question
stringlengths
37
38.8k
group_id
stringlengths
2
6
sentence_embeddings
listlengths
768
768
<p>If two identical masses are somehow "released" into deep space (that is, they're subject to no other gravitation forces but their own, and are initially at rest to each other). What decides whether they collide or orbit each other? I'm imagining for example two 1&nbsp;kg masses initially at rest, say 10&nbsp;m apart. What happens next?</p>
g1495
[ 0.05453384667634964, 0.013671090826392174, 0.01478668861091137, -0.0290574599057436, 0.015452984720468521, 0.04966343566775322, -0.016858050599694252, 0.023914702236652374, -0.033309273421764374, -0.051479071378707886, -0.0189234409481287, -0.0018086344934999943, 0.006468131206929684, -0.04583828151226044, 0.017860962077975273, -0.0020622124429792166, 0.0667206197977066, -0.027617085725069046, 0.010328143835067749, 0.017124351114034653, 0.020038891583681107, 0.031079405918717384, -0.03802301734685898, -0.002023105276748538, -0.025673143565654755, -0.0007981810485944152, 0.01938159391283989, -0.03686971217393875, -0.00767068425193429, 0.00396257359534502, 0.0037011862732470036, 0.029826544225215912, 0.039101820439100266, -0.03435217961668968, -0.011990172788500786, -0.03826075792312622, -0.01179674081504345, -0.015156545676290989, -0.029060257598757744, -0.0140873147174716, 0.05352136120200157, -0.05940108373761177, -0.02606353908777237, -0.009407266043126583, 0.006761088036000729, 0.03554174304008484, -0.058498091995716095, -0.062155310064554214, 0.04223841056227684, 0.0028496705926954746, 0.026421351358294487, 0.10158979147672653, -0.00021578813903033733, -0.02884283848106861, 0.0027347097638994455, -0.0038157117087394, 0.04134027659893036, -0.008551029488444328, 0.04591001570224762, -0.009628488682210445, -0.0019353048410266638, 0.021042797714471817, 0.01452252920717001, -0.027461234480142593, 0.0810299962759018, -0.009400279261171818, -0.060881443321704865, 0.04486459866166115, 0.057355042546987534, -0.02275383472442627, -0.03842288628220558, 0.01770421862602234, -0.008274172432720661, -0.05005238577723503, -0.007264336105436087, 0.0028947952669113874, 0.04372401535511017, 0.018784865736961365, -0.028318246826529503, -0.013116678223013878, -0.025564121082425117, 0.014751240611076355, 0.09564167261123657, 0.03407030925154686, 0.015231591649353504, -0.007844250649213791, -0.010523572564125061, -0.00015991540567483753, -0.052369214594364166, 0.05222100019454956, 0.07257688045501709, -0.02955339476466179, 0.00984159018844366, 0.0058027771301567554, 0.00660098297521472, -0.03519575297832489, 0.06489526480436325, 0.07920445501804352, 0.006693949457257986, -0.04369127377867699, -0.04895944148302078, 0.060532961040735245, -0.005184322129935026, -0.03186642751097679, 0.0206467118114233, -0.006588030140846968, 0.05717587098479271, 0.0558130256831646, 0.008184595964848995, -0.05395699292421341, -0.018651610240340233, -0.03618115931749344, 0.005149682052433491, 0.01438941340893507, -0.027709243819117546, -0.044877372682094574, 0.03776198998093605, 0.0048918211832642555, -0.010697967372834682, 0.0076911658979952335, 0.016505956649780273, -0.04101323336362839, -0.039948269724845886, 0.012182779610157013, -0.054957255721092224, 0.005579225718975067, 0.04063795134425163, 0.026668794453144073, 0.009078972041606903, -0.0100443409755826, 0.01733468659222126, 0.0029050104785710573, 0.05091468617320061, 0.01751805655658245, -0.08030642569065094, -0.026611050590872765, -0.00450653163716197, -0.03152073174715042, 0.001645538373850286, -0.02964789606630802, -0.018795927986502647, -0.01061642449349165, -0.07549332827329636, 0.014250606298446655, -0.030392171815037727, -0.005169462878257036, 0.006989899091422558, -0.0279028732329607, -0.00729339849203825, 0.09815248101949692, 0.008548046462237835, 0.0035618096590042114, 0.038563281297683716, -0.039855342358350754, 0.0101014394313097, 0.007761969696730375, -0.04932798817753792, 0.022362861782312393, -0.02463323064148426, -0.05185580626130104, 0.09262165427207947, -0.029081333428621292, -0.0030791230965405703, -0.003819551318883896, -0.07631201297044754, 0.06100873276591301, 0.028371114283800125, -0.03407548367977142, -0.00800289772450924, -0.004558631684631109, -0.00953161995857954, -0.04755208268761635, -0.04559692367911339, 0.09553384780883789, 0.0047534494660794735, 0.010854151099920273, 0.014966057613492012, -0.021212372928857803, 0.05161512270569801, 0.003885761834681034, 0.017063746228814125, 0.0061712199822068214, -0.0019419420277699828, 0.006087208166718483, 0.013638362288475037, -0.036904606968164444, -0.018913600593805313, 0.003188969334587455, -0.012720983475446701, 0.027017220854759216, -0.021877292543649673, -0.01822078600525856, 0.013144591823220253, 0.010031026788055897, -0.00118209607899189, 0.018417900428175926, -0.013738119043409824, -0.0031548745464533567, -0.042275913059711456, 0.04834747686982155, -0.018412504345178604, 0.026544934138655663, 0.031086428090929985, 0.028008045628666878, -0.025472451001405716, 0.04761841520667076, 0.022773146629333496, 0.051275789737701416, 0.026096217334270477, 0.010918166488409042, 0.03453579917550087, 0.039829131215810776, 0.005704696290194988, -0.0163902435451746, -0.024102922528982162, 0.06234593689441681, -0.030451307073235512, 0.04036429151892662, 0.049172088503837585, -0.05221964791417122, -0.0012621204368770123, 0.01942005567252636, 0.05534124746918678, -0.0440363809466362, 0.028883226215839386, -0.049201883375644684, -0.05699504166841507, -0.0035475334152579308, 0.0301860012114048, 0.0022068191319704056, 0.025446543470025063, 0.023340919986367226, 0.01435774751007557, 0.013033931143581867, 0.046549320220947266, -0.021014025434851646, 0.006665945518761873, 0.0019014592980965972, 0.04983412101864815, 0.037890415638685226, -0.00589439133182168, -0.055404506623744965, -0.02393183298408985, -0.006454660091549158, -0.007624869700521231, -0.09856074303388596, 0.05312223732471466, 0.0072084288112819195, -0.031250856816768646, 0.03149385377764702, -0.0005058980896137655, -0.04361521825194359, -0.07764457911252975, -0.019970914348959923, -0.033792369067668915, -0.00034022863837890327, -0.031673822551965714, 0.04887500777840614, -0.09447874128818512, -0.010156589560210705, -0.001731111784465611, -0.0394907109439373, 0.001756086596287787, 0.015959683805704117, -0.06589136272668839, -0.05537961795926094, 0.06896810233592987, 0.013627661392092705, -0.006370502524077892, 0.0009360597468912601, 0.0006349939503706992, 0.044129181653261185, 0.030943164601922035, 0.036344192922115326, -0.001802633865736425, 0.05652003362774849, -0.016265373677015305, -0.07644076645374298, -0.00404417235404253, -0.00499709090217948, 0.043705470860004425, 0.035787731409072876, -0.024452419951558113, 0.004526233766227961, 0.06939474493265152, -0.02868514694273472, -0.025575166568160057, 0.0451231449842453, 0.008852225728332996, -0.028568154200911522, 0.04035281017422676, 0.035437215119600296, 0.07370758801698685, 0.03528640419244766, 0.001313846674747765, 0.06733161211013794, 0.023975467309355736, 0.038151826709508896, -0.04242702201008797, 0.005678295157849789, 0.005133836530148983, -0.06972553580999374, 0.04375500604510307, 0.028530694544315338, -0.044960375875234604, 0.03270723670721054, -0.030775200575590134, -0.016727492213249207, -0.009404855780303478, -0.02784097194671631, 0.03987935930490494, 0.05775591731071472, 0.0200404841452837, 0.0032647931948304176, -0.058315858244895935, -0.005493387579917908, 0.03225161135196686, -0.024039415642619133, -0.05197739973664284, -0.08370660990476608, -0.08372509479522705, -0.040853261947631836, 0.01535689178854227, -0.023276709020137787, -0.030787460505962372, -0.006152941379696131, -0.04143698140978813, -0.028991298750042915, -0.01829933561384678, -0.008338975720107555, -0.026992619037628174, 0.05215036869049072, -0.05174728110432625, -0.07534671574831009, 0.000056119410146493465, 0.018824778497219086, 0.057446930557489395, 0.0182304996997118, 0.04846534505486488, 0.05739733576774597, 0.01511436514556408, 0.044959284365177155, -0.049999941140413284, 0.02681533433496952, 0.02685774862766266, 0.008934621699154377, 0.07063741236925125, -0.032313697040081024, -0.012823824770748615, -0.04319886863231659, 0.015295964665710926, -0.00844830647110939, 0.01523706503212452, 0.004478118382394314, -0.0061956713907420635, 0.03959885239601135, -0.007046123500913382, 0.017272992059588432, -0.01701824553310871, -0.0076055992394685745, 0.03389885276556015, -0.015019631013274193, -0.06384602934122086, 0.048564884811639786, 0.044340480118989944, -0.02677704393863678, -0.0577506497502327, -0.07835039496421814, 0.0024386753793805838, -0.03906302899122238, 0.019150180742144585, -0.013465417549014091, -0.02154381200671196, 0.027054550126194954, 0.07082968950271606, -0.0803486630320549, 0.06383223831653595, 0.02463238500058651, 0.007606561295688152, -0.02534610405564308, 0.014689530245959759, -0.013094098307192326, -0.03799154981970787, -0.013194096274673939, 0.026162466034293175, 0.05750901997089386, -0.04222512245178223, -0.019693724811077118, -0.017929870635271072, -0.03119908645749092, 0.015400842763483524, -0.035764455795288086, -0.0229561235755682, 0.01152055524289608, 0.08039480447769165, 0.045717835426330566, 0.02719135396182537, -0.017809143289923668, 0.02470855973660946, -0.03756909817457199, 0.013264071196317673, 0.05229649320244789, -0.09361157566308975, -0.03755751997232437, 0.006243464536964893, -0.0258330088108778, 0.0024165473878383636, -0.03990819305181503, -0.0295663271099329, 0.035767413675785065, 0.03452856466174126, 0.02362320013344288, 0.028683843091130257, 0.0007958894711919129, 0.07146554440259933, 0.0016789028886705637, -0.025006990879774094, -0.0019430569373071194, -0.010135412216186523, 0.034695591777563095, -0.05202499404549599, 0.03728589043021202, 0.011030398309230804, -0.003500540740787983, -0.032558977603912354, 0.03604062274098396, 0.08333606272935867, -0.018116291612386703, -0.013629416935145855, -0.013896825723350048, 0.028760164976119995, 0.027962153777480125, -0.007215242832899094, 0.02672780677676201, -0.058411553502082825, 0.0286009032279253, -0.011930537410080433, 0.012592010200023651, -0.005189833696931601, 0.07491917908191681, 0.04867309331893921, 0.01513724122196436, -0.05090264976024628, 0.01745809242129326, 0.03164944052696228, 0.09644493460655212, -0.03284703567624092, -0.047821905463933945, 0.016116945073008537, -0.022610269486904144, -0.0798441544175148, -0.05141289159655571, -0.037140682339668274, -0.047763641923666, -0.01825665310025215, 0.005516642704606056, -0.017200062051415443, 0.031569600105285645, 0.00368979899212718, -0.0311582013964653, 0.019909050315618515, -0.05089216306805611, 0.03816380724310875, 0.00866248644888401, -0.014605799689888954, -0.037773508578538895, 0.039091162383556366, 0.01132272556424141, -0.019370440393686295, 0.01798524521291256, 0.010222484357655048, 0.016091173514723778, -0.0016816473798826337, 0.02235446870326996, -0.02277771383523941, 0.02683677151799202, -0.019736163318157196, -0.04095548018813133, 0.06647887825965881, -0.08411825448274612, -0.019959088414907455, -0.0026883664540946484, 0.044851839542388916, -0.012113871984183788, -0.011064436286687851, 0.024985885247588158, -0.017308782786130905, -0.01802261732518673, 0.04605469852685928, -0.0001556564384372905, -0.034222155809402466, -0.010963386856019497, -0.019637206569314003, -0.027168450877070427, -0.010242301039397717, -0.024091757833957672, -0.01298669446259737, 0.00013899635814595968, 0.007773563265800476, -0.007043093908578157, 0.01802402175962925, 0.03916675224900246, 0.10677874833345413, 0.013400297611951828, -0.023576553910970688, 0.02559610828757286, -0.0062822396866977215, -0.05310140177607536, 0.020096197724342346, 0.012999485246837139, -0.07495824992656708, 0.03443269431591034, -0.003490840084850788, 0.08058558404445648, 0.010296144522726536, -0.026373902335762978, 0.044517166912555695, -0.004815215244889259, 0.029298949986696243, 0.013117793016135693, 0.01716330088675022, -0.00979422964155674, 0.02881687320768833, 0.03541623428463936, 0.024679558351635933, -0.06338001042604446, -0.04123314097523689, 0.04200996086001396, -0.05275529995560646, 0.05294225737452507, -0.02254035696387291, -0.052586302161216736, 0.04976946488022804, -0.027515271678566933, 0.0026686054188758135, -0.0363769568502903, 0.028815841302275658, 0.04041674733161926, 0.05002094432711601, -0.00001547179817862343, -0.004895464517176151, 0.04301042854785919, -0.009472031146287918, 0.06400585919618607, 0.007285266648977995, -0.03623560070991516, -0.028267627581954002, 0.03352854400873184, 0.05113934725522995, -0.06088326498866081, -0.059759434312582016, -0.00023962362320162356, 0.015966981649398804, 0.033455222845077515, -0.02307569794356823, 0.07213050127029419, -0.015467550605535507, 0.023573776707053185, -0.0451260469853878, 0.01610240340232849, 0.00931324902921915, 0.06424551457166672, 0.043767720460891724, -0.020821111276745796, -0.0026750985998660326, -0.05970070883631706, -0.023693716153502464, -0.009992695413529873, 0.03984535112977028, -0.019792113453149796, 0.020145606249570847, -0.018064415082335472, -0.02326659858226776, -0.05293813347816467, 0.019343215972185135, -0.0006255730986595154, -0.05560123547911644, -0.05432935804128647, -0.001439447863958776, -0.03375900164246559, 0.09462395310401917, 0.011535562574863434, 0.05662846192717552, 0.0034860316663980484, -0.026077156886458397, 0.09002701938152313, -0.04052642732858658, -0.04507855698466301, 0.011142558418214321, 0.04601338133215904, -0.036962978541851044, -0.05940337851643562, -0.022103307768702507, 0.019445231184363365, -0.03961459547281265, 0.020414242520928383, -0.028847645968198776, 0.023275624960660934, 0.0001635549560887739, -0.017450246959924698, -0.011141552589833736, 0.022599929943680763, 0.12289848178625107, 0.056615784764289856, -0.0037871396634727716, 0.022886181250214577, -0.07583602517843246, 0.008081071078777313, 0.028383202850818634, 0.04812830686569214, -0.0032872166484594345, -0.05830448865890503, 0.002892283722758293, -0.025082886219024658, -0.0024616927839815617, 0.03964584320783615, -0.021013041958212852, 0.033586286008358, -0.06960690766572952, -0.003626557532697916, -0.003143581096082926, -0.023465324193239212, 0.006421711761504412, -0.07116249948740005, -0.028603296726942062, -0.00399521179497242, -0.0005712596466764808, -0.005536162294447422, 0.031096406280994415, 0.03403483331203461, -0.015010358765721321, -0.007177719846367836, 0.04093366116285324, -0.01203096006065607, -0.02638750523328781, 0.054278429597616196, -0.03140546754002571, 0.036141347140073776, -0.0020452288445085287, -0.03355967253446579, 0.05541219562292099, 0.003066018922254443, 0.03179499879479408, 0.050643809139728546, -0.039566244930028915, -0.03858420252799988, 0.041985396295785904, -0.008703654631972313, -0.03731083869934082, -0.022829236462712288, -0.08358590304851532, -0.07645348459482193, -0.0005468978779390454, 0.0023655355907976627, 0.004007024224847555, 0.044393859803676605, -0.015084884129464626, -0.03838115558028221, -0.009838862344622612, 0.037560172379016876, -0.018866071477532387, -0.0142986960709095, -0.047353122383356094, 0.05312904343008995, -0.02814171276986599, -0.015145881101489067, 0.04166267067193985, -0.06059429794549942, 0.003612687112763524, -0.011205456219613552, -0.012602868489921093, -0.025156689807772636, -0.04122653603553772, 0.007676622364670038, -0.018814701586961746, 0.000483462936244905, -0.011267228983342648, -0.04086722061038017, -0.0038920235820114613, 0.031173303723335266, 0.014421696774661541, -0.018320579081773758, 0.0016109435819089413, 0.0006919092847965658, -0.015781469643115997, 0.06024235859513283, -0.005671313032507896, -0.004561173729598522, -0.05618714168667793, -0.003647839417681098, -0.039365243166685104, 0.056082818657159805, -0.004951817914843559, -0.024658219888806343, -0.04927058145403862, -0.021217230707406998, 0.012852845713496208, 0.020697908475995064, 0.009431574493646622, 0.011429334059357643, -0.01823440194129944, 0.029353495687246323, 0.025264406576752663, 0.006638860795646906, 0.008663469925522804, 0.016299597918987274, 0.021908314898610115, -0.0015599005855619907, -0.001246931846253574, -0.007014596369117498, 0.039257489144802094, 0.03202526271343231, 0.01705756224691868, -0.015518560074269772, -0.029580067843198776, -0.05324135348200798, -0.07523894309997559, -0.00003111028127023019, 0.039033520966768265, 0.009285290725529194, 0.010692598298192024, -0.010464298538863659, 0.01569351740181446, -0.026417717337608337, -0.0014738371828570962, -0.029529094696044922, 0.02468279004096985, -0.03137864172458649, -0.0012668152339756489, -0.006020009517669678, 0.00828471314162016, 0.0038436653558164835, 0.009078532457351685, 0.019505880773067474, 0.03025379590690136, 0.014998243190348148, -0.026125146076083183, -0.029779769480228424, -0.039484795182943344, 0.008223680779337883, -0.05240423232316971, -0.040424469858407974, -0.006637359503656626, -0.01296574529260397, -0.0017309662653133273, 0.024146880954504013, 0.02008259855210781, 0.05916247144341469, 0.04358998313546181, -0.07301564514636993, 0.018368633463978767, -0.04162287712097168, -0.0038568219169974327, 0.041838645935058594, 0.06628555059432983, -0.029157452285289764, -0.04483884572982788, -0.007757837418466806, -0.04267824441194534, -0.026385406032204628, 0.01610817015171051, -0.02971448190510273, -0.020928693935275078, -0.00669756019487977, -0.03522250056266785, 0.0008338416810147464, 0.004443715326488018, 0.012240197509527206 ]
<p>we vistited yesterday a fun park and saw a ride which was a big centrifuge only in vertical. this one had a speed meter but it was broken and i also wanted to know how much g-force is on there...</p> <p>so my first thought was to calculate this with the centrifugal-accerleration. I have $\omega = \frac {0.5*2\pi} 1 [\frac {rad} s]$ and $r= 25[m]$, so the accerleration is $a_z = \omega^2r = \pi^2*25 = ~246$</p> <p>then i can calculate the g force with $g_{force} = \frac {a_z} g$ which gives me about $24g$ that seems fairly too high! </p> <p>what am i missing?</p>
g1496
[ 0.02503235451877117, 0.07148639112710953, -0.01439104974269867, 0.02971320040524006, 0.008623465895652771, 0.035161811858415604, 0.08213444799184799, 0.02244499884545803, -0.13184760510921478, 0.006996327079832554, 0.004346961155533791, -0.020539849996566772, -0.06669019907712936, 0.020686499774456024, 0.06508053839206696, -0.01375196035951376, 0.052429329603910446, -0.04070429131388664, 0.011035933159291744, 0.043274953961372375, 0.022209959104657173, -0.04926660656929016, -0.024575965479016304, -0.04249488562345505, 0.03955092281103134, -0.013538060709834099, 0.014952396042644978, -0.006920387037098408, -0.027935856953263283, 0.024493509903550148, -0.024559082463383675, 0.010373523458838463, -0.049365464597940445, -0.0882098451256752, -0.01144330482929945, 0.012762348167598248, 0.027360405772924423, 0.046025436371564865, 0.053188443183898926, -0.03364363685250282, 0.010042834095656872, -0.011277819983661175, 0.03981984779238701, -0.011585104279220104, 0.02523382008075714, 0.025206217542290688, -0.02690238505601883, -0.001204257132485509, 0.02071685530245304, 0.026538006961345673, -0.050595127046108246, 0.04901045188307762, 0.022246886044740677, 0.04224666580557823, -0.017085649073123932, 0.07270516455173492, 0.039479900151491165, 0.004528802819550037, -0.04118415340781212, 0.0020530640613287687, -0.027462802827358246, -0.03369675204157829, 0.03920356184244156, -0.05276062339544296, 0.008233973756432533, -0.047710154205560684, -0.005576586350798607, 0.008494344539940357, 0.006159428507089615, -0.008621938526630402, -0.01774163544178009, -0.03878798708319664, 0.04699394851922989, -0.01886742189526558, -0.08921337127685547, 0.017894836142659187, -0.015974050387740135, 0.016738558188080788, 0.037109170109033585, -0.018983330577611923, -0.03190910071134567, 0.0028091941494494677, 0.019007712602615356, -0.04584459960460663, 0.03469642624258995, -0.02308986522257328, -0.013860071077942848, 0.016056837514042854, 0.020976059138774872, -0.009459882974624634, 0.07370249927043915, -0.013822752982378006, 0.06642027199268341, 0.026605164632201195, -0.014543654397130013, -0.06604722142219543, -0.026362953707575798, 0.0883084312081337, 0.002989467466250062, -0.004681853111833334, -0.027854755520820618, -0.007485346868634224, 0.004682761151343584, -0.04776208475232124, 0.018817394971847534, -0.03660184517502785, 0.019634433090686798, 0.036800846457481384, -0.01749168522655964, -0.048531923443078995, 0.019732631742954254, -0.016745395958423615, -0.043596331030130386, -0.05960197001695633, 0.0037614016328006983, -0.03638675436377525, 0.037347324192523956, -0.0002755217719823122, 0.007376246619969606, -0.010953892022371292, -0.02561844512820244, 0.05959741398692131, -0.039488285779953, 0.06426411122083664, -0.03148108348250389, -0.01606976054608822, 0.0032772172708064318, 0.02030063606798649, -0.014831884764134884, -0.02704598568379879, 0.037938009947538376, -0.021667635068297386, 0.025327032431960106, 0.0057348692789673805, 0.01447207573801279, -0.005784983746707439, -0.08182711899280548, 0.04338911175727844, -0.06609795987606049, -0.016171347349882126, -0.05235328525304794, -0.058584023267030716, 0.02117992751300335, 0.03639509156346321, 0.030166827142238617, 0.04060380160808563, -0.07376676797866821, 0.03123326040804386, 0.07199804484844208, -0.06693653017282486, 0.02985270507633686, 0.059371281415224075, 0.007439847569912672, -0.06483545899391174, 0.051480431109666824, -0.011242372915148735, 0.06073927506804466, 0.014264577068388462, -0.0037821182049810886, 0.0025683240965008736, 0.07149604707956314, -0.008542036637663841, 0.04223554953932762, 0.028817318379878998, -0.04761965945363045, 0.010351007804274559, -0.024160683155059814, -0.05543725565075874, -0.009391778148710728, -0.0016767384950071573, -0.10217538475990295, -0.010454188100993633, 0.07878921180963516, -0.01072466280311346, -0.002985134022310376, -0.007674958556890488, -0.0009472704259678721, -0.07905080169439316, 0.00825570710003376, 0.06304482370615005, 0.03137144073843956, -0.01135215163230896, 0.026544375345110893, -0.009793109260499477, -0.031592268496751785, -0.030346527695655823, 0.057303715497255325, -0.023795872926712036, -0.05191798880696297, 0.022077208384871483, -0.005487185902893543, -0.007925898768007755, -0.002048494992777705, 0.019489236176013947, -0.033575769513845444, 0.03520329296588898, -0.0070356340147554874, -0.027974503114819527, -0.048724301159381866, 0.03408908098936081, -0.017041850835084915, 0.03606054559350014, 0.04641252011060715, -0.012249183841049671, 0.004402111284434795, -0.03198307007551193, -0.03499434515833855, -0.019861318171024323, 0.031871944665908813, -0.033910490572452545, 0.008070248179137707, -0.008318884298205376, -0.00029660534346476197, -0.02811869978904724, -0.012663907371461391, 0.0022954249288886786, 0.05850660428404808, 0.043750058859586716, 0.0004411896807141602, 0.013470295816659927, 0.028934797272086143, 0.03105415776371956, 0.02621605060994625, -0.002180331153795123, -0.04110100120306015, -0.0032475434709340334, -0.016082460060715675, -0.014724400825798512, 0.004280859604477882, -0.028631584718823433, -0.022616270929574966, 0.037596508860588074, -0.04145367816090584, -0.026599641889333725, 0.020572705194354057, 0.07763762772083282, -0.044159598648548126, -0.002268679905682802, 0.019805628806352615, -0.0008616115665063262, 0.04604716598987579, -0.04203711450099945, 0.021697813645005226, -0.007063938770443201, 0.017417335882782936, 0.011027563363313675, -0.01606893166899681, 0.007403280586004257, 0.033084187656641006, -0.0189542006701231, 0.004950163885951042, -0.018795792013406754, -0.031939052045345306, 0.017087841406464577, 0.02241365984082222, 0.04911243915557861, -0.05281412973999977, 0.01076771691441536, -0.028729788959026337, -0.004803212359547615, 0.0038014540914446115, 0.023930205032229424, -0.002187662525102496, 0.03770937770605087, -0.049115199595689774, -0.012920839712023735, -0.05140973627567291, -0.00921278540045023, 0.005123745184391737, 0.033754490315914154, 0.013305773958563805, 0.05733096972107887, -0.00004675607124227099, 0.03616470471024513, 0.00030227715615183115, -0.07125584036111832, -0.029789818450808525, 0.00905205961316824, 0.026719707995653152, 0.0031438362784683704, -0.0023429549764841795, 0.023122664541006088, -0.0019419500604271889, 0.033731162548065186, 0.051918402314186096, -0.006067272741347551, 0.020878871902823448, 0.05497942119836807, -0.017482846975326538, -0.010646398179233074, -0.05655574053525925, 0.01807163842022419, -0.024256635457277298, -0.020082730799913406, -0.01772390678524971, 0.029300473630428314, 0.036733221262693405, 0.021008210256695747, 0.05859024450182915, -0.03479302302002907, 0.019824184477329254, -0.06004631519317627, 0.006974348332732916, 0.04536090046167374, -0.09672486037015915, -0.025019735097885132, 0.030484942719340324, -0.03480236977338791, -0.030614029616117477, 0.06105612590909004, -0.030715137720108032, 0.037290189415216446, 0.05193355306982994, -0.07416152954101562, -0.060156114399433136, -0.06094604358077049, 0.061239566653966904, -0.06681855767965317, -0.05925806239247322, 0.013555570505559444, 0.01013310719281435, -0.08012473583221436, 0.013353428803384304, -0.019631756469607353, -0.012026497162878513, 0.0813218206167221, -0.0792892575263977, 0.013300671242177486, 0.03698335215449333, -0.08597397059202194, 0.041575659066438675, 0.030263803899288177, -0.0099258441478014, 0.0010403519263491035, -0.026155613362789154, 0.019257282838225365, 0.023814529180526733, -0.009906201623380184, 0.00029417607584036887, 0.01983029954135418, -0.09086689352989197, -0.03312293440103531, -0.014703174121677876, -0.04460371658205986, -0.060409266501665115, 0.005617703311145306, -0.009908435866236687, 0.07844027131795883, 0.005041228141635656, -0.009576392360031605, 0.002516321139410138, -0.03255812078714371, 0.018552379682660103, -0.0823698416352272, -0.0033511773217469454, -0.03230162709951401, 0.009851750917732716, 0.014416740275919437, -0.07103422284126282, 0.03004615008831024, 0.03663679212331772, 0.00780379818752408, -0.026335854083299637, 0.06947550177574158, 0.033048685640096664, -0.06884132325649261, -0.04735497012734413, 0.053150709718465805, -0.03417149931192398, -0.028416389599442482, 0.05237463116645813, -0.013756564818322659, 0.04784001037478447, 0.001672310521826148, 0.02354646846652031, -0.0803292840719223, 0.04758836701512337, -0.04546114057302475, 0.03810948133468628, 0.019921280443668365, 0.00728232366964221, 0.02964175119996071, 0.009840433485805988, -0.04212190955877304, -0.004603625275194645, -0.015731537714600563, -0.03178280219435692, 0.019469941034913063, 0.003084541065618396, -0.03708842024207115, 0.009240436367690563, -0.02136974036693573, -0.002990640001371503, 0.0083300257101655, 0.04241866245865822, 0.031726982444524765, 0.006683265324681997, 0.012053976766765118, -0.02343014068901539, 0.0030251829884946346, 0.0029818143229931593, 0.03269675001502037, 0.043346792459487915, 0.020619165152311325, -0.01919049397110939, 0.005647290963679552, 0.006724619306623936, 0.005654569249600172, 0.008408213965594769, 0.00293421046808362, 0.005577791947871447, 0.021522080525755882, -0.0030691407155245543, -0.055734582245349884, 0.03462620824575424, -0.027203047648072243, 0.02937508188188076, 0.02606862224638462, 0.012355554848909378, 0.00868690013885498, 0.06467171758413315, 0.006865271367132664, 0.048338934779167175, -0.043284475803375244, -0.09661712497472763, 0.03195665404200554, -0.009775977581739426, -0.01965877041220665, -0.025914916768670082, -0.02513885498046875, 0.03643972426652908, -0.016035741195082664, -0.05359763279557228, 0.0352712944149971, -0.04563918337225914, 0.052898842841386795, 0.007524305954575539, 0.045011844485998154, 0.05644044280052185, -0.005330953281372786, 0.05927975848317146, 0.02398509718477726, 0.02954937145113945, -0.03055761568248272, 0.01745077595114708, 0.001568619511090219, -0.025907427072525024, -0.05807731673121452, 0.03359774500131607, -0.007766338996589184, -0.0455814003944397, -0.06004311889410019, -0.010071776807308197, 0.018407151103019714, 0.03328539803624153, 0.02785111963748932, -0.004830777645111084, 0.012244096957147121, -0.055543988943099976, 0.02556326612830162, -0.06814416497945786, 0.019448133185505867, -0.05035775899887085, -0.030538409948349, 0.03485811501741409, -0.005517521873116493, 0.03630931302905083, -0.03600328043103218, -0.002734109992161393, 0.006173111964017153, -0.016990089789032936, -0.019969729706645012, 0.009382426738739014, -0.006423987913876772, -0.04684660956263542, 0.09542224556207657, 0.03540709242224693, 0.04636607691645622, 0.03466920554637909, 0.005683720577508211, 0.008900832384824753, 0.0115888686850667, 0.03037034161388874, -0.04917566105723381, 0.015454886481165886, -0.010817082598805428, -0.014445283450186253, 0.0035672171507030725, 0.01166682131588459, -0.04839269444346428, 0.018933869898319244, 0.024639036506414413, -0.02467818558216095, -0.026949305087327957, -0.030391549691557884, 0.01603139005601406, -0.004731375258415937, -0.011318682692945004, -0.015364820137619972, 0.0213552825152874, -0.051483023911714554, 0.026401730254292488, -0.0425344780087471, -0.03208398446440697, 0.00829911045730114, 0.06574289500713348, -0.004929147660732269, 0.0019345853943377733, 0.01619250513613224, 0.10965035855770111, -0.043052688241004944, -0.02118956670165062, 0.021429354324936867, -0.0450112484395504, 0.006869518663734198, -0.0007083137170411646, 0.038693882524967194, 0.018996333703398705, 0.026200979948043823, -0.020736733451485634, 0.0905587300658226, -0.023328473791480064, 0.04325466603040695, -0.0575723797082901, -0.0906718522310257, 0.004470526240766048, -0.04433218389749527, -0.029432542622089386, 0.017144791781902313, -0.0052905092015862465, 0.044843487441539764, -0.07650884985923767, -0.017237666994333267, -0.03254641965031624, -0.029468102380633354, -0.02487538754940033, 0.07454993575811386, -0.02190571092069149, 0.07191629707813263, -0.005118534900248051, -0.036178797483444214, 0.007729149889200926, -0.034662727266550064, 0.0289903674274683, -0.020896034315228462, 0.01086301077157259, 0.013780583627521992, -0.02929862029850483, 0.033730391412973404, -0.03280116617679596, -0.016910267993807793, 0.014510459266602993, 0.042482778429985046, 0.02415662817656994, -0.007954098284244537, 0.03919490799307823, -0.003936734050512314, 0.00026472637546248734, -0.014969226904213428, 0.03012583963572979, 0.052053581923246384, -0.002780801383778453, 0.006820284761488438, -0.027745140716433525, 0.014636018313467503, -0.012495400384068489, -0.008711450733244419, 0.014535210095345974, 0.06395679712295532, 0.0007501609507016838, -0.031434908509254456, 0.009286553598940372, -0.015100650489330292, 0.042624905705451965, 0.10728402435779572, -0.006980369798839092, 0.0080088060349226, 0.032543957233428955, -0.0193046685308218, 0.02290838025510311, 0.01186642237007618, 0.005779556464403868, 0.03946424648165703, -0.035818297415971756, 0.0017540449043735862, 0.041466739028692245, -0.03713409602642059, -0.014018555171787739, -0.020078258588910103, -0.04660270735621452, 0.010286012664437294, 0.008001510053873062, 0.013422192074358463, 0.014284146018326283, 0.0005648382939398289, -0.014393001794815063, 0.016788331791758537, 0.0007156317587941885, 0.061226896941661835, -0.021859126165509224, 0.040297552943229675, 0.023258766159415245, -0.025039799511432648, -0.023510225117206573, 0.031436312943696976, -0.024334432557225227, -0.03772455453872681, 0.01123321708291769, 0.012871937826275826, -0.04764508083462715, -0.004764509852975607, 0.01632131077349186, 0.005365914199501276, 0.05023646727204323, 0.019892599433660507, 0.00019850872922688723, 0.08486901223659515, -0.0032046325504779816, 0.043559323996305466, 0.018740728497505188, 0.010813894681632519, 0.03353748470544815, 0.04771171882748604, -0.04601135849952698, 0.023063939064741135, -0.014221996068954468, -0.051321420818567276, -0.01071992702782154, 0.05449480563402176, -0.06803948432207108, -0.0029236064292490482, 0.026510899886488914, 0.028234751895070076, -0.012331509031355381, 0.035329680889844894, 0.06476399302482605, -0.0016461164923384786, 0.018803490325808525, 0.04550698399543762, 0.037269193679094315, 0.011254681274294853, 0.007449015974998474, -0.021407542750239372, -0.04998621717095375, -0.019060038030147552, -0.02294749766588211, 0.006091811694204807, 0.04857633262872696, 0.05943220108747482, -0.011171868070960045, 0.06517872959375381, -0.04167835786938667, 0.006798422429710627, -0.002551683457568288, -0.053612418472766876, 0.008243657648563385, 0.022021593526005745, -0.0005105796153657138, 0.039860792458057404, -0.02458920143544674, -0.00999888963997364, -0.027878014370799065, 0.05153452232480049, -0.00020559277618303895, -0.07492624968290329, -0.01019914261996746, -0.09388795495033264, 0.02731120027601719, 0.022307096049189568, 0.00011631380766630173, -0.02811194583773613, -0.0027538184076547623, -0.03486130014061928, -0.054484397172927856, -0.024903004989027977, -0.04842285439372063, -0.05027385428547859, -0.06909418106079102, 0.020734185352921486, 0.009071271866559982, -0.007957154884934425, 0.005584061145782471, -0.021655280143022537, 0.05492939427495003, -0.061870358884334564, 0.02845251001417637, 0.036562949419021606, -0.005587632302194834, 0.00006258986104512587, -0.013154653832316399, -0.057247817516326904, -0.009744022972881794, 0.04166349768638611, -0.022404467687010765, -0.006733774673193693, -0.021663658320903778, -0.01749802567064762, 0.06744398176670074, 0.014702466316521168, -0.02431703545153141, 0.0763486698269844, -0.05172844976186752, -0.029953699558973312, -0.015047894790768623, 0.025783386081457138, 0.04244185984134674, 0.004334254655987024, -0.037568483501672745, 0.03056730329990387, 0.013557736761868, -0.018499912694096565, 0.04596882313489914, -0.053360022604465485, -0.00815413985401392, 0.02600710466504097, 0.004742810968309641, -0.03748184069991112, -0.02018006518483162, 0.04088466614484787, -0.07991974800825119, -0.005359889939427376, 0.0023768555838614702, 0.00015348281885962933, -0.0533563569188118, -0.03170381113886833, 0.0607459731400013, -0.029294589534401894, -0.03233170509338379, 0.017396844923496246, 0.06989838182926178, -0.04601668938994408, -0.012723895721137524, -0.04706554114818573, -0.025812167674303055, -0.034619513899087906, -0.033714111894369125, 0.057626329362392426, -0.050682298839092255, -0.01867699809372425, 0.0007542576058767736, 0.018293078988790512, -0.009598659351468086, -0.015075710602104664, 0.024070825427770615, 0.00896772276610136, 0.03624086081981659, 0.00539569603279233, 0.02799294888973236, 0.011854058131575584, -0.007717722095549107, 0.034526579082012177, 0.005893401801586151, 0.028101669624447823, -0.028748780488967896, -0.0010954263852909207, -0.05927222967147827, -0.01181453000754118, -0.008069446310400963, 0.0010321640875190496, -0.002362376544624567, 0.0009502539760433137, 0.017886878922581673, -0.0035836438182741404, -0.019428467378020287, -0.0008419671794399619, 0.008133314549922943, 0.012063151225447655, -0.034053001552820206 ]
<p>Not having studied General Relativity, I have sometimes been puzzled by references to the behaviour for "classic" black holes &mdash; as they are popularly portrayed &mdash; as being true for black holes which are not rotating and which have no charge. I don't understand the role rotation <em>does</em> play, but at least because it has to do with the motion of massive bodies, I can understand why it <em>could</em> play an important role. But I have no such intuition for electrical charge.</p> <p>How does <em>charge</em> change the behaviour of a black hole, aside from the obvious role of electrostatic force? (It will preferentially attract particles of the opposite charge, obviously.) But it would seem that charge plays a more intriguing role than just this.</p> <p>The current status of the <a href="http://en.wikipedia.org/wiki/Black_hole#Singularity" rel="nofollow">Wikipedia page on black holes</a> claims that you can theoretically avoid the singularity of a charged black hole. It also describes there that there is a theoretical upper bound on the charge/mass ratio of a black hole: that any would-be black hole exceeding it (which is generally thought to be impossible &mdash; see <a href="http://physics.stackexchange.com/q/6650/4976">this related question on trying to force saturation of the charge/mass ratio or black holes</a>) would lack an event horizon (and therefore presumably not be a black hole). Why should that be? Furthermore: from <a href="http://physics.stackexchange.com/q/9516/4976">this other related question on repulsion of pairs of charged black holes</a> (and from Willie Wong's comment, below), ir seems that the size of the event horizon may change depending on how close it is to being extremal! Why would the event horizon of a <em>highly charged</em> black hole be different than the event horizon of a <em>neutral</em> black hole, of similar mass?</p> <p>Is there a clear reason for such an interplay is there between electrodynamics (aside from local Lorentz invariance) and general relativity that bring these things about?</p>
g1497
[ 0.019772455096244812, 0.012392020784318447, 0.010846764780580997, -0.023719169199466705, 0.03831358626484871, 0.04510541632771492, 0.07907190918922424, 0.007642510812729597, -0.039363451302051544, 0.011667609214782715, 0.058698806911706924, -0.003914684522897005, 0.004579548723995686, 0.02083738148212433, -0.02952449955046177, 0.021783554926514626, 0.026904407888650894, -0.014508544467389584, -0.0030812276527285576, 0.0025208364240825176, 0.008087403140962124, -0.023363355547189713, 0.05637218430638313, -0.028296224772930145, -0.033574339002370834, 0.03373083472251892, 0.060114193707704544, -0.009746373631060123, -0.012722899205982685, -0.07423079013824463, 0.07041946798563004, 0.06241988390684128, -0.00374620221555233, 0.008691562339663506, -0.014412185177206993, -0.04867192730307579, 0.0048004621639847755, -0.01733153499662876, 0.010979858227074146, -0.0037236646749079227, 0.016188571229577065, -0.004136092495173216, -0.03797299414873123, -0.029657505452632904, 0.016282498836517334, -0.00492924964055419, 0.03652135655283928, 0.030170129612088203, 0.07325460016727448, 0.02019985392689705, -0.007202154025435448, 0.007272463757544756, 0.05079694464802742, -0.034026455134153366, 0.05054973438382149, -0.04813852161169052, 0.004321407061070204, 0.08463849127292633, 0.01814306154847145, 0.060406409204006195, -0.04048982262611389, 0.010700848884880543, 0.01948198676109314, -0.008142584003508091, 0.0056827133521437645, -0.05890430137515068, -0.04547469690442085, -0.0388014055788517, -0.0440947562456131, 0.01553521677851677, -0.022482911124825478, -0.03550977259874344, -0.05149652063846588, 0.004986396059393883, 0.016049019992351532, 0.03528672084212303, -0.005434786900877953, 0.014989223331212997, 0.023267891258001328, -0.07174649834632874, -0.014200304634869099, 0.005882414989173412, 0.08295425027608871, -0.006286874413490295, 0.08253251761198044, 0.0013040917692705989, -0.0060141184367239475, -0.01124411541968584, 0.027290403842926025, 0.00601683696731925, 0.04830499365925789, -0.03226647526025772, 0.06646360456943512, 0.011589840054512024, -0.02377021685242653, 0.016274727880954742, 0.010671081952750683, 0.03780532255768776, 0.052940625697374344, 0.04532304033637047, -0.08041159808635712, 0.015437149442732334, 0.03151202201843262, 0.03806387260556221, 0.020056553184986115, -0.004178369417786598, -0.014853766188025475, 0.08192762732505798, -0.01570005714893341, -0.0011417386122047901, 0.03605177253484726, -0.04320795461535454, -0.019858714193105698, -0.02754501812160015, -0.08182018250226974, 0.04631398618221283, 0.05580300837755203, -0.08130881935358047, -0.02755129151046276, 0.046281199902296066, -0.058213457465171814, 0.018135463818907738, -0.014244084246456623, 0.036581676453351974, -0.0153038389980793, -0.016246670857071877, 0.011849641799926758, -0.03046024590730667, -0.007450373377650976, 0.03193099424242973, -0.020343750715255737, 0.011123772710561752, 0.0038470225408673286, 0.02576581947505474, -0.024148767814040184, -0.002099629957228899, 0.03993063420057297, -0.052264317870140076, 0.042050790041685104, -0.015261171385645866, 0.026985080912709236, -0.05075680837035179, 0.003505128901451826, 0.005793814081698656, 0.0052329618483781815, 0.007588625885546207, -0.019956424832344055, -0.040340010076761246, 0.05094797536730766, 0.047282665967941284, 0.03360798582434654, 0.08560626208782196, -0.004176904913038015, 0.020292457193136215, 0.03553592786192894, 0.029620502144098282, 0.04575229063630104, 0.0012128676753491163, -0.023931438103318214, 0.037720441818237305, 0.0682479590177536, -0.012760789133608341, -0.03640497103333473, 0.051579613238573074, -0.007206289563328028, -0.05459640175104141, 0.030948562547564507, -0.0433262437582016, 0.021575167775154114, -0.03726349398493767, -0.015611504204571247, 0.014953909441828728, 0.01747831329703331, 0.0816359594464302, 0.04517408087849617, -0.014584211632609367, -0.027153940871357918, -0.04458761587738991, 0.016007451340556145, -0.021138064563274384, -0.06646988540887833, 0.006840186659246683, -0.00248278328217566, 0.013071826659142971, 0.007216311525553465, -0.010021715424954891, 0.00281661213375628, 0.08336081355810165, 0.01876571960747242, -0.002048279857262969, -0.06589441746473312, -0.0010306318290531635, 0.013971465639770031, 0.017103202641010284, -0.013160916976630688, 0.02387009933590889, 0.014801396988332272, 0.016988392919301987, -0.0027683041989803314, 0.052699677646160126, -0.03467213362455368, -0.01266483124345541, -0.026259414851665497, -0.005421860609203577, -0.0034784036688506603, 0.005457563791424036, -0.023335594683885574, 0.0011935554211959243, 0.05433080345392227, -0.03777115419507027, 0.020527848973870277, -0.02978183887898922, 0.026611628010869026, 0.004931075498461723, -0.00816551223397255, -0.03928671032190323, -0.024398205801844597, 0.0014096827944740653, -0.0507972314953804, -0.0014198237331584096, -0.0845070332288742, -0.06495606899261475, -0.003981482237577438, -0.011916160583496094, -0.03331448510289192, 0.025892527773976326, 0.023189442232251167, -0.030076615512371063, -0.03498831391334534, -0.007056109141558409, -0.05358542501926422, 0.05675925686955452, -0.01314525492489338, 0.08518417179584503, 0.058244895190000534, 0.014214224182069302, 0.004000160843133926, -0.041161272674798965, 0.04662574455142021, -0.008042923174798489, 0.037768784910440445, -0.047366343438625336, -0.01713576540350914, 0.009069175459444523, 0.02335323952138424, -0.03036319836974144, 0.06483256816864014, 0.011064581573009491, -0.010137826204299927, 0.04410988837480545, 0.023481108248233795, -0.07217948883771896, -0.006765911355614662, 0.00006940039020264521, 0.02282985858619213, -0.016878413036465645, -0.00042993182432837784, -0.01006600633263588, -0.09058977663516998, -0.0033120564185082912, -0.006208221428096294, 0.020629344508051872, -0.0036700996570289135, 0.057440515607595444, -0.09522517770528793, -0.01469486579298973, -0.06081005930900574, 0.01345763634890318, -0.019392596557736397, -0.001079898327589035, -0.0322553887963295, 0.024920020252466202, 0.014381732791662216, 0.02826981619000435, 0.043176498264074326, -0.02691584639251232, -0.020362526178359985, 0.02441101148724556, 0.05730562284588814, -0.030139867216348648, -0.024515138939023018, -0.01022249087691307, -0.05109290033578873, -0.014996614307165146, 0.02174180932343006, -0.03234665095806122, -0.01555049978196621, 0.00784118752926588, -0.040100663900375366, -0.04186788946390152, -0.016885502263903618, 0.051221929490566254, 0.06654724478721619, 0.01998012512922287, 0.08497335016727448, -0.03559954836964607, -0.04406755790114403, -0.0184856615960598, -0.06060166656970978, 0.026886744424700737, 0.06867838650941849, 0.006897689774632454, -0.028993189334869385, 0.01709105260670185, -0.0102088563144207, 0.07844283431768417, -0.027306104078888893, -0.045059990137815475, -0.028481831774115562, 0.026502057909965515, -0.0289201308041811, 0.004537361208349466, -0.020525943487882614, 0.004333196207880974, -0.06455831974744797, 0.0055230180732905865, 0.004889050964266062, -0.007157891057431698, -0.013313878327608109, 0.002017567167058587, -0.024476006627082825, 0.0443105548620224, -0.006012619007378817, -0.018580332398414612, 0.054870039224624634, 0.05869108438491821, -0.010502699762582779, -0.010877084918320179, -0.04799410328269005, 0.03645098954439163, 0.012574808672070503, 0.021888073533773422, 0.022740621119737625, 0.023571712896227837, -0.024012384936213493, -0.00762363662943244, 0.04311711713671684, 0.008461718447506428, 0.02498319186270237, -0.012760452926158905, 0.05046435073018074, -0.01098339632153511, -0.044712699949741364, -0.04302586615085602, -0.022973716259002686, 0.013978848233819008, -0.02331540361046791, -0.021179797127842903, -0.010766171850264072, -0.031034020707011223, 0.02681575156748295, -0.03658508509397507, 0.054803527891635895, 0.040098726749420166, -0.0010164021514356136, -0.05552035942673683, -0.006532825995236635, 0.03318072855472565, -0.022291801869869232, 0.032670922577381134, 0.05170827731490135, -0.011548315174877644, -0.03549034520983696, -0.035058505833148956, -0.002133056055754423, -0.03597690165042877, -0.004588708747178316, -0.02897985838353634, -0.0366906076669693, -0.0794457346200943, 0.016131972894072533, 0.09472057968378067, -0.00677353935316205, -0.002860599895939231, 0.010951320640742779, -0.07132818549871445, 0.018969064578413963, 0.042167555540800095, 0.01291149016469717, -0.01238129660487175, -0.006316349841654301, -0.020917242392897606, 0.0002205138880526647, 0.016119055449962616, -0.002352980663999915, -0.013983767479658127, -0.032470691949129105, 0.004476622678339481, -0.052500225603580475, -0.05433756485581398, -0.005337613169103861, 0.02491021901369095, 0.03594771772623062, -0.04277161881327629, -0.030397454276680946, -0.01836305670440197, -0.0032216713298112154, -0.048987530171871185, 0.057961564511060715, -0.03567514941096306, 0.04242071509361267, 0.007497111801058054, -0.026848310604691505, 0.002744104713201523, 0.049861397594213486, -0.01802508719265461, 0.02969209849834442, -0.04704466089606285, 0.015387426130473614, -0.040581535547971725, 0.04075586795806885, 0.024111948907375336, -0.017805421724915504, -0.019043605774641037, 0.021923378109931946, -0.0006943128537386656, 0.02516835369169712, 0.042611848562955856, -0.011650960892438889, 0.0022046356461942196, 0.03545205667614937, 0.021661724895238876, 0.026722855865955353, 0.017741933465003967, 0.040315572172403336, 0.050225164741277695, 0.013014508411288261, 0.03918560594320297, -0.018719078972935677, 0.05098099261522293, 0.0019359533907845616, 0.012909974902868271, -0.05988021567463875, -0.01890866830945015, -0.03196152299642563, 0.030220067128539085, -0.021271424368023872, 0.03960743546485901, -0.023490600287914276, 0.015738962218165398, 0.09066475927829742, 0.012808440253138542, -0.012998581863939762, -0.0700024962425232, -0.019090622663497925, 0.012965496629476547, -0.013031858019530773, 0.03900438919663429, -0.01879725232720375, -0.032484304159879684, -0.02462008222937584, -0.013829987496137619, -0.003748478600755334, -0.0637509897351265, -0.002176581183448434, 0.01987483911216259, -0.023943305015563965, 0.006999397650361061, -0.061308059841394424, 0.007639827206730843, -0.05428270250558853, -0.04178139567375183, 0.0077389078214764595, 0.013197218999266624, 0.02608579583466053, -0.026598136872053146, -0.0022831636015325785, -0.0648752897977829, -0.026722965762019157, -0.004373279865831137, -0.06189129874110222, 0.0246741883456707, 0.020823637023568153, 0.0075967623852193356, -0.019426589831709862, 0.0487104095518589, 0.02414356917142868, -0.05553928017616272, -0.06281297653913498, -0.08186020702123642, -0.056936923414468765, -0.02585594542324543, 0.022513899952173233, 0.03224390000104904, 0.01790885254740715, 0.017669212073087692, -0.007002704776823521, -0.0028915093280375004, -0.02090650610625744, 0.02511879988014698, 0.030206823721528053, -0.02252398617565632, 0.007040789816528559, 0.02327203005552292, -0.0116680096834898, 0.016931023448705673, 0.025171194225549698, 0.024146167561411858, -0.0033752338495105505, 0.014634544029831886, -0.002855355618521571, -0.03956654667854309, 0.031258419156074524, 0.016190029680728912, -0.04014774039387703, 0.022623231634497643, 0.0327390618622303, -0.03455318883061409, 0.016570325940847397, 0.06115175038576126, -0.03152773156762123, 0.04101831093430519, 0.02537848800420761, 0.05705010145902634, 0.04394994676113129, -0.0094135208055377, 0.005484110675752163, -0.057548630982637405, 0.04845612496137619, -0.0162492748349905, -0.024287637323141098, -0.03504530340433121, 0.027878673747181892, 0.024784523993730545, 0.016920149326324463, -0.03218496963381767, -0.026487750932574272, -0.016807882115244865, 0.03738480061292648, 0.044436726719141006, -0.006387997884303331, -0.009378988295793533, 0.009097940288484097, -0.05539817735552788, 0.034087058156728745, -0.03305201977491379, 0.0461418442428112, -0.010382751002907753, 0.05906345695257187, -0.018314335495233536, -0.003498608944937587, -0.041544295847415924, -0.007697109133005142, 0.010740911588072777, 0.07607283443212509, 0.014085921458899975, -0.05814637988805771, 0.008958641439676285, 0.01893956959247589, -0.05376805365085602, -0.050750717520713806, 0.05277617275714874, -0.041788890957832336, 0.029018912464380264, -0.001452505006454885, 0.035279370844364166, 0.0560770258307457, -0.07077300548553467, -0.06350088119506836, -0.05418922379612923, 0.04262125864624977, -0.007739054970443249, 0.003948741592466831, 0.04378794506192207, 0.05277688056230545, -0.03793853521347046, 0.04676193371415138, -0.021940719336271286, 0.02921590395271778, 0.009982822462916374, -0.06767796725034714, -0.009759947657585144, 0.042267169803380966, 0.0214785598218441, 0.020458169281482697, -0.01151545811444521, -0.040734730660915375, 0.04138572886586189, -0.027463862672448158, -0.005474437959492207, -0.026144687086343765, -0.023057881742715836, 0.11206050962209702, -0.08921246230602264, -0.0016582218231633306, -0.022211233153939247, -0.025085434317588806, 0.029886312782764435, -0.004891776945441961, -0.015408042818307877, -0.003376775188371539, 0.027955198660492897, 0.06936974823474884, -0.07795247435569763, -0.0831284373998642, -0.018822912126779556, 0.02133198454976082, -0.04338457062840462, 0.014082077890634537, -0.09745365381240845, -0.02980624884366989, 0.05827634036540985, 0.048745423555374146, 0.06698437035083771, 0.07724093645811081, -0.007557115983217955, -0.007909783162176609, -0.0508272685110569, 0.002491250168532133, 0.015621822327375412, -0.05921284481883049, 0.020367233082652092, -0.047669220715761185, -0.015105905011296272, -0.03966418281197548, 0.04672660306096077, -0.004770262166857719, 0.03559809550642967, 0.006725278217345476, -0.033261995762586594, -0.04237939789891243, -0.007790345698595047, 0.014504180289804935, -0.0008932495838962495, 0.03694527968764305, -0.016086865216493607, -0.05514397472143173, 0.020462756976485252, 0.00040793948573991656, 0.017971141263842583, 0.021015280857682228, 0.03500381112098694, -0.052115630358457565, 0.05757655203342438, 0.06837991625070572, 0.00046418988495133817, -0.04091249778866768, 0.0034227652940899134, -0.009179177694022655, -0.07297138124704361, 0.0030781240202486515, -0.010325904004275799, 0.03271299973130226, 0.04437178373336792, -0.056845828890800476, -0.005890720058232546, 0.011949052102863789, 0.03858531266450882, -0.06334593147039413, 0.01834302954375744, -0.010773435235023499, -0.0683424100279808, -0.0014685235219076276, 0.012165072374045849, -0.0179786067456007, -0.01924998126924038, -0.035440318286418915, -0.00010175767238251865, 0.05550557002425194, -0.02904360555112362, -0.007727338932454586, 0.07067058235406876, -0.04158942028880119, -0.028131194412708282, -0.026206884533166885, -0.004699131939560175, 0.029920637607574463, -0.030325306579470634, 0.01219961978495121, -0.0008887720759958029, 0.01327823381870985, -0.03871142864227295, -0.07737645506858826, -0.01371798012405634, -0.04895801469683647, -0.08334405720233917, -0.015628619119524956, 0.05749190226197243, -0.011111410334706306, 0.03012867085635662, 0.03470854461193085, 0.04150654748082161, 0.0076619903557002544, 0.05914239212870598, -0.04157936945557594, 0.027347156777977943, -0.061908893287181854, 0.047090087085962296, 0.020058339461684227, 0.05370432883501053, 0.0017214950639754534, -0.0058792573399841785, -0.03755047544836998, 0.055345192551612854, -0.021147452294826508, 0.01345820352435112, 0.007362829986959696, 0.038841426372528076, 0.020800363272428513, -0.06852526217699051, -0.030906032770872116, -0.010592425242066383, -0.012701689265668392, -0.0278356671333313, 0.02551993355154991, 0.049629706889390945, -0.005944432225078344, -0.06322947889566422, -0.044168513268232346, 0.04258772358298302, 0.031903669238090515, -0.007909558713436127, -0.014777664095163345, -0.026544779539108276, -0.03417721763253212, -0.017024226486682892, -0.02777142822742462, -0.013018406927585602, 0.006565972231328487, -0.020131200551986694, 0.03935947269201279, 0.045998960733413696, 0.009209007024765015, -0.014074348844587803, -0.02546088583767414, -0.05396163463592529, -0.004849886056035757, 0.051932770758867264, -0.0029068607836961746, -0.015647366642951965, 0.00788807962089777, -0.037510406225919724, -0.0339355431497097, 0.03048223815858364, -0.019077278673648834, 0.02917276695370674, 0.02120021916925907, 0.0373271107673645, 0.029234368354082108, 0.02157294750213623, -0.008333458565175533, 0.015945062041282654, -0.03048298880457878, -0.05303386226296425, -0.03377576172351837, 0.008550025522708893, 0.034566767513751984, 0.02979150414466858, 0.055881317704916, 0.04658157005906105, 0.005758875515311956, -0.019365882501006126, -0.05844714120030403, -0.004021807573735714, 0.027636975049972534, -0.0399739071726799, -0.014300445094704628, 0.009366566315293312, -0.0500820018351078, 0.005353977438062429, 0.0015788925811648369, 0.03157243877649307, -0.01698804460465908, -0.058756470680236816, -0.004977883771061897, -0.05486709251999855, 0.025551937520503998, 0.006121993530541658 ]
<p>I am reading up on the Schrödinger equation and I quote:</p> <blockquote> <p><em>Because the potential is symmetric under $x\to-x$, we expect that there will be solutions of definite parity.</em></p> </blockquote> <p>Could someone kindly explain why this is true? And perhaps also what it means physically?</p>
g1498
[ 0.015274706296622753, 0.050965532660484314, -0.009606215171515942, -0.030754592269659042, 0.0714239776134491, 0.006858169101178646, 0.0047497134655714035, 0.07397326081991196, 0.004546002019196749, -0.022104881703853607, -0.005563670769333839, 0.028779415413737297, 0.024207035079598427, -0.0569293387234211, 0.012201901525259018, -0.013135812245309353, 0.0902797058224678, -0.03467130661010742, -0.03137023001909256, 0.02997218631207943, -0.11113638430833817, -0.0016590768937021494, 0.012802252545952797, -0.050642408430576324, 0.026570996269583702, -0.013736006803810596, 0.039768997579813004, -0.09276551753282547, -0.0489303357899189, -0.023652903735637665, 0.015923235565423965, 0.0027850030455738306, 0.040317416191101074, -0.06686922907829285, -0.01956375129520893, -0.007000295910984278, 0.057972390204668045, -0.001964786322787404, 0.052221909165382385, -0.05478281527757645, 0.0899212434887886, 0.016946865245699883, -0.01940314844250679, -0.04980611801147461, -0.05591144785284996, -0.06866216659545898, 0.0068768225610256195, 0.060249995440244675, 0.005952766165137291, -0.028035864233970642, 0.014004703611135483, 0.045585934072732925, 0.053731538355350494, -0.009254295378923416, 0.009025843814015388, 0.002567071234807372, 0.09312432259321213, -0.019388621672987938, -0.007641477044671774, 0.007787083275616169, -0.0009342837729491293, -0.003514775773510337, 0.029889466241002083, 0.017151083797216415, 0.071036197245121, -0.05984928086400032, -0.07316764444112778, 0.0053108083084225655, 0.06279901415109634, 0.009760151617228985, 0.03674868866801262, -0.04383755475282669, 0.006447194144129753, -0.03343794867396355, 0.027685558423399925, -0.0005465949652716517, -0.004648798611015081, -0.018656359985470772, 0.027647972106933594, 0.014007389545440674, 0.0068482812494039536, -0.012186546809971333, 0.028641244396567345, -0.025492839515209198, 0.04614650830626488, 0.0345255509018898, 0.016417525708675385, -0.0329902358353138, -0.030752748250961304, 0.06458360701799393, -0.000015556744983769022, -0.0490582212805748, 0.016628172248601913, 0.049354083836078644, 0.01887638494372368, -0.020210549235343933, -0.0362023189663887, 0.04537440463900566, 0.0029716850258409977, 0.02131362073123455, -0.02818594127893448, 0.06548964232206345, 0.05957883223891258, -0.013507785275578499, 0.057553913444280624, -0.029632901772856712, 0.004483978729695082, 0.03071523644030094, -0.01656041480600834, -0.060622528195381165, 0.0017977013485506177, 0.01288159005343914, -0.05037275701761246, 0.014054028317332268, -0.05709933489561081, 0.020742792636156082, 0.058215219527482986, -0.06697368621826172, 0.007497994229197502, 0.048821210861206055, 0.03632865846157074, 0.01922929473221302, 0.0026927408762276173, 0.029033944010734558, -0.034865718334913254, 0.007856459356844425, 0.029054636135697365, -0.005844444502145052, 0.0013686332385987043, -0.03744244948029518, 0.030491411685943604, -0.01649882271885872, 0.003445485606789589, 0.013646097853779793, 0.04420216754078865, 0.0053876843303442, -0.00834650732576847, 0.007893524132668972, 0.004486445803195238, -0.017007408663630486, -0.02538612298667431, 0.0019198969239369035, -0.009502887725830078, 0.0056101433001458645, -0.05272175371646881, -0.06911715120077133, -0.0628155842423439, -0.027942951768636703, 0.04003147780895233, 0.024681663140654564, 0.0076993596740067005, 0.05973284691572189, -0.017915792763233185, -0.08014990389347076, -0.010342184454202652, -0.04982373118400574, 0.07634754478931427, -0.0012098855804651976, 0.00856265239417553, -0.00516746798530221, 0.02235288918018341, 0.022309089079499245, -0.02646862342953682, 0.04075215756893158, -0.07815273851156235, -0.004826511722058058, -0.046357497572898865, -0.036321964114904404, -0.02342113107442856, -0.03638544678688049, 0.01560879498720169, 0.032439813017845154, 0.023753665387630463, 0.04416915029287338, 0.02908061072230339, 0.07690475881099701, 0.03073766455054283, 0.024724885821342468, -0.011666609905660152, 0.029197731986641884, 0.008780472911894321, -0.05447652190923691, 0.04518627002835274, -0.058081500232219696, -0.04298946633934975, -0.012241664342582226, -0.0024602082557976246, -0.0013296587858349085, -0.047480251640081406, 0.03440897911787033, 0.02646941877901554, 0.01890057697892189, 0.01967284455895424, 0.058959826827049255, 0.0244609322398901, -0.009000408463180065, 0.037390321493148804, -0.031168125569820404, -0.0005467847804538906, -0.011268089525401592, -0.06963302195072174, 0.05527563393115997, 0.0013492545112967491, 0.02478288859128952, -0.001109535456635058, 0.027406539767980576, 0.04686998575925827, -0.0233877282589674, 0.08103781193494797, -0.028724398463964462, 0.01823624223470688, 0.005453701596707106, -0.025617698207497597, -0.05268988013267517, -0.005996423307806253, 0.012645929120481014, -0.038461834192276, 0.018500272184610367, -0.05823241546750069, 0.043666284531354904, -0.022306015715003014, -0.03949777036905289, -0.015085658989846706, 0.07169968634843826, -0.024556143209338188, 0.0013205589493736625, -0.04752170667052269, -0.027161210775375366, -0.05486948788166046, 0.02909083291888237, -0.018667615950107574, -0.03828345984220505, 0.008165819570422173, -0.005995491053909063, 0.0410444475710392, 0.06756184995174408, -0.001769506256096065, -0.009465064853429794, 0.038519494235515594, -0.03605760261416435, -0.013517408631742, -0.019654490053653717, -0.04993924871087074, 0.07536862790584564, 0.022199416533112526, 0.00842277705669403, 0.03145914524793625, -0.027997544035315514, -0.0605093389749527, 0.0018333240877836943, 0.04344649985432625, -0.054276034235954285, -0.01088046282529831, -0.00015079592412803322, -0.008048002608120441, -0.04480950906872749, 0.029461562633514404, 0.04376083239912987, 0.013141307979822159, 0.00004730104046757333, -0.0032728298101574183, 0.025847936049103737, 0.030722936615347862, -0.022918177768588066, -0.04625633731484413, 0.02629377320408821, -0.02214939147233963, 0.027577733621001244, 0.04594726487994194, -0.008232662454247475, 0.006325969006866217, 0.08834236860275269, 0.012644929811358452, 0.011294307187199593, -0.056837599724531174, -0.06107333302497864, -0.003675838466733694, -0.0005731421988457441, 0.03366963937878609, -0.0026601930148899555, -0.04056982696056366, 0.014719597063958645, -0.01840396597981453, -0.014054053463041782, 0.07863136380910873, -0.026197923347353935, -0.056323010474443436, -0.017888955771923065, 0.06572730094194412, 0.026224004104733467, -0.021241312846541405, 0.015488386154174805, 0.07811040431261063, -0.011644636280834675, -0.006053162273019552, 0.0351436622440815, -0.024220559746026993, -0.03483298420906067, -0.044097695499658585, 0.04018175229430199, -0.014363111928105354, 0.0793544128537178, -0.03200747072696686, 0.04383630305528641, 0.03367888182401657, 0.0355101078748703, -0.028685428202152252, -0.016676319763064384, 0.00630055321380496, -0.020302852615714073, -0.028820350766181946, 0.05208759382367134, -0.020871320739388466, -0.0040994384326040745, -0.05739563703536987, 0.028653927147388458, -0.026576390489935875, 0.07012256979942322, 0.016118362545967102, -0.05726001039147377, -0.03527379781007767, -0.005594182293862104, 0.023905035108327866, 0.018694160506129265, -0.01261896826326847, -0.007700684946030378, -0.041680410504341125, -0.006623013410717249, -0.03686198964715004, 0.015810640528798103, 0.018298380076885223, -0.004577742889523506, 0.05499284341931343, 0.004806062206625938, -0.07007620483636856, -0.006672785617411137, -0.026139937341213226, 0.02605586126446724, 0.00726423179730773, -0.035125140100717545, -0.010377125814557076, -0.0995916873216629, -0.04141872748732567, 0.03694053366780281, -0.026942996308207512, 0.029224278405308723, -0.026264505460858345, -0.02861517108976841, 0.04777884483337402, -0.01000175904482603, 0.007621111813932657, 0.03242309391498566, 0.0007640296826139092, -0.020824966952204704, -0.04240529611706734, 0.024943705648183823, -0.03930403292179108, 0.016104815527796745, -0.030946308746933937, 0.049794938415288925, -0.0017072272021323442, -0.02443845197558403, 0.030207892879843712, -0.002620752202346921, 0.05236218497157097, 0.048224035650491714, -0.03516796976327896, -0.0038409156259149313, 0.015127355232834816, -0.032271455973386765, 0.0055996691808104515, -0.018853100016713142, 0.00883584562689066, 0.10870180279016495, 0.07398991286754608, -0.06367363780736923, -0.02616017870604992, -0.0024746283888816833, 0.016164714470505714, -0.017190881073474884, 0.0025950511917471886, -0.014413065277040005, -0.009374001063406467, 0.07105028629302979, 0.026476776227355003, -0.003651924431324005, -0.0005695604486390948, 0.06770254671573639, -0.01423440221697092, -0.026628844439983368, 0.06846784800291061, 0.014846679754555225, -0.008844608440995216, 0.05060623586177826, -0.06794510781764984, 0.021452991291880608, -0.003431876190006733, -0.042828746140003204, -0.034065667539834976, 0.026115629822015762, 0.014303178526461124, -0.051153942942619324, -0.03206196799874306, -0.008746452629566193, 0.026485268026590347, -0.033370256423950195, -0.026617001742124557, -0.017504416406154633, -0.009099741466343403, -0.03126596659421921, 0.04445015266537666, 0.030068358406424522, 0.02061512880027294, 0.0016941678477451205, -0.003917271737009287, 0.008766790851950645, -0.017009755596518517, -0.03234012797474861, 0.06623958051204681, -0.03885404393076897, 0.046972617506980896, -0.017660995945334435, 0.05569394305348396, 0.0013783914037048817, 0.013005956076085567, -0.023086512461304665, 0.018214141950011253, -0.025367464870214462, 0.00275582168251276, -0.010825807228684425, 0.016903426498174667, 0.007486339658498764, -0.0010053419973701239, 0.015807829797267914, -0.027693981304764748, 0.013846999034285545, -0.059816475957632065, -0.020682023838162422, -0.015844255685806274, 0.03956983983516693, 0.08113853633403778, -0.01408927422016859, 0.03467993810772896, -0.004224215634167194, 0.034566570073366165, 0.005859352648258209, -0.020142294466495514, -0.009039984084665775, 0.032038237899541855, -0.04115942493081093, -0.0008312215213663876, 0.02905339002609253, -0.00881281215697527, -0.015600353479385376, 0.0027833012863993645, -0.03401636704802513, -0.03942470625042915, 0.01963762193918228, 0.059396665543317795, -0.009915534406900406, -0.01275078859180212, -0.10941106081008911, -0.01673588529229164, -0.01699010282754898, 0.04725335165858269, 0.03934605047106743, 0.02612486109137535, 0.0013562097446992993, -0.09275969862937927, -0.037322062999010086, 0.0013642976991832256, 0.029797013849020004, 0.005706369411200285, 0.04138576239347458, 0.032710328698158264, 0.009211468510329723, -0.019404608756303787, -0.050720103085041046, -0.021079622209072113, 0.004227437078952789, -0.014945500530302525, -0.0040252371691167355, 0.012525985948741436, 0.008815757930278778, -0.01940878853201866, 0.01769818738102913, 0.0054621947929263115, 0.011038484051823616, -0.05775182321667671, 0.009942068718373775, 0.0583871565759182, 0.05853019282221794, 0.007029810454696417, 0.019297799095511436, -0.03845226392149925, -0.02513926289975643, 0.03248178958892822, 0.009974797256290913, 0.02021118439733982, -0.020813286304473877, -0.0010501191718503833, -0.011524242348968983, 0.03142194077372551, -0.02413419634103775, 0.0048258015885949135, 0.058018215000629425, 0.07316263020038605, -0.020989984273910522, 0.056740373373031616, -0.06785908341407776, -0.003897042479366064, -0.07626032084226608, -0.006159600801765919, 0.02033134549856186, 0.05207430198788643, -0.0526338666677475, -0.009799488820135593, 0.020900022238492966, 0.014441299252212048, -0.06774310767650604, 0.04999670758843422, 0.03249740228056908, 0.010785646736621857, -0.02333829738199711, 0.06341717392206192, 0.022102439776062965, -0.06673091650009155, -0.016831476241350174, 0.005502681247889996, 0.0713769719004631, 0.034762583673000336, 0.030321020632982254, 0.07569904625415802, -0.013748375698924065, 0.07237136363983154, -0.030427372083067894, -0.0014710996765643358, -0.00610551331192255, 0.010045179165899754, 0.0001506657717982307, -0.001427363371476531, 0.007143273483961821, 0.027150653302669525, 0.06444057822227478, 0.006229850463569164, -0.02794499881565571, -0.08417538553476334, 0.03871110826730728, 0.026814382523298264, -0.024506522342562675, -0.015839260071516037, -0.0014250960666686296, -0.07028696686029434, -0.009174746461212635, 0.0013090604916214943, 0.020464086905121803, 0.03847567364573479, -0.03953603282570839, -0.018565047532320023, -0.014642259106040001, 0.06842414289712906, -0.043273523449897766, -0.02151491492986679, 0.013622132129967213, 0.006722487974911928, -0.05055953934788704, -0.02587153948843479, -0.005247313994914293, 0.0017299677710980177, 0.056946054100990295, -0.07747016102075577, 0.02610713057219982, 0.0017306252848356962, 0.034647680819034576, -0.0019206174183636904, -0.06043444573879242, -0.020171932876110077, -0.04573843628168106, 0.01000540517270565, 0.008225121535360813, -0.007887318730354309, -0.03734155744314194, 0.06695868074893951, -0.012905082665383816, -0.026643481105566025, -0.000642463390249759, -0.0028129518032073975, -0.023647114634513855, 0.03953680023550987, 0.03311483561992645, -0.0690535306930542, -0.013326172716915607, -0.015070960856974125, -0.01251555047929287, 0.07586002349853516, -0.01839573308825493, -0.010738656856119633, -0.003521349746733904, -0.037533681839704514, -0.007805014494806528, 0.05354473739862442, -0.03803574666380882, -0.0261508971452713, 0.04678122699260712, -0.02660238742828369, -0.00509649096056819, -0.01658421941101551, 0.017728274688124657, -0.019190801307559013, 0.09171298146247864, 0.022967610508203506, 0.023863736540079117, -0.023156719282269478, -0.057354673743247986, 0.016262589022517204, -0.02861175313591957, 0.017283985391259193, 0.02990945614874363, -0.031244153156876564, 0.0007147947326302528, 0.037283845245838165, -0.02108839340507984, -0.0442475788295269, 0.03323725238442421, 0.08141699433326721, 0.01692306064069271, -0.008611761964857578, 0.02981387823820114, 0.048306334763765335, -0.022493284195661545, -0.0056158131919801235, 0.025082165375351906, -0.00017152797954622656, 0.030610300600528717, -0.029798496514558792, 0.00768782664090395, -0.003488606307655573, -0.016288921236991882, 0.06292112171649933, 0.02112146094441414, 0.0067036752589046955, 0.04616573080420494, 0.07908792048692703, -0.09132523089647293, 0.028913643211126328, 0.08790010958909988, 0.012767015025019646, 0.026346737518906593, -0.06907295435667038, -0.011346935294568539, 0.020264092832803726, -0.0312592014670372, 0.026616739109158516, -0.015829095616936684, -0.012822412885725498, -0.027531372383236885, -0.026780037209391594, -0.04582970216870308, 0.006850604899227619, -0.03190998360514641, -0.028359482064843178, -0.0024770160671323538, -0.019637232646346092, 0.003419842105358839, -0.05168730020523071, 0.03208618983626366, 0.030695997178554535, -0.000386731670005247, 0.004635464865714312, -0.06231718882918358, 0.008103870786726475, 0.002749502891674638, 0.017634589225053787, 0.02180584706366062, -0.001080191694200039, 0.00863137748092413, 0.01398821733891964, -0.027604658156633377, 0.0017078676028177142, 0.007154288701713085, -0.01097308099269867, 0.001142591703683138, -0.024165060371160507, -0.03645966574549675, -0.047234173864126205, 0.003436064813286066, -0.005625941790640354, -0.02020077221095562, 0.06677225977182388, 0.0032289312221109867, -0.01737663522362709, -0.007746612187474966, 0.03558054566383362, -0.02797088585793972, -0.04646039754152298, 0.02410704270005226, -0.017063114792108536, 0.03576851636171341, -0.030839350074529648, -0.0074096741154789925, -0.009225710295140743, -0.027835560962557793, -0.024060824885964394, -0.02612605318427086, -0.009168879128992558, -0.02361029013991356, 0.006131094880402088, -0.046400878578424454, -0.02414296567440033, -0.004275686107575893, 0.0020994001533836126, 0.0008979022386483848, -0.01857258938252926, -0.024053804576396942, 0.08045483380556107, -0.03152180090546608, -0.02920878864824772, -0.054076939821243286, 0.012218538671731949, -0.006353628821671009, 0.04571763426065445, 0.024113059043884277, 0.02114592120051384, -0.044661786407232285, -0.028498714789748192, -0.05710255727171898, -0.0021120328456163406, -0.006671433337032795, -0.02888385020196438, 0.03506585210561752, 0.01078787911683321, 0.0011722331400960684, 0.04373864829540253, 0.015040192753076553, 0.03021383285522461, -0.01330667082220316, -0.024980325251817703, 0.005540771409869194, -0.01033979281783104, -0.010135256685316563, 0.022941822186112404, -0.07058268785476685, -0.02510032244026661, -0.028917914256453514, -0.02418948896229267, 0.015488315373659134, -0.032902345061302185, 0.03669751062989235, -0.020054513588547707, -0.022212840616703033, -0.014546516351401806, -0.021416446194052696, -0.07221096754074097, 0.07345328480005264, 0.04236132279038429, -0.06464379280805588, -0.008370616473257542, 0.008772999048233032, 0.010042178444564342, -0.0022763642482459545, 0.01941847801208496, -0.032995715737342834, -0.030740559101104736, 0.018036801367998123, -0.011646580882370472, -0.051216382533311844, -0.04887692257761955, -0.05907130986452103 ]
<p>when firing a proton (for example) to an atomic nucleus, from a distance $D$, the deflection angle of the proton $\alpha $ to the type of changes atomic nuclei? or always constant?</p>
g1499
[ 0.024351956322789192, -0.056687235832214355, -0.010787093080580235, -0.015072351321578026, 0.09237934648990631, -0.010105714201927185, 0.009027979336678982, 0.026334069669246674, 0.0005527018220163882, -0.029384886845946312, -0.045765697956085205, 0.016761403530836105, -0.0024012948852032423, -0.029659487307071686, 0.07369644939899445, 0.0017970205517485738, 0.005123395472764969, -0.050862666219472885, 0.011097919195890427, 0.027369225397706032, 0.0282516460865736, -0.0005647566867992282, -0.0376632884144783, -0.035731349140405655, 0.07574961334466934, 0.006272970698773861, 0.018756460398435593, -0.02702956460416317, -0.04808596149086952, -0.004329879768192768, 0.017820652574300766, -0.00357779860496521, 0.05252780765295029, 0.004067333415150642, -0.0300199743360281, -0.0665503740310669, 0.02238270826637745, -0.021650316193699837, 0.1211354210972786, -0.024813883006572723, -0.033445198088884354, 0.010023935697972775, 0.006985413376241922, 0.01355582382529974, 0.008689278736710548, -0.040239885449409485, -0.006424030289053917, -0.016116641461849213, -0.07929886877536774, 0.021984072402119637, -0.04838186874985695, 0.002238111337646842, -0.022505076602101326, -0.0566197894513607, 0.0467325784265995, 0.014853439293801785, -0.0140024209395051, 0.017256049439311028, 0.06918419897556305, 0.03696316480636597, -0.0029890318401157856, 0.004973685368895531, -0.028365937992930412, -0.030082138255238533, 0.087028868496418, -0.05712789297103882, -0.04214968904852867, 0.009140076115727425, -0.013146283105015755, -0.03425785154104233, -0.00684591056779027, -0.05403686314821243, -0.04984572157263756, 0.015146798454225063, 0.017942281439900398, 0.007681427989155054, -0.00015158498717937618, -0.04837680608034134, -0.013190087862312794, 0.028646672144532204, -0.04567450284957886, -0.04003553092479706, 0.032432496547698975, -0.013841429725289345, 0.06255166232585907, 0.0352608785033226, 0.06367427855730057, 0.05192474648356438, -0.031407102942466736, 0.028801023960113525, -0.009581688791513443, -0.00660929037258029, -0.02217366360127926, 0.05586014315485954, -0.03441334143280983, -0.04272274300456047, -0.022517060860991478, 0.06483534723520279, 0.027229800820350647, 0.02314031682908535, 0.004484631586819887, 0.01006050780415535, 0.06934767961502075, -0.017745552584528923, -0.01947811245918274, 0.011098023504018784, 0.008902829140424728, -0.03551637381315231, 0.03118843212723732, -0.01868743821978569, -0.02448650449514389, -0.06178848072886467, -0.02067633531987667, -0.02205219864845276, -0.0015368966851383448, -0.05384490638971329, 0.032254766672849655, -0.008599516935646534, 0.040246717631816864, 0.017209423705935478, 0.04693403095006943, -0.019001619890332222, -0.04920276626944542, 0.053507350385189056, -0.03940387815237045, -0.04805382713675499, -0.06976303458213806, 0.0016911490820348263, 0.0417608842253685, -0.02474285662174225, -0.0025233584456145763, -0.026076972484588623, -0.03657851740717888, -0.0031984609086066484, 0.007576747331768274, 0.026743141934275627, 0.025543173775076866, -0.05201146751642227, -0.026583442464470863, 0.011260895989835262, 0.034820109605789185, 0.025305181741714478, 0.001219167374074459, -0.006616429425776005, -0.006458132062107325, -0.0062721059657633305, -0.002135959453880787, -0.024389559403061867, 0.05220455676317215, 0.03436966612935066, 0.038255710154771805, 0.016497405245900154, 0.01735103316605091, 0.011481821537017822, 0.005521363578736782, -0.01774320937693119, -0.010525464080274105, 0.022438105195760727, -0.03822355717420578, -0.013353119604289532, 0.049081336706876755, -0.053456950932741165, -0.06689896434545517, -0.023018628358840942, -0.06913153827190399, -0.009561490267515182, -0.012125293724238873, 0.00989731214940548, 0.03283087536692619, 0.0057943519204854965, -0.05806875601410866, 0.05090297386050224, 0.02725953981280327, -0.012115741148591042, -0.05115076154470444, 0.055810458958148956, -0.016573840752243996, -0.05335530266165733, 0.018437271937727928, 0.01782193034887314, -0.026639116927981377, 0.048396360129117966, 0.029812272638082504, -0.006422051694244146, -0.014558392576873302, 0.008850259706377983, -0.026893196627497673, -0.030404023826122284, -0.03237316384911537, -0.00031572231091558933, -0.015622861683368683, 0.01176008302718401, 0.015816858038306236, 0.034268300980329514, 0.04159729555249214, -0.05658857896924019, 0.03281092643737793, -0.03315277025103569, -0.044486891478300095, 0.046773720532655716, -0.03366783633828163, -0.010627847164869308, 0.06469254195690155, 0.05355700105428696, 0.01291356049478054, 0.0034493154380470514, 0.026105234399437904, -0.00045902462443336844, 0.028395501896739006, 0.012908980250358582, 0.000986321596428752, 0.08883173018693924, -0.0878613069653511, -0.020870201289653778, 0.08345392346382141, 0.0473499670624733, -0.007042015437036753, 0.010871946811676025, 0.00296384678222239, -0.002022472443059087, -0.04312993958592415, 0.040307946503162384, 0.04337260127067566, 0.020839717239141464, -0.029092421755194664, 0.007477415259927511, -0.02397499606013298, 0.03262961655855179, 0.03461109846830368, 0.0023949944879859686, -0.059721894562244415, 0.04126688092947006, -0.038675714284181595, -0.028161467984318733, 0.010206121951341629, 0.013401876203715801, 0.0031379826832562685, 0.015586337074637413, 0.020396627485752106, -0.0643291175365448, 0.0245607178658247, -0.05509507283568382, -0.11059557646512985, -0.020211294293403625, -0.027055975049734116, -0.023923451080918312, 0.025527093559503555, 0.0247359536588192, -0.004281027242541313, -0.009204413741827011, 0.03117953985929489, 0.012976040132343769, -0.04884069040417671, 0.05563301220536232, -0.06213151663541794, -0.012342543341219425, -0.03224732726812363, -0.050449661910533905, -0.015467648394405842, -0.03561920300126076, 0.02237268164753914, -0.09927264600992203, 0.01734957844018936, -0.007542390841990709, -0.02199711464345455, -0.00618624035269022, -0.00606314605101943, 0.07270022481679916, -0.017819911241531372, 0.014576778747141361, -0.028597937896847725, 0.08958771824836731, 0.07263748347759247, 0.08983763307332993, -0.050470877438783646, -0.0049843331798911095, -0.004555138759315014, -0.03273792564868927, -0.0047981576062738895, 0.004986801650375128, -0.040690042078495026, 0.03648079186677933, -0.05838834494352341, 0.04856797307729721, 0.059147972613573074, 0.052442438900470734, -0.014989770948886871, -0.011320722289383411, -0.0309386495500803, -0.009638410061597824, 0.013744895346462727, 0.021395986899733543, 0.028684016317129135, 0.0044820476323366165, -0.023469358682632446, 0.03334071487188339, 0.09396045655012131, -0.01268141157925129, -0.0052892970852553844, 0.05571303516626358, 0.0003995877632405609, 0.017030183225870132, -0.02359727956354618, 0.030220063403248787, 0.00017503504932392389, 0.05740632116794586, -0.009657741524279118, -0.04006136581301689, 0.02693755365908146, 0.03204232081770897, -0.066321961581707, 0.018548009917140007, -0.030425695702433586, 0.030306637287139893, -0.029979053884744644, -0.045819252729415894, 0.005114223342388868, 0.027087638154625893, -0.005096876993775368, 0.05709628388285637, -0.06810755282640457, -0.07830063253641129, -0.0060537089593708515, 0.005500744096934795, 0.02161278948187828, 0.013976825401186943, 0.025597333908081055, 0.06387544423341751, 0.004953292664140463, -0.033155180513858795, -0.0024092423263937235, 0.0019526694668456912, -0.017656156793236732, -0.030490100383758545, -0.03183063119649887, 0.025539875030517578, -0.025118058547377586, 0.03984053432941437, 0.020891336724162102, -0.03559218719601631, 0.023482874035835266, 0.01744680292904377, -0.05349336192011833, 0.006446604151278734, 0.08387112617492676, 0.03504546359181404, -0.023893635720014572, -0.06486206501722336, -0.029439719393849373, 0.009408748708665371, 0.022635506466031075, 0.0075370557606220245, -0.0076395743526518345, 0.04338131844997406, 0.050950076431035995, 0.0005054227076470852, -0.032524581998586655, 0.014004599303007126, -0.03208552673459053, 0.019192907959222794, -0.04408181086182594, -0.04643929377198219, 0.03675045073032379, 0.04755019396543503, -0.03078138642013073, -0.013007942587137222, -0.01667463779449463, 0.04976528882980347, 0.014636624604463577, 0.005062027368694544, -0.030422141775488853, -0.014663724228739738, 0.035972390323877335, 0.006024934817105532, -0.048572514206171036, 0.04920708388090134, 0.025915777310729027, 0.02010933868587017, -0.10092063248157501, 0.033270906656980515, -0.017299974337220192, 0.06271862983703613, 0.009347060695290565, 0.06704208999872208, -0.022401075810194016, 0.043784599751234055, 0.006015473511070013, -0.004781103692948818, 0.022374983876943588, -0.013286617584526539, 0.0036801083479076624, -0.0596691332757473, 0.01920795813202858, 0.009489133022725582, -0.005451773293316364, 0.008236974477767944, -0.03176799416542053, 0.018450601026415825, -0.05781141668558121, 0.04685383662581444, 0.01885259337723255, -0.018561331555247307, -0.02447577379643917, -0.07649319618940353, 0.0519859604537487, -0.012090959586203098, -0.024390241131186485, 0.03392232954502106, -0.046264342963695526, -0.03628026694059372, 0.02128441631793976, -0.007614780217409134, -0.026584429666399956, 0.002691299421712756, -0.0016584009863436222, -0.01452615950256586, 0.02145710401237011, 0.05887686461210251, -0.001847056089900434, -0.010815095156431198, 0.008886564522981644, 0.058601800352334976, -0.017458608373999596, 0.05736679956316948, 0.07285818457603455, 0.013276797719299793, 0.010971811600029469, 0.05457853525876999, 0.010361197404563427, -0.044241346418857574, -0.03545106202363968, -0.02826102450489998, 0.027909813448786736, -0.0037010719534009695, -0.05648283660411835, 0.01952751725912094, -0.015885060653090477, 0.03508695960044861, -0.03104684129357338, 0.047050926834344864, 0.07513675093650818, 0.03648309409618378, -0.022842803969979286, 0.05661080777645111, 0.046197447925806046, 0.04909816384315491, -0.06780387461185455, -0.011174354702234268, 0.019964218139648438, 0.0036385601852089167, -0.057014547288417816, 0.0034138280898332596, -0.03224780410528183, -0.04175306856632233, 0.010800596326589584, -0.03832264244556427, -0.07637631893157959, -0.006144674029201269, 0.01319938711822033, 0.01256037037819624, -0.02503320202231407, -0.016749832779169083, -0.003230299800634384, -0.042694199830293655, -0.00775707233697176, 0.03311144933104515, 0.0025446200743317604, -0.058017902076244354, -0.03804674372076988, 0.0022549384739249945, 0.002628318965435028, 0.005090593826025724, 0.017080776393413544, -0.030931785702705383, 0.05747842416167259, -0.0021653438452631235, 0.003929298371076584, -0.035426486283540726, -0.035760026425123215, -0.062378332018852234, -0.0005515686352737248, -0.023731743916869164, -0.011528974398970604, 0.016535110771656036, -0.015483862720429897, 0.012860574759542942, 0.017105532810091972, -0.025283582508563995, 0.02358420379459858, -0.03158339112997055, 0.04656672850251198, 0.008341502398252487, -0.002373113064095378, -0.022491758689284325, -0.021730968728661537, -0.03698962926864624, 0.007270130794495344, 0.06812288612127304, 0.046477802097797394, 0.0032687662169337273, -0.003431298304349184, -0.017199702560901642, 0.03959006443619728, 0.022956842556595802, -0.03959479182958603, 0.04053446650505066, 0.05727832391858101, -0.0009973670821636915, 0.00398290203884244, -0.04599100351333618, 0.0398864671587944, -0.026340316981077194, 0.047599080950021744, 0.047072187066078186, 0.025602418929338455, -0.024425728246569633, -0.059065744280815125, 0.03551812842488289, -0.06244145706295967, -0.000469892198452726, 0.016979020088911057, -0.021249685436487198, 0.012861162424087524, -0.029131924733519554, 0.023155134171247482, 0.02807067707180977, -0.052609313279390335, 0.009532816708087921, -0.03255859762430191, 0.020143646746873856, 0.009907658211886883, -0.021482596173882484, 0.001871301094070077, -0.011249135248363018, 0.020847950130701065, -0.043663397431373596, -0.00939565896987915, -0.0233292318880558, -0.010026015341281891, -0.014638299122452736, -0.0061179716140031815, -0.001175579964183271, 0.05149373039603233, 0.042781855911016464, -0.019981570541858673, -0.004625754896551371, -0.03766078129410744, -0.0035605300217866898, 0.03652983531355858, -0.04160319268703461, 0.007621890865266323, 0.022048527374863625, -0.024042250588536263, -0.04513274133205414, -0.00593778770416975, -0.013122609816491604, 0.034621238708496094, -0.0174778550863266, 0.009748854674398899, -0.026890702545642853, -0.007445611525326967, 0.04342038556933403, 0.019236205145716667, 0.03168543800711632, 0.036817267537117004, -0.05163336545228958, 0.01095027755945921, -0.019668525084853172, 0.04134756326675415, 0.01787925325334072, 0.012982118874788284, -0.0001667446194915101, 0.008680133149027824, 0.0037751963827759027, 0.03520600497722626, 0.009331518784165382, -0.06876671314239502, -0.047117773443460464, 0.014727568253874779, 0.09777197241783142, 0.018928077071905136, -0.020210720598697662, -0.0004899983177892864, -0.028164410963654518, -0.05668119341135025, 0.03258296102285385, -0.011023049242794514, 0.0411260649561882, -0.0012618487235158682, -0.05518915131688118, -0.00025605253176763654, -0.04354282468557358, -0.014471028000116348, -0.006813389714807272, -0.029506579041481018, 0.00012520980089902878, -0.018126390874385834, -0.008336151950061321, 0.04063398391008377, 0.05884546414017677, 0.0678120031952858, 0.034180399030447006, 0.055160876363515854, 0.010453560389578342, 0.001641969196498394, 0.02901165559887886, -0.0033755050972104073, 0.013619872741401196, 0.06606637686491013, 0.022673653438687325, -0.017364434897899628, 0.030050043016672134, -0.0064788819290697575, -0.02106907218694687, -0.023983832448720932, -0.04381969943642616, 0.020219560712575912, -0.0022433833219110966, -0.09965194761753082, 0.011451317928731441, 0.01786581426858902, 0.02258019521832466, -0.00011960333358729258, -0.012631136924028397, 0.024573884904384613, 0.018610017374157906, -0.02503536082804203, 0.00797447469085455, -0.038550447672605515, 0.013207381591200829, 0.025231821462512016, 0.04488201066851616, -0.02637067437171936, 0.01815183274447918, -0.06964316219091415, 0.09302173554897308, -0.07327553629875183, 0.0788075402379036, 0.028185414150357246, 0.034476738423109055, 0.008976985700428486, 0.09304020553827286, 0.04401025176048279, -0.026118116453289986, -0.05711549147963524, -0.014153903350234032, 0.044437225908041, 0.04758836701512337, -0.08575078099966049, -0.016322720795869827, 0.018390586599707603, -0.004164948593825102, -0.023327762261033058, 0.0769706517457962, 0.004445378668606281, 0.035716209560632706, -0.012815626338124275, -0.01620246097445488, -0.06306397169828415, -0.06234963238239288, -0.04683271050453186, -0.04919930547475815, 0.02649528719484806, -0.06580326706171036, 0.017897682264447212, 0.011669597588479519, 0.01270537730306387, -0.04499674588441849, 0.005800949409604073, 0.00695107551291585, -0.02704155445098877, -0.00444568507373333, -0.01586984656751156, -0.019924301654100418, 0.014369666576385498, 0.016215244308114052, -0.0015023692976683378, -0.034993067383766174, 0.008637038059532642, 0.02586900070309639, 0.08369940519332886, 0.016507642343640327, 0.0045647700317204, -0.03705304488539696, -0.03642832487821579, -0.013410224579274654, -0.03973827138543129, -0.026815209537744522, 0.03388337790966034, -0.011920182034373283, 0.02687446027994156, -0.04571008309721947, 0.025244195014238358, 0.0044418335892260075, -0.03170943632721901, -0.004028474446386099, 0.013780991546809673, 0.05627397820353508, 0.01733618602156639, -0.06037911772727966, -0.015450751408934593, -0.015239882282912731, 0.040112435817718506, 0.03606562688946724, 0.06023792177438736, 0.010378756560385227, -0.06883543729782104, 0.06591760367155075, -0.005483473651111126, -0.06255528330802917, 0.05341213569045067, 0.01239364966750145, 0.05832307040691376, -0.037073422223329544, 0.005183676723390818, 0.009735554456710815, -0.04538079723715782, -0.04577616602182388, 0.01766880415380001, 0.027639100328087807, -0.015324958600103855, -0.05619202181696892, -0.006892870180308819, -0.022161800414323807, 0.02117220312356949, -0.013201271183788776, -0.018370939418673515, 0.009476782754063606, 0.044529449194669724, 0.008795671164989471, -0.006921797059476376, -0.008727749809622765, -0.014036438427865505, -0.00885860901325941, 0.005992418620735407, 0.009333008900284767, 0.00867654848843813, -0.051856718957424164, -0.0625079944729805, 0.001000124029815197, 0.049436792731285095, 0.010494524613022804, -0.01139863021671772, 0.0016552257584407926, 0.0028189104050397873, -0.016687769442796707, 0.020999690517783165, 0.031188946217298508, 0.1042935848236084, 0.026629174128174782, 0.01655850186944008, -0.013344168663024902, 0.03027714602649212, 0.011205185204744339, -0.004893232136964798, -0.02314761094748974, -0.05234062299132347, 0.038777370005846024, -0.04090619087219238, -0.028441932052373886, -0.016942333430051804, -0.045414067804813385, 0.004753244575113058, -0.020610909909009933, -0.012855312786996365, -0.040167052298784256, -0.06493600457906723, 0.008532670326530933 ]
<p>It's actually a teaching conflict at my school. They said that $$\text{Flux}=\frac{q}{\varepsilon_0}.$$ Say for a point charge at the centre of the sphere and let's say we not put water into the sphere, so now $E/ \varepsilon_0=K$. Thus $E= \varepsilon_0 K$. So flux becomes $q/\varepsilon_0 K$. That means that any change in medium changes the flux.</p> <p>However, in FIITJEE I was told that the addition of a medium won't change the flux since the number of electric field lines remains constant for any medium. So changing medium won't change the formula, $\text{flux}=q/\varepsilon_0$.</p> <p>So, does flux actually change with change in medium or not? </p> <p>$K$ is the dielectric constant.</p>
g1500
[ 0.0421331413090229, -0.032705213874578476, 0.0017245728522539139, -0.04047011211514473, 0.04124633967876434, 0.017322244122624397, 0.03609554097056389, -0.0116110285744071, 0.007302861660718918, -0.003881299402564764, -0.04571564868092537, 0.050785861909389496, 0.03141607344150543, 0.007486380636692047, -0.057308606803417206, -0.0020801860373467207, 0.065852589905262, -0.0001267420157091692, -0.029875878244638443, -0.0034129100386053324, -0.06068454310297966, -0.01628485880792141, -0.007221439387649298, -0.02158239111304283, 0.010902862064540386, -0.0212359931319952, 0.04251126945018768, 0.03092302195727825, 0.02476753294467926, -0.02955353632569313, 0.05593258515000343, -0.010856579057872295, 0.029525863006711006, 0.017226791009306908, -0.07380252331495285, -0.05116952210664749, -0.010989220812916756, 0.11743602901697159, 0.03243367001414299, -0.009204832836985588, 0.04887821525335312, 0.016080090776085854, 0.013668965548276901, 0.006756199058145285, -0.04823730140924454, -0.02977614663541317, -0.004160051234066486, -0.013287180103361607, -0.03070320561528206, -0.03288638964295387, -0.053307950496673584, -0.034893181174993515, 0.004977236967533827, 0.02446109429001808, -0.056388020515441895, 0.02077409438788891, 0.009727086871862411, -0.040381211787462234, 0.022367127239704132, 0.029303142800927162, 0.02945576049387455, 0.022480720654129982, -0.010950038209557533, -0.005351307336241007, 0.030144693329930305, 0.0046031419187784195, -0.059366993606090546, 0.00406748428940773, -0.06230534240603447, 0.032681964337825775, -0.05669097229838371, -0.006827758625149727, -0.05136340111494064, 0.006478030700236559, -0.0067776828072965145, 0.023973053321242332, 0.07042863219976425, 0.009675664827227592, 0.02753819338977337, -0.04768115282058716, -0.0322641097009182, 0.0037200304213911295, 0.06521913409233093, 0.03690171614289284, 0.026092614978551865, -0.028892120346426964, 0.008004498668015003, 0.04345167428255081, -0.014390806667506695, -0.018918177112936974, -0.02389703504741192, -0.020069023594260216, 0.0550030954182148, 0.008352458477020264, -0.04730925336480141, -0.07959680259227753, 0.012334661558270454, 0.0040040998719632626, 0.016224578022956848, 0.01214207336306572, -0.03995050862431526, -0.0006588505930267274, 0.0070493207313120365, 0.02808368392288685, -0.053610485047101974, -0.006128939799964428, 0.035739339888095856, 0.008528374135494232, -0.0022662042174488306, -0.026986055076122284, -0.024828249588608742, -0.03146577626466751, -0.03861473873257637, -0.006575345993041992, -0.0817810520529747, -0.013252279721200466, 0.03640167787671089, 0.004475557245314121, 0.017125314101576805, -0.010036082938313484, 0.008524731732904911, -0.029589131474494934, 0.018830951303243637, 0.032480012625455856, -0.030218705534934998, 0.013749483041465282, -0.016252530738711357, 0.04451027512550354, 0.047042228281497955, -0.01326860673725605, -0.04820897430181503, -0.04547567665576935, -0.013451592065393925, 0.009291074238717556, -0.029887156561017036, 0.015347014181315899, 0.004798481706529856, -0.005027077626436949, 0.017715822905302048, -0.009505092166364193, -0.0009671844891272485, -0.02152453362941742, 0.025068191811442375, -0.04545270651578903, -0.04127034544944763, 0.05490121990442276, -0.009331781417131424, -0.013882836326956749, 0.10329356044530869, 0.0011868678266182542, 0.09753047674894333, 0.06778471171855927, 0.03723268583416939, -0.010585164651274681, -0.0029344826471060514, -0.0195863489061594, 0.056042030453681946, 0.01870419830083847, 0.0448184609413147, -0.07412911206483841, 0.02453668601810932, 0.028088726103305817, 0.031477708369493484, 0.023795658722519875, -0.023162182420492172, 0.05974448099732399, 0.012173978611826897, 0.027927860617637634, -0.0415559746325016, -0.017921172082424164, -0.039074111729860306, 0.04788513109087944, 0.03987530246376991, 0.014466684311628342, 0.0044584874995052814, -0.015669453889131546, -0.0055245752446353436, -0.0016841772012412548, -0.0009077276918105781, 0.014451585710048676, -0.034917932003736496, 0.04388182610273361, 0.01920931413769722, -0.09065840393304825, -0.05736808106303215, 0.056412674486637115, -0.015854401513934135, 0.014309153892099857, -0.04009392485022545, -0.027850370854139328, -0.07880330830812454, 0.004680934827774763, -0.02276764251291752, 0.06998570263385773, 0.030463384464383125, -0.0105140907689929, -0.02377309463918209, -0.013642283156514168, -0.04216938093304634, 0.019557630643248558, -0.022466326132416725, 0.05608268082141876, 0.05745368078351021, 0.002712622983381152, 0.03241308778524399, -0.014761079102754593, -0.03310481831431389, -0.05686894431710243, 0.06965231895446777, 0.025151289999485016, 0.05506863072514534, -0.0036571670789271593, -0.024162234738469124, 0.04181195795536041, -0.00406983308494091, -0.002210956532508135, 0.004444930702447891, -0.0009624949307180941, -0.01627250202000141, -0.022487163543701172, -0.06417571008205414, 0.030852923169732094, 0.008270222693681717, -0.03756854683160782, -0.06193126365542412, -0.04880182445049286, 0.04149254783987999, -0.014956201426684856, -0.04612794145941734, 0.03409229964017868, -0.04192081466317177, -0.01768597774207592, -0.009960484690964222, 0.008615591563284397, -0.0014567692996934056, 0.049042146652936935, -0.05997288227081299, 0.0009998860768973827, 0.06224127113819122, -0.03638533502817154, -0.000919653452001512, -0.03217427805066109, -0.015157829970121384, 0.01421631034463644, 0.043396610766649246, -0.02579091116786003, 0.0034303534775972366, -0.00020564709848258644, -0.0270068496465683, 0.007997368462383747, 0.0491313673555851, -0.0710897371172905, 0.037175875157117844, 0.04942355304956436, -0.002208805177360773, 0.008278640918433666, -0.07283636927604675, 0.06075022742152214, -0.013174398802220821, -0.04082150757312775, -0.01043670903891325, -0.03964434191584587, 0.034145697951316833, 0.015512589365243912, -0.03903007507324219, 0.042060207575559616, -0.03834693878889084, 0.08995770663022995, 0.02505221962928772, 0.02702002413570881, 0.006903908681124449, 0.04550839215517044, 0.03975330665707588, 0.03474096953868866, 0.027075868099927902, 0.0148643609136343, 0.01480866502970457, -0.05290021374821663, 0.06906379014253616, -0.04141935333609581, -0.016754470765590668, -0.015598286874592304, -0.04823269695043564, 0.05804114416241646, 0.03406728059053421, -0.0641757920384407, 0.02034579962491989, 0.00890467967838049, -0.09260474145412445, 0.015043805353343487, -0.04089866578578949, 0.05874466896057129, 0.04352688416838646, -0.06419934332370758, 0.005897533614188433, 0.020916901528835297, 0.07033418118953705, -0.06426958739757538, -0.012653722427785397, 0.04267553985118866, 0.013877728953957558, -0.02386433072388172, -0.043407320976257324, -0.018598752096295357, 0.05467265099287033, 0.07644699513912201, -0.011747735552489758, -0.06711281090974808, 0.08974869549274445, 0.00896183680742979, -0.04367094114422798, 0.005627539474517107, -0.03959648683667183, 0.05274384841322899, -0.044303420931100845, 0.03551102802157402, 0.03643687814474106, 0.037629857659339905, 0.030941031873226166, 0.019762687385082245, -0.02110268920660019, 0.004782456438988447, 0.07706480473279953, -0.0351988859474659, 0.023416582494974136, 0.040693338960409164, -0.009434166364371777, -0.03701573982834816, -0.04952580854296684, 0.018749922513961792, -0.034554485231637955, -0.0040413918904960155, -0.023786457255482674, -0.08057676255702972, -0.02459271438419819, 0.0026724576018750668, -0.011463440954685211, -0.010990058071911335, -0.03487914428114891, 0.019111791625618935, 0.0006653558230027556, -0.0176380667835474, -0.06242118403315544, -0.0002695839502848685, -0.013613455928862095, -0.010525153949856758, 0.03725175932049751, -0.059921588748693466, 0.02149815484881401, 0.028015175834298134, 0.060091882944107056, 0.004988955333828926, 0.009209522977471352, 0.009854678064584732, 0.005399747285991907, -0.07737051695585251, 0.03610765561461449, 0.028825543820858, -0.021542968228459358, -0.017764253541827202, 0.038959577679634094, -0.07156889140605927, -0.008912401273846626, -0.020280353724956512, -0.027263067662715912, 0.03167874366044998, 0.020921839401125908, 0.027794843539595604, -0.0321735218167305, 0.004736518952995539, -0.01989753544330597, 0.014903117902576923, -0.053990334272384644, 0.03483123704791069, 0.024371864274144173, -0.018757401034235954, -0.029311249032616615, 0.0283795353025198, -0.059655286371707916, -0.0026157398242503405, 0.014476358890533447, 0.01257555466145277, -0.003969299606978893, -0.029284019023180008, -0.00702683674171567, 0.014150217175483704, 0.018093938007950783, 0.014159568585455418, 0.03380836173892021, 0.0059189205057919025, -0.006083339918404818, 0.012628274038434029, 0.019631875678896904, -0.01640736684203148, -0.024582907557487488, -0.061575718224048615, 0.01938730478286743, -0.037447407841682434, 0.00044181631528772414, -0.01746445894241333, 0.029377423226833344, -0.004536767955869436, -0.04874454438686371, -0.05660949647426605, 0.018956754356622696, -0.009304915554821491, 0.05032685771584511, -0.019268054515123367, 0.028700873255729675, -0.06436223536729813, -0.005611476022750139, -0.022408341988921165, -0.05976184085011482, -0.0698423832654953, -0.024316331371665, 0.013702950440347195, -0.04136813431978226, -0.015790866687893867, 0.05619703233242035, -0.06016518548130989, 0.048792727291584015, 0.004151303321123123, -0.025879157707095146, -0.04583844542503357, 0.048055250197649, 0.02425560913980007, 0.02246720902621746, 0.02294323407113552, 0.03966062515974045, -0.027194302529096603, -0.07249170541763306, 0.02935187518596649, -0.04014262557029724, -0.00028931046836078167, -0.03069252148270607, 0.04235056787729263, -0.05472652614116669, -0.01636851206421852, -0.029004253447055817, -0.014142067171633244, 0.0984581857919693, 0.04058882221579552, 0.021384352818131447, -0.037291157990694046, -0.012218254618346691, 0.019183775410056114, -0.03132948279380798, -0.012663555331528187, -0.03324734792113304, -0.06885538250207901, -0.023898618295788765, 0.03600446134805679, 0.02569587528705597, -0.017002684995532036, -0.008595217950642109, -0.020449362695217133, -0.018006816506385803, 0.013177383691072464, -0.001140993321314454, -0.00043378042755648494, -0.057131391018629074, -0.012201990932226181, 0.04894895851612091, 0.019248927012085915, 0.03036622144281864, 0.00711732916533947, -0.028298286721110344, -0.04048089683055878, -0.0015932557871565223, -0.035646721720695496, 0.010494349524378777, 0.02585325948894024, 0.02854204550385475, 0.009427735581994057, 0.057226382195949554, 0.006856563035398722, 0.0012462902814149857, 0.007075004279613495, -0.005540003534406424, -0.05945824086666107, 0.027338551357388496, -0.032106559723615646, 0.03139704093337059, 0.06548085063695908, -0.036926764994859695, 0.0006863703019917011, -0.011381173506379128, 0.01701800525188446, 0.02424371987581253, -0.043966565281152725, 0.05049259215593338, -0.06293129920959473, 0.046962298452854156, 0.029331324622035027, 0.02191004529595375, 0.05307992547750473, 0.009189048781991005, -0.01767038367688656, 0.008510693907737732, 0.02002389170229435, -0.026023484766483307, -0.026443490758538246, -0.050007160753011703, 0.014972727745771408, -0.03435630723834038, -0.02101765386760235, 0.009483646601438522, 0.03188727796077728, 0.017241662368178368, 0.057364363223314285, 0.018943550065159798, -0.030234528705477715, 0.010842777788639069, 0.010912814177572727, 0.029071329161524773, 0.01607288420200348, -0.05386195704340935, -0.027826664969325066, 0.0254406426101923, -0.005174980964511633, 0.04496454447507858, -0.02769705280661583, 0.040421340614557266, -0.05125539004802704, 0.009002880193293095, 0.020648034289479256, -0.02829916402697563, -0.03627508133649826, 0.04362552985548973, 0.06308877468109131, -0.0007213179487735033, 0.053585343062877655, -0.05579907074570656, 0.008990314789116383, -0.023384736850857735, 0.012687908485531807, -0.02731170877814293, 0.017474189400672913, 0.05284365639090538, 0.06613066792488098, 0.005341424606740475, 0.019137432798743248, -0.006487456150352955, -0.02851860783994198, -0.012250710278749466, 0.0070403763093054295, -0.017968151718378067, -0.005128335207700729, 0.08081028610467911, 0.0197971910238266, -0.06082528084516525, -0.006796537898480892, -0.004099854733794928, -0.029908299446105957, 0.04244149103760719, 0.02813323214650154, -0.028551779687404633, -0.0033989185467362404, -0.006259588059037924, -0.011712221428751945, 0.015627574175596237, 0.041124481707811356, 0.015095926821231842, -0.07240716367959976, 0.03267047554254532, -0.09541810303926468, 0.077873595058918, -0.012464133091270924, 0.017201557755470276, 0.0251305028796196, 0.0035824335645884275, -0.0000030312512535601854, -0.026008659973740578, -0.07633447647094727, 0.012661647982895374, 0.022612672299146652, -0.03195970132946968, -0.02509225904941559, -0.02071552351117134, -0.015263070352375507, 0.007753325626254082, 0.0169199388474226, 0.016866790130734444, -0.06898187845945358, 0.011697574518620968, 0.022733381018042564, -0.003465290879830718, 0.0341472290456295, 0.05905478820204735, -0.00630384823307395, -0.024584036320447922, -0.020320748910307884, 0.024280469864606857, 0.03227484971284866, 0.0006117989541962743, -0.021147098392248154, -0.03281177952885628, 0.01876884512603283, 0.03793995454907417, 0.02042701095342636, 0.0251453910022974, 0.014826251193881035, -0.01255706138908863, -0.012482419610023499, 0.013177281245589256, -0.02597939595580101, 0.04510483890771866, 0.014891508966684341, -0.01918148621916771, 0.03663051873445511, 0.024614792317152023, 0.009445169940590858, 0.004539698362350464, 0.014700779691338539, -0.019292697310447693, -0.01510117668658495, -0.035704147070646286, 0.040121208876371384, -0.009959562681615353, -0.024657513946294785, 0.0080904271453619, -0.06604243814945221, 0.015559349209070206, -0.06333685666322708, 0.03306843340396881, 0.057968802750110626, 0.002607217989861965, 0.006091177463531494, 0.04260442033410072, -0.050102997571229935, -0.028125757351517677, 0.018853245303034782, -0.0271212887018919, 0.02022058703005314, -0.0021869284100830555, -0.0015985759673640132, -0.01562603935599327, 0.03148173913359642, -0.012494094669818878, -0.007382163777947426, -0.04492112249135971, 0.022353433072566986, 0.0755842849612236, 0.06467510014772415, 0.011463670991361141, 0.025661952793598175, -0.021117858588695526, -0.010248717851936817, -0.0589461587369442, 0.040459178388118744, 0.04220224544405937, 0.012636427767574787, 0.017460258677601814, 0.023970428854227066, -0.03165129944682121, 0.031432099640369415, 0.007898489013314247, 0.045445092022418976, -0.006561382673680782, -0.030487611889839172, 0.020050380378961563, -0.016345230862498283, -0.02863485738635063, 0.008713610470294952, 0.047371406108140945, 0.03404349461197853, 0.03723517805337906, -0.05447600036859512, 0.046276483684778214, -0.03119191899895668, 0.0007371165556833148, 0.022232383489608765, 0.010535734705626965, -0.010353689081966877, 0.01088338065892458, 0.05049892142415047, -0.05286535620689392, 0.08522938936948776, 0.05186090245842934, 0.04293302446603775, -0.0024440682027488947, -0.04026538133621216, 0.033298999071121216, -0.037086743861436844, -0.08538737893104553, 0.0025262085255235434, -0.09610310196876526, -0.022179752588272095, 0.05313090234994888, 0.017825359478592873, 0.03281117603182793, -0.011292645707726479, 0.0260010939091444, 0.05205975100398064, 0.03979011997580528, -0.03314407914876938, -0.006732785142958164, -0.007104520685970783, 0.04967528209090233, -0.07121895253658295, 0.0017627512570470572, -0.056751661002635956, -0.03701557219028473, 0.0017637135460972786, -0.03186660259962082, 0.019090689718723297, -0.049205880612134933, 0.005397106055170298, -0.03782184422016144, -0.010530640371143818, 0.03011556901037693, -0.0007410863181576133, 0.09973523765802383, 0.015191217884421349, -0.023330941796302795, 0.013653325848281384, -0.0015324963023886085, 0.05247794836759567, -0.00366216036491096, -0.02125721052289009, -0.07078728824853897, -0.039329953491687775, -0.011952187865972519, -0.07009012997150421, -0.026734817773103714, -0.012687942013144493, -0.03404902294278145, -0.04851343482732773, 0.05613667145371437, -0.004701975733041763, -0.0045176236890256405, 0.025020094588398933, -0.0004219361871946603, 0.005835636053234339, -0.009830023162066936, -0.03604596108198166, 0.04222612455487251, -0.022330518811941147, -0.02243812009692192, 0.04313519597053528, -0.032917559146881104, -0.009083391167223454, -0.010917452163994312, 0.014568000100553036, -0.03785140812397003, 0.008741162717342377, -0.034116603434085846, 0.08564862608909607, 0.010660943575203419, 0.018682338297367096, -0.02245645597577095, -0.0842173770070076, -0.04474936053156853, 0.023110268637537956, 0.045319799333810806, -0.04079210013151169, -0.012058003805577755, 0.012665711343288422, 0.014225715771317482, -0.00554786017164588, -0.041969183832407, -0.023196281865239143, 0.009967273101210594, 0.06756927073001862, 0.011188502423465252, -0.02178528532385826, 0.018867267295718193, 0.05446173995733261 ]
<p>Suppose we have a parallelepiped shaped box full of water on the surface of the sea. Suddenly the box disappears. What is the shape of the waves vs. time caused by the fall of the water contained in the box?</p>
g1501
[ 0.09163281321525574, 0.05897197127342224, 0.0028005267959088087, -0.04522477835416794, 0.05125455558300018, 0.05090320482850075, 0.04549526050686836, -0.027474259957671165, -0.012687096372246742, -0.040525976568460464, 0.001545509323477745, -0.006269835401326418, 0.04622248187661171, 0.06081414967775345, -0.028952766209840775, -0.0017078613163903356, 0.03288602456450462, -0.03441334143280983, -0.031457509845495224, -0.020734108984470367, -0.008307228796184063, 0.0028830338269472122, -0.0081174923107028, 0.03074471652507782, -0.06984750926494598, 0.021973511204123497, 0.04744688794016838, -0.016281602904200554, 0.0070754424668848515, -0.02161606401205063, -0.03598906099796295, 0.02154620923101902, 0.01970626227557659, -0.017663581296801567, -0.04148514196276665, 0.007397510576993227, 0.013730491511523724, 0.0257638618350029, 0.0362582691013813, 0.0618845596909523, 0.004095346201211214, -0.02311844192445278, -0.03388046845793724, 0.032416220754384995, 0.0136376041918993, -0.01384385023266077, -0.033913254737854004, 0.007596401497721672, -0.014771833084523678, -0.07033531367778778, 0.024547994136810303, -0.027111655101180077, 0.02671874314546585, -0.053820203989744186, -0.004741768818348646, -0.003937899600714445, 0.02796359173953533, 0.035733021795749664, 0.004238472785800695, -0.029008150100708008, -0.012537680566310883, 0.045929234474897385, -0.02847772091627121, -0.004200757015496492, 0.08369407057762146, 0.003764510154724121, -0.06382725387811661, -0.006642814259976149, 0.06286802887916565, -0.0310396496206522, 0.019197700545191765, -0.019860200583934784, -0.0134684843942523, -0.041236042976379395, -0.01598004810512066, 0.07168569415807724, -0.02411642111837864, 0.03744478523731232, -0.04728474095463753, 0.015010927803814411, 0.055168360471725464, 0.03190925717353821, -0.05850323662161827, -0.004884531255811453, 0.05647701770067215, -0.022175390273332596, 0.019923122599720955, 0.01961595192551613, -0.01475923229008913, 0.009239534847438335, -0.056587450206279755, -0.06721816956996918, 0.07102350145578384, -0.005454397294670343, 0.010017252527177334, -0.022278141230344772, 0.003562674857676029, -0.00345713016577065, 0.00793197937309742, 0.07214314490556717, -0.006885237991809845, -0.03816703334450722, -0.0402146577835083, -0.060798853635787964, 0.02684836834669113, -0.030652513727545738, 0.009681984782218933, 0.019353611394762993, 0.010157778859138489, -0.05854416266083717, 0.005005354061722755, -0.029117055237293243, 0.00002909617978730239, -0.02915879152715206, -0.014555729925632477, -0.0665915310382843, -0.00052369583863765, 0.01327426265925169, 0.016915202140808105, 0.04797041788697243, -0.01820678450167179, -0.02863241173326969, -0.004850410856306553, 0.09580274671316147, 0.06279507279396057, 0.035558417439460754, 0.0018199948826804757, 0.0636858195066452, 0.012126552872359753, 0.07132801413536072, 0.03043990395963192, 0.0896323099732399, -0.030928298830986023, 0.02352054975926876, 0.0039171697571873665, 0.018759967759251595, -0.06295066326856613, 0.020323902368545532, 0.021971067413687706, -0.01231585256755352, -0.02109786681830883, -0.04070344194769859, -0.003721653949469328, -0.005435767583549023, -0.005986752454191446, -0.003620442468672991, 0.024480221793055534, 0.018770745024085045, 0.000185035343747586, -0.02547680027782917, -0.005867911037057638, 0.03463521599769592, 0.017129316926002502, -0.0023094580974429846, 0.048009783029556274, 0.047617919743061066, -0.011572127230465412, -0.037213798612356186, -0.0020281693432480097, -0.000029025024559814483, 0.047328054904937744, 0.024444788694381714, -0.023347558453679085, 0.06386782228946686, -0.05538465082645416, -0.06157907471060753, 0.030319251120090485, -0.06968298554420471, -0.0008357613696716726, -0.04187730699777603, -0.01708381623029709, -0.03910215198993683, -0.010093022137880325, 0.07085971534252167, -0.013360938057303429, 0.030028607696294785, 0.016915058717131615, -0.06875135004520416, 0.023579083383083344, 0.024480100721120834, -0.009559894911944866, 0.02637675777077675, 0.002630333648994565, -0.01197733823210001, 0.07458531111478806, -0.027942487969994545, 0.0251723974943161, 0.004827199969440699, -0.08938739448785782, -0.04360548034310341, -0.009640813805162907, -0.08450744301080704, 0.015199241228401661, 0.015543160028755665, 0.039469677954912186, -0.024066606536507607, 0.04691633954644203, -0.007168978918343782, -0.0573686845600605, 0.02451794221997261, 0.0020895807538181543, 0.01853976398706436, 0.06828587502241135, 0.022057298570871353, -0.017212223261594772, 0.020828809589147568, 0.01493743620812893, 0.02723027393221855, -0.007966059260070324, -0.010711334645748138, 0.005204199813306332, 0.0025890255346894264, -0.05001683160662651, -0.034651145339012146, -0.017527248710393906, 0.02367592416703701, -0.034478407353162766, 0.09296903014183044, -0.0031560177449136972, -0.0034984739031642675, -0.05881568044424057, 0.010407907888293266, 0.0297315064817667, -0.04088198021054268, 0.02397272363305092, 0.01462803315371275, -0.03271272033452988, 0.0038545196875929832, 0.03599129617214203, -0.014212578535079956, -0.025255316868424416, 0.0010050811106339097, -0.029393576085567474, -0.006474651396274567, -0.015040346421301365, 0.03682365268468857, -0.0051263743080198765, -0.002932068658992648, 0.015317999757826328, -0.0477573536336422, 0.003650790313258767, 0.04143357649445534, -0.0748492181301117, -0.012878481298685074, -0.015528671443462372, -0.00831996463239193, 0.02763628587126732, -0.018885375931859016, 0.029081638902425766, 0.038924988359212875, 0.009536978788673878, -0.018620723858475685, 0.006446778774261475, 0.04921432211995125, 0.05138915032148361, 0.06740745902061462, 0.010336293838918209, 0.04156489297747612, -0.05284116417169571, 0.007455887738615274, 0.009722355753183365, 0.02057638019323349, -0.05292549356818199, 0.017024632543325424, -0.03809763491153717, -0.034891899675130844, 0.026158811524510384, 0.008180554956197739, -0.023979350924491882, -0.0058216555044054985, 0.012622812762856483, 0.056868623942136765, 0.04879311844706535, 0.05759938433766365, -0.002813007915392518, 0.0037540870252996683, 0.0008137863478623331, -0.011384572833776474, -0.08460935950279236, -0.008219263516366482, 0.027464019134640694, 0.020898766815662384, -0.0751051977276802, 0.06229515001177788, 0.0044447677209973335, -0.06357928365468979, 0.03470134362578392, 0.036465808749198914, -0.026771435514092445, 0.04486347734928131, -0.016974395141005516, 0.07167486101388931, 0.0031674380879849195, 0.036282479763031006, -0.012676571495831013, 0.03191347047686577, 0.017097512260079384, -0.015132083557546139, -0.030055083334445953, -0.02120588719844818, 0.003442856017500162, 0.007112374994903803, 0.037698015570640564, -0.05523362010717392, 0.029148472473025322, 0.06705139577388763, 0.03591778501868248, -0.039991408586502075, -0.027673598378896713, 0.014716551639139652, -0.04263480752706528, 0.029956161975860596, 0.004210603889077902, 0.01980196125805378, -0.08281949907541275, -0.005444913636893034, -0.013157439418137074, 0.028851859271526337, -0.04146766662597656, -0.0016311652725562453, -0.06856341660022736, -0.009438085369765759, -0.021990465000271797, 0.0041253636591136456, 0.032465800642967224, -0.02277589961886406, -0.028413712978363037, 0.029667498543858528, -0.03828507289290428, 0.007101194467395544, -0.026709269732236862, -0.09533663839101791, -0.019870523363351822, -0.0033315420150756836, 0.028612995520234108, 0.025298133492469788, 0.03033854439854622, 0.031629521399736404, 0.002803889336064458, 0.05096228048205376, 0.04491850733757019, -0.021849576383829117, -0.009473198093473911, -0.05416414514183998, 0.011077875271439552, -0.008207756094634533, 0.020491933450102806, -0.06805021315813065, 0.005925638135522604, -0.0011502148117870092, -0.005538824945688248, -0.017699379473924637, -0.013793244026601315, -0.0026210329961031675, 0.00987782422453165, 0.050668831914663315, -0.019343029707670212, -0.01572221703827381, 0.028252918273210526, 0.003531241323798895, -0.0549563392996788, -0.04784774035215378, 0.06246650964021683, 0.02073875069618225, -0.00004944109241478145, -0.026455679908394814, 0.013480153866112232, 0.0677509531378746, 0.0006306604482233524, -0.08111676573753357, 0.05495966225862503, -0.020270919427275658, -0.005659041460603476, 0.0327255018055439, 0.04258076846599579, 0.007657161448150873, 0.014988450333476067, 0.013062716461718082, -0.01443026214838028, -0.025706181302666664, 0.08619170635938644, 0.003294741502031684, -0.00032958824886009097, -0.04219214990735054, 0.011273761279881, -0.009385202080011368, -0.029343824833631516, -0.05663151666522026, 0.003281715326011181, -0.05156679078936577, 0.011282279156148434, -0.017553135752677917, 0.0034576680045574903, 0.0024643177166581154, -0.016667596995830536, 0.038786813616752625, -0.006772290449589491, 0.025537878274917603, -0.08037097752094269, -0.0065774680115282536, 0.06210525706410408, 0.03911701962351799, -0.0485544316470623, -0.032524362206459045, 0.06426969915628433, -0.03451284021139145, 0.053450021892786026, -0.04993625730276108, -0.03164718300104141, -0.03107653744518757, -0.0016563805984333158, -0.029160205274820328, -0.03556074574589729, -0.03766926750540733, -0.006190359126776457, 0.03275071457028389, 0.10062599927186966, 0.021654728800058365, 0.005327965598553419, 0.024726053699851036, 0.015337353572249413, 0.049129337072372437, -0.04718499630689621, -0.03701898455619812, -0.09696420282125473, 0.012620813213288784, -0.0076216417364776134, -0.022004954516887665, -0.06188970431685448, -0.043465279042720795, -0.03254879638552666, 0.034819405525922775, 0.015648022294044495, 0.0608549490571022, -0.013728128746151924, 0.021664611995220184, 0.043006982654333115, -0.0014362992951646447, -0.024696078151464462, 0.01722954586148262, 0.01201458927243948, -0.030333422124385834, 0.013811190612614155, 0.0279035996645689, -0.0255050677806139, 0.08640283346176147, 0.005999892950057983, -0.05452553182840347, 0.020774511620402336, -0.07196091115474701, -0.08602118492126465, 0.03929099068045616, 0.04100305214524269, -0.05240985006093979, 0.015370436944067478, 0.018650125712156296, -0.030297784134745598, 0.0155337518081069, -0.02203766629099846, 0.0688215121626854, -0.02336627058684826, -0.03014746680855751, -0.04011372849345207, 0.05608449876308441, 0.05058176815509796, -0.03494703024625778, 0.026547307148575783, -0.05137166753411293, -0.03423850238323212, 0.0644088014960289, 0.01711105927824974, 0.01634557917714119, 0.03303142637014389, 0.021670829504728317, 0.010151533409953117, 0.010167988017201424, 0.0005596989649347961, -0.023723255842924118, 0.023286975920200348, -0.03878171741962433, 0.011510795913636684, -0.05777871236205101, -0.028883570805191994, -0.024482177570462227, -0.02195885218679905, 0.037221476435661316, 0.015239805914461613, 0.047557324171066284, 0.021331779658794403, -0.04249231889843941, 0.0012144377687945962, -0.06913008540868759, 0.016771923750638962, -0.00674355449154973, 0.022643378004431725, -0.04064137116074562, 0.019512861967086792, 0.05925028398633003, -0.002204413991421461, -0.0057416739873588085, -0.020293358713388443, -0.05069155991077423, -0.0001731123629724607, -0.008141287602484226, -0.009850011207163334, 0.0417097769677639, 0.016462674364447594, 0.019742021337151527, -0.013816842809319496, 0.03358288109302521, 0.08289658278226852, -0.07396193593740463, -0.024754801765084267, -0.015509309247136116, 0.0125169288367033, -0.06417428702116013, -0.0579361654818058, 0.01451911311596632, -0.011237284168601036, 0.08588113635778427, -0.011129697784781456, 0.057626187801361084, -0.031494852155447006, 0.010933619923889637, 0.02651963010430336, 0.024277204647660255, -0.07577212154865265, 0.00866848137229681, 0.007824484258890152, -0.02059059962630272, 0.06394386291503906, 0.009309455752372742, 0.00273720221593976, -0.011819644831120968, -0.014191259630024433, -0.056874778121709824, 0.05193301662802696, 0.048329904675483704, 0.08910761028528214, -0.02602212317287922, -0.03741834685206413, 0.007200036197900772, 0.018365507945418358, 0.05546557530760765, 0.02792271599173546, 0.037935953587293625, -0.021358080208301544, 0.003241397440433502, 0.013978502713143826, 0.015570093877613544, -0.037703026086091995, 0.009666533209383488, 0.01858346350491047, 0.04788009822368622, -0.03348233923316002, -0.01234215684235096, 0.004127016756683588, -0.0404948852956295, -0.0454825833439827, -0.05382886156439781, -0.0048662275075912476, 0.020954128354787827, -0.033926595002412796, -0.002837234176695347, 0.02220141515135765, 0.029078185558319092, 0.026328302919864655, 0.03429415076971054, 0.045149803161621094, -0.04256008565425873, 0.016595318913459778, -0.019512420520186424, 0.054339222609996796, -0.014759360812604427, 0.015274690464138985, 0.019886944442987442, 0.010933688841760159, -0.041244592517614365, -0.04611619561910629, 0.04783574119210243, 0.02177717350423336, -0.030907724052667618, 0.03808866813778877, -0.00742762815207243, -0.018521692603826523, -0.002023915993049741, -0.05060367286205292, -0.054995156824588776, 0.030496127903461456, 0.0010129238944500685, 0.0032546173315495253, -0.03374361991882324, -0.027714509516954422, 0.0205595213919878, -0.007379516959190369, 0.0545499287545681, -0.022851504385471344, 0.042899519205093384, -0.010080868378281593, 0.02178771421313286, -0.06688064336776733, -0.010877617634832859, 0.0621405653655529, 0.0070699951611459255, 0.03997649624943733, -0.02015904150903225, 0.01003870740532875, -0.05768771097064018, -0.04652046784758568, -0.03226510435342789, 0.046021562069654465, 0.028262747451663017, -0.058219652622938156, 0.0014421523083001375, -0.03326268866658211, -0.06894057244062424, 0.023709489032626152, -0.04629817232489586, -0.007594718597829342, 0.00853327289223671, 0.04448305815458298, -0.05831720679998398, 0.035788118839263916, 0.0048453230410814285, 0.004912191070616245, 0.023096248507499695, -0.030832571908831596, -0.026667222380638123, -0.022499175742268562, -0.007726829499006271, 0.03124968148767948, -0.024407122284173965, -0.010693526826798916, 0.03260675072669983, -0.0204359982162714, 0.04851769283413887, -0.025058116763830185, 0.08678895235061646, 0.019932402297854424, 0.046400707215070724, 0.05504411458969116, 0.06541266292333603, 0.023475555703043938, -0.03452945128083229, -0.06812037527561188, 0.029708772897720337, 0.02203124761581421, -0.045347508043050766, -0.042144641280174255, -0.05054010450839996, 0.02272898331284523, 0.02096831612288952, -0.021051015704870224, -0.0013057756004855037, 0.023350974544882774, -0.006324608810245991, -0.0031539988704025745, 0.010603129863739014, -0.07468026131391525, -0.01871039904654026, -0.026116812601685524, 0.003950352314859629, 0.004255813080817461, -0.008937517181038857, -0.0137611860409379, 0.015957539901137352, -0.03876622021198273, -0.036065664142370224, -0.03005600906908512, 0.02245277538895607, 0.026428598910570145, 0.01955462247133255, -0.020662127062678337, -0.03685455396771431, 0.039613548666238785, 0.022110512480139732, 0.020695537328720093, -0.02222929336130619, 0.00507874833419919, -0.013432545587420464, 0.001958854729309678, 0.04636083170771599, -0.03744622692465782, -0.01360093243420124, 0.005278655793517828, -0.02700039930641651, -0.03558548912405968, -0.012197554111480713, -0.006724024191498756, -0.001359427347779274, 0.039821360260248184, 0.06630520522594452, -0.016878612339496613, -0.03127158060669899, -0.0045278179459273815, -0.023792723193764687, 0.055922042578458786, 0.038663435727357864, 0.00808919407427311, -0.033314529806375504, -0.01355044450610876, 0.025191763415932655, 0.04271586984395981, 0.05385652929544449, -0.020332330837845802, -0.03709138557314873, -0.0525696687400341, -0.0231033768504858, -0.028504787012934685, -0.03111119568347931, -0.0010861767223104835, 0.058395154774188995, 0.026005607098340988, -0.08951565623283386, 0.010977279394865036, 0.02533675543963909, -0.07740020751953125, 0.022503402084112167, -0.043455708771944046, -0.00687787588685751, -0.07785630226135254, 0.0023555848747491837, -0.03673665598034859, -0.0627761259675026, 0.005762893240898848, -0.027107955887913704, 0.0002905458095483482, -0.024973230436444283, -0.02517417073249817, 0.01308166328817606, -0.039377231150865555, 0.00763593940064311, -0.010219037532806396, 0.028008973225951195, 0.05450516939163208, 0.004939869977533817, 0.029225243255496025, 0.03723986819386482, -0.04576005041599274, -0.02864953689277172, 0.03916920721530914, -0.013968123123049736, -0.02221551537513733, -0.006267841439694166, 0.023765336722135544, -0.04208848252892494, 0.0010435170261189342, 0.04734524339437485, -0.005324564408510923, -0.03905580937862396, 0.012677843682467937, 0.023242885246872902, 0.007194883190095425, 0.026943674311041832, 0.021363049745559692, -0.034731972962617874, 0.01160159520804882, -0.02548154443502426, -0.02417784370481968, -0.061788156628608704, -0.05340810492634773, -0.01403949037194252, 0.061571259051561356, -0.026653330773115158, 0.001387771568261087, 0.007047655992209911, 0.02745679020881653, 0.001715782331302762 ]
<p>One of the most famous experiments in quantum mechanics in the context of wave-particle duality is certainly passing a beam of electrons through two slits, which results in an interference pattern being formed on a screen positioned after them.</p> <p>Now, <strong>starting from the Schrödinger equation</strong> (which we know is obeyed by electrons), how can we derive the formula describing the interference pattern?</p> <p>I am pretty sure we already know the answer, i.e. it is the same pattern generated by light going through two slits (so a sine squared modulated by a sinc envelope), but how do we get it <strong><em>from quantum mechanics</em></strong> ?</p>
g1502
[ -0.005939774680882692, -0.008014513179659843, 0.0006158314645290375, -0.028519731014966965, 0.01602879725396633, 0.020379312336444855, 0.036493465304374695, 0.050198208540678024, 0.029023440554738045, -0.0133175328373909, 0.00012257823254913092, 0.05995389446616173, 0.017648976296186447, 0.02081780880689621, -0.04888917878270149, -0.006848106626421213, 0.07614851742982864, 0.02256866544485092, 0.011117728427052498, 0.05528401955962181, -0.028329625725746155, 0.020982753485441208, -0.008629935793578625, -0.12288176268339157, 0.002514415653422475, -0.013345069251954556, 0.0027853117790073156, -0.06274490058422089, 0.013682710938155651, 0.004993125796318054, 0.01282445341348648, -0.03949722647666931, 0.05097693204879761, -0.04666777700185776, -0.043884437531232834, -0.04721176251769066, 0.006130511406809092, 0.0670836865901947, -0.008266562595963478, 0.03104172833263874, -0.05117745324969292, -0.013241542503237724, -0.05325068533420563, -0.07010495662689209, 0.003960390109568834, -0.05942724272608757, 0.010512900538742542, 0.0366838201880455, 0.022561682388186455, -0.08869361132383347, -0.024921992793679237, 0.060670629143714905, 0.0363016352057457, -0.010917211882770061, 0.015590586699545383, 0.06428984552621841, 0.02233024314045906, -0.021376773715019226, 0.107997365295887, 0.02591913752257824, 0.012725320644676685, -0.008608377538621426, 0.024008531123399734, 0.012428867630660534, 0.048564475029706955, 0.002929899375885725, -0.03462299704551697, -0.004836739972233772, -0.015985585749149323, 0.012536484748125076, 0.01928546652197838, -0.08162037283182144, 0.002905411645770073, -0.01403072476387024, 0.041110679507255554, -0.004407832864671946, 0.02323070541024208, 0.0117987971752882, 0.01591276004910469, 0.025510288774967194, -0.05966303125023842, -0.057243503630161285, -0.03666243329644203, -0.010810949839651585, 0.006516594439744949, -0.0017757235327735543, 0.03547235578298569, -0.04104935750365257, -0.0020677230786532164, 0.002929725218564272, 0.04537227377295494, 0.013429729267954826, 0.037819668650627136, 0.009528685361146927, -0.01107536256313324, -0.03371113911271095, -0.004816621541976929, 0.01809166744351387, -0.005195339675992727, 0.005521493498235941, 0.02553638257086277, -0.07774116843938828, 0.023585623130202293, -0.022894028574228287, -0.024735379964113235, 0.021306639537215233, 0.009296277537941933, -0.019969286397099495, 0.012629068456590176, -0.03241831809282303, -0.055685050785541534, -0.04982819780707359, -0.022438080981373787, -0.03972046449780464, -0.0019476492889225483, -0.032010696828365326, 0.006841676775366068, -0.06986312568187714, -0.0019231688929721713, 0.04399522393941879, 0.005259590223431587, 0.0014320744667202234, -0.03528112545609474, 0.024715114384889603, -0.008939563296735287, 0.03482022508978844, 0.012508914805948734, 0.008069653064012527, 0.04281925410032272, 0.0014554350636899471, 0.07009424269199371, 0.009960291907191277, 0.023908313363790512, 0.006781709846109152, 0.028034310787916183, 0.024456966668367386, 0.03867011144757271, -0.0025855584535747766, 0.030639342963695526, -0.05111259967088699, -0.010417775250971317, -0.07954315841197968, -0.037352509796619415, -0.04157406836748123, 0.015406081452965736, -0.04805922135710716, -0.03909679874777794, -0.0005615868722088635, 0.034274015575647354, -0.015919223427772522, -0.0015566875226795673, 0.062070511281490326, -0.007775142323225737, -0.022204207256436348, -0.009373161941766739, -0.011753790080547333, 0.04756428673863411, -0.02052946388721466, -0.005204787943512201, 0.009402354247868061, 0.06333300471305847, -0.010693110525608063, -0.032222945243120193, 0.02612173557281494, -0.03520125895738602, -0.026400268077850342, -0.0067959618754684925, -0.05136394500732422, 0.03968973830342293, -0.05417238175868988, 0.022381987422704697, -0.00405515544116497, -0.03527610003948212, -0.017383858561515808, 0.011751297861337662, 0.12163282185792923, 0.054033029824495316, -0.03363047167658806, 0.05072883889079094, 0.020653637126088142, -0.03192083165049553, -0.029013896360993385, 0.0136721795424819, -0.01316265668720007, -0.017801886424422264, -0.04580167308449745, 0.010714922100305557, -0.04181849956512451, -0.027014894410967827, 0.012609599158167839, 0.0006946249632164836, -0.043853454291820526, 0.004451384302228689, -0.028133098036050797, -0.009997174143791199, 0.01715978980064392, 0.08818996697664261, -0.010937878862023354, 0.06258577108383179, -0.006876027211546898, 0.009194920770823956, 0.07194866240024567, 0.048811741173267365, -0.001911772065795958, 0.009351934306323528, 0.03925983980298042, -0.014666385017335415, -0.019314656034111977, 0.012820661999285221, -0.0039032127242535353, 0.0030724203679710627, 0.017341382801532745, -0.026425499469041824, 0.0076371291652321815, -0.0022347131744027138, -0.012508213520050049, -0.00262888940051198, -0.020421475172042847, -0.06250122934579849, 0.023625481873750687, -0.01351910550147295, 0.0018053542589768767, -0.03967737406492233, 0.0010120494989678264, 0.014950522221624851, 0.028667086735367775, -0.04227687045931816, -0.02704828605055809, -0.08182921260595322, 0.03072214685380459, -0.05230120196938515, -0.03605346009135246, -0.058398839086294174, -0.05302564799785614, 0.048377301543951035, 0.03960364684462547, -0.031577493995428085, 0.05179320648312569, 0.05003105849027634, -0.048183877021074295, 0.004776631947606802, 0.009465758688747883, -0.027066737413406372, 0.016179636120796204, -0.015259956941008568, -0.015015012584626675, 0.003486697329208255, -0.002804161049425602, -0.04224015772342682, 0.0011274528224021196, 0.01663082465529442, -0.010055124759674072, -0.01891077309846878, -0.0032915391493588686, -0.015360859222710133, -0.08652235567569733, -0.0021195856388658285, 0.009002728387713432, -0.050823092460632324, -0.04982547089457512, 0.04616403207182884, 0.050724294036626816, 0.03992889076471329, 0.015079881064593792, -0.01083199493587017, -0.07952100783586502, 0.08112025260925293, 0.04165629297494888, 0.02830350771546364, -0.06624887883663177, -0.026652691885828972, 0.10982988029718399, 0.031717751175165176, -0.08114403486251831, 0.0477849543094635, -0.02247595600783825, 0.012886658310890198, -0.06989289820194244, 0.03641697019338608, -0.040997136384248734, 0.0022084666416049004, 0.005785319954156876, -0.048123348504304886, 0.036364343017339706, 0.03523510321974754, -0.08929446339607239, 0.07504674792289734, 0.05481300875544548, 0.05118907243013382, 0.029680024832487106, -0.03769593685865402, 0.022794093936681747, 0.01577744260430336, 0.07270420342683792, -0.06547106057405472, -0.017008023336529732, 0.043055254966020584, 0.02777727134525776, -0.02967800945043564, 0.015262925066053867, -0.05036977678537369, 0.010481011122465134, -0.02485557645559311, 0.011106546968221664, 0.03932802751660347, -0.03352759778499603, -0.017895687371492386, -0.038137536495923996, -0.04092680290341377, 0.010611191391944885, -0.009463333524763584, 0.045368071645498276, 0.05235753953456879, 0.014211161993443966, -0.05344408378005028, 0.028493592515587807, -0.04087047651410103, 0.047641463577747345, 0.02602382004261017, -0.005813560914248228, -0.03661913424730301, 0.018053635954856873, 0.0448867604136467, 0.04039481654763222, -0.010221983306109905, -0.025497306138277054, 0.017871834337711334, 0.03077874705195427, -0.005456668324768543, -0.02200576663017273, 0.013048970140516758, -0.017935272306203842, -0.0015729399165138602, -0.0030349851585924625, 0.042726337909698486, -0.04999420419335365, 0.009733896702528, 0.0011338586919009686, 0.004051481373608112, 0.051738131791353226, 0.03839968517422676, -0.010877521708607674, -0.021190714091062546, -0.016143478453159332, 0.0040213665924966335, 0.002753382781520486, 0.004395662806928158, 0.024282703176140785, -0.014273512177169323, -0.04981343820691109, 0.0114818150177598, 0.012051845900714397, 0.004520995542407036, -0.006953987292945385, -0.03760621324181557, 0.015022770501673222, 0.00568933691829443, -0.02223743125796318, 0.054217830300331116, -0.06181400269269943, -0.02276678942143917, -0.016429301351308823, 0.006047770380973816, 0.02095370553433895, -0.025081010535359383, -0.0797792375087738, 0.02406114712357521, 0.014410942792892456, -0.030672136694192886, -0.03184347227215767, -0.02030736394226551, -0.00822362955659628, -0.01966279186308384, 0.029553378000855446, -0.035596780478954315, -0.051441535353660583, -0.0054663908667862415, 0.044969186186790466, -0.021651308983564377, 0.034323014318943024, -0.05071793496608734, 0.004724642261862755, 0.009855692274868488, 0.02416372299194336, 0.04590712487697601, 0.03130099177360535, -0.010454828850924969, 0.03068888932466507, 0.05218710005283356, -0.03149273991584778, 0.009694548323750496, -0.019492099061608315, -0.0690896138548851, 0.033371079713106155, 0.02744309976696968, -0.011825189925730228, 0.035814978182315826, 0.014002234674990177, 0.01142818108201027, -0.00023900943051557988, 0.0855351984500885, -0.016610080376267433, 0.014300122857093811, -0.05342866852879524, -0.03239041566848755, -0.0371844582259655, 0.01255731750279665, -0.052613697946071625, -0.03791099414229393, -0.016029126942157745, -0.008084075525403023, -0.03719884902238846, 0.015261435881257057, -0.04078604280948639, -0.020754965022206306, 0.000052355284424265847, 0.03776489198207855, -0.017737742513418198, 0.034235890954732895, 0.03821782022714615, -0.039501339197158813, 0.07688584178686142, 0.04195660725235939, -0.035964641720056534, -0.010812273249030113, 0.020201418548822403, 0.00043033488327637315, -0.05379824340343475, -0.014964845031499863, -0.05201597884297371, -0.017381684854626656, -0.005603997502475977, -0.011150160804390907, 0.02450404316186905, -0.06251879036426544, -0.013458264991641045, -0.016387922689318657, -0.02513144724071026, 0.03339267894625664, 0.06888967752456665, 0.07357743382453918, -0.066874660551548, 0.02289595827460289, -0.002819695044308901, -0.023271605372428894, 0.045537639409303665, -0.01996360905468464, -0.00287991133518517, 0.01699576899409294, -0.023922668769955635, -0.04791738837957382, 0.009108533151447773, -0.01638895645737648, 0.009595944546163082, -0.036314111202955246, 0.02043132483959198, -0.04149366170167923, 0.04521626606583595, 0.026832135394215584, -0.016822058707475662, -0.02314157225191593, 0.062032852321863174, -0.021184856072068214, 0.026375776156783104, 0.041811503469944, 0.040796030312776566, -0.06655047833919525, -0.004623486194759607, -0.07548156380653381, -0.03810979053378105, 0.05251125246286392, 0.018397308886051178, 0.008733169175684452, -0.023113293573260307, 0.05127784237265587, -0.06015367805957794, -0.1046062558889389, 0.006295709405094385, -0.028109220787882805, 0.005879336968064308, -0.02595917508006096, -0.08939559757709503, 0.023837536573410034, 0.04613004997372627, 0.017665263265371323, -0.03802891820669174, -0.028336280956864357, 0.0704958513379097, 0.0009575166623108089, -0.03209572285413742, -0.04689460247755051, 0.026248237118124962, -0.029237352311611176, -0.0027530211955308914, -0.004526621196419001, -0.04151500388979912, 0.047202564775943756, 0.016481216996908188, -0.007445559371262789, -0.012524520047008991, -0.014728758484125137, 0.008960734121501446, -0.030471619218587875, -0.0019237250089645386, -0.027582556009292603, 0.007414232473820448, 0.00853182002902031, -0.04997032880783081, -0.00945240631699562, -0.012198852375149727, 0.012250760570168495, -0.07843004167079926, -0.032104212790727615, -0.020646853372454643, 0.017106901854276657, -0.025594040751457214, 0.014748385176062584, 0.0051686083897948265, -0.018287962302565575, -0.015168982557952404, 0.06550925970077515, 0.018437087535858154, -0.002254153834655881, -0.030671602115035057, 0.06374836713075638, -0.00949416495859623, -0.07290598750114441, -0.02164643071591854, 0.05001514405012131, 0.015897858887910843, -0.007438416592776775, 0.07197513431310654, -0.08876527100801468, 0.056345462799072266, 0.05635230243206024, -0.05547577515244484, 0.04161882400512695, 0.03809165582060814, -0.0067870477214455605, -0.02051493711769581, 0.0008735056617297232, 0.02125728875398636, 0.03913956508040428, 0.04462980851531029, 0.010793322697281837, -0.001233178423717618, 0.00886699091643095, -0.014475378207862377, 0.03856349363923073, 0.0575307197868824, 0.04924057796597481, 0.0019509348785504699, -0.01410968229174614, 0.033648427575826645, 0.007159825414419174, 0.04880329221487045, 0.020963888615369797, -0.04563222452998161, -0.0167925413697958, -0.004026453942060471, 0.040354613214731216, 0.022221248596906662, 0.014630509540438652, 0.01358200516551733, -0.00036016604281030595, 0.03728930279612541, -0.026412328705191612, -0.014708902686834335, 0.010615653358399868, 0.041061434894800186, 0.0010520991636440158, 0.008659674786031246, -0.0019018430029973388, 0.01754571497440338, 0.00250812666490674, 0.05957278981804848, 0.019517555832862854, -0.044605329632759094, -0.036817703396081924, -0.0057962434366345406, -0.005614123307168484, 0.08238016813993454, 0.009209544397890568, -0.02644062042236328, -0.05101834610104561, 0.0275215245783329, -0.012084098532795906, 0.0007775665144436061, 0.08457044512033463, 0.002704903483390808, -0.06945525109767914, -0.042777568101882935, -7.330072548938915e-7, -0.008478790521621704, 0.02011118270456791, -0.03074333444237709, 0.06628991663455963, 0.008107843808829784, 0.018673231825232506, 0.08439160883426666, -0.028294265270233154, -0.02159958705306053, -0.00950794667005539, 0.015513129532337189, 0.03114503063261509, 0.016332373023033142, 0.029312942177057266, -0.03535233065485954, -0.0114083057269454, -0.02558601275086403, -0.00963614135980606, -0.03156000003218651, -0.045783624053001404, 0.03967598080635071, -0.043716851621866226, -0.053124669939279556, -0.02625643089413643, 0.007673495914787054, 0.029010998085141182, -0.009593725204467773, -0.003074993146583438, -0.028302181512117386, -0.05332280322909355, -0.030652692541480064, 0.0055757551454007626, -0.027635488659143448, 0.018499426543712616, -0.006743375211954117, 0.07043109834194183, -0.0214922484010458, 0.0004295181133784354, -0.023927832022309303, 0.0821327343583107, 0.003755563171580434, -0.004116964526474476, 0.03558049350976944, 0.0231260284781456, 0.04785892739892006, 0.025630725547671318, 0.03547459468245506, 0.005549128167331219, 0.07496283948421478, 0.0676765963435173, -0.01571532152593136, -0.051067762076854706, -0.006436654832214117, -0.00547880819067359, -0.0009720044326968491, -0.0225563682615757, -0.009524662978947163, 0.017963917925953865, -0.023826533928513527, -0.01761080138385296, 0.025852128863334656, 0.033941686153411865, 0.003694813000038266, 0.012821003794670105, 0.012530344538390636, 0.005820837803184986, -0.0736130028963089, -0.05137854442000389, -0.058513570576906204, -0.03815799951553345, 0.008768994361162186, 0.02383028157055378, 0.021531488746404648, -0.010339867323637009, -0.01724652573466301, -0.005451253615319729, -0.030401980504393578, 0.0037376214750111103, -0.05982599034905434, -0.01019364781677723, 0.03681308031082153, -0.016447480767965317, -0.07229730486869812, 0.03285534679889679, 0.039760902523994446, -0.04743700474500656, -0.05235077068209648, 0.03622341528534889, -0.003536490723490715, -0.001957507571205497, -0.013322298415005207, 0.04518807306885719, -0.01001885998994112, 0.054470647126436234, -0.03211140260100365, -0.005437394138425589, 0.01813855767250061, 0.015050916001200676, 0.01861678436398506, -0.018054023385047913, -0.009252318181097507, 0.01466154120862484, 0.03954015299677849, 0.04688423126935959, 0.029419194906949997, 0.009420011192560196, 0.06135764345526695, -0.004860938061028719, 0.05787414312362671, -0.025580745190382004, 0.028531668707728386, 0.027821840718388557, -0.010431885719299316, 0.01568416878581047, -0.04936521500349045, 0.030806465074419975, -0.0024351789616048336, -0.023924216628074646, -0.017249571159482002, -0.010848219506442547, 0.04482583701610565, 0.05231722816824913, 0.003788465168327093, -0.010152002796530724, 0.08287197351455688, -0.00208834046497941, 0.037943847477436066, 0.033388424664735794, 0.034644659608602524, -0.01235420722514391, -0.027071472257375717, 0.006040855776518583, -0.025050023570656776, 0.03893565759062767, 0.0052119106985628605, 0.008509302511811256, 0.043538738042116165, 0.025736220180988312, 0.001977176871150732, -0.008993609808385372, 0.014010646380484104, -0.028214288875460625, -0.017999717965722084, -0.02488129213452339, -0.0075417389161884785, 0.031235221773386, 0.002967618405818939, 0.05151563510298729, -0.03248761594295502, -0.0366595983505249, -0.09964527934789658, -0.021581051871180534, -0.0031085617374628782, -0.0035686963237822056, -0.03835124149918556, 0.011729675345122814, 0.002039844635874033, 0.024680618196725845, -0.0028463827911764383, -0.05452638491988182, 0.05919298902153969, 0.11058554798364639, -0.08439560234546661, 0.001426998875103891, 0.010991135612130165, 0.030260402709245682, -0.02291438728570938, 0.030183708295226097, -0.014904223382472992, 0.0010662480490282178, 0.010511999949812889, -0.02659492753446102, -0.017201393842697144, 0.007250094786286354, -0.04754016920924187 ]
<p>This is a historical question partly, and maybe too broad for this site, but would require some familiarity with modern physics research practice so hopefully appropriate here. </p> <p>Einstein's later years, after general relativity, were (as I understand it) taken up predominantly by his effort to find a unified theory that explains both gravitation and electromagnetism and their interrelation. </p> <p>And from what I understand his approach was mainly mathematical, trying variations of functions and so forth, looking for something that fit - and doing his work predominantly on paper. </p> <p>Had he access to modern computers - programming languages, mathematica, etc. - how might that have changed his progress, and willingness to give up perhaps? And in what ways have computers in general changed / revolutionized theoretical &amp; mathematical physics?</p>
g1503
[ 0.014598474837839603, 0.05957268923521042, 0.006055960897356272, -0.003046636702492833, -0.017260227352380753, 0.02244083397090435, 0.11528163403272629, 0.019156107679009438, -0.033709097653627396, -0.016145627945661545, 0.00457508210092783, -0.02490556426346302, 0.08088751137256622, 0.0174117311835289, 0.022322285920381546, -0.02874162048101425, 0.021266601979732513, -0.017992017790675163, -0.006396932061761618, 0.007074006367474794, 0.06904412060976028, 0.011443761177361012, 0.029964616522192955, -0.06289592385292053, -0.027338434010744095, -0.0034645497798919678, -0.04170823469758034, -0.025893332436680794, -0.04291289672255516, -0.004707581829279661, 0.025196949020028114, -0.017372971400618553, 0.007893329486250877, -0.05342378094792366, -0.0700988844037056, -0.05927708372473717, -0.005831881891936064, 0.038162339478731155, 0.04777182638645172, -0.019234996289014816, 0.06553970277309418, 0.016648272052407265, -0.048768531531095505, -0.012083159759640694, 0.02027158811688423, 0.016314435750246048, -0.05644885078072548, -0.044586844742298126, -0.009711934253573418, 0.011584225110709667, 0.008454293943941593, 0.08033888041973114, 0.046197835355997086, -0.00516647519543767, 0.026702944189310074, 0.019685745239257812, 0.0033990785013884306, 0.051010675728321075, 0.051436897367239, -0.02913573570549488, -0.01521497406065464, 0.015420911833643913, 0.021100535988807678, -0.006181198637932539, 0.00018575202557258308, 0.009041598998010159, 0.010183947160840034, -0.04540494829416275, -0.007703447714447975, -0.028497988358139992, 0.008474428206682205, -0.06476837396621704, 0.025850826874375343, -0.007614010479301214, 0.03433573618531227, -0.0075571779161691666, -0.006853080820292234, -0.0411568284034729, 0.0330626517534256, 0.017588799819350243, -0.03389334678649902, -0.03143882751464844, 0.002510996302589774, -0.0521322637796402, 0.07183865457773209, -0.03334825113415718, -0.050812847912311554, 0.010154462419450283, -0.00632542883977294, 0.030698416754603386, -0.038704682141542435, 0.036323051899671555, 0.016813289374113083, -0.0021609042305499315, -0.0047584460116922855, -0.04531018063426018, 0.02054765820503235, 0.02601613849401474, 0.01804911531507969, 0.026803335174918175, -0.032658446580171585, -0.05340702831745148, 0.06834008544683456, 0.027257617563009262, -0.02596288174390793, 0.029033366590738297, 0.03071114420890808, -0.03476099297404289, -0.006223791278898716, 0.0406637080013752, -0.04356425628066063, -0.015169495716691017, -0.03581720218062401, -0.00016362633323296905, -0.03144941106438637, -0.029092704877257347, 0.003853062866255641, -0.0350089967250824, -0.04627406969666481, 0.05434712395071983, -0.018634827807545662, 0.018490644171833992, -0.0008989509660750628, 0.011824853718280792, -0.006888149306178093, 0.045069847255945206, -0.004501344636082649, 0.028096774592995644, -0.03599662706255913, 0.046852629631757736, 0.025647368282079697, 0.004365439061075449, -0.05181904882192612, 0.05700148269534111, -0.033946070820093155, 0.04427069053053856, -0.02735373191535473, -0.004470644518733025, 0.019585972651839256, -0.025893626734614372, 0.03278769552707672, -0.054207075387239456, -0.025478340685367584, -0.01528218388557434, 0.01887279748916626, 0.04391990974545479, -0.03195834904909134, 0.025649741291999817, -0.0643954873085022, 0.0034778518602252007, -0.023450646549463272, 0.022571055218577385, 0.017765745520591736, -0.03794759884476662, 0.009144394658505917, -0.0031498686876147985, -0.01376316323876381, 0.014767860062420368, -0.02335481531918049, 0.0042462823912501335, 0.04727741703391075, -0.058628350496292114, -0.02489100582897663, 0.029566612094640732, -0.04878733679652214, 0.0672014132142067, -0.00457344064489007, -0.07167920470237732, 0.022336380556225777, -0.016763679683208466, 0.005054282024502754, 0.020057396963238716, 0.030523501336574554, 0.007860994897782803, -0.010346473194658756, 0.03299214318394661, 0.020279189571738243, -0.03468504175543785, 0.017246520146727562, 0.009643630124628544, -0.05190861597657204, -0.044900573790073395, 0.0019600961823016405, -0.022260859608650208, 0.0043161893263459206, -0.05154837295413017, -0.00509229488670826, 0.008654318749904633, -0.014490622095763683, -0.006913012359291315, -0.04380086809396744, -0.03162048012018204, -0.03123672865331173, 0.037263453006744385, -0.0020682604517787695, -0.0027841823175549507, 0.020077774301171303, -0.003350204322487116, -0.0171954482793808, 0.11105003952980042, -0.0562572218477726, 0.07199694216251373, 0.04282669350504875, -0.003356658387929201, -0.030729109421372414, -0.018786953762173653, -0.01366026233881712, -0.05513444170355797, 0.06511294096708298, 0.022031662985682487, 0.02266390435397625, 0.05290047824382782, 0.04094783216714859, 0.006539551541209221, -0.05071272328495979, 0.029955556616187096, -0.020465468987822533, -0.04706675559282303, 0.0005514451186172664, 0.07082941383123398, -0.018668504431843758, -0.01650538668036461, 0.027172135189175606, 0.04411769658327103, -0.007300334982573986, -0.02333369478583336, -0.03889210894703865, 0.0591173879802227, -0.051702823489904404, -0.010606957599520683, -0.05263661593198776, 0.05944627895951271, -0.048276036977767944, -0.009522231295704842, 0.06228569895029068, 0.02553204819560051, -0.035565391182899475, -0.05023611709475517, 0.0940098986029625, -0.025630716234445572, -0.05146874487400055, 0.01692093163728714, -0.006552896928042173, -0.01479210052639246, -0.017290009185671806, 0.0015651910798624158, 0.05245784670114517, 0.025112755596637726, -0.057453885674476624, 0.05147935450077057, 0.024720238521695137, -0.02167934738099575, -0.056443024426698685, 0.04336918890476227, -0.011700283735990524, 0.05048563703894615, 0.02368919365108013, 0.024998707696795464, -0.017222395166754723, 0.006252587772905827, 0.012698770500719547, -0.021997226402163506, -0.03919799253344536, 0.054460588842630386, 0.015415842644870281, 0.004358020611107349, -0.06541208177804947, 0.01161761675029993, 0.005837839562445879, -0.000009299667908635456, 0.020594993606209755, 0.04408853501081467, -0.02911013551056385, -0.004615588579326868, 0.014985323883593082, -0.052303362637758255, -0.005085619632154703, -0.009372586384415627, 0.06349597871303558, -0.02217617630958557, 0.01077460590749979, -0.052313581109046936, -0.049178436398506165, -0.04401162266731262, 0.012814784422516823, -0.04464362561702728, -0.015507812611758709, 0.021304870024323463, 0.04596642777323723, 0.004376515280455351, 0.047279249876737595, 0.017867466434836388, 0.028385214507579803, -0.05215698853135109, -0.03096136450767517, 0.043374963104724884, -0.033948663622140884, -0.04082310572266579, -0.07728619128465652, 0.005675667896866798, 0.003081645118072629, -0.01251786295324564, 0.02009911648929119, 0.012550720945000648, 0.009852472692728043, -0.015530544333159924, -0.07580025494098663, -0.01031086128205061, -0.028819043189287186, -0.038771308958530426, -0.010413016192615032, 0.036679137498140335, 0.046009611338377, -0.02237727865576744, -0.05025472491979599, 0.02555467002093792, 0.005684200208634138, 0.038802873343229294, -0.0016633764607831836, -0.02259523794054985, -0.013618800789117813, 0.04681895300745964, 0.002315242774784565, -0.0646367222070694, 0.06340471655130386, 0.09127464145421982, -0.013069113716483116, -0.0032839966006577015, -0.0003560840559657663, 0.029666395857930183, -0.055548038333654404, -0.0226278193295002, -0.02900635451078415, 0.004905791953206062, -0.0461086742579937, -0.015941333025693893, 0.01011887937784195, -0.03885265812277794, 0.03037349134683609, -0.02430274337530136, 0.01587555557489395, 0.02814512886106968, -0.06909646093845367, -0.0026482478715479374, 0.06887397915124893, 0.019494568929076195, 0.008487384766340256, -0.018123507499694824, -0.007403912488371134, -0.04256705567240715, 0.05074351653456688, 0.00749192014336586, -0.02273278497159481, 0.023349935188889503, 0.032638322561979294, 0.013548308052122593, 0.0023300291504710913, 0.08750586211681366, -0.000394446833524853, 0.06645752489566803, -0.036531295627355576, -0.013294934295117855, -0.019981687888503075, -0.0072399345226585865, -0.06427512317895889, 0.01787029579281807, 0.026398226618766785, 0.0006846753531135619, -0.05867408215999603, -0.012629886157810688, -0.0006372678326442838, 0.06706240773200989, 0.02871481329202652, -0.0029701804742217064, 0.02390776388347149, -0.04196716472506523, 0.043471913784742355, 0.0155512485653162, 0.00418182322755456, 0.02547505870461464, 0.03436660021543503, -0.009919350035488605, 0.008060023188591003, -0.005169199779629707, 0.029091179370880127, -0.05997830256819725, -0.060732871294021606, -0.01656281389296055, 0.0030397241935133934, 0.04890850558876991, 0.03188231587409973, -0.00037141554639674723, -0.024340717121958733, -0.020749418064951897, -0.007879803888499737, 0.033571355044841766, -0.0623973049223423, -0.012892309576272964, 0.007470591459423304, 0.03960004076361656, -0.029322709888219833, 0.028761720284819603, 0.03518711403012276, 0.028188688680529594, 0.011690345592796803, -0.020171333104372025, 0.00822860561311245, -0.029848482459783554, 0.0030966748017817736, -0.03481173887848854, 0.022196855396032333, -0.046723607927560806, -0.015612217597663403, 0.0006772773922421038, -0.014581656083464622, 0.013879693113267422, -0.001074948813766241, 0.007597242947667837, 0.0386824756860733, 0.01875978708267212, 0.041780296713113785, 0.012354811653494835, 0.007183379959315062, -0.027948440983891487, -0.003919016569852829, 0.051248982548713684, 0.049383506178855896, 0.031875643879175186, -0.008920605294406414, 0.02082805521786213, 0.028375135734677315, -0.010015605017542839, 0.0032942930702120066, -0.02054888755083084, -0.03872856870293617, 0.011095285415649414, 0.04291565343737602, 0.028150023892521858, 0.008098067715764046, 0.003307847771793604, 0.10756418853998184, 0.006824889220297337, 0.0014444012194871902, -0.020160816609859467, -0.023951897397637367, -0.0000734005807316862, -0.009427528828382492, -0.002796046668663621, -0.01880434714257717, 0.017631206661462784, -0.07051018625497818, 0.029716819524765015, 0.03428652882575989, 0.03490429371595383, -0.04579930007457733, -0.029859844595193863, -0.03512489050626755, -0.005613002460449934, 0.02973911538720131, 0.024951331317424774, -0.05767165496945381, -0.00010484614176675677, -0.050780195742845535, 0.05769554525613785, 0.028427094221115112, 0.0003936308203265071, -0.07121184468269348, -0.05550020560622215, -0.039890777319669724, -0.012107718735933304, -0.009230543859302998, 0.04121280461549759, 0.07783294469118118, 0.0027277772314846516, 0.0012216799659654498, 0.0250124242156744, -0.055394213646650314, -0.032093483954668045, -0.02439727447926998, 0.010783576406538486, -0.009474067017436028, -0.008842721581459045, 0.011412519961595535, 0.007846512831747532, -0.020669570192694664, -0.0009318714728578925, -0.04070143774151802, 0.013009284622967243, -0.03252028301358223, -0.029402293264865875, 0.05120391398668289, 0.008739806711673737, 0.06996120512485504, -0.03965364396572113, -0.0569763220846653, -0.057485584169626236, -0.08289886265993118, 0.005196303594857454, 0.02470659837126732, 0.017731469124555588, -0.006319704931229353, 0.05558177828788757, 0.0005953289219178259, -0.029215410351753235, -0.025397367775440216, -0.03429558128118515, -0.0533100850880146, -0.05888549983501434, -0.03917853534221649, 0.07480763643980026, -0.0018332309555262327, 0.012564089149236679, -0.039896976202726364, 0.041017044335603714, 0.03254735842347145, 0.005834359209984541, -0.005064216908067465, 0.014913741499185562, 0.04617132246494293, -0.07724303752183914, -0.016458122059702873, -0.0006388176698237658, 0.03823017328977585, 0.055110760033130646, 0.03757859021425247, 0.008877073414623737, -0.0505744107067585, -0.01108804065734148, -0.0037003278266638517, -0.02852514758706093, -0.007417070679366589, -0.013452486135065556, -0.010618338361382484, -0.01876388117671013, -0.01628885231912136, -0.045445241034030914, -0.0258810855448246, -0.023890295997262, 0.022038936614990234, -0.024439826607704163, -0.008582791313529015, 0.011091181077063084, -0.009610794484615326, 0.07531213015317917, 0.00744228158146143, -0.023858075961470604, 0.016601217910647392, 0.011933359317481518, 0.07656487822532654, -0.07111434638500214, -0.025876635685563087, -0.019677037373185158, 0.0026354517322033644, 0.04302363470196724, -0.02222095988690853, 0.06251821666955948, 0.029049338772892952, -0.04529230296611786, 0.03378518298268318, 0.03672219067811966, 0.013381840661168098, -0.04561273008584976, -0.004759278614073992, -0.017620768398046494, 0.0058690751902759075, -0.027335364371538162, 0.04617652669548988, -0.04727170243859291, 0.030424689874053, 0.04917474463582039, 0.004095917567610741, -0.06273595243692398, -0.0033065439201891422, 0.03132361173629761, 0.005491388496011496, 0.018406452611088753, 0.0016470187110826373, -0.04107052832841873, -0.027015404775738716, -0.015024475753307343, -0.00889418926090002, -0.032302528619766235, 0.04143581911921501, -0.021084966138005257, -0.020563991740345955, 0.0009008150664158165, -0.08102302998304367, 0.06465284526348114, 0.056320786476135254, -0.092646025121212, -0.02300681546330452, 0.03422608971595764, -0.008960018865764141, -0.07087430357933044, -0.05598859861493111, 0.004998433403670788, 0.020772671326994896, 0.020417887717485428, -0.03153757005929947, 0.015775810927152634, -0.03569702059030533, 0.03023964911699295, 0.07431706041097641, 0.053986579179763794, 0.021194713190197945, 0.022919517010450363, -0.036623429507017136, -0.0057462663389742374, 0.021442072466015816, -0.03741999715566635, -0.01593075692653656, 0.015976889058947563, 0.005127513315528631, 0.03383685648441315, -0.055900197476148605, 0.0003296670038253069, 0.0554824098944664, -0.006598674692213535, -0.019751563668251038, -0.05097196251153946, 0.0273077841848135, 0.009486118331551552, 0.025086384266614914, -0.05424725264310837, -0.013175541535019875, -0.0019632468465715647, -0.003153386292979121, 0.04010510444641113, 0.04911564290523529, -0.006136697251349688, 0.0168851800262928, 0.06460127979516983, 0.06592188030481339, 0.03420638665556908, 0.03873470425605774, -0.033516786992549896, 0.03401653841137886, -0.013248731382191181, -0.01830347068607807, 0.0016042680945247412, -0.031152300536632538, -0.017225507646799088, -0.015621846541762352, 0.011028937064111233, -0.0259507168084383, -0.06200401112437248, 0.03081217221915722, -0.015193735249340534, -0.035719409584999084, 0.04562056064605713, 0.023638935759663582, -0.036603305488824844, -0.0051066153682768345, 0.00013752267113886774, -0.049729835242033005, 0.01621563546359539, -0.019080733880400658, 0.04753073677420616, 0.03131777420639992, -0.0766705721616745, -0.012792524881660938, -0.0023371886927634478, 0.008957085199654102, 0.0031766036991029978, -0.028969183564186096, 0.024947812780737877, 0.006573468446731567, -0.023745618760585785, 0.009528955444693565, -0.009897129610180855, 0.0558142364025116, -0.0026259268634021282, -0.05336931720376015, 0.026827404275536537, 0.03495143726468086, -0.02906903252005577, -0.032654620707035065, -0.04395259544253349, -0.07864099740982056, 0.009184679947793484, -0.060404613614082336, 0.06093856692314148, -0.01576465554535389, 0.04223601520061493, -0.047651056200265884, 0.025104854255914688, -0.03575767204165459, 0.06259482353925705, -0.019050316885113716, 0.029424920678138733, -0.01703481562435627, -0.03208395838737488, 0.027583450078964233, 0.011653570458292961, 0.012540055438876152, 0.0007651537307538092, 0.029133586212992668, 0.007815489545464516, 0.12117698043584824, 0.025066902860999107, -0.014907206408679485, -0.025832518935203552, 0.021691065281629562, -0.015658190473914146, 0.0033002321142703295, -0.022525152191519737, -0.07879255712032318, -0.00030432495987042785, -0.011923338286578655, 0.05019001290202141, -0.043905481696128845, 0.027427004650235176, 0.08381704986095428, -0.017584800720214844, -0.014596650376915932, 0.07136651128530502, -0.03487361967563629, -0.015398937277495861, -0.0629536584019661, -0.005566127598285675, 0.018816832453012466, -0.019163312390446663, -0.0512751042842865, -0.04844049736857414, 0.013980010524392128, 0.071503184735775, 0.021855121478438377, 0.006196681410074234, -0.017994288355112076, -0.04632459580898285, 0.03882281109690666, -0.03639374300837517, -0.021333379670977592, 0.06498962640762329, -0.039504487067461014, 0.03673751652240753, -0.05462418496608734, 0.012364930473268032, 0.004847830627113581, -0.07673519104719162, -0.04138551279902458, 0.030484771355986595, -0.009280792437493801, 0.018819639459252357, 0.0054049426689744, -0.044072531163692474, -0.021255191415548325, 0.0543321892619133, 0.04705588147044182, -0.03208020702004433, -0.04496238753199577, 0.025068584829568863, -0.00955953262746334, 0.04675110802054405, 0.030537443235516548, 0.02449360489845276, 0.0315876342356205, -0.010927014984190464, -0.019699199125170708, 0.0553736686706543, 0.047514237463474274, 0.021357005462050438, 0.07577653229236603, -0.059125691652297974, -0.06244704872369766, 0.022046878933906555, 0.07395884394645691, 0.03719434514641762 ]
<p>In QFT the principle of stationary action states that we choose fields that will make the action stationary but what if the action has many stationary points? What's the significance of these other solutions?</p>
g1504
[ 0.03650004416704178, 0.031125152483582497, 0.0032480363734066486, 0.00019903101201634854, 0.08552470058202744, -0.052656762301921844, 0.05700339749455452, 0.026300324127078056, 0.0291456151753664, 0.026736024767160416, -0.04318506270647049, -0.021179351955652237, -0.06544821709394455, -0.026705164462327957, -0.00965426117181778, -0.013037819415330887, 0.06029009073972702, 0.024604080244898796, -0.01361661683768034, -0.013404332101345062, 0.018066726624965668, 0.07690633833408356, 0.06353774666786194, -0.010204902850091457, 0.003459178376942873, 0.02785070240497589, 0.015390419401228428, 0.009174097329378128, -0.02480902522802353, -0.01700640469789505, -0.02469750866293907, 0.04988297447562218, 0.008225878700613976, -0.06982620805501938, 0.029708391055464745, -0.030415527522563934, 0.06422585248947144, 0.025124123319983482, -0.006818738300353289, -0.08986074477434158, -0.030095690861344337, -0.009368889033794403, -0.004177926108241081, 0.012420590966939926, -0.01811034232378006, -0.039454713463783264, 0.03930586203932762, -0.006278747692704201, -0.02189062535762787, -0.0010198242962360382, -0.017766844481229782, 0.0201652143150568, 0.03224531561136246, -0.036612629890441895, 0.007576230447739363, 0.059720128774642944, -0.00534424651414156, -0.0024817674420773983, 0.00894693098962307, 0.025020137429237366, 0.012625123374164104, 0.025541450828313828, 0.021012604236602783, 0.05534135550260544, 0.019083142280578613, -0.021998774260282516, 0.0037798520643264055, 0.002213903469964862, -0.020909376442432404, -0.01705343648791313, -0.03876293823122978, -0.05451030284166336, -0.031910404562950134, 0.04746183753013611, -0.005837633274495602, 0.051315464079380035, 0.009192136116325855, 0.026632562279701233, -0.002011573873460293, -0.0046889279037714005, -0.0970679447054863, -0.05040694773197174, 0.049014803022146225, -0.005536311771720648, 0.021244624629616737, 0.0017654960975050926, 0.013092291541397572, 0.021105311810970306, -0.036994919180870056, -0.038340531289577484, 0.008763766847550869, 0.026225827634334564, 0.04176278039813042, 0.06268458813428879, -0.0663977861404419, 0.00933463778346777, 0.034400712698698044, 0.00846460647881031, -0.0804351344704628, 0.014656683430075645, -0.03190236538648605, 0.02370535209774971, -0.01843329332768917, 0.05642155557870865, 0.005375680048018694, -0.060799818485975266, 0.005464123096317053, 0.004278914071619511, -0.026863815262913704, 0.049011483788490295, 0.00028426916105672717, 0.04065275192260742, -0.04240143299102783, 0.008263060823082924, -0.04112650454044342, -0.021943768486380577, 0.04740466549992561, 0.03159983083605766, 0.0381644032895565, 0.028217390179634094, -0.059195492416620255, -0.011901452206075191, -0.01781260408461094, 0.016583945602178574, -0.022373337298631668, -0.016838062554597855, -0.033719174563884735, 0.021404268220067024, -0.00425340561196208, 0.03514513745903969, 0.09917599707841873, 0.024814922362565994, 0.017162645235657692, 0.02239629067480564, -0.010388389229774475, 0.03629465401172638, -0.05241134762763977, 0.010535535402595997, -0.0055799707770347595, 0.031531088054180145, 0.02719041146337986, -0.019197233021259308, -0.0024460821878165007, -0.03743939846754074, -0.031144743785262108, 0.010492794215679169, 0.03149634972214699, 0.024858718737959862, 0.03158942982554436, 0.01064314041286707, -0.019400669261813164, 0.08075226843357086, 0.021334389224648476, -0.004744332283735275, 0.0807804986834526, -0.014424084685742855, 0.008851097896695137, 0.009348771534860134, 0.04721137508749962, -0.04175066202878952, 0.03551895543932915, 0.0024567958898842335, 0.02001996524631977, -0.02312418259680271, -0.06887716054916382, 0.010664046742022038, -0.019700946286320686, -0.04808308556675911, 0.011113543063402176, -0.017792632803320885, -0.07651155441999435, 0.03674188628792763, 0.011879786849021912, 0.055319737643003464, 0.03767196089029312, 0.018773231655359268, 0.007379119750112295, -0.033234234899282455, -0.0010645948350429535, -0.02288629114627838, -0.02543768845498562, 0.019073007628321648, 0.035533249378204346, -0.034753091633319855, -0.027101468294858932, 0.049553282558918, -0.031196169555187225, -0.012296521104872227, -0.09173722565174103, 0.057798001915216446, -0.021702516824007034, -0.03147220239043236, -0.0402451790869236, 0.024221384897828102, 0.02014441229403019, 0.0378895066678524, -0.0077087171375751495, -0.024872416630387306, -0.0488707534968853, -0.06537117809057236, 0.022469177842140198, 0.04675108566880226, -0.042843885719776154, 0.010009515099227428, -0.0025997997727245092, 0.030299406498670578, -0.033604662865400314, 0.029517151415348053, 0.06245901808142662, -0.028190579265356064, 0.016632450744509697, -0.026853082701563835, -0.04995122179389, 0.06424376368522644, 0.0035870932042598724, 0.021271824836730957, -0.03197282552719116, 0.026451753452420235, 0.005735545884817839, 0.0003826453466899693, -0.0038791480474174023, 0.00587554881349206, 0.04491645470261574, 0.03487268090248108, -0.021867308765649796, 0.023973792791366577, -0.015486447140574455, -0.022500619292259216, 0.008354433812201023, 0.030536239966750145, -0.061822663992643356, -0.014949512667953968, -0.021660223603248596, -0.006503020413219929, -0.011908935382962227, -0.056124329566955566, -0.007347882725298405, -0.02259172685444355, 0.04402583837509155, 0.05789363384246826, 0.004342706874012947, -0.00445674080401659, -0.010020045563578606, -0.00008262177288997918, -0.013081892393529415, 0.018903758376836777, -0.001542682177387178, -0.007463239133358002, -0.010101376101374626, 0.03224119916558266, 0.01628822647035122, -0.015036906115710735, 0.037888072431087494, 0.019216792657971382, -0.004570935852825642, -0.018730761483311653, -0.014049039222300053, 0.025266386568546295, 0.02089257724583149, -0.03244146332144737, 0.02043795771896839, 0.02141706645488739, 0.0077269733883440495, -0.01249179057776928, 0.04061086103320122, 0.028057875111699104, 0.04181497544050217, 0.036709047853946686, -0.018261313438415527, -0.0001292848464800045, -0.053303785622119904, -0.009313146583735943, 0.01944710873067379, 0.07419732213020325, -0.02493114210665226, 0.02828872762620449, 0.03284680098295212, -0.06970763206481934, -0.009802688844501972, -0.006843337323516607, 0.04764563590288162, -0.06154767796397209, -0.05629177764058113, 0.04497940465807915, 0.037697844207286835, 0.04319649189710617, -0.0001919614733196795, 0.0012406404130160809, -0.016034996137022972, -0.021486729383468628, 0.0020106977317482233, 0.00865110196173191, 0.06340141594409943, -0.021540280431509018, -0.023237524554133415, 0.0081325126811862, -0.0769919902086258, -0.08325652033090591, 0.021893726661801338, 0.0502503402531147, -0.014035878702998161, 0.04196591675281525, -0.007901406846940517, 0.03520709276199341, 0.058370307087898254, 0.03807726502418518, -0.024258345365524292, -0.07673695683479309, -0.0029312826227396727, -0.04078064113855362, -0.01328499149531126, 0.07614103704690933, -0.06454513967037201, 0.0025813316460698843, -0.063331238925457, 0.0014878954971209168, -0.02558102086186409, 0.02834654040634632, 0.0731515884399414, -0.016172876581549644, -0.05029655247926712, -0.047093987464904785, 0.053607963025569916, -0.040873344987630844, 0.09176194667816162, 0.06386612355709076, -0.029303444549441338, 0.0523943267762661, -0.017270196229219437, -0.023897163569927216, -0.0014387835981324315, 0.026402970775961876, -0.02473646216094494, -0.011668559163808823, 0.01583046279847622, -0.044020846486091614, -0.012251557782292366, 0.02599179744720459, 0.0028060367330908775, -0.015874462202191353, 0.010842052288353443, -0.02859301120042801, -0.04853927344083786, -0.030210431665182114, -0.021828852593898773, -0.008811225183308125, 0.0654301643371582, -0.0009370360057801008, 0.049326445907354355, 0.0293181873857975, -0.0256817489862442, -0.037289414554834366, -0.05599471181631088, -0.003319784067571163, 0.041281893849372864, 0.006145983934402466, -0.008341225795447826, 0.007377489935606718, -0.007960746996104717, -0.015843946486711502, -0.02856580913066864, -0.04133138060569763, -0.007671137806028128, 0.09964863210916519, 0.04635925590991974, -0.003989021293818951, -0.0430414080619812, -0.015445699915289879, 0.014911061152815819, -0.025718562304973602, 0.03465283289551735, -0.012689485214650631, 0.0036750559229403734, 0.01702393963932991, 0.010815281420946121, 0.029881805181503296, -0.014015169814229012, -0.04644828289747238, -0.04587218165397644, -0.02155277319252491, 0.03172540292143822, 0.07320695370435715, -0.0448361411690712, -0.006071575451642275, 0.011026142165064812, 0.07108312100172043, -0.0009420355199836195, 0.035778749734163284, 0.017840705811977386, 0.020986283197999, 0.013518081046640873, -0.012332931160926819, -0.0025144771207123995, -0.06738703697919846, -0.039063576608896255, -0.003505063010379672, -0.0014622177695855498, -0.04481397941708565, 0.08238465338945389, -0.00517824525013566, 0.061805665493011475, -0.012706521898508072, -0.02207868918776512, -0.009580884128808975, 0.014557448215782642, -0.0040571242570877075, 0.023011423647403717, -0.05112770199775696, 0.05401790887117386, -0.023748308420181274, -0.055603157728910446, -0.04783700779080391, -0.016089554876089096, -0.050270628184080124, 0.025821451097726822, 0.008184922859072685, 0.04575914889574051, -0.05340775474905968, 0.00011107515456387773, -0.007901756092905998, 0.060298703610897064, 0.007275715004652739, 0.03346319496631622, -0.07930377125740051, -0.00012031226651743054, 0.05741686373949051, 0.011942081153392792, -0.011752525344491005, -0.0033756450284272432, -0.08598898351192474, 0.0038705142214894295, 0.0010897602187469602, 0.03330076485872269, 0.028415491804480553, -0.053082555532455444, 0.018156519159674644, -0.01624036766588688, 0.005741218104958534, -0.028930088505148888, -0.012456869706511497, 0.01930253393948078, 0.010836927220225334, -0.004621145315468311, 0.0009971766266971827, -0.030220627784729004, 0.028293075039982796, -0.004171903245151043, -0.04916006699204445, -0.04167771711945534, -0.09314556419849396, 0.009144607000052929, -0.010409495793282986, -0.022080447524785995, 0.010896348394453526, -0.028121931478381157, -0.020490536466240883, -0.010284756310284138, -0.007097099907696247, 0.02431802824139595, 0.05843934416770935, -0.020176997408270836, -0.03620024397969246, 0.0010477234609425068, -0.0024700670037418604, 0.046767327934503555, 0.03512211889028549, -0.057918235659599304, -0.01036524772644043, -0.03650696948170662, 0.010890942066907883, 0.05579044669866562, 0.023896774277091026, 0.05485229939222336, 0.05050111562013626, -0.03089064173400402, -0.056305237114429474, 0.02125377207994461, 0.032359957695007324, 0.03702237829566002, -0.06733918190002441, -0.028439095243811607, -0.016057677567005157, 0.037820298224687576, 0.03349432721734047, -0.014149405062198639, -0.06732162833213806, 0.0035496517084538937, -0.0021439273841679096, -0.01009396556764841, -0.022815030068159103, 0.008407875895500183, -0.007059108000248671, 0.06246707960963249, 0.06333698332309723, 0.003358971094712615, -0.028562821447849274, -0.0017743376083672047, 0.023785395547747612, -0.005928618833422661, -0.004144262056797743, -0.003031136468052864, -0.03400120511651039, 0.010432763956487179, 0.006975250318646431, 0.016018908470869064, 0.04226770997047424, 0.07202661037445068, -0.024920500814914703, 0.011529925279319286, 0.00005556486576097086, 0.041637640446424484, -0.0024457317776978016, -0.050883982330560684, -0.001920825568959117, 0.003418185980990529, 0.0410144180059433, -0.04447092488408089, -0.09657230973243713, -0.01158736553043127, 0.02271951548755169, 0.031138891354203224, -0.006138846278190613, -0.046044837683439255, -0.06063257157802582, 0.06817149370908737, -0.027302751317620277, -0.040752675384283066, 0.001879231072962284, -0.050522759556770325, 0.03986293822526932, 0.028605498373508453, 0.03176650032401085, 0.025936653837561607, -0.013286824338138103, -0.019924944266676903, 0.02588927373290062, 0.03946610167622566, -0.012519375421106815, -0.02805132418870926, 0.030617116019129753, -0.059444133192300797, 0.0405532605946064, 0.023011675104498863, 0.01553388498723507, -0.04447410628199577, -0.014777516014873981, -0.026003172621130943, 0.02719637006521225, 0.02716691419482231, -0.03381113335490227, -0.026591742411255836, 0.008750393986701965, -0.0049942065961658955, -0.026262089610099792, -0.0697057768702507, 0.03821755200624466, -0.05755983293056488, -0.003200537757948041, -0.028182359412312508, -0.03764742240309715, 0.006310244090855122, 0.011498231440782547, 0.02170451544225216, -0.04731070250272751, 0.04957732558250427, -0.030994480475783348, -0.01397867500782013, -0.011139122769236565, 0.042107418179512024, -0.004295553080737591, 0.054118748754262924, 0.10193920880556107, 0.025151774287223816, 0.01119202096015215, -0.02420227788388729, -0.009993098676204681, -0.008749113418161869, 0.009703932330012321, -0.11594025045633316, 0.040358733385801315, -0.0793762132525444, 0.09769223630428314, 0.035356100648641586, -0.049513060599565506, 0.02107541449368, 0.06739939004182816, -0.04307521507143974, 0.02776431106030941, 0.009378459304571152, 0.06386768072843552, 0.02901262789964676, 0.0367162823677063, -0.028751280158758163, -0.010008951649069786, 0.01691402681171894, -0.0035124917048960924, 0.022562798112630844, 0.00261360639706254, -0.0421978160738945, -0.0892077088356018, 0.005463915411382914, 0.03621075302362442, 0.014950431883335114, -0.017238125205039978, -0.04533364623785019, 0.105121910572052, -0.02327723428606987, -0.07922187447547913, -0.0017789608100429177, -0.018732815980911255, -0.008700117468833923, 0.003870304673910141, 0.027433905750513077, -0.005864233709871769, 0.01864689402282238, 0.00778191490098834, 0.0022662763949483633, -0.025899220257997513, -0.004693507216870785, -0.016051456332206726, -0.021015875041484833, -0.02645343914628029, -0.014853917062282562, -0.04269849881529808, 0.007391029968857765, 0.023047707974910736, -0.03819495812058449, -0.009321671910583973, -0.019790245220065117, -0.036023177206516266, 0.01256899256259203, -0.015303942374885082, 0.023995788767933846, 0.012295537628233433, -0.04671713337302208, -0.013500760309398174, -0.06668888032436371, -0.018369397148489952, -0.00844096764922142, -0.008390363305807114, -0.050957608968019485, 0.10061702132225037, 0.04700283706188202, -0.046569231897592545, 0.02898557297885418, -0.011082111857831478, 0.04116914048790932, 0.022317366674542427, -0.08447693288326263, -0.04496929049491882, 0.0534193255007267, 0.010517983697354794, -0.05319627374410629, -0.02069721929728985, 0.001464230939745903, 0.01404303964227438, -0.03136110678315163, -0.025671664625406265, -0.027000175788998604, -0.01817929930984974, 0.039131730794906616, -0.0021710668224841356, -0.06701406091451645, 0.011296986602246761, -0.03782032057642937, 0.028320275247097015, 0.07388947159051895, -0.022748125717043877, 0.015597530640661716, -0.017913779243826866, -0.011748767457902431, -0.004277675412595272, -0.05861685797572136, 0.026348020881414413, -0.0018899912247434258, 0.018647894263267517, 0.023199453949928284, -0.002786087803542614, 0.06403329223394394, 0.001337217865511775, 0.039771441370248795, -0.03761469945311546, 0.019082896411418915, -0.07740115374326706, -0.08590710908174515, -0.023162128403782845, 0.024573711678385735, -0.011179116554558277, -0.013599900528788567, -0.04326104745268822, 0.06782607734203339, -0.03370662406086922, 0.027684839442372322, -0.028070980682969093, -0.009230971336364746, 0.04898926243185997, -0.02359357848763466, 0.051831748336553574, -0.013010511174798012, 0.0031462693586945534, 0.03794635087251663, -0.040335312485694885, 0.008013162761926651, -0.03928017243742943, 0.06652180105447769, -0.08719201385974884, 0.017991865053772926, -0.020672209560871124, -0.02811473049223423, -0.015712233260273933, 0.004876930732280016, 0.023755937814712524, -0.011463163420557976, 0.025131726637482643, -0.024093393236398697, 0.007768196985125542, -0.05104571953415871, 0.027553148567676544, 0.04750259220600128, 0.03986818715929985, -0.0376233272254467, 0.030079957097768784, -0.06540513783693314, -0.030161645263433456, 0.008166929706931114, 0.009479695931077003, 0.02169426903128624, -0.019150694832205772, 0.05494476482272148, 0.008669537492096424, -0.022017136216163635, -0.001294592977501452, 0.007190629839897156, 0.03022949956357479, 0.025781068950891495, 0.010267672128975391, -0.03904400020837784, -0.020929355174303055, 0.012379189021885395, -0.014072410762310028, 0.0335647277534008, -0.002616588491946459, 0.038975320756435394, 0.02813764661550522, -0.01654673181474209, -0.011654229834675789, 0.003114938037469983, -0.007226726971566677, 0.066207155585289, -0.00655969837680459, 0.02371075004339218, 0.0010287417098879814, -0.06314459443092346, -0.013452466577291489, -0.031075982376933098, 0.008854941464960575, -0.004308771342039108, 0.057600315660238266, 0.038369257003068924, 0.0031765613239258528, -0.016005514189600945, -0.011749335564672947, -0.0025511838030070066, 0.00036960371653549373, -0.025403428822755814, -0.028097696602344513, 0.01995987631380558, -0.028926324099302292 ]
<p>Through a bit calculation we can derive that in a cavity, the energy density $$u(f,T)=\overline{E(f)}\times G(f)=\frac{8\pi h}{c^3}\frac{f^3}{e^{h\nu /kT}-1}$$ If we take the integral over all frequency, we get $$U(T)=\frac{8πh}{c^3}\frac{(kT)^4}{h^3}{\frac{π^4}{15}}=C_{onst}T^4$$ And Stefan-Boltzmann Law claims that for a perfect black-body $$j^*=\sigma T^4$$ where $j^*$ is the radiant exitance, which is defined as the total energy radiated per unit surface area of a black body across all wavelengths per unit time.</p> <p>And it just so happens that $\frac{\sigma}{C_{onst}}=\frac{c}{4}$, why is that?</p> <p>P.S. The professor told me to refer to some thermodynamics book, where a more general case is discussed. But we don't have that book in our library and the professor's now out of town xD.</p>
g1505
[ 0.020843353122472763, 0.022569244727492332, -0.003132002428174019, -0.022294439375400543, 0.008663797751069069, -0.006653399206697941, 0.05791092664003372, 0.0030669684056192636, -0.03377649188041687, 0.011163653805851936, -0.0071961344219744205, 0.04101433977484703, 0.00935005396604538, -0.006372387520968914, 0.02620016410946846, -0.022954918444156647, 0.047475650906562805, -0.002067627850919962, 0.019521860405802727, -0.0051209768280386925, -0.09734341502189636, -0.023904254660010338, -0.046877168118953705, -0.05059945210814476, 0.05182788148522377, -0.014178549870848656, 0.023562809452414513, -0.010603377595543861, -0.055320534855127335, -0.030621442943811417, 0.030363423749804497, 0.003679860383272171, 0.015209311619400978, -0.017140759155154228, -0.03876494616270065, 0.0025004586204886436, 0.022736886516213417, 0.019686192274093628, 0.014096466824412346, -0.011202936992049217, 0.03564593568444252, -0.048839863389730453, -0.02403826080262661, 0.0024500724393874407, 0.014260838739573956, -0.05433262512087822, -0.04980161413550377, 0.013774346560239792, -0.008394291624426842, 0.03408434987068176, 0.00695214094594121, 0.040599945932626724, 0.11525597423315048, -0.036190927028656006, 0.01603584922850132, -0.0032697024289518595, -0.03958035632967949, -0.00265941652469337, 0.005624324083328247, 0.06640715152025223, 0.02619999460875988, -0.034070271998643875, -0.05639266222715378, 0.029048338532447815, 0.08282110840082169, -0.00846780277788639, 0.02140861377120018, 0.01628384366631508, -0.025178959593176842, -0.025088990107178688, 0.013422428630292416, 0.019703999161720276, -0.042710237205028534, -0.02963472157716751, -0.04841797798871994, 0.0019073465373367071, -0.0019767286721616983, 0.04269596189260483, -0.00509631959721446, 0.002835939172655344, -0.05709691345691681, -0.003928385209292173, -0.006547174416482449, 0.014164034277200699, 0.046571459621191025, -0.0021508345380425453, 0.029944347217679024, 0.05165429785847664, -0.010801786556839943, -0.009423444047570229, -0.0019001057371497154, 0.0015286871930584311, 0.040795326232910156, -0.02577299252152443, 0.023892657831311226, 0.032020244747400284, 0.04657081514596939, 0.03396841883659363, -0.04026288911700249, -0.07886294275522232, -0.015067382715642452, 0.01828610897064209, -0.038277626037597656, 0.018547631800174713, -0.007915107533335686, -0.02631598338484764, -0.0415094792842865, -0.007481703069061041, -0.041777536273002625, 0.06380780786275864, -0.06488537788391113, -0.0458492636680603, -0.0026905713602900505, -0.015122858807444572, -0.03177978843450546, 0.01134765800088644, 0.03578741103410721, -0.031247608363628387, -0.03145164996385574, 0.030837107449769974, -0.028716180473566055, 0.010373489931225777, -0.02854873426258564, 0.03775785118341446, -0.02185586839914322, 0.03555639833211899, -0.01026803720742464, -0.0064185019582509995, -0.0032015254255384207, -0.004180713091045618, -0.011869117617607117, 0.012087242677807808, -0.01439371332526207, 0.02076682262122631, 0.06778856366872787, 0.0566546730697155, -0.00830535776913166, -0.008396518416702747, -0.01836809143424034, 0.01603739708662033, -0.015047414228320122, -0.016625061631202698, 0.00887599028646946, -0.03703104704618454, -0.039476316422224045, -0.013538336381316185, -0.08317070454359055, -0.010352018289268017, -0.022559043020009995, 0.017549650743603706, 0.0035878601484000683, 0.05090634897351265, 0.023969121277332306, 0.03428204357624054, -0.01790223829448223, 0.008146345615386963, 0.008853481151163578, 0.04793298989534378, -0.017307903617620468, 0.011348887346684933, 0.0034560849890112877, 0.022220570594072342, 0.031556710600852966, 0.011597145348787308, -0.07764413207769394, -0.003976421896368265, -0.03280368074774742, -0.08172334730625153, -0.011832580901682377, -0.015876909717917442, -0.012204991653561592, -0.004717306699603796, -0.02768835611641407, 0.05495051294565201, -0.03033338487148285, 0.03969554230570793, 0.015544606372714043, -0.03255966305732727, 0.012449278496205807, 0.05220115929841995, -0.0014511237386614084, -0.03668971359729767, 0.08241870999336243, -0.021489247679710388, 0.045545995235443115, 0.03527768328785896, -0.005809151567518711, -0.006817971356213093, 0.004752084147185087, 0.01682407222688198, -0.03036404214799404, -0.0015605627559125423, 0.020189853385090828, -0.01063972245901823, 0.017536429688334465, 0.048270922154188156, -0.000386614294257015, -0.03302140161395073, 0.0002593174867797643, -0.02747052162885666, 0.010458487085998058, 0.05185557156801224, 0.0676644891500473, -0.040526796132326126, 0.07827803492546082, 0.04382921755313873, 0.0017085650470107794, 0.02569258213043213, 0.0408695824444294, 0.016762668266892433, -0.0195449311286211, -0.028597110882401466, -0.016665512695908546, 0.08380477130413055, 0.0009814441436901689, -0.05568332597613335, -0.042225226759910583, -0.01030459813773632, 0.006654894910752773, 0.015465949662029743, -0.04186199977993965, 0.020330891013145447, -0.004425092600286007, 0.006043582689017057, -0.002358958823606372, 0.0035298108123242855, -0.07570283114910126, -0.02286588028073311, -0.008185946382582188, 0.03773583844304085, -0.10838209837675095, 0.0009064548648893833, 0.00248219957575202, -0.030892526730895042, -0.0012859082780778408, 0.074917271733284, 0.003969485871493816, -0.0006193447043187916, -0.00427747517824173, 0.022279776632785797, 0.04991254210472107, -0.08549073338508606, -0.053400106728076935, -0.038968898355960846, 0.03664751350879669, -0.005372611340135336, -0.0368831604719162, -0.053644709289073944, -0.02392701804637909, -0.03614499047398567, -0.0150400185957551, 0.03346039354801178, 0.02325586974620819, -0.02633797749876976, -0.0071318261325359344, 0.015369961969554424, -0.03428981825709343, 0.01740444079041481, -0.08122242987155914, -0.044595081359148026, 0.015902116894721985, -0.024620773270726204, -0.0007985859992913902, -0.05896734446287155, -0.08852853626012802, 0.023588338866829872, -0.044560112059116364, 0.01264770608395338, 0.05469295009970665, 0.00455020647495985, 0.01811748743057251, 0.1360330581665039, 0.04710271209478378, -0.023310992866754532, 0.02069481462240219, 0.02140263095498085, -0.02331417426466942, -0.0041642580181360245, 0.05945628508925438, -0.006267540622502565, -0.04242391139268875, -0.008006810210645199, -0.12069475650787354, 0.03221314027905464, -0.01682870462536812, -0.06501973420381546, 0.0007403091294690967, 0.01739947311580181, 0.03591574355959892, -0.04614172503352165, 0.03695269674062729, 0.010566736571490765, -0.005784510634839535, 0.05558955669403076, 0.013019083999097347, 0.028542393818497658, 0.01439693383872509, -0.05823124572634697, 0.04142804071307182, 0.04500838369131088, -0.011005767621099949, 0.02820727787911892, -0.013556906953454018, -0.06907603144645691, -0.00959487073123455, 0.018990598618984222, -0.06626065820455551, -0.07378086447715759, -0.005590733606368303, 0.029487477615475655, -0.04163585230708122, -0.031789857894182205, 0.047878820449113846, 0.009907964617013931, -0.017323844134807587, -0.019430195912718773, 0.013310293667018414, 0.014267826452851295, 0.04697970300912857, -0.0038508407305926085, -0.0187324620783329, 0.021731238812208176, 0.0310076717287302, -0.05650930479168892, 0.03374728932976723, -0.014644713141024113, -0.05902800336480141, -0.05840813368558884, -0.023725399747490883, 0.00553086819127202, 0.004145519807934761, -0.011230873875319958, 0.030148116871714592, 0.011097454465925694, -0.03636937215924263, -0.0036439464893192053, -0.030762147158384323, 0.03847845271229744, -0.004242812283337116, -0.012372039258480072, -0.006884908769279718, -0.03233867138624191, 0.04147039353847504, 0.00407066335901618, 0.001350570353679359, 0.05650029703974724, -0.01654702238738537, 0.02122439816594124, 0.014207197353243828, -0.017107555642724037, 0.018086101859807968, -0.019982319325208664, 0.0031064797658473253, 0.0111644072458148, -0.03155084326863289, 0.029309885576367378, 0.04236980527639389, 0.0495811402797699, 0.08095714449882507, -0.01954459398984909, 0.02750583179295063, -0.05437829717993736, 0.0730813592672348, -0.05075320228934288, -0.019413679838180542, -0.036318376660346985, 0.03227615728974342, 0.07867152988910675, -0.0007354922709055245, 0.012770619243383408, -0.036436911672353745, -0.04524962231516838, -0.018361935392022133, 0.05911921709775925, 0.04785382002592087, -0.04534439742565155, -0.017539063468575478, -0.005162748042494059, -0.03148706257343292, 0.029840096831321716, 0.03158801421523094, -0.007701796945184469, 0.018060777336359024, 0.01261878851801157, 0.03708148002624512, 0.017827151343226433, -0.03870706632733345, -0.04842120781540871, 0.07129953801631927, -0.04197848588228226, -0.010906380601227283, -0.016746457666158676, -0.04319168999791145, -0.003268940607085824, -0.037170086055994034, -0.05329862982034683, 0.07314144819974899, -0.02891446277499199, -0.009065501391887665, 0.05092120170593262, 0.013486810959875584, 0.04380954056978226, 0.029100554063916206, -0.04751933366060257, 0.0006960696773603559, 0.026635386049747467, 0.05193471908569336, -0.035971809178590775, -0.052577901631593704, -0.0431009940803051, -0.0021126752253621817, 0.006106559652835131, -0.012999885715544224, -0.026976104825735092, 0.022967448458075523, 0.0006586759118363261, -0.013608007691800594, -0.03282434120774269, 0.040090128779411316, -0.01295560598373413, 0.016829555854201317, -0.03243718668818474, 0.026054268702864647, -0.033872731029987335, 0.011062868870794773, 0.018201759085059166, 0.07045398652553558, 0.0036133439280092716, 0.0002632797695696354, -0.016565026715397835, 0.04555300623178482, -0.03075554035604, 0.004335405770689249, 0.011282535269856453, -0.07310842722654343, 0.03468649834394455, -0.033559650182724, 0.02287116087973118, 0.0029806713573634624, 0.07905034720897675, 0.025644509121775627, -0.061860036104917526, 0.01727238856256008, -0.02952403947710991, 0.02215958945453167, -0.00033959216671064496, 0.028217600658535957, -0.09217621386051178, -0.0045851306058466434, -0.01014720182865858, -0.02063496969640255, 0.021798448637127876, 0.008402024395763874, -0.027528397738933563, -0.00019361548766028136, -0.039830368012189865, -0.029265232384204865, 0.03024487942457199, 0.04352284595370293, 0.04565736651420593, -0.03764520585536957, 0.01750578172504902, 0.001151141943410039, -0.011122455820441246, 0.053987789899110794, -0.05104273557662964, 0.022383572533726692, 0.013818611390888691, 0.01191342156380415, -0.024919910356402397, 0.0364251546561718, 0.06624364107847214, 0.018543949350714684, -0.017584973946213722, -0.04165653511881828, 0.0039236899465322495, 0.03270675614476204, 0.013658909127116203, -0.0400129109621048, 0.005596821662038565, 0.01723383739590645, 0.028685858473181725, 0.024793365970253944, 0.0664549320936203, -0.018772615119814873, 0.051403529942035675, -0.031423766165971756, -0.019796689972281456, -0.019436826929450035, 0.02620522864162922, -0.0030982980970293283, 0.017036933451890945, -0.002619534032419324, -0.013205938041210175, -0.020360196009278297, -0.019089339300990105, 0.09518546611070633, -0.04552847519516945, 0.007215025369077921, 0.04592456296086311, -0.039161503314971924, -0.027108382433652878, -0.003054829081520438, 0.008046700619161129, 0.002368795219808817, 0.07459120452404022, 0.02536408044397831, 0.012646605260670185, 0.0006277503562159836, 0.07216639816761017, 0.03920520469546318, 0.02827708050608635, 0.08748354017734528, 0.015102828852832317, -0.02620869316160679, -0.0310489721596241, -0.010174280032515526, -0.019224409013986588, -0.016502046957612038, -0.043649617582559586, 0.039555538445711136, 0.0066187139600515366, 0.01172352023422718, 0.020180070772767067, 0.0026473337784409523, 0.02025316283106804, -0.02580542117357254, -0.03213142603635788, -0.01578604243695736, 0.007688373792916536, -0.021673277020454407, 0.0008679534075781703, -0.01714237406849861, 0.006102477200329304, -0.042085207998752594, 0.00659985700622201, -0.05585098639130592, 0.02771618217229843, 0.04735309258103371, -0.021577803418040276, 0.03588171675801277, -0.020153041929006577, -0.020653091371059418, 0.03687914460897446, 0.031204814091324806, 0.008232095278799534, -0.04781436547636986, 0.004123048856854439, -0.02465640939772129, -0.014451447874307632, 0.05132132023572922, 0.03487944230437279, -0.024336326867341995, -0.00627988763153553, 0.04548606649041176, 0.000396515941247344, 0.01933765411376953, 0.01988261751830578, -0.04280650243163109, -0.0004643673019018024, 0.034398239105939865, 0.0025050356052815914, 0.027632147073745728, -0.000011245546374993864, 0.04656979814171791, -0.0747569277882576, -0.034381840378046036, -0.06225520372390747, -0.02007966861128807, 0.014436041936278343, -0.012439534068107605, 0.05386161804199219, -0.005268834065645933, -0.020777815952897072, 0.022495539858937263, 0.046734459698200226, -0.005578919313848019, -0.05276651680469513, -0.009732287377119064, -0.03667948395013809, 0.02863417938351631, 0.0019960980862379074, 0.03845126926898956, -0.00865425355732441, -0.018408240750432014, 0.03193740174174309, 0.02067233808338642, 0.009249630384147167, 0.04588822275400162, 0.01164449006319046, 0.020796654745936394, -0.020524805411696434, 0.04989248141646385, -0.01930435746908188, -0.06915519386529922, -0.023271340876817703, 0.015280788764357567, -0.04241211712360382, -0.015463201329112053, 0.013580674305558205, 0.01424124464392662, 0.013146848417818546, -0.006431782618165016, -0.026762908324599266, 0.020535722374916077, -0.009065806865692139, -0.007680762559175491, 0.019780678674578667, -0.013315580785274506, -0.006065304856747389, -0.028853176161646843, 0.05289806053042412, -0.04005807638168335, 0.0398990772664547, 0.009001580066978931, -0.0029443325474858284, 0.026483925059437752, 0.04948047548532486, -0.00019208605226594955, 0.0172308087348938, 0.05197091028094292, 0.0022800147999078035, 0.031925786286592484, -0.014352317899465561, 0.021711153909564018, 0.04352749511599541, -0.029376856982707977, 0.05921144410967827, 0.04989054799079895, -0.007427087519317865, 0.07474779337644577, -0.020178847014904022, -0.017631307244300842, 0.05029527470469475, -0.009877011179924011, 0.028154240921139717, -0.04801943153142929, -0.028281191363930702, -0.05291113629937172, 0.014498374424874783, -0.019833873957395554, 0.006585204973816872, 0.0751027837395668, 0.0295866709202528, -0.03366005793213844, 0.04999365657567978, 0.06688603013753891, -0.053737711161375046, -0.0918494313955307, 0.007615741342306137, 0.035582948476076126, -0.05851917713880539, -0.048106204718351364, 0.00028805420151911676, -0.032073725014925, -0.010809209197759628, 0.011908631771802902, 0.006454943213611841, 0.04922272637486458, -0.051577240228652954, 0.011291136033833027, 0.032958436757326126, 0.05516215041279793, 0.018617326393723488, 0.062134455889463425, -0.011214300990104675, 0.05511145293712616, -0.017719363793730736, 0.018335161730647087, -0.11108052730560303, 0.005804366432130337, 0.0341014638543129, -0.07491786777973175, -0.015039151534438133, -0.033036936074495316, -0.02638288214802742, -0.00604395242407918, 0.08904678374528885, -0.018429957330226898, 0.03541262075304985, 0.01855502836406231, -0.021543234586715698, -0.0924786850810051, 0.019433612003922462, 0.006035017780959606, 0.04228343442082405, -0.07468032091856003, -0.014462434686720371, 0.009450789541006088, 0.052794553339481354, -0.03206007182598114, -0.025009052827954292, 0.011067568324506283, -0.020085791125893593, 0.0053617642261087894, -0.019904207438230515, 0.016234001144766808, -0.006672519724816084, 0.06596430391073227, 0.0027820502873510122, -0.023723630234599113, -0.009372388944029808, -0.024007733911275864, -0.02713916450738907, 0.06566714495420456, 0.016897669062018394, 0.005061888601630926, -0.046843137592077255, -0.008553688414394855, -0.07073908299207687, 0.0395258292555809, -0.06529754400253296, 0.02461238205432892, 0.02227705530822277, 0.022923501208424568, 0.017400044947862625, -0.05133472755551338, 0.06215093284845352, -0.015794822946190834, -0.0714402049779892, 0.01507007610052824, -0.0048188576474785805, -0.01410843525081873, -0.013427579775452614, -0.010303801856935024, -0.048768047243356705, -0.05882004275918007, -0.03403065353631973, 0.06487271934747696, -0.009744200855493546, -0.03242756798863411, 0.013136602938175201, -0.0075937919318675995, -0.007152977399528027, -0.03232138976454735, 0.028307894244790077, 0.028304262086749077, 0.04959442466497421, 0.05740668997168541, 0.04896441102027893, -0.04309717193245888, -0.07598616182804108, 0.008218440227210522, -0.058722175657749176, -0.05220074579119682, -0.05361204594373703, -0.06739497184753418, -0.028101259842514992, 0.04126306623220444, 0.015138763003051281, 0.013795480132102966, -0.006773783825337887, -0.03729488328099251, 0.0322873592376709, 0.034076664596796036, -0.041640233248472214, 0.07181554287672043, -0.018610792234539986, -0.0016934210434556007, 0.04567750170826912, 0.0015644242521375418, -0.008590192534029484, -0.027003705501556396, -0.04341350123286247, 0.02416815236210823, -0.024335158988833427, 0.026832355186343193, -0.009471283294260502 ]
<p>I have known the reason why skate can slide over ice is that water's melting curve in terms of pressure and temperature has a negative slope. If the pressure due to our mass increases sufficiently high, the ice starts to melt.</p> <p>But someone says, according to latest research, it is not true because the time for which we pressure the ice is too short so the ice can't has enough time to melt.</p> <p>Which is more reasonable between the two arguments?</p>
g22
[ 0.0683119148015976, 0.05784103274345398, 0.005673647858202457, 0.0848957970738411, 0.003037851769477129, 0.008647659793496132, 0.0348653569817543, 0.006090661510825157, -0.07303352653980255, 0.021098261699080467, 0.014472553506493568, 0.012070492841303349, 0.029576634988188744, -0.029827550053596497, -0.031692784279584885, 0.021909991279244423, 0.00212842901237309, -0.01650124043226242, 0.027534792199730873, 0.07104935497045517, -0.003110727295279503, 0.001974634360522032, -0.010651807300746441, 0.008599589578807354, -0.11350495368242264, -0.03299259394407272, 0.019619083032011986, 0.014158516190946102, 0.021705565974116325, 0.03934315964579582, 0.0014007462887093425, 0.04013635590672493, -0.002242694841697812, -0.021818548440933228, 0.008238443173468113, -0.05772923305630684, 0.029280953109264374, -0.0293967816978693, 0.015869125723838806, -0.05359329655766487, 0.0014130062190815806, 0.04956622049212456, -0.011207273229956627, 0.048496656119823456, 0.03353675454854965, -0.06443902105093002, 0.02869507111608982, -0.009807651862502098, -0.08112721145153046, -0.018674861639738083, 0.034503791481256485, 0.03614891320466995, 0.026079624891281128, 0.008297464810311794, -0.07657263427972794, 0.026422185823321342, -0.007938736118376255, 0.026254046708345413, -0.036928508430719376, -0.026400765404105186, -0.013554075732827187, 0.04253251105546951, -0.02786288782954216, -0.03209022060036659, 0.033117908984422684, -0.0459018275141716, -0.005742956884205341, -0.00885728094726801, 0.07632314413785934, 0.031043903902173042, -0.005636437330394983, -0.01770903542637825, -0.015458079054951668, 0.011612696573138237, -0.03129861131310463, -0.03503422439098358, -0.01666906103491783, -0.03547622635960579, 0.024820532649755478, 0.016377780586481094, 0.017523696646094322, 0.023652607575058937, -0.0007363699842244387, -0.031254228204488754, 0.0845315009355545, -0.018603438511490822, -0.03443345054984093, 0.02432764321565628, -0.0371866412460804, -0.00012017109838780016, 0.005374959670007229, -0.01534650381654501, 0.028398917987942696, 0.03248777613043785, 0.016729654744267464, -0.0022797330748289824, 0.010992640629410744, 0.037879329174757004, -0.015054316259920597, 0.08261179178953171, -0.09187201410531998, -0.009022507816553116, 0.0005444618873298168, -0.04409653693437576, 0.05644269660115242, 0.0034282344859093428, 0.008425690233707428, -0.014087758027017117, 0.0154845230281353, -0.03894660994410515, 0.03171829134225845, -0.026769550517201424, -0.029907643795013428, -0.01939004845917225, -0.014694477431476116, -0.020597191527485847, -0.0025735334493219852, 0.011160136200487614, -0.007970632053911686, 0.040055882185697556, 0.006071401759982109, -0.041497476398944855, -0.026182474568486214, 0.15025506913661957, 0.02343190461397171, 0.025102153420448303, 0.0072724707424640656, 0.01307669933885336, 0.014864994212985039, 0.03319122642278671, -0.05909283459186554, 0.05219542235136032, -0.04025692492723465, -0.02161179855465889, 0.014372493140399456, 0.10785464197397232, -0.04953540116548538, 0.05087681859731674, -0.061411138623952866, 0.023385822772979736, 0.05107234790921211, 0.029412074014544487, 0.0005639596492983401, 0.010316100902855396, -0.057273898273706436, 0.008789894171059132, -0.051178619265556335, 0.04586585983633995, -0.0444968044757843, 0.006645181216299534, 0.028362704440951347, 0.010956842452287674, 0.038885533809661865, -0.03886599838733673, 0.04043865203857422, 0.038106270134449005, -0.011925335973501205, -0.007918554358184338, 0.03501996025443077, 0.02863413095474243, -0.012177374213933945, -0.0408429279923439, 0.016006065532565117, 0.05223634093999863, -0.04948198050260544, 0.03062114305794239, 0.025001920759677887, 0.022066330537199974, -0.01187208667397499, 0.02639790251851082, -0.007794835604727268, -0.004968229681253433, 0.0229061059653759, 0.05263391137123108, 0.07759442925453186, -0.029678314924240112, 0.07088229060173035, 0.019874989986419678, -0.0007242096471600235, 0.016729649156332016, 0.02435038983821869, 0.0520830862224102, 0.008442427963018417, -0.030958807095885277, 0.06975716352462769, -0.01789594627916813, 0.1010492593050003, 0.01459768507629633, 0.004064219072461128, -0.020221082493662834, -0.010786900296807289, -0.03850669786334038, -0.0015347525477409363, -0.0031567944679409266, 0.016656571999192238, -0.019079983234405518, 0.007019885815680027, -0.018821489065885544, -0.05962288752198219, 0.021309509873390198, -0.0005449537420645356, -0.0004556285566650331, 0.0003322600678075105, -0.025686660781502724, -0.08192319422960281, 0.024742580950260162, 0.01014269981533289, 0.03703617677092552, 0.030872976407408714, -0.0363631434738636, 0.008085840381681919, 0.0486346036195755, -0.032260216772556305, 0.027165604755282402, -0.046220701187849045, 0.020451625809073448, -0.020519396290183067, 0.0069982632994651794, -0.012459415011107922, 0.0012886656913906336, -0.027920514345169067, -0.043164871633052826, -0.026269948109984398, 0.024013448506593704, -0.08426835387945175, -0.037376679480075836, -0.04325496405363083, -0.04076032713055611, 0.029111560434103012, -0.0014718666207045317, -0.014506343752145767, -0.025653818622231483, -0.026173142716288567, -0.01587761379778385, -0.027381887659430504, 0.04704062640666962, -0.018681449815630913, 0.01533094048500061, 0.08239686489105225, 0.03530475124716759, -0.042572904378175735, -0.004165759775787592, -0.06031908094882965, 0.025377290323376656, 0.013276483863592148, -0.04409356415271759, 0.011555729433894157, -0.04007767140865326, 0.048876021057367325, 0.051650263369083405, -0.03424288332462311, 0.01916762813925743, -0.014355075545608997, 0.028405703604221344, 0.06481354683637619, -0.03160751238465309, -0.011763506568968296, 0.00851545948535204, 0.00803976971656084, 0.0143919438123703, 0.03337465599179268, 0.038157131522893906, -0.0653325617313385, 0.027971981093287468, -0.1042008325457573, 0.0045926556922495365, -0.11588156968355179, -0.002715097740292549, 0.04823867604136467, 0.04041876643896103, 0.01599198766052723, -0.02992822416126728, -0.019794177263975143, 0.06629433482885361, -0.0228407122194767, -0.0463331937789917, -0.026952162384986877, -0.010609292425215244, -0.014733191579580307, -0.05173151195049286, 0.047556161880493164, 0.005151999182999134, -0.04572979733347893, -0.018864067271351814, -0.005141282454133034, -0.03240730240941048, -0.06637057662010193, -0.0027084765024483204, -0.07537012547254562, 0.03120635263621807, 0.01568264700472355, -0.005451664794236422, 0.0481407530605793, 0.03623079136013985, 0.0117851747199893, 0.055782806128263474, 0.003068597987294197, -0.013904624618589878, -0.039928317070007324, -0.005458584986627102, 0.019424164667725563, 0.02517775073647499, -0.03508150950074196, 0.02606271579861641, 0.09004741162061691, 0.06238578259944916, 0.0017870661104097962, -0.03836735710501671, 0.004168887622654438, 0.026104317978024483, 0.0179694015532732, 0.07776608318090439, -0.0016642302507534623, 0.04051297903060913, -0.04740938916802406, -0.046666573733091354, -0.029354587197303772, 0.04179234430193901, 0.013497872278094292, -0.011325825937092304, -0.04393499717116356, -0.0016415345016866922, -0.010642464272677898, 0.04939476028084755, 0.02091972716152668, 0.030668489634990692, -0.018867265433073044, 0.01844310201704502, -0.00960599910467863, -0.004392828792333603, 0.012209740467369556, 0.04337005689740181, -0.037984661757946014, -0.024630874395370483, -0.025050194934010506, 0.02342361956834793, 0.09223811328411102, 0.045193810015916824, -0.002890803152695298, 0.023252416402101517, -0.02570783719420433, -0.009782299399375916, -0.023298155516386032, 0.051307931542396545, 0.0035058434586972, -0.00025641598040238023, -0.02560446411371231, 0.0020202784799039364, -0.003366396063938737, -0.014415618032217026, 0.05412540212273598, 0.003087670309469104, -0.03405800089240074, 0.004759049043059349, -0.01837269216775894, 0.010085497982800007, -0.044259559363126755, 0.015361581929028034, 0.0035850757267326117, 0.034726403653621674, 0.025983797386288643, 0.006925011985003948, 0.028522688895463943, 0.06208033859729767, 0.019492875784635544, 0.018571224063634872, -0.010124880820512772, -0.004373474512249231, -0.04131477698683739, 0.031169302761554718, 0.00693072285503149, -0.029750434681773186, 0.007315788883715868, -0.04440832510590553, 0.043944112956523895, -0.047604139894247055, 0.019526835530996323, 0.051555950194597244, -0.03900785371661186, 0.057254016399383545, 0.029841206967830658, 0.043489158153533936, 0.05200830474495888, -0.020844437181949615, -0.015155700035393238, 0.015398811548948288, -0.03188370540738106, -0.002567446092143655, -0.0066200136207044125, 0.025597142055630684, -0.001914871740154922, -0.02726687863469124, 0.0022204280830919743, -0.020897526293992996, -0.017556896433234215, -0.000048313173465430737, -0.040204450488090515, 0.04437192156910896, -0.06595421582460403, -0.07300053536891937, -0.016983753070235252, 0.028533266857266426, 0.010497087612748146, -0.006897181738168001, 0.021314192563295364, -0.023233748972415924, 0.040304653346538544, -0.03950662538409233, -0.03718138486146927, -0.0017886649584397674, 0.05534902215003967, -0.021213246509432793, -0.08273892849683762, 0.01273158099502325, 0.004579989705234766, -0.06017608195543289, -0.026278430595993996, -0.02371499314904213, 0.01374958548694849, 0.010012033395469189, -0.01366840023547411, -0.05791759863495827, -0.02009574882686138, -0.04950690641999245, -0.08212446421384811, 0.035412855446338654, 0.002886456437408924, -0.02764444425702095, -0.03053736872971058, -0.02602154202759266, 0.02530079148709774, 0.04837416857481003, -0.057552777230739594, -0.013497022911906242, 0.037127379328012466, 0.08174484968185425, 0.026318859308958054, -0.008222514763474464, -0.00962002668529749, 0.02884659543633461, -0.03392980620265007, -0.04834865778684616, 0.04685640335083008, 0.05643130838871002, -0.02743053436279297, 0.043248869478702545, 0.011765853501856327, -0.00650798948481679, -0.020032787695527077, -0.0692785233259201, -0.01476450078189373, 0.010792842134833336, -0.013081311248242855, 0.0021735334303230047, -0.03514263406395912, -0.04929134622216225, -0.008830543607473373, 0.046349361538887024, -0.05653764307498932, 0.04605637863278389, 0.04278584569692612, 0.018182996660470963, 0.030245335772633553, 0.0035185092128813267, 0.048027463257312775, -0.007148646283894777, -0.016459854319691658, -0.05286814272403717, 0.014211205765604973, 0.012714200653135777, -0.015335598960518837, 0.041402168571949005, -0.03669613227248192, 0.081143818795681, -0.00027104964829050004, -0.008065958507359028, -0.023669248446822166, 0.022331977263092995, 0.021305924281477928, -0.04529410973191261, -0.008313246071338654, -0.018743695691227913, 0.013528329320251942, -0.05904575437307358, 0.0030629257671535015, 0.005415452178567648, -0.09024705737829208, 0.06053159758448601, 0.0036526299081742764, -0.034395813941955566, 0.005175063852220774, -0.053973305970430374, 0.044785209000110626, 0.02130286581814289, -0.06494452804327011, -0.039987388998270035, -0.02454793080687523, 0.007390907034277916, 0.027498522773385048, 0.0003839487908408046, -0.04302143305540085, -0.0882626548409462, 0.05303787440061569, -0.014530947431921959, 0.0022596362978219986, -0.021249612793326378, 0.04092857241630554, -0.04675368592143059, -0.040652256458997726, -0.038880281150341034, -0.008081487379968166, 0.04902719706296921, 0.012514408677816391, 0.013888335786759853, 0.059002835303545, 0.015522214584052563, -0.039309315383434296, 0.008843514136970043, -0.029210666194558144, 0.0029847510159015656, -0.008984405547380447, -0.03172396495938301, 0.004008796997368336, 0.02393348328769207, -0.048607226461172104, 0.010207219049334526, -0.05899818614125252, -0.022330008447170258, -0.007093031425029039, -0.027484145015478134, 0.031173570081591606, -0.05410357192158699, 0.06818822771310806, 0.03141837567090988, 0.010492740198969841, -0.04577815532684326, -0.029268041253089905, 0.00432416470721364, 0.04728494957089424, 0.0036088719498366117, -0.04175489768385887, 0.020705070346593857, -0.00454735429957509, 0.060988713055849075, -0.008804808370769024, 0.03538474068045616, 0.006972652394324541, 0.03414216637611389, 0.006984775885939598, -0.09732533991336823, -0.03263688459992409, -0.013073516078293324, -0.04825083911418915, -0.03622523322701454, 0.04277082160115242, -0.01009521633386612, 0.003142785746604204, 0.012892760336399078, 0.037038542330265045, -0.02402373217046261, -0.0017959391698241234, -0.05037097632884979, -0.04126444458961487, 0.022610021755099297, 0.04031559079885483, 0.01805952936410904, -0.0022767111659049988, 0.0074441032484173775, 0.009989742189645767, -0.009129654616117477, 0.05467735603451729, 0.012255744077265263, 0.007754397578537464, 0.04298613592982292, -0.04152262210845947, 0.0430208295583725, -0.013993575237691402, -0.00001815996438381262, 0.0013372717658057809, -0.041590366512537, 0.02096135914325714, 0.014824284240603447, -0.06361261010169983, -0.008115094155073166, 0.01691814325749874, 0.036057665944099426, -0.07855463773012161, -0.004357066471129656, -0.005851434543728828, -0.02937227115035057, -0.01919531635940075, -0.003311098786070943, -0.02649320289492607, -0.07104124873876572, 0.000019158525901730172, -0.008928226307034492, 0.02525528520345688, 0.012040502391755581, -0.027113355696201324, -0.008064104244112968, 0.05216896906495094, 0.07680164277553558, 0.07898549735546112, 0.012701775878667831, -0.032306913286447525, -0.025919005274772644, 0.0009884132305160165, 0.06476999819278717, 0.07035365700721741, -0.01633322238922119, -0.054208070039749146, 0.020367875695228577, 0.05535193160176277, -0.044656023383140564, -0.010103272274136543, 0.004270879551768303, -0.04402446001768112, -0.031148482114076614, -0.0004363680782262236, -0.025121454149484634, -0.020264968276023865, 0.009204023517668247, -0.028708918020129204, -0.03548678010702133, 0.019959118217229843, 0.0005931066116318107, -0.015836212784051895, -0.010365087538957596, 0.003410174511373043, -0.0007363305776380002, 0.046841636300086975, -0.03019299916923046, -0.061094749718904495, 0.07797491550445557, -0.012038393877446651, 0.013091065920889378, 0.009039855562150478, 0.02338333986699581, 0.015942147001624107, 0.04207456111907959, 0.02450747787952423, -0.0642363429069519, -0.011757935397326946, 0.033760033547878265, 0.03353004902601242, -0.006629577837884426, -0.05395553633570671, -0.041350800544023514, 0.015219305641949177, -0.019860437139868736, -0.00003951684630010277, -0.024565154686570168, -0.02280571684241295, -0.055516671389341354, -0.008961965329945087, -0.02698906697332859, -0.00419987179338932, 0.04650828614830971, 0.051650188863277435, -0.001056887093000114, -0.02838112600147724, -0.02221018634736538, -0.0025731187779456377, 0.012166551314294338, 0.01980888657271862, -0.03990606591105461, -0.018661201000213623, 0.033168282359838486, 0.012859571725130081, 0.003424344351515174, -0.016549795866012573, -0.00026910248561762273, 0.03417320176959038, -0.05109471455216408, -0.01843411847949028, 0.038368407636880875, -0.022370418533682823, -0.05426301434636116, 0.0010308722266927361, 0.07866468280553818, 0.04029376432299614, -0.006640416570007801, 0.03546345606446266, -0.037750791758298874, -0.034165799617767334, 0.013604401610791683, -0.012373621575534344, 0.027966709807515144, -0.015669655054807663, 0.005399010609835386, -0.010033898986876011, 0.03562150523066521, 0.011700307950377464, 0.027744390070438385, -0.010376166552305222, 0.014346749521791935, 0.014283320866525173, 0.04466572776436806, 0.02385922707617283, 0.009952696040272713, -0.03254583850502968, -0.048643600195646286, 0.031196877360343933, -0.0009495720150880516, -0.06658285111188889, 0.06523986905813217, 0.0009090838138945401, -0.04198293387889862, 0.031235357746481895, -0.03579628840088844, 0.038571104407310486, 0.05589552968740463, 0.014670821838080883, -0.02518407627940178, 0.02500828541815281, 0.014492768794298172, 0.017690854147076607, -0.037934888154268265, -0.06287199258804321, -0.024473432451486588, 0.019446808844804764, -0.0357055701315403, -0.029968125745654106, -0.06566241383552551, -0.025286763906478882, -0.022466961294412613, -0.018087739124894142, -0.01673688180744648, -0.019674697890877724, -0.05077342316508293, -0.036945514380931854, 0.007613806053996086, -0.034416891634464264, -0.009624773636460304, 0.010754012502729893, 0.00688165845349431, 0.013776666484773159, 0.05177994817495346, -0.05672119930386543, 0.0706939548254013, 0.008700835518538952, 0.02783828414976597, 0.005309519823640585, -0.026581991463899612, -0.0036717115435749292, -0.0016300213756039739, 0.04069484770298004, 0.01057280134409666, 0.01725025475025177, 0.01578393392264843, -0.03222210332751274, 0.059242211282253265, 0.01064402423799038, -0.010979444719851017, 0.03898107260465622, 0.012518109753727913, -0.08415663242340088, 0.034877825528383255, -0.019956717267632484, -0.0033845040015876293, -0.0233365036547184, -0.0545663945376873, 0.055491749197244644, -0.03836758807301521, -0.029424622654914856, -0.01810908317565918, 0.0002127321931766346, 0.003615407273173332 ]
<p>The articles I found on radiation in the solar system mostly dealt with solar wind, I wonder about other types. Is there a breakdown that tells me, withhin an order of magnitude, at least what intensity I can expect for a the different spectra - hard gamma through to radio frequencies, and chargede particles - and how this varies depending on my position?</p>
g1506
[ -0.013779254630208015, 0.05724233016371727, -0.025939911603927612, -0.02132268436253071, 0.02713811583817005, 0.012089725583791733, -0.02751024253666401, -0.0073241968639194965, -0.017120886594057083, -0.04639727249741554, 0.06979575753211975, 0.046928346157073975, 0.01255476288497448, -0.009088505059480667, 0.0422324575483799, -0.051260411739349365, 0.052980974316596985, -0.015959594398736954, 0.0607239305973053, 0.06048880144953728, -0.014910162426531315, -0.05535561218857765, -0.01356938574463129, 0.0020212207455188036, -0.02282937802374363, 0.06185843423008919, 0.005267534404993057, -0.02130277082324028, 0.010906637646257877, -0.06708458811044693, 0.0032674104440957308, -0.0051355441100895405, 0.013569564558565617, -0.03255872428417206, -0.04186755418777466, 0.014858239330351353, -0.017787782475352287, 0.013714362867176533, -0.0032383210491389036, 0.023312076926231384, -0.014197693206369877, -0.033020418137311935, 0.022346120327711105, 0.04790182039141655, -0.021824980154633522, -0.024222860112786293, -0.035881172865629196, 0.006793057546019554, -0.03315868601202965, -0.008702488616108894, -0.034389808773994446, -0.02564138174057007, 0.020873283967375755, 0.03149731829762459, 0.06602267175912857, -0.03902418911457062, 0.009190799668431282, -0.05136316642165184, 0.05101318657398224, 0.0012518538860604167, 0.008595333434641361, 0.00686795637011528, -0.06139375641942024, -0.05634622275829315, -0.0167893897742033, -0.0068474384024739265, -0.027088923379778862, 0.030729884281754494, -0.08681495487689972, -0.05393587797880173, 0.04997578635811806, 0.014894946478307247, -0.016354110091924667, -0.06890808790922165, -0.00856921449303627, -0.0354231558740139, 0.013781734742224216, 0.012539306655526161, -0.004074471071362495, 0.04778748378157616, 0.005603700410574675, 0.006920107174664736, 0.013633371330797672, -0.013456066139042377, 0.06680048257112503, -0.005106053780764341, 0.010491597466170788, 0.022529590874910355, 0.025749461725354195, -0.028478527441620827, 0.04711051285266876, 0.014786332845687866, 0.0018998325103893876, -0.05202135816216469, -0.013799114152789116, 0.02785063348710537, -0.01758425310254097, 0.03799821436405182, -0.03530455380678177, -0.00706348055973649, 0.004541177302598953, -0.012844777666032314, 0.011178226210176945, 0.013052660040557384, 0.06093462556600571, -0.011532924138009548, 0.026909589767456055, -0.05149288848042488, 0.028698809444904327, -0.007305372506380081, -0.017727501690387726, -0.016779281198978424, 0.00801610667258501, 0.005257977172732353, -0.05360623449087143, -0.0006125911022536457, 0.03542288765311241, -0.0737464502453804, 0.03744576498866081, 0.09037219732999802, 0.09286794811487198, 0.0724259540438652, -0.04491812735795975, 0.03609621152281761, -0.06128297373652458, -0.07697279006242752, 0.05500069260597229, -0.01011538878083229, 0.003945075906813145, -0.006133799906820059, 0.017742516472935677, -0.05309518426656723, -0.022271402180194855, 0.037266477942466736, 0.07098210602998734, -0.010215583257377148, 0.018003389239311218, -0.012467811815440655, -0.0025005992501974106, -0.029365437105298042, 0.04851676896214485, -0.005132765043526888, -0.00007787391950841993, -0.032678067684173584, -0.04066009446978569, 0.010403480380773544, -0.023425200954079628, -0.005916878115385771, 0.022085899487137794, 0.0033728517591953278, 0.07844994962215424, 0.0164912398904562, 0.015099229291081429, -0.040277548134326935, -0.010387592948973179, 0.014842567965388298, 0.007978804409503937, 0.026050955057144165, -0.04502653330564499, 0.06423402577638626, -0.013394811190664768, -0.02272174507379532, -0.02264656126499176, -0.009291378781199455, -0.05375783145427704, -0.031002815812826157, -0.05339999869465828, -0.028411269187927246, 0.024433616548776627, 0.011620963923633099, -0.0016273099463433027, -0.009403347037732601, 0.05338270589709282, -0.03424365818500519, -0.009888152591884136, 0.02120252512395382, 0.05372465401887894, -0.040167082101106644, 0.02714710868895054, 0.015848981216549873, 0.009952932596206665, 0.022369705140590668, -0.012234861962497234, -0.043827638030052185, 0.023469623178243637, -0.03689468652009964, -0.023950833827257156, -0.011841912753880024, 0.05183044821023941, 0.03634445369243622, -0.003206070279702544, -0.002936168108135462, 0.022352883592247963, -0.0285335723310709, 0.035963043570518494, -0.026177799329161644, -0.032348740845918655, -0.0044779363088309765, -0.013843369670212269, 0.01951722614467144, 0.021607162430882454, 0.07109566777944565, 0.007914118468761444, 0.056846242398023605, 0.009176654741168022, 0.08986736834049225, -0.02733735926449299, -0.01375829428434372, 0.04070674255490303, -0.014276187866926193, 0.04006660729646683, -0.05891988426446915, 0.053891200572252274, 0.0006436651456169784, 0.0042001428082585335, 0.010658408515155315, -0.07509062439203262, 0.00866798497736454, 0.05572592839598656, -0.02839798294007778, -0.0534946545958519, -0.00898029189556837, 0.04430706053972244, 0.00967545248568058, -0.018288537859916687, 0.04956859350204468, -0.05014634504914284, 0.021414903923869133, 0.06353936344385147, 0.04383710026741028, -0.01581549271941185, 0.024603085592389107, -0.028040461242198944, 0.013257146812975407, 0.00010540025687078014, -0.05057542398571968, 0.0035448584239929914, -0.05412984639406204, 0.03147205710411072, -0.014996398240327835, -0.06077605485916138, 0.001419291365891695, -0.020494136959314346, -0.02441905066370964, 0.0356406606733799, -0.025803036987781525, 0.0314798541367054, -0.02590874210000038, -0.03528016805648804, -0.005670038051903248, 0.003787294728681445, -0.04078194499015808, 0.007909826003015041, 0.07166588306427002, -0.057344529777765274, 0.017000529915094376, -0.029068825766444206, 0.055651403963565826, -0.051818352192640305, -0.0014798104530200362, 0.00122301175724715, -0.013587270863354206, -0.023598508909344673, 0.04263797029852867, -0.0019861699547618628, -0.015081631951034069, 0.0472259595990181, 0.02906952239573002, -0.010536718182265759, -0.04205946624279022, 0.056383632123470306, 0.06630928814411163, 0.004123027436435223, 0.011671354062855244, -0.02858053892850876, 0.019431278109550476, -0.021155204623937607, 0.015955744311213493, 0.024234266951680183, -0.04320848733186722, 0.05539738014340401, -0.0123710036277771, 0.03235927224159241, 0.006540537346154451, 0.006257737521082163, -0.06743885576725006, -0.011589186266064644, 0.03803331032395363, -0.008642513304948807, 0.010000600479543209, -0.03887366130948067, -0.05539308488368988, 0.08561088889837265, -0.02787666954100132, -0.04645826667547226, -0.025483887642621994, 0.02986804209649563, 0.03439517691731453, 0.01591409556567669, 0.011731794103980064, 0.0011301718186587095, -0.05829082801938057, 0.009148376993834972, -0.011918754316866398, -0.03011070191860199, 0.0037449190858751535, -0.03945893421769142, -0.04009329900145531, 0.04151487722992897, 0.017593329772353172, -0.051303304731845856, -0.04151541739702225, 0.002149217762053013, 0.03724333643913269, 0.0026421351358294487, 0.0015476684784516692, -0.03881238400936127, 0.0008691884577274323, 0.01481938362121582, 0.01860627345740795, 0.009137767367064953, -0.0654635801911354, 0.04858001694083214, -0.0027859786059707403, -0.035563912242650986, 0.05981158837676048, 0.030634088441729546, -0.062080781906843185, -0.057677384465932846, 0.006361904088407755, 0.012936752289533615, 0.020301420241594315, -0.006062865257263184, 0.0351012721657753, -0.014016576111316681, 0.07041171938180923, -0.010167418047785759, 0.010841463692486286, 0.04889633506536484, 0.027391381561756134, 0.06779280304908752, 0.00475291907787323, -0.02938004396855831, 0.0006813168874941766, -0.053693342953920364, 0.0029636125545948744, 0.01204981654882431, -0.06511101871728897, -0.0378357470035553, -0.023120971396565437, 0.028570745140314102, -0.03610311448574066, -0.013143976218998432, -0.03196485713124275, -0.029717331752181053, -0.0019007171504199505, 0.0163264237344265, 0.033866990357637405, -0.00583895156159997, 0.015182510949671268, 0.04392474889755249, -0.05380868911743164, 0.026155000552535057, -0.02583826333284378, 0.024988971650600433, 0.02290809340775013, -0.00011148317571496591, 0.005964701529592276, -0.02189501002430916, -0.010781940072774887, -0.010129688307642937, 0.008554507046937943, 0.029316550120711327, -0.03820190206170082, -0.0007208989118225873, -0.039689648896455765, 0.037406668066978455, 0.014436846598982811, 0.025531403720378876, 0.017780851572752, -0.001201536739245057, 0.029262423515319824, 0.06780621409416199, 0.00257196300663054, 0.054020825773477554, 0.0008836116176098585, 0.0036572718527168036, 0.05276187136769295, -0.061473309993743896, -0.076632559299469, 0.02000482566654682, -0.11576636880636215, -0.052135828882455826, 0.04333554953336716, 0.05105998367071152, -0.09528892487287521, 0.04443031921982765, 0.01674593985080719, 0.03182916343212128, 0.035765524953603745, 0.04384010285139084, 0.011039686389267445, 0.004999478347599506, -0.02532745711505413, 0.003607361577451229, 0.03347337618470192, -0.0013945228420197964, -0.017256854102015495, -0.05356103554368019, -0.016875362023711205, -0.0014197599375620484, -0.04430540278553963, 0.010815425775945187, -0.026911068707704544, -0.004410043824464083, 0.03861776366829872, -0.0225982628762722, -0.06846025586128235, 0.08192852884531021, 0.01949010044336319, 0.02368856407701969, 0.026257846504449844, 0.030117861926555634, 0.004497865680605173, -0.03679633513092995, 0.08855531364679337, 0.06075182929635048, 0.00966448150575161, -0.012930909171700478, 0.024601323530077934, 0.042525764554739, -0.039478741586208344, -0.036731790751218796, 0.0295968446880579, 0.014036179520189762, 0.02642035484313965, -0.044447895139455795, -0.01690654642879963, -0.02006029710173607, -0.0010416036238893867, 0.06634277105331421, 0.0015463588060811162, 0.04596615210175514, 0.036550141870975494, 0.034426458179950714, 0.05086386203765869, 0.008929101750254631, -0.01102979201823473, -0.033264826983213425, -0.009617995470762253, -0.04322033375501633, -0.029044121503829956, -0.10398779809474945, 0.0014251015381887555, -0.026195498183369637, -0.01860314980149269, -0.021247029304504395, 0.020652838051319122, 0.04647761583328247, -0.00426869373768568, -0.006056154612451792, -0.004999483469873667, 0.09691751003265381, -0.024261383339762688, 0.030855802819132805, 0.021069109439849854, -0.0710611343383789, 0.029856914654374123, -0.06928056478500366, -0.01619308441877365, -0.03021535649895668, 0.017348773777484894, 0.07181793451309204, -0.08938788622617722, -0.041291493922472, 0.012232806533575058, -0.03811477869749069, -0.046562131494283676, -0.0613994300365448, 0.022195957601070404, -0.021912815049290657, 0.004870777018368244, 0.013053257018327713, 0.030391566455364227, -0.025623705238103867, 0.036443017423152924, -0.019794123247265816, 0.011841014958918095, 0.06138985976576805, -0.015401478856801987, -0.02803932875394821, -0.0014004068216308951, -0.00020188975031487644, -0.02927924133837223, -0.028258122503757477, 0.03285299241542816, -0.008172658272087574, -0.08776605129241943, 0.009453066624701023, -0.009250550530850887, 0.004719173535704613, 0.013475666753947735, -0.003932591062039137, 0.014323120005428791, 0.034398920834064484, 0.058783672749996185, 0.052346598356962204, -0.0483594611287117, 0.04795508086681366, 0.031040731817483902, -0.019649861380457878, 0.006847950629889965, -0.031588613986968994, 0.02500465326011181, 0.0014550171326845884, 0.0009520543389953673, -0.06706126779317856, 0.06129844859242439, 0.07301715761423111, -0.061148982495069504, -0.046191032975912094, -0.010238450951874256, 0.019471408799290657, 0.03831310570240021, 0.02076750621199608, -0.006768838036805391, -0.014993821270763874, 0.028288239613175392, 0.01459038257598877, -0.036696624010801315, 0.01264168694615364, 0.032493848353624344, -0.03265563026070595, 0.010090741328895092, 0.06373315304517746, -0.059746649116277695, 0.017158279195427895, 0.041805583983659744, 0.03392505645751953, 0.05160810798406601, -0.06641893088817596, 0.027126867324113846, -0.009617714211344719, 0.016576100140810013, 0.01266784593462944, 0.02023054100573063, -0.0004080391372554004, 0.023714579641819, 0.013169465586543083, 3.3838563240351505e-7, -0.009371969848871231, -0.026142166927456856, 0.04583635926246643, -0.0005263125640340149, -0.06546786427497864, 0.026811230927705765, 0.014951146207749844, 0.028046349063515663, -0.02101198211312294, -0.0204088743776083, -0.03241835907101631, 0.02692430652678013, 0.011602926068007946, -0.036708932369947433, -0.002107394626364112, -0.04090298339724541, 0.01575716771185398, -0.06785913556814194, 0.06160164624452591, 0.04898744076490402, -0.010903541930019855, -0.022915488108992577, 0.02852800115942955, 0.018186982721090317, 0.021694514900445938, -0.06838514655828476, 0.023441802710294724, 0.011171506717801094, -0.008706312626600266, -0.0009030146175064147, 0.05173997953534126, -0.000702560122590512, 0.03453926742076874, 0.015163341537117958, -0.02253357321023941, 0.03439483791589737, -0.0056287990882992744, 0.032697759568691254, -0.0008258202578872442, -0.026692500337958336, 0.04528270661830902, -0.053938232362270355, 0.05737517029047012, 0.02187056466937065, -0.05193217471241951, -0.0018940098816528916, 0.005104661453515291, -0.03550497069954872, 0.028880475088953972, 0.008436023257672787, 0.04094509780406952, 0.024094635620713234, 0.02997458539903164, -0.01042992528527975, 0.057725079357624054, -0.04747778922319412, -0.0049985251389443874, 0.04168146848678589, -0.003792049828916788, 0.04221212491393089, -0.023311639204621315, -0.033380862325429916, -0.025581233203411102, 0.0072996229864656925, -0.028030557557940483, -0.006010717246681452, -0.031877387315034866, 0.007841806858778, 0.01913651078939438, -0.033035460859537125, -0.0021554718259721994, -0.08102917671203613, -0.014617975801229477, -0.010339275002479553, -0.005900465417653322, 0.03995753452181816, -0.006905492395162582, 0.05379068851470947, 0.03136805072426796, -0.026327617466449738, 0.05416913703083992, 0.013566258363425732, 0.06093341112136841, 0.03674564138054848, -0.0028792938683182, -0.034780923277139664, -0.0347619354724884, -0.05936269834637642, -0.03972615674138069, 0.05874946340918541, 0.0003368587058503181, 0.003149763448163867, 0.031640224158763885, -0.04979585483670235, 0.018486620858311653, 0.04132890701293945, -0.004187861457467079, -0.02939598821103573, 0.01827787607908249, -0.0403527207672596, 0.008336723782122135, -0.07158555090427399, 0.054441917687654495, -0.034535471349954605, 0.013026352040469646, 0.07364410907030106, -0.028363436460494995, -0.016510704532265663, 0.02062995173037052, -0.057731110602617264, 0.06260481476783752, 0.008070098236203194, -0.051737431436777115, 0.029413562268018723, -0.014935046434402466, 0.016703005880117416, -0.0033285438548773527, -0.07353654503822327, -0.04725821688771248, -0.024239031597971916, -0.03568698838353157, 0.01939908042550087, -0.02444998174905777, 0.039463408291339874, -0.03831886500120163, -0.04048489034175873, -0.049527719616889954, -0.025714248418807983, -0.00796988233923912, -0.031019534915685654, -0.011452732607722282, 0.028638217598199844, 0.00214519165456295, 0.05397270247340202, 0.033020779490470886, -0.0018652714788913727, -0.09421993792057037, -0.04445207864046097, 0.01065825205296278, -0.02440854348242283, -0.08747194707393646, 0.04093828424811363, 0.02621617168188095, -0.07279269397258759, -0.012325668707489967, -0.029711784794926643, -0.04660434648394585, 0.04553205892443657, 0.051730927079916, 0.008889291435480118, 0.00565492594614625, 0.038275688886642456, -0.011312983930110931, -0.06772206723690033, 0.023214571177959442, 0.04340184107422829, -0.0007244294392876327, 0.022848721593618393, -0.0020758318714797497, -0.006711962632834911, 0.039940766990184784, 0.038388896733522415, -0.022049468010663986, 0.003328492399305105, -0.0053694648668169975, -0.010732075199484825, -0.07388157397508621, -0.009397024288773537, -0.0024475527461618185, 0.04586055874824524, -0.004566092509776354, 0.0035889227874577045, 0.06393395364284515, 0.022078968584537506, 0.037870969623327255, -0.02443769760429859, 0.0014790805289521813, -0.02816845290362835, 0.07045329362154007, -0.027433136478066444, 0.0034291737247258425, 0.011218037456274033, -0.001335221459157765, -0.018884658813476562, -0.03778306394815445, -0.0035373037680983543, 0.015317201614379883, -0.09049823135137558, -0.008094694465398788, 0.03128702566027641, 0.013082282617688179, 0.038380205631256104, -0.04410354420542717, -0.016755934804677963, -0.026411233469843864, -0.016749704256653786, 0.0014128201873973012, -0.058608755469322205, -0.0015872500371187925, -0.06956174969673157, -0.0007494330056942999, 0.0010912101715803146, 0.0363025888800621, 0.049378227442502975, 0.00042872779886238277, -0.02131989598274231, -0.02699856087565422, -0.028419706970453262, -0.010630284436047077, 0.047120533883571625, 0.02842625044286251, -0.03822808340191841, 0.02792956680059433, -0.005559936631470919, -0.0017500071553513408, -0.02301866188645363, 0.014567551203072071, -0.03790506720542908 ]
<p>I've been reading up on nuclear reactors, and understand explanations of how it works, how water is heated to steam, which turns the turbines, etc.. I understand all of the safety features, and how control rods are used, and what they do with spent fuel.</p> <p>However, what I can't figure out (after lookin at many websites and videos) is where the reaction actually starts. The fuel rods contain Uranium pellets, and then they're put in the reactor, where the reaction starts and neutrons start hitting each other to create heat? So is this happening all over the reactor, or just in each fuel rod assembly?</p> <p>Also, you can hold a Uranium pellet in your hand (ideally wearing a glove) and it's not dangerous, so what <em>starts</em> a reaction? A lot of people say the reaction can start by itself, so why do uranium pellets not suddenly heat up and start spreading radiation by themselves? Is it because they haven't been <em>enriched</em>?</p> <p>What if you dropped a Uranium pellet on the floor?</p>
g1507
[ 0.027307892218232155, 0.020346300676465034, 0.0055463784374296665, 0.038578830659389496, 0.04763885587453842, 0.013620711863040924, 0.03276867792010307, 0.10338108241558075, 0.005428382661193609, -0.062134433537721634, -0.019769733771681786, 0.025137629359960556, 0.005762588232755661, 0.0008059758110903203, 0.046253837645053864, -0.07446365058422089, -0.0035427177790552378, -0.002416739473119378, -0.01782517321407795, 0.05026547983288765, 0.01144629716873169, -0.0034121337812393904, -0.029544714838266373, -0.0016931892605498433, -0.06178261339664459, -0.02914569526910782, -0.05437885969877243, -0.02066025882959366, 0.009101837873458862, -0.06568102538585663, -0.014060240238904953, -0.0021128645166754723, 0.0272972472012043, 0.00899315532296896, 0.02299831248819828, -0.07015897333621979, -0.06808001548051834, -0.011401514522731304, -0.008923066779971123, 0.02147519402205944, -0.08389590680599213, -0.020169852301478386, 0.004188793711364269, -0.008600941859185696, -0.019898686558008194, 0.04713663086295128, -0.0577029287815094, -0.018263479694724083, -0.04294285550713539, 0.08282134681940079, 0.0276486836373806, -0.02034935913980007, -0.011164555326104164, -0.0001933929161168635, 0.0202325452119112, -0.0036301910877227783, 0.031040355563163757, 0.02022719383239746, 0.0927535742521286, 0.015959903597831726, 0.02317909151315689, 0.006399885751307011, -0.012164486572146416, -0.04784153774380684, 0.06984160095453262, 0.03541586920619011, -0.02770250104367733, 0.022409629076719284, 0.0605989433825016, 0.0766637995839119, -0.03175180405378342, -0.04550827294588089, -0.03381834924221039, 0.0012708832509815693, -0.007877526804804802, -0.022440452128648758, -0.05234251916408539, -0.010767867788672447, -0.0198175311088562, 0.012780954129993916, -0.004342075902968645, -0.012394768185913563, 0.018327878788113594, -0.004774628207087517, -0.007898421958088875, 0.040119193494319916, -0.053620122373104095, -0.01137066725641489, -0.004621090367436409, 0.013889675959944725, 0.044700585305690765, 0.02501923404633999, 0.004362467676401138, 0.009121501818299294, 0.02639959193766117, -0.04651135578751564, -0.08660263568162918, 0.020355945453047752, -0.009874190203845501, 0.014360882341861725, -0.006675833370536566, -0.03572854772210121, 0.008364532142877579, -0.01334703154861927, -0.024935461580753326, 0.003319151932373643, -0.004567666444927454, 0.005652416497468948, 0.03153048828244209, 0.0309767909348011, -0.05792570114135742, 0.004375350195914507, -0.007711389567703009, 0.01273617148399353, 0.04895405471324921, 0.021999511867761612, 0.05229491740465164, 0.038287773728370667, 0.02953726425766945, 0.023641321808099747, 0.046043116599321365, 0.06828097254037857, -0.10537198185920715, -0.0035148104652762413, -0.03489004075527191, -0.006984189618378878, -0.0023736595176160336, 0.027860790491104126, -0.01637902483344078, 0.08596193790435791, -0.024886947125196457, -0.04430929943919182, -0.08286477625370026, 0.0019865301437675953, 0.09811745584011078, 0.03085322678089142, 0.0035089096054434776, 0.0430460125207901, 0.018084391951560974, 0.0018396874656900764, 0.011544984765350819, 0.043564073741436005, -0.03710382059216499, -0.05831845849752426, -0.035832252353429794, 0.034413792192935944, 0.0037633508909493685, 0.0025176536291837692, 0.008239971473813057, -0.030834101140499115, 0.0028167488053441048, 0.03597429394721985, -0.014380506239831448, -0.0909309983253479, 0.012764682993292809, -0.020109113305807114, 0.017938440665602684, -0.09377618134021759, 0.0886894017457962, -0.01806112937629223, 0.0552600659430027, 0.01491066999733448, 0.009532229043543339, -0.011477956548333168, -0.04159320890903473, 0.0009850258938968182, 0.04018627852201462, -0.06555730104446411, 0.000781642273068428, 0.01890929415822029, -0.056399114429950714, -0.08993328362703323, -0.06006797403097153, 0.04912341758608818, -0.04542527347803116, 0.02640705369412899, 0.11809995025396347, -0.0019499798072502017, 0.0217213723808527, -0.03457821160554886, -0.029314372688531876, -0.04359811544418335, 0.04741756245493889, -0.06704743206501007, 0.035690754652023315, -0.024197451770305634, -0.03418103605508804, 0.006497173570096493, -0.0017455356428399682, 0.04060305655002594, -0.0032583267893642187, -0.03322674706578255, 0.015668019652366638, -0.03683449327945709, 0.005522157996892929, -0.01876033842563629, -0.060970649123191833, -0.06412863731384277, 0.032595738768577576, 0.05252192169427872, 0.006948626600205898, -0.04085495322942734, -0.013627199456095695, 0.003614925080910325, -0.022893918678164482, 0.0012486993800848722, -0.0006404435844160616, 0.04701776057481766, -0.0058169071562588215, 0.024180661886930466, 0.019454795867204666, -0.025357790291309357, 0.030157411471009254, -0.026330003514885902, -0.022278331220149994, 0.05173397809267044, -0.0526757687330246, 0.01340717263519764, 0.010420719161629677, 0.00008769887790549546, 0.028264719992876053, 0.0011814931640401483, -0.017741145566105843, -0.009059435687959194, -0.004001902416348457, 0.04969632998108864, -0.015804734081029892, -0.00008455233182758093, 0.07277998328208923, 0.006638851948082447, -0.06808250397443771, 0.041130296885967255, -0.031001323834061623, -0.06185124069452286, 0.0027483718004077673, -0.03864116594195366, -0.014747727662324905, -0.007336081471294165, 0.011403271928429604, -0.037828363478183746, -0.011212900280952454, -0.008982457220554352, -0.011823659762740135, 0.06134520843625069, -0.003066466888412833, -0.10470797121524811, 0.04191163182258606, -0.04423612356185913, -0.04095214977860451, -0.01826941967010498, 0.00651663588359952, 0.0014081158442422748, 0.027193590998649597, 0.05124254897236824, -0.03122849389910698, -0.03864758834242821, -0.010967683978378773, -0.003199652535840869, -0.04861294478178024, -0.05120472237467766, -0.001593029242940247, 0.0008472418994642794, 0.044452402740716934, 0.033214617520570755, -0.06372103840112686, 0.03661283105611801, -0.035734567791223526, -0.022928405553102493, 0.02491222880780697, 0.011969377286732197, -0.06505092233419418, -0.05379664897918701, 0.007663969416171312, -0.024284521117806435, -0.020748568698763847, -0.029604235664010048, 0.052528560161590576, 0.000496096268761903, 0.04660821333527565, -0.022742532193660736, 0.03799454867839813, 0.009515251033008099, -0.024640750139951706, -0.020297285169363022, 0.030254187062382698, -0.031284864991903305, -0.02900509350001812, -0.012745368294417858, 0.02274010144174099, -0.055703360587358475, -0.01746862195432186, -0.07325150817632675, 0.03548809140920639, 0.008634183555841446, -0.021734174340963364, -0.025797951966524124, 0.040690913796424866, 0.025931309908628464, -0.044893283396959305, -0.0011048540472984314, -0.03122909739613533, -0.03266378864645958, -0.0004930216819047928, -0.041994620114564896, -0.05862561985850334, 0.03163905814290047, -0.03831024467945099, -0.03993600606918335, 0.002992240944877267, -0.012291659601032734, -0.025482285767793655, 0.03428056463599205, -0.010277687571942806, 0.02596786804497242, 0.010042122565209866, -0.007277459371834993, -0.012240683659911156, 0.03939264267683029, 0.06183403357863426, -0.048638079315423965, -0.09266551584005356, -0.02265058644115925, 0.008328981697559357, 0.007430435623973608, -0.024348320439457893, 0.0002996902330778539, 0.047930508852005005, 0.002202781615778804, 0.0036550273653119802, -0.04863949120044708, -0.011102329939603806, 0.05962328985333443, -0.03095323033630848, -0.004793846979737282, -0.04832218959927559, 0.008974096737802029, -0.05503470078110695, 0.07792025059461594, 0.004130946937948465, -0.012731881812214851, 0.06644686311483383, 0.015511702746152878, 0.03278065472841263, 0.03450605645775795, 0.01291700080037117, 0.011988233774900436, 0.027927329763770103, -0.03647792711853981, -0.018124083057045937, -0.0068707275204360485, 0.013808776624500751, 0.016655365005135536, -0.059636957943439484, 0.00044135612552054226, -0.060569193214178085, -0.025124119594693184, 0.002973184222355485, -0.005942024756222963, 0.06277304142713547, -0.018104545772075653, -0.017026716843247414, -0.018851326778531075, -0.017934873700141907, 0.010134580545127392, -0.010908253490924835, 0.028275931254029274, 0.032662633806467056, -0.050921499729156494, 0.014001172035932541, -0.007565174717456102, -0.024558300152420998, 0.019113777205348015, -0.014630182646214962, -0.040189940482378006, 0.006252755410969257, 0.023697106167674065, 0.009302278980612755, 0.05244908854365349, 0.00435192184522748, 0.02484997734427452, -0.04050245136022568, -0.02307196520268917, 0.03183894604444504, 0.02460802160203457, 0.05341571196913719, 0.029902871698141098, -0.009225720539689064, -0.04503540322184563, -0.004668864421546459, 0.0029267705976963043, 0.06171054765582085, -0.04517441242933273, -0.013098807074129581, 0.020989323034882545, 0.034469760954380035, 0.000499397050589323, 0.012892316095530987, 0.032850928604602814, -0.003745372174307704, -0.011270602233707905, -0.034402236342430115, 0.03871021792292595, -0.012347967363893986, -0.06014731526374817, -0.02314266376197338, 0.05298387631773949, -0.03090038150548935, -0.022098857909440994, -0.01454244926571846, 0.0040443832986056805, 0.03744715452194214, 0.06049949675798416, -0.05199436470866203, -0.007876293733716011, -0.02341497875750065, -0.02985946461558342, -0.005605252459645271, 0.006690165959298611, -0.0267315823584795, 0.001614394597709179, -0.025570303201675415, -0.006051420234143734, 0.04047964885830879, 0.0259172935038805, -0.048971615731716156, 0.00823434442281723, 0.03651806712150574, 0.021215105429291725, 0.033663444221019745, -0.02168317697942257, 0.06384565681219101, 0.018795814365148544, -0.01627090945839882, 0.022533977404236794, -0.01882552169263363, 0.03874122351408005, -0.025457728654146194, -0.022759465500712395, 0.037328168749809265, 0.02248721942305565, 0.0678870752453804, 0.05715351551771164, -0.00557035394012928, 0.05123145133256912, 0.026121685281395912, 0.034914400428533554, 0.04011579602956772, -0.029084112495183945, -0.033074475824832916, -0.015957258641719818, -0.030914099887013435, 0.04007331654429436, -0.057766709476709366, -0.06308911740779877, 0.032099656760692596, -0.0005127306212671101, 0.04818429797887802, -0.07373815774917603, 0.001992274774238467, -0.03991362825036049, 0.001854466157965362, -0.05532794073224068, 0.04559509828686714, -0.004487149883061647, -0.02714967168867588, -0.005327897146344185, 0.02054802142083645, -0.01449962705373764, -0.041701167821884155, 0.009184662252664566, 0.020456044003367424, 0.03500094264745712, 0.054726190865039825, -0.01904553547501564, 0.06097448617219925, 0.04645773023366928, 0.02346229925751686, -0.015336839482188225, 0.002497245091944933, 0.0013391375541687012, -0.010758087038993835, 0.030671004205942154, -0.03515781834721565, -0.0027359607629477978, 0.006838011089712381, -0.004738272167742252, 0.020271141082048416, 0.026346450671553612, 0.03407561033964157, 0.01564059965312481, -0.019277440384030342, -0.009425012394785881, -0.014509285800158978, -0.039309531450271606, -0.0073105692863464355, -0.09652694314718246, -0.01860489696264267, 0.011794237419962883, 0.054096996784210205, -0.03623884543776512, -0.013905268162488937, -0.01612454280257225, -0.05409754440188408, 0.06329257041215897, -0.013186663389205933, 0.03086766041815281, 0.005565284285694361, -0.018494680523872375, 0.01607672870159149, -0.025585448369383812, 0.050449762493371964, 0.01773340068757534, -0.05019071698188782, -0.04746275767683983, -0.01668483018875122, -0.0031831138767302036, -0.06046589836478233, -0.029809005558490753, 0.026367316022515297, 0.03102104365825653, -0.04653732478618622, 0.04798230528831482, 0.05513589084148407, -0.0495578832924366, 0.0009470423101447523, -0.0036498387344181538, -0.07279196381568909, 0.04778353124856949, 0.026074618101119995, 0.010447954759001732, 0.003718310734257102, 0.008927922695875168, 0.008395788259804249, 0.06854384392499924, -0.0749330073595047, 0.02151395007967949, 0.01723797805607319, 0.0003038544673472643, 0.06222861632704735, 0.049924012273550034, 0.01903662458062172, 0.007592359557747841, 0.03453488275408745, 0.011320237070322037, -0.026936249807476997, 0.016138844192028046, 0.006850064266473055, 0.030954748392105103, -0.05657445639371872, 0.030635440722107887, 0.00441159401088953, 0.01583215221762657, 0.047887131571769714, 0.010794843547046185, 0.009831570088863373, 0.0028033419512212276, 0.02849210426211357, 0.022486137226223946, 0.03253613039851189, -0.08509976416826248, -0.006964543368667364, 0.05832287669181824, -0.007064764853566885, 0.008299705572426319, 0.04374627396464348, -0.031976573169231415, -0.06208124756813049, -0.03452586755156517, 0.02014179714024067, 0.021644756197929382, 0.059883762151002884, -0.011830098927021027, 0.036059364676475525, -0.038250189274549484, -0.013794535771012306, 0.06951813399791718, -0.028730494901537895, 0.04391064494848251, -0.02258341759443283, 0.009737378917634487, 0.05097587779164314, -0.0086668124422431, -0.01598186604678631, 0.012885901145637035, -0.03664889186620712, 0.01667196862399578, 0.016544895246624947, 0.019469352439045906, 0.001251291367225349, 0.006362727377563715, -0.026905221864581108, 0.00744257215410471, -0.009833559393882751, -0.020957741886377335, 0.0037638989742845297, -0.02152303233742714, -0.006341299507766962, 0.025801070034503937, 0.025143271312117577, 0.04702543839812279, -0.018907399848103523, 0.0050382837653160095, 0.00527511490508914, 0.033660199493169785, -0.028249286115169525, -0.036639630794525146, 0.02562851458787918, -0.026609385386109352, 0.06331085413694382, 0.030893342569470406, 0.0507364496588707, 0.00785942655056715, 0.03736431896686554, 0.003451724536716938, -0.04816264286637306, -0.05631139501929283, -0.03381083160638809, 0.029816919937729836, 0.04817855730652809, 0.041196249425411224, 0.010504503734409809, -0.021262411028146744, 0.08014314621686935, -0.03862236440181732, 0.03057577833533287, 0.025248007848858833, -0.05679979920387268, 0.006533609237521887, 0.08444009721279144, -0.04652205482125282, -0.018685780465602875, -0.0024731005541980267, -0.057299982756376266, 0.035668909549713135, 0.020103825256228447, -0.02879023365676403, 0.03014855459332466, 0.010977160185575485, 0.013445010408759117, 0.022293666377663612, 0.013904989697039127, 0.017798423767089844, 0.016496602445840836, 0.04789642617106438, -0.03064078278839588, 0.030794966965913773, 0.013154304586350918, -0.0017725304933264852, -0.05616588145494461, 0.0062493071891367435, -0.04247097298502922, -0.07171447575092316, -0.07424211502075195, 0.007385418750345707, -0.010362397879362106, 0.0706113800406456, -0.014250743202865124, 0.04286431893706322, 0.009354525245726109, -0.02274918742477894, 0.019030839204788208, 0.027182962745428085, -0.06994307786226273, -0.009081308729946613, -0.001492282492108643, -0.008036027662456036, 0.04503689333796501, 0.013118085451424122, 0.04936233535408974, -0.03274138644337654, -0.01952512003481388, -0.01501438021659851, -0.05968840792775154, 0.054237645119428635, 0.02983478270471096, 0.05229981243610382, 0.04019354283809662, 0.04447203129529953, 0.03477024659514427, -0.0355151928961277, -0.012765323743224144, -0.007312092464417219, 0.013436487875878811, -0.06443974375724792, 0.016924135386943817, 0.03684259578585625, -0.03745300695300102, -0.010617120191454887, -0.029085196554660797, 0.004064814653247595, -0.014933419413864613, 0.0381949283182621, 0.09192916750907898, -0.007248669397085905, -0.010282378643751144, -0.033764373511075974, -0.00856225285679102, -0.029223304241895676, -0.041081588715314865, -0.016551807522773743, 0.010482480749487877, -0.043289296329021454, 0.011305645108222961, -0.023001236841082573, 0.008639813400804996, 0.020384613424539566, 0.023256560787558556, -0.002189165446907282, -0.012107920832931995, -0.00941403117030859, -0.004487421363592148, 0.004667419008910656, 0.028850415721535683, -0.0037610467988997698, -0.06981763988733292, -0.006022877991199493, -0.034587349742650986, 0.00720827654004097, 0.04679201915860176, -0.006272858940064907, -0.014471301808953285, 0.00665854150429368, -0.02049635909497738, -0.015150357969105244, 0.010478712618350983, 0.03689863160252571, 0.05575456842780113, -0.0459674596786499, -0.04180050641298294, 0.042618460953235626, -0.004134839866310358, 0.03198177367448807, -0.018159493803977966, 0.031866926699876785, 0.03415383771061897, -0.0009201282518915832, 0.026311250403523445, -0.05839040130376816, -0.04796966537833214, -0.020266467705368996, 0.013767539523541927, 0.005107474979013205, -0.005410642363131046, 0.0016262324061244726, -0.018138715997338295, -0.04112760350108147, -0.018870003521442413, 0.06210848689079285, -0.00883591640740633, -0.027836816385388374, -0.007862192578613758, 0.03861994668841362, 0.051379356533288956, 0.07300476729869843, 0.03725554049015045, -0.02108762040734291, -0.04627614840865135, 0.07900787889957428, -0.04757165163755417, 0.054364316165447235, -0.006377366371452808, 0.052960749715566635, -0.04377418011426926, -0.048781055957078934, -0.021107425913214684, 0.05205979198217392, -0.06999307870864868, -0.04215412586927414 ]
<p>We know that a piece of ferromagnet, such as iron, can be magnetized by putting in a strong magnetic field to get domains parallel to the field grow. </p> <p>I also remember from pop. culture and MacGyver old tv series that you can magnetize a piece of iron by hitting it hard, with a hammer say, along the same direction.</p> <p>1-Is this way of magnetizing iron scientific? or is it pseudoscience?</p> <p>and if it is scientific then:</p> <p>2-what is the physical principle that will allow iron to get magnetized by hitting? and </p> <p>3-how about nonferromagnetic materials?</p>
g1508
[ 0.06710093468427658, 0.09281488507986069, -0.015955155715346336, 0.017689377069473267, 0.05708727985620499, 0.023867115378379822, -0.01602037437260151, 0.031243707984685898, -0.044504158198833466, -0.0028308897744864225, -0.03525906428694725, -0.007769415155053139, -0.014296375215053558, -0.031334131956100464, -0.011725286021828651, 0.01606561429798603, 0.003903921926394105, 0.014215907081961632, 0.06689692288637161, 0.02743339166045189, 0.02905307523906231, 0.04869123175740242, 0.02548913098871708, -0.04079050570726395, -0.08507633954286575, -0.006490164902061224, 0.0031614003237336874, -0.036114152520895004, 0.03617415577173233, -0.00805484689772129, -0.03143589571118355, -0.014719163067638874, 0.042381808161735535, -0.034984514117240906, -0.031207991763949394, -0.06239742413163185, -0.03718850016593933, 0.010235103778541088, 0.006604422815144062, -0.000860817264765501, 0.01006700936704874, -0.03452394902706146, 0.06756019592285156, -0.028755946084856987, -0.006837988737970591, 0.03388071060180664, -0.03021402284502983, -0.039804719388484955, -0.0025288937613368034, 0.005581521429121494, -0.0024174873251467943, -0.05160937458276749, 0.09677566587924957, -0.0008373480523005128, -0.002513526938855648, -0.0077947527170181274, 0.04283881559967995, 0.020105760544538498, 0.07997490465641022, -0.024690235033631325, 0.03227110207080841, 0.06275998055934906, -0.00889586191624403, -0.007076785899698734, 0.027651796117424965, 0.03463989123702049, -0.044223036617040634, -0.009782257489860058, 0.04825807362794876, 0.012308084405958652, -0.02173786424100399, -0.02498990297317505, -0.004316524602472782, -0.02377743273973465, -0.06206488981842995, -0.004355056211352348, 0.05397680774331093, -0.015980180352926254, 0.022566553205251694, 0.042354945093393326, 0.02602686733007431, -0.06182650104165077, 0.0034981626085937023, -0.023641536012291908, -0.02696704864501953, -0.004571102559566498, -0.020954417064785957, 0.025577664375305176, -0.0004174477362539619, 0.005219235550612211, -0.012851870618760586, 0.01152556948363781, 0.028924748301506042, 0.023097585886716843, -0.01942358911037445, 0.05204389989376068, -0.016815993934869766, 0.01912113092839718, -0.045295871794223785, -0.04904423654079437, -0.052773281931877136, -0.06697148829698563, 0.006556835025548935, -0.028770679607987404, -0.009052546694874763, -0.02438095584511757, 0.07847098261117935, 0.07923565059900284, -0.02665596455335617, 0.03128664568066597, -0.026304109022021294, -0.017306016758084297, -0.02496691793203354, 0.012223836034536362, -0.043341152369976044, 0.0378911979496479, 0.05786169692873955, 0.016159122809767723, 0.0051353806629776955, 0.11232206970453262, 0.06362374126911163, -0.009751645848155022, 0.00871516764163971, 0.025449924170970917, -0.06687840074300766, 0.008194994181394577, -0.0005171357770450413, -0.008729328401386738, -0.02102874405682087, -0.036159440875053406, -0.015330739319324493, -0.014194303192198277, 0.012700758874416351, -0.009930039756000042, -0.032522719353437424, 0.019087299704551697, 0.026352738961577415, 0.013367242179811, 0.011672312393784523, 0.005767199210822582, 0.01611250452697277, -0.057636260986328125, -0.03166252747178078, -0.024693390354514122, -0.016235288232564926, 0.027145029976963997, -0.014559795148670673, -0.017054904252290726, 0.052232202142477036, 0.0519687719643116, 0.03835776075720787, 0.04981573671102524, 0.007600896526128054, -0.04687778279185295, -0.0038757887668907642, -0.014449989423155785, -0.001907046651467681, 0.04174848645925522, 0.08158887177705765, -0.005073022563010454, 0.03767573460936546, 0.002556018065661192, 0.011366470716893673, -0.022387295961380005, 0.02024746499955654, 0.02454950287938118, 0.02265470288693905, 0.0006175428279675543, -0.02537430450320244, 0.020320797339081764, -0.07648735493421555, 0.0417182557284832, -0.000019457727830740623, 0.024317016825079918, -0.02383119985461235, -0.013234499841928482, -0.005439938046038151, -0.08129904419183731, -0.0023274060804396868, -0.05354612320661545, 0.008394928649067879, 0.001538001699373126, 0.02612628974020481, 0.030925849452614784, 0.014315146021544933, 0.021516848355531693, 0.016430268064141273, 0.0001918468769872561, 0.0007804048364050686, 0.022031070664525032, -0.01148410513997078, -0.00794288981705904, 0.019430654123425484, 0.013902910985052586, -0.002760502742603421, -0.043019987642765045, 0.00827278196811676, 0.04741987586021423, -0.009412269107997417, -0.041396915912628174, -0.002484001684933901, 0.06484498828649521, -0.016958268359303474, 0.026150431483983994, -0.04187696799635887, 0.0032547854352742434, -0.031229030340909958, 0.023313608020544052, 0.054815880954265594, 0.012201887555420399, 0.020522568374872208, 0.04678637161850929, 0.005258518271148205, 0.0009132735431194305, -0.0217092614620924, 0.026738358661532402, -0.03921817988157272, 0.00985500868409872, -0.060788143426179886, -0.012775073759257793, 0.02722609043121338, -0.0038114835042506456, -0.0011270663235336542, 0.04021632671356201, 0.029701488092541695, 0.00630919961258769, -0.012668777257204056, 0.033252641558647156, 0.015590131282806396, -0.03721987083554268, 0.000711107044480741, 0.005732148885726929, 0.0006960263708606362, -0.008729707449674606, 0.0576227605342865, 0.06432030349969864, -0.0038488334976136684, -0.009570220485329628, -0.026633739471435547, -0.017454568296670914, 0.014380118809640408, -0.05898351967334747, 0.032350633293390274, -0.018751392140984535, 0.0031490446999669075, -0.07026027888059616, -0.02110232226550579, -0.036429934203624725, 0.020801667124032974, 0.008824633434414864, 0.08024545013904572, -0.02417738363146782, -0.004012498073279858, -0.0382443368434906, -0.02982884831726551, 0.008143508806824684, 0.008364716544747353, 0.06720650941133499, -0.0698501244187355, 0.009038594551384449, 0.007056021597236395, -0.06573802977800369, 0.04955781623721123, 0.010204036720097065, -0.06303023546934128, -0.018742352724075317, -0.0627194195985794, 0.03296273946762085, -0.013064736500382423, 0.039178941398859024, -0.04657221585512161, 0.02475256472826004, 0.041821595281362534, 0.02756255678832531, 0.007981670089066029, -0.030732056125998497, 0.024414673447608948, 0.057944249361753464, 0.035629335790872574, -0.0202761460095644, -0.028080256655812263, 0.01268109679222107, -0.05491749197244644, -0.04242317005991936, 0.01991717889904976, 0.007389673497527838, -0.03792121633887291, -0.06824697554111481, -0.06994771957397461, 0.015759164467453957, -0.039880648255348206, -0.07406356930732727, 0.011669169180095196, -0.03981289640069008, -0.02339901030063629, 0.04887494817376137, 0.052472736686468124, 0.008368502371013165, -0.020366400480270386, 0.047310296446084976, 0.03319701552391052, -0.0033665052615106106, -0.023792698979377747, 0.04935295507311821, 0.023859655484557152, 0.007304464932531118, -0.021036745980381966, -0.028527988120913506, -0.020691167563199997, -0.05587652698159218, -0.04146679863333702, 0.06967778503894806, 0.001853065099567175, 0.075084388256073, -0.022200044244527817, -0.013228374533355236, 0.008582372218370438, 0.01650807447731495, 0.08055897802114487, 0.005731472745537758, -0.01841738075017929, -0.02645295485854149, 0.017562249675393105, -0.02757144719362259, 0.062204062938690186, 0.022358596324920654, 0.015489013865590096, -0.012200293131172657, -0.02589890919625759, 0.01629728265106678, 0.0634663999080658, 0.0739545077085495, -0.09926574677228928, -0.023340431973338127, -0.09014782309532166, 0.020256295800209045, -0.010600531473755836, 0.05156617984175682, 0.03353537246584892, 0.008882644586265087, 0.06643424183130264, -0.05926499143242836, 0.018044816330075264, -0.019848663359880447, 0.016546547412872314, 0.0928853452205658, -0.009205752052366734, -0.01285602431744337, 0.01874949410557747, 0.06593343615531921, 0.04869956895709038, 0.04398885369300842, 0.020774569362401962, 0.0395461842417717, 0.00934145599603653, 0.045058269053697586, 0.07007697224617004, 0.006670057307928801, 0.007514807861298323, -0.027507619932293892, -0.030034169554710388, 0.056440435349941254, -0.02020902745425701, -0.026728350669145584, -0.023839831352233887, 0.029703384265303612, -0.004594364203512669, 0.026137592270970345, 0.01732979342341423, -0.008963491767644882, 0.03360874950885773, -0.0041916025802493095, 0.021935923025012016, 0.04912405461072922, -0.029909031465649605, 0.01712491549551487, -0.03567105159163475, 0.013985258527100086, -0.008684776723384857, -0.025668559595942497, -0.04704030230641365, 0.06661311537027359, 0.006900928448885679, 0.050029776990413666, -0.005191035568714142, -0.0351589173078537, -0.05217975378036499, 0.0690416470170021, 0.007103059906512499, -0.021733589470386505, -0.001773923635482788, -0.00021964880579616874, -0.07334760576486588, 0.045067816972732544, -0.03328603506088257, -0.03005388006567955, -0.062244612723588943, -0.015878191217780113, 0.056781258434057236, -0.02167956531047821, 0.037460461258888245, 0.04426485300064087, -0.03831285238265991, 0.03013322874903679, -0.02564236894249916, 0.0352090522646904, -0.02684561349451542, 0.010866204276680946, 0.025685258209705353, -0.05837409570813179, -0.003187446855008602, -0.0634925365447998, -0.04464505612850189, -0.09087396413087845, 0.0554756224155426, 0.019750716164708138, -0.005830373149365187, 0.015494477935135365, -0.01913902536034584, -0.04605375602841377, 0.03462233021855354, 0.007251246366649866, 0.007951058447360992, -0.016023410484194756, -0.059452131390571594, 0.08238373696804047, -0.009862716309726238, -0.06995497643947601, -0.007448997348546982, 0.04031960666179657, 0.029625460505485535, -0.005782656837254763, 0.04515290632843971, 0.018334975466132164, 0.019038895145058632, -0.003337590489536524, -0.023905843496322632, 0.025933729484677315, 0.02799486741423607, -0.005440868437290192, 0.02150544710457325, 0.058308787643909454, 0.026389673352241516, -0.0034788993652909994, -0.043655876070261, -0.01746668480336666, -0.0535246841609478, 0.047392748296260834, -0.03221391141414642, -0.012624343857169151, -0.012603678740561008, -0.007329089101403952, -0.010323303751647472, -0.028390200808644295, -0.012874416075646877, -0.023298393934965134, -0.02777719870209694, 0.02232477441430092, 0.0011403935495764017, 0.04613560438156128, -0.014350025914609432, -0.022657571360468864, -0.02076210454106331, 0.032959502190351486, -0.041626088321208954, 0.01572241820394993, 0.02083980292081833, -0.09341757744550705, -0.006707349326461554, 0.0566244050860405, 0.016482068225741386, 0.016548333689570427, -0.009677517227828503, 0.006833374034613371, 0.03403843566775322, 0.0025589801371097565, 0.008747703395783901, -0.0560462661087513, -0.013156997039914131, -0.043912991881370544, -0.0004749999789055437, -0.010684814304113388, 0.013793443329632282, -0.026118239387869835, -0.049635149538517, -0.04818416386842728, -0.0319308303296566, 0.0670022964477539, -0.034875232726335526, -0.034213218837976456, -0.008894598111510277, 0.022666890174150467, -0.00987369753420353, -0.013879252597689629, -0.04481717571616173, -0.041606076061725616, -0.024573206901550293, 0.0003572203277144581, -0.03865882381796837, -0.08655530959367752, 0.023450715467333794, 0.006126783788204193, -0.04732505604624748, -0.01167756225913763, 0.0019403542391955853, -0.03345512971282005, 0.08434022963047028, -0.013783405534923077, 0.01266417745500803, 0.011335832066833973, 0.05412358418107033, -0.010046419687569141, -0.010344034992158413, -0.01480698212981224, 0.05000106617808342, 0.007005670573562384, 0.007797378581017256, 0.021957503631711006, 0.0498935803771019, -0.0020530608016997576, -0.024659989401698112, -0.027007536962628365, -0.0006718963268212974, -0.07425105571746826, -0.02186698280274868, -0.0257414560765028, -0.020162567496299744, -0.01317539718002081, 0.025592520833015442, 0.05271833762526512, -0.011018374003469944, -0.013066394254565239, 0.03791887313127518, -0.009996825829148293, -0.05428508296608925, 0.0015452074585482478, 0.02748100645840168, 0.0006662016385234892, -0.005546922329813242, 0.03291124850511551, 0.0220137070864439, -0.023087749257683754, 0.07211999595165253, 0.026216035708785057, -0.012641948647797108, -0.02500646747648716, 0.031229551881551743, -0.014358071610331535, 0.011361350305378437, -0.05441492423415184, -0.0804084837436676, -0.0018170663388445973, 0.009413409046828747, 0.011264344677329063, 0.02468050643801689, 0.01797734946012497, -0.042225778102874756, -0.06927821040153503, 0.049011703580617905, -0.06273611634969711, 0.004485514480620623, -0.018704496324062347, -0.032916657626628876, -0.027323786169290543, -0.014665985479950905, 0.03484097868204117, -0.05941600725054741, -0.029373832046985626, 0.032520994544029236, 0.018030358478426933, -0.028566740453243256, 0.023983439430594444, -0.04608054831624031, 0.021741833537817, 0.02730639837682247, 0.007751681841909885, -0.0009098517475649714, 0.033153973519802094, -0.0065113864839077, -0.029316438362002373, 0.043339937925338745, 0.03749813139438629, 0.007633578032255173, -0.013230436481535435, 0.01791640929877758, 0.009690516628324986, -0.07184188067913055, 0.005914715584367514, 0.0015694515313953161, -0.015134249813854694, -0.0052567776292562485, 0.027820108458399773, -0.04558336362242699, -0.0013891616836190224, -0.0352710597217083, -0.040671203285455704, 0.008615375496447086, 0.08369933813810349, -0.028668025508522987, -0.01224210299551487, -0.0533343069255352, -0.0023724588099867105, -0.004842920228838921, 0.0016529809217900038, 0.016957048326730728, 0.07246202230453491, 0.06086094677448273, -0.039984121918678284, 0.04558292776346207, -0.03905951976776123, -0.06921825557947159, 0.0083248820155859, -0.04376070573925972, 0.013915632851421833, 0.037823501974344254, -0.06183731555938721, -0.0041950056329369545, -0.0844002515077591, 0.01338032353669405, 0.01822935789823532, -0.022891221567988396, -0.06443335860967636, 0.023047495633363724, -0.05834643915295601, 0.01760227046906948, 0.01310950517654419, -0.0022821943275630474, 0.02996344305574894, 0.0318388007581234, -0.02884433977305889, -0.08020185679197311, -0.016453389078378677, -0.010060823522508144, 0.0612044595181942, 0.0027115370612591505, 0.01870480179786682, 0.04509604349732399, 0.011988894082605839, 0.02409759722650051, -0.004278350621461868, -0.028220394626259804, -0.012395170517265797, 0.005528059788048267, 0.03290507197380066, -0.0030045281164348125, 0.024672165513038635, -0.07917553931474686, -0.03265173360705376, -0.011300616897642612, 0.03238217532634735, -0.0630980134010315, -0.00808186549693346, -0.03993343561887741, 0.041146647185087204, -0.013949696905910969, 0.041120413690805435, 0.017754416912794113, 0.009660866111516953, 0.0422399528324604, -0.03125613182783127, -0.056028444319963455, 0.005005465820431709, 0.012410997413098812, -0.0487009659409523, 0.027591058984398842, 0.008416461758315563, -0.043028734624385834, -0.03724416345357895, 0.013287287205457687, 0.010534217581152916, 0.018903430551290512, -0.0008976097451522946, 0.0521405003964901, 0.012415137141942978, 0.03480483591556549, 0.013487152755260468, 0.004518907517194748, -0.046920835971832275, 0.04794817417860031, -0.014881454408168793, -0.037053003907203674, 0.06284193694591522, 0.0024105780757963657, -0.014189437963068485, 0.012037909589707851, 0.014636869542300701, -0.05536308512091637, 0.09834955632686615, -0.023691769689321518, -0.04049013555049896, 0.00009475940896663815, -0.019847232848405838, -0.008788244798779488, 0.03355228155851364, 0.0025002292823046446, -0.0328933522105217, 0.056070081889629364, 0.02504793182015419, -0.03929942101240158, 0.03564775735139847, -0.027772702276706696, 0.04267296567559242, 0.020129311829805374, -0.018362442031502724, 0.02364966832101345, -0.005790290422737598, -0.024000896140933037, 0.01223680004477501, -0.04367157071828842, 0.0046935901045799255, 0.0012142204213887453, 0.02289704419672489, -0.002730743261054158, -0.029488295316696167, -0.0255991630256176, 0.005113919731229544, 0.027280133217573166, -0.02088272199034691, 0.011695648543536663, -0.02130969986319542, -0.03880250081419945, 0.05658798664808273, 0.0635557547211647, -0.027097193524241447, -0.06574900448322296, 0.07076550275087357, 0.05036289244890213, -0.0030552505049854517, -0.01593637838959694, 0.049719762057065964, 0.04607932269573212, -0.047333065420389175, 0.016551882028579712, -0.017847338691353798, -0.00914646778255701, 0.02151060476899147, -0.02606872282922268, 0.0023847222328186035, 0.02751500904560089, -0.018930571153759956, 0.05086218938231468, 0.020625142380595207, -0.047268692404031754, -0.03131142258644104, -0.03420069441199303, 0.005274364724755287, -0.04041103273630142, 0.13073892891407013, -0.014847059734165668, 0.054627083241939545, 0.023155806586146355, -0.01396341435611248, 0.013392889872193336, 0.001544829225167632, -0.008046994917094707, 0.0016979665961116552, -0.056781478226184845, 0.028828762471675873, 0.07210104167461395, -0.03796294704079628, -0.02137853391468525, -0.03807102143764496, -0.010482611134648323, -0.025812311097979546, -0.04952509328722954, 0.015982670709490776, -0.06023207679390907, -0.001728482311591506 ]
<p>We all know the effects of speed on time, and we have a formula for that, but I have a hunch, that time also is relative to pressure, and that by increasing the pressure on matter, in fact time will speed up for that matter. </p> <p>I am not a physics expert ( I have a Masters Degree in Computer Engineering, and have hence taken several physics, math and chemistry classes ) so don't slaughter me, I would appreciate a talkative tone. </p> <p>So I will say some "ideas" in my head that might be stupid, or assumptions from my understanding of how things are that are in fact wrong from an expert view, but please try to understand my <strong>intention</strong> or follow my idea of what I am thinking instead of focusing on details.</p> <p>So, my thinking is that once something starts travelling near the speed of light, or the speed of light, it will start to dissolve, before turning into energy and becoming the lightest of all while dissolving = light, and hence is why it can travel at the speed of light. So if something is to travel at the speed of light, it actually have to be dissolved into energy.</p> <p>The idea I have with pressure, is that if matter, in a pressure chamber, where pressure is turned up, the matter will eventually turn into pure energy as well = light. </p> <p>I also have this thought, that once pressure is applied to matter, the atoms starts to vibrate, move faster, and a reaction that would normally take hundreds of years, can be achieved with quicker results in a pressure chamber because time for all that materia increases, not because of the pressure, but because time is happening faster, which supports my idea of time actually speeding up for those particles. </p> <p>What happens with used reactor fuel in a pressure chamber today? How much can we speed up the halftime?</p> <p>It appears to me that if this was true, it will be the contradiction to speed. A twin X travelling near the speed of light, will come back to visit an older twin Y on earth. </p> <p>However, with pressure, it might just be the opposite, that twin X in the pressure chamber will in fact be older than twin Y outside.</p> <p>Surely turning up pressure on a twin might not be so healthy, but neither is acceleration from 0 to the speed of light in 1s. So pressure is probably not a healthy way to speed up time for matter, it will probably destroy certain things in it. </p> <p>Am I on something here? No?</p>
g1509
[ 0.06434064358472824, 0.036018647253513336, 0.016358250752091408, -0.006365434732288122, 0.04574231430888176, -0.007488083094358444, 0.028206119313836098, 0.0023557539097964764, -0.051203325390815735, 0.025429679080843925, 0.06912774592638016, -0.031811945140361786, 0.0190317053347826, 0.0004176622605882585, 0.0024627097882330418, -0.023897593840956688, 0.10112316906452179, -0.03149311989545822, -0.03161691501736641, 0.015705028548836708, 0.006057382095605135, 0.032255206257104874, -0.008125958032906055, -0.09240119159221649, -0.06329122185707092, 0.004647829569876194, 0.014460559003055096, -0.040087535977363586, -0.0348820760846138, -0.008423030376434326, 0.02895856834948063, -0.04811204597353935, -0.04105931147933006, -0.003912574611604214, 0.0029488992877304554, -0.0797119215130806, 0.015104402787983418, 0.01951112039387226, 0.0740448534488678, 0.01774304360151291, -0.006546239834278822, -0.06444697082042694, 0.00865182839334011, -0.0030535960104316473, -0.0018790914909914136, 0.01556423306465149, 0.010931404307484627, -0.0030395423527806997, -0.035273477435112, 0.01196390949189663, 0.01750735193490982, 0.016351813450455666, -0.026813562959432602, 0.0545642152428627, -0.06674865633249283, 0.022751115262508392, -0.010520302690565586, -0.04276479408144951, 0.06488156318664551, 0.03866880014538765, -0.020973647013306618, -0.01946481503546238, 0.0786590501666069, -0.007670823018997908, 0.044929563999176025, 0.026907946914434433, -0.011570797301828861, -0.027203720062971115, 0.09288138896226883, -0.010136948898434639, -0.0171431303024292, -0.037884946912527084, -0.03617587685585022, -0.015059182420372963, 0.013406098820269108, 0.05501655116677284, 0.044552262872457504, -0.011095092631876469, 0.003827568842098117, 0.00900175515562296, -0.021031389012932777, 0.0018149567767977715, 0.006786101032048464, -0.039736051112413406, -0.01843060739338398, -0.07095102220773697, -0.03530420735478401, -0.029246658086776733, 0.00687971618026495, 0.011832396499812603, 0.013680226169526577, -0.048789359629154205, 0.03870127722620964, -0.009591145440936089, -0.005983543116599321, 0.009162654168903828, 0.008436296135187149, 0.041953589767217636, -0.017907213419675827, 0.06628261506557465, -0.06332317739725113, -0.06078421324491501, 0.055367253720760345, 0.014246462844312191, -0.035152822732925415, -0.06831186264753342, -0.014266090467572212, -0.024909570813179016, -0.013522383756935596, -0.025695951655507088, 0.020250702276825905, 0.01750045083463192, -0.021360790356993675, -0.005970973055809736, -0.026573657989501953, -0.10732445865869522, -0.02102595940232277, 0.02589433267712593, -0.04121387377381325, 0.01863851398229599, 0.034924883395433426, 0.002677326323464513, 0.006793912500143051, 0.019062869250774384, -0.003987305331975222, 0.0013286294415593147, 0.027637500315904617, -0.027165934443473816, -0.022409986704587936, -0.011667261831462383, -0.04442717134952545, 0.04425257071852684, -0.007587288040667772, 0.08129290491342545, 0.005909844767302275, -0.008772686123847961, -0.035444118082523346, 0.035349588841199875, -0.02421863004565239, 0.00959479808807373, 0.012788564898073673, -0.008688016794621944, -0.03333395719528198, 0.005330107640475035, -0.03951235115528107, 0.024431293830275536, -0.047346364706754684, 0.04045504704117775, -0.007749737240374088, 0.03999540954828262, -0.015630565583705902, 0.06722070276737213, -0.018410516902804375, -0.012977180071175098, 0.01669912226498127, 0.03429215028882027, 0.035859718918800354, 0.010295315645635128, -0.00605972483754158, 0.08107168972492218, 0.0679820328950882, 0.009478493593633175, -0.0065923952497541904, -0.01283801905810833, -0.04692356660962105, 0.07100002467632294, 0.0410490408539772, -0.00827296357601881, 0.005886433646082878, -0.03146253526210785, -0.06079120934009552, 0.05109374597668648, 0.023808948695659637, -0.0053641414269804955, 0.05471204221248627, -0.039031319320201874, 0.09283562004566193, -0.0375664122402668, -0.08391230553388596, 0.012951177544891834, 0.0034892873372882605, -0.017785197123885155, -0.02884625643491745, -0.04945548623800278, 0.013324114494025707, 0.0018665270181372762, 0.016167236492037773, 0.018565708771348, -0.10784398764371872, -0.026746243238449097, 0.016259346157312393, -0.01703471876680851, 0.004732096567749977, 0.05091279745101929, 0.010947966948151588, -0.02888013795018196, -0.02191678248345852, -0.03538321331143379, -0.04491712152957916, 0.023239677771925926, -0.07471681386232376, 0.006876027677208185, 0.028877224773168564, -0.009376823902130127, 0.09620647877454758, 0.06285683810710907, -0.014887182973325253, 0.01758103258907795, 0.04507684335112572, 0.03645244240760803, 0.04571419954299927, 0.02545558102428913, -0.017982250079512596, -0.006566055119037628, 0.016344966366887093, -0.0066728610545396805, -0.05353837460279465, -0.015742452815175056, 0.008853121660649776, 0.016221605241298676, -0.0028814508114010096, -0.046091657131910324, 0.008719527162611485, -0.00911856908351183, -0.02350456826388836, -0.05975326523184776, 0.002902744570747018, -0.04384327307343483, -0.02312948927283287, 0.013362049125134945, -0.00021749369625467807, 0.07687211036682129, -0.05238281562924385, -0.0377008356153965, 0.01636308990418911, 0.020294060930609703, -0.04003599286079407, -0.014001814648509026, 0.008557887747883797, -0.014866109006106853, 0.01982034742832184, -0.024326590821146965, -0.014222221449017525, -0.02348897233605385, -0.038698527961969376, -0.07075715065002441, 0.0015797421801835299, -0.08441190421581268, 0.011937463656067848, 0.009759499691426754, 0.035118527710437775, 0.0030267934780567884, -0.0509391725063324, -0.06393837183713913, 0.023893335834145546, -0.01848825253546238, 0.02884574979543686, 0.055014342069625854, -0.08136415481567383, -0.03660638630390167, 0.023593131452798843, 0.06253942102193832, -0.016632618382573128, 0.026290910318493843, -0.050534144043922424, 0.07535655051469803, -0.06761033087968826, 0.014143687672913074, -0.015980301424860954, 0.02650637924671173, -0.021098075434565544, -0.029251540079712868, 0.0325896181166172, -0.0009774514473974705, -0.03178175911307335, 0.001245148596353829, 0.06413371115922928, -0.01718512736260891, 0.019200442358851433, -0.011786236427724361, -0.050165195018053055, 0.012042097747325897, -0.05757652223110199, -0.0023428727872669697, -0.011013288050889969, -0.06216739863157272, 0.0049519469030201435, 0.016199635341763496, 0.023672999814152718, -0.01384909637272358, 0.00235615368001163, 0.06706103682518005, 0.0014584232121706009, 0.019321342930197716, 0.038696035742759705, 0.08272592723369598, 0.041653137654066086, -0.007737372070550919, -0.07640524208545685, -0.03322364017367363, 0.01948675513267517, -0.047173235565423965, 0.0047157700173556805, 0.08422563970088959, 0.04657580703496933, 0.03124314174056053, -0.056233637034893036, 0.009356365539133549, -0.008999624289572239, -0.0038509827572852373, 0.02145267277956009, 0.02368079498410225, -0.02084166184067726, 0.03556833043694496, -0.05215857923030853, -0.002967467065900564, -0.003713700920343399, -0.0024808398447930813, 0.0404021218419075, -0.01304269302636385, 0.00138567213434726, -0.01743689924478531, 0.001492867711931467, -0.05185665935277939, -0.00712181068956852, -0.006371394265443087, 0.008596966974437237, -0.03668450936675072, -0.007209050003439188, -0.012677617371082306, 0.012059919536113739, -0.008274001069366932, 0.003658585948869586, -0.004744459874927998, -0.0973827913403511, -0.00555784534662962, 0.013652293011546135, 0.05249298736453056, -0.0029968100134283304, 0.053135376423597336, 0.031001975759863853, -0.010319050401449203, -0.01622588001191616, 0.08951704204082489, -0.04164433851838112, 0.004406649619340897, 0.00961038377135992, -0.02171914093196392, -0.016053440049290657, 0.03725532442331314, 0.08544370532035828, -0.011748211458325386, -0.026213388890028, 0.005034811794757843, 0.011075446382164955, -0.009950609877705574, 0.017679277807474136, 0.039352767169475555, 0.04555409029126167, -0.07436583191156387, -0.03382834047079086, 0.02145925723016262, 0.03486586734652519, 0.006312589626759291, -0.033529654145240784, -0.0027347938157618046, 0.006253825034946203, 0.033379100263118744, 0.012312388978898525, -0.015805061906576157, 0.07261306047439575, 0.017732765525579453, -0.00627977354452014, 0.0627560168504715, 0.07589215785264969, -0.016277065500617027, 0.005966725293546915, -0.03217856585979462, 0.013861493207514286, 0.0331202857196331, 0.015775443986058235, 0.03479867801070213, 0.036254819482564926, 0.01371560338884592, -0.013983250595629215, 0.01746208406984806, -0.043268393725156784, -0.00802706927061081, -0.008680637925863266, -0.022981133311986923, 0.04702381044626236, 0.0012683572713285685, -0.05039437115192413, -0.003669962752610445, -0.041204940527677536, 0.00591832771897316, 0.023651814088225365, 0.012607049196958542, -0.03664596006274223, -0.039669789373874664, -0.025777986273169518, -0.011531630530953407, 0.025011330842971802, 0.004849117249250412, -0.04136091470718384, 0.04486342892050743, -0.01359346229583025, -0.0680074468255043, 0.016453176736831665, -0.012792354449629784, 0.03878104314208031, -0.050562240183353424, -0.021343732252717018, 0.0016180254751816392, -0.00783650204539299, 0.02674214169383049, -0.005151786375790834, -0.014405329711735249, 0.018507376313209534, 0.02645198442041874, 0.00798661820590496, 0.03441969305276871, 0.05404072254896164, -0.01954478770494461, -0.017796294763684273, 0.02819129265844822, 0.06670384854078293, 0.003732840297743678, -0.0166530329734087, -0.04359860718250275, 0.04003922641277313, 0.01879776641726494, -0.010810771957039833, 0.005419967230409384, 0.022953251376748085, 0.06641042977571487, 0.01622958481311798, 0.008473465219140053, 0.030945563688874245, 0.08046533912420273, 0.050185978412628174, 0.012805749662220478, 0.07943994551897049, 0.005299542099237442, -0.04687907174229622, 0.0811299979686737, -0.043631501495838165, -0.02338852919638157, -0.031008277088403702, -0.03189530223608017, -0.0635884553194046, 0.06507201492786407, 0.014401651918888092, -0.0011119446717202663, -0.024631120264530182, -0.0030625429935753345, -0.05090891569852829, 0.054186705499887466, 0.010211460292339325, 0.041535891592502594, -0.039061859250068665, 0.04756536707282066, 0.06035337969660759, -0.0076901670545339584, -0.04457557573914528, 0.00848967395722866, -0.020532909780740738, -0.040786098688840866, -0.004046204034239054, -0.021147433668375015, -0.03482790291309357, -0.026183608919382095, -0.00108054478187114, 0.037581756711006165, 0.011341341771185398, -0.003127782139927149, 0.005985479801893234, -0.024444298818707466, 0.012577293440699577, -0.001905588898807764, 0.01296672411262989, 0.014383450150489807, 0.05838272348046303, -0.02169744297862053, 0.01638406328856945, -0.013630731962621212, -0.039211831986904144, 0.05406682565808296, 0.041119612753391266, -0.003417724510654807, 0.02107211761176586, -0.012513123452663422, 0.0035108388401567936, 0.009038090705871582, -0.019162282347679138, 0.03134873881936073, 0.06380487233400345, 0.06612177193164825, -0.0027789759915322065, -0.003433645935729146, -0.008084259927272797, 0.003470269963145256, 0.01732437126338482, -0.037049610167741776, -0.004982596263289452, -0.023913094773888588, 0.0445748008787632, 0.016810815781354904, -0.021890638396143913, 0.06235450133681297, 0.03849972039461136, 0.04343177005648613, -0.005444650538265705, 0.04009614512324333, 0.016506224870681763, 0.002012416021898389, -0.030497856438159943, 0.010042206384241581, 0.0025924204383045435, -0.0620286650955677, -0.002119355369359255, 0.02014755830168724, 0.06444232165813446, -0.0017031206516548991, 0.014519640244543552, 0.02740379236638546, -0.0696592628955841, 0.021267695352435112, 0.030558791011571884, 0.000524539384059608, 0.004426517058163881, -0.014931147918105125, 0.06287804245948792, -0.03883987292647362, -0.052713073790073395, 0.05369015038013458, 0.016846003010869026, -0.0020263257902115583, 0.0320286899805069, -0.026408681645989418, -0.0730963721871376, -0.01301585417240858, 0.0052176592871546745, 0.03105061873793602, 0.00644787959754467, 0.030942972749471664, -0.04683971032500267, -0.04319895803928375, 0.00568884564563632, -0.013040219433605671, -0.03074822388589382, -0.03369656950235367, -0.007090247236192226, -0.04258165508508682, 0.028549646958708763, -0.01984996721148491, 0.04129842296242714, -0.04780134558677673, 0.01636407896876335, 0.03897770494222641, 0.022032355889678, 0.08764222264289856, -0.03847905993461609, 0.05404488369822502, 0.026700589805841446, -0.052058447152376175, 0.0191622506827116, -0.043618667870759964, -0.0006064914050512016, 0.0019617194775491953, 0.04987773671746254, 0.03831982985138893, 0.0005741704953834414, -0.012966150417923927, 0.018247533589601517, -0.028548676520586014, 0.01568419672548771, -0.07553406804800034, -0.07674862444400787, -0.04387877508997917, -0.022752685472369194, 0.0011584794847294688, -0.03097059577703476, -0.018478039652109146, 0.03953610360622406, -0.04582768678665161, 0.0021106775384396315, -0.010438906028866768, 0.041999444365501404, 0.002787855686619878, 0.0260980986058712, 0.01838645152747631, -0.037426549941301346, -0.0711677223443985, -0.030458834022283554, 0.01359233446419239, -0.01994488015770912, -0.02271822839975357, -0.009990404359996319, 0.05036433786153793, -0.011314117349684238, -0.004762784577906132, 0.016036732122302055, 0.004831366706639528, -0.013296485878527164, -0.010397006757557392, -0.028658291324973106, 0.003535340540111065, 0.05507415905594826, -0.001436147023923695, -0.007338059134781361, 0.006692338269203901, 0.029630146920681, 0.025567177683115005, -0.021085774526000023, -0.022429561242461205, 0.0051348344422876835, 0.007536088582128286, 0.016188576817512512, 0.019558753818273544, 0.06164700910449028, 0.04729136824607849, 0.021058978512883186, -0.043259087949991226, -0.00046622828813269734, -0.03626824542880058, -0.042516548186540604, 0.017490142956376076, -0.010512075386941433, -0.00208770832978189, 0.04340187832713127, -0.06700633466243744, 0.004417053889483213, 0.016556039452552795, -0.013330921530723572, -0.03979852795600891, -0.02120819315314293, 0.060691870748996735, -0.003849255619570613, 0.010372371412813663, 0.05100031942129135, -0.044322703033685684, -0.013326121494174004, 0.02603081800043583, 0.0016975043108686805, 0.023274537175893784, 0.032178957015275955, -0.0038608130998909473, -0.0443534255027771, 0.005942143499851227, -0.008494487963616848, -0.07079324126243591, -0.050423331558704376, 0.01579108275473118, -0.01707112230360508, -0.023947523906826973, -0.04131722077727318, -0.0013653234345838428, 0.04689299315214157, -0.012781896628439426, -0.05236637964844704, -0.07099643349647522, -0.026860738173127174, -0.006646470166742802, -0.03609936311841011, 0.033790040761232376, -0.020721139386296272, -0.09553993493318558, 0.02261008322238922, -0.03955753520131111, 0.0040810806676745415, -0.016652092337608337, 0.02693091332912445, -0.02623049169778824, -0.013621184974908829, 0.006354024633765221, 0.007573848590254784, -0.010411303490400314, 0.049413349479436874, 0.04394499957561493, -0.01465294323861599, 0.05031406506896019, -0.044821884483098984, 0.0029647110495716333, -0.006451437249779701, 0.06828329712152481, -0.06528878957033157, -0.03379145637154579, -0.10661845654249191, -0.01679409109055996, -0.0012908850330859423, 0.050802234560251236, -0.03154342994093895, 0.0460379421710968, 0.004049334675073624, 0.01608947291970253, 0.08691317588090897, 0.008866180665791035, -0.0009513467084616423, 0.014488332904875278, -0.05734255909919739, -0.04121522605419159, 0.034526608884334564, -0.047172993421554565, -0.02802318148314953, 0.015158560127019882, -0.014778654091060162, 0.024906650185585022, -0.04985535517334938, 0.013499527238309383, -0.003668480319902301, 0.028689779341220856, -0.0275235828012228, -0.021663907915353775, 0.056202951818704605, -0.052593495696783066, -0.000641614431515336, -0.05793940648436546, -0.0050656176172196865, 0.01657971926033497, -0.021467849612236023, -0.02786724641919136, -0.05323604494333267, -0.03996846079826355, 0.0388149656355381, 0.014914706349372864, 0.00527110043913126, -0.04852884262800217, 0.01786763034760952, 0.005783095024526119, 0.025808144360780716, 0.005808878690004349, 0.03366938233375549, -0.010969692841172218, -0.0029895990155637264, 0.030831124633550644, 0.05118172615766525, -0.008307397365570068, -0.06087707728147507, 0.049940165132284164, -0.0641697496175766, -0.025680746883153915, -0.046426352113485336, 0.054850202053785324, 0.01180076040327549, -0.0487506203353405, -0.021491365507245064, 0.07666493952274323, 0.03741657733917236, -0.014956318773329258, 0.035885315388441086, 0.0768611878156662, -0.011243020184338093, 0.013581099919974804, 0.008450464345514774, 0.014930899254977703, -0.038715194910764694, 0.0015122108161449432, 0.0033347357530146837, -0.06515226513147354, -0.0071784923784434795, 0.02129964902997017, 0.051205363124608994, -0.011752150021493435, -0.014501750469207764, -0.005219929851591587, -0.03520961478352547, -0.017463870346546173 ]
<p>I read about Goodwin's "proof" that $\pi = 3.20$, it's BS and I know that. What I am wondering is whether his technique may have stumbled on something ( a warped space) years before Einstein. So I guess my question is this: </p> <p>Is it possible that somewhere in the universe (say the vicinity of a neutron star) where (due to the warped space) the ratio of the circumference to the radius is measured as something other than 3.14...? </p> <p>Following from that, is it possible that we only measure $\pi$ as 3.14... because of the way <em>our</em> local space time is curved by the earth?</p>
g1510
[ 0.03870629519224167, 0.03667772188782692, 0.0014631046215072274, -0.08871990442276001, -0.012482833117246628, 0.016882065683603287, -0.003496011719107628, 0.012214619666337967, 0.015043750405311584, 0.01577983982861042, 0.02128659561276436, 0.00956033542752266, -0.008654840290546417, 0.01219055987894535, -0.004821751266717911, -0.039474476128816605, 0.050585146993398666, -0.019089803099632263, 0.0260090883821249, -0.01034870557487011, 0.009899438358843327, -0.07484567910432816, 0.04115346446633339, -0.07936800271272659, 0.038630712777376175, -0.03158845007419586, 0.031487926840782166, 0.0044968873262405396, -0.013105343095958233, -0.03979765623807907, 0.017213977873325348, -0.0043432931415736675, -0.01878473348915577, -0.05303439125418663, 0.0006669267895631492, -0.031713999807834625, -0.024569425731897354, 0.009272043593227863, 0.07095662504434586, 0.00021569123782683164, -0.04058549553155899, 0.008578496053814888, 0.009947912767529488, -0.011893403716385365, 0.04170439764857292, 0.04141480475664139, -0.0173810962587595, 0.04564998298883438, 0.03265543282032013, 0.011800922453403473, -0.06155326962471008, 0.01869734190404415, 0.04787595197558403, 0.006079779006540775, -0.025366993620991707, 0.0027049011550843716, -0.00942670926451683, -0.0003121708577964455, 0.10027426481246948, 0.02607116848230362, -0.027740713208913803, -0.005632015876471996, 0.05771789327263832, 0.009729139506816864, 0.027514278888702393, -0.003386319847777486, -0.007110342383384705, -0.004742890130728483, 0.009964540600776672, -0.06043562293052673, 0.010779446922242641, -0.06029197946190834, 0.021158913150429726, -0.0553477518260479, -0.0497327521443367, 0.0420527383685112, 0.013911976478993893, 0.00870998203754425, -0.025871457532048225, 0.04131082445383072, -0.038479287177324295, 0.001394467893987894, -0.03399244695901871, 0.02146824635565281, 0.04379953071475029, -0.04527151212096214, 0.01194485928863287, 0.029431337490677834, 0.007105708587914705, 0.045943744480609894, -0.007215140853077173, -0.021437449380755424, 0.024610713124275208, -0.015082894824445248, -0.034661777317523956, -0.011362235061824322, 0.005902251228690147, 0.058577653020620346, -0.06185280159115791, 0.07139556109905243, -0.07643132656812668, 0.002306611742824316, 0.04944637790322304, -0.03807494044303894, -0.010442061349749565, 0.026899779215455055, 0.02507285214960575, -0.020138608291745186, -0.0016137714264914393, -0.035234235227108, 0.008576692081987858, -0.0469033345580101, 0.01708073541522026, -0.01955295167863369, -0.037845928221940994, -0.056128211319446564, 0.010549564845860004, 0.005136410240083933, -0.045483581721782684, 0.13797640800476074, 0.008975278586149216, 0.029932858422398567, 0.02840346097946167, 0.05827492102980614, -0.027514617890119553, 0.050433870404958725, -0.011276881210505962, 0.010689894668757915, 0.07395189255475998, 0.018826676532626152, -0.038211170583963394, 0.030893441289663315, -0.03941037133336067, 0.009618142619729042, -0.043575722724199295, 0.09614285826683044, 0.002021451247856021, 0.018310807645320892, -0.05140634998679161, 0.044403076171875, -0.02623618394136429, -0.05451872944831848, 0.05024397000670433, -0.00931460689753294, -0.013216592371463776, -0.02003880962729454, -0.04117150604724884, -0.0062247756868600845, 0.0016926038078963757, 0.01028926856815815, -0.0049775345250964165, 0.034086186438798904, 0.009507528506219387, -0.0013123549288138747, -0.02624286152422428, -0.013880844227969646, -0.0005382210947573185, 0.016023889183998108, 0.007438887841999531, 0.004960737191140652, 0.04277646914124489, -0.052387725561857224, 0.009275127202272415, 0.03451710194349289, -0.03660916909575462, 0.015914982184767723, -0.02284984290599823, -0.04282320663332939, -0.04888703301548958, -0.031142085790634155, -0.06141230836510658, -0.002593916840851307, 0.08156810700893402, -0.02757723443210125, -0.05523417517542839, 0.016897916793823242, -0.01345484796911478, -0.05872642248868942, 0.0007687879260629416, 0.031993553042411804, -0.002025771886110306, 0.03609180822968483, -0.0015024616150185466, -0.0041446564719080925, 0.011637896299362183, 0.015209372155368328, 0.010419607162475586, -0.039870209991931915, 0.04993187263607979, -0.01934584602713585, 0.011560182087123394, -0.002707973588258028, 0.012101768516004086, 0.036696504801511765, 0.03942926973104477, 0.016340581700205803, 0.014415365643799305, -0.009608663618564606, 0.027717724442481995, 0.027745231986045837, -0.0036311426665633917, 0.046505916863679886, 0.06530945003032684, 0.015696287155151367, -0.009718626737594604, -0.0185258612036705, 0.014371703378856182, -0.016436897218227386, 0.049682360142469406, 0.06346408277750015, 0.046054862439632416, 0.001971843186765909, -0.011412513442337513, 0.01615583337843418, -0.019282618537545204, 0.014042345806956291, -0.00716187572106719, 0.002031392650678754, 0.005349377170205116, 0.01893715187907219, 0.013116140849888325, 0.0185255017131567, 0.06950435787439346, -0.04083836078643799, 0.02162911742925644, -0.03201120346784592, -0.03603360429406166, 0.00985702220350504, -0.012524356134235859, -0.0026420182548463345, -0.0751345083117485, 0.03698137030005455, -0.01735229603946209, 0.04550003632903099, 0.024538571015000343, 0.04221023619174957, -0.0012265670811757445, -0.04806668311357498, 0.009452885948121548, 0.03785068914294243, 0.026458770036697388, -0.03112930990755558, -0.06186416372656822, 0.02867717668414116, 0.04981473460793495, -0.032973963767290115, 0.04260885342955589, -0.04354511573910713, -0.030507998540997505, -0.011817020364105701, -0.02163873426616192, 0.013565938919782639, -0.007348346523940563, 0.023898912593722343, -0.010229545645415783, 0.020470714196562767, -0.01129493210464716, 0.10150279849767685, -0.053423184901475906, -0.02203405648469925, 0.019964218139648438, 0.025469528511166573, 0.01778520457446575, 0.033936578780412674, 0.03650179132819176, -0.06533355265855789, -0.0712520107626915, 0.01840103045105934, -0.05173274874687195, 0.015124395489692688, 0.011681260541081429, 0.04010689631104469, 0.0019518391927704215, 0.035455238074064255, -0.04267413914203644, -0.003336295485496521, 0.018290886655449867, -0.062417205423116684, 0.01294614002108574, -0.027587777003645897, 0.006378193385899067, 0.08443742245435715, -0.09196045994758606, -0.020660120993852615, 0.006355480756610632, 0.015111375600099564, -0.09334489703178406, -0.018663130700588226, 0.025614434853196144, 0.03715004771947861, -0.014951575547456741, -0.004096170421689749, 0.03216796740889549, -0.005152883939445019, 0.009093702770769596, 0.06313663721084595, 0.03705814853310585, 0.007268092129379511, 0.013550962321460247, -0.008645576424896717, -0.01712820492684841, -0.0559251569211483, -0.01914091221988201, -0.02520580217242241, 0.025728536769747734, -0.0013668598840013146, 0.0019865126814693213, -0.00911757256835699, -0.05323433130979538, -0.008976778015494347, -0.04252554476261139, 0.005166521295905113, -0.019829845055937767, 0.019555727019906044, -0.05757041648030281, -0.02237921953201294, -0.03706642612814903, 0.026714371517300606, 0.00875508040189743, 0.05392885580658913, 0.03340502828359604, 0.015462172217667103, -0.07145462930202484, -0.10056623816490173, 0.07856161147356033, 0.023596759885549545, -0.06051357835531235, 0.002926871180534363, -0.027835961431264877, -0.03320692852139473, -0.04800555109977722, -0.06078434735536575, -0.034978535026311874, -0.0294256079941988, -0.017264870926737785, 0.0012001305585727096, -0.027391737326979637, 0.046403978019952774, 0.06496115773916245, -0.0063078696839511395, -0.034061845391988754, -0.0110981659963727, -0.02809743396937847, -0.008241366595029831, 0.020815720781683922, 0.061570219695568085, -0.020536230877041817, 0.0030458266846835613, 0.01741768792271614, -0.022135967388749123, 0.03902733698487282, -0.011745283380150795, 0.0089634470641613, -0.06222739443182945, 0.09566778689622879, 0.03196136653423309, 0.011513023637235165, 0.025184422731399536, 0.0015353454509750009, -0.04985862597823143, 0.012360421940684319, -0.026612024754285812, -0.004147262312471867, -0.06489817053079605, -0.011775771155953407, -0.028759457170963287, 0.006095870863646269, 0.0028278937097638845, 0.008284403942525387, -0.004448667634278536, -0.05926321819424629, -0.010748272761702538, 0.021057307720184326, 0.040203120559453964, 0.07672901451587677, -0.07370031625032425, -0.0364520326256752, 0.042340949177742004, -0.0006486454512923956, 0.03304911404848099, 0.009295698255300522, 0.0036946202162653208, 0.021575666964054108, 0.017748558893799782, -0.06242439150810242, -0.02375822328031063, -0.02882365882396698, -0.07897185534238815, 0.03689311072230339, -0.030083540827035904, 0.031590864062309265, -0.011067556217312813, -0.011960068717598915, 0.014786437153816223, 0.023120371624827385, -0.015769340097904205, 0.009776362217962742, -0.009617852978408337, -0.006838886067271233, 0.018271038308739662, -0.008445287123322487, 0.027793588116765022, 0.05956771597266197, 0.036010969430208206, 0.0051377578638494015, -0.009598148986697197, 0.0729270800948143, 0.043290670961141586, 0.01272520050406456, -0.012327522970736027, 0.0012408652110025287, -0.010265818797051907, 0.010117175988852978, -0.0867067202925682, 0.020574068650603294, -0.034194331616163254, -0.013441001996397972, -0.0052659292705357075, 0.020022371783852577, -0.0018453859956935048, -0.018343212082982063, 0.04727445915341377, 0.0013668849132955074, 0.019732801243662834, 0.012112338095903397, 0.08463910967111588, -0.026097621768712997, -0.03322451561689377, 0.01801530458033085, -0.010579020716249943, 0.044082704931497574, 0.006423548329621553, 0.015360429883003235, 0.04462800547480583, 0.0237472802400589, -0.01158246211707592, -0.019668934866786003, 0.03132269158959389, 0.0023305262438952923, -0.01316019706428051, 0.004069880116730928, -0.02287045121192932, 0.036814987659454346, 0.008502759039402008, -0.007826759479939938, 0.025579780340194702, -0.07610360532999039, -0.011552046984434128, 0.007207727059721947, -0.0008199680014513433, -0.005155512131750584, -0.0404798649251461, -0.012214913964271545, 0.04494922235608101, 0.043369557708501816, -0.024472372606396675, -0.03680652379989624, 0.034427180886268616, -0.017155712470412254, 0.026297224685549736, -0.02181931771337986, 0.026052972301840782, 0.010939277708530426, 0.05685914680361748, 0.022055072709918022, 0.008733361028134823, -0.04584643244743347, -0.01970026083290577, -0.0033900055568665266, 0.013704076409339905, 0.021480415016412735, 0.019746260717511177, -0.02161269634962082, -0.01601133495569229, -0.014142565429210663, -0.018139546737074852, -0.06253940612077713, 0.040232352912425995, -0.07963980734348297, -0.012319362722337246, 0.020568614825606346, 0.013228755444288254, -0.02900918945670128, -0.026595009490847588, -0.008470353670418262, 0.08864637464284897, -0.06437930464744568, 0.011461704969406128, 0.006936889607459307, -0.06324883550405502, 0.045513689517974854, -0.025064583867788315, 0.0643601194024086, -0.007545675616711378, -0.04079335555434227, 0.014856628142297268, -0.0067831976339221, -0.0722895935177803, -0.053639695048332214, 0.03133607655763626, 0.038708217442035675, 0.03487169370055199, -0.003704648930579424, -0.04140442982316017, 0.017528273165225983, -0.0007067591068334877, 0.01017098966985941, -0.03010258823633194, -0.007682165130972862, 0.08573414385318756, -0.011884630657732487, 0.022182313725352287, 0.0317072831094265, -0.01441275142133236, 0.06658349931240082, -0.0660507008433342, 0.012995686382055283, 0.06976128369569778, -0.03277740254998207, -0.011588165536522865, -0.06547661870718002, 0.022647300735116005, 0.043134212493896484, 0.019004106521606445, -0.0016893502324819565, 0.012105165980756283, 0.0015767525183036923, -0.005307975225150585, 0.015066796913743019, -0.012106574140489101, 0.0009625415550544858, -0.029281098395586014, -0.029882896691560745, -0.022077536210417747, 0.023526882752776146, -0.023756111040711403, -0.015282204374670982, 0.04795387014746666, 0.07147657871246338, -0.030495155602693558, 0.023952864110469818, -0.04243357479572296, 0.030138298869132996, 0.01707194186747074, -0.03997983783483505, 0.02986006997525692, -0.06433561444282532, 0.023475784808397293, 0.03186795487999916, -0.047639161348342896, -0.004251569043844938, 0.00396896805614233, -0.07116305083036423, -0.003160925582051277, -0.0453103631734848, 0.010125751607120037, 0.047437380999326706, -0.0110903549939394, -0.046154819428920746, 0.025669971480965614, 0.060584355145692825, -0.05359369516372681, 0.008011078462004662, 0.04528820142149925, -0.0558202862739563, -0.04081002622842789, 0.051776062697172165, 0.009678400121629238, 0.021368851885199547, -0.005238426383584738, -0.03451215848326683, -0.0731784924864769, 0.012667683884501457, 0.0246513020247221, 0.0030061753932386637, -0.03355298936367035, -0.07764820754528046, -0.012203313410282135, -0.026561979204416275, 0.04219161346554756, 0.00197697919793427, 0.0011613504029810429, 0.024523138999938965, 0.011042336001992226, -0.0012916288105770946, 0.022698689252138138, 0.02602836675941944, 0.042747169733047485, 0.023988045752048492, -0.046437881886959076, 0.006286515388637781, -0.010336077772080898, -0.03466722369194031, -0.03754153847694397, -0.00040321325650438666, -0.01724446751177311, -0.00820905901491642, -0.025877468287944794, -0.08341331034898758, 0.02374163828790188, 0.003799930913373828, 0.03917459398508072, 0.09886869788169861, -0.016301365569233894, 0.04277757182717323, 0.017483826726675034, -0.04898746684193611, 0.0019433608977124095, 0.051892589777708054, -0.013068838976323605, 0.02186696045100689, 0.06940121203660965, 0.022261735051870346, 0.017656872048974037, 0.0016660111723467708, -0.020807845517992973, 0.08191404491662979, -0.04883590340614319, 0.004799514077603817, -0.02927354909479618, 0.09516840428113937, 0.0024707233533263206, -0.018219465389847755, -0.048185549676418304, 0.030430249869823456, 0.04428433999419212, -0.02545294351875782, -0.017671696841716766, -0.007278882898390293, 0.01810605451464653, 0.0065042125061154366, 0.031489986926317215, -0.011116672307252884, 0.028792649507522583, -0.007520023733377457, 0.0198921300470829, -0.020011112093925476, 0.022581614553928375, 0.031868577003479004, 0.012238377705216408, -0.02725994773209095, -0.0413239561021328, 0.0031778013799339533, -0.02330886572599411, -0.051758479326963425, 0.03660022094845772, -0.027908721938729286, 0.03223145008087158, -0.04426729306578636, 0.01548399031162262, 0.0636766329407692, 0.004618754610419273, 0.0012208545813336968, -0.007566157262772322, -0.05325441434979439, -0.006025516893714666, -0.003893936285749078, -0.005349958315491676, -0.012235316447913647, -0.09146922081708908, 0.022450242191553116, -0.050503723323345184, 0.0023209245409816504, -0.0197971910238266, -0.053813014179468155, -0.013121708296239376, 0.002911373507231474, -0.023150445893406868, -0.02919134683907032, -0.036142051219940186, 0.05324186384677887, -0.028041897341609, -0.104573555290699, 0.023735271766781807, 0.028262799605727196, 0.022472159937024117, -0.011374437250196934, -0.058884333819150925, -0.028738874942064285, 0.014818892814218998, -0.004391560796648264, 0.06983184069395065, -0.02137494832277298, 0.03870813921093941, -0.08046551793813705, -0.011893179267644882, -0.05114518105983734, -0.03847566619515419, 0.028536062687635422, 0.02989516779780388, 0.013733084313571453, 0.006281311623752117, 0.026765218004584312, 0.010252839885652065, 0.06163603812456131, -0.019689247012138367, -0.004026082344353199, 0.07499836385250092, -0.00934577826410532, -0.03081485815346241, 0.03346570208668709, -0.031007932499051094, 0.03392241150140762, -0.017781458795070648, 0.016428081318736076, 0.0016175527125597, -0.04953314736485481, 0.010580060072243214, -0.02874481864273548, -0.0014188627246767282, 0.04073229432106018, 0.05312993377447128, -0.013165234588086605, 0.031109968200325966, 0.0410534143447876, 0.03439347445964813, -0.04638109728693962, -0.03173644095659256, 0.004912537056952715, -0.0678359866142273, -0.030921125784516335, -0.02674158476293087, -0.020260073244571686, -0.07459431886672974, -0.01184877660125494, 0.020447589457035065, 0.018897999078035355, -0.0036435588262975216, 0.04260795935988426, -0.014535043388605118, 0.03822904825210571, 0.044579245150089264, 0.0058167604729533195, -0.05414237082004547, -0.061541710048913956, -0.0329538956284523, 0.02270139567553997, -0.023424841463565826, -0.029872430488467216, -0.0003142083587590605, 0.01899085007607937, 0.023645073175430298, 0.008223620243370533, -0.016918634995818138, -0.017977602779865265, -0.007769663818180561, -0.031377244740724564, 0.0614745132625103, -0.048982247710227966, -0.06494759023189545, -0.017093300819396973, 0.03927012160420418, 0.0062578399665653706, 0.07419385015964508, 0.06562221050262451, -0.011232541874051094, -0.020058462396264076, 0.020846428349614143, -0.03540705516934395, -0.012792667374014854, -0.014152100309729576, 0.033578451722860336, 0.08515655994415283, 0.00847345869988203, 0.005106859840452671, -0.036492720246315, 0.026638643816113472, 0.025173595175147057 ]
<p>How can I recognize clearly when I deal with capacitors in parallel or capacitors in series? Can follow a "rule" or a intuitive method? I have to do difficult exercises regarding system of capacitors so I must understand when I have capacitors in parallel or in series. Can you explain me in a simple way?</p>
g1511
[ 0.027333471924066544, 0.06308599561452866, -0.00832308828830719, -0.025936398655176163, 0.012258106842637062, -0.04545995593070984, 0.059625331312417984, 0.016245728358626366, -0.005636763293296099, -0.0004799558955710381, -0.07821929454803467, 0.09017589688301086, 0.016239110380411148, 0.030590875074267387, 0.04114535450935364, -0.04397071525454521, 0.02115204744040966, 0.014526915736496449, -0.0017410720465704799, 0.026572762057185173, 0.018015319481492043, 0.04534769058227539, -0.02004382386803627, 0.005476666148751974, -0.059692464768886566, 0.03100086748600006, -0.05497649684548378, -0.009270541369915009, -0.0036466249730437994, -0.06672322750091553, 0.005056004039943218, 0.0003952127299271524, 0.06657958775758743, -0.019388046115636826, 0.016377151012420654, -0.04720788449048996, 0.046161383390426636, -0.0064181433990597725, 0.010058040730655193, 0.02809082716703415, 0.016321619972586632, 0.003380072070285678, 0.015050625428557396, 0.026468582451343536, -0.04673929885029793, 0.019361944869160652, -0.05303315073251724, -0.03035462461411953, -0.01760450378060341, -0.0297738965600729, 0.02744649350643158, -0.02321912907063961, 0.02353728376328945, 0.040201954543590546, 0.009770405478775501, -0.0035178018733859062, 0.040894269943237305, 0.035078272223472595, 0.10758250206708908, -0.024665292352437973, 0.02587192691862583, 0.060214564204216, -0.015723418444395065, 0.017974501475691795, 0.05112031474709511, 0.022524604573845863, 0.026091599836945534, 0.022313756868243217, -0.01827956922352314, 0.01398539263755083, 0.0063185859471559525, -0.08129480481147766, 0.058183230459690094, 0.009289190173149109, -0.021084174513816833, 0.0029872229788452387, 0.012795521877706051, -0.03055533394217491, 0.008342303335666656, 0.027186457067728043, 0.027755362913012505, -0.005517106503248215, 0.06490291655063629, -0.021623948588967323, 0.03283528611063957, -0.010097512975335121, 0.010421841405332088, -0.04026730731129646, -0.05841045081615448, 0.02517855167388916, -0.014919870533049107, 0.015233969315886497, -0.007325270678848028, 0.034276608377695084, 0.00559247424826026, -0.0007585475104860961, -0.01401272788643837, 0.042015619575977325, 0.004835032392293215, -0.01109501626342535, -0.02942774072289467, 0.07593706995248795, -0.04012256860733032, -0.05487746745347977, -0.04268202558159828, 0.034923382103443146, 0.07801022380590439, -0.014844345860183239, -0.0003154755395371467, -0.06264076381921768, -0.060165926814079285, 0.03092571534216404, -0.024335386231541634, 0.02243814989924431, -0.030733857303857803, 0.013535425066947937, 0.05979486182332039, -0.02229374833405018, 0.010259602218866348, 0.05632530152797699, -0.038712792098522186, -0.03800224885344505, 0.0018533198162913322, -0.018386639654636383, -0.007396710570901632, -0.044392526149749756, 0.06317130476236343, -0.017375033348798752, 0.00863721501082182, 0.006439820863306522, 0.027761666104197502, -0.012516462244093418, -0.017857113853096962, 0.02045282907783985, -0.010899358429014683, 0.01956360973417759, 0.06251685321331024, -0.05374492332339287, 0.01624804548919201, -0.020315034314990044, -0.0446135513484478, 0.019420674070715904, -0.051810577511787415, -0.027854613959789276, 0.058531519025564194, -0.04063750058412552, -0.039931055158376694, -0.03485899046063423, -0.006833544000983238, 0.015772216022014618, 0.040331095457077026, 0.0524594821035862, -0.04439335688948631, -0.059583477675914764, 0.022322777658700943, -0.002261166460812092, 0.014525936916470528, 0.03194442763924599, 0.03976544737815857, -0.030887344852089882, -0.0583474338054657, 0.014229665510356426, -0.06628638505935669, 0.021949615329504013, -0.03954968601465225, -0.07452651113271713, -0.020334821194410324, 0.0010663967113941908, 0.035378843545913696, -0.06735692173242569, -0.009497483260929585, -0.021768908947706223, -0.026241714134812355, 0.03654353693127632, 0.07163860648870468, 0.04604720324277878, 0.07551240921020508, 0.014876076951622963, 0.05290628969669342, -0.037622082978487015, -0.030038731172680855, -0.008682441897690296, 0.0242603812366724, 0.005998088978230953, -0.04557221010327339, 0.02848179079592228, 0.03131842240691185, 0.04081973060965538, -0.04259573295712471, 0.021981574594974518, -0.047996796667575836, -0.00009990840044338256, 0.029949495568871498, 0.061554573476314545, 0.004199843388050795, -0.04558341205120087, 0.00973445363342762, 0.009410060942173004, -0.03931255638599396, -0.08492603898048401, 0.04015646502375603, -0.01073954813182354, 0.014980258420109749, 0.04565355181694031, 0.019077269360423088, 0.02767457813024521, -0.021246248856186867, -0.03191909193992615, 0.06303764134645462, 0.010274440981447697, 0.0009570585680194199, 0.007897083647549152, -0.03127499669790268, 0.038016464561223984, -0.01824432797729969, -0.017808323726058006, -0.0225785244256258, 0.019422030076384544, -0.019977565854787827, 0.024574164301156998, -0.02205992490053177, -0.04896965250372887, -0.03756681829690933, -0.007087963167577982, -0.036197490990161896, -0.002567281248047948, -0.021652033552527428, 0.02515522763133049, -0.02921440824866295, -0.019118739292025566, -0.06953878700733185, -0.010890494100749493, -0.01660800725221634, -0.0031466754153370857, -0.023635994642972946, -0.0008194563561119139, 0.05749320238828659, -0.047367118299007416, 0.03334181010723114, 0.022961949929594994, -0.007729313801974058, -0.0031803185120224953, 0.051655784249305725, -0.017188774421811104, -0.022285789251327515, -0.0190457534044981, 0.04053765907883644, -0.013949616812169552, -0.01445835828781128, -0.0015692334854975343, 0.01600046455860138, 0.003503601299598813, -0.010208501480519772, 0.0053985887207090855, -0.0034535888116806746, 0.002626106608659029, 0.041391074657440186, 0.008839531801640987, 0.03293856233358383, 0.0448765903711319, -0.02195027843117714, -0.0223236121237278, -0.04831034317612648, 0.0843793973326683, 0.007105862256139517, -0.031897567212581635, -0.010690692812204361, -0.012821446172893047, 0.04348631948232651, -0.009294813498854637, -0.016895635053515434, 0.06356418132781982, 0.03756096586585045, -0.04082193598151207, 0.012856184504926205, -0.04796510934829712, 0.04844478517770767, -0.03654369339346886, 0.003850640496239066, 0.04494562745094299, -0.007594988215714693, -0.05096832290291786, 0.0034201378002762794, -0.07226472347974777, 0.036894604563713074, -0.006794655229896307, 0.017117025330662727, -0.047395750880241394, 0.0026416184846311808, 0.061601266264915466, -0.044963251799345016, -0.09466393291950226, -0.057468097656965256, -0.03932363539934158, -0.010026192292571068, 0.04616755247116089, 0.023259609937667847, 0.007625237572938204, 0.020551785826683044, 0.05363403633236885, 0.017855534330010414, 0.010936922393739223, -0.00048102776054292917, -0.020704032853245735, 0.06805043667554855, 0.04716842249035835, 0.007290976122021675, -0.0032063734252005816, -0.02623859979212284, 0.02586502954363823, -0.03575431928038597, -0.006976916454732418, 0.042119454592466354, -0.014060146175324917, -0.018754595890641212, 0.07754894345998764, 0.020873330533504486, 0.006003006361424923, -0.07225195318460464, -0.04963691905140877, 0.005423638503998518, -0.03161715343594551, 0.068376824259758, 0.02545647695660591, -0.035636644810438156, 0.01069684699177742, 0.005279057193547487, -0.04187522083520889, -0.03148237243294716, 0.011327615939080715, -0.036295678466558456, -0.035298410803079605, 0.031000833958387375, -0.005835465621203184, -0.04772281274199486, -0.05340966954827309, -0.02402074821293354, -0.006472697015851736, 0.00265981862321496, 0.015088564716279507, 0.03298138827085495, -0.0029894753824919462, -0.021962400525808334, -0.060664672404527664, -0.01985195465385914, -0.015569430775940418, 0.01818275637924671, 0.046812500804662704, 0.05264424532651901, -0.04844313859939575, 0.0356273390352726, 0.013199309818446636, 0.015099328011274338, 0.02814491279423237, -0.04281369596719742, -0.00308037712238729, 0.026504207402467728, 0.054079413414001465, -0.048006005585193634, 0.014689717441797256, 0.008188719861209393, -0.036442071199417114, 0.0063536702655255795, 0.044346053153276443, 0.000939411111176014, -0.03853652626276016, 0.03003288246691227, 0.08171176165342331, -0.043431542813777924, -0.06401030719280243, -0.016187695786356926, 0.025812899693846703, -0.01385707687586546, 0.0036605503410100937, 0.0041315145790576935, -0.07248499989509583, -0.032749008387327194, 0.024961747229099274, 0.0043237172067165375, 0.019299769774079323, -0.0032365485094487667, -0.06188337504863739, -0.03775348141789436, -0.054977767169475555, 0.05081823095679283, -0.026462385430932045, 0.0702660009264946, 0.08124446123838425, -0.015155086293816566, 0.016050659120082855, 0.004988004919141531, -0.04677319899201393, -0.049621280282735825, 0.010836193338036537, -0.011053496971726418, -0.004284970462322235, -0.01250622607767582, 0.031144697219133377, -0.010831156745553017, 0.032474834471940994, -0.08430728316307068, -0.0592101514339447, 0.01250920258462429, -0.02111024782061577, 0.012362423352897167, 0.020345564931631088, 0.01790446974337101, -0.058925922960042953, 0.08082365989685059, -0.0063034165650606155, -0.04483186826109886, -0.0014079413376748562, 0.023011505603790283, 0.007798136677592993, -0.027860932052135468, 0.004326244350522757, 0.06249687820672989, 0.0024907251354306936, 0.04410485923290253, 0.05125012993812561, 0.008202691562473774, -0.0010112945456057787, -0.04787684604525566, -0.030796153470873833, -0.03519618511199951, 0.03232355788350105, 0.05434392765164375, 0.014196264557540417, -0.009290821850299835, 0.034707341343164444, -0.02313019521534443, -0.007770082447677851, 0.05565493553876877, 0.019326796755194664, -0.0070055024698376656, 0.01624755933880806, 0.0012422200525179505, 0.05935368314385414, -0.024031076580286026, 0.045212410390377045, 0.05372482165694237, -0.005125673487782478, -0.06544531136751175, -0.049049459397792816, -0.029767630621790886, 0.031257662922143936, -0.032331760972738266, 0.017878685146570206, -0.059312522411346436, -0.04819760099053383, -0.0600086934864521, 0.03409552946686745, -0.0643368810415268, -0.05192065238952637, -0.02052185870707035, -0.0162576362490654, -0.02736230194568634, -0.04270591959357262, 0.00996255874633789, -0.005108821205794811, 0.026722420006990433, -0.01471336092799902, -0.012499254196882248, -0.022233903408050537, -0.03558580204844475, 0.02279840223491192, -0.04847048968076706, -0.029704678803682327, -0.056457530707120895, 0.02387544885277748, 0.031143348664045334, 0.01616387814283371, 0.021081674844026566, 0.004593466874212027, 0.030815565958619118, -0.026180123910307884, 0.029329143464565277, -0.005421311594545841, -0.045949965715408325, 0.01950846053659916, 0.04586714506149292, -0.0557083934545517, -0.0025128591805696487, -0.011435608379542828, -0.05634261295199394, -0.017498638480901718, 0.02755686081945896, 0.008514881134033203, 0.015430805273354053, 0.0042920405976474285, 0.035675812512636185, 0.05975766107439995, 0.03105812706053257, 0.09807999432086945, -0.06503576785326004, -0.046058353036642075, 0.005142965354025364, 0.03929727524518967, -0.017562249675393105, -0.0023119684774428606, 0.002141013275831938, 0.03375973924994469, 0.0416727289557457, 0.019755370914936066, -0.02595444582402706, 0.021795446053147316, 0.03062698245048523, -0.03856991231441498, 0.01428765058517456, 0.02640562504529953, 0.05401988700032234, 0.05424506589770317, 0.0032263160683214664, 0.043648187071084976, 0.019889486953616142, 0.011240741237998009, 0.006504040211439133, -0.004600650630891323, -0.04571783170104027, 0.0003832518414128572, 0.04786548390984535, 0.03498674929141998, -0.040597572922706604, 0.024442072957754135, -0.021000780165195465, -0.05905616655945778, -0.017651723697781563, -0.003486908506602049, 0.05324060469865799, 0.03411098197102547, 0.059107743203639984, -0.0010818946175277233, -0.014558756723999977, -0.0257197767496109, -0.050247255712747574, -0.057863593101501465, 0.0013757396955043077, -0.0018069627694785595, 0.06449834257364273, 0.04917219653725624, -0.04327714815735817, 0.01372301485389471, -0.02441568486392498, 0.042610250413417816, -0.019572114571928978, -0.04196755215525627, 0.06847400963306427, 0.012719333171844482, 0.0753641277551651, -0.004987309221178293, -0.011271623894572258, -0.012664273381233215, 0.000155814501340501, -0.037722211331129074, 0.07898741960525513, 0.0003710634773597121, 0.03211437910795212, -0.037019032984972, 0.025822408497333527, -0.01584593951702118, -0.05747935548424721, 0.060243912041187286, 0.022765247151255608, -0.0634041428565979, -0.0522233247756958, -0.03079783171415329, -0.00859727431088686, 0.04509231448173523, 0.058197811245918274, 0.013250265270471573, 0.026538705453276634, -0.0649675652384758, 0.009028882719576359, 0.03207777068018913, 0.06010691076517105, 0.033837925642728806, -0.005981067195534706, 0.04748969525098801, 0.07061260938644409, 0.010386656038463116, -0.023223763331770897, 0.004009537864476442, 0.009866050444543362, -0.018248531967401505, 0.02151551842689514, 0.07515350729227066, 0.06168541684746742, 0.024674510583281517, 0.009445580653846264, 0.007823359221220016, 0.0006834585219621658, -0.021698877215385437, 0.03689763322472572, 0.01760454848408699, 0.04912751913070679, 0.015876280143857002, 0.00046799599658697844, 0.07756564021110535, 0.024465128779411316, 0.0031199047807604074, 0.027345679700374603, -0.03126238286495209, -0.004721136298030615, -0.02497558481991291, -0.04802747815847397, -0.017849596217274666, -0.024349870160222054, 0.013610868714749813, -0.07007001340389252, 0.04232632368803024, -0.012844284065067768, -0.003420918481424451, 0.038496069610118866, 0.03190236911177635, -0.04057130590081215, 0.02296660654246807, 0.02399740181863308, 0.011358695104718208, 0.005647057201713324, -0.03979906439781189, 0.06589609384536743, 0.006616540253162384, 0.006738249212503433, 0.031124098226428032, 0.01972207985818386, 0.056610360741615295, 0.021520668640732765, 0.07287672907114029, 0.06557268649339676, -0.04496898129582405, -0.023755725473165512, 0.020438073202967644, -0.0290067195892334, 0.06879530847072601, 0.015405859798192978, 0.003642334835603833, -0.05918099731206894, -0.04182619974017143, 0.0030517014674842358, -0.006759460084140301, -0.038293421268463135, -0.00945365708321333, -0.00003958849629270844, 0.0242198146879673, 0.04197760671377182, -0.011699126102030277, 0.04350649565458298, -0.012779830023646355, -0.03092852793633938, -0.01753046363592148, -0.012319712899625301, -0.05961897596716881, -0.02149639092385769, 0.023644044995307922, -0.00434895372018218, 0.026792777702212334, 0.037952955812215805, 0.007790182251483202, 0.0021040376741439104, -0.03730403631925583, -0.0690271407365799, -0.009850380942225456, -0.015135794878005981, -0.026461075991392136, -0.007832708768546581, 0.04450177401304245, 0.0030126511119306087, -0.0182788148522377, -0.014130447059869766, -0.054261334240436554, -0.04218340665102005, -0.026669561862945557, 0.015027227811515331, 0.03738066926598549, 0.05007984861731529, -0.008765379898250103, -0.01912510022521019, -0.012021969072520733, -0.08176403492689133, -0.010940483771264553, -0.04655066132545471, -0.03865622729063034, 0.031800176948308945, -0.012307846918702126, 0.007570371963083744, 0.027766533195972443, -0.023632952943444252, -0.013420568779110909, -0.026343751698732376, -0.009219272993505001, -0.04929329454898834, -0.03289168328046799, 0.04128700867295265, -0.08255168795585632, 0.00781110767275095, -0.0139931570738554, 0.04790375754237175, 0.022856317460536957, -0.034192562103271484, 0.030813513323664665, 0.02613849937915802, -0.009530315175652504, -0.005165485665202141, 0.00827284250408411, -0.048060692846775055, -0.029067575931549072, -0.06664960831403732, -0.032804492861032486, 0.019196949899196625, 0.012167626060545444, -0.04386555776000023, 0.02253369241952896, 0.04345360025763512, 0.02458396553993225, -0.0340275876224041, -0.029590245336294174, -0.06522339582443237, -0.02993161417543888, -0.047701265662908554, 0.03606817126274109, -0.05874200910329819, -0.023950917646288872, 0.041872479021549225, -0.031050750985741615, -0.016413327306509018, -0.02072797156870365, 0.026751846075057983, 0.020422518253326416, -0.034163136035203934, -0.013705361634492874, 0.04834483191370964, 0.0005036367219872773, 0.02402445301413536, 0.08976025879383087, -0.030823102220892906, 0.03570405766367912, 0.005817979574203491, -0.02136487141251564, -0.017782624810934067, -0.014304051175713539, -0.03000856377184391, -0.0447380505502224, -0.006766428705304861, -0.022866223007440567, -0.02959752455353737, -0.035403523594141006, -0.0029513996560126543, -0.026169579476118088, 0.04574941098690033, -0.047573626041412354, -0.05759689211845398, -0.02116987854242325, 0.008772007189691067, 0.0031879583839327097, -0.01098974235355854, 0.019182568415999413, 0.035289570689201355, -0.01885376125574112, 0.03265650197863579, -0.015575616620481014, -0.039743032306432724, 0.008333016186952591, -0.033551618456840515, 0.0008454152848571539, 0.021184053272008896, -0.0026453484315425158, -0.07085193693637848, -0.06979047507047653 ]
<p>I have been asked this question by a student, but I was able and in the same time incapable to give a good answer for this without equations, so do you have ideas how one can explain this in a simple way? </p> <p>(Answers like we can take time as an imaginary, or our space is actually pseudo-Euclidean will be hard to grasp for new students.)</p> <p>Note that the problem is <em>not</em> in visualizing the 4th dimension, that an easy thing to explain. The problem is more related to why we are in 3D that moving along 1D time dimension? In Differential geometry this interpreted by fiber bundles, but how to explain it to usual student.</p>
g1512
[ 0.027434973046183586, 0.09524757415056229, -0.005485732574015856, -0.027042163535952568, -0.04279820993542671, 0.01872449927031994, 0.07138945907354355, 0.004631248768419027, -0.02466646395623684, -0.00009476513514528051, 0.004990461282432079, -0.0027528314385563135, 0.04909226670861244, 0.049881886690855026, 0.022590195760130882, -0.027289777994155884, 0.0006899567670188844, -0.04605614021420479, -0.02323051728308201, -0.012284236028790474, 0.0202297642827034, 0.002566229086369276, 0.038830533623695374, -0.03176771104335785, -0.05276334658265114, -0.04076629877090454, 0.04758353531360626, -0.030311034992337227, -0.02193998359143734, 0.015741456300020218, 0.06797807663679123, 0.01106900256127119, 0.01217231061309576, -0.021146882325410843, -0.048506371676921844, -0.018278570845723152, 0.015107293613255024, -0.0033134694676846266, 0.05750716105103493, -0.023029755800962448, -0.018508486449718475, -0.026975853368639946, 0.009451078251004219, 0.02266032062470913, 0.012013566680252552, 0.04519346356391907, -0.029875146225094795, -0.012756501324474812, -0.021465478464961052, 0.005826094653457403, 0.031167516484856606, 0.03886204585433006, -0.007344501093029976, 0.026176558807492256, 0.002157538430765271, -0.014516105875372887, 0.023536037653684616, -0.027811110019683838, 0.0580611526966095, 0.031925324350595474, 0.009005093015730381, 0.006464078556746244, 0.054246701300144196, 0.038828782737255096, 0.073091059923172, -0.05757110193371773, -0.04269648343324661, -0.027983911335468292, 0.05332201346755028, -0.035203754901885986, 0.0240043755620718, 0.008477594703435898, 0.027255363762378693, 0.006685940083116293, -0.020707931369543076, 0.011492622084915638, 0.0736946389079094, 0.020885465666651726, -0.039389073848724365, -0.020188963040709496, -0.04406505078077316, 0.03502792492508888, -0.02307315357029438, -0.03896968066692352, 0.11446385085582733, 0.021871207281947136, 0.02550087496638298, -0.04413636401295662, 0.002822439419105649, 0.007365120109170675, -0.033866871148347855, 0.013053318485617638, 0.03195402771234512, 0.03302722051739693, -0.029249874874949455, -0.07221587747335434, -0.06614899635314941, 0.10046298801898956, -0.04223185405135155, -0.01697356067597866, -0.02957095019519329, 0.005455715581774712, 0.03358633071184158, -0.044917505234479904, 0.007407729979604483, -0.030971653759479523, 0.008215234614908695, 0.015383034944534302, -0.011565047316253185, -0.021573863923549652, -0.02042238600552082, -0.04066677764058113, -0.022189997136592865, 0.04894572123885155, 0.012711945921182632, -0.013285201974213123, 0.03247103840112686, -0.03853027522563934, 0.0034819578286260366, 0.05025121197104454, 0.04140407592058182, 0.003487256122753024, 0.00762610649690032, 0.04470669850707054, 0.018217692151665688, 0.029008643701672554, 0.012962806038558483, -0.000502297654747963, 0.04414929822087288, 0.012217591516673565, -0.012468528933823109, 0.048697277903556824, 0.007125687785446644, 0.03390895202755928, -0.04999880865216255, 0.04391666501760483, -0.017975851893424988, -0.03877768665552139, -0.009290876798331738, 0.06786791235208511, -0.017259150743484497, -0.0769433081150055, -0.015241662040352821, -0.038880083709955215, -0.05682665482163429, 0.01935315504670143, -0.025656666606664658, -0.0393574982881546, -0.04772103950381279, 0.019964447245001793, 0.01850062608718872, 0.1076832190155983, 0.036187127232551575, -0.008886195719242096, 0.037542086094617844, 0.015280233696103096, -0.007037478964775801, 0.0023173727095127106, 0.03556545451283455, -0.020252980291843414, 0.04159439727663994, 0.00915581826120615, -0.03792475536465645, -0.007752397563308477, -0.04593754559755325, 0.007796439807862043, 0.004483127500861883, -0.0682251900434494, -0.01377373281866312, -0.09753847122192383, -0.03215436264872551, 0.018761923536658287, 0.009815225377678871, 0.01619872823357582, -0.0062980931252241135, 0.03655603155493736, -0.04747616872191429, -0.016106491908431053, -0.07658243179321289, 0.013500545173883438, 0.022749274969100952, -0.005662006326019764, 0.007900653406977654, -0.04955608397722244, 0.042653512209653854, 0.03671550750732422, 0.001422810135409236, 0.019258422777056694, -0.03304409980773926, -0.005089994054287672, -0.009183193556964397, -0.0351831279695034, 0.03240756690502167, 0.0439663864672184, -0.02779454179108143, -0.03368546813726425, 0.023936469107866287, -0.04835706204175949, -0.043358076363801956, 0.0290431696921587, 0.022174188867211342, -0.00581701286137104, 0.049346841871738434, 0.041092418134212494, 0.03587302565574646, -0.012114412151277065, -0.006345028523355722, -0.020718280225992203, 0.06974419951438904, -0.041280053555965424, 0.07594497501850128, -0.0052740792743861675, -0.0029767367523163557, 0.040706098079681396, -0.03498023375868797, -0.035270869731903076, 0.01698913797736168, -0.00968722254037857, 0.011154413223266602, 0.03664180263876915, -0.028232617303729057, -0.059147417545318604, 0.010493213310837746, -0.02485242299735546, 0.021873774006962776, -0.05266236886382103, -0.04889127239584923, -0.05472801625728607, -0.012164689600467682, 0.07453972846269608, -0.04079611971974373, -0.014174725860357285, 0.006586040370166302, 0.015399812720716, 0.0628603994846344, 0.019998138770461082, -0.04473154991865158, 0.04578768089413643, 0.024923304095864296, 0.02355218678712845, 0.05019689351320267, 0.009413781575858593, 0.030140792950987816, 0.002398299751803279, 0.01629037968814373, -0.02750730887055397, 0.07793217897415161, -0.021439148113131523, -0.012178939767181873, 0.017344938591122627, 0.0311286561191082, -0.0161865446716547, 0.011843855492770672, -0.005404181312769651, 0.013718408532440662, 0.025682300329208374, 0.016010669991374016, 0.012731971219182014, -0.03261356055736542, -0.029804490506649017, -0.015389504842460155, 0.030863778665661812, 0.010800211690366268, 0.05394844338297844, -0.053595785051584244, -0.06304304301738739, -0.02572612091898918, 0.05658447742462158, -0.03516071289777756, -0.014169231988489628, 0.0330369733273983, 0.008273439481854439, 0.008230148814618587, 0.024578802287578583, -0.038686152547597885, 0.0005694912979379296, 0.026485556736588478, -0.0349397286772728, -0.0038035206962376833, -0.021152762696146965, -0.020059650763869286, 0.018406085669994354, -0.05329579859972, 0.007759946398437023, 0.0533871203660965, -0.08287430554628372, 0.04120079427957535, 0.0226773489266634, -0.053802840411663055, 0.019385237246751785, -0.07754982262849808, 0.017952464520931244, -0.03268484026193619, -0.011875543743371964, -0.02636607550084591, 0.04753253981471062, 0.02370874211192131, 0.012514044530689716, -0.015917107462882996, -0.03175397589802742, -0.05491932854056358, 0.020665394142270088, 0.033071521669626236, 0.0028196144849061966, 0.04100775718688965, -0.02053111605346203, 0.003149924799799919, -0.06804124265909195, -0.045960016548633575, -0.008459309116005898, 0.012326146475970745, 0.014925776049494743, -0.04081223905086517, 0.018833450973033905, -0.027659954503178596, -0.004275714047253132, -0.05694551020860672, -0.0066087618470191956, 0.03699799254536629, 0.008192149922251701, -0.015047723427414894, -0.018202077597379684, -0.08534667640924454, -0.008910921402275562, 0.0037188446149230003, -0.04650493338704109, -0.003326552454382181, -0.04557926952838898, -0.025510793551802635, 0.024170296266674995, -0.016468357294797897, -0.05210334435105324, -0.035542868077754974, -0.036088548600673676, -0.03327294439077377, -0.06158781796693802, -0.06848813593387604, -0.0017851353622972965, 0.019402649253606796, -0.03923593461513519, -0.03573789820075035, -0.03991008922457695, -0.006920841988176107, 0.01595790684223175, 0.019474230706691742, 0.01613142341375351, 0.009151438251137733, 0.018833227455615997, -0.012526558712124825, -0.020134558901190758, -0.006078632548451424, 0.044828660786151886, 0.02845790982246399, -0.08009640127420425, 0.03430234268307686, 0.05710650607943535, 0.0638938918709755, 0.0646929144859314, -0.017275461927056313, -0.05592770501971245, 0.030299268662929535, -0.010014173574745655, -0.031376760452985764, -0.013782351277768612, 0.031477272510528564, 0.007026569917798042, 0.027006542310118675, 0.06929688155651093, 0.029921891167759895, 0.04718759283423424, 0.05186501145362854, -0.0017063894774764776, 0.01772729679942131, 0.05383121222257614, 0.04134408012032509, 0.011728021316230297, -0.01026887260377407, -0.0007446930394507945, 0.0044691781513392925, -0.020740531384944916, 0.016975577920675278, 0.03583076223731041, 0.0546695776283741, -0.028328068554401398, 0.033235762268304825, 0.016653208062052727, -0.02730548195540905, 0.000624525302555412, -0.032009512186050415, -0.015529325231909752, 0.07668758928775787, 0.029765337705612183, -0.021824678406119347, -0.03815529868006706, 0.01140615064650774, -0.015202966518700123, 0.02680601179599762, 0.029395682737231255, -0.06276744604110718, -0.10665323585271835, 0.022291263565421104, 0.03274054080247879, 0.007297596428543329, 0.022117283195257187, -0.012375853955745697, -0.04644748196005821, 0.030339522287249565, -0.034560076892375946, 0.04814423993229866, -0.028149062767624855, -0.006190472282469273, -0.015927400439977646, 0.053217023611068726, -0.03381215035915375, 0.04446502774953842, 0.02985394559800625, 0.009840273298323154, 0.004718448035418987, 0.002047286368906498, 0.04331807792186737, 0.031556349247694016, 0.06325416266918182, -0.020869145169854164, -0.007808273658156395, -0.001301457523368299, 0.06074421480298042, 0.05464036762714386, -0.01683860458433628, -0.05760674551129341, -0.014959110878407955, -0.04187506064772606, 0.009336155839264393, -0.040458403527736664, 0.04350772127509117, -0.05136733129620552, -0.010447083041071892, -0.04258273169398308, 0.023355741053819656, 0.020754290744662285, 0.026703571900725365, 0.01790536567568779, 0.018833616748452187, 0.031821731477975845, -0.022173341363668442, -0.014847896061837673, 0.03031282313168049, 0.005119518376886845, -0.04665577784180641, -0.041900813579559326, -0.001130892662331462, -0.034972429275512695, 0.08977977931499481, -0.000304104556562379, -0.00915623176842928, 0.03837282955646515, -0.0017869080184027553, -0.023765768855810165, 0.01429592352360487, -0.006923591252416372, 0.027016716077923775, -0.048752766102552414, 0.0372968390583992, -0.010980651713907719, 0.017347302287817, -0.0026135065127164125, -0.04373028129339218, -0.03137853369116783, -0.048135578632354736, -0.02682223916053772, 0.06317846477031708, 0.03351067006587982, 0.02133314684033394, -0.04774373397231102, -0.022579893469810486, 0.02739051915705204, 0.0164581798017025, 0.006331538315862417, 0.04179420322179794, 0.01669212058186531, -0.04772869870066643, -0.013706408441066742, -0.05034860223531723, 0.08077304065227509, -0.016404272988438606, 0.033825866878032684, 0.010878687724471092, -0.04692833125591278, 0.00968895386904478, -0.03162036091089249, -0.034314654767513275, -0.032811012119054794, -0.024822287261486053, -0.00814582034945488, 0.024447325617074966, -0.04768170788884163, -0.046204451471567154, -0.004865606315433979, 0.008863051421940327, -0.028498783707618713, -0.024787941947579384, -0.04872923344373703, 0.009126296266913414, -0.007960560731589794, -0.03677282854914665, -0.005390830338001251, 0.03843026980757713, 0.0651002824306488, -0.038464415818452835, -0.07098577171564102, 0.05721740797162056, 0.01946217007935047, -0.01797381415963173, -0.01601928472518921, 0.026676513254642487, 0.022653305903077126, -0.039687760174274445, -0.0049264682456851006, 0.020235735923051834, 0.0792437344789505, 0.04862998053431511, -0.03200427442789078, 0.10397990792989731, 0.04789568856358528, 0.00279033905826509, 0.006922440137714148, -0.00826652068644762, -0.04250311478972435, 0.0018895453540608287, 0.02603263594210148, 0.06156622990965843, 0.059914376586675644, -0.012598560191690922, -0.0016302171861752868, -0.03800508379936218, -0.02650005929172039, 0.03760354965925217, 0.041233669966459274, -0.03714105486869812, 0.04822878539562225, 0.010535250417888165, -0.06831283122301102, -0.032842814922332764, -0.0236134584993124, 0.07695260643959045, -0.035194095224142075, -0.021870149299502373, 0.04480476304888725, 0.012846382334828377, 0.025690410286188126, -0.028316622599959373, -0.003011024557054043, -0.020872248336672783, 0.027947578579187393, -0.026858825236558914, -0.010655582882463932, -0.017319077625870705, -0.01128297671675682, -0.0359593890607357, -0.048972293734550476, -0.053680915385484695, -0.010873486287891865, 0.030399082228541374, -0.0006479714647866786, -0.019510047510266304, -0.020050721243023872, -0.03562387451529503, 0.07468608766794205, 0.016541756689548492, 0.05763787776231766, 0.000009444170245842542, -0.002139081945642829, -0.060177285224199295, 0.051819659769535065, 0.0018736817874014378, 0.0027803191915154457, -0.04107410088181496, 0.05988465994596481, -0.033259470015764236, -0.04969175532460213, 0.014427910558879375, 0.018149428069591522, -0.010792352259159088, 0.06523009389638901, -0.03582313656806946, 0.011315972544252872, 0.023861665278673172, 0.018553759902715683, -0.03130915015935898, -0.01110016368329525, -0.02666012942790985, -0.0744142085313797, 0.022025609388947487, -0.007349696476012468, -0.027424423024058342, -0.012309628538787365, 0.0095391059294343, -0.02104940637946129, 0.06999896466732025, 0.014430302195250988, -0.03437246009707451, -0.009990793652832508, 0.04677598178386688, -0.0014683330664411187, -0.030890682712197304, 0.012941250577569008, 0.025427045300602913, -0.011516052298247814, -0.0017980021657422185, 0.036233965307474136, 0.042848143726587296, 0.0127843813970685, 0.05937839299440384, -0.0023312640842050314, 0.07442155480384827, 0.03619355335831642, -0.06313610076904297, 0.01297636516392231, -0.03564674034714699, 0.07273420691490173, -0.009298560209572315, 0.0354190394282341, -0.04293874278664589, 0.06572777032852173, 0.03674556314945221, 0.010199030861258507, 0.01740250550210476, -0.06895578652620316, -0.02261948026716709, 0.04846738651394844, 0.03241049498319626, -0.00884003471583128, -0.053356289863586426, 0.01012435369193554, 0.06813599914312363, -0.013809996657073498, 0.009728910401463509, -0.06587345153093338, 0.03921143710613251, 0.004079523030668497, 0.014944897964596748, -0.004987524822354317, -0.02318185567855835, 0.014725292101502419, -0.05031532421708107, -0.012210664339363575, -0.05805561691522598, -0.005243141204118729, -0.046073585748672485, 0.0010631154291331768, 0.006549970246851444, 0.02713252231478691, -0.027505720034241676, 0.0013306998880580068, -0.013987155631184578, -0.03237675502896309, -0.07486851513385773, -0.02193848043680191, -0.011475549079477787, -0.054807454347610474, -0.06734584271907806, -0.050742194056510925, 0.028077324852347374, -0.043270815163850784, 0.023482713848352432, -0.002283659530803561, 0.03562866151332855, 0.009137574583292007, 0.015885312110185623, 0.015651030465960503, -0.01144864410161972, 0.008355632424354553, 0.03571891412138939, 0.016926271840929985, 0.02531462162733078, -0.006861236412078142, 0.0061302101239562035, -0.0045941793359816074, 0.03115563839673996, 0.029142873361706734, 0.006850639823824167, 0.008286748081445694, 0.06096493825316429, 0.014034073799848557, -0.030155668035149574, -0.04703700542449951, -0.007024046964943409, -0.003036836627870798, -0.00944988802075386, -0.046067945659160614, 0.002430224558338523, 0.02347579598426819, 0.05185478925704956, -0.026861386373639107, 0.01844637468457222, 0.014868729747831821, -0.02737976610660553, 0.10453186929225922, -0.03377946838736534, -0.03672122210264206, -0.036252934485673904, -0.0692426860332489, -0.023975590243935585, -0.00538150779902935, -0.007683234289288521, -0.017635399475693703, -0.05649489909410477, -0.04513946920633316, 0.00032625297899357975, -0.01706795021891594, 0.04152822494506836, 0.004936684388667345, 0.07646961510181427, -0.025824232026934624, -0.014894423075020313, -0.004349065013229847, -0.03312511369585991, -0.03040853701531887, -0.053045399487018585, -0.003419819986447692, -0.036096904426813126, -0.010904932394623756, -0.05378943681716919, -0.005285002291202545, -0.0569428950548172, 0.01125821378082037, -0.05233713984489441, -0.003187372349202633, -0.10847962647676468, 0.0308719202876091, 0.005064728669822216, 0.01767056994140148, 0.02220802940428257, 0.03074321523308754, 0.06634487956762314, -0.04485494643449783, 0.029690256342291832, -0.025164175778627396, 0.004087849520146847, 0.0394883006811142, 0.013225475326180458, 0.01148303598165512, -0.0030761281959712505, -0.009065892547369003, 0.015020682476460934, 0.03634895384311676, -0.0032140647526830435, 0.0026069735176861286, 0.025000011548399925, 0.05642233416438103, 0.028780600056052208, -0.026735279709100723, 0.05543722212314606, -0.03883451968431473, -0.02883925288915634, 0.03461506962776184, -0.050607793033123016, -0.006648743525147438, 0.03801043704152107, 0.004534181207418442, -0.00579336192458868, -0.011225172318518162, -0.06286447495222092, 0.011415993794798851, 0.05946345999836922, 0.0031235849019140005, -0.035221733152866364, -0.03943152725696564, 0.032140422612428665 ]
<p>I'm thinking about trying to do a numerical simulation of some very simple QM problems.</p> <p>How much space do I need? To simulate the Hilbert space?</p> <p>I'd like to eventually simulate the absorption or emission of a photon by a hydrogen atom. So at least three particles (two fermions, one boson). Let's generalize that to three particles with arbitrary spin, so I can look at three photons or three electrons if I want to.</p> <p>In order to do a numerical simulation I need to replace the continuous spacetime with a rectangular grid or lattice. I'd like to eventually get more precision, but let's start with just ten cells per dimension to begin with. So including time, I need ten thousand cells in a four dimensional lattice. `</p> <p>How many cells do I need to simulate the Hilbert space? and what goes in each cell? </p> <p>If I put restrictions on the shape of the wavefunction, does that help?</p>
g1513
[ -0.003685977542772889, 0.03247271478176117, 0.00756578054279089, -0.06037778779864311, -0.016344184055924416, -0.03536584973335266, -0.012712438590824604, 0.023490289226174355, -0.04473775625228882, -0.006075753364712, -0.007841872051358223, -0.01693333312869072, 0.0011834254255518317, 0.020522553473711014, -0.007575074210762978, 0.018944496288895607, 0.0323307178914547, 0.04435041546821594, -0.039134543389081955, -0.017507458105683327, 0.036794766783714294, 0.006203431636095047, -0.021907545626163483, -0.06948519498109818, -0.023652590811252594, 0.02993689849972725, 0.02270236611366272, -0.02844277396798134, 0.028930239379405975, 0.05622975900769234, -0.03243032097816467, 0.016561565920710564, -0.00100346514955163, -0.040996067225933075, -0.0073215654119849205, 0.026367126032710075, 0.01999904401600361, 0.00905731413513422, 0.003063475014641881, -0.030977550894021988, 0.012720871716737747, -0.0640745609998703, 0.021622097119688988, 0.009375198744237423, 0.04458296298980713, 0.007402337156236172, 0.007909676060080528, 0.011820889078080654, 0.025739090517163277, 0.029562614858150482, -0.023465903475880623, -0.0008355254540219903, 0.03147245943546295, -0.0012497433926910162, -0.0014095180667936802, 0.057224828749895096, -0.044124145060777664, -0.06629873067140579, 0.03405959531664848, 0.05329778417944908, 0.005347640719264746, 0.01613740250468254, -0.05210549011826515, -0.03087250143289566, 0.009138655848801136, 0.03109121136367321, -0.024855487048625946, -0.0027207941748201847, -0.028761016204953194, 0.021353168413043022, 0.02759196050465107, -0.02610989287495613, -0.019750721752643585, 0.016874652355909348, -0.02275746874511242, -0.00781609583646059, -0.04493754357099533, 0.019983218982815742, 0.029528029263019562, 0.014468938112258911, -0.06399193406105042, -0.05550113692879677, 0.02189345844089985, -0.02191096916794777, -0.012486835941672325, 0.020630165934562683, -0.041600849479436874, -0.02350589632987976, -0.011059235781431198, 0.03744916245341301, 0.03137199208140373, 0.03747578710317612, 0.07589813321828842, 0.06294960528612137, 0.019826615229249, -0.011247329413890839, -0.02168414182960987, 0.08056963235139847, 0.04305434226989746, 0.008690120652318, -0.014568958431482315, -0.037402063608169556, 0.033444758504629135, -0.057409562170505524, -0.060428768396377563, 0.01356144156306982, 0.029372556135058403, 0.041305091232061386, 0.05161655321717262, -0.004738638177514076, -0.04449697211384773, -0.036356110125780106, -0.04091402515769005, -0.018825124949216843, -0.08855663239955902, 0.009171237237751484, 0.032477423548698425, -0.03741094097495079, 0.01870948262512684, 0.03850013390183449, 0.002011963166296482, 0.03486974909901619, 0.10051041841506958, 0.00808495469391346, 0.03839065134525299, -0.013536027632653713, -0.022520339116454124, 0.07642753422260284, 0.03205330669879913, 0.04450616240501404, -0.01449477020651102, 0.03339191898703575, -0.07872378826141357, 0.03948824852705002, 0.02207214944064617, 0.042386896908283234, -0.01292023342102766, 0.018816452473402023, -0.019384989514946938, 0.009520718827843666, 0.0019170282175764441, -0.03034815564751625, -0.0015788839664310217, -0.03874341771006584, 0.01858365722000599, -0.07097160071134567, 0.004165989346802235, -0.03152237832546234, -0.018708841875195503, -0.03412459418177605, 0.024105075746774673, 0.04130697622895241, 0.026823049411177635, -0.005701924674212933, -0.0014883165713399649, 0.035914670675992966, 0.04652814194560051, -0.060493774712085724, 0.01618688926100731, -0.025522083044052124, 0.020207591354846954, 0.04077426344156265, -0.011869894340634346, 0.009566131047904491, -0.014546222053468227, -0.0016557350754737854, 0.06756997108459473, -0.07292108982801437, 0.007540369406342506, -0.02697552740573883, 0.04569521173834801, -0.011450499296188354, 0.01565496250987053, 0.033304546028375626, -0.051611997187137604, 0.030171852558851242, 0.01398316491395235, -0.04996627941727638, 0.008701721206307411, 0.01422086264938116, 0.053145136684179306, 0.028811711817979813, -0.036102741956710815, -0.03760363906621933, -0.015771349892020226, 0.024844586849212646, 0.017205461859703064, -0.0158950574696064, -0.0277731753885746, -0.00170669867657125, 0.011955352500081062, 0.004790326580405235, 0.04776782542467117, -0.02725924365222454, 0.0215916708111763, 0.030058370903134346, 0.048154205083847046, -0.010776851326227188, -0.036252524703741074, 0.015406861901283264, 0.028495091944932938, 0.03635454177856445, 0.0740216001868248, 0.06065134331583977, 0.08736744523048401, 0.0017308564856648445, -0.036767374724149704, 0.038078423589468, -0.01856408640742302, -0.011913544498383999, 0.011567660607397556, 0.013220683671534061, -0.014998199418187141, 0.050289738923311234, 0.024159444496035576, 0.021906442940235138, -0.07049214094877243, -0.022300679236650467, -0.008330601267516613, 0.09393532574176788, 0.0005316605675034225, -0.051191650331020355, 0.014468264766037464, -0.01816621422767639, -0.02041056379675865, 0.005948983132839203, 0.023201435804367065, 0.007343441713601351, -0.04049481451511383, 0.045797184109687805, -0.09322153031826019, -0.009827652014791965, -0.001724725472740829, -0.09871205687522888, -0.016678638756275177, 0.034661199897527695, -0.07986655086278915, -0.007419784553349018, 0.05459621548652649, 0.0001407012459821999, 0.061572425067424774, 0.038452547043561935, -0.020056530833244324, -0.009329737164080143, 0.029241815209388733, -0.06220582500100136, 0.015081262215971947, -0.035758960992097855, -0.03341880068182945, -0.027569685131311417, -0.044570062309503555, -0.026295047253370285, -0.013587324880063534, 0.02495831437408924, -0.04747529700398445, -0.04101474955677986, -0.019871892407536507, 0.0038232519291341305, -0.07497023791074753, -0.010541948489844799, -0.005361396353691816, -0.052969254553318024, -0.004469574429094791, 0.04375658929347992, 0.020777031779289246, 0.007802802603691816, 0.005553921218961477, -0.023064419627189636, 0.015081466175615788, 0.0032972735352814198, 0.02053762413561344, 0.055340688675642014, 0.06274450570344925, 0.009030045010149479, 0.006802100222557783, -0.03893154114484787, 0.0003222961677238345, -0.0007087007397785783, 0.013585308566689491, -0.04075479879975319, -0.060902055352926254, -0.0768573209643364, -0.07458910346031189, 0.043039046227931976, 0.05120259150862694, -0.03745124489068985, 0.0025322125293314457, 0.009429454803466797, -0.02067112736403942, -0.03418666496872902, -0.03745007514953613, 0.04750482365489006, -0.017516352236270905, 0.03534010797739029, -0.047462962567806244, -0.023030882701277733, 0.010792381130158901, -0.015586642548441887, -0.004150530323386192, 0.08667533844709396, -0.012966280803084373, 0.02586175687611103, 0.02862580493092537, -0.014423721469938755, 0.003024657256901264, -0.004058284685015678, -0.020180679857730865, -0.019951600581407547, 0.001077650231309235, 0.012801972217857838, 0.03929740563035011, 0.03037564642727375, -0.03990824148058891, 0.022976767271757126, -0.05695340782403946, -0.05800609290599823, -0.025074806064367294, -0.04786791652441025, 0.03536910563707352, -0.03709445521235466, -0.010070163756608963, -0.039423320442438126, 0.02263869345188141, -0.028925668448209763, 0.051947835832834244, 0.10384931415319443, 0.028132779523730278, -0.04390751197934151, -0.03305177763104439, -0.036184947937726974, -0.011679017916321754, 0.005582198966294527, 0.008266774006187916, 0.038230713456869125, 0.007920063100755215, -0.047936055809259415, -0.021176185458898544, -0.05059628188610077, 0.014604609459638596, -0.0712389349937439, 0.004985014908015728, -0.03358433023095131, 0.025733599439263344, -0.036281097680330276, -0.00277382112108171, -0.06545469164848328, -0.02355312369763851, 0.007486368529498577, -0.04016575217247009, -0.02171885035932064, -0.0027989947702735662, -0.0631355568766594, 0.005807900335639715, -0.024740850552916527, 0.027095267549157143, 0.006368305068463087, -0.004474331624805927, 0.03360418602824211, 0.05658910796046257, 0.028856554999947548, -0.002666311804205179, -0.06285451352596283, -0.014087648130953312, 0.01383617240935564, -0.030228054150938988, -0.010796565562486649, 0.046774592250585556, 0.030645154416561127, -0.0211135633289814, -0.004379503428936005, -0.02723880670964718, 0.04343661665916443, -0.05740461125969887, -0.026699962094426155, 0.02273213304579258, -0.007336931768804789, 0.008092197589576244, -0.03154657036066055, 0.02616797760128975, 0.009496220387518406, -0.07744916528463364, 0.007447594776749611, 0.03596194088459015, -0.027657296508550644, -0.00163935124874115, 0.04039657488465309, 0.06182342395186424, -0.00736354710534215, -0.045658472925424576, -0.0026019313372671604, 0.03175042197108269, -0.08447310328483582, -0.020647238940000534, -0.042868658900260925, -0.031630776822566986, -0.026218494400382042, -0.0024049540515989065, -0.029074039310216904, -0.038498520851135254, 0.04006899893283844, 0.02856474183499813, -0.03791099786758423, 0.022030185908079147, 0.0025708519387990236, 0.03460366651415825, -0.009468779899179935, 0.02378280647099018, -0.015377247706055641, 0.002885041292756796, 0.007474965415894985, -0.015191773883998394, -0.0038102976977825165, 0.019912123680114746, -0.0310272928327322, 0.021169502288103104, -0.02637970633804798, -0.02026044949889183, 0.01668573170900345, -0.026615338400006294, -0.015451635234057903, 0.014191037975251675, 0.04207003861665726, -0.046237729489803314, 0.0009790527401492, 0.018053356558084488, 0.0021079732105135918, 0.013266715221107006, -0.03491847217082977, -0.013886568136513233, -0.011452893726527691, 0.039460331201553345, 0.026637906208634377, -0.0069734943099319935, 0.07823865115642548, -0.0602928064763546, -0.039193328469991684, -0.058071319013834, -0.008111153729259968, 0.01153579168021679, -0.01836523599922657, 0.0299949049949646, 0.005239694379270077, 0.01109828520566225, 0.0033481817226856947, 0.03786078095436096, -0.016194386407732964, -0.09128038585186005, -0.04644954949617386, -0.030047612264752388, -0.020904479548335075, 0.07368938624858856, 0.009375731460750103, -0.05288877338171005, 0.006682506296783686, -0.02045583538711071, 0.0404948890209198, -0.01611454039812088, 0.037202138453722, 0.09395650029182434, 0.10617946833372116, -0.03132135421037674, 0.031525079160928726, -0.015376978553831577, -0.002258618362247944, -0.013030773028731346, -0.024699704721570015, -0.06618748605251312, 0.02217390015721321, 0.0026733162812888622, -0.002142759971320629, 0.057447951287031174, -0.03647400066256523, 0.029607601463794708, 0.0019190785242244601, 0.0009200643980875611, -0.03932011127471924, -0.021458188071846962, -0.034903623163700104, -0.008388150483369827, 0.027880746871232986, 0.022020187228918076, -0.0237231757491827, 0.07130841165781021, 0.09113585203886032, 0.026052096858620644, -0.016069160774350166, 0.03303210809826851, 0.018377674743533134, 0.025889955461025238, -0.024967001751065254, 0.0010503616649657488, -0.04613817110657692, 0.01509115844964981, 0.009625902399420738, 0.0036747960839420557, -0.016385596245527267, 0.01385645940899849, -0.06020078435540199, -0.026966094970703125, 0.043338339775800705, -0.0037229841109365225, -0.0042680553160607815, 0.0332953967154026, -0.04077925160527229, -0.0735577642917633, 0.030927879735827446, 0.00453681917861104, -0.01992976851761341, -0.0174892395734787, 0.04141005501151085, -0.007081962656229734, -0.005678783170878887, 0.013676322996616364, -0.04121372103691101, 0.013740843161940575, -0.0076705580577254295, -0.045651283115148544, 0.03862760215997696, -0.04608185589313507, -0.013786448165774345, 0.02572794444859028, 0.011180567555129528, 0.00911603681743145, -0.054198767989873886, 0.013460694812238216, 0.02446483075618744, -0.03624793142080307, -0.038304585963487625, -0.016135437414050102, 0.012323821894824505, 0.055927176028490067, 0.029062293469905853, -0.056201640516519547, 0.0011268907692283392, -0.05877671763300896, 0.047978900372982025, 0.05086725950241089, -0.04907118156552315, 0.07243666052818298, 0.018609827384352684, 0.014281737618148327, 0.02116214670240879, 0.005177633836865425, 0.044360775500535965, -0.023706378415226936, -0.0002307120885234326, -0.0050423648208379745, 0.009510952979326248, 0.0362716019153595, -0.05131229758262634, -0.03429742157459259, -0.05015510320663452, -0.008303675800561905, -0.024629484862089157, -0.000676511786878109, 0.07745762169361115, -0.004003793932497501, -0.033226240426301956, -0.0008435378549620509, 0.03368644788861275, 0.035271063446998596, -0.0023909397423267365, -0.0019085017265751958, -0.11887908726930618, -0.002878696657717228, 0.027750201523303986, -0.06129423901438713, 0.019797462970018387, 0.062083758413791656, 0.026685766875743866, 0.007260128855705261, -0.025265932083129883, -0.01961592584848404, 0.030046861618757248, 0.02880493365228176, 0.002941025421023369, 0.04109082370996475, 0.007106347940862179, -0.03992171213030815, 0.03476075455546379, 0.016107123345136642, 0.054310206323862076, 0.028202736750245094, -0.008641017600893974, 0.06931062787771225, 0.07857204973697662, 0.01725139282643795, 0.0011684923665598035, 0.060174550861120224, 0.0203336700797081, -0.026467066258192062, -0.021580196917057037, 0.002760295057669282, -0.0799330472946167, 0.00886805634945631, 0.03129434585571289, 0.02795284055173397, -0.00871363840997219, -0.038967348635196686, 0.011021214537322521, 0.017310695722699165, 0.040470194071531296, 0.01029486209154129, -0.025536339730024338, 0.02890198864042759, -0.000274049787549302, -0.03635390102863312, -0.05702492967247963, 0.04212453216314316, -0.028775835409760475, 0.0011958765098825097, -0.006658179685473442, 0.0027996685821563005, 0.06301505863666534, 0.013164760544896126, -0.07674837112426758, 0.06682321429252625, -0.015585698187351227, 0.029934167861938477, 0.025147439911961555, 0.041045840829610825, -0.003119982313364744, 0.0017664240440353751, -0.047866471111774445, 0.03898473456501961, 0.040467776358127594, -0.02107597328722477, 0.05205334350466728, 0.06798487156629562, -0.041644591838121414, 0.008895950391888618, -0.09160082787275314, 0.011143852025270462, 0.0007589994929730892, -0.04257000982761383, 0.01776970736682415, -0.07515560835599899, -0.026723986491560936, 0.005188551731407642, 0.017325256019830704, -0.010670891031622887, -0.028688017278909683, 0.024563858285546303, 0.007187645882368088, -0.03187616541981697, -0.007851120084524155, 0.09419845789670944, 0.010828712955117226, -0.0072248815558850765, 0.03921053558588028, 0.03743932768702507, 0.030682595446705818, -0.07210732996463776, -0.030795827507972717, -0.054898157715797424, 0.04370689019560814, -0.013674620538949966, -0.0006655469187535346, -0.01010042242705822, -0.03261030465364456, -0.024097036570310593, -0.06529455631971359, -0.060363516211509705, -0.04701829329133034, 0.019813954830169678, 0.03029739297926426, -0.0032113250344991684, -0.00018893476226367056, 0.0017813610611483455, -0.007079168688505888, -0.03543026000261307, 0.02488953247666359, -0.03875116631388664, 0.013376055285334587, 0.004588425625115633, -0.01607431471347809, -0.006350431591272354, 0.08560826629400253, 0.010707990266382694, -0.031190358102321625, 0.017992673441767693, -0.01824439875781536, -0.029661530628800392, 0.017975198104977608, 0.000893083808477968, -0.001364162308163941, 0.05472948029637337, -0.03256462141871452, 0.021115997806191444, -0.004366620443761349, 0.005814296659082174, -0.03086913377046585, -0.006060698069632053, -0.03269001096487045, 0.024346712976694107, 0.06306314468383789, 0.0921926498413086, -0.032409995794296265, 0.06642381846904755, 0.03856992349028587, -0.007995889522135258, -0.020816119387745857, 0.03665729984641075, -0.010115627199411392, 0.015437291003763676, -0.040325816720724106, -0.027782855555415154, -0.05512356385588646, 0.03681621327996254, -0.029042934998869896, -0.00005844572660862468, 0.033692389726638794, -0.019886339083313942, 0.00239915051497519, 0.051622532308101654, -0.029036913067102432, -0.02455199509859085, 0.013991402462124825, 0.05357644334435463, -0.07746298611164093, -0.02347194030880928, -0.03709833323955536, -0.02501611039042473, 0.018931256607174873, 0.03251774236559868, -0.012409658171236515, -0.009514063596725464, 0.008065563626587391, 0.009387419559061527, 0.03286243975162506, -0.01286241039633751, 0.016202345490455627, -0.02544003166258335, 0.006529160309582949, 0.029156722128391266, -0.005044339224696159, -0.027477536350488663, 0.007974017411470413, -0.015513872727751732, 0.018370425328612328, 0.004793030209839344, -0.028166741132736206, -0.01136529166251421, -0.02316814847290516, -0.013338305987417698, 0.019952984526753426, -0.05966615304350853, 0.05695348232984543, 0.10623820871114731, 0.0044281273148953915, -0.05128958076238632, 0.0023172390647232533, 0.02281978726387024, 0.06124954670667648, 0.0795392170548439, -0.08763790130615234, 0.02296534553170204, 0.040954455733299255, 0.0301950816065073, -0.013688530772924423, 0.00573726836591959, 0.004570625722408295, 0.017676927149295807, 0.03474390506744385, -0.021378813311457634, -0.009135426953434944, 0.02822844311594963, 0.015455766580998898 ]
<p>I wanted to know why there is a hole in the ball (basketball, volleyball, handball) to fill the ball with air. Why can't the ball come with filled in air and fully sealed so that there is no loss of air?</p>
g1514
[ 0.05734784156084061, 0.026002436876296997, 0.0037597985938191414, 0.04352257028222084, -0.036850400269031525, 0.07811412215232849, 0.05108187720179558, 0.03068884275853634, -0.012357196770608425, -0.009985096752643585, -0.00046672954340465367, -0.006700187921524048, 0.01061301026493311, 0.0017292239936068654, -0.010479453951120377, -0.017821364104747772, -0.050543736666440964, -0.060312192887067795, 0.004741236567497253, -0.022832369431853294, 0.010424894280731678, 0.01734112575650215, 0.0065360101871192455, -0.015518279746174812, -0.053650449961423874, -0.007617723196744919, 0.023095659911632538, -0.07644293457269669, -0.010952750220894814, -0.022460144013166428, 0.056818488985300064, 0.031299103051424026, 0.007785223890095949, -0.03731909021735191, 0.007007668726146221, 0.00012589538528118283, 0.01462866086512804, -0.04662107303738594, -0.040738027542829514, -0.021948538720607758, -0.019746743142604828, -0.0023213678505271673, -0.016989072784781456, 0.033267006278038025, -0.022894995287060738, -0.00761311175301671, -0.013019289821386337, 0.051030825823545456, 0.005937275942414999, -0.032420482486486435, -0.005605421029031277, 0.005350652150809765, -0.058764826506376266, -0.01778838410973549, -0.007586671970784664, -0.0032332453411072493, 0.017702411860227585, 0.021318934857845306, 0.04842018708586693, -0.019842108711600304, -0.05846071243286133, 0.03665575757622719, -0.05503188818693161, 0.05800776183605194, 0.03512485697865486, -0.009332502260804176, -0.0360218845307827, -0.04475628584623337, 0.042145200073719025, 0.051079005002975464, 0.05511414632201195, -0.04279347509145737, 0.008265134878456593, -0.01816014014184475, -0.0029944938141852617, -0.0022226031869649887, -0.01563008688390255, 0.08232136070728302, 0.05032092332839966, -0.010516141541302204, 0.031164372339844704, 0.048436056822538376, 0.0391702726483345, -0.020565737038850784, 0.048610467463731766, -0.00861520878970623, -0.06942872703075409, -0.07874663174152374, -0.03397069498896599, -0.02062683366239071, 0.012055360712110996, 0.007548714522272348, 0.08138604462146759, 0.04286099597811699, -0.0405992791056633, 0.0002165092882933095, -0.06504229456186295, 0.06930853426456451, -0.032280486077070236, -0.005326863843947649, 0.056069761514663696, -0.05419616401195526, 0.05117521807551384, 0.001652141218073666, 0.011971171014010906, 0.019694024696946144, 0.013046196661889553, 0.04886743053793907, 0.004974678624421358, 0.0007042900542728603, -0.009653742425143719, 0.013366028666496277, -0.03802209347486496, -0.008316043764352798, 0.007914860732853413, 0.026602914556860924, 0.104422926902771, 0.03430454060435295, 0.03545593097805977, 0.08141940832138062, -0.02218368463218212, 0.008783329278230667, -0.007849829271435738, -0.04218588024377823, -0.02348460629582405, -0.0042059035040438175, 0.01193966343998909, -0.03187383711338043, -0.016917791217565536, -0.05435879901051521, -0.020191865041851997, -0.0190938301384449, -0.017137905582785606, -0.019151143729686737, 0.005667351186275482, 0.006909361574798822, -0.03063846193253994, 0.03528369590640068, 0.011488523334264755, 0.030628997832536697, 0.024251097813248634, 0.018761046230793, 0.012879619374871254, 0.026393303647637367, -0.02614845708012581, 0.014831400476396084, 0.04686347767710686, -0.019619449973106384, -0.033337414264678955, -0.010895810090005398, 0.026219099760055542, 0.04934864491224289, -0.019633391872048378, -0.0013500552158802748, -0.007884767837822437, -0.005756886675953865, 0.008244827389717102, -0.02478916384279728, 0.02753913588821888, 0.03260888531804085, 0.04765372350811958, 0.06508738547563553, 0.007188747636973858, 0.0885206088423729, -0.11052406579256058, 0.07720895856618881, -0.004554782994091511, -0.050473347306251526, -0.04038284718990326, -0.04027600958943367, -0.05781133845448494, -0.011807793751358986, -0.028145669028162956, 0.09699288755655289, 0.008212429471313953, 0.024927537888288498, 0.03026367351412773, -0.023833142593503, 0.03802475705742836, -0.03865208476781845, -0.04966434836387634, -0.03535286709666252, 0.00882493145763874, -0.06156981736421585, -0.027924157679080963, 0.03685510531067848, 0.04243313521146774, -0.04123231768608093, -0.02414170280098915, -0.0277608260512352, 0.04871877282857895, -0.04117972403764725, -0.005932650528848171, 0.02594994194805622, -0.002031833166256547, 0.053803879767656326, 0.09600236266851425, -0.023231035098433495, -0.0960298404097557, 0.03602328896522522, -0.002855085302144289, -0.01561339944601059, 0.057132117450237274, -0.034547802060842514, -0.00854330975562334, -0.016700129956007004, -0.021785732358694077, 0.0825430303812027, 0.005023539531975985, 0.06649228930473328, 0.0072532822377979755, -0.023549702018499374, 0.07098143547773361, 0.055278025567531586, 0.06812475621700287, 0.010052388533949852, -0.03988439217209816, 0.008785117417573929, -0.043726906180381775, -0.04017481580376625, 0.01398997288197279, -0.022591950371861458, -0.033135753124952316, -0.046604715287685394, -0.0547868013381958, 0.006749178282916546, -0.013206737115979195, 0.017484987154603004, -0.047895852476358414, 0.017549600452184677, -0.05263712257146835, -0.013822002336382866, 0.011265167035162449, 0.06220564618706703, 0.03916123881936073, 0.014041334390640259, -0.0015094602713361382, 0.06552186608314514, 0.048757750540971756, -0.014822571538388729, -0.02116859145462513, -0.003075697459280491, 0.01153557375073433, -0.021078111603856087, 0.04491030424833298, -0.05914567783474922, -0.006259057205170393, -0.036330558359622955, 0.02822043187916279, 0.05805839225649834, -0.02671230398118496, 0.006238861009478569, -0.007679179310798645, -0.0016986201517283916, -0.02756151743233204, -0.05202968418598175, 0.0017279010498896241, 0.005014133173972368, 0.0017486534779891372, -0.1019698902964592, -0.0599568635225296, -0.05140737071633339, -0.011218694038689137, -0.016508078202605247, -0.03134257718920708, 0.03709119185805321, -0.011577784083783627, -0.02952134609222412, -0.0042694080621004105, 0.03162664547562599, -0.014781995676457882, 0.038198478519916534, 0.03150537610054016, 0.02341979742050171, -0.005183837376534939, -0.03203367069363594, -0.004205574281513691, -0.015485214069485664, 0.015938635915517807, -0.03926185891032219, -0.042360611259937286, 0.0488654263317585, -0.06916674971580505, 0.01095904316753149, 0.03246430307626724, -0.023186352103948593, -0.048304483294487, 0.01624731719493866, -0.040993161499500275, 0.002320653758943081, 0.00041674869135022163, 0.043852824717760086, -0.014874660409986973, -0.009445302188396454, 0.02670913003385067, 0.0349743478000164, 0.004277635365724564, 0.003927932120859623, -0.053265709429979324, 0.046694375574588776, -0.0255732499063015, -0.009319422766566277, -0.020960310474038124, -0.006684249732643366, 0.0241914764046669, 0.06674956530332565, -0.018914317712187767, 0.017626408487558365, -0.03682135418057442, 0.03487376123666763, 0.033074989914894104, 0.03528371453285217, -0.004248084966093302, 0.021016567945480347, -0.09343843907117844, 0.013906111009418964, 0.0015888279303908348, 0.020463727414608, 0.011096559464931488, -0.004442176315933466, -0.0000883375687408261, 0.005348440259695053, 0.03157922998070717, -0.00834632944315672, 0.021523235365748405, -0.01210820209234953, 0.015887336805462837, 0.006418971810489893, -0.003755084704607725, -0.07611802220344543, -0.01229611225426197, 0.006709232460707426, -0.018529007211327553, -0.027477771043777466, -0.03679855167865753, 0.002963984152302146, -0.05340082198381424, -0.05214732512831688, 0.025502903386950493, -0.05474211275577545, -0.009705191478133202, -0.00003237871715100482, 0.0067397854290902615, 0.003995839040726423, -0.008508507162332535, -0.013396057300269604, 0.06228480860590935, -0.01796376146376133, 0.008792459964752197, -0.037170909345149994, 0.07895724475383759, 0.033129483461380005, 0.014886297285556793, -0.04384681209921837, -0.013421256095170975, 0.003200993174687028, 0.035140395164489746, 0.0034328026231378317, 0.010560999624431133, 0.015270247124135494, 0.030944490805268288, -0.03500719740986824, -0.023099930956959724, 0.013301927596330643, -0.006960940081626177, 0.0011075761867687106, 0.031060298904776573, -0.03794202208518982, -0.04242613539099693, 0.008962716907262802, -0.006607661955058575, 0.019137023016810417, -0.05317308381199837, 0.050772249698638916, 0.07355146110057831, -0.07144305109977722, 0.0007652773056179285, 0.015117624774575233, -0.081963449716568, -0.05055717006325722, 0.06840609759092331, -0.027491411194205284, -0.02885538339614868, 0.03520592302083969, 0.030815530568361282, 0.02168760821223259, -0.00004731838635052554, 0.010559242218732834, -0.002303927205502987, -0.06654604524374008, 0.015861177816987038, 0.01413069199770689, 0.015409518033266068, 0.03347189724445343, 0.004294845275580883, -0.014212413690984249, -0.04355208948254585, -0.025410007685422897, -0.029806016013026237, 0.014259238727390766, 0.05020696297287941, 0.04329672083258629, 0.002166695659980178, -0.020197957754135132, 0.03440997004508972, 0.008514690212905407, 0.061970870941877365, -0.02124827727675438, 0.008520599454641342, -0.01926269941031933, -0.019050223752856255, 0.06450365483760834, -0.038044266402721405, -0.057201582938432693, 0.0048533170484006405, -0.0025797553826123476, -0.009365077130496502, 0.033402957022190094, 0.029766982421278954, -0.013306341134011745, -0.008760170079767704, -0.009630681946873665, 0.0024707315023988485, 0.003563195001333952, 0.001578167313709855, 0.07429738342761993, -0.005838034674525261, -0.05841176584362984, 0.01951155625283718, -0.004428255837410688, -0.008618566207587719, 0.01912645809352398, -0.03117741271853447, -0.06617555767297745, 0.022908274084329605, -0.030599504709243774, -0.05118517950177193, 0.016266794875264168, 0.01378956064581871, 0.02565285563468933, 0.03976645693182945, -0.007850362919270992, 0.026074053719639778, -0.04211905226111412, 0.01601819507777691, -0.009900226257741451, -0.04968004301190376, -0.0038475990295410156, -0.05252659320831299, -0.038889896124601364, -0.013976079411804676, 0.03948168084025383, 0.04182296618819237, -0.001896294066682458, -0.022759603336453438, -0.008693011477589607, -0.022547854110598564, -0.03375845029950142, 0.00015901905135251582, 0.0195242278277874, -0.027522144839167595, -0.010040918365120888, 0.009982690215110779, 0.033137816935777664, 0.05668630823493004, -0.0025577922351658344, 0.059973910450935364, -0.02905048429965973, 0.0034255378413945436, -0.04645777866244316, 0.012492488138377666, 0.078671395778656, -0.042279742658138275, 0.07243894785642624, -0.003383704461157322, 0.011503264307975769, -0.05871135741472244, 0.0019113090820610523, 0.12204812467098236, -0.0492517426609993, -0.0263653676956892, 0.012447284534573555, -0.03906027972698212, 0.08484143018722534, -0.03619640693068504, -0.07424339652061462, -0.021060839295387268, 0.006184796337038279, 0.0256817489862442, -0.0009992477716878057, 0.03546138480305672, 0.016465947031974792, -0.014519775286316872, 0.0017079660901799798, -0.02011682093143463, -0.007316106464713812, 0.035423509776592255, -0.06070975586771965, -0.007282393518835306, -0.025805842131376266, -0.04468689486384392, -0.10705974698066711, 0.0014101077103987336, 0.024042906239628792, 0.0010819790186360478, 0.021798795089125633, -0.04152941703796387, 0.03372257575392723, 0.0030405211728066206, -0.0016163643449544907, -0.01325216330587864, -0.03884763643145561, 0.019399933516979218, 0.010148986242711544, 0.013688195496797562, -0.0032694104593247175, -0.0020000210497528315, -0.021138232201337814, -0.0036865295842289925, 0.0548979714512825, -0.00018562798504717648, -0.016895389184355736, 0.050508223474025726, 0.02243240736424923, 0.00040782050928100944, 0.05231386050581932, -0.04087873548269272, -0.048131655901670456, 0.01884768344461918, 0.033026017248630524, -0.03253420814871788, -0.00770164979621768, 0.03144160285592079, -0.031221216544508934, -0.04899745061993599, -0.02398233488202095, -0.03294825926423073, -0.02927253767848015, 0.06318280845880508, 0.0012109209783375263, -0.012946568429470062, -0.013596361503005028, -0.010757206939160824, 0.0729449912905693, 0.04702715203166008, -0.0299614779651165, -0.0068769874051213264, -0.010525621473789215, 0.03798617795109749, -0.041330043226480484, -0.00027395327924750745, 0.04688410088419914, -0.052644651383161545, 0.0019851180259138346, -0.017449619248509407, 0.0028623922262340784, 0.0280766598880291, 0.020384477451443672, -0.003728217678144574, -0.041545405983924866, 0.006363308057188988, 0.011501922272145748, -0.04483375325798988, 0.008671719580888748, 0.01743306964635849, 0.03337531164288521, -0.010634806007146835, -0.002250749384984374, 0.03449802100658417, -0.07209460437297821, -0.03075472265481949, -0.008574938401579857, 0.0489610992372036, 0.03349435329437256, 0.029435204342007637, 0.002572490833699703, 0.03404511511325836, -0.019497094675898552, -0.002399839460849762, 0.0012179387267678976, 0.0543927364051342, -0.0024445175658911467, 0.04202532768249512, -0.00513409823179245, 0.04345397278666496, 0.03757361322641373, -0.039897624403238297, -0.02297424152493477, 0.0017588409828022122, 0.011311828158795834, -0.01467014942318201, 0.024885881692171097, 0.020731600001454353, -0.07520151883363724, 0.001246259780600667, -0.027814188972115517, 0.013414817862212658, 0.02630356140434742, -0.0042466064915061, -0.012728557921946049, 0.025998534634709358, 0.015278924256563187, -0.018595097586512566, -0.026577474549412727, -0.010414659976959229, 0.01703687198460102, 0.020543072372674942, -0.02923167496919632, 0.007881896570324898, -0.006175527349114418, -0.04249808192253113, 0.028616728261113167, -0.0012785078724846244, 0.003394306870177388, -0.008305962197482586, -0.049360066652297974, 0.037589624524116516, -0.009079706855118275, 0.026535741984844208, -0.043867919594049454, -0.053367625921964645, 0.03028935007750988, -0.01404428668320179, 0.026900235563516617, 0.026287928223609924, -0.03414404019713402, -0.08834927529096603, 0.03849481791257858, 0.011559260077774525, -0.04169381782412529, -0.01584003120660782, -0.008470986969769001, -0.046289097517728806, 0.011058635078370571, -0.02225179597735405, 0.06139542907476425, -0.02610786259174347, 0.014303191564977169, 0.04974651336669922, -0.0012235849862918258, -0.026498127728700638, 0.04114207252860069, 0.026263512670993805, 0.08173613250255585, -0.027818402275443077, 0.02133908122777939, 0.02388458512723446, -0.025151772424578667, -0.02515912428498268, 0.0054550678469240665, -0.057930316776037216, -0.025910621508955956, -0.05389546975493431, -0.049474261701107025, -0.011805745773017406, 0.010934585705399513, -0.03744128346443176, -0.06808463484048843, 0.041131921112537384, -0.015910465270280838, 0.025437701493501663, -0.007943389937281609, 0.025081757456064224, 0.04463304206728935, -0.014439263381063938, 0.010619577951729298, 0.09720184653997421, -0.04127000644803047, 0.035214103758335114, 0.0051409052684903145, 0.03873820602893829, -0.021222688257694244, 0.007569378241896629, 0.024779649451375008, -0.035860154777765274, 0.03433874249458313, -0.012481417506933212, 0.08825431764125824, 0.009871336631476879, -0.04355228692293167, -0.08597417920827866, 0.0802759975194931, -0.03384161368012428, 0.003982793539762497, 0.003470291383564472, 0.015670079737901688, 0.005554376635700464, 0.004821436945348978, 0.07455296814441681, -0.03432345390319824, 0.03698623552918434, 0.038367703557014465, 0.06813975423574448, 0.04084646701812744, -0.0009804326109588146, -0.004707195330411196, 0.04888065159320831, -0.007400082424283028, -0.05651673302054405, -0.07761918008327484, -0.03315485268831253, -0.026693807914853096, -0.025849509984254837, -0.03291405364871025, -0.012495897710323334, 0.02347489632666111, -0.01799989677965641, 0.04107717052102089, -0.044527214020490646, 0.048564836382865906, 0.010443388484418392, -0.042424727231264114, 0.02480883151292801, -0.03604092076420784, 0.0013678079703822732, 0.030751565471291542, -0.02182035706937313, 0.031062796711921692, 0.024945702403783798, -0.062081675976514816, -0.03705086186528206, -0.03687654063105583, -0.027362432330846786, 0.010825400240719318, -0.017040133476257324, -0.006247917655855417, -0.01949024386703968, 0.04093027859926224, -0.032673005014657974, 0.004918343853205442, 0.0030637753661721945, -0.07818921655416489, 0.057639047503471375, 0.026738611981272697, 0.0015911012887954712, -0.030040191486477852, 0.020032430067658424, 0.033957432955503464, -0.03688528388738632, 0.025302259251475334, -0.00033379081287421286, 0.008571267127990723, 0.05787228047847748, -0.0657460168004036, 0.009295282885432243, -0.06301020830869675, -0.05460561439394951, 0.04461323469877243, 0.06451800465583801, 0.025830574333667755, 0.0204971581697464, -0.03322719410061836, -0.057583827525377274, 0.0590205192565918, 0.05565759167075157, -0.012077265419065952, -0.015531330369412899, 0.04339950159192085, -0.004336555954068899, -0.05773906409740448, 0.029175089672207832, 0.04235399514436722, 0.01859784685075283, 0.0005746764945797622, 0.018018310889601707, 0.020269354805350304, -0.0014284899225458503, -0.002666708780452609 ]
<p>I'm wondering if there is a textbook that describes the handiwork of a particle physics analysis. There are a bunch of books about theory, about the experimental aspects like detectors, and about statistical methods, but I haven't seen one that focused on the actual work of an analyzer.</p> <p>I mean stuff like:</p> <ul> <li>How to conduct a search vs. a measurement</li> <li>What backgrounds to consider for a final state, and how to model them</li> <li>What distributions to look at -- pT of various objects or MET are obvious, but there are things like transverse masses, $\cos \theta^*$, aplanarity, the Florida variable (seriously), or ptBalance, that you first have to know about</li> <li>How to choose signal regions, sidebands</li> <li>How to determine systematic errors concretely</li> <li>How to perform a cutflow</li> <li>How to do tag-and-probe</li> <li>How to perform a multivariate analysis, and how to choose btw. techniques</li> <li>How to set limits, and how to perform combinations</li> </ul> <p>Most of this stuff is covered in various books, but mostly from a different perspective. For example, its nice to know how to solve an integral with Monte Carlo methods, and what the factorization theorem does. But for someone working on an analysis its more useful to know what the main differences between MC generators are, and how to deal with negative event weights in various situations. Similarly, there are a couple of textbooks about statistics for high energy physics, but those I've found tend to focus on derivations, instead of practical issues of the analysis.</p> <p>Does anyone know of a book that fits my description?</p> <p><em>(Note I don't believe this fits very well under the current <a href="http://meta.physics.stackexchange.com/questions/4697/are-resource-recommendations-allowed">book policy</a>. Resource recommendation questions tend to be fairly broad, and thus the answers have to be very descriptive. In this case, the question is already descriptive, so a brief answer would also be OK, even a negative answer (a la "I've been a expert for 20 years and can say for certain that such a book doesn't exist").)</em></p>
g1515
[ 0.04645068198442459, 0.013148055411875248, 0.03846707567572594, -0.02308865264058113, 0.03326090797781944, -0.04400813207030296, 0.00007800867024343461, 0.06086459755897522, -0.009639013558626175, 0.021893590688705444, 0.04858529567718506, -0.036006245762109756, 0.03878972679376602, -0.022617993876338005, -0.048662472516298294, -0.042926039546728134, 0.007654211018234491, 0.0010160228703171015, 0.0015455251559615135, 0.05995143949985504, 0.02417934313416481, 0.06585375219583511, -0.028000395745038986, -0.025232071056962013, -0.021955672651529312, 0.005384107120335102, -0.11985030770301819, -0.027163395658135414, 0.005083049181848764, -0.018291212618350983, -0.02966039441525936, -0.030606182292103767, -0.0016038583125919104, -0.04943399503827095, -0.018131371587514877, -0.07523351907730103, 0.0556550957262516, 0.025561358779668808, 0.038547247648239136, 0.04564576968550682, 0.009295308031141758, 0.006285510025918484, 0.006757135968655348, -0.04338007792830467, -0.008081372827291489, -0.016760170459747314, -0.024218803271651268, 0.043325427919626236, -0.04298422485589981, 0.04754731431603432, -0.02593955770134926, 0.0035698646679520607, 0.04486944153904915, 0.023514045402407646, 0.0717722624540329, -0.018993202596902847, 0.03194547817111015, 0.0017427896382287145, 0.11018172651529312, -0.04146725311875343, 0.03482486680150032, 0.037443067878484726, -0.07549946755170822, -0.03180704265832901, 0.008590469136834145, -0.055869463831186295, 0.01044486928731203, -0.0464278906583786, -0.020386481657624245, 0.028902269899845123, 0.013389996252954006, -0.023592472076416016, -0.022688664495944977, -0.0028823697939515114, -0.0018435105448588729, -0.03066335804760456, -0.02565894089639187, -0.021365221589803696, 0.0018369491444900632, 0.03377123922109604, -0.05063435807824135, 0.009466132149100304, 0.036541469395160675, -0.0121967988088727, 0.08351453393697739, 0.009678386151790619, -0.004713262896984816, -0.005001433659344912, -0.05696592852473259, -0.034473203122615814, -0.027485249564051628, 0.06190359592437744, 0.05670035257935524, -0.02227441594004631, -0.06073812395334244, -0.026706308126449585, -0.021573323756456375, 0.004382249899208546, -0.0013807888608425856, 0.02772849053144455, -0.013438357040286064, 0.01812799461185932, -0.009782200679183006, 0.01898849755525589, -0.016956787556409836, -0.01051937323063612, 0.003019202733412385, 0.011016445234417915, -0.003526092739775777, -0.009782601147890091, -0.05416681244969368, 0.019475096836686134, 0.002411646069958806, -0.002303974935784936, -0.07393168658018112, -0.028831826522946358, 0.05768526345491409, 0.006410921923816204, 0.018093591555953026, 0.040578607469797134, 0.05463280528783798, 0.04919571056962013, -0.03697055205702782, 0.0015765498392283916, -0.07454841583967209, -0.008126739412546158, 0.020564455538988113, 0.013930722139775753, -0.019967157393693924, 0.0037377167027443647, 0.03834589943289757, -0.045084111392498016, -0.031343549489974976, 0.03407583385705948, -0.011884483508765697, 0.060583557933568954, -0.0018448357004672289, 0.05905859172344208, 0.05621936544775963, 0.0016015515429899096, -0.011529279872775078, -0.012915365397930145, -0.035811979323625565, -0.017601417377591133, 0.02328449860215187, 0.0997927188873291, -0.04189271479845047, 0.02321365661919117, -0.01646573282778263, 0.0520419217646122, -0.01320992223918438, 0.024347346276044846, -0.024062274023890495, -0.04254760593175888, 0.04017885401844978, 0.040655165910720825, 0.026812519878149033, 0.005546554457396269, 0.024232670664787292, -0.01706079952418804, 0.07215362787246704, -0.020856553688645363, -0.04294995591044426, 0.04469316825270653, -0.0391174741089344, -0.004355288576334715, -0.015853162854909897, -0.05677960440516472, 0.04113759100437164, -0.03187815472483635, 0.007254065480083227, -0.008310598321259022, 0.047556955367326736, 0.06257717311382294, -0.03277421370148659, 0.05789083242416382, 0.028807364404201508, -0.010447300039231777, 0.016092319041490555, 0.05439576134085655, -0.010743530467152596, 0.004362707957625389, 0.018610049039125443, -0.025859646499156952, -0.03143955394625664, -0.02618652954697609, -0.0602492094039917, 0.009377201087772846, 0.033191680908203125, -0.02209898829460144, -0.017785362899303436, 0.013365894556045532, 0.008196583017706871, 0.006220508366823196, 0.032998621463775635, -0.01605825498700142, -0.016720609739422798, -0.042754217982292175, -0.012353415600955486, -0.00637015700340271, 0.01348666101694107, 0.023637602105736732, 0.022076589986681938, 0.04988720268011093, 0.04068578779697418, 0.017063405364751816, 0.025146787986159325, -0.012407303787767887, -0.0391613207757473, -0.01521249394863844, 0.021592359989881516, -0.008255240507423878, 0.05564981326460838, 0.0073350779712200165, 0.008468610234558582, -0.007804769556969404, -0.08984902501106262, 0.019026096910238266, 0.0076757557690143585, -0.0038932249881327152, -0.08911854028701782, -0.03412066400051117, -0.04222904145717621, 0.05552895739674568, -0.03469334542751312, 0.022100169211626053, -0.03862917423248291, 0.00440875394269824, -0.02324734255671501, 0.012762283906340599, -0.06003769114613533, 0.025923658162355423, 0.005885672755539417, -0.02158159576356411, -0.006187146995216608, -0.03601471334695816, -0.005761104170233011, -0.06418967247009277, 0.03899484872817993, 0.0117957117035985, -0.019039608538150787, 0.0027487415354698896, -0.013361413031816483, -0.009027833119034767, 0.013001754879951477, -0.041299376636743546, 0.067036472260952, 0.01896136812865734, -0.06317359209060669, -0.029898153617978096, -0.0021070698276162148, -0.009561960585415363, 0.036204151809215546, -0.04153639078140259, 0.025451961904764175, -0.024939807131886482, 0.006886347196996212, 0.022781075909733772, -0.024112023413181305, -0.026815805584192276, 0.01650184579193592, -0.02988528460264206, -0.034108761698007584, 0.038061533123254776, 0.02164202369749546, 0.005171892698854208, -0.059520870447158813, 0.05340747535228729, -0.04174917936325073, -0.014774341136217117, 0.00748471962288022, -0.01884661614894867, 0.005837585311383009, -0.027322951704263687, 0.0545002743601799, 0.04982593655586243, 0.012432669289410114, -0.012158031575381756, 0.04646198824048042, -0.04688388481736183, 0.008947650901973248, -0.0544448159635067, 0.028256313875317574, 0.027965908870100975, 0.002636004239320755, -0.013340492732822895, -0.018623294308781624, -0.09752447158098221, -0.023248475044965744, -0.027669284492731094, 0.028271794319152832, -0.017873764038085938, -0.005383830517530441, 0.01213220413774252, -0.029308117926120758, 0.020454825833439827, 0.048693396151065826, -0.04092341288924217, -0.04739832878112793, 0.01390861812978983, 0.007950514554977417, -0.009432693012058735, 0.020098665729165077, 0.016985313966870308, 0.04353521391749382, 0.052831560373306274, -0.021011382341384888, -0.041425690054893494, -0.059413690119981766, 0.0007250570924952626, -0.04070562124252319, 0.012776096351444721, 0.0019026299705728889, 0.03377046436071396, 0.027450669556856155, 0.0019659108947962523, 0.014563610777258873, -0.009659336879849434, -0.0367322638630867, -0.027439333498477936, 0.01580451801419258, 0.016918284818530083, 0.1289011836051941, -0.053915344178676605, 0.00012319587403908372, -0.03645296394824982, -0.020353857427835464, -0.011291206814348698, -0.043870437890291214, -0.021163268014788628, 0.025653764605522156, -0.07967149466276169, 0.01945384219288826, 0.012945120222866535, -0.014505712315440178, -0.046169981360435486, 0.010640868917107582, -0.03548448160290718, 0.030998555943369865, -0.0059623257257044315, 0.03645031899213791, -0.026231858879327774, -0.016548894345760345, 0.0274202898144722, -0.012060163542628288, 0.0051338402554392815, -0.012916379608213902, 0.00779722910374403, 0.03746182098984718, -0.025355808436870575, 0.05264676734805107, 0.030287131667137146, 0.0030029546469449997, 0.00247272034175694, -0.03410685807466507, -0.008928557857871056, 0.04674755781888962, 0.022989856079220772, 0.03140580654144287, 0.010647338815033436, -0.040436893701553345, -0.009393799118697643, -0.0024565202184021473, 0.0032285451889038086, -0.03595584258437157, 0.045318424701690674, -0.016738614067435265, 0.003791708266362548, -0.0015579377068206668, -0.020969469100236893, 0.028416622430086136, 0.044484276324510574, -0.052033960819244385, 0.022560415789484978, -0.06442748010158539, -0.06368137896060944, 0.017032556235790253, 0.0182048287242651, 0.012211010791361332, -0.026712484657764435, 0.007603942416608334, 0.022381780669093132, 0.00961705856025219, -0.0015940758166834712, 0.06736373901367188, -0.0076675619930028915, -0.04959908127784729, 0.05761987343430519, 0.011788194999098778, -0.005817831959575415, 0.025563227012753487, -0.07239841669797897, -0.05830223113298416, -0.00245465780608356, 0.057377614080905914, -0.043343640863895416, 0.020961327478289604, -0.01997167244553566, 0.03492528945207596, 0.06969279050827026, -0.06433930993080139, 0.009486543014645576, 0.036367081105709076, -0.02633104845881462, 0.007612388115376234, 0.033363256603479385, 0.023130906745791435, -0.00752969179302454, -0.06754572689533234, -0.014060216024518013, -0.01916639693081379, 0.019101114943623543, 0.03442620858550072, -0.01630527898669243, -0.041783176362514496, -0.011271674185991287, -0.026296930387616158, -0.0027706134133040905, 0.0608678013086319, 0.01944095268845558, -0.028963204473257065, -0.013702670112252235, 0.012711379677057266, -0.008269302546977997, -0.003292257897555828, 0.044697973877191544, 0.04280306026339531, 0.008148830384016037, -0.04422759264707565, -0.018388396129012108, 0.03873612731695175, -0.02807265892624855, 0.01555514894425869, -0.01419367827475071, -0.036402903497219086, -0.035495366901159286, -0.041818272322416306, 0.020819349214434624, 0.025529539212584496, 0.014380719512701035, 0.05906748026609421, 0.018623223528265953, 0.047557197511196136, 0.0932023897767067, -0.039598576724529266, 0.04668831452727318, 0.005650637671351433, 0.0003862332087010145, -0.0357959121465683, 0.0006459600990638137, 0.018631212413311005, 0.005536053329706192, -0.07648802548646927, -0.015261677093803883, -0.008046362549066544, -0.0010051550343632698, 0.032762620598077774, 0.012033073231577873, 0.03772137314081192, -0.01584775745868683, 0.02346595749258995, -0.019542859867215157, -0.01794840209186077, -0.005366600584238768, -0.058836955577135086, 0.021115649491548538, -0.040110066533088684, -0.003889691084623337, -0.06258881092071533, -0.05843159183859825, -0.027484696358442307, 0.03501323238015175, 0.032448332756757736, -0.041024100035429, 0.056726764887571335, -0.056623250246047974, -0.04300392419099808, -0.00831869337707758, -0.015776941552758217, 0.0000016035211274356698, 0.02531629242002964, -0.04078769311308861, 0.010745597071945667, 0.031070655211806297, -0.0120056988671422, 0.04335615783929825, -0.049846671521663666, -0.003285316750407219, 0.011186668649315834, -0.03962986543774605, -0.008849256671965122, 0.014072833582758904, 0.07791101187467575, -0.06241995468735695, -0.061856284737586975, -0.02838432788848877, 0.07230529189109802, 0.043353643268346786, 0.0292575154453516, 0.019238894805312157, 0.028230492025613785, -0.06213371828198433, -0.03274798393249512, 0.00884341076016426, -0.009705477394163609, -0.019815271720290184, 0.008398674428462982, -0.00518072908744216, 0.019702592864632607, -0.006714374292641878, 0.004654339514672756, 0.10050030797719955, -0.013541176915168762, 0.013746168464422226, -0.0008075383957475424, 0.05053124576807022, -0.002384292660281062, 0.045924410223960876, -0.02683580480515957, -0.0025693171191960573, -0.009477689862251282, 0.011888361535966396, -0.009627232328057289, 0.0006214826134964824, 0.01896943338215351, -0.020216079428792, -0.03854165971279144, 0.0071380785666406155, -0.03758726269006729, 0.031572844833135605, 0.022142333909869194, -0.023097233846783638, -0.04474414885044098, 0.08675360679626465, -0.035040561109781265, -0.030029257759451866, 0.0013602223480120301, 0.032324183732271194, 0.00968577153980732, 0.049335356801748276, -0.0067798784002661705, 0.005299659911543131, 0.017885735258460045, 0.02589094452559948, 0.03592827543616295, 0.021559439599514008, 0.026955045759677887, 0.028982123360037804, 0.04103513062000275, -0.08539576083421707, -0.04382048174738884, -0.01755511201918125, 0.028492406010627747, -0.05517992377281189, 0.007609107065945864, 0.01348799467086792, 0.05137389525771141, -0.02780553139746189, 0.03583044931292534, -0.02773541770875454, -0.0445319227874279, -0.06385497003793716, 0.015140031464397907, 0.02296837605535984, 0.007827021181583405, 0.02441439963877201, -0.03782260790467262, -0.09355833381414413, -0.00129022728651762, 0.0013091249857097864, -0.008338048122823238, -0.016786616295576096, -0.0068121072836220264, 0.03595595806837082, 0.039994217455387115, 0.08405143767595291, 0.03902200609445572, 0.004705250728875399, 0.014008844271302223, -0.029410434886813164, 0.07523784786462784, 0.06190598011016846, 0.002424846636131406, -0.040069010108709335, -0.019613824784755707, 0.041679225862026215, -0.007148916367441416, 0.04425424709916115, -0.0511089451611042, -0.010885967873036861, -0.050105176866054535, 0.008058669045567513, -0.005488857626914978, -0.0099949911236763, -0.019972166046500206, -0.04712137579917908, 0.033483438193798065, -0.0013367122737690806, -0.009248827584087849, -0.011689583770930767, -0.032067928463220596, 0.020208360627293587, -0.06969165056943893, 0.01163728628307581, 0.042023129761219025, 0.052961524575948715, -0.018313074484467506, 0.00839800201356411, -0.03983556851744652, 0.005656375549733639, -0.020607294514775276, -0.01649812050163746, 0.00951846782118082, 0.025546614080667496, 0.02191447839140892, -0.06084425747394562, -0.007232016883790493, -0.004625184927135706, -0.035503678023815155, -0.06129372492432594, 0.051366791129112244, 0.022743139415979385, 0.031169015914201736, -0.08548106998205185, -0.025538034737110138, 0.01337004080414772, -0.01741938851773739, 0.05544092133641243, 0.06960273534059525, -0.08198018372058868, -0.0023745130747556686, 0.027643313631415367, 0.04020009562373161, 0.04767467826604843, -0.02772899530827999, 0.06601975858211517, -0.02523544616997242, 0.02336926944553852, 0.01571226678788662, 0.0426737479865551, 0.02310958318412304, 0.006954972166568041, 0.03234872594475746, -0.06578882783651352, -0.028364161029458046, -0.08764763921499252, -0.034092482179403305, 0.02860163152217865, -0.059930551797151566, 0.03601459041237831, 0.03084423393011093, 0.02448972314596176, -0.01244440395385027, -0.034366216510534286, -0.007346196100115776, 0.07711563259363174, 0.03903918340802193, 0.047054190188646317, 0.06029960513114929, -0.07018325477838516, 0.004442168865352869, -0.02218281291425228, 0.04472316429018974, 0.060910556465387344, 0.0027635719161480665, 0.03416520729660988, 0.003924419172108173, 0.011182809248566628, 0.04645349830389023, -0.02750440686941147, -0.05359664931893349, 0.013127034530043602, -0.07351977378129959, 0.04256519675254822, 0.054608650505542755, -0.03861192613840103, 0.005894183646887541, 0.01179179735481739, -0.010956249199807644, -0.06318455189466476, 0.037028905004262924, 0.06811556965112686, -0.02660166658461094, -0.0036401732359081507, -0.01589912176132202, -0.008012439124286175, -0.09735870361328125, -0.02093546837568283, -0.033901944756507874, 0.014249307103455067, -0.06791286915540695, -0.019308164715766907, 0.05466466769576073, -0.0576946847140789, -0.027975602075457573, -0.008413963951170444, 0.05879638344049454, -0.01570567488670349, 0.028684576973319054, 0.003418168518692255, 0.0026100301183760166, -0.0032983117271214724, 0.002719742711633444, -0.019378527998924255, -0.03739174082875252, -0.0412643663585186, -0.02603635936975479, -0.019086971879005432, 0.040732160210609436, 0.026505110785365105, -0.049188029021024704, -0.008945818990468979, 0.014996901154518127, -0.012191074900329113, -0.05126279965043068, 0.004424421116709709, -0.003779506543651223, 0.02824379876255989, 0.03316431865096092, -0.0035553453490138054, 0.007165861316025257, -0.01511446200311184, -0.017857283353805542, -0.02948126755654812, 0.05949206277728081, -0.02951297163963318, 0.024489864706993103, 0.07417377084493637, 0.021904461085796356, 0.051801227033138275, 0.02291725017130375, 0.021846314892172813, -0.04339662194252014, 0.047850944101810455, -0.02368711307644844, -0.015614708885550499, 0.06629165261983871, -0.03781330958008766, 0.011174416169524193, -0.0026813256554305553, 0.016089128330349922, -0.00401935214176774, -0.030012231320142746, -0.020380334928631783, -0.08130679279565811, -0.07316694408655167, -0.03413686901330948, 0.030805034562945366, 0.0025960789062082767, 0.003583473851904273, -0.025783279910683632, 0.031175430864095688, 0.052720747888088226, 0.03888699784874916, -0.022425683215260506, -0.03813394904136658, 0.00984808336943388, 0.042351581156253815, 0.025126975029706955, 0.0036949231289327145, 0.047097913920879364, 0.01512286439538002, 0.04921700060367584, -0.01567970961332321, -0.014641297049820423, -0.011921590194106102, 0.019172823056578636, -0.005917894653975964 ]
<p>I was studying a <a href="http://en.wikipedia.org/wiki/GRE_Physics_Test" rel="nofollow">GRE Physics Test</a> problem where optical light with a wavelength of 500&nbsp;nm travels through a gas with refractive index $n$.</p> <p>If we look at the equations for wave motion and index of refraction</p> <p>$$c=\lambda_0\nu\quad\text{(in vacuum)}$$</p> <p>$$v = \lambda\nu\quad\text{(in medium)}$$</p> <p>$$n = c/v$$</p> <p>we see that, if the frequency is constant, the <strong><em>wavelength decreases in the medium compared to vacuum</em></strong>. Is this a consistent property at all frequencies and for all mediums with refractive index real and greater than 1?</p> <p>Are there dielectrics which change the frequency (still for <code>n</code> > 1), and is there an example of that?</p>
g1516
[ 0.007033993490040302, -0.00590644683688879, 0.021665755659341812, 0.026176780462265015, 0.020132770761847496, -0.004302127752453089, -0.03256518393754959, -0.0061986977234482765, -0.009134572930634022, 0.016318591311573982, 0.05004478618502617, 0.02769576571881771, -0.004049865063279867, 0.028021398931741714, -0.01527527067810297, -0.01763479970395565, 0.05416860431432724, 0.014113635756075382, 0.0023436183109879494, -0.026401957497000694, -0.04599400609731674, 0.013196500018239021, -0.05626726523041725, -0.08967211842536926, 0.02596048265695572, 0.0021596287842839956, 0.08932948857545853, -0.007156522944569588, -0.010882058180868626, -0.025184284895658493, 0.06129506602883339, -0.032923806458711624, 0.07898140698671341, -0.018267519772052765, 0.010262886062264442, -0.010547523386776447, 0.057827871292829514, -0.0017808099510148168, 0.06506361067295074, 0.04647938907146454, -0.02304772101342678, 0.02113499492406845, 0.0063734035938978195, 0.033493772149086, 0.03252438083291054, -0.01744360476732254, -0.04543459415435791, 0.009981725364923477, 0.0019347845809534192, -0.03837193548679352, -0.014137154445052147, 0.029184605926275253, 0.021232033148407936, -0.007529251277446747, 0.011475793085992336, 0.02212592028081417, -0.09267980605363846, 0.028334852308034897, 0.042762622237205505, 0.02551911026239395, -0.015101910568773746, -0.03584958612918854, 0.009406334720551968, -0.0012553149135783315, 0.027700230479240417, -0.02188650518655777, -0.03277256339788437, -0.003989093936979771, -0.0004659847472794354, -0.01618623174726963, -0.060757946223020554, -0.024462750181555748, -0.0703200101852417, -0.05025156959891319, 0.0043229092843830585, 0.01998492330312729, 0.019014185294508934, 0.0002106797619489953, -0.056667279452085495, 0.007839354686439037, -0.05874696001410484, -0.003290396649390459, 0.0053043365478515625, 0.042013317346572876, -0.01980188675224781, -0.09296160191297531, 0.022952968254685402, 0.0006480702431872487, 0.04004420340061188, 0.021819913759827614, 0.04085063561797142, 0.0404559001326561, 0.037486184388399124, 0.06398285925388336, 0.07201699912548065, 0.003936192486435175, -0.036015089601278305, 0.0866527333855629, 0.03462963178753853, -0.024592313915491104, -0.01211860217154026, -0.0194444227963686, 0.022981567308306694, 0.009273539297282696, 0.006577192340046167, -0.019405117258429527, 0.00450988719239831, 0.00584822753444314, -0.02762077935039997, 0.02673712931573391, 0.014149386435747147, -0.05854180455207825, -0.04780586063861847, -0.07207159698009491, -0.050539400428533554, 0.005120984278619289, 0.014667877927422523, -0.05773895978927612, 0.04601859673857689, 0.03971840441226959, 0.024126924574375153, 0.012564169242978096, 0.004122308921068907, 0.023693399503827095, -0.029970407485961914, -0.00027245740056969225, 0.03386592119932175, 0.00878599751740694, 0.006705425214022398, 0.003195331431925297, -0.03988493233919144, -0.01508161798119545, -0.04783233255147934, 0.010029059834778309, -0.016066834330558777, 0.0040129562839865685, 0.05481964722275734, 0.021816667169332504, 0.00023708888329565525, 0.012533764354884624, 0.024997413158416748, 0.00954551249742508, 0.024245403707027435, -0.030662033706903458, -0.038183048367500305, -0.014035544358193874, 0.010334023274481297, 0.006758681498467922, 0.07481426000595093, -0.02306717447936535, 0.016891542822122574, 0.07444605231285095, 0.04734193533658981, -0.018655074760317802, -0.04160946235060692, -0.012397675774991512, 0.010107414796948433, -0.01547358836978674, -0.0017001189989969134, -0.022531097754836082, 0.016999471932649612, -0.00810376089066267, 0.03274502977728844, 0.022042954340577126, 0.011925768107175827, 0.0020603612065315247, -0.05216594040393829, -0.009137149900197983, -0.006489168386906385, -0.08323775231838226, -0.050203483551740646, 0.011746070347726345, -0.030588632449507713, 0.1052679643034935, -0.002387923886999488, 0.0562523677945137, 0.076134093105793, 0.006976961623877287, -0.046357348561286926, 0.010071213357150555, -0.020745381712913513, -0.047117769718170166, -0.0009860052959993482, -0.07723537087440491, 0.031819429248571396, 0.039359886199235916, -0.025318516418337822, -0.040676821023225784, -0.10907845199108124, -0.047758083790540695, -0.04468441382050514, 0.010071827098727226, -0.008786322548985481, 0.04381581395864487, 0.02364756353199482, -0.019995007663965225, -0.06469432264566422, -0.04634513705968857, -0.05350101366639137, -0.007377583999186754, -0.04763982445001602, 0.04006609693169594, 0.11274248361587524, 0.020612724125385284, 0.04851248115301132, -0.040968168526887894, 0.007558708544820547, -0.04934963956475258, 0.008501444011926651, 0.03971328213810921, 0.03518382087349892, 0.0738513171672821, 0.002998973010107875, -0.005720109213143587, 0.02357429638504982, 0.049333199858665466, 0.002269924618303776, 0.006112241186201572, 0.04007894545793533, 0.031139740720391273, -0.04044531285762787, 0.012113578617572784, -0.03302546963095665, 0.024296099320054054, -0.022748645395040512, -0.09607676416635513, -0.02703155390918255, 0.021793430671095848, 0.044089581817388535, -0.020807011052966118, 0.004706425592303276, 0.028473850339651108, 0.024444550275802612, 0.002262088470160961, 0.013981591910123825, 0.03125529736280441, -0.04342912510037422, -0.011063680984079838, 0.050183944404125214, -0.020924217998981476, -0.011452609673142433, -0.035898059606552124, -0.06770742684602737, 0.011163423769176006, -0.02728630229830742, 0.010154987685382366, -0.05489431321620941, -0.06777869164943695, 0.03481420874595642, 0.01995800994336605, 0.015184142626821995, -0.0010294661624357104, 0.011048133485019207, 0.017368784174323082, -0.014641827903687954, 0.024237658828496933, 0.001568591920658946, 0.07179448008537292, -0.01929198019206524, -0.03040364943444729, -0.006758091505616903, 0.007007864769548178, 0.019356243312358856, -0.003414591308683157, -0.018521206453442574, -0.001622272189706564, 0.0038720525335520506, 0.10542379319667816, -0.013526846654713154, 0.008960597217082977, 0.008733796887099743, 0.051288194954395294, 0.020816266536712646, -0.004551572725176811, 0.050242893397808075, 0.020186172798275948, 0.01567726954817772, -0.04380803182721138, 0.04190784692764282, -0.018936604261398315, -0.024157725274562836, -0.0012984748464077711, -0.09429097920656204, 0.005056131165474653, 0.022262781858444214, -0.07258933782577515, 0.024919483810663223, -0.02449246682226658, -0.0260971300303936, 0.06248065456748009, -0.02225535362958908, 0.0760703757405281, 0.03342422842979431, 0.02783254347741604, -0.05260021612048149, 0.05238199979066849, 0.05866178497672081, 0.0005420040106400847, 0.01393054984509945, 0.00332861440256238, -0.000682021607644856, -0.07162030041217804, -0.030285287648439407, 0.027174009010195732, 0.027457982301712036, 0.007712258491665125, -0.061690542846918106, -0.07587775588035583, 0.011748149059712887, 0.04125814512372017, 0.029939506202936172, 0.04675973951816559, 0.03492825850844383, -0.006130673922598362, -0.03961235657334328, 0.051834993064403534, 0.01998022198677063, -0.007813352160155773, -0.008496991358697414, 0.004685424268245697, -0.003309412859380245, -0.06153115630149841, 0.034141991287469864, -0.03263481333851814, 0.039507269859313965, -0.027874236926436424, -0.0029804084915667772, 0.025187360122799873, -0.06304564327001572, -0.006478199735283852, -0.016310136765241623, 0.027042068541049957, -0.016689419746398926, -0.025286007672548294, -0.00002164014040317852, -0.007345485966652632, -0.042009588330984116, 0.019390495494008064, 0.04310256615281105, 0.010371105745434761, -0.03786144405603409, -0.024788247421383858, -0.039173103868961334, 0.014973201788961887, 0.004799182061105967, 0.0508585162460804, 0.014388361014425755, -0.008948825299739838, -0.001068675541318953, 0.036218080669641495, 0.04159088805317879, -0.0204086322337389, 0.049919333308935165, -0.021103786304593086, -0.08222173899412155, -0.031179599463939667, 0.0567476823925972, 0.030652597546577454, 0.0707135871052742, -0.06284838169813156, 0.00715829711407423, -0.005856187082827091, -0.008552305400371552, -0.016743149608373642, -0.02761087194085121, -0.025502918288111687, 0.016455963253974915, 0.0758487805724144, 0.01164625771343708, 0.012060900218784809, -0.0065496983006596565, -0.02045935019850731, -0.005429713521152735, 0.05618669092655182, 0.0018265125108882785, 0.01926092803478241, -0.011530628427863121, 0.02496509999036789, -0.03113449551165104, 0.05702460929751396, 0.024395739659667015, -0.027575373649597168, 0.03523058071732521, -0.005790199153125286, 0.008038186468183994, -0.02117461897432804, -0.02863299660384655, -0.029120618477463722, 0.00944145955145359, -0.060889195650815964, -0.02640727534890175, -0.044735342264175415, -0.017252618446946144, 0.04371931403875351, -0.01005598809570074, -0.034533578902482986, 0.03525109961628914, -0.047734335064888, 0.011432910338044167, 0.0214990247040987, 0.022382374852895737, -0.004878771957010031, -0.056427471339702606, -0.021036414429545403, -0.020177951082587242, 0.033945437520742416, 0.050023239105939865, 0.002733806148171425, -0.05662642791867256, 0.00046119585749693215, -0.01309849414974451, -0.01741977222263813, -0.0411297008395195, -0.08514998853206635, 0.016864806413650513, 0.06686913222074509, 0.003178397659212351, -0.04835984483361244, -0.008632994256913662, -0.010381796397268772, 0.005400368943810463, 0.08034545928239822, -0.00033673871075734496, 0.011293180286884308, 0.033322498202323914, 0.018779795616865158, 0.059442680329084396, -0.008096441626548767, 0.0026065434794873, -0.0587526373565197, -0.07952842116355896, -0.04063016548752785, -0.007591910194605589, 0.023145295679569244, 0.025680851191282272, 0.036259885877370834, -0.04193570837378502, -0.0362112782895565, 0.029256517067551613, 0.05796807259321213, 0.09248709678649902, -0.008819946087896824, 0.03239228576421738, -0.06150880828499794, 0.016942530870437622, 0.05299752205610275, -0.038493990898132324, 0.008960437029600143, -0.038964517414569855, -0.002106053987517953, -0.0398717001080513, -0.014086423441767693, -0.004089461639523506, -0.032347671687603, -0.032938387244939804, -0.03967219218611717, -0.06644366681575775, 0.04474059119820595, 0.040602996945381165, -0.02705887332558632, -0.014084464870393276, 0.02956344559788704, 0.00968762394040823, -0.00020945363212376833, 0.03329192101955414, 0.0046285539865493774, 0.005784241948276758, -0.005970493424683809, -0.023061413317918777, -0.029310651123523712, 0.031248051673173904, -0.04324302449822426, 0.054562557488679886, 0.015013973228633404, 0.05794385075569153, -0.004490796476602554, -0.017479484900832176, -0.010878019034862518, -0.03284665197134018, -0.07890704274177551, 0.0005766351241618395, -0.030360331758856773, 0.1139100193977356, 0.04144022986292839, -0.04664295166730881, -0.002137698931619525, -0.033548299223184586, 0.058697640895843506, -0.021043287590146065, -0.06453089416027069, -0.01946338638663292, -0.027876392006874084, 0.003231878625229001, 0.011198803782463074, -0.04467112198472023, 0.010426290333271027, 0.05698184296488762, 0.012574474327266216, -0.0231134332716465, -0.027521446347236633, -0.011958745308220387, -0.02309598959982395, 0.040468763560056686, -0.017068466171622276, -0.03494717553257942, -0.008033841848373413, -0.0011277716839686036, 0.05136233568191528, -0.024859044700860977, 0.039201196283102036, -0.0028100458439439535, -0.006628105416893959, 0.03377130255103111, 0.024772023782134056, 0.012612313963472843, -0.014935797080397606, -0.04451586678624153, -0.009603495709598064, -0.011155619286000729, -0.031675081700086594, 0.026300396770238876, -0.029997488483786583, 0.06660284847021103, -0.032313667237758636, 0.02337665855884552, 0.016036083921790123, 0.008466656319797039, -0.030026379972696304, -0.0029558632522821426, 0.03630245104432106, 0.022467058151960373, 0.020631354302167892, 0.024182872846722603, -0.06481597572565079, 0.013098769821226597, 0.02147909440100193, 0.015762828290462494, -0.009099171496927738, -0.03582305461168289, 0.024961473420262337, -0.026306530460715294, 0.033469393849372864, 0.034594010561704636, -0.006827263627201319, -0.032397281378507614, 0.009663162752985954, 0.02060069516301155, -0.003873191075399518, 0.0226692333817482, 0.020913448184728622, 0.038815148174762726, -0.041592709720134735, -0.028958497568964958, -0.009921366348862648, -0.011117849498987198, -0.005492343567311764, 0.017018264159560204, -0.0015579423634335399, -0.0067122322507202625, -0.034879423677921295, 0.03533173352479935, 0.011839059181511402, 0.03675377368927002, -0.03180685639381409, 0.00832895003259182, -0.09656400978565216, 0.011314373463392258, -0.03804592043161392, 0.06487672030925751, 0.016248153522610664, -0.07826206088066101, 0.02901008166372776, -0.06115233898162842, -0.055289529263973236, 0.0024016883689910173, -0.02427992969751358, -0.04064640775322914, -0.0629393458366394, 0.012801424600183964, 0.002797013381496072, 0.0384959913790226, -0.04311778396368027, 0.035675644874572754, 0.01563672348856926, -0.07796795666217804, -0.03937018662691116, 0.01726442389190197, 0.03601078316569328, 0.04207855090498924, -0.010993517935276031, -0.04749823734164238, -0.008121569640934467, -0.01872260868549347, -0.0027440085541456938, -0.004814397543668747, -0.062437545508146286, -0.010458212345838547, -0.01287094783037901, -0.008271856233477592, 0.04353780671954155, 0.05897404998540878, -0.005945854354649782, 0.013555826619267464, 0.016933178529143333, -0.05265836790204048, 0.020598484203219414, -0.002983140992000699, -0.022748040035367012, 0.06419182568788528, 0.03265963867306709, -0.0055963932536542416, 0.022374866530299187, 0.0316297672688961, -0.005573904141783714, -0.0621018223464489, -0.08138510584831238, -0.02309422381222248, 0.06827256083488464, 0.0013488872209563851, 0.007425731047987938, 0.007054075598716736, -0.08521458506584167, -0.01409816648811102, 0.015018886886537075, 0.014370552264153957, 0.03472600877285004, -0.04663404822349548, -0.024374572560191154, 0.06535857915878296, -0.02328597754240036, 0.023050563409924507, 0.01277642510831356, -0.017754264175891876, 0.010202388279139996, 0.013942885212600231, 0.03326216712594032, -0.08263830840587616, -0.0058494433760643005, 0.037345223128795624, 0.0014148630434647202, 0.033201757818460464, 0.025042645633220673, 0.023068813607096672, 0.013849751092493534, 0.008229009807109833, 0.0012932791141793132, 0.07207024842500687, -0.028575338423252106, -0.025059137493371964, -0.010354682803153992, 0.004324786365032196, -0.05439078435301781, -0.01246748585253954, 0.05462014302611351, -0.003550482215359807, 0.039016950875520706, -0.03364114090800285, -0.00869562104344368, 0.03953258693218231, -0.061264846473932266, -0.026677267625927925, -0.029064714908599854, -0.0004855395236518234, 0.01671755313873291, -0.030287684872746468, 0.06782744824886322, 0.007260738406330347, -0.07285463809967041, 0.023270199075341225, -0.03421173617243767, 0.04717163369059563, 0.011594030074775219, 0.0633469969034195, -0.028994880616664886, -0.0022502157371491194, 0.011036179959774017, -0.0743771344423294, 0.057200707495212555, 0.03270110487937927, -0.056122083216905594, -0.018540721386671066, 0.013141544535756111, 0.02900087460875511, -0.06068676337599754, 0.015398302115499973, 0.012692592106759548, -0.08054280281066895, 0.05848052352666855, 0.038521796464920044, -0.030221620574593544, -0.0051152464002370834, -0.05894192308187485, 0.04040471091866493, 0.014573506079614162, 0.037664834409952164, -0.06694509088993073, 0.016479840502142906, 0.0016493559814989567, 0.00781870074570179, -0.08145805448293686, -0.06059686839580536, -0.005876789800822735, -0.04005032777786255, 0.002987345913425088, -0.020243948325514793, 0.02122393064200878, -0.041489649564027786, -0.054675497114658356, 0.0013920130440965295, 0.02653965912759304, 0.03578706458210945, -0.012720145285129547, 0.024364445358514786, 0.03554569557309151, 0.04972357302904129, -0.01323957834392786, -0.02359456568956375, -0.01036220695823431, 0.01163681410253048, -0.03139927610754967, -0.020987359806895256, -0.028935236856341362, 0.032414283603429794, -0.02351723425090313, -0.031930845230817795, -0.023379765450954437, -0.004730225540697575, -0.02503289468586445, 0.010312939062714577, 0.014596897177398205, -0.03688517212867737, 0.023337068036198616, -0.027483081445097923, 0.004388364963233471, 0.01726868748664856, -0.01284447405487299, 0.0028338429983705282, 0.03323384374380112, 0.029997045174241066, 0.032724883407354355, -0.0035160300321877003, -0.006318282335996628, 0.006721752230077982, 0.060739096254110336, 0.020927535369992256, 0.0022565312683582306, 0.006668558344244957, 0.02264886349439621, 0.05015525221824646, -0.005336999427527189, -0.03436281159520149, 0.0028360860887914896, -0.009558741003274918, 0.05655749514698982, 0.006580164190381765, -0.02571587637066841, 0.01627187989652157, 0.02770034782588482, 0.027310796082019806, -0.01001445297151804, 0.015147870406508446, -0.0257113017141819, 0.035839203745126724, -0.013584972359240055, -0.014177627861499786, -0.016858432441949844, 0.010228876024484634, 0.028738534078001976 ]
<p>One can expand any periodic function in sines and cosines. When calculating the coefficients $a_0$, $a_n$, and $b_n$ one find that $a_1&gt;a_2&gt;...&gt;a_n&gt;...$, similarly for $b_n$. </p> <p>Is there an intuitive reason to understand this, I mean why would one expect this to happen? It looks miraculous and mysterious to me that the coefficients came out "ordered" in a way that made the convergence manifest.</p>
g1517
[ 0.038095708936452866, -0.002063998021185398, 0.021358033642172813, -0.02136976085603237, 0.01149367168545723, -0.029148058965802193, 0.0047121779061853886, 0.0060691130347549915, 0.027084290981292725, -0.03865103796124458, -0.04923343285918236, 0.039872732013463974, 0.03145488724112511, -0.00269151758402586, 0.00910626258701086, -0.020480846986174583, -0.03257061913609505, 0.03829197585582733, -0.003224926767870784, 0.06190263107419014, -0.008903378620743752, 0.03687484562397003, 0.029761221259832382, -0.03915402665734291, 0.014769074507057667, -0.007617921102792025, -0.007196377031505108, -0.017564671114087105, -0.02260933443903923, -0.010635585524141788, 0.062412917613983154, -0.01004058588296175, -0.00403869803994894, -0.007365025579929352, -0.01664847694337368, 0.05204271897673607, 0.007689425256103277, -0.02402401901781559, 0.08435246348381042, 0.03701210021972656, -0.02958538383245468, 0.023958738893270493, 0.037822261452674866, 0.007893388159573078, -0.026868250221014023, -0.024307092651724815, 0.0010090710129588842, -0.015692435204982758, -0.024282781407237053, -0.09878003597259521, -0.022729527205228806, 0.007383979391306639, 0.06125795096158981, 0.005435657687485218, 0.0038571024779230356, 0.09123283624649048, 0.010595710948109627, -0.03413974493741989, 0.02198549546301365, 0.030771279707551003, 0.027357760816812515, 0.006223159842193127, 0.0617852509021759, -0.02720649540424347, 0.02711925096809864, -0.022988097742199898, 0.04354472458362579, 0.055382195860147476, 0.009459411725401878, -0.008003207854926586, -0.022058596834540367, -0.073489710688591, 0.006857296451926231, -0.047334469854831696, -0.04729335010051727, -0.011145006865262985, 0.009551226161420345, 0.015281228348612785, -0.043427933007478714, 0.01294238306581974, -0.014504866674542427, -0.011919904500246048, -0.009145276620984077, 0.08222631365060806, 0.00997835397720337, -0.048418078571558, 0.0632721334695816, 0.00023641860752832144, 0.046726301312446594, 0.042560383677482605, -0.013743084855377674, 0.009080229327082634, -0.02486347034573555, -0.01042312104254961, -0.041245702654123306, -0.02405952662229538, -0.0072630890645086765, 0.04926622658967972, 0.03169897943735123, -0.03300189599394798, -0.02575378119945526, 0.05052020773291588, 0.03610195592045784, 0.03061535209417343, -0.07025668770074844, -0.012581810355186462, 0.04243640601634979, -0.026382241398096085, 0.027226092293858528, 0.016103394329547882, -0.0608467236161232, 0.0042650094255805016, -0.01900385692715645, -0.05761287733912468, 0.0050551616586744785, 0.04373994842171669, 0.005917295813560486, 0.056136976927518845, 0.055779483169317245, 0.040664687752723694, 0.012859715148806572, -0.05477345734834671, -0.014934824779629707, 0.04855197295546532, -0.03348870947957039, 0.049984902143478394, 0.054576996713876724, 0.02348906174302101, 0.04688228294253349, -0.0851982980966568, 0.01699872687458992, 0.030959615483880043, 0.013288200832903385, 0.07680310308933258, 0.06604501605033875, -0.018088746815919876, -0.004260997287929058, -0.05642165616154671, -0.01990017667412758, 0.00909027922898531, -0.03252428397536278, -0.09196677058935165, 0.0452926866710186, -0.046914055943489075, -0.025731166824698448, 0.018196765333414078, -0.041941989213228226, -0.055401287972927094, -0.08361106365919113, 0.05222175642848015, -0.04009883478283882, 0.05659755319356918, -0.02550368756055832, 0.012860938906669617, 0.0020823520608246326, -0.014559755101799965, 0.04137934744358063, -0.0369531475007534, -0.005214597564190626, 0.010601699352264404, 0.00407239468768239, -0.017500782385468483, -0.05750380456447601, 0.022135017439723015, -0.08824881166219711, 0.006074853707104921, -0.027462594211101532, -0.03142767772078514, -0.0704604834318161, -0.023451292887330055, -0.019449561834335327, 0.03447837010025978, -0.017152834683656693, 0.016642676666378975, -0.031230011954903603, 0.08101223409175873, 0.030680213123559952, -0.011393149383366108, 0.03849121183156967, 0.00408298522233963, -0.04897220432758331, 0.05354789271950722, -0.027862902730703354, -0.008361917920410633, 0.021118583157658577, -0.023530391976237297, -0.012877306900918484, 0.019796645268797874, -0.08263058215379715, 0.007107088342308998, 0.0209940318018198, 0.005805716384202242, 0.006464997306466103, 0.013394263572990894, -0.03218579292297363, -0.022745488211512566, -0.010474861599504948, -0.0280768945813179, -0.03591287508606911, -0.007297647185623646, 0.012595984153449535, 0.034741420298814774, 0.032263390719890594, -0.009628310799598694, 0.002003770088776946, 0.009345677681267262, -0.004211197607219219, -0.014249919913709164, 0.006815739907324314, 0.0687597468495369, -0.009134653024375439, -0.06462714076042175, -0.01964101567864418, 0.06368926167488098, -0.00570620596408844, -0.005563292186707258, 0.0030455882661044598, -0.03542144224047661, 0.0643225908279419, 0.008962666615843773, 0.021838495507836342, -0.053931720554828644, -0.032637692987918854, -0.015717295929789543, -0.021571870893239975, 0.02656410075724125, -0.029715988785028458, -0.015651604160666466, 0.02943463623523712, 0.019590549170970917, -0.05854758247733116, -0.0013081220677122474, 0.010406631976366043, 0.008600634522736073, -0.023473422974348068, 0.012981096282601357, -0.014468849636614323, 0.03396064415574074, 0.01865237206220627, 0.03459450602531433, 0.025560108944773674, -0.05467220023274422, 0.03647901490330696, -0.010984755121171474, 0.011004793457686901, -0.014012981206178665, -0.021404793485999107, -0.00584601191803813, -0.05068580061197281, 0.05302136763930321, 0.034470658749341965, -0.0376213937997818, 0.010609140619635582, 0.07766830176115036, -0.0313933826982975, -0.05028543993830681, -0.02000356838107109, -0.02740858867764473, -0.026566943153738976, -0.06781937927007675, -0.030679408460855484, 0.05765407904982567, 0.043069638311862946, 0.02578197978436947, -0.030051536858081818, -0.0026294237468391657, 0.004718835465610027, -0.024301353842020035, 0.055088188499212265, -0.05973192676901817, 0.0031806016340851784, 0.016207845881581306, 0.05120980739593506, 0.011258377693593502, -0.08024357259273529, 0.0004996546194888651, 0.009034148417413235, -0.010756997391581535, 0.025146370753645897, -0.019038543105125427, -0.04128263518214226, -0.013352111913263798, -0.05544259771704674, 0.016852758824825287, 0.021697044372558594, 0.00836960133165121, 0.008668165653944016, 0.05302385613322258, -0.04067317396402359, 0.044337693601846695, 0.01852838322520256, 0.026910625398159027, -0.013507151044905186, -0.007039907854050398, 0.016123594716191292, 0.04113072156906128, 0.03563065454363823, -0.03669418767094612, -0.025042112916707993, 0.07451189309358597, 0.021948695182800293, 0.011044317856431007, -0.027461128309369087, -0.04428819939494133, -0.01564340479671955, -0.004882884211838245, 0.002867982257157564, 0.019753817468881607, -0.012386530637741089, -0.020543577149510384, 0.02343735657632351, -0.014074099250137806, -0.02651253156363964, 0.013879475183784962, -0.03449808806180954, -0.01360981073230505, 0.04932431876659393, 0.051059529185295105, 0.09281721711158752, 0.033815789967775345, -0.0368913896381855, -0.05639195069670677, -0.03832348808646202, -0.06905502825975418, 0.010168221779167652, 0.00014584310702048242, 0.0037889110390096903, -0.042896024882793427, 0.02819942682981491, 0.010764050297439098, -0.05516032129526138, -0.021403133869171143, -0.0161889661103487, -0.034929465502500534, 0.01856299489736557, -0.05144418776035309, -0.0214654840528965, 0.005476197227835655, 0.015131848864257336, 0.024684347212314606, -0.037182554602622986, -0.008134753443300724, -0.00048669957322999835, -0.05510680377483368, 0.021009955555200577, -0.00352027197368443, 0.055021755397319794, 0.040964532643556595, 0.015212297439575195, -0.02968410775065422, -0.006303762085735798, -0.00969015620648861, 0.02550455369055271, -0.02418731339275837, 0.027146996930241585, 0.03250126168131828, -0.01996954157948494, -0.029892636463046074, -0.02574772946536541, -0.02369147539138794, 0.054593879729509354, 0.02776452898979187, -0.049634046852588654, 0.028963221237063408, 0.0006029701908119023, 0.009063998237252235, 0.033228274434804916, 0.102303147315979, 0.023665646091103554, 0.03107612021267414, 0.026214493438601494, -0.012707347050309181, -0.015839334577322006, -0.038085270673036575, 0.06660443544387817, 0.0010768345091491938, -0.006613710895180702, 0.015088317915797234, 0.0038695225957781076, 0.014903557486832142, -0.023264234885573387, -0.03134344890713692, 0.015119451098144054, 0.0025618523359298706, -0.013991928659379482, 0.03008888103067875, -0.046620529145002365, -0.007526409346610308, -0.03849978372454643, -0.017135469242930412, 0.046957820653915405, -0.0034690124448388815, 0.041476957499980927, -0.0030350384768098593, 0.058104876428842545, -0.12626484036445618, -0.045159440487623215, -0.03071293793618679, -0.01637822575867176, -0.02785804308950901, -0.001766412635333836, -0.045294564217329025, -0.018450554460287094, -0.002812465652823448, -0.01993468776345253, 0.007493910379707813, 0.06352104991674423, 0.03232715278863907, -0.0032971110194921494, -0.09656038135290146, -0.017359517514705658, 0.04266340658068657, -0.024410594254732132, 0.0031325947493314743, 0.05876033753156662, 0.08656027168035507, 0.025192871689796448, -0.032515931874513626, -0.023579522967338562, -0.006882453802973032, -0.06466494500637054, 0.045927993953228, -0.03668291121721268, -0.013523093424737453, 0.026383299380540848, 0.018352553248405457, -0.031186573207378387, -0.015443447977304459, 0.010917454957962036, 0.002843359252437949, 0.015612083487212658, 0.028625616803765297, 0.07099727541208267, -0.04022872820496559, -0.0646832138299942, -0.00010948201088467613, -0.014784028753638268, 0.0834498256444931, 0.024065952748060226, 0.0815902054309845, 0.032032452523708344, -0.00011434160842327401, -0.010943619534373283, -0.017392247915267944, 0.04428777098655701, -0.0668017789721489, -0.03551569581031799, -0.012435728684067726, 0.0427158884704113, -0.024554455652832985, 0.03147995099425316, 0.0035267004277557135, 0.05122610554099083, 0.00573007483035326, 0.030659934505820274, -0.03732949495315552, -0.023330500349402428, 0.03617652505636215, -0.036280952394008636, 0.04226630926132202, 0.017356401309370995, -0.024432701990008354, 0.006356512662023306, -0.00554937869310379, 0.05638160556554794, 0.060094404965639114, 0.04217066988348961, -0.029793288558721542, -0.03501234948635101, 0.024020450189709663, -0.029367521405220032, 0.02005934715270996, 0.02932838536798954, -0.00298940553329885, 0.020510761067271233, -0.09922587126493454, -0.012306337244808674, 0.0011196318082511425, 0.0017890947638079524, -0.02302202768623829, 0.028073180466890335, -0.016982099041342735, 0.06763002276420593, 0.07584384083747864, -0.04796478524804115, -0.019503153860569, 0.002703309990465641, -0.08746828138828278, 0.020351430401206017, -0.06001216173171997, 0.025232473388314247, -0.012375175952911377, 0.03963153436779976, 0.015852374956011772, -0.005584103520959616, 0.025260483846068382, 0.052052244544029236, -0.027272218838334084, -0.023131409659981728, -0.014683881774544716, -0.030903853476047516, 0.04777214303612709, -0.028840741142630577, 0.005734533537179232, 0.03397621959447861, 0.05829290300607681, 0.01957126520574093, -0.028900116682052612, 0.01578311063349247, 0.003382012015208602, 0.0041883522644639015, -0.011276704259216785, -0.00870443508028984, 0.053804345428943634, 0.030269496142864227, -0.04658516123890877, -0.015206711366772652, -0.00514643220230937, -0.05211568996310234, -0.09181158989667892, 0.024408914148807526, -0.0007975685875862837, 0.02282078005373478, -0.03785818815231323, 0.006227806210517883, 0.019924791529774666, -0.02411631867289543, -0.029923930764198303, 0.012395047582685947, 0.011413807049393654, 0.02432570792734623, 0.04660319909453392, 0.00981292687356472, -0.01443361397832632, 0.011051601730287075, 0.012349715456366539, -0.02544698677957058, 0.025876278057694435, -0.017611514776945114, 0.00031985348323360085, -0.028661008924245834, 0.011112944222986698, 0.00670323520898819, 0.03812791779637337, 0.021473539993166924, 0.008322061039507389, 0.02361597865819931, 0.03539755195379257, 0.015358764678239822, -0.013587001711130142, -0.02425442263484001, 0.04914751276373863, -0.04697433486580849, 0.011233293451368809, -0.03159959241747856, 0.060044895857572556, 0.02441900409758091, -0.028218910098075867, -0.04382649436593056, -0.027468565851449966, 0.02072204276919365, -0.01837591826915741, -0.018237296491861343, -0.07650575041770935, 0.0195838063955307, -0.014194575138390064, 0.03281102702021599, 0.058729104697704315, 0.0017324179643765092, 0.04658890143036842, 0.01653435453772545, -0.018303245306015015, 0.04597761854529381, 0.029100997373461723, 0.043935611844062805, 0.04448848217725754, -0.0409901961684227, -0.018265968188643456, 0.012907657772302628, -0.07401210814714432, 0.03248051181435585, -0.001647785771638155, -0.008014511317014694, 0.0713578388094902, -0.04937027767300606, 0.014201338402926922, -0.04226923733949661, 0.0595322921872139, 0.10676367580890656, -0.06915690004825592, -0.021753130480647087, -0.011320848017930984, 0.0067586335353553295, -0.007889138534665108, 0.018522163853049278, -0.025971783325076103, -0.0030798569787293673, 0.027977511286735535, -0.01124151423573494, -0.025185050442814827, 0.06836257129907608, -0.009412446059286594, 0.09927447885274887, -0.051205310970544815, -0.056532878428697586, -0.05433088168501854, 0.010642343200743198, 0.01887158863246441, -0.012509712018072605, 0.046678654849529266, -0.042559392750263214, 0.07449878007173538, 0.06518375128507614, 0.03757854923605919, -0.011387321166694164, -0.042075518518686295, -0.025897953659296036, 0.025168515741825104, -0.013204408809542656, 0.022989626973867416, 0.01899419166147709, -0.013970185071229935, -0.037960898131132126, -0.040130384266376495, -0.018849041312932968, 0.00163802329916507, -0.015714991837739944, 0.016582606360316277, 0.042323037981987, -0.015342061407864094, -0.05518128722906113, 0.06388899683952332, -0.06580659002065659, 0.0004532302846200764, 0.019811296835541725, 0.02440224401652813, -0.06939786672592163, -0.0029683709144592285, 0.056849319487810135, 0.058189649134874344, -0.013149268925189972, -0.02957087755203247, 0.022855408489704132, -0.017934275791049004, -0.004845489747822285, 0.04793637990951538, -0.009667858481407166, -0.04222635179758072, -0.05586646497249603, 0.008744069375097752, 0.013054614886641502, -0.055845145136117935, -0.007394581101834774, 0.04417077824473381, -0.017990363761782646, -0.015666887164115906, 0.020252933725714684, -0.021283317357301712, 0.02446621097624302, 0.02156558819115162, -0.0451735258102417, 0.06177681311964989, 0.01454769168049097, 0.02786119468510151, 0.022577522322535515, 0.020900335162878036, 0.03834746778011322, -0.048345085233449936, -0.008101277984678745, -0.0729808509349823, 0.013208366930484772, 0.020697565749287605, -0.016672374680638313, -0.0030700552742928267, 0.006245046854019165, 0.03551698103547096, -0.049149882048368454, -0.005036742892116308, 0.0007873692666180432, 0.007188040297478437, 0.052451424300670624, -0.02553570456802845, 0.01959133706986904, 0.03828101232647896, -0.014971298165619373, 0.034867607057094574, -0.022785987704992294, 0.04077770188450813, -0.0025439609307795763, -0.01911739818751812, -0.014779595658183098, -0.01232477929443121, -0.023070886731147766, 0.012252256274223328, 0.06441125273704529, -0.0038673817180097103, -0.03492586687207222, 0.005771144293248653, -0.03274578973650932, 0.016734493896365166, -0.03339521586894989, -0.015550339594483376, -0.03689746931195259, -0.05176879093050957, 0.03693322092294693, 0.01150974165648222, -0.010412467643618584, -0.025703761726617813, -0.033759914338588715, -0.05606928840279579, -0.039848051965236664, -0.002335975645110011, 0.043071068823337555, 0.00044227318721823394, -0.0017786369426175952, 0.03706594929099083, 0.00858831126242876, -0.02551036700606346, 0.021099379286170006, 0.03701716288924217, -0.04288164898753166, -0.03741280362010002, 0.02566349506378174, -0.07874051481485367, -0.0234267208725214, -0.02847965806722641, -0.023002685979008675, 0.0032734463457018137, -0.00764997536316514, 0.026227355003356934, -0.03162579610943794, 0.0007995902560651302, -0.03692403435707092, -0.03167403116822243, 0.002823491347953677, -0.012639880180358887, 0.005006890278309584, -0.020916350185871124, -0.03505157306790352, -0.03330468758940697, -0.03298014774918556, -0.025378018617630005, 0.026862001046538353, -0.0146369319409132, -0.004400851670652628, -0.010196059010922909, -0.05037210136651993, -0.002184729091823101, 0.06969088315963745, 0.022354329004883766, -0.0507272407412529, 0.037846118211746216, 0.0059072645381093025, 0.04797043651342392, 0.0500711165368557, 0.005689158570021391, -0.021267391741275787, 0.06606334447860718, 0.022534992545843124, -0.01809455268085003, 0.022906513884663582, 0.014856354333460331, -0.07763582468032837, 0.004057347308844328, 0.0064820824190974236, -0.08051863312721252, -0.06467609852552414, 0.024048395454883575 ]
<p>Here is the problem:</p> <p><img src="http://i.stack.imgur.com/iojG5.jpg" alt="Here is the problem"></p> <p>In the above figure I want help on finding the potential difference between X and Y. It is getting quite confusing due to the battery in the middle. I found the current in both the loops using Kirchhoff's Voltage law but then I'm confused on the proper method to find the potential drop between the two loops.</p>
g1518
[ 0.013284445740282536, 0.0203989427536726, -0.0041458806954324245, -0.0042496332898736, 0.03138468787074089, -0.018258480355143547, -0.023384395986795425, -0.0026756301522254944, -0.038397520780563354, 0.019701598212122917, -0.0047156368382275105, 0.034803979098796844, -0.057468004524707794, 0.04903837665915489, 0.08043880760669708, -0.017744343727827072, 0.05946952477097511, -0.005301887169480324, 0.033904362469911575, 0.0010854116408154368, 0.0017634634859859943, 0.03002074919641018, -0.05373019725084305, 0.012094647623598576, -0.03864385560154915, -0.013720156624913216, -0.004202302545309067, 0.03730238601565361, -0.08193740993738174, 0.019709322601556778, -0.0003269494045525789, 0.006199417635798454, 0.061419226229190826, -0.008408046327531338, -0.02692321501672268, 0.006718968041241169, 0.03664205223321915, 0.03869711980223656, -0.028254110366106033, 0.03628196939826012, -0.04338786005973816, 0.016052016988396645, 0.054653242230415344, 0.04827167093753815, 0.015210676938295364, -0.06901190429925919, -0.02389993518590927, -0.0024385242722928524, -0.01396856177598238, -0.03051629476249218, -0.006248122081160545, 0.049389541149139404, 0.02293250896036625, -0.007532055955380201, 0.01831653155386448, -0.023148316890001297, 0.00453822361305356, -0.010646460577845573, 0.014524058438837528, -0.004751705098897219, 0.03292272984981537, 0.06388475000858307, 0.03316490352153778, 0.029215361922979355, -0.02368053048849106, -0.006889563053846359, -0.01616518758237362, -0.02566451206803322, -0.04245976358652115, 0.008763186633586884, -0.017046114429831505, -0.042894914746284485, -0.01605462282896042, -0.02065877988934517, -0.026753423735499382, 0.019909437745809555, 0.07442136853933334, -0.018321912735700607, 0.041644755750894547, -0.010455845855176449, -0.03598334267735481, -0.038694001734256744, 0.030174652114510536, 0.06241053715348244, 0.04479636996984482, 0.014060797169804573, 0.006143242120742798, 0.002396522555500269, -0.04141935333609581, -0.015293827280402184, -0.005371622275561094, 0.021251976490020752, 0.08962655067443848, -0.030169373378157616, 0.01041039451956749, -0.04888530820608139, -0.002713837893679738, 0.036144111305475235, 0.06941713392734528, 0.045383021235466, 0.011012238450348377, -0.02612963132560253, -0.010738229379057884, -0.013252426870167255, -0.06494341045618057, 0.024399464949965477, 0.0028891307301819324, -0.03937605768442154, -0.06903386116027832, -0.036370791494846344, -0.05392894148826599, -0.10113391280174255, -0.0159007515758276, -0.034504376351833344, 0.025800976902246475, 0.02086048573255539, 0.004709611181169748, -0.04434099793434143, 0.033757083117961884, 0.00847973208874464, -0.0348418653011322, 0.006574548780918121, 0.009878515265882015, 0.010329732671380043, 0.05037720873951912, 0.0111157251521945, -0.017132332548499107, -0.017485933378338814, 0.04477729648351669, 0.028418781235814095, 0.04069211333990097, -0.01741870306432247, 0.003385629039257765, 0.0077078090980648994, -0.01328330859541893, 0.0025746633764356375, -0.0034253604244440794, -0.01901189237833023, -0.010889465920627117, -0.006801980547606945, 0.026254475116729736, -0.057778894901275635, -0.025371979922056198, -0.022584041580557823, -0.01581157185137272, 0.04066357761621475, -0.03735760971903801, 0.024277759715914726, 0.0338754802942276, -0.06001828610897064, 0.034689754247665405, 0.03315882757306099, -0.019404549151659012, -0.0006720697856508195, -0.013502691872417927, -0.05085429921746254, 0.028414970263838768, 0.027864309027791023, 0.03073994256556034, 0.005789403337985277, -0.05224626511335373, 0.02249751426279545, 0.02478724531829357, -0.01696866564452648, -0.06243547797203064, -0.014909371733665466, 0.059489067643880844, -0.023779025301337242, -0.014730378054082394, -0.03168801963329315, -0.02579631470143795, -0.04133731126785278, 0.028266191482543945, 0.043266620486974716, 0.06185803562402725, 0.08229324221611023, 0.027833547443151474, -0.024896737188100815, 0.03823215141892433, 0.04150613397359848, -0.03576416149735451, 0.036256641149520874, -0.005008085630834103, 0.0166504867374897, -0.0001346472854493186, -0.0179255623370409, 0.020309090614318848, 0.03472451865673065, -0.10101867467164993, -0.08470836281776428, -0.06909745931625366, -0.02269343100488186, 0.005963588133454323, -0.025531047955155373, -0.05861468240618706, 0.04072989895939827, 0.06084239482879639, -0.06489482522010803, -0.025294555351138115, -0.04272586852312088, -0.04619860649108887, -0.03077460080385208, 0.045711446553468704, 0.06455614417791367, -0.030824627727270126, 0.002201347379013896, 0.005628928542137146, -0.030375061556696892, 0.0141569459810853, -0.031943824142217636, -0.09643208980560303, -0.012166938744485378, 0.028850480914115906, 0.01907314918935299, -0.03281570225954056, -0.03806976601481438, -0.012961318716406822, 0.06177373230457306, -0.03508685156702995, 0.007771739736199379, 0.015153399668633938, -0.02208491414785385, 0.04418648034334183, -0.02144518308341503, -0.012755263596773148, 0.003916169051080942, 0.03844450041651726, -0.014691661112010479, -0.05785192549228668, -0.0157917533069849, -0.05639704316854477, 0.003080965718254447, -0.005851005204021931, -0.039893586188554764, 0.0015190416015684605, -0.010572180151939392, -0.007133408449590206, 0.007585189770907164, -0.021523449569940567, -0.005122761707752943, -0.0025844660121947527, 0.010234221816062927, 0.03072294220328331, 0.10745414346456528, 0.05691683292388916, 0.009916550479829311, 0.01676735281944275, 0.03156154230237007, -0.0039460258558392525, 0.002693797927349806, 0.03780484199523926, 0.02124253287911415, -0.062021270394325256, 0.014434649609029293, -0.039402883499860764, -0.015593517571687698, 0.00991868320852518, 0.005541146267205477, -0.014266693964600563, -0.03270576894283295, -0.056751642376184464, -0.008544747717678547, -0.024637077003717422, 0.042318154126405716, -0.0351971872150898, -0.018749313428997993, -0.023491350933909416, -0.07295127213001251, -0.0036808173172175884, -0.057647015899419785, -0.037728678435087204, -0.010875990614295006, -0.009133875370025635, -0.05452582985162735, -0.022279389202594757, -0.03212851658463478, 0.009609316475689411, -0.05789417028427124, 0.06389665603637695, 0.017702247947454453, 0.038015905767679214, -0.0004387556982692331, -0.014686879701912403, 0.1084364503622055, 0.011472289450466633, -0.03817092627286911, 0.03939750790596008, 0.05595439299941063, 0.03253142535686493, 0.00900576077401638, -0.03741537407040596, 0.003090690588578582, 0.03317065164446831, -0.032616026699543, 0.01619878225028515, 0.01701543480157852, -0.006705091800540686, -0.005971597973257303, -0.02268882468342781, -0.04406784102320671, 0.04255755990743637, 0.004971277434378862, 0.0520259290933609, 0.022897152230143547, 0.010806579142808914, -0.026118382811546326, 0.06163943186402321, 0.019604986533522606, 0.05760304257273674, 0.043131500482559204, -0.020033812150359154, -0.010395011864602566, 0.06747995316982269, -0.07495295256376266, 0.03266708925366402, 0.011037671007215977, -0.059991881251335144, 0.005239866673946381, 0.0013875263975933194, 0.0013166677672415972, 0.005475284997373819, -0.01901468075811863, 0.032438624650239944, 0.08198232203722, -0.00951601006090641, 0.040928978472948074, -0.03249220550060272, -0.014744024723768234, -0.036658115684986115, -0.0003872938104905188, -0.041214652359485626, -0.003945560194551945, 0.040731094777584076, -0.030521150678396225, 0.024859333410859108, -0.03737180680036545, 0.018497493118047714, 0.0031479864846915007, -0.03721604868769646, -0.026209238916635513, 0.006746831350028515, 0.005129154305905104, -0.04014613479375839, -0.03398969769477844, -0.042190615087747574, -0.028558211401104927, -0.020124401897192, 0.036984313279390335, 0.0006013642996549606, -0.04522372782230377, 0.013112961314618587, -0.01566370390355587, 0.03787120431661606, 0.0016997969942167401, -0.019003188237547874, -0.06217489391565323, -0.048687949776649475, -0.008129257708787918, -0.06143511086702347, 0.08873847872018814, -0.018478509038686752, -0.02577289380133152, 0.0068379975855350494, -0.0063930959440767765, 0.026668444275856018, -0.025738967582583427, -0.012588265351951122, 0.040205925703048706, 0.012791935354471207, -0.08871810138225555, 0.014897690154612064, 0.006985637824982405, 0.00043089763494208455, -0.04675144702196121, -0.028297707438468933, -0.08128691464662552, 0.051250990480184555, -0.003806775901466608, 0.021531967446208, 0.06704230606555939, -0.0023461838718503714, 0.02459392137825489, 0.024503003805875778, 0.021364105865359306, 0.08371679484844208, -0.002235983032733202, 0.03365897759795189, 0.05610508844256401, -0.010329135693609715, -0.02347729355096817, -0.0124054541811347, 0.013584406115114689, -0.05678296834230423, -0.016626685857772827, -0.022356893867254257, 0.009400889277458191, 0.02304350957274437, -0.023965591564774513, -0.03050185926258564, 0.036406517028808594, 0.010361459106206894, 0.025284795090556145, 0.030850447714328766, -0.03996608778834343, 0.0206416267901659, -0.042570311576128006, 0.06998033821582794, -0.03892476111650467, 0.07102028280496597, 0.020519137382507324, -0.026541495695710182, -0.027926715090870857, 0.06668350100517273, -0.011449187062680721, 0.010384783148765564, -0.01161701325327158, 0.048536721616983414, 0.03308723121881485, 0.047687508165836334, 0.013975937850773335, 0.016980942338705063, 0.03755910322070122, -0.032184213399887085, -0.06575264781713486, -0.020323259755969048, 0.002277991035953164, 0.01661340706050396, 0.021512480452656746, 0.04283099249005318, 0.00032339885365217924, -0.05246232450008392, 0.08394433557987213, -0.07310096174478531, 0.014319922775030136, -0.0472300760447979, 0.07750001549720764, -0.05539262667298317, -0.031717460602521896, -0.02039276249706745, 0.06141912192106247, 0.10245285928249359, 0.0008603589958511293, -0.05164984241127968, -0.0044302260503172874, -0.01568436622619629, 0.062731072306633, -0.06465774029493332, -0.01775473915040493, -0.0032192154321819544, -0.059695325791835785, -0.045897360891103745, -0.017500726506114006, -0.0036915724631398916, -0.07259364426136017, -0.017675988376140594, 0.026850566267967224, 0.05029168352484703, -0.02917507477104664, 0.02754134312272072, 0.07390380650758743, 0.01768527925014496, -0.01698850281536579, -0.005814520642161369, -0.05215921252965927, 0.05784536898136139, -0.019782980903983116, -0.061762988567352295, -0.027016477659344673, -0.04456054046750069, -0.01589440368115902, 0.005938253365457058, -0.00095143704675138, -0.014755114912986755, 0.06061122566461563, 0.0027851727791130543, -0.043225422501564026, -0.0007198759121820331, -0.01166126225143671, -0.023171082139015198, 0.00266436068341136, -0.10308346897363663, 0.02929975837469101, 0.008747212588787079, 0.06689747422933578, -0.004723526071757078, 0.02701609395444393, -0.029896020889282227, 0.022689487785100937, -0.007584806531667709, -0.02421928197145462, 0.08169450610876083, 0.06534659117460251, 0.024365965276956558, -0.03863009437918663, 0.0428021140396595, 0.028627531602978706, 0.03641539439558983, 0.04105772450566292, -0.023494252935051918, 0.01731143891811371, -0.026625653728842735, -0.002678674878552556, 0.012598487548530102, 0.014406824484467506, -0.04625701159238815, 0.05225197598338127, 0.04081147164106369, 0.036462411284446716, 0.017649240791797638, -0.010664800181984901, -0.023168163374066353, -0.035524532198905945, 0.011967863887548447, 0.014088957570493221, 0.012142189778387547, 0.03264099732041359, -0.03673990070819855, -0.01432134211063385, -0.0028515032026916742, -0.04905017837882042, 0.08080361038446426, 0.03858570381999016, 0.008891437202692032, -0.027803117409348488, 0.03825635835528374, -0.038880765438079834, -0.05119521543383598, -0.013658663257956505, 0.0029822008218616247, -0.0383182093501091, -0.01897008717060089, 0.02629568800330162, -0.014700429514050484, -0.005608090665191412, 0.015634698793292046, -0.03961733356118202, 0.05237293615937233, -0.03856566920876503, -0.01515176985412836, 0.016258729621767998, 0.03721218928694725, 0.03292202576994896, -0.02200518548488617, 0.02383236028254032, -0.024553190916776657, -0.03878452256321907, -0.018667997792363167, -0.04985419660806656, 0.04067336022853851, -0.014445570297539234, 0.012123974040150642, 0.03926519677042961, 0.022831769660115242, 0.034535787999629974, 0.015085394494235516, 0.038591355085372925, -0.013995442539453506, 0.002291128970682621, -0.04454730451107025, 0.016278905794024467, 0.04073704034090042, -0.015494143590331078, -0.025908546522259712, -0.00293134618550539, 0.056994736194610596, 0.014266750775277615, -0.04358306899666786, 0.03324125334620476, 0.038431331515312195, 0.017171362414956093, 0.006441180594265461, 0.012644590809941292, -0.027012985199689865, 0.008316024206578732, 0.04460418224334717, 0.03719085454940796, -0.015044727362692356, 0.004756156820803881, 0.030918357893824577, -0.0015728120924904943, -0.022473927587270737, 0.012482802383601665, 0.0042025544680655, -0.01964949071407318, 0.024178611114621162, 0.03979017212986946, 0.007617021445184946, -0.05810590833425522, 0.003526373766362667, 0.0080866115167737, -0.02776166796684265, 0.019875744357705116, 0.032912854105234146, -0.04466918483376503, 0.011812826618552208, -0.03916675224900246, 0.03181634843349457, 0.02212500385940075, 0.007116093300282955, 0.02648753486573696, 0.005697319284081459, 0.0006324934074655175, -0.000331586372340098, 0.010246609337627888, -0.03384292125701904, -0.01403664518147707, -0.005598966497927904, 0.011238470673561096, -0.06297945976257324, -0.041363537311553955, 0.010803856886923313, -0.010394536890089512, -0.029615459963679314, -0.025342967361211777, 0.017069494351744652, 0.03840438276529312, 0.020300447940826416, 0.03349655494093895, 0.009409812279045582, 0.0162213072180748, 0.013478861190378666, 0.007732739672064781, -0.04477016627788544, 0.03649948909878731, 0.03970508277416229, 0.025225786492228508, -0.051486216485500336, -0.012617493979632854, 0.02535136230289936, -0.02125280350446701, -0.014065130613744259, -0.020894572138786316, 0.019563306123018265, 0.0291728675365448, 0.01107440609484911, 0.038755256682634354, -0.03480498492717743, 0.005792409181594849, 0.02934914082288742, -0.013966625556349754, 0.03563902899622917, 0.01757926121354103, -0.007155765313655138, 0.028983019292354584, 0.019970402121543884, -0.08516356348991394, 0.03940392658114433, 0.014927822165191174, -0.04052213206887245, -0.001267052604816854, 0.026741450652480125, -0.007971884682774544, -0.03597065806388855, 0.0031001076567918062, 0.0007399902096949518, 0.02082034945487976, 0.05369864031672478, 0.0038298610597848892, 0.08089368790388107, -0.05558595061302185, -0.021028047427535057, -0.04222023859620094, -0.01656302995979786, 0.05657701566815376, 0.031185738742351532, 0.0558914951980114, -0.04578932374715805, 0.009631618857383728, -0.005931034684181213, -0.0076476894319057465, -0.05180320143699646, -0.048892054706811905, 0.000029452674425556324, 0.005149378906935453, 0.00677808653563261, 0.016039716079831123, 0.03620398789644241, -0.020805105566978455, -0.04919007793068886, -0.03898590803146362, 0.0036181204486638308, -0.019259817898273468, -0.07997552305459976, -0.00740669434890151, -0.056147657334804535, 0.03622722998261452, -0.03212880715727806, -0.023726845160126686, -0.0029657098930329084, 0.034148357808589935, 0.01630999520421028, 0.057443767786026, 0.009133406914770603, -0.04333363100886345, -0.05017611011862755, 0.046560756862163544, 0.027129070833325386, 0.009965638630092144, 0.08603664487600327, 0.017121003940701485, 0.0395907498896122, -0.03316989168524742, 0.026395360007882118, 0.030116397887468338, -0.04241206869482994, -0.01537901721894741, -0.06629956513643265, -0.0008154598763212562, -0.015334103256464005, -0.0015130630927160382, 0.02516636997461319, 0.05358963459730148, -0.05939584597945213, -0.07682833075523376, 0.02797882817685604, 0.016319148242473602, 0.0011194233084097505, 0.019500412046909332, -0.0021024716552346945, 0.04045013710856438, 0.009260302409529686, -0.021803168579936028, 0.0036495965905487537, -0.06998387724161148, -0.05187412351369858, -0.062314312905073166, -0.008444263599812984, 0.02833321876823902, -0.008713140152394772, 0.012478142976760864, 0.03714393079280853, 0.014526821672916412, -0.02188742160797119, -0.051258333027362823, 0.007643030025064945, -0.008126678876578808, -0.027227038517594337, 0.018612023442983627, 0.028349991887807846, 0.03964526951313019, 0.030260343104600906, -0.05624924600124359, -0.017622750252485275, -0.05904868245124817, -0.0008454130729660392, 0.008005230687558651, -0.02253250777721405, 0.055564239621162415, 0.048486776649951935, -0.05690034106373787, -0.01298471074551344, -0.06354684382677078, -0.07853749394416809, 0.04391687735915184, 0.021092137321829796, -0.024663319811224937, -0.007534470409154892, 0.0724080353975296, 0.010289816185832024, 0.016695016995072365, -0.04192383214831352, -0.009969075210392475, -0.08971681445837021, 0.05654267966747284, 0.048943161964416504, -0.0013469057157635689, 0.009038534946739674, -0.011643961071968079 ]
<p>I have often seen diagrams, like <a href="http://en.wikipedia.org/wiki/Lens_%28optics%29#Imaging_properties">this one</a> on Wikipedia for a thin convex lens that show three lines from a point on the object converging at the image. Do all the other lines from that point on the object that pass through the lens converge at the same point on the image?</p> <p>*<em>Updated question: *</em> to say, "from that point on the object"</p>
g1519
[ 0.03011160157620907, -0.04393274337053299, 0.026087390258908272, -0.0028942376375198364, 0.05066298320889473, -0.0017292007105425, -0.009894927963614464, 0.006452036090195179, -0.01686861552298069, -0.03555857017636299, 0.0002299539337400347, -0.0004220072878524661, 0.09488923102617264, -0.023412222042679787, -0.009751971811056137, -0.03595893085002899, 0.056962303817272186, -0.06520015001296997, -0.007149542216211557, 0.0720583125948906, 0.0007018111064098775, 0.06705248355865479, -0.011083564721047878, -0.017384875565767288, 0.001387845491990447, 0.013387000188231468, 0.021474502980709076, -0.0003947569348383695, -0.07351794093847275, -0.029820039868354797, 0.007934275083243847, -0.020183565095067024, 0.04309942200779915, -0.05581483617424965, 0.0024409638717770576, 0.02812434732913971, 0.004418432712554932, 0.016073618084192276, 0.032205965369939804, 0.025226306170225143, 0.022109420970082283, -0.008100052364170551, -0.022575439885258675, -0.02050488255918026, -0.008605048060417175, -0.07279621064662933, -0.023206593468785286, -0.000693218840751797, -0.01989593915641308, 0.0017361148493364453, -0.03383702412247658, 0.0844583809375763, -0.02563638612627983, -0.03868686035275459, -0.0046347761526703835, 0.07271195948123932, -0.012479265220463276, 0.0166382547467947, 0.05481681972742081, -0.024612553417682648, -0.017549261450767517, 0.0029789377003908157, -0.008331811055541039, 0.03812512010335922, 0.09300797432661057, -0.016977626830339432, -0.05801756680011749, -0.008517800830304623, 0.03732721135020256, -0.014919053763151169, 0.016624905169010162, -0.02962792105972767, 0.032301418483257294, -0.07175219058990479, -0.06913930922746658, 0.013663838617503643, 0.018939368426799774, -0.0563255175948143, -0.015091522596776485, 0.0032160559203475714, -0.03908253088593483, -0.010875359177589417, -0.03150758519768715, 0.021721728146076202, 0.12485089898109436, 0.04188279062509537, 0.06020331382751465, 0.00008760210766922683, -0.017368467524647713, 0.036160677671432495, 0.021890366449952126, 0.06847450882196426, -0.03277651220560074, 0.028078634291887283, 0.021968353539705276, -0.019278908148407936, 0.0003023981407750398, -0.00898011215031147, 0.025717204436659813, -0.010041607543826103, -0.05062036216259003, -0.014516317285597324, 0.012562674470245838, -0.008656241931021214, -0.043141815811395645, 0.020914245396852493, 0.041837990283966064, -0.038983751088380814, -0.02889278158545494, -0.010537305846810341, -0.060976333916187286, -0.10944196581840515, -0.013558849692344666, 0.012388595379889011, -0.06997061520814896, -0.07398112863302231, 0.036189693957567215, 0.004736096598207951, -0.0225168876349926, 0.02373691461980343, 0.011047877371311188, -0.009984972886741161, 0.004517444409430027, 0.07592437416315079, -0.031679652631282806, 0.011471141129732132, 0.0241349246352911, -0.023264842107892036, 0.03533116728067398, 0.019156794995069504, 0.03986551985144615, -0.0034147112164646387, 0.011283710598945618, -0.03760985657572746, -0.0007588986773043871, 0.02881658636033535, -0.01883758418262005, -0.043744053691625595, 0.06328333914279938, 0.01103257853537798, -0.015808774158358574, -0.05259726196527481, -0.021466027945280075, -0.024915777146816254, -0.0029239545110613108, -0.015460916794836521, 0.02442462369799614, 0.02600529044866562, 0.08264315128326416, 0.02318655699491501, -0.027856765314936638, 0.03357706591486931, 0.003973075188696384, 0.014149298891425133, 0.01023091934621334, -0.02053210325539112, -0.0072739762254059315, 0.014160078018903732, 0.03527549281716347, -0.038849618285894394, -0.01665898784995079, -0.022369595244526863, 0.020039226859807968, -0.0012509204680100083, -0.07908667623996735, -0.06708969175815582, -0.0012132255360484123, -0.07831985503435135, 0.03819996863603592, -0.09102615714073181, 0.0004352118994574994, 0.03294670581817627, -0.0054182447493076324, -0.0453411228954792, 0.021079404279589653, 0.035997822880744934, 0.0068448204547166824, -0.014446018263697624, 0.049624934792518616, 0.014727921225130558, -0.09111706167459488, 0.05372102931141853, -0.018017297610640526, -0.02572507970035076, 0.02875477261841297, 0.024146774783730507, -0.007975881919264793, -0.027598589658737183, -0.017905307933688164, 0.027021093294024467, -0.02600540593266487, -0.0036338164936751127, -0.01761804148554802, 0.06420052796602249, 0.01789775677025318, -0.03672337904572487, 0.03506792336702347, -0.06987461447715759, -0.029874807223677635, -0.01976022496819496, 0.012422247789800167, 0.013770240359008312, 0.02107684127986431, 0.08734003454446793, -0.026365354657173157, -0.002832551719620824, 0.013628670014441013, 0.018221965059638023, 0.029038557782769203, 0.028441939502954483, -0.0006755533977411687, 0.032020218670368195, 0.032384712249040604, -0.014401799067854881, -0.07306461781263351, -0.026212844997644424, 0.02258811704814434, -0.003138369182124734, -0.02449388988316059, 0.017106574028730392, 0.006352169904857874, 0.054161302745342255, 0.02152414061129093, -0.04294205829501152, -0.02674010954797268, -0.02631947584450245, -0.03215771168470383, -0.04262540861964226, 0.0018236895557492971, -0.010462379083037376, -0.05410588160157204, -0.04413465037941933, 0.02378738857805729, -0.06873664259910583, 0.06834228336811066, 0.0037996035534888506, -0.05019374564290047, 0.023533865809440613, -0.010199788957834244, 0.01381630264222622, 0.0024466661270707846, 0.018821673467755318, -0.008799384348094463, -0.020440226420760155, 0.02389753982424736, -0.061393432319164276, 0.013502227142453194, 0.010394095443189144, -0.004691397771239281, 0.08374486118555069, 0.02751300483942032, 0.0315047912299633, 0.010489177890121937, 0.08995978534221649, 0.006992725655436516, -0.015501071698963642, 0.004902678541839123, 0.010206605307757854, -0.02539670839905739, 0.003724628360942006, -0.04148121550679207, 0.015469093807041645, -0.03238152340054512, -0.03968518227338791, -0.05483654886484146, -0.020791368559002876, -0.009364480152726173, 0.01791669987142086, 0.03874807804822922, 0.021595550701022148, -0.0035237076226621866, 0.04931621253490448, 0.01932552270591259, 0.005152571480721235, 0.0009034690447151661, 0.01156567595899105, -0.0037108485121279955, -0.009893516078591347, -0.008736205287277699, -0.055239446461200714, 0.010317792184650898, 0.02515973336994648, -0.018870333209633827, 0.03200354427099228, 0.04200658202171326, -0.034807976335287094, 0.03165244683623314, 0.02533319778740406, 0.03351912274956703, 0.033971719443798065, -0.021214736625552177, 0.08158417791128159, 0.04674520716071129, 0.02745799534022808, -0.03188806772232056, 0.011921138502657413, 0.049998074769973755, 0.0248197503387928, 0.022946210578083992, 0.019292684271931648, -0.06363580375909805, -0.022665545344352722, -0.007417954038828611, -0.03234706446528435, 0.08918334543704987, 0.014572824351489544, -0.030482692644000053, -0.08247760683298111, 0.03079734928905964, 0.003263510297983885, 0.013313458301126957, -0.022734884172677994, 0.01453818567097187, 0.022733861580491066, 0.014088038355112076, -0.01010994054377079, 0.013055296614766121, 0.01172216609120369, 0.005495657678693533, 0.05926055461168289, -0.06108279898762703, 0.027484485879540443, -0.01757207326591015, -0.026603996753692627, 0.011487172916531563, 0.01927962899208069, 0.011203402653336525, -0.009866442531347275, 0.04254135116934776, 0.02764800563454628, -0.023020915687084198, -0.026919592171907425, -0.03596789762377739, 0.0377083420753479, 0.03049650229513645, -0.010357570834457874, -0.013225924223661423, -0.016736911609768867, 0.07401450723409653, 0.048127416521310806, 0.03536875545978546, 0.005403139628469944, 0.007441903930157423, -0.029889479279518127, 0.05332334339618683, -0.037142314016819, -0.008184005506336689, 0.00970334094017744, -0.0036403872072696686, -0.04710560292005539, 0.03577284514904022, 0.02936801128089428, 0.0012636632891371846, -0.07333897799253464, -0.05231282860040665, 0.02488858997821808, 0.013401873409748077, 0.027314526960253716, 0.016018206253647804, -0.0120448162779212, 0.0734083354473114, 0.001306873164139688, 0.03124612756073475, -0.03825641795992851, 0.0022435104474425316, 0.01920739933848381, 0.003078626934438944, 0.036087557673454285, 0.08122298866510391, 0.05500751733779907, 0.03703468665480614, -0.05050971731543541, -0.05403288081288338, 0.031076885759830475, -0.0463319793343544, 0.03648514300584793, 0.042797841131687164, -0.008658889681100845, -0.08691643923521042, 0.04677623510360718, 0.021352792158722878, 0.002717742696404457, 0.0376477874815464, 0.048801109194755554, -0.033094439655542374, 0.01184540893882513, -0.04500721022486687, -0.0733596459031105, 0.07089550793170929, 0.0053421794436872005, 0.021176589652895927, -0.06784199178218842, 0.009635179303586483, -0.013226162642240524, 0.04345947504043579, -0.06488462537527084, -0.016143901273608208, 0.02008494734764099, -0.012566382065415382, 0.03387861326336861, 0.041695963591337204, 0.05964171886444092, -0.004449920728802681, -0.012769903987646103, -0.017695782706141472, -0.04217526316642761, 0.03383754938840866, 0.042107634246349335, 0.008692567236721516, -0.026687368750572205, -0.0032969878520816565, -0.015478878282010555, 0.05854294076561928, -0.02633427269756794, 0.05988806113600731, 0.042099449783563614, -0.0022888043895363808, -0.007472475524991751, -0.032576438039541245, 0.03336293250322342, -0.04726696386933327, 0.013272978365421295, -0.05043598264455795, -0.0008182601304724813, -0.04359620064496994, 0.04494761303067207, 0.05121254548430443, -0.0014315791195258498, -0.04277019947767258, 0.025562457740306854, 0.02168967016041279, 0.005982148461043835, 0.01162754837423563, 0.029524419456720352, -0.06015443056821823, 0.01959598809480667, -0.03213769942522049, 0.07156284153461456, -0.00455459812656045, -0.021942371502518654, -0.043979957699775696, -0.026156116276979446, 0.029513224959373474, -0.044269002974033356, -0.0005312055582180619, -0.000686216342728585, -0.0401553213596344, 0.04007123038172722, -0.0010508507257327437, 0.002703605219721794, -0.06704186648130417, 0.014389343559741974, -0.06904532015323639, -0.017659315839409828, -0.021785994991660118, -0.026792647317051888, 0.0023403363302350044, 0.014748469926416874, 0.02415672317147255, -0.05668224021792412, 0.042155832052230835, 0.025632642209529877, 0.03553464263677597, -0.01380455307662487, 0.03833361715078354, -0.049921490252017975, 0.011634967289865017, 0.0032371636480093002, -0.028276171535253525, 0.006653380114585161, 0.005504828877747059, 0.0730038583278656, 0.09384110569953918, 0.04488657787442207, 0.015429059974849224, -0.0021176906302571297, 0.0027639251202344894, 0.023736124858260155, -0.0069371480494737625, -0.03529690206050873, -0.030965164303779602, -0.02158866636455059, 0.03394680842757225, -0.010439417324960232, -0.016678586602211, 0.03982986882328987, -0.013791842386126518, 0.011652061715722084, 0.019422326236963272, 0.021653519943356514, 0.027647366747260094, -0.04824386164546013, 0.003548838198184967, -0.021420056000351906, -0.014176216907799244, -0.059474878013134, 0.07028499990701675, 0.0201577078551054, 0.009104728698730469, 0.010055448859930038, -0.031092064455151558, -0.010098169557750225, -0.06606107950210571, -0.0034503822680562735, -0.03626697137951851, 0.015163283795118332, 0.05564315244555473, -0.07690563052892685, 0.024240976199507713, 0.05586886405944824, 0.027888726443052292, -0.014603844843804836, 0.027803458273410797, -0.006700416561216116, -0.03282609209418297, -0.015201836824417114, -0.09545375406742096, 0.005196981132030487, -0.02112143114209175, -0.013444380834698677, 0.010000793263316154, -0.008180972188711166, -0.03579310327768326, -0.019528884440660477, 0.03251132369041443, -0.0025147367268800735, -0.010075479745864868, -0.0006708730943500996, 0.06559305638074875, 0.008304879069328308, -0.04681314155459404, 0.048634327948093414, 0.02359856851398945, -0.00819915160536766, 0.010251668281853199, -0.005707739386707544, -0.028319742530584335, -0.011840999126434326, 0.02845134027302265, 0.041147615760564804, 0.006612628698348999, 0.05185145139694214, 0.012941204011440277, 0.10265672951936722, 0.018555615097284317, -0.04574861004948616, 0.0038831422571092844, -0.006438712123781443, 0.015038092620670795, 0.015327715314924717, 0.012001372873783112, 0.03261278569698334, -0.048880673944950104, 0.019840100780129433, -0.009361011907458305, 0.01531209982931614, 0.01368314865976572, -0.03576097637414932, 0.025465482845902443, -0.05390944704413414, 0.014850900508463383, -0.00879074726253748, -0.014397324994206429, -0.0010540478397160769, -0.03245006874203682, -0.048089295625686646, -0.03285521641373634, 0.07473652064800262, 0.03799811005592346, 0.02464158833026886, 0.0209715124219656, -0.04623756185173988, 0.017970560118556023, -0.0071602026000618935, 0.05611608922481537, 0.030729973688721657, -0.003162490436807275, -0.007237092591822147, -0.013265946879982948, 0.0185166597366333, 0.0017002893146127462, -0.01662217266857624, 0.014430519193410873, -0.0355432964861393, -0.007397051434963942, 0.03984728455543518, -0.030634017661213875, -0.02920491434633732, -0.004672538489103317, -0.03124089166522026, -0.0034706792794167995, 0.005742642097175121, 0.002263192320242524, -0.02207910642027855, 0.04898611083626747, -0.00914180651307106, 0.007322574034333229, 0.06792256236076355, -0.026791885495185852, 0.039079271256923676, -0.015933247283101082, 0.04390638321638107, 0.018651068210601807, -0.043333280831575394, -0.01514510065317154, 0.0330832302570343, -0.02802152931690216, -0.0037138755433261395, 0.030454974621534348, -0.07048224657773972, 0.027581844478845596, 0.03691231831908226, 0.02904035896062851, 0.012141605839133263, 0.014426208101212978, 0.01205847691744566, -0.04653771221637726, -0.019803175702691078, -0.01848234422504902, -0.04488426074385643, 0.020992040634155273, -0.0577489472925663, -0.005555484909564257, -0.010156919248402119, -0.03835725411772728, -0.004179661627858877, 0.018485454842448235, 0.01904090866446495, 0.017308052629232407, 0.03738601505756378, 0.0010820570169016719, -0.013345817103981972, -0.02139187790453434, 0.004042827989906073, -0.012087821029126644, 0.0297537948936224, -0.02449893206357956, 0.012935953214764595, 0.030830640345811844, 0.07096666842699051, 0.024085920304059982, -0.013836800120770931, 0.004537311848253012, 0.03395300358533859, 0.008144931867718697, -0.017102200537919998, 0.0011775778839364648, -0.06261947005987167, -0.07863651216030121, -0.005926333833485842, 0.023495333269238472, 0.03221180662512779, -0.03399424999952316, 0.05138050392270088, -0.0481666661798954, 0.05302105098962784, -0.005600091069936752, -0.028467340394854546, 0.0158123467117548, -0.035531364381313324, -0.011171484366059303, 0.0019382430473342538, -0.030316567048430443, -0.04129638150334358, -0.021448295563459396, -0.014854307286441326, 0.007671985309571028, -0.09662513434886932, -0.01614558883011341, -0.0025620674714446068, 0.03007563017308712, -0.009994473308324814, -0.017002075910568237, 0.0937165841460228, -0.007005167193710804, 0.025393787771463394, -0.07105635106563568, 0.07400833815336227, -0.012385985814034939, 0.03422718495130539, 0.03433789685368538, 0.04663265496492386, 0.048986539244651794, -0.05351077765226364, -0.058003608137369156, -0.021174924448132515, -0.029553471133112907, -0.025143295526504517, -0.008459266275167465, -0.06672298163175583, 0.03686647117137909, -0.01090936828404665, 0.05083532631397247, -0.03656009957194328, 0.007323430851101875, -0.019520683214068413, 0.06775358319282532, 0.023591769859194756, -0.022319946438074112, 0.06027037277817726, -0.011512493714690208, 0.014531689696013927, -0.03771704062819481, -0.03554685786366463, 0.026962917298078537, -0.02293434925377369, -0.056141577661037445, -0.0029706533532589674, 0.026346849277615547, 0.007233451586216688, -0.042978908866643906, -0.03950444608926773, -0.00080831692321226, 0.028472337871789932, -0.03869754448533058, 0.027031034231185913, -0.03306140378117561, -0.036852963268756866, -0.04587406665086746, 0.028240757063031197, -0.06189078465104103, 0.04268387332558632, -0.021059922873973846, -0.06944899260997772, -0.03222837671637535, 0.021360086277127266, -0.005191737785935402, -0.006728956010192633, -0.018831580877304077, -0.015140320174396038, -0.07428249716758728, 0.023880524560809135, -0.04337447136640549, 0.022203870117664337, 0.00547361234202981, 0.04153167083859444, -0.00448928726837039, -0.07612461596727371, -0.008221561089158058, -0.0618041567504406, 0.04812829568982124, -0.037527721375226974, -0.0028135960455983877, -0.032209526747465134, 0.02343624457716942, -0.003837047377601266, -0.02078399248421192, -0.008114781230688095, 0.0735170766711235, 0.023881828412413597, -0.01585262082517147, 0.01423543319106102, 0.0498548224568367, 0.005948700476437807, 0.001501147635281086, -0.05201392248272896, -0.03319517523050308, 0.01971242018043995, 0.06449870765209198, 0.008733118884265423, -0.04625494033098221, -0.061444271355867386, -0.0015095977578312159, -0.006002434063702822, -0.019231397658586502, -0.08130200207233429, -0.06147516146302223, 0.0075929248705506325 ]
<p>I was at a lecture yesterday and there was a demo of a van de graff generator. He held the smaller metal globe which is attached by a wire, about 4cm from the main globe. This created a spark between the two globes. At the same time the spark happened the speakers in the hall would click loudly, the projector (on the other side of the room) would turn yellow and the text moved down, then flashed black and back to normal. And the plasma globe that was next to the van de graff generator which was switched off (but on at the wall) would briefly turn on. </p> <p>Is it possible for a spark to do that? Or is there something else happening at the same time? </p>
g1520
[ 0.03165609762072563, 0.03879407048225403, -0.01335430983453989, -0.06713100522756577, 0.04104415327310562, 0.00013033229333814234, -0.004953073803335428, 0.02525428496301174, -0.020344268530607224, -0.007063702214509249, -0.03431401774287224, 0.05154280364513397, -0.005402466282248497, 0.013206756673753262, -0.0039027039892971516, -0.023441487923264503, 0.05415576696395874, -0.003050336381420493, -0.07336433231830597, 0.03188714012503624, -0.037179458886384964, -0.012736649252474308, -0.021207600831985474, -0.07110706716775894, -0.023865526542067528, 0.03313882648944855, -0.004698525182902813, -0.0006619062623940408, 0.00841535720974207, -0.07485172152519226, -0.03515412658452988, -0.01007379125803709, -0.021244686096906662, -0.060767777264118195, -0.02367440052330494, 0.010320410132408142, 0.01127078291028738, 0.021139109507203102, -0.026254354044795036, -0.015127327293157578, -0.006757912691682577, 0.012334820814430714, 0.038798872381448746, -0.00073266337858513, 0.03300373628735542, 0.010070273652672768, 0.0233784019947052, 0.0447864904999733, -0.011248826049268246, -0.06694697588682175, -0.06302741914987564, 0.02439625933766365, 0.008712264709174633, 0.0016445257933810353, 0.03396829217672348, 0.002376678166911006, 0.0038610242772847414, -0.06713008880615234, 0.06541059166193008, 0.014780453406274319, -0.05167270824313164, 0.04347024857997894, 0.040312785655260086, -0.011228124611079693, 0.01389981061220169, -0.03624657541513443, -0.050065863877534866, -0.0006907638162374496, 0.028501544147729874, 0.02012951485812664, -0.041475649923086166, 0.04521408677101135, -0.014607740566134453, 0.00011791680299211293, 0.013282393105328083, 0.00792887806892395, 0.013061179779469967, -0.011578546836972237, 0.018077531829476357, 0.071930892765522, -0.032346319407224655, -0.0045066107995808125, -0.0165427066385746, 0.01036557462066412, 0.027832094579935074, -0.02539599873125553, -0.05575387552380562, -0.04325760155916214, -0.04371442273259163, -0.06183195859193802, 0.08824556320905685, 0.003815404139459133, 0.01456813421100378, 0.0006942397449165583, -0.0596940815448761, 0.04482799768447876, 0.008342341519892216, 0.04644495248794556, 0.04800258204340935, 0.0376349613070488, -0.06497349590063095, -0.09121543914079666, 0.011976812966167927, -0.013836024329066277, -0.02465178817510605, -0.04378514364361763, 0.07095175236463547, -0.027796905487775803, -0.03316464647650719, -0.02492094784975052, 0.02114233560860157, -0.10295306146144867, -0.02925281412899494, -0.023282837122678757, -0.03561045229434967, -0.021187519654631615, 0.03314385935664177, -0.022591523826122284, 0.0020201553124934435, 0.030502628535032272, 0.030588986352086067, -0.08370110392570496, -0.07060205936431885, 0.06637417525053024, 0.06937745213508606, -0.05300652235746384, 0.06039922311902046, -0.05464236065745354, -0.018703700974583626, 0.013859466649591923, 0.003828026819974184, -0.0015217267209663987, -0.031072480604052544, 0.036674465984106064, 0.02207794412970543, 0.02776554599404335, 0.08850226551294327, 0.05210133641958237, 0.01655106619000435, 0.03224031999707222, 0.020690038800239563, -0.05951473116874695, -0.04034866765141487, -0.06884677708148956, -0.01117648370563984, 0.06565960496664047, 0.018890226259827614, 0.0014777631731703877, 0.017639873549342155, -0.025340301916003227, -0.03090827167034149, -0.032033976167440414, 0.001325691002421081, -0.011829238384962082, 0.05884389951825142, -0.02530084177851677, 0.018747854977846146, -0.010522332973778248, -0.013612351380288601, -0.015908731147646904, 0.008161177858710289, -0.015150430612266064, 0.0012316110078245401, -0.0000879523140611127, 0.0065809632651507854, -0.021870139986276627, 0.06716756522655487, -0.024072594940662384, -0.045953843742609024, -0.009243904612958431, -0.03803466632962227, 0.0021185274235904217, 0.0014243097975850105, 0.020687859505414963, 0.024090580642223358, 0.02686488628387451, 0.0324300117790699, -0.04087026044726372, 0.020578762516379356, -0.006153642665594816, -0.09488913416862488, -0.007673483807593584, -0.04656438156962395, -0.00885874591767788, 0.034513067454099655, 0.01772249862551689, 0.0015410823980346322, 0.004007468465715647, -0.04455939307808876, 0.034120988100767136, -0.08566626906394958, 0.006219787523150444, -0.04068969562649727, 0.02077198401093483, -0.011087531223893166, -0.045832544565200806, -0.007843667641282082, -0.003007320687174797, -0.025472573935985565, 0.00914138276129961, -0.018912773579359055, 0.018355460837483406, 0.04567735269665718, 0.0368194505572319, -0.0006029541837051511, 0.002157271374017, -0.03121473453938961, 0.0028184622060507536, -0.0004547139396890998, -0.030653683468699455, 0.04529574513435364, 0.04532230272889137, -0.018738189712166786, 0.020065922290086746, -0.024897677823901176, -0.0328398160636425, -0.016995517536997795, -0.06058650463819504, 0.019999539479613304, -0.012720917351543903, -0.03448650985956192, 0.04468464478850365, 0.041514214128255844, 0.0040726130828261375, 0.013368473388254642, 0.03281357139348984, -0.004289637785404921, -0.05927987024188042, -0.01890755631029606, 0.00003054136686841957, 0.012496563605964184, 0.0011311990674585104, 0.019854489713907242, -0.031129924580454826, -0.004359459970146418, 0.041918642818927765, -0.010386745445430279, -0.0548686720430851, -0.03438621759414673, -0.02565542235970497, 0.035366687923669815, -0.06609898060560226, 0.04946400597691536, -0.05097352713346481, -0.006171794608235359, -0.05133451148867607, -0.0014024109113961458, 0.04534570500254631, 0.023529207333922386, 0.055816650390625, 0.0726855993270874, -0.03858489170670509, 0.009232546202838421, 0.03154197707772255, -0.05313992127776146, -0.034995585680007935, -0.01243996899574995, 0.013380485586822033, 0.02017890103161335, -0.041703756898641586, -0.027512362226843834, -0.04699236899614334, -0.013152207247912884, 0.009189662523567677, 0.0012256692862138152, -0.05633126199245453, -0.01879596710205078, -0.04745642840862274, -0.017756082117557526, -0.033356763422489166, 0.011484001763164997, 0.024787891656160355, 0.004854019731283188, -0.012075170874595642, -0.014101642183959484, 0.03112076409161091, 0.016024140641093254, 0.00932475458830595, 0.07138258963823318, 0.008841685019433498, -0.06536782532930374, 0.027070987969636917, -0.05965140834450722, 0.03774762898683548, 0.009535345248878002, -0.03639807924628258, -0.014539921656250954, 0.03945476561784744, -0.05241719260811806, 0.012803223915398121, -0.11242896318435669, -0.02494523674249649, 0.10738907754421234, 0.020288731902837753, 0.005609660875052214, 0.031073225662112236, 0.025358235463500023, -0.016752390190958977, -0.015786055475473404, -0.0020840864162892103, 0.030290963128209114, -0.07859122008085251, -0.012315272353589535, 0.05957762897014618, 0.02163087949156761, 0.01595405302941799, -0.0396503247320652, 0.014246598817408085, 0.05314231291413307, 0.05484844744205475, -0.01679343357682228, 0.04213432967662811, 0.04423569142818451, 0.02225748635828495, 0.004125417675822973, 0.029601097106933594, 0.011276530101895332, 0.029704848304390907, 0.012140875682234764, 0.07933631539344788, -0.03179142624139786, -0.041396141052246094, -0.017154665663838387, -0.005112165585160255, 0.0225447416305542, 0.06082569807767868, 0.044549163430929184, 0.011506673879921436, -0.020699573680758476, 0.01758154109120369, -0.07566016167402267, -0.018596747890114784, -0.08367909491062164, -0.026016348972916603, 0.03214046359062195, 0.017546186223626137, 0.0044717807322740555, 0.03809215500950813, -0.010488628409802914, 0.06983215361833572, 0.04076744616031647, 0.03308211639523506, -0.009427876211702824, -0.02578251250088215, 0.029502063989639282, 0.04518833011388779, -0.02082596719264984, -0.05526131018996239, 0.007217808160930872, -0.03562219813466072, 0.05501585453748703, 0.04966757819056511, 0.006330952979624271, -0.04863017424941063, 0.0065613556653261185, -0.02519713155925274, 0.02074277028441429, 0.024968445301055908, -0.05475315451622009, 0.0007515919860452414, -0.027290355414152145, -0.015067743137478828, 0.025367215275764465, -0.0314716212451458, -0.0025431490503251553, -0.004109634552150965, -0.032013941556215286, 0.024741986766457558, 0.0038284931797534227, -0.060253601521253586, 0.05299779400229454, 0.0038249522913247347, -0.040303949266672134, 0.08645708113908768, 0.0009437483968213201, 0.019660281017422676, 0.020091384649276733, -0.0020259430166333914, -0.02809475176036358, 0.06656654179096222, -0.007462720386683941, -0.008523539640009403, 0.07217338681221008, 0.010671433061361313, 0.05946485325694084, -0.002865525661036372, 0.029204590246081352, 0.0023269650992006063, 0.019969893619418144, -0.04428312927484512, 0.04236917570233345, 0.026808546856045723, 0.017614293843507767, 0.013450673781335354, 0.03968258202075958, -0.013920167461037636, -0.008070936426520348, 0.012013796716928482, 0.05167912319302559, -0.006838356144726276, -0.01637599617242813, 0.017285963520407677, -0.005278346594423056, -0.06941433995962143, 0.022471774369478226, -0.024192044511437416, 0.002054390497505665, -0.011750301346182823, 0.06617753952741623, -0.051814332604408264, 0.01156210619956255, -0.019574284553527832, -0.00411222456023097, -0.03541205823421478, -0.013589159585535526, 0.03369683399796486, 0.06695494055747986, 0.046008918434381485, -0.01048746146261692, 0.02837797813117504, 0.022633081302046776, 0.01812017150223255, 0.016105549409985542, 0.044163476675748825, -0.00813270267099142, 0.03594833239912987, 0.0008604543982073665, -0.01430993340909481, -0.01575079932808876, 0.028599483892321587, 0.02673409879207611, 0.029348069801926613, -0.022756576538085938, 0.022760959342122078, 0.002932968782261014, 0.05520603060722351, -0.05239409953355789, 0.03693138062953949, -0.010127425193786621, 0.08544643968343735, 0.10618463903665543, -0.03647036477923393, 0.08428359031677246, 0.010229148901998997, 0.020908158272504807, 0.04036076366901398, -0.026983223855495453, 0.012892934493720531, -0.033532269299030304, -0.003900371491909027, -0.021549280732870102, -0.03889933228492737, -0.04591350257396698, -0.04979091137647629, 0.04586654528975487, -0.014012412168085575, -0.03923078998923302, 0.024646224454045296, -0.06782930344343185, -0.015615777112543583, 0.00120713678188622, -0.057504769414663315, 0.020582929253578186, 0.033300209790468216, 0.06718295812606812, -0.048185743391513824, -0.08890882879495621, -0.08115550875663757, -0.008664742112159729, -0.06601991504430771, 0.009547793306410313, 0.03155382350087166, -0.05344802886247635, 0.062361940741539, 0.01476028747856617, -0.05196426063776016, 0.01956791616976261, 0.015511151403188705, 0.024204405024647713, -0.014010246843099594, 0.005376793444156647, 0.03229200467467308, 0.015253167599439621, -0.006857126485556364, 0.01904762163758278, -0.001769289723597467, -0.04373921453952789, 0.08129668980836868, 0.021008135750889778, -0.021258587017655373, 0.09814604371786118, 0.01827080361545086, 0.01593596301972866, 0.008411513641476631, -0.0037822206504642963, -0.05998003110289574, 0.018396655097603798, 0.012282849289476871, -0.01423870399594307, 0.031850382685661316, 0.0012905708281323314, -0.041114795953035355, -0.006909704301506281, 0.019408607855439186, 0.018934208899736404, -0.03196235001087189, -0.039203252643346786, -0.011390963569283485, 0.037687040865421295, 0.058402467519044876, -0.0846327617764473, 0.0021099296864122152, 0.001892455155029893, 0.040377601981163025, 0.039484474807977676, -0.023125439882278442, -0.09834257513284683, -0.07483673840761185, -0.02461567521095276, 0.025666551664471626, 0.02755468152463436, -0.06793399155139923, -0.017773667350411415, -0.027885615825653076, -0.01719680428504944, 0.07885689288377762, 0.00811673328280449, 0.017511093989014626, 0.025427743792533875, 0.05296826735138893, 0.039417751133441925, -0.01399815734475851, -0.014800039120018482, -0.01958201453089714, -0.00798235647380352, -0.02804633602499962, 0.0077485088258981705, -0.016098085790872574, -0.04244979843497276, 0.022600729018449783, 0.010420887731015682, -0.011200307868421078, 0.04417048394680023, 0.006466907449066639, -0.0026458713691681623, -0.02404867485165596, -0.018679281696677208, -0.04049481078982353, 0.010958260856568813, -0.03284649923443794, 0.03962638974189758, 0.0493781603872776, 0.005982790142297745, 0.03668275848031044, 0.01698032021522522, 0.0011375832837074995, -0.030729331076145172, -0.011245513334870338, 0.04072072356939316, -0.04586891457438469, 0.05689585953950882, -0.045598216354846954, -0.012060759589076042, -0.0038268782664090395, 0.04232810437679291, 0.038707077503204346, 0.006949520204216242, -0.02367839217185974, 0.023839017376303673, 0.04617465287446976, 0.06919310241937637, -0.03426002711057663, -0.036732058972120285, -0.020655376836657524, -0.007858979515731335, -0.005735630635172129, 0.030977504327893257, 0.04051939770579338, -0.01908421702682972, -0.01970004476606846, -0.0017503182170912623, 0.024704352021217346, 0.04445066303014755, -0.0000649142821202986, -0.030510056763887405, 0.00634431978687644, -0.025816863402724266, 0.017681322991847992, -0.015150056220591068, -0.05405690148472786, -0.03541186824440956, 0.04277660697698593, -0.030825776979327202, 0.0316196009516716, -0.005115893203765154, 0.002534666331484914, -0.012969803996384144, 0.003127017989754677, -0.002897589234635234, -0.006815493106842041, 0.018912658095359802, 0.019306140020489693, 0.017685897648334503, -0.06223638728260994, -0.014353948645293713, 0.012183424085378647, -0.0258705485612154, 0.0433172769844532, 0.03907536342740059, -0.0006548147648572922, 0.00902959331870079, -0.011897657066583633, 0.012664052657783031, -0.034668464213609695, 0.007240972947329283, -0.030451275408267975, -0.03868847340345383, -0.0741068571805954, 0.052657321095466614, 0.049341559410095215, 0.006837481167167425, -0.021751174703240395, -0.03059437684714794, -0.066118024289608, 0.006374484859406948, 0.014717422425746918, -0.05298558250069618, -0.015387400984764099, 0.024478094652295113, -0.01647944003343582, -0.015217242762446404, -0.017368772998452187, -0.06862136721611023, 0.030037516728043556, 0.03633640334010124, 0.021105214953422546, -0.003363450989127159, -0.015466849319636822, 0.043981920927762985, -0.05727475881576538, 0.037791889160871506, -0.05209802836179733, -0.0026061879470944405, 0.028968757018446922, 0.06410381942987442, 0.018195660784840584, -0.007642748765647411, -0.033242642879486084, -0.051246169954538345, 0.01416696049273014, 0.052637968212366104, -0.034822918474674225, -0.037797316908836365, 0.018663890659809113, -0.03296361118555069, 0.045881543308496475, 0.017384769394993782, 0.05167711526155472, 0.03989803045988083, -0.005487504880875349, -0.019676929339766502, -0.007107777055352926, -0.032760847359895706, -0.0008078640094026923, 0.008905744180083275, 0.022798750549554825, -0.00039734074380248785, -0.019108213484287262, -0.0438806526362896, -0.002253121929243207, -0.003031110391020775, -0.03473050892353058, -0.06166744604706764, -0.008607950061559677, -0.02564222365617752, -0.0013872261624783278, 0.0467832125723362, 0.04084929823875427, 0.07276395708322525, 0.018930815160274506, 0.007139439694583416, -0.017826370894908905, -0.07015927881002426, -0.0002851677709259093, -0.0032005624379962683, -0.009032554924488068, -0.028458626940846443, 0.06458872556686401, 0.02323591522872448, -0.003599110757932067, -0.01617482677102089, -0.01775452494621277, 0.014571205712854862, 0.01497241947799921, 0.014268110506236553, -0.005132468417286873, 0.04782714322209358, -0.006756818387657404, -0.027824509888887405, -0.03153045102953911, -0.015425276011228561, -0.01094084233045578, 0.01630348525941372, 0.0055126468650996685, 0.015789780765771866, 0.01992381177842617, 0.026380490511655807, -0.013785636983811855, -0.010629150085151196, -0.007068713195621967, 0.03629516065120697, 0.0173186082392931, -0.020080428570508957, 0.021827423945069313, 0.01827545277774334, 0.00928928330540657, 0.03536945953965187, 0.030836720019578934, 0.006205922458320856, 0.05361580848693848, -0.01874287612736225, 0.023040464147925377, -0.03901084512472153, -0.042407456785440445, 0.046832695603370667, 0.05302365496754646, -0.0014870860613882542, 0.005534498952329159, 0.052064020186662674, 0.011021415702998638, 0.008319702930748463, -0.0076169781386852264, 0.039148006588220596, -0.02575671300292015, -0.04977354779839516, -0.031512338668107986, 0.01486898586153984, -0.045668818056583405, 0.034196313470602036, 0.016497375443577766, -0.008058415725827217, -0.026840699836611748, -0.05148052051663399, 0.017445947974920273, 0.023077864199876785, -0.00195324863307178, 0.001335735316388309, 0.07560481876134872, 0.04297104477882385, -0.018053168430924416, -0.009011066518723965, -0.09493929147720337, 0.02642742171883583, -0.05396377667784691, 0.027531331405043602, -0.024160737171769142, -0.0839233547449112, 0.052571363747119904, 0.0009629693813621998, -0.02138243429362774, -0.062406595796346664, -0.0002787476987577975, -0.012153436429798603, -0.042783159762620926, -0.007595260627567768, -0.04210641607642174, 0.03005814738571644, 0.025352487340569496 ]
<p>As far as I've read online, there isn't a good explanation for the <a href="http://en.wikipedia.org/wiki/Born_rule" rel="nofollow">Born Rule</a>. Is this the case? Why does taking the square of the wave function give you the Probability? Naturally it removes negatives and imaginary numbers, but why is it the square, not the fourth or some higher power?</p>
g23
[ 0.05598004162311554, 0.02041914500296116, -0.0011792124714702368, -0.03427769988775253, 0.036064840853214264, 0.008750575594604015, 0.05846250057220459, 0.06518708169460297, -0.004856436513364315, -0.0383671335875988, -0.013202999718487263, 0.00030700775096192956, 0.03605944290757179, 0.00777406757697463, 0.013000022619962692, -0.002814903622493148, 0.0320502445101738, 0.04916699603199959, 0.057097434997558594, 0.03666834905743599, -0.015709688887000084, 0.005010866094380617, -0.004711208865046501, -0.029081890359520912, 0.022440718486905098, -0.05434105917811394, 0.056078631430864334, -0.04294632747769356, 0.00814757402986288, -0.01607917994260788, 0.0368608720600605, 0.036770034581422806, 0.09919477999210358, -0.010877449065446854, -0.033043161034584045, 0.052499253302812576, 0.05700722709298134, 0.008286244235932827, 0.014524873346090317, 0.0060461899265646935, -0.029174158349633217, 0.004102332517504692, -0.029854770749807358, 0.01396612823009491, -0.032936230301856995, 0.014640141278505325, -0.01799652725458145, 0.058052290230989456, -0.013048014603555202, -0.05610457435250282, -0.014242613688111305, -0.022978438064455986, 0.04059174284338951, 0.03287263959646225, 0.026195883750915527, 0.009306719526648521, 0.008919734507799149, 0.0030634377617388964, 0.032172225415706635, 0.00914592295885086, 0.015106677077710629, -0.012419421225786209, 0.005910908337682486, 0.035283662378787994, 0.02914758026599884, 0.01103125885128975, -0.01036762073636055, 0.0053753117099404335, 0.004581207409501076, 0.06000827997922897, 0.0035186437889933586, -0.06624850630760193, -0.03625211492180824, -0.042772326618433, 0.012931224890053272, 0.010191735811531544, 0.029259884729981422, 0.03128846734762192, -0.00247374945320189, 0.06037348508834839, -0.02035956084728241, -0.03401375189423561, 0.006005804054439068, 0.028951531276106834, 0.007134763989597559, 0.011614936403930187, 0.06601981073617935, -0.07256129384040833, 0.02857312560081482, -0.01179383136332035, -0.002703793114051223, -0.0339960977435112, 0.0384257473051548, -0.016967084258794785, 0.015684982761740685, 0.012273508124053478, -0.02725319378077984, 0.04893723875284195, -0.00394954951480031, 0.0031823106110095978, 0.009231054224073887, 0.005980389658361673, 0.049430593848228455, -0.03887306898832321, -0.03036658838391304, 0.012485499493777752, -0.01426810771226883, -0.03569139912724495, -0.04746400937438011, -0.023635001853108406, -0.018976274877786636, -0.03847301006317139, 0.006266963668167591, -0.03700777143239975, -0.058891575783491135, 0.02142864465713501, -0.006502533331513405, -0.05247172713279724, -0.027223272249102592, 0.04069538414478302, -0.027405498549342155, 0.003265364794060588, 0.00662418594583869, 0.047498151659965515, -0.01793091744184494, 0.0064887660555541515, 0.010811740532517433, 0.02611023560166359, 0.04065726324915886, 0.027130216360092163, 0.05298731476068497, 0.0040117716416716576, -0.019955968484282494, 0.022479422390460968, -0.005547734443098307, 0.031421855092048645, 0.050533439964056015, 0.005716055631637573, 0.027003251016139984, 0.03038962557911873, -0.01515646930783987, -0.01505148783326149, 0.06759686768054962, -0.059738676995038986, 0.03991125524044037, -0.02769334614276886, 0.04516831785440445, -0.010231482796370983, -0.0018685159739106894, -0.0293545164167881, -0.02193540520966053, 0.027752207592129707, 0.010273962281644344, -0.01758619397878647, 0.00023013541067484766, 0.009449895471334457, 0.034789714962244034, 0.04391147196292877, -0.030560344457626343, -0.02901282161474228, 0.0509403720498085, -0.00016374822007492185, -0.05685045197606087, 0.045037247240543365, -0.07046669721603394, -0.0332954041659832, -0.03396148234605789, -0.07049136608839035, -0.013098183088004589, -0.0354604572057724, 0.03012431226670742, -0.033627141267061234, -0.04994940012693405, 0.015675978735089302, 0.009928733110427856, 0.0264920461922884, -0.015586061403155327, -0.012598566710948944, 0.008221451193094254, 0.015981750562787056, -0.041172292083501816, -0.010519538074731827, -0.008793913759291172, -0.003345953533425927, 0.0045892419293522835, -0.05723924562335014, 0.026343978941440582, 0.047859612852334976, 0.0022883156780153513, 0.04270403832197189, -0.03739561885595322, -0.08520596474409103, -0.0371922068297863, 0.016229018568992615, 0.01439368724822998, -0.023518938571214676, -0.000005217445504968055, -0.0032628560438752174, -0.031819701194763184, 0.07785047590732574, 0.021605027839541435, 0.05614795908331871, 0.05189965292811394, -0.034621067345142365, 0.040362026542425156, 0.0026487521827220917, -0.006785884033888578, 0.03591296821832657, -0.002336102072149515, -0.020804589614272118, -0.008746420033276081, 0.009858816862106323, 0.031018191948533058, 0.03483488783240318, -0.017774134874343872, 0.024846864864230156, -0.015100260265171528, 0.024160631000995636, -0.02031446434557438, -0.0027467194013297558, -0.02237100340425968, -0.0024193187709897757, 0.01701524294912815, 0.02554575353860855, 0.006267051212489605, 0.05306617543101311, -0.030292324721813202, -0.013440165668725967, -0.009564033709466457, 0.05527068302035332, -0.09799809008836746, -0.07403581589460373, -0.06097479164600372, 0.01956329680979252, 0.0012970267562195659, 0.009118037298321724, -0.026470638811588287, -0.01858346164226532, 0.0360451303422451, 0.06230179965496063, -0.01355806179344654, -0.016139568760991096, 0.01762082800269127, 0.026461215689778328, 0.04274122789502144, -0.059839360415935516, 0.036912258714437485, -0.018367411568760872, -0.024753736332058907, 0.02621660754084587, -0.024915123358368874, 0.008362837135791779, -0.03392907604575157, 0.0427933894097805, 0.0041493200697004795, 0.007005860563367605, -0.036696817725896835, 0.0038874654565006495, -0.04755434766411781, -0.031723830848932266, 0.013432856649160385, 0.013659083284437656, 0.004245278425514698, 0.007045308127999306, -0.029124723747372627, -0.03883180022239685, -0.04699045047163963, -0.00869620032608509, 0.012882249429821968, 0.021636640653014183, 0.0021214105654507875, 0.08963913470506668, -0.018459506332874298, 0.04110291227698326, -0.014266196638345718, -0.02146325260400772, -0.0072474549524486065, -0.018213612958788872, -0.01836835779249668, 0.02660171128809452, 0.0072203828021883965, 0.0034552616998553276, -0.09093563258647919, 0.04472160339355469, 0.017413951456546783, -0.0790858045220375, 0.05804076045751572, 0.013851890340447426, -0.028611643239855766, -0.002454788889735937, -0.022018689662218094, 0.05136173963546753, -0.016217347234487534, -0.03861725330352783, 0.01619701087474823, 0.02888002060353756, -0.0011448283912613988, -0.082003153860569, -0.03363081067800522, 0.05435666814446449, 0.03735979646444321, 0.002014372730627656, -0.002230447018519044, -0.041054174304008484, 0.005747275892645121, 0.04118993878364563, 0.027893180027604103, -0.03526011481881142, -0.011595587246119976, -0.007756858132779598, 0.012270580045878887, 0.05500898137688637, -0.029715009033679962, -0.024201713502407074, 0.009551450610160828, -0.016271235421299934, -0.07807028293609619, 0.020327705889940262, 0.09157483279705048, -0.05909423157572746, -0.06416542828083038, -0.0401705838739872, -0.04266364499926567, 0.05819232016801834, 0.020946605131030083, 0.01512523926794529, -0.06955170631408691, 0.034601327031850815, 0.03180255740880966, -0.03436504676938057, 0.03805724158883095, 0.03696616366505623, -0.009201071225106716, 0.021185217425227165, -0.0863371416926384, -0.03141589090228081, 0.007520376238971949, -0.003970741759985685, -0.011838550679385662, 0.015329035930335522, 0.047998733818531036, 0.019003717228770256, -0.030361942946910858, 0.005749212112277746, 0.009543499909341335, 0.027511021122336388, 0.030492648482322693, 0.03299124911427498, 0.007575801108032465, -0.018231693655252457, -0.02345007099211216, -0.014666355215013027, 0.024818668141961098, 0.008219437673687935, 0.020376810804009438, 0.04741353541612625, 0.006391036324203014, 0.04112505912780762, 0.031384795904159546, 0.0071426802314817905, -0.013307981193065643, -0.025157539173960686, 0.0481606088578701, 0.038912806659936905, 0.009021192789077759, -0.00371204293332994, -0.018431812524795532, 0.08347376435995102, 0.02200787328183651, 0.001352116814814508, -0.03077697940170765, -0.04594452306628227, -0.03979609161615372, 0.028323285281658173, 0.013652274385094643, 0.016950303688645363, -0.007627454586327076, 0.07396291941404343, -0.023421868681907654, -0.02421308495104313, 0.07622406631708145, -0.0007757377461530268, -0.0048252735286951065, -0.028668100014328957, 0.032015543431043625, -0.056870169937610626, -0.06603389978408813, -0.03312092274427414, -0.013625087216496468, -0.036851994693279266, 0.038618311285972595, 0.03552012890577316, 0.003478622529655695, 0.04333965480327606, 0.040996696799993515, -0.014085252769291401, 0.010448331013321877, -0.03500736132264137, -0.01885232701897621, 0.04441620409488678, -0.003986697643995285, 0.042760688811540604, 0.019175946712493896, 0.02404153347015381, 0.05223473906517029, 0.007901988923549652, 0.06581215560436249, -0.011991757899522781, -0.02965530753135681, 0.018484845757484436, -0.05689361318945885, 0.032876111567020416, -0.0020131219644099474, -0.07584924250841141, 0.037539564073085785, 0.03815004974603653, 0.09245779365301132, -0.026462577283382416, 0.0026213068049401045, 0.026478854939341545, 0.03219906985759735, -0.016893304884433746, -0.017018580809235573, 0.01218467392027378, -0.038763970136642456, -0.013467620126903057, 0.048836421221494675, -0.05292673781514168, -0.004036856349557638, -0.04018685966730118, 0.0101028922945261, 0.017736002802848816, 0.00024566909996792674, -0.007256676908582449, -0.04473947361111641, -0.044553834944963455, -0.03820827975869179, 0.03763023018836975, 0.012340747751295567, 0.009637377224862576, 0.0498804971575737, -0.03082585148513317, -0.00041800434701144695, 0.04091461002826691, 0.059311311691999435, 0.045962944626808167, -0.0012822868302464485, -0.05547274649143219, -0.02089664526283741, 0.00042263109935447574, 0.027694648131728172, 0.01216199155896902, 0.012115219607949257, -0.10003101825714111, 0.0443735308945179, -0.016730686649680138, -0.09012535214424133, 0.012297182343900204, 0.00936257652938366, -0.008742048405110836, -0.026726705953478813, -0.030415700748562813, -0.013087396509945393, 0.011100491508841515, 0.053934648633003235, -0.0010611019097268581, -0.054388754069805145, 0.012626376934349537, -0.04614276438951492, 0.056367579847574234, -0.00569241913035512, -0.029242319986224174, 0.01954581029713154, 0.056908246129751205, -0.058549292385578156, -0.06971380114555359, -0.0013531714212149382, -0.03617439046502113, 0.001736372010782361, -0.0726836770772934, -0.014651712030172348, -0.03575938194990158, 0.024233520030975342, -0.005518058780580759, -0.014024066738784313, -0.012109871953725815, 0.030997972935438156, -0.03062940016388893, -0.014742542989552021, -0.041927918791770935, 0.04684850201010704, -0.023766139522194862, 0.015915943309664726, 0.012183302082121372, 0.01132170483469963, -0.0569726936519146, 0.026741506531834602, -0.03937234356999397, -0.026841918006539345, -0.04714721813797951, -0.09955360740423203, -0.06776232272386551, -0.05862640216946602, 0.023925352841615677, -0.059376541525125504, 0.03215472400188446, 0.04770227149128914, -0.04733191058039665, 0.011654259636998177, -0.022162897512316704, 0.04395320639014244, -0.09662945568561554, 0.05443441495299339, -0.03853173553943634, 0.03153642639517784, -0.035347070544958115, -0.054223716259002686, -0.015812845900654793, 0.02806933782994747, 0.09584009647369385, 0.03143641725182533, 0.04651526361703873, -0.01700344868004322, -0.043174196034669876, 0.01853903941810131, -0.049744028598070145, -0.015180687420070171, -0.026252951472997665, 0.04515756294131279, 0.038559697568416595, 0.0007425892981700599, 0.019796591252088547, 0.029036812484264374, 0.08520448207855225, -0.020584624260663986, -0.008996406570076942, -0.04553554579615593, 0.014306660741567612, 0.023298103362321854, -0.03292696550488472, 0.05473642796278, 0.018626151606440544, 0.026046592742204666, 0.02120331861078739, -0.03404548764228821, 0.012093852274119854, -0.034730661660432816, -0.01727023534476757, 0.01903981901705265, 0.05211019515991211, -0.05048927292227745, -0.02935873344540596, 0.010854873806238174, -0.021628407761454582, -0.029738349840044975, 0.05127086490392685, -0.021781325340270996, 0.040690455585718155, 0.011126933619379997, -0.03940114378929138, 0.011012827046215534, 0.029598798602819443, -0.03181702271103859, -0.012525354512035847, 0.016659099608659744, -0.012229622341692448, 0.03981413692235947, 0.06347166001796722, -0.029148224741220474, 0.056758660823106766, 0.02995329722762108, -0.029454831033945084, -0.02322053164243698, 0.025549406185746193, -0.04876846820116043, 0.04094421863555908, 0.006215485744178295, -0.040016792714595795, -0.030056994408369064, -0.0279352106153965, -0.005171476863324642, 0.05124913528561592, 0.03138604387640953, -0.09465348720550537, -0.036699362099170685, 0.01598065346479416, 0.018901215866208076, -0.0011356015456840396, 0.0008508765022270381, 0.051152169704437256, -0.022961590439081192, -0.0663975179195404, -0.025712957605719566, -0.0030130664817988873, -0.013845660723745823, -0.028873059898614883, 0.04695825278759003, 0.0149074736982584, -0.015623064711689949, -0.06520602107048035, -0.030896242707967758, -0.061850424855947495, 0.022800840437412262, -0.004332167096436024, 0.051535021513700485, 0.0298269335180521, 0.017709316685795784, -0.0330742672085762, -0.03116256184875965, 0.0476992167532444, -0.037674497812986374, -0.01692846603691578, -0.02358485385775566, -0.003440055064857006, -0.00440631527453661, -0.08441843837499619, -0.021211380138993263, 0.008658369071781635, 0.005560350604355335, -0.00045926746679469943, 0.02469412423670292, -0.0011513408971950412, -0.013791329227387905, -0.014762183651328087, 0.08454379439353943, -0.022363554686307907, -0.004245631862431765, -0.022708214819431305, 0.014875472523272038, 0.025682954117655754, -0.030570993199944496, -0.060195956379175186, 0.01287617813795805, 0.03235552832484245, -0.028607305139303207, 0.017893033102154732, -0.054535992443561554, -0.021920470520853996, 0.06623956561088562, -0.015134354121983051, -0.07642465084791183, 0.05760956183075905, 0.06848013401031494, 0.0032017850317060947, -0.06601463258266449, 0.04709811881184578, 0.013671155087649822, -0.02895853854715824, -0.08655163645744324, 0.0007736557745374739, -0.014649800956249237, 0.024491172283887863, -0.06535821408033371, -0.010492943227291107, -0.019869886338710785, 0.010244688019156456, 0.007384077645838261, 0.010578617453575134, 0.00022429192904382944, -0.03561363369226456, -0.018016614019870758, -0.01614798791706562, 0.007035747170448303, 0.0337224081158638, -0.005776623729616404, 0.016264937818050385, -0.002342754043638706, -0.023872746154665947, 0.00787318218499422, -0.01164995413273573, -0.006271151825785637, 0.0029262423049658537, -0.054405298084020615, 0.0027944210451096296, 0.011523786932229996, 0.013447821140289307, -0.007074577733874321, -0.0011556028621271253, 0.018301505595445633, 0.01637316681444645, -0.020234035328030586, -0.008649059571325779, -0.05237506330013275, -0.0414564348757267, 0.035865020006895065, 0.018147481605410576, -0.07807651907205582, 0.01797102764248848, -0.012080423533916473, 0.015794726088643074, -0.007427384611219168, 0.014148707501590252, 0.010349810123443604, 0.020047863945364952, 0.024114184081554413, -0.030542492866516113, 0.06789674609899521, 0.02244480326771736, 0.054906215518713, 0.07369539886713028, -0.001493041287176311, 0.0005249484092928469, -0.043820641934871674, -0.07797620445489883, 0.036829959601163864, -0.020351463928818703, 0.04106038808822632, -0.06489226967096329, -0.005594430025666952, -0.04626189172267914, -0.011998025700449944, -0.01817566715180874, -0.023852795362472534, -0.02815765142440796, 0.041429903358221054, 0.03680165112018585, 0.024735476821660995, 0.0037199645303189754, -0.022775758057832718, -0.05378851294517517, 0.04765011742711067, -0.0051864697597920895, -0.03553187474608421, -0.00981251522898674, -0.00798406545072794, 0.016169149428606033, 0.027415594086050987, -0.034082550555467606, -0.029033636674284935, 0.028671743348240852, -0.07149519771337509, 0.0010411087423563004, 0.025521492585539818, 0.054566483944654465, -0.001326330821029842, -0.001586562255397439, -0.04423549398779869, 0.03980490192770958, -0.0045947241596877575, 0.039490580558776855, 0.020527135580778122, 0.030611200258135796, 0.07069792598485947, -0.09299976378679276, -0.03423616290092468, -0.04087351635098457, -0.05262872204184532, 0.03886635974049568, 0.030188681557774544, -0.03128930926322937, 0.003948079887777567, 0.024707764387130737, -0.027489811182022095, 0.1069970354437828, 0.024127503857016563, -0.014003518968820572, 0.059409741312265396, -0.004025860223919153, 0.05463174358010292, -0.0600033663213253, 0.05838228762149811, -0.03921111673116684, 0.012696905992925167, -0.005730882287025452, -0.006691711489111185, -0.03813987970352173, -0.004822119139134884, 0.02968495711684227 ]
<p>While reading a paper I ran into this particular way of writing a $\cal{N}=3$ fields (in a theory with $N_f$ hypermultiplets) that I couldn't relate to anything I had seen before in the text-books (typically Weinberg's) The claim is that $q^{Aa}$ and $\psi_{\alpha}^{Aa}$ are scalar and fermions such that $a,b$ are $SU(R)_R$ indices, $A,B$ are denoting them to transform in the fundamental representation of $USp(2N_f)$ (why?) and $\alpha, \beta$ are $SO(2,1)$ spinor indices (theory is in $2+1$) </p> <p>Apparently these fields satisfy some reality conditions given by, the following equations,</p> <p>$(q^\dagger)_{Aa} = \omega_{AB}\epsilon_{ab}q^{Bb}$</p> <p>and</p> <p>$\bar{\psi} ^\alpha _{Aa} = \omega_{AB} \epsilon_{ab} \epsilon ^{\alpha \beta} \psi _{\beta} ^{Bb}$</p> <p>(where $\omega$ is some symplectic form, which I have no clue about) </p> <p>I find the above equations very unfamiliar. For one thing why do the scalar and the fermion have $R$ charge indices? (I am only familiar with the supercharges having a R-symmetry when the central charges are absent) Also I don't understand the $USp(2N_f)$ index. </p> <p>Apparently this can be related to usual $\cal{N}=2$ fields $(Q,\tilde{Q})$ as,</p> <p>$q^{A1} = (Q,\tilde{Q})$</p> <p>and</p> <p>$q^{A2} = (-\bar{\tilde{Q}}, \bar{Q})$</p> <p>I am completely unfamiliar with such a relationship or this thinking of $\cal{N}=2$ fields as being thought of as a pair of $Qs$. </p> <p>Once I understand the meaning of the above I will post another about its curious way of writing the supersymmetry transformation and the lagrangian with this field content. </p>
g1521
[ 0.05486360564827919, 0.010816831141710281, -0.03094586357474327, -0.028511855751276016, 0.07006106525659561, 0.007520178332924843, 0.023915361613035202, 0.0032515372149646282, 0.0020941360853612423, -0.005152993369847536, -0.060261014848947525, 0.017112497240304947, -0.011212848126888275, 0.006023092195391655, -0.006621732842177153, -0.02252225950360298, 0.07463575154542923, 0.026985859498381615, 0.02027595415711403, -0.05394245684146881, -0.01809077337384224, 0.048287566751241684, 0.012840919196605682, -0.05775147303938866, 0.0034297907259315252, -0.025846583768725395, 0.006762668956071138, -0.015610294416546822, -0.02948688343167305, -0.07812128961086273, 0.004689901601523161, 0.06521996110677719, -0.0032197257969528437, -0.05452345684170723, -0.02546832337975502, -0.06082348898053169, 0.06453274190425873, 0.014616734348237514, 0.0003572329005692154, -0.015694864094257355, -0.05084676668047905, 0.015637746080756187, 0.038242779672145844, 0.0037439404986798763, -0.02705858275294304, 0.0313132144510746, -0.030780699104070663, 0.009813361801207066, -0.02418021857738495, -0.01654656045138836, 0.052016131579875946, 0.019581427797675133, 0.057267285883426666, -0.02245328202843666, -0.04146810248494148, 0.02471453696489334, 0.036755722016096115, -0.05062214657664299, 0.05832875892519951, 0.07339843362569809, -0.010648813098669052, -0.02038915641605854, 0.03628016635775566, 0.030520813539624214, 0.06682230532169342, 0.05081985890865326, -0.040431346744298935, -0.0023276349529623985, 0.02478662133216858, -0.018063059076666832, -0.0007153209298849106, -0.05478770285844803, 0.024283038452267647, 0.04083891212940216, 0.03142281994223595, 0.03431877866387367, -0.04333844035863876, -0.01046909112483263, 0.020364178344607353, 0.02744210697710514, -0.019439352676272392, -0.06391587108373642, 0.021782999858260155, 0.04787216708064079, 0.005108581855893135, -0.05897744745016098, 0.01657315343618393, 0.003985195886343718, -0.00910218432545662, -0.0037362128496170044, -0.05370483919978142, -0.031224023550748825, 0.007059060037136078, 0.04879821464419365, -0.014034798368811607, 0.0034345739986747503, -0.006001378409564495, -0.001895759254693985, -0.05485352873802185, -0.016768943518400192, -0.04869833216071129, 0.07970306277275085, 0.04555758833885193, -0.005288328975439072, -0.04232895374298096, 0.005424938630312681, 0.026831181719899178, 0.008753477595746517, 0.014450391754508018, 0.0428466796875, -0.07950080186128616, 0.07773754745721817, -0.00575113482773304, 0.0002341033541597426, -0.08601333945989609, -0.03224065527319908, -0.0037190502043813467, -0.04106563329696655, 0.016951613128185272, 0.02911747433245182, -0.008328953757882118, 0.010451557114720345, 0.03903210535645485, 0.026368994265794754, 0.014345047064125538, -0.040932558476924896, 0.004846055060625076, 0.04760264605283737, 0.006038039922714233, -0.03017820231616497, 0.005391658283770084, -0.05904961749911308, -0.05203908681869507, 0.005698483902961016, 0.04923881217837334, 0.0651685893535614, -0.0005419092485681176, 0.01734801195561886, -0.014199306257069111, -0.018906166777014732, -0.014456982724368572, -0.0010286574251949787, 0.008305163122713566, -0.03637852147221565, -0.05296797677874565, -0.02357104979455471, -0.004436828196048737, -0.038871802389621735, 0.036735739558935165, -0.00534405093640089, 0.011532433331012726, 0.08220148831605911, -0.018188947811722755, 0.01285755168646574, -0.021450407803058624, 0.043396566063165665, -0.006740076933056116, -0.033661749213933945, 0.006388155743479729, -0.010195949114859104, 0.04308895394206047, -0.022040920332074165, 0.021997258067131042, -0.01099594309926033, 0.0030077341943979263, -0.027258438989520073, 0.05019078776240349, -0.018126696348190308, -0.017845820635557175, -0.04929427430033684, -0.02167639508843422, 0.07180818170309067, 0.03778649494051933, 0.0018585894722491503, -0.013091392815113068, 0.06253962218761444, -0.0008446527644991875, 0.009676714427769184, 0.008715485222637653, -0.005618791561573744, -0.08311215043067932, 0.0032076118513941765, 0.021687433123588562, -0.0008027718868106604, 0.008944550529122353, 0.00871944334357977, -0.037550728768110275, 0.10050959140062332, -0.010083329863846302, 0.020053330808877945, -0.0027969395741820335, 0.04061617702245712, 0.04531588405370712, 0.07570353150367737, 0.013953384943306446, 0.05456696078181267, 0.014339715242385864, 0.006772383116185665, -0.02105015330016613, -0.036154262721538544, -0.005419682711362839, 0.004975167103111744, -0.014002881944179535, -0.039140734821558, 0.03699365258216858, 0.04687737673521042, -0.04913295805454254, 0.006368957459926605, 0.05688796564936638, -0.03352219611406326, 0.02152353525161743, -0.04948032647371292, -0.01270523015409708, 0.03855329751968384, -0.012895558029413223, -0.02635318413376808, -0.0063684550113976, -0.049947597086429596, -0.0034400480799376965, 0.023623136803507805, 0.0558801144361496, -0.051233842968940735, 0.0687708780169487, 0.026740165427327156, -0.012424956075847149, 0.057896409183740616, 0.000880510953720659, -0.004271527752280235, 0.008779352530837059, -0.04868210479617119, -0.11880963295698166, 0.0005702953203581274, 0.004392771050333977, -0.031690340489149094, -0.00903627835214138, -0.0033087506890296936, 0.0005784331005997956, 0.05223238840699196, 0.031977709382772446, 0.032150547951459885, 0.06617195159196854, -0.008957444690167904, 0.009797881357371807, 0.04568207636475563, 0.03742152079939842, 0.015790598466992378, 0.02806292101740837, 0.017959434539079666, -0.07668627798557281, 0.014121525920927525, -0.00542455492541194, -0.02743123285472393, -0.009676586836576462, 0.014698580838739872, -0.00047434965381398797, -0.038055647164583206, 0.057485416531562805, 0.022535905241966248, -0.023743394762277603, -0.03381427377462387, 0.01870773173868656, 0.008346744813024998, -0.008745325729250908, -0.010910584591329098, -0.05677482485771179, 0.007724226452410221, 0.001841760240495205, 0.019164390861988068, -0.022244859486818314, 0.010000654496252537, -0.09043145179748535, 0.012142229825258255, 0.007969476282596588, -0.037349313497543335, -0.006367078982293606, -0.046112194657325745, -0.047482267022132874, -0.019985340535640717, 0.005411739926785231, -0.08664587140083313, -0.04570600762963295, -0.00741273257881403, 0.012321737594902515, 0.021462351083755493, -0.01060014683753252, -0.0034942792262881994, -0.034448932856321335, -0.024104125797748566, 0.048848748207092285, 0.06478860974311829, 0.05057116225361824, 0.05476789548993111, 0.017170937731862068, -0.028262384235858917, -0.03753942996263504, -0.02427106536924839, -0.01676270179450512, -0.028999056667089462, -0.030651777982711792, 0.016164330765604973, 0.004211623687297106, 0.035124342888593674, 0.021050840616226196, 0.017817584797739983, 0.034548770636320114, -0.01200238149613142, -0.061388734728097916, -0.0007889624685049057, 0.0010539734503254294, 0.032359082251787186, -0.035937823355197906, 0.020680267363786697, -0.0017397808842360973, 0.004252099897712469, -0.05430395528674126, -0.001479240832850337, 0.011886955238878727, 0.003544042818248272, 0.05882326513528824, -0.03134935721755028, -0.09884892404079437, -0.050311651080846786, 0.05890136957168579, 0.01834404282271862, 0.00032788485987111926, 0.01674017123878002, -0.041241202503442764, 0.024121858179569244, -0.00928021501749754, -0.0714346170425415, 0.004292100202292204, 0.014671675860881805, 0.034723859280347824, -0.06528037041425705, -0.08076847344636917, 0.04066376015543938, -0.08529958873987198, 0.06555437296628952, 0.029370205476880074, -0.053660038858652115, 0.021351035684347153, -0.03717741370201111, -0.07252460718154907, -0.02119024284183979, -0.006881066132336855, 0.005521249026060104, -0.03319356217980385, -0.037398383021354675, 0.011437099426984787, -0.029352763667702675, -0.04981989040970802, 0.0532994344830513, 0.03859923779964447, 0.003095746273174882, -0.0019136664923280478, -0.003307443344965577, 0.04143579676747322, -0.004951464477926493, 0.010506988503038883, 0.004396466072648764, 0.05922960862517357, 0.0015629197005182505, -0.02641909196972847, 0.02956818975508213, -0.024128898978233337, 0.00962801743298769, -0.06874069571495056, -0.01559535600244999, -0.05192266404628754, -0.019193368032574654, 0.03197572007775307, 0.004912453703582287, -0.009051003493368626, 0.013752540573477745, -0.050176311284303665, -0.06480956822633743, -0.01640954241156578, -0.050188012421131134, -0.041290491819381714, 0.0022103760857135057, -0.004276161082088947, -0.0056053828448057175, 0.03823788836598396, 0.011624373495578766, 0.009009779430925846, 0.01493079960346222, -0.025751609355211258, 0.00728303287178278, -0.0531667098402977, -0.020438656210899353, 0.007616320624947548, 0.004944527987390757, -0.04648546874523163, 0.0003600733762141317, -0.0015914636896923184, -0.01425119023770094, 0.05797727406024933, -0.03118131123483181, -0.020785467699170113, 0.03443662449717522, -0.011974894441664219, -0.017936890944838524, 0.00015278253704309464, -0.08597342669963837, -0.020894527435302734, -0.0060520595870912075, 0.022670339792966843, -0.023028112947940826, 0.02661173790693283, -0.02974211797118187, -0.015560293570160866, -0.0292584840208292, 0.07742322981357574, -0.04205503314733505, 0.07296954095363617, -0.008351457305252552, -0.04406518116593361, -0.01655496470630169, 0.007929692976176739, -0.014555544592440128, 0.015531528741121292, 0.0027386725414544344, 0.03503327816724777, 0.005782695487141609, 0.06984178721904755, 0.018978629261255264, 0.02548377588391304, 0.005821188911795616, -0.012100528925657272, 0.020904649049043655, 0.04803718253970146, 0.08208243548870087, -0.014777831733226776, 0.033068545162677765, -0.03866800665855408, -0.0206083282828331, -0.11295180767774582, 0.010094728320837021, -0.002559712389484048, 0.028688078746199608, 0.08809354156255722, -0.013815226964652538, 0.004867930430918932, -0.037574801594018936, -0.018213259056210518, 0.012118084356188774, -0.05597424507141113, 0.026935772970318794, -0.02367793396115303, 0.0034944298677146435, 0.013269798830151558, 0.050750572234392166, -0.02385527826845646, -0.032774168998003006, 0.0316506028175354, -0.025029713287949562, -0.00218865554779768, 0.026113636791706085, 0.05873098969459534, 0.010790840722620487, -0.036273371428251266, 0.02634158916771412, -0.011464259587228298, -0.05039724335074425, 0.05383149906992912, 0.04181927815079689, -0.08010464906692505, 0.0051603130996227264, -0.04945186898112297, -0.061054304242134094, 0.0603686198592186, -0.07611034065485, -0.053595349192619324, -0.06570778787136078, 0.04604262486100197, 0.003279112745076418, 0.011701189912855625, 0.0015154272550716996, -0.06250505149364471, 0.006485302001237869, 0.009275121614336967, 0.030338948592543602, 0.027121812105178833, 0.01703612320125103, -0.029923217371106148, 0.009221679531037807, -0.014653072692453861, -0.01799873262643814, -0.04352450370788574, -0.01684979721903801, -0.01661783643066883, 0.029272867366671562, 0.038580767810344696, 0.07101362198591232, 0.009001784026622772, 0.023035675287246704, 0.03826523199677467, 0.009174367412924767, -0.006180312018841505, 0.018269386142492294, -0.028862716630101204, 0.04664233326911926, 0.012087148614227772, 0.03844231739640236, -0.0030894309747964144, 0.06635405868291855, 0.10167716443538666, 0.020635681226849556, 0.017291102558374405, 0.015389862470328808, 0.06302949786186218, -0.05800716578960419, 0.03740303963422775, 0.01001223735511303, -0.009883223101496696, 0.0618584081530571, -0.0025910071562975645, -0.001275661401450634, -0.009159569628536701, -0.06120847538113594, 0.012777388095855713, 0.015351904556155205, 0.03779080510139465, -0.02251114882528782, 0.05358006805181503, 0.06659909337759018, -0.022625654935836792, -0.07005076110363007, 0.03631497547030449, 0.0449543222784996, -0.031004218384623528, -0.041654523462057114, -0.0013309214264154434, -0.008976736105978489, 0.07640335708856583, -0.03460545092821121, 0.036162976175546646, -0.03533713147044182, 0.017854975536465645, 0.00364370783790946, -0.04470401257276535, -0.03550694137811661, -0.024469390511512756, -0.0038790253456681967, -0.006692562717944384, -0.020377904176712036, 0.015044583939015865, -0.04001546651124954, 0.014061516150832176, -0.04621969163417816, -0.015293636359274387, -0.04321020096540451, -0.023901596665382385, 0.011472574435174465, 0.03585262596607208, 0.03158363699913025, 0.06534811854362488, -0.03595464304089546, -0.042404890060424805, 0.0017842845991253853, -0.01247379556298256, -0.0158915463835001, 0.0022457705345004797, 0.009390948340296745, -0.006119697354733944, 0.011568189598619938, 0.009128856472671032, -0.06907568871974945, 0.05268007889389992, 0.0007839572499506176, -0.00746178301051259, 0.0360717736184597, 0.020211655646562576, 0.018296457827091217, 0.0166753102093935, 0.02789943479001522, -0.027277374640107155, 0.0001663817383814603, -0.0019133485620841384, -0.02393941953778267, 0.04909592121839523, 0.00897076353430748, 0.007350030820816755, -0.041445087641477585, 0.03518476337194443, 0.032158490270376205, -0.059586819261312485, 0.008191385306417942, 0.025591842830181122, -0.037594713270664215, -0.030136657878756523, 0.038718923926353455, -0.04098496213555336, -0.06367675215005875, -0.016434958204627037, 0.03310400992631912, 0.030206527560949326, 0.010082956403493881, -0.016634026542305946, -0.025851674377918243, 0.043644387274980545, 0.0510348342359066, 0.02886827476322651, -0.04328879714012146, 0.06416298449039459, 0.045521218329668045, 0.008583319373428822, -0.004653418902307749, 0.011707133613526821, 0.03744874522089958, -0.008463097736239433, 0.007964258082211018, -0.051714248955249786, 0.028007574379444122, 0.03494388982653618, -0.038212887942790985, -0.015133559703826904, 0.04124453663825989, -0.05218220129609108, 0.008089534007012844, 0.04469529539346695, 0.024735044687986374, 0.0035311169922351837, -0.029880408197641373, 0.04029540717601776, -0.0026341713964939117, -0.002024365123361349, 0.025043342262506485, 0.054416630417108536, 0.0031865278724581003, -0.006719909142702818, -0.03788204863667488, 0.07553991675376892, 0.02462591789662838, 0.015411187894642353, 0.016091104596853256, -0.04116753116250038, 0.052805591374635696, 0.0016288006445392966, 0.03721323981881142, -0.003671804443001747, 0.05947171151638031, 0.023455152288079262, -0.03125215321779251, -0.01012791134417057, -0.0498468391597271, 0.02800792269408703, 0.013893057592213154, -0.07713574916124344, 0.012203049845993519, 0.06860539317131042, 0.015170872211456299, -0.03949730470776558, -0.025853026658296585, -0.03162829205393791, -0.03950418904423714, -0.008512793108820915, 0.033217381685972214, 0.0001843169011408463, -0.05613791197538376, -0.006863391492515802, 0.016961099579930305, 0.0014425446279346943, -0.030938470736145973, -0.004400661680847406, 0.06448602676391602, 0.018318962305784225, -0.013440994545817375, 0.051036205142736435, -0.021565405651926994, 0.009468956850469112, -0.018926573917269707, 0.004704388324171305, -0.015429492108523846, -0.050505444407463074, -0.02535049058496952, -0.01878395304083824, 0.03931146487593651, 0.025744888931512833, -0.0008321114000864327, -0.014918320812284946, 0.050386108458042145, 0.036864664405584335, -0.053150713443756104, -0.0541350357234478, 0.020858561620116234, 0.0041710748337209225, 0.010389004833996296, -0.030709771439433098, 0.071352019906044, 0.0286506786942482, -0.06259925663471222, 0.006184681318700314, 0.009357500821352005, -0.054964181035757065, 0.02581222914159298, -0.024421220645308495, 0.050005797296762466, 0.013476351276040077, 0.04898726940155029, 0.012083183974027634, -0.061810750514268875, -0.004579359199851751, -0.0046807448379695415, 0.017682328820228577, 0.04191865399479866, 0.006634599529206753, 0.019017433747649193, -0.05092883110046387, -0.02454986236989498, -0.021010272204875946, 0.009260518476366997, 0.010042955167591572, 0.02886345051229, 0.07354457676410675, 0.03607737272977829, -0.004205604083836079, -0.05139845982193947, -0.040357235819101334, -0.04133002832531929, 0.005740248132497072, 0.004922193940728903, -0.01802521012723446, -0.052556030452251434, -0.012136044912040234, -0.017016157507896423, 0.03248682618141174, 0.004634777083992958, 0.011187383905053139, 0.005664148833602667, -0.05837582051753998, 0.002649516798555851, -0.07731889188289642, 0.03686242550611496, -0.0325777530670166, 0.00400342745706439, -0.02055056393146515, -0.0021769371815025806, 0.008569380268454552, -0.030847977846860886, -0.0011664533521980047, -0.011846108362078667, 0.003911168780177832, -0.008874977938830853, -0.049978528171777725, -0.04096786305308342, -0.03299097344279289, -0.008456188254058361, -0.05033969134092331, -0.03959322348237038, 0.04740339517593384, -0.0044144135899841785, -0.01853037253022194, 0.07568328827619553, 0.09047472476959229, 0.001345335622318089, -0.027640724554657936, 0.047305673360824585, 0.02848571166396141, 0.0015013947850093246, 0.0024109715595841408, -0.01884404942393303, 0.016658790409564972, 0.01569594256579876, -0.020160753279924393, -0.059353865683078766, -0.014259548857808113, 0.04468982666730881 ]
<p>A thin spherical shell made of plastic carries a uniformly distributed negative charge of -Q coulombs. Two large thin disks made of glass carry uniformly distributed positive and negative charges S coulombs and -S coulombs. The radius of the plastic spherical shell is R1, and the radius of the glass disks is R2. The distance from the center of the spherical shell to the positive disk is d.</p> <p>I want to know how to find two things:</p> <ul> <li><p>The potential difference V1-V2. Point 1 is at the center of the plastic sphere, and point 2 is just outside the sphere.</p></li> <li><p>The potential difference V2-V3. Point 2 is just below the sphere, and point 3 is right beside the positive glass disk.</p></li> </ul>
g1522
[ 0.07309333980083466, -0.018761081621050835, -0.008209314197301865, -0.031085379421710968, 0.07031811028718948, 0.0099677424877882, 0.0031757985707372427, 0.007353996858000755, -0.044204361736774445, 0.043840114027261734, -0.04347043111920357, 0.016673773527145386, 0.020421788096427917, 0.010183580219745636, 0.005719861947000027, -0.06120649352669716, 0.03055962175130844, -0.04483500495553017, -0.03078528679907322, 0.04475897178053856, -0.011106899939477444, -0.013636868447065353, -0.00043055848800577223, -0.02568621002137661, -0.005712846294045448, -0.00044424974475987256, -0.024670295417308807, 0.07162117213010788, -0.053790364414453506, 0.011110379360616207, 0.021608540788292885, -0.048441462218761444, 0.03535707667469978, -0.046596407890319824, -0.008647720329463482, -0.0004003413487225771, 0.07982634007930756, 0.04509644955396652, -0.058633413165807724, 0.04223657771945, 0.0025815607514232397, -0.030660759657621384, 0.09280168265104294, -0.019160566851496696, 0.005971572361886501, -0.08041619509458542, 0.01241732481867075, 0.052406616508960724, 0.0009717601933516562, -0.03359333425760269, 0.0034775955136865377, 0.03897395730018616, 0.07345779240131378, -0.017686808481812477, -0.02119329757988453, -0.010176185518503189, 0.016181066632270813, -0.05376451462507248, 0.04093390330672264, -0.009307856671512127, 0.0246195700019598, 0.0015590956900268793, -0.021589459851384163, 0.019337831065058708, 0.05103403702378273, 0.021022455766797066, -0.020571894943714142, -0.003510033944621682, -0.04158283770084381, -0.06027372553944588, -0.0047592357732355595, -0.055324163287878036, -0.00013743271119892597, -0.05983617156744003, -0.03507377952337265, 0.006352128926664591, 0.040776576846838, 0.010315834544599056, 0.037277188152074814, -0.014941202476620674, -0.0594620406627655, -0.040649060159921646, 0.05270705372095108, 0.017316941171884537, 0.06214003637433052, 0.019639411941170692, 0.006845160387456417, 0.011358987540006638, -0.03360169008374214, 0.008694794028997421, 0.025762012228369713, 0.003956681117415428, 0.0628698468208313, 0.006391835864633322, -0.02234344556927681, -0.003297233721241355, 0.007096670567989349, 0.029233068227767944, -0.0010544859105721116, -0.0028020006138831377, 0.03401768207550049, 0.011722659692168236, -0.0031316522508859634, 0.05481822043657303, -0.057560715824365616, 0.02763456106185913, 0.02050154283642769, -0.01281881146132946, 0.007691844366490841, 0.029028762131929398, -0.034465450793504715, -0.05983179435133934, -0.02687685377895832, -0.06519722193479538, 0.043220795691013336, -0.004830868914723396, 0.058057766407728195, -0.05160420015454292, -0.02522440254688263, 0.044086866080760956, -0.00537219550460577, 0.0720764771103859, 0.010890810750424862, 0.036019593477249146, 0.034625932574272156, -0.018905755132436752, -0.00025498741888441145, -0.00574718602001667, 0.02644430845975876, -0.003527608932927251, 0.03643719106912613, -0.03328344225883484, -0.03664734959602356, -0.013784322887659073, -0.025620926171541214, 0.073415108025074, 0.00909640733152628, 0.043126724660396576, -0.00288434443064034, -0.04433176666498184, -0.014394650235772133, -0.05382972210645676, -0.01373356208205223, -0.020641056820750237, -0.03127111494541168, 0.03257611021399498, 0.020091978833079338, -0.01857483945786953, -0.017552940174937248, -0.017490630969405174, 0.04096560925245285, 0.05865408480167389, -0.0034954994916915894, 0.03232266381382942, -0.026697492226958275, -0.054586704820394516, 0.023905685171484947, 0.013822074979543686, 0.05173817276954651, -0.012851589359343052, -0.03543371707201004, 0.014165166765451431, 0.041537970304489136, -0.0035729960072785616, -0.04761800169944763, 0.025837048888206482, 0.030243128538131714, 0.049769286066293716, -0.002262056339532137, -0.08133666217327118, -0.036516398191452026, -0.058440983295440674, 0.07669290900230408, 0.056357815861701965, 0.014201497659087181, 0.03227976709604263, -0.008764440193772316, -0.029685162007808685, 0.007450451143085957, 0.08967329561710358, -0.04393015429377556, -0.056267593055963516, 0.05933152139186859, 0.035731542855501175, 0.011815199628472328, -0.007390812039375305, 0.02156638167798519, 0.03698484227061272, -0.05854571983218193, 0.011500258930027485, -0.04936709627509117, -0.01854703202843666, -0.010578864254057407, -0.014477182179689407, 0.00725146196782589, 0.009420478716492653, 0.06017507612705231, -0.033821120858192444, -0.021790336817502975, -0.019932685419917107, -0.02742035500705242, 0.039019014686346054, 0.040711164474487305, 0.047439198940992355, 0.020274238660931587, -0.00027410671464167535, 0.007986551150679588, -0.03474795073270798, 0.039480872452259064, 0.010372744873166084, -0.046800121665000916, -0.0007387903751805425, 0.005091198720037937, -0.04079081863164902, 0.0007503569358959794, 0.01275957003235817, 0.005913582630455494, 0.019928747788071632, -0.03188307210803032, -0.03193843364715576, -0.030647601932287216, 0.011928899213671684, 0.035406891256570816, -0.05293603613972664, 0.03802121430635452, 0.027540018782019615, 0.05112385004758835, 0.026803672313690186, -0.02489466965198517, -0.04004020616412163, -0.08501170575618744, -0.06661133468151093, 0.04030100628733635, -0.024254171177744865, -0.01016363874077797, 0.02985704317688942, -0.060304783284664154, 0.005720023065805435, -0.015385209582746029, 0.015635259449481964, -0.01555115357041359, -0.0067985751666128635, -0.031719740480184555, 0.100735142827034, 0.006100353319197893, -0.020131543278694153, 0.015248733572661877, 0.0009693678002804518, -0.015964465215802193, 0.09054365009069443, 0.03203146904706955, 0.037112850695848465, -0.039288707077503204, 0.019717726856470108, 0.01731208898127079, -0.018679045140743256, -0.019312659278512, 0.00473380833864212, 0.026981016620993614, -0.05596088245511055, -0.0405525304377079, -0.056467801332473755, 0.009545224718749523, 0.03801259770989418, -0.039428699761629105, -0.015688881278038025, -0.08786477148532867, 0.029370803385972977, 0.03504360839724541, -0.02658836916089058, 0.04441298171877861, 0.03416348993778229, 0.05573126673698425, 0.012163556180894375, 0.02376212179660797, -0.025596611201763153, 0.021988196298480034, -0.005642388015985489, 0.029151510447263718, -0.0035910268779844046, 0.034761492162942886, -0.015455775894224644, -0.015306987799704075, 0.057631965726614, 0.016003021970391273, -0.07532422244548798, 0.02902967855334282, 0.06573724746704102, 0.028531735762953758, -0.020372845232486725, -0.01786508411169052, 0.04401738569140434, 0.08426602929830551, -0.06059786677360535, 0.003672028426080942, 0.04373970627784729, 0.0685521587729454, -0.03762269765138626, -0.011570350266993046, -0.03714677691459656, 0.020161157473921776, -0.04009194299578667, 0.030546242371201515, -0.0016677480889484286, 0.050774771720170975, 0.005434677004814148, 0.015383891761302948, -0.015298509038984776, 0.051119789481163025, 0.005582157056778669, 0.008695484139025211, 0.005496905650943518, 0.056913621723651886, -0.010145284235477448, -0.0013255546800792217, 0.035637304186820984, -0.01828158274292946, 0.021453801542520523, 0.017775891348719597, 0.024780822917819023, -0.020736124366521835, -0.0359787791967392, 0.008753160014748573, 0.003791091265156865, -0.002441505901515484, 0.022572029381990433, -0.0845198929309845, -0.05559767782688141, -0.011819785460829735, -0.039860039949417114, -0.04637002572417259, 0.009890544228255749, -0.0019444719655439258, -0.048608679324388504, 0.0015474914107471704, -0.038963932543992996, 0.016992080956697464, 0.025003710761666298, 0.02674075774848461, 0.009752855636179447, 0.0009007026674225926, -0.043076593428850174, -0.08514554053544998, -0.012969751842319965, -0.0763731449842453, -0.0045442585833370686, -0.01782565377652645, 0.01566079631447792, 0.013002952560782433, -0.014112543314695358, -0.016978157684206963, -0.011286450549960136, 0.029705828055739403, 0.004810331389307976, 0.022626424208283424, -0.018167661502957344, -0.027184082195162773, -0.0018528271466493607, -0.007691572420299053, 0.024988602846860886, -0.026668796315789223, -0.039424505084753036, -0.013812115415930748, -0.01347269956022501, 0.03569229692220688, 0.008229081518948078, -0.03023572266101837, -0.022364895790815353, -0.0039816065691411495, -0.014181703329086304, -0.02061270922422409, -0.0019179945811629295, 0.021771609783172607, -0.05568509176373482, 0.06617749482393265, -0.03340979665517807, -0.03157258406281471, -0.016715025529265404, 0.012268830090761185, -0.005502445623278618, 0.03968420624732971, 0.007653867360204458, 0.04475267976522446, -0.006221413612365723, 0.012534987181425095, 0.007648414932191372, -0.010453613474965096, -0.0050423783250153065, 0.01710428297519684, -0.05492342635989189, -0.0082091661170125, -0.019263457506895065, -0.07016605883836746, 0.022167855873703957, 0.006316601298749447, -0.016207806766033173, 0.07102565467357635, -0.006402603350579739, -0.0034445880446583033, 0.038776032626628876, -0.023416072130203247, 0.0011478684609755874, -0.00303415535017848, -0.026382435113191605, -0.012132025323808193, -0.029122859239578247, 0.02344479039311409, -0.056313566863536835, -0.01816183142364025, -0.022869110107421875, -0.016867564991116524, -0.0853700116276741, 0.041548263281583786, -0.046288300305604935, -0.02894776314496994, -0.05543138459324837, 0.01995280757546425, 0.024765435606241226, 0.020992238074541092, 0.029583698138594627, -0.017770636826753616, 0.025368986651301384, -0.009685656055808067, -0.0299777053296566, -0.008253155276179314, 0.022981252521276474, 0.043474212288856506, 0.03395210579037666, 0.033677030354738235, -0.053088169544935226, -0.04064568877220154, 0.049376510083675385, -0.02590523473918438, 0.05425487458705902, -0.05212819203734398, 0.0212272796779871, -0.06223954260349274, -0.024823706597089767, -0.006366977468132973, 0.028766965493559837, 0.024578653275966644, -0.015017996542155743, -0.009136885404586792, -0.03279873728752136, -0.028853459283709526, 0.0685136690735817, -0.02741454541683197, -0.006073853932321072, 0.016057999804615974, -0.05917498469352722, -0.05416898429393768, -0.026521187275648117, -0.04082006588578224, -0.04175791144371033, -0.009208746254444122, -0.0012853899970650673, 0.0008898474043235183, -0.015306440182030201, 0.006575973704457283, -0.021109111607074738, 0.005612973123788834, 0.00488815875723958, 0.01586465910077095, -0.0376746729016304, 0.01705199107527733, -0.03345370665192604, -0.053582627326250076, 0.02630528435111046, -0.036341238766908646, -0.019546151161193848, 0.02257329598069191, 0.05288245901465416, 0.041643548756837845, 0.02960960380733013, 0.0017974540824070573, -0.0037652812898159027, 0.008487408049404621, -0.02770170569419861, -0.000793636660091579, -0.011003290303051472, -0.039622712880373, 0.026983078569173813, -0.0008095834637060761, 0.005478274077177048, -0.004313459619879723, 0.05513077601790428, -0.0015598653117194772, 0.001978457672521472, 0.03302226588129997, 0.0027633917052298784, 0.025197314098477364, -0.016173331066966057, 0.04490580037236214, 0.04090363532304764, 0.027318380773067474, 0.013792460784316063, 0.006618978921324015, 0.04221348837018013, -0.07143047451972961, 0.05706942453980446, -0.037641528993844986, 0.009481719695031643, 0.008561341091990471, 0.0358726941049099, -0.028065577149391174, 0.030897466465830803, 0.05411851406097412, 0.04250754043459892, 0.05752236768603325, -0.04591922089457512, 0.00601129699498415, -0.0010729285422712564, 0.09137803316116333, 0.02457086369395256, -0.04999746382236481, 0.03540494292974472, -0.007780055981129408, 0.013752755708992481, -0.03771376237273216, 0.02167203277349472, 0.05677251145243645, 0.029151322320103645, 0.015556011348962784, -0.07077892869710922, 0.020638378337025642, -0.022472821176052094, -0.030996399000287056, -0.05469571799039841, 0.055888690054416656, 0.002992143388837576, 0.0010489142732694745, -0.017446134239435196, -0.07556145638227463, -0.010217621922492981, 0.018089527264237404, -0.039229970425367355, -0.04525195062160492, -0.025864215567708015, 0.03607064113020897, -0.03000793233513832, 0.020179275423288345, -0.0533604733645916, 0.03553325682878494, 0.003240397199988365, -0.04527334123849869, -0.028215689584612846, -0.005027316976338625, -0.022346703335642815, 0.04157992824912071, 0.03864216431975365, -0.024289041757583618, 0.028220679610967636, 0.02280057594180107, 0.01159727293998003, 0.03241942450404167, -0.02018846571445465, -0.04444050043821335, -0.05152227357029915, -0.0100641380995512, 0.01259575504809618, 0.04911063611507416, -0.053487688302993774, 0.010218543000519276, 0.03427615389227867, -0.026674412190914154, -0.09312594681978226, -0.02388160303235054, 0.0036404095590114594, 0.06404322385787964, 0.011523841880261898, -0.010068959556519985, 0.004538733512163162, 0.00877425167709589, -0.0444890558719635, 0.07910649478435516, 0.01761164329946041, -0.0031005621422082186, 0.01594614051282406, -0.009573513641953468, -0.0003351234772708267, -0.007538514211773872, 0.05418706685304642, 0.006503227166831493, -0.008378995582461357, 0.013430634513497353, 0.08387890458106995, 0.02526932954788208, -0.08234947919845581, 0.011241435073316097, -0.08997654914855957, 0.033084187656641006, -0.052586473524570465, -0.018766827881336212, -0.05397487431764603, -0.03363639861345291, -0.012621642090380192, 0.006177568808197975, -0.0006307697622105479, -0.046964120119810104, 0.046144649386405945, 0.035190172493457794, -0.004909974057227373, 0.019298575818538666, -0.01387710589915514, 0.029525786638259888, 0.015101484954357147, -0.051223594695329666, 0.031565479934215546, -0.006531770806759596, -0.014872916042804718, -0.022696780040860176, 0.0702236145734787, -0.024584295228123665, 0.0008132588118314743, 0.02055644802749157, 0.027550050988793373, -0.0028026809450238943, 0.0272899828851223, -0.01519340556114912, 0.0007466392708010972, 0.04269901663064957, 0.0035219865385442972, -0.06439747661352158, -0.023306993767619133, 0.04835515096783638, 0.0056654345244169235, -0.06474178284406662, -0.027305562049150467, -0.0005730930715799332, 0.006094700191169977, 0.040310442447662354, -0.02347959391772747, 0.037083420902490616, 0.03668520599603653, 0.05802040547132492, 0.08614207059144974, 0.0011121068382635713, 0.04641670733690262, 0.021672602742910385, 0.05100538581609726, 0.018066735938191414, 0.02294701524078846, 0.07615052908658981, 0.014547551050782204, 0.0014287522062659264, 0.020924577489495277, 0.07254906743764877, -0.025082413107156754, -0.009198585525155067, 0.02419080026447773, 0.02295672707259655, 0.009173915721476078, 0.018851641565561295, 0.01003965176641941, -0.023887425661087036, 0.0006742499535903335, 0.0233148280531168, 0.03193151205778122, -0.002442464930936694, -0.02511385641992092, -0.01882646046578884, 0.003948948811739683, -0.03963625431060791, 0.0029024069663137197, -0.03932127729058266, 0.04906175285577774, -0.061006173491477966, -0.06548547744750977, -0.0029121257830411196, -0.05966616049408913, -0.0022311415523290634, 0.016552725806832314, -0.07364659756422043, 0.037078287452459335, 0.006401619408279657, 0.051976412534713745, 0.007171347737312317, 0.019703812897205353, -0.039554234594106674, -0.06114666908979416, 0.005486015230417252, 0.035503704100847244, -0.040821824222803116, -0.030568543821573257, -0.051031261682510376, 0.05448745936155319, -0.0720917135477066, -0.017714032903313637, 0.08652222901582718, 0.05158661678433418, 0.005885249003767967, -0.0016247188905254006, -0.021423431113362312, 0.010401682928204536, -0.074088454246521, 0.00985848717391491, -0.007622328586876392, 0.048941776156425476, 0.04221615940332413, -0.02387647144496441, -0.03792034462094307, -0.032346129417419434, -0.004260796122252941, -0.01140088215470314, 0.005220899358391762, 0.017232121899724007, -0.036694228649139404, 0.02695496939122677, -0.023515550419688225, -0.018963875249028206, 0.04111914336681366, 0.044455163180828094, -0.010489733889698982, -0.061695147305727005, 0.021289018914103508, 0.020596902817487717, -0.027439141646027565, 0.0853140726685524, -0.021305736154317856, 0.0422581247985363, 0.011586048640310764, 0.011392639949917793, 0.042208101600408554, -0.08788571506738663, -0.048690315335989, -0.07362443208694458, 0.0024431846104562283, 0.0042097363620996475, 0.017192495986819267, -0.008257672190666199, -0.048062585294246674, -0.011384754441678524, -0.04558412358164787, 0.007701422553509474, -0.026330312713980675, 0.02814852073788643, -0.008772325702011585, 0.008310317993164062, -0.02110905759036541, -0.018508607521653175, 0.0027660145424306393, -0.05709286406636238, -0.005202319007366896, -0.037758927792310715, -0.047418154776096344, -0.004904912319034338, -0.034395623952150345, 0.07085119932889938, 0.12204471975564957, -0.029513396322727203, 0.0037262006662786007, -0.020275570452213287, -0.0681280568242073, 0.028940794989466667, -0.01162661612033844, -0.020044934004545212, 0.015177853405475616, 0.02693529799580574, 0.001736139296554029, -0.027613429352641106, -0.01634160801768303, 0.007411214988678694, -0.02830659970641136, 0.06484972685575485, 0.036146167665719986, -0.04402245208621025, -0.011767866089940071, 0.0499475859105587 ]
<p>Can one measure the Higgs field? Or is the higgs field not measurable?</p> <p>I know that the higgs boson is a indication for the presence of the higgs field. But it is the only way of the presence of the higgs field?</p> <p>When the higgs field is not measurable, what is the reason?</p>
g1523
[ 0.007086026482284069, 0.06435329467058182, 0.031945016235113144, -0.04317173361778259, 0.05325046181678772, 0.03474600985646248, -0.04049697518348694, 0.09263554215431213, -0.012302245944738388, -0.04721583053469658, -0.09021437913179398, -0.002728048013523221, -0.08265352249145508, 0.05613522604107857, 0.03909740224480629, -0.017139168456196785, 0.034221623092889786, -0.058491300791502, 0.020307309925556183, 0.04705208167433739, 0.0076322187669575214, 0.026844874024391174, 0.01971934363245964, 0.023312658071517944, -0.019300615414977074, -0.009692425839602947, 0.009957215748727322, -0.03832714259624481, 0.05234408751130104, 0.0076188333332538605, -0.009444382041692734, -0.027880586683750153, 0.027134522795677185, -0.08209621906280518, 0.04721711575984955, -0.06565328687429428, 0.043738123029470444, 0.025282051414251328, 0.0332815907895565, 0.010919230990111828, -0.026371736079454422, 0.058684512972831726, -0.017786581069231033, -0.04281020164489746, -0.03868909925222397, 0.0675317719578743, -0.019182730466127396, 0.025426527485251427, 0.03931763023138046, -0.015017768368124962, 0.0032477418426424265, -0.06264616549015045, 0.02222357876598835, 0.05885959416627884, 0.04267687350511551, 0.0021488789934664965, 0.02830459550023079, 0.006945809815078974, 0.058227408677339554, -0.020776348188519478, 0.05469402298331261, 0.03893069177865982, -0.010925902053713799, -0.0364418588578701, 0.03350522369146347, 0.059240613132715225, -0.05091366544365883, -0.0018697226187214255, -0.033003468066453934, -0.02195071429014206, 0.01425883173942566, -0.02362678572535515, 0.011990451253950596, 0.020209385082125664, -0.04843607544898987, 0.02446155436336994, -0.025677183642983437, 0.023165293037891388, -0.0037872835528105497, 0.015391719527542591, 0.005153548438102007, -0.05425417795777321, 0.013566779904067516, -0.004624024964869022, 0.048590708523988724, -0.028325317427515984, 0.025753309950232506, -0.07009812444448471, 0.011094747111201286, -0.006289321463555098, -0.04243466630578041, 0.009930562227964401, 0.06308607012033463, 0.0025781530421227217, -0.01459379494190216, -0.02586337737739086, -0.017510855570435524, 0.006870867218822241, -0.05477769300341606, -0.00313020427711308, -0.07493441551923752, 0.0029051683377474546, -0.03979892283678055, -0.025967653840780258, 0.033214960247278214, -0.045456066727638245, 0.04373284429311752, -0.0015719342045485973, 0.021156273782253265, -0.07321296632289886, -0.03929959610104561, -0.02460462786257267, -0.020809195935726166, 0.01283492986112833, -0.04115656763315201, 0.020737914368510246, 0.08471165597438812, -0.01818710006773472, -0.04313598573207855, 0.06084320694208145, -0.016177713871002197, 0.037235893309116364, 0.053943995386362076, -0.01642872579395771, -0.05403748154640198, -0.004233229905366898, -0.036664191633462906, -0.014002978801727295, -0.04707126319408417, 0.05545894801616669, 0.05918489024043083, 0.05647880584001541, 0.004211890511214733, 0.035980597138404846, -0.029815824702382088, 0.06703072786331177, 0.0681329071521759, 0.0457381047308445, 0.04611241817474365, 0.008718619123101234, -0.01659555546939373, -0.018006524071097374, 0.008819437585771084, 0.003200939390808344, 0.054495666176080704, -0.01541303563863039, 0.04687093570828438, 0.01668539084494114, -0.000018545710190664977, 0.061338238418102264, 0.02016892097890377, 0.03846778720617294, 0.01418372057378292, -0.0007525267428718507, 0.013537474907934666, -0.010104038752615452, 0.02322492003440857, 0.021219495683908463, -0.010999254882335663, 0.02647784724831581, 0.03163260594010353, 0.004521410912275314, 0.022837696596980095, -0.03585592284798622, -0.0015665325336158276, -0.006944465450942516, 0.016331598162651062, -0.021566281095147133, 0.02679753489792347, -0.013702424243092537, -0.023101747035980225, 0.008126744069159031, -0.04472459480166435, 0.0486145094037056, 0.018476290628314018, 0.032141730189323425, -0.008152857422828674, -0.011085914447903633, 0.001102300127968192, 0.033077776432037354, -0.0198423620313406, -0.0042020054534077644, 0.0635298639535904, -0.034329332411289215, -0.05723927915096283, -0.012265214696526527, -0.014199637807905674, -0.06124049797654152, 0.0397566594183445, 0.03792697936296463, -0.026102708652615547, -0.012714486569166183, 0.0010808806400746107, 0.022683218121528625, 0.011582843959331512, 0.003376229200512171, 0.026407921686768532, -0.010095878504216671, 0.01575342006981373, -0.025100629776716232, 0.029860084876418114, -0.019226664677262306, -0.005128172691911459, 0.024303652346134186, 0.03692677989602089, -0.037567079067230225, -0.039670106023550034, 0.001859484356828034, 0.041976407170295715, -0.02625267393887043, -0.009428265504539013, -0.04443744570016861, -0.015995236113667488, -0.032193366438150406, -0.03604226931929588, 0.03837883099913597, -0.01068092044442892, 0.04207523167133331, 0.03399674966931343, -0.029394807294011116, -0.03195464238524437, -0.01863047108054161, 0.04173186421394348, -0.0032508205622434616, -0.007107341196388006, 0.09502068907022476, -0.021354874595999718, 0.005816067568957806, -0.059775274246931076, 0.03003324195742607, -0.017089810222387314, -0.0737689882516861, -0.009478584863245487, 0.007635787129402161, -0.00653607863932848, 0.020058754831552505, 0.0038352247793227434, -0.015045523643493652, 0.05191775783896446, 0.06297039240598679, -0.0030571133829653263, -0.06461615115404129, -0.017485857009887695, 0.02920059859752655, 0.05713239312171936, 0.003686130279675126, 0.05822718143463135, 0.0382096990942955, -0.01796320080757141, -0.007090091705322266, 0.03368030861020088, -0.013061191886663437, -0.002653886331245303, -0.03861602768301964, 0.0336272269487381, 0.005758190527558327, 0.10277976095676422, -0.010299467481672764, -0.07693567126989365, -0.040476731956005096, 0.014186744578182697, -0.05833997204899788, 0.011659229174256325, 0.044833987951278687, -0.01482265256345272, -0.020963795483112335, 0.02467942424118519, -0.006277007050812244, -0.04078209027647972, -0.02513544075191021, -0.0500352643430233, 0.004240721929818392, -0.004191060084849596, -0.00034160175709985197, 0.0012370118638500571, -0.03595193475484848, -0.07478822022676468, 0.0483233816921711, 0.031171968206763268, -0.04574758931994438, -0.031529419124126434, 0.014103404246270657, 0.007043040357530117, 0.036906395107507706, -0.008165608160197735, 0.026393353939056396, -0.012968942523002625, -0.13388164341449738, 0.014032164588570595, 0.07524355500936508, 0.042360570281744, -0.04357418790459633, -0.0028131017461419106, 0.023232175037264824, -0.05666886642575264, 0.016067666932940483, -0.014631801284849644, 0.00757446326315403, 0.038320135325193405, -0.019310595467686653, 0.0124575886875391, 0.03139603137969971, -0.05090255290269852, -0.03767426311969757, 0.056022658944129944, -0.0504482164978981, -0.029557302594184875, 0.002046887995675206, -0.02947758510708809, -0.032612938433885574, -0.029632870107889175, 0.02733374387025833, -0.004842303227633238, 0.018346605822443962, 0.002073396695777774, 0.001421631663106382, -0.005575888324528933, 0.09370067715644836, -0.027524935081601143, -0.02516353875398636, -0.014442864805459976, -0.010295568034052849, -0.01636078581213951, -0.008442031219601631, 0.010336159728467464, 0.01973802037537098, 0.00299619953148067, 0.039656639099121094, -0.040107790380716324, -0.0632418766617775, 0.005803507287055254, -0.031302209943532944, -0.04685847833752632, 0.02471069246530533, -0.021069172769784927, -0.0023184753954410553, 0.012782642617821693, 0.03389705345034599, 0.004530185833573341, 0.04910939186811447, 0.02500614896416664, 0.007638945244252682, -0.10933669656515121, -0.006216526962816715, -0.05497998371720314, -0.013097954913973808, -0.005516963079571724, -0.03352862596511841, 0.03865007311105728, -0.03950704261660576, 0.051665350794792175, 0.04698348417878151, 0.006123578641563654, -0.01075720600783825, -0.04411378130316734, 0.0018131975084543228, -0.027253631502389908, 0.008198919706046581, 0.012443365529179573, 0.005774803459644318, 0.027067862451076508, -0.0025694684591144323, 0.0057898820377886295, 0.02264166623353958, -0.0512317419052124, -0.029179386794567108, 0.004904375411570072, -0.029397621750831604, 0.007257502060383558, 0.013682868331670761, -0.018292967230081558, -0.017184557393193245, 0.04585903510451317, 0.0646880492568016, -0.020238297060132027, -0.10519423335790634, 0.061524223536252975, -0.0537746325135231, 0.011700642295181751, -0.005720715969800949, -0.050771914422512054, 0.07346799969673157, 0.03500160947442055, -0.004345880355685949, 0.023558175191283226, -0.042177874594926834, -0.01009705476462841, 0.017415326088666916, -0.007874892093241215, -0.010662342421710491, -0.05193200334906578, -0.026439888402819633, -0.0007857337477616966, 0.051657553762197495, 0.045475367456674576, -0.014987819828093052, 0.05565295368432999, 0.05090312287211418, 0.058531615883111954, -0.01239679753780365, 0.005361136514693499, -0.020195577293634415, 0.004356287885457277, -0.0440686009824276, 0.017552940174937248, -0.006152910180389881, 0.04859068617224693, 0.02187306433916092, 0.003915784880518913, -0.02016984485089779, -0.04245048761367798, 0.0033198613673448563, -0.025912167504429817, -0.01724197156727314, 0.0004917137557640672, -0.039250049740076065, 0.03733775392174721, 0.0036691445857286453, 0.03880451247096062, 0.023391060531139374, 0.06837103515863419, 0.004013137426227331, -0.001900634029880166, -0.02741878107190132, -0.06710640341043472, 0.10967814177274704, -0.007846452295780182, 0.06995247304439545, -0.05407670885324478, -0.028144586831331253, 0.04328029602766037, -0.016569295898079872, 0.0315803624689579, 0.01882723905146122, -0.024430030956864357, 0.03737030550837517, -0.06283318251371384, -0.006443341728299856, 0.007659501396119595, -0.01567126251757145, 0.0075874896720051765, -0.005646538455039263, 0.0007369743543677032, 0.02963988669216633, -0.08215565979480743, 0.01533959899097681, -0.03114052675664425, -0.007327517960220575, -0.029238440096378326, -0.038802120834589005, -0.024762768298387527, 0.006264647468924522, -0.06149134039878845, 0.008053810335695744, -0.00215909187681973, -0.036803439259529114, 0.029861466959118843, 0.010258294641971588, -0.025754248723387718, 0.005935759283602238, -0.07044325768947601, 0.0007177258376032114, 0.06041928753256798, 0.04413451626896858, 0.0026621976867318153, -0.03912872448563576, -0.07256817817687988, -0.028570309281349182, -0.007577862124890089, -0.01792917214334011, 0.005405867006629705, -0.036181509494781494, 0.0659511536359787, 0.05506718531250954, 0.018284199759364128, 0.025455426424741745, -0.03584516420960426, 0.010870514437556267, -0.045628830790519714, -0.046038344502449036, 0.028674231842160225, 0.015649134293198586, -0.008997303433716297, -0.004707684740424156, -0.044695787131786346, -0.004188295919448137, -0.04254642874002457, 0.034413326531648636, 0.015507292933762074, 0.0016389376251026988, 0.017774397507309914, 0.06478004902601242, 0.050931431353092194, 0.010559487156569958, 0.02421187423169613, -0.030942142009735107, -0.06610824912786484, -0.02245062217116356, -0.011306125670671463, 0.031807638704776764, -0.023832228034734726, 0.030826391652226448, -0.0068209487944841385, 0.0307152159512043, -0.024365898221731186, 0.0582909882068634, 0.01772058568894863, -0.04126164689660072, 0.0548873208463192, -0.011717226356267929, -0.019286636263132095, -0.0017933719791471958, -0.039921849966049194, 0.0038332142867147923, 0.04463420808315277, -0.03818368911743164, 0.008677590638399124, 0.0056921737268567085, -0.058748017996549606, 0.011471226811408997, -0.049178190529346466, -0.008815430104732513, 0.03507135063409805, -0.026976626366376877, 0.014613845385611057, -0.05594693496823311, -0.0715765431523323, -0.023070642724633217, 0.07861639559268951, -0.004783557262271643, 0.0469667911529541, 0.05566007271409035, 0.03288886323571205, 0.002069511916488409, -0.020556867122650146, -0.057194195687770844, 0.01827229931950569, -0.038710933178663254, 0.022927086800336838, 0.03749590367078781, 0.006124578416347504, -0.009471438825130463, 0.045686986297369, -0.01251172460615635, 0.010881501249969006, 0.03663905709981918, -0.02413012646138668, 0.0036862518172711134, 0.04951833188533783, -0.029528016224503517, -0.05129069834947586, 0.0480363629758358, -0.02501498907804489, -0.0011853709584102035, -0.02370641939342022, 0.01978885941207409, -0.0016324227908626199, 0.056889936327934265, 0.023890478536486626, -0.015593241900205612, 0.031254686415195465, 0.030371366068720818, -0.020618077367544174, 0.009174207225441933, 0.005397234112024307, 0.04843074083328247, 0.020784173160791397, -0.007146034389734268, 0.04165378957986832, -0.014890079386532307, -0.05274322256445885, -0.013827107846736908, 0.006550765596330166, 0.018222210928797722, 0.005288553889840841, 0.03929669409990311, 0.007746681105345488, 0.057576339691877365, -0.05465805158019066, 0.00022866265499033034, -0.006559113040566444, 0.0453433059155941, 0.014882659539580345, -0.048438407480716705, 0.043136026710271835, 0.016624752432107925, 0.014426562935113907, -0.010382902808487415, 0.01595822535455227, 0.07979816198348999, -0.009783312678337097, -0.01016161311417818, -0.03081558085978031, 0.0068115065805613995, -0.05184483155608177, -0.030873620882630348, -0.03302113711833954, 0.020529290661215782, -0.028705617412924767, -0.01940634287893772, 0.0016843711491674185, -0.03300442174077034, 0.0022403590846806765, -0.051064882427453995, 0.02361265756189823, 0.08749233186244965, 0.014305473305284977, 0.0428437814116478, -0.010925279930233955, -0.019636468961834908, 0.0018889975035563111, 0.018413668498396873, 0.024359676986932755, 0.01165272481739521, 0.03397426754236221, -0.02542106993496418, 0.022305572405457497, -0.02153722196817398, -0.037623193114995956, 0.01701793447136879, 0.007530075032263994, -0.016579698771238327, 0.03783747926354408, -0.0031588361598551273, -0.022953514009714127, -0.0032450822181999683, -0.021165208891034126, 0.0266906525939703, -0.071779265999794, -0.0200016051530838, 0.02001195400953293, 0.01624261401593685, 0.005857483483850956, 0.04197213053703308, 0.03150225803256035, 0.02460946887731552, -0.007933782413601875, 0.011470071040093899, -0.03971919044852257, -0.012833600863814354, 0.017127584666013718, 0.03364959731698036, -0.006113164592534304, -0.0261127520352602, -0.04843468964099884, 0.02821025252342224, 0.034260306507349014, 0.007816419936716557, -0.07636506110429764, -0.030614499002695084, -0.030005333945155144, 0.03353864699602127, -0.01792377419769764, -0.0951540395617485, 0.0067217908799648285, 0.023203495889902115, -0.01899324730038643, -0.007733152713626623, 0.0075342110358178616, -0.014525706879794598, -0.03903187811374664, -0.06797412037849426, -0.004458761774003506, -0.04350365325808525, -0.004819532390683889, -0.01771794632077217, 0.0031914561986923218, -0.029495103284716606, -0.00849002692848444, -0.01718570664525032, 0.009522665292024612, -0.09034883230924606, -0.061614345759153366, 0.02568294294178486, -0.04780861362814903, -0.04366637021303177, -0.004287054296582937, 0.027388744056224823, -0.030866824090480804, -0.015126745216548443, -0.05725373327732086, 0.024550162255764008, -0.001730815740302205, 0.012291993945837021, -0.02300579473376274, -0.05865021049976349, 0.015560069121420383, 0.004243322182446718, 0.014081931672990322, -0.04820460453629494, -0.00746488943696022, 0.002014435362070799, 0.061439674347639084, -0.09024421870708466, 0.019277261570096016, -0.0018991879187524319, -0.0076730214059352875, 0.04167426377534866, -0.015245867893099785, -0.06327159702777863, -0.00802886113524437, -0.0056798141449689865, 0.01784294843673706, -0.0199595894664526, 0.044177062809467316, -0.014642775058746338, -0.0002425720012979582, 0.033269356936216354, -0.08559849113225937, -0.04287439212203026, 0.03298288956284523, 0.07299168407917023, 0.03372874855995178, 0.00915225874632597, -0.017197342589497566, -0.022093161940574646, -0.055133577436208725, -0.013020465150475502, -0.011005107313394547, -0.06485054641962051, 0.03386199474334717, -0.0007786080823279917, -0.0025945333763957024, -0.013683347962796688, -0.055644236505031586, -0.00845490675419569, -0.02533593401312828, 0.03218039870262146, 0.06921947747468948, 0.053824249655008316, 0.03420860692858696, 0.05209675431251526, -0.019641514867544174, -0.04692002013325691, -0.07913193851709366, 0.0254955030977726, 0.06115129962563515, 0.019976483657956123, 0.038607753813266754, 0.011796061880886555, -0.04836883395910263, 0.003090165089815855, 0.04257306084036827, 0.025107335299253464, 0.011003104969859123, -0.05292542278766632, 0.015144901350140572, -0.034301307052373886, 0.049225736409425735, 0.003880921984091401, -0.006288529839366674, 0.05425690859556198, 0.008920353837311268, 0.06864633411169052, -0.01140435878187418, -0.03057815320789814, 0.01593450829386711, 0.04346364364027977, 0.006359769031405449, -0.009071314707398415, 0.059907324612140656, -0.02888670563697815, 0.03285060077905655, 0.0012671257136389613, -0.05709777772426605, -0.015122286975383759, 0.04077142849564552, -0.0028710090555250645 ]
<p>Really short question, but I cannot find anything on the internet.</p> <p>What is meant <em>proton polarisation</em>?</p> <p>Is it to do with the spin of the proton? I guess the spin of the proton is obtained from the vector addition of the 3 quarks' individual spins, so it can't be 0... Can we have <em>unpolarised</em> protons then?</p> <p>Thanks!</p>
g1524
[ 0.008448106236755848, -0.02011570706963539, -0.004265739116817713, -0.025981854647397995, 0.09704276919364929, 0.029205258935689926, -0.06924422830343246, 0.0708855390548706, 0.011805725283920765, -0.011812756769359112, 0.0025157304480671883, 0.012271510437130928, -0.05503964424133301, -0.06256190687417984, -0.022053442895412445, 0.020523732528090477, -0.025939419865608215, 0.028583748266100883, 0.019021959975361824, -0.025633614510297775, -0.024930439889431, 0.028141610324382782, 0.016488922759890556, -0.06337140500545502, 0.01127686444669962, -0.04433687776327133, -0.014395741745829582, -0.0565926656126976, -0.030740367248654366, 0.04214668273925781, 0.00614981260150671, -0.03995358198881149, -0.01661192625761032, -0.009253297001123428, -0.025343336164951324, -0.052896615117788315, 0.0783788189291954, 0.017438681796193123, 0.05318542197346687, -0.0039340718649327755, 0.010761426761746407, 0.012997833080589771, -0.006087132729589939, -0.006982041988521814, -0.02034005895256996, -0.008724983781576157, 0.02600056678056717, -0.00774731021374464, -0.02673874795436859, 0.02231656201183796, -0.04316846653819084, -0.01975896582007408, 0.04656941816210747, 0.047549087554216385, 0.05248909071087837, 0.020888401195406914, 0.011525393463671207, -0.026220662519335747, 0.09337176382541656, 0.05196747928857803, -0.018745316192507744, -0.014944949187338352, 0.005751606542617083, 0.04865497350692749, -0.0177140012383461, -0.06639537960290909, -0.04387595131993294, 0.0140464436262846, -0.037104297429323196, 0.10878919064998627, -0.00439403997734189, -0.05107291787862778, -0.01205054298043251, -0.04462806135416031, 0.006049640476703644, 0.05876987427473068, 0.016674943268299103, -0.026432419195771217, 0.0716523751616478, 0.00013156207569409162, 0.012153259478509426, 0.023448146879673004, -0.0209308173507452, -0.014989035204052925, 0.07589798420667648, 0.007790127769112587, -0.029453683644533157, -0.013947620987892151, -0.01602095365524292, -0.012068227864801884, 0.01731298677623272, -0.05060529336333275, -0.013672802597284317, 0.020258277654647827, -0.042134229093790054, -0.01704533025622368, 0.02276034466922283, 0.014792589470744133, -0.032190293073654175, 0.014856291003525257, -0.021275248378515244, 0.01902260072529316, -0.009896895848214626, -0.06735856831073761, 0.018127979710698128, 0.04963494464755058, 0.004867508076131344, -0.0011859657242894173, 0.08094938844442368, 0.0061157625168561935, -0.03552333265542984, 0.003156694583594799, -0.052416909486055374, 0.06539931148290634, -0.05260200798511505, -0.015313156880438328, 0.06422636657953262, -0.016825929284095764, 0.05304526910185814, 0.036280158907175064, 0.0348697267472744, 0.022589484229683876, -0.06688641011714935, 0.13293933868408203, -0.05548033118247986, -0.014835763722658157, 0.033254481852054596, 0.06759579479694366, 0.03781525790691376, -0.0183767918497324, 0.0034624466206878424, -0.039656199514865875, -0.0043361918069422245, -0.013177501037716866, -0.02312271110713482, -0.0014516968512907624, 0.02558564953505993, 0.0249626524746418, 0.004021645989269018, 0.028911883011460304, 0.01652715727686882, 0.019900398328900337, -0.00811105128377676, -0.021712753921747208, -0.00034667307045310736, -0.0499119907617569, -0.0027912871446460485, -0.025691969320178032, -0.00011097596870968118, 0.08964686095714569, 0.053043123334646225, 0.04448404908180237, 0.04055929556488991, -0.014874360524117947, 0.000756449531763792, -0.06123770400881767, 0.04208732396364212, -0.005323813762515783, -0.031765807420015335, 0.022542966529726982, 0.06653154641389847, -0.07490099221467972, -0.01607009954750538, -0.002998670795932412, -0.06517481803894043, 0.011837148107588291, 0.059381935745477676, -0.02199763059616089, 0.0213868860155344, -0.03835800662636757, -0.01953921839594841, 0.016406897455453873, -0.03355643153190613, 0.027065547183156013, 0.05177346616983414, 0.053441137075424194, 0.007352936547249556, -0.03435661643743515, 0.007930215448141098, 0.019004736095666885, -0.03649989143013954, 0.01821877434849739, -0.0037289545871317387, 0.005879363976418972, -0.004313930403441191, -0.03670646250247955, -0.015273427590727806, 0.05120610073208809, -0.01325071882456541, 0.013770741410553455, -0.004028043244034052, 0.022674931213259697, 0.0034113412257283926, -0.03327389806509018, -0.007020127028226852, -0.00950821116566658, -0.01930496096611023, -0.03602707013487816, 0.004684796091169119, 0.06867363303899765, 0.00043640987132675946, -0.015306252986192703, 0.02788352407515049, 0.02640586905181408, 0.04034039005637169, -0.03634147346019745, 0.05596601963043213, 0.016371840611100197, 0.10471154749393463, 0.008474738337099552, -0.016364889219403267, 0.004710478242486715, -0.009783844463527203, -0.014942488633096218, -0.02204265259206295, 0.02817041240632534, 0.02545730024576187, 0.0888989269733429, -0.010327833704650402, -0.012231183238327503, -0.03361263498663902, -0.01765304058790207, 0.00011511927004903555, 0.01161293312907219, -0.07447027415037155, 0.023542482405900955, -0.06493014097213745, -0.005918765440583229, -0.027334285899996758, 0.034777361899614334, -0.02427123859524727, -0.06532643735408783, 0.010775096714496613, 0.030634835362434387, 0.006418498698621988, 0.018180230632424355, -0.03485061973333359, -0.009701716713607311, -0.016032641753554344, 0.011384360492229462, -0.016656925901770592, -0.0019430061802268028, -0.0013305108295753598, 0.05613233894109726, 0.03315705806016922, -0.00624764384701848, 0.059522002935409546, 0.005405575968325138, -0.02309601940214634, 0.006903401575982571, 0.042365651577711105, 0.005284555722028017, 0.01450307946652174, -0.01436710637062788, -0.02492515929043293, -0.029500357806682587, -0.031995195895433426, 0.03711716830730438, -0.08112458139657974, -0.05372341349720955, 0.04300805181264877, -0.06707315891981125, 0.026850558817386627, 0.030222171917557716, -0.0003181339125148952, 0.0046151671558618546, 0.043330296874046326, 0.004405349493026733, 0.029340090230107307, -0.022557005286216736, -0.03419790789484978, 0.0598762184381485, 0.025411082431674004, -0.007985222153365612, -0.01588081382215023, -0.07308369129896164, -0.02818770334124565, 0.0052221729420125484, -0.028830459341406822, -0.029831070452928543, -0.0595858134329319, 0.04195493459701538, -0.04056444764137268, -0.03528374433517456, -0.0343136303126812, -0.002122592180967331, -0.017675278708338737, -0.0026341185439378023, -0.03519636392593384, -0.018358401954174042, -0.03972170129418373, -0.046113021671772, 0.04944545775651932, -0.0447784923017025, 0.030744316056370735, -0.032676782459020615, 0.05576407536864281, -0.031560905277729034, -0.020375052466988564, 0.0779849961400032, 0.09681351482868195, 0.04879353195428848, -0.02261458896100521, -0.03239789977669716, 0.035072680562734604, 0.013730726204812527, -0.05551309883594513, -0.03395761549472809, -0.06933671236038208, 0.01342177577316761, -0.049137845635414124, 0.07800840586423874, -0.023380769416689873, 0.08739478141069412, 0.020738456398248672, -0.0325792022049427, -0.06779727339744568, 0.029230214655399323, 0.026034291833639145, 0.007371955085545778, -0.09047944098711014, -0.040127944201231, 0.03288421779870987, -0.01272623147815466, 0.09395348280668259, -0.01608763448894024, -0.005030249711126089, 0.03297388553619385, -0.028091279789805412, -0.016935328021645546, 0.030278196558356285, -0.02700144797563553, 0.024252278730273247, 0.04171345382928848, -0.13356322050094604, -0.023047611117362976, -0.013686785474419594, -0.005311311688274145, 0.010091050527989864, -0.03215847536921501, 0.02524789422750473, -0.023292673751711845, -0.02116248570382595, -0.033709313720464706, -0.011693927459418774, 0.02360963076353073, -0.010684037581086159, -0.029119716957211494, 0.009420506656169891, 0.03223561868071556, -0.006000807974487543, 0.060116712003946304, 0.021279409527778625, 0.055814843624830246, 0.002884319983422756, -0.013637948781251907, -0.07512775808572769, 0.0315551720559597, -0.010777081362903118, -0.011075489223003387, 0.022227786481380463, -0.060726042836904526, 0.022884178906679153, -0.009494016878306866, -0.019476447254419327, 0.0028468812815845013, -0.035277921706438065, -0.0182656142860651, -0.005165961571037769, -0.004789619706571102, 0.012486767023801804, -0.0912880077958107, -0.011713841930031776, -0.01604072004556656, -0.005433104000985622, -0.04054442048072815, -0.002289813244715333, 0.03631529211997986, -0.11409485340118408, 0.008568458259105682, -0.007641332224011421, 0.06060006842017174, 0.04295286536216736, 0.05658607557415962, -0.024570662528276443, 0.03708123788237572, -0.04458050802350044, -0.005842557642608881, -0.02293408289551735, -0.020025670528411865, -0.004305337555706501, 0.026214443147182465, 0.030662279576063156, 0.026046868413686752, 0.012910137884318829, -0.07604258507490158, 0.002945950487628579, -0.06118595600128174, -0.00998249463737011, 0.06937622278928757, -0.022051997482776642, -0.005533766932785511, 0.03758610412478447, -0.006928320974111557, 0.09075325727462769, -0.030788004398345947, 0.005369287915527821, 0.028018461540341377, 0.05308086425065994, -0.042587194591760635, -0.014148548245429993, 0.037063270807266235, -0.00420156167820096, -0.02035842090845108, 0.03380824625492096, 0.054707735776901245, -0.022294238209724426, -0.012591361999511719, -0.038591168820858, -0.01972087472677231, -0.02046496421098709, 0.02297341078519821, -0.006632145494222641, -0.006034239660948515, -0.00011185680341441184, 0.04379330202937126, 0.04005061835050583, -0.0415092371404171, -0.027128497138619423, -0.01321601215749979, 0.01207652222365141, -0.02786726877093315, 0.008896693587303162, -0.0018840052653104067, 0.009384235367178917, -0.026627566665410995, -0.0029628481715917587, 0.017127301543951035, -0.03840119019150734, -0.017235910519957542, 0.07779113203287125, 0.016083717346191406, 0.033540040254592896, -0.0030531142838299274, 0.0038463652599602938, -0.036582984030246735, -0.06081320345401764, -0.030309779569506645, -0.012206783518195152, -0.031660787761211395, -0.0007563225226476789, 0.021963102743029594, -0.06436705589294434, -0.013523565605282784, -0.0030813964549452066, 0.06345182657241821, -0.006269169971346855, 0.02895469218492508, 0.006250720005482435, 0.024579400196671486, -0.14213137328624725, -0.00841599516570568, -0.05369763448834419, -0.0012186060193926096, -0.03499939292669296, 0.043825287371873856, -0.04670622944831848, 0.016514187678694725, -0.03758203238248825, 0.027311017736792564, 0.0028506123926490545, -0.023564981296658516, 0.003911261912435293, 0.020304376259446144, -0.0011075944639742374, 0.011380272917449474, -0.02390299364924431, -0.025315996259450912, 0.002036364981904626, -0.0246780663728714, -0.004127338528633118, -0.02075725793838501, 0.03549054637551308, -0.030440548434853554, -0.010296833701431751, 0.01667540892958641, -0.03538476675748825, -0.04780124872922897, -0.01466717105358839, -0.0453917421400547, 0.0046251555904746056, 0.04933590441942215, 0.014467946253716946, -0.006884829141199589, -0.00010012117854785174, -0.025850512087345123, -0.04072267934679985, 0.011855910532176495, 0.013935983180999756, 0.002683360828086734, 0.003209400689229369, -0.029985884204506874, -0.01208814699202776, 0.005998518317937851, -0.009844565764069557, -0.024467797949910164, 0.07683942466974258, -0.07303568720817566, -0.0002513225772418082, -0.036707643419504166, 0.025604506954550743, -0.022785652428865433, 0.015112511813640594, 0.03252582252025604, 0.02214135229587555, 0.042081981897354126, -0.050927817821502686, 0.012894838117063046, 0.02678300067782402, -0.007062673568725586, -0.0294811874628067, -0.013854713179171085, 0.0019971360452473164, -0.052323296666145325, -0.017142128199338913, -0.007454602047801018, -0.04453369602560997, 0.02501741237938404, -0.002650235313922167, 0.03913406655192375, 0.0493425652384758, 0.023080216720700264, 0.08927007764577866, 0.023083483800292015, -0.00020375382155179977, -0.07636119425296783, -0.0032868115231394768, -0.0095289321616292, 0.030802816152572632, 0.022809026762843132, 0.0055332425981760025, -0.010155659168958664, -0.010630316101014614, 0.06570548564195633, 0.02564922906458378, 0.00891124363988638, 0.00463443249464035, 0.011942807585000992, 0.01560937985777855, -0.11873794347047806, -0.023086601868271828, -0.01373562216758728, 0.012045534327626228, -0.08279770612716675, -0.04874039441347122, 0.026988742873072624, 0.03166895732283592, -0.056289222091436386, -0.019039489328861237, -0.06411319226026535, -0.028688084334135056, -0.041458215564489365, 0.00034976706956513226, -0.0210911575704813, -0.03350554034113884, 0.00432971678674221, -0.053641967475414276, 0.011676739901304245, -0.0058699422515928745, 0.024352174252271652, -0.010203264653682709, 0.015653615817427635, -0.054992809891700745, 0.08055540174245834, 0.005346050951629877, 0.015500353649258614, 0.03995273634791374, -0.02682305872440338, 0.011080696247518063, 0.050492022186517715, 0.04077589511871338, 0.02733045443892479, 0.06713984161615372, -0.00928296148777008, 0.011847561225295067, 0.03592057526111603, -0.03809065744280815, -0.009392411448061466, 0.04446202144026756, 0.014825982972979546, -0.03605420142412186, 0.043104659765958786, -0.06748203188180923, -0.023158468306064606, 0.026918796822428703, 0.03749484196305275, 0.01743597537279129, 0.008736040443181992, 0.011315370909869671, -0.05680951103568077, -0.0600646436214447, 0.0509960763156414, 0.013853777199983597, 0.07731755822896957, 0.008118590340018272, 0.0073615191504359245, 0.02922993153333664, -0.051903605461120605, 0.0029601200949400663, 0.02616005204617977, -0.0006253556348383427, -0.02649780362844467, -0.02610193006694317, -0.03970986232161522, 0.0052920132875442505, -0.054838985204696655, -0.02985469438135624, -0.006315851118415594, 0.02255401574075222, -0.01591324992477894, -0.025077050551772118, -0.027936695143580437, -0.03130437806248665, -0.033430714160203934, 0.02532104030251503, 0.012234280817210674, 0.04666215553879738, 0.05073051527142525, -0.003005113685503602, 0.03182177618145943, 0.01374692004173994, 0.010616839863359928, 0.010426347143948078, 0.042709220200777054, -0.017679020762443542, 0.019874118268489838, -0.044371966272592545, 0.03897697478532791, 0.08718160539865494, 0.014642924070358276, -0.0057593341916799545, 0.024046223610639572, 0.024427106603980064, -0.021091777831315994, -0.015272931195795536, 0.037713658064603806, -0.028878653421998024, 0.0009132000850513577, -0.051666393876075745, -0.03648054599761963, -0.02133057825267315, -0.015185080468654633, 0.024427203461527824, 0.03591331094503403, 0.01428300328552723, -0.006144282408058643, 0.027115490287542343, 0.04655352234840393, 0.04346292465925217, -0.027457328513264656, -0.028347088024020195, -0.0053519378416240215, -0.02609940618276596, 0.0055617401376366615, 0.0050066267140209675, 0.03421679139137268, -0.016524743288755417, -0.0033202634658664465, 0.04085760936141014, -0.027970511466264725, -0.0320950485765934, -0.044289764016866684, -0.023144811391830444, -0.012603911571204662, -0.007564428262412548, -0.05367708578705788, 0.011836939491331577, 0.021085472777485847, 0.02978084236383438, 0.039307475090026855, 0.0006965897046029568, -0.02510671503841877, -0.04218299314379692, -0.01920013129711151, -0.01383487693965435, -0.009721984155476093, -0.01678907312452793, -0.020334932953119278, 0.021004486829042435, 0.022856395691633224, 0.05209891125559807, -0.0250661913305521, 0.05616963282227516, -0.0038912338204681873, 0.0014783961232751608, -0.003737319028005004, 0.010463534854352474, 0.003276068950071931, 0.03250555694103241, -0.04665985330939293, 0.05147944763302803, -0.003525983775034547, 0.025653932243585587, 0.01866391859948635, 0.025362012907862663, 0.00280595850199461, 0.003917260095477104, 0.012331807054579258, -0.02580379694700241, 0.0274162869900465, 0.05331151559948921, 0.0014010906452313066, -0.03818075731396675, 0.019223755225539207, 0.02490200102329254, -0.0004826904332730919, -0.04384881630539894, 0.016342412680387497, 0.0385512039065361, -0.010056267492473125, 0.005218888632953167, 0.051372453570365906, 0.01375770103186369, -0.04970287159085274, -0.045725155621767044, 0.007451673969626427, -0.016563229262828827, 0.019899528473615646, 0.06624402105808258, 0.0577075220644474, 0.03460664674639702, 0.03250350430607796, -0.02699872851371765, 0.05553962662816048, 0.009752593003213406, -0.01203567162156105, -0.006104564759880304, -0.0017571585485711694, -0.011108599603176117, 0.05685419961810112, -0.015717539936304092, -0.02621486596763134, 0.01377126295119524, -0.006837064400315285, -0.0031173191964626312, -0.005521958228200674, -0.025570470839738846, 0.07575857639312744, 0.027984293177723885, 0.014698379673063755, 0.0019327731570228934, 0.01537175104022026, 0.00832515861839056, 0.05427093803882599, 0.051852110773324966, -0.04535980150103569, -0.019908249378204346, -0.0028828263748437166, -0.039358604699373245, -0.0200330950319767, 0.01256786659359932, 0.006212332751601934, -0.013029849156737328, -0.011803881265223026, 0.011176333762705326, -0.0060655176639556885, -0.05469530448317528, 0.029827933758497238 ]
<p>Approaching the speed of sound in an aircraft is relatively difficult, because the closer you get to Mach 1, the denser the pressure is around you (sound accumulates causing vibrations).</p> <p>Is there a similar effect as you approach the speed of light? Does the Doppler Effect apply for light as it does with sound? Will light accumulate around your aircraft causing heat? </p> <p>Speaking strictly hypothetical.</p>
g1525
[ 0.03562847897410393, 0.038473110646009445, 0.024802854284644127, 0.011206776835024357, 0.030337389558553696, -0.0036589319352060556, 0.02296367660164833, 0.020230794325470924, -0.048676785081624985, 0.003146921982988715, 0.0012182941427454352, -0.002484968863427639, -0.010734658688306808, 0.09789493680000305, -0.012219900265336037, -0.029892820864915848, 0.032144129276275635, -0.028790809214115143, 0.007358378730714321, 0.020187050104141235, 0.004984155762940645, 0.010389819741249084, 0.009961206465959549, -0.05477409064769745, -0.045647285878658295, 0.008277404122054577, -0.042993564158678055, -0.02550751343369484, -0.05826813355088234, 0.000912967836484313, -0.015201826579868793, -0.0646127313375473, 0.05455882102251053, 0.013966066762804985, -0.016182364895939827, -0.04016038402915001, -0.005217151250690222, 0.04294314235448837, 0.0052534607239067554, -0.01535243820399046, 0.042425934225320816, -0.011626566760241985, 0.007719981484115124, -0.024031853303313255, 0.05510283634066582, 0.04605542868375778, 0.0009853050578385592, 0.027111023664474487, -0.007871177978813648, 0.03752224147319794, 0.008862796239554882, -0.01332764234393835, 0.0033878155518323183, 0.029827650636434555, -0.00876996386796236, 0.020598962903022766, -0.009382806718349457, -0.027211109176278114, 0.046795085072517395, 0.07000233978033066, -0.00935770571231842, 0.0649222731590271, -0.01374906301498413, 0.049377888441085815, 0.024927103891968727, -0.013961237855255604, 0.030685478821396828, -0.06364854425191879, 0.04117520526051521, -0.021383361890912056, -0.016301460564136505, -0.04172998666763306, -0.045209698379039764, -0.031658101826906204, -0.039550524204969406, 0.020062733441591263, 0.01856454834342003, -0.046220678836107254, 0.023889005184173584, 0.017437785863876343, 0.0006721836980432272, -0.005431598052382469, 0.08390314131975174, -0.020043672993779182, -0.0020294426940381527, -0.05885224789381027, -0.019242480397224426, 0.006582753267139196, 0.0270921029150486, -0.008035692386329174, 0.03215281665325165, -0.02897658757865429, 0.02115866169333458, -0.0009356808732263744, -0.007746806833893061, -0.009562462568283081, -0.009596923366189003, 0.02111174911260605, -0.045579973608255386, -0.02357795648276806, 0.028771035373210907, -0.022304875776171684, 0.008756047114729881, 0.03426928073167801, -0.038109418004751205, -0.029554834589362144, 0.022257918491959572, -0.003459573956206441, -0.02237921766936779, -0.04412734881043434, -0.014218567870557308, -0.06069891154766083, 0.04048694297671318, -0.04845118150115013, -0.0853029265999794, -0.02653825841844082, 0.013748032972216606, 0.01713697426021099, -0.07058358937501907, 0.006557338871061802, 0.04206855967640877, 0.013788494281470776, 0.012841866351664066, 0.03292911872267723, 0.062428127974271774, 0.06116748973727226, -0.01663302630186081, -0.013635814189910889, -0.013473345898091793, -0.02446134202182293, -0.03954041749238968, 0.06765487790107727, -0.003847540821880102, 0.029754983261227608, 2.2054980775010335e-7, 0.004117240663617849, -0.010497907176613808, 0.01847936399281025, -0.007091273553669453, 0.005437441635876894, 0.11392535269260406, -0.038325753062963486, 0.042760513722896576, -0.03753457963466644, -0.04593345522880554, 0.03538889065384865, 0.0010821664473041892, -0.006406864151358604, 0.04186549782752991, 0.013413704000413418, -0.015791673213243484, -0.002298197941854596, 0.02335761860013008, -0.05387962609529495, -0.06172401085495949, 0.06261308491230011, 0.006285415031015873, 0.06349178403615952, 0.004058368969708681, 0.05228103697299957, 0.043958235532045364, -0.002297659171745181, 0.04559948295354843, -0.022366221994161606, -0.032832033932209015, 0.04553458094596863, -0.022701125591993332, -0.03488565981388092, -0.004061826039105654, -0.01568722352385521, 0.009297634474933147, 0.03668572008609772, -0.011822731234133244, 0.05152038484811783, 0.03987400606274605, -0.015471715480089188, 0.10616939514875412, -0.01940874755382538, -0.04186871647834778, -0.03022230602800846, -0.03477964922785759, -0.026618627831339836, -0.005662478972226381, -0.10469312965869904, -0.037130557000637054, -0.008232589811086655, 0.010815797373652458, -0.036437321454286575, -0.09708727896213531, 0.030519625172019005, -0.0537123940885067, -0.06678099930286407, -0.001958848675712943, 0.014324155636131763, -0.036868173629045486, -0.03050641529262066, -0.00028135505272075534, -0.015074613504111767, -0.05637369304895401, 0.01949138380587101, -0.034845221787691116, 0.05316486209630966, 0.03965277597308159, -0.05981936305761337, 0.021032454445958138, 0.010115537792444229, -0.017429597675800323, -0.05614396929740906, 0.05171419307589531, -0.008439024910330772, 0.03854820877313614, -0.00413886783644557, 0.028970904648303986, 0.026302682235836983, 0.01810491643846035, 0.01335522998124361, -0.040883924812078476, -0.011528540402650833, 0.0266479030251503, 0.019097864627838135, 0.023868687450885773, 0.03527034446597099, -0.011966168880462646, -0.0006442285957746208, -0.021251888945698738, -0.048602230846881866, -0.07627975940704346, -0.0330372080206871, 0.0048810443840920925, 0.04201211780309677, -0.050787732005119324, -0.008979720063507557, 0.008882242254912853, -0.02783868834376335, 0.009616387076675892, 0.010220805183053017, 0.021148452535271645, 0.00836621318012476, -0.014971664175391197, 0.06997096538543701, 0.0005716366576962173, 0.012066815048456192, -0.02258257195353508, 0.04095904901623726, -0.011988194659352303, -0.016388310119509697, -0.05293992906808853, -0.03941473364830017, 0.03571946918964386, -0.016648123040795326, 0.04900004342198372, 0.0071877664886415005, -0.01462340634316206, -0.02899581380188465, 0.006887586321681738, -0.018758734688162804, -0.004060700535774231, 0.02106558531522751, 0.006598880048841238, -0.007866163738071918, -0.054429568350315094, 0.008944355882704258, -0.034097179770469666, -0.04933987557888031, -0.025272654369473457, 0.05685130134224892, 0.027258804067969322, -0.040027182549238205, -0.007405449170619249, -0.009100626222789288, -0.043262116611003876, 0.0057986825704574585, 0.02235526032745838, -0.0012369039468467236, 0.0385141521692276, -0.026520295068621635, -0.006652409676462412, 0.01387277152389288, 0.011320767924189568, 0.016716275364160538, -0.002623267937451601, -0.05358987674117088, -0.02246887981891632, -0.0067415800876915455, 0.04871935769915581, -0.06911680102348328, -0.0044682021252810955, -0.004348707385361195, 0.051781922578811646, -0.04161350056529045, 0.005616145674139261, 0.006991232745349407, 0.0022736540995538235, -0.012071973644196987, 0.04776056483387947, 0.05488641932606697, 0.04108476638793945, 0.01997257024049759, 0.0050830296240746975, 0.0022895156871527433, 0.04290006682276726, -0.039516158401966095, -0.016850832849740982, 0.012504879385232925, -0.05933700501918793, 0.023353902623057365, -0.06708239018917084, -0.045426588505506516, 0.002519310684874654, -0.012918363325297832, 0.0030723914969712496, 0.02803160808980465, 0.009053174406290054, 0.00660387659445405, -0.01869148015975952, -0.01109020784497261, 0.009207579307258129, -0.024254880845546722, 0.03936324641108513, 0.022600896656513214, 0.019522851333022118, -0.023793557658791542, 0.0011407526908442378, -0.040176693350076675, 0.006321446970105171, -0.010751919820904732, 0.1008317768573761, 0.046115197241306305, -0.025821978226304054, -0.016491388902068138, 0.022750169038772583, -0.04676448553800583, -0.04472232609987259, -0.005713335704058409, -0.03981618955731392, -0.015268176794052124, -0.0017207108903676271, 0.05061471089720726, 0.04886312782764435, 0.06317369639873505, 0.056575752794742584, -0.026852020993828773, -0.004223930649459362, -0.006145418621599674, -0.025730974972248077, 0.029651690274477005, 0.03548133373260498, 0.0028340208809822798, -0.0014195659896358848, 0.005649372469633818, 0.06426243484020233, -0.05588145554065704, -0.0600561760365963, -0.02143891341984272, -0.03509950265288353, -0.026076316833496094, 0.0644143596291542, 0.04168862849473953, -0.014291331171989441, 0.007351632229983807, -0.019260136410593987, 0.028004616498947144, 0.03896775096654892, -0.042434658855199814, -0.00015447361511178315, -0.043812334537506104, -0.04192698001861572, 0.012933008372783661, 0.016318203881382942, 0.006414717063307762, -0.008144795894622803, -0.0024738197680562735, -0.06690050661563873, 0.06650274246931076, 0.0033421590924263, -0.004826189950108528, 0.015113091096282005, -0.044027213007211685, -0.016598153859376907, 0.007123906165361404, -0.01341574639081955, 0.03500083088874817, 0.0255527775734663, -0.027718808501958847, -0.005654525943100452, -0.022115075960755348, -0.017694924026727676, -0.02878570556640625, -0.0030261266510933638, -0.026237037032842636, -0.04489568993449211, -0.04420653358101845, -0.001558667398057878, 0.05360864847898483, -0.017688028514385223, -0.018799342215061188, -0.0070382640697062016, -0.013317933306097984, -0.05359676107764244, 0.039501938968896866, 0.07679564505815506, 0.0026825289241969585, 0.006321579683572054, 0.016164308413863182, -0.04367268830537796, -0.008935770019888878, -0.012697277590632439, -0.032120198011398315, -0.05887734144926071, 0.0021678549237549305, -0.005044071469455957, -0.039279088377952576, -0.06141386926174164, -0.01804083213210106, -0.024076486006379128, 0.020563272759318352, 0.0386781208217144, -0.009225537069141865, 0.04101424291729927, 0.05648370459675789, 0.0033932949882000685, 0.011348240077495575, 0.060082826763391495, 0.04758566617965698, -0.03283577039837837, -0.007246637251228094, 0.04370351508259773, -0.010396676138043404, 0.006627698894590139, -0.0764969065785408, 0.020963983610272408, -0.04593253508210182, 0.01848907768726349, 0.04488423839211464, -0.027500592172145844, 0.13042475283145905, 0.03444237634539604, 0.003706005634739995, 0.031741101294755936, -0.018845759332180023, -0.05013757944107056, 0.014652001671493053, 0.04386621713638306, -0.006784732919186354, -0.046616047620773315, 0.08033779263496399, -0.004429567605257034, -0.03639761731028557, -0.02152331918478012, -0.002319870050996542, -0.09301963448524475, 0.04023025929927826, -0.056137144565582275, 0.0045609320513904095, -0.01684044860303402, 0.01260929461568594, -0.06041602045297623, 0.007301999256014824, 0.023425942286849022, -0.025010526180267334, 0.042117226868867874, -0.01285614725202322, -0.02275959402322769, -0.0034919462632387877, -0.026486540213227272, 0.011718637309968472, -0.019047606736421585, -0.019239800050854683, -0.06782253831624985, 0.016143089160323143, -0.011073741130530834, -0.004364198539406061, -0.0080832215026021, 0.06782253831624985, -0.01066745538264513, 0.039950188249349594, -0.02170621044933796, -0.0125100864097476, -0.017670173197984695, -0.05085771530866623, 0.027692824602127075, 0.02401200868189335, 0.042682718485593796, -0.04315555468201637, 0.02339531108736992, -0.015389598906040192, 0.010333632118999958, 0.04488683119416237, -0.004128357395529747, -0.03326172009110451, 0.010866637341678143, -0.03011269122362137, -0.1045750230550766, 0.015780646353960037, -0.050985805690288544, 0.07354685664176941, 0.04061416536569595, -0.01054451521486044, -0.03335820138454437, -0.027333971112966537, -0.04100906848907471, 0.021047478541731834, 0.04276672378182411, 0.00953125674277544, -0.0056713721714913845, 0.0017886993009597063, 0.055689986795186996, -0.03459104523062706, -0.01696830801665783, 0.10089604556560516, 0.00880140345543623, 0.0342012457549572, 0.02505570463836193, 0.02847917191684246, 0.02422749437391758, -0.04635053128004074, 0.027387753129005432, 0.053335607051849365, 0.053134702146053314, -0.04662046208977699, 0.04323185235261917, -0.05520356446504593, -0.025737417861819267, 0.023081030696630478, 0.02567426860332489, 0.007773843593895435, -0.049752864986658096, 0.009979049675166607, 0.019487347453832626, 0.04389398545026779, 0.029925845563411713, 0.015478257089853287, 0.053654298186302185, 0.007401564158499241, 0.01943320408463478, -0.002261555287986994, -0.006660770624876022, -0.039551991969347, -0.02649972401559353, 0.04678604379296303, -0.01662980020046234, 0.04191334918141365, -0.024614134803414345, 0.08332464843988419, 0.030909888446331024, -0.011803681030869484, 0.03491969406604767, 0.015641391277313232, 0.007779906969517469, -0.011965068057179451, -0.00691475672647357, -0.026772579178214073, -0.023251207545399666, 0.04557812586426735, -0.0007030675187706947, -0.00657616276293993, -0.001084455056115985, -0.05009494721889496, 0.05230998620390892, 0.008494568057358265, 0.014072911813855171, 0.042746253311634064, 0.024954212829470634, -0.025566089898347855, 0.023620225489139557, 0.01382236834615469, 0.03767712414264679, -0.07449658215045929, 0.051409684121608734, 0.06694188714027405, -0.003198885126039386, -0.027730723842978477, 0.0034525874070823193, -0.019121425226330757, 0.028173957020044327, 0.03728912025690079, -0.017021993175148964, -0.05299276113510132, -0.04650665074586868, -0.03167952224612236, -0.04553396627306938, -0.00007686456956434995, -0.0021811570040881634, -0.03599514439702034, 0.028723210096359253, -0.027252614498138428, 0.016032464802265167, 0.045366812497377396, 0.04930547624826431, -0.013790200464427471, -0.05273544043302536, -0.04185347259044647, -0.028708966448903084, -0.002408851869404316, -0.031968455761671066, -0.06802808493375778, 0.007079636678099632, 0.04980671778321266, 0.012298434972763062, 0.035033632069826126, 0.08113779872655869, -0.017511365935206413, 0.06843668967485428, -0.032955899834632874, -0.002193802036345005, 0.01868465729057789, -0.0144578842446208, -0.01685979962348938, 0.0516422763466835, -0.03405404090881348, -0.027329938486218452, 0.014328012242913246, 0.0505790039896965, -0.06090255081653595, -0.0010540592484176159, 0.038846276700496674, 0.012161772698163986, -0.10982847213745117, 0.0626431331038475, -0.005053509026765823, 0.0052979812026023865, -0.02085200697183609, 0.06003174930810928, -0.05190573260188103, -0.012752307578921318, 0.012354722246527672, -0.06755413860082626, -0.01697544753551483, 0.006405180785804987, 0.04291205108165741, 0.06521494686603546, 0.0016602654941380024, 0.0056380946189165115, 0.08769966661930084, 0.02532714419066906, 0.005729292519390583, 0.07023933529853821, -0.048325203359127045, 0.022786429151892662, 0.010862741619348526, 0.03412266820669174, 0.011988600715994835, -0.01203153096139431, 0.00929948315024376, -0.02824828401207924, 0.002846823073923588, 0.05534997582435608, -0.020726976916193962, 0.03101455047726631, -0.03878546133637428, -0.06221917271614075, -0.07012412697076797, -0.018615463748574257, 0.0017176283290609717, 0.021426526829600334, -0.01842072419822216, -0.006412358954548836, 0.006369481328874826, -0.033851880580186844, -0.05352483689785004, -0.010818669572472572, -0.010366301983594894, -0.06669865548610687, 0.025596454739570618, -0.030321544036269188, 0.06617848575115204, 0.04743644967675209, -0.09688612818717957, -0.024055548012256622, 0.027736060321331024, 0.03555617853999138, -0.07281307876110077, 0.01872216910123825, 0.004845148418098688, -0.00024900215794332325, 0.04436521977186203, -0.04136175289750099, -0.002976340474560857, 0.017931833863258362, 0.012680450454354286, 0.011466071009635925, 0.015838734805583954, 0.0184787567704916, -0.015000203624367714, 0.03519907966256142, 0.005862345453351736, -0.03405341878533363, -0.019923128187656403, -0.0030733742751181126, -0.06848045438528061, -0.06513125449419022, -0.00047202440327964723, -0.009964244440197945, -0.03932524845004082, -0.04457402229309082, -0.044866811484098434, 0.05189020186662674, 0.03414583206176758, -0.06702371686697006, 0.0446227490901947, -0.09791404008865356, -0.02745402790606022, 0.034984637051820755, 0.004316465929150581, 0.01850283145904541, -0.02873920649290085, 0.037259604781866074, 0.0340428426861763, -0.008669888600707054, 0.018162330612540245, 0.07605090737342834, 0.037495099008083344, -0.0004927165573462844, 0.04480648413300514, -0.011928687803447247, -0.03426114842295647, 0.021834591403603554, -0.01598486863076687, 0.011412262916564941, 0.008523968979716301, 0.019444407895207405, -0.019731814041733742, -0.04459865018725395, -0.04100298509001732, 0.03070962429046631, -0.02292843908071518, 0.0019997928757220507, 0.00041809745016507804, 0.000691996596287936, -0.04716257378458977, 0.056150585412979126, 0.015180493704974651, 0.01689518429338932, -0.015131969936192036, -0.05646335706114769, -0.03130864351987839, 0.07038670033216476, 0.013664490543305874, 0.0274495929479599, 0.03478245437145233, -0.01534677017480135, 0.008899559266865253, 0.05694979056715965, 0.015037120319902897, 0.047496140003204346, -0.02537330612540245, 0.039650529623031616, 0.030444642528891563, 0.027265112847089767, 0.021486777812242508, -0.009459348395466805, 0.03660811483860016, -0.05284186825156212, 0.024251995608210564, 0.04543258249759674, 0.005792576353996992, -0.04308004677295685, -0.06162374094128609, -0.023634379729628563, -0.04915915057063103, -0.03054429218173027, 0.00046338385436683893, -0.016948724165558815, -0.007716783322393894, -0.0064192162826657295, -0.020695984363555908, -0.02926221676170826, -0.01064387522637844 ]
<p>(I apologize if this question is too theoretical for this site.)</p> <p>This is related to the answer <a href="http://physics.stackexchange.com/a/11124">here</a>, although I came up with it independently of that. $\:$ Suppose we <br> have a unit mass planet at each integer point in 1-d space. $\:$ As described in that answer, the sum <br>of the forces acting on any particular planet is absolutely convergent. $\;\;$ Suppose we move planet_0 <br> to point $\epsilon$, where $\: 0&lt; \epsilon&lt; \frac12 \:$. $\;\;$ For similar reasons, those sums will still be absolutely convergent. <br> Now we let Newtonian gravity apply. $\:$ What will happen?</p> <p><br><br></p> <p>If it's unclear what an answer might look like, you could consider the following more specific questions: <br><br><br> planet_0 will start out moving right, and all of the other planets will start out moving to the left. <br> Will there be a positive amount of time before any of them turn around? <br> (As opposed to, for example, each planet_n for $\: n\neq 0 \:$ turning around at time 1/|n|.)</p> <p>Will there be a positive amount of time before any collisions occur?</p> <p>"Obviously" (at least, I hope I'm right), planet_0 will collide with planet_1. $\:$ Will that be the first collision?</p> <p>How long will it be before there are any collisions? $\:\:$ (perhaps just an approximation for small $\:\epsilon\:$) <br><br></p>
g1526
[ 0.02433723770081997, 0.07566865533590317, -0.00577067444100976, -0.007343311328440905, 0.05237726494669914, 0.0007616732618771493, 0.03602784126996994, -0.03086908534169197, -0.04065297916531563, -0.05174893140792847, -0.03167236968874931, 0.004286203533411026, -0.0019764425233006477, 0.010185597464442253, -0.008597391657531261, -0.010567180812358856, 0.03951891139149666, 0.0023080825340002775, -0.04031363129615784, 0.03882833942770958, -0.014737491495907307, 0.01452991645783186, -0.0193001888692379, -0.010132445953786373, 0.00628832308575511, -0.016594426706433296, 0.006610850337892771, 0.06162060797214508, -0.03925051540136337, -0.016994476318359375, 0.0130960987880826, -0.007082309108227491, 0.008041753433644772, -0.03328591585159302, -0.01747850887477398, -0.017641955986618996, 0.016833772882819176, 0.00015377534145954996, 0.07385113090276718, -0.052834369242191315, 0.018719883635640144, -0.056911420077085495, 0.02036065049469471, 0.0011835854966193438, 0.017363665625452995, -0.03516162931919098, 0.0010233336361125112, -0.06604613363742828, 0.04493395611643791, 0.030580291524529457, -0.03633514791727066, 0.035902708768844604, -0.01717468351125717, -0.03392096981406212, -0.008044355548918247, 0.09789418429136276, 0.04984288290143013, -0.058024726808071136, 0.007839092053472996, 0.020856939256191254, 0.039211954921483994, -0.017720524221658707, 0.004827443975955248, -0.02099771611392498, 0.06367353349924088, 0.00047822570195421576, -0.04106641188263893, 0.050711680203676224, 0.08197656273841858, -0.003715069033205509, 0.0008517426322214305, -0.0006197771872393787, -0.003911866806447506, -0.06047215685248375, -0.018755551427602768, 0.06307759881019592, 0.005195912439376116, -0.002243814757093787, -0.002352483104914427, -0.006738725584000349, -0.021408258005976677, -0.01294298842549324, 0.030270874500274658, -0.0427713617682457, 0.05597583204507828, -0.02949969470500946, 0.01357948686927557, -0.004851059056818485, -0.05133841931819916, 0.034743983298540115, 0.025815268978476524, -0.017679529264569283, -0.04678720608353615, -0.0016005183570086956, -0.029106104746460915, -0.024159368127584457, -0.03054763376712799, 0.040835004299879074, 0.04930707812309265, -0.004869689233601093, 0.00241981353610754, -0.012049219571053982, -0.00133485475089401, -0.0177813358604908, 0.0126111451536417, -0.04211124777793884, 0.019711961969733238, 0.013158894143998623, 0.002060615224763751, -0.056551918387413025, -0.050941452383995056, -0.04904579371213913, 0.02636817656457424, -0.0436650849878788, -0.07372593134641647, 0.02510189265012741, 0.020148037001490593, -0.006759026553481817, 0.023234650492668152, 0.09115079790353775, -0.017518801614642143, 0.007781110238283873, -0.03509429842233658, 0.02798830345273018, -0.06713912636041641, -0.04718465358018875, 0.036819230765104294, 0.036210283637046814, 0.06426563113927841, 0.0026643723249435425, 0.03173555061221123, 0.006404042709618807, -0.02037273906171322, -0.006824801675975323, -0.03749215230345726, -0.00374789210036397, -0.04656323790550232, -0.0036386523861438036, 0.029942650347948074, 0.001798257464542985, -0.012864172458648682, -0.07122445851564407, -0.022040963172912598, 0.016988493502140045, -0.036287467926740646, 0.03014790639281273, -0.00479226466268301, -0.044890981167554855, 0.05364098399877548, 0.053642768412828445, -0.05293506383895874, 0.055665839463472366, 0.004161639604717493, -0.017011653631925583, 0.03774106130003929, 0.01472656149417162, 0.010097073391079903, 0.048894692212343216, -0.0023575297091156244, -0.05681052431464195, -0.005547999404370785, -0.011168583296239376, -0.02020253799855709, -0.020300446078181267, -0.06701698154211044, 0.06281521916389465, -0.05751800164580345, -0.07169108837842941, 0.044539693742990494, -0.022774536162614822, -0.03901483491063118, -0.014811469241976738, 0.007984857074916363, -0.0158675629645586, -0.008811981417238712, 0.005381312686949968, -0.0052530355751514435, -0.017272653058171272, -0.025391310453414917, -0.008677951991558075, 0.05275775119662285, -0.050296034663915634, 0.03707265853881836, 0.011462888680398464, 0.013483265414834023, -0.014623248018324375, -0.037475328892469406, 0.04027596861124039, -0.017698129639029503, 0.0132672730833292, -0.03446068614721298, -0.0026637001428753138, -0.0014059633249416947, 0.038652170449495316, -0.008215904235839844, 0.0021009924821555614, -0.04773420840501785, -0.053351495414972305, -0.03733961284160614, -0.03243062272667885, 0.007714190986007452, 0.036981213837862015, 0.01933293603360653, 0.05296899750828743, 0.0029995571821928024, 0.04829660803079605, -0.016823265701532364, 0.05972599983215332, 0.02731173485517502, 0.04449565336108208, 0.02240189164876938, -0.0754954144358635, -0.02490662783384323, 0.04530205577611923, -0.05589132755994797, -0.02833370678126812, -0.04414208605885506, 0.0045847357250750065, 0.015878846868872643, 0.019970035180449486, -0.01081191934645176, -0.017161892727017403, -0.018685463815927505, -0.009757806546986103, 0.005030694883316755, -0.02832901105284691, -0.07421289384365082, -0.043193984776735306, 0.014654012396931648, 0.0007886426756158471, -0.0009969426319003105, 0.09550579637289047, -0.010668258182704449, -0.037809278815984726, 0.013627720065414906, 0.025518376380205154, 0.03885585069656372, 0.03224712982773781, -0.005639357026666403, -0.02996656484901905, 0.04005511850118637, -0.03947964683175087, -0.022085200995206833, -0.010227366350591183, 0.05740887299180031, -0.05710243806242943, -0.009174532257020473, -0.012295966036617756, -0.03873814642429352, 0.03938162699341774, -0.007939825765788555, 0.0009409892372786999, -0.03532116860151291, 0.05283118784427643, 0.045652709901332855, -0.03125971555709839, 0.035224318504333496, 0.006848746445029974, 0.0033124687615782022, -0.03086511418223381, 0.0017838074127212167, -0.030733345076441765, 0.01128930039703846, 0.04255000874400139, -0.04972835257649422, 0.008305990137159824, -0.03337201103568077, 0.015541017055511475, 0.013109104707837105, 0.018201494589447975, -0.023019321262836456, -0.001627039280720055, 0.03426921367645264, 0.09018958359956741, -0.027486998587846756, 0.0013246882008388638, 0.009981106966733932, 0.002318277955055237, -0.022245733067393303, 0.018837133422493935, -0.044676415622234344, 0.01695483736693859, -0.005044958554208279, 0.01379437930881977, 0.066672682762146, -0.08140073716640472, 0.056270159780979156, -0.005337454844266176, -0.025510165840387344, 0.031100310385227203, 0.033531706780195236, 0.08769860118627548, 0.07459844648838043, 0.0038705950137227774, 0.00808828603476286, 0.07829979807138443, -0.0032840638887137175, -0.012538851238787174, 0.010562331415712833, 0.03575863689184189, 0.014190247282385826, 0.0006069102673791349, -0.013187366537749767, 0.02052365615963936, 0.024251988157629967, 0.03985024243593216, -0.05796894431114197, -0.03483855351805687, -0.024164624512195587, -0.04283585026860237, -0.01984860934317112, 0.09106584638357162, -0.015816593542695045, -0.0072356928139925, -0.05814220383763313, -0.058150794357061386, 0.08490753173828125, 0.021446797996759415, -0.01328113954514265, 0.0028623719699680805, -0.022785015404224396, -0.09364107251167297, 0.0021134186536073685, -0.010402405634522438, -0.0008203212055377662, 0.005556466057896614, -0.062018606811761856, -0.04879458248615265, -0.0017474069027230144, 0.03692524507641792, -0.008188672363758087, 0.026580069214105606, 0.0076749627478420734, 0.02312592603266239, -0.07291753590106964, -0.010415875352919102, 0.02411777898669243, -0.007999911904335022, 0.0037528190296143293, 0.08684699982404709, -0.01651635579764843, 0.004185700789093971, -0.030813073739409447, -0.023862194269895554, 0.012230840511620045, 0.02514047734439373, 0.07458017021417618, -0.01465305220335722, 0.0022451654076576233, 0.008863248862326145, 0.027541788294911385, -0.0404958613216877, 0.047518711537122726, -0.009717433713376522, 0.009835566394031048, 0.08302397280931473, 0.01840551756322384, -0.03970733657479286, -0.05341736599802971, 0.017400380223989487, -0.000354450021404773, -0.010759237222373486, -0.04479314759373665, 0.04114672541618347, 0.03362647444009781, -0.010161137208342552, -0.023424135521054268, -0.007590446621179581, 0.05737297236919403, 0.032439958304166794, 0.0747687965631485, -0.011179744265973568, 0.025575684383511543, 0.01628965698182583, 0.07087421417236328, -0.07081916183233261, 0.08731333166360855, -0.0061690667644143105, 0.05157199874520302, 0.015292773023247719, 0.043641503900289536, 0.037770338356494904, -0.05687201768159866, 0.059661898761987686, 0.025849880650639534, 0.0497639924287796, -0.045391008257865906, -0.08678235113620758, 0.049027103930711746, -0.0022683455608785152, 0.04908812791109085, -0.08920823037624359, 0.051698628813028336, -0.008273170329630375, 0.0479157529771328, -0.04663952440023422, -0.018611811101436615, -0.018058130517601967, -0.0358661450445652, -0.01777716912329197, 0.0646948590874672, 0.026653138920664787, -0.036402828991413116, -0.010686804540455341, -0.012280960567295551, -0.012473626993596554, -0.002084263600409031, 0.03167760744690895, -0.008583199232816696, -0.06635285913944244, 0.04542386159300804, 0.011884383857250214, -0.011669456027448177, -0.025510061532258987, -0.016176559031009674, 0.0364740788936615, -0.02223193272948265, 0.00393853010609746, 0.0447402149438858, 0.02263817936182022, -0.03252577409148216, 0.036017343401908875, 0.00007912215369287878, -0.03938942402601242, -0.006196662783622742, -0.010091427713632584, 0.05547553300857544, 0.02451903745532036, -0.00817289762198925, -0.02040974050760269, -0.03032592311501503, 0.047651711851358414, 0.01307395938783884, 0.01911200024187565, -0.0407843291759491, 0.0763520672917366, 0.025556178763508797, -0.006181515287607908, 0.02014494501054287, 0.01922299899160862, 0.037669405341148376, 0.08097545057535172, 0.012183005921542645, 0.019619761034846306, -0.008525872603058815, 0.07713550329208374, -0.020343173295259476, -0.08033879101276398, 0.03293101117014885, -0.01820140704512596, -0.007464939262717962, 0.029824985191226006, -0.01200255285948515, -0.030690116807818413, -0.03598105162382126, -0.02845109812915325, -0.02302587404847145, 0.05587432160973549, -0.02251613140106201, 0.039511341601610184, 0.012448405846953392, -0.023842591792345047, 0.0377238504588604, 0.011985431425273418, 0.0034296035300940275, -0.03288821503520012, 0.009150724858045578, -0.011085156351327896, -0.0704384371638298, 0.025479480624198914, -0.03752266243100166, 0.04876459017395973, 0.042275890707969666, 0.046031855046749115, -0.032409947365522385, 0.02383018471300602, 0.014940300025045872, 0.025849947705864906, 0.03203463926911354, -0.025025593116879463, 0.004560805857181549, -0.03288862854242325, 0.0052050696685910225, 0.0035019624046981335, 0.012818695977330208, 0.008073764853179455, 0.002372296527028084, -0.035074759274721146, 0.024221444502472878, -0.04570130631327629, 0.018473107367753983, 0.0005082222633063793, 0.0114073371514678, -0.035160940140485764, -0.021332480013370514, 0.04471414163708687, -0.06248359754681587, -0.009527839720249176, 0.020207304507493973, 0.002052765805274248, -0.025484632700681686, 0.03313061594963074, -0.03634357079863548, -0.009020606055855751, -0.008008673787117004, 0.04098615050315857, 0.02616170421242714, -0.0017622241284698248, -0.02402482181787491, 0.02064448408782482, 0.0051915268413722515, 0.05253088101744652, -0.025962039828300476, 0.05722428485751152, -0.017356492578983307, 0.008653668686747551, -0.005229693837463856, -0.02955368161201477, -0.09521200507879257, -0.04848882183432579, 0.025474324822425842, -0.011818934231996536, -0.030474795028567314, 0.015565046109259129, 0.049862805753946304, 0.01848178170621395, -0.011340252123773098, -0.010581893846392632, -0.056604087352752686, 0.05276269465684891, 0.015280338935554028, -0.0416254885494709, 0.04713767021894455, -0.006824140902608633, -0.05942863970994949, 0.010925079695880413, 0.045593444257974625, -0.0010347780771553516, 0.09341412037611008, 0.04207528382539749, -0.0348808690905571, 0.019279373809695244, 0.023302588611841202, -0.0038237357512116432, -0.012851608917117119, 0.033232856541872025, 0.006189489271491766, 0.07225546985864639, 0.011772985570132732, -0.06654072552919388, -0.013980049639940262, 0.012286459095776081, -0.02111639827489853, -0.05656968057155609, -0.0184941366314888, 0.06058121472597122, 0.02643284574151039, -0.04015196114778519, 0.016093308106064796, -0.05648154765367508, -0.002158432500436902, -0.0310268122702837, -0.009990273043513298, -0.056842952966690063, -0.01895342953503132, 0.0010881328489631414, 0.007200267631560564, -0.02627224661409855, 0.0349932424724102, 0.03744659945368767, 0.02763259969651699, -0.0024105922784656286, 0.023914197459816933, 0.01743434928357601, 0.02974659949541092, -0.014060437679290771, -0.037657901644706726, -0.08109021186828613, -0.04313844069838524, 0.0032807854004204273, 0.027394024655222893, -0.030481768772006035, 0.032437823712825775, -0.005891455803066492, -0.021499650552868843, 0.040843211114406586, -0.0005101790884509683, -0.02715466171503067, 0.012086034752428532, -0.02919890359044075, 0.002767636440694332, -0.04387778788805008, 0.04338950291275978, -0.011951989494264126, -0.031480371952056885, -0.017029868438839912, 0.02833094261586666, 0.0058889021165668964, -0.00004657885438064113, 0.0024332471657544374, -0.0011191362282261252, 0.03531177341938019, 0.054775163531303406, -0.021029191091656685, -0.046070646494627, -0.027679909020662308, -0.055740032345056534, -0.0036762626841664314, 0.02728104218840599, 0.051824938505887985, 0.015582005493342876, 0.025369755923748016, 0.05470318719744682, 0.010614984668791294, 0.03195350617170334, -0.008401909843087196, 0.0013108800631016493, 0.005605950020253658, 0.028230782598257065, 0.005331903696060181, 0.04054078459739685, -0.05905212089419365, -0.011888425797224045, -0.06302447617053986, -0.02988041192293167, 0.01746409945189953, 0.019658705219626427, -0.007378046400845051, 0.05944487825036049, -0.007132425904273987, 0.029673567041754723, -0.0234546922147274, -0.03423500806093216, 0.07322447001934052, 0.017529714852571487, 0.06215117871761322, -0.037579186260700226, -0.023418620228767395, 0.028787046670913696, 0.02485189028084278, -0.028014477342367172, -0.01933855190873146, -0.026046061888337135, 0.005229418631643057, -0.013849042356014252, 0.03979320451617241, -0.0028002408798784018, -0.0353039912879467, -0.04946359992027283, -0.015752658247947693, -0.04043978825211525, -0.01671672984957695, 0.02156473696231842, 0.05236075073480606, -0.0908326804637909, 0.0011202347232028842, -0.009546879678964615, -0.0009095011628232896, 0.022883214056491852, -0.019456544890999794, 0.03238679841160774, -0.013424909673631191, -0.0850178524851799, -0.0005136713152751327, -0.036482084542512894, 0.0565725602209568, 0.008404483087360859, 0.0004122481623198837, 0.00561284925788641, -0.08727437257766724, 0.06163182854652405, -0.0047044637612998486, -0.026100384071469307, 0.041762273758649826, 0.04096224159002304, 0.03242753446102142, -0.04132239893078804, -0.05545913800597191, 0.03132709488272667, 0.01364374253898859, 0.010811809450387955, -0.01807050034403801, -0.03526189550757408, 0.0070328316651284695, -0.04820128530263901, -0.0034858807921409607, -0.025930222123861313, 0.018424205482006073, -0.041677240282297134, -0.02990829199552536, 0.06073041260242462, 0.04472143575549126, 0.011118488386273384, -0.022391391918063164, -0.036740824580192566, -0.022164955735206604, 0.031913578510284424, 0.018635600805282593, -0.023684164509177208, -0.00791089702397585, -0.04205256700515747, -0.03434247523546219, -0.018219485878944397, -0.05942274257540703, 0.026077186688780785, 0.021086569875478745, -0.030920226126909256, -0.027303626760840416, -0.023066746070981026, 0.03597111627459526, 0.05328108370304108, 0.020278599113225937, -0.0013558572391048074, -0.038985323160886765, 0.004080641083419323, -0.03584691882133484, -0.020034007728099823, 0.00996336992830038, 0.06248495355248451, 0.02522275038063526, 0.0022158571518957615, 0.01266690343618393, -0.00958644412457943, -0.0929577574133873, -0.06120535358786583, 0.008870949037373066, -0.05788940191268921, -0.08002855628728867, 0.04899691417813301, -0.04444015026092529, -0.051854945719242096, 0.010136949829757214, -0.014893854968249798, 0.022776732221245766, 0.010771612636744976, 0.0031342485453933477, 0.017467981204390526, -0.0623968169093132, -0.03365594148635864, -0.002540408633649349, -0.0853666365146637, -0.07840058207511902, 0.04098324105143547, 0.02071179635822773, 0.02110769972205162, 0.042123548686504364, 0.005425428971648216, 0.044550321996212006, 0.03106946498155594, -0.007291227113455534, 0.03543870896100998, 0.0552644319832325, 0.019561128690838814, 0.018848281353712082, 0.0353236086666584, 0.002670357935130596, -0.026395879685878754, -0.008641858585178852, -0.0485537089407444, -0.012478005141019821, -0.01565477065742016, -0.020964892581105232, -0.02862459607422352, -0.02893928810954094, 0.01548541896045208, -0.04906018450856209, -0.031378865242004395, 0.030447134748101234 ]
<p>We know that the light gets refracted when it enter a medium low/high refractive index. </p> <p>But why light is not refracted when it comes out from the vertex of a prism.</p>
g1527
[ 0.04601446911692619, 0.0370369553565979, 0.021933933719992638, 0.029215369373559952, -0.0006139234756119549, -0.022904351353645325, 0.02436733804643154, 0.017780810594558716, 0.034819748252630234, -0.011453552171587944, 0.018398521468043327, 0.08569630980491638, 0.016781380400061607, -0.06249059736728668, 0.021371670067310333, -0.003459947183728218, 0.005486315116286278, -0.005325257312506437, 0.06664519757032394, 0.06843006610870361, -0.08279377967119217, -0.0027717852499336004, -0.03796358406543732, -0.07438588887453079, -0.02437780797481537, 0.005708910059183836, 0.06627307832241058, -0.029948463663458824, -0.04828383028507233, 0.009812858887016773, 0.0331740602850914, -0.04033679515123367, 0.06070110574364662, -0.06255415081977844, 0.03375349938869476, -0.01607339270412922, 0.012448166497051716, -0.02155046910047531, 0.04551250860095024, 0.0005131115904077888, -0.029940130189061165, 0.0054913852363824844, -0.05803897604346275, -0.022336475551128387, 0.03041309490799904, 0.007279039826244116, 0.030244620516896248, -0.014839590527117252, -0.04538436606526375, -0.0645519345998764, -0.049934323877096176, 0.029731599614024162, 0.017691180109977722, -0.005149471573531628, 0.01566990092396736, 0.0012024840107187629, -0.009286525659263134, 0.061398763209581375, 0.06678194552659988, -0.003581816563382745, 0.011304788291454315, -0.015281755477190018, 0.013904835097491741, 0.051171738654375076, -0.00047016580356284976, -0.02753935381770134, -0.028964146971702576, -0.0011648231884464622, 0.021242834627628326, 0.0342765748500824, -0.011374481953680515, -0.02911379374563694, -0.02290280908346176, 0.034710753709077835, -0.027976611629128456, 0.004252767190337181, -0.00007202590495580807, 0.0031285881996154785, -0.048873621970415115, 0.025862524285912514, -0.00002410844354017172, -0.006200047209858894, -0.05196433514356613, -0.044294580817222595, 0.02981271967291832, 0.037535347044467926, 0.04760081693530083, -0.047343723475933075, -0.04688151553273201, -0.006509775295853615, 0.07108213752508163, -0.006742902100086212, 0.08076609671115875, 0.03325749561190605, -0.033534858375787735, 0.012969656847417355, -0.03755217418074608, -0.01824266090989113, -0.003941036760807037, 0.02647193893790245, 0.01301189512014389, -0.046746451407670975, 0.003800817532464862, 0.04662488028407097, 0.06941720843315125, -0.029611362144351006, 0.02253451943397522, -0.0067122820764780045, -0.0607687272131443, -0.012064111419022083, -0.02280402183532715, -0.01621311902999878, -0.03813648223876953, -0.0703200176358223, -0.08230902999639511, -0.010943440720438957, 0.11006484925746918, -0.006838138215243816, 0.029431013390421867, 0.04320857673883438, 0.021589605137705803, 0.03189503028988838, -0.012683998793363571, 0.10413950681686401, 0.02744321897625923, 0.033336374908685684, 0.06674925982952118, -0.02854190208017826, 0.03187016025185585, 0.01477066706866026, -0.036627452820539474, -0.020137378945946693, -0.028082692995667458, 0.0281264316290617, 0.037734925746917725, 0.029027597978711128, 0.07994969934225082, -0.011777881532907486, 0.011139518581330776, -0.0008525245357304811, -0.0307368952780962, 0.04661478474736214, -0.01303237397223711, -0.0649997889995575, 0.02357109636068344, -0.012126409448683262, -0.02066582441329956, 0.032453034073114395, 0.0317898765206337, 0.05008626729249954, 0.015451617538928986, 0.06661438941955566, 0.05282428860664368, 0.0031375582329928875, -0.021691180765628815, -0.05624838545918465, 0.06819251924753189, -0.030329328030347824, -0.021252108737826347, -0.03087424486875534, 0.051800962537527084, -0.00868155900388956, -0.041665203869342804, 0.014679859392344952, -0.021793430671095848, -0.07565125077962875, -0.04252563416957855, -0.08937583118677139, -0.036218106746673584, -0.06493500620126724, -0.046516481786966324, 0.03748249635100365, -0.019710656255483627, 0.04970231652259827, 0.012946626171469688, 0.05272341147065163, 0.03824029862880707, 0.01534265000373125, 0.00692139845341444, 0.03445698320865631, -0.022787338122725487, 0.03240960091352463, -0.04153319448232651, -0.05311662331223488, -0.02063903957605362, -0.010723636485636234, 0.014989057555794716, 0.00986408069729805, -0.007777155376970768, -0.02436470426619053, 0.03967559337615967, -0.020839253440499306, -0.03001304902136326, 0.02021002769470215, 0.013026153668761253, -0.06488122791051865, -0.03612011671066284, -0.052012477070093155, -0.05637989565730095, 0.004380676429718733, 0.00042266392847523093, -0.03013615868985653, -0.01843939535319805, 0.013443121686577797, -0.000585859757848084, 0.03261689096689224, -0.05650379881262779, 0.02537705935537815, 0.05699320510029793, -0.004781773313879967, 0.0008207184146158397, 0.02865481562912464, 0.0467522107064724, -0.00010892371938098222, 0.008629124611616135, 0.011022238060832024, -0.00064130499958992, 0.012884956784546375, 0.03213908150792122, -0.00020465378474909812, -0.021656431257724762, 0.02847188711166382, -0.05533437430858612, -0.0015006408793851733, -0.038321711122989655, -0.0152288768440485, -0.06836740672588348, -0.010337424464523792, 0.003224866231903434, 0.02732049487531185, -0.010404371656477451, -0.036500994116067886, -0.03234437480568886, -0.010496385395526886, -0.021539373323321342, -0.006185624282807112, -0.04184050112962723, 0.028834713622927666, 0.029152778908610344, -0.06391569972038269, -0.01871013268828392, -0.0420694500207901, -0.04892547056078911, 0.026743033900856972, -0.03205239400267601, -0.05651151388883591, 0.022893989458680153, -0.03173596411943436, -0.001444549299776554, 0.03493906557559967, 0.04582870006561279, 0.03405940905213356, -0.007334697991609573, -0.0058837211690843105, -0.04468698427081108, -0.033664945513010025, -0.006007015239447355, 0.037772901356220245, -0.0401226170361042, -0.005055666901171207, -0.01226370595395565, -0.058585673570632935, -0.017832033336162567, -0.019030075520277023, -0.022820185869932175, 0.01234850101172924, 0.0192627664655447, 0.028336772695183754, 0.024311251938343048, 0.008284558542072773, -0.0432201623916626, 0.07741940021514893, 0.05580038204789162, -0.046801451593637466, 0.02151123806834221, -0.01865190640091896, -0.08044683933258057, 0.03559844195842743, 0.026448916643857956, -0.010364821180701256, -0.04490942135453224, -0.03625793009996414, -0.03343324735760689, -0.004888174124062061, 0.06546303629875183, -0.0040975953452289104, -0.0332450345158577, 0.012498422525823116, 0.02345525659620762, -0.06227700784802437, -0.0549837201833725, 0.045343779027462006, 0.011210219003260136, -0.017706427723169327, 0.025865696370601654, -0.05073232203722, -0.024794507771730423, 0.012239694595336914, -0.007162052672356367, 0.042995743453502655, -0.0286399032920599, 0.005082510877400637, 0.009026280604302883, 0.005761086009442806, 0.001951422542333603, 0.026459870859980583, -0.05600987747311592, -0.0819762721657753, -0.005235706921666861, 0.034118812531232834, 0.07000459730625153, 0.026167280972003937, -0.035092100501060486, 0.056776080280542374, -0.01226027775555849, 0.05889573693275452, -0.03761628642678261, 0.08993908762931824, 0.03102135844528675, 0.04599321633577347, -0.033797722309827805, 0.005369916558265686, -0.02504698932170868, 0.03138517960906029, -0.012520832940936089, -0.06957294791936874, -0.059907883405685425, 0.0647059753537178, 0.019074223935604095, 0.016274962574243546, 0.03715113177895546, -0.03802638128399849, -0.054906200617551804, 0.03869349882006645, 0.03458308428525925, -0.007500131148844957, -0.025461506098508835, 0.031043877825140953, 0.004642477724701166, 0.051717642694711685, 0.04486817121505737, -0.02638823911547661, -0.08865074813365936, -0.01564747840166092, -0.00023331194825004786, -0.029799027368426323, -0.002721224445849657, -0.05610751360654831, -0.006482949946075678, -0.00975150428712368, 0.032225605100393295, 0.005137604661285877, -0.019132480025291443, -0.042365334928035736, -0.08099392801523209, -0.02335040643811226, -0.0717347115278244, 0.05507206916809082, 0.06036435440182686, 0.018954666331410408, 0.045604441314935684, -0.009338042698800564, 0.042969077825546265, -0.03012041561305523, -0.013756629079580307, -0.002741977572441101, 0.01637491211295128, 0.03255029767751694, 0.0028243076521903276, 0.07918840646743774, 0.014362523332238197, -0.046815454959869385, -0.02279537543654442, 0.06326187402009964, -0.01809324137866497, 0.008474666625261307, 0.004997642245143652, 0.03871416673064232, -0.03099917434155941, 0.028113888576626778, 0.027326550334692, -0.035960402339696884, 0.0406230129301548, -0.029634268954396248, -0.02802279219031334, -0.036903947591781616, 0.008214462548494339, 0.008287567645311356, -0.019483407959342003, 0.002480960451066494, 0.01479522418230772, 0.020931171253323555, 0.019108811393380165, 0.03685562312602997, 0.03690924122929573, 0.01746971346437931, 0.016636980697512627, -0.04437369480729103, -0.011639214120805264, -0.018853547051548958, 0.05070624500513077, 0.03167909383773804, -0.020249633118510246, 0.017525507137179375, 0.07339520752429962, 0.02525540627539158, -0.016042713075876236, 0.015214365907013416, 0.003969679120928049, -0.007231034804135561, 0.027042482048273087, 0.032775457948446274, -0.02838730812072754, -0.04582121595740318, 0.04528858885169029, 0.042546942830085754, 0.02372545562684536, -0.01150897890329361, -0.00884233508259058, 0.018392805010080338, -0.01327493879944086, 0.01775040477514267, 0.02820184826850891, 0.01683305762708187, 0.04912754148244858, 0.07795481383800507, 0.010284260846674442, -0.0527951680123806, -0.0510922372341156, -0.05868256464600563, 0.01734369434416294, 0.02598877251148224, -0.039321646094322205, -0.07104089856147766, 0.04675186425447464, 0.052945517003536224, -0.014201787300407887, 0.050181616097688675, 0.0019451187690719962, 0.02259957231581211, 0.04010951146483421, 0.05589183419942856, 0.06040843203663826, -0.0021599424071609974, 0.02905351296067238, 0.022498605772852898, -0.05959537997841835, 0.06687050312757492, -0.032193005084991455, 0.0019278271356597543, -0.03250347450375557, -0.04641720652580261, -0.025934480130672455, -0.039099402725696564, -0.08225488662719727, -0.0036685094237327576, -0.031246136873960495, 0.02513701841235161, -0.01684846542775631, 0.0778835266828537, -0.0012248356360942125, 0.01283744815737009, 0.02822929248213768, -0.0044249617494642735, 0.050166770815849304, 0.0034775035455822945, -0.01190017256885767, 0.008044304326176643, -0.003775679739192128, -0.022129934281110764, -0.01534588448703289, 0.014433558098971844, 0.04695988446474075, 0.019458714872598648, 0.07070571929216385, -0.023694731295108795, -0.0371185839176178, 0.023715877905488014, -0.002687370404601097, -0.024890925735235214, 0.007771916221827269, 0.0031162560917437077, -0.008060500957071781, 0.006780541501939297, 0.0022934298031032085, 0.010207200422883034, -0.05746716633439064, -0.021053167060017586, -0.04546422138810158, -0.012461465783417225, -0.02220880798995495, -0.030399076640605927, -0.01713542826473713, 0.019434252753853798, 0.05102698132395744, -0.03427787497639656, 0.039022356271743774, 0.012514755129814148, 0.004666685592383146, -0.01937977224588394, -0.07845108211040497, -0.04030896723270416, -0.024266758933663368, -0.033612869679927826, -0.0199002455919981, -0.031155657023191452, 0.03965672105550766, -0.02954169549047947, 0.03556593134999275, 0.04495079442858696, 0.029638968408107758, -0.12326521426439285, 0.05857906863093376, 0.03536427766084671, 0.041816674172878265, -0.031235380098223686, -0.034320682287216187, 0.015833742916584015, 0.026737358421087265, 0.03189432993531227, -0.06512242555618286, 0.012605044059455395, -0.0007227592286653817, -0.05033755302429199, 0.037044957280159, 0.010947776027023792, -0.013160698115825653, -0.056757837533950806, 0.03867291286587715, -0.023095909506082535, -0.00861401204019785, 0.05710982531309128, 0.01839641109108925, 0.015658659860491753, -0.01764441654086113, -0.02059788629412651, 0.004237293731421232, 0.017970681190490723, -0.012379246763885021, -0.002629909897223115, -0.06344714015722275, 0.015361764468252659, -0.00022060872288420796, 0.050676293671131134, 0.0008763874648138881, 0.019568264484405518, -0.030419252812862396, 0.040764473378658295, 0.01725679449737072, 0.04200584813952446, 0.00132957031019032, 0.010486165061593056, -0.024071060121059418, -0.040308233350515366, -0.012176905758678913, -0.00968219805508852, 0.013755585998296738, -0.025510186329483986, -0.0058888704515993595, -0.0409495085477829, 0.014797945506870747, 0.036182425916194916, -0.005343793425709009, -0.0026647516060620546, 0.004737691022455692, -0.05250377953052521, 0.01240242924541235, 0.036093294620513916, -0.007279128301888704, -0.008267316967248917, -0.0028348853811621666, -0.020098404958844185, 0.015229647979140282, 0.03150130808353424, -0.013441173359751701, 0.04861169308423996, -0.04210749268531799, 0.015060975216329098, 0.00944252498447895, -0.009185503236949444, 0.04154583439230919, 0.04349740594625473, 0.01899060234427452, -0.02416231296956539, -0.05280688777565956, -0.01790616661310196, 0.011021451093256474, 0.021591689437627792, 0.013050816021859646, -0.013068768195807934, 0.028747642412781715, -0.01464384701102972, -0.005867487750947475, 0.03698395565152168, -0.011733289808034897, -0.035930782556533813, 0.011172144673764706, 0.061636243015527725, -0.03685365989804268, -0.027583137154579163, 0.0444449707865715, -0.02206915058195591, 0.07936827093362808, -0.020096732303500175, 0.04818079248070717, 0.0145464101806283, 0.013786212541162968, -0.032527562230825424, 0.06835311651229858, 0.026203308254480362, 0.004162922501564026, 0.057252805680036545, 0.0018556638387963176, -0.03710731863975525, -0.03926903381943703, -0.06691709160804749, -0.06560396403074265, 0.019341960549354553, -0.013083570636808872, -0.12590107321739197, -0.014076531864702702, -0.03322206437587738, 0.050756167620420456, -0.03351077809929848, 0.01703246496617794, 0.040087830275297165, -0.013080444186925888, -0.02357335202395916, 0.032503604888916016, 0.03977837786078453, 0.021428506821393967, -0.016564277932047844, -0.016423571854829788, 0.06908318400382996, -0.02438279613852501, -0.017670659348368645, -0.07241004705429077, -0.013790907338261604, 0.015127208083868027, 0.03600878268480301, 0.036770131438970566, 0.027040326967835426, -0.010563508607447147, 0.012346858158707619, -0.008694421499967575, 0.04635236784815788, -0.012796525843441486, -0.05384041741490364, -0.0569065697491169, -0.03395413979887962, -0.015002936124801636, -0.0449846051633358, 0.004797385539859533, 0.05173664167523384, -0.033563852310180664, 0.04225151613354683, -0.09531120955944061, 0.046898793429136276, -0.010097948834300041, -0.05436408519744873, -0.02365129627287388, 0.038899701088666916, 0.009175640530884266, 0.011771113611757755, -0.02040768414735794, 0.006876217667013407, 0.04051552712917328, -0.024540117010474205, 0.012414077296853065, 0.019037920981645584, 0.0071760197170078754, -0.05345406010746956, -0.048682838678359985, 0.033509984612464905, -0.020310772582888603, -0.01235199999064207, -0.009145811200141907, -0.005874980241060257, 0.013016919605433941, -0.0034517492167651653, -0.03135323151946068, 0.046205148100852966, 0.009009649977087975, -0.01882127672433853, -0.0294979028403759, 0.0337444469332695, -0.03200030326843262, 0.021286094561219215, 0.03383512794971466, -0.03808717057108879, -0.020901521667838097, -0.004160753451287746, 0.030657395720481873, 0.0038064580876380205, -0.04699009284377098, 0.03084699809551239, 0.011712467297911644, -0.009454707615077496, 0.005638113711029291, -0.003929563332349062, -0.01056644693017006, 0.008428164757788181, -0.01732884906232357, 0.004300760570913553, 0.028241580352187157, 0.012370246462523937, -0.010307949036359787, 0.0911460742354393, 0.0064023640006780624, -0.023293474689126015, 0.04845394566655159, -0.06426533311605453, 0.0035373636055737734, 0.029922323301434517, -0.0181003175675869, 0.029702365398406982, 0.009227617643773556, 0.013794965110719204, -0.025656724348664284, -0.04014153778553009, -0.0357738621532917, -0.01215924508869648, -0.008677522651851177, -0.07808785140514374, -0.021150214597582817, -0.03199175372719765, 0.032327570021152496, -0.028197484090924263, -0.048577193170785904, -0.015688110142946243, 0.034035179764032364, 0.06324438005685806, -0.013230690732598305, 0.004100381396710873, -0.027366846799850464, -0.037078723311424255, 0.01208545546978712, -0.05564124137163162, 0.019579023122787476, 0.02569565549492836, -0.001540740136988461, 0.03511134907603264, -0.016760116443037987, -0.034297876060009, 0.047123998403549194, -0.00009849214984569699, -0.008955739438533783, 0.023662874475121498, 0.015193391591310501, 0.005117037333548069, -0.02213573269546032, -0.013994243927299976, -0.008902355097234249, 0.07222918421030045, 0.045374322682619095, -0.07612726837396622, 0.047770846635103226, 0.009606728330254555, -0.0026061630342155695, -0.011179741472005844, -0.0018667642725631595, 0.003217011457309127, 0.0029603007715195417, 0.01796022430062294, 0.0012385430745780468, -0.01737396791577339, -0.039223987609148026, -0.01810411736369133 ]
<p>Consider the quantum system $\mathcal{B}(\mathbb{C}^d\otimes\mathbb{C}^d)$ and $|\psi\rangle=\frac{1}{\sqrt{d}}\sum_{i=0}^{d-1}|i,i\rangle$ be the (standard) maximally entangled state. Consider the state </p> <p>$\rho_\lambda=\lambda \frac{\mathbb{I}_{d^2}}{d^2}+(1-\lambda)|\psi\rangle\langle\psi|.$</p> <p>Now for some values of $\lambda$ this state is entangled (example $\lambda=0$ it is $|\psi\rangle\langle\psi|$) and hence its entanglement can be detected by partial transpose operation. </p> <p>Can $\rho(\lambda)$ be an entangled state which is positive under partial transpose (known in literature as PPT entangled state) for some values $\lambda$? My intuition tells me that this is the case. However, I was told (without reference) that this is not the case and for the values of $\lambda$ we get only separable states or not PPT entangled states. I could not find the corresponding paper. May be I am not giving the proper string for searching. Advanced thanks for any suggestion, reference or comment.</p>
g1528
[ -0.011666988953948021, -0.007641754113137722, 0.01131437812000513, -0.039415329694747925, -0.02520008571445942, -0.01994728483259678, -0.02232743799686432, 0.02866554632782936, -0.006906070746481419, 0.027189098298549652, -0.03020843304693699, -0.029144205152988434, -0.042356088757514954, -0.012261983938515186, -0.01287796813994646, 0.006604690570384264, 0.05023433268070221, 0.00417221849784255, 0.021782930940389633, -0.05243682116270065, -0.06359070539474487, 0.0016525725368410349, -0.008779718540608883, -0.008653854951262474, 0.017611457034945488, -0.041318707168102264, 0.0035647135227918625, 0.0055616493336856365, -0.03746014088392258, -0.023473164066672325, -0.08005217462778091, -0.05257971212267876, -0.006780583411455154, 0.016009841114282608, -0.04756981134414673, -0.0329296849668026, 0.04384339600801468, -0.052827730774879456, 0.02887372300028801, 0.0030180702451616526, -0.027293561026453972, 0.017316313460469246, -0.02768513932824135, -0.048337969928979874, 0.01333377230912447, -0.05267195776104927, 0.10083238035440445, 0.02874193899333477, -0.010041283443570137, -0.022909050807356834, 0.004878235515207052, 0.011317584663629532, 0.034160394221544266, -0.008531177416443825, 0.05913515388965607, 0.010870827361941338, -0.005613875575363636, -0.044892050325870514, 0.03632016479969025, -0.030386706814169884, 0.024136105552315712, -0.04742499440908432, 0.023280644789338112, 0.0004239944682922214, -0.016797548159956932, 0.015085531398653984, -0.011165203526616096, -0.0476362407207489, 0.017913656309247017, 0.010883568786084652, -0.011762218549847603, -0.01591242477297783, 0.05258423835039139, 0.007952823303639889, 0.03353895992040634, -0.015750106424093246, 0.00761695671826601, -0.07365438342094421, 0.03759949654340744, -0.024142306298017502, 0.020370149984955788, -0.053721483796834946, 0.004848667420446873, -0.009216499514877796, 0.017196400091052055, 0.044272128492593765, -0.007535827811807394, -0.027674848213791847, -0.08413698524236679, 0.05796268954873085, -0.024356229230761528, -0.03993014618754387, 0.0449986569583416, 0.053742144256830215, -0.027296392247080803, -0.009658019058406353, 0.03164883330464363, 0.00009104894706979394, -0.014022071845829487, 0.01659269444644451, -0.0016373844118788838, -0.011297543533146381, 0.04546308517456055, 0.0181549321860075, 0.0028967796824872494, 0.017242804169654846, 0.0002655104617588222, -0.035242270678281784, -0.013722309842705727, -0.034932706505060196, 0.008463088423013687, -0.005400822963565588, -0.03993584215641022, -0.02894752286374569, -0.05165795236825943, 0.04417438060045242, 0.0060282424092292786, -0.023057691752910614, -0.06710751354694366, 0.05004335939884186, 0.03126603364944458, 0.01727956160902977, 0.001201690873131156, 0.07599782943725586, -0.02396620437502861, 0.026045532897114754, -0.054360516369342804, -0.028707411140203476, 0.06277512013912201, 0.012008960358798504, 0.049131497740745544, 0.03024567849934101, -0.0027922315057367086, 0.011351830326020718, -0.027943262830376625, 0.006468815729022026, 0.0811062753200531, 0.04050359129905701, 0.028531868010759354, -0.03586110845208168, -0.0364423431456089, 0.01764647476375103, -0.010577143169939518, 0.06095367670059204, 0.058621857315301895, -0.016694769263267517, -0.01602010242640972, -0.0004211550112813711, 0.0029387292452156544, 0.039420828223228455, 0.030315661802887917, -0.04471078887581825, 0.0034713733475655317, 0.008259214460849762, -0.03752422705292702, 0.05334470048546791, 0.0267811082303524, 0.018014919012784958, 0.006601586937904358, 0.035907670855522156, 0.01429432351142168, 0.029524048790335655, -0.011919060721993446, -0.04236385598778725, 0.022612839937210083, -0.013739872723817825, -0.024888886138796806, -0.03468269854784012, 0.011966862715780735, -0.059238675981760025, 0.044765979051589966, 0.04716017097234726, -0.00584446033462882, -0.0400797538459301, 0.057111456990242004, 0.0031180924270302057, -0.000756514782551676, 0.04008418321609497, 0.018345419317483902, -0.009978956542909145, -0.037497393786907196, -0.015416310168802738, -0.02525041438639164, 0.048993922770023346, -0.013868867419660091, -0.030130116268992424, -0.045594945549964905, 0.025996733456850052, -0.03401016443967819, 0.028470439836382866, -0.05158349499106407, 0.008853308856487274, 0.05962410941720009, 0.016950730234384537, 0.002077733865007758, -0.034099336713552475, 0.005658815149217844, -0.017327675595879555, -0.029545092955231667, 0.02101939171552658, 0.009525811299681664, 0.010110180824995041, 0.025996821001172066, -0.00019551593868527561, 0.010420526377856731, -0.006266921758651733, 0.0006027781055308878, -0.0000516353829880245, 0.00207176199182868, -0.0032223707530647516, 0.0022586670238524675, -0.03342542052268982, -0.02867649309337139, 0.02438700571656227, -0.031237738206982613, -0.00991737563163042, 0.0033826823346316814, 0.052943453192710876, -0.014136948622763157, -0.02202155999839306, -0.01987391710281372, 0.0023440641816705465, 0.011123515665531158, 0.046035271137952805, 0.011151289567351341, 0.0789678543806076, -0.05391521006822586, 0.04269416257739067, -0.02279166877269745, 0.03337028622627258, 0.02206883765757084, 0.001232264214195311, 0.021190404891967773, 0.007682824041694403, 0.02888851799070835, 0.07009070366621017, 0.011987531557679176, 0.061066724359989166, -0.04766826704144478, -0.05883745104074478, 0.04396780580282211, 0.016001354902982712, -0.060036297887563705, 0.03088761493563652, 0.028338797390460968, 0.019251978024840355, -0.008263970725238323, 0.0049950252287089825, -0.0006242467788979411, 0.037188753485679626, -0.014827016741037369, -0.014808489009737968, 0.024835849180817604, 0.039285529404878616, 0.01125566940754652, -0.011875372380018234, -0.012835484929382801, 0.031033558771014214, 0.017888879403471947, 0.020751463249325752, -0.004426803905516863, -0.02809811197221279, -0.03482908755540848, -0.042136579751968384, -0.05111485347151756, 0.03885174170136452, -0.04671870544552803, -0.01189536415040493, -0.06341268122196198, 0.03845254331827164, -0.003021716373041272, 0.07915978133678436, 0.029129644855856895, 0.08730269968509674, 0.02851284109055996, -0.05054469779133797, -0.028933852910995483, -0.009755932725965977, -0.05075438693165779, 0.009443938732147217, -0.050531648099422455, 0.0069525535218417645, -0.00846631545573473, 0.05992254614830017, 0.012778572738170624, -0.09873773902654648, 0.004341083113104105, -0.014542493037879467, 0.01894195005297661, 0.08707047998905182, -0.01787576638162136, 0.013170578517019749, -0.004771794658154249, 0.010121900588274002, -0.01647072844207287, -0.006015198305249214, -0.006959735415875912, -0.056374192237854004, 0.04820698872208595, 0.04171227291226387, -0.03143243119120598, -0.04247518256306648, -0.035356950014829636, 0.06637058407068253, 0.10050636529922485, -0.009612525813281536, -0.05442395061254501, 0.03204542398452759, -0.009392143227159977, -0.00340190134011209, -0.06861894577741623, 0.00807261560112238, 0.06911975890398026, -0.04848531261086464, -0.002884938847273588, -0.003082138719037175, -0.00980678666383028, -0.03372429683804512, -0.053624410182237625, -0.03465718775987625, 0.011459454894065857, -0.011079173535108566, -0.0034887483343482018, -0.024523403495550156, 0.06956710666418076, -0.047381442040205, 0.006363825872540474, 0.02088138647377491, -0.08708877861499786, -0.014852646738290787, 0.030047308653593063, -0.019832735881209373, 0.07034501433372498, 0.0024423140566796064, -0.026613658294081688, -0.013159478083252907, -0.03823170065879822, 0.0008206940838135779, 0.015085030347108841, 0.005157939624041319, -0.00648257602006197, -0.0013931588036939502, -0.027508186176419258, 0.004112299997359514, 0.06467796117067337, -0.06771161407232285, -0.015493875369429588, 0.05160831660032272, 0.08906286209821701, 0.04527420550584793, -0.01149044930934906, 0.10260369628667831, 0.04066202789545059, 0.0262060035020113, -0.006384288426488638, 0.05799340829253197, 0.08163921535015106, 0.010322798043489456, -0.03699243813753128, 0.004861636087298393, 0.055680740624666214, -0.005762887187302113, -0.003450081218034029, -0.0249799694865942, -0.005200006999075413, 0.008811517618596554, -0.012897627428174019, -0.02276180498301983, 0.01780223287642002, 0.03785541281104088, -0.030460022389888763, 0.02172943204641342, 0.02017095685005188, 0.021845364943146706, 0.0007195177604444325, -0.08648645132780075, -0.0032198154367506504, -0.010785402730107307, 0.0026936165522783995, -0.0015782105037942529, 0.03753936290740967, -0.005157758016139269, 0.01598670706152916, -0.012558606453239918, -0.003714738879352808, 0.01638972945511341, 0.005790221504867077, -0.006323099602013826, 0.042934924364089966, -0.0012636963510885835, 0.059575848281383514, -0.03518491983413696, -0.03091210499405861, 0.0027793908957391977, 0.020225858315825462, 0.09704272449016571, 0.042546745389699936, 0.020177410915493965, 0.0019421842880547047, 0.00032249095966108143, -0.04863603040575981, -0.05934550613164902, 0.003237797413021326, 0.009581523947417736, 0.004174391273409128, -0.08912096917629242, 0.022726990282535553, 0.03990641236305237, -0.008940460160374641, -0.007514238823205233, 0.02802819199860096, 0.00630928622558713, -0.0167176965624094, -0.021839629858732224, -0.060386933386325836, 0.0520232692360878, 0.004160914570093155, -0.04890403151512146, 0.004255997948348522, -0.006512421183288097, 0.014934259466826916, 0.030979963019490242, -0.02486109547317028, 0.054242704063653946, 0.019792597740888596, -0.00864881370216608, 0.05133131891489029, 0.057201698422431946, -0.0012233324814587831, -0.021821465343236923, -0.014053032733500004, -0.00871986523270607, -0.07974279671907425, 0.037811968475580215, -0.05496525019407272, -0.026617389172315598, -0.04525665193796158, 0.041361864656209946, -0.052177295088768005, -0.050619687885046005, 0.035707395523786545, -0.03352532163262367, -0.03475860133767128, 0.017314838245511055, 0.01456106174737215, 0.004727199673652649, -0.019526872783899307, -0.03823254629969597, -0.005052728112787008, -0.047415681183338165, 0.020853372290730476, 0.035276398062705994, 0.02344273030757904, -0.04027462750673294, -0.025902368128299713, -0.005725177936255932, -0.016851024702191353, 0.015459965914487839, 0.04313432425260544, 0.04345441609621048, 0.0012848025653511286, -0.00201402953825891, 0.018221240490674973, 0.03158827871084213, 0.05604439973831177, 0.030194878578186035, -0.06828907132148743, 0.022273289039731026, -0.023264829069375992, -0.058374013751745224, -0.0077163889072835445, 0.009590929374098778, 0.02026025764644146, 0.024004703387618065, -0.007762192748486996, -0.022013232111930847, -0.02869947999715805, 0.006348936818540096, -0.004751407541334629, -0.036407798528671265, 0.010679990984499454, -0.0539902001619339, -0.003970562946051359, -0.00093834288418293, 0.03789673373103142, 0.049919210374355316, 0.022298524156212807, -0.022053426131606102, -0.05035518854856491, -0.057507503777742386, 0.0186858419328928, 0.07988830655813217, 0.01569250039756298, 0.018348705023527145, 0.010460512712597847, -0.001868348103016615, -0.04642976075410843, -0.05289151147007942, -0.03078550100326538, 0.06472618132829666, -0.023292364552617073, 0.009308337233960629, 0.05865629389882088, 0.03289513662457466, -0.0033863787539303303, 0.02372458204627037, 0.029477067291736603, -0.0048169540241360664, -0.05314791947603226, 0.02235317789018154, -0.08691160380840302, -0.005031192675232887, -0.07000745832920074, -0.025919415056705475, -0.04260922223329544, -0.0039594583213329315, -0.03840174153447151, 0.04481969401240349, -0.021360168233513832, -0.022159116342663765, 0.04037559777498245, -0.010404528118669987, -0.002191566862165928, -0.02231600135564804, 0.025959987193346024, 0.03186113014817238, -0.050708167254924774, -0.03614317625761032, 0.015591803006827831, -0.010032852180302143, 0.06605971604585648, 0.014681586064398289, 0.05379357561469078, -0.0016526508843526244, 0.02721490152180195, -0.04847799614071846, -0.025530440732836723, 0.02335653267800808, 0.05731694772839546, 0.030548810958862305, 0.020981552079319954, -0.06166675686836243, -0.07560055702924728, 0.047250840812921524, -0.04107065498828888, -0.011525032110512257, -0.05412116274237633, -0.013842646963894367, -0.0986182764172554, 0.010381634347140789, -0.0018424279987812042, 0.06531146168708801, -0.0841265544295311, -0.034808021038770676, 0.06666555255651474, 0.02474145218729973, 0.011478684842586517, 0.00029510920285247266, -0.000009206572940456681, 0.01736338809132576, 0.008978498168289661, -0.01540782954543829, 0.013140209950506687, 0.018611518666148186, -0.0318753719329834, -0.02546636201441288, -0.012659795582294464, -0.019968900829553604, 0.04135207459330559, 0.048366252332925797, -0.02397661842405796, -0.0037102920468896627, -0.0451328381896019, -0.008095759898424149, -0.011042972095310688, -0.04813080281019211, -0.06751314550638199, -0.05923507735133171, 0.047010548412799835, 0.007400735281407833, -0.048552047461271286, 0.003926683682948351, -0.014111649245023727, -0.0005902844714000821, -0.012137582525610924, 0.00024399971880484372, -0.0422806441783905, -0.007240377366542816, -0.017070062458515167, 0.07976782321929932, -0.04184155911207199, 0.037691302597522736, -0.04504920169711113, -0.010054492391645908, 0.041573189198970795, -0.03934822604060173, 0.012821285985410213, -0.032589543610811234, 0.0017611193470656872, -0.035243310034275055, 0.06819694489240646, -0.045628130435943604, -0.002755694556981325, -0.04242411628365517, 0.007346775848418474, 0.05523369833827019, -0.048640862107276917, 0.020643524825572968, 0.006865683943033218, 0.05240751802921295, 0.03805975243449211, -0.02330143004655838, -0.032640207558870316, -0.02624831534922123, -0.02568221092224121, -0.08429131656885147, 0.010541994124650955, 0.04266371577978134, -0.002869832329452038, -0.0035683773458003998, 0.10360326617956161, -0.03480277210474014, -0.003129218704998493, -0.01683070883154869, -0.007018800359219313, 0.08030292391777039, -0.023224713280797005, -0.05100240185856819, 0.03223034366965294, 0.034832801669836044, 0.052565596997737885, -0.0012782601406797767, 0.0045667896047234535, -0.015417790971696377, -0.011427213437855244, 0.007662175688892603, -0.04053034260869026, 0.01872057467699051, 0.05381278693675995, 0.03696213662624359, 0.010002698749303818, 0.04160250723361969, 0.09473921358585358, -0.020503249019384384, -0.02762572653591633, 0.036071762442588806, 0.02492539957165718, 0.011550034396350384, -0.05871060490608215, -0.0023537620436400175, 0.04268038272857666, 0.02159956656396389, -0.08032623678445816, 0.0017854534089565277, -0.02810630574822426, -0.022443708032369614, -0.0378136932849884, 0.019212480634450912, 0.08184754103422165, -0.09462647140026093, 0.014391589909791946, -0.05187954753637314, -0.04048356041312218, -0.004218027926981449, 0.015564458444714546, 0.02202804945409298, 0.045474499464035034, -0.0028355030808597803, -0.029673706740140915, -0.08295264095067978, 0.04125085100531578, -0.02560737356543541, -0.001085264957509935, 0.030680963769555092, 0.05954089015722275, -0.038323771208524704, 0.009553731419146061, 0.029930399730801582, -0.05338043347001076, 0.0042230817489326, -0.033367570489645004, 0.016443192958831787, -0.02716265618801117, 0.0006329810130409896, -0.007433826569467783, -0.02293815091252327, 0.028807006776332855, 0.05096444487571716, -0.017544660717248917, 0.015943793579936028, 0.013249069452285767, -0.027499523013830185, 0.03837141767144203, 0.01744084805250168, -0.017370767891407013, 0.0428507961332798, 0.009915925562381744, 0.029836837202310562, 0.06085763871669769, 0.006930687464773655, -0.0034202653914690018, 0.011383642442524433, -0.05896029993891716, 0.019433654844760895, 0.009970694780349731, -0.01606343500316143, -0.021348392590880394, -0.030284332111477852, 0.013259654864668846, 0.031787414103746414, 0.03409804776310921, 0.012361463159322739, 0.06148126721382141, 0.011586949229240417, 0.027034472674131393, -0.025448475033044815, -0.0363643541932106, 0.01863238215446472, 0.013818271458148956, -0.003518161829560995, 0.0521387904882431, 0.045414552092552185, -0.06113016605377197, -0.02160884067416191, -0.03417826071381569, -0.011030352674424648, 0.006655808072537184, 0.05268711596727371, -0.014925805851817131, -0.03637668490409851, 0.04575875401496887, -0.06881820410490036, -0.03919884189963341, -0.029378069564700127, -0.03305283561348915, 0.0248002577573061, 0.0031467482913285494, 0.03499329462647438, -0.024653596803545952, 0.029649710282683372, -0.04465454816818237, -0.07430373877286911, -0.01778401806950569, 0.0030249617993831635, 0.048525359481573105, 0.013581660576164722, -0.0541403703391552, 0.007465626113116741, 0.020313074812293053, -0.021666700020432472, 0.004311214666813612, 0.005221178289502859, -0.024022888392210007, 0.013307980261743069, -0.007599543314427137, 0.050456225872039795, 0.09669476002454758, -0.023490604013204575, 0.00824242178350687, -0.0169973187148571, -0.012953494675457478, -0.03153322637081146, -0.013489688746631145, -0.024516141042113304, -0.0482325553894043, -0.014578101225197315, -0.008565777912735939, 0.036753099411726 ]
<p>I'm currently learning about symmetry between particles. For a simple case of two non-interacting particles at $x_1$ and $x_2$, we know that the wavefunction can be written as $\psi_{n_1, n_2} = \phi_{n_1}(x_1) \phi_{n_2}(x_2)$</p> <p>Let's consider two cases in ground state and first excited state.</p> <p>(a) Two particles are not identical, and have spin zero</p> <p>(b) Two identical particles, each with spin zero</p> <p>We know that the energy is given by $E_n = (n_1 + n_2 + 1)\hbar \omega$.</p> <p><strong>For case (a)</strong></p> <p>Since they are not identical, the wavefunction at ground state would be $\phi_1(x_1) \phi_1 (x_2)$ right? Then the degeneracy would be 0 right? Since $n_1 = n_2 = 1$.</p> <p>For the first excited state, the wavefunction would be $\phi_2(x_1)\phi_1(x_2)$, assuming $E_2(x_1) &lt; E_2(x_2)$, meaning we just take whatever is lower. The degeneracy would be 0, since they are distinguishable?</p> <p><strong>For case (b)</strong></p> <p>Now they are identical, ground state wavefunction would still be $\phi_1(x_1)\phi_1(x_2)$ right? Degeneracy of ground state would be 0, since $n_1=n_2=1$?</p> <p>But for the first excited state, the degeneracy would be 2, since either $n_1=2$ and $n_2=1$ or $n_1=1$ and $n_2=2$? Spin 0 particles are bosons, so the wavefunction must be symmetric right? So I'm thinking $\psi = \frac{1}{2} \left[ \phi_2(x_1)\phi_1(x_2) + \phi_1(x_1)\phi_2(x_2)\right]$</p> <p>The concept of symmetry and exchange symmetry is still new to me, I'd appreciate any response!</p>
g1529
[ -0.006014454178512096, -0.01866224780678749, 0.008924535475671291, -0.012104308232665062, 0.09641287475824356, -0.013395789079368114, 0.033299874514341354, 0.06159639731049538, -0.030415300279855728, -0.01279276143759489, -0.024061283096671104, 0.030216200277209282, -0.030615709722042084, -0.0240323543548584, -0.009249705821275711, 0.058577604591846466, 0.06833285093307495, 0.041884955018758774, -0.01948108896613121, 0.02155868522822857, 0.015565534122288227, 0.021349068731069565, -0.05399421975016594, -0.0341058075428009, 0.03270367532968521, -0.07403626292943954, -0.023356664925813675, -0.040500298142433167, -0.021795744076371193, 0.02120145410299301, 0.011107518337666988, 0.05654734745621681, 0.004342655185610056, 0.012299704365432262, 0.01212075911462307, -0.000641396502032876, -0.004326166119426489, -0.012482273392379284, 0.009598270989954472, 0.0011317917378619313, 0.037740785628557205, 0.036701031029224396, -0.01696150377392769, -0.027705064043402672, 0.036813266575336456, 0.018793044611811638, 0.003384921234101057, -0.03440586477518082, -0.04437774792313576, -0.03391822800040245, 0.04999195784330368, 0.02872096188366413, 0.07801622152328491, 0.052128709852695465, -0.009714825078845024, -0.014760240912437439, 0.018415525555610657, -0.014214703813195229, 0.06065269187092781, 0.0434592142701149, -0.007038456853479147, 0.025255506858229637, 0.008772875182330608, 0.03753945231437683, 0.0032843383960425854, -0.008658177219331264, -0.024493325501680374, -0.016492119058966637, 0.012217126786708832, 0.029738452285528183, -0.021826619282364845, -0.008364241570234299, -0.005471103824675083, 0.0258251391351223, -0.010857474990189075, -0.025083592161536217, -0.009055168367922306, -0.003931023180484772, 0.006198761984705925, -0.013869395479559898, -0.05348712578415871, -0.017824843525886536, 0.008047498762607574, 0.03602691739797592, 0.027443453669548035, -0.035578787326812744, -0.04146430641412735, -0.02416948787868023, -0.024530597031116486, 0.03886871039867401, 0.024540312588214874, -0.030536871403455734, 0.056244853883981705, -0.002657830249518156, -0.00045128678902983665, -0.003294913796707988, 0.020757269114255905, 0.04709960147738457, -0.04181371629238129, 0.0009358921670354903, -0.007229459006339312, -0.008087576366961002, 0.02027903124690056, -0.004165478050708771, 0.06224169209599495, -0.034572385251522064, 0.031010271981358528, 0.019524578005075455, -0.0393979586660862, -0.02855149284005165, 0.030389875173568726, 0.011394445784389973, -0.0012900963192805648, 0.009011516347527504, -0.05402763932943344, -0.01752047799527645, 0.03843449056148529, -0.055107053369283676, -0.039837952703237534, 0.02674352563917637, 0.0353013351559639, 0.006255862768739462, -0.005748449359089136, 0.07606767863035202, 0.028258714824914932, -0.030748696997761726, -0.025791622698307037, -0.017943549901247025, 0.04703690856695175, -0.03134704753756523, -0.013721976429224014, -0.05197712779045105, 0.03856956586241722, 0.058249760419130325, -0.03168940544128418, 0.044467732310295105, 0.023893272504210472, 0.03451471030712128, -0.015623961575329304, -0.03492427244782448, 0.0012011686339974403, -0.02503657527267933, -0.013301942497491837, -0.0029382207430899143, 0.00868867989629507, -0.00569279957562685, -0.02915930189192295, -0.09495566040277481, -0.024813061580061913, 0.08044859766960144, -0.017383543774485588, 0.05266334116458893, 0.029185406863689423, 0.04229820892214775, 0.028416167944669724, -0.019445296376943588, 0.035442497581243515, -0.055745288729667664, -0.014257574453949928, 0.0055250669829547405, 0.06750830262899399, -0.01002212893217802, 0.05267692729830742, -0.028680795803666115, -0.041823163628578186, -0.041790351271629333, 0.045869819819927216, -0.08919522911310196, 0.002090832684189081, -0.11021097749471664, -0.015097073279321194, 0.019899263978004456, 0.0030324114486575127, 0.052212052047252655, -0.002682543359696865, 0.01403131429105997, -0.08311812579631805, -0.06192323565483093, 0.008872780948877335, 0.019667942076921463, -0.028502559289336205, -0.007897943258285522, -0.007553705945611, 0.027551602572202682, -0.03891611471772194, 0.04959741234779358, 0.03834762051701546, 0.008664119988679886, -0.08801249414682388, 0.007210562005639076, 0.0035746926441788673, 0.036408595740795135, -0.018336644396185875, 0.03032618574798107, -0.012429481372237206, 0.03318142518401146, -0.013349885120987892, -0.014067226089537144, -0.006315145641565323, 0.009235064499080181, -0.008885092101991177, 0.05909455195069313, 0.04071423411369324, -0.015411265194416046, 0.03263569995760918, -0.005897213239222765, 0.0403616838157177, -0.004619155079126358, 0.048053573817014694, -0.028427526354789734, -0.00929262861609459, -0.021931186318397522, -0.05206798017024994, 0.011813424527645111, 0.00471235066652298, -0.02029036171734333, -0.024561772122979164, -0.002996087772771716, -0.0320771187543869, -0.019862975925207138, -0.0019832507241517305, -0.016909386962652206, 0.07224425673484802, 0.0450204573571682, -0.038352686911821365, 0.03200680762529373, -0.029613476246595383, 0.005571228452026844, -0.07776178419589996, 0.04254131391644478, -0.04983492195606232, 0.03990522772073746, -0.011596047319471836, -0.028429754078388214, 0.026228491216897964, 0.037061646580696106, -0.02378533035516739, -0.013621670193970203, 0.07339630275964737, -0.00915807019919157, -0.021905044093728065, -0.008411236107349396, -0.0534350648522377, 0.0506717711687088, 0.02769427001476288, -0.0055360388942062855, -0.03350427746772766, 0.02841157279908657, 0.031148845329880714, -0.007994710467755795, 0.013193088583648205, -0.0034495852887630463, -0.06736978143453598, -0.018116416409611702, -0.012209178879857063, -0.06476937234401703, 0.0074394322000443935, 0.0008389381691813469, -0.05554362013936043, -0.07773101329803467, 0.0016236603260040283, -0.033758800476789474, -0.0027463254518806934, 0.00038786334334872663, -0.02794969640672207, 0.00758526474237442, 0.037405651062726974, 0.0009683861862868071, -0.03264310956001282, -0.04555832967162132, 0.024866988882422447, 0.08607372641563416, -0.00553806172683835, 0.06109217181801796, -0.037090104073286057, -0.04936860501766205, -0.019527330994606018, 0.03108247183263302, 0.01672687940299511, -0.029183808714151382, -0.03934251517057419, -0.03238556906580925, -0.015384177677333355, 0.014610299840569496, 0.09660045057535172, -0.124477319419384, -0.04800690338015556, -0.005266072228550911, -0.00473359739407897, 0.041969556361436844, -0.009846300818026066, 0.039944227784872055, 0.0481114536523819, -0.017170654609799385, -0.008483168669044971, 0.005706647410988808, -0.009988640435039997, -0.04394994676113129, -0.016308337450027466, 0.07077325135469437, -0.013675002381205559, -0.04286019131541252, 0.015136437490582466, 0.0010327297495678067, 0.030458519235253334, -0.04747713357210159, -0.04488169401884079, -0.035619478672742844, -0.03902500122785568, 0.027858195826411247, -0.05949192866683006, 0.057180460542440414, -0.01703883707523346, 0.039345916360616684, -0.023233264684677124, 0.034975193440914154, -0.04185862839221954, -0.0026556795928627253, -0.03303442895412445, -0.03561987355351448, -0.052290014922618866, -0.02447456121444702, 0.02091148868203163, -0.02610488049685955, 0.029105696827173233, 0.036413129419088364, -0.0234361682087183, 0.002777315676212311, -0.09844154864549637, 0.009706102311611176, 0.015154801309108734, -0.0076146721839904785, -0.011681262403726578, -0.045110080391168594, -0.016106467694044113, -0.00974068883806467, -0.008783952333033085, -0.034199535846710205, -0.016307983547449112, 0.031739477068185806, -0.026934828609228134, -0.0037967688404023647, -0.014736033044755459, -0.04983256012201309, 0.024214312434196472, -0.028027404099702835, -0.035098735243082047, 0.005251919385045767, -0.028459476307034492, 0.05378207936882973, -0.005840715486556292, 0.026055075228214264, 0.022121623158454895, 0.010999462567269802, -0.023000292479991913, -0.06232935190200806, 0.023356324061751366, 0.020940516144037247, -0.017444605007767677, 0.05567707121372223, 0.04287855699658394, -0.027125664055347443, 0.02159455418586731, 0.007928435690701008, -0.023343199864029884, -0.044908564537763596, -0.04280689358711243, -0.05298623442649841, 0.03522418811917305, -0.024634839966893196, -0.030551690608263016, 0.012345698662102222, 0.02121109329164028, -0.050159599632024765, -0.012915482744574547, -0.028919601812958717, 0.02423100918531418, -0.039928555488586426, -0.05301140248775482, 0.030783072113990784, -0.014047262258827686, -0.00875303614884615, 0.029296398162841797, -0.002740402240306139, 0.06619469821453094, 0.05477014183998108, -0.0019655495416373014, 0.007017308846116066, 0.043569184839725494, 0.019608663395047188, 0.021872369572520256, -0.019655440002679825, 0.0007055533351376653, 0.08133360743522644, 0.04719919338822365, 0.02986682392656803, 0.007491540629416704, -0.032261401414871216, -0.017406269907951355, 0.02803635783493519, -0.02331037074327469, -0.024454040452837944, -0.042989157140254974, -0.0759628415107727, 0.024135880172252655, -0.0017310971161350608, 0.02810272015631199, -0.01120405737310648, -0.03703998029232025, 0.0011788877891376615, 0.03338731452822685, 0.022305238991975784, 0.04057782515883446, -0.028949525207281113, -0.04581310972571373, -0.003167290473356843, -0.008985106833279133, -0.04959990084171295, -0.0027971090748906136, -0.00878988392651081, 0.018466314300894737, 0.028192689642310143, 0.02121124602854252, 0.02867666445672512, 0.005979887209832668, 0.06732779741287231, 0.015719817951321602, -0.005156060215085745, -0.069047711789608, -0.023178299888968468, 0.00195723376236856, 0.019249863922595978, 0.007239705882966518, -0.007583573926240206, -0.0742964968085289, 0.0030425176955759525, -0.0585007444024086, 0.010907996445894241, 0.02768923155963421, 0.033920519053936005, 0.0710044801235199, 0.02482854388654232, -0.037146419286727905, 0.01596534438431263, 0.03209025040268898, 0.025762630626559258, -0.07315079867839813, -0.042413078248500824, 0.004094178322702646, -0.0422419048845768, -0.02193289063870907, 0.014970230869948864, -0.02068421058356762, -0.049038249999284744, -0.04401872307062149, -0.02200712077319622, 0.0043307943269610405, 0.072532057762146, -0.03804508596658707, 0.007215116638690233, -0.057969775050878525, 0.019624052569270134, 0.025750145316123962, -0.06238789111375809, 0.00914473831653595, 0.0394105464220047, -0.06583073735237122, 0.005853955168277025, -0.00783978495746851, 0.011347430758178234, 0.00978586170822382, -0.07073256373405457, 0.03781905770301819, -0.02447308413684368, 0.012085072696208954, 0.02931756153702736, -0.014941192232072353, -0.01363933552056551, 0.01997685804963112, -0.017324721440672874, -0.04263141378760338, 0.0123570142313838, 0.0717802345752716, 0.009229504503309727, 0.02288288250565529, 0.0008710316033102572, -0.0209242831915617, 0.05409373342990875, -0.04069507122039795, -0.0408967062830925, -0.003834208007901907, -0.02374269813299179, -0.011443466879427433, -0.01778539828956127, 0.07396019995212555, -0.014889036305248737, 0.00840328074991703, 0.0034263317938894033, -0.058577679097652435, 0.03360266610980034, -0.03571663424372673, -0.004131509456783533, -0.010638564825057983, 0.015147337689995766, 0.009395898319780827, 0.046220917254686356, 0.023721493780612946, -0.009988534264266491, -0.03256503492593765, -0.0007180430693551898, 0.0026758769527077675, -0.04952666908502579, 0.029118739068508148, 0.0298905111849308, -0.008818775415420532, 0.05231534317135811, -0.014575990848243237, -0.004401335958391428, -0.01695859432220459, -0.006913390476256609, 0.02932038903236389, 0.034128788858652115, 0.016017792746424675, -0.031493984162807465, -0.015503231436014175, 0.003960253670811653, -0.0027478118427097797, 0.019739607349038124, -0.03878879174590111, 0.08494484424591064, 0.04588553309440613, 0.025920839980244637, 0.028909439221024513, -0.002588183619081974, 0.053293392062187195, -0.013780195266008377, -0.04573465883731842, 0.009336910210549831, 0.03877837955951691, 0.028554363176226616, -0.014195154421031475, 0.017610784620046616, 0.05650685355067253, -0.010191578418016434, -0.08375963568687439, 0.040209006518125534, -0.014854814857244492, -0.017298443242907524, -0.017099402844905853, -0.032097335904836655, -0.02758512832224369, -0.006732478272169828, -0.0006777903181500733, -0.01636527292430401, 0.04737615957856178, 0.05627822503447533, 0.02101832628250122, -0.005163717549294233, 0.0330311618745327, -0.03410038724541664, 0.028798719868063927, -0.041993968188762665, 0.06643151491880417, -0.013542057015001774, 0.016310814768075943, -0.006157867144793272, -0.03943028301000595, -0.05801860988140106, -0.01978737860918045, -0.03089912422001362, -0.041757356375455856, -0.010162060149013996, -0.005011498928070068, -0.03219933807849884, 0.017009569332003593, 0.04850010946393013, -0.021174831315875053, -0.061853259801864624, -0.011579027399420738, -0.00012845096352975816, 0.0061034224927425385, 0.042411770671606064, 0.03368721529841423, 0.0023633611854165792, -0.035545628517866135, 0.05743079632520676, 0.04368530586361885, -0.05401657149195671, 0.05226500332355499, 0.03635711222887039, -0.041018374264240265, -0.09219791740179062, -0.028459148481488228, 0.0008995868265628815, 0.02598908357322216, 0.015084905549883842, 0.008787334896624088, -0.060982704162597656, 0.012944931164383888, 0.016653355211019516, 0.05817433074116707, 0.0029227843042463064, 0.02560598775744438, 0.025951558724045753, 0.03611407428979874, 0.04046841710805893, -0.035869039595127106, 0.03169111907482147, -0.02437411993741989, -0.009469483979046345, -0.009803323075175285, -0.017659056931734085, -0.03353526070713997, -0.06628739088773727, 0.03336566314101219, -0.043069589883089066, 0.024853311479091644, 0.05145348235964775, 0.022047236561775208, 0.03319455683231354, -0.004174685105681419, 0.006465427111834288, -0.03620709106326103, -0.048497915267944336, 0.10140209645032883, 0.047617919743061066, -0.02523522637784481, 0.0120124826207757, 0.03662966936826706, 0.015264356508851051, 0.03290674462914467, -0.007096109911799431, 0.03911057114601135, 0.012736566364765167, -0.03972780331969261, 0.003374001942574978, -0.01793433353304863, -0.008411693386733532, 0.032854821532964706, 0.04212946817278862, -0.01277089398354292, 0.04463104531168938, 0.10366524755954742, -0.015319989994168282, -0.058961786329746246, 0.023087967187166214, 0.049879807978868484, 0.029532816261053085, -0.07938802987337112, 0.009368496015667915, -0.020155254751443863, -0.06513047963380814, -0.030883826315402985, -0.005002938210964203, -0.010497129522264004, -0.009608029387891293, 0.046050552278757095, -0.03533690795302391, 0.0533449687063694, 0.0005670543177984655, -0.018941637128591537, -0.0004697031690739095, -0.024830766022205353, -0.005049429833889008, 0.008569595403969288, 0.028889883309602737, 0.037159424275159836, 0.0372314490377903, -0.02598346211016178, -0.02662433683872223, -0.015429371036589146, -0.09661296010017395, -0.0703350380063057, 0.024964015930891037, -0.02877824194729328, -0.014294837601482868, 0.01523315254598856, 0.03348309174180031, -0.0016798139549791813, -0.018369004130363464, 0.05366406962275505, -0.05312386155128479, -0.04315491020679474, 0.03895975649356842, -0.04349488019943237, 0.025155697017908096, -0.008320454508066177, -0.012647024355828762, -0.020370887592434883, 0.04320772737264633, -0.056648895144462585, -0.011548119597136974, 0.017725909128785133, -0.026724020019173622, -0.04648316651582718, 0.03216565400362015, 0.05704676732420921, 0.018450912088155746, 0.0340813472867012, 0.006695165764540434, 0.038809292018413544, -0.0291349608451128, 0.02416185662150383, 0.003990489058196545, 0.012781464494764805, -0.06694687157869339, 0.006476013921201229, -0.05071012303233147, -0.007602397818118334, 0.00893945712596178, 0.03546345233917236, 0.02526828460395336, 0.013040406629443169, 0.0372975617647171, -0.007453021593391895, 0.011861312203109264, -0.08954722434282303, 0.01752188615500927, 0.07016023248434067, 0.040581099689006805, -0.0018461054423823953, 0.013935750350356102, 0.004281012807041407, -0.018187889829277992, -0.0293076541274786, -0.027045810595154762, 0.008573174476623535, 0.024352747946977615, 0.06476584821939468, 0.05448593571782112, -0.013144494034349918, 0.10857263952493668, -0.03754992410540581, 0.05739661306142807, -0.01907804049551487, -0.008645878173410892, 0.006591594312340021, -0.026887215673923492, -0.0423426516354084, 0.04452765733003616, -0.011438300833106041, 0.003885142505168915, -0.026925014331936836, -0.03653755784034729, -0.021962709724903107, 0.0634327307343483, 0.022741463035345078, 0.025776933878660202, 0.09250737726688385, -0.014618736691772938, 0.027436811476945877, 0.0024157424923032522, -0.016918137669563293, 0.08245661109685898, 0.07063785195350647, -0.03143256530165672, 0.006768812891095877, 0.05890168622136116, -0.015397852286696434, -0.03428757190704346, -0.0012888731434941292, -0.007155919913202524, -0.008758017793297768, -0.00808060821145773, -0.05564136803150177, 0.0019289253978058696, -0.034681547433137894, 0.09730347245931625 ]
<p>The force for revolution of earth is provided by the gravitational force of attraction between earth and the sun. What provides the force(torque) for the rotation of earth? </p>
g1530
[ 0.03238454833626747, 0.0700017660856247, -0.013292071409523487, 0.020003773272037506, 0.019998518750071526, 0.044999860227108, 0.06093394383788109, -0.04885780066251755, -0.0017669000662863255, -0.0015423574950546026, 0.028264150023460388, -0.013041718862950802, 0.01818498596549034, -0.033823512494564056, 0.051003772765398026, 0.047086331993341446, 0.08800530433654785, 0.0311777014285326, 0.06062236428260803, 0.04788951203227043, 0.023352472111582756, -0.01886412687599659, -0.04317193850874901, -0.054093021899461746, 0.010883194394409657, 0.023147130385041237, 0.036232057958841324, -0.01211201399564743, -0.05179652199149132, -0.034789830446243286, 0.04231850057840347, -0.008833624422550201, 0.046472903341054916, -0.04373079910874367, -0.021319063380360603, -0.04483089968562126, -0.012944968417286873, 0.028219876810908318, 0.024543246254324913, -0.052265528589487076, -0.00793411210179329, 0.008602709509432316, 0.009861966595053673, 0.021119341254234314, 0.04153711721301079, -0.07271576672792435, 0.01264864020049572, 0.03255512937903404, -0.014032138511538506, -0.022719141095876694, -0.029074791818857193, -0.0301816388964653, -0.0006578831817023456, -0.045894961804151535, -0.003741677151992917, 0.005907264072448015, 0.04874132201075554, -0.03450687974691391, -0.03804173693060875, 0.016789177432656288, -0.0350811704993248, -0.014930513687431812, -0.002081759972497821, -0.03746148943901062, 0.004262219648808241, -0.014082340523600578, 0.010316048748791218, -0.0015637101605534554, 0.02699912153184414, 0.02192194201052189, 0.014885490760207176, -0.016512082889676094, -0.006369098089635372, -0.005464750807732344, -0.00507479440420866, -0.02715240977704525, 0.018239475786685944, 0.02546267956495285, 0.004109365865588188, -0.01714518293738365, 0.00794311799108982, 0.0337042398750782, 0.013829601928591728, -0.024230558425188065, 0.07694502174854279, -0.05204283818602562, 0.008866938762366772, 0.07225395739078522, 0.007559661753475666, 0.025310087949037552, 0.055197373032569885, 0.004044262692332268, 0.07608585059642792, 0.013449093326926231, -0.037094082683324814, -0.027869250625371933, 0.009984051808714867, 0.0643225908279419, -0.007493828888982534, 0.021922431886196136, -0.014087614603340626, -0.04483349621295929, -0.028722483664751053, -0.06485041975975037, 0.0698220506310463, 0.0164957195520401, 0.016083499416708946, -0.031027918681502342, -0.05376151204109192, -0.0297092255204916, 0.020223503932356834, -0.02000066637992859, 0.004119083750993013, -0.06007329747080803, -0.023875098675489426, -0.06445445120334625, 0.08089236915111542, -0.020203718915581703, 0.053491491824388504, 0.07768499106168747, 0.0014070194447413087, 0.01210896298289299, -0.056545987725257874, 0.10610315948724747, -0.03882138803601265, -0.037298157811164856, 0.02586107887327671, 0.009400919079780579, 0.02318197302520275, -0.02215571328997612, 0.02208801545202732, 0.0009153152350336313, -0.02441786788403988, -0.011720862239599228, 0.029451876878738403, -0.011990435421466827, -0.013483566232025623, 0.010574178770184517, -0.001085462048649788, 0.05960650369524956, -0.010056727565824986, 0.01589978300035, 0.030078371986746788, -0.0037371055223047733, -0.015689704567193985, 0.056291092187166214, 0.0038452548906207085, 0.0294358991086483, 0.051050253212451935, 0.02522629126906395, -0.00513793621212244, 0.018071215599775314, 0.014185250736773014, -0.0473746657371521, 0.029834838584065437, -0.05784828960895538, 0.05831480026245117, -0.03107346035540104, -0.022348647937178612, 0.036024343222379684, 0.042410023510456085, -0.06012196093797684, 0.001382665359415114, -0.027847403660416603, -0.004851224832236767, 0.021062646061182022, -0.04357091337442398, -0.015717148780822754, -0.04411573335528374, 0.014786683954298496, -0.01859191246330738, -0.0004942412488162518, 0.019527191296219826, -0.003030071035027504, -0.0030735190957784653, -0.011596053838729858, 0.025079047307372093, -0.04684225842356682, -0.01669364795088768, 0.013084941543638706, 0.04072175547480583, -0.019967077299952507, 0.02896755188703537, 0.05705029517412186, -0.014271324500441551, -0.004413212183862925, 0.027799127623438835, -0.03648346662521362, -0.052497491240501404, 0.004591336473822594, 0.00035260809818282723, -0.012306846678256989, -0.01478513702750206, 0.004871123470366001, 0.0077598607167601585, -0.0035365496296435595, 0.01613546535372734, -0.025002453476190567, -0.06054593250155449, 0.0734173059463501, -0.03947759419679642, 0.04141814634203911, 0.055453307926654816, -0.029523126780986786, -0.007876296527683735, -0.04144766926765442, 0.01577761583030224, 0.024129092693328857, 0.08890973031520844, 0.03300083428621292, 0.05329558998346329, 0.022652775049209595, 0.007153527811169624, -0.020473221316933632, -0.05278624966740608, -0.02363433688879013, 0.0050466652028262615, -0.0016691709170117974, -0.03489143028855324, -0.017027447000145912, -0.016487369313836098, 0.03331426903605461, -0.036632515490055084, 0.008730907924473286, -0.05281732231378555, 0.001807362656109035, 0.01021326333284378, -0.0028600976802408695, 0.03877478092908859, 0.010255052708089352, -0.03891168162226677, -0.051613982766866684, 0.06158486753702164, 0.04382868483662605, 0.03530026972293854, 0.07579504698514938, 0.02506011351943016, -0.03060564212501049, -0.02207881584763527, -0.011973503977060318, 0.001528367749415338, 0.031869709491729736, 0.0022423735354095697, -0.013221396133303642, 0.025235218927264214, -0.05815275013446808, 0.04808508977293968, 0.039939288049936295, 0.060401178896427155, -0.005322491284459829, 0.08360074460506439, -0.04769865795969963, -0.05010589212179184, 0.030267134308815002, -0.000891129660885781, 0.013750978745520115, -0.03998417779803276, 0.06579168885946274, -0.04016263782978058, -0.031454045325517654, -0.032735250890254974, 0.0014292673440650105, 0.017434684559702873, 0.06249335780739784, -0.06621131300926208, 0.012323189526796341, -0.047925617545843124, 0.02495887503027916, 0.012024223804473877, -0.004592259880155325, -0.03915071859955788, -0.00612766994163394, -0.037845924496650696, 0.04321654886007309, -0.06344625353813171, -0.0846032127737999, -0.02602788805961609, -0.01842189021408558, -0.03683483600616455, -0.015664665028452873, 0.04003666713833809, -0.02199428342282772, 0.028517290949821472, 0.044714733958244324, 0.027275200933218002, -0.0002161612210329622, -0.06024797633290291, 0.030857324600219727, -0.0629756823182106, -0.03174501284956932, -0.041849054396152496, 0.03661658242344856, 0.08339682966470718, -0.02681523747742176, 0.016438810154795647, 0.003953394014388323, -0.004001376684755087, -0.021530073136091232, -0.03687359392642975, 0.05404960736632347, 0.04602055624127388, -0.041405338793992996, -0.011895655654370785, 0.03519099950790405, -0.03144662082195282, 0.036955930292606354, 0.011972520500421524, -0.06341712921857834, -0.04464966431260109, 0.013598584569990635, -0.07803981751203537, 0.011729804798960686, -0.056389499455690384, -0.06555656343698502, -0.03513506054878235, -0.03952276334166527, -0.02581094019114971, -0.006409055553376675, 0.026113785803318024, -0.023531552404165268, -0.019000496715307236, -0.0909981057047844, -0.02184339426457882, -0.0424710288643837, 0.019399583339691162, 0.06587452441453934, -0.10919736325740814, -0.000691393855959177, -0.03560860827565193, -0.07444245368242264, 0.03525306284427643, 0.06995899230241776, -0.046286121010780334, 0.0352068655192852, -0.043302569538354874, 0.028345922008156776, 0.022891392931342125, -0.012152261100709438, 0.012892600148916245, 0.04467514902353287, -0.02262992225587368, 0.029777860268950462, -0.07270154356956482, -0.03476846590638161, 0.008424614556133747, 0.051975056529045105, -0.0334501788020134, -0.03820086643099785, 0.028358103707432747, 0.011638229712843895, 0.009245254099369049, -0.04617296904325485, -0.003941153641790152, 0.0025389278307557106, 0.028088940307497978, 0.03484012931585312, 0.034050412476062775, 0.0013085397658869624, -0.07753205299377441, -0.0010197957744821906, -0.016854722052812576, -0.022273702546954155, -0.013727683573961258, 0.03181379660964012, 0.027104754000902176, -0.004519820678979158, 0.01753906160593033, -0.005398637615144253, -0.024323519319295883, 0.00348100159317255, 0.04376314580440521, 0.0014229987282305956, -0.006756125949323177, -0.013292456977069378, 0.05160947144031525, -0.06713130325078964, 0.0030657409224659204, -0.07850846648216248, 0.0037204469554126263, 0.01815750077366829, 0.062432534992694855, 0.017893832176923752, -0.037439391016960144, 0.04770132899284363, 0.033228036016225815, 0.010032251477241516, 0.009739808738231659, -0.015101381577551365, 0.05194836109876633, -0.011995458975434303, -0.01998610980808735, -0.057067062705755234, 0.012546271085739136, -0.01572316884994507, 0.022736500948667526, -0.057667676359415054, 0.03385213017463684, 0.027559641748666763, -0.02557259425520897, -0.031348817050457, -0.0036923622246831656, 0.02372242882847786, -0.00762619124725461, 0.017215708270668983, 0.0009941908065229654, 0.05261242017149925, 0.015835300087928772, -0.012715468183159828, 0.04563382267951965, 0.025929104536771774, -0.00339097180403769, 0.03377551957964897, -0.02162194810807705, -0.02259347401559353, 0.02697494439780712, 0.0018097971333190799, 0.007902787998318672, 0.01855352893471718, 0.03389056399464607, 0.0003146592353004962, -0.008847026154398918, 0.04869116470217705, 0.029435060918331146, 0.002391572343185544, -0.033217474818229675, 0.026404133066534996, 0.050013359636068344, -0.021948395296931267, 0.01387840323150158, -0.045926518738269806, -0.031017793342471123, -0.044103410094976425, 0.021241530776023865, -0.01675308123230934, -0.010992852039635181, -0.0039041696581989527, 0.01860348880290985, -0.02060559205710888, 0.01328863762319088, -0.020266778767108917, 0.027190307155251503, 0.03944762423634529, 0.03924131020903587, -0.004959598649293184, -0.0429467037320137, 0.11487078666687012, 0.02340129390358925, -0.04667358845472336, 0.0028847919311374426, -0.007433874066919088, -0.013873769901692867, -0.04054474085569382, -0.006611802615225315, 0.044086433947086334, -0.022778868675231934, 0.07842087745666504, -0.026845306158065796, 0.009474006481468678, -0.021485228091478348, -0.005445635411888361, -0.0233412254601717, 0.00024928475613705814, -0.028063056990504265, 0.044336214661598206, 0.0384429395198822, 0.01221530046314001, -0.021040815860033035, 0.0286030825227499, 0.006153726018965244, 0.013736325316131115, 0.021488048136234283, 0.005989627446979284, 0.038753483444452286, 0.04023014381527901, -0.004409531131386757, -0.009807695634663105, 0.01811448484659195, -0.045544352382421494, 0.04438969865441322, -0.05272681638598442, -0.003467640606686473, 0.02420041710138321, 0.030223965644836426, -0.00953923724591732, -0.004692830611020327, -0.03372150659561157, 0.04216031730175018, -0.0383705273270607, -0.007879785262048244, -0.018091585487127304, -0.03190136328339577, 0.018384715542197227, -0.03800500929355621, -0.11420268565416336, -0.009004798717796803, 0.07145725935697556, -0.012289999052882195, 0.008669791743159294, 0.020579606294631958, 0.03451928496360779, 0.002186077181249857, -0.002733953995630145, -0.021540949121117592, 0.019887514412403107, -0.03858591988682747, 0.019116295501589775, 0.02324848808348179, 0.040417302399873734, -0.02686281129717827, 0.03673655539751053, -0.026418084278702736, -0.008909621275961399, -0.008879789151251316, 0.048386577516794205, 0.01354174967855215, 0.019485121592879295, 0.030422065407037735, 0.013911068439483643, 0.008965473622083664, 0.029410921037197113, 0.030265819281339645, -0.023991264402866364, 0.05111891031265259, -0.061319541186094284, 0.025520596653223038, -0.0094316890463233, -0.023515921086072922, 0.035253316164016724, 0.017703546211123466, 0.05586592108011246, -0.004868888296186924, 0.026347825303673744, 0.03352544829249382, -0.06641877442598343, 0.04457513988018036, -0.02077779918909073, 0.05482595041394234, 0.0020470970775932074, 0.055541738867759705, -0.06651466339826584, -0.0295266006141901, -0.027112482115626335, 0.07114661484956741, -0.024281231686472893, 0.02584707736968994, 0.04695529490709305, -0.012937946245074272, 0.035032548010349274, 0.016909992322325706, 0.03664317727088928, -0.013915911316871643, 0.05527639761567116, -0.012132406234741211, -0.031908970326185226, -0.09216861426830292, 0.013979442417621613, 0.039010338485240936, -0.031513672322034836, -0.022879956290125847, -0.031088871881365776, 0.05153089761734009, 0.04313168302178383, -0.010394747368991375, -0.020022667944431305, -0.04856496304273605, -0.03692298009991646, 0.02176794782280922, -0.03180842101573944, 0.004065568093210459, 0.017303863540291786, -0.00958136934787035, 0.008392883464694023, -0.0078404750674963, 0.015880320221185684, 0.03653518483042717, 0.001245894585736096, -0.02262093313038349, -0.03237217292189598, -0.09251772612333298, -0.022951483726501465, 0.044344428926706314, -0.029019629582762718, -0.009846986271440983, -0.06635073572397232, -0.03992079943418503, -0.024414559826254845, -0.08100508153438568, -0.03505304083228111, 0.025655856356024742, -0.06177910044789314, -0.006092519965022802, 0.058924827724695206, -0.04370056837797165, -0.019222766160964966, 0.035375580191612244, 0.024020623415708542, 0.025010237470269203, 0.056658774614334106, 0.03619663789868355, 0.005750216543674469, 0.02429668977856636, 0.003978738095611334, 0.08165396749973297, 0.024665463715791702, 0.06967423111200333, -0.07537964731454849, -0.02304968237876892, -0.07415571063756943, -0.006379322148859501, -0.029427776113152504, 0.023046288639307022, 0.0013666070299223065, -0.016917385160923004, -0.0027374872006475925, 0.00601104274392128, 0.030130451545119286, 0.02861264906823635, 0.029611600562930107, -0.005729916505515575, -0.004489605315029621, -0.01677520014345646, -0.03780850023031235, 0.011332698166370392, -0.07445324957370758, 0.01460475567728281, 0.00364343891851604, -0.06703390181064606, 0.03089384362101555, 0.035311050713062286, -0.01604011282324791, 0.003530945163220167, 0.015988390892744064, -0.016760369762778282, 0.02418137900531292, 0.06532847881317139, 0.05629974976181984, -0.06246095895767212, 0.013941032811999321, 0.0018132338300347328, 0.04111681878566742, -0.05599111318588257, 0.006272510159760714, -0.005061026196926832, 0.022797171026468277, -0.059850484132766724, -0.011009177193045616, -0.009479493834078312, -0.034001510590314865, -0.00934186577796936, 0.011907885782420635, 0.0014557442627847195, -0.02152804285287857, 0.0023542053531855345, 0.015976546332240105, -0.03983089327812195, 0.03386002779006958, -0.02194569818675518, -0.03768303990364075, -0.01178416796028614, -0.05747661739587784, -0.013545945286750793, -0.008845597505569458, -0.028295358642935753, 0.007923648692667484, -0.05301026999950409, 0.016854984685778618, -0.01985805481672287, -0.0009048692299984396, -0.0020037812646478415, 0.008876160718500614, -0.018609782680869102, 0.019247842952609062, 0.018029673025012016, -0.009320354089140892, -0.05840247496962547, 0.024037232622504234, 0.009723412804305553, -0.03996162489056587, 0.015427203848958015, -0.02986213006079197, -0.045351915061473846, 0.0459757074713707, -0.01673956774175167, 0.020065123215317726, 0.01298657339066267, -0.018955426290631294, 0.027313191443681717, 0.000815928156953305, 0.025731969624757767, 0.019514814019203186, -0.02546703815460205, 0.06615812331438065, -0.04027208313345909, 0.004797026980668306, -0.022006195038557053, -0.006224676501005888, -0.011483496986329556, -0.019636932760477066, 0.0035179562401026487, 0.011113548651337624, -0.0077944728545844555, -0.05756540969014168, -0.020438415929675102, -0.0008163846214301884, 0.009651745669543743, 0.01220516487956047, 0.017685355618596077, -0.040919262915849686, -0.04711059853434563, 0.018406031653285027, 0.059703681617975235, -0.03624171391129494, 0.03717947006225586, 0.009852797724306583, -0.021983003243803978, 0.07700824737548828, -0.02041357196867466, 0.08726294338703156, 0.02305380441248417, -0.04825712740421295, -0.014224318787455559, -0.032611120492219925, 0.03770872578024864, -0.0627836287021637, -0.07616479694843292, -0.010997069999575615, 0.002003022003918886, -0.04570680856704712, 0.026422543451189995, -0.02458970993757248, 0.019191578030586243, -0.007733884733170271, 0.005000536795705557, 0.008047046139836311, -0.036935605108737946, 0.057041801512241364, -0.02353045716881752, -0.02838597632944584, 0.007451002951711416, 0.06520151346921921, -0.010174699127674103, -0.07713957875967026, -0.0525626614689827, -0.033994268625974655, 0.0440216064453125, 0.0023655169643461704, -0.02602154202759266, 0.08165840804576874, 0.04694683477282524, -0.03236692026257515, -0.01383888442069292, 0.0020970352925360203, -0.021917786449193954, -0.08279053866863251, -0.0027926971670240164, -0.01251098234206438, -0.03993961215019226, 0.02004990167915821, 0.05541164427995682, -0.012380770407617092, 0.0010553378378972411, -0.0037396475672721863, 0.04573328047990799, -0.05336078256368637, 0.053810711950063705, -0.03409183770418167, -0.045332908630371094, 0.056291498243808746 ]
<p>What kind of significant impacts have originated from $E=mc^2$.</p> <p>Generally, it is regarded as the most famous equation of all time. Except for nuclear energy (fission and fusion) I do not know any other way in which this equation has made an impact on the world. </p> <p>Can somebody list some developments and impacts based on this equation?</p>
g1531
[ 0.02373756840825081, 0.04350244626402855, -0.006414168514311314, 0.011595964431762695, 0.007687150500714779, -0.004545076750218868, 0.025370657444000244, 0.07110711187124252, 0.02092009037733078, -0.00951689574867487, 0.0028754794038832188, 0.016729440540075302, 0.11374126374721527, 0.04787531495094299, 0.09451840072870255, -0.021975573152303696, 0.030770685523748398, 0.00836713332682848, -0.015000035986304283, 0.08216864615678787, -0.023960333317518234, -0.025195689871907234, 0.006087729707360268, -0.030428584665060043, -0.006819434463977814, -0.02567031979560852, 0.0650813952088356, 0.006203183438628912, -0.0248294398188591, 0.012926374562084675, 0.012361578643321991, -0.022705769166350365, 0.07646757364273071, -0.013956557959318161, -0.10788745433092117, -0.0027699607890099287, 0.01242105569690466, 0.024569271132349968, 0.09460274130105972, -0.030711384490132332, -0.006795957218855619, -0.00861541461199522, -0.012992716394364834, 0.03205089271068573, 0.010375812649726868, -0.004379295744001865, -0.0666472390294075, -0.021336646750569344, -0.03337911516427994, -0.026261700317263603, 0.017850754782557487, -0.023687319830060005, 0.12464667111635208, 0.015073486603796482, -0.02175566740334034, -0.024324335157871246, -0.004914064891636372, -0.015012312680482864, 0.09205023944377899, 0.07182008028030396, -0.005879517644643784, 0.012512384913861752, -0.03214221075177193, -0.017464861273765564, 0.05857035517692566, -0.031228024512529373, -0.033170368522405624, 0.022680943831801414, 0.007286489941179752, 0.024140236899256706, 0.01506887935101986, -0.08069772273302078, 0.01175819244235754, 0.014393332414329052, 0.002885744208469987, -0.020747382193803787, 0.05126771330833435, 0.003546688938513398, 0.008063036948442459, -0.010795393027365208, -0.06075982004404068, -0.007327533792704344, 0.023900650441646576, -0.036186184734106064, 0.0806308165192604, -0.08521437644958496, 0.04566853493452072, 0.07462746649980545, -0.027751531451940536, -0.04662025347352028, 0.0018821241101250052, 0.007851656526327133, -0.04779956489801407, -0.035129934549331665, -0.020642215386033058, -0.05125356838107109, 0.03535206988453865, -0.04471898078918457, 0.021396035328507423, 0.08826135843992233, -0.003899065777659416, -0.08093608170747757, -0.025251461192965508, 0.05669286102056503, 0.03623810037970543, 0.006160118151456118, -0.040376219898462296, 0.00937297660857439, 0.02081676945090294, 0.011027702130377293, -0.047560784965753555, -0.0008260169997811317, -0.00040938466554507613, 0.04065544530749321, -0.06533351540565491, -0.03962722793221474, 0.0165397971868515, -0.019543560221791267, -0.07342302799224854, 0.05444270372390747, 0.07007879763841629, -0.017870482057332993, -0.010439524427056313, -0.009133039973676205, -0.036933913826942444, -0.013455242849886417, -0.006630346179008484, -0.010838531889021397, 0.054062556475400925, -0.029763612896203995, -0.02120419219136238, 0.01507316343486309, 0.028913844376802444, -0.020237049087882042, 0.039185091853141785, 0.03228393942117691, -0.07947733998298645, 0.038296669721603394, 0.022792542353272438, 0.005401928909122944, 0.022210534662008286, -0.04814966395497322, 0.01923903077840805, 0.025065602734684944, -0.10621917992830276, 0.01515435054898262, 0.028623389080166817, -0.011008664965629578, -0.0004016118182335049, 0.009246318601071835, -0.021778466179966927, 0.01311753410845995, -0.04273173585534096, -0.0046210805885493755, -0.024812357500195503, 0.026884861290454865, -0.04452333599328995, -0.030403971672058105, -0.0463855117559433, 0.01972181722521782, -0.020168500021100044, 0.02888358384370804, 0.026066340506076813, -0.009176360443234444, -0.01316280011087656, 0.018172629177570343, 0.07378948479890823, -0.0448664128780365, 0.01110140047967434, 0.04627475142478943, -0.02582576312124729, -0.019319824874401093, 0.028334712609648705, 0.05383141711354256, -0.026572702452540398, -0.015571282245218754, 0.026641104370355606, -0.06117939203977585, 0.012175136245787144, 0.004291366320103407, -0.026665717363357544, -0.005045307334512472, 0.016543911769986153, 0.012761364690959454, 0.023483961820602417, -0.01009874977171421, -0.0026827589608728886, 0.04541989043354988, -0.02094443514943123, 0.03998974710702896, -0.04561144486069679, 0.029913945123553276, 0.009152700193226337, -0.010700025595724583, 0.004794273991137743, 0.018499067053198814, 0.0096260542050004, 0.042607251554727554, -0.022450843825936317, 0.014467736706137657, -0.025608593598008156, 0.03968144208192825, 0.0037008984945714474, 0.031128447502851486, 0.007847370579838753, 0.015599537640810013, 0.028997821733355522, 0.004464115481823683, -0.0073896050453186035, -0.04686427116394043, 0.022411441430449486, -0.002089843852445483, -0.019738435745239258, -0.014592424035072327, 0.004674137104302645, 0.01884506270289421, -0.06188158318400383, 0.028950052335858345, -0.02796807698905468, 0.06004112958908081, -0.05040090158581734, -0.002123217098414898, 0.015699487179517746, 0.020868150517344475, 0.07531367987394333, 0.004319400060921907, -0.04978575184941292, -0.05620327591896057, -0.018926644697785378, -0.047149233520030975, -0.06999225169420242, 0.06575998663902283, 0.014449797570705414, 0.009753530845046043, 0.0008331905701197684, 0.0006046670605428517, -0.005795558914542198, -0.0019255932420492172, 0.05220825597643852, 0.011980039067566395, 0.039172377437353134, -0.018537312746047974, 0.0028381808660924435, -0.018292011693120003, -0.001746509806253016, -0.05375101417303085, 0.047432493418455124, 0.006112088914960623, 0.024882620200514793, -0.019502772018313408, 0.03333297371864319, -0.040455739945173264, -0.08892177045345306, -0.014098160900175571, 0.029629811644554138, -0.011393807828426361, 0.007758688181638718, 0.06462293118238449, -0.07005777955055237, 0.03774293512105942, -0.037296708673238754, 0.029611827805638313, 0.01761181652545929, 0.0168142132461071, 0.008601847104728222, 0.003878055140376091, -0.02903624251484871, 0.01610168255865574, -0.006389659829437733, -0.032529979944229126, -0.00849698856472969, 0.014760983176529408, -0.07500212639570236, 0.021597864106297493, -0.0043909018859267235, -0.0884992927312851, 0.02282150834798813, -0.07616381347179413, 0.023856746032834053, -0.022701717913150787, -0.028067663311958313, -0.03115398995578289, -0.028869252651929855, 0.025537796318531036, 0.011809210292994976, -0.048413436859846115, -0.00013719355047214776, 0.03086257167160511, 0.03809399902820587, -0.01241645310074091, 0.0015794039936736226, -0.009883006103336811, -0.011797287501394749, 0.01751510612666607, -0.004148746840655804, 0.03746970742940903, 0.007042312994599342, -0.04520498216152191, -0.01781255379319191, -0.05045856162905693, 0.031468503177165985, -0.016785556450486183, 0.011887501925230026, 0.01796146295964718, -0.06909970194101334, -0.038254812359809875, 0.030532166361808777, -0.022316914051771164, 0.05122761055827141, 0.008515109308063984, -0.06746510416269302, 0.06473005563020706, -0.007393761537969112, 0.03576507046818733, -0.08588793128728867, 0.0039002415724098682, 0.05908932536840439, 0.016399141401052475, 0.05147403106093407, -0.035619836300611496, -0.011844905093312263, -0.09062747657299042, 0.013264705426990986, -0.03099503181874752, 0.010219627059996128, 0.04006103426218033, -0.007815469056367874, -0.04661869630217552, 0.004649067297577858, 0.03382917121052742, -0.03879806026816368, -0.003346385434269905, -0.014405613765120506, -0.015217423439025879, -0.03792811557650566, -0.020139606669545174, -0.024527352303266525, 0.0275525264441967, 0.023767830803990364, 0.05469411611557007, 0.004244014620780945, -0.08600657433271408, -0.03090139850974083, -0.022020168602466583, 0.0038221972063183784, -0.0268267709761858, -0.02108074352145195, -0.021836359053850174, 0.0026437737978994846, -0.04904872551560402, 0.03694574907422066, -0.01646336540579796, -0.012461771257221699, 0.025237400084733963, 0.03942708671092987, -0.008484389632940292, -0.011503132991492748, 0.022568240761756897, 0.002261687768623233, 0.039942316710948944, -0.04180654138326645, -0.054584112018346786, -0.018115665763616562, 0.04515528306365013, 0.018616046756505966, -0.024906817823648453, -0.006746840197592974, 0.008471544831991196, -0.04429231584072113, -0.037751454859972, 0.022475969046354294, 0.06858925521373749, 0.05176016688346863, 0.012067154049873352, 0.02439628727734089, 0.009021874517202377, -0.011076548136770725, 0.04360010474920273, -0.037452708929777145, 0.016212372109293938, -0.004856047686189413, -0.05650816112756729, 0.005822568666189909, -0.017063355073332787, 0.02142961695790291, -0.08127400279045105, -0.04602638632059097, -0.03392544016242027, -0.005158491898328066, -0.019197028130292892, 0.01741107925772667, -0.05301683768630028, -0.035780590027570724, 0.06316564232110977, 0.03169385343790054, -0.008695906959474087, -0.020762333646416664, -0.01800508238375187, 0.055583663284778595, 0.019656172022223473, 0.009049669839441776, -0.05228210240602493, 0.06937845796346664, 0.002066456712782383, 0.015715906396508217, 0.010332670994102955, 0.06915128976106644, -0.03846464306116104, 0.034054193645715714, -0.041727062314748764, 0.048013944178819656, -0.000045308875996852294, -0.04104873910546303, -0.05537787079811096, 0.020695382729172707, -0.046559445559978485, 0.010433381423354149, -0.04462454840540886, -0.003469676710665226, 0.023198232054710388, 0.03543402999639511, -0.0037283324636518955, -0.05083450675010681, 0.024985529482364655, 0.018152384087443352, 0.01233504805713892, 0.03397205471992493, -0.021542662754654884, -0.003077025758102536, 0.07068932801485062, 0.0011664611520245671, 0.08329999446868896, -0.031883373856544495, 0.006121649872511625, -0.018375281244516373, 0.007669905200600624, 0.009162023663520813, -0.020629115402698517, -0.037298575043678284, 0.03366042673587799, 0.120432049036026, -0.03737422451376915, -0.020353974774479866, 0.05100324749946594, 0.009370074607431889, 0.02964969538152218, -0.0022951362188905478, -0.03958754241466522, -0.004530640318989754, 0.04172306880354881, -0.024003831669688225, -0.04552964121103287, 0.017027609050273895, 0.00921681523323059, -0.0052986182272434235, -0.01701376773416996, -0.010689595714211464, -0.04573986306786537, 0.06430014222860336, 0.05339411273598671, -0.05759098008275032, -0.01650301367044449, 0.001215868047438562, 0.005788260605186224, 0.017658626660704613, -0.06393102556467056, -0.05707475170493126, -0.0066683413460850716, -0.052362602204084396, 0.040868960320949554, 0.00015856687969062477, -0.000032221374567598104, 0.017637845128774643, -0.041073091328144073, -0.002739730989560485, 0.022437775507569313, -0.07669084519147873, -0.029590383172035217, 0.03326357156038284, -0.025094402953982353, -0.008377541787922382, -0.05194418504834175, -0.030455751344561577, 0.006687269080430269, 0.0107047650963068, 0.03825923427939415, -0.04494943469762802, 0.05413390323519707, 0.02641741745173931, -0.05276477336883545, 0.027858160436153412, 0.03740767389535904, 0.004491699393838644, -0.058957815170288086, 0.028407247737050056, 0.015884341672062874, -0.012105991132557392, -0.01767306961119175, 0.04738296940922737, -0.07000462710857391, -0.004333148710429668, 0.06714123487472534, -0.0437692366540432, 0.03237329423427582, -0.01110779494047165, -0.013528317213058472, 0.07695920765399933, -0.02430654875934124, 0.030178319662809372, 0.0540730357170105, 0.01565392315387726, -0.042523130774497986, 0.022500064224004745, -0.04025857523083687, 0.02869458682835102, 0.008328578434884548, -0.051410574465990067, -0.004557181149721146, 0.06414103507995605, -0.03480539843440056, 0.011191724799573421, -0.048515453934669495, 0.06720633059740067, 0.01031502801924944, 0.02821383811533451, -0.03954216092824936, -0.036832649260759354, -0.017090415582060814, 0.03806338459253311, -0.005970225669443607, -0.023927804082632065, -0.04290560260415077, -0.008699645288288593, -0.014916332438588142, 0.028412362560629845, -0.009005667641758919, -0.013775686733424664, -0.0013565024128183722, 0.03220866620540619, -0.019103605300188065, 0.023525437340140343, -0.01266233529895544, 0.04491424933075905, 0.010824811644852161, 0.008002430200576782, 0.029733680188655853, 0.02203092724084854, 0.017937134951353073, 0.006462789140641689, -0.04388248547911644, -0.003544594394043088, 0.010600653477013111, 0.07818394899368286, -0.01238428894430399, 0.03860354796051979, 0.021138211712241173, 0.025740360841155052, 0.03950214385986328, 0.0029632465448230505, -0.023277265951037407, -0.017904596403241158, 0.03267347812652588, 0.017643390223383904, 0.023199412971735, -0.020922617986798286, -0.05885162204504013, 0.03691050037741661, 0.005839251913130283, 0.03164657950401306, 0.07526349276304245, 0.02901952713727951, 0.020871903747320175, 0.05207138881087303, 0.004778323695063591, 0.028566181659698486, 0.020686933770775795, -0.02500195987522602, -0.0003003337769769132, 0.009104958735406399, 0.00458769453689456, 0.01809230074286461, -0.020011693239212036, -0.005739880725741386, -0.020227845758199692, -0.023250672966241837, -0.011758009903132915, 0.022081568837165833, 0.011760389432311058, 0.011391662992537022, -0.026313472539186478, 0.046900514513254166, 0.027831459417939186, -0.022153789177536964, -0.05032297596335411, -0.031137768179178238, -0.05044190585613251, -0.009659548290073872, 0.029617635533213615, 0.0420326367020607, -0.0005936482339166105, -0.002880011685192585, 0.027696242555975914, -0.014441578648984432, -0.002981215715408325, 0.05592147260904312, -0.02584218792617321, -0.07500117272138596, 0.005557318218052387, -0.011177673935890198, 0.025646114721894264, -0.051225561648607254, -0.0028628595173358917, 0.02328830026090145, -0.0032969187013804913, -0.033783357590436935, -0.0419958271086216, -0.006456876173615456, -0.01004828792065382, -0.0023983700666576624, -0.022565556690096855, -0.057691339403390884, -0.03893149644136429, -0.010960237123072147, -0.05080130323767662, 0.022739268839359283, 0.01898912526667118, 0.03116489015519619, -0.01798437349498272, 0.02755768410861492, -0.05327662453055382, 0.0036749092396348715, 0.0501323938369751, 0.05766340345144272, 0.040347225964069366, -0.03806106001138687, -0.002809143392369151, -0.0026838111225515604, -0.0053591313771903515, -0.005116892978549004, 0.02535172924399376, -0.028271902352571487, 0.010285565629601479, -0.01544265914708376, -0.03535778447985649, -0.035933658480644226, 0.016890229657292366, 0.05141837149858475, 0.007086816243827343, -0.08936933428049088, 0.023164208978414536, -0.040721628814935684, -0.035777539014816284, 0.030695032328367233, 0.006333652418106794, 0.03085523098707199, -0.005364684388041496, -0.0136756282299757, 0.0029880311340093613, 0.05681484937667847, -0.047245092689991, -0.0033771481830626726, 0.029610835015773773, 0.03138335049152374, -0.006702815648168325, -0.0045392271131277084, 0.0032373694702982903, 0.029019564390182495, -0.08172475546598434, 0.03701794147491455, 0.013638697564601898, 0.015719283372163773, -0.05145510286092758, -0.07001349329948425, -0.028086839243769646, -0.048222459852695465, -0.003218140220269561, -0.05325082316994667, -0.003556744661182165, -0.02851574495434761, 0.0419643335044384, 0.037768784910440445, 0.041669685393571854, -0.003913543652743101, -0.09092099219560623, -0.039407022297382355, 0.04130800440907478, -0.04763193428516388, 0.03728039190173149, -0.020935844630002975, 0.053296130150556564, -0.024638600647449493, 0.002546885749325156, 0.01656290702521801, -0.03754780814051628, 0.03081434965133667, 0.023759372532367706, -0.04785282164812088, 0.09496132284402847, -0.019278045743703842, 0.033647939562797546, 0.020618755370378494, -0.04292326793074608, -0.010213153436779976, -0.02968098782002926, 0.009997020475566387, 0.05333489179611206, 0.030485471710562706, 0.02293446473777294, -0.05315522104501724, -0.008234306238591671, -0.024995988234877586, -0.0005818022764287889, 0.03833040967583656, -0.00480447756126523, 0.0060822563245892525, 0.0050060641951859, -0.0022651709150522947, 0.018013177439570427, 0.013041992671787739, 0.05593062564730644, 0.03031947650015354, 0.051956381648778915, -0.04989062622189522, -0.04299697279930115, -0.026266252622008324, -0.0482107475399971, -0.0331888347864151, -0.022410636767745018, -0.02456299215555191, 0.02651064842939377, 0.04183341935276985, 0.028394421562552452, 0.01008665468543768, 0.0627780482172966, 0.004009098745882511, -0.000964236562140286, 0.009854655712842941, 0.045479338616132736, -0.035474423319101334, 0.0009364320430904627, 0.012079425156116486, -0.04654404893517494, -0.03389003872871399, -0.004957737401127815, -0.017810756340622902, -0.00829168688505888, -0.03082520328462124, 0.0727669820189476, 0.011436183005571365, 0.014619690366089344, 0.027147630229592323, 0.01592201739549637, -0.026741590350866318, 0.04408172145485878, 0.07516264170408249, -0.04539190232753754, 0.011014055460691452, 0.023206213489174843, -0.022634074091911316, -0.028583835810422897, 0.00985206849873066, 0.012167135253548622, -0.01554917637258768, -0.00782011542469263, -0.002222406445071101, -0.05328594148159027, -0.02723182551562786, 0.026601679623126984 ]
<p>The process of exchange of energy between a photon and an electron only occur after a specific energy called work-function of the material. Thus, the energy transferred is quantised due to the fact that the electron can reside only in quantised orbits. </p> <p>But, why doesn't the process happen in steps? I mean the electron getting excited to a higher orbit and before the electron gets de-excited another photon gives it energy to escape from the metal. Is it theoretically possible?</p>
g1532
[ 0.017167558893561363, 0.043676119297742844, -0.0015042753657326102, 0.018868012353777885, 0.06549722701311111, -0.002613009652122855, 0.002083347411826253, 0.03755815699696541, -0.027179941534996033, 0.009448044002056122, -0.013675512745976448, 0.04354988783597946, 0.009582273662090302, -0.05488454923033714, -0.0009081278694793582, -0.010060497559607029, 0.028852222487330437, -0.0006211717263795435, 0.04683926701545715, 0.06304992735385895, -0.01422192808240652, 0.011701332405209541, 0.024656066671013832, -0.04263368621468544, -0.032247647643089294, 0.010038506239652634, -0.009864557534456253, -0.04640936106443405, 0.02597011812031269, -0.007645351346582174, 0.0016554429894313216, -0.03306027874350548, 0.057626090943813324, -0.036123838275671005, -0.031215762719511986, -0.034139618277549744, 0.04150707274675369, 0.029725955799221992, 0.03043905645608902, 0.0198358241468668, -0.001041698851622641, -0.050322141498327255, -0.003595881862565875, -0.01230692956596613, 0.03638973832130432, -0.02687973342835903, 0.03112867660820484, -0.03793757036328316, -0.0008228198275901377, -0.04071930795907974, 0.023137666285037994, 0.06679404526948929, 0.061502717435359955, 0.023579759523272514, 0.07168389111757278, 0.003610435873270035, 0.006554223597049713, -0.01712666265666485, 0.09230154007673264, -0.012464925646781921, 0.02467512898147106, 0.02122742310166359, 0.04649408906698227, 0.051228731870651245, 0.03913802653551102, 0.030243903398513794, -0.041468337178230286, -0.022530129179358482, 0.026284251362085342, -0.0009353485074825585, 0.02308513969182968, -0.0071759833954274654, -0.03687787428498268, 0.002160770818591118, 0.07355410605669022, -0.02974877506494522, 0.005980572663247585, -0.03460448607802391, -0.0030094606336206198, -0.015896061435341835, -0.053680017590522766, -0.007464039139449596, 0.008073168806731701, -0.0003904018667526543, -0.007962857373058796, 0.020237984135746956, 0.0054574222303926945, -0.02654235064983368, -0.03842736408114433, 0.0021052430383861065, 0.042930182069540024, -0.025741754099726677, 0.05897141993045807, 0.027339419350028038, -0.06363798677921295, 0.018982404842972755, -0.05251879245042801, 0.07269613444805145, -0.03908899053931236, -0.03571930155158043, -0.028432250022888184, -0.07286327332258224, 0.006947382818907499, -0.015983402729034424, 0.0327230766415596, -0.06119715794920921, -0.045990049839019775, -0.022156693041324615, 0.027099210768938065, 0.07287713885307312, -0.013530616648495197, 0.012249797582626343, -0.06682436913251877, -0.021935660392045975, 0.023354588076472282, 0.053245410323143005, 0.0655764490365982, -0.03349260613322258, -0.057692404836416245, 0.017203297466039658, 0.012431243434548378, -0.0212447140365839, -0.00480102701112628, 0.013070614077150822, 0.016691410914063454, -0.003770506475120783, -0.008343935944139957, -0.010814842768013477, 0.021799521520733833, -0.009732423350214958, 0.03409323841333389, 0.02124880440533161, -0.03234409540891647, 0.04781562462449074, 0.027356479316949844, 0.00028073182329535484, 0.0415603406727314, 0.014674094505608082, -0.019635984674096107, -0.01747882179915905, 0.014825327321887016, -0.047769609838724136, -0.041046272963285446, -0.019433343783020973, -0.04366005212068558, 0.03611430153250694, -0.04281416907906532, 0.030643587931990623, 0.01278554368764162, 0.01838592439889908, -0.008985786698758602, 0.04277884215116501, 0.030456963926553726, -0.027405530214309692, 0.05424133315682411, -0.04052295908331871, 0.06319709867238998, -0.030800122767686844, 0.00985716562718153, 0.0035201043356209993, 0.06937709450721741, -0.03675656020641327, -0.005338536109775305, -0.03980478644371033, -0.03152989223599434, 0.004814149346202612, 0.006553418468683958, -0.05711906775832176, 0.010590741410851479, -0.06628430634737015, 0.015075269155204296, -0.053120534867048264, -0.0368158295750618, 0.03916974365711212, -0.026200970634818077, 0.09098643064498901, -0.003965811338275671, 0.014735461212694645, -0.03390287235379219, -0.005652269348502159, -0.014094109646975994, -0.04617338627576828, 0.03731417655944824, -0.0405547209084034, 0.0748237818479538, -0.005715533159673214, -0.004621079191565514, 0.019327620044350624, -0.017744889482855797, 0.0287124402821064, 0.0057241967879235744, 0.025471540167927742, 0.05482878163456917, -0.05749620497226715, -0.02008931338787079, -0.0009110370883718133, -0.021642068400979042, -0.024182675406336784, -0.004756387788802385, -0.040027301758527756, 0.022752057760953903, 0.055753130465745926, -0.016831059008836746, -0.009694032371044159, 0.07602420449256897, 0.012325025163590908, -0.03816431015729904, 0.00969566497951746, 0.007464647758752108, -0.01875174790620804, 0.05827067047357559, 0.00922432728111744, -0.0045910305343568325, -0.01950209215283394, -0.01903340592980385, 0.007764908485114574, 0.00369637506082654, -0.018129801377654076, 0.0326712429523468, 0.013337446376681328, 0.011015570722520351, 0.002556721679866314, 0.03203543648123741, 0.044214993715286255, -0.021029694005846977, 0.005679421592503786, -0.004709929693490267, -0.022418439388275146, -0.03697539493441582, 0.012296954169869423, -0.07854939997196198, 0.044947948306798935, -0.030496492981910706, -0.03610525652766228, 0.0006180151831358671, 0.01869112253189087, -0.014363976195454597, 0.015736136585474014, -0.007285841275006533, 0.03258105367422104, 0.0379997082054615, -0.006337518338114023, -0.022556250914931297, -0.011003023013472557, -0.02055804245173931, -0.072346530854702, 0.01838773488998413, 0.024271957576274872, -0.035296808928251266, -0.028893552720546722, 0.06675882637500763, -0.053772781044244766, -0.03890316188335419, -0.03931928798556328, -0.05157005786895752, -0.0704074278473854, -0.036045998334884644, 0.027162974700331688, -0.03817083686590195, -0.03519639000296593, -0.03169103339314461, -0.0026285056956112385, 0.02615394815802574, -0.033978819847106934, -0.012978794984519482, -0.014901554211974144, -0.02855188213288784, -0.01561603881418705, -0.025263965129852295, -0.043692316859960556, -0.06632281094789505, 0.05582621321082115, -0.010467284359037876, 0.021560560911893845, -0.0265868678689003, -0.007781956344842911, -0.0030432757921516895, -0.012685186229646206, 0.03590622916817665, -0.04724947363138199, -0.08482149243354797, -0.014793505892157555, -0.04032748565077782, -0.011470936238765717, -0.007824649102985859, -0.027206238359212875, -0.023114677518606186, 0.028754092752933502, 0.05773989483714104, -0.08456708490848541, -0.04499494656920433, -0.024952726438641548, 0.03315183147788048, 0.018962720409035683, -0.06296327710151672, 0.03237972408533096, 0.060137368738651276, -0.016114063560962677, -0.0716756209731102, 0.06539741158485413, -0.0028421974275261164, -0.019929222762584686, -0.04855268448591232, -0.011473762802779675, 0.06394357979297638, 0.012343522161245346, -0.02841549925506115, 0.01017893198877573, -0.04723493754863739, -0.04307325929403305, 0.023189527913928032, 0.048329055309295654, -0.0055228956043720245, 0.02101464942097664, -0.05586088076233864, -0.034248922020196915, -0.032764919102191925, -0.01690572313964367, 0.027861494570970535, -0.01891314424574375, -0.041401445865631104, -0.0100959911942482, -0.013112439773976803, -0.015233159065246582, 0.02963637374341488, 0.013451777398586273, -0.05514713004231453, -0.0659329816699028, -0.008924206718802452, 0.021453915163874626, 0.0359475240111351, 0.033614154905080795, -0.04322471097111702, -0.0024423860013484955, -0.025397738441824913, -0.05119618773460388, -0.012712727300822735, 0.035789310932159424, 0.007212918717414141, 0.043270599097013474, -0.0049781580455601215, 0.020290585234761238, -0.03163330629467964, 0.04284147918224335, 0.06653232127428055, -0.014882064424455166, 0.02540515922009945, -0.000880889652762562, 0.012975416146218777, -0.010995449498295784, 0.01947745680809021, -0.03132101893424988, 0.002604446606710553, -0.003471111413091421, -0.03541714325547218, 0.030275681987404823, 0.0032144207507371902, 0.04607550799846649, 0.07838906347751617, -0.05653410777449608, -0.013852654956281185, -0.024560073390603065, 0.09225466847419739, -0.03182661533355713, -0.01838654838502407, 0.025998584926128387, -0.007110590115189552, 0.02203749120235443, 0.015724601224064827, -0.017145462334156036, 0.0049347770400345325, -0.04656122624874115, -0.028838176280260086, -0.028496868908405304, 0.0757816955447197, -0.056549400091171265, 0.04143386706709862, 0.02056056633591652, -0.04690355435013771, 0.00977342389523983, -0.038598354905843735, -0.022983834147453308, 0.04583144560456276, 0.0034639674704521894, 0.020873039960861206, 0.050733037292957306, -0.059322115033864975, -0.0051774694584310055, -0.012719962745904922, -0.012860962189733982, 0.04850279912352562, -0.010789329186081886, 0.004766884259879589, 0.010100486688315868, -0.0015706318663433194, -0.014752251096069813, 0.02518555149435997, -0.07398245483636856, 0.042756304144859314, 0.019370215013623238, 0.013342327438294888, 0.0038978930097073317, -0.06586349755525589, 0.010889346711337566, 0.01698470115661621, 0.02319147251546383, 0.06451188772916794, -0.017655011266469955, -0.018615471199154854, -0.027009734883904457, -0.040833014994859695, 0.007967428304255009, 0.019825506955385208, 0.023863278329372406, 0.0032901018857955933, 0.003216023789718747, -0.02566058747470379, 0.012999390251934528, -0.03244291990995407, 0.025392722338438034, -0.05287950113415718, 0.044060274958610535, 0.06410802155733109, 0.04181985557079315, -0.01858774945139885, 0.06541728228330612, 0.009866836480796337, -0.001670575002208352, 0.015607599169015884, -0.034804876893758774, 0.05232764035463333, 0.030241360887885094, 0.019291125237941742, -0.016969092190265656, -0.07513746619224548, 0.06644853204488754, -0.017950095236301422, 0.08541291207075119, -0.03321443498134613, 0.10356787592172623, 0.11811747401952744, 0.037625983357429504, -0.021468982100486755, 0.040769897401332855, 0.046653248369693756, -0.001993756042793393, -0.019521217793226242, -0.011957577429711819, 0.0035232817754149437, -0.07106425613164902, -0.03723074868321419, -0.0027612075209617615, -0.07056859135627747, -0.0005185132613405585, 0.06220860406756401, -0.04748659208416939, -0.024933021515607834, -0.030844470486044884, 0.01993461884558201, 0.06346849352121353, -0.02318521961569786, 0.020146099850535393, 0.015702413395047188, 0.04771086946129799, -0.04680830240249634, 0.004162161611020565, -0.07387679815292358, 0.03683946281671524, -0.018834279850125313, 0.018868574872612953, -0.007705186028033495, 0.0257048849016428, 0.017805393785238266, 0.038713134825229645, 0.019796662032604218, -0.032568152993917465, -0.0512772761285305, -0.04329927638173103, 0.04780314117670059, 0.015522914007306099, 0.013763499446213245, 0.020285017788410187, 0.02502783201634884, 0.01570896990597248, -0.039592206478118896, 0.016429640352725983, -0.06508480757474899, 0.021039824932813644, 0.016038237139582634, -0.06341453641653061, 0.022533679381012917, -0.0020035100169479847, -0.029008138924837112, -0.00988058652728796, 0.021023981273174286, 0.01981610432267189, 0.020698266103863716, 0.04011191055178642, 0.026397714391350746, 0.016049137338995934, -0.06303219497203827, 0.00846737902611494, -0.11015757918357849, -0.010408422909677029, 0.031543973833322525, -0.01122811809182167, 0.04466467350721359, -0.020815476775169373, -0.05162365362048149, -0.03350784629583359, -0.022602209821343422, 0.006222811993211508, -0.04876402020454407, 0.03889741003513336, 0.023169301450252533, 0.0037770068738609552, 0.02023700624704361, -0.03299509733915329, 0.002720791380852461, -0.04590989276766777, -0.013238085433840752, 0.009033619426190853, -0.0019706967286765575, -0.05276035517454147, 0.07147085666656494, 0.010126080363988876, -0.048385098576545715, -0.03388986736536026, 0.02246958017349243, 0.02277304418385029, 0.01783783733844757, -0.015959804877638817, -0.012057594954967499, 0.0703410729765892, -0.016036756336688995, -0.04207080230116844, 0.04735637828707695, -0.003557930001989007, -0.03214254602789879, 0.06843587011098862, 0.013316506519913673, -0.05558924004435539, 0.05226432904601097, 0.081187404692173, 0.03176448121666908, -0.03919123113155365, 0.004023796878755093, 0.030435098335146904, 0.005193606484681368, -0.04824100807309151, 0.03509945422410965, -0.015018937177956104, 0.009707823395729065, -0.014978168532252312, 0.010240769013762474, 0.04558641090989113, 0.023418400436639786, -0.033737875521183014, -0.009010298177599907, -0.023750968277454376, 0.0771845355629921, 0.029255332425236702, 0.031136687844991684, 0.030901851132512093, 0.05699459835886955, -0.016931794583797455, -0.018948804587125778, 0.01270625926554203, 0.0021342861000448465, 0.03319002687931061, 0.03799954056739807, 0.010231182910501957, -0.022751525044441223, 0.00022868625819683075, -0.030292928218841553, 0.04061325639486313, -0.029187120497226715, -0.039078302681446075, -0.06017610803246498, -0.03049394302070141, 0.020978331565856934, 0.05637815222144127, -0.019885744899511337, 0.0201755091547966, -0.06397023051977158, 0.041849832981824875, 0.004719981923699379, -0.002123780082911253, 0.03545823693275452, 0.015960320830345154, -0.054637983441352844, 0.014595850370824337, 0.02412087842822075, -0.046224646270275116, -0.001516795251518488, -0.02268025279045105, -0.0024459874257445335, -0.004021254368126392, -0.0006574048311449587, 0.08443862944841385, -0.0028007018845528364, -0.021564563736319542, -0.013822329230606556, -0.035709310322999954, 0.023855464532971382, 0.021261343732476234, 0.013745523989200592, 0.026357438415288925, 0.04213828220963478, 0.04371156543493271, -0.021910449489951134, -0.027751322835683823, -0.0008902093395590782, -0.010630721226334572, -0.015678105875849724, -0.03839818760752678, 0.012877975590527058, 0.04013865441083908, 0.06347344815731049, 0.0025848925579339266, -0.002503409516066313, -0.01395012903958559, 0.039458464831113815, -0.029414664953947067, 0.03210318461060524, 0.04524116590619087, -0.08316357433795929, 0.046280257403850555, 0.06355325877666473, 0.007963293232023716, -0.03864113241434097, 0.047852858901023865, -0.04878998547792435, 0.037859730422496796, -0.01655396819114685, 0.046816859394311905, -0.012503042817115784, -0.06800214946269989, 0.030853213742375374, -0.04345877096056938, -0.03810093551874161, -0.008440949022769928, 0.09211135655641556, 0.03728516027331352, -0.02063179388642311, 0.032643675804138184, 0.0024416763335466385, 0.01774774119257927, -0.034523725509643555, 0.015283819288015366, -0.004788321442902088, -0.047531209886074066, -0.020436903461813927, -0.010175470262765884, 0.010939763858914375, 0.010474532842636108, -0.03139694407582283, 0.04148295149207115, 0.006796928588300943, -0.03661331534385681, 0.021499553695321083, -0.045619938522577286, -0.02299109846353531, 0.018023362383246422, 0.06818848103284836, 0.02332698553800583, 0.02596820704638958, -0.052500490099191666, -0.019023390486836433, -0.06883316487073898, -0.04308750107884407, -0.030125116929411888, -0.02373478002846241, 0.028312580659985542, -0.03276778385043144, 0.031238382682204247, 0.014736268669366837, 0.07262618839740753, -0.04006243124604225, 0.003671714337542653, -0.013642502948641777, -0.034800272434949875, 0.006695083808153868, -0.017688171938061714, 0.0011222719913348556, -0.03511534258723259, -0.02006681263446808, 0.02184183895587921, -0.016837596893310547, 0.05235912278294563, -0.011180290952324867, -0.0005132099031470716, 0.059178758412599564, 0.00523590762168169, 0.004905681125819683, 0.06750982254743576, 0.02434476651251316, -0.05231872573494911, 0.028702586889266968, 0.044007085263729095, 0.03282887116074562, -0.025443382561206818, 0.0032235521357506514, 0.006469548214226961, -0.00034704903373494744, 0.011800132691860199, 0.023762425407767296, -0.026898996904492378, -0.05039051175117493, 0.0046895346604287624, 0.0558590292930603, 0.024222495034337044, -0.059821657836437225, 0.04104321449995041, -0.00029122125124558806, -0.02808164805173874, -0.0600554533302784, 0.07892182469367981, 0.018501412123441696, 0.018821340054273605, -0.010809540748596191, 0.023844419047236443, -0.03960540145635605, -0.05417288467288017, 0.007542613428086042, 0.0001706839830148965, 0.0011670304229483008, -0.06205221638083458, -0.007768395356833935, -0.01916654035449028, 0.05222576484084129, 0.010642747394740582, -0.023644959554076195, -0.05475135147571564, -0.006015774328261614, -0.02098066546022892, 0.0028592643793672323, -0.0546867772936821, 0.016905246302485466, 0.00041794340359047055, 0.040636878460645676, -0.012400267645716667, 0.004235829226672649, -0.01975933276116848, 0.006236220709979534, -0.02026420272886753, -0.019013457000255585, 0.00433714222162962, 0.01082207914441824, -0.04378674924373627, -0.030298789963126183, 0.038570307195186615, -0.05369141325354576, 0.03098275139927864, 0.11172705143690109, -0.014195183292031288, -0.013156235218048096, 0.014938030391931534, -0.017595477402210236, 0.024085571989417076, -0.044956274330616, 0.006880815140902996, -0.06268057227134705, -0.05291218310594559, -0.01192608941346407, -0.042282551527023315, -0.017303232103586197, 0.037505775690078735 ]
<p>Why is electron presented in books, pictures as a sphere, when in fact it's not?</p>
g1533
[ 0.014657057821750641, 0.031775619834661484, 0.004768473096191883, -0.03911852464079857, 0.05475744232535362, 0.0458870530128479, -0.004149820189923048, 0.0095795514062047, 0.02115624025464058, 0.016334347426891327, 0.0642370656132698, 0.026883572340011597, 0.06352215260267258, 0.028967274352908134, -0.017795654013752937, -0.05600600689649582, 0.017268231138586998, -0.02581569366157055, 0.03383803740143776, 0.03543589264154434, 0.00985789205878973, 0.005790615454316139, 0.03928446024656296, 0.009836899116635323, -0.022431248798966408, 0.03574759513139725, -0.016292184591293335, -0.05436687171459198, 0.05417560040950775, 0.017081836238503456, 0.017181143164634705, -0.0011621161829680204, 0.014393983408808708, 0.0095760403200984, -0.018517836928367615, -0.04045592248439789, 0.02851785533130169, 0.04482662305235863, 0.011743826791644096, -0.011653137393295765, 0.003382378024980426, -0.06057453155517578, -0.044891808182001114, 0.028335560113191605, -0.019567986950278282, 0.023431943729519844, 0.001536123687401414, 0.03090752847492695, 0.003192487871274352, -0.011373981833457947, 0.020908283069729805, 0.030401328578591347, 0.027951577678322792, 0.012780316174030304, 0.09858708083629608, -0.03610944747924805, -0.009084869176149368, 0.040902525186538696, 0.08293591439723969, 0.023179728537797928, -0.006857665255665779, 0.05018658936023712, -0.005064059980213642, 0.040024284273386, 0.04613559693098068, 0.006637711077928543, -0.08303479105234146, 0.034024033695459366, -0.021438878029584885, 0.0187356136739254, 0.026094455271959305, -0.12237685918807983, -0.009805133566260338, -0.005864695180207491, 0.008671348914504051, -0.011438678950071335, -0.03966667130589485, 0.004876295570284128, 0.051654014736413956, 0.00794134009629488, 0.021209407597780228, 0.019857458770275116, -0.004127058200538158, 0.024141309782862663, 0.1054033562541008, 0.029197415336966515, -0.02087206207215786, -0.05163278430700302, -0.019557446241378784, -0.04618129879236221, 0.058398690074682236, -0.028755495324730873, 0.03585940971970558, -0.002995592774823308, -0.041349008679389954, -0.033360160887241364, -0.037483181804418564, -0.014039919711649418, -0.017598530277609825, 0.07647918909788132, -0.051605261862277985, -0.03883027657866478, 0.012089344672858715, 0.04202061519026756, -0.02141636051237583, 0.0017068202141672373, -0.020132925361394882, -0.03850904479622841, 0.04112273082137108, -0.029437657445669174, -0.016881253570318222, -0.03367297723889351, -0.037232883274555206, -0.007503226399421692, -0.0387115553021431, 0.012520254589617252, 0.0893758088350296, -0.004471499007195234, 0.016499526798725128, 0.050653230398893356, 0.04153350368142128, 0.011204554699361324, 0.05845412239432335, 0.021385345607995987, -0.048248689621686935, -0.03610721603035927, 0.05226302891969681, -0.035686884075403214, 0.04297785833477974, -0.07772736996412277, -0.01631600223481655, 0.00552665488794446, -0.05368984118103981, 0.03742685168981552, 0.00513598183169961, 0.07299495488405228, -0.030211346223950386, -0.029893046244978905, 0.008075305260717869, 0.017289521172642708, 0.0012186473468318582, 0.006914204452186823, -0.007660985924303532, -0.051442451775074005, -0.0016492779832333326, 0.00225803442299366, -0.0055105797946453094, -0.030538570135831833, 0.02263249084353447, 0.0285896398127079, -0.02492855116724968, 0.06597138196229935, 0.04912562668323517, -0.011277629062533379, -0.00044772509136237204, -0.06382371485233307, 0.092678502202034, 0.006542386021465063, 0.032305892556905746, 0.022748781368136406, 0.03105073608458042, -0.00652574235573411, -0.05028470978140831, 0.00946133118122816, -0.047541067004203796, 0.01008656807243824, -0.00685218395665288, -0.051588162779808044, 0.01069204043596983, -0.08687057346105576, -0.0075156609527766705, 0.010933224111795425, -0.0024428695905953646, 0.05222154036164284, -0.033511314541101456, 0.0012521117459982634, 0.008166973479092121, -0.0044455332681536674, 0.023791251704096794, 0.00878943596035242, -0.017594095319509506, -0.03906894102692604, 0.048060692846775055, 0.00026020314544439316, -0.003410118166357279, 0.023745940998196602, 0.006263309624046087, 0.06086588650941849, 0.005900758318603039, 0.03877852484583855, -0.018604835495352745, -0.031559985131025314, 0.0062929666601121426, 0.03928910195827484, 0.0031196584459394217, -0.025682568550109863, 0.021923013031482697, -0.019907046109437943, -0.08722595125436783, 0.03443905711174011, -0.008756052702665329, 0.05207085236907005, -0.026723679155111313, 0.04331032559275627, 0.0050614504143595695, -0.02310778759419918, -0.0522141270339489, -0.027380289509892464, 0.032303616404533386, -0.01559342909604311, 0.026913758367300034, 0.01991782896220684, -0.01197933591902256, 0.026787664741277695, -0.005695404019206762, -0.030830202624201775, -0.008181340992450714, -0.02389947511255741, -0.04394078627228737, 0.0017339251935482025, -0.05624166876077652, -0.0367257185280323, 0.0017983440775424242, -0.04106973484158516, 0.04900113493204117, 0.030933406203985214, -0.019347388297319412, -0.0223834365606308, -0.026173025369644165, 0.016021115705370903, -0.09023553878068924, -0.023835744708776474, 0.0016814101254567504, 0.0054513802751898766, 0.013288088142871857, -0.026594020426273346, -0.028840351849794388, -0.029375916346907616, 0.008924647234380245, -0.03368644416332245, -0.0065561262890696526, 0.0020699722226709127, 0.00809424091130495, -0.037717435508966446, 0.04698360711336136, -0.007762848865240812, 0.03455055505037308, -0.036122456192970276, -0.036970678716897964, 0.012308556586503983, -0.010111518204212189, -0.04347784072160721, -0.06550263613462448, 0.05953557416796684, 0.021129194647073746, 0.03588221222162247, -0.04711019620299339, -0.017924362793564796, -0.013408888131380081, 0.0032303098123520613, -0.04354919120669365, -0.027044234797358513, 0.03681466728448868, -0.026195254176855087, -0.070027194917202, -0.05322432145476341, 0.006092417053878307, 0.021505841985344887, 0.05759843438863754, -0.030179891735315323, -0.052194494754076004, 0.06481079012155533, -0.04069705307483673, -0.04025288298726082, -0.008653043769299984, -0.03440365195274353, -0.015683574602007866, 0.014951697550714016, -0.0014404685935005546, -0.040635041892528534, -0.0062113674357533455, 0.02469519153237343, -0.006321896333247423, 0.025183284655213356, 0.034949012100696564, -0.025039367377758026, -0.025331901386380196, 0.011925037950277328, 0.011082570068538189, -0.04802060127258301, -0.029059456661343575, -0.03353893756866455, 0.0026428597047924995, -0.014132410287857056, -0.004535140935331583, 0.018052471801638603, 0.07984770834445953, 0.016710106283426285, -0.03370269387960434, -0.024954089894890785, -0.0113666458055377, 0.011214219033718109, 0.0041830469854176044, 0.08004813641309738, 0.04048462584614754, -0.010033243335783482, -0.015889916568994522, -0.052149832248687744, -0.04598570987582207, -0.034813616424798965, 0.03883397579193115, -0.006729358807206154, -0.039066508412361145, 0.06638438999652863, -0.040694836527109146, 0.017534861341118813, -0.03647018224000931, 0.025612127035856247, 0.03633135184645653, 0.007103873882442713, -0.06424266844987869, 0.02524791657924652, 0.03967871889472008, -0.017331156879663467, 0.0041947499848902225, 0.037223443388938904, -0.00840820837765932, -0.029296429827809334, 0.052078720182180405, -0.013023764826357365, 0.02260805107653141, -0.02426593191921711, 0.0171422827988863, -0.014686188660562038, -0.04584187641739845, -0.04183502495288849, -0.05757378041744232, 0.035498108714818954, 0.04064420983195305, -0.015827681869268417, -0.00651771854609251, -0.0017458578804507852, -0.06268972903490067, 0.006028627976775169, 0.061136625707149506, 0.007674155756831169, -0.10788217186927795, -0.09618993103504181, 0.016346924006938934, -0.037911806255578995, 0.03415091708302498, 0.09475351125001907, 0.02861621417105198, 0.028477080166339874, 0.008259812369942665, -0.005599603056907654, 0.006791479419916868, -0.001830770750530064, -0.022364793345332146, -0.053140584379434586, 0.005793616641312838, 0.01217973604798317, 0.024696489796042442, -0.029231654480099678, -0.018114201724529266, 0.00676771393045783, 0.008286467753350735, 0.09820307791233063, -0.008717612363398075, -0.033945001661777496, -0.03811423480510712, -0.018384691327810287, 0.006667437497526407, 0.050300661474466324, 0.050629258155822754, -0.06043347343802452, -0.049220010638237, 0.0574028417468071, -0.0430416576564312, -0.0755479633808136, 0.020469294860959053, -0.04496961086988449, 0.01804497465491295, -0.006664308253675699, 0.047359105199575424, -0.01093591284006834, 0.01659201830625534, -0.008470064960420132, -0.009264534339308739, -0.024522582069039345, -0.005106447730213404, 0.002466018544510007, -0.0178131852298975, 0.03675417974591255, -0.025171581655740738, -0.0037162303924560547, 0.06466981768608093, -0.05273525416851044, 0.0612785629928112, 0.019420763477683067, 0.004859624896198511, -0.03245134279131889, 0.024673765525221825, -0.019470900297164917, 0.014032289385795593, 0.02423601597547531, 0.042081620544195175, -0.03515060245990753, 0.02803855761885643, -0.031132366508245468, 0.021448614075779915, 0.054371174424886703, -0.01364203542470932, -0.034544456750154495, 0.0004785957280546427, -0.004739202558994293, -0.020358102396130562, -0.01951136812567711, -0.06008012220263481, -0.013590780086815357, -0.006064246874302626, 0.054261598736047745, -0.010563855990767479, 0.004717590287327766, 0.007214829325675964, 0.06404539942741394, -0.0010698596015572548, 0.0051271081902086735, -0.027558283880352974, 0.011356210336089134, 0.016130125150084496, 0.0018846056191250682, 0.024247897788882256, 0.02986433357000351, -0.017963245511054993, -0.01834111288189888, -0.033535368740558624, 0.03881792351603508, -0.002911651972681284, 0.05055316537618637, 0.08252447098493576, -0.05435803160071373, 0.06741505861282349, 0.001110220910049975, 0.013545196503400803, -0.004618728533387184, -0.04784464091062546, 0.052294906228780746, -0.05601274222135544, 0.025805747136473656, 0.015091659501194954, -0.06024269759654999, -0.006556638050824404, 0.04710542410612106, -0.017130881547927856, -0.04552574083209038, -0.032244570553302765, -0.016063548624515533, -0.027912992984056473, -0.019532546401023865, -0.07458057999610901, -0.01860102452337742, -0.042985595762729645, 0.06308261305093765, -0.018777919933199883, 0.025056054815649986, -0.0972578376531601, -0.0030873704236000776, -0.020969614386558533, -0.031199665740132332, 0.04212768375873566, 0.027583161368966103, 0.010940318927168846, 0.011145726777613163, 0.10256856679916382, 0.03274276480078697, -0.01926720142364502, -0.04276775196194649, -0.0155844921246171, -0.028087835758924484, -0.02640618570148945, -0.009255516342818737, 0.030316704884171486, 0.03711798042058945, -0.019126415252685547, 0.03506229445338249, -0.0020615968387573957, 0.05927250534296036, -0.01354384794831276, 0.005693586077541113, 0.039283689111471176, -0.02420620620250702, 0.002494565676897764, -0.050355467945337296, 0.0007734548416920006, 0.019874321296811104, 0.06687264144420624, 0.00892221461981535, 0.030113641172647476, 0.03882315754890442, -0.0653613731265068, -0.03790706768631935, -0.04268112778663635, 0.022545520216226578, 0.038868680596351624, 0.0144176771864295, 0.06870066374540329, -0.004168797750025988, 0.03475131094455719, -0.040966372936964035, 0.049994636327028275, -0.0517936572432518, 0.006224428303539753, 0.011395896784961224, 0.039103586226701736, -0.026662444695830345, -0.06436934322118759, -0.01486156601458788, 0.04529346898198128, 0.010344396345317364, 0.023885654285550117, -0.024705465883016586, 0.04228977859020233, -0.053241729736328125, 0.01718886010348797, 0.023859649896621704, 0.018866200000047684, -0.02202369086444378, 0.07571069896221161, 0.08843729645013809, 0.03135700896382332, -0.029556358233094215, 0.01127899531275034, 0.014101793058216572, -0.0005837954231537879, -0.018662048503756523, -0.027760913595557213, 0.05109467729926109, 0.07374341040849686, -0.024565845727920532, -0.02533506229519844, -0.030004343017935753, -0.001654586405493319, 0.027494363486766815, 0.01600794494152069, 0.011696118861436844, 0.028037359938025475, 0.03334818780422211, 0.055285241454839706, 0.04313838481903076, 0.03698071464896202, 0.027580201625823975, -0.009278042241930962, -0.05356457084417343, 0.013073486275970936, 0.011989974416792393, 0.014072559773921967, -0.022892732173204422, -0.028439225628972054, -0.020847350358963013, 0.0065616099163889885, 0.007580563426017761, -0.005789698101580143, 0.02807597629725933, 0.019917232915759087, -0.008860825560986996, -0.007089788559824228, -0.0036200133617967367, 0.005335038527846336, 0.050908997654914856, -0.043048661202192307, -0.016469240188598633, 0.021843763068318367, -0.03113759681582451, 0.018238073214888573, -0.015005981549620628, 0.035534944385290146, 0.02398492395877838, -0.03452659770846367, -0.03294563665986061, 0.03493531420826912, 0.003617015201598406, -0.028539378196001053, -0.007814222015440464, 0.03171918913722038, -0.015455901622772217, -0.020625874400138855, 0.014948573894798756, 0.02979899011552334, -0.02795265056192875, 0.02154635265469551, -0.02279183641076088, -0.0024219604674726725, 0.014099251478910446, 0.007926874794065952, -0.03593984618782997, -0.04077386483550072, 0.01648353412747383, -0.056544363498687744, 0.010187050327658653, 0.03788963705301285, -0.007990029640495777, 0.028724566102027893, 0.023211900144815445, 0.08456165343523026, 0.02341517247259617, -0.0077234720811247826, 0.01858580857515335, -0.01023206114768982, 0.03308692201972008, -0.03600773587822914, 0.040693383663892746, -0.027963604778051376, -0.005225899163633585, -0.03434716537594795, -0.07101590931415558, -0.002928932895883918, -0.02214020863175392, -0.03992027789354324, -0.02395852655172348, -0.030805159360170364, -0.01756184548139572, -0.0017717266455292702, 0.00007614721107529476, 0.02513916790485382, 0.002630062634125352, -0.057124167680740356, 0.08528473973274231, 0.05584074184298515, 0.0036226168740540743, -0.04262983053922653, 0.020210301503539085, 0.02256784774363041, 0.04903338849544525, 0.03135741129517555, 0.008225818164646626, -0.04468799754977226, -0.04133608937263489, 0.00693127466365695, -0.04327069967985153, -0.0966402217745781, -0.004449720028787851, 0.060397084802389145, -0.012625014409422874, -0.030947178602218628, -0.008708360604941845, 0.035110048949718475, 0.01359011884778738, -0.052140869200229645, -0.023975390940904617, 0.0507187619805336, 0.007693285122513771, -0.013428617268800735, -0.05396392568945885, 0.010587869212031364, -0.0019271232886239886, 0.005324155557900667, 0.028659744188189507, -0.030321160331368446, -0.057627443224191666, -0.05119463801383972, 0.012417315505445004, 0.003943284973502159, -0.005029344465583563, -0.031486619263887405, 0.003871635999530554, -0.06489492207765579, -0.06441690027713776, 0.011820625513792038, -0.020299728959798813, -0.04792489856481552, 0.025741949677467346, 0.021940156817436218, 0.018519235774874687, -0.018834371119737625, -0.021420300006866455, -0.00023822988441679627, 0.03452305868268013, -0.0015958513831719756, -0.018017364665865898, 0.010576293803751469, 0.061164602637290955, 0.05866609141230583, -0.015566721558570862, -0.05914931744337082, -0.10810191184282303, -0.09749054908752441, -0.015085956081748009, 0.011134105734527111, 0.01875614933669567, 0.049482882022857666, 0.0016449952963739634, 0.035121042281389236, -0.010095585137605667, 0.011005036532878876, -0.0000616081670159474, -0.012121971696615219, -0.019100917503237724, -0.010667110793292522, -0.04542127624154091, 0.027866022661328316, -0.012826110236346722, -0.019198834896087646, 0.01740417070686817, 0.034778278321027756, 0.024223240092396736, 0.05301085487008095, 0.06563399732112885, -0.022108817473053932, -0.03604166954755783, 0.013123865239322186, 0.04803169518709183, 0.0191896241158247, -0.001210788614116609, 0.04952104389667511, 0.013254387304186821, 0.01964193768799305, 0.03912947699427605, -0.028583809733390808, 0.00487337913364172, 0.026682496070861816, 0.019893387332558632, -0.015157189220190048, 0.009096119552850723, 0.08449018001556396, -0.03761449083685875, 0.057572439312934875, -0.015209456905722618, 0.002542793285101652, 0.03364304453134537, -0.024310756474733353, 0.0668170377612114, 0.040282730013132095, 0.010739795863628387, -0.0669446587562561, 0.0161603856831789, 0.027645383030176163, -0.07379360496997833, 0.004663180094212294, -0.02283424325287342, 0.012998837046325207, 0.018458718433976173, -0.0020395866595208645, -0.01509412843734026, -0.07824676483869553, -0.03195636346936226, -0.07486780732870102, -0.06498339772224426, 0.01855897158384323, -0.016948329284787178, -0.004889953415840864, -0.012450924143195152, -0.02221381478011608, 0.007673422805964947, 0.0024908168707042933, 0.008325694128870964, 0.012150357477366924, 0.006739817559719086, -0.0103913564234972, 0.0369812436401844, -0.0013299168786033988, -0.03578156977891922, 0.046205244958400726, 0.01557995192706585, -0.01632094942033291, -0.05625336617231369, -0.0567612498998642, 0.041858479380607605 ]
<p>Is it possible to know whether a lightning bolt travel from the ground to the sky or from the sky to the ground? </p> <p>Alternatively, it could be both sides approaching</p>
g1534
[ 0.010698692873120308, 0.039166487753391266, 0.020086856558918953, -0.037344712764024734, 0.06400690227746964, -0.005350435618311167, 0.001046957215294242, 0.0061104558408260345, 0.0029994684737175703, -0.028965158388018608, -0.026300426572561264, 0.0008495768997818232, 0.035211388021707535, 0.0049718511290848255, -0.020732862874865532, -0.044905368238687515, 0.11269795149564743, -0.05054941400885582, 0.009954532608389854, 0.037018198519945145, 0.05101044103503227, 0.03304293006658554, 0.025177432224154472, -0.025671113282442093, -0.01276889443397522, -0.06077778711915016, -0.05902335047721863, -0.024144155904650688, -0.049300290644168854, -0.034307822585105896, -0.006916303653270006, 0.015342660248279572, 0.059882715344429016, -0.053215883672237396, -0.03106934018433094, -0.033022839576005936, 0.01940864510834217, 0.004190458450466394, 0.013255560770630836, 0.020219020545482635, 0.01226021721959114, -0.013564853928983212, 0.02202458493411541, -0.03363526612520218, 0.027151165530085564, -0.017841264605522156, 0.019712207838892937, 0.037861067801713943, 0.005775149445980787, -0.003016925882548094, -0.05905035138130188, 0.03850458934903145, -0.006292460951954126, 0.07337100803852081, -0.03972626477479935, 0.020466042682528496, 0.06284336000680923, -0.03388885036110878, 0.10144033282995224, 0.009370710700750351, 0.011176270432770252, 0.01649738848209381, 0.002277995692566037, -0.0333058126270771, 0.045077670365571976, -0.03109259158372879, -0.0863596573472023, -0.03817618265748024, 0.0698021799325943, -0.04274587333202362, 0.0408603735268116, -0.037429746240377426, -0.009731722995638847, 0.03014593943953514, 0.018358081579208374, -0.021744709461927414, 0.004491863772273064, 0.026071690022945404, 0.042383696883916855, 0.058910537511110306, 0.003856104798614979, -0.061714716255664825, -0.04384621977806091, 0.011785090900957584, -0.01897379942238331, 0.028739091008901596, 0.029010597616434097, -0.019931433722376823, -0.017655281350016594, -0.03663552552461624, -0.030233340337872505, 0.0001970704470295459, 0.077536940574646, 0.008692661300301552, -0.03273546323180199, -0.015348532237112522, -0.016336722299456596, 0.016133500263094902, 0.01158366072922945, 0.0075016929768025875, -0.0713096335530281, -0.024423273280262947, -0.014605137519538403, 0.007371812127530575, 0.02991931326687336, -0.04374292865395546, 0.02241293527185917, -0.04431774839758873, -0.027760732918977737, -0.05958988890051842, 0.014408771879971027, -0.03972506523132324, 0.015203500166535378, 0.023143574595451355, -0.023480772972106934, -0.041030529886484146, 0.030638786032795906, 0.010501847602427006, 0.007005975116044283, 0.03565638139843941, -0.01164225209504366, -0.011580919846892357, -0.03505200147628784, 0.0697537362575531, 0.0030549601651728153, 0.006339872255921364, 0.02905360236763954, -0.01035870611667633, -0.03637637197971344, -0.03180009871721268, -0.02898101508617401, 0.008180275559425354, 0.038378942757844925, 0.018700897693634033, 0.000993215711787343, 0.03650234639644623, 0.08150478452444077, 0.061857353895902634, -0.03917134180665016, 0.05175856500864029, 0.08968427777290344, -0.023345069959759712, 0.018734466284513474, -0.04896737262606621, 0.021961500868201256, 0.010923604480922222, -0.03569870442152023, 0.011175102554261684, 0.004862796515226364, 0.012956325896084309, -0.02475283481180668, 0.006442445795983076, -0.03500806912779808, 0.02517046593129635, -0.034346748143434525, -0.07545045018196106, -0.004084140527993441, 0.0002533181686885655, -0.02976551279425621, -0.007220356725156307, 0.023542111739516258, -0.024470916017889977, 0.034829478710889816, -0.0417194627225399, 0.006942286621779203, -0.02437782473862171, 0.0009988972451537848, 0.024812160059809685, 0.053154971450567245, -0.01793813891708851, -0.00943212304264307, 0.04420456662774086, 0.06258896738290787, 0.0197429321706295, 0.1146216168999672, 0.03798120841383934, 0.003989451564848423, -0.012453204952180386, 0.017098523676395416, 0.019845062866806984, -0.005406922195106745, 0.0028894010465592146, -0.03181565925478935, -0.006826150696724653, 0.0007108022109605372, -0.053074341267347336, -0.013311183080077171, -0.03682449460029602, 0.019285673275589943, -0.017054855823516846, -0.03715376928448677, -0.08986011892557144, -0.04403330385684967, 0.022295786067843437, 0.013188890181481838, -0.05596417933702469, 0.011815489269793034, 0.014707486145198345, -0.04901282861828804, -0.07765379548072815, 0.03512416034936905, 0.03846444562077522, 0.009339806623756886, 0.013451039791107178, -0.005852285772562027, -0.007535313721746206, 0.024934783577919006, 0.002166556427255273, 0.03924987465143204, -0.05197160691022873, -0.02784612588584423, -0.01913609728217125, 0.03807387128472328, 0.052687615156173706, 0.022074030712246895, -0.034476105123758316, 0.009940190240740776, 0.010431171394884586, -0.03292769938707352, 0.03718309849500656, -0.0162497591227293, 0.06607827544212341, 0.01071716845035553, -0.004070420283824205, -0.010338664054870605, 0.04537792503833771, -0.020612675696611404, 0.030404875054955482, -0.019284702837467194, -0.00029503690893761814, -0.02319576032459736, 0.004416779149323702, 0.003645347896963358, -0.021120846271514893, 0.06537488847970963, 0.045267753303050995, 0.016819274052977562, 0.004464037716388702, 0.02293066494166851, -0.09707339853048325, -0.010626406408846378, -0.033339984714984894, 0.03851836174726486, 0.01685725897550583, 0.08152613788843155, -0.0306678656488657, -0.014853074215352535, 0.04240592569112778, -0.026922356337308884, 0.01835023984313011, 0.06064211204648018, 0.022051053121685982, -0.06463941186666489, 0.03963654488325119, -0.037998609244823456, -0.06434588134288788, 0.03327692300081253, -0.045028991997241974, -0.0732363909482956, -0.03158196434378624, -0.04729972779750824, -0.043474216014146805, 0.002978394040837884, 0.006165162194520235, -0.02141907624900341, -0.00719722593203187, -0.04983796179294586, 0.02256254479289055, 0.004774901550263166, -0.0607922188937664, 0.03756452351808548, -0.009874640963971615, 0.0514618381857872, -0.012055938132107258, -0.0389433391392231, -0.00023887830320745707, -0.036085840314626694, -0.0031864417251199484, 0.011862064711749554, -0.005330163054168224, -0.021686850115656853, -0.020757602527737617, 0.00011685703793773428, 0.052829641848802567, 0.03457126021385193, 0.001317040529102087, -0.013703501783311367, 0.00998864509165287, -0.027853695675730705, 0.043347012251615524, -0.03493692725896835, -0.028952263295650482, 0.06341129541397095, -0.04177045449614525, -0.022952333092689514, -0.017686232924461365, 0.018542371690273285, -0.015292465686798096, 0.0020804633386433125, -0.020595520734786987, -0.01520912442356348, -0.009232784621417522, -0.004470906686037779, 0.023043930530548096, 0.05813930183649063, 0.0681181401014328, -0.036673933267593384, 0.007009222637861967, 0.05789389833807945, -0.008950285613536835, 0.00650499202311039, 0.09693589061498642, 0.024536702781915665, 0.011796601116657257, -0.0035969573073089123, -0.006543445400893688, -0.010190595872700214, 0.06575000286102295, 0.04043075814843178, 0.08329759538173676, 0.030261356383562088, -0.027287686243653297, 0.013092701323330402, 0.10102976858615875, 0.02725028432905674, -0.007290493231266737, -0.011330699548125267, 0.047146912664175034, -0.0545278899371624, -0.05071074515581131, -0.0894058346748352, 0.040499813854694366, 0.0023345735389739275, -0.018511870875954628, 0.02397928759455681, 0.0009038478601723909, 0.03136695921421051, -0.005739742890000343, 0.04304703325033188, 0.04504271596670151, 0.04971954971551895, -0.026372302323579788, -0.05202459916472435, 0.026804927736520767, 0.016541266813874245, 0.03010062873363495, -0.020864229649305344, 0.022847497835755348, 0.030571183189749718, -0.021551309153437614, 0.024867793545126915, -0.03344738483428955, -0.010006590746343136, -0.009900439530611038, 0.052890826016664505, 0.019175926223397255, 0.021768108010292053, 0.04161728546023369, 0.010691477917134762, 0.03732334449887276, -0.024094944819808006, 0.014375594444572926, -0.003583956975489855, -0.01820140890777111, 0.026646729558706284, -0.014344277791678905, -0.023017678409814835, 0.03825892508029938, -0.027895387262105942, -0.005983274895697832, 0.02368946000933647, 0.03986747935414314, -0.0169292613863945, 0.03037962131202221, 0.017282413318753242, -0.02978336252272129, 0.04213706776499748, -0.06162390857934952, 0.0020450770389288664, 0.03818581625819206, 0.01885293424129486, 0.0026221098378300667, 0.01932602748274803, -0.011920405551791191, 0.01591872237622738, -0.046569738537073135, 0.05185519531369209, -0.054621074348688126, 0.014721868559718132, 0.005843101069331169, 0.040262237191200256, -0.01284987572580576, -0.031117405742406845, -0.03705072030425072, 0.0031074995640665293, 0.01845579780638218, 0.043197035789489746, 0.0761660635471344, 0.0058750263415277, 0.024426201358437538, 0.0804186761379242, -0.023239865899086, 0.01087118312716484, -0.02768394723534584, -0.03204681724309921, 0.03833929821848869, 0.015253002755343914, -0.03151160478591919, 0.0033879776019603014, -0.0307371336966753, 0.038818418979644775, -0.019587181508541107, -0.03330022469162941, -0.03990711644291878, 0.05703644081950188, -0.01866944506764412, 0.021029740571975708, 0.021879570558667183, 0.06416147947311401, -0.022505536675453186, 0.04872860386967659, 0.06640452891588211, 0.04335455596446991, -0.02508205734193325, -0.03260115534067154, 0.09294014424085617, 0.022822994738817215, -0.0204582829028368, -0.026755960658192635, 0.020869458094239235, -0.0007761016022413969, 0.0274310614913702, 0.01660795509815216, -0.0028059612959623337, -0.020171843469142914, 0.03671502694487572, -0.002618067665025592, -0.0055856527760624886, 0.0856916680932045, 0.018353192135691643, 0.042432792484760284, 0.029568955302238464, -0.005906999576836824, -0.0087807048112154, -0.040676265954971313, 0.04325958341360092, 0.00353794451802969, -0.02391655743122101, -0.014622122049331665, -0.026252659037709236, -0.0865134745836258, 0.0014212847454473376, -0.07612456381320953, 0.01868320070207119, -0.05775120481848717, 0.014598196372389793, 0.004509659018367529, -0.006597114726901054, -0.023202527314424515, -0.012880859896540642, -0.011394989676773548, -0.07984846830368042, 0.020048201084136963, 0.04702642560005188, -0.005461086984723806, 0.04146860912442207, -0.03303174301981926, -0.04444139450788498, -0.057818811386823654, -0.02123822644352913, -0.02685588039457798, 0.008164945058524609, 0.0015761021059006453, 0.02745545655488968, -0.022278625518083572, -0.05064007639884949, -0.0209177378565073, -0.014865506440401077, 0.011832606047391891, -0.003874672343954444, -0.010425920598208904, 0.0004286456387490034, 0.00520916236564517, -0.039822790771722794, 0.01724831387400627, -0.013593311421573162, 0.031448639929294586, 0.027647407725453377, 0.016585586592555046, -0.02859528362751007, -0.0012445916654542089, -0.03246074169874191, -0.0359790176153183, -0.03942236676812172, -0.065680593252182, -0.020739760249853134, -0.004032494965940714, 0.024668553844094276, -0.010602557100355625, 0.023270396515727043, -0.06100139394402504, -0.005820794031023979, 0.05559640750288963, 0.03684614971280098, 0.011289761401712894, 0.05763840675354004, 0.0206913985311985, -0.0342329666018486, -0.04853805899620056, 0.06186387315392494, -0.03122171387076378, -0.057257652282714844, -0.029061738401651382, 0.0501362644135952, 0.023960469290614128, -0.022271594032645226, 0.01563619077205658, 0.06549302488565445, 0.018795564770698547, -0.009526504203677177, 0.007867732085287571, -0.021628443151712418, 0.026776527985930443, -0.010440309531986713, -0.004410878289490938, -0.008485945872962475, -0.013009843416512012, -0.029278768226504326, -0.011641439981758595, -0.008972753770649433, -0.00001981370041903574, 0.07233171910047531, -0.007655226159840822, -0.04043017327785492, 0.013063378632068634, -0.06759459525346756, 0.01629607193171978, -0.025103943422436714, 0.003538507502526045, -0.01799008622765541, -0.0198019091039896, -0.04540131613612175, 0.031280115246772766, 0.025904390960931778, 0.01613887958228588, -0.025194218382239342, -0.04974236339330673, -0.031028365716338158, 0.028648998588323593, -0.06810645014047623, 0.009587256237864494, 0.03675996884703636, -0.07299958169460297, 0.04422406852245331, 0.02016746997833252, 0.0442647859454155, -0.002371135400608182, -0.0021404544822871685, 0.04251720756292343, -0.035082802176475525, 0.052641142159700394, 0.0017655187984928489, -0.022700969129800797, -0.013954735361039639, 0.027099279686808586, -0.024921270087361336, -0.026836777105927467, -0.0417068749666214, 0.030332105234265327, 0.01247385237365961, 0.02312394790351391, -0.05116584897041321, -0.0035955137573182583, 0.0069746896624565125, 0.035393744707107544, 0.0028729834593832493, 0.01639619842171669, 0.044496092945337296, 0.022127751260995865, -0.003038619877770543, 0.04638585075736046, 0.04267191141843796, 0.021726910024881363, -0.07248886674642563, 0.005152312573045492, 0.019234787672758102, -0.0034000552259385586, 0.019048616290092468, 0.011353406123816967, 0.03188399225473404, -0.057540163397789, -0.019793985411524773, 0.0011808094568550587, -0.07566728442907333, -0.08616112917661667, -0.024851473048329353, 0.0348733626306057, 0.020900683477520943, -0.011982631869614124, 0.10369771718978882, -0.005275188013911247, -0.033702343702316284, 0.040807414799928665, -0.027100944891572, 0.05325353890657425, -0.01990818791091442, 0.03565891087055206, 0.03847488760948181, 0.03855683654546738, -0.05684523284435272, -0.02404971607029438, -0.00037961467751301825, 0.03688541054725647, 0.0012346645817160606, -0.03391389548778534, 0.019086528569459915, -0.03407835215330124, -0.015940504148602486, -0.0011497404193505645, -0.04259709268808365, 0.044271085411310196, 0.005999683402478695, -0.07379812747240067, 0.011386104859411716, -0.038954127579927444, -0.012550058774650097, -0.0270013939589262, 0.040299613028764725, -0.017313452437520027, 0.018462786450982094, 0.0036329582799226046, 0.03222988545894623, -0.00250362535007298, 0.028335705399513245, 0.050230711698532104, 0.008652887307107449, -0.010873078368604183, -0.01922890916466713, -0.022703206166625023, -0.004424574784934521, -0.008943259716033936, -0.03705050051212311, -0.04376610741019249, 0.01402284111827612, -0.07118207961320877, 0.0004059993661940098, 0.03647645562887192, -0.08735408633947372, -0.08100389689207077, -0.024408230558037758, -0.0060972366482019424, -0.003846313338726759, -0.041729867458343506, -0.026306699961423874, -0.012906617484986782, 0.025703350082039833, -0.010157630778849125, 0.04640881344676018, 0.02764805406332016, -0.04239099472761154, 0.006955898366868496, -0.011627310886979103, -0.03368285670876503, -0.006628493778407574, 0.03991753235459328, -0.024440789595246315, -0.02625958062708378, -0.04432278871536255, -0.06560955941677094, -0.015015347860753536, -0.012884932570159435, -0.0066629135981202126, -0.027118660509586334, 0.029836300760507584, -0.039683833718299866, -0.011259094811975956, -0.028258105739951134, -0.01833358407020569, -0.0015098005533218384, -0.024582406505942345, 0.021399885416030884, 0.05963144078850746, -0.06057160720229149, 0.042991023510694504, 0.022327832877635956, 0.038365066051483154, 0.04862085357308388, -0.05542442202568054, -0.02129274792969227, -0.07742524147033691, -0.017998429015278816, 0.04906069114804268, 0.0032268750946968794, -0.0600765161216259, -0.042739614844322205, -0.010777115821838379, 0.018863944336771965, -0.0027005712036043406, 0.01059645228087902, -0.012576508335769176, -0.024920495226979256, 0.029683995991945267, 0.04430743306875229, 0.00020479076192714274, 0.023476405069231987, -0.0698331892490387, -0.004017455503344536, 0.02637753076851368, -0.07315307855606079, 0.003504799911752343, 0.028030242770910263, 0.051519498229026794, -0.007121522445231676, 0.06364688277244568, -0.03034055233001709, 0.06671416759490967, 0.06021701171994209, 0.047211553901433945, 0.00028515554731711745, 0.046602457761764526, -0.01836216263473034, -0.03828917071223259, -0.035969771444797516, -0.04508804529905319, -0.03721463307738304, 0.05846211686730385, -0.006689704488962889, 0.02943195030093193, -0.013947688974440098, -0.04890621080994606, 0.03619179129600525, 0.010537097230553627, 0.0035619630943983793, -0.049555446952581406, -0.06658914685249329, 0.018063852563500404, 0.021690061315894127, -0.061993397772312164, 0.036366771906614304, -7.157614163588732e-7, -0.033293262124061584, -0.029778802767395973, -0.024084972217679024, -0.02662622183561325, -0.02076491340994835, -0.06096172705292702, 0.02985440380871296, 0.06757081300020218, 0.017451094463467598, -0.04681115597486496, 0.012556225061416626, 0.008134563453495502, -0.02233942411839962, 0.036742232739925385, 0.03141020983457565, 0.08013684302568436, -0.04707132652401924, 0.003869937267154455, -0.005537719931453466, 0.02410227246582508, -0.05031200870871544, -0.05646030604839325, 0.02156832255423069, 0.0025424673222005367, -0.03362800553441048, -0.027195610105991364, -0.03657511994242668, 0.020861748605966568 ]
<p>I'm having trouble understanding what a problem I have is seeking.</p> <p>To simplify the problem:</p> <blockquote> <p>A particle reaches a speed of 1.6 m/s in a 5.0 micrometer launch. The speed is reduced to zero in 1.0 mm by the air. Assume constant acceleration and find the acceleration in terms of g during a) the launch and b) the speed reduction. </p> </blockquote> <p>The basic strategy to find acceleration I am using is to calculate two velocity equations: one between (0 m/s, 0 m) and (1.6 m/s, 5.0 micrometers); the second between (1.6 m/s, 5.0 micrometers) and (0 m/s, 1.0 mm). Then I will derive the acceleration value for each. Because acceleration is constant I can expect a linear velocity equation. </p> <p>What is confusing me is that we are to assume constant acceleration. Thus the acceleration equation will merely be some real number. So, what exactly is expected if it is to be in terms of g? Is my strategy to find acceleration incorrect?</p>
g1535
[ 0.08252213895320892, 0.022990895435214043, 0.01374494843184948, 0.045457832515239716, 0.02467486634850502, -0.008762182667851448, 0.013966470025479794, 0.021519413217902184, -0.06946216523647308, -0.032212335616350174, -0.030915074050426483, 0.0386723093688488, -0.014355916529893875, 0.05583967640995979, 0.028793055564165115, -0.017948249354958534, -0.007602017838507891, -0.02699030563235283, -0.023497795686125755, 0.024022024124860764, 0.07802844792604446, -0.025740675628185272, -0.04141940921545029, -0.06640518456697464, 0.043967168778181076, -0.024213971570134163, -0.01057369913905859, -0.004645117558538914, -0.06205827742815018, -0.018423236906528473, 0.052779801189899445, -0.019129233434796333, 0.01548295933753252, -0.02992170676589012, -0.029961399734020233, -0.06338869780302048, 0.036428261548280716, 0.03464508801698685, -0.028243567794561386, -0.02238701656460762, 0.03779921308159828, -0.061166997998952866, 0.02457796037197113, 0.00880331639200449, 0.08835361897945404, 0.049598708748817444, 0.004375409334897995, -0.0014707365771755576, -0.010708292946219444, -0.07174278050661087, -0.026201386004686356, 0.06902474910020828, 0.008980896323919296, -0.060896825045347214, -0.027420375496149063, 0.06085043027997017, -0.003496218239888549, -0.024734681472182274, -0.0016438765451312065, 0.04674091190099716, -0.014687050133943558, -0.03628057613968849, -0.011174573563039303, -0.07981991022825241, 0.07623021304607391, -0.02128461003303528, -0.02069881558418274, -0.0006515728891827166, -0.022505538538098335, 0.012635888531804085, 0.022784335538744926, -0.07271572202444077, 0.005736574064940214, -0.06609302014112473, -0.0770389512181282, -0.06476826220750809, -0.01813526079058647, -0.05204053968191147, -0.004594530910253525, 0.05289280042052269, -0.026283757761120796, 0.05590086802840233, 0.04041702300310135, 0.016262654215097427, -0.004241026006639004, 0.00498442817479372, -0.0006272276514209807, 0.034197594970464706, -0.02919021062552929, -0.04378926753997803, 0.022121084854006767, 0.05393688380718231, 0.05016655474901199, 0.0083736851811409, -0.045858848839998245, -0.02651713788509369, -0.03886782377958298, 0.05749252066016197, 0.053896281868219376, 0.010241073556244373, 0.02030550129711628, -0.03000650554895401, 0.03202766552567482, -0.0017981346463784575, 0.01683979295194149, -0.018859725445508957, 0.03871084377169609, 0.03079530969262123, -0.019921956583857536, -0.02907981351017952, 0.0021439967676997185, -0.02066868357360363, -0.05669277533888817, -0.07267988473176956, -0.030599668622016907, -0.049153588712215424, 0.05642236769199371, 0.03688618540763855, -0.023468537256121635, 0.06876115500926971, -0.020327700302004814, 0.031265389174222946, -0.03259739652276039, 0.049327701330184937, -0.0009728122968226671, -0.04605461657047272, -0.013736484572291374, 0.013122730888426304, 0.0037635699845850468, 0.01970496028661728, 0.0223738644272089, -0.03155849501490593, 0.03948969393968582, 0.024832258000969887, -0.0782284066081047, -0.024667054414749146, 0.003024943405762315, 0.026225784793496132, -0.0070453486405313015, 0.017113016918301582, -0.036158714443445206, -0.0271246749907732, 0.005641936790198088, -0.014679721556603909, -0.05905238166451454, 0.0183853879570961, -0.04117336869239807, 0.015157906338572502, 0.023897357285022736, 0.039296168833971024, -0.0004913050215691328, 0.05098659172654152, 0.015637416392564774, 0.04034983366727829, 0.04495435580611229, -0.004927799105644226, 0.01656503975391388, 0.03165338560938835, -0.022293493151664734, 0.026848459616303444, 0.058095838874578476, -0.027293313294649124, 0.014923102222383022, 0.030478384345769882, -0.10860490798950195, 0.04743707552552223, 0.010230066254734993, -0.05265787988901138, 0.019612547010183334, -0.011865369975566864, -0.0005268985987640917, -0.05403595417737961, 0.03184504806995392, 0.05938689038157463, -0.018586713820695877, -0.040189728140830994, 0.11497648805379868, 0.015505471266806126, -0.04835978150367737, -0.001181158353574574, 0.020036453381180763, -0.022560911253094673, 0.03289920464158058, -0.04171420633792877, -0.0059481170028448105, -0.02592095360159874, 0.014413513243198395, 0.042907122522592545, -0.05908660963177681, -0.00307178171351552, 0.011663225479424, -0.040178507566452026, 0.003240308491513133, 0.017895163968205452, -0.06386294215917587, 0.005994962528347969, 0.029042262583971024, -0.0074077183380723, -0.03960433974862099, 0.05564241483807564, 0.025604207068681717, 0.03844044730067253, -0.0029850974678993225, -0.030368341132998466, 0.10288027673959732, -0.05236455425620079, -0.01807517558336258, -0.046339988708496094, 0.000724491139408201, 0.008997336030006409, 0.005310930777341127, 0.027901582419872284, 0.00754134077578783, 0.05364115908741951, 0.057002417743206024, -0.03878679499030113, 0.03800269961357117, 0.03662891685962677, 0.02367253601551056, -0.013977659866213799, -0.007460263557732105, -0.035009127110242844, -0.016264822334051132, -0.0253891684114933, -0.025550488382577896, -0.04842778667807579, 0.020804669708013535, -0.02968839555978775, -0.026774218305945396, 0.0075372024439275265, -0.040225375443696976, 0.02625480853021145, -0.025782303884625435, -0.016909150406718254, 0.018801763653755188, -0.007329442072659731, -0.018190637230873108, 0.012603404000401497, 0.038394294679164886, 0.02950626239180565, -0.04514310881495476, -0.014099379070103168, -0.029564380645751953, -0.003104801755398512, 0.003277932293713093, -0.09796726703643799, -0.003383444622159004, -0.025623593479394913, -0.0008415282354690135, 0.00003337578527862206, -0.02156367339193821, 0.04013890027999878, 0.00431118905544281, -0.018934711813926697, 0.012231767177581787, -0.026362905278801918, -0.00044588459422811866, -0.010992882773280144, -0.01848389208316803, -0.015029621310532093, -0.03384929150342941, 0.013952015899121761, -0.03333041071891785, 0.037316516041755676, -0.04840494319796562, -0.015085898339748383, -0.024963587522506714, 0.019061099737882614, 0.0065587954595685005, 0.022267205640673637, -0.04111171141266823, -0.02187042310833931, -0.013719700276851654, 0.022126929834485054, -0.008411812596023083, -0.018531540408730507, 0.0731894001364708, -0.011403790675103664, 0.06079882010817528, 0.07468751072883606, -0.0030183184426277876, -0.06323154270648956, -0.0645766407251358, 0.04060320183634758, 0.03670347109436989, -0.0641733929514885, 0.05435755476355553, 0.03147569298744202, 0.029157355427742004, -0.026531938463449478, -0.01855386793613434, 0.025150639936327934, 0.020556095987558365, 0.008887371979653835, 0.003661524271592498, 0.05725214630365372, 0.025382069870829582, -0.016345368698239326, 0.028798989951610565, -0.004738160874694586, -0.013967995531857014, -0.05923541262745857, 0.032561734318733215, -0.008591463789343834, -0.04225935414433479, 0.009233372285962105, -0.02947041019797325, -0.06086784601211548, -0.05295975133776665, -0.011319652199745178, -0.023804165422916412, 0.05511745437979698, 0.00851448718458414, -0.003434265498071909, 0.026564856991171837, -0.007807111367583275, 0.002579291118308902, 0.024020200595259666, 0.038974471390247345, 0.03646305203437805, -0.04967586323618889, -0.11550495028495789, 0.029321232810616493, 0.03210166096687317, 0.02150978334248066, -0.006417319644242525, 0.004267141222953796, 0.020681429654359818, -0.043969351798295975, -0.027062341570854187, 0.008759958669543266, -0.011896043084561825, 0.01111635286360979, 0.006393541116267443, 0.024467527866363525, -0.08270378410816193, -0.01213592104613781, -0.005933851003646851, 0.0379713773727417, -0.006431620568037033, 0.007927182130515575, 0.0008134135860018432, -0.07345927506685257, 0.006305810064077377, 0.02287699468433857, -0.041612885892391205, 0.017871061339974403, 0.015004665590822697, 0.01136013399809599, -0.030530860647559166, 0.041754499077796936, -0.06322481483221054, 0.011627706699073315, -0.018154321238398552, -0.039252713322639465, -0.003369417041540146, 0.0259060338139534, 0.01819118857383728, -0.0058568427339196205, -0.0000377165742975194, -0.01616712473332882, -0.03160300478339195, -0.02756272256374359, 0.06898114830255508, 0.03089124523103237, -0.06549804657697678, -0.02827128767967224, 0.03144817799329758, -0.004725721199065447, -0.03805676847696304, 0.0025978251360356808, 0.007009745109826326, 0.020790517330169678, -0.00549060944467783, -0.057592060416936874, -0.05301172286272049, -0.026239359751343727, 0.04031822085380554, -0.014796453528106213, -0.02028225176036358, 0.04043453559279442, 0.03939734399318695, 0.010476474650204182, -0.019287696108222008, 0.014012442901730537, -0.00973169319331646, 0.013641956262290478, -0.0026723293121904135, 0.014282655902206898, -0.05966797098517418, 0.01545016374439001, -0.01676618866622448, -0.05991223454475403, 0.04231555387377739, 0.003782696556299925, 0.016683241352438927, -0.06072653457522392, -0.010406957939267159, -0.026174165308475494, 0.06640877574682236, -0.019850051030516624, -0.012056099250912666, 0.02161404676735401, 0.007536729332059622, -0.03735622763633728, 0.03161453455686569, 0.057648077607154846, 0.028196442872285843, 0.02907101996243, 0.048375654965639114, 0.0026355779264122248, 0.04000191017985344, -0.04360775649547577, -0.032491639256477356, -0.019280893728137016, -0.02087290771305561, -0.012569338083267212, -0.03972705453634262, -0.009288045577704906, 0.01955895684659481, 0.056120164692401886, 0.03924746811389923, 0.0029905925039201975, -0.04670041427016258, -0.05316120386123657, 0.04537821561098099, 0.0010435094591230154, 0.04566196724772453, 0.007645787671208382, -0.027449849992990494, 0.006025037262588739, 0.010700419545173645, -0.009395292028784752, 0.0634513571858406, 0.02247283048927784, 0.10717657208442688, -0.0015133707784116268, 0.03268812224268913, 0.011641186662018299, 0.0005795448087155819, 0.02570824697613716, 0.03418530896306038, -0.000949399487581104, 0.0244733989238739, -0.004671529401093721, 0.052082739770412445, 0.0020727929659187794, -0.013333815149962902, -0.03224733844399452, 0.006946067791432142, 0.036652572453022, 0.025475801900029182, 0.014992404729127884, -0.034193847328424454, -0.05958351492881775, -0.017308494076132774, -0.015607422217726707, -0.02056870050728321, 0.037031907588243484, 0.031045913696289062, 0.009756692685186863, 0.022684870287775993, -0.005576188210397959, -0.022526782006025314, 0.0027777820359915495, -0.019610492512583733, -0.041286300867795944, 0.022280747070908546, -0.06032480672001839, -0.05799946188926697, -0.007173066958785057, -0.03993993252515793, -0.033997830003499985, -0.025030195713043213, 0.0046308282762765884, 0.013608066365122795, -0.04148804396390915, 0.03272976353764534, 0.05793626233935356, 0.04335341975092888, -0.034477587789297104, -0.055374596267938614, -0.014780573546886444, -0.0059041827917099, 0.01583744026720524, 0.05282168462872505, 0.013768408447504044, -0.009531735442578793, 0.06553129106760025, -0.027614401653409004, 0.07749529927968979, 0.003650550963357091, -0.025325793772935867, -0.05056720972061157, -0.045224230736494064, -0.014752106741070747, 0.02945547364652157, 0.013831219635903835, 0.015074136666953564, 0.011291873641312122, -0.02755114622414112, -0.04459303617477417, 0.006539734546095133, 0.0025128216948360205, -0.011678007431328297, 0.038860470056533813, 0.03712627291679382, 0.013124709017574787, 0.01194673776626587, 0.050859082490205765, 0.07113274186849594, 0.030180685222148895, 0.040373191237449646, -0.0005635814159177244, -0.03952031582593918, -0.026106050238013268, 0.03718021139502525, -0.0139443539083004, -0.021315041929483414, -0.03427663445472717, 0.04826793447136879, -0.015130962245166302, -0.015507588163018227, -0.025600742548704147, 0.008194169029593468, 0.030892038717865944, -0.00768134044483304, 0.043414175510406494, -0.01409123931080103, 0.05206656455993652, -0.004214854910969734, 0.0013310187496244907, 0.00431340467184782, -0.02481258660554886, -0.013864759355783463, 0.0049044410698115826, -0.00915445014834404, -0.02220260351896286, 0.04023991897702217, -0.030478626489639282, -0.11641263961791992, 0.010156565345823765, -0.027989964932203293, 0.03996451944112778, -0.0014960796106606722, -0.009696601890027523, -0.00500109838321805, 0.008883311413228512, 0.01703611947596073, -0.0795292779803276, -0.01379743218421936, -0.02355566807091236, 0.03250671923160553, 0.015564783476293087, -0.02158462442457676, 0.04614945128560066, 0.017538370564579964, 0.058439336717128754, -0.015004118904471397, 0.0075892554596066475, 0.040618497878313065, -0.03141063451766968, 0.02274710312485695, 0.002058862242847681, 0.0067163193598389626, -0.03551284596323967, 0.036900363862514496, -0.03456110134720802, 0.05386578291654587, -0.021766390651464462, -0.03554341942071915, 0.02115246281027794, -0.01688624732196331, 0.016641445457935333, 0.05753925070166588, 0.032198768109083176, -0.005991559941321611, -0.024788450449705124, -0.08849810808897018, 0.07755030691623688, 0.015277082100510597, 0.020840154960751534, -0.009819350205361843, -0.0228553619235754, -0.019711406901478767, -0.015398561954498291, -0.04341689497232437, -0.04333417862653732, 0.044727545231580734, -0.011044650338590145, 0.0380813293159008, -0.000353459850884974, -0.040956638753414154, -0.02944316901266575, -0.10225632786750793, -0.05101395398378372, 0.03375023603439331, -0.03301726654171944, -0.017875852063298225, 0.002211138606071472, 0.08417827636003494, 0.02492285706102848, 0.026707949116826057, -0.02041427604854107, 0.020002570003271103, -0.02596472203731537, -0.032451331615448, 0.012956500984728336, 0.05261560156941414, -0.06468995660543442, -0.03129901736974716, 0.003033386543393135, 0.02742249146103859, 0.0019487751414999366, 0.054387856274843216, -0.0023200989235192537, -0.02871556580066681, 0.007423081900924444, -0.0002176491980208084, 0.002483644289895892, 0.04130540415644646, 0.029347635805606842, -0.01113692857325077, -0.00566127011552453, 0.08818857371807098, -0.000013683795259566978, -0.01049766130745411, 0.039730340242385864, 0.043564267456531525, -0.014245913363993168, -0.004028475843369961, -0.04085556045174599, -0.0033553221728652716, 0.01546508353203535, 0.011313543654978275, 0.02408999390900135, 0.033181026577949524, 0.0796041190624237, 0.02749829925596714, 0.007362978532910347, 0.026389053091406822, -0.03379328176379204, -0.01634656824171543, 0.014163733460009098, -0.033387620002031326, -0.051326852291822433, -0.005289169959723949, -0.00579923577606678, -0.019889242947101593, -0.040005650371313095, -0.047418128699064255, -0.06316428631544113, -0.019846847280859947, 0.01781860925257206, 0.0288715697824955, 0.035225264728069305, 0.044478416442871094, 0.004686740692704916, 0.056347548961639404, -0.04749827831983566, -0.049414027482271194, -0.06322449445724487, 0.004795459099113941, 0.04585077986121178, -0.018527572974562645, 0.029168151319026947, -0.02302522584795952, -0.0208018459379673, 0.04871976748108864, -0.024475598707795143, -0.016352122649550438, -0.012681740336120129, -0.023294968530535698, 0.02671363204717636, -0.004463592078536749, 0.0657569095492363, -0.020414849743247032, 0.029078848659992218, -0.020880859345197678, -0.01533211674541235, 0.021005192771553993, 0.04761818051338196, -0.04744984954595566, 0.00474821450188756, 0.021428387612104416, 0.04224032908678055, -0.03231259807944298, 0.012708800844848156, 0.02150258980691433, -0.03897416591644287, -0.05601662024855614, 0.037739671766757965, 0.05809548869729042, -0.06417269259691238, 0.015836047008633614, -0.0022651602048426867, 0.0008831115555949509, 0.045799657702445984, -0.0037076997105032206, -0.0318821519613266, 0.029782230034470558, -0.00967948604375124, 0.0476340726017952, 0.057401545345783234, -0.03797552362084389, 0.03940208628773689, 0.0013339967699721456, -0.02528977394104004, -0.0162662360817194, 0.009622943587601185, -0.03137527406215668, -0.03314775601029396, 0.05388582497835159, -0.012860064394772053, 0.04486602917313576, 0.013884002342820168, -0.03666490316390991, -0.016175871714949608, 0.03780093416571617, -0.04640429466962814, -0.010719343088567257, 0.003128005424514413, 0.04861822724342346, -0.07780387997627258, 0.04120927304029465, -0.06925052404403687, -0.03751349449157715, 0.04668838158249855, -0.011448943056166172, 0.050727713853120804, 0.04612862318754196, -0.0074503556825220585, 0.0391281396150589, 0.0498633086681366, 0.005228162743151188, -0.02110919915139675, 0.01753135584294796, -0.0014080447144806385, -0.038129959255456924, 0.07050292938947678, -0.023546388372778893, 0.011562931351363659, -0.03541059046983719, 0.028746875002980232, 0.014258679933845997, -0.02652277797460556, 0.03736744448542595, 0.06011136621236801, 0.035070113837718964, -0.047792594879865646, 0.05337086319923401, -0.04251118749380112, -0.09083568304777145, 0.034262001514434814, 0.04544636234641075, -0.053613826632499695, -0.0015468928031623363, 0.04918472468852997, -0.05698830634355545, -0.037500083446502686, -0.02780522033572197, -0.023438772186636925, -0.02214042842388153, 0.020505132153630257, -0.03305257484316826, 0.00792052410542965, -0.052682314068078995, 0.02342808246612549 ]
<p>How does the nonlinear absorption coefficient depend on the band gap? How can that coefficient be calculated theoretically? (Preferably with an example)</p>
g1536
[ 0.00753599451854825, -0.009764873422682285, 0.016233965754508972, 0.04128272831439972, -0.0019549913704395294, 0.017317036166787148, -0.020676108077168465, 0.057717472314834595, 0.0074345823377370834, -0.004075098782777786, -0.00023367814719676971, 0.028449438512325287, 0.027275217697024345, 0.013139715418219566, 0.08611734956502914, 0.015657495707273483, 0.020954113453626633, 0.045170076191425323, 0.016663169488310814, 0.0385885089635849, -0.058535464107990265, 0.0027736478950828314, -0.0580233596265316, -0.08634445071220398, -0.02571074478328228, 0.053118009120225906, 0.050716012716293335, 0.026346830651164055, 0.0004044279339723289, -0.015090635046362877, 0.004051382187753916, 0.003754529170691967, 0.03654646873474121, -0.006240712013095617, -0.027740469202399254, 0.10135834664106369, 0.0011557501275092363, -0.012292950414121151, 0.044846903532743454, 0.06765860319137573, -0.0070002018474042416, 0.004078842233866453, -0.009014330804347992, 0.0010802056640386581, -0.034427106380462646, -0.08229309320449829, -0.01965416595339775, -0.023491699248552322, -0.02884007804095745, -0.05790377035737038, -0.02560698427259922, 0.027609551325440407, 0.056083232164382935, 0.03827962279319763, 0.04429776966571808, -0.014118689112365246, -0.03144439682364464, 0.016778727993369102, -0.017600269988179207, -0.024277914315462112, -0.030264826491475105, 0.027998588979244232, 0.013286109082400799, 0.0004044085799250752, 0.04257646203041077, -0.04217515140771866, -0.01969337649643421, -0.02261759340763092, 0.007158793043345213, -0.10652779787778854, -0.02951372042298317, 0.04575474560260773, -0.0572061762213707, -0.038391295820474625, -0.016902348026633263, 0.00011491785699035972, -0.02926279976963997, 0.03678785637021065, -0.006724451202899218, 0.07132349908351898, -0.03255157172679901, -0.0017050286987796426, 0.03275832533836365, 0.05238333344459534, 0.02179703116416931, -0.05587069317698479, 0.02310679666697979, -0.0005267256638035178, -0.04074203595519066, -0.023935630917549133, 0.013679583556950092, -0.024618135765194893, -0.010014794766902924, -0.030975772067904472, 0.06748982518911362, -0.032490577548742294, -0.0354277677834034, 0.01330261304974556, -0.028974346816539764, 0.0032254676334559917, 0.04979846999049187, -0.031181734055280685, 0.020571377128362656, 0.026182666420936584, -0.04516006261110306, 0.03551008924841881, 0.041294194757938385, -0.0035748325753957033, -0.054842423647642136, -0.01609324850142002, -0.04039055481553078, -0.02735896222293377, 0.04697471484541893, -0.02113994210958481, -0.01879597268998623, -0.03044520877301693, 0.036229997873306274, -0.040289439260959625, 0.021572940051555634, 0.03809787333011627, -0.049135275185108185, 0.07361014932394028, -0.021113183349370956, 0.054664794355630875, 0.0036295524332672358, 0.0002929614274762571, 0.013164659962058067, 0.031202415004372597, 0.024215223267674446, 0.012077037245035172, 0.025848157703876495, -0.01173305045813322, -0.030008604750037193, 0.030094914138317108, 0.007069128565490246, -0.012604276649653912, -0.007652870379388332, -0.033495064824819565, -0.04483868554234505, 0.015847045928239822, -0.001476009376347065, -0.04667988792061806, 0.026989184319972992, -0.0578869953751564, -0.013435859233140945, 0.0027590387035161257, -0.06176844239234924, -0.011604118160903454, -0.03514399006962776, -0.02431805618107319, 0.006482168100774288, -0.008876119740307331, 0.06548309326171875, -0.05303886905312538, 0.022574832662940025, -0.0005179802537895739, 0.07557439059019089, 0.0021123860497027636, -0.03178892657160759, 0.012911940924823284, 0.030745193362236023, -0.04072153940796852, -0.007598212920129299, 0.01511793490499258, -0.10366616398096085, -0.04265514761209488, 0.03152686357498169, -0.11517307907342911, -0.017329547554254532, -0.006038303021341562, 0.04769017547369003, 0.02512628771364689, 0.02055881917476654, -0.024564146995544434, 0.039556894451379776, 0.09403644502162933, 0.04693939536809921, -0.007200173567980528, 0.01836162991821766, 0.04221012815833092, -0.009450121782720089, 0.03835362568497658, 0.043026089668273926, 0.002290723379701376, 0.012971856631338596, -0.05872511491179466, 0.02276432514190674, 0.02117641642689705, -0.022292708978056908, 0.024295657873153687, 0.018729258328676224, 0.04527870565652847, 0.05446883291006088, -0.03194585070014, -0.05353504419326782, 0.007287578657269478, 0.0380866639316082, 0.016935378313064575, -0.03340756148099899, -0.027281498536467552, -0.033742133527994156, 0.026681315153837204, 0.03386581316590309, -0.009103501215577126, 0.06592224538326263, 0.030999822542071342, -0.04099567234516144, -0.009076524525880814, 0.02175270952284336, -0.036617472767829895, -0.03344471752643585, 0.005129275843501091, -0.029501501470804214, -0.03429201990365982, 0.011459232307970524, 0.0006861088913865387, 0.013579529710114002, -0.0015149173559620976, -0.024662524461746216, 0.04045545682311058, -0.0018174498109146953, -0.023462023586034775, -0.016124913468956947, 0.02162017486989498, -0.056019559502601624, -0.019998298957943916, -0.027795754373073578, 0.024354267865419388, 0.02480003982782364, 0.013684275560081005, -0.024283461272716522, 0.0011192058445885777, -0.045790378004312515, -0.02408214472234249, -0.024751069024205208, 0.07325536012649536, 0.017202816903591156, -0.021481569856405258, -0.005195422563701868, -0.04706282913684845, -0.00486423633992672, 0.052514538168907166, 0.01144708227366209, 0.023509232327342033, -0.03674093261361122, -0.022150933742523193, -0.009747461415827274, -0.024228980764746666, -0.07038968801498413, -0.011536262929439545, -0.0013461436610668898, 0.009973806329071522, -0.01223414670675993, -0.0025492713321000338, -0.004973690491169691, -0.02481199987232685, -0.014812732115387917, 0.01759677194058895, 0.005494560115039349, -0.03335653990507126, -0.023738596588373184, 0.03527134284377098, -0.02097729593515396, -0.01853804849088192, -0.006946256384253502, -0.06750304251909256, -0.045139338821172714, -0.026471631601452827, 0.00532585009932518, -0.008783992379903793, 0.024564970284700394, 0.029350798577070236, 0.011458762921392918, 0.030277805402874947, 0.0205532293766737, -0.00984963309019804, -0.01412624679505825, -0.03169505298137665, 0.015557650476694107, -0.07334819436073303, -0.0008783906232565641, 0.016019541770219803, -0.040435049682855606, 0.02936737798154354, 0.025725584477186203, -0.05220478028059006, 0.07703512161970139, 0.010362865403294563, -0.009146376512944698, 0.0017856304766610265, -0.07254050672054291, -0.015890326350927353, -0.05134549364447594, 0.04060807824134827, -0.04428347572684288, 0.0159293320029974, 0.05511663109064102, -0.10372194647789001, -0.061531055718660355, 0.0277838334441185, 0.03478135168552399, -0.05370226874947548, 0.023543288931250572, -0.012365857139229774, 0.03653835132718086, 0.014834372326731682, -0.03583601489663124, -0.019616704434156418, 0.008033659309148788, 0.03922533988952637, -0.041722286492586136, 0.01708785630762577, 0.037513259798288345, 0.0043080048635602, -0.033681031316518784, -0.009887531399726868, 0.004816023632884026, -0.01512952707707882, 0.04124847427010536, 0.02088569663465023, 0.0001547611755086109, -0.09408373385667801, -0.02215474843978882, -0.044268883764743805, 0.027104834094643593, -0.08987811952829361, -0.027673671022057533, -0.104745052754879, -0.022688282653689384, -0.02141873724758625, 0.012187951244413853, -0.03373376652598381, 0.05666755139827728, 0.018605435267090797, 0.01994992420077324, -0.012688927352428436, 0.011424084194004536, 0.034157585352659225, -0.046728577464818954, 0.03308364003896713, 0.0013122300151735544, -0.05187392979860306, -0.04052447900176048, -0.04851463809609413, -0.004263375420123339, 0.008102741092443466, 0.03568171337246895, 0.02172304131090641, -0.020238026976585388, -0.030076593160629272, 0.0044076815247535706, -0.024860486388206482, -0.00006305387069005519, -0.035210981965065, -0.020353877916932106, 0.006501694675534964, 0.035770878195762634, 0.008176209405064583, 0.03222893550992012, -0.004433075897395611, 0.05397939682006836, -0.03273918107151985, 0.03192058578133583, -0.0016611091559752822, -0.045717015862464905, 0.01027857419103384, -0.01960708387196064, -0.005350410472601652, 0.023463785648345947, 0.015012698248028755, -0.038585953414440155, 0.026251908391714096, -0.02596452087163925, 0.026471421122550964, 0.05227116122841835, -0.05649283155798912, 0.03583763912320137, 0.03872423246502876, -0.005381914786994457, 0.04197729378938675, -0.00735336821526289, 0.00823806319385767, 0.010936095379292965, 0.005846372805535793, 0.0766603946685791, -0.049766868352890015, 0.024354228749871254, 0.03289148584008217, -0.024624621495604515, -0.004724327940493822, 0.020384877920150757, -0.043807271867990494, -0.00469548674300313, -0.017736049368977547, 0.006600508466362953, -0.04652305319905281, -0.023376256227493286, -0.009573354385793209, 0.011772850528359413, 0.020797070115804672, 0.030465444549918175, 0.039235033094882965, 0.0594230480492115, -0.00451740762218833, 0.02754233591258526, 0.06172821298241615, 0.013865466229617596, -0.0251790601760149, -0.05862573906779289, -0.01442775409668684, -0.020485134795308113, 0.03671799227595329, -0.04624896124005318, -0.03720305860042572, -0.006938486360013485, 0.07923135161399841, -0.019117798656225204, -0.019823754206299782, 0.02159089222550392, 0.010668712668120861, 0.004527474287897348, -0.024382678791880608, -0.04049510508775711, 0.01627703197300434, -0.011975173838436604, 0.020107099786400795, 0.07306525856256485, 0.004562468267977238, 0.0265971589833498, -0.01968029886484146, 0.05379144847393036, -0.0019519844790920615, 0.00004582213659887202, -0.003278799820691347, -0.04336630925536156, 0.007528198882937431, -0.028341446071863174, -0.018752172589302063, 0.05025836080312729, -0.0046430774964392185, 0.05511382594704628, -0.011852085590362549, 0.006966182962059975, -0.012953562662005424, -0.011707035824656487, -0.0020590857602655888, -0.03981521353125572, 0.030292313545942307, 0.00012488666106946766, 0.022934073582291603, -0.027815403416752815, -0.014252398163080215, -0.017289429903030396, -0.05392579361796379, -0.019444074481725693, 0.005754227750003338, -0.062306251376867294, 0.019689692184329033, 0.0845719575881958, -0.005880639422684908, -0.01833791472017765, -0.003895744914188981, -0.03583487495779991, -0.02553984709084034, 0.014491001144051552, -0.015314308926463127, 0.03827793896198273, 0.020852340385317802, 0.018365127965807915, -0.002837738022208214, 0.02448424883186817, -0.013177318498492241, 0.0007743040914647281, 0.05459606274962425, 0.01491538155823946, -0.059842731803655624, -0.012772634625434875, -0.0030686743557453156, 0.03697708249092102, -0.07276087999343872, 0.014096474274992943, 0.006823538802564144, 0.06114984303712845, 0.08428391069173813, 0.015638992190361023, -0.02526453696191311, -0.03279682621359825, -0.00032543318229727447, -0.011237015947699547, -0.07638128101825714, 0.038004085421562195, 0.0370173417031765, -0.08115116506814957, -0.012577982619404793, 0.022746123373508453, -0.0042081549763679504, 0.06383024156093597, 0.054074712097644806, -0.0030471887439489365, 0.03732563182711601, -0.03823298215866089, 0.001838178257457912, -0.013654043897986412, 0.01060086116194725, 0.017525291070342064, 0.08141805231571198, 0.04056619852781296, -0.04029570892453194, -0.010672912932932377, 0.07063312828540802, 0.024489261209964752, -0.0007547390414401889, -0.029718976467847824, 0.02599574625492096, -0.003998253028839827, 0.004440079443156719, 0.0018633458530530334, 0.03373732790350914, -0.013814468868076801, -0.020749637857079506, -0.011186524294316769, 0.023507418110966682, 0.004828187637031078, 0.016854820773005486, 0.013292219489812851, -0.009994409047067165, -0.042890653014183044, 0.021914547309279442, 0.04412049800157547, -0.0348777249455452, -0.019718503579497337, 0.010707410983741283, -0.03636578097939491, -0.0009556253789924085, 0.08840087056159973, 0.002869955962523818, -0.016701873391866684, -0.01771968975663185, -0.06076069921255112, 0.021178174763917923, -0.019839318469166756, -0.00964144617319107, 0.03613246977329254, 0.07832162827253342, 0.039017390459775925, -0.02756316214799881, 0.005121173802763224, 0.05988653749227524, 0.004136867821216583, 0.0068223318085074425, 0.006781258154660463, -0.040046241134405136, -0.030447686091065407, 0.03039432317018509, 0.06395217031240463, 0.03351003676652908, 0.02400333806872368, 0.0068212589249014854, -0.0018137333681806922, -0.03952465206384659, 0.04621762037277222, 0.07670285552740097, 0.00008935540972743183, -0.04781889542937279, 0.01400251965969801, 0.03223360329866409, 0.052328091114759445, -0.011169648729264736, 0.06412384659051895, -0.06118900701403618, -0.020900225266814232, -0.012211361899971962, -0.003028338775038719, 0.02900184504687786, 0.022483421489596367, 0.08040981739759445, 0.013371028006076813, -0.0017502581467851996, -0.006725595332682133, -0.008747700601816177, 0.01960158161818981, -0.0013404223136603832, 0.019635023549199104, -0.004696606192737818, -0.03454889729619026, 0.04365703463554382, -0.03454015776515007, 0.016581781208515167, 0.03387446328997612, 0.00031892003607936203, 0.02122962288558483, -0.028874535113573074, 0.05274486169219017, -0.05267391353845596, 0.050629422068595886, -0.040728162974119186, -0.009185252711176872, 0.0011565056629478931, -0.008016487583518028, -0.017361493781208992, 0.030171165242791176, -0.011229123920202255, 0.023265305906534195, -0.02042320743203163, 0.06120031327009201, -0.04158385843038559, 0.042540647089481354, -0.004816525150090456, -0.048418667167425156, 0.009356729686260223, -0.038448136299848557, 0.019960269331932068, 0.10710741579532623, 0.0100331399589777, 0.031671274453401566, -0.060844749212265015, 0.012427630834281445, 0.03253574296832085, -0.036947332322597504, 0.07149363309144974, -0.049712926149368286, -0.056448500603437424, 0.0036135963164269924, 0.001403349102474749, 0.02173895761370659, 0.05201491713523865, -0.09056406468153, -0.022007299587130547, 0.022492730990052223, -0.03213903680443764, 0.00843699462711811, 0.002662145532667637, 0.09828419238328934, -0.016732733696699142, 0.019397208467125893, 0.03913978114724159, -0.01616363599896431, -0.02127097360789776, 0.005510337185114622, 0.006624584086239338, -0.03063478320837021, 0.006086322478950024, 0.05853768810629845, 0.020729990676045418, -0.014682305045425892, 0.027151530608534813, -0.045432861894369125, -0.01958272233605385, 0.013854959979653358, -0.04525160789489746, 0.020482467487454414, -0.05345211923122406, -0.004658573307096958, -0.002786151133477688, -0.01702200248837471, 0.03637821972370148, -0.019335385411977768, 0.08300045132637024, 0.05962315574288368, 0.010417322628200054, -0.03447569161653519, -0.05560220405459404, 0.06258097290992737, 0.0047042458318173885, 0.04074421525001526, -0.019686482846736908, 0.09045020490884781, -0.09533695876598358, 0.02930288389325142, -0.03484703600406647, 0.0016893659485504031, -0.07004161924123764, 0.0573369562625885, -0.020404908806085587, 0.014307419769465923, 0.007495359051972628, -0.05712653324007988, 0.008123423904180527, -0.048044249415397644, 0.015106051228940487, -0.04182910919189453, 0.005804221145808697, 0.01715880259871483, -0.07788063585758209, -0.02677466720342636, 0.036034416407346725, -0.06579288840293884, 0.036488357931375504, 0.03828735277056694, 0.01538150291889906, -0.05331358313560486, -0.01291199866682291, 0.04872141033411026, -0.05088408291339874, -0.017127418890595436, -0.00034896255237981677, -0.01040733978152275, 0.010998951271176338, -0.022034499794244766, 0.012494820170104504, -0.004418393597006798, -0.010684054344892502, -0.040797483175992966, -0.05478570982813835, 0.06900104135274887, -0.015507942996919155, 0.011506481096148491, -0.003448868403211236, -0.04953249916434288, -0.0340084433555603, 0.018776454031467438, -0.004341270308941603, 0.03588046878576279, 0.007163454778492451, 0.0071882400661706924, -0.004114475101232529, -0.04413943365216255, -0.005602618679404259, -0.05162699148058891, 0.03479134663939476, 0.042954083532094955, -0.020893417298793793, 0.04752320051193237, -0.05135015770792961, -0.014396432787179947, -0.06477039307355881, -0.019471952691674232, 0.0048530143685638905, 0.042481373995542526, 0.013317869044840336, -0.028294174000620842, 0.010591350495815277, -0.05635863542556763, -0.015704097226262093, -0.015064483508467674, 0.012847903184592724, 0.023779485374689102, 0.03516785427927971, 0.04847210273146629, 0.007654344197362661, 0.029127413406968117, -0.0749111995100975, -0.0015632093418389559, -0.025773128494620323, 0.030465831980109215, -0.020336266607046127, -0.006291207857429981, -0.029905937612056732, 0.06089804694056511, -0.01716454327106476, 0.00485791452229023, -0.0029111735057085752, 0.020527131855487823, 0.05710463598370552, 0.058800484985113144, -0.04600130021572113, -0.10113599896430969, 0.010860011912882328, 0.001721679698675871, 0.0029040540102869272, 0.029646558687090874, 0.006585356313735247, -0.05702606961131096, 0.015385154634714127, 0.018257437273859978, -0.01739070564508438, -0.05523722991347313, -0.028952764347195625 ]
<p>The latent heat of vaporization of water is what we normally use to calculate the heat transfer that occurs at 373 K when liquid water transits to vapor phase. But there are curves for latent heat of vaporization at different temperatures. What is meant by latent heat of vaporization at a temperature different from its boiling point?</p>
g1537
[ 0.027833012863993645, -0.027346298098564148, 0.0018579495372250676, 0.026821115985512733, -0.0227371733635664, 0.009174036793410778, -0.0399533286690712, 0.01876687817275524, 0.0026422853115946054, 0.002509873593226075, -0.04031701385974884, 0.05511051043868065, 0.003838790813460946, -0.022347215563058853, -0.015436415560543537, -0.01765645667910576, 0.061733026057481766, -0.02595687471330166, -0.005006376653909683, 0.03098340332508087, 0.0007002092897891998, -0.08546020835638046, -0.0006237393827177584, -0.004594981670379639, -0.05805038660764694, -0.05392809584736824, -0.014510825276374817, 0.014535502530634403, -0.005227758549153805, 0.006232717540115118, 0.02211163006722927, 0.007836278527975082, 0.013886907137930393, -0.03961164131760597, -0.03976544737815857, -0.035547249019145966, -0.03751729056239128, -0.006866909097880125, 0.05005284398794174, -0.014367733150720596, 0.05423782020807266, 0.07139570266008377, 0.04226268455386162, 0.06323430687189102, 0.017042024061083794, -0.013505714945495129, 0.0005939236143603921, 0.009207292459905148, -0.049017198383808136, 0.003928463440388441, 0.04531882703304291, 0.048306867480278015, -0.013625760562717915, -0.0010052809957414865, -0.05706540867686272, -0.0002785985416267067, -0.03945494070649147, -0.00039927958277985454, 0.040996063500642776, 0.03376780077815056, 0.08723218739032745, 0.06648579984903336, 0.004162766970694065, -0.004634262528270483, 0.058001626282930374, -0.028449801728129387, -0.083173468708992, -0.042144134640693665, -0.01368621364235878, 0.016626352444291115, -0.014590803533792496, -0.060435060411691666, -0.04275428131222725, 0.01586940884590149, -0.05301133170723915, -0.059416960924863815, -0.006182066164910793, -0.049741506576538086, -0.006277079228311777, 0.012576524168252945, -0.011858581565320492, 0.005425812676548958, 0.008567456156015396, 0.024108434095978737, 0.033932238817214966, -0.024272581562399864, -0.008798723109066486, 0.0052014910615980625, -0.043885450810194016, -0.012321310117840767, -0.04449904337525368, 0.061717480421066284, 0.09759166091680527, 0.03382905200123787, -0.0019130237633362412, 0.04542925953865051, -0.0005484282155521214, 0.03241103142499924, -0.03434937447309494, 0.013756228610873222, -0.0009834429947659373, -0.036506712436676025, 0.03371964022517204, -0.017358381301164627, 0.004113451577723026, -0.0495072603225708, 0.0005644014454446733, 0.012300487607717514, -0.03748862445354462, 0.01416105404496193, 0.0008586895419284701, -0.04300084337592125, -0.022307995706796646, -0.018886785954236984, 0.010568365454673767, 0.014952790923416615, -0.02945704758167267, -0.027845902368426323, -0.0018287006532773376, 0.02513369731605053, 0.0005472684279084206, 0.01141197420656681, -0.02356400527060032, 0.11421559005975723, 0.021304462105035782, 0.013278163969516754, 0.007025484461337328, -0.09128911048173904, 0.01706814579665661, 0.023762645199894905, 0.015074843540787697, 0.05174519866704941, 0.004405871033668518, 0.02070102095603943, 0.078375905752182, 0.0013818570878356695, 0.008870408870279789, 0.03990898281335831, 0.012361032888293266, 0.006749083753675222, 0.049496788531541824, 0.0007092709420248866, 0.0003050698433071375, -0.025616087019443512, -0.04796764999628067, 0.009101444855332375, -0.014988764189183712, 0.02115727961063385, 0.003939949441701174, -0.026741063222289085, -0.03158902749419212, 0.000450323976110667, 0.04382910951972008, 0.02686387673020363, -0.0386744849383831, 0.009577666409313679, 0.0012276830384507775, -0.036285802721977234, 0.044238604605197906, -0.04996229335665703, -0.0023858456406742334, -0.05704422667622566, 0.07153577357530594, 0.027478044852614403, -0.03222555294632912, -0.02478194609284401, -0.03824685886502266, 0.017356421798467636, -0.006887242663651705, -0.07209263741970062, -0.08794613182544708, 0.03562344238162041, -0.04897857457399368, -0.058326151221990585, 0.04797393083572388, 0.0162887554615736, 0.027751056477427483, 0.022892087697982788, -0.01812264882028103, -0.020525742322206497, -0.013804900459945202, 0.011842334643006325, 0.031397804617881775, -0.02111099101603031, -0.026051998138427734, 0.03973059356212616, 0.031913597136735916, -0.05585480108857155, -0.037710387259721756, -0.01335815992206335, -0.03498843312263489, -0.008439307101070881, 0.007780040148645639, 0.000838668376673013, -0.013669239357113838, -0.06424885243177414, -0.06035788729786873, 0.0011443847324699163, -0.057637959718704224, -0.05481603741645813, -0.024219920858740807, -0.006694883573800325, 0.000420015916461125, 0.00030965395853854716, 0.009024307131767273, 0.015128672122955322, -0.011135468259453773, 0.011426321230828762, 0.018304169178009033, 0.036595143377780914, 0.03363051265478134, 0.018221529200673103, 0.018068235367536545, -0.002299322048202157, -0.05816735699772835, 0.08410268276929855, -0.006095578894019127, -0.014884905889630318, -0.009359871968626976, -0.012572440318763256, -0.02176802232861519, 0.031962547451257706, -0.030170245096087456, 0.04882360249757767, -0.047888390719890594, 0.02429601363837719, -0.04757241532206535, -0.0473964661359787, -0.0004630997427739203, 0.00907248817384243, -0.011943326331675053, -0.009003937244415283, -0.01494964212179184, -0.052865881472826004, 0.014858962036669254, -0.05942379683256149, 0.030054759234189987, -0.011773748323321342, 0.02544630505144596, 0.04680691659450531, 0.04047391191124916, -0.03371821343898773, 0.009628836996853352, 0.07257093489170074, 0.04474787786602974, 0.004522583447396755, -0.021453820168972015, -0.03751543164253235, -0.022067634388804436, 0.0027424998115748167, -0.010836878791451454, 0.010170066729187965, -0.02566632628440857, 0.09837643802165985, -0.007756001316010952, -0.02371917851269245, -0.06399019062519073, -0.0010874225990846753, -0.059986624866724014, -0.013341812416911125, 0.015274645760655403, -0.005030850414186716, 0.036585673689842224, -0.013359665870666504, -0.013644975610077381, 0.050817497074604034, 0.0027708359993994236, 0.021541092544794083, -0.05350585654377937, -0.03195680305361748, 0.0031804568134248257, 0.03448311612010002, 0.01435207761824131, 0.08660072088241577, 0.049572356045246124, -0.016228612512350082, 0.004990316461771727, 0.018473852425813675, 0.0005210498929955065, -0.05580730736255646, -0.03469321131706238, -0.011498747393488884, -0.03308585286140442, 0.024108417332172394, 0.022550910711288452, -0.09305927902460098, 0.04013581573963165, 0.07926414906978607, 0.030100863426923752, -0.03664081543684006, 0.05388711020350456, 0.007090122904628515, -0.037791259586811066, 0.009970900602638721, -0.006886124145239592, -0.04818372055888176, 0.020133402198553085, -0.04504932463169098, -0.05169058218598366, -0.023104112595319748, -0.01779046468436718, 0.006959006190299988, -0.01085918489843607, -0.00803097989410162, 0.00764200696721673, -0.00834578089416027, -0.017882214859128, -0.07542462646961212, 0.004221991635859013, -0.044466692954301834, -0.018456866964697838, -0.06628622859716415, -0.05318094417452812, -0.02022402547299862, 0.003469048300758004, -0.024904342368245125, -0.03181922435760498, 0.053862620145082474, 0.07792350649833679, -0.001461434061639011, -0.07332839071750641, -0.020652974024415016, 0.054379407316446304, 0.03104848600924015, 0.0036635531578212976, 0.03711306303739548, 0.03427092358469963, -0.024869035929441452, -0.0436832495033741, 0.017544925212860107, -0.027161503210663795, 0.016583092510700226, -0.08642687648534775, -0.035760655999183655, 0.005096306558698416, -0.009342875331640244, -0.007246257737278938, 0.045323584228754044, -0.007168369833379984, 0.02798631601035595, 0.022675413638353348, -0.04555346444249153, -0.05407331883907318, 0.039678167551755905, -0.006672181189060211, -0.01845087669789791, 0.001981642795726657, 0.007017523515969515, 0.01641467586159706, 0.007600295823067427, 0.03269486874341965, -0.03589438647031784, -0.0437837615609169, -0.06230532005429268, -0.028720611706376076, 0.008662586100399494, -0.06526163965463638, -0.07241913676261902, -0.01617339998483658, 0.06334005296230316, 0.029798617586493492, 0.0019554970785975456, 0.05259087681770325, 0.0192379392683506, -0.007314885500818491, -0.03794660046696663, 0.011145674623548985, 0.027777524664998055, 0.005331648979336023, 0.032202381640672684, 0.0026071297470480204, -0.026923509314656258, -0.0322372242808342, 0.0061966003850102425, 0.013760264031589031, 0.02613717131316662, 0.019436510279774666, 0.008884336799383163, -0.046398259699344635, 0.026558537036180496, 0.0075287469662725925, -0.015325488522648811, 0.04752129688858986, 0.011008466593921185, 0.02282150276005268, -0.020239785313606262, -0.04660521075129509, 0.01524334866553545, 0.038370173424482346, -0.06907997280359268, -0.00018479066784493625, 0.01836039498448372, 0.03547848016023636, 0.00891963578760624, 0.02104051224887371, -0.012882606126368046, 0.042788948863744736, 0.07570023834705353, 0.016781629994511604, -0.022250637412071228, -0.010833505541086197, -0.012399647384881973, 0.05593865364789963, -0.0020887863356620073, -0.01617308147251606, -0.031995225697755814, 0.07754053175449371, -0.0462268702685833, 0.012100189924240112, -0.07752513140439987, -0.011876669712364674, 0.06800764799118042, -0.02195645682513714, -0.03275167942047119, -0.033919911831617355, -0.032908473163843155, 0.04797110706567764, -0.029634179547429085, -0.010399582795798779, 0.04621676355600357, -0.045348700135946274, -0.013891997747123241, 0.016410985961556435, 0.021358361467719078, 0.08075021207332611, -0.003261106787249446, 0.09244811534881592, 0.019537605345249176, -0.0415283739566803, -0.06981812417507172, 0.01087083388119936, 0.02883976697921753, 0.013079517520964146, 0.06370116770267487, 0.011177252046763897, -0.0015053709503263235, 0.07389258593320847, 0.009899638593196869, -0.0076844170689582825, -0.015235485509037971, -0.014251410961151123, 0.03410810977220535, -0.020450515672564507, 0.04414312541484833, -0.05448269844055176, -0.008748715743422508, 0.05921159312129021, -0.051272280514240265, 0.03413393348455429, -0.05808098614215851, -0.008091272786259651, 0.0757235586643219, -0.031135663390159607, 0.04537634551525116, -0.06828224658966064, -0.0022313648369163275, 0.016563385725021362, 0.005743328481912613, -0.04817749187350273, 0.026402730494737625, -0.01957355998456478, -0.0015877202386036515, -0.020565230399370193, -0.006650273688137531, 0.03831596300005913, -0.034373972564935684, -0.015730053186416626, -0.017260469496250153, 0.024171914905309677, 0.08258368819952011, 0.03605404496192932, 0.0517086498439312, 0.04320491850376129, 0.08446446061134338, 0.054402995854616165, -0.027026209980249405, 0.0546928271651268, -0.052249256521463394, 0.01918891631066799, 0.006174086593091488, 0.029895219951868057, 0.02425624243915081, -0.0038470826111733913, 0.04735839366912842, -0.021349215880036354, -0.011798422783613205, -0.006335175596177578, 0.03271206468343735, 0.013559255748987198, -0.054972488433122635, -0.03301359340548515, -0.022561848163604736, 0.0064216190949082375, 0.0263129360973835, -0.014219819568097591, -0.005520051345229149, 0.019926652312278748, 0.03129332512617111, 0.03880900889635086, 0.03582486882805824, -0.06363538652658463, 0.027611710131168365, 0.008102797903120518, -0.05074746534228325, 0.04601145163178444, 0.007312836591154337, 0.01491306722164154, 0.02221365086734295, -0.05691497027873993, 0.010088193230330944, 0.052525684237480164, 0.005556899588555098, -0.06760440021753311, 0.00800290796905756, 0.02828914113342762, 0.027163855731487274, 0.010021431371569633, -0.0339224673807621, 0.030355285853147507, -0.006176828406751156, -0.0039654443971812725, -0.02029533125460148, -0.009124466218054295, 0.023297198116779327, 0.014580576680600643, -0.016112158074975014, -0.04139968752861023, -0.037778034806251526, -0.03402472287416458, -0.035349003970623016, -0.027884116396307945, 0.04251308739185333, 0.05556900054216385, 0.05012671276926994, -0.009119125083088875, 0.0043164086528122425, -0.027590051293373108, 0.01592150144279003, 0.08449029922485352, 0.013522152788937092, -0.040880732238292694, -0.057229671627283096, 0.024847259745001793, 0.0006393304793164134, 0.04861421510577202, 0.031360603868961334, 0.015013162977993488, 0.003976785112172365, -0.009771697223186493, 0.03161986172199249, -0.003013128647580743, -0.01841176114976406, -0.004993252921849489, -0.04988178238272667, 0.007282766979187727, 0.009486625902354717, 0.04388813674449921, -0.04314957931637764, -0.022327708080410957, -0.019350294023752213, -0.0412759892642498, -0.013165581971406937, 0.01651245914399624, 0.04605157673358917, -0.029221808537840843, -0.03103022277355194, -0.0167979933321476, -0.0416187159717083, 0.004619703162461519, -0.005080574192106724, -0.015004361979663372, 0.02944735810160637, 0.001371976686641574, -0.023989776149392128, 0.004366179462522268, 0.020428922027349472, -0.006557764019817114, -0.05211823061108589, -0.018147941678762436, 0.014591888524591923, -0.02725371904671192, -0.021019695326685905, -0.004818321205675602, 0.03189873695373535, -0.03010634146630764, -0.0005656052380800247, -0.012939514592289925, 0.016773736104369164, -0.08548415452241898, 0.09038226306438446, 0.008913032710552216, 0.04214705526828766, -0.027520058676600456, -0.006587829440832138, -0.01238096971064806, 0.03708460554480553, -0.012151213362812996, 0.07992154359817505, -0.005130616016685963, 0.009315201081335545, 0.005470604170113802, 0.00286503997631371, 0.017161067575216293, -0.061850566416978836, 0.003066825680434704, -0.0012827473692595959, 0.03569035232067108, 0.0296158604323864, 0.01335941068828106, 0.0028993040323257446, 0.026210492476820946, 0.04360367730259895, 0.028859153389930725, -0.0726977065205574, -0.006312266457825899, -0.03387228399515152, -0.048595722764730453, 0.028137030079960823, -0.06373562663793564, -0.016405198723077774, -0.01955980248749256, -0.003080688649788499, 0.035317908972501755, 0.004126504994928837, 0.053096234798431396, 0.03950657323002815, -0.058064915239810944, 0.04554222151637077, -0.03268089145421982, 0.007309558801352978, -0.0025864760391414165, -0.00846210215240717, -0.006908366456627846, 0.002065785462036729, 0.009943301789462566, 0.048471201211214066, -0.043187256902456284, -0.017795683816075325, -0.015503794886171818, 0.06076209992170334, 0.01274502370506525, -0.01190621592104435, 0.0024748174473643303, 0.05012744665145874, -0.029374852776527405, 0.025868326425552368, -0.015543689951300621, -0.040175557136535645, -0.0770326629281044, -0.04489240050315857, -0.013399221003055573, -0.0552961640059948, 0.020360101014375687, 0.005371877923607826, 0.010685120709240437, 0.019599581137299538, 0.024321017786860466, -0.012345586903393269, -0.003804787527769804, 0.015003728680312634, 0.01668255589902401, 0.04447557032108307, 0.05218343064188957, 0.06462999433279037, 0.04556688293814659, 0.07074771076440811, 0.061376288533210754, -0.05392429977655411, 0.01770203933119774, -0.04338027536869049, -0.04057789593935013, -0.039795562624931335, -0.014952103607356548, -0.04020623117685318, -0.011488717049360275, 0.02071092277765274, 0.05805907025933266, -0.0007251696661114693, -0.03632507473230362, 0.0048464396968483925, -0.0471784844994545, 0.0067901634611189365, 0.018703853711485863, -0.04623601958155632, -0.014558566734194756, -0.006784587167203426, -0.05870833992958069, 0.03235723450779915, 0.07313813269138336, 0.026345085352659225, -0.0013327636988833547, 0.0020105105359107256, 0.016947077587246895, -0.0165907833725214, -0.009651141241192818, 0.016982167959213257, 0.054912269115448, -0.046832311898469925, 0.02883818745613098, 0.010122321546077728, 0.040545132011175156, -0.025952080264687538, -0.0035104125272482634, 0.015334161929786205, 0.02963048778474331, 0.07720019668340683, 0.038539763540029526, 0.06013911962509155, -0.0445728562772274, -0.04156450927257538, -0.031048502773046494, -0.0046697319485247135, 0.03256061673164368, -0.01513274572789669, -0.029063774272799492, -0.027802051976323128, -0.02247723750770092, -0.043474968522787094, -0.006548188626766205, -0.04460068792104721, 0.0013662890996783972, -0.008224532008171082, -0.04713265597820282, -0.03057997301220894, 0.027912836521863937, -0.038103919476270676, -0.011615198105573654, -0.012549033388495445, -0.05926128104329109, 0.026445845142006874, 0.00868148636072874, 0.08085820823907852, 0.02406839281320572, 0.01160492841154337, -0.016360385343432426, 0.05160605534911156, -0.002760988427326083, 0.04422982782125473, 0.10738108307123184, 0.013989969156682491, 0.04216345027089119, 0.01311518531292677, 0.04431360587477684, -0.03366096317768097, 0.057867418974637985, -0.04960702359676361, -0.011430352926254272, 0.036556243896484375, 0.048896998167037964, -0.03365888446569443, -0.0044853296130895615, -0.04474212974309921, -0.016594691202044487, 0.027798617258667946, 0.0005280246259644628, -0.041691336780786514, -0.057983167469501495, 0.047629959881305695, -0.010805592872202396, -0.038619108498096466, -0.051547568291425705, -0.016993578523397446, 0.0600813589990139, 0.04852341488003731, -0.0009311731555499136, 0.01941704750061035, -0.054844118654727936, 0.00864927377551794 ]
<p>If we consider a classical field theory for a massless particle of integer spin $s$, in a curved space-time, one finds that it is "naturally" conformal in a space-time of dimension $2+2s$</p> <p>For instance, the free massless scalar field theory is conformal in $2$ dimensions, the electromagnetic field theory is conformal in $4$ dimensions, etc...</p> <p>But does it work for half-integer spin, for instance is a spin $\frac{1}{2}$ field theory conformal in a $3$ dimensional space-time , and is a spin $\frac{3}{2}$ field theory conformal in a $5$ dimensional space-time ?</p>
g1538
[ 0.015823455527424812, -0.04295074939727783, 0.030918719246983528, 0.002400824101641774, -0.0043089743703603745, 0.0028879386372864246, 0.005684392061084509, -0.028940027579665184, -0.03464697673916817, 0.00910202693194151, -0.01923178695142269, 0.03037233091890812, 0.017190901562571526, -0.015883592888712883, -0.042710695415735245, 0.021076444536447525, 0.035220153629779816, 0.023022975772619247, 0.05863368511199951, 0.00687640905380249, -0.0001384144416078925, -0.018925143405795097, 0.04114687815308571, 0.010274549946188927, -0.04497212544083595, 0.04551905393600464, 0.008156095631420612, -0.007940194569528103, 0.012279029004275799, -0.031224049627780914, -0.004713309928774834, 0.05167488753795624, 0.0247084591537714, -0.026374926790595055, -0.018656423315405846, -0.02565927989780903, -0.0016428478993475437, 0.01293839793652296, 0.018765006214380264, 0.02118772827088833, -0.024019356817007065, 0.0002968203625641763, 0.02571018412709236, -0.0061445520259439945, 0.005405936390161514, 0.054874271154403687, 0.012268968857824802, 0.07941557466983795, -0.021514080464839935, 0.022771378979086876, -0.013126331381499767, 0.0305820032954216, 0.004952453076839447, 0.0010841808980330825, -0.044497329741716385, -0.02349761128425598, 0.006584388669580221, 0.03537619486451149, 0.08392529934644699, 0.048394784331321716, -0.030579008162021637, 0.04941437393426895, -0.004689539782702923, 0.06498709321022034, 0.007384961470961571, 0.04799361154437065, -0.07346230745315552, -0.0356476753950119, 0.03262340649962425, -0.022671451792120934, -0.012788289226591587, -0.06762877106666565, 0.004360633436590433, -0.03235244005918503, -0.029032642021775246, 0.09259245544672012, 0.0016320940339937806, 0.001801390666514635, -0.04699581116437912, -0.03526763245463371, -0.02683923952281475, -0.022553754970431328, 0.0010877985041588545, -0.012247277423739433, 0.07631088048219681, -0.019491462036967278, -0.0659460723400116, 0.006573356222361326, -0.05601426586508751, 0.016391530632972717, 0.027900131419301033, 0.006334950216114521, -0.000850493845064193, 0.0066771614365279675, 0.031036628410220146, 0.00550164794549346, 0.0030139859300106764, -0.01922069862484932, -0.01478287111967802, 0.02157195843756199, -0.03649936243891716, 0.02383744902908802, 0.07116631418466568, 0.022488143295049667, -0.03373956307768822, -0.006310440134257078, -0.0017833352321758866, 0.03668402135372162, 0.06980540603399277, -0.020967679098248482, 0.0022603352554142475, 0.03329189494252205, -0.0397682823240757, 0.027684181928634644, -0.01641322486102581, 0.04087766259908676, 0.03533933684229851, -0.024351993575692177, 0.028798958286643028, 0.036257512867450714, 0.011872805655002594, 0.03199930861592293, 0.07339366525411606, 0.040175873786211014, -0.0398954302072525, 0.01673104800283909, -0.034519314765930176, -0.003178276354447007, 0.005919836927205324, -0.014079414308071136, 0.006694610696285963, 0.036851368844509125, -0.0029336579609662294, 0.014236987568438053, -0.02490806207060814, 0.038538139313459396, -0.03523944690823555, -0.011367091909050941, 0.046890828758478165, -0.05274338275194168, -0.013823405839502811, -0.03736228495836258, 0.03524033725261688, 0.009946411475539207, -0.028889140114188194, 0.020174948498606682, 0.022580748423933983, -0.07439247518777847, -0.01079811342060566, 0.06500686705112457, -0.034821849316358566, 0.05315675586462021, 0.02935265190899372, -0.04139311611652374, -0.00733816297724843, 0.03163376823067665, -0.012506628409028053, -0.01128238532692194, 0.020084895193576813, -0.022391118109226227, 0.054567817598581314, -0.004061931278556585, 0.029892075806856155, -0.001115348655730486, -0.040416765958070755, -0.002562537556514144, -0.02814151532948017, -0.024664005264639854, -0.029963849112391472, -0.039809051901102066, -0.012613052502274513, 0.0003453285316936672, 0.05224815011024475, 0.062359366565942764, -0.008469165302813053, 0.03322635963559151, -0.09721958637237549, -0.024243704974651337, 0.017656235024333, -0.008078783750534058, -0.02512555941939354, -0.046585168689489365, -0.04925863817334175, -0.019121060147881508, -0.008683995343744755, 0.027943046763539314, 0.03212345018982887, 0.04905855655670166, -0.022549379616975784, -0.025676855817437172, 0.009015879593789577, 0.005206218454986811, -0.0003874339163303375, 0.07380836457014084, -0.0004814418207388371, -0.01431962475180626, 0.016899950802326202, -0.0035628555342555046, 0.013152270577847958, 0.020941603928804398, 0.03526972606778145, 0.06181700900197029, 0.00644727423787117, 0.0014584104064852, 0.001297426293604076, -0.0413438156247139, 0.01693056896328926, -0.058384526520967484, 0.044630710035562515, 0.0015909612411633134, 0.08755526691675186, 0.014354998245835304, -0.03510216996073723, 0.02292432263493538, -0.02286878228187561, -0.01750335283577442, -0.034396957606077194, -0.017434855923056602, -0.04066406562924385, 0.08423741161823273, -0.006028157193213701, -0.006305641494691372, 0.05580533295869827, -0.040828920900821686, -0.0021717066410928965, -0.018132006749510765, -0.0305692907422781, -0.029689840972423553, -0.02027103304862976, 0.011893108487129211, -0.02645282819867134, -0.0803246945142746, 0.0014120902633294463, -0.00007979790098033845, 0.035386331379413605, 0.02916177734732628, -0.05442780628800392, -0.008959378115832806, 0.05037153512239456, -0.0023007411509752274, 0.04611620306968689, 0.03832161799073219, -0.04161125421524048, 0.028419289737939835, 0.024597004055976868, 0.021286696195602417, 0.005278041586279869, -0.024838512763381004, -0.02556747943162918, 0.007823538966476917, 0.02959480695426464, 0.012247354723513126, -0.051928166300058365, 0.02565084956586361, -0.029618775472044945, 0.03323329985141754, -0.01992873288691044, 0.06793829798698425, -0.11026254296302795, -0.03319554403424263, -0.022569293156266212, -0.012010730803012848, -0.015520489774644375, 0.04256855323910713, -0.00499681057408452, -0.025615554302930832, 0.021912211552262306, 0.06421972811222076, -0.01164489146322012, 0.02323777973651886, -0.0008695893920958042, 0.10834075510501862, -0.04645087942481041, 0.04475603625178337, -0.030524784699082375, -0.009714443236589432, -0.021954450756311417, 0.033792052417993546, -0.00881288107484579, -0.015547010116279125, 0.008657757192850113, -0.05600254610180855, -0.032393764704465866, 0.019580606371164322, 0.03304700925946236, -0.03589826822280884, -0.03712613880634308, -0.001810600864700973, 0.013378453440964222, 0.048520155251026154, 0.0028160533402115107, 0.0032556159421801567, 0.01766715943813324, -0.05956186726689339, 0.024103878065943718, 0.01986914686858654, 0.005081875249743462, -0.0050894212909042835, -0.00581554789096117, 0.07524343580007553, 0.01341209001839161, -0.0033176641445606947, 0.0049608368426561356, 0.01111667975783348, -0.02239467389881611, -0.027825409546494484, -0.05313153937458992, -0.060131434351205826, -0.021034065634012222, -0.06509684771299362, -0.046840790659189224, 0.06501199305057526, 0.04015105962753296, -0.01372998021543026, -0.0632031038403511, -0.06100001558661461, 0.009609728120267391, 0.03075835481286049, 0.027513816952705383, -0.00187157082837075, -0.007283104117959738, -0.00010463640501257032, 0.0021151418332010508, 0.0019436810398474336, 0.004043801221996546, 0.006013279780745506, 0.012257760390639305, -0.019330868497490883, -0.06337180733680725, 0.017319729551672935, 0.02846849337220192, 0.004748068284243345, -0.006951343268156052, -0.04485703632235527, -0.05266404524445534, 0.008004959672689438, -0.04543920233845711, 0.026528650894761086, -0.004093779716640711, -0.01486033946275711, -0.044319506734609604, -0.009713815525174141, -0.07927447557449341, -0.01523219607770443, -0.0034747333265841007, 0.019869068637490273, -0.033265285193920135, -0.021313682198524475, -0.02336130291223526, 0.03543250635266304, 0.0071354457177221775, -0.033540744334459305, 0.0018387845484539866, -0.010392077267169952, 0.0269052442163229, -0.01658443920314312, 0.02998972125351429, 0.09678211808204651, -0.01958392560482025, -0.01728852465748787, -0.0009685104014351964, -0.009583264589309692, 0.048098236322402954, 0.007641549687832594, -0.013901623897254467, 0.01775277592241764, 0.020399557426571846, -0.035508204251527786, 0.07570282369852066, 0.02724236622452736, 0.015661155804991722, 0.012671928852796555, 0.01053707767277956, -0.02034015953540802, -0.030085943639278412, -0.020006969571113586, -0.047853294759988785, 0.0114707350730896, -0.05487570911645889, 0.002703622682020068, 0.03460819646716118, 0.03894990682601929, 0.002775277243927121, 0.05740775167942047, -0.024471763521432877, 0.028328148648142815, -0.06204022467136383, -0.014178052544593811, -0.04182258993387222, 0.02517351135611534, 0.024698292836546898, 0.004357638768851757, 0.01008178573101759, -0.05776314064860344, 0.0017939454410225153, 0.002302467357367277, 0.03367595374584198, -0.054416969418525696, 0.008065350353717804, -0.04493587091565132, -0.0056234002113342285, 0.04009218513965607, -0.0016403320478275418, -0.015079677104949951, 0.0228353813290596, 0.005826715845614672, -0.030323684215545654, -0.02241935022175312, 0.02361936867237091, -0.0635138601064682, -0.05984833836555481, 0.017307234928011894, -0.03732878714799881, -0.053844865411520004, 0.006830934900790453, 0.009106630459427834, -0.027712704613804817, -0.05461044982075691, -0.020370302721858025, -0.005414183717221022, 0.019838716834783554, 0.009594040922820568, -0.015541726723313332, -0.005433341022580862, -0.010463041253387928, 0.006051434203982353, 0.033643558621406555, -0.010734445415437222, -0.04652782529592514, 0.007931478321552277, 0.00016824189515318722, 0.009982407093048096, 0.019288383424282074, 0.015831585973501205, -0.07948865741491318, 0.05737956985831261, -0.027095163241028786, 0.018205363303422928, -0.019486749544739723, 3.2719108844503353e-7, 0.03953634202480316, -0.02403940074145794, 0.04720548540353775, -0.034330353140830994, -0.0040915715508162975, 0.014175903052091599, -0.004649769980460405, -0.04707217589020729, 0.034790366888046265, -0.02027186192572117, 0.03097829781472683, 0.011753072962164879, -0.011126099154353142, 0.019315768033266068, -0.03363751992583275, -0.042996279895305634, -0.0034664554987102747, -0.0004929974093101919, 0.06402142345905304, 0.029465507715940475, -0.07558796554803848, -0.013762337155640125, -0.03662028908729553, -0.02260689064860344, -0.025045527145266533, 0.03859463706612587, -0.02387826144695282, -0.05112491548061371, -0.1040724664926529, 0.023672230541706085, 0.058606769889593124, -0.014275923371315002, -0.02217201329767704, -0.03936413675546646, -0.023939114063978195, 0.04752710834145546, -0.005975652020424604, -0.006569175980985165, -0.05116228014230728, -0.06598620861768723, 0.01392455119639635, -0.0807674378156662, -0.047687966376543045, 0.042806271463632584, -0.016139760613441467, 0.017658459022641182, 0.0314418263733387, -0.0067976657301187515, 0.03253036364912987, -0.03597269952297211, 0.016886049881577492, 0.013723371550440788, -0.07770859450101852, 0.00006709533045068383, 0.0017898224759846926, 0.05506877601146698, -0.03699333965778351, -0.10761253535747528, -0.02864323928952217, -0.041132114827632904, -0.046174462884664536, -0.01183524914085865, 0.029473019763827324, 0.03632981330156326, -0.0467018261551857, 0.034692052751779556, 0.05644569173455238, -0.0028676665388047695, -0.07545272260904312, 0.04206772521138191, 0.01506150420755148, -0.04899098724126816, 0.011492956429719925, 0.05339936539530754, 0.0574783980846405, -0.023253746330738068, -0.02952161245048046, -0.007487327326089144, 0.08369257301092148, -0.040320366621017456, -0.013125640340149403, -0.029343586415052414, 0.07319521903991699, 0.017159273847937584, 0.03985877335071564, 0.060586582869291306, -0.04841005057096481, -0.03714010491967201, 0.003827734850347042, 0.05386317893862724, 0.006652999669313431, -0.061172328889369965, 0.024361850693821907, 0.04937434569001198, -0.0021620020270347595, -0.03637691214680672, -0.011612646281719208, 0.0023009334690868855, 0.029737666249275208, 0.08894132822751999, -0.0606440007686615, -0.06106763705611229, 0.007581578567624092, -0.04499814286828041, 0.01256990060210228, 0.01206695381551981, 0.05843639373779297, -0.03144180402159691, 0.0349283404648304, -0.01319857407361269, -0.06157809495925903, 0.02994394674897194, -0.06244109198451042, -0.03663022816181183, -0.01039567869156599, 0.0708257257938385, 0.015310181304812431, -0.019810296595096588, 0.00109487387817353, 0.027406856417655945, -0.00905347615480423, -0.0347987525165081, 0.04672004282474518, -0.02337675541639328, -0.019650710746645927, -0.003884881269186735, 0.014176587574183941, -0.07956529408693314, 0.08282192796468735, -0.053732264786958694, -0.04853565990924835, 0.033873893320560455, 0.020045073702931404, 0.02759622223675251, -0.029813507571816444, -0.02313537523150444, -0.02249123342335224, -0.05156135931611061, -0.049149040132761, 0.019358651712536812, 0.028551198542118073, 0.0073027946054935455, 0.0045792534947395325, -0.06120043620467186, 0.034707505255937576, 0.053540922701358795, -0.029176944866776466, 0.004585866816341877, -0.007301511242985725, 0.01416224054992199, -0.05530666932463646, -0.01737120933830738, 0.020411033183336258, 0.038769643753767014, -0.005946357734501362, 0.0025784061290323734, -0.04000285640358925, -0.015471460297703743, -0.024234676733613014, 0.028009556233882904, -0.0087274219840765, 0.0262454766780138, 0.05300944298505783, 0.044298022985458374, 0.002966452157124877, 0.03911340981721878, -0.05587088316679001, -0.006379930302500725, 0.020780792459845543, -0.005785288754850626, -0.03258296102285385, 0.00030911932117305696, -0.028298938646912575, 0.06222248077392578, -0.038095537573099136, -0.0233332309871912, 0.03187060356140137, -0.006252543069422245, -0.032450780272483826, 0.027706842869520187, 0.06910552084445953, 0.040932707488536835, -0.0032994577195495367, -0.04504963010549545, -0.014248648658394814, -0.005290009547024965, 0.045262064784765244, -0.01210255641490221, 0.034255895763635635, -0.015301174484193325, -0.026772785931825638, 0.0005762019427493215, 0.05005958676338196, 0.06403063982725143, 0.017953865230083466, 0.013122286647558212, -0.028989562764763832, 0.000993853434920311, 0.038096170872449875, 0.037185583263635635, -0.003708310890942812, -0.009686470031738281, 0.03341636806726456, 0.010029207915067673, -0.049438610672950745, -0.008483054116368294, 0.007208013907074928, 0.0023991574998944998, -0.05387788638472557, 0.05465254932641983, 0.029336733743548393, 0.0403200164437294, 0.0415680855512619, -0.007569471374154091, -0.04691912606358528, -0.015975499525666237, 0.010972213000059128, 0.08027007430791855, -0.013417129404842854, -0.039827991276979446, 0.008595552295446396, -0.023531267419457436, -0.01683448813855648, -0.05935440585017204, -0.05648808553814888, 0.037132371217012405, -0.010841135866940022, -0.01207614317536354, 0.061248403042554855, 0.006260757800191641, -0.039961569011211395, 0.012025224976241589, -0.019463853910565376, 0.061992231756448746, 0.06532500684261322, -0.04504626989364624, -0.04458695277571678, 0.053519561886787415, 0.009037423878908157, -0.010936511680483818, 0.03340717777609825, 0.020654596388339996, -0.00407348433509469, -0.008866964839398861, -0.041627056896686554, 0.030052468180656433, 0.006704014725983143, 0.003494741627946496, 0.002004384296014905, 0.02314251847565174, -0.003611344378441572, -0.01074211299419403, 0.04247250407934189, -0.019689884036779404, 0.0642157569527626, 0.01577925868332386, 0.013958720490336418, 0.022096624597907066, 0.012610356323421001, 0.01904365047812462, 0.048747431486845016, 0.02827717363834381, -0.030439257621765137, -0.0096354428678751, 0.06901684403419495, -0.03989565744996071, -0.0581664964556694, -0.00933601800352335, -0.04502522200345993, -0.026857759803533554, 0.020457228645682335, 0.04802653193473816, 0.017709091305732727, 0.08256647735834122, 0.03288629278540611, -0.013958401046693325, -0.04693220183253288, 0.0016039882320910692, 0.11409088969230652, -0.05533343181014061, -0.0494004562497139, -0.0034324468579143286, -0.004987691529095173, 0.004006559029221535, 0.0027262107469141483, 0.04315515607595444, -0.06520892679691315, -0.025559041649103165, 0.04972152039408684, -0.04238056764006615, 0.032155513763427734, -0.02424112893640995, -0.05938755348324776, 0.03799640014767647, -0.05197249352931976, -0.006426883861422539, -0.03727841004729271, -0.00125168077647686, 0.00844201073050499, -0.07317359745502472, -0.030635302886366844, 0.06934447586536407, 0.01954101212322712, -0.022358346730470657, -0.06226488947868347, 0.060237251222133636, 0.0014124350855126977, 0.006658940576016903, -0.028073832392692566, 0.04479275271296501, -0.026551958173513412, 0.031361911445856094, 0.028750643134117126, 0.061063073575496674, 0.0759463906288147, -0.052245013415813446, -0.0004449887783266604, -0.00481690838932991, 0.035163529217243195, 0.058392468839883804, 0.0002654126728884876, 0.013403311371803284, -0.015814386308193207, 0.0647454783320427, 0.014809295535087585, -0.010332594625651836, -0.0012829892802983522, 0.04711636155843735 ]
<p>I have the cross-sections as a function of $\sqrt{s}$ for a process with a $u$-quark and $u$-antiquark in the initial state (eg.: $u \bar{u} \to e^- e^+$). I have a standard parton distribution function table (say, CTEQ). With these, how do I find the corresponding cross-sections for a process with protons in the initial state (e.g. $p p \to e^- e^+$ as at the LHC)?</p> <p>Specifically, should I use some sort of convolution? How?</p>
g1539
[ 0.060691218823194504, -0.031233880668878555, 0.006149915046989918, -0.05486211180686951, 0.010225381702184677, -0.015179585665464401, 0.005067332182079554, 0.07406917959451675, -0.025698650628328323, 0.01257739681750536, 0.03144310414791107, 0.01224703248590231, 0.05956512689590454, 0.0079876109957695, -0.03621741384267807, -0.02742544189095497, 0.02363261580467224, 0.009129941463470459, -0.015355413779616356, 0.005649247206747532, 0.026714220643043518, 0.021048905327916145, 0.01847316510975361, -0.0026286221109330654, 0.025799062103033066, -0.014860861003398895, -0.0904611125588417, 0.05903508514165878, -0.08221547305583954, 0.023038992658257484, -0.03134892135858536, -0.0528201125562191, 0.008317053318023682, -0.023193201050162315, 0.005690578371286392, 0.011698552407324314, 0.07816141843795776, -0.05612217262387276, 0.022221319377422333, -0.017252612859010696, -0.011518340557813644, -0.02424602396786213, 0.02092350833117962, 0.004145822022110224, 0.03363685682415962, 0.0042602247558534145, -0.03303772583603859, 0.01941678673028946, -0.03744872659444809, 0.023546364158391953, -0.02435207925736904, 0.07138676941394806, 0.022970693185925484, 0.0014965118607506156, 0.031299442052841187, 0.024767689406871796, 0.007240735925734043, 0.004290484357625246, 0.04957066476345062, -0.0095698656514287, 0.06503831595182419, 0.023212796077132225, 0.0237048901617527, -0.08835744857788086, 0.06335078179836273, 0.0079013891518116, 0.06078909710049629, 0.054746098816394806, -0.030562398955225945, 0.02854043059051037, -0.05437576770782471, -0.014586168341338634, -0.011460987851023674, 0.010680112987756729, -0.02764120325446129, -0.0238414965569973, -0.008814835920929909, -0.006470485590398312, 0.02493356727063656, 0.049840282648801804, -0.04458511620759964, -0.002171855652704835, 0.05653202161192894, -0.050254639238119125, 0.0022791537921875715, 0.018968356773257256, -0.012584419921040535, -0.0169381033629179, -0.07302546501159668, -0.019495658576488495, 0.03194320574402809, -0.0014885974815115333, -0.025809556245803833, -0.006401605438441038, -0.00464423093944788, -0.015711305662989616, -0.07401645928621292, 0.02482789382338524, -0.012861543335020542, 0.012117075733840466, 0.023061830550432205, 0.02730901539325714, 0.029709046706557274, -0.052412357181310654, -0.015011456795036793, -0.012323010712862015, 0.015538872219622135, -0.012265476398169994, 0.041965551674366, -0.005798028316348791, -0.035832300782203674, 0.015602560713887215, -0.034608371555805206, 0.0030791035387665033, -0.000047604065912310034, -0.025685526430606842, 0.023257888853549957, 0.013362672179937363, 0.0013309282949194312, 0.01901393197476864, 0.014582441188395023, -0.020007770508527756, -0.009595688432455063, 0.0964171439409256, -0.03391335532069206, 0.019700292497873306, -0.048855140805244446, 0.0336519293487072, 0.00654316833242774, 0.03460995480418205, -0.000011065439139201771, -0.018768325448036194, 0.03977202996611595, 0.045118264853954315, 0.004004734568297863, 0.000288245762931183, 0.021161893382668495, 0.06465140730142593, -0.01005722675472498, -0.011362966150045395, 0.029787825420498848, 0.05168798938393593, -0.03450123220682144, 0.0013919693883508444, -0.00715969642624259, -0.024652233347296715, -0.036450181156396866, -0.07540206611156464, -0.0452888086438179, 0.040264032781124115, -0.04823718219995499, -0.005388171412050724, 0.0056387027725577354, -0.015547829680144787, 0.0012200248893350363, -0.010041099041700363, 0.0066061438992619514, -0.029293904080986977, -0.04203679412603378, -0.04552185535430908, 0.06323239207267761, -0.019488321617245674, -0.011874314397573471, -0.00007018446194706485, -0.014052601531147957, -0.05357498675584793, 0.019214125350117683, -0.06324146687984467, 0.0033701250795274973, -0.005191094242036343, 0.031937021762132645, 0.008111725561320782, -0.01650538109242916, 0.05204178765416145, -0.026185378432273865, 0.03401082009077072, 0.05291149392724037, -0.011034300550818443, 0.059447962790727615, 0.03471934050321579, 0.050696294754743576, -0.024276183918118477, -0.005829363130033016, 0.006936460733413696, 0.029453381896018982, -0.01818433217704296, -0.004918464459478855, 0.0655689388513565, 0.026343945413827896, 0.026323089376091957, 0.020131105557084084, -0.0022756876423954964, -0.017146257683634758, -0.061105307191610336, 0.0017784680239856243, -0.02449706755578518, -0.03281978517770767, -0.05256437137722969, 0.007164414972066879, -0.0013562155654653907, -0.008788916282355785, -0.03166819363832474, 0.019850172102451324, 0.04195992276072502, 0.031203046441078186, 0.005653700791299343, 0.0051787300035357475, -0.019401803612709045, 0.004808639641851187, 0.008432031609117985, -0.012708052061498165, -0.011973590590059757, -0.030435550957918167, 0.011702482588589191, -0.04784305766224861, -0.0016565241385251284, 0.015099389478564262, -0.009177474305033684, -0.0362863689661026, 0.08783420920372009, -0.10115858912467957, -0.017782488837838173, 0.005842320621013641, -0.029332712292671204, 0.04167909175157547, 0.08701039850711823, 0.02590903826057911, 0.018284277990460396, -0.04383418336510658, -0.03214189410209656, -0.07957489043474197, 0.02811034396290779, -0.03240131959319115, -0.033175621181726456, -0.0455947183072567, -0.029530517756938934, 0.00042917722021229565, 0.021856874227523804, 0.029345406219363213, 0.048791103065013885, -0.022491442039608955, -0.032149944454431534, 0.014057795517146587, 0.003377578454092145, 0.03378057852387428, -0.030345246195793152, 0.0489848367869854, -0.030561860650777817, -0.03256714716553688, -0.02166457660496235, 0.00865117460489273, 0.020930761471390724, 0.008013480342924595, -0.014517061412334442, -0.03546878695487976, -0.062061529606580734, 0.03215491399168968, 0.012390321120619774, -0.010767408646643162, -0.03035539761185646, -0.04041282832622528, -0.008150453679263592, 0.004289313219487667, 0.03564251959323883, 0.005021248012781143, -0.03423433005809784, -0.01591493934392929, -0.016641022637486458, -0.025348195806145668, -0.016243446618318558, -0.03819121792912483, 0.04319853335618973, 0.02786056511104107, -0.009144320152699947, 0.05237821117043495, -0.023022502660751343, -0.007114375475794077, -0.055309489369392395, -0.03275691717863083, -0.026189539581537247, 0.0019810195080935955, -0.047496698796749115, -0.01114447321742773, -0.02061602659523487, 0.01820415072143078, -0.02375136688351631, 0.03184351697564125, 0.009085430763661861, -0.016594551503658295, -0.011867230758070946, 0.019452322274446487, -0.063247449696064, -0.034869235008955, -0.005686210934072733, 0.007151681464165449, -0.0018416834063827991, 0.05647222325205803, -0.015159589238464832, 0.005719320848584175, 0.006228286307305098, -0.029024897143244743, -0.010606888681650162, 0.05260985717177391, 0.025839485228061676, 0.00374209089204669, 0.0692346841096878, -0.030176114290952682, 0.03425982594490051, -0.020413145422935486, -0.0016588098369538784, 0.0008949937182478607, -0.0010310873622074723, 0.01726052165031433, 0.010881476104259491, 0.02647099830210209, -0.08045103400945663, 0.07607987523078918, 0.0019557331688702106, 0.0038701724261045456, -0.0471029095351696, -0.0409507192671299, -0.015131565742194653, 0.06725423783063889, -0.057392705231904984, 0.04821520671248436, -0.007761591579765081, -0.02552461065351963, 0.0093617495149374, 0.010815702378749847, -0.07037106156349182, 0.005490873008966446, 0.05657477676868439, 0.04905133321881294, 0.00883438903838396, -0.0766872689127922, -0.03628849238157272, 0.027732666581869125, -0.009695942513644695, 0.02194773033261299, 0.0035070565063506365, 0.020968995988368988, -0.058198247104883194, -0.0326010137796402, 0.002097425749525428, 0.037618398666381836, -0.0724673792719841, 0.0021625522058457136, 0.10342460125684738, 0.008360432460904121, -0.03759942203760147, -0.025881273671984673, 0.06113867834210396, 0.030892210081219673, 0.027604972943663597, -0.0030359134543687105, 0.04037419706583023, 0.04154760763049126, -0.0889069139957428, 0.044577401131391525, 0.02227734588086605, 0.0277382992208004, -0.057730190455913544, 0.024822266772389412, 0.07008308172225952, -0.019473372027277946, -0.00529038580134511, -0.005399653222411871, 0.0354774072766304, 0.054244302213191986, -0.001892873435281217, 0.037615817040205, -0.03387993201613426, 0.04931056499481201, -0.04242754355072975, -0.042475223541259766, -0.005825065076351166, -0.05920474976301193, 0.03698885813355446, -0.04835518077015877, -0.0004227125900797546, -0.008115214295685291, 0.03115987777709961, 0.0338769406080246, 0.00592302531003952, 0.012310449033975601, -0.03850478306412697, -0.052229490131139755, -0.04316461831331253, 0.06610601395368576, 0.05273059010505676, 0.058955419808626175, -0.044223226606845856, -0.07756604999303818, 0.05824104696512222, 0.009342510253190994, -0.023490332067012787, 0.0318562351167202, 0.0016770190559327602, -0.020976051688194275, 0.03579948469996452, -0.06596475094556808, -0.04460519179701805, 0.05020226538181305, -0.040327463299036026, 0.03878509998321533, -0.04421020671725273, 0.018478592857718468, -0.03636936843395233, -0.0509864017367363, -0.050511494278907776, -0.0006781488773413002, 0.007725181523710489, 0.005151959136128426, -0.009561688639223576, -0.043478019535541534, -0.025394095107913017, -0.02486877143383026, -0.03983302041888237, -0.01235867477953434, -0.001889644656330347, -0.011891958303749561, 0.013278535567224026, 0.054392602294683456, 0.04300370439887047, -0.055702805519104004, -0.004040578380227089, 0.030354982241988182, 0.014899928122758865, 0.019760748371481895, 0.00455264188349247, 0.014443443156778812, 0.006306400988250971, 0.0399942509829998, 0.0415336936712265, -0.013566236011683941, 0.0017282030312344432, -0.013989035040140152, -0.023992814123630524, -0.020551320165395737, -0.007487058639526367, 0.029489561915397644, 0.012295651249587536, -0.033572569489479065, 0.03342287614941597, 0.04050435125827789, 0.034911688417196274, -0.04573158174753189, -0.037139687687158585, -0.04419553652405739, -0.038974929600954056, -0.025951240211725235, -0.010169248096644878, -0.05982484295964241, -0.02736053243279457, 0.029127653688192368, 0.051794297993183136, 0.07016302645206451, 0.03986668959259987, 0.021194815635681152, 0.05204896256327629, -0.05870754271745682, -0.013929679989814758, 0.009527336806058884, -0.0461638979613781, -0.07001850008964539, 0.07329480350017548, -0.0964888408780098, 0.04685097932815552, -0.025850139558315277, -0.0005469272728078067, 0.02121759206056595, -0.0344228595495224, 0.028896568343043327, -0.05364350229501724, -0.02949192188680172, 0.07996999472379684, -0.01569429039955139, 0.014096387661993504, -0.015845835208892822, 0.004793344531208277, -0.002631201408803463, -0.0395471453666687, -0.009760484099388123, -0.07842104136943817, -0.03316744044423103, 0.02358008734881878, -0.01862611621618271, -0.044209402054548264, -0.008407850749790668, 0.035163722932338715, -0.026940587908029556, 0.01625378429889679, 0.03318512439727783, 0.05057185888290405, 0.08056992292404175, -0.006212814711034298, 0.042288172990083694, -0.012648370116949081, 0.01729070581495762, 0.05156547948718071, -0.014197239652276039, -0.03726416453719139, -0.046498458832502365, 0.0416095107793808, -0.003877907060086727, 0.031061386689543724, 0.03256497532129288, 0.01719062589108944, 0.002664644503965974, -0.03415079414844513, 0.09448088705539703, 0.030923964455723763, 0.03258105367422104, 0.008797811344265938, -0.053994908928871155, 0.04803887754678726, -0.02705399878323078, 0.08739984780550003, -0.016789188608527184, -0.05251207575201988, 0.041154731065034866, 0.0057771638967096806, 0.059661995619535446, -0.019296759739518166, -0.006809226702898741, -0.05110170692205429, 0.01671822927892208, 0.001984574133530259, 0.03067442774772644, 0.0037657716311514378, 0.02919277921319008, 0.006254962179809809, 0.0007718726410530508, 0.06937702745199203, -0.02295045368373394, -0.04788537323474884, -0.017537198960781097, -0.013328835368156433, 0.015614309348165989, -0.015313969925045967, -0.03276776149868965, -0.02539180777966976, 0.006402480881661177, -0.03372296318411827, -0.06056195870041847, -0.02781512588262558, -0.00244308914989233, 0.012295900844037533, 0.028230898082256317, -0.03599289432168007, -0.002491076709702611, -0.01590513437986374, -0.005216194782406092, -0.07301890105009079, -0.018422605469822884, 0.0430707149207592, 0.053713273257017136, 0.009079341776669025, 0.03453671932220459, -0.005267668981105089, 0.03159426152706146, -0.06625155359506607, 0.04194548726081848, -0.014243288896977901, 0.02064298465847969, -0.012612460181117058, -0.033208057284355164, -0.005653777625411749, -0.02168290689587593, 0.007833578623831272, 0.04527336359024048, -0.07858118414878845, -0.016952218487858772, -0.02869618497788906, -0.01701100543141365, 0.029794346541166306, -0.02003760077059269, -0.011265028268098831, -0.0016500757774338126, 0.0384477861225605, 0.003440640401095152, 0.009330672211945057, 0.013805681839585304, 0.009316720999777317, 0.0031071496196091175, 0.041221387684345245, 0.017144102603197098, -0.0033786019776016474, 0.004770624451339245, 0.059797924011945724, -0.05599270388484001, -0.013491827063262463, -0.006066266447305679, 0.04605802521109581, 0.05075763165950775, 0.003065133234485984, 0.004431618377566338, -0.004227933008223772, 0.0045737638138234615, 0.031950995326042175, -0.04362727329134941, -0.012494524009525776, 0.015646839514374733, -0.036298464983701706, 0.02455860748887062, -0.011226077564060688, 0.010200736112892628, 0.04180401563644409, 0.01726642996072769, -0.008024495095014572, 0.017706576734781265, -0.0026265496853739023, 0.0014822058146819472, 0.006232414394617081, 0.013907989487051964, -0.03742152824997902, -0.04746106639504433, -0.007677949033677578, 0.02435421012341976, -0.040539346635341644, 0.05959299951791763, 0.007770121097564697, -0.05052435025572777, -0.022781874984502792, 0.02956554852426052, 0.01916917786002159, -0.0006162015488371253, 0.011184610426425934, 0.07073965668678284, -0.046291809529066086, 0.013082632794976234, 0.030647411942481995, 0.05585501343011856, -0.025870639830827713, -0.050503041595220566, 0.07116006314754486, 0.009540088474750519, 0.024367112666368484, -0.003993380349129438, -0.0031814533285796642, 0.022014306858181953, 0.0165584534406662, 0.04766033589839935, -0.021342869848012924, -0.08497293293476105, -0.015853028744459152, -0.008684406988322735, 0.014032523147761822, -0.09548921883106232, 0.008314322680234909, 0.0485052689909935, 0.004071155097335577, 0.02488241344690323, -0.01585957407951355, 0.036923859268426895, 0.05562949925661087, 0.04772401228547096, 0.004335586912930012, 0.04557224363088608, -0.01839778758585453, -0.003328329650685191, -0.055974580347537994, -0.03667536750435829, -0.005589557811617851, 0.06717003136873245, -0.011475909501314163, -0.0009048397769220173, -0.025228239595890045, 0.040556035935878754, -0.0590534470975399, 0.007803446613252163, -0.04912952706217766, -0.06382963806390762, 0.04007032513618469, 0.04234924912452698, -0.03192148357629776, -0.00311078317463398, 0.06109694018959999, -0.009757786989212036, -0.009380427189171314, -0.04980693757534027, -0.02607090212404728, -0.062239039689302444, -0.011021136306226254, 0.014090914279222488, 0.027107806876301765, -0.06337257474660873, -0.03132827579975128, 0.02825167030096054, 0.03984018415212631, -0.027607308700680733, -0.04386569932103157, 0.01678864285349846, -0.02066916972398758, 0.013864885084331036, 0.031450800597667694, 0.02934444509446621, -0.057802796363830566, 0.002724114805459976, 0.04553387314081192, 0.07685507088899612, 0.021190639585256577, -0.0011213473044335842, -0.010024764575064182, 0.01942211575806141, -0.042086970061063766, -0.0001971623714780435, -0.06779227405786514, 0.05596967041492462, -0.04860782250761986, -0.00853420328348875, 0.04517862945795059, -0.0394204780459404, 0.00595454266294837, 0.022778842598199844, 0.03472959250211716, -0.049882885068655014, -0.001922867028042674, 0.04146600142121315, 0.08945033699274063, -0.08845652639865875, -0.013905517756938934, 0.003508474910631776, 0.021246323361992836, 0.05453534051775932, 0.024177005514502525, 0.0071967062540352345, 0.04652169346809387, -0.034018952399492264, 0.056729208678007126, -0.009349755942821503, -0.03215211257338524, -0.012139545753598213, 0.010046396404504776, -0.03300262242555618, -0.11834723502397537, 0.0009118131129071116, -0.038384292274713516, 0.017705969512462616, 0.0025970765855163336, -0.05347997695207596, -0.041691988706588745, -0.0034379479475319386, -0.014592532068490982, 0.015543107874691486, -0.03501356020569801, 0.023914672434329987, -0.04350028187036514, 0.04486268386244774, 0.001724195433780551, 0.039901070296764374, -0.043319184333086014, 0.023109961301088333, 0.02437784895300865, -0.028398782014846802, -0.03938925638794899, 0.039316680282354355, 0.03927677497267723, -0.036231428384780884, 0.03860308229923248, 0.006568268872797489, 0.046210166066884995, 0.0012765431310981512, 0.031149238348007202, -0.01592794433236122, 0.030184807255864143, 0.007164344657212496, -0.023610839620232582 ]
<p>It is said that the universe is expanding and the galaxies are moving apart. I understand that the space between every two galaxies is increasing. Doesn't this seem to imply that the galaxies will have relative motion and so have a moving velocity. According to relativity and the modern belief in physics, it is said that everything depends on relative motion and nothing else (I am talking about the concepts such as Time Dilation etc.). So in brief I would like to ask that why is it said that galaxies do not move even though the distance between them is increasing.</p>
g1540
[ 0.0016691378550603986, 0.0202640313655138, 0.01967446133494377, -0.006946874316781759, 0.0299626924097538, 0.02257372811436653, 0.005594342481344938, 0.023631006479263306, -0.01623525843024254, -0.03610127046704292, 0.047179050743579865, -0.03332166001200676, -0.020924760028719902, 0.029070986434817314, 0.017320912331342697, -0.004618760664016008, -0.022475646808743477, -0.03778889402747154, -0.015054596588015556, 0.015842044726014137, -0.06914391368627548, 0.00530615821480751, 0.01855161041021347, -0.03612448275089264, 0.0005926443845964968, -0.005755350459367037, 0.012301445007324219, -0.06495805084705353, 0.008841527625918388, 0.021782679483294487, 0.05263431742787361, -0.002010691212490201, -0.006172118242830038, -0.04326806962490082, 0.046589549630880356, -0.0006401428254321218, 0.025871049612760544, -0.031981006264686584, 0.03877897560596466, -0.021152900531888008, -0.02136574126780033, 0.032470542937517166, -0.012169865891337395, -0.03335851803421974, 0.09244121611118317, -0.020245738327503204, -0.018198788166046143, -0.021669097244739532, 0.02557554468512535, 0.025065135210752487, -0.0651470348238945, 0.007665717508643866, -0.020969554781913757, 0.029726194217801094, 0.003974271938204765, -0.012060469947755337, 0.03489931300282478, -0.008154956623911858, 0.052234552800655365, -0.0029080722015351057, -0.018307263031601906, 0.002720525721088052, 0.057635631412267685, -0.02253839001059532, 0.022945784032344818, -0.009668702259659767, -0.058369580656290054, -0.038877252489328384, 0.06645429879426956, 0.029521621763706207, -0.029882948845624924, 0.0031638441141694784, -0.0602661669254303, -0.017411641776561737, -0.042112622410058975, 0.026141662150621414, 0.03767434507608414, -0.046290408819913864, -0.009354698471724987, -0.008620592765510082, -0.010418242774903774, -0.03693225979804993, 0.036091774702072144, 0.01178043894469738, 0.03377704322338104, -0.029256626963615417, -0.0035870890133082867, 0.0061036949045956135, -0.004314027726650238, 0.031911399215459824, 0.00718518253415823, -0.0012377920793369412, 0.07688458263874054, 0.012900999747216702, -0.023285500705242157, -0.034738119691610336, -0.11308599263429642, 0.06136073172092438, 0.015277405269443989, 0.0001978436775971204, -0.05071765556931496, -0.006955150049179792, 0.0656166523694992, -0.03617851808667183, 0.009895887225866318, -0.02751612290740013, 0.01109170913696289, 0.03766656666994095, 0.007827281020581722, -0.06125001981854439, 0.001511981594376266, -0.02471238747239113, 0.04009268432855606, -0.04097774252295494, -0.01589829847216606, -0.005041790660470724, 0.027510996907949448, 0.055254679173231125, 0.057867761701345444, 0.02264745533466339, -0.009040876291692257, 0.03539518266916275, -0.03211529552936554, -0.04686642065644264, -0.021718714386224747, -0.055182576179504395, 0.05798996984958649, -0.016094820573925972, 0.05202935263514519, 0.013579887337982655, 0.06474565714597702, 0.055571649223566055, -0.011840058490633965, 0.03822924196720123, -0.04523322358727455, -0.04023892059922218, 0.02521730586886406, 0.007607122417539358, -0.03023727610707283, 0.019103845581412315, 0.0036101611331105232, -0.01432094071060419, 0.06957139074802399, -0.04798917472362518, -0.019500140100717545, 0.002427938859909773, -0.01077813096344471, 0.052823152393102646, 0.029628558084368706, -0.02442106418311596, 0.023015592247247696, 0.05922580882906914, -0.04439708963036537, -0.0235606636852026, -0.015340662561357021, 0.0026787209790199995, 0.040883395820856094, 0.02420496940612793, -0.02433578297495842, -0.015018916688859463, 0.06525474041700363, -0.02094688080251217, 0.00503062317147851, -0.010176394134759903, -0.04096507653594017, 0.07933107763528824, -0.002706690924242139, -0.02789628691971302, 0.011849592439830303, 0.02453586645424366, -0.05685769394040108, 0.008824743330478668, -0.01762651652097702, 0.0833682045340538, 0.02327299304306507, 0.03236524388194084, 0.05876270681619644, 0.023459741845726967, -0.041018296033144, -0.023345697671175003, -0.03824267536401749, -0.03963809460401535, -0.008293881081044674, -0.030472073704004288, -0.021950537338852882, -0.01362074539065361, -0.05478006973862648, -0.06302390992641449, -0.030681870877742767, -0.02193862572312355, -0.002988212974742055, -0.013903962448239326, 0.022638019174337387, -0.013042685575783253, -0.004524329677224159, 0.022381186485290527, -0.01049648504704237, -0.008570387028157711, -0.013768999837338924, 0.04629030451178551, -0.002194263506680727, 0.01742394082248211, 0.017679814249277115, -0.013727004639804363, 0.05044883117079735, -0.043217115104198456, -0.07063652575016022, 0.008194523863494396, 0.07611298561096191, 0.02150266058743, 0.0376095250248909, -0.04373627156019211, 0.03749030828475952, -0.004076602403074503, 0.018889399245381355, -0.02225358411669731, 0.020714951679110527, -0.002115332754328847, -0.02537406049668789, 0.007547762710601091, 0.0015220153145492077, -0.012376515194773674, 0.03424576297402382, -0.05251983553171158, 0.05031672865152359, -0.056803327053785324, -0.06982740014791489, 0.013312963768839836, -0.009473283775150776, 0.06247669458389282, -0.075558602809906, -0.022055378183722496, 0.038246653974056244, -0.0034131361171603203, 0.032630499452352524, 0.003932540770620108, -0.008196488954126835, 0.011004765518009663, 0.034959204494953156, 0.04171125590801239, 0.03076540119946003, -0.02712578885257244, -0.011762741953134537, 0.016351254656910896, 0.0431269146502018, -0.07552404701709747, 0.07139012217521667, -0.04926979914307594, -0.04480919614434242, 0.02640368789434433, 0.06972067058086395, -0.03667617589235306, 0.015482151880860329, -0.057299770414829254, 0.009075469337403774, -0.012900426983833313, 0.0015864894958212972, 0.06823933869600296, -0.06018836423754692, -0.01984863169491291, 0.013841028325259686, -0.01309429481625557, 0.10072622448205948, 0.006091744638979435, -0.053960204124450684, 0.03435152396559715, -0.03861869499087334, 0.02410796470940113, -0.03180073946714401, -0.07362180948257446, -0.01636357232928276, -0.008057443425059319, 0.007014511153101921, 0.04136206954717636, -0.015387484803795815, 0.04357946664094925, 0.016108432784676552, -0.03110434301197529, 0.007379670161753893, -0.0043807863257825375, -0.021285928785800934, -0.009323998354375362, -0.0753253847360611, -0.046464379876852036, 0.0017487845616415143, -0.035861991345882416, -0.01449812576174736, -0.012349716387689114, 0.030612431466579437, -0.0020982760470360518, 0.009066512808203697, 0.02394811436533928, 0.034534305334091187, -0.022410541772842407, 0.02764626033604145, 0.05646643787622452, -0.04570569097995758, 0.027934925630688667, -0.05824112147092819, -0.012051758356392384, 0.029446659609675407, -0.03468819335103035, 0.015197685919702053, -0.02323547936975956, 0.03478112071752548, 0.036335840821266174, 0.000909301801584661, 0.0036167434882372618, -0.03590356186032295, -0.026174116879701614, 0.0010729337809607387, 0.012130212038755417, 0.01652957871556282, 0.041274599730968475, -0.012253116816282272, 0.05480894818902016, 0.004958067089319229, 0.03691139444708824, 0.03828814625740051, 0.050471194088459015, -0.00709436135366559, 0.015190530568361282, -0.0646417886018753, -0.0374409444630146, 0.05817704275250435, -0.015032821334898472, -0.007294367533177137, -0.061635687947273254, -0.04704797640442848, -0.008717472665011883, -0.025047581642866135, -0.004909863229840994, -0.008797022514045238, -0.03893020749092102, -0.054388418793678284, 0.0068239434622228146, 0.01673521101474762, -0.01547865942120552, 0.048157550394535065, 0.00021742346871178597, 0.0215492881834507, -0.00553755322471261, -0.018200799822807312, 0.09434656798839569, -0.03194611892104149, 0.08105117827653885, 0.06299182772636414, -0.020865527912974358, -0.009077687747776508, -0.023288575932383537, 0.035748597234487534, 0.008297867141664028, 0.005133897066116333, -0.03314335644245148, -0.04971375688910484, -0.027428383007645607, -0.008031664416193962, -0.026240570470690727, 0.001576690236106515, -0.000380861310986802, 0.026936708018183708, 0.009746993891894817, -0.036101169884204865, -0.0015179048059508204, -0.04280645400285721, 0.018282389268279076, -0.024626126512885094, -0.021532848477363586, -0.003178029553964734, 0.025141196325421333, 0.01905234530568123, -0.035701580345630646, -0.04060015827417374, 0.0020417480263859034, 0.07116684317588806, -0.027464257553219795, 0.09734375774860382, 0.03179820254445076, -0.009001386351883411, -0.006402445957064629, 0.031910963356494904, 0.002600207692012191, 0.004703558515757322, 0.059903450310230255, 0.008342566899955273, -0.010489728301763535, -0.0494471937417984, 0.010137641802430153, -0.01083742082118988, -0.04458955302834511, 0.09929376095533371, -0.021778540685772896, 0.004288002382963896, 0.011475445702672005, 0.012035705149173737, -0.04871610552072525, 0.02046263962984085, 0.040404099971055984, 0.08614762127399445, 0.009330852888524532, 0.01121559739112854, 0.010756297968327999, -0.052086662501096725, 0.01754874177277088, -0.0228570569306612, 0.04499898478388786, 0.01689564622938633, 0.010342523455619812, -0.01567464880645275, -0.011281074024736881, -0.004482903517782688, -0.00003674430990940891, 0.021164678037166595, -0.0500744953751564, 0.03532684966921806, 0.007795375306159258, 0.004137041047215462, -0.040724266320466995, -0.007918917573988438, 0.03923533484339714, 0.015393799170851707, 0.06297065317630768, 0.03242310509085655, -0.019371051341295242, -0.016118550673127174, 0.07088736444711685, 0.02138771489262581, -0.004453998524695635, 0.0006366325542330742, 0.0022545296233147383, -0.019731471315026283, 0.046533308923244476, 0.0403815358877182, 0.03165508806705475, -0.02551240101456642, 0.04058711975812912, -0.026057880371809006, 0.09305823594331741, 0.013224594295024872, -0.006033639423549175, 0.06511036306619644, 0.0032156577799469233, 0.014720261096954346, 0.03628735616803169, 0.030004100874066353, 0.06421177089214325, -0.09508878737688065, 0.005842506419867277, -0.04228147119283676, -0.03857007995247841, -0.028020717203617096, 0.05292491242289543, -0.039998918771743774, 0.006912000477313995, 0.002147446386516094, -0.030084358528256416, 0.015520158223807812, -0.0073565468192100525, 0.008275537751615047, 0.05541371926665306, -0.038473036140203476, 0.07330018281936646, 0.050993748009204865, 0.043610092252492905, 0.013658388517796993, -0.00825510360300541, 0.011832267977297306, -0.05094347894191742, -0.02143554762005806, 0.09635365754365921, -0.019137505441904068, 0.013627476990222931, -0.019441066309809685, 0.023083750158548355, -0.0255719181150198, 0.05869019776582718, 0.007255850825458765, 0.00633698794990778, -0.00044588404125534, -0.04012509435415268, -0.03188728913664818, -0.0610206164419651, 0.044494543224573135, -0.02502954751253128, 0.010239780880510807, 0.004565344657748938, 0.0027104883920401335, 0.04745635762810707, 0.019732562825083733, -0.0526043064892292, 0.058541081845760345, -0.04202627018094063, 0.026444394141435623, 0.02314569801092148, -0.02199988253414631, -0.023017719388008118, -0.01734241656959057, 0.021680641919374466, -0.005006978288292885, -0.02357248216867447, 0.017724094912409782, 0.025177055969834328, 0.0010506573598831892, -0.046321213245391846, -0.015550448559224606, 0.01015601959079504, 0.013775847852230072, -0.0050753578543663025, -0.041842155158519745, -0.01831664703786373, -0.01901880092918873, 0.051552001386880875, 0.014312788844108582, 0.013707315549254417, 0.019807377830147743, -0.06887935101985931, 0.006714561488479376, -0.03633864223957062, 0.049357783049345016, -0.006122023332864046, -0.011199221014976501, -0.027762161567807198, 0.043037049472332, -0.02419920451939106, 0.10652157664299011, -0.008050058968365192, 0.0031884012278169394, 0.028636839240789413, 0.06115762144327164, 0.00939162541180849, 0.02191958948969841, 0.0029929038137197495, 0.011596986092627048, -0.021506687626242638, -0.043356992304325104, -0.029050592333078384, 0.004825277253985405, -0.03119586780667305, -0.017454223707318306, -0.011542937718331814, 0.00955759547650814, 0.02008928172290325, -0.043149515986442566, 0.06609055399894714, -0.0694352313876152, 0.049101732671260834, -0.010303412564098835, -0.06926073879003525, 0.09427022933959961, -0.04197344556450844, -0.033178992569446564, 0.031032424420118332, -0.030305424705147743, -0.0366591215133667, -0.03888313099741936, 0.08837001770734787, 0.045455452054739, -0.030613048002123833, 0.004044565372169018, -0.049802616238594055, 0.02419932186603546, -0.02734154276549816, -0.07339660823345184, -0.009821465238928795, 0.03009769693017006, -0.08367019891738892, -0.00907188095152378, -0.02916417457163334, 0.04106178507208824, 0.030326049774885178, -0.06092928722500801, 0.019856469705700874, 0.00029520285897888243, 0.027329271659255028, 0.0023300955072045326, 0.021307021379470825, -0.024125337600708008, -0.03471825644373894, -0.05305220186710358, -0.028600312769412994, 0.05526842549443245, -0.01780627854168415, 0.034679755568504333, -0.05317043885588646, -0.05426480621099472, 0.031863950192928314, 0.032401442527770996, -0.012568201869726181, 0.030583839863538742, -0.01293187215924263, -0.023783519864082336, 0.04232929274439812, -0.006605448666960001, -0.01439847331494093, -0.003477988764643669, -0.027176206931471825, -0.014242365956306458, -0.03794749453663826, -0.019587354734539986, 0.0027406574226915836, 0.003529960522428155, -0.020576687529683113, 0.048998720943927765, -0.010209726169705391, -0.006290882360190153, -0.019749272614717484, -0.05104227736592293, 0.029025118798017502, 0.04153696075081825, 0.01797039434313774, 0.008700392208993435, 0.01548562478274107, 0.06346313655376434, 0.02344411425292492, -0.004189695697277784, -0.04823239892721176, 0.024818090721964836, -0.02739511802792549, -0.023025065660476685, -0.02157665602862835, 0.00938743632286787, 0.01348991971462965, -0.012111146934330463, 0.032351747155189514, 0.017779897898435593, 0.027613915503025055, -0.129540354013443, -0.007929968647658825, 0.005799110047519207, 0.0012760884128510952, 0.01226099394261837, 0.009341318160295486, 0.016992146149277687, 0.0200785044580698, 0.0022969197016209364, -0.023104621097445488, -0.05531049519777298, 0.01849464327096939, 0.023779243230819702, -0.021038031205534935, 0.029348306357860565, -0.06083935499191284, 0.04536096751689911, -0.01923242397606373, -0.011212159879505634, -0.01985161378979683, -0.03124682419002056, -0.038258764892816544, -0.04086456820368767, 0.010580471716821194, -0.05208733677864075, -0.09284970909357071, 0.0165831558406353, 0.017793729901313782, -0.058129798620939255, -0.008741901256144047, -0.045822083950042725, -0.06140590459108353, -0.03774707391858101, -0.032758407294750214, -0.06768881529569626, -0.021600421518087387, -0.043618544936180115, 0.045604776591062546, 0.006047169212251902, 0.05972085893154144, 0.032088588923215866, 0.002636545104905963, -0.014955324120819569, 0.006430806126445532, 0.04372233897447586, -0.0039023221470415592, -0.02113458886742592, 0.02200547605752945, -0.00671266159042716, -0.03143366426229477, -0.036757826805114746, -0.01996709033846855, 0.10044685751199722, -0.02043173648416996, -0.04643556475639343, 0.05707889795303345, -0.026755740866065025, 0.0417771190404892, 0.0072091673500835896, 0.07149803638458252, 0.0028567942790687084, -0.04923398420214653, -0.0022602849639952183, -0.04445766657590866, -0.006387420929968357, -0.050252825021743774, -0.057779230177402496, -0.009947109036147594, -0.011259917169809341, 0.0488729253411293, 0.05466489866375923, 0.03410720452666283, -0.01747988536953926, -0.05303012207150459, -0.011413782835006714, -0.046264633536338806, -0.003363941330462694, 0.013631298206746578, 0.027092527598142624, 0.02835501730442047, -0.03955782949924469, 0.05863723158836365, -0.021960169076919556, -0.0026329716201871634, 0.011261167004704475, 0.00039635025314055383, 0.02603180706501007, -0.036983031779527664, -0.02788272127509117, -0.06100290268659592, 0.015460220165550709, 0.00890451017767191, -0.002189882565289736, -0.039421167224645615, 0.023153377696871758, -0.03761224076151848, 0.044770751148462296, -0.05073646456003189, -0.03254004940390587, 0.004061105661094189, 0.005840853787958622, -0.037475768476724625, 0.006819996051490307, -0.013310041278600693, 0.002601612126454711, 0.00732105178758502, -0.0469411201775074, -0.0004855079168919474, -0.07362562417984009, 0.05510987341403961, 0.017479265108704567, -0.030279865488409996, 0.02870127558708191, 0.041194360703229904, 0.014583119191229343, -0.008132971823215485, -0.017321674153208733, 0.04020414128899574, 0.00019400090968701988, -0.08256766200065613, 0.04704327881336212, 0.04079422354698181, 0.013814806938171387, 0.023871008306741714, 0.01078999973833561, 0.07328270375728607, 0.0018994661513715982, 0.05760500952601433, 0.010817321948707104, -0.011400236748158932, -0.007527566980570555, -0.007439758162945509, -0.06198229268193245, -0.009135568514466286, -0.011032717302441597, 0.023173140361905098, 0.02039264887571335, -0.03747858107089996, -0.0008179524447768927, -0.03753947094082832, -0.05223902314901352, 0.00961106177419424 ]
<p>To derive Bose-Einstein and Fermi-Dirac distribution, we need to apply grand canonical ensemble:$Z(z,V,T)=\displaystyle\sum_{N=0}^{\infty}[z^N\sideset{}{'}\sum\limits_{\{n_j\}}e^{-\beta\sum\limits_{j}n_j\epsilon_j}]$. There is a constraint $\sideset{}{'}\sum\limits_{\{n_j\}}$ for quantum particles(bosons and fermions) in grand canonical ensemble:$\sum\limits_{j}n_j=N$, but why is there no such a constraint for classical particels?</p>
g1541
[ -0.03345644846558571, 0.03986959159374237, -0.00870445091277361, -0.08667667955160141, 0.017254386097192764, 0.007285146042704582, 0.06811346858739853, 0.03061792440712452, -0.024364884942770004, -0.006291104946285486, -0.0055745006538927555, 0.06894505023956299, -0.06555904448032379, 0.06422596424818039, 0.030562033876776695, 0.018324555829167366, -0.03650960326194763, 0.03714023530483246, -0.01705058664083481, -0.04069564491510391, 0.008253530599176884, -0.012703360989689827, 0.02339237742125988, -0.03218754008412361, 0.07961888611316681, -0.025716662406921387, -0.004178598988801241, -0.010525299236178398, 0.003393968101590872, 0.02216106280684471, 0.021076058968901634, -0.002989943837746978, 0.05496464669704437, 0.031924061477184296, 0.06528397649526596, -0.02627549134194851, 0.04920801520347595, -0.03766258805990219, 0.014979388564825058, -0.019216982647776604, -0.018178123980760574, -0.011594772338867188, -0.027470234781503677, 0.007846205495297909, 0.00036985016777180135, 0.05701605975627899, -0.006056418176740408, -0.008769501931965351, -0.033623263239860535, -0.003956689964979887, 0.04800913855433464, 0.031078577041625977, -0.024778902530670166, 0.022271020337939262, -0.010838601738214493, 0.0027359023224562407, 0.015291723422706127, -0.025293415412306786, 0.0703466534614563, 0.03794523701071739, 0.0024521141313016415, -0.0171428881585598, -0.0261074248701334, 0.031559720635414124, 0.02906007692217827, -0.007269286084920168, -0.02097177691757679, 0.0183003768324852, 0.01733608916401863, 0.005014203488826752, -0.032970964908599854, -0.08030493557453156, 0.03175313398241997, 0.025704938918352127, -0.004289439879357815, -0.02040816657245159, 0.010385645553469658, 0.07257939130067825, -0.01660626009106636, -0.03423849493265152, -0.05010847747325897, -0.05085492506623268, 0.07450036704540253, 0.02336733788251877, -0.0036940230056643486, -0.0029496755450963974, -0.04125358164310455, -0.07106034457683563, -0.00961163267493248, 0.027350828051567078, -0.004060403443872929, -0.06997599452733994, 0.016567861661314964, 0.007446909323334694, 0.031572505831718445, -0.07545530796051025, -0.019021810963749886, 0.029806500300765038, -0.03932282701134682, -0.010124072432518005, 0.004753547254949808, 0.04190044850111008, 0.0393451564013958, 0.0045328992418944836, -0.06415703147649765, -0.04648742824792862, -0.011617569252848625, 0.003698941320180893, -0.023511016741394997, -0.016833331435918808, -0.01645606942474842, -0.01881975494325161, 0.02075507864356041, -0.021692248061299324, -0.07046579569578171, -0.0046286070719361305, 0.04532927647233009, -0.0504021979868412, -0.014052072539925575, 0.07262366265058517, -0.03727186843752861, 0.020325155928730965, 0.02254815213382244, 0.04063689336180687, -0.06307116150856018, -0.02616790495812893, -0.019585298374295235, 0.0386725552380085, -0.006059084087610245, -0.04585432633757591, 0.009360297583043575, 0.01158311776816845, 0.0208324883133173, -0.018489647656679153, 0.03932996839284897, 0.02644590102136135, -0.0448269285261631, -0.00170954130589962, 0.02330728992819786, 0.04145490378141403, -0.01054711826145649, -0.00457916921004653, 0.04532163590192795, 0.013261036947369576, 0.014559173956513405, -0.06357559561729431, -0.029783403500914574, -0.030765313655138016, -0.069669209420681, 0.07099678367376328, -0.019969476386904716, 0.04031716287136078, 0.0030676673632115126, 0.004332424141466618, -0.019887544214725494, 0.04733394458889961, 0.021862292662262917, 0.000042711977584986016, -0.010259323753416538, -0.022637464106082916, -0.016938993707299232, 0.026498831808567047, -0.08407776802778244, 0.024265769869089127, 0.015550961717963219, 0.040972452610731125, 0.024775220081210136, 0.026879971846938133, -0.0026270532980561256, -0.028006065636873245, -0.022456666454672813, 0.0463394932448864, -0.08187360316514969, 0.05072840303182602, 0.04043829068541527, 0.016116594895720482, -0.06114906817674637, -0.0010426269145682454, 0.03051511012017727, 0.012076189741492271, -0.033419571816921234, -0.03977293148636818, -0.002302935579791665, -0.013150288723409176, -0.000785976299084723, -0.015763379633426666, -0.0035109601449221373, 0.05114084109663963, 0.019582225009799004, 0.002354213036596775, -0.005238712299615145, -0.009404405951499939, 0.053875237703323364, -0.0010402899933978915, -0.0027811159379780293, -0.03797532990574837, 0.04371274635195732, -0.0983741506934166, -0.02026894874870777, 0.08991015702486038, -0.05650119483470917, -0.004260283894836903, 0.05706134811043739, -0.0032607754692435265, 0.043863922357559204, 0.01590259186923504, -0.023850534111261368, 0.004779424984008074, 0.026481883600354195, -0.07219953089952469, -0.007615242153406143, -0.06557081639766693, 0.01817062310874462, 0.04523129761219025, -0.015218298882246017, -0.04940493777394295, -0.0008129340712912381, -0.04982565715909004, 0.027394087985157967, 0.06443130224943161, -0.10714246332645416, -0.04590771719813347, -0.0111207515001297, -0.02042059227824211, 0.040332261472940445, 0.060168687254190445, 0.049763139337301254, -0.00039491517236456275, -0.003912847489118576, 0.08014607429504395, -0.08910147845745087, 0.013107438571751118, -0.0386323444545269, -0.05619792640209198, -0.005491233896464109, -0.009223653003573418, 0.02698446623980999, 0.00809544324874878, 0.01494579203426838, 0.035267192870378494, -0.0073999459855258465, -0.043008312582969666, 0.008361008018255234, 0.0073381997644901276, 0.022875919938087463, 0.04709027707576752, -0.037592604756355286, -0.010516589507460594, 0.01333717629313469, -0.04947344586253166, 0.030501479282975197, -0.0073002097196877, -0.03355487063527107, 0.008976048789918423, 0.03727417066693306, 0.0023635528050363064, 0.0020473129115998745, 0.00803481787443161, -0.04960052669048309, -0.04243459925055504, 0.020197778940200806, -0.008341707289218903, -0.02103545516729355, 0.013163896277546883, 0.018197033554315567, 0.02240542136132717, 0.04239601641893387, -0.0033559438306838274, -0.020954936742782593, 0.08977688103914261, 0.006760336458683014, 0.09058818966150284, -0.009026218205690384, 0.03914324939250946, 0.001293136621825397, -0.009353814646601677, -0.01558858621865511, -0.022251462563872337, -0.02447001077234745, 0.008872829377651215, -0.0788675844669342, 0.038617104291915894, 0.03658698871731758, 0.03649000823497772, 0.03634478151798248, -0.03247510641813278, -0.01006914209574461, -0.013683700934052467, 0.03117118589580059, -0.01999635435640812, 0.010401356033980846, 0.017033325508236885, 0.04020877927541733, 0.018575454130768776, -0.018599659204483032, -0.023554254323244095, -0.03202245756983757, -0.013387483544647694, 0.007787482347339392, 0.08357104659080505, 0.04902799054980278, -0.07017679512500763, 0.006351060699671507, -0.004742823075503111, 0.02095956727862358, 0.010468583554029465, -0.021688878536224365, 0.03243500366806984, -0.0011720844777300954, -0.04247898980975151, 0.016846338286995888, 0.06089133769273758, -0.0013604164123535156, -0.022512976080179214, 0.03375086188316345, -0.04112359508872032, -0.02292407862842083, -0.03924946114420891, 0.04873333498835564, -0.11156015843153, 0.021159440279006958, -0.008173241280019283, 0.04467742145061493, -0.007360782008618116, 0.04645718261599541, -0.005105474032461643, -0.05638602748513222, -0.03396144509315491, -0.012395069003105164, 0.010792195796966553, 0.020528672263026237, 0.015792176127433777, 0.06064285337924957, 0.02885463461279869, -0.0022440929897129536, -0.02445111609995365, 0.04306400567293167, -0.026316771283745766, 0.03260267153382301, -0.036929577589035034, -0.08241399377584457, -0.00496703153476119, -0.021982461214065552, 0.03870025649666786, 0.005561057012528181, -0.019483836367726326, -0.033516038209199905, 0.07722973078489304, 0.020950807258486748, 0.0043772137723863125, -0.05058753862977028, -0.003728382522240281, 0.047701332718133926, 0.02258630469441414, -0.04332631081342697, 0.03369725123047829, 0.037392452359199524, -0.007108774036169052, 0.07193779200315475, 0.01242738962173462, 0.04088809713721275, -0.061301130801439285, -0.003505919361487031, 0.0003524709027260542, 0.044339537620544434, -0.019570203498005867, 0.01833265647292137, 0.002535724313929677, -0.019244207069277763, -0.002145731821656227, 0.021785587072372437, 0.007823728956282139, -0.00234454614110291, 0.044052381068468094, 0.0347159169614315, -0.040980495512485504, 0.0016211309703066945, 0.051591478288173676, -0.011411020532250404, -0.038827136158943176, -0.01422267034649849, 0.011711536906659603, 0.07005967199802399, 0.04547546058893204, 0.03423568978905678, 0.002888737479224801, -0.010690784081816673, -0.05283883213996887, -0.0065594203770160675, 0.014367172494530678, -0.024638162925839424, -0.03408874571323395, -0.0005902376142330468, -0.0067695314064621925, -0.034476637840270996, 0.04481589421629906, 0.03819706663489342, 0.032726533710956573, 0.013820258900523186, 0.022026769816875458, -0.06773710995912552, 0.011629240587353706, 0.001844213460572064, -0.014252682216465473, 0.012443984858691692, -0.01846654899418354, -0.05708269029855728, -0.0072090900503098965, -0.011880829930305481, 0.004607631359249353, 0.02546222321689129, 0.021374501287937164, 0.020376648753881454, 0.009797424077987671, 0.03621074929833412, -0.06696291267871857, 0.013668195344507694, -0.04802173376083374, 0.03137657791376114, -0.027932098135352135, -0.014258109033107758, -0.04035782441496849, 0.05210212990641594, 0.0022332898806780577, 0.04029543697834015, 0.08757958561182022, -0.03169780597090721, -0.014687208458781242, -0.009383352473378181, -0.02185479737818241, -0.02773425728082657, -0.004397315438836813, -0.038900721818208694, 0.02244308590888977, -0.030231909826397896, 0.0040650516748428345, -0.07250042259693146, -0.038760099560022354, -0.03268110007047653, 0.010432119481265545, 0.04963618144392967, -0.023703454062342644, 0.01893395185470581, -0.005472609773278236, 0.028658540919423103, 0.10595972090959549, -0.049549903720617294, -0.0249831210821867, -0.0484071709215641, 0.008405345492064953, 0.05712603032588959, 0.013826688751578331, -0.0207048486918211, 0.0005369556602090597, 0.03929554298520088, -0.0020774975419044495, -0.03447476774454117, 0.0026323837228119373, 0.03171195462346077, 0.032639406621456146, -0.05608552694320679, 0.0020061051473021507, -0.020984183996915817, 0.03483515605330467, 0.06749046593904495, -0.007992679253220558, -0.06337638944387436, 0.013074938207864761, -0.04673798009753227, -0.022191911935806274, -0.031171146780252457, 0.006859200075268745, 0.04346546530723572, -0.0413297675549984, -0.012510445900261402, 0.05126683786511421, -0.03486960381269455, -0.02792951837182045, -0.021488379687070847, -0.003374790772795677, -0.03719855472445488, -0.017058057710528374, -0.03455079346895218, 0.007389395497739315, -0.017026321962475777, 0.032386261969804764, 0.014361276291310787, -0.030157949775457382, -0.016900628805160522, -0.044492583721876144, -0.00869816169142723, -0.009987812489271164, 0.01058490015566349, 0.007349069695919752, 0.06351592391729355, 0.0023979770485311747, -0.03721879422664642, -0.03500200808048248, 0.009549889713525772, 0.029850132763385773, -0.010470470413565636, -0.030585316941142082, 0.04027668759226799, 0.025417635217308998, -0.025049522519111633, 0.09698738902807236, 0.06617514789104462, 0.020257839933037758, -0.02670796401798725, 0.025667622685432434, 0.018479477614164352, -0.024543754756450653, 0.05215892568230629, -0.0026444068644195795, -0.05873088911175728, 0.0036508245393633842, 0.08164682984352112, -0.027050914242863655, -0.008073306642472744, -0.03453262895345688, 0.04476287215948105, 0.005806232802569866, 0.017572320997714996, 0.016676999628543854, -0.008960897102952003, -0.04154855012893677, -0.041026365011930466, -0.02018437348306179, 0.01822076179087162, 0.03279147297143936, -0.0009657797636464238, -0.06390950083732605, -0.05537441372871399, -0.011386086232960224, 0.02423514612019062, 0.01114580500870943, -0.008581406436860561, -0.013058057054877281, -0.0033156576100736856, -0.010399440303444862, -0.004844678565859795, -0.08145622164011002, 0.007340989541262388, -0.013639479875564575, -0.012023959308862686, -0.001201967359520495, -0.03010261245071888, 0.024443145841360092, 0.0353073850274086, -0.03011404722929001, -0.008975788950920105, -0.004447944462299347, -0.03309791535139084, 0.0005601877928711474, 0.03741415590047836, 0.04596038907766342, 0.010467654094099998, -0.011335548013448715, -0.04422943666577339, 0.03662172332406044, -0.03581716865301132, -0.06847318261861801, 0.03437792509794235, -0.03077433630824089, -0.007187193259596825, -0.02637852542102337, -0.018877828493714333, -0.0012713732430711389, 0.00947709009051323, 0.07055667787790298, 0.017708217725157738, -0.007894701324403286, 0.05277778208255768, 0.0057847341522574425, 0.03609687089920044, -0.041792429983615875, -0.032608214765787125, -0.023867696523666382, -0.004198115319013596, -0.0027263823430985212, -0.010839158669114113, 0.006233665626496077, 0.009592568501830101, -0.01823144219815731, -0.04393962025642395, 0.04196620732545853, -0.017436720430850983, 0.009619513526558876, 0.005711845587939024, 0.03443775698542595, -0.004947897978127003, -0.028818003833293915, -0.013317685574293137, -0.018078429624438286, -0.06486029177904129, -0.041931990534067154, 0.011265955865383148, -0.0735601857304573, -0.01065786276012659, -0.02422817051410675, -0.018940553069114685, 0.011108780279755592, -0.0044381096959114075, 0.04287099465727806, 0.08812086284160614, -0.019605381414294243, -0.05148906633257866, 0.0037590491119772196, 0.002400474390015006, 0.08096464723348618, -0.0144041758030653, -0.0021307498682290316, 0.03193674236536026, -0.002142006764188409, 0.0267806276679039, -0.020310809835791588, -0.018548931926488876, 0.020657861605286598, -0.06593160331249237, 0.027726726606488228, 0.03925648331642151, -0.027911897748708725, -0.038626257330179214, -0.033189207315444946, 0.07037316262722015, 0.03504995256662369, -0.009232818149030209, 0.021019503474235535, 0.0725104883313179, 0.006599846761673689, 0.03716791048645973, 0.006101707927882671, -0.01754358783364296, 0.014793516136705875, -0.04885527864098549, 0.05169100686907768, -0.042385995388031006, 0.0072065736167132854, 0.04756949469447136, -0.02839670144021511, -0.040109045803546906, 0.0024819797836244106, 0.05219430476427078, 0.031383272260427475, -0.07607368379831314, 0.001829882268793881, 0.06074264273047447, 0.047486480325460434, -0.08765678852796555, -0.035643912851810455, 0.06933087855577469, -0.002535078441724181, 0.04405416175723076, 0.007245270069688559, -0.03114704042673111, -0.07244212180376053, 0.034528110176324844, -0.027264917269349098, -0.00004791644823853858, -0.10776172578334808, -0.04337386041879654, -0.011654932983219624, 0.006747294683009386, 0.02000529132783413, 0.025421129539608955, 0.028596017509698868, -0.011431785300374031, -0.07247698307037354, -0.013017729856073856, -0.040975626558065414, 0.0609053336083889, -0.00784095749258995, -0.014064903371036053, 0.015079669654369354, 0.048743247985839844, -0.019079577177762985, 0.006701011210680008, 0.023719189688563347, 0.021682078018784523, -0.009881779551506042, 0.017744125798344612, -0.009025356732308865, -0.06199140474200249, -0.01827588677406311, 0.016690609976649284, -0.022204047068953514, 0.03794039413332939, -0.01869715191423893, 0.044260237365961075, 0.059242311865091324, -0.038804225623607635, -0.05576010048389435, 0.030742885544896126, 0.008752838708460331, 0.020049769431352615, 0.023335207253694534, 0.03604598343372345, 0.012861614115536213, 0.04513949900865555, 0.03005860559642315, 0.015635371208190918, 0.0020129678305238485, -0.04702463373541832, -0.03290272876620293, 0.04516519233584404, -0.02144470624625683, 0.013993600383400917, -0.041649963706731796, -0.03466188535094261, -0.021142397075891495, -0.029131188988685608, -0.0038153291679918766, -0.03852362185716629, 0.051186271011829376, 0.03246290981769562, -0.007771797012537718, -0.03884686529636383, 0.01921168528497219, 0.006271356716752052, -0.03540812432765961, 0.011264096014201641, -0.04005103185772896, 0.006351121235638857, -0.0010080351494252682, -0.02796301431953907, -0.04337216913700104, 0.004285389557480812, -0.02432899735867977, 0.006209033075720072, 0.04178744927048683, -0.05746881291270256, -0.024274248629808426, -0.06468340009450912, 0.0575057789683342, -0.008802995085716248, 0.054904110729694366, 0.04088252782821655, 0.06030102074146271, 0.01658809185028076, -0.004296818282455206, -0.04431791231036186, 0.005563347600400448, 0.028953732922673225, 0.00952201522886753, -0.003454744815826416, -0.0036800203379243612, -0.06443065404891968, -0.032695308327674866, 0.03908663988113403, 0.020209386944770813, -0.04733775183558464, -0.005482476204633713, 0.02740848995745182, 0.009066388942301273, 0.04609131067991257, -0.028672518208622932, 0.09233485907316208, 0.04973326995968819, 0.02632867358624935, 0.0674499124288559, -0.023047370836138725, -0.014736470766365528, -0.002079371362924576, -0.014816667884588242, -0.06846724450588226, -0.013359966687858105, -0.0015542191686108708, -0.022528093308210373 ]
<p>The figure shows an LR circuit with a switch and a 240-volt battery. At the instant the switch is closed the current in the circuit and the potential difference between points a and b, Vab, are</p> <p><img src="http://i.stack.imgur.com/Xs9ak.png" alt="enter image description here"></p> <p>Choices : </p> <pre><code>a. 0 A, 0 V b. 0 A, -240 V c. 0 A, +240 V d. 0.024 A, 0 V e. 0.024 A, +240 V </code></pre> <p>Answer : c. 0 A, +240 V</p> <hr> <p><strong>My Questions</strong></p> <ul> <li><p>When the battery discharging, the voltage will drop continuously, the voltage across a and b at the start instant should be equal to the original voltage of the battery 240V. However, how can we determine whether Vab is +240V or -240V?</p></li> <li><p>Moreover, if the potential different at the start instant is 240V, why should the current equals 0A?</p></li> </ul> <hr> <p>Thank you for your help.</p>
g1542
[ 0.05878721922636032, -0.06026165932416916, -0.0016404202906414866, 0.01643490232527256, 0.07983729988336563, 0.0018620147602632642, 0.039702557027339935, 0.03690686449408531, -0.06247232109308243, 0.01104892697185278, -0.04062921926379204, 0.04988783970475197, -0.018650328740477562, 0.051800817251205444, 0.059606023132801056, -0.010384663939476013, 0.016768109053373337, -0.024223176762461662, 0.040790051221847534, -0.023968005552887917, 0.02158106118440628, 0.04442109540104866, -0.0416518859565258, 0.024470798671245575, -0.013359837234020233, -0.06911393254995346, -0.007703876122832298, 0.025141747668385506, -0.03772289305925369, -0.050461120903491974, -0.04417908191680908, 0.0010259933769702911, 0.09195465594530106, -0.015620769932866096, -0.02252444066107273, 0.008089057169854641, -0.007971955463290215, -0.001456106430850923, -0.031157013028860092, 0.037822425365448, -0.0032134659122675657, 0.024939952418208122, 0.06899930536746979, 0.030752884224057198, -0.017715999856591225, -0.07576627284288406, 0.0006429702043533325, -0.00853912252932787, 0.002980408724397421, -0.021275123581290245, -0.02184879034757614, -0.018108412623405457, -0.022228920832276344, 0.02213837206363678, 0.0010788108920678496, 0.003234184579923749, 0.020229455083608627, 0.002344654407352209, -0.007731546647846699, 0.028824804350733757, 0.013379567302763462, -0.014803820289671421, 0.06909488141536713, 0.03575284034013748, 0.023421037942171097, -0.026000667363405228, -0.008701187558472157, -0.012991185300052166, -0.005503514315932989, 0.010541459545493126, -0.028982263058423996, -0.07512611895799637, -0.015955200418829918, -0.010427864268422127, -0.018528928980231285, 0.03267883509397507, 0.03050352819263935, -0.003320922376587987, 0.06972827017307281, 0.01071212813258171, -0.10168696939945221, -0.05157526209950447, 0.039608314633369446, 0.08534683287143707, -0.01007807720452547, 0.029049929231405258, 0.018341977149248123, 0.007069658022373915, -0.01346442848443985, 0.01266868319362402, 0.048693183809518814, -0.009911230765283108, 0.07111844420433044, -0.04712449759244919, -0.04860178753733635, -0.022206149995326996, 0.011944049037992954, 0.05736483633518219, 0.03320079669356346, 0.02351187914609909, 0.0016684496076777577, -0.052133433520793915, -0.006862517911940813, -0.019585149362683296, -0.07350007444620132, 0.03636535629630089, 0.012608259916305542, -0.05861881747841835, -0.07336214184761047, -0.0189251359552145, -0.048978786915540695, -0.09151114523410797, -0.03568938747048378, -0.01914769969880581, -0.005690534133464098, 0.03261984884738922, 0.04174434393644333, -0.005935871973633766, -0.005133342929184437, -0.04151260107755661, -0.047781798988580704, 0.012559834867715836, -0.04131878912448883, -0.027103954926133156, -0.007104343269020319, 0.007975278422236443, -0.03957439586520195, -0.00828376691788435, 0.02351919189095497, 0.040217623114585876, 0.045230261981487274, 0.012900551781058311, -0.007866248488426208, 0.0005080148694105446, 0.0026905867271125317, 0.03277895227074623, 0.07486458867788315, -0.0009168075048364699, -0.0018170084804296494, 0.004293886478990316, -0.009386473335325718, -0.02090875431895256, -0.042530935257673264, 0.010730020701885223, -0.0509217269718647, 0.07052849978208542, -0.032948967069387436, -0.0007964428514242172, 0.040034063160419464, -0.01196421030908823, 0.05394051969051361, 0.06897392123937607, -0.046843525022268295, -0.023551616817712784, -0.0063280691392719746, -0.05027412250638008, 0.013684074394404888, -0.00034018157748505473, 0.006782345939427614, 0.008408776484429836, 0.012977968901395798, 0.0018253647722303867, -0.031557705253362656, -0.03326030448079109, -0.02562771551311016, 0.011767768301069736, 0.06571035832166672, -0.004841242916882038, 0.0029922574758529663, 0.0072236815467476845, -0.05490721017122269, 0.0289651807397604, 0.03591824322938919, 0.004082841798663139, 0.1073913499712944, 0.10725037008523941, 0.03625672683119774, 0.022959379479289055, 0.09015676379203796, 0.03498376905918121, -0.01255081221461296, -0.024730512872338295, 0.051465779542922974, -0.005888361483812332, -0.04357459396123886, -0.01911197602748871, -0.0008494617068208754, 0.012914873659610748, -0.05100792646408081, -0.05458521842956543, -0.019656198099255562, -0.02849026769399643, -0.04543863609433174, -0.03455018252134323, -0.041071560233831406, 0.01797676831483841, 0.03153486177325249, -0.041601020842790604, -0.03842892870306969, -0.02394365705549717, -0.021150439977645874, 0.0372031033039093, 0.037235017865896225, 0.12020862847566605, -0.00920436717569828, 0.013737496919929981, -0.0024741142988204956, -0.004493254702538252, -0.014451023191213608, 0.009634343907237053, -0.03224917873740196, 0.012764137238264084, 0.00425878819078207, 0.014441005885601044, -0.03409520164132118, 0.0033279515337198973, -0.07409694790840149, 0.04098165035247803, -0.05062512308359146, 0.013315490446984768, 0.008978758938610554, 0.0007385078934021294, 0.034499794244766235, 0.016869641840457916, -0.03520442545413971, 0.021050145849585533, 0.010754830203950405, -0.05883108079433441, -0.013292995281517506, -0.005900306161493063, -0.013412756845355034, 0.01585223712027073, -0.053306944668293, -0.030615637078881264, -0.0172293521463871, 0.013869705609977245, -0.016461387276649475, -0.0021862273570150137, -0.03254310041666031, -0.0289230328053236, 0.07399160414934158, -0.0025380265433341265, 0.06487604975700378, 0.10757733881473541, -0.004985778592526913, -0.03548704832792282, 0.04697435349225998, -0.020501477643847466, -0.02865692786872387, 0.024657733738422394, -0.03760466352105141, 0.03382488340139389, -0.01949021965265274, 0.04532838985323906, -0.09215099364519119, -0.0379069484770298, 0.009099421091377735, 0.008315974846482277, 0.0065323482267558575, -0.035597413778305054, -0.0187077596783638, -0.019776947796344757, 0.03929071128368378, 0.06964195519685745, -0.00653211772441864, -0.010290611535310745, -0.04895361140370369, -0.02765047550201416, 0.005165747832506895, -0.0676577016711235, 0.005706325173377991, 0.044000294059515, -0.006627566646784544, 0.0030181531328707933, 0.007664461620151997, -0.022426428273320198, 0.01264091208577156, -0.046690646559000015, 0.08052294701337814, 0.011650808155536652, 0.045673295855522156, -0.02768712118268013, -0.053649988025426865, -0.005490434821695089, -0.0019401200115680695, 0.021044733002781868, 0.024189621210098267, 0.016115033999085426, 0.002022838918492198, -0.005160253029316664, -0.038029611110687256, -0.00951966643333435, 0.026094188913702965, -0.0670548602938652, 0.0007671884377487004, -0.0010626886505633593, 0.014542358927428722, -0.008225806057453156, -0.0592605397105217, -0.025897081941366196, -0.011578747071325779, -0.05169913172721863, 0.005800934974104166, -0.013483112677931786, 0.00391455227509141, 0.002648791763931513, 0.0030414811335504055, 0.030685752630233765, 0.0633373111486435, 0.06362734735012054, -0.05311458185315132, -0.03679317608475685, -0.016110088676214218, -0.08527718484401703, 0.0056098513305187225, -0.029735691845417023, 0.002424076432362199, 0.05322887375950813, -0.021860992535948753, -0.019186297431588173, -0.005934652406722307, -0.010370675474405289, 0.0321323499083519, 0.07014451175928116, 0.013373232446610928, 0.010755211114883423, -0.02918672189116478, 0.026616454124450684, -0.05982163920998573, -0.022213591262698174, -0.04252604395151138, 0.037291739135980606, 0.0004183074343018234, 0.014300024136900902, 0.009757758118212223, -0.024445461109280586, 0.009452380239963531, 0.03903121501207352, -0.02499617077410221, -0.004378298297524452, 0.012840664014220238, -0.012260118499398232, -0.06194514408707619, -0.000013595442396763247, 0.029805613681674004, -0.004671055823564529, -0.009468861855566502, -0.003779623657464981, -0.027377964928746223, -0.022271132096648216, 0.005485178902745247, -0.009351217187941074, -0.01992822252213955, -0.020732779055833817, 0.0011500472901389003, -0.003145436989143491, -0.0690474882721901, 0.034490231424570084, -0.039716508239507675, 0.018655147403478622, -0.035237930715084076, -0.03367667272686958, 0.040731027722358704, 0.01687169447541237, 0.04678865522146225, -0.06119387596845627, -0.007968004792928696, 0.01674017123878002, -0.006250677164644003, -0.05748732015490532, 0.04949229583144188, -0.022391481325030327, 0.02925649844110012, 0.022112106904387474, 0.037728868424892426, -0.0057611926458776, 0.05788819491863251, 0.0013957732589915395, -0.03942765295505524, 0.09312591701745987, 0.017152145504951477, 0.047680508345365524, 0.03895634412765503, -0.03416725993156433, 0.012816016562283039, 0.013462689705193043, -0.01163404993712902, 0.005570775829255581, 0.040852662175893784, -0.02582591399550438, 0.01026106346398592, 0.048177532851696014, -0.034815527498722076, 0.02511781081557274, -0.01951519213616848, 0.02033282443881035, 0.049426767975091934, 0.01567174308001995, -0.07212463021278381, 0.04865916445851326, -0.0217740498483181, 0.04942356050014496, 0.018583467230200768, -0.026205193251371384, 0.00870634987950325, -0.045179303735494614, 0.039301369339227676, -0.02378755994141102, 0.06008215621113777, 0.011306541971862316, -0.017706867307424545, -0.02938544563949108, -0.01465240865945816, -0.05842049792408943, -0.027652934193611145, 0.01571437530219555, 0.06447605788707733, 0.05468914285302162, 0.07972323149442673, 0.049051232635974884, 0.00573174562305212, 0.03314773738384247, 0.03133372217416763, -0.05468660220503807, 0.03123622201383114, -0.017552947625517845, 0.05834845080971718, 0.01348752249032259, 0.06767219305038452, -0.038913801312446594, 0.0417960025370121, 0.0643022432923317, -0.03590770810842514, 0.021134261041879654, -0.03167823702096939, 0.06978059560060501, -0.07205377519130707, 0.030616939067840576, 0.037979111075401306, 0.030212989076972008, 0.06634317338466644, -0.03606967628002167, 0.0012271987507119775, 0.009695552289485931, -0.02742062136530876, 0.0462060421705246, -0.0900663211941719, -0.02007739618420601, 0.04289834573864937, -0.06624921411275864, -0.04248899221420288, 0.013291290029883385, 0.004809623584151268, -0.06092457100749016, -0.04008028656244278, -0.009609851986169815, 0.02599501796066761, -0.026440948247909546, -0.01766045019030571, 0.03321905806660652, 0.0468812920153141, -0.041737161576747894, 0.020790504291653633, 0.016409724950790405, 0.036158159375190735, 0.005726624745875597, 0.009050708264112473, -0.017280306667089462, -0.03962548449635506, -0.060951076447963715, 0.03516504913568497, 0.02181818336248398, -0.0005307624232955277, 0.052804719656705856, -0.0015709648141637444, -0.009661925956606865, 0.04009784013032913, -0.02330891788005829, -0.043820831924676895, -0.032827071845531464, -0.05310523137450218, -0.042438339442014694, -0.023173512890934944, 0.03062969259917736, 0.001928931102156639, -0.017767230048775673, -0.034401487559080124, -0.010613879188895226, -0.0069753145799040794, 0.0217253677546978, 0.04814238101243973, 0.0655096098780632, 0.07382228970527649, -0.024283036589622498, 0.052016161382198334, -0.018397558480501175, 0.011842785403132439, 0.03928903862833977, -0.050916630774736404, 0.031468044966459274, -0.050291940569877625, -0.020576659590005875, -0.001949323108419776, 0.016479704529047012, -0.042647410184144974, 0.08174538612365723, -0.045474011451005936, -0.006228746380656958, -0.012752005830407143, -0.05635562911629677, -0.022587232291698456, -0.002001263666898012, 0.03320200741291046, 0.047758448868989944, 0.006858660373836756, 0.02520599029958248, -0.051301632076501846, -0.03190834820270538, -0.07513196766376495, -0.007509319111704826, 0.008096378296613693, 0.0037787461187690496, 0.09323248267173767, -0.024831591174006462, -0.029440511018037796, -0.03947756439447403, 0.009382076561450958, -0.022752586752176285, 0.003890451043844223, 0.019783280789852142, -0.00026873612659983337, 0.06564094126224518, -0.01742052100598812, -0.012514796108007431, -0.00332144508138299, -0.002882561646401882, 0.02898244746029377, -0.029589824378490448, -0.003543086117133498, -0.006195372436195612, -0.0018591700354591012, -0.0021414707880467176, -0.0009341309196315706, 0.059113264083862305, -0.02426619827747345, -0.05881144851446152, -0.06661701947450638, -0.053725410252809525, -0.015968618914484978, -0.023393157869577408, -0.04528910666704178, 0.048457540571689606, -0.00211475626565516, 0.05518791079521179, 0.04649576172232628, -0.01363853458315134, 0.016618497669696808, 0.0037087725941091776, -0.0357229970395565, 0.005038725212216377, 0.03947066888213158, -0.03525605425238609, 0.00844677072018385, -0.00590880773961544, 0.048821981996297836, -0.06257827579975128, -0.03729914501309395, 0.01941855065524578, 0.002415209077298641, -0.010695341043174267, 0.012114073149859905, -0.030207889154553413, 0.02409196086227894, -0.0760331004858017, 0.040142133831977844, 0.02085699886083603, -0.0530489981174469, -0.037651535123586655, 0.029480718076229095, 0.05085378885269165, -0.000933328177779913, 0.02554255910217762, 0.014187107793986797, -0.03713260963559151, 0.041456278413534164, 0.043950293213129044, 0.005229039583355188, -0.0979936346411705, -0.02652917429804802, 0.0342521145939827, 0.014863146468997002, 0.03707970678806305, 0.015579747967422009, -0.04872989282011986, 0.023700233548879623, -0.003366850083693862, -0.0011228182120248675, 0.0028692984487861395, -0.025043262168765068, 0.031105879694223404, 0.023467790335416794, 0.04311813414096832, -0.029555251821875572, 0.028332555666565895, -0.015132450498640537, 0.0022259256802499294, -0.021601412445306778, 0.0060456860810518265, 0.0025284322910010815, -0.032428078353405, 0.0032559032551944256, 0.009655538946390152, -0.019822316244244576, -0.008784491568803787, 0.014290978200733662, -0.012737387791275978, 0.010841453447937965, 0.056241270154714584, -0.030973639339208603, 0.06996549665927887, -0.00692779803648591, 0.008939431980252266, -0.031712718307971954, 0.02460145764052868, 0.05425184965133667, 0.06731975078582764, -0.01573803648352623, 0.04299384728074074, 0.01833116076886654, -0.009837068617343903, -0.02545183338224888, -0.0007485119276680052, -0.004215933382511139, 0.039442118257284164, 0.03305184096097946, 0.029747620224952698, -0.050492946058511734, -0.0036599887534976006, 0.024127664044499397, -0.013758793473243713, -0.0014975958038121462, 0.03155680000782013, 0.001055129338055849, 0.03818179666996002, 0.035975586622953415, -0.04673905298113823, 0.002055507153272629, 0.006807117257267237, -0.004015438724309206, 0.03563310578465462, 0.041959311813116074, -0.0013183365808799863, -0.0404818020761013, 0.0404190793633461, -0.006557870656251907, 0.04391264170408249, 0.007071135565638542, 0.0244697704911232, 0.01886231265962124, -0.024008071050047874, 0.022329101338982582, -0.030326295644044876, -0.039898186922073364, 0.01190088875591755, 0.03957254812121391, 0.032401613891124725, -0.028925821185112, -0.06729982048273087, -0.019103096798062325, -0.07422616332769394, -0.03573169559240341, -0.0646648108959198, -0.006757792085409164, 0.028756318613886833, 0.0424850657582283, 0.023074127733707428, -0.009181497618556023, 0.0078085921704769135, 0.03850633651018143, -0.02641483023762703, 0.0022440245375037193, 0.03787986561655998, -0.07420952618122101, -0.006226820405572653, -0.054369889199733734, 0.05863218754529953, -0.048038724809885025, -0.00844963826239109, 0.015583966858685017, 0.009447591379284859, -0.01366437878459692, 0.04351317882537842, 0.0067204744555056095, 0.03307097405195236, -0.02551874704658985, 0.006721514742821455, -0.014512541703879833, -0.011273582465946674, 0.042199742048978806, 0.0021873738151043653, 0.033427562564611435, -0.024509437382221222, 0.03554808720946312, 0.030204925686120987, -0.02760346606373787, -0.0178365521132946, -0.025055546313524246, 0.004099850542843342, -0.05148917809128761, 0.004123856779187918, 0.02661534585058689, 0.048768866807222366, 0.01679561659693718, -0.03289312496781349, -0.01736346445977688, 0.04139348119497299, -0.02840419113636017, 0.0058904606848955154, -0.01066316943615675, 0.0627853125333786, 0.0009882072918117046, -0.02069981023669243, -0.030228616669774055, -0.033985186368227005, -0.010249658487737179, -0.004661877639591694, -0.046521276235580444, 0.007700816262513399, -0.03607060760259628, -0.007060143630951643, -0.038550738245248795, -0.030084777623414993, -0.012836193665862083, -0.003046068362891674, -0.04470786824822426, 0.031682245433330536, 0.004180454649031162, 0.03813675045967102, 0.0011732735438272357, 0.007889130152761936, -0.03041604533791542, -0.04970376193523407, 0.0026394769083708525, -0.033477235585451126, 0.03489716351032257, -0.03599551320075989, -0.07470912486314774, 0.022921429947018623, 0.051933180540800095, -0.037967242300510406, 0.01370426919311285, -0.04305465891957283, -0.07357736676931381, 0.01989736221730709, 0.029931435361504555, -0.0011994153028354049, -0.05514319986104965, 0.004349247552454472, -0.010044319555163383, 0.02247883751988411, -0.05212041363120079, -0.018042325973510742, 0.0016142671229317784, 0.011800287291407585, 0.019313545897603035, -0.012098869308829308, -0.06150388345122337, 0.0008202496683225036 ]
<p>The spatially flat FRW metric in cartesian co-ordinates is given by: $$ds^2 = -dt^2 + a^2(t)(dx^2 + dy^2 + dz^2)$$ As I understand it there are Killing vectors in the $x$, $y$, $z$ directions implying that momentum is conserved but there is no Killing vector in the $t$-direction which implies that energy is not conserved. I don't know much about Killing vectors. Is this correct?</p> <p>If I transform the time co-ordinate $t$ to conformal time $\tau$ using the relationship: $$d\tau = \frac{dt}{a(t)}$$ the metric now becomes: $$ds^2 = a^2(\tau)(-d\tau^2 + dx^2 + dy^2 + dz^2)$$ Does this metric now have a Killing vector in the $\tau$-direction as well as in the $x$, $y$ and $z$ directions?</p>
g1543
[ 0.016381453722715378, -0.05983256921172142, -0.023043060675263405, -0.012074800208210945, 0.07367721945047379, -0.0045104180462658405, 0.030356068164110184, -0.00562985148280859, -0.07233847677707672, -0.016390850767493248, 0.03761562705039978, -0.039844952523708344, 0.10034792125225067, -0.00909317284822464, -0.015063771978020668, -0.025212211534380913, 0.02618688903748989, 0.019820624962449074, 0.00834502000361681, 0.01777327060699463, -0.0286902766674757, -0.04193907976150513, 0.016441700980067253, 0.006527754012495279, 0.07158021628856659, -0.03378773108124733, 0.09997281432151794, -0.040782779455184937, -0.03764985501766205, -0.06112845987081528, 0.0908144861459732, 0.07891396433115005, 0.022338267415761948, -0.02022557333111763, -0.007455696351826191, -0.03345205634832382, 0.05702595040202141, 0.02001059614121914, 0.0724298283457756, 0.0014636929845437407, 0.015109751373529434, -0.029054801911115646, 0.03708367422223091, 0.015340744517743587, 0.015046434476971626, -0.008542971685528755, -0.07125137001276016, -0.02016383782029152, 0.0013154147891327739, -0.014348194003105164, -0.006190068554133177, 0.023717187345027924, -0.02400330640375614, -0.046959325671195984, -0.026853861287236214, -0.04080032557249069, 0.006260729860514402, -0.024593528360128403, 0.00779807660728693, 0.03522736579179764, -0.041946638375520706, -0.012698126025497913, 0.0037238169461488724, -0.001722404034808278, 0.0561203807592392, -0.07953611761331558, -0.012268420308828354, -0.03698445484042168, 0.027573756873607635, 0.01801876351237297, 0.03794677555561066, 0.02928955852985382, 0.024584084749221802, -0.055902354419231415, 0.022455962374806404, 0.07814823091030121, 0.008247485384345055, 0.001950161182321608, -0.04042525589466095, -0.08094564080238342, -0.11178002506494522, 0.02473403327167034, 0.030830956995487213, 0.038168635219335556, 0.06663055717945099, -0.03086371161043644, -0.024999825283885002, 0.04006568714976311, -0.005445575341582298, -0.0034555767197161913, 0.008995421230793, 0.0011449046432971954, 0.041790641844272614, -0.029778482392430305, 0.005991610232740641, 0.03037976287305355, -0.08808564394712448, 0.05351804569363594, 0.012937692925333977, -0.04885488376021385, 0.004454679321497679, 0.029440145939588547, -0.019942017272114754, -0.004387084860354662, 0.03913900628685951, -0.060863953083753586, 0.03291405364871025, 0.0028171089943498373, -0.036617547273635864, -0.04551493003964424, 0.030520837754011154, 0.03437528759241104, -0.03538445383310318, 0.03173373267054558, 0.009298211894929409, -0.02015424519777298, 0.04003443941473961, -0.07314600050449371, 0.01431370247155428, -0.0022206457797437906, 0.0010187228908762336, 0.0034999139606952667, -0.025097951292991638, 0.0331440195441246, -0.002564833965152502, -0.02302638627588749, -0.0027954999823123217, -0.00917916838079691, 0.030741875991225243, 0.0005744174704886973, -0.0014070417964830995, -0.000106922845588997, 0.024297714233398438, 0.030280446633696556, -0.04550500214099884, 0.02242269553244114, 0.013737181201577187, 0.0454099103808403, 0.032044947147369385, 0.007856368087232113, -0.033606596291065216, -0.021665021777153015, 0.06317397207021713, -0.03068825602531433, -0.04911864921450615, 0.0001065602627932094, -0.031467095017433167, -0.04849591851234436, 0.082561194896698, -0.0529409795999527, -0.00784442201256752, 0.11392901837825775, -0.01690710335969925, -0.006550158374011517, -0.0002913238713517785, -0.04039670154452324, -0.05313955619931221, -0.03826649859547615, -0.04444862902164459, -0.044107835739851, 0.11112214624881744, 0.0009853054070845246, 0.0622251033782959, 0.012610301375389099, -0.004787647631019354, 0.03306202590465546, -0.018012363463640213, -0.041940245777368546, -0.00022166148119140416, -0.026848003268241882, -0.05173022300004959, 0.0320223867893219, 0.022767581045627594, 0.04487594589591026, 0.01931699924170971, -0.0016471821581944823, -0.10325340926647186, 0.02437068708240986, -0.0020837541669607162, -0.023187989369034767, -0.02336796745657921, -0.019622376188635826, 0.01232974138110876, -0.033685993403196335, 0.05150580406188965, 0.028619881719350815, -0.0014609626960009336, -0.006555250845849514, -0.06953492760658264, 0.0035496316850185394, 0.026037635281682014, 0.013675443828105927, -0.00048741247155703604, 0.06533194333314896, 0.024253034964203835, 0.016317350789904594, 0.007661448325961828, -0.032535627484321594, 0.022769078612327576, 0.010128742083907127, -0.028368892148137093, -0.002201431430876255, 0.026079272851347923, 0.04643489420413971, 0.04238898679614067, 0.009989812038838863, -0.0025732656940817833, 0.005746925249695778, 0.020795125514268875, 0.006786368787288666, -0.019549768418073654, -0.025930432602763176, -0.011625826358795166, 0.01952771097421646, -0.015646226704120636, -0.03740066662430763, -0.0041746157221496105, 0.08211074024438858, -0.06176481768488884, -0.002346963156014681, -0.03357940912246704, -0.0024434556253254414, 0.018712840974330902, 0.001125961891375482, -0.013922546990215778, -0.038782909512519836, -0.06586805731058121, -0.03997861593961716, 0.005063613411039114, -0.01879252679646015, -0.02640116773545742, 0.014170876704156399, 0.010908600874245167, -0.020204422995448112, 0.04720767214894295, 0.005506015848368406, -0.006089022383093834, 0.035632647573947906, 0.031089646741747856, 0.043336525559425354, -0.029774151742458344, -0.036948952823877335, -0.05057169124484062, 0.003015979193150997, 0.01828651875257492, 0.05997101962566376, 0.05477510392665863, -0.0008652778924442828, 0.02275734394788742, -0.02757246419787407, 0.031168030574917793, -0.009827605448663235, -0.024321580305695534, 0.026493752375245094, 0.0355948843061924, 0.028591260313987732, -0.01857745088636875, -0.016556423157453537, -0.1302906721830368, 0.007167771924287081, -0.008473090827465057, -0.07643365859985352, -0.006337478756904602, 0.024860450997948647, -0.022800162434577942, 0.01597994565963745, -0.014239948242902756, 0.04581854119896889, -0.009584272280335426, 0.0019084920641034842, -0.0003928912919946015, 0.04514162242412567, 0.04013867676258087, 0.07930316030979156, -0.04744299128651619, 0.011774227023124695, -0.004279475659132004, -0.029012128710746765, -0.03558359295129776, 0.005102610215544701, -0.03352150321006775, -0.019559664651751518, -0.04049769043922424, 0.04095100611448288, 0.018938573077321053, -0.01401720754802227, -0.0036780594382435083, 0.018320709466934204, -0.02137821726500988, -0.029211748391389847, -0.046593062579631805, 0.04178283363580704, -0.007938765920698643, -0.051889434456825256, -0.001107473042793572, 0.03903137519955635, 0.03022799640893936, 0.0033942440059036016, -0.01081786397844553, 0.024643629789352417, 0.012377173639833927, 0.008455699309706688, 0.029219670221209526, -0.01105905044823885, 0.03278671205043793, 0.031571172177791595, -0.0549723356962204, -0.07001028209924698, -0.022511346265673637, -0.008855978026986122, 0.0009271648013964295, 0.018411749973893166, -0.0012849339982494712, 0.0003439050051383674, -0.05730879679322243, -0.016081534326076508, -0.03419610857963562, -0.05766991898417473, -0.06347855180501938, 0.017642289400100708, 0.013451837003231049, 0.03556595370173454, -0.030029548332095146, 0.01809568516910076, 0.01382792554795742, 0.044792789965867996, -0.06976477801799774, 0.025030488148331642, -0.02900169976055622, 0.04151102900505066, -0.036816470324993134, 0.014308035373687744, 0.05212785303592682, -0.024752380326390266, -0.01851155050098896, -0.001921441056765616, -0.04588359594345093, 0.05059389770030975, 0.0437435619533062, 0.01636599190533161, -0.05329933762550354, -0.023540904745459557, -0.004282851237803698, -0.0013995278859511018, 0.006557921413332224, 0.0468762069940567, -0.004488533362746239, 0.02121792733669281, -0.0029903051909059286, -0.01738453097641468, 0.0036758522037416697, -0.04120781645178795, -0.0055186087265610695, -0.06551359593868256, 0.00008366168185602874, 0.03275754675269127, 0.04403425008058548, 0.05458110198378563, 0.015924736857414246, 0.008915326558053493, 0.029217928647994995, -0.0007228690083138645, -0.03816669434309006, -0.0065699913538992405, -0.029142720624804497, -0.008965675719082355, -0.04901103302836418, -0.012792821042239666, -0.05043955519795418, -0.02005213499069214, 0.051798757165670395, 0.027571970596909523, 0.0021656767930835485, 0.11098435521125793, 0.01032167486846447, -0.011950007639825344, 0.011026548221707344, -0.0005631573149003088, -0.0068930936977267265, 0.027158627286553383, -0.0008481381228193641, -0.04588624835014343, -0.02440999075770378, 0.016459446400403976, 0.03493162989616394, -0.034588444977998734, -0.07136152684688568, -0.02211759425699711, 0.031149843707680702, 0.04733451083302498, 0.0024627691600471735, 0.006662121508270502, 0.020390605553984642, -0.019564641639590263, -0.0064522321335971355, -0.014461237005889416, 0.0378258042037487, 0.031756509095430374, 0.00234970566816628, 0.036394212394952774, -0.02463715337216854, 0.04937763139605522, -0.04238881170749664, -0.03840727359056473, 0.032849013805389404, 0.06397878378629684, -0.009034930728375912, 0.009774282574653625, 0.001492629642598331, -0.04112541303038597, 0.018516138195991516, -0.0021016255486756563, 0.0001045313329086639, -0.08318623155355453, 0.04504718631505966, -0.038770582526922226, 0.014691394753754139, 0.0278728436678648, 0.025792306289076805, -0.0002352912415517494, 0.020424382761120796, 0.01774517260491848, 0.010587072931230068, -0.00464234221726656, 0.01710783690214157, 0.03953738883137703, 0.04389812424778938, -0.05833141878247261, -0.055864088237285614, 0.009073484688997269, -0.005765434820204973, 0.003048039972782135, 0.04649197682738304, 0.04665413871407509, -0.05289684608578682, 0.01979823224246502, -0.013451064005494118, -0.0322992205619812, 0.02790314517915249, 0.09137867391109467, 0.04723029583692551, -0.050612032413482666, -0.020157014951109886, -0.045602574944496155, -0.023419080302119255, 0.04155965521931648, 0.046864740550518036, -0.0874830111861229, 0.007728181779384613, -0.052318863570690155, -0.026756644248962402, 0.071391761302948, 0.010508534498512745, -0.012770198285579681, 0.011067412793636322, -0.024953262880444527, -0.028174396604299545, 0.0031561232171952724, 0.0035776325967162848, 0.02462112531065941, -0.06532606482505798, 0.00431415718048811, 0.028062352910637856, -0.00872267596423626, -0.0049595762975513935, -0.03127692639827728, -0.01713290810585022, 0.03249843791127205, -0.02347758039832115, -0.021410100162029266, 0.03478162735700607, 0.013000547885894775, -0.04442295432090759, 0.014971207827329636, -0.05862428620457649, 0.05441345274448395, 0.022309409454464912, 0.02073219232261181, 0.012886269018054008, -0.04026123136281967, 0.005428685341030359, -0.031917769461870193, 0.009878662414848804, 0.00003641970761236735, 0.05456330627202988, 0.062072113156318665, 0.019434209913015366, -0.021517198532819748, 0.05450208857655525, -0.026094848290085793, 0.02100607566535473, 0.012552556581795216, 0.002795587060973048, 0.04736286774277687, 0.0388336218893528, 0.06307999789714813, 0.026864228770136833, -0.07517316937446594, -0.007652014493942261, 0.008600443601608276, -0.052285633981227875, 0.014348054304718971, 0.00609858613461256, -0.040115442126989365, -0.011171157471835613, 0.05764606222510338, 0.11423037946224213, -0.0008554878877475858, -0.06443163752555847, 0.04238487780094147, -0.024848682805895805, 0.0029067520517855883, 0.003154143923893571, 0.02449464611709118, 0.0223053228110075, -0.03768550604581833, 0.0021954660769551992, 0.004067029803991318, 0.03126494586467743, 0.01864379644393921, 0.02960028499364853, -0.0068020932376384735, 0.015455246903002262, -0.028388872742652893, 0.029343003407120705, 0.009860851801931858, -0.07294024527072906, -0.0019110735738649964, -0.042507123202085495, 0.004098954144865274, 0.003947918303310871, -0.028508080169558525, -0.054025109857320786, 0.036467745900154114, -0.016438666731119156, -0.0554487407207489, -0.008042944595217705, 0.017076401039958, 0.028315769508481026, -0.02652137354016304, -0.02395162731409073, -0.013113333843648434, -0.005665530916303396, 0.05840251222252846, -0.04591283202171326, 0.0420290008187294, -0.002470441395416856, -0.04443832486867905, -0.03780923783779144, -0.03160128369927406, -0.06489550322294235, -0.019235748797655106, 0.00903937965631485, -0.030718762427568436, 0.004408556967973709, 0.003956892527639866, 0.04462375491857529, -0.015728948637843132, -0.04356728121638298, -0.03582284599542618, -0.017040980979800224, 0.014762288890779018, 0.0045300982892513275, 0.032619670033454895, 0.016720052808523178, -0.014176319353282452, -0.05088689178228378, -0.04612419009208679, 0.05082271993160248, -0.004190113395452499, 0.008974496275186539, -0.007738750893622637, -0.026263050734996796, 0.030400104820728302, -0.0015663536032661796, -0.017762556672096252, -0.034183960407972336, 0.013020409271121025, -0.05300722271203995, 0.015239064581692219, 0.025796903297305107, -0.033351462334394455, 0.016270233318209648, -0.09717505425214767, -0.0043555512093007565, 0.014952994883060455, -0.06592796742916107, -0.009721806272864342, -0.01418454572558403, -0.005886467639356852, -0.005798413883894682, 0.019330376759171486, -0.03235222399234772, 0.02164316363632679, -0.02059752307832241, -0.022092139348387718, 0.017080796882510185, 0.03214136138558388, -0.05761435255408287, -0.009610575623810291, -0.08486232906579971, 0.0369449108839035, 0.05139121413230896, -0.0028248445596545935, 0.0584503673017025, 0.04709494858980179, -0.016177374869585037, 0.042881667613983154, 0.03808063268661499, -0.0019880332984030247, -0.006610522046685219, 0.07480142265558243, -0.005311334040015936, 0.03133826330304146, 0.007577249780297279, -0.005620792042464018, 0.03713148832321167, 0.029445134103298187, -0.019434219226241112, 0.011190707795321941, 0.03608664497733116, -0.019957559183239937, -0.01028265431523323, 0.03400280326604843, 0.021908022463321686, 0.021147342398762703, -0.01263173297047615, 0.007824831642210484, -0.005977459717541933, 0.010129486210644245, -0.020316503942012787, -0.004492383915930986, -0.05330485850572586, 0.013408279046416283, 0.025044336915016174, 0.07000216841697693, -0.010945259593427181, 0.024975810199975967, 0.033772408962249756, 0.013870667666196823, 0.013030809350311756, 0.055062174797058105, -0.011591671966016293, -0.047285985201597214, -0.06487812846899033, 0.011486954987049103, 0.01854264736175537, -0.010949837043881416, -0.020458895713090897, 0.021744301542639732, 0.020432153716683388, -0.0220924224704504, -0.03378821909427643, 0.013568677008152008, -0.03258433938026428, -0.02971600368618965, -0.02733287774026394, 0.018588436767458916, 0.023870369419455528, 0.019708314910531044, 0.03969906270503998, -0.04564294219017029, 0.030350783839821815, 0.020262490957975388, -0.0243613813072443, 0.03431135043501854, -0.0017180175054818392, 0.016582095995545387, 0.06138291582465172, -0.01168970949947834, -0.011139298789203167, -0.028301309794187546, -0.012404085136950016, 0.009474924765527248, 0.016690699383616447, -0.003654851345345378, -0.05195491388440132, 0.03904469311237335, -0.028483374044299126, -0.010238594375550747, 0.0005034329369664192, 0.03146982938051224, -0.007137421052902937, 0.0015639923512935638, -0.016056552529335022, 0.03507464751601219, 0.05480660870671272, -0.0653226301074028, 0.001276760478504002, 0.010928546078503132, -0.06498832255601883, 0.04893682897090912, 0.012067659758031368, 0.036188606172800064, 0.0014526558807119727, -0.05446314439177513, 0.01130523532629013, 0.042201846837997437, -0.05240761861205101, 0.01804785057902336, 0.03828790411353111, 0.021040424704551697, -0.01905020885169506, 0.015545115806162357, 0.0030328233260661364, 0.035085394978523254, -0.021944474428892136, -0.10933557897806168, 0.03936832398176193, 0.016283700242638588, 0.02843860536813736, 0.03758727014064789, -0.014917777851223946, 0.02043372392654419, -0.0012614780571311712, -0.030966293066740036, -0.05243941769003868, 0.002171920845285058, 0.010386348702013493, -0.07725678384304047, -0.03584638983011246, -0.028594668954610825, 0.02096014842391014, -0.06093503162264824, -0.009757869876921177, -0.00913125928491354, -0.021960129961371422, 0.009568254463374615, 0.0826532170176506, -0.014332837425172329, -0.037521906197071075, -0.0612872950732708, -0.05744281783699989, 0.05574314296245575, 0.008795267902314663, 0.027646556496620178, 0.03195146098732948, -0.012253370136022568, 0.038036003708839417, 0.020106714218854904, -0.01466948539018631, -0.024159567430615425, -0.0009834746597334743, 0.019689153879880905, -0.06307122856378555, -0.00194768444634974, 0.04794743284583092, 0.05499792471528053, 0.014091582037508488, 0.0012032625963911414, 0.07424761354923248, 0.0793692022562027, -0.03376659378409386, -0.019748594611883163, 0.052282270044088364, -0.00943938922137022, 0.07093578577041626, -0.05555884167551994, 0.046655166894197464, -0.07998770475387573, -0.02222209796309471, -0.0029786163941025734, -0.03261062130331993, 0.009569426067173481, 0.008470804430544376, -0.04515162110328674, 0.004398826509714127, 0.005125872325152159 ]
<p>The Lagrangian of the Yang-Mills fields is given by $$ \mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu} D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+ \bar{c}^a(\partial\cdot D^{ab})c^b $$ where the metric is $(-,+,+,+)$, and the conventions are the following: $$ [D_{\mu},D_{\nu}]=-igF_{\mu\nu},\quad D_{\mu}=\partial_{\mu}-igA^a_{\mu}t^a, \quad D^{ab}_{\mu}=\delta^{ab}\partial_{\mu}-gf^{abc}A^c_{\mu} $$</p> <p>Let $\epsilon$ be an infinitesimal anticummuting parameter, and consider the BRST transformation: $$ \delta\psi=ig\epsilon c^at^a\psi,\quad \delta A^a_{\mu}=\epsilon D^{ab}_{\mu}c^b,\quad \delta c^a=-\frac{1}{2}g\epsilon f^{abc}c^bc^c,\quad \delta\bar{c}^a=\frac{1}{\xi}\epsilon\partial^{\mu}A^a_{\mu} $$</p> <p>I have calculated the corresponding Noether current as $$ j_{BRST}^{\mu}=-g\bar{\psi}\gamma^{\mu}c^at^a\psi-F^{a\mu\nu}D^{ab}_{\nu}c^b- \frac{1}{\xi}(\partial\cdot A^a)D^{ab\mu}c^b+ \frac{1}{2}gf^{abc}(\partial^{\mu}\bar{c}^a)c^bc^c $$</p> <p>I am not sure whether the result is correct or not, so I would like to check that $\partial_{\mu}j^{\mu}_{BRST}=0$. Even though I have used the equation of motion $$ \partial_{\mu}F^{a\mu\nu}=-g\bar{\psi}\gamma^{\nu}t^a\psi- gf^{abc}A^b_{\mu}F^{c\mu\nu}-\frac{1}{\xi}\partial^{\nu} (\partial\cdot A^a)-gf^{abc}(\partial^{\nu}\bar{c}^b)c^c $$ $$ (i\gamma^{\mu}D_{\mu}-m)\psi=0,\quad \partial^{\mu}D^{ab}_{\mu}c^b=0 $$ and spent about four hours, I still cannot get it right. Could someone help me check this? Thanks a lot.</p>
g1544
[ 0.04021183401346207, -0.02043968439102173, -0.014667476527392864, -0.07278773933649063, 0.03226766362786293, 0.035191670060157776, 0.09540977329015732, 0.03529541566967964, -0.03530155494809151, -0.03642610087990761, 0.008153021335601807, 0.07705533504486084, 0.033209871500730515, -0.00404129596427083, 0.0049125091172754765, 0.007002610247582197, 0.014447344467043877, -0.008455796167254448, 0.05239006504416466, -0.07522483915090561, -0.026018740609288216, 0.020958906039595604, 0.03510790690779686, -0.04903974011540413, 0.0017268770607188344, 0.016993412747979164, 0.03351876139640808, -0.029469341039657593, -0.0070846714079380035, 0.01185179315507412, -0.0272836871445179, 0.013171281665563583, 0.040871985256671906, -0.03778300806879997, -0.033205680549144745, -0.01599590666592121, 0.0738169252872467, 0.02685278095304966, 0.031636204570531845, 0.034373145550489426, 0.0365033857524395, -0.04151266813278198, 0.050747524946928024, 0.05856919288635254, 0.02930225431919098, 0.0046700527891516685, -0.03453820198774338, -0.015353431925177574, -0.04249521717429161, 0.02279384806752205, 0.051292601972818375, 0.0112577173858881, 0.03620358556509018, -0.04352305084466934, -0.007795686833560467, 0.025633592158555984, -0.033169206231832504, 0.02259303629398346, -0.021823318675160408, 0.0280840452760458, 0.006866614334285259, -0.08458273857831955, 0.002351638861000538, -0.010679763741791248, 0.013687453232705593, -0.05597276985645294, -0.034843552857637405, -0.027537913993000984, 0.016687313094735146, -0.0061721354722976685, -0.018574679270386696, -0.0001441344356862828, 0.007193828001618385, 0.0103622330352664, -0.004853891208767891, -0.009411252103745937, -0.0688200294971466, 0.024576587602496147, 0.012643369846045971, -0.08280563354492188, -0.010625088587403297, -0.017316201701760292, 0.002523664152249694, 0.01630113646388054, 0.065273217856884, -0.10361441224813461, 0.004475743044167757, 0.006531369406729937, 0.020189739763736725, 0.020895356312394142, -0.05538876727223396, 0.023943128064274788, 0.019253842532634735, -0.08237393945455551, 0.01931208185851574, -0.021510574966669083, 0.01469465158879757, 0.01487327367067337, -0.053289707750082016, -0.021437937393784523, -0.04436436668038368, 0.020644651725888252, -0.003337017260491848, 0.0015374710783362389, -0.035130150616168976, 0.02628297358751297, -0.0019486711826175451, -0.015858059749007225, -0.0670347511768341, -0.06569283455610275, -0.00996871292591095, -0.0034284694120287895, 0.036089152097702026, -0.01713866926729679, -0.07135529816150665, 0.005336342845112085, -0.029208434745669365, -0.008682426996529102, -0.03835093602538109, 0.047004856169223785, -0.04668397083878517, -0.004960172809660435, -0.033078182488679886, 0.038969870656728745, -0.003502471838146448, -0.03210996091365814, -0.04789112135767937, 0.038451582193374634, 0.03718110918998718, -0.004079750273376703, -0.044666022062301636, 0.04257709160447121, -0.014061206951737404, -0.01881803758442402, -0.03426613286137581, -0.004050484858453274, 0.0021580734755843878, 0.016654865816235542, -0.0004705839673988521, 0.051515787839889526, 0.002220479305833578, -0.05721469968557358, 0.0022502404171973467, -0.027302417904138565, -0.01619465835392475, 0.04898928105831146, -0.03278346359729767, -0.07061842828989029, -0.014787559397518635, -0.0038179962430149317, 0.03485087677836418, 0.05501912534236908, 0.038171250373125076, 0.025154152885079384, 0.009969840757548809, -0.014027249068021774, 0.031202729791402817, -0.05237143486738205, -0.006545751355588436, 0.0064768921583890915, 0.00545371463522315, -0.07423991709947586, 0.07865002006292343, 0.019764592871069908, -0.03815753757953644, 0.030273154377937317, 0.017944211140275, 0.03810932859778404, 0.008929267525672913, -0.08088809251785278, -0.05428078770637512, -0.01159400213509798, -0.007109129801392555, -0.02460479736328125, 0.06009889766573906, 0.011338573880493641, -0.038152359426021576, -0.04695338010787964, -0.019317718222737312, -0.02015104331076145, -0.030802827328443527, -0.022602571174502373, 0.012225557118654251, -0.03395015373826027, -0.029016250744462013, -0.03872081637382507, 0.011931171640753746, 0.02415389008820057, 0.020140737295150757, 0.012179787270724773, -0.0007748616044409573, 0.024124111980199814, -0.019781725481152534, 0.06085289269685745, 0.022848518565297127, 0.062446027994155884, 0.028139954432845116, -0.07151550054550171, 0.034190546721220016, -0.040704503655433655, -0.0035284929908812046, 0.0315386988222599, 0.02073916792869568, -0.011752191931009293, 0.011944483034312725, -0.033169522881507874, 0.029025277122855186, 0.017527863383293152, 0.011347413063049316, 0.0003683745744638145, -0.001002403674647212, -0.03513207659125328, 0.02693117782473564, -0.00626758998259902, -0.0342513732612133, -0.014601746574044228, 0.01865602843463421, 0.003927712794393301, -0.07046426832675934, 0.07518226653337479, 0.03089793026447296, -0.014295264147222042, 0.05458028241991997, -0.00590179767459631, -0.027616390958428383, 0.005773633718490601, -0.004883602727204561, 0.005673246458172798, -0.004010251257568598, 0.02270812913775444, -0.01687474548816681, 0.0235389843583107, 0.027410071343183517, 0.015254924073815346, 0.011715629138052464, 0.026177342981100082, -0.03845934197306633, 0.027559859678149223, 0.015561242587864399, 0.01237583253532648, 0.05950534716248512, 0.0038128800224512815, 0.030996475368738174, 0.030493570491671562, 0.046789441257715225, 0.0937328115105629, 0.044908538460731506, -0.004296281840652227, 0.029050549492239952, -0.028241993859410286, 0.022980868816375732, -0.02787073142826557, -0.053156185895204544, 0.050122976303100586, 0.00820137094706297, 0.008646768517792225, 0.027932986617088318, -0.015623428858816624, -0.033626921474933624, -0.0422159843146801, 0.026713063940405846, -0.06090051308274269, -0.03474581241607666, 0.09939399361610413, -0.03816937282681465, -0.03500005975365639, -0.025889350101351738, 0.004203522577881813, -0.020410414785146713, 0.04385824501514435, -0.0007012196583673358, 0.04741554334759712, 0.06214310973882675, -0.018441036343574524, -0.03885349631309509, -0.0015143537893891335, -0.013428612612187862, -0.019886385649442673, 0.015134126879274845, -0.01614150032401085, -0.017893513664603233, -0.016131656244397163, 0.028207002207636833, 0.04754163697361946, 0.00020526701700873673, -0.11222875863313675, -0.01496883574873209, -0.013694492168724537, -0.03616742044687271, -0.022422082722187042, -0.0042382278479635715, 0.04896553233265877, 0.019684283062815666, 0.01122015155851841, -0.036098580807447433, 0.028681021183729172, 0.03271139785647392, -0.053052451461553574, -0.023477964103221893, 0.033667244017124176, -0.028106169775128365, -0.008574467152357101, -0.0038496905472129583, -0.00596314063295722, -0.006237474735826254, -0.03154721111059189, -0.03298281133174896, -0.013481605798006058, -0.04156779870390892, 0.017537182196974754, -0.017288297414779663, -0.028365127742290497, 0.059466395527124405, -0.02302040345966816, -0.03225600719451904, -0.017513960599899292, 0.023063132539391518, -0.04106483981013298, 0.0027581448666751385, 0.023414205759763718, -0.018409350886940956, -0.03592364862561226, -0.0013524473179131746, 0.028454530984163284, -0.038241397589445114, 0.03208880126476288, -0.03639458864927292, 0.018654050305485725, -0.08200293779373169, -0.0027912890072911978, -0.02796299010515213, -0.039377421140670776, 0.002997998846694827, 0.011854060925543308, -0.014303070493042469, -0.017756110057234764, -0.009546779096126556, 0.0197644904255867, 0.04104486107826233, -0.01423534844070673, -0.05365677550435066, 0.007802744396030903, -0.020515499636530876, 0.0590972863137722, -0.0017214181134477258, -0.010142889805138111, -0.016244860365986824, -0.020349597558379173, 0.03091079741716385, -0.03385471925139427, -0.037739500403404236, -0.026806341484189034, -0.0019690159242600203, -0.026002489030361176, -0.02266397699713707, -0.04643452167510986, 0.046098995953798294, 0.039660267531871796, 0.017732076346874237, 0.019313644617795944, 0.004478211048990488, 0.00954868271946907, -0.04732441529631615, -0.0011706583900377154, -0.028006430715322495, -0.022784719243645668, -0.059317272156476974, 0.004181989468634129, -0.0050346022471785545, -0.046117112040519714, 0.023179763928055763, -0.04533509165048599, 0.00974456686526537, 0.02226891927421093, -0.04615819826722145, -0.03150651231408119, 0.0557016022503376, 0.017088331282138824, -0.012457293458282948, 0.04514171928167343, 0.001169297844171524, 0.025215379893779755, -0.022268950939178467, 0.030994415283203125, -0.012471260502934456, 0.03258578106760979, 0.014699244871735573, -0.009478387422859669, 0.03614422306418419, -0.060545459389686584, 0.05648207664489746, 0.0060851541347801685, -0.011733472347259521, 0.028663471341133118, 0.0022456913720816374, -0.009240079671144485, 0.0034863215405493975, 0.03348773345351219, 0.029362494125962257, -0.009344281628727913, -0.01588101126253605, 0.0009382827556692064, 0.04033423960208893, -0.00019993510795757174, -0.026758845895528793, 0.010257044807076454, 0.004562779329717159, 0.03911646455526352, 0.047609806060791016, -0.010200878605246544, -0.073371522128582, -0.00832809042185545, 0.011665279045701027, -0.07197079807519913, 0.027155676856637, -0.025246750563383102, -0.02015869691967964, -0.07793502509593964, -0.01412868406623602, -0.04158305376768112, 0.0693262442946434, -0.0504893884062767, 0.05919073522090912, -0.041281528770923615, 0.06953676789999008, 0.07507068663835526, 0.0812651515007019, 0.021537089720368385, -0.046021174639463425, -0.047424059361219406, -0.00716684153303504, 0.039428409188985825, -0.03791329637169838, 0.06069992855191231, -0.06666605174541473, 0.056142669171094894, 0.011980533599853516, -0.0056715854443609715, 0.041116323322057724, 0.06934928148984909, 0.0626511499285698, -0.032228436321020126, 0.09340564161539078, 0.0012251598527655005, -0.008077668957412243, 0.05061444267630577, -0.02342362515628338, -0.059131450951099396, 0.002492761006578803, -0.012385592795908451, -0.004934223834425211, 0.003742723725736141, -0.014741227962076664, -0.013966359198093414, -0.005687023513019085, -0.0063806623220443726, 0.03793815150856972, 0.037287283688783646, -0.022570578381419182, 0.019022740423679352, -0.026828575879335403, -0.04857948049902916, -0.022719664499163628, 0.016762055456638336, 0.040125079452991486, -0.056467559188604355, -0.026500383391976357, 0.011407957412302494, -0.04080760478973389, -0.13067364692687988, 0.03327538073062897, -0.002363968873396516, 0.013613617978990078, -0.016951415687799454, -0.0010935323080047965, 0.02145509049296379, -0.01689094491302967, -0.01350726280361414, -0.02424001321196556, -0.006091632880270481, 0.029552672058343887, -0.05992585048079491, 0.037202782928943634, -0.0006836279644630849, -0.0038328811060637236, 0.04413820058107376, -0.0013782919850200415, 0.024332666769623756, -0.006407816428691149, -0.08751873672008514, -0.011439112946391106, -0.00825339462608099, 0.010762621648609638, 0.0018137232400476933, 0.027125637978315353, 0.05222151055932045, -0.012287679128348827, 0.048672646284103394, -0.003131377510726452, 0.06111602112650871, -0.07286660373210907, 0.0778631642460823, -0.013438095338642597, -0.03899458795785904, 0.03183576837182045, 0.08262394368648529, 0.0337713398039341, 0.014540528878569603, -0.039185672998428345, 0.024510541930794716, -0.05221349745988846, -0.01952337846159935, 0.037712469696998596, -0.02670259214937687, 0.0377013124525547, -0.007368193473666906, -0.016224464401602745, -0.026858579367399216, -0.008568629622459412, -0.04878498613834381, 0.0797860324382782, 0.018448954448103905, -0.0017687167273834348, -0.012993836775422096, -0.07263792306184769, 0.05131535604596138, -0.05566256865859032, -0.024662818759679794, -0.058794938027858734, 0.02419322356581688, 0.017168881371617317, 0.004962095525115728, 0.0034010529052466154, -0.0258871391415596, 0.05353919416666031, -0.03367357701063156, -0.007500942330807447, -0.0467628538608551, 0.0006479283911176026, -0.004361720290035009, -0.003254976822063327, 0.006098496727645397, 0.0005914407083764672, -0.06991063803434372, -0.07007576525211334, 0.06515231728553772, -0.02167859673500061, -0.0005383552052080631, -0.015042333863675594, -0.031889159232378006, -0.00820212997496128, 0.0033570979721844196, 0.049683161079883575, 0.00019241662812419236, -0.009004289284348488, 0.02793417125940323, 0.015882091596722603, 0.02957497164607048, -0.04666144400835037, 0.01936432160437107, 0.022946618497371674, -0.014148863032460213, -0.0009237696067430079, 0.021465100347995758, 0.002497995737940073, 0.035730522125959396, -0.048001471906900406, -0.051096636801958084, 0.04886148124933243, -0.025085411965847015, -0.020219113677740097, 0.049687281250953674, -0.007098299916833639, 0.013382494449615479, -0.028889384120702744, 0.041253916919231415, -0.027655022218823433, -0.06490311026573181, 0.009738647378981113, 0.019295882433652878, 0.025818202644586563, 0.00995014701038599, 0.011811980977654457, -0.05015692114830017, 0.023451847955584526, 0.02046758122742176, -0.03953240439295769, 0.004058999940752983, 0.008218474686145782, 0.06755200773477554, -0.006369831971824169, 0.03240697458386421, 0.0432787649333477, 0.04964783787727356, 0.05843750387430191, 0.012458279728889465, -0.03745900094509125, -0.03998320922255516, 0.0007179159438237548, 0.008222652599215508, 0.09082802385091782, 0.03545115143060684, -0.03533075377345085, -0.021465733647346497, 0.05106230452656746, 0.024675097316503525, -0.020234202966094017, 0.0025236548390239477, 0.01066978182643652, 0.0016068060649558902, 0.04839425906538963, -0.027225442230701447, 0.012072687037289143, 0.030804648995399475, 0.069864422082901, -0.0644816905260086, 0.004175208043307066, 0.09607065469026566, -0.0057382164523005486, 0.022002503275871277, 0.06888628751039505, 0.03473253920674324, 0.0020348874386399984, -0.048077043145895004, -0.0035537502262741327, 0.024995891377329826, 0.01650463230907917, 0.006289162207394838, -0.015729498118162155, -0.02417559176683426, 0.0323779359459877, 0.023269139230251312, -0.062312424182891846, -0.028532877564430237, -0.003136181039735675, 0.0712457075715065, -0.04089125990867615, 0.031715117394924164, 0.054822888225317, 0.025788431987166405, -0.01635769009590149, 0.007165566552430391, 0.01290501095354557, -0.02598199062049389, -0.09305650740861893, -0.01739991270005703, -0.024013781920075417, 0.008231939747929573, -0.057163454592227936, 0.022631434723734856, 0.005507464054971933, 0.0050759464502334595, 0.015464444644749165, 0.024620244279503822, -0.05556730926036835, -0.032720208168029785, 0.004471501801162958, 0.015717865899205208, 0.019918134436011314, -0.01751367747783661, -0.0135545888915658, -0.05467256158590317, -0.005145679693669081, -0.024037126451730728, 0.009989924728870392, 0.039637427777051926, -0.027100756764411926, -0.008583718910813332, 0.06829667836427689, -0.002316887956112623, -0.032901130616664886, 0.01965979114174843, -0.027511676773428917, 0.02855147235095501, 0.00936237070709467, -0.04991069808602333, 0.03995111212134361, 0.06152622401714325, -0.05220137909054756, -0.023821229115128517, -0.011860758997499943, 0.005902581382542849, -0.04022764042019844, 0.04396658390760422, -0.06833814084529877, 0.0012358807725831866, 0.03657061606645584, -0.016288798302412033, 0.01846943236887455, 0.051474470645189285, -0.026680201292037964, 0.021638207137584686, -0.01900516450405121, 0.0014791906578466296, -0.0062616742216050625, 0.0062730927020311356, 0.047595445066690445, 0.03997056558728218, 0.08801291882991791, -0.0026270896196365356, 0.0236678346991539, -0.03438413143157959, -0.041134513914585114, 0.030452966690063477, -0.01882195845246315, 0.026756642386317253, -0.007611881010234356, -0.04640810564160347, -0.04668635502457619, 0.03255186975002289, 0.001567860716022551, 0.013543019071221352, 0.010015950538218021, 0.029429849237203598, 0.07112691551446915, 0.041545070707798004, 0.024919556453824043, 0.02331625297665596, 0.005940469913184643, 0.0020564189180731773, -0.0053699021227657795, 0.02723384089767933, -0.00901797879487276, -0.027506018057465553, -0.05990004166960716, 0.01297497283667326, -0.0056677572429180145, -0.004524351097643375, 0.03208049014210701, -0.031629715114831924, -0.09915322810411453, -0.039524488151073456, -0.0529080368578434, -0.021124107763171196, -0.04028117284178734, 0.004879982676357031, -0.0034618715289980173, -0.037684280425310135, 0.08284465968608856, 0.030359409749507904, 0.005488038063049316, -0.050938643515110016, -0.03301583230495453, 0.03364051505923271, -0.013378951698541641, -0.014260311610996723, 0.0385848730802536, 0.05402468517422676, 0.019627081230282784, -0.00877327285706997, 0.07813221961259842, 0.034271616488695145, 0.024949034675955772, 0.021768633276224136, 0.013705659657716751, -0.015914311632514, 0.03966906666755676, -0.002228153171017766, 0.04212724044919014, 0.029944032430648804, -0.04696075618267059, -0.07643851637840271, 0.04890088737010956, 0.04929650202393532, 0.014981287531554699, -0.006075621582567692, -0.022990340366959572, 0.011643038131296635 ]
<p>Any finite &amp; non empty set of masses has a computable center of gravity: $\vec{OG} = \frac{\sum_i m_i \vec{OM}_i}{\sum_i m_i}$ .</p> <p>Does the contrapositive permits to conclude that a mass system with physical evidence that it doesn't have a gravity center is an infinite set of mass (i.e. of cardinal larger than $\aleph_0$) ?</p> <p>On the other hand, an infinite set of masses may have a computable center of gravity. Ex. : within a 2D infinite plan, an infinite set of equal masses linearly distributed along the x and y axis will have a gravity center at its origin O. Unfortunately, this example doesn't have a center of gravity since the integral of masses in this particular topology doesn't converge. </p>
g1545
[ 0.019085122272372246, 0.035464391112327576, -0.012458950281143188, -0.05726082995533943, 0.007956819608807564, 0.0423683263361454, 0.03278357535600662, -0.035115547478199005, -0.05574658885598183, 0.019646555185317993, -0.013702795840799809, -0.049763601273298264, 0.04153123497962952, 0.03780277445912361, -0.05059675872325897, 0.014422099106013775, 0.00602383678779006, 0.043563149869441986, 0.052454546093940735, 0.016988443210721016, 0.05518016964197159, -0.00555275147780776, 0.04411185905337334, 0.02006950043141842, 0.045875273644924164, 0.009305374696850777, 0.09763738512992859, 0.003628459991887212, -0.05241226404905319, -0.019248487427830696, 0.008626174181699753, -0.01663973741233349, 0.028391435742378235, -0.02264561876654625, -0.03823729604482651, -0.03586683049798012, -0.023111965507268906, -0.037825554609298706, -0.055725015699863434, -0.012901118025183678, -0.018313530832529068, 0.010006871074438095, 0.0017134140944108367, -0.012107928283512592, -0.053590137511491776, 0.0439487062394619, -0.023042157292366028, 0.007626062724739313, 0.01040744036436081, -0.037435248494148254, -0.025172261521220207, 0.061695244163274765, 0.025138840079307556, 0.026144932955503464, -0.049995094537734985, 0.017409181222319603, 0.037401601672172546, 0.022058991715312004, -0.01806624047458172, -0.009788271971046925, 0.02332199551165104, 0.014672517776489258, 0.00047323855687864125, -0.053477924317121506, 0.018745459616184235, 0.01921910047531128, -0.011994517408311367, 0.014341223984956741, -0.04282046854496002, 0.013560823164880276, 0.016734743490815163, -0.002720925258472562, 0.007375688757747412, -0.02849636599421501, -0.007490535266697407, 0.033657245337963104, -0.017548924311995506, 0.02858234941959381, -0.04992469400167465, 0.015542223118245602, 0.008947485126554966, -0.024804020300507545, 0.02073667198419571, -0.02538522146642208, 0.01754770800471306, -0.027145422995090485, 0.010509641841053963, -0.03129760921001434, -0.054108042269945145, 0.0367133691906929, -0.00019723904551938176, 0.0031615926418453455, 0.03222079202532768, 0.041285574436187744, 0.028656229376792908, -0.03052370622754097, 0.02034829743206501, 0.01878354139626026, -0.0413409061729908, -0.02086484245955944, 0.0386725477874279, 0.02355578914284706, -0.032630350440740585, -0.044235460460186005, 0.026886576786637306, 0.005767900962382555, 0.012143665924668312, 0.032969728112220764, 0.01362374983727932, -0.005251804832369089, 0.004721971694380045, -0.025734106078743935, -0.049354977905750275, 0.02106569893658161, -0.0777106061577797, -0.027833279222249985, 0.08324695378541946, -0.029718637466430664, -0.005356811452656984, -0.004293020814657211, -0.04690738394856453, 0.007396333385258913, 0.007382729556411505, 0.028352633118629456, -0.03931356593966484, -0.02179585210978985, -0.0018182245548814535, 0.01586596481502056, 0.02945014461874962, -0.03452781215310097, -0.042232852429151535, -0.026470080018043518, -0.017509913071990013, 0.010672405362129211, -0.013625511899590492, -0.040693242102861404, -0.029734574258327484, -0.07050880044698715, -0.0199033934623003, 0.02433743327856064, -0.026922766119241714, 0.010967223905026913, 0.005053957924246788, -0.02488759160041809, 0.007435952313244343, -0.02600722387433052, -0.004055430646985769, 0.010837280191481113, 0.0390002466738224, 0.058616556227207184, -0.030801329761743546, 0.0578010268509388, -0.02973957173526287, -0.04021207615733147, 0.005991039332002401, 0.019098546355962753, -0.0007136509520933032, 0.026234949007630348, 0.05221414566040039, -0.019698550924658775, 0.04295099154114723, 0.017681745812296867, -0.00354252802208066, 0.01791861467063427, -0.018428361043334007, -0.021415740251541138, 0.023439161479473114, 0.04144616425037384, -0.03687993809580803, -0.04104595631361008, -0.06019643321633339, 0.0277462899684906, -0.0028760640416294336, 0.02350655198097229, -0.00874307006597519, -0.029397396370768547, -0.009924717247486115, 0.0013196903746575117, 0.04699001461267471, -0.0395628847181797, -0.05434803664684296, 0.027102729305624962, -0.023841174319386482, 0.04600036144256592, -0.00952884741127491, -0.022493885830044746, -0.014864452183246613, 0.05581570416688919, -0.032671697437763214, -0.012382656335830688, -0.023939045146107674, 0.06141839548945427, -0.04143086448311806, 0.150021031498909, 0.004836807958781719, -0.013914464972913265, 0.01057068444788456, 0.03093312680721283, -0.03421374410390854, 0.061391472816467285, 0.006765034049749374, 0.0363624207675457, 0.06464245915412903, -0.01890524849295616, -0.023881476372480392, 0.02101447433233261, -0.022429488599300385, 0.02425631694495678, 0.009631688706576824, 0.02448114939033985, 0.0151227917522192, 0.0019145335536450148, 0.03302804008126259, 0.033550869673490524, 0.015798097476363182, -0.0035938324872404337, -0.005676334258168936, 0.00401461822912097, 0.026180554181337357, -0.019089391455054283, -0.020970724523067474, -0.003868070198222995, 0.046510692685842514, -0.002357104094699025, -0.002063714200630784, -0.0030393083579838276, -0.028390973806381226, -0.021931832656264305, 0.006454772781580687, -0.0021023962181061506, -0.0021713548339903355, -0.0006386998575180769, 0.0015726772835478187, -0.023948151618242264, 0.02221057191491127, -0.04120348393917084, 0.017329595983028412, 0.002680964767932892, 0.03049452044069767, 0.03479361906647682, 0.036259669810533524, -0.04677228629589081, 0.011674356646835804, -0.019054314121603966, 0.04385868087410927, -0.07358420640230179, 0.013069245964288712, 0.02235085517168045, -0.021530676633119583, 0.015776488929986954, -0.09168574959039688, 0.01165400817990303, -0.037728164345026016, 0.0330270454287529, 0.019546309486031532, -0.011320609599351883, 0.03969552367925644, -0.031579192727804184, -0.06862596422433853, -0.012504170648753643, -0.011760330758988857, -0.057641416788101196, 0.02663419023156166, 0.023416290059685707, -0.039584964513778687, 0.025052299723029137, -0.020481783896684647, -0.009826558642089367, 0.014489960856735706, 0.0315789058804512, -0.010175111703574657, -0.01318295020610094, 0.06572578102350235, 0.08232295513153076, -0.02322179637849331, 0.01041017472743988, -0.005926461424678564, 0.015018792822957039, 0.0015742148971185088, 0.02011810801923275, 0.042230915278196335, -0.01552540808916092, 0.002228150609880686, 0.06294860690832138, 0.03614383190870285, -0.0385562926530838, -0.0846746414899826, 0.04656768962740898, -0.046155981719493866, -0.03436759486794472, 0.04265984892845154, 0.042374905198812485, 0.05476975440979004, 0.035164974629879, -0.025048531591892242, 0.09974607825279236, 0.008529107086360455, 0.01291336677968502, -0.01822848804295063, 0.024378087371587753, 0.008950414136052132, 0.09109233319759369, 0.02780161052942276, 0.047155119478702545, 0.010339288972318172, 0.04139913618564606, -0.0077612935565412045, -0.02613999880850315, 0.0021993047557771206, -0.08758752048015594, -0.005945674609392881, 0.04427249729633331, 0.05716884508728981, -0.021660421043634415, 0.030158525332808495, 0.048801422119140625, 0.026117270812392235, -0.02487361989915371, -0.052298013120889664, -0.043418653309345245, -0.05709387734532356, 0.009938403964042664, 0.002836343366652727, -0.004043450579047203, 0.015171765349805355, 0.02311822958290577, -0.04132774472236633, 0.03864285722374916, 0.0059735714457929134, 0.01052925456315279, -0.015223412774503231, -0.008380050770938396, 0.005254011135548353, 0.054722126573324203, -0.06184585765004158, -0.04473048448562622, 0.030472226440906525, 0.04031812772154808, 0.030050333589315414, -0.019754724577069283, -0.06940868496894836, 0.0864168107509613, -0.02839503437280655, -0.02681398019194603, 0.0507645346224308, 0.04099515080451965, -0.003820122918114066, 0.028446108102798462, 0.032840825617313385, -0.04288269579410553, 0.016711238771677017, -0.01186041347682476, 0.04134049639105797, 0.07403379678726196, -0.03216996788978577, 0.0022405737545341253, -0.023995565250515938, -0.002218860201537609, -0.04499657079577446, 0.031648289412260056, 0.01987225003540516, -0.026709428057074547, -0.02037355676293373, 0.016174374148249626, 0.046136874705553055, 0.014079298824071884, -0.02388927899301052, -0.022679341956973076, 0.03434094414114952, -0.03286861255764961, 0.018395042046904564, -0.03368344157934189, 0.04638403654098511, 0.01655407063663006, 0.049354031682014465, -0.09016428142786026, 0.009402204304933548, 0.04086139798164368, 0.011606174521148205, 0.03904073312878609, 0.09513732045888901, -0.02755247987806797, 0.009761522524058819, -0.0010436831507831812, -0.0007000871701166034, 0.031413525342941284, 0.002991387853398919, -0.019579928368330002, 0.01231268048286438, 0.013184804469347, 0.04019324481487274, -0.04087058827280998, -0.008380603976547718, 0.007281000725924969, 0.00945496279746294, -0.007036556489765644, -0.06826018542051315, -0.04089788347482681, 0.04351207986474037, 0.04738161712884903, 0.029518840834498405, -0.015226074494421482, -0.019202567636966705, -0.020703930407762527, -0.05866031348705292, 0.033793799579143524, 0.011348648928105831, -0.004941464867442846, 0.015508494339883327, 0.009088524617254734, 0.04691717401146889, -0.05036994442343712, 0.051014494150877, -0.04139670357108116, 0.0802251473069191, -0.010658042505383492, -0.04507627338171005, -0.03313238173723221, 0.038618046790361404, 0.008514412678778172, -0.05442025139927864, 0.026798415929079056, -0.029848657548427582, -0.04850205034017563, 0.04260856658220291, 0.04894968494772911, -0.06251493096351624, -0.016289882361888885, -0.06542710959911346, 0.010671046562492847, 0.02669443190097809, 0.08269879966974258, 0.03532798960804939, 0.07724147289991379, 0.0005501223495230079, 0.061119843274354935, -0.008898962289094925, 0.035302404314279556, -0.020102104172110558, 0.011397244408726692, 0.0018778931116685271, 0.00839136354625225, -0.0623568594455719, -0.04658528417348862, -0.003479904495179653, 0.07779262959957123, -0.015619548968970776, -0.03750158101320267, -0.03540246933698654, 0.028243031352758408, -0.037968460470438004, 0.01522067841142416, 0.016451554372906685, -0.024377478286623955, -0.04057230055332184, -0.017799286171793938, -0.018258467316627502, 0.018554214388132095, -0.047607604414224625, -0.05567097291350365, -0.015736235305666924, -0.05120076984167099, 0.023527882993221283, 0.03457096591591835, 0.041457369923591614, 0.0180373378098011, -0.01356228906661272, -0.04252931475639343, -0.016318151727318764, -0.04416566342115402, 0.0128975510597229, 0.09195567667484283, 0.04053351655602455, 0.0024184181820601225, -0.01270829327404499, 0.036860521882772446, 0.008808562532067299, -0.012204358354210854, -0.024219587445259094, -0.024520637467503548, -0.04617943614721298, 0.02109747938811779, -0.015947045758366585, -0.021996697410941124, 0.02469046041369438, 0.054649606347084045, -0.021501561626791954, -0.006119170691817999, 0.01609937660396099, 0.02787994220852852, 0.028125526383519173, 0.002011307515203953, 0.006269531790167093, -0.040622223168611526, -0.006735240574926138, -0.07078776508569717, -0.013787844218313694, -0.024859542027115822, 0.04207918792963028, 0.031223976984620094, -0.030783426016569138, 0.07706314325332642, 0.022546881809830666, 0.0635777935385704, -0.04183070361614227, 0.056127484887838364, 0.013342144899070263, -0.03892041742801666, -0.033418286591768265, 0.03480613976716995, 0.003527401015162468, 0.0022731581702828407, 0.03103841096162796, 0.04993911460042, 0.04335248842835426, 0.023568594828248024, -0.06457773596048355, -0.03920019418001175, -0.003238888457417488, -0.006547017488628626, 0.020480912178754807, -0.00486574973911047, 0.034739840775728226, -0.01895551010966301, 0.01943373680114746, -0.01962946355342865, 0.02511557750403881, -0.08703431487083435, -0.07551604509353638, 0.029743745923042297, 0.03654461354017258, -0.02174696885049343, 0.03447963669896126, -0.03365297615528107, -0.04274497553706169, -0.022157765924930573, -0.023944199085235596, 0.00030150398379191756, 0.03395436331629753, -0.0162070170044899, -0.04253115504980087, -0.05161985009908676, -0.0024155143182724714, 0.042077597230672836, -0.019080346450209618, 0.0005528891342692077, -0.01116026658564806, -0.04454268515110016, 0.02481864020228386, -0.10068607330322266, -0.033981069922447205, 0.04680955782532692, 0.027096791192889214, 0.017601080238819122, -0.034078653901815414, 0.0019838297739624977, -0.04575389623641968, 0.06317049264907837, -0.05353343114256859, -0.03213392570614815, -0.011386915110051632, 0.002020847052335739, 0.03971724584698677, -0.03033684752881527, -0.03206658735871315, 0.028126344084739685, -0.050088852643966675, -0.05632305517792702, 0.013568595051765442, -0.037975721061229706, 0.02264321781694889, 0.00705411983653903, 0.0336935892701149, 0.02879873290657997, 0.06943683326244354, 0.06122800335288048, -0.041790880262851715, -0.04588371887803078, 0.06440392881631851, -0.04671967402100563, 0.012905596755445004, -0.04859473183751106, 0.04353391006588936, -0.06093602254986763, 0.07532384246587753, 0.002862585475668311, -0.04662366211414337, 0.01028480939567089, -0.00392165407538414, -0.03341164439916611, -0.01891365274786949, -0.012529375031590462, 0.006546838209033012, -0.010296051390469074, -0.03498827666044235, -0.05630118027329445, -0.013769879005849361, 0.011419796384871006, -0.005330545827746391, -0.023309238255023956, 0.013087840750813484, -0.030220532789826393, 0.06640192121267319, 0.048272401094436646, -0.015768051147460938, -0.004988199565559626, -0.04255048558115959, 0.002485901117324829, 0.016978885978460312, -0.05572909861803055, -0.005385467316955328, 0.00042889994801953435, -0.023580370470881462, -0.03688989579677582, 0.024544671177864075, 0.014947814866900444, -0.024557815864682198, -0.0020083743147552013, -0.05826651677489281, -0.014655771665275097, 0.08726003021001816, -0.03251197189092636, -0.040164630860090256, -0.02212420105934143, -0.024728596210479736, 0.01765674166381359, 0.03012002445757389, 0.019394315779209137, 0.076943039894104, 0.020279353484511375, 0.016115935519337654, 0.06297577172517776, -0.005544958636164665, 0.015618088655173779, -0.019055170938372612, -0.0015922028105705976, -0.03871819004416466, 0.03034631535410881, 0.04292077571153641, -0.0032646183390170336, -0.06094195693731308, 0.006770484149456024, -0.033206477761268616, 0.02564580924808979, 0.008786330930888653, -0.0446661002933979, 0.07712855935096741, 0.016011197119951248, -0.028147365897893906, -0.0410328209400177, -0.06108763813972473, 0.010600442066788673, 0.004166061524301767, 0.03674808144569397, -0.09116010367870331, -0.017674149945378304, -0.030705060809850693, 0.008589685894548893, 0.007592000532895327, -0.029616108164191246, -0.08448046445846558, 0.05736665427684784, -0.03449356183409691, -0.016073349863290787, -0.02887459471821785, 0.04381826892495155, 0.020857220515608788, -0.03138861432671547, -0.037958357483148575, 0.000935448391828686, -0.019187036901712418, -0.047664299607276917, -0.055673662573099136, 0.009921311400830746, 0.007152801379561424, -0.012010934762656689, 0.014955299906432629, -0.07075989246368408, -0.017944492399692535, 0.017994025722146034, 0.006099543068557978, 0.0316154807806015, -0.005832584574818611, 0.038767825812101364, -0.01907382905483246, -0.007898658514022827, 0.00529996445402503, 0.005630741827189922, 0.021971022710204124, -0.033569272607564926, 0.024383820593357086, 0.010968837887048721, 0.03380901739001274, 0.012999820522964, -0.025879863649606705, -0.018194813281297684, -0.017691314220428467, 0.047582149505615234, 0.026628676801919937, -0.006637263111770153, 0.034489281475543976, -0.04849700629711151, -0.05717059597373009, 0.0462992824614048, 0.005948125850409269, 0.0182828176766634, -0.019262652844190598, -0.0030866777524352074, -0.02933666855096817, -0.0009597951429896057, 0.048495784401893616, -0.04660864174365997, -0.038088347762823105, 0.006028345320373774, -0.0011853420874103904, 0.024070831015706062, -0.004179796669632196, 0.013939859345555305, -0.001835552742704749, -0.029853150248527527, -0.013380895368754864, -0.01789478212594986, -0.0015122556360438466, -0.08669541031122208, -0.06678808480501175, -0.005942788440734148, 0.002960730344057083, 0.005838838405907154, -0.05987123027443886, 0.07059933245182037, -0.023743173107504845, 0.03252210095524788, -0.04103884473443031, -0.018104346469044685, -0.06851180642843246, -0.020280679687857628, -0.05481116473674774, -0.002372076502069831, -0.042341601103544235, -0.02522188238799572, -0.06623831391334534, -0.05259067937731743, 0.013809297233819962, 0.013368042185902596, 0.04982822388410568, 0.04485887661576271, -0.05353527516126633, -0.009827863425016403, 0.08710753172636032, 0.038196515291929245, 0.03759010136127472, 0.009227381087839603, 0.011934561654925346, 0.018982183188199997, -0.03799894452095032, 0.008586086332798004, 0.04618039354681969, -0.007657210808247328, 0.04703417792916298, 0.027001937851309776, -0.036562416702508926, 0.030219905078411102, 0.032412875443696976, -0.055234916508197784, -0.0788799524307251, 0.06018693000078201, 0.00944491382688284, 0.03315073996782303 ]
<p>Why do the propellers on helicopter appear to be so slow when the propellers is going at full speed? Can you please explain this particular optical illusion to me? </p>
g1546
[ 0.06030181050300598, 0.03048197366297245, 0.012088148854672909, 0.06090101599693298, 0.049782510846853256, 0.03466979041695595, 0.055105023086071014, 0.03833584859967232, -0.00424276664853096, 0.036051344126462936, 0.045612867921590805, -0.010442530736327171, -0.03086807020008564, 0.04303255304694176, -0.0013780355220660567, 0.011825330555438995, 0.01467962097376585, -0.0433327816426754, -0.014104724861681461, 0.0432603545486927, 0.056684862822294235, 0.03928166627883911, -0.039084725081920624, -0.004226590506732464, -0.015725335106253624, 0.030565297231078148, -0.05125224590301514, -0.017733942717313766, 0.006929939147084951, 0.02160661108791828, -0.007195021025836468, -0.00202085729688406, 0.011535285972058773, 0.04381362348794937, -0.018031755462288857, -0.01571858674287796, 0.016765909269452095, -0.002170141087844968, 0.029368188232183456, 0.051382895559072495, 0.0089741051197052, 0.025946063920855522, 0.0006348887691274285, -0.017260625958442688, -0.004218138754367828, -0.02667178027331829, -0.010109547525644302, 0.009047865867614746, -0.038137320429086685, -0.021942568942904472, 0.02577127330005169, 0.020568164065480232, 0.0034657777287065983, 0.027218645438551903, 0.05160319805145264, 0.04077506437897682, 0.014835728332400322, 0.046173542737960815, 0.05421732738614082, 0.03448968380689621, -0.04786662757396698, 0.02132026106119156, 0.0032901836093515158, 0.05565698444843292, -0.005250659305602312, -0.034887876361608505, 0.06014874577522278, -0.06903642416000366, 0.039289720356464386, -0.007755502127110958, -0.07108396291732788, -0.011265423148870468, -0.049588244408369064, -0.045070525258779526, -0.08586334437131882, -0.008950590156018734, -0.028670717030763626, -0.02871902659535408, 0.051864903420209885, 0.039502307772636414, 0.04818642884492874, 0.022755710408091545, -0.06413391977548599, 0.012780786491930485, 0.016603685915470123, 0.05535699054598808, -0.031710464507341385, -0.06878262758255005, -0.015715694054961205, -0.02548687718808651, 0.03162618726491928, -0.014516725204885006, 0.01840396225452423, 0.04190340265631676, -0.00193318712990731, -0.02416771836578846, -0.051101669669151306, 0.09777972847223282, -0.03504570573568344, 0.010415332391858101, -0.022993292659521103, 0.046551741659641266, 0.032599274069070816, 0.02893516980111599, -0.04627939313650131, 0.04450227692723274, 0.002654461422935128, 0.00811055488884449, 0.030683288350701332, -0.02718415856361389, 0.009901193901896477, -0.06341998279094696, 0.018609734252095222, -0.01784978248178959, -0.04825475811958313, -0.0645664855837822, 0.032544542104005814, 0.0074289035983383656, 0.014511220157146454, 0.008055659011006355, 0.05788005143404007, -0.034474801272153854, -0.05221595615148544, 0.011434191837906837, 0.09378935396671295, 0.03166934475302696, 0.039103131741285324, -0.027957482263445854, -0.008014638908207417, -0.008842064067721367, 0.07552129030227661, 0.011128764599561691, -0.031827326864004135, -0.010172302834689617, 0.0025931112468242645, -0.05429493635892868, -0.014372695237398148, 0.006127458065748215, 0.039954930543899536, 0.041615065187215805, 0.06589088588953018, -0.0528995655477047, 0.03169923275709152, 0.004829748068004847, 0.0015876718098297715, 0.011079919524490833, 0.015902502462267876, -0.00038501067319884896, 0.0512685589492321, -0.028681015595793724, -0.0094615388661623, 0.05514372140169144, 0.06896384060382843, -0.05227567255496979, -0.011887229979038239, 0.020626099780201912, -0.00430284533649683, 0.05974096804857254, -0.02360299788415432, 0.09369600564241409, 0.04105920344591141, 0.02304038591682911, 0.00502746133133769, 0.054516684263944626, -0.09339842200279236, 0.01910477876663208, 0.02796182595193386, -0.06052372604608536, -0.022799154743552208, 0.02017209492623806, 0.030932480469346046, -0.02533566579222679, 0.008448341861367226, 0.02929484285414219, 0.08646415174007416, -0.016494063660502434, 0.08132894337177277, -0.005356099456548691, -0.023523563519120216, 0.05709882825613022, -0.05523483082652092, -0.027728401124477386, -0.013497080653905869, -0.006415810436010361, 0.005499768536537886, -0.04364732280373573, 0.04275559261441231, 0.03923792392015457, -0.09537645429372787, 0.012871821410953999, -0.021249156445264816, -0.037510067224502563, -0.002225729404017329, -0.011986767873167992, -0.02750464342534542, -0.021069081500172615, 0.009688659571111202, -0.07080384343862534, -0.019610650837421417, 0.008304121904075146, 0.04462418705224991, -0.026747412979602814, 0.06731285899877548, -0.013228490948677063, -0.00516838813200593, -0.024127958342432976, 0.036609407514333725, -0.01967141032218933, 0.05504632368683815, -0.016718760132789612, 0.02660900540649891, 0.018273813650012016, 0.006208994425833225, 0.020376138389110565, 0.017230169847607613, 0.021357623860239983, 0.012199513614177704, 0.011966340243816376, -0.006502038333564997, 0.024611694738268852, 0.036129724234342575, -0.05777902901172638, -0.023565499112010002, -0.001227129134349525, -0.015659846365451813, 0.0036560199223458767, -0.049814168363809586, -0.020716706290841103, -0.00567896431311965, 0.06478922814130783, 0.01200147159397602, -0.052124928683042526, 0.022914879024028778, 0.01725626550614834, 0.013552917167544365, -0.02768179401755333, 0.008084508590400219, 0.039431534707546234, -0.009271005168557167, -0.03984472155570984, -0.02995830960571766, -0.006019972264766693, 0.007340232841670513, -0.0023447435814887285, -0.03516855463385582, -0.06200351193547249, -0.025594163686037064, -0.06042426452040672, -0.022824855521321297, 0.036141712218523026, 0.04928932711482048, -0.0048191240057349205, -0.0018740547820925713, 0.06277451664209366, 0.01051183883100748, -0.04777749255299568, -0.05353950709104538, 0.004800055176019669, -0.010153948329389095, 0.026294464245438576, -0.03199305385351181, 0.0860452726483345, -0.0007810257375240326, 0.01530509628355503, -0.08205896615982056, 0.0009859391720965505, -0.02298508770763874, -0.005894678644835949, 0.01948830485343933, -0.012615657411515713, -0.0030547017231583595, 0.054679468274116516, 0.02625924162566662, -0.018199477344751358, -0.024560902267694473, -0.02011798322200775, -0.02547813020646572, 0.010691002942621708, -0.05629059672355652, 0.03316405788064003, -0.02140733413398266, -0.03678233176469803, 0.0032633498776704073, 0.022440660744905472, -0.006753781344741583, -0.07930461317300797, -0.02039440907537937, 0.0021051231306046247, -0.02975858747959137, 0.017627360299229622, -0.09169105440378189, 0.010259748436510563, -0.01834687404334545, -0.017190903425216675, 0.021734390407800674, 0.042089566588401794, 0.07383587956428528, -0.013745618052780628, -0.007430184166878462, 0.020906012505292892, 0.06471692025661469, -0.015066780149936676, 0.00865140650421381, 0.03377268835902214, 0.049668122082948685, 0.038663312792778015, 0.038261137902736664, -0.03888477385044098, -0.06545545905828476, 0.050832297652959824, -0.00818695966154337, 0.037689708173274994, -0.009685591794550419, -0.0208579208701849, 0.041054658591747284, -0.015003734268248081, -0.05739516392350197, -0.0022956563625484705, -0.026750560849905014, 0.015752175822854042, 0.015631860122084618, -0.0546775721013546, -0.0361299030482769, 0.021050697192549706, 0.003356870962306857, -0.040828146040439606, 0.026881977915763855, -0.02038518711924553, 0.014145654626190662, -0.07522693276405334, 0.04548044502735138, -0.04317156597971916, -0.014338458888232708, -0.027439327910542488, -0.05665593966841698, -0.01762847602367401, -0.04381747543811798, 0.05207965895533562, 0.01380480919033289, -0.06644567102193832, 0.060826487839221954, 0.024379437789320946, -0.07920754700899124, -0.005861263256520033, -0.030611323192715645, -0.0025913261342793703, -0.01035231351852417, -0.00012874115782324225, 0.002265142509713769, -0.02081272006034851, 0.01738869771361351, 0.039249811321496964, -0.007721849717199802, -0.04808797687292099, -0.011647850275039673, 0.04935631901025772, -0.03219131752848625, -0.016674019396305084, 0.06575950235128403, 0.01215681154280901, 0.049479033797979355, 0.032507576048374176, 0.005333119072020054, -0.03307410329580307, -0.01762658916413784, -0.052023034542798996, -0.01129638310521841, 0.009264597669243813, -0.03165224939584732, 0.04290930926799774, 0.01842522993683815, 0.03893868997693062, -0.036764033138751984, 0.02506459318101406, -0.0318136066198349, -0.02973676659166813, 0.03737783432006836, 0.021684659644961357, -0.0028432568069547415, 0.005913271568715572, 0.024581361562013626, -0.013026577420532703, -0.008691770024597645, 0.005984082818031311, 0.05353701487183571, -0.012046759016811848, 0.011599037796258926, -0.061811357736587524, 0.04186294227838516, -0.06526488810777664, 0.01229101698845625, -0.020527033135294914, 0.016176870092749596, 0.01917758770287037, 0.032938335090875626, 0.04640995338559151, -0.011271967552602291, 0.006955635733902454, 0.012211180292069912, -0.003023386700078845, -0.04403664544224739, -0.04956315830349922, -0.023380324244499207, -0.004030001349747181, 0.00016478626639582217, -0.012113384902477264, 0.03643873706459999, 0.06666333973407745, -0.0007566501735709608, 0.011264746077358723, -0.0016603772528469563, 0.07956329733133316, -0.030037835240364075, -0.036818601191043854, -0.013570832088589668, 0.035145994275808334, 0.030977757647633553, 0.008256708271801472, 0.02314925752580166, 0.04660383611917496, -0.05017315223813057, -0.03237327188253403, -0.002625163411721587, -0.006487817037850618, -0.05444841459393501, 0.02332528494298458, 0.02729911357164383, 0.0008483671117573977, 0.009143438190221786, -0.017074696719646454, 0.06444799154996872, 0.008145558647811413, -0.003927465528249741, 0.03241308405995369, -0.030123619362711906, 0.08179571479558945, 0.04120849072933197, 0.046486545354127884, 0.050459299236536026, 0.006243165582418442, 0.009182477369904518, 0.020754458382725716, 0.032658372074365616, 0.017746012657880783, 0.008354859426617622, -0.011193164624273777, 0.015846000984311104, -0.006150195375084877, 0.01677979901432991, -0.05431777611374855, -0.08119907975196838, 0.0225584264844656, -0.026200242340564728, -0.026486916467547417, -0.0036437532398849726, -0.008887098170816898, -0.08226451277732849, 0.0374671071767807, 0.002796010347083211, -0.00031541514908894897, -0.004205002449452877, 0.053790003061294556, -0.04423331841826439, -0.008608520962297916, 0.02406981773674488, 0.04117852821946144, -0.05822637304663658, -0.039086222648620605, -0.030612457543611526, -0.008360331878066063, -0.06694253534078598, 0.0018507413333281875, 0.0017700776224955916, 0.0766737163066864, -0.009980618953704834, 0.012277372181415558, -0.03751032426953316, -0.003943671006709337, -0.05578070133924484, -0.008380313403904438, -0.05470725893974304, -0.0357053205370903, 0.05090084299445152, -0.05926669389009476, -0.01703854463994503, -0.049398232251405716, 0.02494829334318638, 0.05794854089617729, -0.021310437470674515, -0.04820818454027176, 0.05217454582452774, 0.017366982996463776, -0.07875024527311325, -0.008349431678652763, 0.013605006970465183, -0.0001211889975820668, -0.0036451653577387333, -0.047505807131528854, -0.008593089878559113, -0.010152370668947697, -0.02001596800982952, 0.003246097592636943, -0.004699754063040018, -0.016747500747442245, -0.0041005657985806465, -0.00787916500121355, 0.019140243530273438, -0.04367757588624954, -0.0026756443548947573, 0.025646673515439034, -0.01746746338903904, 0.04240564629435539, 0.0013315301621332765, 0.0046723079867661, 0.0035371591802686453, -0.043695125728845596, 0.036526359617710114, 0.040307436138391495, -0.007046565413475037, 0.0012477997224777937, 0.017594680190086365, 0.00046867996570654213, -0.024505918845534325, 0.017065180465579033, 0.03429386019706726, -0.006997686345130205, -0.0426325723528862, -0.006302600726485252, 0.017304006963968277, 0.039875347167253494, -0.0204795952886343, -0.0056939758360385895, 0.04877433180809021, 0.014275881461799145, 0.0029925103299319744, -0.004903117660433054, 0.05309489741921425, -0.054536741226911545, 0.004864925984293222, 0.006431393790990114, -0.009684785269200802, 0.010310783050954342, -0.035235319286584854, 0.08640621602535248, -0.002071513794362545, 0.03030915930867195, 0.06660566478967667, -0.0008797268383204937, 0.058186426758766174, -0.005687212571501732, -0.01193042192608118, -0.011969972401857376, -0.05640508979558945, -0.01221536286175251, -0.022342154756188393, 0.025860771536827087, -0.025641733780503273, -0.02698884904384613, -0.04910459741950035, -0.031322818249464035, 0.015254437923431396, 0.08230426162481308, 0.023370793089270592, -0.07367272675037384, -0.012881188653409481, -0.002559565706178546, -0.003203397151082754, 0.04225126653909683, 0.03456496447324753, -0.05004841461777687, -0.02293042093515396, -0.0028293610084801912, -0.013166450895369053, 0.044875506311655045, -0.016188262030482292, 0.03435128554701805, 0.029965544119477272, -0.03063991293311119, -0.07857903093099594, -0.023739002645015717, 0.01725715957581997, 0.00886248704046011, 0.031094316393136978, -0.015096657909452915, -0.012882457114756107, -0.0287036020308733, -0.01993369683623314, 0.004324603360146284, 0.040881071239709854, -0.019082410261034966, -0.054868023842573166, 0.07144368439912796, -0.05536733567714691, -0.1115204468369484, 0.042606983333826065, -0.022534487769007683, -0.0547369047999382, 0.07336019724607468, -0.03869463875889778, -0.0789605975151062, 0.025606833398342133, -0.10339071601629257, 0.08911212533712387, -0.004320697858929634, 0.014283386990427971, 0.002128841355443001, -0.003422617446631193, -0.023282064124941826, 0.02969241887331009, 0.04796740785241127, 0.007371950428932905, 0.00582905113697052, -0.016847772523760796, -0.062377117574214935, -0.03597494959831238, 0.03199233114719391, -0.02341921441257, -0.04487070068717003, 0.013182491064071655, -0.037043940275907516, 0.06252555549144745, -0.027091989293694496, -0.030054772272706032, -0.02235245518386364, 0.013599599711596966, -0.03637572377920151, -0.05738614872097969, 0.003954441286623478, 0.005190967116504908, -0.0037648554425686598, 0.01246639434248209, -0.04308873787522316, 0.01793752610683441, 0.0369429811835289, 0.04037418216466904, -0.003171705175191164, -0.01338306162506342, 0.016499996185302734, 0.02828405052423477, 0.05006469786167145, 0.0432133823633194, 0.008288484998047352, -0.014088846743106842, -0.005850421264767647, -0.06165507435798645, -0.002216771012172103, 0.0633527860045433, -0.08435919880867004, -0.024459196254611015, -0.023160438984632492, -0.028478873893618584, -0.019649267196655273, 0.0036973825190216303, 0.0013844281202182174, 0.027836062014102936, -0.005823501851409674, -0.03864651545882225, -0.01256183534860611, 0.03466878458857536, -0.04129992052912712, -0.007182447239756584, -0.00887299608439207, -0.05573129281401634, -0.021484922617673874, 0.017271680757403374, -0.0011805524118244648, -0.00870297197252512, -0.027990277856588364, -0.06054777279496193, 0.0260337945073843, 0.02940327301621437, 0.024602575227618217, -0.02320953644812107, -0.005062525160610676, 0.035397909581661224, 0.009832181967794895, -0.02859351597726345, -0.008020578883588314, 0.013352532871067524, -0.04510199651122093, -0.042167779058218, 0.08355078101158142, 0.05233382061123848, 0.023676954209804535, -0.06746932864189148, 0.031553175300359726, -0.031285565346479416, 0.008582155220210552, -0.018783817067742348, -0.07830354571342468, 0.010045061819255352, 0.01608901284635067, 0.02557087503373623, -0.018011698499321938, 0.027757778763771057, 0.058889154344797134, 0.06509153544902802, 0.01531614363193512, -0.023068353533744812, 0.013407000340521336, -0.04077070578932762, -0.018105167895555496, 0.06822647899389267, 0.012130163609981537, 0.0065245600417256355, -0.03026619367301464, 0.012366500683128834, 0.032159991562366486, 0.025512514635920525, -0.025959407910704613, -0.03874974325299263, -0.0174686461687088, -0.02347586117684841, 0.003877989947795868, -0.01730242930352688, -0.05217253416776657, -0.0025105266831815243, -0.061501920223236084, -0.0889858826994896, -0.029716352000832558, 0.036033280193805695, 0.026726743206381798, -0.028133884072303772, -0.053203728049993515, 0.01859869807958603, -0.008659553714096546, 0.03433070704340935, -0.021139957010746002, -0.024133387953042984, -0.009135791100561619, -0.004321117885410786, 0.008846725337207317, -0.022571943700313568, 0.02745109237730503, -0.05559622496366501, -0.010200689546763897, 0.008135242387652397, -0.0019315172685310245, -0.016759464517235756, 0.003502767765894532, -0.01040436327457428, -0.02783813513815403, 0.019406475126743317, -0.0056938487105071545, 0.03725951910018921, 0.025201968848705292, 0.02992437034845352, -0.0475870817899704, 0.04842592403292656, -0.010839206166565418, 0.03370700031518936, 0.07396838068962097, -0.024142596870660782, 0.033114876598119736, 0.06054065003991127, -0.012198383919894695, -0.03165202960371971, 0.01693810150027275, -0.04512946680188179, 0.01640661247074604, -0.01889871247112751, -0.025886042043566704, 0.005095777101814747, -0.023309487849473953, -0.002551642945036292, -0.03853967785835266, -0.03354377672076225, 0.02320175990462303 ]
<p>$u^{\mu}$ - 4-velocity</p> <p>$b^{\mu}$ - 4-vector of magnetic field</p> <p>$ u_{\mu}u^{\mu}=-1, \qquad u_{\mu}b^{\mu}=0 $</p> <p>$$ u_{\beta}u^{\alpha}\nabla_{\alpha}b^{\beta}-u_{\beta}b^{\alpha}\nabla_{\alpha}u^{\beta}+\nabla_{\alpha}b^{\alpha}=0 $$ I don't understand why this equation gives this $$ u^{\alpha}u^{\beta}\nabla_{\alpha}b^{\beta}+\nabla_{\alpha}b^{\alpha}=0 $$</p> <p>Help me please!</p>
g1547
[ 0.01432870328426361, 0.029878247529268265, -0.010284011252224445, 0.04476747289299965, 0.10427679866552353, 0.011478938162326813, 0.07958412915468216, 0.05205950886011124, -0.03426090627908707, -0.011131721548736095, -0.012766103260219097, 0.06781134009361267, -0.06559587270021439, 0.0014441104140132666, 0.06493675708770752, -0.017965786159038544, -0.01246519573032856, -0.011840424500405788, 0.00879181269556284, -0.021588532254099846, -0.03671209514141083, 0.07188371568918228, 0.04478095844388008, -0.030737053602933884, 0.041673097759485245, -0.0505659319460392, -0.017533041536808014, -0.017439784482121468, -0.01413977611809969, -0.04209151864051819, 0.022762151435017586, 0.025701619684696198, 0.08508234471082687, -0.022297337651252747, -0.02232922986149788, -0.009048137813806534, 0.02837718091905117, -0.01117387879639864, -0.0008812681771814823, -0.05824552848935127, -0.0038056345656514168, -0.009938092902302742, 0.0151916379109025, 0.023047981783747673, 0.03949510306119919, -0.019869491457939148, -0.021944940090179443, -0.050793081521987915, -0.033987291157245636, 0.07055273652076721, 0.006841626949608326, -0.029350176453590393, 0.10168295353651047, -0.02713075466454029, -0.023732038214802742, 0.048557162284851074, 0.01606661267578602, 0.0011267696972936392, -0.04163621366024017, 0.07660108804702759, 0.052750226110219955, -0.0365232452750206, 0.02962285280227661, 0.02054908126592636, 0.023683153092861176, -0.06480376422405243, -0.028751304373145103, -0.0038595013320446014, -0.03346910700201988, 0.03043258748948574, -0.018275057896971703, -0.06727691739797592, -0.0073466552421450615, -0.02099727839231491, -0.029467053711414337, -0.015661850571632385, 0.014847840182483196, 0.010139504447579384, -0.02411477640271187, -0.057837482541799545, -0.02755068615078926, 0.06786864250898361, -0.0034225801937282085, 0.07732080668210983, -0.017887504771351814, -0.012950291857123375, 0.00942980032414198, 0.0419880747795105, -0.038763031363487244, -0.07129985839128494, -0.019358722493052483, -0.007572927046567202, -0.013545452617108822, 0.016833936795592308, 0.011973096057772636, -0.05276956036686897, 0.01546966377645731, 0.059815045446157455, -0.005737897474318743, 0.02710595354437828, -0.01754576712846756, 0.0450383760035038, -0.01872353069484234, 0.03128001093864441, -0.011231042444705963, 0.00012089256051694974, -0.011307374574244022, 0.03242881968617439, -0.040445391088724136, 0.007978199981153011, -0.049505144357681274, -0.05769011378288269, -0.03545473515987396, 0.052363503724336624, 0.0019526276737451553, -0.004135788418352604, -0.0073232282884418964, -0.03826361149549484, 0.0104279275983572, 0.016391420736908913, -0.0008852769387885928, -0.009470747783780098, -0.025962868705391884, 0.047143518924713135, 0.015603728592395782, -0.02992500551044941, -0.023033782839775085, 0.061055321246385574, 0.03746756538748741, -0.015606735832989216, 0.008737550117075443, -0.03710415959358215, 0.05081590637564659, 0.00620632478967309, 0.010589278303086758, 0.018717102706432343, 0.013207059353590012, 0.04924345761537552, -0.021785348653793335, 0.05375725403428078, 0.006999810226261616, -0.032034505158662796, 0.011132815852761269, -0.06330627202987671, -0.07340709120035172, 0.053241707384586334, -0.008486718870699406, -0.07611671090126038, 0.04319420084357262, 0.02568124793469906, -0.016571061685681343, 0.09230391681194305, -0.024231577292084694, 0.0639423355460167, -0.04935089498758316, 0.0013663200661540031, 0.033730413764715195, 0.005351255182176828, -0.013882885687053204, -0.025493059307336807, 0.09619984030723572, -0.02167350798845291, 0.067942313849926, 0.00031822622986510396, -0.054464440792798996, 0.028946109116077423, 0.06634066998958588, -0.01876046136021614, 0.002907153684645891, 0.021367661654949188, -0.036715224385261536, -0.015198255889117718, 0.041817136108875275, 0.07026129215955734, -0.013389339670538902, 0.039031870663166046, 0.029541200026869774, -0.007639527786523104, -0.003911613021045923, -0.0033205198124051094, 0.0027325875125825405, -0.04091385751962662, 0.05936189368367195, -0.046509746462106705, -0.008646632544696331, -0.002422366291284561, -0.003967308904975653, 0.1044309064745903, -0.04501570761203766, 0.030761033296585083, -0.020324045792222023, -0.05811508372426033, -0.03153874725103378, -0.018057135865092278, -0.004122926853597164, 0.056223075836896896, -0.015810828655958176, -0.01256941631436348, -0.07957060635089874, 0.04741721972823143, -0.048669666051864624, 0.08204134553670883, 0.045824289321899414, -0.04788631573319435, 0.009713932871818542, -0.05948926880955696, -0.024524010717868805, 0.06526128947734833, 0.04384598881006241, 0.006467916537076235, 0.04420305788516998, -0.012617673724889755, -0.02600424736738205, 0.02678803727030754, -0.02723420225083828, -0.02837885543704033, 0.058585964143276215, 0.015153494663536549, -0.04550309479236603, 0.05746457725763321, -0.03185581788420677, -0.011782589368522167, 0.049217648804187775, 0.002377120079472661, -0.02377679944038391, 0.011081538163125515, -0.02659100480377674, -0.003840835066512227, 0.033265311270952225, -0.04754926636815071, -0.007604527287185192, 0.02702350914478302, 0.04387770593166351, 0.027660218998789787, -0.0012836884707212448, 0.0009334745700471103, 0.00861082598567009, 0.03639819845557213, -0.020475013181567192, -0.03153572604060173, 0.01518287044018507, 0.008243082091212273, 0.009473294019699097, 0.004512396641075611, 0.030843544751405716, 0.008494090288877487, 0.056968580931425095, -0.07135839015245438, 0.0098672304302454, 0.027220245450735092, 0.045854467898607254, -0.03199931979179382, 0.05162404850125313, -0.0007404775824397802, -0.030713753774762154, -0.0014351896243169904, 0.020689332857728004, 0.05576512590050697, -0.05975805222988129, -0.048762090504169464, 0.022577518597245216, -0.02957220748066902, 0.014124404639005661, 0.03851912543177605, -0.0627220943570137, 0.008755529299378395, -0.04636022821068764, 0.008844408206641674, 0.07147029042243958, 0.01541919820010662, -0.03471169248223305, 0.040184926241636276, -0.011603748425841331, 0.040210213512182236, -0.04404861107468605, 0.022821824997663498, 0.0016078567132353783, 0.008010463789105415, 0.02532661147415638, 0.035919979214668274, -0.029801763594150543, 0.0062612323090434074, -0.02534637786448002, -0.0344197116792202, -0.006303289905190468, -0.04627355933189392, -0.0649070143699646, 0.01886371336877346, 0.021377714350819588, -0.03214242309331894, 0.006118998397141695, 0.013163210824131966, 0.018238164484500885, -0.009908623993396759, 0.011734199710190296, 0.05721046403050423, 0.00799562782049179, -0.05399034917354584, -0.026293767616152763, 0.016897963359951973, -0.014153329655528069, 0.0030672645661979914, -0.02876714989542961, -0.046987202018499374, -0.023907696828246117, -0.0002186968340538442, -0.039257727563381195, -0.06719296425580978, -0.03368285298347473, 0.01639121025800705, -0.03071225807070732, -0.014103807508945465, 0.014604981057345867, -0.031145431101322174, 0.001781389582902193, 0.0039522601291537285, -0.00005913318454986438, 0.013267331756651402, 0.07001067698001862, -0.0029130626935511827, -0.03601049259305, -0.10949426889419556, 0.024886183440685272, 0.0014549910556524992, 0.004145238548517227, -0.04454784840345383, -0.004527417477220297, -0.007058892399072647, -0.005273822695016861, 0.0019913632422685623, -0.04354310408234596, -0.004564695525914431, 0.05388059467077255, 0.022031504660844803, -0.018462810665369034, -0.005640133284032345, -0.009374833665788174, 0.03597293421626091, -0.02541152946650982, -0.026889456436038017, -0.03532618656754494, -0.047825079411268234, -0.03179113566875458, -0.0022326819598674774, 0.0006159021286293864, 0.004062458407133818, 0.06935952603816986, -0.03006759099662304, 0.029606005176901817, 0.024360135197639465, 0.018112046644091606, 0.06209670007228851, 0.03155846148729324, 0.005996280815452337, -0.003756867488846183, -0.00579542713239789, 0.02156877890229225, 0.00937865674495697, -0.002037976635619998, -0.008888441137969494, -0.032394520938396454, -0.016259152442216873, -0.03257603198289871, 0.0629526898264885, -0.00534722488373518, 0.04661722481250763, 0.014452922157943249, 0.0454627200961113, -0.055969104170799255, -0.00954821053892374, 0.0046526165679097176, -0.017412304878234863, 0.0007094808970578015, 0.004058815073221922, 0.020162122324109077, -0.045016564428806305, -0.020271338522434235, -0.050094254314899445, -0.0329226553440094, 0.015695510432124138, 0.0860922709107399, -0.02032962627708912, 0.023255834355950356, 0.04116855189204216, 0.01023788284510374, 0.0027379244565963745, -0.003742361208423972, -0.02612769417464733, 0.03590359538793564, -0.03847341239452362, 0.04673323780298233, 0.02477363497018814, 0.03193959966301918, -0.03116636350750923, -0.0034501361660659313, -0.036291949450969696, -0.03238793835043907, -0.012086599133908749, -0.04482568800449371, -0.014643682166934013, -0.03649071231484413, -0.0036425800062716007, -0.007805126253515482, 0.015582798048853874, -0.021109288558363914, -0.014731726609170437, -0.0010039432672783732, 0.017322059720754623, 0.06707815080881119, -0.007078681141138077, 0.0028634117916226387, -0.002900520572438836, -0.013298535719513893, -0.01911371573805809, 0.02230611816048622, 0.03956650197505951, -0.03863764926791191, 0.0315517820417881, 0.002608047565445304, -0.02983972430229187, 0.03615016117691994, 0.009872708469629288, 0.0329158715903759, -0.07930394262075424, 0.007711510639637709, 0.015683699399232864, 0.0686766654253006, 0.05393507331609726, -0.0027612363919615746, -0.0054118144325912, -0.014161762781441212, 0.07188324630260468, -0.012394017539918423, 0.031819745898246765, -0.08911377191543579, 0.08670491725206375, -0.026621541008353233, 0.04403657093644142, 0.008929254487156868, 0.060375411063432693, -0.01470615342259407, -0.0042902762070298195, 0.0782812312245369, -0.024074245244264603, -0.0259644016623497, 0.026124432682991028, 0.001039683585986495, -0.09607627242803574, -0.044771984219551086, -0.030189815908670425, -0.04688625782728195, 0.06344889849424362, -0.012198047712445259, -0.019677359610795975, 0.019427822902798653, -0.011083763092756271, -0.006654643919318914, 0.035607822239398956, 0.028874384239315987, 0.05182977393269539, -0.06194949895143509, 0.04915132746100426, 0.022843552753329277, -0.012106098234653473, -0.021999849006533623, -0.037460070103406906, 0.00625011557713151, -0.01443459838628769, -0.01596173271536827, -0.006982566323131323, 0.03905210271477699, 0.009160799905657768, 0.010182514786720276, 0.013270414434373379, 0.02636287920176983, 0.08349107205867767, -0.04969918355345726, 0.02448802813887596, -0.051832448691129684, -0.046358492225408554, 0.00832351017743349, -0.02285470999777317, 0.03160039708018303, 0.009303666651248932, -0.016812661662697792, 0.0067164162173867226, -0.0173118244856596, -0.025073599070310593, 0.005172476638108492, -0.004512427840381861, -0.006667113397270441, 0.014424330554902554, -0.01326857041567564, -0.0016648779856041074, -0.018542179837822914, -0.05309334769845009, -0.02122381702065468, 0.02339509129524231, -0.01806003972887993, -0.02150835283100605, -0.04394654184579849, -0.025372404605150223, -0.049211256206035614, 0.030231935903429985, 0.030323771759867668, 0.07425400614738464, 0.02599680796265602, 0.03056945465505123, 0.02635014057159424, 0.051730941981077194, 0.010936498641967773, -0.0637257993221283, 0.06771238893270493, -0.013220113702118397, -0.03960870951414108, -0.0022986631374806166, 0.020312076434493065, -0.03305577486753464, 0.04081360250711441, -0.012183643877506256, 0.06039794906973839, -0.0010303712915629148, 0.026446787640452385, 0.026531849056482315, 0.020449168980121613, 0.028855064883828163, -0.038895636796951294, -0.004784451797604561, -0.006419855169951916, 0.04266231879591942, -0.004951935261487961, -0.008612203411757946, 0.05116069316864014, -0.0078039527870714664, 0.041914112865924835, -0.0082998713478446, 0.02478201873600483, -0.09003717452287674, -0.020520498976111412, 0.039270274341106415, -0.008971760980784893, -0.04961307346820831, 0.011156893335282803, 0.02231830358505249, -0.02671552263200283, 0.028423108160495758, 0.00804886594414711, -0.011387697421014309, 0.009679388254880905, -0.037790197879076004, -0.06222331523895264, -0.043217796832323074, 0.018261317163705826, -0.02558409608900547, -0.009915878996253014, -0.04072965309023857, -0.04343804717063904, 0.02765069156885147, -0.04091041535139084, -0.005488050635904074, 0.05625675991177559, -0.06118658185005188, -0.03155384585261345, 0.009335326962172985, 0.014541573822498322, -0.0935850664973259, 0.0038528922013938427, -0.02400944009423256, 0.048925720155239105, -0.004101783502846956, -0.046147141605615616, 0.031867027282714844, -0.06457031518220901, -0.02455727569758892, 0.036529701203107834, 0.05865662172436714, 0.011294287629425526, -0.028352167457342148, -0.08650275319814682, 0.01914721354842186, 0.02550749108195305, 0.011675110086798668, -0.014161075465381145, -0.006771528627723455, 0.014485697261989117, 0.025974849238991737, -0.049773842096328735, -0.02477083168923855, 0.023847563192248344, -0.04598444700241089, -0.008359236642718315, 0.029183683916926384, 0.007214009296149015, -0.03162575885653496, -0.06131990998983383, -0.011430872604250908, -0.012172725982964039, -0.01076972484588623, -0.007743432652205229, -0.03850266709923744, 0.025276396423578262, -0.015391127206385136, -0.07409679144620895, 0.0021851249039173126, -0.006514217704534531, 0.007602795958518982, -0.01928388699889183, -0.06128137558698654, -0.002328895963728428, 0.009762351401150227, -0.017901478335261345, 0.044545937329530716, -0.053613923490047455, 0.07986999303102493, -0.0022031476255506277, -0.023005835711956024, -0.010785971768200397, 0.03667209669947624, 0.0114592919126153, 0.026959169656038284, 0.009768176823854446, -0.0008106293971650302, 0.004224656615406275, -0.03574438765645027, 0.08210179954767227, -0.011614665389060974, -0.047661829739809036, 0.0033854986540973186, -0.001062853028997779, -0.03626150265336037, -0.0074071637354791164, -0.013055036775767803, -0.053831737488508224, 0.04320807754993439, 0.0029008614365011454, 0.046351123601198196, 0.0030092208180576563, 0.016070885583758354, -0.008773187175393105, 0.0876755490899086, -0.02345195785164833, 0.049157675355672836, -0.010217552073299885, -0.0010306640760973096, -0.034251850098371506, -0.04243314638733864, -0.02951839193701744, -0.007619738113135099, -0.09909912198781967, 0.007031978107988834, 0.00431394949555397, 0.02347341924905777, -0.012720095925033092, 0.00116567627992481, -0.03597698733210564, -0.04335543513298035, 0.0185410026460886, 0.03518533334136009, 0.04568514972925186, 0.02231127955019474, 0.011640127748250961, -0.04934411868453026, -0.05301829054951668, 0.028760619461536407, 0.0701889842748642, 0.03427644819021225, -0.007446111645549536, 0.006795549765229225, 0.07398038357496262, -0.02787802368402481, 0.008087920024991035, 0.029457660391926765, -0.016175583004951477, 0.003583008423447609, -0.00595265906304121, -0.010536747984588146, 0.007250359281897545, -0.010467533953487873, 0.00660597113892436, -0.021413598209619522, -0.01664852164685726, 0.01904904656112194, 0.013807141222059727, -0.007640200201421976, -0.021923119202256203, -0.012991190887987614, 0.02025391347706318, 0.0330299511551857, 0.0538044199347496, 0.03369951248168945, -0.03005870245397091, 0.041516151279211044, 0.09225808829069138, -0.003119108732789755, -0.019119391217827797, -0.01017659530043602, -0.05638543888926506, 0.00337975868023932, 0.015821686014533043, 0.0299497302621603, 0.014848095364868641, -0.029633404687047005, 0.012257792986929417, 0.03828319534659386, 0.04476294666528702, 0.012280412949621677, -0.008135187439620495, -0.008125700987875462, -0.044395893812179565, -0.05347337946295738, -0.022849392145872116, -0.014175285585224628, 0.015216419473290443, 0.013927689753472805, 0.010788544081151485, 0.0033384414855390787, -0.01766027696430683, 0.0413251593708992, -0.03759792819619179, -0.02059847302734852, -0.00840554665774107, -0.005485911387950182, 0.010463858023285866, -0.09334464371204376, -0.03962066397070885, -0.028529133647680283, 0.004588044714182615, -0.001128547010011971, 0.011608843691647053, -0.05088813602924347, -0.05743418633937836, -0.03775930777192116, -0.07198616862297058, 0.005864741746336222, -0.04885517433285713, -0.01613776944577694, -0.018898867070674896, 0.010993839241564274, 0.07703939825296402, -0.01744712144136429, 0.014592614024877548, -0.02280784770846367, 0.0051923952996730804, 0.02170524187386036, -0.020288599655032158, 0.01930432952940464, -0.04502236098051071, 0.04547703638672829, 0.06005125492811203, -0.061103709042072296, 0.07773364335298538, 0.03520270064473152, -0.04821484163403511, 0.03375830873847008, 0.052137281745672226, -0.044936403632164, 0.021825794130563736, 0.01525895670056343, -0.027499552816152573, 0.02071191929280758, 0.0071627553552389145, -0.038652218878269196, -0.011159363202750683, 0.00798521563410759, -0.020327800884842873, 0.0093447370454669, -0.05393124744296074, 0.03900146484375 ]
<p>OK, so my textbook says that in time dilation and length contraction, the proper time and the proper length is "That which is in the frame of reference of the observer at rest relative to the event". </p> <p>This means that the proper time/length is that which is observed by the observer moving close to the speed of light, and the dilated time and contracted length is that which is observed by an observer moving relative to the event, i.e. is watching something move close to the speed of light. Am I correct so far?</p> <p>So, for example, if we have a beam of protons moving with a velocity of 0.99c and a stationary electron watching them, the proper time/length is that which the protons observe whereas the dilated time/contracted length is that which the electrons would see. </p> <p>Assuming I am correct so far (which I very well may not be, please tell me if I'm wrong), I have just been confused by an exam question. Here it is:</p> <blockquote> <p>In an experiment, a beam of protons moving along a straight line at a constant speed of $1.8$x$10^8$$ms^{-1}$ took 95ns to travel between two detectors at a fixed distance $d_0$ apart. Calculate the distance $d_0$ between the two detectors in the frame of reference of the detectors.</p> </blockquote> <p>Well, according to my understanding above, this would be the contracted distance, since the observer (detectors) are in motion relative to the event. However, they calculate the distance using $d=vt$, which would mean it's the proper distance.</p> <p>Someone please explain. </p>
g1548
[ 0.041245412081480026, -0.0037753235083073378, 0.02929248847067356, 0.009845430962741375, 0.020231392234563828, -0.022149745374917984, 0.013345259241759777, 0.04795306548476219, 0.016361668705940247, 0.025210309773683548, -0.019758259877562523, 0.026865264400839806, 0.00865393690764904, -0.031405266374349594, 0.03740318492054939, -0.057977452874183655, 0.11011648923158646, 0.006348281167447567, -0.037653397768735886, 0.055724307894706726, -0.0007622862467542291, 0.0419592447578907, 0.009773398749530315, -0.04094022512435913, -0.030723076313734055, -0.014250845648348331, -0.0138965779915452, 0.04346298798918724, -0.052241016179323196, -0.05141590163111687, 0.040394362062215805, -0.0003903841716237366, 0.01084230188280344, -0.021047651767730713, 0.010478243231773376, -0.0568571574985981, 0.009834357537329197, 0.00286359922029078, 0.0394037626683712, -0.01023036614060402, 0.03914183750748634, 0.011790035292506218, -0.04224814102053642, -0.07327325642108917, 0.08438628166913986, 0.03977809101343155, -0.024862445890903473, -0.00845443643629551, 0.041110046207904816, -0.012238738127052784, -0.03964299336075783, 0.06654408574104309, -0.038784075528383255, -0.003665580879896879, 0.009857062250375748, 0.06316959112882614, -0.010853100568056107, -0.01594395563006401, 0.055205851793289185, 0.035042595118284225, 0.05108077824115753, 0.007308811880648136, -0.010808294638991356, 0.004357882775366306, 0.06259553134441376, 0.005349938757717609, -0.004814876243472099, -0.014336678199470043, -0.009607315994799137, 0.040414951741695404, -0.04858439788222313, -0.0648317039012909, -0.025875937193632126, 0.014565731398761272, -0.021100308746099472, -0.032865989953279495, 0.022469479590654373, -0.013089772313833237, 0.0020389407873153687, -0.01341757457703352, -0.06748642027378082, -0.02676258608698845, 0.03233477100729942, 0.02247084118425846, 0.06923703104257584, 0.009884732775390148, -0.06415156275033951, -0.009183326736092567, -0.03543046861886978, 0.04036923497915268, -0.013721502386033535, -0.08384385704994202, 0.05867885798215866, 0.025439927354454994, -0.0002803116221912205, 0.03840561956167221, -0.0202237069606781, 0.038572970777750015, 0.022429242730140686, 0.07058407366275787, -0.031665705144405365, -0.0028394749388098717, -0.04175439104437828, 0.013630812987685204, -0.03490116447210312, -0.021637102589011192, -0.053652696311473846, -0.04649903252720833, -0.02710188925266266, -0.07050085812807083, -0.036442939192056656, -0.07615665346384048, 0.012965588830411434, -0.009848937392234802, -0.06502149999141693, -0.01472537498921156, 0.05037541687488556, 0.06341097503900528, 0.0009848072659224272, 0.027074771001935005, 0.02803366631269455, 0.010948728770017624, -0.010035688988864422, 0.02682517282664776, -0.01038915105164051, 0.007038685027509928, 0.013255800120532513, 0.02401736006140709, -0.016736699268221855, 0.02485746145248413, -0.018694939091801643, 0.04798885062336922, -0.02391737326979637, 0.017629284411668777, -0.0311350729316473, 0.022253111004829407, 0.043600376695394516, 0.017104709520936012, -0.015785858035087585, 0.016654927283525467, 0.017544511705636978, -0.015070770867168903, -0.023310771211981773, -0.07030310481786728, 0.008797761052846909, 0.0743863582611084, -0.06189223378896713, -0.021359695121645927, 0.030143680050969124, 0.015091359615325928, -0.022682420909404755, 0.06890031695365906, -0.055696628987789154, -0.05148281902074814, -0.022854305803775787, -0.013593747280538082, 0.04492476209998131, -0.07354196906089783, 0.003050066763535142, 0.03994916379451752, 0.03304902836680412, -0.014904491603374481, -0.03929346054792404, -0.006429323460906744, -0.051594458520412445, -0.0032279060687869787, 0.0027697563637048006, -0.01619700714945793, 0.043406061828136444, -0.0784769356250763, -0.08945954591035843, 0.001042370218783617, 0.07140137255191803, 0.044903289526700974, -0.04742889478802681, 0.10161858052015305, 0.008213731460273266, -0.03114420920610428, -0.07197178900241852, -0.013579937629401684, -0.040956079959869385, -0.012391027063131332, -0.00465774443000555, -0.037145595997571945, -0.041981421411037445, 0.008528287522494793, -0.024897847324609756, -0.0317414328455925, -0.04548502713441849, 0.006237047724425793, 0.0007423398783430457, -0.016033539548516273, -0.01707911118865013, 0.004125767387449741, -0.06875386834144592, -0.022002797573804855, -0.0043650539591908455, -0.0537588894367218, -0.009113415144383907, 0.001751946285367012, -0.05513548105955124, -0.03412741795182228, 0.011499378830194473, 0.012897335924208164, 0.036436714231967926, 0.005440316628664732, -0.020868491381406784, 0.006552543956786394, 0.02369578741490841, 0.006788298487663269, 0.03723401203751564, 0.01148948073387146, -0.0008374464232474566, 0.048248931765556335, -0.012653390876948833, -0.055674996227025986, -0.04150431230664253, 0.06293310970067978, -0.015403226017951965, 0.009689508005976677, -0.036056455224752426, -0.0067238593474030495, 0.0640849769115448, -0.06192665919661522, 0.004699566401541233, -0.028464656323194504, -0.015407634899020195, -0.021845322102308273, -0.007610198110342026, 0.047792017459869385, -0.11646085232496262, 0.02534549869596958, -0.021510865539312363, 0.028891224414110184, 0.045704979449510574, 0.05283629521727562, -0.006649114657193422, 0.016316602006554604, 0.03170251101255417, -0.06577274948358536, 0.05448778346180916, -0.015470041893422604, -0.0063897003419697285, 0.007865484803915024, 0.024266131222248077, 0.01608993299305439, 0.08385320007801056, 0.0008046877337619662, -0.020902151241898537, -0.03401341661810875, -0.026087909936904907, -0.0043728966265916824, 0.01208446267992258, 0.027158411219716072, -0.003951227758079767, -0.04076837748289108, -0.020930327475070953, 0.03862427920103073, -0.10744404047727585, -0.002217665547505021, 0.026060765609145164, 0.011762896552681923, 0.020435018464922905, -0.0019422994228079915, -0.03007541224360466, -0.016963008791208267, 0.000029462386009981856, 0.059251513332128525, 0.018580593168735504, -0.027829932048916817, 0.041776735335588455, -0.03969904035329819, 0.018477775156497955, -0.02509780041873455, 0.012244637124240398, -0.026423513889312744, -0.02346327155828476, -0.0472714900970459, -0.021709119901061058, -0.06716760993003845, -0.027152445167303085, -0.03401185944676399, -0.05807260423898697, -0.027729352936148643, -0.014374073594808578, -0.00402954313904047, -0.06731871515512466, -0.03374448046088219, -0.016187580302357674, 0.00550168938934803, -0.029002288356423378, 0.05362211540341377, 0.0330149307847023, 0.027563950046896935, 0.03829867020249367, 0.007334139198064804, 0.042702313512563705, 0.012340491637587547, -0.04314829781651497, 0.029494501650333405, -0.009637854993343353, -0.015541109256446362, -0.029027866199612617, 0.036783359944820404, 0.07657867670059204, 0.012829047627747059, -0.04873126372694969, -0.05986863747239113, -0.03309459984302521, 0.01792162097990513, -0.039936989545822144, 0.018733996897935867, -0.0144116235896945, -0.005502018611878157, 0.024060282856225967, -0.05942244827747345, -0.002878219587728381, 0.045753300189971924, -0.04403209686279297, -0.010768536478281021, 0.035275861620903015, -0.0012580358888953924, -0.026138173416256905, -0.0027615251019597054, 0.02804514579474926, -0.027634533122181892, 0.013309339992702007, 0.0013401621254161, -0.03819918632507324, -0.023372294381260872, 0.01451320294290781, -0.04356234148144722, -0.0010224697180092335, -0.045747220516204834, -0.018112391233444214, -0.04720243439078331, 0.003703860566020012, 0.10426551848649979, 0.04484454169869423, 0.0000281581833405653, 0.024599988013505936, 0.040277253836393356, -0.03155847266316414, 0.012752602808177471, 0.05353128910064697, -0.018419215455651283, -0.041108887642621994, -0.014784898608922958, -0.020962579175829887, -0.03460758551955223, 0.04441743344068527, -0.018659450113773346, -0.05330868437886238, -0.015840355306863785, -0.004780873656272888, 0.05007793754339218, -0.009030367247760296, 0.01414374727755785, -0.034351807087659836, -0.027073480188846588, -0.009387660771608353, 0.036434464156627655, -0.004335569683462381, 0.011446668766438961, -0.051853593438863754, -0.015775363892316818, -0.01703788712620735, 0.1092148944735527, 0.059537485241889954, -0.021159427240490913, 0.014513729140162468, 0.012697091326117516, -0.05057419091463089, 0.0240702535957098, -0.015072262845933437, -0.0038372210692614317, -0.029433023184537888, 0.07622837275266647, -0.00646175304427743, 0.025325598195195198, -0.03582363575696945, 0.011161486618220806, 0.023980142548680305, -0.004258059896528721, 0.038350868970155716, -0.02180507965385914, 0.0071167186833918095, -0.013493835926055908, -0.01537579670548439, -0.011828016489744186, 0.031622931361198425, -0.08139418810606003, -0.04574180021882057, -0.028599794954061508, 0.019704658538103104, -0.020167844370007515, 0.07296518236398697, 0.04258878156542778, 0.0015302152605727315, -0.0009911034721881151, -0.005657037254422903, 0.06299915909767151, -0.04132336750626564, -0.06152528524398804, -0.005479584913700819, 0.04073457047343254, 0.006279839668422937, 0.02071634866297245, 0.053102243691682816, 0.012243960052728653, -0.05142608657479286, 0.002025088295340538, -0.04571682587265968, 0.023049378767609596, 0.012982676737010479, 0.018756050616502762, -0.04730415344238281, -0.03134624660015106, 0.019547339528799057, 0.02749062515795231, 0.009045254439115524, 0.0395234040915966, 0.029160151258111, -0.05691885948181152, -0.025161826983094215, 0.09777248650789261, 0.026581406593322754, 0.031552962958812714, 0.008954821154475212, -0.0027447124011814594, 0.01165954302996397, 0.016833176836371422, 0.009795116260647774, 0.04471728205680847, -0.027541814371943474, 0.03757542371749878, 0.02693195454776287, 0.07012056559324265, 0.035052139312028885, 0.05654985457658768, 0.025961369276046753, -0.0008810339495539665, 0.007668737787753344, 0.0027751349844038486, -0.02979290299117565, -0.008057690225541592, -0.07923451066017151, -0.0684240534901619, -0.028846895322203636, -0.044301364570856094, -0.007288149558007717, 0.06788570433855057, -0.018531424924731255, -0.015237306244671345, 0.0544944703578949, -0.020769387483596802, 0.0005825921543873847, 0.02262396551668644, 0.026741405948996544, -0.024121906608343124, -0.042441096156835556, 0.03542914614081383, -0.008177965879440308, -0.022483311593532562, 0.00406427588313818, -0.02939544804394245, -0.02127818390727043, -0.016524016857147217, -0.07998204231262207, 0.06523031741380692, 0.00914052501320839, -0.0056854188442230225, -0.004411447327584028, -0.011716369539499283, 0.03208938613533974, -0.0017458858201280236, -0.025852764025330544, 0.022378133609890938, 0.02387923374772072, -0.02682567574083805, -0.013069512322545052, -0.030306069180369377, -0.0039001749828457832, 0.0008648752118460834, 0.0367734432220459, 0.03580567613244057, 0.0005595101392827928, 0.0011312293354421854, 0.08853050321340561, -0.04450187459588051, 0.02127407118678093, -0.03654349967837334, 0.0222256388515234, -0.029015904292464256, -0.035716984421014786, 0.011907425709068775, 0.02542271465063095, 0.03696102276444435, 0.0262301042675972, -0.04328114539384842, 0.022523008286952972, 0.014845345169305801, -0.014671939425170422, 0.005091454833745956, -0.05258695408701897, 0.00010432572162244469, 0.04542863741517067, 0.019995898008346558, -0.085300013422966, 0.0010443917708471417, 0.03507877141237259, 0.01890009455382824, 0.03578636422753334, 0.009985309094190598, -0.014546824619174004, -0.05732274800539017, 0.040580689907073975, 0.0013917838223278522, -0.03730049729347229, 0.007951730862259865, 0.020809348672628403, 0.02754862792789936, 0.060109999030828476, 0.01939058117568493, 0.008029735647141933, -0.051324859261512756, -0.027633043006062508, 0.023561980575323105, 0.006107347551733255, 0.021231384947896004, -0.008603970520198345, 0.0017166795441880822, 0.03717424347996712, 0.03395730257034302, -0.023832304403185844, 0.04527242109179497, -0.018548371270298958, -0.03886478766798973, -0.0006260276422835886, -0.013125930912792683, -0.04896822199225426, 0.008530382066965103, 0.04587573930621147, 0.03375940024852753, 0.026557104662060738, 0.016866959631443024, 0.0026559007819741964, -0.024429848417639732, 0.00852674525231123, -0.027421923354268074, 0.006275303196161985, 0.009531509131193161, -0.002058787737041712, -0.06658631563186646, 0.009223188273608685, 0.017098382115364075, 0.054362520575523376, -0.03733758628368378, -0.07943827658891678, -0.024715248495340347, 0.015556514263153076, 0.003878266317769885, -0.030354293063282967, 0.011369062587618828, -0.01770530827343464, -0.02220034785568714, -0.038689736276865005, 0.0023296137806028128, 0.001498559257015586, 0.0005696786683984101, 0.009793506935238838, -0.019723081961274147, 0.029500098899006844, 0.007245949469506741, 0.05139824375510216, 0.060618966817855835, -0.005755084566771984, -0.04423544183373451, -0.07657978683710098, -0.03307341784238815, 0.014775851741433144, -0.002482219599187374, -0.018764449283480644, -0.029614821076393127, 0.0400272011756897, -0.00047848219401203096, -0.006636056583374739, -0.007530441042035818, 0.009666548110544682, 0.008972061797976494, -0.0010453809518367052, -0.002619449980556965, 0.00642402283847332, -0.04538106173276901, -0.06511922180652618, 0.04080132767558098, 0.023115921765565872, -0.004436412826180458, -0.03426802530884743, 0.07696571946144104, -0.03196710720658302, 0.04435013234615326, 0.026746677234768867, -0.07006021589040756, 0.04882079362869263, 0.007040644064545631, -0.025922860950231552, 0.05705130100250244, 0.04359504207968712, 0.028554486110806465, -0.022368334233760834, -0.0015703501412644982, 0.0026352431159466505, 0.03226641193032265, -0.011148212477564812, -0.02169717475771904, -0.016039375215768814, -0.01871594600379467, 0.011515399441123009, 0.016371021047234535, 0.029824379831552505, -0.0006009506760165095, 0.016893483698368073, -0.0012595150619745255, -0.018996208906173706, 0.08000965416431427, -0.0070703765377402306, 0.027174998074769974, -0.019171562045812607, 0.029402680695056915, 0.00757686048746109, -0.024498604238033295, -0.0292649008333683, 0.045948658138513565, 0.08151256293058395, 0.06299280375242233, -0.0022089271806180477, 0.07872260361909866, 0.05410027503967285, 0.03875363990664482, 0.02651911787688732, -0.05590430647134781, -0.01954049989581108, -0.025174561887979507, -0.019731717184185982, -0.07196220010519028, 0.04103752225637436, -0.005635200999677181, -0.03686162456870079, 0.014369565062224865, -0.02970939874649048, 0.0004130757588427514, -0.04957103356719017, 0.08348063379526138, -0.0030698475893586874, -0.02121018059551716, 0.020023010671138763, -0.04020318761467934, -0.032581865787506104, -0.06477583199739456, 0.018139487132430077, -0.019210539758205414, 0.036589086055755615, -0.04700203239917755, 0.012713856063783169, 0.02983436919748783, -0.08309151232242584, -0.031445614993572235, -0.010226752609014511, -0.043389610946178436, 0.018541719764471054, 0.006440138444304466, 0.006253357045352459, 0.0006062987959012389, -0.020245976746082306, 0.03978446125984192, 0.02072218246757984, 0.053767140954732895, 0.03002951852977276, 0.007539908867329359, -0.007113456726074219, 0.06019670143723488, -0.035000991076231, -0.008538949303328991, -0.045267216861248016, -0.008590435609221458, -0.006594375241547823, -0.11098100244998932, 0.015092250891029835, 0.009694209322333336, 0.026021722704172134, 0.005164592992514372, 0.017681516706943512, -0.010607313364744186, 0.026481591165065765, -0.02525097131729126, 0.13960270583629608, 0.014113015495240688, 0.01370988879352808, -0.01438514981418848, 0.05063104256987572, 0.020395245403051376, 0.034960806369781494, 0.05134410411119461, 0.03103077970445156, 0.03202872350811958, -0.018396073952317238, -0.0027816700749099255, -0.043556202203035355, 0.011305699124932289, 0.008636916056275368, -0.017846887931227684, 0.0029654409736394882, 0.03888436034321785, -0.03820214420557022, -0.004501231946051121, -0.016626406461000443, 0.03351856395602226, 0.0292921494692564, -0.03921538591384888, -0.03199627250432968, -0.011388355866074562, 0.010229609906673431, -0.05566556379199028, 0.02038654126226902, -0.03130944073200226, 0.009861416183412075, 0.007902728393673897, -0.008854713290929794, 0.009691985324025154, 0.015384986996650696, 0.01337776705622673, -0.023960744962096214, -0.023112637922167778, -0.03930263593792915, 0.04016305133700371, -0.00386145175434649, -0.02318602055311203, -0.021815214306116104, 0.06195799633860588, 0.01937715895473957, -0.039264317601919174, -0.04734992980957031, -0.002227413235232234, -0.02813190221786499, -0.09367547929286957, 0.02541784755885601, 0.03466024994850159, 0.07395783066749573, -0.010705963708460331, -0.008089634589850903, 0.040984801948070526, 0.00818273052573204, 0.035830698907375336, 0.028754040598869324, 0.004890593234449625, 0.0017437883652746677, 0.033887770026922226, 0.019585831090807915, 0.057709384709596634, -0.01413301844149828, 0.029907792806625366, 0.025804677978157997, 0.006991223432123661, 0.007114285137504339, -0.0023365176748484373, -0.029774222522974014, 0.0028524769004434347 ]
<p>I would like to know how one could show and prove that a given motion is simple harmonic motion.</p> <p>Once given an answer, I'll apply that technique to an example I am trying to figure out. </p> <p>Thank you in advance!</p> <p>I believe a motion can be proved simple harmonic, if the relation between its is as such: $$ a_x = - \omega^2\cdot x $$</p> <p>And as such the period time is: $$ T =\frac{2\pi}{\omega} $$</p> <p>Question-so-far: How do you prove such for a given force $F = \frac{G\cdot m_e \cdot M}{R_E} \cdot r$ ? Or any force that has non-trivial constants?</p>
g1549
[ 0.0819549709558487, -0.008659051731228828, 0.015152281150221825, 0.005343773867934942, 0.05060180649161339, -0.033214837312698364, 0.04250975325703621, -0.03838764876127243, -0.008863388560712337, -0.02268863655626774, -0.0396869070827961, -0.0044368356466293335, -0.009846838191151619, 0.030414719134569168, -0.010967962443828583, -0.025444410741329193, 0.05026724562048912, -0.016186458989977837, -0.001347976503893733, 0.02627146616578102, 0.03001417964696884, 0.015484519302845001, -0.017269732430577278, -0.02724708989262581, 0.049306973814964294, 0.013926896266639233, -0.000964721548371017, -0.015464557334780693, -0.005639954004436731, -0.05712807923555374, 0.005977586843073368, 0.004343464970588684, 0.060515716671943665, 0.036080241203308105, -0.010556972585618496, -0.02986603043973446, 0.042778000235557556, -0.038696419447660446, 0.06347393989562988, 0.002088022418320179, 0.01078522577881813, -0.045034658163785934, 0.014099165797233582, 0.07308612018823624, 0.0429462231695652, 0.0030970561783760786, -0.010131575167179108, -0.007984247989952564, -0.08030997216701508, 0.019544772803783417, 0.0134471096098423, 0.008864265866577625, 0.034884028136730194, -0.03912929445505142, -0.029181869700551033, -0.00035540509270504117, 0.014333151280879974, 0.007183023728430271, -0.0030678051989525557, -0.016575008630752563, -0.03651486337184906, 0.0022631424944847822, 0.02160869725048542, 0.03279375284910202, 0.002095626899972558, 0.021896827965974808, -0.0054061985574662685, -0.03224954381585121, 0.04333225265145302, 0.02766352705657482, -0.06737156212329865, -0.011235217563807964, 0.03371322900056839, -0.01101500354707241, -0.04060036689043045, 0.0010037124156951904, 0.0019346491899341345, 0.002036697929725051, -0.017577102407813072, -0.06608899682760239, -0.007724050432443619, 0.007330769207328558, -0.004153884947299957, 0.014370637014508247, 0.021564582362771034, -0.05092440918087959, -0.0032262131571769714, 0.0037028647493571043, 0.020899362862110138, 0.020544743165373802, 0.0366719625890255, -0.003526495536789298, 0.03701439127326012, 0.04170555993914604, -0.0058935522101819515, -0.030648021027445793, -0.061486367136240005, 0.05295601114630699, 0.04794149473309517, -0.004127635154873133, -0.03319882974028587, -0.009575321339070797, -0.01679122820496559, 0.018086610361933708, 0.027738381177186966, -0.06311727315187454, 0.01537108700722456, 0.020149746909737587, -0.0249486044049263, -0.010643060319125652, -0.009985806420445442, 0.00061726727290079, -0.0069540031254291534, -0.0701264962553978, 0.01398005522787571, -0.0100586311891675, 0.052763525396585464, 0.040698591619729996, 0.03296990692615509, 0.06686737388372421, -0.04861302673816681, 0.06920580565929413, 0.023181281983852386, 0.015213988721370697, -0.06564199179410934, -0.016687143594026566, 0.0355832614004612, 0.05579181760549545, 0.016228312626481056, -0.008135584183037281, 0.021544402465224266, 0.006998137570917606, 0.01683020032942295, 0.023237129673361778, -0.026821324601769447, 0.014185174368321896, 0.04556339234113693, -0.039646752178668976, 0.006989969406276941, 0.008721761405467987, -0.011390524916350842, -0.013773847371339798, 0.02134852297604084, -0.04966781288385391, -0.02189844846725464, 0.06483092904090881, -0.006686475593596697, -0.05723462998867035, 0.029764041304588318, 0.06382761150598526, -0.005325264297425747, 0.033530984073877335, 0.03403821587562561, -0.056971728801727295, 0.08343148231506348, 0.002031395910307765, 0.04550940543413162, 0.025073595345020294, -0.03339530900120735, 0.003413570113480091, 0.016672536730766296, 0.019347012042999268, 0.08031699806451797, -0.026989853009581566, -0.01870741695165634, 0.02813577838242054, -0.05981459096074104, -0.008168787695467472, -0.01765524409711361, 0.018372004851698875, -0.051237497478723526, -0.021462086588144302, 0.009805617853999138, 0.0712694451212883, 0.027179688215255737, -0.020499758422374725, -0.03676699846982956, -0.06913014501333237, -0.002677330980077386, -0.02036857418715954, 0.03569244220852852, 0.025473041459918022, -0.02784409560263157, -0.026830853894352913, 0.0023575490340590477, -0.005141475237905979, 0.035961128771305084, -0.008170553483068943, -0.02743387594819069, 0.0517842061817646, -0.06519316881895065, -0.010986095294356346, -0.006240637041628361, -0.0005629501538351178, -0.05335212126374245, 0.039582304656505585, -0.030325571075081825, -0.029969366267323494, -0.04346441477537155, -0.028491849079728127, 0.004632231779396534, 0.004554557614028454, 0.05773931369185448, -0.005752770695835352, 0.006358565296977758, 0.04827584698796272, -0.00479561323300004, -0.03310404345393181, 0.008210818283259869, 0.026907047256827354, 0.00764553714543581, 0.00667810533195734, -0.0026877610944211483, -0.011499281972646713, -0.020457107573747635, 0.022303007543087006, 0.024049052968621254, -0.050012677907943726, -0.04815461486577988, 0.027578968554735184, -0.015406553633511066, -0.026746071875095367, -0.04936531186103821, -0.005402296781539917, -0.04310648515820503, 0.017106307670474052, -0.010752909816801548, -0.011400673538446426, -0.05389106646180153, 0.04001776874065399, -0.012734685093164444, 0.03175390884280205, 0.0020983926951885223, 0.012449163943529129, 0.007304060738533735, 0.024064956232905388, -0.02166902832686901, -0.029987378045916557, -0.005474156700074673, 0.04462790861725807, -0.05846058577299118, -0.09921132773160934, 0.008663802407681942, -0.05343935638666153, 0.023425128310918808, -0.0052479044534265995, 0.048990242183208466, 0.006558976136147976, 0.04518728703260422, -0.011213300749659538, -0.010508735664188862, -0.033440906554460526, 0.001963926013559103, 0.01872888207435608, 0.022700022906064987, -0.012670530937612057, 0.02831759862601757, 0.04389461502432823, 0.006369234994053841, -0.04062080383300781, 0.006970984861254692, -0.024166487157344818, 0.02632782980799675, 0.023316586390137672, -0.08255940675735474, -0.024451764300465584, -0.035919614136219025, 0.03524116054177284, -0.06407464295625687, -0.03573319688439369, -0.006841619033366442, -0.004814618732780218, 0.007783799897879362, 0.02810344658792019, -0.09248531609773636, -0.029031086713075638, 0.0331520140171051, -0.018202155828475952, 0.007258401717990637, 0.013495384715497494, -0.006258899811655283, -0.023691868409514427, -0.0329991951584816, 0.008137725293636322, 0.050889234989881516, -0.025852104648947716, 0.013764696195721626, 0.024133725091814995, -0.03126269951462746, 0.0002686798688955605, -0.051769986748695374, -0.018164973706007004, -0.02910284325480461, -0.008361926302313805, -0.05928638577461243, 0.020662715658545494, 0.026842348277568817, -0.045528594404459, 0.050282593816518784, 0.009506705217063427, 0.05676325410604477, 0.017312392592430115, 0.01800951547920704, 0.022255757823586464, 0.032934777438640594, -0.017983224242925644, 0.02012733370065689, -0.045078180730342865, -0.05413144454360008, 0.07669562101364136, 0.05173426494002342, 0.046899572014808655, 0.010647203773260117, 0.026775803416967392, -0.060345955193042755, 0.0369873009622097, -0.02928767539560795, -0.04133600369095802, -0.026082323864102364, 0.011858614161610603, -0.024351000785827637, -0.09515494853258133, -0.04667157307267189, -0.040107809007167816, 0.08041643351316452, 0.0000917619836400263, -0.04073885828256607, -0.035778939723968506, -0.06960681080818176, -0.031181009486317635, 0.03136100247502327, 0.02570965513586998, 0.019238267093896866, 0.003826464293524623, -0.0219641774892807, -0.009922635741531849, -0.019277092069387436, 0.010904845781624317, 0.024564066901803017, 0.023498594760894775, 0.054288845509290695, -0.002382233738899231, -0.06669095158576965, -0.0009059891453944147, -0.05280816927552223, 0.022981662303209305, -0.016508979722857475, 0.01687990315258503, 0.04099353030323982, -0.04511827602982521, 0.007824435830116272, -0.05604245513677597, 0.07569973170757294, -0.029781483113765717, -0.012491405010223389, 0.006879875436425209, 0.03834402933716774, 0.03600144758820534, -0.021934140473604202, -0.05543055012822151, 0.03532470017671585, 0.006108906120061874, 0.006554132327437401, 0.03890642151236534, 0.029108960181474686, -0.011178922839462757, 0.008056143298745155, 0.050375815480947495, 0.0686049833893776, -0.008713583461940289, 0.0487309992313385, -0.04463521018624306, 0.0031343407463282347, 0.007534970063716173, 0.019789796322584152, -0.07852718234062195, 0.02155267633497715, 0.058754414319992065, -0.0178719162940979, 0.053769759833812714, 0.041526149958372116, -0.007978943176567554, 0.007867136038839817, 0.04745945334434509, -0.009176908060908318, -0.01723121479153633, 0.012127935886383057, 0.047554243355989456, 0.05355917662382126, -0.04471983760595322, 0.04042120650410652, -0.01250773761421442, 0.0012699489016085863, 0.003759135492146015, 0.01727946661412716, -0.049134645611047745, 0.06088007986545563, -0.012697486206889153, -0.047433871775865555, -0.02027135342359543, -0.027994027361273766, -0.0072863721288740635, 0.00273798662237823, -0.009648725390434265, -0.04101055860519409, 0.05240795016288757, -0.004889240022748709, -0.010200238786637783, 0.06092623621225357, -0.052102647721767426, -0.01603102497756481, -0.044664397835731506, 0.014906001277267933, -0.028988322243094444, -0.012799724005162716, 0.022574031725525856, -0.007186328526586294, 0.00012719356163870543, -0.0033050556667149067, -0.02177395299077034, -0.03735482692718506, 0.0690319761633873, -0.021030334755778313, -0.026907794177532196, -0.04469751939177513, 0.07844187319278717, 0.07612142711877823, -0.02113962359726429, 0.03654048219323158, -0.027367645874619484, -0.006949467118829489, -0.027017317712306976, 0.031390972435474396, -0.019191551953554153, -0.055786553770303726, -0.0019838656298816204, -0.037594228982925415, 0.03611277788877487, -0.021676303818821907, 0.020579183474183083, 0.07525239884853363, 0.04168424755334854, 0.06947251409292221, -0.07942898571491241, -0.0060689374804496765, 0.029551224783062935, -0.01407228410243988, -0.05142892897129059, -0.03189308941364288, -0.0625867173075676, 0.05177517235279083, 0.015919936820864677, 0.006059102714061737, 0.006888515781611204, -0.048567913472652435, -0.037084512412548065, -0.018795480951666832, 0.004849513527005911, -0.06688947230577469, 0.015948308631777763, -0.00012698746286332607, -0.008874686434864998, 0.07035880535840988, 0.004918153863400221, 0.06930219382047653, 0.027014529332518578, -0.015472025610506535, -0.03811148554086685, -0.0018665704410523176, -0.001707119750790298, -0.011958276852965355, 0.006400394719094038, 0.012669169344007969, -0.02850462682545185, -0.023484770208597183, -0.048614826053380966, 0.01964442990720272, 0.05073487013578415, 0.023123323917388916, -0.036506157368421555, 0.06400373578071594, -0.0007455874001607299, -0.005709582008421421, 0.030623018741607666, 0.02365013398230076, -0.0688997209072113, -0.05407777056097984, 0.004022350534796715, 0.005796865094453096, -0.02280326373875141, 0.010225650854408741, 0.015682945027947426, 0.0064505115151405334, 0.04177333787083626, -0.04014169052243233, 0.01135170552879572, -0.014130660332739353, -0.006342087406665087, -0.022381043061614037, -0.01181691512465477, -0.060131870210170746, 0.029336383566260338, 0.052260447293519974, 0.03700868412852287, 0.0048154196701943874, 0.04462733119726181, 0.06047839671373367, -0.030783774331212044, -0.02269783616065979, 0.07867846637964249, 0.00014936219668015838, 0.08292662352323532, -0.07866548001766205, 0.03508047014474869, 0.018157780170440674, 0.006378163583576679, -0.0197090245783329, -0.028572436422109604, -0.023285632953047752, -0.0394730344414711, 0.032610319554805756, 0.005452255252748728, 0.04759170487523079, -0.033665500581264496, 0.03864525258541107, -0.010523208416998386, -0.015589993447065353, -0.02271936647593975, 0.026720596477389336, 0.05129288136959076, 0.009801401756703854, -0.04713089391589165, 0.037381913512945175, -0.06467893719673157, -0.010398981161415577, 0.024325838312506676, 0.04539196565747261, -0.01566796563565731, -0.015113022178411484, 0.055099233984947205, -0.02202688530087471, -0.038310736417770386, 0.0010843129130080342, 0.005413264501839876, -0.059953995048999786, -0.000056044391385512426, 0.0016134536126628518, 0.0067099761217832565, 0.018446581438183784, -0.03270818665623665, -0.029552659019827843, 0.025362974032759666, -0.07131271064281464, -0.029897416010499, -0.026236871257424355, 0.027705445885658264, 0.0026001441292464733, -0.09044542908668518, -0.00009582855273038149, -0.00006077456782804802, 0.027720429003238678, 0.019216258078813553, -0.006052154116332531, 0.008916657418012619, 0.030716555193066597, -0.022013479843735695, 0.062060825526714325, -0.0077720326371490955, 0.017043154686689377, 0.04471360519528389, -0.031429894268512726, 0.058760758489370346, -0.05927380546927452, -0.0246893223375082, 0.002749752253293991, -0.027170106768608093, -0.020895686000585556, -0.016796136274933815, -0.09850352257490158, -0.005639266222715378, -0.0018237625481560826, 0.015064847655594349, 0.014409179799258709, 0.011153987608850002, -0.06566261500120163, 0.0892515480518341, -0.018094511702656746, -0.03422170877456665, 0.01303975097835064, 0.04487204551696777, -0.04171799123287201, -0.011975576169788837, -0.020193180069327354, -0.025235256180167198, 0.005120506044477224, 0.0034251247998327017, 0.0019012336852028966, 0.039969611912965775, 0.0457952506840229, 0.06784667819738388, -0.0341903492808342, -0.011394144035875797, 0.0707513839006424, -0.008950430899858475, -0.021085137501358986, 0.08650673180818558, 0.02207568660378456, -0.015796050429344177, 0.027069350704550743, 0.012850895524024963, -0.033754460513591766, 0.005867532454431057, 0.018001185730099678, -0.007769075222313404, -0.020425885915756226, -0.04648032411932945, -0.0053266300819814205, -0.01289817038923502, 0.02696400135755539, -0.02597559615969658, 0.015353121794760227, 0.05073673278093338, 0.034113965928554535, 0.002792653627693653, 0.07634596526622772, -0.0010803407058119774, -0.04628109559416771, 0.03445742279291153, 0.044458214193582535, -0.04283332824707031, 0.022576726973056793, -0.00015424513549078256, 0.012056899257004261, 0.05880197137594223, -0.027538683265447617, -0.020339932292699814, -0.08019693195819855, 0.06949262320995331, 0.0519910603761673, -0.007288910914212465, -0.00503352377563715, 0.054146308451890945, 0.01861744001507759, -0.019580388441681862, -0.0824187844991684, -0.011149153113365173, 0.040348175913095474, 0.015361394733190536, -0.052033040672540665, 0.005250433925539255, 0.009562593884766102, -0.011360004544258118, 0.029511718079447746, -0.0014022373361513019, -0.033498696982860565, 0.04432982951402664, 0.01589842140674591, 0.009769954718649387, -0.011899232864379883, -0.04294843226671219, -0.022998495027422905, 0.04477338865399361, -0.004786408506333828, -0.03567038103938103, -0.016916053369641304, 0.08313558250665665, -0.03119218535721302, -0.01771923154592514, -0.00859649945050478, -0.028834693133831024, 0.05973154306411743, 0.06954183429479599, 0.044806234538555145, -0.007898557931184769, -0.043534260243177414, 0.01096516102552414, 0.0014914821367710829, 0.02536194957792759, 0.026216929778456688, -0.029671119526028633, -0.08037083595991135, 0.006000543478876352, -0.014218173921108246, -0.004643908701837063, -0.025449078530073166, 0.025049805641174316, -0.05455872416496277, -0.008220675401389599, -0.02172304317355156, -0.026687297970056534, -0.013025188818573952, 0.0544329434633255, -0.04991579055786133, -0.01948886550962925, 0.026644600555300713, -0.036037627607584, 0.042641591280698776, 0.014286361634731293, 0.02414841577410698, 0.01011113915592432, -0.04788210615515709, -0.05670377239584923, -0.006160775665193796, 0.011231467127799988, -0.00663702841848135, -0.014853314496576786, -0.047222625464200974, -0.020735569298267365, -0.0578378364443779, 0.047710053622722626, 0.0911431536078453, 0.03842155635356903, -0.05156724900007248, -0.03660578653216362, 0.013003343716263771, 0.044806621968746185, -0.015865815803408623, 0.029373202472925186, 0.061933357268571854, -0.035640571266412735, -0.012826502323150635, 0.0020509527530521154, 0.001617054338566959, -0.0448409840464592, -0.06502384692430496, 0.04012277349829674, 0.0016466421075165272, -0.06847226619720459, 0.01539671327918768, -0.03386962413787842, 0.03429633378982544, -0.029753461480140686, 0.028573565185070038, 0.05296356976032257, -0.02921472117304802, -0.019402706995606422, -0.002290659584105015, -0.04076026752591133, -0.04100145027041435, 0.0737459808588028, -0.005074203480035067, -0.04046444222331047, -0.003980874549597502, -0.0013164259726181626, 0.017286671325564384, -0.0202752947807312, -0.012178591452538967, 0.0816018357872963, -0.02506200224161148, -0.002287986222654581, -0.006749738473445177, 0.06739132851362228, -0.049626536667346954, -0.01782713271677494, 0.010566442273557186, -0.04513058811426163, -0.047395918518304825, 0.03224561735987663, 0.06411022692918777, -0.011013546958565712, -0.05153927952051163, 0.08777453750371933, -0.03044571913778782, -0.016735436394810677, -0.024289602413773537, -0.0608743317425251, 0.007160142995417118, 0.01517051737755537 ]
<p>David Albert is a philosopher of Science at Columbia. His book "Time and Chance" includes this example (p 36). </p> <p>A gas is confined on one side of a box with a removable wall. "Draw the wall out, <em>slowly</em>, and <em>perpendicular</em> to its surface, like a piston. Now it happens to be the case, it happens to be a consequence of the Newtonian laws of motion, that a billiard ball which bounces off a receding wall will move more slowly <em>after</em> the collision than <em>before</em> it. (Footnote. Proof: consider the fame of reference in which the wall is at rest.) And so gas particles that bounce off the wall as it it's being drawn out will have their kinetic energy somewhat <em>depleted</em>."</p> <p>Why is that? We are assuming that an externally applied force is pulling the wall out. It's not the gas that is pushing the wall out. So why is energy lost. Why doesn't that violate conservation of energy.</p> <p>Another way to look at it is to assume a series of walls very close to each other. Remove them one by one parallel to the surface. There will be no change in the total kinetic energy of the gas. Why is this different?</p>
g1550
[ 0.09926041960716248, 0.027991587296128273, 0.01394143421202898, 0.03829459100961685, 0.018551189452409744, 0.0016119341598823667, 0.07725272327661514, 0.04440407082438469, -0.07809542119503021, -0.05213136598467827, -0.003372013568878174, -0.03304476663470268, -0.020257415249943733, -0.004562703426927328, 0.005974704399704933, -0.0036462710704654455, 0.051383063197135925, -0.027024095878005028, 0.010612056590616703, 0.09071265906095505, -0.042557213455438614, 0.009304983541369438, 0.012836850248277187, -0.018748227506875992, 0.021361788734793663, -0.025834225118160248, 0.06181013956665993, -0.06376940757036209, -0.03210857883095741, -0.04109055921435356, 0.02474120818078518, -0.0026231349911540747, 0.037832047790288925, -0.05003087595105171, -0.03562134876847267, -0.023748572915792465, 0.05864376947283745, -0.03013312816619873, 0.07425568252801895, -0.028208501636981964, 0.033972594887018204, 0.019748397171497345, 0.022546833381056786, 0.0383477546274662, 0.04165070131421089, 0.004537962377071381, -0.010588356293737888, -0.025801636278629303, -0.009170668199658394, -0.03230397403240204, -0.022011853754520416, 0.006838338449597359, -0.02302633225917816, -0.008544973097741604, 0.017112331464886665, 0.007645917125046253, -0.005683181807398796, 0.0012911277590319514, 0.06195477396249771, -0.0003959363966714591, 0.032935965806245804, 0.017334705218672752, 0.018388906493782997, 0.014226814731955528, 0.07030615210533142, -0.04806942865252495, -0.04603629931807518, 0.031392887234687805, 0.027751635760068893, -0.01642746850848198, 0.022801999002695084, -0.028095528483390808, 0.010161008685827255, -0.04393335059285164, 0.04172497242689133, 0.029123077169060707, 0.003335224464535713, -0.004133199341595173, -0.03155751898884773, 0.0008125464082695544, -0.0555676706135273, 0.03202763944864273, -0.02526070922613144, 0.015132012777030468, 0.08089292049407959, -0.005165908485651016, -0.039671264588832855, 0.007872837595641613, -0.017982183024287224, -0.003580091055482626, 0.0049896566197276115, 0.0033174464479088783, 0.14490032196044922, -0.015959013253450394, -0.05809415504336357, 0.02048683911561966, -0.04149138554930687, 0.023669691756367683, 0.01840747334063053, 0.023160794749855995, -0.046498093754053116, -0.06998205929994583, -0.03155210614204407, -0.020640891045331955, 0.011994554661214352, -0.010207870975136757, -0.00016676865925546736, 0.029823238030076027, -0.06113012135028839, -0.04009197652339935, 0.051942020654678345, -0.06634591519832611, -0.006651736795902252, -0.053318072110414505, -0.013646377250552177, -0.04584488272666931, 0.09705165028572083, 0.010748478583991528, 0.0039360132068395615, 0.07529893517494202, -0.02004166506230831, 0.053503260016441345, -0.01968051865696907, 0.007045550271868706, -0.031322263181209564, -0.005076931789517403, 0.015078992582857609, 0.010280291549861431, 0.026622770354151726, 0.005227392539381981, 0.017010794952511787, 0.01231162715703249, 0.0021032625809311867, 0.031159736216068268, 0.03453447297215462, -0.006585685536265373, -0.01267782412469387, -0.003932317718863487, 0.005820665042847395, -0.048462145030498505, 0.05436933413147926, 0.05042827129364014, -0.012762060388922691, -0.02253539115190506, -0.02805473655462265, 0.050624143332242966, -0.04412422701716423, 0.0019948501139879227, 0.01750536821782589, -0.02605893649160862, -0.002835616935044527, 0.020691119134426117, -0.008716830052435398, -0.03237342834472656, 0.10804980248212814, -0.002087728353217244, 0.029210539534687996, 0.01204754039645195, -0.02876203879714012, 0.017740881070494652, 0.07679981738328934, -0.003929816652089357, 0.02635922282934189, -0.00024325090635102242, -0.04293232038617134, 0.030705736950039864, 0.026753006502985954, -0.05870640650391579, 0.029598688706755638, -0.05021882429718971, -0.05881720036268234, -0.04419715702533722, 0.01869204454123974, 0.05293003097176552, -0.028193587437272072, 0.0642714649438858, 0.023107552900910378, -0.051827047020196915, -0.03331223875284195, -0.04549137130379677, 0.032455574721097946, -0.03340226411819458, 0.021497096866369247, -0.013596946373581886, 0.032858286052942276, 0.018045030534267426, 0.015782874077558517, 0.06032702699303627, -0.08022879809141159, -0.03734906017780304, -0.026293663308024406, 0.006195846013724804, 0.00785781443119049, -0.026050344109535217, 0.0029249133076518774, 0.019596494734287262, 0.00021335604833438993, -0.04977629333734512, -0.0870373472571373, 0.02701256424188614, -0.05368911474943161, 0.01787128672003746, 0.00872459914535284, -0.0013661757111549377, 0.028470845893025398, 0.02780766971409321, -0.041526831686496735, 0.0574159137904644, -0.009421920403838158, -0.07619855552911758, 0.0189589224755764, 0.03508669137954712, -0.024760017171502113, 0.03403853997588158, 0.023266470059752464, 0.007825619541108608, -0.01531014870852232, 0.025988468900322914, -0.02311141975224018, -0.007597990334033966, -0.06092869117856026, 0.011110221035778522, -0.013921794481575489, -0.0646263062953949, -0.015423715114593506, -0.021006563678383827, -0.07251165807247162, 0.0036574744153767824, -0.05874626338481903, 0.025396816432476044, -0.04401889815926552, 0.0025082705542445183, -0.013330730609595776, 0.03511703386902809, 0.0448153093457222, 0.01742498204112053, 0.05195673927664757, 0.02222100831568241, 0.032479383051395416, -0.01161144021898508, 0.037608176469802856, -0.07115067541599274, -0.07127730548381805, -0.05106974020600319, 0.01798105239868164, -0.023294202983379364, 0.03722207248210907, -0.035021618008613586, 0.04654126241803169, 0.01909010484814644, 0.027224089950323105, -0.003783659776672721, -0.03497372940182686, -0.010566630400717258, 0.0371527336537838, -0.004597590770572424, -0.007237797603011131, -0.004007596988230944, 0.007774864789098501, -0.05091104656457901, 0.0030127468053251505, -0.017549891024827957, 0.005936663597822189, 0.05521067604422569, -0.025484707206487656, -0.02736813761293888, -0.04437776282429695, 0.05651184916496277, 0.0162025298923254, 0.0006023980677127838, -0.0012057600542902946, 0.06950446218252182, 0.022745409980416298, 0.04126860946416855, 0.007215921301394701, -0.007216352503746748, 0.05434362590312958, -0.026591306552290916, 0.008241417817771435, -0.023449376225471497, -0.02855520509183407, 0.03185190632939339, -0.08770899474620819, 0.0066209826618433, 0.003944072872400284, -0.04867938160896301, 0.014649206772446632, -0.014452371746301651, -0.017872730270028114, 0.006903638131916523, 0.005767525639384985, 0.11969298869371414, 0.009295384399592876, 0.011089115403592587, 0.004810317885130644, 0.07656626403331757, -0.008474862203001976, -0.03516450896859169, -0.06845136731863022, 0.0024410299956798553, -0.04068979620933533, -0.017270134761929512, -0.025971395894885063, 0.041235968470573425, 0.03399382159113884, 0.039515212178230286, -0.08331798017024994, -0.04467311501502991, 0.008731169626116753, -0.038806404918432236, 0.03937358781695366, 0.03797880560159683, 0.021821020171046257, 0.028960345312952995, -0.06530633568763733, -0.05422447621822357, -0.0019619232043623924, -0.03128894791007042, 0.013771933503448963, 0.04306894168257713, -0.016203027218580246, 0.04069628566503525, 0.012615310959517956, 0.008983226493000984, -0.0022962933871895075, 0.009303973987698555, -0.06061870604753494, 0.009941491298377514, -0.03630905970931053, 0.0014192549278959632, 0.02088220790028572, 0.0016428789822384715, 0.007272940594702959, -0.023104656487703323, -0.047555796802043915, -0.03739473223686218, -0.022107712924480438, -0.0031120632775127888, 0.010883661918342113, 0.05250200256705284, -0.02425839751958847, 0.02994103543460369, -0.04414141923189163, -0.0031092604622244835, -0.0022468070965260267, 0.01240846049040556, 0.036072779446840286, 0.01813969761133194, 0.01605651155114174, -0.07927802205085754, 0.07717522233724594, -0.005798263940960169, 0.0525650717318058, -0.005235492717474699, -0.02102627605199814, 0.008747803047299385, -0.010716614313423634, 0.01391827967017889, -0.013247265480458736, 0.026096796616911888, 0.004605232737958431, -0.0371958427131176, -0.019915873184800148, -0.0010832302505150437, -0.017765384167432785, -0.005735104903578758, 0.015776649117469788, 0.04604518041014671, 0.03382686898112297, -0.02608622796833515, 0.0073198662139475346, 0.05296218767762184, -0.030061258003115654, 0.027559561654925346, 0.0397845022380352, -0.021719196811318398, 0.03090086579322815, -0.013079388998448849, 0.01026854757219553, 0.003938187845051289, 0.04697537422180176, 0.008467823266983032, -0.05342172831296921, -0.0022662982810288668, 0.04101521149277687, 0.038214586675167084, -0.022015951573848724, 0.005618839990347624, 0.025415129959583282, -0.027192391455173492, -0.009484442882239819, 0.03164030238986015, -0.033876530826091766, 0.00791547168046236, 0.017478520050644875, 0.02298513799905777, 0.03709620609879494, -0.010879901237785816, -0.058465249836444855, 0.005178742576390505, -0.025534730404615402, 0.018940946087241173, -0.03867347911000252, 0.01864948868751526, 0.018753208220005035, -0.03513982519507408, 0.07572255283594131, -0.037600744515657425, 0.02442305162549019, -0.0006895209662616253, -0.012503786012530327, -0.036037370562553406, -0.06602812558412552, -0.032901082187891006, -0.0190986767411232, -0.0025187169667333364, 0.015444972552359104, 0.03710128366947174, 0.03401154279708862, 0.022748667746782303, 0.026899248361587524, 0.020147638395428658, -0.05430508032441139, 0.005777577869594097, 0.041765403002500534, 0.07692409306764603, 0.03812675550580025, 0.0012148472014814615, -0.020092204213142395, -0.01852574199438095, 0.045159582048654556, 0.042275868356227875, -0.01700015738606453, -0.017693504691123962, -0.027487287297844887, 0.018739555031061172, -0.02427411638200283, 0.0399111807346344, 0.009818833321332932, 0.08233337104320526, 0.03557981550693512, 0.0019418878946453333, 0.0028800375293940306, 0.007432090118527412, 0.01987466774880886, 0.07748663425445557, -0.03315141797065735, -0.0257957074791193, -0.02610613964498043, -0.0203536506742239, -0.017288686707615852, 0.03127415105700493, 0.012962506152689457, -0.006979686673730612, -0.00018429048941470683, -0.04495473951101303, -0.07864677906036377, 0.018553584814071655, -0.007920843549072742, 0.05352082476019859, -0.05832279473543167, 0.02880934439599514, 0.03871190920472145, -0.00702225835993886, -0.027547653764486313, 0.0003259840596001595, 0.005574969109147787, 0.023738456889986992, -0.044669244438409805, -0.010562809184193611, 0.033527784049510956, 0.030031723901629448, -0.0324854850769043, 0.024242199957370758, -0.027574308216571808, -0.021278895437717438, -0.011208313517272472, 0.0054331934079527855, 0.08037745952606201, -0.05784543603658676, 0.004618034698069096, -0.024348067119717598, 0.013037694618105888, 0.05530671402812004, -0.018663795664906502, 0.011581102386116982, -0.054714757949113846, -0.012486934661865234, -0.037322912365198135, 0.027429621666669846, 0.05840370059013367, 0.04733707010746002, -0.037370678037405014, -0.03504851832985878, 0.04592736065387726, -0.0054223136976361275, 0.048171982169151306, -0.022079521790146828, -0.014529809355735779, 0.00914008915424347, -0.08275962620973587, 0.008139720186591148, -0.02776506543159485, -0.03626873716711998, -0.026836257427930832, 0.039195697754621506, -0.006582535803318024, -0.016697535291314125, -0.00391886942088604, 0.017767705023288727, -0.03585902228951454, -0.026509607210755348, 0.022951828315854073, 0.02694595791399479, 0.03162456676363945, -0.024237707257270813, 0.04926583543419838, -0.04414936900138855, -0.040743082761764526, -0.01801311783492565, 0.042306385934352875, -0.013447609730064869, 0.023753376677632332, -0.015208026394248009, 0.01053689606487751, 0.0791463553905487, -0.052702177315950394, -0.01733378693461418, -0.035293251276016235, 0.05028189718723297, -0.005483299493789673, -0.029715511947870255, 0.017876598984003067, 0.04296250268816948, -0.09019794315099716, 0.022318916395306587, -0.03673231974244118, -0.0035375943407416344, 0.04444078356027603, -0.04672566428780556, 0.011727329343557358, -0.0469660647213459, 0.032397713512182236, 0.045909956097602844, 0.0677579864859581, 0.010290322825312614, -0.05995041877031326, 0.009519075974822044, -0.001673188991844654, -0.056768354028463364, -0.0014312410494312644, 0.02455791085958481, -0.048564814031124115, 0.0038502011448144913, 0.006903571076691151, 0.028074556961655617, 0.017134223133325577, -0.060923874378204346, -0.004855581093579531, -0.004545084200799465, -0.030051784589886665, 0.027473224326968193, 0.025332853198051453, -0.005868094507604837, 0.058107730001211166, -0.0313015878200531, -0.00410475954413414, 0.0019674955401569605, 0.02665007673203945, 0.03159615769982338, 0.0361257940530777, 0.0043624588288366795, 0.02928468957543373, 0.03299528360366821, 0.022974634543061256, 0.010367444716393948, -0.07274831831455231, -0.02419256791472435, -0.09634464979171753, -0.007393829058855772, 0.010915739461779594, -0.08680194616317749, 0.01759599894285202, -0.07576055824756622, -0.02723013050854206, -0.012740638107061386, 0.01831071265041828, -0.012554536573588848, 0.045303765684366226, -0.02142183482646942, 0.03843340277671814, -0.06261453032493591, -0.0005313385627232492, -0.027171296998858452, -0.040275949984788895, -0.029527904465794563, -0.043757688254117966, 0.011942041106522083, -0.027572965249419212, 0.030009159818291664, -0.020448951050639153, 0.024632493034005165, -0.0027942408341914415, -0.04498957097530365, 0.04998211935162544, 0.05853414535522461, -0.028042316436767578, -0.009046980179846287, -0.02698487415909767, 0.026545938104391098, -0.06152934953570366, 0.07922720164060593, 0.0032125823199748993, -0.017619283869862556, 0.0033541503362357616, -0.015058674849569798, 0.01034252718091011, 0.00924515351653099, -0.012493765912950039, -0.0027738348580896854, 0.014263881370425224, 0.011235052719712257, 0.07010916620492935, -0.04560565948486328, 0.023293446749448776, -0.03008698672056198, -0.12189153581857681, 0.043641429394483566, 0.048661086708307266, 0.033380139619112015, -0.005211528390645981, 0.01258591003715992, -0.04205641895532608, 0.026156896725296974, -0.014922552742064, 0.023761652410030365, -0.0870661586523056, 0.025499187409877777, 0.03059394657611847, -0.026996705681085587, -0.03401849791407585, 0.0005081712733954191, 0.013543735258281231, 0.02161695621907711, -0.031433120369911194, -0.00479429867118597, -0.004475449677556753, -0.0255277156829834, -0.05339321494102478, -0.016387848183512688, -0.032490190118551254, -0.006488539278507233, -0.029126714915037155, -0.005218156147748232, -0.024671098217368126, 0.01165071502327919, -0.058486245572566986, -0.028536168858408928, 0.04564218968153, -0.06199146807193756, -0.024474065750837326, -0.026804324239492416, 0.012095581740140915, 0.001404771232046187, -0.008166743442416191, 0.03353094682097435, 0.013529490679502487, -0.04385983198881149, 0.03607754781842232, -0.010575871914625168, 0.013701333664357662, -0.05824398994445801, -0.04304629936814308, 0.026915058493614197, -0.009913260117173195, 0.06904052197933197, 0.037026140838861465, 0.004065582528710365, 0.013385728001594543, -0.023616848513484, 0.014304458163678646, 0.01066546980291605, -0.04383358731865883, -0.039623528718948364, -0.00345821026712656, 0.07516392320394516, -0.00706924544647336, 0.0300404392182827, 0.01422155275940895, -0.007500321604311466, 0.020309392362833023, 0.032397300004959106, 0.05112660676240921, 0.0326295830309391, 0.005721984896808863, -0.008961902931332588, 0.04670881852507591, 0.006316053215414286, 0.0005228336085565388, -0.013283881358802319, -0.03447384759783745, 0.004147622734308243, 0.0279886145144701, -0.015266490168869495, -0.007747616618871689, 0.018994903191924095, 0.02102656289935112, -0.021271295845508575, -0.032530538737773895, 0.006125939078629017, 0.009365521371364594, 0.010736493393778801, 0.0472334660589695, -0.02583656832575798, 0.0450122095644474, -0.02023926004767418, -0.014240603893995285, 0.03931863605976105, 0.05029908940196037, -0.04162812978029251, 0.03204748407006264, -0.010559892281889915, -0.021909326314926147, -0.06269443780183792, 0.028797652572393417, 0.01042028795927763, -0.03586190566420555, -0.01779296062886715, -0.0742497518658638, 0.00814888533204794, -0.018782205879688263, -0.01833394728600979, 0.05605556443333626, 0.05302683264017105, -0.020652489736676216, 0.011068356223404408, 0.01877015084028244, -0.001002795877866447, -0.014088176190853119, -0.00872271228581667, 0.0004714843234978616, -0.023987995460629463, -0.014483035542070866, -0.016594173386693, 0.008227800950407982, -0.10774417966604233, -0.03009626641869545, 0.03277778625488281, 0.03128354996442795, 0.04755278304219246, 0.06763651967048645, -0.043130502104759216, -0.03353254497051239, 0.006461389362812042, 0.034068647772073746, -0.06940289586782455, 0.01784314401447773, 0.03179381042718887, 0.005583799444139004, -0.0321941040456295, 0.002998132025822997, 0.027867427095770836, 0.0008853357867337763, -0.039051420986652374, 0.006706686690449715, -0.08875567466020584, 0.020238930359482765, 0.03110673278570175 ]
<p>I've been told to revise the derivation that proves $\frac{\mathrm{d}P}{\mathrm{d}r} =\frac{GM(r)p(r)}{r^2}$ where brackets indicate a function of, P is pressure and p is density. Rather helpfully he hasn't given us it to revise, so if anyone knows it I'd be really grateful. Thanks. </p>
g1551
[ 0.02648051828145981, -0.010683038271963596, -0.03133224695920944, -0.04691833630204201, 0.026900174096226692, 0.022906893864274025, 0.07198087126016617, -0.013072746805846691, -0.06361249089241028, -0.0015559657476842403, -0.028104811906814575, 0.01365096215158701, 0.008771865628659725, -0.019830171018838882, 0.02950415574014187, 0.035223592072725296, -0.0030306135304272175, 0.01608848012983799, -0.03120005503296852, -0.022438382729887962, -0.08217545598745346, -0.0434192530810833, 0.04880385100841522, -0.026746204122900963, 0.09531394392251968, -0.05587135627865791, 0.03031444363296032, 0.023188475519418716, -0.04773513600230217, 0.0003154205624014139, 0.023163044825196266, 0.04740489646792412, 0.03340344876050949, -0.03692632168531418, -0.06477586179971695, -0.03237420693039894, 0.040701307356357574, 0.04246983677148819, -0.006821314338594675, -0.0580323301255703, -0.0067869313061237335, -0.0027694522868841887, 0.01446319930255413, 0.014707343652844429, -0.018859071657061577, 0.006349294912070036, -0.08537214994430542, 0.0004885850939899683, -0.08516036719083786, 0.01182689517736435, 0.043521784245967865, 0.07601170241832733, 0.02143002487719059, -0.05809486657381058, -0.09699948132038116, 0.01960902288556099, -0.012242819182574749, -0.07014725357294083, 0.030916975811123848, 0.00975937768816948, -0.05119173228740692, 0.00773715740069747, -0.009051215834915638, -0.012655665166676044, -0.006596936844289303, -0.004138346761465073, 0.009868111461400986, -0.037697456777095795, 0.04658270627260208, 0.0049782926216721535, 0.011019705794751644, -0.03578033670783043, 0.0580458901822567, 0.014227606356143951, -0.0022950577549636364, -0.04406356066465378, 0.018298305571079254, 0.014788434840738773, 0.04197118058800697, -0.043411146849393845, 0.023736299946904182, -0.00611572340130806, 0.05186418816447258, -0.00423765042796731, 0.020181013271212578, -0.02796504832804203, 0.022098293527960777, 0.015520313754677773, 0.007250724360346794, 0.030281687155365944, 0.017939867451786995, -0.012151788920164108, 0.0034235708881169558, 0.018934987485408783, 0.014493581838905811, -0.0024070783983916044, -0.04960094764828682, -0.029129432514309883, -0.020129205659031868, 0.00601112050935626, 0.016607018187642097, -0.019230986014008522, 0.03438619524240494, 0.015357260592281818, 0.011526347137987614, 0.018786421045660973, 0.017783723771572113, 0.0020526000298559666, 0.023014960810542107, -0.07680030912160873, -0.024810267612338066, 0.04040391743183136, -0.03701874986290932, -0.017434032633900642, 0.0027107391506433487, -0.06156836450099945, 0.007740242872387171, 0.021567773073911667, -0.05457812920212746, 0.06876504421234131, 0.016061291098594666, -0.01490680780261755, 0.034090928733348846, 0.04962361603975296, -0.013824548572301865, 0.011278551071882248, -0.02298176847398281, 0.003596838563680649, 0.0722842812538147, 0.01464043091982603, -0.008168156258761883, 0.03771160915493965, 0.008364811539649963, -0.041796501725912094, -0.00500612985342741, -0.0017333475407212973, -0.04001912102103233, 0.02490176446735859, -0.027048146352171898, 0.004458798095583916, -0.0015356865478679538, -0.012922555208206177, -0.03823496773838997, -0.004593027755618095, 0.003168267197906971, -0.020014328882098198, 0.01741449348628521, 0.02100364863872528, 0.009048694744706154, 0.0025134002789855003, 0.023780684918165207, 0.04203426465392113, -0.004585376475006342, -0.021695705130696297, 0.04466182366013527, 0.04548797756433487, 0.027810445055365562, -0.033123645931482315, 0.01590699516236782, 0.0019368744688108563, 0.006374819204211235, -0.03525172546505928, -0.02031102031469345, 0.07253079116344452, -0.0006037375424057245, 0.05186210200190544, 0.02651945687830448, -0.07553481310606003, -0.0518982820212841, -0.037417490035295486, -0.0010747265769168735, 0.05998758226633072, 0.033585306257009506, -0.011064011603593826, -0.006522487848997116, 0.04030223190784454, -0.004915381316095591, -0.03161236643791199, 0.033320315182209015, 0.017690010368824005, 0.04808727651834488, -0.029824595898389816, 0.02114037424325943, -0.04024158790707588, 0.026200667023658752, -0.004610354546457529, 0.030448637902736664, -0.033442605286836624, -0.03470269963145256, -0.0012408675393089652, -0.03915325179696083, 0.05784346163272858, -0.006113232113420963, 0.0454406701028347, 0.030236631631851196, 0.04949689283967018, -0.006308660842478275, -0.06939106434583664, 0.007421507034450769, 0.09383474290370941, -0.03949999064207077, 0.008916685357689857, 0.08313219249248505, -0.026374749839305878, 0.04738370329141617, 0.03814562037587166, -0.013106117025017738, -0.02237963303923607, 0.03134642168879509, 0.049073271453380585, -0.011524135246872902, -0.08278188109397888, 0.02435942552983761, 0.017192034050822258, -0.009231222793459892, -0.09145043045282364, 0.014831023290753365, 0.043262239545583725, 0.021848957985639572, 0.004839942790567875, -0.08870972692966461, 0.047319088131189346, -0.018905164673924446, 0.04849905148148537, -0.02989155612885952, 0.015125692822039127, 0.016272230073809624, -0.005077427718788385, 0.0007880739285610616, 0.0014686265494674444, -0.05865568667650223, -0.011952906847000122, -0.06993323564529419, -0.009947240352630615, 0.030341321602463722, 0.03351446986198425, -0.0604734867811203, -0.051871541887521744, 0.02187957800924778, -0.0038875797763466835, -0.05294666811823845, -0.0042055160738527775, -0.029898671433329582, -0.008206415921449661, 0.007912938483059406, 0.02062743343412876, 0.05222659185528755, 0.07010889053344727, 0.06412806361913681, 0.0005362883093766868, -0.0035834917798638344, 0.04550415650010109, -0.0026777286548167467, 0.010307610966265202, 0.010471006855368614, -0.004542096983641386, -0.033002570271492004, -0.03150596842169762, 0.08068867772817612, -0.054311756044626236, -0.014216823503375053, -0.04495924711227417, -0.036525025963783264, 0.03113214112818241, -0.11258160322904587, 0.03150219842791557, 0.0012080767191946507, -0.009000989608466625, 0.058195095509290695, 0.042711060494184494, 0.04858950898051262, -0.014796051196753979, 0.0371105782687664, 0.03196682408452034, -0.04607906565070152, -0.02827633172273636, 0.0111860865727067, -0.014629988931119442, -0.009096791967749596, 0.02920590341091156, 0.0574420802295208, -0.02265756204724312, 0.01940276101231575, 0.026234684512019157, 0.037600353360176086, -0.03364481031894684, 0.016630886122584343, 0.012505747377872467, 0.010525364428758621, 0.04144613444805145, 0.03326515108346939, -0.008858160115778446, -0.004988022148609161, -0.018800614401698112, -0.028250759467482567, 0.0382523275911808, 0.006526040844619274, -0.05696508288383484, 0.0026623958256095648, -0.0010613430058583617, 0.02248874306678772, -0.021681275218725204, -0.0019348778296262026, 0.021054476499557495, -0.008195745758712292, -0.015000246465206146, -0.00666239857673645, 0.03880240395665169, -0.005125134717673063, -0.03525794669985771, 0.021102668717503548, 0.00008761807839618996, 0.005348420701920986, -0.017324097454547882, -0.0027420225087553263, -0.0387767031788826, 0.027821028605103493, -0.0036220115143805742, -0.004500962793827057, -0.005151920951902866, -0.014457007870078087, -0.00093148770974949, 0.00010662584827514365, -0.028655990958213806, -0.00261694542132318, 0.022129205986857414, -0.07318603992462158, -0.009184345602989197, -0.003975075203925371, -0.04875017702579498, 0.04499368369579315, -0.0019993579480797052, -0.003002801211550832, -0.0418977364897728, -0.062487468123435974, -0.035328906029462814, -0.015726527199149132, 0.0772632509469986, 0.003347654826939106, -0.03555014356970787, 0.007771763484925032, -0.012956416234374046, -0.0005123570444993675, -0.003946223296225071, -0.028325388208031654, 0.020091362297534943, -0.010974937118589878, 0.03941839933395386, 0.026993706822395325, 0.025533560663461685, -0.04032012075185776, -0.027730943635106087, 0.026919368654489517, -0.000539202825166285, 0.02867971919476986, 0.014238812029361725, 0.043939195573329926, 0.008890433236956596, -0.010905456729233265, -0.019100431352853775, 0.021175140514969826, -0.06334557384252548, 0.015350161120295525, 0.05969288572669029, 0.033114850521087646, -0.021946974098682404, 0.0424705445766449, 0.016412148252129555, -0.05758103355765343, -0.01686237007379532, 0.011865939944982529, -0.07837045937776566, 0.05807759240269661, 0.06517140567302704, 0.052108973264694214, -0.037794798612594604, -0.023154906928539276, 0.005298807751387358, -0.0035606129094958305, 0.07166410237550735, 0.04181543365120888, -0.013240950182080269, 0.034545186907052994, 0.024505624547600746, 0.005672837141901255, 0.025024503469467163, -0.05587492883205414, 0.02148684486746788, 0.01048376876860857, -0.00954595860093832, 0.007653149776160717, -0.009398315101861954, -0.02845994383096695, 0.03998996689915657, -0.010862739756703377, -0.018406594172120094, 0.012394586578011513, 0.05221837759017944, -0.06087317690253258, 0.033598482608795166, -0.047008972615003586, -0.042410679161548615, 0.0332341305911541, -0.03505527228116989, -0.04830249026417732, -0.018687576055526733, 0.005719961132854223, -0.049155447632074356, 0.03004971705377102, 0.005625048186630011, -0.007688230834901333, -0.06390393525362015, 0.02090809866786003, 0.008988650515675545, 0.013302247039973736, -0.009675680659711361, 0.019498668611049652, 0.026098808273673058, 0.03510598465800285, 0.005960918962955475, 0.008577356114983559, -0.00016203755512833595, 0.02153598703444004, -0.009287470951676369, 0.050232384353876114, 0.059847671538591385, 0.048928771167993546, -0.010328834876418114, -0.008839148096740246, -0.02357325330376625, 0.04385592043399811, -0.02362031675875187, -0.04595768824219704, 0.0037317676469683647, -0.05601740628480911, 0.06144870072603226, -0.04383590817451477, -0.016698600724339485, -0.05320047214627266, 0.05852143093943596, 0.017448004335165024, -0.018137702718377113, 0.01926177740097046, 0.01474368292838335, 0.048083677887916565, 0.005092645063996315, 0.020109646022319794, -0.02912304922938347, 0.03136781230568886, 0.06015437841415405, 0.010802756994962692, 0.0004378811572678387, 0.051813606172800064, -0.01731267385184765, 0.07352432608604431, -0.012562504969537258, -0.004788023419678211, -0.04459714516997337, -0.02964038774371147, -0.010381189174950123, -0.028836075216531754, 0.019815737381577492, -0.02305891551077366, 0.02733376994729042, -0.006546431221067905, 0.016904672607779503, -0.046900346875190735, 0.004640647675842047, 0.0136281568557024, -0.017931891605257988, -0.03382040187716484, -0.013301659375429153, -0.056578636169433594, -0.02929227612912655, 0.022921226918697357, 0.04075552523136139, 0.014762534759938717, -0.03040677309036255, 0.02945576049387455, -0.0546085499227047, 0.0030652149580419064, 0.022770337760448456, -0.01238268706947565, -0.011196543462574482, 0.010568967089056969, 0.05943508446216583, 0.00028996748733334243, -0.015246960334479809, -0.06037207320332527, -0.04044639319181442, -0.006468739826232195, -0.030961306765675545, -0.02886359579861164, 0.02339857816696167, -0.021859778091311455, 0.01781822368502617, 0.0176504198461771, -0.005939052440226078, 0.02230275794863701, 0.014720840379595757, -0.055647555738687515, -0.01234898716211319, 0.03141041100025177, -0.006104236003011465, -0.02398049831390381, 0.07415971904993057, 0.0641169548034668, -0.006756934337317944, -0.013475324027240276, 0.0475768968462944, -0.01559300534427166, -0.0207737497985363, 0.07915332168340683, 0.013084614649415016, -0.015566850081086159, 0.003972596954554319, -0.05144510790705681, -0.029131650924682617, -0.0068786959163844585, -0.06906760483980179, 0.04836291819810867, -0.04358875751495361, 0.06857173889875412, -0.04023565351963043, -0.007896849885582924, 0.01856229081749916, -0.06412027776241302, -0.060876552015542984, 0.017094917595386505, 0.015352482907474041, -0.035863298922777176, -0.052688777446746826, 0.040600672364234924, -0.006261995527893305, -0.07097899913787842, -0.0485471710562706, -0.054819025099277496, 0.01893739588558674, 0.0656837746500969, -0.06518635153770447, 0.019921086728572845, 0.03713241219520569, -0.009526929818093777, 0.04095527157187462, -0.07994405925273895, 0.0169074684381485, 0.0032074085902422667, -0.012406239286065102, 0.03087640181183815, -0.02656366117298603, -0.01562112383544445, 0.00039020422264002264, -0.04668596014380455, -0.033869341015815735, 0.03844060003757477, -0.0012986627407371998, 0.006313304416835308, -0.04075101017951965, -0.01781420037150383, 0.04318590462207794, -0.03997515141963959, -0.024441206827759743, -0.048952553421258926, 0.00894062127918005, -0.030431542545557022, -0.08420053869485855, 0.02161799930036068, 0.024517327547073364, 0.027168070897459984, -0.002283307258039713, -0.011900385841727257, 0.05130986496806145, 0.02464120090007782, 0.04173947125673294, 0.04324391111731529, -0.00034364720340818167, -0.012921048328280449, -0.048090074211359024, 0.011470370925962925, -0.054018836468458176, -0.026683753356337547, 0.027407033368945122, 0.058034755289554596, -0.013129575178027153, -0.05105062201619148, 0.02513490431010723, 0.009062436409294605, -0.011595692485570908, 0.021717647090554237, 0.027693476527929306, -0.004826318938285112, 0.046262506395578384, -0.036730676889419556, 0.007537536323070526, 0.004610228817909956, -0.03418737277388573, 0.03800485283136368, 0.07978102564811707, 0.07596743851900101, -0.012220066040754318, 0.03655299171805382, 0.06633642315864563, -0.000015214036466204561, -0.07380405813455582, 0.03133831173181534, -0.02440851926803589, -0.03421616926789284, 0.010910127311944962, -0.056596964597702026, 0.01005446258932352, 0.008092197589576244, 0.02089737541973591, 0.051232919096946716, 0.01573055051267147, 0.07014156877994537, -0.034715957939624786, -0.0038604955188930035, 0.08919493854045868, 0.007436385378241539, -0.018903791904449463, 0.061980776488780975, 0.012862219475209713, 0.0022668326273560524, -0.0627656951546669, -0.00607910193502903, 0.032871901988983154, -0.0012186848325654864, -0.049982063472270966, 0.023259034380316734, 0.015924125909805298, -0.006592539604753256, 0.01808708906173706, -0.008899879641830921, -0.013470199890434742, -0.014784500934183598, 0.04674218222498894, -0.024704497307538986, 0.052675023674964905, 0.03957401588559151, 0.042861320078372955, -0.028385503217577934, -0.015048530884087086, -0.027088329195976257, -0.028472665697336197, -0.04659479483962059, -0.06874214112758636, 0.0681840106844902, -0.017969438806176186, -0.06649395078420639, 0.018838807940483093, 0.06030640751123428, 0.0423734188079834, -0.0031567157711833715, 0.060084473341703415, -0.0364641435444355, 0.0010304814204573631, -0.010970886796712875, 0.02782214991748333, 0.018311413004994392, -0.032992757856845856, -0.022613046690821648, 0.020901618525385857, 0.009481282904744148, 0.028983980417251587, -0.06013607978820801, 0.004835769534111023, -0.014214645139873028, -0.05308648198843002, -0.0028100688941776752, -0.03138954937458038, 0.0442214235663414, -0.02276461198925972, -0.005746763665229082, 0.0016020863549783826, -0.03876946493983269, 0.05915259197354317, 0.005199627950787544, 0.016078591346740723, 0.005731811281293631, 0.029566513374447823, 0.017358161509037018, 0.0072524407878518105, -0.015374536626040936, -0.09427595883607864, -0.028358908370137215, 0.002330801449716091, 0.007972180843353271, -0.04522452503442764, -0.0003688535944093019, 0.0826784074306488, -0.017350967973470688, 0.001327713718637824, 0.01762237958610058, 0.03826852887868881, -0.03533022105693817, -0.016973471269011497, 0.027277447283267975, -0.029060205444693565, 0.01954825595021248, -0.023289086297154427, 0.018459705635905266, -0.03651362657546997, -0.08475367724895477, -0.04531542956829071, -0.024202194064855576, -0.00847628340125084, 0.021260900422930717, 0.015565753914415836, -0.013287706300616264, -0.03424156829714775, 0.06717592477798462, -0.08684515208005905, -0.07223434746265411, -0.019818609580397606, 0.05089893564581871, 0.036790236830711365, -0.04577629268169403, -0.00038598282844759524, 0.005960919428616762, -0.07399781793355942, 0.002840573899447918, -0.04049167409539223, -0.03458312526345253, -0.09974971413612366, -0.046725671738386154, -0.025145474821329117, -0.048931825906038284, -0.00005583142410614528, 0.04992585629224777, 0.03740961104631424, -0.020375335589051247, -0.025889180600643158, -0.0011189824435859919, 0.030995631590485573, 0.012932601384818554, 0.005054181441664696, 0.028256110846996307, -0.010765234008431435, 0.06727277487516403, 0.01367965154349804, -0.019726527854800224, -0.014197064563632011, 0.040704332292079926, -0.02618662267923355, 0.04668683558702469, -0.03203963488340378, -0.044950976967811584, 0.03557926416397095, 0.04776182025671005, -0.0432993583381176, -0.005982321221381426, 0.03550785034894943, -0.02279573492705822, -0.05407166853547096, -0.002766205230727792, -0.06729473918676376, 0.02101803943514824, 0.0473410002887249, 0.06846842169761658, -0.006385960150510073, 0.06232934817671776, 0.006207003258168697, 0.030721960589289665, -0.010305856354534626, -0.002049496164545417, 0.00888690073043108, -0.0030634505674242973, 0.014451870694756508 ]
<p>With all the recent discoveries of supermassive black holes being at the center of nearly every galaxy, and the proposed "at least one planet" around (probably) every star.</p> <p>Does this affect the estimated total mass of our universe?</p> <p>Is Dark Matter necessary when planets and black holes are included in the calculation?</p>
g1552
[ 0.0055452315136790276, 0.015843715518712997, 0.01087905466556549, -0.0037186734843999147, 0.03274763748049736, 0.02802390791475773, -0.02310379222035408, 0.045942146331071854, 0.015841929242014885, -0.034101732075214386, 0.01618051342666149, -0.06516142934560776, 0.004506635945290327, 0.04817593842744827, -0.03186926618218422, -0.004853866528719664, -0.04424169287085533, -0.028536081314086914, -0.014100245200097561, 0.010475937277078629, -0.0019091333961114287, -0.05759614706039429, 0.01536592561751604, -0.07448586076498032, -0.014117940329015255, -0.004426306113600731, 0.045954395085573196, -0.016159338876605034, -0.02358928695321083, 0.045848023146390915, -0.00451638363301754, -0.0059605930000543594, -0.04057316854596138, 0.009270470589399338, -0.01097430381923914, -0.05135752260684967, 0.019522925838828087, 0.0106987114995718, 0.033184297382831573, -0.054368529468774796, 0.02183474786579609, -0.02335815317928791, -0.005576093215495348, -0.00037494298885576427, -0.04970113933086395, 0.0024216475430876017, -0.03470453992486, 0.010646582581102848, 0.022099317982792854, -0.005938038229942322, -0.003946604672819376, -0.04961474612355232, 0.048345018178224564, 0.03392363339662552, -0.03280293568968773, 0.04290948063135147, 0.012585463002324104, -0.05800550803542137, 0.003916524350643158, 0.00532749155536294, -0.01181353535503149, -0.007295970804989338, -0.0005689045647159219, 0.008584382012486458, -0.016192371025681496, 0.02338181436061859, -0.03788115456700325, -0.02185010351240635, -0.018794720992445946, -0.013263313099741936, 0.02484964393079281, 0.016524922102689743, 0.04735325276851654, -0.02605573460459709, -0.03089536540210247, 0.07902101427316666, -0.029812274500727654, 0.012907776050269604, -0.045422572642564774, 0.015556812286376953, 0.012148477137088776, -0.05490687116980553, 0.0955321341753006, 0.002091670408844948, 0.026908209547400475, -0.04311143606901169, -0.03074933961033821, -0.01765088364481926, -0.01117080170661211, 0.034628573805093765, 0.03980636969208717, 0.0009592819260433316, 0.04008757695555687, -0.00954399537295103, 0.05435069650411606, 0.04928242787718773, -0.01032137032598257, 0.020310644060373306, 0.005870357155799866, 0.029111240059137344, -0.06942213326692581, 0.05645160749554634, -0.018215935677289963, -0.04962877184152603, 0.038832493126392365, 0.014942722395062447, 0.03544621914625168, -0.008579963818192482, 0.014179346151649952, -0.008060978725552559, -0.05017271265387535, -0.04907822608947754, -0.010092901065945625, 0.0052185142412781715, -0.10510940104722977, -0.05861850827932358, 0.06798243522644043, -0.03790990635752678, -0.0029162310529500246, 0.02583743818104267, -0.004210885614156723, 0.002088935347273946, 0.05585567653179169, 0.008656108751893044, -0.010458186268806458, -0.1239500343799591, -0.028203178197145462, 0.007303269580006599, 0.01663210615515709, -0.06051076203584671, -0.01684807986021042, 0.010562371462583542, 0.01278992835432291, 0.042220909148454666, -0.012263021431863308, 0.003436032449826598, -0.029795082286000252, 0.033629849553108215, -0.039303723722696304, 0.026446301490068436, 0.02473375014960766, 0.039117224514484406, 0.022109342738986015, 0.022195791825652122, -0.029185641556978226, -0.0029135835357010365, -0.061255477368831635, -0.009749776683747768, -0.004446843639016151, -0.05413752421736717, 0.032497406005859375, 0.01356506533920765, 0.011150659061968327, -0.03687671199440956, -0.008332308381795883, 0.01467280462384224, -0.00888026412576437, 0.006617785431444645, 0.002634103875607252, -0.017833586782217026, 0.04598376899957657, -0.03325868770480156, -0.0022978789638727903, 0.00147704454138875, 0.010963916778564453, -0.008390405215322971, -0.03359440714120865, -0.05247775837779045, -0.02600979618728161, 0.02297883667051792, -0.009672047570347786, 0.05527140572667122, -0.01583111472427845, -0.009771435521543026, 0.04755501449108124, -0.016745494678616524, 0.05706895515322685, -0.046773817390203476, -0.034886330366134644, 0.03373187407851219, 0.031847964972257614, -0.004465373698621988, -0.028474759310483932, -0.035976607352495193, -0.013482647016644478, -0.043525490909814835, 0.010019234381616116, 0.02985248900949955, 0.02169698290526867, 0.05298595130443573, -0.024513375014066696, 0.06170304864645004, 0.09270112961530685, 0.05865715444087982, 0.016754858195781708, -0.0019240546971559525, 0.024898715317249298, 0.042683154344558716, 0.000981185119599104, 0.015817418694496155, 0.0030890856869518757, 0.023749113082885742, -0.04339766874909401, -0.05184435844421387, 0.030385697260499, -0.006492171436548233, -0.020912542939186096, 0.05163968726992607, 0.02312910184264183, -0.01719120889902115, 0.05362962558865547, 0.016947612166404724, -0.002670304151251912, 0.014682663604617119, -0.05821054428815842, 0.040113527327775955, -0.0430590994656086, 0.05285898968577385, 0.025826964527368546, 0.030342023819684982, -0.047555796802043915, 0.00009325958671979606, -0.02967587672173977, 0.016313830390572548, 0.018734224140644073, 0.025266112759709358, -0.004749082028865814, -0.04878383129835129, 0.01115960069000721, -0.007295313291251659, -0.013931344263255596, -0.009265118278563023, 0.04740258306264877, 0.029801350086927414, 0.06939836591482162, 0.01529299933463335, 0.029925039038062096, -0.038233932107686996, -0.0022261100821197033, 0.05671730637550354, 0.038823001086711884, -0.03403135761618614, -0.032295212149620056, 0.03544450178742409, 0.019432343542575836, -0.01535067055374384, -0.012933256104588509, -0.045001838356256485, -0.038664840161800385, 0.029044346883893013, -0.04797741025686264, -0.016748493537306786, 0.028787557035684586, -0.0491342693567276, 0.007049177773296833, -0.00666318042203784, -0.002358753001317382, 0.04104568809270859, -0.05177350714802742, 0.021520527079701424, 0.06349194049835205, -0.0490131676197052, -0.0023882249370217323, 0.002510315738618374, -0.038792118430137634, -0.00324835442006588, -0.05859429016709328, -0.041901785880327225, 0.030576450750231743, 0.031098077073693275, 0.03522220626473427, -0.03381374478340149, 0.0385778471827507, -0.01863826811313629, 0.012280619703233242, 0.04937858134508133, -0.027566611766815186, 0.0016014358261600137, 0.07194077968597412, 0.02827027067542076, -0.0025345096364617348, 0.005895914044231176, -0.07859456539154053, 0.003916750196367502, 0.005353685002774, -0.027210835367441177, -0.0711570456624031, -0.05803539976477623, -0.025410234928131104, -0.031636737287044525, 0.05796542018651962, 0.03879600763320923, 0.03336210548877716, 0.051678597927093506, 0.07012732326984406, 0.044178109616041183, 0.03182283043861389, 0.03151120990514755, 0.006466764956712723, -0.027421148493885994, 0.04283370077610016, -0.005374387372285128, 0.011518953368067741, 0.020733365789055824, -0.000732945220079273, 0.04943076893687248, -0.02856704592704773, 0.006370768882334232, 0.04872339218854904, -0.07590080797672272, 0.03236684948205948, 0.05879843980073929, 0.03896349295973778, 0.09830275923013687, -0.0026986694429069757, 0.00950224045664072, 0.029206758365035057, -0.023006586357951164, -0.02447751723229885, 0.05829748138785362, -0.006815736182034016, 0.02927439659833908, -0.01605316810309887, -0.019743984565138817, 0.038399551063776016, 0.05827092006802559, 0.006894110236316919, -0.022660519927740097, -0.08244983106851578, 0.01898919977247715, 0.013456445187330246, -0.019483791664242744, -0.048890650272369385, 0.08556073904037476, -0.0635095164179802, 0.029991762712597847, 0.02848551608622074, -0.05070945620536804, 0.027422232553362846, 0.034643273800611496, 0.0004190196341369301, -0.027767829596996307, -0.023698879405856133, 0.006303863134235144, 0.016102716326713562, 0.04581848904490471, -0.026706168428063393, -0.07625053822994232, 0.003324685152620077, -0.063267782330513, 0.010771488770842552, 0.01950584538280964, 0.007460610009729862, 0.03111490234732628, 0.040481071919202805, 0.014623675495386124, 0.029831888154149055, 0.047446198761463165, 0.013080489821732044, -0.001257437514141202, 0.018640920519828796, -0.015834501013159752, -0.01869346760213375, -0.0032082453835755587, 0.028354475274682045, -0.026011252775788307, 0.0008800691575743258, -0.07000482827425003, -0.020084599032998085, -0.0202769972383976, -0.021174892783164978, 0.015118761919438839, -0.009811336174607277, -0.03468891978263855, 0.029571933671832085, -0.007379128132015467, 0.05340888351202011, 0.051509540528059006, 0.008635448291897774, 0.0299544595181942, 0.03472231328487396, 0.05175047367811203, -0.0002206058125011623, 0.0036111322697252035, -0.02583421766757965, -0.024756500497460365, -0.0034013683907687664, -0.05838550254702568, 0.01679433509707451, -0.07079958915710449, 0.014329535886645317, -0.058164507150650024, 0.022465823218226433, -0.03730246424674988, 0.0026103334967046976, -0.01817876286804676, 0.006882013287395239, -0.015839016065001488, 0.08447469770908356, 0.021952999755740166, 0.03547152504324913, -0.02506130188703537, 0.03884917497634888, -0.013829242438077927, 0.04210580140352249, 0.03430929780006409, 0.017539318650960922, -0.031886544078588486, -0.0006154724396765232, -0.00680380966514349, 0.02318856120109558, 0.02142970822751522, -0.015910351648926735, 0.035709723830223083, 0.04138537868857384, 0.0037624239921569824, -0.011382805183529854, -0.05035584792494774, -0.008240475319325924, -0.0025160794612020254, 0.007726113311946392, -0.011508239433169365, -0.07310266047716141, -0.02143235318362713, -0.02101428247988224, 0.0035193199291825294, -0.013025844469666481, -0.06086847186088562, 0.0031905346550047398, 0.057475700974464417, 0.026876704767346382, -0.008952031843364239, 0.04270394518971443, 0.04872691258788109, -0.009187211282551289, 0.03752954676747322, 0.0426996573805809, 0.008230593986809254, -0.0009221331565640867, -0.038598496466875076, 0.011637932620942593, -0.010539037175476551, -0.050233688205480576, -0.005484532564878464, 0.0073822010308504105, 0.01452989038079977, -0.04630599543452263, -0.025254128500819206, -0.013448463752865791, 0.004223096650093794, -0.051436956971883774, 0.006386220455169678, -0.005253934767097235, -0.03333429619669914, -0.038566991686820984, 0.03924435004591942, -0.00337949488312006, 0.07048109173774719, -0.05628436803817749, 0.03121880069375038, -0.06732193380594254, 0.027050277218222618, -0.006972531322389841, 0.06666730344295502, 0.0471661277115345, -0.07457317411899567, -0.023130152374505997, -0.02451462112367153, -0.03906361386179924, 0.012140298262238503, -0.03926416486501694, -0.005927813705056906, 0.018339741975069046, 0.045241888612508774, -0.049130942672491074, -0.012828809209167957, -0.06992295384407043, -0.07372366636991501, -0.000620074279140681, -0.008833503350615501, -0.0032500613015145063, 0.00959848053753376, 0.06799633800983429, -0.00431530736386776, 0.004002625588327646, 0.09499697387218475, -0.04684925079345703, -0.010820343159139156, -0.047788798809051514, -0.0002371304581174627, -0.03092133440077305, -0.03545781970024109, 0.041132569313049316, -0.025023864582180977, -0.04231516271829605, 0.05468070134520531, -0.021458225324749947, -0.1038631871342659, -0.02862883359193802, 0.04662621021270752, 0.029777711257338524, 0.10619465261697769, 0.02844930626451969, -0.038393378257751465, -0.025268202647566795, 0.004703714977949858, -0.05854753404855728, -0.00787053070962429, 0.04053553193807602, -0.0040529887191951275, 0.024789420887827873, 0.01166292279958725, -0.015964707359671593, 0.04295707866549492, -0.028349973261356354, -0.08396194875240326, 0.04694792255759239, 0.011513660661876202, 0.03325205296278, -0.028724856674671173, -0.023308565840125084, -0.035525623708963394, 0.02648984082043171, 0.047845639288425446, 0.07424819469451904, -0.002816458698362112, -0.010472269728779793, 0.002454242669045925, 0.02470576949417591, -0.010854285210371017, 0.04959879443049431, -0.036270223557949066, 0.0536302775144577, -0.036045871675014496, 0.03269018232822418, -0.013684708625078201, -0.010545235127210617, 0.01336455624550581, 0.07910170406103134, 0.00875716470181942, 0.008336938917636871, -0.00029720974271185696, 0.0638466328382492, 0.021401777863502502, 0.04843365401029587, -0.003405826399102807, -0.001793421688489616, 0.02294284477829933, 0.010120349936187267, -0.07019494473934174, -0.01405299175530672, 0.07030510157346725, 0.01259465143084526, 0.045023221522569656, -0.057114969938993454, 0.056101854890584946, 0.006556582637131214, 0.010012106969952583, -0.008855856955051422, -0.031717583537101746, -0.049591097980737686, 0.0017904307460412383, -0.008356956765055656, 0.013881920836865902, -0.03863753005862236, 0.004966733977198601, 0.03553000092506409, -0.038853008300065994, 0.0038713158573955297, -0.09827399253845215, -0.012627306394279003, -0.02352319471538067, -0.04377097263932228, -0.01851649396121502, -0.013742775656282902, 0.014682925306260586, -0.0356769934296608, -0.005585620645433664, 0.002210243372246623, -0.03874998167157173, 0.03989521786570549, -0.050133492797613144, 0.037306420505046844, -0.07767646759748459, 0.062332384288311005, -0.0013884671498090029, -0.06749733537435532, 0.0686943382024765, -0.00005325265374267474, -0.03037005104124546, 0.03849545121192932, 0.0173569954931736, 0.030752327293157578, 0.0033820990938693285, -0.06473449617624283, -0.03168993070721626, -0.004993318580091, -0.018929682672023773, 0.013588955625891685, -0.043176304548978806, 0.011933498084545135, 0.027277417480945587, 0.04090956971049309, -0.0028353938832879066, 0.040660228580236435, -0.04655229672789574, -0.045389559119939804, -0.007206448353827, 0.04738238826394081, 0.01531577855348587, 0.05018661171197891, -0.03822341933846474, -0.020542260259389877, 0.03377188742160797, -0.013100738637149334, -0.025102632120251656, -0.04681042954325676, -0.022891519591212273, -0.013959801755845547, -0.017690366134047508, 0.01762327551841736, 0.037277426570653915, -0.019002022221684456, -0.0652194395661354, 0.042353998869657516, 0.011331943795084953, -0.014154239557683468, 0.020436499267816544, 0.030710594728589058, 0.03190220147371292, 0.0269462950527668, 0.04695864021778107, 0.004066576715558767, -0.006057131104171276, -0.014803105965256691, 0.050505563616752625, 0.04466515779495239, 0.013997857458889484, 0.009632889181375504, -0.03341606259346008, -0.021631840616464615, -0.0943896472454071, -0.0034417049027979374, 0.05420534312725067, -0.013413424603641033, -0.011232457123696804, 0.04594147205352783, 0.019148055464029312, -0.009556785225868225, 0.011585792526602745, -0.02772710658609867, -0.06026817113161087, -0.015406865626573563, 0.03188195452094078, -0.03705950826406479, -0.03466300293803215, -0.01897161640226841, -0.024268003180623055, -0.014963855035603046, 0.005432088393718004, 0.003581713419407606, -0.04072337597608566, -0.05345362797379494, -0.056496091187000275, 0.02503592148423195, -0.0019930393900722265, 0.06137986481189728, 0.009448107331991196, -0.03528689220547676, 0.004984146915376186, -0.0013506632531061769, -0.021315058693289757, -0.08890128880739212, -0.0037963660433888435, 0.01497064158320427, -0.048590037971735, -0.029354089871048927, -0.06997624784708023, -0.0043680304661393166, 0.018576616421341896, 0.055544838309288025, 0.0018789825262501836, -0.039601974189281464, 0.05573304370045662, -0.02580721490085125, 0.013548699207603931, 0.00852158572524786, -0.024721378460526466, 0.003236308228224516, -0.02290402725338936, 0.03675318881869316, -0.028309384360909462, 0.016565343365073204, -0.002839029999449849, -0.017600692808628082, 0.021250156685709953, 0.05234941467642784, 0.09008437395095825, 0.028381390497088432, -0.017056182026863098, -0.05301975458860397, -0.030622098594903946, 0.00777631439268589, 0.009469578042626381, 0.0473041906952858, 0.06898022443056107, -0.023843884468078613, 0.014639820903539658, -0.005904538091272116, 0.017385827377438545, 0.06854897737503052, 0.0069371480494737625, -0.023487422615289688, 0.009358123876154423, -0.023725522682070732, -0.029156534001231194, 0.03165002539753914, -0.029745958745479584, -0.03443010523915291, -0.04628531634807587, -0.019385408610105515, 0.005854576826095581, 0.023905517533421516, -0.018040090799331665, -0.011948850005865097, -0.020849820226430893, -0.004814453423023224, 0.05962713062763214, -0.01315240003168583, -0.01892434060573578, 0.011230682022869587, 0.017604392021894455, -0.039547398686409, 0.007770083379000425, -0.006574478466063738, -0.029207807034254074, 0.025271756574511528, -0.001293358625844121, -0.02310384437441826, -0.007606993429362774, -0.0010191391920670867, -0.09457653760910034, 0.04415585845708847, 0.011323124170303345, -0.009864513762295246, -0.03125516697764397, -0.030838703736662865, -0.017149100080132484, 0.05210909619927406, 0.06140528991818428, -0.03182597458362579, 0.004190067760646343, 0.018393976613879204, 0.021903621032834053, -0.03196762874722481, -0.019939573481678963, -0.01502638217061758, -0.09358489513397217, -0.09479866176843643, 0.04100165516138077, 0.04017525911331177, 0.010634264908730984, 0.02497801184654236, -0.01441937405616045, 0.039577025920152664, -0.008568312041461468, 0.051885735243558884, 0.024638373404741287 ]
<p>An object of mass m is slowly lowered into a black hole of mass 1000 m. Is the amount of braking energy larger than $0.6 mc^2$? </p> <p>Now what if, after lowering the mass close to the event horizon, we wait the black hole to shrink to mass 100 m, by emitting Hawking radiation, and then we lower the mass some more? Is the braking energy of the second lowering process larger than $0.5 mc^2$? </p> <p>I wonder can we extract more than $E=mc^2$ energy from mass m?</p> <p>(In this thought experiment we use a wire and a winch, or anything that works)</p>
g1553
[ 0.019282815977931023, 0.021884018555283546, 0.0391804464161396, 0.018225770443677902, -0.00939443614333868, 0.010952262207865715, 0.025958778336644173, 0.07213477045297623, -0.0576293021440506, -0.014950239099562168, -0.016445700079202652, 0.006324961315840483, 0.00048809245345182717, 0.023822667077183723, 0.016246968880295753, 0.004253391642123461, 0.05873766541481018, -0.06090608984231949, 0.004789539147168398, 0.006227539386600256, -0.004451674874871969, 0.018530502915382385, -0.008362972177565098, -0.022573215886950493, -0.015408802777528763, 0.015100915916264057, 0.017762739211320877, 0.04817117378115654, -0.049597982317209244, 0.0218758974224329, 0.031057702377438545, -0.015250897035002708, 0.003906375262886286, -0.017935989424586296, -0.052603527903556824, -0.007313352543860674, 0.049101121723651886, 0.025011355057358742, -0.02823726274073124, 0.04815589264035225, 0.049469172954559326, -0.07249635457992554, 0.04849676787853241, 0.001993732526898384, 0.04218218848109245, -0.04055861011147499, 0.03813272342085838, -0.03096858039498329, 0.01999479904770851, -0.02168232575058937, 0.03930538520216942, 0.019759658724069595, 0.03955014795064926, 0.0362764336168766, 0.016955537721514702, 0.021495142951607704, -0.016200263053178787, -0.04258819296956062, 0.03571547195315361, 0.017698654904961586, -0.029765551909804344, -0.008834900334477425, 0.034508660435676575, -0.01444549672305584, 0.05871337279677391, -0.023247724398970604, -0.06712005287408829, -0.010002288036048412, 0.009844760410487652, 0.039155714213848114, 0.018824901431798935, 0.01818954572081566, -0.030378183349967003, -0.02543828636407852, 0.007991115562617779, 0.030265163630247116, 0.007254014257341623, 0.005461281631141901, 0.010090136900544167, 0.0019748848862946033, -0.04830263555049896, -0.03231652081012726, 0.027462827041745186, 0.05268145725131035, 0.07298943400382996, 0.01066617388278246, -0.03426480293273926, 0.04108985885977745, -0.0299075860530138, 0.0460442416369915, 0.059269074350595474, -0.02248801477253437, 0.06719692796468735, -0.005965124350041151, 0.03257981315255165, 0.019430868327617645, -0.0014011274324730039, 0.049431655555963516, -0.026096602901816368, 0.02318137139081955, -0.034455958753824234, -0.013234111480414867, 0.0006424603634513915, -0.0116183552891016, 0.022304465994238853, -0.023151637986302376, -0.021255647763609886, 0.014120802283287048, -0.006159380543977022, 0.0548119843006134, 0.0054264855571091175, -0.11386275291442871, -0.02548833005130291, -0.04480794072151184, -0.08618564158678055, -0.03244846314191818, 0.0821123793721199, -0.01282585971057415, -0.09749919176101685, 0.02281278558075428, -0.014712048694491386, 0.003014258574694395, -0.030859852209687233, 0.04192142188549042, 0.04160555079579353, -0.032522521913051605, -0.02884645387530327, 0.021403737366199493, 0.016996776685118675, -0.007797707803547382, -0.006608795374631882, 0.010718823410570621, 0.02295491099357605, 0.014122853986918926, -0.04144493117928505, 0.03044239804148674, -0.023562733083963394, 0.013106424361467361, 0.020246589556336403, -0.020012717694044113, 0.01408624928444624, -0.006937600206583738, -0.010420171543955803, 0.017902350053191185, -0.032321035861968994, 0.07227418571710587, -0.04297221079468727, 0.014411162585020065, 0.0026129947509616613, 0.024006055667996407, -0.00165939808357507, 0.03941575437784195, 0.010167314670979977, -0.061960507184267044, 0.04336908087134361, 0.05490230768918991, 0.053134169429540634, 0.02500683069229126, 0.014605220407247543, 0.0605153813958168, 0.04880816489458084, -0.020646505057811737, 0.051737915724515915, 0.03215985372662544, -0.06513726711273193, 0.05654986575245857, 0.011407251469790936, 0.0039142705500125885, 0.04897090420126915, -0.00769363297149539, -0.044774141162633896, -0.05504561960697174, 0.027947964146733284, 0.07522660493850708, -0.006998495664447546, 0.00006493806722573936, 0.049976449459791183, -0.037924062460660934, -0.07402569055557251, 0.02000339701771736, 0.022970907390117645, -0.0016652120975777507, -0.018178807571530342, 0.008711361326277256, 0.09061426669359207, -0.03299890086054802, 0.03274014592170715, 0.05761367082595825, 0.027483999729156494, 0.0013712870422750711, -0.044658362865448, -0.051859479397535324, 0.03864704817533493, 0.021003099158406258, 0.015721386298537254, 0.00030326846172101796, 0.020676249638199806, -0.014766337350010872, 0.005976774264127016, 0.061854287981987, -0.002637149067595601, 0.0038505946286022663, -0.057391390204429626, -0.008568210527300835, 0.03346334770321846, -0.01455239299684763, 0.03378891572356224, -0.02558254823088646, -0.005694904830306768, -0.04499821737408638, 0.039376214146614075, 0.013404295779764652, 0.01508066151291132, -0.03417167812585831, -0.05189596116542816, 0.04273364320397377, -0.01563829556107521, 0.03729182481765747, 0.03766034543514252, 0.009803486056625843, -0.041831716895103455, -0.004445705562829971, 0.036356404423713684, -0.024992328137159348, 0.016716554760932922, 0.031520210206508636, -0.059852235019207, -0.08017084747552872, -0.027234207838773727, -0.04270366206765175, -0.028323659673333168, 0.10777369886636734, 0.0009526103385724127, -0.010618544183671474, 0.044080089777708054, -0.021620910614728928, -0.008939290419220924, 0.009516896679997444, 0.0027000224217772484, -0.012177547439932823, 0.048011865466833115, -0.0031012771651148796, -0.01842670701444149, -0.03905656933784485, -0.003452804870903492, -0.04656059667468071, -0.0352286659181118, 0.045220132917165756, 0.004753146320581436, -0.014546405524015427, 0.005524506792426109, -0.011153137311339378, -0.0068355766125023365, 0.000334997836034745, 0.02712065912783146, 0.005366106051951647, -0.03965529054403305, 0.06814397871494293, -0.05590743571519852, -0.0013453661231324077, 0.03668222948908806, -0.010805035941302776, 0.033849749714136124, 0.023517636582255363, -0.06743612140417099, -0.019543934613466263, -0.03806838393211365, -0.04501218721270561, 0.047790370881557465, 0.03835776448249817, -0.01824021525681019, -0.0249907448887825, 0.04958166554570198, 0.0004139607772231102, -0.013637452386319637, -0.009394470602273941, -0.011652904562652111, -0.042101986706256866, 0.05254450812935829, -0.031703002750873566, -0.05245006084442139, 0.01048898883163929, -0.10285931825637817, -0.006337504368275404, -0.01961914636194706, -0.060474835336208344, -0.021644389256834984, 0.017362205311655998, -0.02460055612027645, -0.030920371413230896, -0.04622466117143631, 0.030979780480265617, 0.04697057232260704, 0.021486040204763412, 0.025624610483646393, 0.08833753317594528, 0.03231842815876007, 0.022462503984570503, -0.024306654930114746, 0.04299885034561157, 0.0038353032432496548, -0.06948642432689667, 0.0006506339996121824, 0.011356868781149387, -0.05454801768064499, 0.04924952983856201, 0.0014796325704082847, -0.014756811782717705, -0.025790732353925705, -0.037391841411590576, 0.00653380062431097, 0.028507525101304054, 0.012025982141494751, 0.0340750589966774, -0.07545571029186249, -0.04036666080355644, 0.02627534605562687, -0.04143562167882919, 0.0005367227713577449, -0.011692749336361885, 0.003551310393959284, -0.009252311661839485, 0.014069528318941593, -0.019691450521349907, 0.030916444957256317, 0.05931323021650314, -0.028652353212237358, -0.026290765032172203, -0.023742185905575752, 0.00038796706940047443, -0.016934797167778015, 0.03468719869852066, -0.044545404613018036, 0.031945474445819855, -0.0013765412149950862, 0.0157791581004858, 0.0008436011848971248, 0.022237403318285942, 0.0502006821334362, 0.06748757511377335, 0.02808964066207409, -0.00644468329846859, -0.013796359300613403, 0.0026484846603125334, 0.02421530708670616, 0.04585660994052887, -0.030760744586586952, -0.022620465606451035, -0.01948743686079979, -0.06015576794743538, 0.004989388398826122, -0.035188574343919754, 0.013176944106817245, -0.04325078800320625, -0.010080182924866676, -0.04795307293534279, -0.004463921766728163, -0.024414662271738052, 0.06528996676206589, -0.010371237061917782, 0.020244291052222252, -0.005947797559201717, -0.014157813042402267, 0.00923766940832138, 0.00894478801637888, -0.031657516956329346, -0.02446938492357731, 0.007911487482488155, 0.004516970831900835, -0.035145312547683716, 0.006094005424529314, -0.01657881774008274, -0.04475108161568642, 0.03933503106236458, -0.005019152536988258, -0.03481286019086838, 0.06654372066259384, 0.02748255804181099, 0.028336191549897194, -0.030448397621512413, 0.025525080040097237, -0.029342129826545715, -0.029813630506396294, -0.028667185455560684, -0.016111671924591064, -0.015223933383822441, -0.029678260907530785, -0.04832380637526512, 0.025770260021090508, -0.009541415609419346, -0.03388402238488197, -0.04142366722226143, -0.02104511670768261, -0.07024182379245758, -0.020103760063648224, 0.03411462903022766, 0.01579403690993786, -0.07555867731571198, 0.034393370151519775, 0.018267106264829636, -0.004114890471100807, 0.06093127280473709, 0.009356839582324028, 0.03243963420391083, 0.025278711691498756, 0.015505007468163967, 0.06322956830263138, 0.013328704982995987, 0.03928247094154358, 0.011277497746050358, 0.055996619164943695, -0.1078016385436058, -0.03391048312187195, -0.07376261800527573, 0.020385321229696274, -0.04116411507129669, 0.03922518342733383, 0.009988292120397091, 0.009003807790577412, 0.012591134756803513, -0.0004348409129306674, 0.0024153944104909897, -0.05595646798610687, 0.02360539697110653, -0.04987920820713043, -0.002558947540819645, -0.026284681633114815, 0.01289813406765461, -0.014050908386707306, 0.005475207231938839, 0.06766156107187271, -0.002430699998512864, -0.05759694427251816, -0.008406336419284344, -0.041741058230400085, 0.06464788317680359, 0.020633427426218987, -0.023916201665997505, -0.005051664542406797, 0.02421376295387745, 0.03952905163168907, -0.0011472883634269238, -0.03552902489900589, -0.00511059258133173, 0.051922816783189774, 0.0827149972319603, 0.07453307509422302, -0.03379794955253601, 0.011509853415191174, 0.013977390713989735, -0.033208563923835754, -0.029334114864468575, -0.028677325695753098, 0.01341300830245018, 0.04917900636792183, 0.012325452640652657, -0.05870522931218147, 0.06362677365541458, 0.007746854797005653, 0.026272818446159363, 0.000758803857024759, 0.006806519813835621, 0.05560925602912903, 0.023800382390618324, 0.012792873196303844, -0.060448966920375824, -0.0341443195939064, -0.003990863915532827, -0.007816886529326439, 0.037507202476263046, -0.07214383035898209, 0.029376287013292313, -0.0003929354716092348, 0.03241182863712311, -0.004489500541239977, -0.026024147868156433, -0.025350045412778854, -0.06022519990801811, 0.04638104513287544, -0.0430867001414299, -0.01889169029891491, -0.0023856270126998425, 0.020850535482168198, -0.07742244750261307, -0.035079143941402435, 0.02686912566423416, -0.08849842101335526, 0.03933769091963768, 0.028812414035201073, -0.012792859226465225, 0.022667039185762405, 0.01980392076075077, -0.02625245600938797, 0.0030263604130595922, 0.0005499544786289334, 0.01111212931573391, 0.003953567240387201, -0.04533810541033745, -0.019071970134973526, -0.007579875644296408, -0.01745535247027874, -0.05300680547952652, 0.013837712816894054, 0.012173891067504883, -0.01824105717241764, -0.009018896147608757, 0.028457988053560257, -0.012248367071151733, 0.009338684380054474, 0.09900295734405518, -0.07367689907550812, 0.05285629257559776, 0.014163453131914139, 0.038454242050647736, 0.007267962209880352, -0.025091858580708504, 0.024426447227597237, 0.022128915414214134, 0.05259792134165764, -0.028236674144864082, 0.05325805023312569, -0.015489296056330204, 0.004320225678384304, 0.041181113570928574, -0.002987821586430073, 0.004130697809159756, -0.046807851642370224, 0.04678550735116005, -0.01692149229347706, 0.006347749847918749, 0.022854428738355637, 0.014980892650783062, 0.018367048352956772, -0.0065745338797569275, 0.022609664127230644, 0.0722908154129982, -0.007256684359163046, -0.012758857570588589, 0.013843811117112637, -0.019262898713350296, 0.015752345323562622, -0.02116846852004528, 0.06720004230737686, 0.03320707753300667, 0.07292795926332474, -0.03308618441224098, -0.021482175216078758, -0.004107350949198008, 0.0005763746448792517, -0.07496484369039536, -0.062010347843170166, 0.001276788767427206, -0.0011919450480490923, 0.03443865105509758, -0.010926934890449047, 0.03974400460720062, 0.032247766852378845, -0.025235189124941826, 0.01677335798740387, -0.006638974417001009, -0.002079183701425791, -0.02530800737440586, 0.022160829976201057, -0.014921898022294044, 0.07406250387430191, -0.07082861661911011, 0.010548739694058895, -0.02433529496192932, 0.07475122064352036, -0.027689127251505852, -0.033303115516901016, 0.021879563108086586, -0.0035965400747954845, -0.006647042464464903, 0.015226120129227638, 0.005983771290630102, 0.022426290437579155, 0.024118084460496902, 0.005445545073598623, -0.03393416479229927, -0.014671258628368378, -0.01881464011967182, 0.02263760194182396, -0.052012041211128235, -0.021301135420799255, 0.033430684357881546, -0.06621339917182922, -0.007042171899229288, 0.016610173508524895, 0.023249700665473938, 0.007861264050006866, -0.005076624918729067, 0.002815015846863389, -0.06069827824831009, -0.09382136166095734, -0.0029722799081355333, -0.040817826986312866, -0.08506181836128235, -0.022118184715509415, 0.006240513641387224, -0.009015283547341824, -0.004759815987199545, 0.029700536280870438, -0.01753312349319458, -0.0022630973253399134, 0.0404575951397419, -0.03754691407084465, 0.02361341565847397, 0.05154573917388916, -0.021221918985247612, -0.0152951804921031, -0.026113232597708702, 0.026758505031466484, 0.002548730466514826, -0.03581465780735016, 0.07982785999774933, 0.0550713948905468, -0.006029590964317322, -0.003562911879271269, -0.04443281143903732, -0.002264602342620492, -0.0106781255453825, 0.021604755893349648, -0.07058168202638626, -0.020034046843647957, 0.022693362087011337, 0.005532130133360624, -0.03798184171319008, 0.07164668291807175, 0.0357496403157711, 0.0027432411443442106, 0.006825687829405069, -0.010768730193376541, 0.015138526447117329, 0.017398254945874214, 0.04990540072321892, 0.00453497190028429, 0.03644086793065071, -0.03636729717254639, -0.004975531715899706, 0.014116364531219006, -0.0014089831383898854, -0.007246633991599083, 0.04502548277378082, -0.030452970415353775, 0.018969323486089706, 0.039545733481645584, 0.05397772416472435, 0.0010363697074353695, -0.01845163106918335, 0.0028165741823613644, -0.03713535517454147, -0.06371276825666428, -0.032614368945360184, -0.052242621779441833, -0.04194752871990204, -0.055131517350673676, -0.0011671888642013073, 0.05193714052438736, -0.050721392035484314, 0.024422189220786095, -0.013037302531301975, -0.01493358239531517, 0.004400170873850584, -0.01001907978206873, 0.04684726893901825, -0.017391817644238472, -0.025175413116812706, 0.022775903344154358, -0.0107664093375206, 0.00535382516682148, -0.04293502867221832, -0.12775005400180817, -0.041357722133398056, -0.043058138340711594, -0.057304833084344864, -0.025688860565423965, 0.016399987041950226, -0.014152574352920055, 0.012926469556987286, 0.030560482293367386, -0.006370036397129297, -0.012241649441421032, -0.01023758202791214, 0.002281095599755645, 0.08711457252502441, -0.08747997134923935, 0.0598139725625515, -0.0018167862435802817, 0.012163283303380013, -0.02588719315826893, 0.029182054102420807, 0.021162258461117744, -0.01396067626774311, 0.004008893389254808, -0.008854033425450325, 0.02614201232790947, -0.0025135024916380644, -0.0062615592032670975, -0.005235227756202221, -0.01542819943279028, 0.023606857284903526, 0.021276025101542473, 0.008447709493339062, -0.08634909987449646, 0.07168484479188919, -0.045214977115392685, -0.027894606813788414, -0.05709191784262657, -0.014140692539513111, 0.01340806670486927, 0.0390985831618309, -0.040989022701978683, 0.033860087394714355, 0.0045306626707315445, -0.04199356213212013, 0.008794083259999752, -0.010347164236009121, 0.00023134949151426554, -0.007749286480247974, 0.019398478791117668, 0.0678754523396492, -0.026353565976023674, -0.05356259271502495, 0.0018704140093177557, -0.01689814403653145, -0.007285736966878176, -0.014567484147846699, -0.04722486808896065, -0.022655585780739784, 0.009937187656760216, -0.025408420711755753, -0.00784680712968111, -0.053105637431144714, 0.06371912360191345, -0.0391446016728878, -0.005661888513714075, 0.037645116448402405, -0.025968872010707855, 0.020187009125947952, -0.003661799943074584, -0.09397801756858826, 0.004138778895139694, -0.0018260441720485687, 0.01868000626564026, -0.009573490358889103, 0.006810366176068783, 0.03451058641076088, 0.08704472333192825, 0.006010924465954304, 0.0363159142434597, -0.048133641481399536, -0.05153573676943779, 0.015110749751329422, 0.05616164207458496, 0.00047755311243236065, 0.003190029878169298, 0.009180665947496891, -0.09302234649658203, -0.017015809193253517, -0.03564884141087532, 0.003021292155608535, -0.043217599391937256, -0.03141236677765846, 0.007436620537191629, -0.03187842294573784, 0.06275390088558197, 0.04703514650464058 ]
<p>Well, that's easy: the sand is wet, and my shoes are wet, and hydrogen bonding adheres the wet sand to my wet feet and to my shoes.</p> <p>But then I walk home, and my shoes dry, and the sand on them dries, and some of the sand falls off. But some does not. It's really stuck: even several days later I can turn the shoe upside-down and it won't fall off. What holds it on?</p> <p>Sand sticks to my feet after my feed dry and the sand dries. Is this the same?</p>
g1554
[ 0.01699099875986576, 0.0075452374294400215, 0.006180893629789352, -0.012938370928168297, 0.04200214892625809, 0.035723570734262466, -0.02975935861468315, 0.04571636766195297, -0.010063199326395988, -0.06518227607011795, -0.016335664317011833, 0.008865962736308575, -0.024199163541197777, -0.014817728661000729, 0.03924155607819557, 0.04032478109002113, 0.030371660366654396, -0.011351238004863262, 0.017136437818408012, -0.016554268077015877, 0.00033054035156965256, 0.03547179698944092, -0.037651240825653076, -0.022174542769789696, -0.07065022736787796, -0.06614162027835846, 0.013965348713099957, -0.00036757643101736903, -0.001616634544916451, 0.04904023930430412, -0.00965490099042654, -0.02653004601597786, 0.064300537109375, -0.05571844428777695, -0.021746203303337097, -0.02496793493628502, 0.0051079802215099335, -0.047750432044267654, 0.018138904124498367, -0.040324147790670395, 0.005946718621999025, 0.031792689114809036, -0.015518211759626865, 0.035774510353803635, 0.015362756326794624, -0.023212559521198273, -0.019179517403244972, -0.010275207459926605, 0.016873518005013466, -0.03122374229133129, 0.00650784233585, 0.031920429319143295, 0.0025571873411536217, -0.004027138464152813, 0.0198469627648592, -0.0605919174849987, 0.011033456772565842, 0.047802627086639404, 0.03520916774868965, 0.02513028308749199, -0.023855242878198624, -0.018622828647494316, -0.022056257352232933, 0.08688366413116455, -0.027824394404888153, -0.022557243704795837, -0.021495366469025612, -0.004326161462813616, 0.013006018474698067, 0.01432908233255148, 0.009013039059937, 0.01489745732396841, 0.01330363005399704, -0.061410438269376755, -0.02349955402314663, -0.0036504294257611036, 0.036883167922496796, -0.0031612636521458626, 0.010649279691278934, 0.008673182688653469, 0.005321576725691557, 0.026185626164078712, -0.04801466315984726, 0.014402051456272602, -0.017607761546969414, 0.025748126208782196, -0.01591498591005802, -0.035940639674663544, -0.03928804397583008, 0.011581302620470524, -0.0023479422088712454, 0.04849458485841751, 0.010525074787437916, 0.07511169463396072, -0.05296001210808754, -0.01704573445022106, -0.03598079830408096, 0.0637451633810997, 0.02807494066655636, -0.01805836521089077, -0.014675365760922432, -0.07946498692035675, 0.08865038305521011, -0.009984306991100311, 0.04883464425802231, -0.011905106715857983, 0.03002883866429329, 0.03468557447195053, 0.053620610386133194, -0.05542294308543205, -0.026501258835196495, 0.026983341202139854, 0.0000598820042796433, -0.03269460052251816, 0.029079515486955643, -0.001651430269703269, -0.022325677797198296, -0.005734583362936974, 0.01585174724459648, -0.05679174140095711, -0.00541076110675931, -0.032163698226213455, 0.005368969403207302, 0.033963922411203384, 0.015869421884417534, -0.005624055862426758, 0.019669873639941216, 0.008784250356256962, 0.0029707790818065405, 0.016248460859060287, 0.010006919503211975, -0.0007693154038861394, 0.036342062056064606, -0.04747195914387703, -0.08692535012960434, -0.017040152102708817, -0.005880055483430624, 0.007989744655787945, -0.0018113978439942002, -0.022064121440052986, 0.026241110637784004, 0.0082982387393713, 0.05337394028902054, 0.060563210397958755, -0.022133493795990944, 0.05649774521589279, 0.027420058846473694, 0.02894214726984501, 0.023629043251276016, 0.049754273146390915, -0.04053638130426407, 0.049072157591581345, -0.030173830687999725, 0.03471534699201584, 0.042564138770103455, -0.034847281873226166, 0.055008791387081146, -0.03301617503166199, 0.03735937550663948, 0.041563522070646286, 0.06588894873857498, 0.01689944602549076, 0.009547517634928226, 0.01664254069328308, 0.012984401546418667, 0.029969383031129837, 0.05866127088665962, -0.011557596735656261, -0.03325429558753967, 0.06524413824081421, 0.03789359703660011, -0.04278912395238876, -0.019141260534524918, 0.022003784775733948, -0.031164634972810745, 0.03619531914591789, 0.03952900692820549, -0.05919934809207916, 0.0158609040081501, 0.043079156428575516, 0.046830516308546066, -0.03113989718258381, 0.01711616851389408, 0.05487529933452606, -0.017217431217432022, 0.060640137642621994, 0.024558788165450096, -0.05122250318527222, -0.04310513660311699, -0.03596946597099304, -0.027815906330943108, -0.040288571268320084, -0.027986891567707062, -0.03410650044679642, -0.01261819712817669, -0.01945520006120205, 0.00326280458830297, -0.08778182417154312, 0.12761901319026947, -0.03281493857502937, 0.02153020165860653, 0.026988640427589417, -0.002500479808077216, -0.006565872114151716, 0.05399326980113983, -0.04822921007871628, -0.00981755368411541, -0.014564217068254948, -0.05644819140434265, 0.023189159110188484, 0.006734997965395451, 0.0032943207770586014, -0.03418085724115372, 0.02199111133813858, 0.03504776209592819, -0.02953716553747654, 0.017526444047689438, 0.09395256638526917, -0.07061600685119629, -0.012238653376698494, -0.02475021779537201, -0.01594545878469944, 0.04863478243350983, 0.019484350457787514, 0.05276038125157356, 0.018012650310993195, -0.05065349116921425, -0.013709169812500477, -0.014443538151681423, 0.06333019584417343, 0.01829472929239273, -0.06997402012348175, -0.008776013739407063, 0.03321114927530289, 0.03432629629969597, 0.011793743818998337, 0.041331399232149124, 0.04009381681680679, 0.00451430631801486, 0.027792656794190407, -0.006116601172834635, -0.03317723795771599, -0.00028962857322767377, -0.012164641171693802, 0.04136238619685173, 0.02935822121798992, 0.029126852750778198, -0.024053940549492836, 0.004221638664603233, 0.007455506362020969, 0.09983690083026886, 0.01204755064100027, 0.0002008075825870037, 0.003654755186289549, 0.012785718776285648, 0.0002981311408802867, -0.08650650829076767, -0.013480973429977894, -0.06462142616510391, -0.08322155475616455, -0.024551864713430405, -0.04075603559613228, 0.014384860172867775, 0.026836181059479713, -0.025555482134222984, -0.0037597715854644775, -0.02335260808467865, 0.021352099254727364, 0.022792473435401917, -0.0019133532186970115, -0.022279296070337296, 0.014437612146139145, 0.007215533871203661, -0.025250263512134552, -0.046615440398454666, 0.021622490137815475, 0.0029580872505903244, -0.07935430854558945, 0.02845017984509468, -0.016116313636302948, 0.029190104454755783, 0.013504359871149063, 0.020807793363928795, -0.006480848416686058, -0.01820162683725357, -0.016244901344180107, -0.04214976355433464, 0.03884771838784218, 0.010743120685219765, 0.033227670937776566, -0.0032020790968090296, 0.029728494584560394, 0.08173032850027084, -0.012337666004896164, 0.014557060785591602, -0.019157417118549347, 0.009694760665297508, 0.01862853579223156, -0.0348823145031929, 0.0742633193731308, 0.0460905060172081, 0.00910973735153675, 0.03998180851340294, -0.015135184861719608, 0.0043312073685228825, -0.02272500842809677, 0.013494234532117844, -0.003285185433924198, 0.024234149605035782, -0.012404374778270721, 0.0005022308323532343, -0.01018037460744381, -0.0021789483726024628, -0.01952964812517166, -0.021834518760442734, 0.03887536749243736, -0.014163007959723473, -0.008872210048139095, -0.007178385742008686, 0.015813514590263367, -0.007024673279374838, 0.02761172130703926, -0.03922460600733757, 0.02126174420118332, 0.022996703162789345, 0.03156772255897522, -0.03147183731198311, 0.00391756696626544, 0.0043632169254124165, -0.010348299518227577, 0.029939809814095497, 0.09428462386131287, -0.01440117135643959, -0.06354016065597534, -0.029152780771255493, 0.02586548589169979, -0.024874910712242126, -0.007313720416277647, -0.014562321826815605, -0.034949593245983124, -0.046260297298431396, 0.08182091265916824, -0.003889065468683839, -0.03027215413749218, 0.009603088721632957, 0.0081751998513937, 0.10276367515325546, -0.008165602572262287, -0.03342081233859062, -0.041201651096343994, 0.00553250964730978, 0.009039596654474735, 0.033089473843574524, -0.030068594962358475, -0.012852109968662262, 0.028634460642933846, -0.031331852078437805, -0.05774913728237152, -0.01790757104754448, 0.0035121189430356026, -0.0054965247400105, 0.009948487393558025, -0.011937727220356464, -0.02304800972342491, -0.0007015589508228004, -0.004235975909978151, -0.01224773470312357, 0.011384793557226658, -0.03200099617242813, -0.0003263275430072099, 0.006665663328021765, 0.017859073355793953, -0.009055516682565212, 0.05768980830907822, -0.03782640025019646, -0.005081164184957743, -0.01759173348546028, -0.052971869707107544, -0.00003457923958194442, 0.0031375500839203596, -0.008553887717425823, 0.1095273345708847, -0.03696297109127045, 0.03869093954563141, 0.01913723163306713, 0.009432706981897354, -0.004537447355687618, 0.005106489174067974, 0.01740168407559395, 0.021907072514295578, -0.02571183629333973, 0.05478494614362717, 0.044227972626686096, -0.0785457044839859, -0.024976888671517372, -0.036941662430763245, 0.009408567100763321, 0.08124041557312012, -0.041410595178604126, -0.05153326690196991, 0.01081888098269701, 0.048893123865127563, -0.05719311907887459, -0.04387310519814491, 0.046202272176742554, 0.005209301598370075, 0.022593136876821518, -0.024302976205945015, -0.006780788768082857, -0.030142592266201973, 0.06811192631721497, 0.028997985646128654, -0.043456368148326874, 0.015686575323343277, -0.018934836611151695, 0.004577204119414091, -0.015856154263019562, 0.048961617052555084, -0.05754419043660164, -0.06238224357366562, 0.01282540149986744, 0.027377063408493996, 0.04991242662072182, -0.03088427148759365, 0.050914227962493896, 0.0027589083183556795, -0.03777173161506653, 0.003936342895030975, 0.03561815991997719, 0.005485787522047758, -0.03531327471137047, 0.009700753726065159, 0.0735388919711113, -0.04073309153318405, -0.012028643861413002, 0.034776680171489716, 0.057845864444971085, -0.04019329324364662, -0.06176401674747467, 0.029182516038417816, 0.016534388065338135, 0.04983656853437424, -0.009995252825319767, -0.020250560715794563, 0.009815833531320095, 0.013168158940970898, 0.02140216901898384, -0.017741436138749123, -0.0020810794085264206, -0.0037201540544629097, -0.05955258756875992, -0.019563918933272362, 0.019984548911452293, -0.018437344580888748, -0.0012251002481207252, 0.028477743268013, -0.056573536247015, -0.011816952377557755, -0.0315418615937233, 0.021241186186671257, -0.01594489812850952, -0.025994576513767242, 0.01141077745705843, 0.046955693513154984, 0.00884251669049263, -0.04502454772591591, 0.055280908942222595, -0.010029250755906105, 0.013223554939031601, 0.022902190685272217, 0.05701424553990364, -0.02125575579702854, -0.004094075411558151, 0.03854823112487793, -0.022666607052087784, -0.0030517408158630133, -0.015245884656906128, 0.02283092401921749, 0.043350815773010254, -0.061783771961927414, 0.036188602447509766, -0.0220639668405056, -0.03216572105884552, 0.03371698036789894, -0.06335846334695816, -0.03412838652729988, 0.037029460072517395, 0.033562932163476944, -0.012798071838915348, 0.022630533203482628, 0.022457368671894073, -0.0558810755610466, 0.04235995188355446, -0.0196559838950634, -0.0769040435552597, -0.03534122556447983, -0.04933331161737442, 0.006126496009528637, -0.0037608607672154903, -0.008115535601973534, -0.023601163178682327, -0.0656294897198677, 0.08269459754228592, -0.019515087828040123, 0.047725360840559006, 0.03227350115776062, 0.02468970976769924, 0.002386293839663267, -0.010661568492650986, -0.0033991041127592325, 0.033870697021484375, 0.02725043147802353, -0.03361034393310547, 0.02581283636391163, 0.00904090330004692, -0.0682036504149437, 0.03035869635641575, 0.021829240024089813, -0.03829915449023247, 0.04329119250178337, 0.021034443750977516, -0.021240681409835815, 0.016554977744817734, -0.03339206054806709, -0.023070506751537323, -0.06742330640554428, -0.046880513429641724, -0.014651570469141006, -0.022207409143447876, 0.03138665854930878, 0.002187997568398714, 0.020745405927300453, 0.08275559544563293, 0.025780875235795975, 0.0050176773220300674, -0.005457498133182526, 0.03221963718533516, 0.02491021901369095, 0.012892920523881912, -0.011168701574206352, 0.013235099613666534, 0.04924585670232773, 0.06927458941936493, 0.05856647342443466, -0.006327157840132713, -0.0043710325844585896, 0.004130054730921984, -0.09733740985393524, 0.0792250856757164, 0.023781925439834595, -0.005733857862651348, 0.018891511484980583, -0.04864947870373726, -0.03371547535061836, -0.025489548221230507, -0.014367176219820976, -0.024438956752419472, -0.06281960755586624, -0.032976653426885605, -0.05088510364294052, 0.057496268302202225, -0.0025331974029541016, -0.013189484365284443, 0.012916982173919678, 0.012896797619760036, -0.030475033447146416, 0.005701160524040461, -0.0023128739558160305, -0.03540056198835373, -0.02294704131782055, -0.01971735619008541, 0.01360595878213644, 0.08250393718481064, -0.001506224856711924, -0.11167113482952118, 0.04709199443459511, -0.044756773859262466, 0.04406774789094925, -0.05642849579453468, -0.012702809646725655, 0.0314108282327652, -0.005911317653954029, 0.011548313312232494, -0.01546782348304987, -0.023515406996011734, -0.011423426680266857, -0.02863127738237381, -0.031650856137275696, -0.021237105131149292, -0.009142853319644928, -0.021720819175243378, 0.06193830445408821, -0.03999381884932518, 0.006644642446190119, -0.02539019100368023, 0.005334232002496719, 0.03635266050696373, -0.03398003429174423, 0.016175951808691025, 0.003936336375772953, 0.004342018160969019, -0.023776749148964882, 0.10588730126619339, 0.00426289951428771, 0.024820882827043533, -0.014283213764429092, 0.01259708683937788, 0.02348397672176361, -0.003061395836994052, -0.00025423101033084095, -0.0205547995865345, 0.004393286537379026, 0.01485129352658987, 0.027771886438131332, 0.004214344080537558, -0.032773979008197784, 0.05860143154859543, 0.05646248906850815, -0.0031615153420716524, 0.01755073107779026, -0.11211953312158585, 0.02197709120810032, 0.0015856806421652436, -0.005057619884610176, -0.02403835952281952, -0.03347272798418999, 0.02855929359793663, 0.002207475481554866, 0.008564641699194908, -0.020251987501978874, 0.0025034728460013866, -0.012487203814089298, -0.027647050097584724, 0.0021727574057877064, -0.017707806080579758, 0.02865387313067913, -0.06243152543902397, 0.012042789719998837, -0.1045391857624054, 0.062473878264427185, 0.00021690200082957745, -0.03919316083192825, -0.005534854717552662, 0.04201461002230644, -0.02145170420408249, -0.055796824395656586, -0.017007090151309967, -0.07865319401025772, -0.013737106695771217, 0.01278536394238472, 0.05631142482161522, -0.030941907316446304, -0.017771072685718536, 0.009270195849239826, 0.008362333290278912, 0.049271631985902786, -0.06550326198339462, 0.05229144170880318, -0.02252480387687683, 0.01915731281042099, 0.0116040650755167, -0.026686793193221092, -0.007347069680690765, 0.04693104326725006, 0.0041265059262514114, 0.07099045813083649, -0.02723146229982376, 0.01639378070831299, 0.01836153119802475, 0.04692722111940384, -0.03416723757982254, -0.016002565622329712, 0.02161511965095997, -0.022376583889126778, 0.020588001236319542, 0.010539926588535309, 0.0050615835934877396, 0.04765855520963669, -0.0011373887537047267, -0.025043657049536705, 0.03141959011554718, 0.011705831624567509, 0.035972077399492264, -0.04318303242325783, -0.03753654658794403, -0.018027544021606445, 0.014466030523180962, -0.028182271867990494, 0.050697941333055496, -0.06109491363167763, 0.0387096144258976, 0.014422914944589138, -0.02355349436402321, 0.03074493259191513, -0.056328851729631424, -0.025338977575302124, 0.02645655907690525, -0.06386205554008484, 0.02699938416481018, -0.01880420744419098, -0.009379833936691284, -0.011210329830646515, 0.0458526648581028, 0.05107431858778, 0.06782107800245285, -0.056162651628255844, -0.0926746353507042, -0.039783526211977005, -0.04918733239173889, -0.07963914424180984, 0.01442556083202362, -0.02647351659834385, -0.010752419009804726, -0.011893090792000294, 0.004057320300489664, -0.02942729741334915, -0.017726773396134377, 0.004068236332386732, -0.06311781704425812, -0.030753426253795624, -0.025568166747689247, 0.012099134735763073, 0.08150865137577057, 0.02298019640147686, -0.03347262367606163, -0.001970430836081505, -0.006101822480559349, -0.04895693436264992, -0.02037893608212471, 0.019229575991630554, -0.05655251815915108, 0.03857642039656639, 0.0291743241250515, -0.015430374071002007, -0.0114032793790102, 0.0303611122071743, 0.048304952681064606, -0.017104173079133034, -0.03929450362920761, -0.006537557579576969, -0.03657141700387001, -0.042453840374946594, 0.003670704085379839, -0.0006468680803664029, 0.027823882177472115, -0.04004480689764023, 0.017532970756292343, 0.03583119809627533, 0.04161899536848068, -0.004146961495280266, -0.057329725474119186, 0.0002528959885239601, 0.018626563251018524, -0.02824532985687256, -0.02475631795823574, -0.03320610150694847, -0.06568968296051025, -0.010100943967700005, 0.11041249334812164, -0.025522775948047638, 0.04478972777724266, -0.029073290526866913, -0.07353474199771881, -0.031564969569444656, 0.029993100091814995, 0.002440491458401084, -0.021823495626449585, -0.0063425349071621895 ]
<p>Can anyone give an example of when infinite-dimensional <a href="http://en.wikipedia.org/wiki/Hilbert_space" rel="nofollow">Hilbert spaces</a> are required to describe a physical system? The standard answer to this question is yes, and I'm sure some of you will be quick to point out several clear examples:</p> <p>Ex. 1: Photon number states $\left\{ |0\rangle,|1\rangle,...,|n\rangle \right\}$</p> <p>Ex. 2: Harmonic oscillator number states (same as above).</p> <p>Ex. 3: Continuous-variable basis of a single free particle $\left\{ |x\rangle \right\} \forall x \in \mathbb{R}$</p> <p>From the infinite number of basis vectors in these examples, it is generally concluded that the dimension of the Hilbert space is also infinite.</p> <p>However, it is clear that a photon number state such as $|\psi\rangle=|100\rangle$ is unphysical (to be clear, this is the <a href="http://en.wikipedia.org/wiki/Fock_state" rel="nofollow">Fock number state</a> with $n=100$, not a tripartite state with one photon in one channel). If you dispute this, I would suggest you try preparing such a state in a single-mode fiber in an optics lab. For this reason, we can apply a (somewhat arbitrary) cutoff value of $n$ and recover a finite-dimensional Hilbert space.</p> <p>Similarly, the <a href="http://en.wikipedia.org/wiki/Cardinality" rel="nofollow">cardinality</a> of the basis set for a free particle is actually $\mathbb{N}$, not $\mathbb{R}$ (due to the properties of the function space), and although this set of orthogonal functions is infinite, we can also apply a similar cutoff for any reasonably behaved wavefunction.</p> <p>Can anyone give an example of a system described by an infinite-dimensional vector space for which such a cutoff cannot be applied?</p>
g1555
[ -0.023460976779460907, 0.05286616086959839, 0.01932504028081894, -0.10361243784427643, -0.03762198984622955, -0.008543538860976696, 0.03897419571876526, 0.020893363282084465, 0.01412908174097538, -0.034103166311979294, 0.034154437482357025, -0.06699661165475845, 0.009156306274235249, 0.012839467264711857, 0.0028024730272591114, -0.05136064067482948, 0.047575704753398895, 0.04026807099580765, -0.023210151121020317, -0.051493383944034576, -0.018954133614897728, 0.026972724124789238, -0.0034422981552779675, -0.022537708282470703, -0.009719477035105228, -0.04264187812805176, 0.07318609207868576, -0.04869067296385765, -0.029323037713766098, -0.0018360315589234233, 0.0009801576379686594, -0.05011295527219772, -0.0002120656572515145, -0.006824171170592308, -0.027307845652103424, 0.0038111526519060135, 0.004471392370760441, 0.04086406156420708, 0.015488050878047943, 0.043896593153476715, -0.00921108853071928, -0.005041616968810558, 0.017649348825216293, -0.0207702424377203, -0.010183134116232395, 0.04010026901960373, 0.019768020138144493, 0.01780509017407894, -0.016534222289919853, 0.04963657632470131, 0.026818955317139626, 0.01715107634663582, 0.030933253467082977, 0.04070718586444855, 0.08168836683034897, -0.02250044420361519, -0.0307640228420496, 0.01858227699995041, 0.039023760706186295, 0.009575048461556435, 0.01550289522856474, 0.03640807047486305, -0.004686238244175911, -0.03553161025047302, 0.015974298119544983, -0.035366617143154144, -0.029688097536563873, 0.0013019166653975844, -0.026975704357028008, 0.010799549520015717, 0.020552290603518486, -0.02868388593196869, -0.01106702908873558, -0.013568619266152382, 0.015482673421502113, 0.025199493393301964, -0.04327170550823212, 0.01555576641112566, -0.019735554233193398, 0.08826059848070145, -0.06889693439006805, -0.0134505033493042, 0.043847739696502686, -0.03493688628077507, 0.030085144564509392, 0.07744010537862778, 0.0515909343957901, 0.018692394718527794, -0.024505048990249634, 0.07719704508781433, -0.009745143353939056, 0.06680779904127121, 0.063810795545578, 0.02981158345937729, 0.0055305324494838715, -0.04579240083694458, -0.0046776775270700455, 0.033201463520526886, 0.025125248357653618, -0.006493197288364172, -0.014038540422916412, 0.04289652407169342, 0.02497507631778717, -0.04885384812951088, -0.01018135529011488, 0.050753626972436905, 0.04305404797196388, -0.008458989672362804, 0.01813051849603653, -0.011977123096585274, -0.05590689182281494, -0.0063351173885166645, -0.04912655055522919, -0.039108846336603165, -0.08384224027395248, 0.023394564166665077, 0.0661131888628006, -0.021691592410206795, -0.07220335304737091, 0.03724588453769684, 0.039295002818107605, 0.004545337054878473, 0.033051494508981705, 0.06340022385120392, -0.026654072105884552, 0.08361203223466873, 0.00007082048250595108, 0.06158560514450073, 0.04005609452724457, -0.03369807079434395, -0.01888643018901348, -0.019096732139587402, -0.024433882907032967, -0.01055638212710619, -0.04008036106824875, -0.03700415417551994, 0.014599156565964222, -0.004264418501406908, 0.03122856467962265, 0.07701920717954636, -0.025236893445253372, -0.07755421102046967, -0.009851155802607536, -0.021667074412107468, 0.024195030331611633, -0.0010609518503770232, 0.016631558537483215, -0.020345032215118408, 0.052832625806331635, 0.01451460737735033, -0.021145664155483246, 0.05821662023663521, 0.043538518249988556, 0.008245413191616535, -0.01633039116859436, 0.0053677065297961235, 0.03658832609653473, -0.0009147356613539159, -0.011710552498698235, -0.024707233533263206, 0.019615933299064636, 0.0872027799487114, -0.01342436671257019, -0.014550484716892242, -0.02596583217382431, -0.022155027836561203, 0.0033004831057041883, -0.032941438257694244, -0.017671169713139534, -0.029105044901371002, -0.011333934962749481, -0.004904207307845354, 0.03610854968428612, 0.02280823327600956, 0.021490301936864853, 0.0327787920832634, 0.016192764043807983, -0.016036298125982285, -0.0016115771140903234, -0.012330323457717896, -0.008048689924180508, 0.04288739338517189, 0.003616530913859606, 0.03273475170135498, 0.04866761341691017, 0.03978835791349411, -0.03478559851646423, 0.026395998895168304, -0.014566723257303238, 0.00583028607070446, -0.07199152559041977, -0.014606917276978493, 0.02674177661538124, 0.0005863948608748615, -0.011102289892733097, 0.0032697534188628197, 0.03827156871557236, -0.04104166105389595, -0.07040911167860031, -0.0037287971936166286, -0.020508063957095146, 0.06112530082464218, -0.0065650190226733685, 0.04182717204093933, -0.0024514258839190006, -0.031259603798389435, 0.0025008395314216614, 0.012302335351705551, -0.030820585787296295, -0.035757023841142654, 0.06186739355325699, -0.02501402236521244, -0.036574091762304306, 0.017732538282871246, 0.01843356154859066, -0.04713018238544464, -0.04265962913632393, -0.04424777626991272, -0.025246137753129005, 0.0424126535654068, 0.021822959184646606, -0.006227023433893919, 0.06458666175603867, 0.018019650131464005, 0.007905672304332256, -0.059435971081256866, -0.03365704417228699, 0.009986834600567818, -0.008109251037240028, 0.04709077998995781, -0.04975973069667816, -0.03877837210893631, -0.005495873745530844, -0.03272244706749916, -0.004594397731125355, 0.03267929330468178, -0.024472106248140335, 0.0075516849756240845, 0.005103835836052895, 0.02589915320277214, 0.060247648507356644, 0.008291766978800297, -0.02660057507455349, 0.01391987968236208, 0.0037821196019649506, -0.07142483443021774, -0.0317583829164505, -0.007854389026761055, -0.03912651538848877, 0.0031188023276627064, -0.07221096009016037, -0.0052758981473743916, 0.051386427134275436, 0.024475039914250374, 0.0005123871378600597, 0.0002650533278938383, 0.05949230492115021, 0.01281729619950056, -0.05557464435696602, -0.05757896602153778, -0.008673961274325848, -0.04088569059967995, -0.02447661943733692, 0.02352304197847843, -0.008762894198298454, 0.024140739813447, -0.009708261117339134, 0.04209277033805847, -0.0260627381503582, 0.022670671343803406, 0.0251315925270319, 0.07522834092378616, 0.04284967854619026, 0.0035860708449035883, 0.0029315899591892958, 0.03009250946342945, -0.033179279416799545, -0.005003478843718767, 0.018720993772149086, -0.03743736818432808, -0.03687376528978348, -0.015522741712629795, -0.04184109345078468, 0.014026710763573647, 0.04434676095843315, -0.06577150523662567, 0.025669990107417107, 0.057057324796915054, -0.03733320161700249, -0.04883601889014244, -0.019542120397090912, 0.05291057005524635, -0.010480055585503578, 0.0026670340448617935, -0.06996815651655197, 0.020787987858057022, 0.03634057193994522, -0.055302929133176804, -0.02042538858950138, 0.08586443215608597, 0.006495203357189894, -0.02244100719690323, 0.013043636456131935, -0.053529512137174606, -0.004580018576234579, 0.006126367952674627, -0.05490453168749809, -0.031043021008372307, -0.03698541596531868, 0.008870305493474007, 0.0028071177657693624, 0.062717005610466, -0.008002100512385368, -0.023645441979169846, 0.029887303709983826, -0.010690937750041485, -0.0013273356016725302, -0.013417894020676613, -0.0022885112557560205, 0.016320807859301567, -0.03150772303342819, 0.00780667457729578, 0.046232566237449646, -0.0031365465838462114, 0.05463564023375511, 0.08339700102806091, -0.0701211541891098, -0.0021013827063143253, -0.05814075469970703, 0.007244061678647995, 0.06776774674654007, -0.048934802412986755, 0.015095707960426807, -0.006865165662020445, -0.029128868132829666, -0.05019975081086159, -0.053544290363788605, -0.042944829910993576, 0.061987485736608505, -0.029665399342775345, -0.019965067505836487, 0.0007473279256373644, -0.000630528200417757, -0.01797196827828884, 0.042563315480947495, -0.0029934528283774853, -0.03026551380753517, 0.04800178110599518, -0.036680229008197784, -0.005916044116020203, 0.00011741978960344568, 0.008703527972102165, 0.0343499481678009, 0.009307142347097397, -0.04282650724053383, 0.017256449908018112, 0.057986076921224594, 0.06438340246677399, 0.046233586966991425, -0.01885993406176567, 0.0008961766725406051, -0.04416031390428543, 0.05014609172940254, -0.010250718332827091, -0.003254585200920701, 0.02640244923532009, 0.03200804069638252, -0.031355902552604675, -0.008027276955544949, -0.018705865368247032, -0.01078504417091608, -0.01663905754685402, -0.04398429021239281, 0.02667677402496338, -0.012793591246008873, -0.0439712218940258, -0.009931334294378757, -0.07742772251367569, -0.0647776648402214, 0.027862880378961563, 0.02824891172349453, 0.027174346148967743, 0.10690672695636749, 0.015236208215355873, 0.02078886702656746, 0.012603622861206532, -0.016672857105731964, 0.017705898731946945, 0.01895405352115631, 0.0553155243396759, 0.06392853707075119, -0.04273573309183121, 0.028738820925354958, -0.01312277466058731, 0.017427615821361542, -0.008427662774920464, -0.050475966185331345, -0.05155866593122482, -0.0133695462718606, 0.06542263925075531, 0.005865201354026794, -0.06339648365974426, 0.04567767679691315, 0.019624173641204834, -0.00012746632273774594, -0.03448282554745674, 0.030627824366092682, 0.017243655398488045, -0.04126812145113945, -0.011384645476937294, -0.02127758599817753, 0.001571261789649725, 0.02130076289176941, -0.0686427652835846, 0.045295391231775284, 0.006340209860354662, -0.01824556663632393, -0.029923800379037857, 0.03549415245652199, 0.001450439216569066, -0.03947601839900017, 0.0631755143404007, -0.023548996075987816, -0.014588971622288227, 0.039333611726760864, -0.006305679213255644, -0.01756053976714611, 0.0009277086355723441, -0.02963240258395672, -0.013161425478756428, 0.08323473483324051, 0.014207885600626469, 0.00927197840064764, 0.05512933060526848, -0.014378838241100311, 0.04622076079249382, -0.059770554304122925, 0.011715547181665897, 0.0542437806725502, 0.01967609114944935, 0.02624274231493473, -0.005605801474303007, 0.012336955405771732, 0.0010132845491170883, -0.022990988567471504, 0.06258644908666611, 0.009873709641397, -0.031298138201236725, -0.05337654799222946, 0.01633036695420742, 0.026384321972727776, 0.03869861736893654, -0.06975496560335159, -0.04979199916124344, 0.02901352196931839, -0.037081800401210785, -0.06826002150774002, 0.05392809212207794, 0.04080872982740402, 0.01969272829592228, -0.03729316592216492, -0.03208988159894943, -0.08863818645477295, 0.03294668719172478, -0.0237966887652874, 0.02352292649447918, -0.024649355560541153, 0.017871519550681114, -0.05268187075853348, -0.014565411023795605, 0.05083930119872093, 0.032963547855615616, 0.04812269285321236, 0.015015995129942894, -0.008917148225009441, -0.03598590940237045, -0.04377426952123642, -0.014889959245920181, -0.0658346489071846, -0.005649658851325512, -0.015083706006407738, -0.04264724627137184, 0.0954364538192749, 0.032178688794374466, 0.0379754938185215, 0.031955327838659286, -0.025567442178726196, -0.004409863147884607, -0.05337236821651459, 0.00790638942271471, -0.007882090285420418, 0.007263224106281996, 0.013002932071685791, -0.005778593011200428, 0.0003638822236098349, -0.07042160630226135, 0.02415613830089569, -0.031009821221232414, -0.02634161338210106, 0.033608581870794296, -0.04825449734926224, -0.028001947328448296, 0.04224349930882454, -0.014983032830059528, -0.021946456283330917, -0.024134039878845215, 0.054890673607587814, -0.013057353906333447, 0.010621128603816032, 0.013435020111501217, 0.01759590394794941, 0.008252507075667381, 0.03928479552268982, 0.03574901446700096, 0.05071071535348892, 0.006587883923202753, -0.03967629745602608, 0.03343188017606735, 0.015150743536651134, -0.05136635899543762, -0.011825032532215118, -0.04662708193063736, 0.032291337847709656, -0.0138403894379735, 0.0007066756952553988, 0.06441804766654968, -0.02148732729256153, -0.054954733699560165, -0.05417567119002342, 0.048048827797174454, 0.08577299118041992, 0.04606672003865242, -0.015530015341937542, -0.012711657211184502, -0.05785217508673668, -0.040367722511291504, 0.01611592248082161, -0.016110794618725777, 0.021157564595341682, 0.030566271394491196, -0.012234645895659924, -0.018629498779773712, 0.03463489189743996, 0.03210168331861496, 0.02819574810564518, -0.016079016029834747, 0.020171698182821274, -0.02000999078154564, -0.0371585488319397, -0.03102661669254303, -0.06887554377317429, -0.01739547774195671, -0.007570888847112656, -0.028127677738666534, 0.0424685925245285, -0.0036768948193639517, -0.0045502278953790665, 0.03779904916882515, -0.03945501893758774, -0.023360950872302055, -0.0005466287257149816, 0.03287883847951889, 0.031116627156734467, -0.03035161830484867, -0.03881647810339928, 0.017799416556954384, -0.007765642367303371, -0.04238580912351608, 0.015097352676093578, 0.05113162472844124, 0.0009163542417809367, 0.024071771651506424, 0.005352649837732315, 0.02559259533882141, 0.0021339503582566977, 0.004423124715685844, 0.002755149267613888, -0.024684865027666092, -0.026195097714662552, 0.015094056725502014, 0.002058201003819704, 0.03298348933458328, 0.056933023035526276, -0.054443784058094025, 0.0015517924912273884, 0.031076915562152863, -0.031880076974630356, -0.05058880150318146, 0.026862293481826782, -0.0015338041121140122, -0.09292428195476532, -0.051792073994874954, -0.014955420047044754, -0.038687922060489655, -0.009870033711194992, -0.01756342500448227, -0.007050537969917059, -0.01426141057163477, -0.04265148937702179, 0.0038762097246944904, 0.034039806574583054, -0.0020467445719987154, -0.01881008967757225, 0.036078907549381256, -0.006564797833561897, 0.047241199761629105, -0.06088784337043762, -0.05585506558418274, 0.038165006786584854, -0.022557931020855904, -0.019486475735902786, -0.02465229295194149, -0.06104534491896629, 0.017969567328691483, 0.013936880975961685, -0.10455537587404251, 0.04720781743526459, -0.019500838592648506, -0.023499075323343277, 0.037602946162223816, 0.07144492119550705, -0.03897973895072937, 0.022093024104833603, -0.021689539775252342, -0.008065279573202133, 0.0858900174498558, -0.0046137492172420025, 0.03297220170497894, 0.05012734606862068, -0.04779760167002678, 0.013505217619240284, -0.03389297425746918, 0.03287636488676071, 0.0310482420027256, -0.004226134158670902, 0.0075098853558301926, -0.07316940277814865, -0.01818147860467434, 0.006958331447094679, -0.02757452055811882, 0.0021045904140919447, 0.005387214012444019, 0.07055865973234177, -0.018976211547851562, 0.0024361382238566875, 0.03142228350043297, 0.0176572035998106, -0.018793946132063866, -0.06013566628098488, 0.013790073804557323, 0.008112133480608463, 0.0052107092924416065, -0.020387478172779083, -0.018628420308232307, -0.019549686461687088, 0.0065766568295657635, -0.011025501415133476, -0.015589946880936623, 0.010691437870264053, 0.0006329882307909429, -0.02872183732688427, -0.006231250241398811, -0.007829046808183193, 0.008590742945671082, -0.03585755452513695, 0.016863174736499786, 0.007279002573341131, -0.06518804281949997, 0.009027174673974514, -0.03484797105193138, 0.03743348643183708, 0.01492336019873619, -0.026810841634869576, 0.025615449994802475, 0.04911182448267937, 0.04885067045688629, 0.008921896107494831, 0.07902415096759796, -0.02584799937903881, -0.025700923055410385, 0.020348388701677322, 0.04704725742340088, -0.016561364755034447, -0.04825380817055702, -0.0422472320497036, -0.0403396300971508, -0.008050834760069847, 0.02109920233488083, 0.025244833901524544, 0.022851116955280304, 0.002864812035113573, 0.013668317347764969, 0.005579836666584015, -0.07073039561510086, 0.043631672859191895, -0.007443001493811607, 0.05664889141917229, -0.015218738466501236, 0.061683811247348785, -0.02293792925775051, 0.03819442540407181, -0.0016114016762003303, -0.04716848209500313, -0.05856749787926674, 0.030248915776610374, -0.0035548375453799963, -0.009513013064861298, -0.05774805694818497, 0.028832897543907166, -0.001492342329584062, -0.021755550056695938, 0.01674751192331314, -0.07195571810007095, 0.030161987990140915, -0.018533648923039436, -0.008191073313355446, -0.017627425491809845, -0.018007267266511917, 0.04040711745619774, -0.03628820553421974, -0.03808058425784111, 0.00786090362817049, -0.0150049589574337, 0.017256593331694603, 0.01028228085488081, 0.00816483236849308, -0.021211259067058563, -0.02324501983821392, 0.008386798202991486, 0.03687166050076485, -0.01385276485234499, -0.005862260702997446, -0.0162458885461092, 0.020826052874326706, -0.04702979326248169, 0.011627121828496456, -0.07203994691371918, 0.00959530659019947, 0.028574028983712196, 0.0064331768080592155, -0.03570280596613884, -0.04853497073054314, 0.006692615337669849, -0.03214377164840698, 0.02637539617717266, 0.031234608963131905, -0.03119325451552868, -0.003324719611555338, 0.03516131639480591, 0.020588837563991547, -0.03151487559080124, 0.029123948886990547, -0.03547666221857071, 0.10794823616743088, 0.05150177329778671, 0.016737276688218117, 0.04210004583001137, 0.03868239372968674, 0.1323617696762085, -0.020594540983438492, -0.0015412665670737624, 0.015073643997311592, 0.016472376883029938, -0.014856808818876743, -0.04029934108257294, -0.07984240353107452, -0.022244097664952278, 0.04063773900270462 ]
<p>Let's consider an electron-positron pair with total spin equal to zero. When it annihilates it can not emit only one photon because it would have zero momentum and nonzero energy. The pair emits two photons with opposite momenta but on the momentum-energy plain it looks like the particle goes through a forbidden state (red path on the picture below).</p> <p>The first question is: How is it possible? I suppose this is because of the energy-time uncertainty. The annihilation process is instant (at least looks like on Feynman diagram) and the energy of the intermediate state is not determined. Is it correct?</p> <p>If we can go through any forbidden state, why doesn't the annihilation go the blue path? This is the second question.</p> <p>And the third question: Why do electron-hole pairs in semiconductors always emit photons with energy equal to the band gap? Is it just because the interaction with one photon has higher probability or there is a fundamental difference?</p> <p><img src="http://i.stack.imgur.com/XtNu2.png" alt="enter image description here"></p>
g1556
[ 0.02551313489675522, -0.004188080318272114, 0.022498298436403275, 0.04296565428376198, 0.028501512482762337, 0.034291937947273254, 0.007850130088627338, 0.043363504111766815, 0.014926668256521225, 0.02947389893233776, 0.06712950021028519, -0.00961228832602501, 0.009155021980404854, -0.07543956488370895, -0.018204301595687866, 0.01093378383666277, 0.05402108654379845, -0.016020702198147774, 0.010135389864444733, 0.012949451804161072, -0.0470295175909996, -0.01996786892414093, -0.028436215594410896, -0.07170114666223526, 0.0012761336984112859, -0.036812037229537964, 0.0042905439622700214, -0.03772810101509094, 0.00840602908283472, 0.014339088462293148, 0.030369022861123085, -0.0062506902031600475, 0.03803393989801407, 0.0036540674045681953, 0.048456545919179916, -0.03667085990309715, 0.05054401233792305, 0.007266185712069273, -0.025027969852089882, 0.030256615951657295, 0.03516926243901253, -0.017272206023335457, -0.009225735440850258, -0.03151442110538483, 0.006807111203670502, -0.033499106764793396, 0.0023834677413105965, 0.0298575721681118, 0.06577493995428085, -0.007196189370006323, 0.028200805187225342, 0.029025359079241753, 0.04903370141983032, -0.02617725543677807, 0.03642132878303528, 0.025721611455082893, -0.006276597734540701, 0.01347330305725336, 0.0161756481975317, 0.026758160442113876, -0.00291477725841105, 0.007922912016510963, 0.00945835281163454, 0.020353632047772408, 0.040567319840192795, -0.03965330868959427, 0.005108050536364317, -0.006062462460249662, -0.024440446868538857, 0.07907428592443466, -0.04463999345898628, -0.018209198489785194, -0.02432406134903431, -0.05828443542122841, 0.051099903881549835, -0.006776797119528055, -0.010344387963414192, -0.030439402908086777, 0.03756919503211975, 0.016611333936452866, -0.06030048429965973, -0.0014850490260869265, 0.04594244062900543, -0.07899397611618042, 0.005251233000308275, 0.010321976616978645, 0.0020114912185817957, -0.03236355260014534, -0.015934107825160027, 0.010807358659803867, 0.03129138424992561, -0.061246272176504135, 0.09727931767702103, 0.00043644028482958674, 0.02804047241806984, 0.0055506289936602116, 0.005280146840959787, 0.09450017660856247, 0.013924830593168736, 0.021767666563391685, -0.012429170310497284, -0.017702922224998474, 0.020280731841921806, -0.011746798641979694, -0.0025645841378718615, -0.04582870006561279, -0.017394285649061203, 0.01565767265856266, 0.01948629505932331, 0.035826198756694794, -0.034235164523124695, 0.015791771933436394, -0.027433253824710846, -0.08014794439077377, -0.014124242588877678, 0.04577367752790451, 0.03198977932333946, -0.03246138244867325, -0.0031443603802472353, 0.041217923164367676, -0.013162080198526382, 0.01747991144657135, -0.030824529007077217, 0.06459282338619232, -0.01387559249997139, 0.018549537286162376, -0.005804462358355522, 0.01939678005874157, 0.02251151204109192, 0.011432540602982044, 0.013013845309615135, -0.04723910987377167, 0.018393339589238167, 0.0655815526843071, 0.00496583292260766, 0.006438595242798328, 0.09526071697473526, 0.011121116578578949, 0.025413520634174347, -0.01946200244128704, -0.016782185062766075, -0.03223331645131111, -0.047045350074768066, -0.005927559453994036, 0.010481100529432297, -0.002617886522784829, -0.03834586590528488, -0.019743692129850388, -0.016113156452775, 0.056076206266880035, 0.05297359451651573, 0.013847465626895428, 0.0051485514268279076, -0.006761584430932999, 0.015331566333770752, -0.03657447546720505, 0.06192440912127495, -0.03440917655825615, -0.050597481429576874, 0.026272401213645935, 0.04148932918906212, -0.014565437100827694, 0.018322449177503586, 0.011763970367610455, -0.01600758545100689, -0.021220125257968903, 0.06595378369092941, -0.0459897518157959, -0.022264786064624786, -0.03641441464424133, -0.046203043311834335, -0.010497846640646458, -0.019226333126425743, 0.07460922002792358, 0.0006784717552363873, 0.016365328803658485, -0.028766512870788574, 0.01591487228870392, -0.04663696512579918, 0.01353823859244585, 0.00791841559112072, 0.03244001418352127, 0.04563598334789276, 0.05098511278629303, 0.02324952743947506, 0.013335582800209522, -0.01340304221957922, 0.045008230954408646, -0.02504381351172924, 0.02368868887424469, -0.01008523814380169, -0.009318842552602291, -0.0018707113340497017, -0.006991134956479073, -0.02398538589477539, 0.019289707764983177, -0.04117068648338318, -0.09569796174764633, 0.04484495520591736, -0.015865502879023552, -0.05420590937137604, 0.029765158891677856, -0.032815705984830856, -0.020053742453455925, 0.032078079879283905, -0.018429454416036606, 0.0005089907790534198, -0.04487624391913414, -0.001530407345853746, 0.005428558215498924, 0.006847625598311424, -0.002239636378362775, -0.020356619730591774, 0.06877879053354263, -0.008722657337784767, -0.060068707913160324, 0.005372649058699608, -0.008151323534548283, -0.016112592071294785, -0.010881437920033932, -0.04502386599779129, -0.06778145581483841, 0.033763427287340164, -0.06417994201183319, -0.04351115599274635, 0.02985548786818981, -0.051320042461156845, -0.008825156837701797, -0.05893813446164131, 0.04913419485092163, -0.08535170555114746, 0.01945309154689312, 0.008684384636580944, -0.011562854051589966, 0.018158726394176483, -0.0024328490253537893, 0.007897167466580868, 0.00492403469979763, 0.017757173627614975, 0.019989073276519775, 0.008704460225999355, -0.014782869257032871, -0.09556405246257782, 0.05303361639380455, 0.02170906960964203, -0.06887451559305191, 0.03953208774328232, -0.03341291472315788, -0.031885746866464615, 0.03289994224905968, 0.02892407774925232, -0.017618805170059204, -0.006218890193849802, 0.00602493342012167, 0.009568426758050919, -0.031436726450920105, -0.019756663590669632, 0.023118462413549423, -0.04187816381454468, 0.0024097501300275326, -0.052298977971076965, 0.016327746212482452, -0.013363326899707317, -0.00304883299395442, -0.010302131995558739, 0.02867734245955944, -0.000044871885620523244, -0.027814211323857307, 0.010537322610616684, -0.027812369167804718, 0.0003639901988208294, 0.1053263396024704, -0.004724311642348766, 0.005812555551528931, 0.07053795456886292, 0.015140796080231667, -0.013369826599955559, 0.0015805090079084039, 0.04373738542199135, -0.07060264050960541, -0.07706495374441147, 0.04153910651803017, -0.07069246470928192, 0.007376951165497303, 0.04512442275881767, -0.04494692385196686, 0.04107186198234558, 0.024320824071764946, -0.021967681124806404, 0.01759154722094536, -0.08782459050416946, 0.016651403158903122, 0.03666314855217934, 0.03383512794971466, -0.022635051980614662, -0.03296276926994324, -0.011168689467012882, -0.06833251565694809, -0.04711995646357536, 0.037976305931806564, 0.06924314051866531, -0.028493285179138184, -0.05270787701010704, 0.009305957704782486, 0.07507264614105225, -0.05891577526926994, -0.05066387727856636, -0.06528379768133163, -0.04041704535484314, 0.01862798072397709, -0.0737791508436203, 0.08198434859514236, 0.003681367728859186, 0.008480129763484001, 0.026590393856167793, 0.01668957993388176, -0.029333606362342834, 0.04154668375849724, 0.018911374732851982, -0.003622742835432291, -0.008753825910389423, 0.008252061903476715, -0.0013124380493536592, -0.011131991632282734, 0.0644962266087532, -0.02145138569176197, -0.07764500379562378, -0.05933872610330582, -0.06375101953744888, -0.014699527062475681, 0.020373595878481865, -0.025688763707876205, -0.04093390330672264, -0.03966294974088669, -0.004175678826868534, -0.031027577817440033, 0.04988962411880493, 0.08702061325311661, -0.0054538496769964695, 0.02619842439889908, -0.02831985615193844, -0.02980717457830906, -0.03176343813538551, 0.017394499853253365, 0.012540167197585106, 0.022012125700712204, -0.0019899928011000156, -0.02777027152478695, 0.04565824568271637, -0.041466355323791504, 0.05351778864860535, -0.021339911967515945, 0.029670225456357002, -0.0010740294819697738, -0.019791865721344948, 0.020491456612944603, 0.00001264702314074384, 0.01664266362786293, 0.020262539386749268, -0.018076138570904732, 0.013866061344742775, 0.005751988384872675, 0.031553514301776886, -0.0365074947476387, -0.0395759679377079, -0.03815088048577309, -0.09248960763216019, -0.008432591333985329, 0.061835408210754395, -0.06689450144767761, -0.044662415981292725, -0.00004387761509860866, -0.02960962988436222, -0.012328087352216244, 0.011534183286130428, 0.00231648120097816, -0.017559459432959557, 0.04433658346533775, -0.028621574863791466, 0.07295512408018112, 0.005194175522774458, -0.08650382608175278, 0.03483683615922928, 0.018948961049318314, 0.020980510860681534, 0.04083351418375969, 0.0024839413817971945, -0.005191763862967491, 0.01384530309587717, -0.03937528654932976, 0.054978951811790466, -0.019551606848835945, -0.030325448140501976, 0.013935375958681107, 0.04671754315495491, 0.019224265590310097, 0.012600140646100044, -0.0990295261144638, 0.019548380747437477, 0.01513766497373581, -0.04868943616747856, 0.0010878497269004583, -0.07044873386621475, -0.029401525855064392, 0.030684255063533783, 0.02180837281048298, 0.022419195622205734, -0.01077501941472292, 0.027360180392861366, -0.020103026181459427, -0.0002569003263488412, 0.11098787933588028, 0.029474135488271713, 0.007739092223346233, 0.03587479144334793, -0.006950495298951864, -0.04852443188428879, -0.011853916570544243, -0.0019288694020360708, -0.005935370922088623, 0.012222294695675373, 0.03342093154788017, 0.0458153635263443, -0.062262069433927536, -0.013932894915342331, 0.06876718997955322, 0.010539720766246319, -0.03765987977385521, 0.011806069873273373, -0.009295050986111164, 0.042927615344524384, 0.023060880601406097, -0.002253451617434621, 0.0040017347782850266, -0.05101420730352402, 0.04456550255417824, -0.006299002096056938, -0.0016183179104700685, 0.03115013614296913, 0.05645674094557762, 0.05784163996577263, -0.029885999858379364, 0.03973924741148949, -0.023249542340636253, 0.03227038308978081, 0.025251097977161407, -0.012339695356786251, -0.04161953553557396, 0.03371397778391838, -0.05959707126021385, -0.020038016140460968, -0.036737002432346344, -0.035266369581222534, -0.056127846240997314, -0.028462784364819527, 0.002196985064074397, -0.034744273871183395, 0.05876748263835907, 0.013817732222378254, 0.08045951277017593, -0.061042074114084244, -0.01695512980222702, -0.03588856756687164, 0.008874832652509212, 0.02228119596838951, -0.007551182061433792, -0.03898417949676514, 0.011263733729720116, -0.055229634046554565, 0.029127666726708412, 0.01643448695540428, -0.026276439428329468, 0.013713018968701363, 0.0564689002931118, -0.02308378927409649, -0.020635312423110008, -0.03863140940666199, 0.021055158227682114, -0.0031147815752774477, -0.01853349059820175, 0.014034981839358807, -0.03513077273964882, 0.013932918198406696, 0.009448546916246414, 0.0006479044095613062, 0.020438749343156815, -0.028887012973427773, 0.024101346731185913, 0.05205737054347992, -0.007456877734512091, 0.015711622312664986, -0.025203846395015717, -0.005743242334574461, -0.02371477708220482, 0.03743238374590874, 0.030239159241318703, -0.026096675544977188, 0.0643346831202507, -0.01845436356961727, 0.04248668625950813, -0.03041643276810646, -0.057419538497924805, 0.01123341266065836, -0.029653841629624367, 0.01946336403489113, 0.011669748462736607, 0.06972592324018478, -0.04774632677435875, -0.00832322333008051, -0.01680431142449379, -0.052289802581071854, -0.010890473611652851, 0.04809911921620369, 0.006891152821481228, -0.019394734874367714, 0.034783702343702316, -0.010366703383624554, -0.01652427390217781, 0.0013774944236502051, -0.006014121696352959, -0.007737739011645317, 0.05161022022366524, 0.02903805859386921, 0.01471913792192936, 0.03305453807115555, -0.08530780673027039, 0.013576723635196686, 0.03587425500154495, -0.00446681585162878, 0.03389438986778259, 0.03606740012764931, 0.03518974781036377, -0.021082650870084763, 0.010737821459770203, -0.01919720694422722, -0.07194721698760986, -0.0327373668551445, -0.00667587062343955, -0.03199257701635361, -0.022881582379341125, 0.002100136363878846, -0.06629234552383423, -0.00269450549967587, 0.0813227966427803, -0.06257995218038559, 0.001646950375288725, -0.02670583873987198, -0.02484104223549366, -0.02776928059756756, 0.023659324273467064, -0.01529934722930193, 0.024804171174764633, 0.017112696543335915, -0.007913978770375252, 0.030353985726833344, 0.057892005890607834, -0.014848285354673862, 0.0051175374537706375, -0.03327303007245064, -0.02255234681069851, 0.0451400950551033, -0.026036720722913742, 0.015422315336763859, 0.030069425702095032, 0.038408759981393814, 0.009787019342184067, -0.01563570462167263, -0.0133541040122509, -0.06113995984196663, 0.004538074601441622, 0.014504339545965195, 0.012682423926889896, -0.00015124316269066185, -0.0032717951107770205, -0.03532586619257927, 0.027093831449747086, 0.0174185112118721, 0.01337901595979929, -0.04955735430121422, -0.07471409440040588, 0.015150750987231731, 0.0934017077088356, 0.003921056631952524, -0.00837628822773695, 0.03686986491084099, 0.06447650492191315, -0.05974752828478813, -0.005633392836898565, 0.07608839869499207, 0.06189378350973129, -0.09162313491106033, -0.03940454125404358, 0.015835685655474663, 0.03794989362359047, -0.0253529604524374, -0.022240152582526207, -0.0006632257718592882, -0.03963163495063782, -0.04032471403479576, 0.0049372585490345955, -0.029476536437869072, -0.0005178165738470852, -0.0046819280833005905, 0.03437861427664757, 0.0028884566854685545, 0.08361075073480606, -0.011640294454991817, -0.018265966325998306, 0.01019371673464775, 0.01685621775686741, -0.03651856631040573, -0.02599930763244629, -0.024732012301683426, 0.01023702509701252, -0.02489330805838108, -0.006331463344395161, 0.000602391897700727, 0.03910861164331436, -0.014724141918122768, 0.023293515667319298, 0.02169402316212654, -0.03214428201317787, 0.016766559332609177, -0.028200829401612282, 0.05679744482040405, 0.04727669805288315, -0.056972384452819824, 0.05883431062102318, 0.0632065162062645, -0.04874197021126747, 0.0036236727610230446, -0.04708544909954071, 0.036654721945524216, 0.00821672473102808, -0.009162564761936665, 0.06796438246965408, -0.04432167485356331, -0.026117196306586266, -0.016161128878593445, -0.01821758598089218, 0.08014766126871109, 0.04851813241839409, 0.06757092475891113, 0.03382150083780289, 0.010352322831749916, 0.04542868956923485, -0.0011090199695900083, -0.04972860962152481, -0.020744023844599724, 0.029256997630000114, 0.00866959523409605, -0.03138798102736473, 0.012958655133843422, 0.002020386978983879, 0.01298236008733511, 0.008448777720332146, -0.013081338256597519, -0.010574729181826115, -0.01209305226802826, 0.020265670493245125, 0.0041216276586055756, -0.014299031347036362, -0.022577926516532898, 0.005434901919215918, 0.0049982559867203236, -0.03040885552763939, 0.016255104914307594, -0.00950308796018362, -0.0032954213675111532, -0.04934530705213547, -0.01522907242178917, -0.0630788803100586, -0.06036584824323654, 0.00001106843410525471, 0.0037304062861949205, -0.05904269218444824, -0.011415976099669933, 0.0739574283361435, -0.03845549002289772, -0.0658273994922638, -0.0195061843842268, 0.0040338304825127125, -0.015548943541944027, -0.04728633910417557, 0.04475998133420944, 0.0454411506652832, -0.01575285941362381, 0.02976359613239765, -0.010743007995188236, 0.015315948985517025, -0.015775566920638084, -0.05649665743112564, 0.041914284229278564, 0.0332704521715641, -0.0008462952682748437, -0.015517830848693848, 0.01942834071815014, 0.003498456906527281, -0.011082357726991177, 0.00013875440345145762, 0.01683504320681095, 0.0003266149142291397, 0.04223141819238663, 0.028963370248675346, 0.01075031142681837, -0.01609654352068901, 0.058016613125801086, -0.008829412050545216, -0.002891437616199255, -0.027301548048853874, 0.03904128447175026, 0.009782454930245876, 0.01394135132431984, -0.020975405350327492, -0.029843313619494438, 0.001131945289671421, -0.041550084948539734, 0.05233728513121605, 0.005496566649526358, -0.003244847059249878, -0.009780743159353733, 0.0028004345949739218, -0.045786187052726746, 0.049636609852313995, -0.02261614426970482, -0.0073892902582883835, 0.0878513753414154, 0.05775879696011543, 0.03766835108399391, -0.045444414019584656, -0.04110259562730789, 0.015439340844750404, -0.053732506930828094, -0.004175943788141012, -0.03326481208205223, -0.02017941139638424, -0.030867911875247955, 0.05259200185537338, 0.05217833071947098, 0.019469913095235825, -0.038108352571725845, -0.07577509433031082, 0.03221973404288292, -0.028276212513446808, 0.01845530979335308, -0.01034728717058897, 0.013874686323106289, 0.0011552345240488648, 0.028627753257751465, -0.000985148479230702, -0.009170944802463055, 0.021814461797475815, -0.06607569009065628, 0.0997120812535286, 0.07665041834115982, -0.017518451437354088, 0.0193864144384861, -0.02679286152124405, 0.004121060017496347, 0.002952195005491376, -0.04034315422177315, 0.03010023944079876, -0.052024830132722855, -0.00942467711865902, 0.0025640784297138453, -0.05005744472146034, -0.006773853208869696, 0.006814439315348864 ]
<p><img src="http://i.stack.imgur.com/v7mfP.png" alt="enter image description here"></p> <p>The question asked was "what should be the acceleration such that the pressure at both the points marked by thick dots be equal? the vessel is <strong>open</strong> and cubic with side 5m?" </p> <p>Initially i considered the diagram to be resembling the figure B where $$\tan(\theta)=a/g$$ but then i realized since the both points are the midpoints of the respective sides, the height of the liquid above the lower point must be half of the height above the point on the side. I took the diagram then to resemble D. Then i got the answer as $a=2g$. Is this CORRECT?<br> <strong>If this had been a closed vessel what would the answer have been?</strong> Figure C That is my question.</p>
g1557
[ 0.0660032257437706, -0.014172147028148174, 0.016754809767007828, -0.03536711633205414, 0.05493238568305969, 0.022261297330260277, 0.09406778961420059, -0.01784694194793701, -0.04529528692364693, -0.010318368673324585, 0.022203585132956505, 0.05533934757113457, 0.05924080312252045, -0.012350304052233696, 0.03627687320113182, -0.022821156308054924, 0.030408283695578575, -0.08171603828668594, -0.014565832912921906, 0.021664613857865334, -0.04396970570087433, 0.037067193537950516, -0.06557302176952362, -0.046786438673734665, -0.013632647693157196, -0.07929616421461105, 0.016960276290774345, 0.005529155023396015, -0.0820629671216011, -0.031545285135507584, -0.0016205661231651902, 0.026280615478754044, 0.06419756263494492, -0.04378308728337288, -0.07669419795274734, -0.0127858342602849, 0.02158561535179615, 0.05719435587525368, 0.0019105869578197598, -0.042604751884937286, 0.03471044450998306, -0.05223580077290535, 0.01744619756937027, -0.026924774050712585, -0.0014538104878738523, -0.014217847026884556, -0.02588227018713951, -0.004057153128087521, -0.027114737778902054, -0.020138749852776527, -0.020955638960003853, 0.07221899926662445, -0.00744498148560524, -0.02254544571042061, -0.04766394570469856, 0.13094952702522278, -0.026910066604614258, 0.003769983071833849, 0.03112928941845894, 0.07262791693210602, -0.058005619794130325, -0.01888268254697323, 0.03282972425222397, -0.02319030649960041, 0.04395560547709465, -0.058390527963638306, 0.00921468436717987, 0.01968356780707836, -0.015630895271897316, 0.011035757139325142, 0.05887577682733536, -0.08060609549283981, -0.0008855451014824212, -0.018747033551335335, -0.09180968999862671, 0.005637961905449629, -0.056116484105587006, -0.029216719791293144, 0.030664410442113876, -0.03453325480222702, -0.05133321136236191, 0.03724522516131401, 0.05033186450600624, -0.019185680896043777, 0.05988437309861183, 0.02769698016345501, 0.0020474321208894253, -0.04751821607351303, -0.02425168827176094, 0.024963095784187317, 0.015783442184329033, 0.007045638747513294, 0.050594836473464966, -0.01528076734393835, 0.04596727341413498, -0.006556530948728323, 0.039251040667295456, 0.010087035596370697, 0.05160067602992058, 0.028598980978131294, -0.039621107280254364, -0.07040000706911087, -0.007943795993924141, 0.0178486630320549, -0.02700926549732685, -0.00423142546787858, 0.06820350885391235, -0.00480657396838069, 0.005519465077668428, -0.04051167145371437, -0.002824509982019663, -0.04927045851945877, -0.03371185064315796, -0.0332983024418354, -0.0051146000623703, -0.05730609968304634, 0.061438508331775665, 0.031353194266557693, -0.01742757484316826, 0.04502459987998009, 0.0145194660872221, 0.012827171944081783, 0.04906370863318443, 0.08319124579429626, 0.056758347898721695, -0.011181912384927273, -0.02000764012336731, -0.0026879331562668085, -0.02153485268354416, -0.018685370683670044, 0.02937171794474125, 0.005321466829627752, 0.032837528735399246, -0.01107221469283104, 0.013602732680737972, -0.007024181075394154, -0.0672970563173294, 0.015603553503751755, -0.006645440123975277, -0.00382293201982975, 0.007329094223678112, -0.020130610093474388, -0.04478229209780693, 0.022820672020316124, -0.020168542861938477, 0.013752244412899017, 0.004378743469715118, -0.014056862331926823, 0.06818772852420807, -0.0059379287995398045, -0.009031862020492554, 0.039630502462387085, -0.01322666835039854, -0.01521910261362791, 0.03847401589155197, 0.01438717357814312, 0.051935456693172455, -0.002204138319939375, -0.006515332497656345, 0.017622817307710648, 0.03446913883090019, 0.015407087281346321, 0.049777232110500336, 0.047317370772361755, -0.050385281443595886, -0.003517518751323223, 0.038729339838027954, -0.049062564969062805, 0.04862525314092636, -0.024610914289951324, -0.04491138830780983, -0.006773203611373901, 0.05963341146707535, -0.04338895156979561, 0.025937935337424278, 0.010936387814581394, 0.04578835517168045, -0.008622820489108562, 0.006150717381387949, 0.043597377836704254, -0.00929905567318201, -0.0047333380207419395, 0.04419449716806412, -0.04355339705944061, -0.011773623526096344, -0.04765818268060684, -0.0021835898514837027, -0.00663576927036047, -0.06713081896305084, 0.029754893854260445, 0.016892988234758377, -0.04542990401387215, -0.061517857015132904, 0.07637513428926468, -0.011110718362033367, -0.05384141579270363, 0.08930043131113052, 0.005656163673847914, -0.04279866814613342, 0.0034905439242720604, 0.010788444429636002, 0.07364271581172943, 0.05790116637945175, 0.023035423830151558, -0.013613668270409107, 0.0680840015411377, -0.03725964576005936, 0.0011403969256207347, 0.041429080069065094, 0.034703247249126434, -0.01897408626973629, 0.058138903230428696, -0.007335328496992588, 0.037555206567049026, -0.027287457138299942, -0.007315499242395163, 0.007308408617973328, 0.008751356974244118, -0.019275330007076263, 0.0027883287984877825, -0.017725810408592224, -0.04911372810602188, -0.01965825818479061, 0.003284515580162406, -0.04155934602022171, -0.04260639846324921, 0.038694996386766434, -0.053961075842380524, -0.017048921436071396, -0.021406598389148712, -0.005712171550840139, -0.005565903149545193, -0.011633548885583878, -0.06405710428953171, 0.023611385375261307, 0.0016931967111304402, -0.06767844408750534, 0.0408736914396286, 0.011329916305840015, 0.031069491058588028, 0.005737990140914917, -0.014117465354502201, -0.0008864095434546471, -0.03510957956314087, -0.010513098910450935, 0.010243924334645271, 0.018298020586371422, 0.003754415549337864, 0.010190406814217567, 0.04112475365400314, 0.00524268439039588, 0.002613477874547243, 0.014818336814641953, 0.035249821841716766, 0.0278376005589962, -0.02227436937391758, -0.031160658225417137, 0.02870369143784046, -0.018284233286976814, -0.031078509986400604, -0.0029681248124688864, -0.007246574852615595, -0.01697968877851963, -0.01654033362865448, -0.06281935423612595, -0.0058841402642428875, -0.0497729517519474, -0.08868782967329025, 0.042016513645648956, 0.00661318888887763, -0.0008216515416279435, -0.00036528907367028296, -0.020612798631191254, 0.078776054084301, -0.010247398167848587, -0.01931222714483738, 0.016903603449463844, 0.013253694400191307, 0.0167910885065794, 0.027098791673779488, -0.037050794810056686, -0.018014373257756233, -0.0031859618611633778, 0.061320770531892776, 0.009069896303117275, -0.01218956708908081, 0.03817971423268318, 0.026138868182897568, 0.024180766195058823, 0.046447448432445526, -0.028763143345713615, 0.01695704087615013, 0.024057216942310333, 0.03736017271876335, 0.0024997254367917776, 0.049040649086236954, 0.018809569999575615, -0.031149333342909813, -0.02499232068657875, -0.018292903900146484, -0.0011525880545377731, -0.0345429852604866, -0.012813509441912174, 0.061819445341825485, 0.04311300441622734, 0.016335897147655487, -0.023661470040678978, -0.05642091482877731, -0.03415868058800697, 0.08463773876428604, -0.06614000350236893, -0.01074754074215889, -0.01985948719084263, -0.04116428643465042, -0.025292325764894485, -0.009839554317295551, 0.010853675194084644, 0.010864276438951492, 0.005909984931349754, 0.05537477880716324, -0.03550586476922035, -0.04793789982795715, 0.008390669710934162, 0.051987212151288986, -0.0076621295884251595, -0.0304024126380682, -0.02025877684354782, 0.046829309314489365, -0.021140189841389656, -0.03602819889783859, 0.005346143618226051, -0.04072391241788864, -0.047517329454422, -0.010274337604641914, 0.04188436642289162, -0.033793140202760696, 0.03495073691010475, 0.07795041799545288, 0.03240661323070526, -0.00376281444914639, -0.03061094880104065, -0.016692794859409332, 0.006836266256868839, -0.07089020311832428, -0.003398239379748702, 0.0008208089857362211, 0.019669368863105774, 0.02551840804517269, -0.022309202700853348, -0.019747287034988403, 0.036401715129613876, -0.033019740134477615, 0.0020277658477425575, -0.002262803725898266, 0.01490254420787096, -0.0018531786045059562, 0.04697423055768013, -0.020501887425780296, -0.03840683028101921, -0.022334417328238487, -0.010422032326459885, 0.007732021622359753, -0.008828352205455303, 0.04921373352408409, -0.006915208883583546, -0.025167176499962807, -0.060224927961826324, 0.09013021737337112, -0.020886965095996857, -0.015932057052850723, 0.010645193979144096, -0.035373199731111526, -0.024671705439686775, -0.004831543657928705, 0.0172440018504858, -0.029422152787446976, -0.04160017892718315, -0.01603587158024311, -0.02484889328479767, 0.08801233768463135, 0.0572337806224823, -0.01559855043888092, -0.017534760758280754, -0.019642429426312447, 0.002126140985637903, 0.008686123415827751, -0.012750635854899883, 0.011091339401900768, 0.026704270392656326, -0.09771359711885452, 0.04169440641999245, -0.034566447138786316, -0.0405006967484951, 0.01201699860394001, -0.0052976058796048164, 0.01398152019828558, 0.03914347290992737, 0.062303416430950165, -0.04529884457588196, -0.023366661742329597, 0.0015244274400174618, -0.03337383270263672, 0.006396298296749592, -0.018998583778738976, -0.04983730614185333, -0.03262623772025108, 0.023536378517746925, -0.03011731617152691, 0.03877867013216019, 0.020888162776827812, 0.059708934277296066, 0.0040724813006818295, -0.003848307766020298, -0.07175251096487045, -0.032113246619701385, 0.03142793849110603, 0.044362738728523254, 0.00473707215860486, -0.025137310847640038, 0.004104977939277887, 0.038365695625543594, 0.03460626304149628, 0.02674049884080887, -0.044487908482551575, 0.027204345911741257, 0.00672090332955122, 0.01695857383310795, 0.025153420865535736, 0.00511622428894043, -0.03594769164919853, 0.012667495757341385, 0.021351920440793037, 0.010482813231647015, 0.02439560927450657, -0.0022290281485766172, 0.08304475247859955, 0.020186802372336388, 0.021122699603438377, 0.028760917484760284, 0.013603690080344677, -0.013477222993969917, 0.024007366970181465, 0.056344807147979736, -0.03164752572774887, 0.04693552479147911, 0.038531091064214706, -0.024160973727703094, -0.024721598252654076, -0.06128639727830887, -0.03451845422387123, -0.050882160663604736, 0.029184646904468536, -0.006547222379595041, 0.002361167222261429, -0.02088957652449608, -0.03748740628361702, 0.031726788729429245, 0.004167672712355852, -0.03392791748046875, 0.04958251863718033, -0.010573914274573326, 0.0018938366556540132, -0.01691390946507454, 0.0030007234308868647, 0.08566640317440033, -0.04812989383935928, -0.01579131931066513, -0.005259764846414328, -0.0072604152373969555, -0.013630546629428864, 0.0006615556194446981, -0.006180635187774897, 0.03491223603487015, -0.0031550973653793335, -0.02609235979616642, 0.04879452660679817, 0.03744220733642578, 0.03766565024852753, 0.016114478930830956, -0.041343674063682556, -0.007815835066139698, 0.031205857172608376, 0.03440815210342407, 0.04421118274331093, 0.020285872742533684, 0.03579498454928398, -0.010387763381004333, -0.018315793946385384, 0.017560278996825218, 0.013849088922142982, 0.046334683895111084, -0.01554095558822155, -0.019680358469486237, -0.01358164381235838, -0.01315916795283556, -0.03809436038136482, 0.05055759474635124, -0.00805284921079874, 0.00517862057313323, 0.013669236563146114, -0.06034119799733162, -0.025538144633173943, -0.014922958798706532, 0.010204507037997246, -0.02668934501707554, 0.00666374247521162, -0.03139367327094078, -0.048172179609537125, 0.049136169254779816, 0.07602498680353165, -0.0054412418976426125, 0.006754320580512285, 0.07377123832702637, 0.012309418991208076, -0.010794543661177158, -0.0041677034460008144, 0.006230676546692848, 0.026497239246964455, -0.030157465487718582, -0.022715168073773384, 0.09049080312252045, -0.0012503806501626968, -0.018922554329037666, 0.031352706253528595, -0.002937770914286375, 0.030029861256480217, -0.022554660215973854, -0.013899412006139755, 0.0303402878344059, -0.00669117970392108, -0.04414674639701843, 0.06007670983672142, -0.022789394482970238, -0.05282255634665489, -0.03639524057507515, -0.007143337279558182, 0.03846586495637894, -0.026986971497535706, 0.09405069798231125, -0.029260069131851196, -0.02971341833472252, 0.009781422093510628, -0.010780428536236286, 0.05754881724715233, 0.018074192106723785, 0.02159777656197548, -0.07149529457092285, -0.0143433203920722, -0.012257606722414494, -0.02137581817805767, -0.037711452692747116, -0.011855176649987698, 0.005671895574778318, -0.0004092676390428096, 0.031674571335315704, -0.001586636994034052, -0.03660571947693825, -0.03714846819639206, 0.04637736827135086, -0.012862544506788254, 0.012307178229093552, -0.006114582531154156, -0.011102505959570408, 0.08236417174339294, -0.01107290294021368, -0.08633395284414291, -0.04325222596526146, 0.08334033936262131, 0.06543425470590591, -0.032575301826000214, 0.016942782327532768, 0.005485358648002148, 0.030245861038565636, -0.0075493487529456615, 0.08344998955726624, 0.026851583272218704, -0.03537117689847946, 0.06373815983533859, -0.043908439576625824, 0.03627622500061989, -0.02561461739242077, 0.04975053295493126, 0.019070323556661606, 0.012338959611952305, 0.000765428354497999, -0.025960523635149002, -0.040796928107738495, -0.01254828367382288, 0.008317549712955952, -0.002914746757596731, -0.0462481826543808, -0.004229300655424595, -0.019404714927077293, 0.002819065935909748, 0.014923442155122757, -0.014946434646844864, -0.005929481238126755, 0.015867266803979874, -0.03601071983575821, 0.037604715675115585, -0.02086336351931095, 0.040333788841962814, -0.020451903343200684, -0.01873110793530941, 0.018595146015286446, -0.005016823764890432, 0.023451056331396103, 0.020810624584555626, -0.04889443889260292, -0.05994415655732155, -0.03748844936490059, 0.025640306994318962, 0.003535938449203968, 0.0076177166774868965, 0.0163470096886158, -0.025763750076293945, 0.004970137495547533, 0.004977857228368521, 0.005892412271350622, 0.033483054488897324, 0.012341816909611225, -0.009853987023234367, -0.03778017684817314, -0.07032115757465363, 0.05653553083539009, 0.013062304817140102, -0.014604727737605572, 0.004498648457229137, -0.011691301129758358, 0.012757127173244953, -0.013132179155945778, -0.04210874065756798, -0.021545322611927986, 0.0007319650612771511, 0.009017459116876125, 0.04879602789878845, -0.034035902470350266, 0.04743858426809311, 0.07768793404102325, 0.04802282527089119, -0.012510777451097965, -0.013097904622554779, 0.005217585247009993, 0.0033649224787950516, -0.005827878601849079, -0.0645979717373848, 0.056364499032497406, -0.032535213977098465, -0.05143473297357559, 0.026414040476083755, -0.02448602020740509, -0.03878964111208916, -0.10745301097631454, 0.0278497152030468, -0.021324675530195236, -0.0163018349558115, 0.01573498733341694, 0.007200031541287899, 0.02151346020400524, -0.03158996254205704, 0.01816771924495697, -0.009563449770212173, 0.03191071376204491, -0.002818488283082843, -0.06029282510280609, 0.008527086116373539, -0.03309664502739906, -0.002809001598507166, -0.04378746077418327, 0.00011317835742374882, -0.01324254460632801, -0.004308911040425301, -0.014966809190809727, 0.00380893936380744, 0.026067091152071953, 0.01711958833038807, -0.013208972290158272, -0.0350169911980629, 0.021732622757554054, 0.012393483892083168, -0.0016421778127551079, -0.011707580648362637, -0.0006162075442261994, -0.01872745342552662, -0.04254450649023056, -0.049912452697753906, -0.05406215414404869, -0.013855195604264736, 0.07570455223321915, 0.020340988412499428, 0.02896691858768463, 0.051864247769117355, 0.0022639452945441008, 0.006378914229571819, 0.025488998740911484, 0.029178926721215248, -0.004694825503975153, 0.0661688894033432, -0.00727484654635191, -0.004819087218493223, 0.04239857569336891, -0.0037979260087013245, -0.04631834477186203, -0.00293860980309546, -0.007997018285095692, 0.021171806380152702, 0.01863345317542553, 0.017089998349547386, -0.04832528159022331, -0.03556153550744057, 0.044842831790447235, -0.0387740395963192, 0.042670559138059616, -0.015294070355594158, 0.11015880107879639, 0.02609366923570633, -0.04480436444282532, -0.06850352138280869, -0.014014489017426968, -0.017668673768639565, -0.08618161827325821, 0.010367123410105705, -0.03599230945110321, -0.09419481456279755, 0.016541266813874245, -0.030575908720493317, -0.04552621766924858, -0.006624228786677122, -0.044787243008613586, -0.0029069986194372177, -0.035639438778162, 0.009106608107686043, 0.0008674891432747245, 0.039344627410173416, -0.029103267937898636, -0.030483396723866463, 0.017359357327222824, 0.001985938288271427, 0.031155264005064964, 0.012898816727101803, -0.027013137936592102, -0.03559396043419838, 0.0010602837428450584, 0.008740565739572048, 0.0037091209087520838, -0.030617091804742813, -0.033257801085710526, 0.05057928338646889, 0.034487299621105194, -0.040466565638780594, 0.053507059812545776, 0.02105048857629299, -0.028810400515794754, 0.028950979933142662, 0.07484977692365646, -0.07868815213441849, -0.033547841012477875, 0.0737583339214325, -0.014598998241126537, -0.08274020999670029, -0.06628966331481934, 0.035985253751277924, 0.027256431058049202, -0.027605045586824417, 0.0275037232786417, -0.013077734038233757, -0.05127575621008873, 0.0017337020253762603 ]
<p>My question is fairly simple, but I do need clarification on how to get the inverse of the <a href="http://en.wikipedia.org/wiki/Lennard-Jones_potential" rel="nofollow">Lennard-Jones</a> potential V(x).</p> <p>I am working with the following expression: $$ V(x) = e\times[(R/x)^{12} -2\times(R/x)^6] $$</p> <p>So given a value $V$, how can I find $x(V)$ ?</p>
g1558
[ 0.018077803775668144, 0.02150403894484043, -0.014728118665516376, -0.0511305145919323, 0.0026960577815771103, -0.022092992439866066, -0.03886565938591957, -0.0030007087625563145, -0.018228663131594658, 0.02922537550330162, -0.055489178746938705, 0.050879303365945816, -0.014340805821120739, 0.03499689698219299, 0.0038252361118793488, -0.018030978739261627, 0.04969547688961029, 0.019790247082710266, 0.04606427997350693, -0.0052956221625208855, 0.006277678534388542, -0.04868873208761215, 0.029792750254273415, -0.030263694003224373, 0.038665082305669785, -0.0807400569319725, 0.01257973164319992, 0.07615577429533005, -0.057975783944129944, -0.021039078012108803, -0.008181912824511528, -0.036375291645526886, 0.07109413295984268, -0.014195295050740242, -0.023697149008512497, -0.007955520413815975, 0.04953284189105034, 0.03629636764526367, -0.007776832208037376, 0.061898890882730484, 0.004786696285009384, 0.014870461076498032, 0.04624521732330322, 0.11872980743646622, 0.019826378673315048, -0.02318519353866577, -0.005140421446412802, 0.0649496465921402, 0.0005294834263622761, -0.06940014660358429, 0.02992449887096882, 0.02175179310142994, -0.02088048681616783, 0.00898023508489132, 0.01428547129034996, 0.007906829938292503, -0.009639633819460869, 0.036212820559740067, -0.011955857276916504, 0.035890839993953705, 0.02162889763712883, -0.03879977762699127, -0.022102877497673035, 0.0536925382912159, 0.018965695053339005, -0.022880438715219498, -0.020061127841472626, 0.015487249940633774, -0.02167452685534954, -0.023457789793610573, 0.009003393352031708, -0.011267715133726597, -0.03956758975982666, -0.027225488796830177, -0.06674778461456299, -0.010098466649651527, 0.03171907737851143, -0.03442605584859848, -0.018614133819937706, 0.0087244538590312, -0.004274995066225529, -0.040748726576566696, 0.07899035513401031, 0.05018883943557739, 0.0424007847905159, -0.018628288060426712, 0.0584154948592186, 0.047167934477329254, -0.06375302374362946, -0.019316010177135468, 0.006362105719745159, 0.003562833881005645, 0.0800858661532402, 0.0020425303373485804, 0.02056967094540596, -0.011736364103853703, -0.030113620683550835, 0.019252456724643707, -0.08592703193426132, -0.024391043931245804, 0.03731366619467735, -0.05007055401802063, 0.009639209136366844, -0.10127682983875275, -0.008112491108477116, -0.014637789689004421, 0.08717382699251175, -0.019378233700990677, -0.03682377561926842, -0.03579502925276756, -0.04583248496055603, 0.009156274609267712, -0.039408013224601746, -0.03826439008116722, -0.013275008648633957, 0.018385596573352814, 0.062441080808639526, -0.032680053263902664, -0.033307116478681564, 0.06238539144396782, -0.029467903077602386, 0.0782790407538414, 0.007896862924098969, 0.07932247221469879, 0.03860834985971451, 0.027973132207989693, -0.009755527600646019, 0.03510728478431702, 0.009187985211610794, 0.04690389707684517, 0.025518056005239487, 0.00965750589966774, 0.04922321066260338, 0.008373521268367767, -0.014205912128090858, 0.023013712838292122, -0.043905872851610184, 0.04503551498055458, -0.02741420269012451, -0.005689085926860571, -0.026096804067492485, -0.0398847870528698, -0.018525080755352974, 0.0012204140657559037, -0.04348224028944969, -0.00939518678933382, -0.006367384921759367, -0.03646315261721611, 0.032671958208084106, -0.009577729739248753, -0.03271660581231117, 0.0027506358455866575, 0.050260353833436966, -0.017613165080547333, -0.04228439927101135, -0.003231606213375926, 0.015040606260299683, -0.02303188480436802, -0.021461132913827896, 0.0211925245821476, 0.047598566859960556, 0.006886360701173544, 0.026270758360624313, 0.035832662135362625, -0.030031418427824974, -0.00824658665806055, 0.05776171758770943, -0.0372888408601284, -0.0056933253072202206, -0.06025294214487076, 0.006712351925671101, -0.011364645324647427, 0.059857454150915146, 0.028165394440293312, 0.01810055784881115, 0.012388531118631363, 0.017168937250971794, -0.004719396121799946, -0.06504173576831818, 0.06611432880163193, -0.04000355675816536, -0.021778402850031853, 0.01921316795051098, -0.005193645134568214, 0.01829361356794834, -0.07947713136672974, 0.05358659103512764, 0.07784697413444519, 0.02218317613005638, 0.002076679840683937, 0.03449865058064461, -0.008959340862929821, -0.021197957918047905, 0.007358829025179148, -0.03073805384337902, 0.02964019775390625, 0.0409715510904789, -0.09730972349643707, -0.011111999861896038, 0.02121277153491974, 0.006070314906537533, -0.020106999203562737, 0.030538218095898628, 0.08865030109882355, 0.012565315701067448, -0.03829248249530792, -0.00926439929753542, -0.03768099844455719, -0.016811640933156013, 0.001415830571204424, -0.020837746560573578, -0.009211888536810875, 0.009419994428753853, 0.0501813106238842, 0.03776872530579567, -0.04277695715427399, -0.028940962627530098, 0.034220531582832336, -0.04284852370619774, 0.01426682248711586, -0.02003517746925354, -0.03041398711502552, -0.041549209505319595, 0.07865829765796661, -0.00529091851785779, 0.03350198641419411, 0.03966246172785759, -0.011494004167616367, -0.055607184767723083, -0.021118948236107826, -0.03110327757894993, -0.02717348374426365, -0.006614415440708399, -0.012281326577067375, -0.006455698981881142, 0.006401835009455681, -0.0006371368654072285, -0.04120856150984764, -0.009200322441756725, 0.06243018060922623, -0.006990951020270586, -0.03881172090768814, -0.017374219372868538, 0.08440742641687393, 0.007364306133240461, 0.03709603101015091, 0.03130945935845375, 0.0023616908583790064, -0.01454592403024435, 0.04279741644859314, 0.008703080005943775, 0.017099425196647644, -0.03720952570438385, -0.044478170573711395, -0.007109462283551693, -0.009732924401760101, 0.004838069435209036, -0.014460567384958267, -0.04274208843708038, -0.0010202574776485562, 0.0003687555145006627, 0.030759042128920555, -0.009538298472762108, 0.018506204709410667, -0.01782291941344738, -0.004348553717136383, 0.025127606466412544, -0.03746708482503891, 0.01383383758366108, 0.04537992924451828, -0.003367179771885276, 0.021373355761170387, 0.0587368868291378, -0.020055536180734634, 0.0035858002956956625, -0.06871329247951508, -0.019607165828347206, -0.06659475713968277, 0.06224416196346283, 0.011880199424922466, -0.018940430134534836, -0.0002244524221168831, -0.0030111174564808607, 0.08710313588380814, -0.008888316340744495, 0.003566030878573656, 0.015436109155416489, 0.031296614557504654, -0.0044134086929261684, 0.004498711787164211, -0.06742685288190842, -0.02613029070198536, 0.0043388125486671925, -0.02996429055929184, -0.08194512128829956, -0.052399490028619766, 0.03494250774383545, -0.0901346206665039, -0.012473869137465954, -0.04042261466383934, 0.026283591985702515, -0.030776167288422585, -0.022288091480731964, -0.007187080569565296, 0.005599339492619038, -0.03304816409945488, -0.00936661846935749, -0.0015273465542122722, -0.004516440909355879, -0.017398914322257042, -0.023421846330165863, 0.010500135831534863, 0.02975420281291008, -0.0033379271626472473, -0.013537916354835033, 0.043683070689439774, -0.00575720751658082, -0.02673426829278469, 0.015122904442250729, -0.02818146161735058, -0.032051440328359604, -0.055601973086595535, 0.02828255668282509, 0.05217284709215164, 0.050820451229810715, -0.0250893272459507, -0.05470265448093414, -0.030240679159760475, 0.005604912992566824, 0.028727056458592415, 0.022396864369511604, 0.021025964990258217, 0.022933680564165115, -0.023678775876760483, -0.008470875211060047, -0.0035903167445212603, -0.03655104711651802, 0.025769079104065895, -0.01367577537894249, -0.046571314334869385, 0.02146468497812748, -0.004471823573112488, -0.023587079718708992, 0.016668634489178658, 0.0174342580139637, -0.02213285118341446, -0.013535802252590656, 0.06451131403446198, -0.005885320715606213, -0.02377879060804844, -0.06245856732130051, -0.03010840341448784, 0.03342307358980179, -0.016522763296961784, 0.07236231118440628, 0.0052512758411467075, -0.023675713688135147, 0.034037455916404724, 0.008256287313997746, 0.03252939507365227, -0.03560614585876465, -0.01058290433138609, -0.008057753555476665, 0.04432513937354088, 0.09312716126441956, -0.03852422907948494, 0.000033963515306822956, 0.02316991612315178, -0.029323356226086617, -0.011713404208421707, 0.03705482557415962, -0.011428392492234707, 0.06687140464782715, 0.036623477935791016, -0.06309626251459122, -0.05301060900092125, -0.04038858786225319, 0.05809645354747772, 0.035608597099781036, 0.004693709779530764, 0.0319434329867363, 0.006641428451985121, 0.0020829408895224333, 0.04804444685578346, -0.003548000007867813, -0.010259906761348248, -0.03838741034269333, 0.009418168105185032, 0.05762575566768646, -0.022248469293117523, -0.0014692351687699556, 0.03353685885667801, -0.07853474467992783, 0.042575206607580185, -0.03430094197392464, -0.013140889815986156, 0.007149318233132362, -0.04610292986035347, -0.06392166018486023, 0.012571866624057293, 0.05937337502837181, -0.011695055291056633, 0.022415589541196823, 0.0544319674372673, -0.03830917179584503, -0.013663506135344505, 0.05787985771894455, -0.08076619356870651, -0.0011069264728575945, -0.001950992038473487, -0.07632241398096085, -0.012726102955639362, 0.06256944686174393, -0.04408926144242287, -0.04466438665986061, 0.025772036984562874, 0.08032234758138657, -0.01847929321229458, -0.0008885907009243965, 0.011020507663488388, 0.029954487457871437, -0.003938064444810152, 0.03585314378142357, -0.027975821867585182, -0.06616713106632233, 0.04106830060482025, 0.027004843577742577, 0.0011253991397097707, 0.01622297614812851, 0.0005526565364561975, 0.00419520353898406, 0.06207594275474548, -0.06570090353488922, 0.03528787940740585, -0.04130587354302406, -0.01450984925031662, 0.019469045102596283, -0.004143768455833197, 0.010390684008598328, 0.016160137951374054, -0.010657710954546928, -0.03916611522436142, -0.045591890811920166, 0.008539874106645584, -0.006279332097619772, 0.0032750950194895267, 0.0029194410890340805, -0.04324764385819435, 0.027444861829280853, -0.08003274351358414, -0.028660228475928307, -0.020247118547558784, 0.014638794586062431, -0.04422564432024956, 0.018697110936045647, 0.032907307147979736, 0.01500498503446579, 0.007802607025951147, -0.019768130034208298, -0.005707967560738325, -0.005253118462860584, -0.05021355673670769, -0.025995438918471336, 0.017182817682623863, 0.05438806489109993, -0.010572608560323715, -0.06727849692106247, 0.05334613472223282, -0.006885605864226818, -0.030698154121637344, 0.005679329391568899, 0.011629519052803516, -0.0027590955141931772, 0.003083473304286599, 0.02438356727361679, -0.04445204511284828, 0.010469074361026287, 0.026808468624949455, -0.009458823129534721, 0.0519917830824852, -0.060607437044382095, 0.008301197551190853, 0.004577294923365116, -0.021378951147198677, -0.03772915154695511, 0.0012602729257196188, -0.01753593236207962, 0.017853764817118645, 0.019208470359444618, 0.038341403007507324, -0.017903180792927742, 0.035526104271411896, -0.006426104344427586, -0.04099000245332718, -0.020786842331290245, -0.018341904506087303, 0.011189698241651058, 0.009158547036349773, 0.01986847259104252, 0.03336888924241066, -0.025847604498267174, 0.003073439933359623, -0.029690120369195938, 0.04491923376917839, 0.0048066554591059685, 0.05079063028097153, 0.051800064742565155, -0.02371324971318245, 0.00024655627203173935, -0.02037382312119007, 0.048546139150857925, -0.015617665834724903, 0.037100352346897125, 0.01725124381482601, -0.021495072171092033, 0.014349741861224174, -0.053473930805921555, 0.05142875760793686, -0.06474461406469345, -0.03087347187101841, 0.04217975214123726, 0.037949010729789734, 0.02245495468378067, -0.023791873827576637, -0.01723376475274563, -0.09186295419931412, -0.01379601564258337, -0.0241280235350132, 0.019415447488427162, -0.009834015741944313, -0.013877667486667633, 0.05896245315670967, -0.022658295929431915, -0.02286011166870594, 0.007189965806901455, -0.02109869383275509, -0.004584506619721651, 0.01206230092793703, 0.0038285045884549618, -0.04341752082109451, 0.03383425995707512, -0.007539734710007906, -0.015510630793869495, 0.006652218289673328, -0.038770344108343124, -0.010811262764036655, -0.026389984413981438, -0.024906469509005547, 0.05348169058561325, 0.013053571805357933, 0.0010893750004470348, -0.03717074543237686, -0.005448379088193178, 0.018755076453089714, 0.0343482680618763, -0.0056357476860284805, 0.02917613834142685, 0.005391347222030163, -0.027906527742743492, -0.030467770993709564, 0.028262000530958176, -0.015510566532611847, -0.01556376088410616, 0.04631330072879791, -0.037487275898456573, -0.022346483543515205, 0.030138950794935226, 0.00961742177605629, 0.039076898247003555, 0.05478747561573982, 0.0013486541574820876, -0.06390643864870071, 0.038500718772411346, -0.015280605293810368, 0.03205566480755806, 0.047339826822280884, 0.04136347770690918, -0.08939811587333679, -0.03692012280225754, 0.04686753451824188, -0.026188015937805176, -0.034374065697193146, -0.03767787292599678, -0.030425788834691048, -0.033494699746370316, 0.04615054279565811, 0.017188822850584984, -0.08819960802793503, 0.00016348464123439044, 0.03159283101558685, -0.0010949732968583703, 0.025104286149144173, -0.03880283609032631, -0.037925686687231064, 0.012855554930865765, -0.0030291073489934206, -0.008723854087293148, 0.021935991942882538, 0.022213030606508255, -0.035742878913879395, 0.028656797483563423, 0.04103471711277962, 0.058466587215662, -0.006876844447106123, -0.012199283577501774, 0.022238854318857193, -0.01084977202117443, 0.017817720770835876, -0.0022511219140142202, -0.022091832011938095, -0.000423830293584615, 0.012681851163506508, -0.0025520739145576954, 0.0007356717833317816, 0.0056344554759562016, 0.010820813477039337, 0.05915364623069763, 0.01682913862168789, -0.0030660538468509912, 0.008676299825310707, 0.029254240915179253, -0.008525816723704338, -0.020904559642076492, 0.030590802431106567, 0.0700828805565834, 0.027366237714886665, -0.01953538879752159, -0.020101435482501984, 0.04499603435397148, -0.01834268681704998, 0.025019163265824318, -0.05023525282740593, -0.013665116392076015, 0.05740861967206001, -0.014581655152142048, 0.03354737162590027, -0.009514020755887032, 0.05018242821097374, 0.06257262080907822, 0.013940418139100075, -0.011858227662742138, 0.03813415393233299, -0.028920238837599754, 0.04654517397284508, -0.04497096315026283, -0.03188064694404602, -0.009683332405984402, 0.06041920930147171, -0.03859250620007515, 0.049357473850250244, 0.12267306447029114, -0.037547990679740906, 0.018793398514389992, -0.01272561401128769, -0.006315809674561024, -0.010470450855791569, 0.059057965874671936, 0.04582779482007027, 0.01894867792725563, -0.0615561380982399, -0.03662488982081413, -0.01913302205502987, -0.07451750338077545, 0.0019365159096196294, 0.022902898490428925, -0.009051196277141571, 0.008161857724189758, -0.006789328996092081, 0.003334689885377884, -0.028062405064702034, -0.005218865349888802, -0.04665231332182884, -0.00010495645256014541, -0.012036647647619247, -0.013963337056338787, 0.02095484733581543, 0.01533557754009962, 0.015341401100158691, -0.08023418486118317, 0.020268963649868965, 0.012528179213404655, 0.061480551958084106, -0.02845435030758381, -0.0389278270304203, 0.008395059034228325, -0.005946378689259291, -0.02881046012043953, -0.023858625441789627, -0.01789660006761551, 0.00476079573854804, -0.054646432399749756, 0.08719814568758011, 0.024818245321512222, -0.02506956271827221, 0.012357443571090698, -0.03055436909198761, 0.027869034558534622, -0.006174866575747728, -0.016393061727285385, 0.039773128926754, 0.0033124370966106653, -0.039060141891241074, 0.012139704078435898, 0.006429531145840883, 0.00541977072134614, -0.004724467173218727, -0.029269061982631683, -0.02762073464691639, -0.03447243198752403, -0.046352092176675797, -0.04351417347788811, -0.047628097236156464, -0.0028235141653567553, -0.05141686648130417, 0.09593016654253006, 0.08288707584142685, 0.040376584976911545, 0.002426822204142809, -0.03356645256280899, 0.0011528354370966554, 0.006304360460489988, -0.00995459035038948, -0.009580276906490326, -0.01088531594723463, -0.07215943187475204, -0.0331757478415966, -0.06469044834375381, 0.061300862580537796, -0.005698815919458866, 0.026024125516414642, 0.04472362995147705, 0.0006622799555771053, -0.035208526998758316, -0.0628066211938858, 0.05538446083664894, -0.061519499868154526, 0.028707437217235565, 0.014312881976366043, 0.0535370372235775, 0.044126931577920914, -0.05379147455096245, -0.08163988590240479, 0.05509449914097786, 0.005290172528475523, 0.022827478125691414, -0.014188782311975956, 0.007885003462433815, 0.02429257147014141, 0.05338907986879349, -0.04047994688153267, -0.003165068570524454, -0.043797578662633896, 0.009178966283798218, 0.05069570988416672, 0.05248351767659187, -0.03008207120001316, -0.015426861122250557, 0.05973540246486664, -0.042944107204675674, -0.028245631605386734, -0.0641322210431099, 0.0016407687216997147, -0.04991535842418671, 0.06581937521696091, 0.0026178755797445774, -0.06110432744026184, -0.04349851608276367, 0.00857116375118494 ]
<p>I'm currently consuming a course on QFT where we need to define the unitary time-evolution to get the time evolution of the wave function in the interaction picture:</p> <p>$\hat{U}(t_1,t_0) = \exp\left(\frac{i}{\hbar}\hat{H}_0t_1\right)\exp\left(-\frac{i}{\hbar}\hat{H}(t_1-t_0)\right)\exp\left(-\frac{i}{\hbar}\hat{H}_0t_0\right)$ .</p> <p>Now one can show that this operator follows a Schrödinger equation by simply taking the derivative to time:</p> <p>$i\hbar\frac{d}{dt}\hat{U}(t,t_0) = \hat{H}_1^I(t)\hat{U}(t,t_0)$ .</p> <p>Where $\hat{H}_1^I$ is the perturbation to our free-field Hamiltonian $\hat{H}_0$.</p> <p>Now I started wondering whether $\hat{U}(t_1,t_0)$ shouldn't also follow a Heisenberg equation since it's an operator.</p> <p>I believe it shouldn't since $\hat{U}(t_1,t_0)$ gives a unitairy time-evolution which is a transformation, while the Heisenberg equation applies to observables. I was woundering if someone could confirm my reasoning or disprove it?</p>
g1559
[ 0.007331631146371365, 0.0325617678463459, -0.0028024455532431602, -0.01790762133896351, 0.031369492411613464, 0.022487802430987358, 0.06844158470630646, 0.07531598955392838, 0.031009305268526077, -0.023479243740439415, -0.03018866293132305, -0.01177993044257164, -0.017106181010603905, 0.04312320798635483, 0.014828057959675789, -0.01597968302667141, 0.07103332877159119, 0.028449881821870804, -0.001294026616960764, 0.006143151316791773, -0.06088712438941002, 0.04808024689555168, 0.037799544632434845, -0.014598081819713116, 0.020496021956205368, -0.0784880593419075, 0.01887449063360691, -0.0008039165404625237, 0.03268460929393768, -0.003043007804080844, 0.013322148472070694, 0.043592531234025955, 0.04279303550720215, -0.016354741528630257, 0.02970672771334648, -0.06766138225793839, 0.06845609098672867, 0.015951629728078842, 0.05862810090184212, -0.005340200383216143, 0.0037774168886244297, 0.0368681326508522, -0.021656567230820656, 0.02257446199655533, 0.03823382034897804, 0.007836530916392803, 0.03615296632051468, 0.05057579651474953, -0.016018355265259743, 0.05635597184300423, 0.022479107603430748, 0.03796675428748131, 0.06083225831389427, -0.023842832073569298, 0.0010814607376232743, 0.01634124480187893, 0.02564157173037529, 0.03159402310848236, 0.007380190305411816, 0.04906105622649193, 0.02953164279460907, -0.03239767253398895, 0.024996433407068253, 0.012935852631926537, 0.07296338677406311, 0.007368465885519981, 0.005917643196880817, -0.019581714645028114, -0.022689931094646454, 0.0035461641382426023, -0.04987424239516258, -0.04246290773153305, -0.019599659368395805, 0.09443313628435135, 0.06725698709487915, -0.014787103049457073, 0.016391543671488762, -0.08192441612482071, 0.001602636300958693, -0.03790741786360741, -0.11005374044179916, 0.025080876424908638, 0.0023071751929819584, 0.001612186781130731, 0.0009536391007713974, -0.04620955139398575, 0.0014398943167179823, 0.0119725801050663, 0.021478651091456413, 0.0668749287724495, 0.006852366961538792, -0.010100765153765678, 0.023184433579444885, -0.01029843371361494, -0.021934421733021736, -0.047729890793561935, -0.03376968204975128, 0.03894123062491417, 0.007893781177699566, 0.040431488305330276, -0.08236397802829742, 0.01881702058017254, 0.023860998451709747, -0.0395209826529026, 0.021155158057808876, -0.043663110584020615, -0.045439980924129486, -0.04292898252606392, -0.026108190417289734, 0.004928637761622667, -0.003335363930091262, 0.0351966954767704, -0.009363137185573578, -0.020481739193201065, -0.02699151635169983, 0.01737096533179283, -0.0020942457485944033, -0.02828085422515869, -0.029905851930379868, 0.0006400453858077526, -0.013642657548189163, -0.0026394538581371307, -0.02089618891477585, 0.05354508385062218, -0.010039658285677433, -0.030692940577864647, -0.03500080108642578, 0.0089768311008811, 0.0263977013528347, 0.034195732325315475, 0.03623344749212265, 0.020643606781959534, -0.0032499930821359158, 0.06619513779878616, 0.027277296409010887, 0.05843019112944603, -0.006719054654240608, 0.02307198941707611, -0.0030826993752270937, 0.024759585037827492, 0.010951582342386246, -0.0784793347120285, -0.03993230685591698, -0.02262565866112709, 0.001966206356883049, 0.0001675033854553476, 0.030443448573350906, -0.0713147222995758, 0.04653586074709892, 0.02715010941028595, -0.01135783176869154, 0.06425304710865021, 0.00021875297534279525, 0.011865087784826756, 0.008795596659183502, -0.0030963567551225424, 0.04222855716943741, -0.013624710030853748, 0.07877326756715775, 0.011541461572051048, 0.04062656685709953, -0.006906790193170309, 0.07051091641187668, 0.0008504451252520084, 0.021571315824985504, -0.009477684274315834, 0.02619301527738571, -0.01619640924036503, 0.04309592396020889, -0.049592092633247375, 0.0016263627912849188, 0.03148304298520088, 0.013281937688589096, 0.07882265746593475, 0.008821112103760242, 0.030391506850719452, -0.0063057541847229, 0.035351358354091644, -0.0830661952495575, 0.06969202309846878, -0.03221464157104492, -0.06840798258781433, 0.00788627378642559, -0.05726935714483261, 0.03813641518354416, 0.022867439314723015, 0.00850983988493681, 0.055777933448553085, -0.04401908442378044, 0.03310972824692726, -0.027563419193029404, -0.0622723363339901, 0.0444122850894928, -0.031874097883701324, 0.006552638951689005, 0.05569729208946228, -0.005496690049767494, -0.05712348595261574, -0.02630164474248886, 0.004427330568432808, 0.01611456274986267, 0.024900805205106735, 0.0030934058595448732, 0.0019100726349279284, -0.0037746750749647617, -0.023630289360880852, -0.0054357824847102165, 0.03900057077407837, -0.008691562339663506, -0.10331381112337112, -0.015226885676383972, -0.013364269398152828, -0.02576017566025257, 0.05532625690102577, -0.011456784792244434, -0.001477102399803698, -0.008756821975111961, -0.027725642547011375, -0.018844733014702797, 0.033954620361328125, 0.011695723049342632, 0.032270487397909164, 0.02243500016629696, 0.0026789612602442503, 0.02448277920484543, -0.016011551022529602, -0.03408500552177429, -0.020223254337906837, -0.06300915032625198, -0.002535950392484665, 0.015164719894528389, 0.044131021946668625, -0.015739839524030685, -0.05516605079174042, 0.056569140404462814, 0.07762719690799713, 0.015680458396673203, -0.016884448006749153, 0.0036090670619159937, 0.03737921640276909, -0.015426788479089737, -0.0136346984654665, -0.03152166306972504, -0.024788150563836098, 0.04878201335668564, -0.060680489987134933, -0.01717599667608738, -0.033585693687200546, 0.004974613431841135, -0.03591446951031685, 0.030555129051208496, -0.06653264164924622, 0.017760802060365677, -0.04566521570086479, -0.05256710574030876, -0.018775276839733124, 0.02362298034131527, 0.023618431761860847, -0.02977561764419079, -0.045299120247364044, 0.056564029306173325, 0.033638712018728256, -0.050476234406232834, 0.04868476092815399, 0.00238788197748363, -0.019965162500739098, -0.03960959240794182, 0.02398032881319523, 0.0033340861555188894, -0.039772890508174896, 0.016682513058185577, 0.05069107562303543, -0.036826565861701965, 0.023369839414954185, -0.04986901581287384, -0.0695536732673645, -0.02804204262793064, 0.003073897212743759, 0.004133355338126421, -0.024307146668434143, -0.002683912171050906, -0.02930571883916855, -0.06934050470590591, 0.024456176906824112, 0.041123613715171814, -0.03599299117922783, -0.00466269813477993, 0.009911157190799713, 0.02981637977063656, -0.02389439381659031, -0.03636099025607109, 0.052596189081668854, -0.027358459308743477, 0.01712760515511036, -0.03749961033463478, -0.004049906972795725, 0.0342966727912426, -0.09266533702611923, -0.043123144656419754, 0.04973699897527695, -0.08186467736959457, -0.015575829893350601, 0.023048819974064827, 0.04448322951793671, 0.0482194758951664, -0.024941496551036835, -0.04593471437692642, -0.08920522779226303, -0.06335769593715668, -0.035315919667482376, -0.0701020285487175, 0.07149774581193924, -0.058566100895404816, -0.005255973432213068, -0.013740316964685917, -0.036729272454977036, -0.03350233659148216, 0.005826928187161684, 0.0030433470383286476, -0.014322759583592415, -0.041084788739681244, -0.06269770860671997, -0.016568606719374657, -0.006615960039198399, 0.018846679478883743, -0.03097708895802498, -0.007638846058398485, -0.02372419461607933, 0.0256904698908329, -0.06193815544247627, 0.03152964264154434, -0.01905498467385769, 0.07581409066915512, 0.031614210456609726, -0.015449528582394123, -0.005590840242803097, 0.06312388181686401, 0.02287455089390278, 0.008352665230631828, -0.00425714673474431, 0.029896067455410957, -0.05584762990474701, -0.007698655594140291, 0.061278488487005234, -0.03711985424160957, -0.029865534976124763, 0.018469056114554405, -0.012973962351679802, -0.032010726630687714, 0.021556681022047997, 0.009383901953697205, 0.006192289292812347, 0.017184996977448463, 0.011085515841841698, 0.023162411525845528, 0.005041930358856916, 0.04040085896849632, 0.07726231217384338, 0.05735659599304199, -0.0177423395216465, -0.04946066066622734, -0.03238894045352936, 0.054562799632549286, 0.042251598089933395, -0.010253651067614555, -0.0009404195589013398, -0.006817572750151157, 0.04053959622979164, 0.04041450470685959, -0.03192393481731415, -0.019200075417757034, 0.022946903482079506, 0.0020438332576304674, -0.006776805035769939, 0.012461056001484394, -0.02224363572895527, 0.0638175830245018, -0.007532608229666948, 0.0373484268784523, 0.020753979682922363, 0.009822339750826359, 0.006748754531145096, -0.01171181071549654, 0.08902586996555328, 0.09429501742124557, 0.031019223853945732, -0.004243474919348955, -0.02241288311779499, -0.016512850299477577, 0.010689480230212212, -0.004208808299154043, 0.01477490272372961, 0.0208484698086977, -0.03873284161090851, 0.008550978265702724, -0.018812330439686775, 0.025542715564370155, -0.010468684136867523, -0.02107752487063408, 0.02130129188299179, -0.004152064677327871, -0.08832640945911407, 0.004753091372549534, -0.020531753078103065, -0.0015520589658990502, 0.004757162649184465, 0.050111375749111176, -0.06457528471946716, -0.017049318179488182, -0.04696023091673851, -0.05226605758070946, -0.005698396824300289, 0.00683229835703969, -0.001438380335457623, -0.026713231578469276, -0.000779524736572057, 0.007242964114993811, -0.033728159964084625, -0.017848024144768715, -0.009681479074060917, 0.04432520642876625, 0.006082721520215273, 0.0366937555372715, 0.011392751708626747, -0.08895380795001984, -0.02155240997672081, 0.009310527704656124, 0.02521268092095852, -0.0783919245004654, -0.06117691099643707, -0.001796152675524354, 0.003940402530133724, -0.0033802452962845564, -0.0010448778048157692, -0.09030520170927048, 0.0517912432551384, -0.01851864717900753, 0.05232657492160797, 0.01010151021182537, -0.011131138540804386, 0.0587376207113266, -0.03839651495218277, 0.03394724056124687, -0.015085945837199688, -0.01634213700890541, 0.02120523527264595, 0.0021862625144422054, -0.019947059452533722, 0.0019741186406463385, -0.0339517779648304, -0.015694521367549896, 0.08957554399967194, -0.03238755092024803, -0.01858101785182953, -0.007052782457321882, -0.06264504045248032, -0.01645764335989952, -0.0010417535668238997, 0.02501537837088108, 0.021000254899263382, -0.06200983002781868, -0.04808957874774933, 0.010524346493184566, -0.028392335399985313, -0.02833409607410431, -0.051817215979099274, -0.032948628067970276, 0.02822435460984707, -0.0405820831656456, 0.017549611628055573, 0.028942452743649483, 0.012190837413072586, 0.0446915403008461, 0.004443873185664415, -0.010854802094399929, -0.012568727135658264, 0.0116103021427989, -0.049803707748651505, 0.030486399307847023, -0.08214737474918365, 0.03720417991280556, 0.027301698923110962, 0.04259214550256729, 0.014378710649907589, -0.022832795977592468, 0.04946121945977211, -0.03523433580994606, 0.009245938621461391, 0.007841607555747032, -0.026320714503526688, 0.04989340156316757, -0.030860867351293564, 0.05109826475381851, 0.017705274745821953, 0.022636180743575096, 0.0049162316136062145, 0.0022692931815981865, 0.01761458069086075, 0.055496737360954285, -0.05819360539317131, -0.06088578328490257, -0.0095136146992445, -0.03190910816192627, 0.05370587110519409, -0.025635942816734314, 0.05201628431677818, 0.04990806058049202, 0.011497646570205688, -0.021382706239819527, 0.010448915883898735, 0.04333355650305748, -0.03409193456172943, 0.00029495867784135044, 0.018358241766691208, -0.0033660123590379953, 0.03800216689705849, -0.05136813968420029, -0.004700982943177223, -0.021004918962717056, -0.061896324157714844, 0.04036799445748329, 0.041687000542879105, 0.026109831407666206, -0.029190564528107643, 0.02505820244550705, 0.04692539945244789, -0.008501960895955563, -0.03304437920451164, -0.04369545355439186, 0.06592799723148346, 0.0680968165397644, 0.029476508498191833, 0.0010520156938582659, 0.008711585775017738, 0.01907344162464142, 0.015835223719477654, 0.018775030970573425, 0.01215082686394453, 0.024191036820411682, 0.04138680174946785, 0.014572348445653915, -0.011278489604592323, 0.016971226781606674, -0.0014897375367581844, 0.015990139916539192, -0.0052911750972270966, -0.03454011678695679, 0.01050508487969637, -0.006685303524136543, 0.0005106297903694212, -0.03965015709400177, -0.06718233972787857, -0.03345876559615135, -0.027633877471089363, 0.06315647065639496, 0.035170961171388626, -0.0033388850279152393, -0.07178227603435516, 0.018338797613978386, 0.022250065580010414, 0.05412580445408821, 0.024026641622185707, 0.016045618802309036, -0.017550067976117134, 0.03042014315724373, -0.0022943185176700354, -0.0006095792050473392, -0.021059226244688034, 0.023107586428523064, 0.04282839223742485, -0.004572542384266853, 0.02176091820001602, -0.044156547635793686, 0.0007163303671404719, 0.0005305216764099896, 0.015343945473432541, 0.01585053838789463, -0.07474444061517715, -0.06851111352443695, -0.014663557521998882, -0.027783257886767387, -0.04623217508196831, -0.024025047197937965, -0.042880069464445114, -0.04198595881462097, -0.014553070068359375, 0.010972322896122932, 0.0294906347990036, 0.047478001564741135, 0.09105435013771057, -0.02221909910440445, 0.04062885418534279, -0.03816545009613037, -0.014130378141999245, 0.05721057578921318, -0.014412988908588886, 0.01411364134401083, -0.0009055139380507171, -0.059277746826410294, -0.04496832191944122, 0.002743628341704607, -0.006030396092683077, 0.03185338154435158, 0.011592735536396503, -0.021184368059039116, 0.0361073799431324, -0.013130802661180496, 0.008677744306623936, 0.06590773165225983, -0.005186283960938454, -0.041748955845832825, 0.012013300321996212, -0.03738007694482803, 0.009860982187092304, -0.028912531211972237, -0.050647884607315063, -0.008843856863677502, 0.04945029690861702, -0.029787136241793633, 0.05747193098068237, 0.06639920920133591, 0.028188364580273628, 0.006974855903536081, -0.030909569934010506, -0.028392253443598747, 0.031559351831674576, 0.001895075780339539, 0.00641106441617012, 0.03138025104999542, -0.03261275216937065, -0.015625659376382828, 0.009468569420278072, -0.0285666324198246, 0.03474085405468941, -0.052544523030519485, 0.03444504365324974, -0.033710841089487076, 0.018337486311793327, -0.017222708091139793, 0.02407650463283062, 0.028073126450181007, -0.000051767961849691346, 0.04367108270525932, 0.001530545181594789, -0.05067065730690956, 0.00789959542453289, 0.05078158155083656, 0.004746729973703623, -0.09430085867643356, 0.029127884656190872, 0.052887074649333954, 0.037181686609983444, -0.0715390145778656, 0.005296176765114069, 0.012520032934844494, -0.017554843798279762, -0.04397476091980934, 0.0107713108882308, 0.028992341831326485, -0.019353963434696198, -0.01512142177671194, -0.01833258382976055, -0.07820114493370056, 0.015453148633241653, 0.01538951974362135, 0.044541433453559875, 0.03200135752558708, 0.002275021281093359, 0.03526651859283447, -0.0033181016333401203, -0.023405950516462326, -0.026140384376049042, -0.0009684626711532474, -0.042681194841861725, 0.03267820551991463, -0.010478246957063675, -0.03532102331519127, 0.07782401889562607, -0.01722736842930317, 0.036011047661304474, 0.0002900918771047145, 0.04751775041222572, -0.005586553364992142, -0.04197519272565842, -0.035115115344524384, 0.004623202607035637, -0.005119004752486944, -0.03864124417304993, -0.04165830835700035, 0.02903994917869568, -0.09128786623477936, 0.0459623746573925, 0.006039173807948828, -0.02054869756102562, -0.03074273280799389, 0.012762703001499176, 0.03812335059046745, 0.00207356340251863, -0.008199461735785007, 0.048777028918266296, -0.01502188853919506, -0.005227070301771164, 0.010679916478693485, -0.02758694440126419, 0.016480963677167892, 0.009420838207006454, 0.009328204207122326, -0.06931384652853012, -0.020017998293042183, -0.010423368774354458, -0.006171609740704298, -0.005866223946213722, 0.03629366680979729, -0.02850702591240406, 0.05073435604572296, -0.03346514329314232, -0.011659020557999611, 0.01983468420803547, 0.010197200812399387, -0.045109279453754425, 0.0024387675803154707, 0.024460678920149803, -0.04805314540863037, -0.04721790552139282, -0.037973515689373016, -0.02839442528784275, 0.01214565709233284, -0.011648067273199558, -0.009167108684778214, -0.04670116305351257, -0.01791551522910595, 0.004238392226397991, -0.05007394775748253, -0.005190967582166195, 0.0019976473413407803, 0.00439898855984211, -0.04092266410589218, 0.028962142765522003, 0.0413326732814312, -0.06591162830591202, 0.03792577609419823, -0.05717639625072479, 0.03489452227950096, -0.019047601148486137, 0.02092738449573517, 0.012350893579423428, 0.010891156271100044, -0.04133477434515953, 0.028740718960762024, -0.055837325751781464, 0.03909606859087944, 0.03124609962105751, -0.01723853312432766, 0.038663607090711594, -0.014819784089922905, -0.09307347238063812, -0.017114441841840744, 0.057003725320100784, 0.0026415318716317415, 0.03237563371658325, -0.018807081505656242, 0.0015176613815128803, -0.018909355625510216, -0.046525172889232635, -0.008660209365189075, -0.0550101101398468, -0.020914742723107338, 0.03790810704231262 ]
<p>In the 19th century, most astronomers adopted an island universe model, in which our galaxy was the only object in an infinite space. They didn't know that the "spiral nebulae" were other galaxies. This model had the advantage of being dynamically stable (unlike Newton's infinite and uniform cosmology), and of avoiding the fact that Poisson's equation doesn't have unique solutions for an infinite and uniform universe. Ca. 1830, the geologist Lyell advocated a theory of uniformitarianism, in which the universe would have had uniform conditions going back infinitely far in time. There was some debate between Lyell and physicists such as Kelvin, who objected that the sun would have run out of energy, the earth would have lost its internal heat, and so on, but this was inconclusive because they didn't know enough thermodynamics and didn't know about the atomic nucleus.</p> <p>But by 1850, the second law of thermodynamics had been formulated, and this would seem to have been solid proof that the universe could not possibly have existed for an infinite time in the past. (This level of understanding of thermodynamics would also, I'd imagine, allow them to show that stars would gradually evaporate out of the galaxy, since the velocity distribution would have a high-velocity tail.) Kelvin did attack Lyell with the second law, but it doesn't sound like people at the time appreciated that this was a decisive argument.</p> <p>With the benefit of hindsight, we can say that it was decisive, and from 1850 to 1905, people should have been considering only cosmological models that used Newtonian mechanics and that stretched back a finite time into the past. Are such models possible?</p> <p>For example, I suppose you could make a Newtonian big bang, in which, as many students today imagine, there was an explosion at a specific point in otherwise empty space. Extrapolating the motion of all particles back in time using the laws of physics, one would find their trajectories all converging on a point, then diverging from it again on the other side, i.e., it would look like a big crunch/big bang "singularity," -- it would be a singularity of the matter density, temperature, etc. Thermodynamically, it would look like an extreme thermodynamic fluctuation, which is no worse than the thermodynamic implausibility of the low-entropy big bang in modern GR-based theories. There would be an upper bound on ages of objects in today's universe, because everything was destroyed in the singularity.</p> <p>Another possibility I can imagine is that you could start off with a universe containing an infinite amount of matter and an infinite amount of energy thermodynamically available to do work. After an infinite time, you would have expended an infinite amount of energy to do work, but you would still have an infinite amount left. The modern counterpart of this kind of thinking would be calculations of whether you can do an infinite calculation in various cosmological models (Dyson 1979, Krauss 1999).</p> <p>Related: <a href="http://physics.stackexchange.com/questions/6897/why-didnt-newton-have-a-cosmological-constant">Why didn&#39;t Newton have a cosmological constant</a></p> <p><em>References</em></p> <p>Dyson, Time without end: Physics and biology in an open universe, Reviews of Modern Physics 51 (1979), pp. 447–460, doi:10.1103/RevModPhys.51.447; described in <a href="http://math.ucr.edu/home/baez/end.html">http://math.ucr.edu/home/baez/end.html</a></p> <p>Krauss and Starkman, 1999, Life, The Universe, and Nothing: Life and Death in an Ever-Expanding Universe, <a href="http://arxiv.org/abs/astro-ph/9902189">http://arxiv.org/abs/astro-ph/9902189</a></p>
g1560
[ 0.007731188088655472, -0.008277244865894318, 0.03126413747668266, -0.09459526836872101, 0.024469055235385895, 0.014336757361888885, -0.033965833485126495, 0.009525211527943611, -0.004029603209346533, -0.02690701186656952, 0.04039118066430092, -0.05103563889861107, 0.05626344308257103, 0.027037136256694794, 0.03673669323325157, -0.020561113953590393, 0.0130469910800457, -0.04142703488469124, 0.00452082185074687, 0.05264733359217644, -0.016502059996128082, -0.0061178249306976795, 0.06203870102763176, -0.017409363761544228, -0.05962333455681801, -0.03963693603873253, 0.017838837578892708, -0.008852245286107063, -0.0057454295456409454, -0.024878494441509247, -0.0015999836614355445, -0.04918839782476425, 0.016994256526231766, -0.03666582703590393, -0.00825728103518486, 0.02000385895371437, -0.056619081646203995, -0.0034459286835044622, 0.04972207918763161, -0.037086401134729385, -0.013136015273630619, -0.008904150687158108, 0.005355142056941986, 0.005230616312474012, 0.008578091859817505, -0.005495562683790922, -0.03125628083944321, 0.02438802644610405, 0.03821716457605362, 0.04465770348906517, -0.05418841540813446, 0.026612747460603714, 0.018154889345169067, -0.06116523966193199, -0.017547495663166046, 0.03070136345922947, 0.010682079941034317, 0.002812305698171258, 0.03519096225500107, 0.032900162041187286, -0.04870985075831413, -0.02003004588186741, 0.051520779728889465, -0.0055694873444736, 0.02030843496322632, 0.0051756505854427814, -0.029377296566963196, -0.00231600902043283, 0.02111252397298813, -0.0026633450761437416, -0.0028432481922209263, -0.055410660803318024, -0.03264257311820984, -0.05706234276294708, -0.037576161324977875, 0.04378034919500351, -0.025665180757641792, -0.03172184154391289, -0.0448751337826252, -0.047069501131772995, -0.07886022329330444, 0.02178153209388256, 0.00454835407435894, 0.040140826255083084, -0.01452953927218914, -0.03749346360564232, 0.031104499474167824, -0.03306138888001442, -0.038923878222703934, 0.03240551799535751, -0.06089184433221817, 0.07888995856046677, 0.08242529630661011, -0.00879821740090847, 0.00954391248524189, -0.06275499612092972, 0.017474845051765442, 0.01936308480799198, 0.008931200951337814, 0.03652254864573479, -0.05421920865774155, -0.039855971932411194, 0.049564752727746964, -0.03577745705842972, -0.0042019253596663475, -0.0100106718018651, 0.013668819330632687, 0.029351988807320595, -0.027559086680412292, -0.04410902410745621, 0.02138441801071167, -0.018214507028460503, -0.04875760152935982, -0.02261790819466114, -0.05498617887496948, -0.021427080035209656, 0.025648506358265877, 0.022929873317480087, 0.007170278113335371, 0.029039422050118446, -0.02592836506664753, 0.03845801204442978, -0.043712157756090164, 0.029482703655958176, -0.04203081130981445, -0.0019667241722345352, -0.01387593150138855, -0.0419580303132534, 0.018465526401996613, -0.064778633415699, 0.01367900799959898, 0.06556934863328934, -0.050309617072343826, 0.024449901655316353, 0.01800515688955784, 0.01012213621288538, -0.0566745288670063, 0.01491096243262291, 0.0029006502591073513, -0.005227258428931236, -0.0069708796218037605, -0.08683663606643677, -0.025818677619099617, 0.0665215253829956, 0.007804033812135458, 0.055258024483919144, -0.008592326194047928, 0.04575235769152641, -0.010831366293132305, 0.047878388315439224, -0.023469336330890656, 0.06875397264957428, 0.0442170649766922, 0.06654155254364014, -0.07377003133296967, 0.005278963595628738, -0.01603912189602852, 0.03572563827037811, 0.0016212161863222718, -0.07641972601413727, 0.021842435002326965, 0.008607651107013226, 0.006796351633965969, -0.017772704362869263, -0.05021676793694496, 0.09328333288431168, -0.017973488196730614, -0.07445976138114929, 0.03942333906888962, 0.014974910765886307, -0.06175921484827995, -0.042905014008283615, 0.009311306290328503, 0.018359331414103508, -0.0036901202984154224, -0.031862664967775345, 0.05855736881494522, -0.017011456191539764, 0.006742085330188274, -0.05846920982003212, -0.015010477975010872, -0.010816482827067375, 0.004911553114652634, 0.006190930958837271, 0.009969828650355339, 0.020127208903431892, 0.004830518737435341, -0.0066815633326768875, 0.04850802943110466, -0.013653949834406376, 0.012198965065181255, -0.05152735859155655, -0.026097245514392853, 0.016333220526576042, 0.02165605127811432, -0.008669235743582249, 0.09264832735061646, -0.02477564662694931, -0.06011303886771202, -0.005941079929471016, 0.000293765653623268, 0.03566120192408562, 0.040775567293167114, 0.02186918444931507, -0.013451860286295414, -0.0314650684595108, -0.03202220797538757, 0.02396039292216301, 0.03416862338781357, -0.033454637974500656, -0.009360913187265396, 0.011794441379606724, -0.01711263880133629, 0.04341432824730873, 0.020349305123090744, -0.06110180541872978, -0.03287854045629501, 0.03119063936173916, -0.008737818337976933, 0.04489118978381157, -0.003742627799510956, 0.03984474390745163, 0.046655576676130295, 0.02179177850484848, 0.11704479902982712, -0.07735612243413925, -0.011578555218875408, -0.03372758999466896, -0.05125933140516281, 0.04746478796005249, -0.04233180359005928, 0.02058863453567028, 0.022081393748521805, 0.0038411186542361975, 0.001211637514643371, 0.027191054075956345, 0.01353394240140915, -0.01733458787202835, -0.005901508964598179, 0.010852377861738205, 0.003991307690739632, -0.003251588437706232, -0.06106266379356384, -0.02387181483209133, 0.03057570941746235, -0.10671144723892212, 0.02463892288506031, -0.03207040950655937, 0.0052636717446148396, 0.03908275067806244, 0.006250816863030195, -0.011110382154583931, -0.05479053407907486, -0.015257633291184902, -0.0010276236571371555, -0.00987179484218359, 0.06782318651676178, 0.042959120124578476, -0.06999503821134567, -0.004429078195244074, 0.05842776596546173, -0.057635579258203506, 0.027364268898963928, 0.03763284534215927, -0.0009272726019844413, 0.013521945104002953, -0.04581649973988533, -0.004239997826516628, -0.05487549304962158, -0.035815875977277756, 0.04616079851984978, -0.009524923749268055, 0.013774973340332508, 0.0017808238044381142, -0.022908220067620277, 0.02975105307996273, -0.023778598755598068, 0.0010738983983173966, 0.04324944689869881, -0.00571255199611187, 0.007386123761534691, 0.005317271687090397, -0.05812039598822594, 0.04855960234999657, 0.02309238910675049, -0.05515790730714798, -0.014927112497389317, 0.05969717353582382, 0.07824079692363739, -0.017797043547034264, 0.029038826003670692, 0.04421217367053032, -0.06806749105453491, 0.019146017730236053, -0.0744723454117775, 0.03157047554850578, -0.016077794134616852, -0.006118165794759989, -0.01770690828561783, -0.03317782282829285, -0.010248107835650444, -0.04632312431931496, 0.014796636998653412, 0.052737221121788025, -0.026649612933397293, 0.003392671700567007, -0.0243008341640234, -0.01197925303131342, -0.009149106219410896, -0.06435878574848175, 0.024679549038410187, 0.03224238380789757, 0.0031070243567228317, 0.042745042592287064, -0.018904540687799454, 0.02563418447971344, -0.004374126438051462, -0.004432851914316416, 0.08185743540525436, 0.00011126606841571629, 0.03223433345556259, 0.026767609640955925, 0.03304425999522209, -0.07228218019008636, 0.07141111046075821, 0.032336682081222534, -0.09543713927268982, -0.045529987663030624, -0.08376780897378922, 0.016111651435494423, -0.05329855531454086, -0.04123317822813988, 0.006064039189368486, -0.014093171805143356, -0.04909687489271164, 0.011798263527452946, 0.007974933832883835, 0.002788941841572523, 0.04793223738670349, 0.011834106408059597, -0.01685323566198349, -0.006220331881195307, -0.030171407386660576, 0.01316166203469038, 0.026139074936509132, 0.02897135727107525, -0.0015205037780106068, -0.0035013470333069563, 0.011567051522433758, 0.015089243650436401, 0.0710853636264801, -0.009028461761772633, -0.0018662451766431332, -0.0010927737457677722, 0.026337603107094765, 0.03869112208485603, 0.037559740245342255, 0.06844917684793472, 0.044027652591466904, -0.0011550617637112737, -0.008918868377804756, -0.002336171455681324, 0.027412302792072296, -0.03963745757937431, 0.037948139011859894, 0.037675417959690094, -0.01326783373951912, -0.048180777579545975, 0.02954491786658764, 0.022586438804864883, 0.025178853422403336, 0.03293602541089058, -0.03280576318502426, -0.001092389808036387, 0.02137773483991623, -0.01710112765431404, 0.09366212040185928, 0.041184913367033005, -0.022091420367360115, 0.03612628951668739, -0.00595825957134366, -0.020829275250434875, 0.020655997097492218, 0.09353891760110855, -0.01231699250638485, 0.03185097128152847, -0.018626296892762184, -0.047555696219205856, 0.03527576103806496, 0.003732869168743491, 0.09933976829051971, -0.030828475952148438, 0.0497923344373703, -0.018215958029031754, -0.0014511581975966692, -0.039725612848997116, -0.042094361037015915, -0.04110892489552498, 0.04854033514857292, -0.0001255781389772892, -0.006383642088621855, -0.012198008596897125, -0.04241286963224411, 0.004330541472882032, -0.049076564610004425, -0.0007087000412866473, 0.007289031054824591, -0.06554587930440903, -0.04057101160287857, -0.06089817360043526, -0.024035504087805748, 0.025159362703561783, 0.002218654379248619, -0.026295935735106468, 0.02251279354095459, -0.04863925278186798, 0.048012107610702515, -0.05178464949131012, 0.009376579895615578, 0.008546176366508007, -0.030752621591091156, 0.02939433977007866, -0.04385284334421158, -0.03711779788136482, 0.03284088894724846, -0.022235730662941933, 0.008796853944659233, -0.017070796340703964, -0.05862874910235405, -0.03504267334938049, 0.01765771210193634, 0.024103626608848572, 0.009420235641300678, 0.036244507879018784, -0.006845744326710701, 0.03793071582913399, -0.030819809064269066, 0.04845264181494713, 0.042457155883312225, 0.020794453099370003, 0.06406977027654648, -0.06294514983892441, 0.03717661648988724, 0.06129780411720276, 0.017661202698946, 0.07385629415512085, 0.04160856083035469, -0.04934985935688019, -0.03896905481815338, -0.006348467897623777, 0.02465682663023472, 0.00861077569425106, -0.01350712962448597, 0.06700177490711212, -0.015702685341238976, -0.019373217597603798, -0.03510623797774315, 0.031487297266721725, 0.04008612781763077, 0.05657123401761055, -0.023793146014213562, -0.005077056121081114, -0.018752479925751686, 0.046254467219114304, 0.018634334206581116, -0.013267002068459988, -0.01579429768025875, -0.005029761232435703, -0.04685306176543236, -0.039649613201618195, -0.009043015539646149, 0.037063539028167725, 0.06428328156471252, 0.014274438843131065, -0.036144472658634186, -0.015441911295056343, 0.01598457247018814, -0.07019165903329849, -0.04955589026212692, 0.03185056149959564, -0.05891267582774162, -0.03350444138050079, 0.04462144523859024, 0.029072081670165062, 0.0010471954010426998, 0.0007315432885661721, -0.04263202100992203, 0.03350052610039711, -0.005478672217577696, 0.029433434829115868, -0.008826100267469883, -0.021950596943497658, 0.09732819348573685, 0.020824085921049118, 0.012288445606827736, 0.01576731540262699, 0.07331489026546478, 0.0009702445240691304, -0.028729278594255447, 0.03864414989948273, -0.06572827696800232, 0.07457276433706284, 0.0049513899721205235, -0.029685452580451965, -0.01917336881160736, -0.013679025694727898, -0.027779387310147285, -0.005420436151325703, 0.008882082998752594, -0.019794533029198647, 0.01600136235356331, 0.018358856439590454, 0.018748914822936058, 0.06392107903957367, 0.05800239369273186, -0.030389968305826187, -0.056363124400377274, -0.05864858254790306, -0.05460060015320778, -0.04668591916561127, -0.015408498235046864, 0.003437203587964177, 0.07219842076301575, 0.018110085278749466, 0.016181524842977524, 0.038707319647073746, -0.007697233930230141, -0.04902973026037216, 0.03277978301048279, -0.013286062516272068, 0.0378699004650116, 0.0025586476549506187, -0.003299311501905322, -0.014407499693334103, -0.02893741801381111, 0.07724526524543762, -0.06275082379579544, 0.06398454308509827, -0.014013501815497875, -0.006949331611394882, 0.018797097727656364, 0.0008392593008466065, 0.0221855528652668, -0.0404934398829937, 0.002950186375528574, 0.03772309795022011, -0.029731901362538338, 0.036100149154663086, 0.03457898274064064, -0.05549802631139755, -0.016420092433691025, 0.011941496282815933, 0.026564758270978928, 0.016645116731524467, -0.030642304569482803, 0.019691774621605873, 0.01051553525030613, -0.020630180835723877, -0.01723240129649639, -0.004056211560964584, -0.020358571782708168, 0.06290670484304428, 0.03255724906921387, 0.022961897775530815, -0.02449301816523075, -0.05210374668240547, -0.017456861212849617, -0.06934457272291183, 0.03479808568954468, 0.008831683546304703, 0.006099403835833073, -0.007880924269557, 0.03045489639043808, -0.021545356139540672, 0.03197435662150383, -0.01657768152654171, -0.0421782061457634, -0.010090501978993416, -0.03181358426809311, 0.010687320493161678, 0.003373790765181184, -0.014995992183685303, 0.015130957588553429, -0.02950727567076683, -0.003456069389358163, 0.012372818775475025, -0.006630023941397667, 0.009343128651380539, 0.014855777844786644, -0.03332066163420677, 0.050204478204250336, -0.02851800061762333, -0.010706682689487934, -0.013446648605167866, -0.013767975382506847, 0.016208898276090622, 0.02853616140782833, -0.02355251833796501, -0.08310756087303162, 0.005593776702880859, -0.01973147690296173, -0.03356395289301872, -0.010519727133214474, -0.009297232143580914, 0.02018667943775654, 0.021935658529400826, -0.03828490898013115, 0.012250516563653946, 0.07434435933828354, 0.00015532891848124564, -0.025444023311138153, -0.01579197309911251, 0.004032791126519442, -0.05157621577382088, 0.01572650671005249, -0.01460000965744257, 0.005928074009716511, 0.025225739926099777, -0.021264253184199333, 0.011474787257611752, 0.039382290095090866, 0.05047696828842163, 0.02828170359134674, 0.01892407424747944, 0.045063622295856476, -0.0012050052173435688, -0.051348790526390076, 0.06861507147550583, 0.06203627586364746, 0.0170920267701149, 0.028400149196386337, -0.010786883533000946, 0.03315449878573418, 0.022907627746462822, -0.025962894782423973, -0.0017031775787472725, -0.014479135163128376, -0.030452609062194824, -0.039322443306446075, -0.04119857773184776, -0.01947677694261074, -0.03347465395927429, 0.057227302342653275, 0.05621447041630745, 0.0007997170905582607, 0.0296205822378397, 0.013740683905780315, -0.0008622475434094667, -0.0508243702352047, -0.03536221385002136, -0.003353134961798787, -0.033872831612825394, -0.06178112328052521, 0.011844036169350147, -0.04432361200451851, 0.005696509964764118, 0.01842193678021431, -0.03889649361371994, 0.023974256590008736, -0.04289963096380234, 0.008296498097479343, -0.030836621299386024, 0.01165981125086546, -0.031613826751708984, 0.04916458576917648, 0.03996375948190689, 0.005289485678076744, -0.059172626584768295, 0.02451559156179428, -0.01075560599565506, 0.020258186385035515, 0.05067424848675728, -0.04964381828904152, -0.021261466667056084, 0.011386662721633911, -0.039309293031692505, -0.026393428444862366, 0.007225467823445797, 0.06890584528446198, 0.00980293471366167, 0.0025824320036917925, 0.06466963142156601, -0.0064086285419762135, 0.03325560688972473, -0.02894994243979454, 0.030231881886720657, 0.022194212302565575, 0.02563614584505558, -0.022120313718914986, 0.00837562046945095, -0.07345345616340637, -0.00040723884012550116, -0.02584412693977356, 0.02668905258178711, 0.045394111424684525, 0.010645480826497078, 0.06248828023672104, 0.03367653116583824, 0.050936076790094376, -0.07810501754283905, -0.007264289539307356, 0.0009162876522168517, -0.012828771956264973, 0.004629680421203375, 0.006804203148931265, -0.04642268642783165, -0.007034475449472666, 0.004616063553839922, 0.010914575308561325, 0.032578155398368835, 0.016811473295092583, 0.05206296220421791, -0.011458225548267365, 0.027536215260624886, 0.01777714677155018, -0.006904635578393936, -0.055268917232751846, -0.03671953082084656, -0.0016718442784622312, -0.03735826164484024, -0.04418632760643959, 0.026089496910572052, 0.007577710319310427, -0.008603070862591267, 0.018997596576809883, 0.010950920172035694, 0.001752481795847416, -0.03277023509144783, -0.030296986922621727, -0.022361477836966515, 0.00801736768335104, 0.00951020885258913, -0.014068644493818283, -0.017384978011250496, -0.0728071853518486, 0.014632762409746647, -0.02522723749279976, -0.022541671991348267, -0.04005401208996773, -0.030101709067821503, -0.007035775575786829, 0.023546671494841576, -0.005212096963077784, -0.01764470525085926, 0.008548644371330738, -0.045532260090112686, -0.062222670763731, -0.02188015915453434, 0.051474444568157196, -0.03905230388045311, 0.007540897931903601, 0.0576351061463356, -0.004408953711390495, 0.008662533946335316, 0.06716406345367432, 0.026222381740808487, 0.04597729071974754, -0.019430896267294884, 0.03924058377742767, 0.02648916095495224, -0.049596332013607025, 0.04347681999206543, 0.04848157986998558, -0.018281148746609688, -0.006333472672849894, -0.06050015240907669, 0.04753268137574196, 0.014422636479139328 ]
<p>In the last 40 years (approximately) people have been "discovering", "rediscovering" and "studying" SUSY as a powerful tool and "symmetry principle". </p> <p>Question: </p> <p>What if SUSY is not realized in Nature at the end? Is SUSY the only path to "relate" fermions and bosons or what else? Remark: SUSY has not been discovered yet, so keep you totally conservative. What if there is no SUSY?</p> <p>Bonus:</p> <p>What are the merits of SUSY? What are its main issues? I do know some answers to this, but I think it could very enlightening if we "listed" pros and contras of current supersymmetric theories to see where we are NOW. </p>
g1561
[ 0.027558738365769386, 0.051161233335733414, 0.027181832119822502, 0.017670486122369766, -0.009821549989283085, -0.01610225811600685, -0.02916146069765091, 0.044800907373428345, 0.006683950312435627, -0.03319740667939186, -0.012344586662948132, -0.04650377109646797, 0.004913428332656622, 0.0688643679022789, 0.003764171851798892, -0.012363598681986332, 0.026476221159100533, -0.05935116857290268, 0.04514763876795769, -0.05030512064695358, 0.02300465665757656, 0.021928375586867332, 0.019062308594584465, 0.0033717486076056957, -0.05086953565478325, -0.008152867667376995, 0.054531581699848175, -0.0045766811817884445, 0.06078077107667923, -0.004766758531332016, 0.020185301080346107, -0.01701417565345764, 0.047530464828014374, 0.001768154208548367, 0.02683720551431179, -0.05187537521123886, 0.03073858469724655, 0.05375120788812637, -0.008462300524115562, -0.010165682062506676, 0.006873590871691704, -0.028454581275582314, -0.03213873505592346, -0.057489216327667236, -0.014593186788260937, 0.024798789992928505, -0.007967117242515087, -0.02870466187596321, 0.07755424082279205, -0.050629813224077225, 0.05312489718198776, 0.011200901120901108, 0.035249412059783936, -0.007665429264307022, 0.0018311097519472241, 0.010972504504024982, 0.08540063351392746, 0.011272348463535309, 0.029423099011182785, 0.02145320363342762, 0.005074908956885338, 0.0613938644528389, 0.002977237571030855, 0.04665353149175644, 0.06149866431951523, 0.04986114054918289, -0.0836763009428978, 0.01831556297838688, 0.03434807434678078, 0.021565591916441917, -0.0051804655231535435, -0.04472106695175171, 0.010062865912914276, 0.03285621106624603, -0.000040562732465332374, 0.039654143154621124, -0.004729012493044138, 0.0254405178129673, -0.04508752375841141, -0.011471147648990154, 0.007105735130608082, -0.03582889214158058, 0.006926448550075293, 0.03105762042105198, 0.005583587102591991, -0.06684579700231552, -0.020687974989414215, 0.02848517894744873, -0.005574291106313467, 0.022560205310583115, -0.06855038553476334, -0.011712543666362762, 0.027003776282072067, -0.07741712033748627, -0.008120703510940075, 0.03664293885231018, 0.07847005128860474, 0.0031438262667506933, -0.009690780192613602, -0.02572023496031761, -0.018248364329338074, -0.03867867961525917, 0.03262319788336754, 0.008868563920259476, 0.01840326003730297, -0.02952554076910019, 0.05302863195538521, -0.023517325520515442, 0.019900759682059288, 0.013263675384223461, -0.04737807810306549, 0.017751863226294518, 0.026303481310606003, 0.04368503391742706, -0.09671502560377121, -0.013195347040891647, 0.02865809015929699, -0.044721782207489014, 0.02490544691681862, 0.03655853122472763, 0.020619794726371765, -0.020611485466361046, -0.007611487992107868, -0.028782637789845467, -0.03644851967692375, -0.001954469596967101, -0.05462200567126274, 0.018980352208018303, -0.017619773745536804, -0.0051699173636734486, -0.03328938037157059, -0.014366291463375092, -0.021145449951291084, 0.06797147542238235, -0.017186058685183525, 0.024980148300528526, -0.012817608192563057, -0.003928125835955143, 0.04437025636434555, -0.02806367725133896, -0.004336945712566376, -0.011147188022732735, -0.03300650045275688, 0.07083120942115784, -0.02052689902484417, 0.005635744426399469, -0.016756700351834297, 0.02767150290310383, -0.05605805292725563, 0.056181900203228, -0.01584469899535179, 0.042393989861011505, -0.020885568112134933, -0.02765965647995472, 0.012031921185553074, -0.0636088028550148, 0.007080904673784971, -0.027813274413347244, 0.022140948101878166, -0.07501807808876038, 0.05565731227397919, 0.03135628253221512, -0.028035495430231094, 0.01166452094912529, -0.05150633305311203, -0.027834024280309677, -0.007432082202285528, -0.0743405744433403, 0.008048420771956444, -0.024846136569976807, -0.11676812916994095, -0.03209563344717026, -0.027324967086315155, 0.05551811680197716, -0.023745877668261528, -0.008973570540547371, 0.010076605714857578, -0.011777755804359913, -0.0026130073238164186, 0.02762286737561226, -0.06567725539207458, -0.004189866594970226, 0.027095695957541466, 0.017794843763113022, -0.016210444271564484, 0.0062512559816241264, -0.005519060883671045, -0.005854195449501276, 0.00460836011916399, 0.030637800693511963, 0.007450025528669357, -0.012933376245200634, -0.007248742505908012, 0.07787878066301346, -0.07023370265960693, 0.002953639253973961, 0.01945405639708042, 0.014246040023863316, -0.010945135727524757, -0.04063074290752411, -0.042311251163482666, 0.059608593583106995, 0.01163196749985218, -0.012826330028474331, 0.024278899654746056, 0.0007216246449388564, -0.03857434168457985, 0.011601605452597141, 0.010074594058096409, -0.02990115061402321, 0.049128152430057526, -0.01566997729241848, 0.00770076597109437, -0.03239351883530617, -0.05655593052506447, -0.03711717948317528, -0.0434715673327446, 0.015769025310873985, -0.006517881061881781, 0.050158340483903885, 0.004743896424770355, -0.02580849826335907, 0.02418476901948452, 0.04241829365491867, 0.020710553973913193, 0.05558694154024124, -0.07795988023281097, -0.0829085037112236, -0.04477870464324951, 0.011696421541273594, -0.07034299522638321, -0.0006939467857591808, 0.03371106833219528, -0.03274039551615715, 0.015393488109111786, 0.012917482294142246, -0.00387846352532506, -0.038423918187618256, 0.11159218102693558, -0.022970499470829964, -0.0037684724666178226, -0.03689877688884735, 0.023179316893219948, 0.04180687293410301, 0.10012920945882797, 0.01722489483654499, 0.05013354867696762, -0.014197410084307194, 0.011482891626656055, -0.000012479448741942178, 0.04882649704813957, 0.017597738653421402, 0.0006980975740589201, 0.02211601659655571, -0.018178094178438187, 0.04110397771000862, 0.01831926219165325, 0.060034483671188354, -0.0020214850082993507, -0.05655141919851303, 0.01263057254254818, -0.046513162553310394, -0.0037732834462076426, -0.03407490253448486, -0.010508710518479347, 0.04307316988706589, -0.01572098582983017, -0.017012061551213264, -0.0208427757024765, 0.052336350083351135, -0.020818186923861504, -0.005201092921197414, 0.0009261139784939587, -0.030894069001078606, 0.02182925119996071, 0.053311001509428024, -0.04944721609354019, 0.03720821067690849, 0.0436006635427475, -0.006526484154164791, 0.029323795810341835, 0.011081245727837086, -0.026242468506097794, 0.04749569296836853, 0.027748864144086838, 0.017984721809625626, 0.01689821295440197, -0.03515491634607315, -0.010916593484580517, 0.05085106939077377, -0.008863420225679874, -0.07267595827579498, 0.0008253981941379607, 0.06135706603527069, -0.04742388054728508, 0.021277280524373055, 0.013869291171431541, -0.04392173886299133, -0.043611034750938416, 0.021151859313249588, 0.017624465748667717, 0.022267337888479233, 0.03505535423755646, 0.03726232051849365, 0.035259079188108444, -0.0006698528886772692, -0.12606742978096008, -0.027904506772756577, 0.0224772896617651, -0.049336306750774384, -0.007974482141435146, 0.044248711317777634, -0.0048042223788797855, 0.030146287754178047, -0.02793785370886326, 0.03273753076791763, -0.0077356682159006596, 0.03158014267683029, 0.04743848741054535, -0.036553677171468735, -0.0442885085940361, 0.043437469750642776, 0.06570476293563843, -0.0012729264562949538, 0.044257890433073044, 0.04191873222589493, -0.01868823543190956, 0.02406955696642399, -0.07062767446041107, -0.016731057316064835, -0.013419761322438717, -0.007527741137892008, -0.029232092201709747, -0.004195136949419975, -0.06160881742835045, 0.007625086698681116, -0.028594456613063812, -0.03233371302485466, 0.028018806129693985, 0.034324631094932556, -0.005350358318537474, -0.05597570538520813, 0.004533732309937477, 0.007574868388473988, 0.016278615221381187, -0.016664916649460793, -0.04403730109333992, -0.03765203058719635, 0.02428651787340641, -0.01363008376210928, -0.007382931187748909, 0.047369297593832016, 0.041020799428224564, 0.05863381549715996, -0.029629673808813095, 0.04674854502081871, 0.02960619144141674, 0.02559678629040718, 0.013257532380521297, -0.017196740955114365, -0.02696908637881279, -0.008943149819970131, 0.020968057215213776, 0.024388104677200317, -0.013023441657423973, 0.03577226400375366, 0.03443098068237305, -0.04661890119314194, -0.007020868360996246, -0.033149655908346176, -0.0020535634830594063, -0.02680344693362713, -0.012529212050139904, 0.034867119044065475, 0.0063418177887797356, -0.05441677197813988, -0.016751909628510475, 0.017080094665288925, -0.01911238767206669, 0.024568447843194008, 0.022388124838471413, 0.054922524839639664, 0.006234149448573589, -0.049641769379377365, 0.03614268824458122, 0.04995585232973099, -0.07647005468606949, -0.009170806035399437, -0.042608972638845444, 0.05674166977405548, 0.024297509342432022, 0.02899066172540188, -0.017308756709098816, 0.005368069279938936, 0.018707534298300743, 0.034572988748550415, -0.006203940603882074, -0.03737519681453705, -0.03835683688521385, -0.0014950144104659557, -0.00478461803868413, -0.002279452048242092, -0.033377062529325485, -0.013462144881486893, -0.0015005908207967877, -0.01702680066227913, 0.02803138643503189, -0.028879927471280098, 0.03186560794711113, -0.011033209040760994, 0.05409165844321251, 0.06440018862485886, 0.04527563601732254, -0.026242434978485107, 0.028842192143201828, -0.04404483363032341, -0.06546240299940109, -0.09408415853977203, 0.004863582085818052, 0.004090767819434404, 0.06815183907747269, 0.0026418075431138277, 0.0274201650172472, -0.028407862409949303, 0.006542140617966652, -0.045668382197618484, 0.016798680648207664, -0.0009640361531637609, -0.018812181428074837, 0.012612581253051758, -0.014167608693242073, 0.025730334222316742, -0.02613004297018051, 0.008200012147426605, -0.0039978185668587685, -0.013141673058271408, 0.0020126979798078537, -0.030768128111958504, -0.05987389013171196, 0.06434356421232224, 0.061868298798799515, -0.001734089688397944, 0.018817678093910217, 0.02387271448969841, -0.0202677920460701, -0.01728813163936138, -0.027413932606577873, -0.011141032911837101, 0.0014933425700291991, 0.006916815415024757, -0.018761171028017998, 0.04921167716383934, -0.05482637509703636, -0.013096336275339127, -0.12065106630325317, -0.06772275269031525, 0.0006894113612361252, 0.016675366088747978, 0.018951518461108208, 0.014139899052679539, -0.04542730003595352, -0.03983891382813454, 0.08516789227724075, -0.022639989852905273, 0.055213142186403275, 0.028064701706171036, -0.04298959672451019, -0.018906764686107635, 0.004138143267482519, -0.029862841591238976, -0.04005570709705353, -0.02488797903060913, 0.0330909788608551, 0.03575165197253227, 0.010929403826594353, -0.022604402154684067, -0.045196957886219025, -0.02581346221268177, 0.03159484639763832, 0.027299636974930763, -0.0020044876728206873, -0.07570433616638184, 0.07199167460203171, -0.023820318281650543, -0.03392444923520088, -0.012087492272257805, -0.04344547912478447, 0.00777904037386179, -0.06287205219268799, -0.02887478657066822, -0.017642978578805923, -0.020138420164585114, 0.0013385211350396276, -0.024484233930706978, 0.0034799559507519007, 0.0021249204874038696, 0.0023445093538612127, -0.03190603479743004, -0.025207342579960823, 0.0034422646276652813, 0.005118101369589567, 0.04586018621921539, 0.03771951049566269, 0.08659792691469193, 0.01470791082829237, 0.024776693433523178, 0.12421966344118118, -0.07303162664175034, 0.01358016300946474, -0.030108273029327393, 0.06060135364532471, -0.020747322589159012, -0.05581294000148773, 0.01676061935722828, 0.008015191182494164, 0.02869652956724167, 0.0013992155436426401, -0.01119090337306261, 0.012609629891812801, -0.01366123091429472, -0.047324661165475845, 0.06654848903417587, 0.026540689170360565, -0.02924301289021969, 0.016598429530858994, 0.01170127559453249, -0.028787491843104362, 0.0195304062217474, 0.05139505863189697, -0.015304747968912125, 0.037481993436813354, -0.01514405757188797, 0.08713159710168839, 0.014900915324687958, 0.0738830491900444, -0.013366210274398327, -0.032792869955301285, -0.002605476649478078, -0.029943153262138367, -0.01271743606775999, -0.027407683432102203, 0.0215990599244833, 0.0326787531375885, 0.026374805718660355, 0.0034994545858353376, -0.053650639951229095, -0.035599514842033386, 0.015512695536017418, -0.023227130994200706, -0.037002597004175186, -0.06079932674765587, 0.036671679466962814, -0.04011514410376549, 0.02997593767940998, -0.0034318286925554276, -0.025805337354540825, 0.012020177207887173, 0.014342310838401318, 0.031351376324892044, -0.012850319035351276, -0.02584565244615078, -0.030568677932024002, -0.02811727114021778, 0.03425252065062523, -0.01015289593487978, -0.02697380818426609, -0.0022286386229097843, -0.04360513016581535, 0.021001720800995827, 0.06685619801282883, -0.04317488148808479, 0.03349442780017853, 0.1020718589425087, 0.00874211173504591, 0.019662916660308838, 0.007552793715149164, 0.0000851108125061728, 0.009255828335881233, 0.010730388574302197, -0.015969671308994293, 0.02679160051047802, -0.008958376944065094, 0.025302743539214134, 0.024840621277689934, 0.02759466879069805, 0.04819534346461296, -0.008568596094846725, -0.004808989819139242, 0.014199350029230118, 0.044461775571107864, 0.011341837234795094, 0.010453149676322937, -0.03284979611635208, 0.015175084583461285, -0.028785232454538345, -0.03693779930472374, 0.010140159167349339, -0.004586347378790379, -0.014341911301016808, -0.0052601974457502365, -0.006820318289101124, -0.011753224767744541, 0.06782770901918411, 0.032179199159145355, -0.007733894512057304, 0.09674767404794693, 0.00045966668403707445, 0.016813304275274277, 0.023293478414416313, -0.02231743559241295, 0.024692824110388756, 0.004299593158066273, -0.005526339169591665, -0.001405012677423656, 0.04575112462043762, -0.024089569225907326, -0.0017321670893579721, -0.022105909883975983, -0.0669618770480156, 0.03501873090863228, -0.014407866634428501, 0.009066091850399971, -0.0034504891373217106, -0.022056473419070244, 0.004872589372098446, 0.0667361170053482, -0.009350113570690155, 0.03413447365164757, 0.0551244355738163, 0.010951136238873005, -0.011452125385403633, -0.002236907137557864, 0.11783803254365921, -0.007050882559269667, -0.05776812136173248, 0.021592143923044205, -0.013193884864449501, 0.016449419781565666, 0.04514271765947342, -0.01453347411006689, -0.01206397358328104, -0.014195489697158337, -0.006821752991527319, -0.013454407453536987, -0.021938486024737358, 0.02609802596271038, 0.011907046660780907, 0.012187585234642029, -0.047616660594940186, -0.04507768899202347, -0.017503000795841217, -0.0535450242459774, -0.032830528914928436, -0.036260563880205154, 0.008011246100068092, -0.05213787034153938, -0.02279178984463215, -0.034028783440589905, 0.042159244418144226, -0.06756607443094254, -0.031336259096860886, 0.01746116206049919, 0.01737956330180168, -0.058753181248903275, -0.0077894870191812515, 0.04129830002784729, 0.014499611221253872, -0.019358739256858826, 0.0017975945957005024, -0.01678214594721794, -0.0494077168405056, -0.055409882217645645, 0.010551419109106064, -0.0013221179833635688, -0.011761308647692204, 0.004074267111718655, -0.03500005230307579, 0.013106114231050014, -0.041941236704587936, -0.012279887683689594, -0.0024278215132653713, -0.029530799016356468, -0.048723895102739334, 0.000023192398657556623, -0.045362915843725204, 0.031992435455322266, 0.022597316652536392, -0.004181209020316601, -0.0611603669822216, -0.04844794049859047, -0.059543050825595856, -0.03604045882821083, 0.019850151613354683, -0.06575754284858704, 0.018695779144763947, -0.024588508531451225, 0.03725190833210945, 0.021095899865031242, -0.010047302581369877, -0.005835685413330793, 0.009764891117811203, -0.013802203349769115, -0.012518716976046562, 0.03132381662726402, 0.045121029019355774, 0.04782679304480553, -0.0937575027346611, -0.02129080332815647, -0.06700466573238373, 0.02356887049973011, 0.04572434350848198, 0.05624472722411156, 0.04282330721616745, 0.08033530414104462, 0.025045495480298996, 0.010191217064857483, 0.018252963200211525, -0.06190798059105873, 0.025027485564351082, -0.020362038165330887, -0.03134685754776001, -0.017178134992718697, -0.03201567381620407, 0.044962916523218155, -0.03306227922439575, 0.00352734187617898, -0.048290230333805084, -0.003574829548597336, 0.035000063478946686, -0.026971811428666115, 0.074908047914505, 0.057647526264190674, 0.006431737449020147, -0.03951697424054146, -0.08249243348836899, 0.0029443642124533653, -0.0307439174503088, 0.010819325223565102, -0.060130782425403595, -0.013139829970896244, 0.004711140878498554, -0.004384749103337526, 0.027835583314299583, -0.022088689729571342, -0.017601747065782547, -0.027669794857501984, -0.029315002262592316, 0.007128471042960882, 0.028011953458189964, -0.022220684215426445, 0.013696900568902493, 0.002044167136773467, -0.02691115438938141, 0.0693720355629921, 0.050429388880729675, 0.05614553391933441, 0.030669119209051132, 0.014145942404866219, -0.013480021618306637, 0.051445648074150085, 0.006540253758430481, -0.023134412243962288, 0.02717812918126583, 0.019517237320542336, -0.002739246701821685, 0.01773853600025177, -0.02236153557896614, -0.03108709678053856 ]
<p>So electrons of specific atoms have a minimum amount of energy needed to escape the atom, called the work function, W. Now let's say that you emit a certain frequency of light, and $hf&lt;W$. However, from my understanding, this work function is just a form of kinetic energy, and if an electron has enough kinetic energy, its inertia will be greater than the centripetal force and the electron will escape. So even though $hf&lt;W$, the object being illuminated will still heat up from the light. This heating up means that the material is gaining internal energy, which means that the electrons are gaining kinetic energy. If the material gets hot enough and the electrons keep gaining speed, couldn't the they escape anyway even though $hf&lt;W$? Thanks! </p>
g1562
[ -0.008458995260298252, 0.032133955508470535, 0.017005164176225662, 0.04669209569692612, 0.006631527096033096, -0.04689515754580498, 0.002922752173617482, 0.03503819927573204, -0.05572150647640228, 0.010613550432026386, -0.040214139968156815, 0.042760469019412994, 0.02345769666135311, -0.07464520633220673, -0.006567759905010462, -0.000583590823225677, 0.05989864468574524, -0.03162506967782974, 0.035705938935279846, 0.06380625814199448, -0.002762345364317298, 0.04890180379152298, -0.014406579546630383, -0.07423541694879532, 0.020343901589512825, 0.003065257566049695, -0.00219742557965219, -0.042008377611637115, -0.021414343267679214, 0.0148830721154809, 0.016467776149511337, -0.0017746399389579892, 0.006372719071805477, -0.09780359268188477, -0.024379799142479897, 0.008315137587487698, 0.07130054384469986, 0.04770635440945625, 0.004070968367159367, 0.02584759332239628, -0.030067119747400284, -0.00521373376250267, 0.012253032065927982, 0.013677014969289303, 0.04603636637330055, 0.036535169929265976, 0.00759863993152976, 0.017276043072342873, -0.009159020148217678, -0.01949053630232811, 0.022907201200723648, 0.049557048827409744, 0.013846030458807945, -0.010689658112823963, -0.017949871718883514, -0.024307027459144592, -0.014089355245232582, -0.07548132538795471, 0.08485787361860275, 0.017131585627794266, 0.0380462221801281, 0.012992598116397858, 0.009040266275405884, -0.027806928381323814, 0.03329014033079147, -0.04919036477804184, 0.0007201186381280422, 0.011931875720620155, 0.001212072093039751, 0.007495676167309284, -0.026218023151159286, 0.018908170983195305, -0.030347181484103203, -0.03336343541741371, 0.0027494318783283234, 0.02519887313246727, 0.03902420029044151, -0.09610994905233383, 0.019693924114108086, 0.00911285262554884, -0.04598351567983627, 0.004052962176501751, -0.01557620707899332, 0.024121083319187164, 0.0167990792542696, 0.020659582689404488, -0.00659504160284996, -0.040942706167697906, -0.015342910774052143, -0.00936252623796463, 0.06980285793542862, 0.0050614397041499615, 0.07366055995225906, 0.003761952044442296, -0.03322235494852066, -0.0017092389753088355, -0.036387842148542404, 0.028030814602971077, -0.022437624633312225, -0.010885260999202728, 0.017152125015854836, -0.13031114637851715, 0.035731326788663864, -0.027504166588187218, 0.0028807963244616985, -0.028190376237034798, -0.01092887856066227, -0.05502825975418091, -0.026757486164569855, 0.05862893536686897, 0.002635400276631117, -0.03363354876637459, -0.03621289134025574, -0.10186289995908737, -0.03242475166916847, 0.004513164516538382, 0.005727675743401051, -0.05532117933034897, -0.03932725638151169, 0.044986478984355927, -0.0038935879711061716, 0.00014438640209846199, 0.017170578241348267, 0.03790857642889023, 0.004114228766411543, 0.048407528549432755, 0.002389138098806143, -0.027857568114995956, 0.0005595141556113958, -0.046647291630506516, 0.028630675747990608, 0.055792566388845444, -0.00020701689936686307, 0.05813511461019516, 0.0046369112096726894, 0.061279602348804474, 0.007076611276715994, 0.05370967462658882, 0.00386417587287724, -0.008547049015760422, 0.029083648696541786, -0.045199599117040634, 0.0070988875813782215, -0.035397496074438095, -0.04203953593969345, 0.013617193326354027, -0.05172780156135559, 0.007967743091285229, 0.07551044970750809, 0.05510537326335907, -0.034314170479774475, 0.10619324445724487, 0.022759057581424713, -0.020540647208690643, 0.029536478221416473, -0.06123509258031845, 0.09818510711193085, -0.024320773780345917, -0.006131390109658241, -0.02321668714284897, 0.08219411969184875, -0.021285174414515495, 0.06403040885925293, -0.007063480094075203, -0.0319322794675827, -0.0038680019788444042, -0.014918058179318905, -0.06131758540868759, -0.012869492173194885, -0.054297756403684616, -0.05590541288256645, -0.037837810814380646, -0.007914111949503422, 0.01790054515004158, -0.026231130585074425, 0.024926774203777313, 0.053393930196762085, 0.0016924067167565227, -0.05160868912935257, -0.00558917922899127, -0.03845600038766861, -0.04157193750143051, 0.04348081722855568, -0.03217053785920143, 0.017496207728981972, 0.011412594467401505, -0.011599281802773476, 0.035033825784921646, -0.05480222776532173, 0.02956550195813179, -0.014506169594824314, -0.021678194403648376, 0.03156743943691254, -0.04129737988114357, -0.05028153583407402, -0.05946711450815201, -0.029849359765648842, -0.013297243043780327, -0.0178100373595953, -0.03734109550714493, 0.024594614282250404, 0.04574570432305336, -0.03852415084838867, -0.010373777709901333, 0.05213547870516777, -0.012869871221482754, -0.05411263182759285, -0.014647705480456352, 0.0235239677131176, -0.005275748670101166, 0.033197756856679916, -0.01850906014442444, -0.011435155756771564, 0.049758221954107285, -0.002370127011090517, -0.021775653585791588, -0.06485476344823837, 0.022839106619358063, -0.0006047636270523071, -0.02265237644314766, -0.03140808269381523, -0.013162611052393913, 0.003536198753863573, 0.025841230526566505, -0.034120772033929825, 0.02429215796291828, -0.06639094650745392, -0.03039737604558468, -0.003834571223706007, 0.059734977781772614, -0.09314524382352829, 0.05861572176218033, -0.00790851004421711, -0.050704825669527054, 0.009873089380562305, 0.027561571449041367, -0.02966424822807312, 0.050217404961586, 0.002849341370165348, 0.02228722721338272, -0.007124531548470259, -0.006522766780108213, -0.006796895992010832, -0.051520369946956635, 0.00937147531658411, -0.0012326230062171817, -0.0033284351229667664, -0.026065019890666008, 0.0012948410585522652, 0.010025052353739738, 0.03326193243265152, -0.03977632895112038, -0.07845590263605118, 0.029121827334165573, -0.03404659405350685, -0.03152119740843773, -0.10107561945915222, 0.008895525708794594, -0.06864822655916214, -0.06687340885400772, 0.007924489676952362, 0.03292872756719589, 0.027371184900403023, 0.016505753621459007, -0.04889484494924545, 0.004221232607960701, -0.021295759826898575, -0.009214506484568119, 0.021220987662672997, -0.02231806516647339, -0.029882322996854782, 0.04239047318696976, -0.03581847622990608, -0.004146241117268801, 0.014728427864611149, -0.053760647773742676, -0.046722255647182465, -0.06489214301109314, 0.034219857305288315, -0.01065735425800085, -0.019833799451589584, -0.00760524021461606, -0.089585080742836, -0.023418797180056572, -0.05977658927440643, -0.02126714587211609, -0.015366947278380394, 0.026845762506127357, 0.0032192810904234648, -0.06296705454587936, -0.03676178678870201, 0.05160130560398102, 0.0031158854253590107, 0.032210107892751694, -0.025702379643917084, -0.0048685320653021336, 0.07217580825090408, -0.023148566484451294, -0.06801897287368774, 0.04081372171640396, 0.030829040333628654, -0.02747945301234722, -0.04239537939429283, 0.015075769275426865, -0.015000986866652966, 0.03790753334760666, -0.04970496892929077, -0.030253540724515915, -0.023655537515878677, -0.004777344409376383, 0.05989958718419075, 0.03764757141470909, -0.011190149933099747, 0.010732846334576607, -0.008363936096429825, 0.016435716301202774, -0.026370694860816002, 0.0027899339329451323, 0.006784772500395775, -0.019123665988445282, 0.0032824722584336996, 0.0028694174252450466, -0.015471747145056725, -0.0463002510368824, 0.007157766725867987, -0.02083323523402214, 0.0010877277236431837, -0.12055516988039017, 0.019423749297857285, -0.001699879765510559, 0.01638721488416195, 0.056694041937589645, -0.042375821620225906, -0.02635890059173107, 0.023173553869128227, -0.02782651036977768, 0.004317376296967268, 0.0605023056268692, 0.028916431590914726, 0.07125275582075119, 0.054841384291648865, 0.02777353674173355, -0.047267116606235504, 0.01472808513790369, 0.027854181826114655, 0.008040792308747768, -0.04623693600296974, -0.01312804501503706, 0.003691063728183508, 0.014177379198372364, 0.05020248889923096, -0.04094403237104416, -0.01898461952805519, 0.003781835548579693, -0.0009900105651468039, -0.004964795429259539, 0.01187826693058014, -0.004113669507205486, 0.013588492758572102, -0.002876686630770564, -0.018954582512378693, -0.006058124825358391, 0.09000983834266663, -0.00817184615880251, -0.05377981439232826, 0.018022652715444565, 0.036373525857925415, 0.1141706332564354, 0.004593788646161556, -0.056551698595285416, -0.013539861887693405, -0.0032018262427300215, -0.009818759746849537, 0.02832985110580921, -0.011770421639084816, -0.0035224594175815582, 0.029060661792755127, -0.0032471176236867905, -0.08492922782897949, -0.010081984102725983, -0.03774440661072731, -0.018644388765096664, 0.018900590017437935, 0.023050284013152122, 0.0588233545422554, 0.02422371320426464, -0.0499453991651535, 0.005908432882279158, 0.007055257447063923, -0.01922007091343403, -0.021744437515735626, 0.015088123269379139, -0.00822426937520504, -0.015296908095479012, 0.007989848963916302, -0.017925594002008438, 0.03987963870167732, -0.03505326807498932, 0.03984340280294418, -0.016218936070799828, 0.08220695704221725, 0.023768985643982887, -0.007378595881164074, -0.016460292041301727, 0.042378537356853485, 0.024805909022688866, 0.0406489372253418, -0.031344830989837646, 0.018504660576581955, -0.05357254669070244, -0.039379701018333435, 0.009840080514550209, -0.009363302029669285, 0.020291471853852272, 0.028171414509415627, -0.040087368339300156, -0.0044031087309122086, -0.015485755167901516, 0.005216856952756643, 0.03348299115896225, -0.013612483628094196, 0.008137045428156853, 0.0573088675737381, 0.0160541869699955, -0.023304197937250137, 0.07804437726736069, 0.05884651094675064, 0.05519654601812363, -0.028055675327777863, -0.07841046154499054, 0.022486712783575058, 0.009913573041558266, 0.01048512477427721, -0.017077239230275154, -0.06300149857997894, 0.027520781382918358, -0.024087728932499886, 0.05922389030456543, 0.005233295261859894, 0.0680181160569191, 0.05214816704392433, 0.014404197223484516, 0.035253144800662994, 0.016311243176460266, 0.013244775123894215, 0.06508108973503113, -0.024855932220816612, -0.02190241776406765, 0.0019729614723473787, -0.031033990904688835, -0.0284514669328928, 0.0008633645484223962, 0.005810999311506748, 0.014630308374762535, 0.04547131806612015, -0.007410329766571522, -0.04047098010778427, -0.0348614826798439, 0.025580499321222305, 0.048044733703136444, -0.017098193988204002, -0.046114180237054825, 0.018463151529431343, 0.018158121034502983, 0.029531210660934448, 0.0010044585214927793, -0.04718644171953201, -0.011515999212861061, -0.0491207055747509, 0.035217493772506714, 0.02887192741036415, 0.020931879058480263, 0.05072309076786041, 0.02174275368452072, 0.025524459779262543, -0.06589940935373306, 0.008008291944861412, -0.035243213176727295, 0.013343806378543377, -0.02022874914109707, 0.01745251566171646, 0.012208784930408001, 0.007713434752076864, 0.06729207187891006, 0.011143410578370094, -0.014972306787967682, -0.0833117663860321, 0.04371116682887077, 0.004281069152057171, -0.04406154155731201, 0.03050459735095501, 0.03630511462688446, -0.006051223259419203, -0.004760497249662876, -0.04704003781080246, 0.054944414645433426, 0.05382131040096283, 0.0527956485748291, -0.00039737479528412223, 0.04890073463320732, -0.0487329326570034, -0.01616416871547699, -0.04939410090446472, -0.011445466428995132, 0.0392313078045845, 0.00894477590918541, 0.04696504399180412, 0.007217684295028448, 0.005406232550740242, -0.0284443162381649, -0.018767215311527252, -0.00007235518569359556, 0.03493557125329971, -0.01367830391973257, 0.004215538501739502, -0.03232444077730179, -0.018934298306703568, -0.021861888468265533, 0.019891971722245216, 0.010929299518465996, 0.04305229336023331, 0.02153182215988636, 0.027110975235700607, -0.022016432136297226, 0.04281282424926758, 0.030135484412312508, -0.026669524610042572, 0.01018484216183424, 0.006122938357293606, 0.07394552230834961, 0.051915135234594345, 0.014477564021945, -0.012732384726405144, 0.015322410501539707, 0.0025240725371986628, 0.018489787355065346, 0.026879511773586273, -0.0034365493338555098, -0.007937702350318432, 0.040819667279720306, 0.0183718279004097, -0.014865820296108723, 0.03882700949907303, 0.015612488612532616, 0.05291374772787094, 0.019238770008087158, 0.04247979447245598, -0.028360815718770027, -0.01412146259099245, -0.010235889814794064, 0.0079564293846488, 0.0742049589753151, 0.040728017687797546, 0.02210438996553421, 0.04071256145834923, 0.050186049193143845, 0.03408900275826454, 0.0010724007152020931, -0.014086153358221054, -0.053937237709760666, 0.054859235882759094, 0.023464877158403397, 0.0366569459438324, 0.02740051969885826, 0.08515536785125732, -0.01184407714754343, 0.0062613822519779205, 0.01220280397683382, -0.00995327066630125, 0.04446776583790779, 0.002550703240558505, -0.02114429697394371, 0.0012530327076092362, 0.017535556107759476, -0.02521335333585739, 0.0406680665910244, -0.037005700170993805, -0.043388403952121735, -0.06645510345697403, -0.027212947607040405, 0.030329221859574318, 0.023609613999724388, -0.029227381572127342, -0.055690836161375046, -0.006812920793890953, 0.028252258896827698, -0.03731738403439522, 0.013291210867464542, 0.04277346283197403, -0.025086119771003723, -0.03325329348444939, -0.01587364822626114, 0.009351768530905247, 0.04811154678463936, -0.021033652126789093, -0.026518605649471283, -0.05174563080072403, -0.024945447221398354, 0.006046099588274956, 0.04586672782897949, 0.05285841226577759, -0.0017698330339044333, 0.005976161919534206, -0.0653136596083641, 0.023876264691352844, 0.0015931359957903624, -0.015612970106303692, 0.030501490458846092, -0.025949925184249878, -0.028809884563088417, -0.07423155009746552, -0.014126140624284744, 0.04728290066123009, 0.026377052068710327, 0.012808186933398247, 0.015371168032288551, 0.0517289899289608, 0.034909479320049286, 0.05368591099977493, -0.030225368216633797, -0.0019701295532286167, 0.0008450117311440408, 0.06069537624716759, -0.036635782569646835, -0.00018744439876172692, 0.002539955312386155, -0.07024207711219788, 0.06351155042648315, 0.04036325961351395, 0.0063790688291192055, -0.02599387988448143, 0.055127426981925964, -0.02012050896883011, 0.02866028994321823, -0.05405624210834503, -0.01552407257258892, 0.04277103766798973, -0.021864911541342735, 0.025512579828500748, 0.05403032898902893, -0.041129276156425476, -0.03391824662685394, 0.0293143130838871, 0.021241305395960808, -0.09794697910547256, 0.010715188458561897, 0.004173500929027796, -0.04457659646868706, -0.03699229285120964, 0.0005283883074298501, -0.0281254593282938, -0.03279103338718414, -0.03008330427110195, 0.01792478933930397, 0.01197828259319067, -0.019675614312291145, -0.07828108221292496, -0.03478531911969185, -0.06385566294193268, -0.015096019953489304, -0.007565660867840052, -0.0003631860890891403, 0.06330843269824982, -0.021356068551540375, 0.049203332513570786, 0.06323110312223434, -0.020340625196695328, -0.030676379799842834, -0.043152548372745514, -0.036899346858263016, -0.022396145388484, -0.0008793912129476666, 0.006659805309027433, 0.00598638691008091, -0.013889314606785774, 0.036342572420835495, -0.06231576204299927, 0.05289126932621002, -0.015600142069160938, -0.05020655319094658, -0.018822817131876945, -0.008517499081790447, 0.013972800225019455, -0.01892665959894657, 0.016640949994325638, 0.0009141350165009499, -0.032084301114082336, -0.02929007075726986, -0.005692099686712027, 0.015311403200030327, -0.02752426080405712, 0.028441591188311577, 0.05364272743463516, 0.006769013125449419, -0.036661263555288315, 0.06799859553575516, 0.04608314484357834, -0.03857364133000374, 0.0497995987534523, 0.058740101754665375, 0.012201713398098946, -0.032598063349723816, 0.03429630398750305, -0.008158020675182343, -0.017758727073669434, 0.05599305406212807, 0.027132093906402588, -0.053394246846437454, -0.040856484323740005, 0.0014034721534699202, 0.03197021782398224, 0.025617292150855064, 0.017028968781232834, 0.006827539298683405, 0.050175298005342484, -0.009315621107816696, -0.01797335222363472, 0.000911217590328306, 0.01292545534670353, -0.04304664582014084, 0.00987508799880743, 0.04769141599535942, -0.0295876432210207, -0.00950078945606947, -0.0008828385616652668, 0.035311099141836166, -0.018460778519511223, -0.042678095400333405, 0.0034477205481380224, -0.009408571757376194, -0.017337217926979065, 0.0013390586245805025, 0.004847673233598471, -0.02807149849832058, 0.010029762983322144, 0.001663444098085165, 0.0201583169400692, -0.03355332463979721, 0.07753591984510422, 0.004648367874324322, -0.01030309870839119, 0.004736579488962889, 0.010925267823040485, -0.04790570214390755, -0.006582041271030903, -0.033199381083250046, -0.009462881833314896, -0.009335017763078213, 0.019631972536444664, 0.05323409289121628, -0.050797346979379654, -0.02236654795706272, -0.06249324977397919, 0.012219403870403767, 0.04993154853582382, -0.04742153361439705, -0.006098020356148481, 0.015750408172607422, -0.019083095714449883, 0.017098018899559975, 0.006241047289222479, -0.004119617864489555, -0.026521798223257065, -0.00823906809091568, 0.0673798993229866, -0.06484627723693848, 0.024411773309111595, -0.003865255741402507 ]
<p>I have this problem. I have an ideal gas that goes through an irreversible adiabatic decompression. I have the initial state (P,T,V), and the final pressure, and I have to calculate the entropy difference of the proccess. So, what I know is that I can make up any reversible proces bewteen the initial and final state because entropy is a state function, and integrate the heat over that process, but I can't solve it. I'm aplying $P_1V_1^\lambda=P_2V_2^\lambda$ to get the final state, but as I am creating the final point of the adiabatic, I get entropy difference of $0$ for an invented reversible path. That way of getting the final state is not correct, right? I have $PV=nRT$ but I only have the final $P$ so I need another equation.</p> <p>EDIT: I have tried also to use $\Delta U=W\Rightarrow C_v\Delta T=P_{ext}\Delta V$, get $T_{final}$, and go on, but I don't get the correct result either. I thought this was general: $dU=C_vdT$, when can I apply that equation?</p>
g1563
[ 0.003328594844788313, -0.041195571422576904, 0.0033302835654467344, -0.0344834104180336, 0.02426350861787796, -0.05248190835118294, -0.014501688070595264, 0.07178337872028351, -0.04415876790881157, 0.03678872063755989, -0.02157340757548809, 0.05764090642333031, 0.03687421232461929, -0.08734128624200821, 0.04413653910160065, 0.012898311950266361, 0.0339626744389534, 0.009425893425941467, -0.0055315508507192135, -0.027247829362750053, 0.001883162185549736, -0.04696007817983627, 0.03589032590389252, -0.05498193949460983, 0.04093846306204796, -0.05674995109438896, -0.03370760753750801, 0.023427553474903107, -0.06250432878732681, 0.07192352414131165, -0.013194291852414608, 0.006781057454645634, 0.008758687414228916, -0.027902524918317795, -0.06485879421234131, -0.07336273789405823, 0.05403449386358261, 0.006181538105010986, 0.04788852483034134, -0.10989756882190704, 0.011999053880572319, 0.004398074466735125, 0.028320418670773506, 0.003180968575179577, 0.02369474433362484, -0.004936874378472567, -0.018283484503626823, -0.015638336539268494, -0.043816667050123215, 0.03251553326845169, 0.06078409031033516, 0.08749071508646011, -0.01054813340306282, -0.07424905151128769, 0.0021235698368400335, 0.004943338222801685, -0.014132984913885593, -0.04910243675112724, 0.03563448786735535, -0.014615954831242561, 0.0342542827129364, -0.033202242106199265, -0.006386689376085997, -0.019880643114447594, -0.00553037179633975, -0.016195472329854965, -0.0004969552392140031, 0.0018905518809333444, 0.00022839497250970453, -0.03055926039814949, -0.018497252836823463, -0.03301704674959183, 0.022110171616077423, -0.0322648286819458, 0.03196951746940613, -0.03875035047531128, 0.004372172988951206, -0.0740506649017334, -0.012128676287829876, 0.013274137862026691, -0.06939667463302612, -0.04042813181877136, 0.0477667972445488, -0.047307174652814865, -0.0254188422113657, -0.012362932786345482, 0.028554342687129974, 0.017909444868564606, -0.032504625618457794, 0.03044159896671772, -0.0012823258293792605, -0.0005009606247767806, 0.03004586324095726, 0.05753157287836075, -0.0283016636967659, 0.04994596168398857, -0.010534795932471752, 0.008853939361870289, -0.027617687359452248, -0.0008687725639902055, -0.016829466447234154, -0.05284993723034859, -0.005778837483376265, -0.007936348207294941, -0.02299628034234047, -0.0628337413072586, 0.0035542564000934362, -0.0365133099257946, -0.021230453625321388, 0.020891709253191948, -0.004324864596128464, 0.01521155796945095, -0.005087627563625574, -0.011932752095162868, -0.010710882022976875, -0.03413494676351547, 0.04079902172088623, -0.008614351972937584, -0.018252085894346237, 0.030548853799700737, 0.009238192811608315, 0.02855321206152439, 0.021336039528250694, 0.006410167086869478, 0.031797416508197784, 0.06868674606084824, -0.011276504956185818, -0.06804955750703812, 0.03596140071749687, 0.013065950013697147, 0.030259016901254654, 0.052734021097421646, -0.01062690932303667, 0.028066348284482956, -0.04232870787382126, -0.009643151424825191, -0.010346055030822754, 0.003916324116289616, -0.030962646007537842, 0.024604350328445435, 0.008831287734210491, -0.01612873189151287, -0.03912471607327461, 0.00793891679495573, -0.05129096284508705, -0.038446251302957535, -0.04974415898323059, -0.039343882352113724, -0.005782702472060919, -0.05812995508313179, 0.06319340318441391, -0.010720279067754745, 0.026339180767536163, -0.01414495799690485, -0.008339260704815388, -0.009437122382223606, 0.042703308165073395, 0.02459229715168476, 0.048596374690532684, -0.011273817159235477, 0.06077976152300835, 0.017311682924628258, 0.0663665235042572, -0.009775801561772823, 0.00951800961047411, 0.05519808828830719, 0.0008326579118147492, -0.0009188608964905143, 0.029083214700222015, -0.046343617141246796, -0.026322076097130775, -0.05177025496959686, -0.002600555308163166, 0.030879292637109756, 0.041752249002456665, 0.058813583105802536, 0.02532513067126274, 0.033913321793079376, -0.021094029769301414, -0.05820159241557121, 0.05553515627980232, 0.014384148642420769, 0.07365012913942337, 0.004522977862507105, 0.05478068068623543, 0.06237752363085747, -0.016273856163024902, -0.0006217533373273909, -0.10359363257884979, -0.02008434198796749, 0.03992323577404022, 0.08056412637233734, 0.021494580432772636, 0.04346701130270958, -0.005041377153247595, -0.026909397915005684, 0.008228731341660023, -0.059779804199934006, -0.09395872801542282, -0.005846905987709761, 0.02243565022945404, 0.025459835305809975, 0.048790063709020615, 0.05195816606283188, 0.0077402638271451, 0.04877595603466034, -0.043728169053792953, 0.012993494980037212, -0.008133001625537872, 0.022359855473041534, 0.030708996579051018, -0.02288012020289898, -0.029659263789653778, -0.018847063183784485, 0.011936081573367119, 0.02445506863296032, 0.02166590467095375, 0.019359461963176727, 0.0328800231218338, -0.030425984412431717, -0.0466705858707428, 0.024692203849554062, 0.020101677626371384, 0.036260347813367844, -0.008571241982281208, 0.005016871728003025, -0.030858634039759636, -0.022807486355304718, -0.02010541595518589, 0.011021304875612259, -0.016018474474549294, 0.009120157919824123, 0.005093025974929333, -0.04161017760634422, -0.001764706103131175, -0.01105897594243288, 0.013010844588279724, 0.03672834485769272, 0.03196258842945099, -0.016375409439206123, 0.0032580646220594645, -0.06147042289376259, 0.0002520395501051098, 0.08339198678731918, 0.03632676228880882, 0.017469031736254692, -0.024891776964068413, 0.018278436735272408, -0.006633753422647715, -0.0342763252556324, -0.004547782242298126, 0.03406595066189766, -0.03785787522792816, 0.016018712893128395, 0.019157834351062775, -0.04313843697309494, 0.04133429750800133, -0.027692366391420364, 0.021200597286224365, -0.015773065388202667, -0.003996971063315868, 0.029694290831685066, 0.03142162412405014, 0.03774728626012802, -0.0803971216082573, 0.04585396498441696, 0.0347677506506443, -0.023600641638040543, 0.004796938970685005, -0.012026604264974594, 0.020437752828001976, 0.00632744375616312, -0.03275839611887932, 0.027887949720025063, 0.05784474313259125, -0.011550724506378174, 0.011728604324162006, -0.029138321056962013, 0.009004722349345684, -0.00808471068739891, 0.0024935011751949787, 0.002637146972119808, -0.02486485056579113, 0.04969662427902222, 0.05037076398730278, -0.083786241710186, 0.021086983382701874, 0.11387291550636292, 0.015593432821333408, -0.007049059495329857, 0.01778913475573063, 0.01136492658406496, 0.020344920456409454, 0.02378147654235363, -0.018111875280737877, 0.03547980636358261, 0.004408466629683971, -0.05403994396328926, 0.005695055238902569, -0.026547681540250778, 0.025540340691804886, -0.054249417036771774, -0.01503017544746399, 0.027029966935515404, 0.04686599224805832, 0.01234253216534853, -0.05668490007519722, -0.020284289494156837, 0.025153111666440964, 0.023974211886525154, -0.026002394035458565, -0.0011027598520740867, -0.017760511487722397, -0.1111164391040802, 0.04185948520898819, -0.03349485993385315, 0.05526554584503174, -0.08026450872421265, 0.034331031143665314, 0.016452593728899956, -0.0010945949470624328, -0.06921414285898209, 0.059900913387537, 0.004355795681476593, 0.06494461745023727, -0.002825886942446232, -0.06221157684922218, -0.0187666192650795, -0.030360396951436996, -0.05334838107228279, -0.018250133842229843, 0.01448323205113411, -0.037261828780174255, -0.04994064196944237, -0.028335316106677055, -0.029305685311555862, -0.04133732616901398, 0.014208356849849224, -0.007715980987995863, -0.02753297984600067, 0.004407050553709269, 0.01379713136702776, 0.05486251413822174, 0.029807832092046738, 0.015700841322541237, -0.04031355679035187, 0.0037926272489130497, 0.03666485846042633, 0.01537636760622263, 0.04385099560022354, 0.05957441404461861, -0.0028673941269516945, 0.04840928688645363, -0.010879051871597767, -0.027712222188711166, 0.03899560496211052, 0.09135208278894424, -0.019948311150074005, 0.01359962671995163, -0.027542823925614357, 0.011606269516050816, -0.040070053189992905, -0.009247911162674427, -0.004592273849993944, 0.0013397197471931577, 0.016483647748827934, 0.017252309247851372, 0.027020059525966644, -0.06257636845111847, -0.013777371495962143, -0.008723367005586624, -0.03052436001598835, -0.0038885343819856644, -0.003037611721083522, 0.004948883783072233, -0.08269978314638138, 0.02199554070830345, 0.02617802657186985, -0.001746320049278438, 0.028834514319896698, 0.025242619216442108, 0.013329867273569107, -0.021388500928878784, -0.047856174409389496, -0.006491169333457947, 0.06595948338508606, -0.0027056154794991016, 0.019061032682657242, 0.022563567385077477, -0.020754698663949966, 0.02024170570075512, -0.001988464966416359, -0.011738020926713943, -0.01898188143968582, 0.03537174314260483, 0.07567285746335983, 0.032904572784900665, 0.015897266566753387, -0.06839694827795029, 0.01721673645079136, -0.05436793342232704, -0.0054372334852814674, -0.009371929802000523, -0.012225567363202572, -0.015587780624628067, -0.046242374926805496, 0.008965987712144852, -0.03419813886284828, -0.012772555463016033, 0.004479677882045507, 0.0017792879370972514, -0.004814332816749811, -0.01445253286510706, -0.027019869536161423, -0.03603750467300415, -0.02115134708583355, -0.03905161842703819, -0.024718280881643295, 0.034590788185596466, 0.007170551922172308, -0.017855623736977577, 0.04464314877986908, -0.008976197801530361, 0.0512075200676918, 0.010463274084031582, 0.022273695096373558, 0.0698198527097702, 0.009746243245899677, 0.005788220092654228, -0.04205700010061264, -0.008236417546868324, 0.01743144541978836, -0.03210512176156044, 0.014955568127334118, -0.017104847356677055, 0.06207048147916794, 0.008320223540067673, 0.010670562274754047, -0.004096886608749628, 0.00870839785784483, 0.0856136605143547, 0.02487235888838768, -0.04030115529894829, 0.016727682203054428, -0.0036675443407148123, 0.01956282928586006, 0.03418080881237984, -0.04054209217429161, 0.03127509728074074, -0.03349268063902855, -0.03541800379753113, -0.0020520067773759365, -0.012055016122758389, -0.07024270296096802, 0.004934626631438732, 0.016344737261533737, 0.01912005804479122, 0.07551997900009155, -0.02552420273423195, 0.021002622321248055, -0.01074290182441473, -0.025232283398509026, 0.005580521654337645, 0.006407623644918203, -0.005365336313843727, 0.005092316772788763, -0.05554836243391037, 0.052477866411209106, -0.00420353002846241, -0.014778686687350273, 0.0483589693903923, 0.022991497069597244, -0.024403508752584457, 0.06641805917024612, -0.025611719116568565, 0.012735412456095219, 0.012644140049815178, -0.05207075923681259, 0.019661933183670044, 0.02435426041483879, -0.024171598255634308, 0.029461335390806198, 0.04708683490753174, 0.062127236276865005, 0.023140165954828262, 0.0018060739384964108, -0.027995647862553596, -0.010841545648872852, -0.0030094715766608715, -0.04060917720198631, 0.004106215201318264, 0.09652507305145264, 0.06493650376796722, -0.012651876546442509, -0.00012645091919694096, -0.02483380399644375, -0.07790780067443848, -0.01242909673601389, -0.015165039338171482, 0.04292502626776695, -0.07527477294206619, -0.014837163500487804, 0.008994749747216702, 0.001413947669789195, -0.028049971908330917, -0.00823846273124218, 0.006384668406099081, 0.08267421275377274, -0.030501794070005417, 0.000252262077992782, 0.038865722715854645, 0.006631141062825918, 0.020336803048849106, -0.023394940420985222, -0.0008778264163993299, 0.033918846398591995, -0.005410254932940006, -0.06500697135925293, 0.00032619040575809777, -0.10961013287305832, 0.08173806220293045, -0.03084297850728035, 0.046801235526800156, 0.02708391472697258, 0.031145302578806877, 0.0040037259459495544, -0.016432374715805054, -0.04671022295951843, -0.026159534230828285, 0.02642836421728134, -0.030637625604867935, -0.013727410696446896, 0.01801140420138836, -0.03336648643016815, -0.03281502425670624, -0.02647579275071621, -0.029385380446910858, 0.011831599287688732, 0.06224928796291351, -0.0035957188811153173, 0.013903282582759857, -0.039035532623529434, -0.021127715706825256, 0.020798934623599052, -0.05683039501309395, -0.049687549471855164, -0.025284871459007263, -0.025475336238741875, -0.0381002314388752, 0.023974409326910973, -0.001827159314416349, -0.01638738624751568, 0.0022718170657753944, -0.0635254979133606, 0.030898509547114372, -0.030926035717129707, 0.038899317383766174, 0.018150536343455315, -0.013695399276912212, 0.030516522005200386, 0.019469091668725014, 0.002267431700602174, 0.06729534268379211, 0.06679298728704453, -0.004310372285544872, -0.062099892646074295, 0.02225579507648945, -0.04070541262626648, -0.023419562727212906, 0.021243063732981682, 0.01747702807188034, 0.034707311540842056, 0.016025371849536896, 0.012248141691088676, 0.023527467623353004, -0.0058039030991494656, -0.053375232964754105, -0.09956322610378265, -0.025673363357782364, -0.006826579105108976, -0.06266413629055023, -0.011965734884142876, 0.057958006858825684, -0.00798796582967043, -0.04438255727291107, 0.026128284633159637, -0.03190889582037926, -0.024961065500974655, -0.004594490863382816, 0.061235152184963226, 0.014254563488066196, -0.018245825543999672, -0.01857956498861313, -0.007593877147883177, -0.011408724822103977, -0.01139085739850998, -0.02642064541578293, -0.053544554859399796, -0.001320533687248826, 0.07862059026956558, 0.015345058403909206, 0.031094253063201904, -0.014403017237782478, -0.07102661579847336, -0.008062723092734814, 0.03797240927815437, 0.0037167107220739126, 0.05853302404284477, 0.04988836124539375, -0.02864120714366436, -0.013901644386351109, 0.03732696920633316, 0.04778138920664787, -0.020094703882932663, -0.002968014217913151, -0.02206401340663433, -0.043854523450136185, 0.074692502617836, -0.030983516946434975, 0.02008800394833088, 0.006518586538732052, -0.0028928802348673344, 0.029698362573981285, -0.01444822084158659, 0.0808468908071518, 0.05690450221300125, -0.028860172256827354, 0.03647809103131294, 0.0209036897867918, 0.03957730531692505, -0.008170216344296932, -0.0050222259014844894, 0.006405882071703672, 0.010437996126711369, 0.011475486680865288, 0.006485185585916042, -0.023427793756127357, 0.032757509499788284, 0.04877953976392746, 0.018651705235242844, -0.00586760463193059, -0.001528994645923376, -0.02224092371761799, 0.04442210868000984, -0.0220728050917387, 0.0059239002875983715, 0.0099267503246665, -0.022094249725341797, -0.07470738142728806, -0.03792319819331169, 0.04853714257478714, -0.013151250779628754, -0.018683405593037605, -0.00974937155842781, -0.014227611944079399, 0.07154927402734756, 0.014072855934500694, 0.014534722082316875, 0.022163327783346176, 0.00008503348362864926, 0.041128069162368774, -0.036604851484298706, -0.0018441674765199423, 0.041366126388311386, 0.027399446815252304, 0.02638760767877102, 0.052435506135225296, -0.014518539421260357, 0.014349045231938362, -0.03338925167918205, 0.015084200538694859, -0.048697665333747864, -0.05600551888346672, 0.03454374149441719, 0.01783958077430725, 0.015815429389476776, 0.02814987115561962, 0.028783945366740227, 0.00043614552123472095, -0.04143417626619339, -0.03645028918981552, 0.0009623395744711161, -0.015131216496229172, -0.06973158568143845, -0.038874756544828415, 0.0002602428721729666, -0.007577105890959501, 0.07012853771448135, -0.03719416633248329, 0.025697000324726105, -0.0325905904173851, 0.06825656443834305, 0.03985181078314781, -0.05364425852894783, -0.05030445009469986, 0.03646503761410713, 0.03106234408915043, 0.02611629106104374, 0.019525954499840736, -0.03339596837759018, 0.05762910097837448, -0.060373738408088684, 0.0005373824387788773, 0.021772164851427078, -0.04886494576931, -0.005512518808245659, -0.06384981423616409, -0.0029969774186611176, 0.009090468287467957, 0.017902761697769165, 0.060995329171419144, -0.014816745184361935, -0.003988928161561489, -0.019855761900544167, -0.02560928650200367, -0.049162957817316055, -0.0801047533750534, -0.020608672872185707, 0.015544827096164227, -0.005285175982862711, 0.001934582251124084, 0.017618780955672264, -0.04494481906294823, -0.05791332572698593, -0.024156730622053146, -0.01090653520077467, -0.058536265045404434, -0.021346254274249077, -0.000014160584214550909, -0.03928973898291588, 0.014619536697864532, 0.06912685930728912, -0.00476469099521637, -0.001934944186359644, -0.0015273551689460874, 0.00787264946848154, -0.00813000276684761, -0.009857475757598877, 0.07568065822124481, 0.008262147195637226, -0.04669193550944328, -0.05289367586374283, 0.03951629623770714, 0.0016501806676387787, 0.05449656397104263, -0.03333102539181709, -0.02526715025305748, -0.000736070447601378, 0.09239795058965683, -0.038144346326589584, 0.03890461474657059, -0.06566240638494492, -0.04483408480882645, -0.09332115203142166, -0.03345135226845741, -0.01537604071199894, 0.04316842928528786, 0.007081770803779364, 0.026820573955774307, -0.014477360993623734, -0.02518269792199135, 0.015575162135064602, -0.018579553812742233, 0.044397853314876556, -0.002765759825706482, -0.0019780939910560846, -0.013869278132915497, 0.004635122139006853 ]
<p>I am having trouble understanding electromagnetic radiation (or waves in general, be it EM or sound). If I have a 1 Watt speaker, is it infinitely divided and spread out so that everyone in every direction around the speaker can hear it?</p> <p>I do not believe they have "height", to reach more than one person at once, but if they did they would probably collide at one point. How do sound waves travel "backwards" (i.e. you are behind a speaker), are they scattered by air particles or itself so that people behind could hear it (at reduced amplitude)?</p> <p>I am just unsure how to wrap my head around it.</p>
g1564
[ -0.017748747020959854, 0.02527673915028572, -0.01725669950246811, 0.041948188096284866, 0.05089156702160835, 0.0564626008272171, 0.00997559167444706, 0.06267988681793213, -0.006043555680662394, -0.027046794071793556, -0.001665884512476623, 0.057430706918239594, -0.03532123938202858, 0.06671564280986786, 0.0033079322893172503, -0.03568276762962341, 0.021169669926166534, 0.025487352162599564, -0.030535846948623657, 0.050510555505752563, 0.015479293651878834, -0.009744061157107353, -0.02064329944550991, -0.0500868484377861, -0.019762776792049408, -0.014309522695839405, 0.003727405797690153, 0.011439566500484943, -0.012060410343110561, -0.08888224512338638, -0.019788915291428566, -0.03111972101032734, 0.042621269822120667, -0.01564342901110649, -0.011258076876401901, -0.03822667896747589, -0.024636942893266678, -0.011610984802246094, -0.007126613054424524, 0.08108629286289215, 0.039842039346694946, -0.01927720196545124, 0.008718769066035748, -0.038328807801008224, 0.00031873901025392115, 0.02859342470765114, -0.028411412611603737, -0.010606946423649788, -0.009782439097762108, -0.006103192921727896, -0.03506363183259964, -0.044770754873752594, 0.03857157751917839, 0.10386782884597778, -0.004146968014538288, 0.005568522494286299, -0.046532776206731796, -0.052276816219091415, 0.158909872174263, 0.03213762864470482, 0.01836998015642166, 0.08270648866891861, -0.0563189871609211, -0.03393111750483513, 0.0024565882049500942, -0.03294253349304199, -0.03338240832090378, -0.039437856525182724, 0.03990659490227699, -0.04276464879512787, 0.07690789550542831, -0.049493782222270966, -0.04460500553250313, -0.05694165080785751, 0.02412351220846176, 0.00474996492266655, -0.0023426287807524204, 0.0010737135307863355, 0.005529272835701704, 0.0569637306034565, 0.026027482002973557, -0.031394459307193756, 0.044868405908346176, -0.015005869790911674, 0.014908663928508759, -0.01491310354322195, 0.0018445682944729924, -0.012796984054148197, 0.01927245408296585, -0.07483339309692383, 0.0002474183274898678, -0.041961897164583206, 0.04825523495674133, 0.04197379946708679, -0.016432732343673706, -0.022811882197856903, -0.05113242566585541, 0.016750304028391838, 0.016680417582392693, 0.004672760143876076, -0.03777588531374931, -0.01452610082924366, 0.029306085780262947, 0.005506917834281921, -0.028448056429624557, 0.09174422919750214, 0.005853821057826281, 0.023390164598822594, 0.009500526823103428, 0.0298122838139534, -0.06394979357719421, -0.06840863078832626, 0.017506193369627, -0.028534259647130966, -0.05503897741436958, -0.03221170976758003, 0.05221123248338699, 0.008558127097785473, 0.09836239367723465, 0.07529950886964798, 0.07319438457489014, 0.03856419026851654, -0.029767446219921112, 0.04227356240153313, -0.024096854031085968, 0.015436965972185135, -0.024738922715187073, -0.032826781272888184, 0.021053239703178406, 0.03458753973245621, 0.008830455131828785, 0.04230296239256859, -0.011752909980714321, -0.008793224580585957, 0.01709570176899433, 0.006137693766504526, 0.010951021686196327, 0.016528569161891937, 0.02362203411757946, 0.018362125381827354, 0.055817026644945145, -0.021198846399784088, -0.0012633467558771372, -0.07617052644491196, -0.04661588370800018, -0.0007395268767140806, -0.0016571934102103114, -0.03803372383117676, 0.011373735964298248, 0.016784556210041046, 0.018523182719945908, 0.08129242062568665, 0.003829585388302803, -0.007037099450826645, 0.015936246141791344, 0.03230008855462074, 0.038589391857385635, -0.00281725125387311, -0.02517264522612095, 0.048825453966856, 0.023951208218932152, 0.053512927144765854, -0.026637636125087738, -0.01214397232979536, -0.01309577003121376, 0.00817140843719244, -0.012585639022290707, -0.044812340289354324, 0.01657230034470558, -0.007848751731216908, -0.014716475270688534, -0.0058272769674658775, 0.02105339989066124, 0.05303429067134857, -0.044636987149715424, 0.0494927279651165, 0.057174038141965866, -0.043792326003313065, -0.012274367734789848, -0.009592072106897831, -0.06417663395404816, 0.0020442979875952005, 0.020955007523298264, -0.028665728867053986, 0.0254829078912735, -0.04001808539032936, -0.046048156917095184, 0.004305483307689428, 0.012740813195705414, -0.013665552251040936, -0.025302596390247345, -0.08029305934906006, -0.006751989014446735, -0.011758384294807911, 0.004252943675965071, -0.046650130301713943, -0.008388280868530273, 0.0375099815428257, -0.0034426692873239517, -0.018365882337093353, -0.007126260083168745, 0.013551449403166771, 0.06430072337388992, 0.052686139941215515, 0.08053266257047653, 0.006068916525691748, -0.008018377237021923, 0.004583866335451603, -0.019219642505049706, -0.021315021440386772, -0.007906664162874222, -0.06175275519490242, 0.06046602129936218, 0.0042515103705227375, -0.007862968370318413, 0.0065233283676207066, -0.08145864307880402, -0.016322577372193336, -0.012258677743375301, 0.009983329102396965, -0.05207356810569763, -0.021440133452415466, -0.0009472088422626257, -0.024933071807026863, -0.00011339702905388549, 0.0030508581548929214, -0.0289860051125288, -0.02941691316664219, 0.007094072178006172, -0.02101341262459755, -0.03514983877539635, 0.08625917881727219, -0.005131760146468878, -0.017056865617632866, 0.053465843200683594, 0.018266869708895683, -0.051979225128889084, -0.012906764633953571, -0.03762048855423927, -0.021385401487350464, -0.008802130818367004, -0.022877464070916176, 0.02094409242272377, 0.009531361982226372, 0.0323449969291687, -0.0588216595351696, 0.06313341110944748, -0.029253559187054634, -0.02348610758781433, -0.013074617832899094, 0.03713241219520569, -0.044785596430301666, -0.004942227620631456, 0.023138076066970825, 0.0193575881421566, -0.05275793746113777, -0.03373676538467407, 0.05363010987639427, -0.04190370813012123, 0.005871226079761982, 0.019658254459500313, -0.06292873620986938, -0.01026693545281887, -0.028779787942767143, -0.05480276793241501, -0.00245018326677382, 0.019744016230106354, 0.008336042985320091, -0.00000513258419232443, -0.0037930356338620186, -0.007907598279416561, 0.04017914459109306, 0.02433418296277523, -0.014304453507065773, -0.023145083338022232, -0.0390702486038208, 0.029332144185900688, 0.002235760446637869, 0.06217360496520996, 0.0010355573613196611, 0.00909283198416233, 0.03404509648680687, -0.015150210820138454, -0.08925241976976395, 0.03690915182232857, -0.080553337931633, -0.014291473664343357, -0.009732130914926529, 0.02789030596613884, -0.016177883371710777, -0.05271988362073898, -0.07636722177267075, 0.09840985387563705, 0.004902615677565336, -0.018708523362874985, 0.06648488342761993, 0.012666442431509495, -0.0813656896352768, -0.04226505383849144, -0.01737171784043312, 0.0169132798910141, -0.03006022982299328, 0.04140955209732056, -0.03893943130970001, -0.023372923955321312, 0.045531824231147766, -0.027908965945243835, -0.01921245828270912, 0.009855413809418678, 0.029549842700362206, -0.049054164439439774, 0.060547247529029846, -0.004214076325297356, -0.016860466450452805, 0.004162779543548822, -0.019602136686444283, 0.007875890471041203, -0.022172963246703148, 0.03096613846719265, 0.020154569298028946, -0.059274692088365555, -0.04068741202354431, 0.017051488161087036, -0.014293146319687366, 0.048447903245687485, 0.03779733180999756, 0.027361609041690826, -0.0011363935191184282, -0.0509529784321785, -0.026628131046891212, -0.02570738084614277, -0.03441547974944115, 0.0008552803774364293, -0.02787856198847294, -0.008447877131402493, -0.023139713332057, 0.021415673196315765, 0.030367998406291008, 0.03728005290031433, 0.042960070073604584, 0.05814202129840851, -0.01775767095386982, -0.0011089619947597384, 0.001463899970985949, 0.01490688230842352, 0.037282004952430725, 0.006359976716339588, -0.0038019001949578524, 0.039632052183151245, -0.022426050156354904, 0.026988064870238304, 0.002102125668898225, -0.04292589798569679, 0.019631261005997658, -0.05918797478079796, 0.02723151259124279, 0.04947340115904808, 0.03662325441837311, 0.016977878287434578, -0.03271432965993881, 0.029627760872244835, -0.012648887000977993, 0.056234829127788544, -0.015563479624688625, -0.00743910763412714, -0.03442632779479027, 0.016173483803868294, 0.003104157978668809, 0.027623970061540604, -0.0016348797362297773, 0.02688545361161232, -0.0016274689696729183, -0.02758943848311901, -0.010562078095972538, -0.01082959957420826, -0.03789680451154709, 0.03590559586882591, 0.025253739207983017, -0.027374878525733948, 0.03956286236643791, -0.009354965761303902, 0.028713317587971687, 0.02767235040664673, -0.018872695043683052, 0.0030152183026075363, 0.04102485999464989, -0.010786084458231926, -0.0376581996679306, -0.04570263996720314, -0.010156930424273014, -0.0038673377130180597, -0.04930486902594566, -0.038068193942308426, -0.01760387234389782, -0.0035925861448049545, -0.04349534958600998, -0.005948872771114111, -0.01340592559427023, -0.030586466193199158, 0.08971309661865234, 0.037485357373952866, -0.0034725177101790905, 0.027009950950741768, -0.037271223962306976, 0.022148072719573975, 0.03255736455321312, 0.027605349197983742, 0.002588739385828376, -0.06123116984963417, 0.004875178914517164, -0.011828047223389149, 0.07232560962438583, -0.025030307471752167, -0.08454948663711548, 0.049422167241573334, 0.06801778078079224, 0.052963659167289734, -0.030287768691778183, 0.010417995974421501, 0.051325973123311996, 0.010538593865931034, 0.035962194204330444, -0.017135802656412125, -0.025712044909596443, -0.049345459789037704, 0.07711847126483917, 0.095106340944767, -0.0009369229665026069, -0.04394412785768509, 0.00784369558095932, 0.0011181728914380074, 0.02412964403629303, -0.06605681777000427, -0.016336847096681595, 0.003744172863662243, -0.018689069896936417, 0.013293605297803879, 0.04295167326927185, 0.030810203403234482, 0.014498253352940083, 0.05246356874704361, -0.0471491813659668, -0.02357265166938305, 0.006255962420254946, 0.005358568392693996, 0.008356081321835518, 0.002379982965067029, -0.04200976341962814, -0.03865659236907959, 0.04316652566194534, -0.07388358563184738, 0.0730285495519638, -0.0748153105378151, -0.07426764816045761, 0.03370263800024986, -0.01319154817610979, -0.017706509679555893, -0.05147417634725571, 0.06673264503479004, -0.04019211605191231, -0.03946191444993019, -0.03691941499710083, 0.044244736433029175, 0.005930290091782808, 0.004654179327189922, -0.01319909282028675, 0.026997758075594902, -0.06478619575500488, -0.070158451795578, 0.054463744163513184, -0.02696630172431469, -0.006745039951056242, -0.018813909962773323, 0.012196440249681473, -0.016578618437051773, 0.01676836423575878, -0.05592010170221329, -0.004555645398795605, -0.035367343574762344, -0.006254763808101416, 0.05339441075921059, -0.030228061601519585, -0.008116348646581173, 0.019159844145178795, -0.005602649413049221, 0.06864689290523529, 0.01625395193696022, 0.096589595079422, 0.03385159373283386, -0.0031624934636056423, -0.0012110942043364048, -0.014471174217760563, -0.00845006387680769, -0.06208694353699684, -0.05335913598537445, -0.05215125530958176, -0.009865552186965942, -0.02491188794374466, -0.00032375039882026613, -0.05085654929280281, 0.007849025540053844, -0.06176347658038139, -0.021350093185901642, -0.037168748676776886, -0.020712876692414284, -0.008624405600130558, 0.038433775305747986, -0.016211386770009995, -0.0178153645247221, 0.055574268102645874, -0.001852478482760489, -0.005882976111024618, -0.03690177947282791, -0.0007671394268982112, 0.02291705831885338, -0.0534466914832592, -0.06321590393781662, 0.03711848706007004, -0.023948095738887787, 0.06985494494438171, -0.03240465372800827, 0.030405553057789803, 0.01179778203368187, 0.011260632425546646, -0.004991078283637762, -0.007322756107896566, -0.0477517768740654, 0.03570808842778206, 0.010367252863943577, 0.0483785942196846, 0.01178468856960535, 0.04343520477414131, 0.00032762708724476397, -0.02500775456428528, -0.018288012593984604, -0.016972454264760017, 0.0483100600540638, -0.01959911361336708, 0.02112548053264618, 0.044597920030355453, 0.010849167592823505, -0.003346213838085532, -0.006748116109520197, 0.04728701338171959, 0.011494732461869717, 0.014478583820164204, -0.013296311721205711, 0.015085605904459953, 0.04479818791151047, 0.04180116951465607, 0.004374319221824408, 0.007370661944150925, 0.0607009157538414, 0.04561645910143852, 0.03660246357321739, -0.014418143779039383, 0.023151958361268044, -0.03958960250020027, 0.027352917939424515, -0.04270249605178833, 0.012083517387509346, -0.022362904623150826, -0.011347143910825253, -0.05550761520862579, 0.01681925170123577, -0.02502238005399704, 0.03331539407372475, -0.029609767720103264, 0.0012345401337370276, 0.06561295688152313, 0.030805416405200958, 0.015648523345589638, 0.04663310572504997, -0.0028113306034356356, 0.00601570401340723, -0.011509881354868412, 0.012242973782122135, -0.07476887851953506, -0.06499355286359787, 0.005822876468300819, 0.035161808133125305, 0.017887607216835022, -0.002742429729551077, -0.010334016755223274, -0.010515214875340462, 0.013328896835446358, -0.00986514613032341, -0.023766102269291878, 0.08317863941192627, -0.056230559945106506, -0.026576094329357147, -0.0571708157658577, -0.00069584627635777, 0.009756883606314659, -0.045202866196632385, -0.039689429104328156, 0.07005907595157623, 0.031329162418842316, 0.00668463995680213, 0.001644651871174574, 0.03833095729351044, -0.000915332930162549, -0.021963562816381454, 0.000554831640329212, 0.04958867281675339, -0.02182934805750847, -0.038783423602581024, -0.011482737958431244, -0.014479570090770721, 0.007492529693990946, 0.005429775919765234, -0.009115987457334995, 0.01633968949317932, -0.06535851955413818, -0.03153497353196144, -0.03604791685938835, -0.0674426332116127, -0.04859871044754982, 0.030949490144848824, 0.007279403507709503, 0.001632759696803987, -0.07633934170007706, -0.028215250000357628, -0.009681765921413898, 0.018290696665644646, 0.01765580102801323, 0.05162025988101959, 0.002759403781965375, 0.06803900003433228, -0.002000069012865424, 0.02571793459355831, 0.007900082506239414, 0.038599517196416855, 0.02330203913152218, 0.02891058661043644, 0.014588444493710995, -0.0029806059319525957, 0.006875281687825918, -0.021842267364263535, 0.03225670009851456, -0.008213912136852741, 0.029594970867037773, -0.01026899553835392, 0.07196475565433502, -0.010962646454572678, 0.03980698063969612, 0.004463690798729658, 0.02264382690191269, 0.0026928142178803682, -0.024302253499627113, -0.040030963718891144, -0.08857955783605576, -0.027863839641213417, 0.044356342405080795, -0.016725139692425728, -0.014492192305624485, -0.004178095143288374, 0.018448933959007263, -0.013330514542758465, -0.009439320303499699, 0.01644553244113922, -0.013275455683469772, -0.024631865322589874, 0.06760917603969574, -0.035971082746982574, 0.01015095878392458, 0.03790455684065819, -0.017674559727311134, -0.001754560275003314, 0.012873511761426926, 0.032584816217422485, -0.03396362066268921, -0.021308643743395805, -0.019931454211473465, -0.006002965848892927, 0.015906453132629395, -0.05285615473985672, 0.020784562453627586, -0.015865180641412735, -0.008983707055449486, 0.023977501317858696, -0.016535721719264984, 0.006735083181411028, -0.0461873784661293, 0.041139986366033554, 0.0066744317300617695, -0.039320819079875946, 0.03584049642086029, 0.024968145415186882, -0.028649138286709785, -0.04904954507946968, -0.016271840780973434, -0.016999810934066772, 0.00276157702319324, 0.00011694926797645167, 0.004211712162941694, 0.04609072208404541, 0.06761191785335541, 0.011827745474874973, 0.03617174178361893, 0.04820209741592407, -0.05550937354564667, 0.014281331561505795, -0.01986384578049183, 0.022783735767006874, -0.016252264380455017, 0.04588991403579712, -0.019295545294880867, -0.0007298904820345342, -0.006818669848144054, 0.0012980100000277162, 0.056512538343667984, 0.002009702380746603, -0.008527139201760292, 0.030914021655917168, 0.06843281537294388, -0.031707875430583954, 0.07746554166078568, -0.003743153065443039, -0.052774909883737564, 0.005927876569330692, 0.03997993841767311, 0.007896672934293747, -0.005931485909968615, 0.009503219276666641, 0.028726769611239433, 0.023552611470222473, 0.0032469455618411303, 0.00048674666322767735, 0.013352742418646812, -0.027780553326010704, 0.0219433531165123, -0.022475605830550194, -0.02579048089683056, 0.019845779985189438, 0.0327540747821331, 0.018748586997389793, -0.033457186073064804, 0.010404707863926888, -0.03220460191369057, 0.06984782963991165, 0.010885856114327908, -0.027433540672063828, -0.0002080372505588457, -0.05281875282526016, -0.038473427295684814, -0.006833896040916443, -0.009673512540757656, -0.012951888144016266, -0.060791175812482834, -0.026720494031906128, 0.05199936032295227, 0.011042087338864803, 0.08524462580680847, 0.048187561333179474, -0.02822437509894371, 0.0727258175611496, -0.006849358323961496, 0.004781996365636587, -0.04224541783332825, -0.06355714797973633, -0.037933044135570526, 0.0009037503041327, -0.04232282564043999, -0.05313773825764656, 0.015800852328538895, -0.05212990567088127, -0.013899256475269794 ]
<p>I often see the term "net mechanical efficiency" used in literature, but I am not quite sure what it means, and what the difference is between it and "normal" efficiency. Take this sentence for example: <code>... increased the effectiveness, while reducing net mechanical efficiency.</code> What does exactly does this mean?</p>
g1565
[ 0.05248389393091202, 0.048247821629047394, 0.01741619221866131, -0.013097265735268593, 0.02104385383427143, -0.042463093996047974, 0.022994982078671455, 0.026213936507701874, -0.06612886488437653, 0.019087539985775948, 0.0009729366283863783, -0.04684249311685562, -0.0017401757650077343, -0.02131095714867115, -0.004826236050575972, 0.017482932657003403, -0.011187520809471607, 0.004056595265865326, 0.025912366807460785, 0.054496683180332184, -0.030917417258024216, 0.012579723261296749, -0.01552076917141676, -0.004081730730831623, -0.020444272086024284, 0.08538787066936493, -0.04689895361661911, -0.00946471281349659, -0.030839096754789352, 0.013049144297838211, -0.02585458569228649, -0.04153928905725479, -0.023339619860053062, -0.01387662161141634, -0.13106031715869904, 0.040900327265262604, 0.01725475862622261, 0.018330849707126617, 0.04561451077461243, -0.07198086380958557, 0.022915620356798172, -0.03780925273895264, -0.04652116075158119, -0.024099508300423622, -0.037788260728120804, -0.001016111928038299, -0.016036931425333023, -0.049719128757715225, -0.03968502953648567, -0.045430026948451996, 0.015567071735858917, -0.04534434527158737, 0.05797560513019562, -0.00022987418924458325, 0.10403632372617722, 0.0007539241923950613, 0.010121443308889866, 0.012675915844738483, -0.023048939183354378, -0.002907987218350172, 0.018933312967419624, 0.0010006839875131845, 0.01758057251572609, -0.0388973206281662, -0.02460876852273941, 0.014402460306882858, 0.015453187748789787, 0.015967726707458496, 0.06201140210032463, -0.00717894034460187, -0.0536641851067543, 0.04825141653418541, -0.046030689030885696, -0.012015997432172298, -0.0022537189070135355, -0.009856038726866245, -0.026877937838435173, -0.0026551561895757914, 0.0058217281475663185, 0.028869329020380974, 0.01679234951734543, -0.011663589626550674, -0.024839289486408234, 0.0158056803047657, 0.05217742547392845, 0.0021496338304132223, -0.03320685401558876, -0.02168223261833191, -0.07998821884393692, 0.06004466116428375, 0.042139939963817596, -0.05150113254785538, 0.052676983177661896, -0.007502253632992506, -0.06911949068307877, 0.022480882704257965, 0.03841613233089447, -0.01588289998471737, -0.02967166341841221, 0.010428391396999359, -0.029292335733771324, -0.05933942645788193, 0.031629741191864014, -0.0588299036026001, -0.012140844948589802, 0.0691005289554596, 0.04555431008338928, -0.043032530695199966, -0.04388583451509476, 0.022023795172572136, 0.03665011748671532, 0.05296199768781662, -0.028460243716835976, -0.04050803929567337, -0.04639420285820961, -0.05724702402949333, 0.09667623043060303, 0.0274567399173975, -0.06029578298330307, -0.011590355075895786, 0.02000471018254757, 0.05234510824084282, -0.05178190395236015, 0.00537208141759038, 0.036582786589860916, -0.010277682915329933, 0.013366878032684326, -0.05004429444670677, 0.0033060547430068254, -0.03144155442714691, 0.05430988594889641, 0.029583176597952843, 0.019175130873918533, -0.009782996028661728, -0.007052070926874876, 0.036544930189847946, 0.014441401697695255, -0.017315246164798737, 0.05004376173019409, -0.023929359391331673, -0.012336383573710918, -0.061534058302640915, -0.022826863452792168, -0.0019925052765756845, 0.004049563780426979, 0.026923837140202522, -0.026354610919952393, 0.04510282352566719, 0.0010429919930174947, -0.00306609901599586, 0.006015271879732609, -0.003200214123353362, -0.021429892629384995, -0.09498953819274902, 0.04862789437174797, 0.002573286881670356, 0.0005320897325873375, 0.0033813200425356627, 0.0035872720181941986, 0.09774201363325119, 0.04606890305876732, 0.015953246504068375, 0.020455852150917053, 0.02001001499593258, -0.08183752000331879, -0.0064938864670693874, 0.026451656594872475, -0.04905177652835846, 0.008601441979408264, -0.0238181184977293, 0.0017115436494350433, -0.014023669064044952, 0.002581970766186714, 0.0815407782793045, -0.002320846077054739, 0.039509568363428116, 0.07426510006189346, 0.009048741310834885, -0.05384816601872444, 0.02221931330859661, -0.03047911450266838, 0.034275371581315994, 0.027576642110943794, -0.016523338854312897, -0.058424368500709534, -0.029158495366573334, 0.041500747203826904, -0.01282530464231968, -0.04440287873148918, 0.0010587758151814342, -0.061667975038290024, 0.013117335736751556, 0.10747411847114563, 0.03178895637392998, -0.08734355866909027, 0.015042824670672417, -0.03202272206544876, 0.01084841601550579, -0.013625909574329853, -0.05818232148885727, -0.009144585579633713, 0.01058723870664835, -0.018826311454176903, -0.05782192945480347, -0.03595639392733574, -0.00503722345456481, -0.016634855419397354, 0.01782217063009739, 0.060691528022289276, 0.030056683346629143, 0.01376744732260704, 0.023932378739118576, 0.033260777592659, 0.027648847550153732, 0.0026626840699464083, 0.028262797743082047, -0.07720824331045151, -0.04109516367316246, -0.040514737367630005, -0.05184132605791092, 0.005814705044031143, -0.036299146711826324, -0.00041401918861083686, 0.05102704465389252, -0.05857759714126587, -0.0368817113339901, 0.044996362179517746, 0.016732780262827873, 0.0003769159084185958, 0.00004150688255322166, 0.023071199655532837, 0.038552988320589066, -0.024679627269506454, -0.05557675287127495, -0.0009576068259775639, 0.06978444755077362, 0.018988918513059616, 0.03733415529131889, 0.015047837980091572, 0.009033003821969032, 0.04435783997178078, -0.057210080325603485, -0.015884777531027794, -0.01913793943822384, -0.005103781819343567, -0.051505960524082184, 0.01371554471552372, -0.01887959986925125, -0.03400226682424545, -0.0038693544920533895, 0.056653764098882675, -0.011718535795807838, -0.004824803210794926, -0.014603056013584137, 0.005155582446604967, 0.006192763336002827, -0.02494024485349655, -0.02668757364153862, -0.02219497039914131, 0.03395087271928787, -0.02896440401673317, 0.008466549217700958, -0.012146287597715855, 0.05503673478960991, 0.018724048510193825, -0.05112067237496376, -0.01936233416199684, -0.024964161217212677, 0.029404323548078537, 0.045084498822689056, 0.007929673418402672, -0.009110304526984692, -0.024863772094249725, -0.043698765337467194, -0.0028897433076053858, -0.04871316999197006, -0.021009787917137146, 0.0026572425849735737, 0.01096938457340002, -0.05036409571766853, 0.04088438302278519, -0.020748332142829895, 0.0006559950415976346, 0.03886072337627411, -0.0023882535751909018, -0.07019948959350586, 0.009258340112864971, -0.028880862519145012, -0.018943537026643753, -0.029047328978776932, -0.02637934498488903, -0.03708355873823166, 0.009849007241427898, -0.05522102117538452, 0.02083405666053295, -0.013387993909418583, 0.0009485414484515786, -0.008281446993350983, 0.016639480367302895, -0.05269875377416611, -0.0694613978266716, 0.011746231466531754, -0.03653963655233383, 0.008482892997562885, -0.026726888492703438, 0.0783073902130127, -0.008198809809982777, 0.025975212454795837, -0.03134961426258087, 0.026730716228485107, -0.01763506606221199, 0.02644294686615467, 0.05057059973478317, 0.05863256752490997, -0.11043549329042435, 0.052885983139276505, 0.0008474893984384835, -0.03845924884080887, -0.024506710469722748, 0.008523627184331417, 0.04621371999382973, -0.09146840870380402, 0.02072739601135254, 0.021029843017458916, -0.04870833829045296, 0.005267035216093063, -0.013791976496577263, 0.01473369263112545, -0.03206932172179222, -0.008552995510399342, -0.0011129669146612287, 0.01029223296791315, -0.04085613787174225, -0.030468137934803963, -0.023633403703570366, 0.006746822502464056, -0.030691536143422127, 0.0561768114566803, 0.02519499883055687, 0.015571575611829758, 0.08721868693828583, 0.050532739609479904, -0.04610497131943703, -0.01767834462225437, 0.01268831081688404, 0.023513691499829292, -0.04568491503596306, -0.027897082269191742, -0.019407154992222786, -0.029634002596139908, 0.06433436274528503, -0.012200426310300827, 0.021981706842780113, -0.05220643803477287, -0.060994233936071396, -0.02194233611226082, -0.03636044263839722, -0.02738986350595951, -0.020809827372431755, 0.026140527799725533, -0.002269973512738943, -0.012950700707733631, -0.00048296249588020146, 0.010415427386760712, -0.035582445561885834, 0.014484144747257233, 0.046048860996961594, -0.005906098056584597, -0.04342340677976608, -0.047913406044244766, -0.026299605146050453, 0.03230758756399155, -0.008016902953386307, 0.0019857778679579496, -0.005473674274981022, 0.034916482865810394, 0.023800848051905632, 0.0016877527814358473, 0.04422016069293022, 0.03018319606781006, 0.04329231381416321, -0.009325790219008923, -0.04308611899614334, 0.03568797931075096, 0.015236378647387028, -0.04165554791688919, -0.04657312110066414, 0.03883139789104462, 0.052847519516944885, 0.024796687066555023, -0.05000035837292671, 0.027953611686825752, -0.0432131253182888, 0.014588871970772743, 0.028504628688097, 0.0184160266071558, -0.030376214534044266, 0.029527701437473297, 0.03449685499072075, 0.03815566375851631, 0.0008146046311594546, -0.01002610195428133, 0.016858994960784912, 0.06238223984837532, -0.004375777672976255, -0.05086372792720795, 0.06361836940050125, 0.07113970816135406, -0.015538551844656467, -0.011871975846588612, 0.011102880351245403, -0.049897510558366776, -0.03023265302181244, -0.02144007384777069, 0.006370519753545523, 0.016520392149686813, -0.00969010405242443, 0.031114567071199417, -0.0194403063505888, 0.041302427649497986, -0.004508095793426037, -0.004136273637413979, -0.002318629063665867, -0.022029098123311996, 0.0041908021084964275, 0.06789004802703857, 0.017020056024193764, -0.0006076422869227827, 0.031978920102119446, -0.06994666159152985, 0.03399769589304924, 0.056032903492450714, -0.038734689354896545, 0.03941313922405243, -0.009758791886270046, 0.05377785116434097, 0.007860942743718624, 0.031852684915065765, 0.07190781831741333, -0.010301236063241959, 0.022967789322137833, 0.022405115887522697, -0.013492417521774769, -0.026931969448924065, 0.02134030871093273, -0.03599487617611885, 0.03496366739273071, 0.02648705430328846, -0.07470081001520157, -0.03146776556968689, -0.07302354276180267, 0.05204188823699951, -0.011632874608039856, -0.030364252626895905, 0.030079500749707222, -0.015390617772936821, 0.01857386715710163, -0.0355193167924881, -0.03771107643842697, -0.028595078736543655, -0.031479813158512115, 0.0197812020778656, -0.05627213791012764, 0.020197376608848572, 0.001978303538635373, 0.055961549282073975, 0.020743105560541153, -0.017521673813462257, -0.04361896961927414, 0.06056210771203041, 0.022651303559541702, 0.021173719316720963, 0.026797153055667877, -0.026231534779071808, -0.009415803477168083, 0.038073550909757614, 0.012579922564327717, -0.013261903077363968, 0.03791035711765289, 0.02632744424045086, -0.017510555684566498, -0.013772436417639256, 0.009808411821722984, -0.023427756503224373, 0.029916904866695404, -0.0004001581110060215, 0.01387875247746706, 0.007107078563421965, 0.020536918193101883, -0.04628228768706322, 0.08041734248399734, 0.04705824330449104, -0.003005144651979208, -0.02592785283923149, -0.061846740543842316, 0.008019107393920422, 0.0188575629144907, -0.02426311746239662, 0.015188704244792461, 0.00399619759991765, -0.03322974964976311, 0.022751759737730026, -0.010245653800666332, 0.02620009332895279, 0.004893707111477852, 0.06416682153940201, -0.048572760075330734, -0.02320685237646103, -0.0029543517157435417, 0.016678618267178535, 0.023932309821248055, 0.004726737271994352, -0.03434498608112335, 0.041609711945056915, 0.0347956120967865, 0.03585275635123253, 0.040393464267253876, -0.009583828039467335, -0.001144603593274951, -0.02412482723593712, 0.04078032076358795, -0.019999036565423012, -0.006808174774050713, -0.000594496144913137, -0.011900530196726322, 0.002266343217343092, -0.05013326555490494, 0.03513491898775101, 0.009133659303188324, 0.010283812880516052, 0.020830683410167694, 0.04176679998636246, -0.018403170630335808, 0.033944472670555115, -0.008387221023440361, -0.018996231257915497, -0.021730734035372734, -0.04639394208788872, 0.02576487511396408, 0.009393946267664433, -0.01410392764955759, -0.020594097673892975, -0.035422198474407196, 0.02473476156592369, 0.011654386296868324, 0.021355828270316124, -0.0005234019481576979, -0.05036125332117081, 0.011987521313130856, -0.03177575767040253, -0.002232020953670144, -0.002380314515903592, 0.017502497881650925, -0.06538645178079605, 0.05367862060666084, 0.11531447619199753, -0.006458524614572525, -0.006120199803262949, 0.048750609159469604, -0.03639593347907066, -0.01493798103183508, 0.08233970403671265, -0.00007637911767233163, 0.003737150225788355, 0.045382142066955566, -0.0361783467233181, -0.045983683317899704, -0.012492001987993717, 0.010007735341787338, -0.025146473199129105, 0.0323241725564003, 0.016883857548236847, -0.00932373944669962, 0.08230076730251312, 0.03394235298037529, -0.02066897042095661, -0.007745669223368168, -0.040049295872449875, -0.04097628965973854, -0.03035084344446659, 0.003389916382730007, -0.06192803010344505, -0.02498478814959526, -0.03756354749202728, -0.038770291954278946, 0.0266722422093153, -0.023852767422795296, 0.022094782441854477, -0.0035679342690855265, 0.012391977943480015, -0.024270685389637947, 0.04340887442231178, 0.0007534811738878489, 0.03140055388212204, 0.012558627873659134, -0.005766882095485926, -0.03791278600692749, 0.05886417254805565, 0.04893207550048828, 0.03759925812482834, 0.011329992674291134, -0.00020390472491271794, 0.0722370594739914, -0.032334599643945694, 0.03247824311256409, 0.0799756720662117, 0.021042464300990105, -0.030100086703896523, -0.036784108728170395, -0.028044426813721657, -0.043464742600917816, 0.024660998955368996, 0.0010798679431900382, 0.011642917059361935, 0.012731127440929413, 0.015266196802258492, -0.0524870939552784, -0.027983710169792175, 0.009203811176121235, -0.009763898327946663, -0.03172358125448227, -0.07544281333684921, 0.08587299287319183, -0.010503208264708519, -0.0005830827867612243, 0.006478951778262854, -0.010049375705420971, -0.014951351098716259, 0.011823256500065327, -0.015963850542902946, -0.03327643871307373, 0.013725795783102512, -0.025162722915410995, 0.07934655994176865, -0.023939630016684532, -0.04468584805727005, -0.04604441672563553, 0.05789732560515404, 0.07409515231847763, 0.02588766999542713, -0.0015331441536545753, 0.0024622278288006783, 0.01723211258649826, -0.01785559393465519, -0.046043746173381805, 0.002051649149507284, 0.005795912351459265, -0.02313286066055298, -0.026262465864419937, 0.0001947871205629781, -0.05436287447810173, -0.038137853145599365, -0.026891963556408882, 0.03636929765343666, -0.05691096931695938, 0.03771233186125755, -0.041377488523721695, 0.03915968909859657, -0.012718130834400654, -0.03603134676814079, -0.03908410668373108, 0.009294001385569572, 0.034327905625104904, 0.044115133583545685, 0.0468360111117363, 0.02145206555724144, 0.00965024158358574, -0.013539282605051994, -0.03680260479450226, -0.010744021274149418, 0.00017671061505097896, -0.003885604441165924, 0.025829659774899483, -0.007362675853073597, -0.001361078000627458, 0.010124096646904945, -0.023596221581101418, -0.038559138774871826, -0.009174064733088017, -0.04106973484158516, 0.03225525841116905, 0.024469660595059395, 0.001525496831163764, -0.028411712497472763, 0.031276531517505646, 0.05637536942958832, -0.06616951525211334, 0.030839987099170685, -0.013567027635872364, -0.0037016442511230707, -0.0046034618280828, -0.023966673761606216, 0.02904636599123478, 0.018138771876692772, -0.051260922104120255, 0.05568519979715347, 0.05627045780420303, 0.0945264995098114, 0.04268798604607582, -0.004396709613502026, -0.03111223690211773, 0.0023329092655330896, -0.02439802512526512, 0.04141169413924217, -0.02367491088807583, 0.025308160111308098, -0.02228310890495777, 0.0020843995735049248, -0.032972343266010284, 0.03797617927193642, -0.05539669096469879, -0.037946444004774094, 0.0838659480214119, 0.029349178075790405, -0.03579861670732498, 0.010248100385069847, 0.05746311694383621, -0.026333210989832878, -0.04248896613717079, 0.08925548195838928, 0.02844606712460518, 0.06300806254148483, 0.03407401219010353, -0.04248690977692604, -0.0799810066819191, 0.0016025551594793797, -0.035752300173044205, 0.017960693687200546, 0.010799934156239033, -0.008865274488925934, 0.0075155096128582954, -0.05590002238750458, -0.013614239171147346, 0.020571043714880943, 0.02143796533346176, 0.010604409500956535, 0.018791332840919495, 0.030630677938461304, -0.0009170803823508322, 0.04527191445231438, 0.014702633954584599, -0.0008487533777952194, -0.030669579282402992, 0.001528963795863092, -0.02620149962604046, 0.023528655990958214, 0.035576388239860535, 0.021669497713446617, 0.028982719406485558, -0.03541427105665207, 0.0304463729262352, -0.02846801094710827, -0.011470110155642033, 0.024080168455839157, 0.04142709821462631, -0.033149201422929764, -0.06942181289196014, 0.08410566300153732, 0.00025005271891131997, 0.02469276450574398, 0.007542181760072708, 0.033539753407239914, -0.02748045139014721, -0.08097460120916367, -0.04482695832848549, -0.001698338775895536, -0.0031939512118697166, -0.009719768539071083 ]
<p>It is usually said that existence of discrete spacetime violates Lorentz symmetry. What quantity is used to quantify such violation? I mean could someone points a reference for a derivation that shows such analysis.</p> <p>My other question is that: if, and this is a big fat if, OPERA result was true (and I believe it is not) would that prove that spacetime is discrete? (this is like the inverse to the 1st part of this post, if space-time is discrete then Lorentz symmetry is violated, what if Lorentz symmetry is violated, does that imply space-time is discrete? or not necessarily?)</p>
g1566
[ 0.011389605700969696, 0.012377564795315266, 0.0036506105680018663, -0.031912051141262054, 0.007921824231743813, 0.014902302995324135, 0.02698427252471447, 0.04299532622098923, -0.017535684630274773, -0.03789327293634415, -0.017480282112956047, -0.02077355794608593, 0.019721616059541702, 0.048082880675792694, 0.011968356557190418, -0.01992117054760456, 0.027938928455114365, 0.021302975714206696, -0.045016344636678696, -0.06037316843867302, 0.03587207943201065, 0.0166619885712862, 0.00802550744265318, -0.0691036731004715, 0.05035198852419853, -0.037814877927303314, 0.07946543395519257, -0.011209234595298767, -0.03176342695951462, 0.016769330948591232, 0.016234371811151505, 0.01184731163084507, 0.016623642295598984, -0.057254523038864136, -0.004179755225777626, -0.07633723318576813, -0.04282362014055252, 0.0026812043506652117, 0.02225983887910843, 0.0211743526160717, 0.003213413991034031, 0.016552941873669624, -0.006416943855583668, -0.014376413077116013, -0.020209630951285362, -0.05100727453827858, -0.050622258335351944, 0.031194308772683144, 0.025565121322870255, -0.0342332161962986, 0.03899838402867317, -0.003132185898721218, 0.10104001313447952, -0.08502217382192612, -0.03885413706302643, 0.00826797541230917, 0.00714645441621542, -0.01578780822455883, 0.049147654324769974, 0.09069529175758362, -0.00006506082718260586, -0.000998100033029914, -0.01757444255053997, 0.03676556050777435, 0.031910985708236694, 0.00020630197832360864, -0.024938758462667465, -0.0199736338108778, 0.036108147352933884, -0.03659853711724281, 0.01400725170969963, -0.06093057245016098, 0.05491095036268234, -0.01947941444814205, -0.0438830740749836, 0.045254118740558624, -0.017216674983501434, 0.08370868861675262, -0.03752090781927109, -0.028234751895070076, -0.027366187423467636, -0.0051839109510183334, 0.019215375185012817, 0.0380120612680912, 0.0786462128162384, -0.005355735309422016, -0.02331945113837719, -0.05437025800347328, 0.021189061924815178, 0.027042768895626068, 0.0443386472761631, -0.0705065056681633, 0.037488795816898346, 0.004528949037194252, -0.01267766673117876, -0.015326196327805519, 0.03369302675127983, 0.09123043715953827, -0.020642589777708054, -0.0016439700266346335, 0.006390809081494808, -0.014595276676118374, 0.0053744870238006115, -0.056403402239084244, 0.012795715592801571, 0.00582909444347024, 0.03698912262916565, 0.01741078868508339, -0.013739044778048992, 0.0056044780649244785, -0.018406305462121964, -0.03436248376965523, -0.022679483518004417, -0.02045387029647827, -0.00726526090875268, 0.03766496106982231, 0.02911832556128502, -0.09880027174949646, 0.002282902132719755, 0.04687730595469475, 0.03872763738036156, 0.031213784590363503, -0.03330120071768761, 0.04303647205233574, -0.03524681553244591, -0.009155891835689545, -0.04570332169532776, 0.007805229630321264, 0.038109686225652695, -0.03966138884425163, -0.026792768388986588, 0.04083899036049843, 0.022104531526565552, 0.030163707211613655, -0.06020864099264145, 0.008736852556467056, -0.01594935916364193, -0.031062573194503784, -0.031121505424380302, 0.004088335670530796, 0.036381516605615616, -0.02831636741757393, 0.03664993494749069, -0.014793099835515022, -0.0031675498466938734, 0.0029502788092941046, -0.041153568774461746, -0.07180333882570267, 0.010201828554272652, 0.0146704176440835, 0.0020060527604073286, 0.055314529687166214, 0.019502606242895126, -0.05595805123448372, 0.039653707295656204, -0.014204871840775013, 0.0018878380069509149, -0.0030838509555906057, 0.014109817333519459, 0.010659773834049702, 0.046949081122875214, -0.01870100013911724, 0.01031268946826458, 0.003793952986598015, -0.02829229272902012, 0.004803521558642387, 0.005122365429997444, -0.04600517824292183, -0.020630760118365288, 0.003875282360240817, -0.04122614115476608, -0.03267507627606392, 0.05217772722244263, 0.023584043607115746, 0.023735975846648216, 0.07790957391262054, -0.015173354186117649, 0.017930174246430397, -0.011175991967320442, -0.005115025211125612, -0.014112605713307858, -0.034836895763874054, -0.03942389413714409, -0.049337733536958694, -0.001510685309767723, 0.01219317689538002, 0.028277065604925156, -0.059479836374521255, -0.06065690517425537, 0.030525125563144684, 0.013618127442896366, 0.027462063357234, 0.053274720907211304, 0.041338302195072174, 0.04774180427193642, -0.011820279993116856, -0.018842661753296852, -0.02079256810247898, 0.02411867491900921, 0.005761754233390093, 0.016587860882282257, 0.03192776069045067, 0.0511772446334362, -0.03339874744415283, 0.03309062123298645, 0.03827367350459099, -0.08421023190021515, 0.002246940042823553, 0.038149189203977585, -0.034752119332551956, 0.05191517621278763, -0.049208350479602814, 0.010830940678715706, -0.01146185863763094, -0.0664329007267952, 0.01171362679451704, -0.013996371068060398, 0.015655700117349625, -0.03951805830001831, 0.037264641374349594, 0.04335548356175423, -0.039200253784656525, 0.057555846869945526, 0.04563833773136139, -0.03481818735599518, -0.03453690558671951, 0.006287050433456898, -0.09294740855693817, -0.002351767150685191, 0.02477646991610527, -0.05078940838575363, 0.0010300972498953342, -0.00645711924880743, -0.023596597835421562, 0.025531897321343422, 0.08897148072719574, 0.036425646394491196, 0.005773095414042473, 0.0585750974714756, -0.021270787343382835, 0.020600279793143272, 0.049887191504240036, -0.04216688871383667, 0.03556063398718834, 0.07741161435842514, -0.022134102880954742, -0.025014927610754967, -0.051050640642642975, 0.009515460580587387, 0.020415520295500755, -0.03746093064546585, -0.019159743562340736, -0.01870911195874214, -0.009845699183642864, 0.030515963211655617, -0.052233513444662094, 0.012057777494192123, 0.09417672455310822, -0.08776455372571945, 0.0023469130974262953, -0.012014666572213173, -0.017131708562374115, -0.018757518380880356, 0.012805359438061714, 0.00014217836724128574, -0.05339745059609413, -0.001976877683773637, 0.03107190504670143, -0.04287559539079666, -0.007870317436754704, -0.013291901908814907, 0.04082099348306656, 0.0050639137625694275, 0.04353080317378044, 0.03899778798222542, -0.01752324402332306, 0.04666708782315254, -0.0711994543671608, 0.03173765167593956, -0.029394155368208885, 0.04960924759507179, -0.0018941122107207775, -0.06311870366334915, 0.06518736481666565, 0.021874409168958664, 0.0020015505142509937, -0.05719022825360298, -0.04424713924527168, -0.04565669596195221, 0.031878773123025894, 0.013111836276948452, 0.01317459624260664, -0.04398632422089577, -0.0754610002040863, -0.07321809232234955, 0.03072907030582428, -0.019609913229942322, -0.037785645574331284, 0.016428910195827484, -0.029433706775307655, 0.0007898660842329264, 0.0007971538580022752, 0.04349813610315323, 0.02227308414876461, 0.007920688949525356, -0.0026234248653054237, -0.015732288360595703, -0.036746084690093994, 0.03965108096599579, -0.08807038515806198, 0.04285013675689697, 0.05456499755382538, -0.01910988986492157, -0.02443259209394455, -0.0011944328434765339, 0.00706055061891675, -0.027812935411930084, 0.0362703762948513, 0.027802735567092896, -0.015906522050499916, -0.004387224093079567, 0.004837529268115759, -0.029167545959353447, 0.013404568657279015, 0.028935333713889122, -0.10399606078863144, 0.014159518294036388, 0.011607425287365913, 0.03204856440424919, 0.041093505918979645, 0.02542269602417946, -0.019410358741879463, 0.007788076531141996, -0.018622716888785362, -0.03704141452908516, 0.0012182496720924973, -0.052341099828481674, -0.010439380072057247, -0.023564396426081657, -0.012695487588644028, 0.00007977744098752737, 0.012219469994306564, -0.03647218272089958, -0.008429313078522682, 0.011302298866212368, 0.06799254566431046, 0.03008025884628296, -0.03769500181078911, 0.036115024238824844, 0.05163028836250305, 0.0024546657223254442, -0.07773946225643158, -0.004055507015436888, -0.030665859580039978, -0.019083300605416298, 0.005094608757644892, 0.04303047060966492, 0.02280016429722309, 0.03660072386264801, -0.02551279403269291, 0.011768217198550701, -0.01558416336774826, 0.0391346774995327, -0.035742782056331635, 0.026949573308229446, 0.04752769693732262, -0.007228414993733168, -0.032780516892671585, -0.02981691248714924, 0.002986334031447768, 0.021986952051520348, 0.035480570048093796, 0.01287114154547453, 0.017421267926692963, 0.06974052637815475, -0.04918501526117325, -0.012534505687654018, 0.04449889063835144, 0.021062826737761497, 0.04511520266532898, 0.05687592551112175, 0.04852142930030823, 0.05013603717088699, 0.01472613774240017, 0.0314948670566082, -0.0048213438130915165, -0.04652449116110802, 0.010834933258593082, -0.02011427842080593, -0.08307157456874847, 0.006413021590560675, -0.04649981111288071, -0.03481174260377884, 0.004450513981282711, -0.005744682624936104, -0.03395535796880722, -0.0132360914722085, 0.045676883310079575, 0.014718702994287014, 0.03473580256104469, 0.001213081763125956, 0.04441985860466957, 0.001215417287312448, -0.029386764392256737, 0.022377049550414085, 0.016885749995708466, 0.028723586350679398, -0.004005693830549717, -0.016048166900873184, 0.037496019154787064, -0.03593938425183296, 0.009696456603705883, 0.002527892356738448, -0.09204338490962982, 0.009287579916417599, 0.04034361243247986, -0.006266037002205849, -0.049060601741075516, 0.05322755500674248, 0.0427846685051918, -0.015065823681652546, 0.04232923313975334, -0.04109298065304756, -0.041521765291690826, -0.05471016839146614, 0.03798598051071167, 0.0921265259385109, 0.036441460251808167, -0.04445481300354004, -0.02658923901617527, -0.010443512350320816, 0.017101801931858063, 0.012268380261957645, 0.0809282660484314, -0.01394047960639, -0.024103280156850815, -0.024515366181731224, 0.1005452424287796, -0.030725792050361633, -0.03890042006969452, 0.08157498389482498, -0.017461972311139107, 0.06108659878373146, 0.019741130992770195, -0.017453258857131004, 0.0333452969789505, -0.028307311236858368, -0.04718993231654167, -0.025677774101495743, 0.01087705697864294, 0.02435469441115856, 0.03096499666571617, -0.03320281207561493, -0.023058392107486725, -0.021883506327867508, 0.021853366866707802, -0.0017940483521670103, -0.020033802837133408, 0.00934572983533144, 0.05956520140171051, -0.014375124126672745, -0.004534500651061535, 0.059180472046136856, 0.0719594657421112, 0.04939650744199753, -0.020516060292720795, -0.01702469401061535, -0.04365437850356102, -0.03671911731362343, 0.026383254677057266, 0.0008678477024659514, -0.01335079874843359, -0.011932190507650375, 0.00019105708634015173, 0.01467205211520195, 0.022720929235219955, -0.09123212844133377, 0.005534251220524311, -0.07095058262348175, -0.07111767679452896, -0.052811089903116226, -0.057912472635507584, 0.01438088994473219, 0.021310672163963318, -0.03163390979170799, 0.043481919914484024, 0.02303140051662922, -0.02101617492735386, 0.03813699632883072, -0.014859918504953384, 0.004060993902385235, -0.013620572164654732, 0.06797071546316147, -0.01174788735806942, -0.020556287840008736, 0.003642440540716052, -0.0173142421990633, -0.0332251600921154, -0.020954497158527374, -0.006634959485381842, -0.03733403980731964, 0.057340484112501144, 0.08859557658433914, -0.04621880501508713, -0.024583401158452034, 0.04809623956680298, 0.008571791462600231, 0.03000670298933983, -0.0628163293004036, 0.020665185526013374, 0.03939514607191086, 0.06258302181959152, -0.014368437230587006, -0.0035951812751591206, 0.0014047638978809118, 0.006135336123406887, 0.0058547998778522015, -0.010843999683856964, -0.0022078421898186207, -0.020878665149211884, -0.10728852450847626, 0.02509377710521221, -0.00874436553567648, -0.03449666127562523, 0.010508265346288681, 0.00991299282759428, -0.048789385706186295, 0.0084834611043334, -0.01564077101647854, -0.04415732994675636, 0.033088408410549164, 0.0631885901093483, -0.02784627117216587, -0.027441153302788734, -0.005795351695269346, -0.014306476339697838, 0.05326367914676666, -0.03119197115302086, 0.042145535349845886, 0.034716248512268066, -0.02016543410718441, 0.009032991714775562, 0.05286885425448418, 0.021032247692346573, -0.03912527859210968, 0.002286047674715519, -0.016152385622262955, 0.03329688683152199, 0.025290032848715782, -0.02593260630965233, -0.07484255731105804, 0.01343278307467699, -0.015911536291241646, 0.0017661037854850292, -0.016677187755703926, 0.054628193378448486, 0.014346089214086533, -0.01807473786175251, -0.07090828567743301, 0.018173029646277428, 0.025643877685070038, 0.04908449947834015, 0.010651852004230022, -0.008904301561415195, 0.008170570246875286, -0.046328477561473846, 0.03904880955815315, -0.0005939629045315087, 0.025793462991714478, 0.010640853084623814, -0.03909815475344658, 0.06694391369819641, 0.0172397643327713, 0.014280353672802448, -0.013619714416563511, 0.025853797793388367, 0.03420088812708855, -0.08369152247905731, -0.06038661301136017, 0.00858302041888237, 0.03656850382685661, -0.01375564280897379, 0.02608427032828331, -0.017140120267868042, -0.029784347862005234, 0.06854967027902603, 0.016612930223345757, 0.000714251771569252, -0.01417135912925005, -0.046835362911224365, 0.01327746082097292, -0.025171680375933647, -0.015463813208043575, -0.04497208818793297, 0.02074328623712063, 0.0031686113215982914, -0.0070242309011518955, 0.015981677919626236, -0.03837541118264198, 0.0032896550837904215, 0.02110806107521057, -0.022472038865089417, 0.039238445460796356, -0.011372311040759087, -0.008106960915029049, 0.007076905574649572, -0.036684174090623856, -0.0019069755217060447, -0.025770897045731544, 0.012690110132098198, 0.01316886767745018, 0.012696534395217896, -0.03945320099592209, 0.038339901715517044, -0.0036979292053729296, -0.015313134528696537, -0.02651284821331501, -0.03128783032298088, -0.03305255249142647, 0.055427975952625275, 0.00010247838508803397, -0.0028546431567519903, -0.042517732828855515, -0.008110039867460728, 0.02009410411119461, 0.07390638440847397, 0.024739546701312065, -0.01083680335432291, 0.0008189394138753414, -0.05291859805583954, -0.045839548110961914, 0.009754062630236149, 0.008315084502100945, 0.004226956982165575, -0.04881979897618294, -0.006041365675628185, -0.014987152069807053, -0.01047284435480833, 0.003922821953892708, -0.010973972268402576, 0.006270142737776041, 0.03639516234397888, 0.0413934588432312, -0.05962910130620003, -0.031242666766047478, 0.023480990901589394, 0.05976241081953049, -0.0019920002669095993, -0.018280785530805588, -0.01760024204850197, 0.02000248245894909, -0.00944565050303936, -0.023661309853196144, 0.010676223784685135, -0.028114913031458855, 0.0012416242389008403, -0.031719714403152466, 0.014153243973851204, 0.023633519187569618, -0.04124089330434799, 0.004045850597321987, 0.002894133096560836, -0.0730375126004219, -0.013774257153272629, -0.028634414076805115, 0.014184257946908474, -0.015602411702275276, 0.027253681793808937, 0.0340045802295208, -0.028998257592320442, -0.017321962863206863, -0.05631883442401886, -0.003727180417627096, 0.020295079797506332, -0.0018153343116864562, -0.043738316744565964, -0.014418202452361584, 0.01881670206785202, -0.03713635727763176, 0.012771711684763432, 0.02692786604166031, 0.013285394757986069, -0.03428512439131737, 0.049936022609472275, -0.052064381539821625, -0.03152592107653618, 0.013134419918060303, -0.01074970979243517, 0.006701005157083273, 0.011285507120192051, -0.020925866439938545, 0.024258967489004135, 0.036128152161836624, -0.07534768432378769, -0.03411988168954849, -0.011020790785551071, 0.06624095141887665, 0.0029026949778199196, 0.004650328308343887, 0.004259673412889242, 0.02793031930923462, 0.02306010201573372, -0.02730296179652214, 0.01715157739818096, 0.05482517555356026, 0.06408464163541794, 0.030172988772392273, -0.045945920050144196, -0.06357452273368835, -0.03153606876730919, 0.017126072198152542, 0.021539650857448578, 0.027401020750403404, -0.04250113293528557, 0.06984519958496094, -0.05030679330229759, -0.04604664072394371, 0.010344419628381729, 0.10623210668563843, -0.01615513302385807, 0.031206849962472916, 0.014615487307310104, 0.054025568068027496, -0.07580123096704483, -0.018579714000225067, -0.028102530166506767, 0.026536891236901283, -0.02230202592909336, -0.00027127633802592754, -0.012186231091618538, -0.00023754764697514474, 0.03225839138031006, -0.037837110459804535, 0.06257419288158417, -0.02291608788073063, 0.04464072361588478, 0.009197277016937733, 0.011017430573701859, 0.03300899639725685, 0.038044992834329605, -0.026848243549466133, 0.005861696321517229, -0.01333206333220005, 0.012081671506166458, -0.030210861936211586, 0.025480911135673523, -0.042099568992853165, 0.013145902194082737, 0.03678945451974869, -0.01274194661527872, -0.0006874558166600764, 0.04019732028245926, 0.0010097324848175049, 0.005637339316308498, 0.0348946638405323, -0.09372948110103607, 0.008156202733516693, -0.03607123717665672, 0.030430812388658524, 0.02518738992512226, 0.03211243078112602, 0.0028501113411039114, 0.022038791328668594, 0.014197191223502159, -0.09389660507440567, -0.03769805654883385, 0.0010137103963643312, 0.01573466882109642 ]
<p>I'm having some trouble calculating the 2nd order energy shift in a problem. I am given the pertubation:</p> <p>$\hat{H}'=\alpha \hat{p}$,</p> <p>where $\alpha$ is a constant, and $\hat{p}$ is given by:</p> <p>$p=i\sqrt{\frac{\hbar m\omega }{2}}\left( {{a}_{+}}-{{a}_{-}} \right)$,</p> <p>where ${a}_{+}$ and ${a}_{-}$ are the usual ladder operators.</p> <p>Now, according to my book, the 2nd order energy shift is given by:</p> <p>$E_{n}^{2}=\sum\limits_{m\ne n}{\frac{{{\left| \left\langle \psi _{m}^{0} \right|H'\left| \psi _{n}^{0} \right\rangle \right|}^{2}}}{E_{n}^{0}-E_{m}^{0}}}$</p> <p>Now, what I have tried to do is to calculate the term inside the power of 2. And so far I have done this:</p> <p>$\begin{align} &amp; E_{n}^{1}=\alpha i\sqrt{\frac{\hbar m\omega }{2}}\int{\psi _{m}^{*}\left( {{{\hat{a}}}_{+}}-{{{\hat{a}}}_{-}} \right)}\,{{\psi }_{n}}\,dx=\alpha i\sqrt{\frac{\hbar m\omega }{2}}\left( \int{\psi _{m}^{*}\,{{{\hat{a}}}_{+}}{{\psi }_{n}}\,dx-\int{\psi _{m}^{*}\,{{{\hat{a}}}_{-}}{{\psi }_{n}}\,dx}} \right) \\ &amp; =\alpha i\sqrt{\frac{\hbar m\omega }{2}}\left( \sqrt{n+1}\int{\psi _{m}^{*}\,{{\psi }_{n+1}}\,dx-\sqrt{n}\int{\psi _{m}^{*}\,{{\psi }_{n-1}}\,dx}} \right) \end{align} $</p> <p>As you can see, I end up with the two integrals. But I don't know what to do next ? 'Cause if $m &gt; n$, and only by 1, then the first integral will be 1, and the other will be zero. And if $n &gt; m$, only by 1, then the second integral will be 1, and the first will be zero. Otherwise both will be zero. And it seems wrong to have to make two expressions for the energy shift for $n &gt; m$ and $m &gt; n$.</p> <p>So am I on the right track, or doing it totally wrong ?</p> <p>Thanks in advance.</p> <p>Regards</p>
g1567
[ 0.04757639393210411, -0.028346644714474678, 0.0014772923896089196, -0.017003346234560013, -0.0004224030126351863, -0.01894168183207512, -0.034298308193683624, 0.03933717682957649, -0.0992782786488533, -0.012413500808179379, -0.005543090868741274, 0.041511110961437225, -0.06559226661920547, -0.005785265937447548, 0.012083347886800766, -0.01494776364415884, 0.028952686116099358, 0.02805900201201439, -0.03594484180212021, -0.0191655270755291, -0.0352700874209404, 0.02707691490650177, -0.03525715693831444, -0.03727814555168152, 0.020121732726693153, -0.02327205054461956, 0.02793373167514801, 0.004877096973359585, -0.014615919440984726, -0.021526573225855827, 0.011230170726776123, 0.02674092911183834, 0.055776674300432205, -0.020294373854994774, -0.051350947469472885, 0.0469202883541584, 0.06969892233610153, -0.025904390960931778, -0.00197301572188735, 0.001125453389249742, -0.018638188019394875, -0.034920308738946915, 0.03745598345994949, 0.029109051451086998, -0.0035492032766342163, -0.029204078018665314, -0.027947552502155304, 0.008180171251296997, 0.000891552830580622, 0.0044030495919287205, 0.05354539677500725, 0.03555634617805481, 0.041216447949409485, 0.0007060106727294624, 0.0068857017904520035, -0.023796504363417625, -0.017048774287104607, -0.009217341430485249, 0.05014503374695778, 0.002146058948710561, 0.016949238255620003, -0.058477580547332764, 0.020876817405223846, -0.03905485197901726, -0.007059165276587009, -0.0541454516351223, -0.026635998860001564, -0.004313500598073006, -0.001782629988156259, 0.019308743998408318, -0.012372637167572975, -0.05576262250542641, 0.02111865021288395, -0.004712664522230625, -0.04072641581296921, -0.10678907483816147, -0.01639423705637455, -0.03472377732396126, -0.020000508055090904, -0.040596846491098404, -0.013767986558377743, 0.013568820431828499, -0.0277700237929821, 0.03442820906639099, -0.009242154657840729, 0.015910368412733078, -0.02010396309196949, 0.07639148831367493, -0.011382405646145344, 0.05179404839873314, -0.006151359993964434, 0.04208506643772125, 0.051134753972291946, -0.011120329611003399, 0.02248513512313366, -0.03679981455206871, -0.037235114723443985, 0.015105240978300571, 0.016339760273694992, 0.0002831408055499196, -0.004729741252958775, 0.003639416303485632, 0.044646862894296646, 0.019120177254080772, 0.021932773292064667, -0.03173834830522537, 0.04187490791082382, 0.022489340975880623, 0.011336252093315125, 0.020607635378837585, 0.005301814526319504, 0.04324837401509285, 0.017155202105641365, -0.05199064314365387, -0.005689006764441729, -0.03535555675625801, 0.07570074498653412, -0.046097055077552795, 0.02843189612030983, -0.02189611829817295, 0.047909706830978394, 0.004309677518904209, 0.004836084321141243, 0.058595411479473114, 0.03220958635210991, 0.012204973958432674, -0.09175132215023041, -0.05442629009485245, 0.0553036630153656, -0.004181993193924427, -0.00030415007495321333, -0.04585536569356918, 0.031018108129501343, 0.045184604823589325, -0.02167554199695587, 0.007569262757897377, -0.023622216656804085, -0.046103548258543015, 0.023120004683732986, -0.00910555012524128, 0.03181067854166031, -0.07014364749193192, 0.02905750274658203, -0.01960362307727337, -0.038202691823244095, 0.016147762537002563, 0.04320870339870453, -0.05747454613447189, 0.04527519643306732, -0.007625982165336609, -0.01770906150341034, 0.05612880364060402, 0.00542902247980237, -0.04139728471636772, 0.08243585377931595, 0.019070914015173912, 0.04169986769556999, -0.033614516258239746, 0.03883957490324974, 0.037805601954460144, 0.011582883074879646, 0.009317168965935707, 0.06439217180013657, -0.040328480303287506, 0.01766214333474636, 0.04495074227452278, 0.0617125928401947, 0.011619525961577892, -0.0233522430062294, -0.04677829518914223, -0.012597404420375824, -0.004605722613632679, 0.026339026167988777, 0.02731464058160782, 0.05071864649653435, 0.0792630985379219, 0.006071116775274277, 0.07867621630430222, -0.05678488686680794, 0.08425286412239075, -0.053855109959840775, -0.02431011013686657, -0.032651010900735855, -0.054993052035570145, -0.012172482907772064, -0.009576493874192238, -0.03304389864206314, -0.008592821657657623, 0.00028973649023100734, -0.012404314242303371, -0.03192728012800217, 0.011093229055404663, 0.06245037168264389, 0.02132892981171608, -0.05122112110257149, 0.0761825367808342, 0.08033176511526108, -0.04373751953244209, -0.012748358771204948, -0.030436838045716286, 0.06564560532569885, 0.003782642772421241, 0.024033445864915848, -0.0007751831435598433, 0.09926986694335938, 0.02814871445298195, 0.022532276809215546, 0.00831905473023653, -0.036684442311525345, -0.016540896147489548, -0.020140044391155243, 0.000008346710274054203, 0.0009774100035429, 0.035409897565841675, -0.02057180181145668, 0.03228834271430969, -0.0030987753998488188, 0.012667857110500336, -0.05026828497648239, 0.018200162798166275, -0.011098329909145832, 0.004061398562043905, 0.041828352957963943, 0.03729965165257454, -0.0029683797620236874, 0.03658672422170639, 0.009326730854809284, -0.009911122731864452, -0.04868105426430702, -0.01095788087695837, -0.020239463075995445, 0.04301130026578903, -0.01006094366312027, -0.04868859052658081, 0.010310569778084755, -0.04067390039563179, -0.03306714817881584, 0.06472364813089371, 0.04613453522324562, 0.04675445705652237, 0.04539947584271431, 0.0061720493249595165, -0.005082086194306612, -0.02370704896748066, -0.01162707433104515, 0.011072315275669098, 0.08910471946001053, -0.00035763747291639447, -0.04486692324280739, -0.007559085264801979, 0.0030578412115573883, -0.03782736882567406, -0.07844264805316925, 0.06148771196603775, -0.0689893290400505, -0.045388080179691315, -0.05759251490235329, 0.012005473487079144, -0.0103055564686656, -0.05081772059202194, 0.019491059705615044, -0.0466664619743824, 0.04278736934065819, 0.0338621623814106, -0.01979716122150421, -0.038551609963178635, -0.04973476752638817, 0.013230819255113602, 0.048190485686063766, 0.0012730431044474244, -0.0009240499348379672, 0.034640103578567505, -0.05474235862493515, 0.021576235070824623, 0.016216116026043892, -0.04286540672183037, 0.016793495044112206, -0.08939571678638458, 0.025543702766299248, 0.039436325430870056, -0.0629190132021904, -0.04671755060553551, -0.04234074056148529, 0.098057322204113, 0.002440271433442831, -0.07868744432926178, 0.0011624995386227965, 0.012409863993525505, -0.002290361560881138, 0.026360131800174713, 0.025810766965150833, 0.008312721736729145, -0.03144979476928711, 0.01573077030479908, -0.014885165728628635, -0.01219581812620163, 0.02793206088244915, -0.0007753389654681087, -0.03583936020731926, 0.01564253866672516, 0.03616880625486374, 0.053553998470306396, -0.026851341128349304, -0.019596915692090988, 0.03899567946791649, -0.018147749826312065, -0.03998676687479019, -0.05584986135363579, 0.014600364491343498, 0.04517478495836258, 0.0019887778908014297, -0.03514167293906212, 0.043022818863391876, -0.00273783877491951, 0.01980050839483738, 0.022665202617645264, 0.02210758998990059, -0.07800193876028061, 0.006493903696537018, -0.011482637375593185, -0.04034319147467613, -0.006930377334356308, 0.01443394459784031, 0.011256665922701359, -0.00046490863314829767, 0.013417393900454044, -0.04659761115908623, 0.01016745250672102, -0.04897218197584152, 0.005258290097117424, 0.02369258739054203, 0.011309790425002575, -0.030521433800458908, -0.01681353710591793, -0.006764812394976616, -0.0463065430521965, -0.02284589223563671, 0.007438970729708672, -0.055405326187610626, 0.04437822476029396, -0.008598017506301403, -0.0326300673186779, 0.003257493022829294, 0.01877504028379917, 0.014649486169219017, -0.024173157289624214, -0.013975403271615505, 0.08739627152681351, -0.023754840716719627, -0.015892228111624718, 0.05055495724081993, -0.05761781707406044, 0.020239124074578285, 0.029118185862898827, 0.02100510150194168, -0.003329490777105093, -0.029992757365107536, -0.005147100891917944, -0.0029595105443149805, 0.026602474972605705, -0.003417437430471182, -0.05127374082803726, -0.009739830158650875, 0.01422944851219654, -0.03830426186323166, -0.004723434802144766, -0.02375323325395584, 0.017651889473199844, -0.03431111201643944, 0.006828153971582651, 0.028537031263113022, 0.011234662495553493, -0.05024659261107445, -0.0304153673350811, -0.0027139149606227875, -0.05498285964131355, 0.025054654106497765, -0.00006676821794826537, -0.016276810318231583, 0.06680494546890259, 0.026855826377868652, -0.00894954614341259, -0.03339269012212753, 0.042096998542547226, 0.03358132392168045, 0.008105631917715073, 0.011646367609500885, -0.024234328418970108, 0.04915795847773552, -0.000603770837187767, 0.003618749091401696, 0.02214406058192253, -0.03481976315379143, -0.05878279730677605, -0.02667258307337761, -0.034298427402973175, 0.005503557622432709, 0.026779646053910255, -0.0663907453417778, 0.05639779940247536, -0.023231398314237595, -0.03604787960648537, 0.012455129064619541, 0.004941114224493504, -0.006580702494829893, 0.036368999630212784, 0.040650833398103714, 0.07336696982383728, 0.008562627248466015, 0.011876631528139114, -0.013493026606738567, 0.01693940907716751, -0.04414835199713707, -0.0660412609577179, 0.0025698847603052855, -0.04843994975090027, 0.010331341065466404, -0.009734832681715488, -0.0023764874786138535, 0.01799439825117588, -0.011599796824157238, 0.02400861494243145, -0.007558118086308241, -0.05780475586652756, -0.014020062051713467, 0.0160842202603817, 0.03637333959341049, 0.0004929788992740214, 0.004182951524853706, -0.024410482496023178, 0.006249739322811365, 0.03697887435555458, 0.08124193549156189, 0.017255302518606186, -0.0624113529920578, -0.02149755321443081, -0.008400578051805496, 0.030725650489330292, -0.034350182861089706, -0.010932342149317265, 0.06046884506940842, 0.025084786117076874, -0.03834868595004082, 0.05939391255378723, 0.01198426354676485, 0.017772767692804337, -0.01646442338824272, -0.057887040078639984, 0.07742585986852646, 0.05853588134050369, 0.0002756601315923035, 0.015242109075188637, 0.018680457025766373, 0.011344991624355316, -0.026128407567739487, 0.017177147790789604, 0.00286870077252388, -0.010796274058520794, 0.027555344626307487, -0.00886574201285839, -0.020950743928551674, 0.004646788351237774, -0.04249771684408188, -0.023710330948233604, 0.02484794333577156, -0.0008820230723358691, -0.07580982893705368, 0.02765805646777153, -0.023104339838027954, -0.03555256128311157, 0.0055720326490700245, 0.007694943342357874, -0.018578246235847473, -0.020587166771292686, 0.029268475249409676, 0.0138673922047019, -0.012048721313476562, -0.03059546649456024, 0.057572804391384125, -0.0005941771087236702, -0.052497703582048416, -0.011696860194206238, 0.042491309344768524, 0.04728066921234131, -0.018683459609746933, -0.008122328668832779, -0.036038171499967575, 0.007199801970273256, 0.051140785217285156, -0.02530754916369915, 0.022052526473999023, 0.08160706609487534, -0.02244589477777481, -0.03677841275930405, 0.001654884428717196, 0.035619575530290604, 0.03529243543744087, 0.0473458506166935, 0.044583167880773544, 0.05457979068160057, -0.021441781893372536, 0.07058541476726532, -0.049427732825279236, -0.026484422385692596, -0.00552880996838212, 0.0118362195789814, 0.09332618862390518, 0.018257440999150276, -0.0034083533100783825, 0.02459138259291649, -0.0129150515422225, 0.023379186168313026, -0.01167868822813034, -0.016074353829026222, 0.04826439172029495, 0.002650289563462138, 0.0030290393624454737, -0.0002784099488053471, -0.03500065580010414, -0.02989242784678936, 0.08438102900981903, 0.007670786697417498, 0.04704194515943527, -0.06781410425901413, 0.0480947382748127, 0.05236212536692619, -0.03955010697245598, -0.018391339108347893, -0.04187661409378052, 0.005636515095829964, -0.0019935534801334143, -0.004341117572039366, -0.046621501445770264, -0.00217126845382154, -0.04530327022075653, -0.01833547279238701, -0.018542978912591934, -0.008839422836899757, -0.012088553979992867, 0.0025988041888922453, -0.021419130265712738, 0.025241073220968246, -0.0014525902224704623, -0.008593806996941566, 0.009656299836933613, -0.001759501756168902, 0.008561003021895885, -0.04626915976405144, 0.011789970099925995, 0.03162681683897972, -0.008004238829016685, 0.00015619373880326748, 0.0069497330114245415, 0.01373431459069252, 0.024994557723402977, 0.023012394085526466, 0.03049633279442787, -0.03710254654288292, -0.0034117817413061857, 0.014037834480404854, 0.02425134927034378, -0.017052380368113518, -0.007206232752650976, -0.03184380754828453, 0.011453283950686455, -0.03700755164027214, 0.024723876267671585, 0.01050535123795271, -0.03442198410630226, -0.0067295413464307785, 0.03089381940662861, 0.044156573712825775, 0.03312190622091293, -0.019402174279093742, 0.00046865319018252194, 0.023205965757369995, -0.04980338364839554, -0.02064698375761509, -0.01995060406625271, 0.0029199509881436825, -0.04911718890070915, 0.030093319714069366, -0.043587926775217056, 0.0008120970451273024, -0.08435189723968506, 0.04814601689577103, -0.005947642493993044, -0.02527383714914322, 0.0944976955652237, -0.022921467199921608, -0.030319934710860252, 0.047289878129959106, -0.05275812745094299, -0.057848792523145676, -0.018116842955350876, 0.0040740035474300385, -0.0063285245560109615, -0.009351963177323341, 0.007668243255466223, 0.1291026473045349, 0.02434282936155796, -0.03319542482495308, 0.04824530705809593, -0.009403591975569725, 0.02654978446662426, -0.02039773017168045, -0.01234985888004303, 0.08760971575975418, -0.013798351399600506, 0.0560363233089447, -0.040932293981313705, -0.02626020833849907, -0.002934100804850459, -0.022311225533485413, -0.019151922315359116, -0.03523986041545868, -0.02033652365207672, 0.051007453352212906, 0.0068576755002141, -0.010419275611639023, 0.052307918667793274, 0.004330174066126347, 0.05116422101855278, -0.02400382049381733, 0.05013376846909523, -0.03111654706299305, -0.04847244545817375, 0.011278421618044376, 0.06253320723772049, -0.06833350658416748, -0.03973262384533882, -0.033613432198762894, -0.02512829378247261, 0.023153014481067657, 0.010081819258630276, 0.03118414245545864, -0.04974113777279854, 0.007172601763159037, -0.05250290408730507, 0.08322910964488983, -0.03836286440491676, 0.04856408014893532, -0.02117783948779106, -0.07574683427810669, -0.038664113730192184, 0.0269782617688179, -0.024759475141763687, 0.024163249880075455, -0.08390174061059952, 0.019916653633117676, 0.043344318866729736, -0.028157958760857582, -0.016478054225444794, -0.009690290316939354, -0.026887105777859688, 0.04820633679628372, -0.00878491997718811, 0.015178486704826355, 0.0514056459069252, -0.05631939694285393, -0.014589741826057434, 0.0279715396463871, -0.038187623023986816, 0.06880225241184235, 0.03651880845427513, 0.09033322334289551, 0.0317862331867218, 0.003496679477393627, 0.007073403801769018, -0.019019978120923042, -0.04162267595529556, 0.050320886075496674, -0.05286774784326553, 0.019254380837082863, 0.02072746679186821, 0.00006663005478912964, 0.02883351780474186, 0.02041136845946312, -0.003712849924340844, -0.023446720093488693, 0.0030427100136876106, -0.031123468652367592, -0.023242225870490074, -0.021654445677995682, 0.030337944626808167, 0.01183346938341856, 0.0072118788957595825, 0.024970872327685356, -0.023459918797016144, 0.022389288991689682, -0.018259158357977867, -0.01002730242908001, -0.042990755289793015, -0.014971685595810413, 0.0004914494347758591, 0.029000313952565193, 0.015551012940704823, 0.023716464638710022, 0.07490024715662003, -0.012502359226346016, 0.04743709787726402, -0.06796358525753021, -0.03609805554151535, 0.006411764770746231, -0.021946260705590248, -0.004723286721855402, -0.029390469193458557, -0.027774598449468613, -0.0463416688144207, -0.013490281067788601, 0.02141428552567959, -0.0055851442739367485, 0.04394132271409035, 0.0006252351449802518, 0.06521767377853394, 0.03110911138355732, -0.06322727352380753, -0.013938149437308311, -0.0015824949368834496, 0.0056456150487065315, -0.03565723076462746, 0.0365675613284111, -0.04581503942608833, -0.009846250526607037, -0.014814228750765324, -0.011592763476073742, -0.03526972606778145, 0.007758247200399637, -0.04009421169757843, -0.006714216433465481, 0.008565017953515053, 0.007594497874379158, -0.02129044011235237, -0.0022686407901346684, -0.04476833716034889, -0.018648259341716766, 0.07223428040742874, -0.0478595606982708, 0.04914889857172966, -0.11130177974700928, 0.00038682992453686893, -0.01924830675125122, 0.027927573770284653, -0.022288644686341286, 0.03801223263144493, -0.07484228909015656, -0.036300674080848694, -0.020554035902023315, 0.08843769878149033, -0.018960267305374146, -0.005241176579147577, 0.010765652172267437, 0.04912170395255089, 0.06367034465074539, -0.002925089793279767, -0.042916860431432724, -0.022176537662744522, 0.03283524885773659, -0.03158743306994438, 0.0007386512006632984, -0.0629427433013916, -0.016774993389844894, -0.03611815348267555, 0.027202080935239792, 0.03328555449843407, -0.04274902120232582, -0.05123993381857872, -0.0004107987624593079 ]
<p>In Statistical Mechanics, we often postulate that for an isolated system, the phase-space density of all accessible microstates (i.e all microstates consistent with the energy) is the same. This is equivalent to assuming that the system is ergodic. This postulate leads us to the assertion that at any given time, the system is most likely to be found in that macrostate which has the maximum number of consistent microstates, and from then on, we calculate the entropy for this macrostate and get the fundamental relation for entropy, and hence, other thermodynamic quantities. My question now is: Is this assumption of equal a-priori probabilities too strong to obtain the second assertion? In other words, can we not say that the macrostate with the maximum number of microstates <em>is</em> the observed thermodynamic state, while being non-committal as to whether indeed they are all equally probable or not? Or am I losing some information by not considering their probability distribution (maybe, say fluctuations)?</p>
g1568
[ 0.029158849269151688, 0.012441322207450867, 0.011153160594403744, -0.036110129207372665, -0.022877000272274017, -0.013394364155828953, -0.02053879201412201, 0.028633661568164825, -0.0013074679300189018, -0.008807091973721981, 0.0047249267809093, -0.02008236013352871, 0.012791337445378304, 0.017560342326760292, -0.038321394473314285, 0.028155412524938583, 0.06330592930316925, 0.0023001166991889477, 0.0007907913532108068, 0.06930797547101974, -0.03756193444132805, -0.027437442913651466, -0.008814464323222637, -0.022348612546920776, 0.04643524810671806, -0.003499200101941824, 0.04076305031776428, 0.005171072203665972, -0.025998147204518318, -0.03851914778351784, 0.03602386265993118, -0.013115154579281807, 0.04009956121444702, -0.09378820657730103, -0.01835128664970398, -0.039719630032777786, 0.04217712581157684, 0.030255334451794624, -0.0008683566702529788, -0.0320068895816803, 0.013773752376437187, 0.04227609187364578, -0.011851015500724316, -0.026541270315647125, -0.013577545061707497, 0.011565071530640125, 0.04986753687262535, 0.002484353957697749, -0.026925422251224518, -0.007940531708300114, 0.04167860001325607, 0.048988595604896545, 0.08924911916255951, 0.012664047069847584, -0.009428130462765694, 0.015957651659846306, 0.03447657823562622, -0.010593162849545479, 0.008298121392726898, 0.026256777346134186, 0.058413222432136536, -0.03570986166596413, -0.03709292411804199, -0.03295401856303215, 0.009870944544672966, 0.02907768078148365, -0.04277973249554634, 0.006199719849973917, 0.03660482168197632, -0.03969262167811394, -0.017957378178834915, -0.049477048218250275, 0.0009448120254091918, -0.04652456194162369, -0.015645794570446014, 0.024996399879455566, 0.030034396797418594, -0.01919892244040966, 0.04610894247889519, 0.008388123475015163, -0.023040538653731346, -0.03272692486643791, 0.08626552671194077, -0.03446771949529648, 0.02553054504096508, -0.011205880902707577, 0.03949886932969093, -0.02000240981578827, 0.010165905579924583, 0.05678224936127663, -0.046281736344099045, 0.055339738726615906, 0.07920435816049576, 0.04767557233572006, -0.019181881099939346, -0.00471317395567894, -0.06092149019241333, 0.03362710401415825, -0.010643424466252327, 0.04991789162158966, -0.017322136089205742, 0.01119012851268053, -0.019076017662882805, -0.041252996772527695, -0.04381527751684189, -0.05748172476887703, -0.02147115394473076, -0.017391499131917953, -0.0036799407098442316, -0.0076440428383648396, 0.03265254572033882, 0.03622780740261078, -0.014897102490067482, -0.006907468196004629, -0.06059060990810394, 0.0186216589063406, 0.0731375440955162, -0.04959426820278168, -0.033091045916080475, 0.04065307229757309, -0.02967722713947296, -0.007382200565189123, 0.023584701120853424, 0.09350457042455673, -0.024576133117079735, 0.042403146624565125, -0.033717408776283264, 0.0258378516882658, -0.005497202277183533, -0.006404015701264143, 0.012982267886400223, 0.018297040835022926, 0.03894292935729027, 0.009621315635740757, -0.01737542822957039, 0.011062685400247574, -0.019230810925364494, 0.002308577997609973, -0.03403177112340927, 0.013885087333619595, -0.05631867051124573, -0.013262846507132053, -0.006459790747612715, -0.00487543735653162, 0.0003696935891639441, 0.024704596027731895, -0.04592091962695122, -0.02701462060213089, 0.03732620179653168, 0.052839528769254684, -0.0029783188365399837, 0.016354043036699295, -0.035984355956315994, -0.03363722190260887, -0.02849625237286091, 0.02256118506193161, 0.0016486746026203036, -0.04538315534591675, -0.02927449531853199, 0.01720561645925045, -0.0036064598243683577, -0.005589611362665892, 0.04376908764243126, 0.00672031519934535, -0.013968529179692268, -0.008264045231044292, 0.024440182372927666, -0.04246125742793083, 0.0013410942628979683, -0.014886056073009968, 0.032481636852025986, -0.009180889464914799, 0.03298107907176018, 0.017739245668053627, -0.015057872049510479, 0.01907403953373432, 0.0014526291051879525, -0.029370510950684547, 0.06468898057937622, -0.005211786832660437, 0.0024369945749640465, 0.03208165243268013, 0.047490786761045456, -0.013323071412742138, -0.01102380733937025, -0.047856710851192474, 0.022578852251172066, 0.05736420676112175, -0.02533591352403164, 0.039888232946395874, -0.03559478372335434, -0.012851681560277939, -0.08144073933362961, 0.04040732607245445, 0.0531889833509922, -0.03761475533246994, 0.003269737819209695, -0.030265485867857933, -0.009166786447167397, -0.045119695365428925, 0.04544734209775925, -0.02408594824373722, -0.00970267504453659, -0.028263913467526436, 0.014553855173289776, 0.04725789278745651, -0.02725321426987648, 0.038440484553575516, -0.021055832505226135, 0.011129897087812424, 0.020290490239858627, -0.09433197975158691, -0.049210794270038605, 0.06606276333332062, 0.015897421166300774, -0.044695209711790085, 0.05012444406747818, -0.023231886327266693, 0.005905654281377792, -0.020169315859675407, 0.009288882836699486, 0.008919904008507729, 0.03841675817966461, 0.031370632350444794, 0.02500109374523163, 0.03834046423435211, -0.07306746393442154, 0.0032052304595708847, -0.02904428541660309, 0.05998019874095917, -0.008315745741128922, 0.010590351186692715, 0.025145992636680603, 0.023851288482546806, -0.011160382069647312, 0.06460040807723999, 0.011803222820162773, 0.03272728994488716, 0.005094097927212715, 0.03924236446619034, 0.01927661895751953, -0.05348331481218338, -0.03654532879590988, 0.03873150795698166, 0.022749952971935272, -0.0040099299512803555, -0.00015356465883087367, 0.008997914381325245, 0.04352885112166405, 0.010823004879057407, -0.04912932217121124, 0.0272692684084177, 0.0000621043800492771, 0.0016170339658856392, -0.011483870446681976, -0.04174492135643959, 0.015358350239694118, 0.02160811796784401, -0.0880807414650917, -0.015528973191976547, 0.028572145849466324, 0.009955025278031826, 0.007215113379061222, -0.01211176160722971, -0.0340830534696579, -0.034881796687841415, -0.02037317119538784, -0.023219911381602287, -0.04249706491827965, 0.0018809119937941432, 0.0455390028655529, 0.04980489984154701, -0.00844651274383068, 0.07794688642024994, 0.07042883336544037, 0.017973965033888817, 0.03456791862845421, -0.008874669671058655, -0.007452805992215872, -0.030878540128469467, -0.07301697880029678, -0.019881192594766617, -0.01625746674835682, 0.010631672106683254, 0.011934103444218636, -0.02492361329495907, 0.03624716401100159, -0.027381718158721924, 0.02476477064192295, 0.029669499024748802, 0.021280363202095032, 0.01430528238415718, 0.034092534333467484, 0.05777571722865105, -0.06911180168390274, 0.0026735239662230015, -0.025621693581342697, -0.02904037944972515, 0.04050289839506149, 0.03311198577284813, -0.0018346033757552505, 0.006215325556695461, 0.03356454521417618, -0.047732096165418625, 0.034703873097896576, 0.06162960082292557, -0.07992617040872574, -0.07168694585561752, -0.033580102026462555, -0.015126173384487629, -0.05138210952281952, 0.05770955979824066, -0.014034786261618137, -0.041717033833265305, -0.08644668757915497, 0.0734267458319664, 0.057942744344472885, 0.013077723793685436, 0.03515523299574852, -0.02607118897140026, 0.01964547298848629, 0.03870992362499237, 0.01745009422302246, -0.023594360798597336, 0.03581628203392029, -0.026659728959202766, -0.0383581705391407, -0.009667095728218555, -0.1055692732334137, -0.006905451416969299, 0.05492734536528587, -0.017953554168343544, 0.04342281445860863, -0.02538355439901352, -0.08392805606126785, -0.06306272000074387, -0.058804143220186234, -0.04642200469970703, 0.011531706899404526, 0.04970581829547882, -0.029377257451415062, 0.012297148816287518, -0.02538403309881687, 0.012726101092994213, 0.012066290713846684, 0.01781587302684784, 0.013959350995719433, 0.0215506199747324, 0.05768130347132683, 0.00008290066034533083, 0.0199098140001297, -0.037246737629175186, 0.031112704426050186, 0.03316608443856239, -0.005442128516733646, 0.034467797726392746, 0.006475380156189203, -0.054997339844703674, 0.057760730385780334, -0.02076183259487152, 0.024040093645453453, -0.06256363540887833, 0.03860413283109665, -0.08572206646203995, 0.01611034758388996, 0.014635630883276463, -0.013187129981815815, 0.02832147292792797, 0.03749918192625046, -0.023612383753061295, 0.012327035889029503, -0.03562846779823303, 0.022693168371915817, -0.030868005007505417, 0.08104053884744644, -0.06183917447924614, 0.06868436187505722, 0.030447831377387047, -0.043684881180524826, 0.0022002235054969788, 0.041620709002017975, -0.01948033645749092, 0.0065443143248558044, -0.01624414324760437, 0.032811593264341354, 0.01261375192552805, -0.03691243380308151, 0.04087220877408981, -0.018276726827025414, -0.05665067210793495, -0.019238751381635666, -0.0568009689450264, -0.05040399730205536, 0.01909421943128109, 0.02335510030388832, 0.026655476540327072, 0.03872563689947128, -0.027240410447120667, 0.061267364770174026, 0.05571422353386879, 0.005727545823901892, -0.021210232749581337, -0.03445662558078766, -0.03696465492248535, 0.01641767844557762, -0.036299075931310654, -0.034768715500831604, -0.0006508439546450973, -0.018754970282316208, -0.0554623007774353, 0.023182909935712814, -0.0015739614609628916, 0.0427207350730896, -0.0223679281771183, -0.05352356284856796, 0.011786725372076035, -0.011149406433105469, -0.09179582446813583, 0.03342372551560402, 0.044219836592674255, 0.006841939873993397, -0.03402428701519966, -0.035736389458179474, -0.03852221742272377, 0.0049826218746602535, 0.058402929455041885, 0.07541662454605103, 0.0008807200938463211, -0.03466850146651268, -0.029281260445713997, 0.029529066756367683, 0.026208318769931793, 0.01538087334483862, 0.043113164603710175, -0.029442675411701202, -0.01932167261838913, -0.04518808424472809, 0.030723895877599716, -0.008469962514936924, -0.026723839342594147, -0.01912936009466648, -0.029552042484283447, -0.008400448597967625, 0.02464752271771431, 0.01592460833489895, 0.004030526150017977, 0.0007118211360648274, -0.019246524199843407, 0.003667025361210108, -0.030767805874347687, 0.01926453225314617, -0.051928628236055374, 0.008142405189573765, 0.00950316060334444, -0.026950707659125328, -0.015528310090303421, -0.038031067699193954, 0.03478662297129631, 0.0005755784222856164, 0.04395843669772148, 0.035754796117544174, 0.006915489677339792, 0.023597117513418198, 0.05063249170780182, 0.020157627761363983, -0.02959447167813778, -0.049525581300258636, 0.031035421416163445, -0.06966372579336166, -0.047741979360580444, 0.05121864378452301, 0.028991015627980232, 0.02641284093260765, -0.005976748187094927, -0.01649615913629532, -0.0014037073124200106, 0.016781114041805267, -0.008059000596404076, 0.01884973607957363, 0.04033168777823448, -0.0283870417624712, -0.018274612724781036, 0.007895167917013168, 0.03398726508021355, 0.03617006540298462, 0.04193943366408348, 0.0062414174899458885, -0.05259579420089722, -0.017956526950001717, 0.018744278699159622, 0.029224226251244545, 0.057249244302511215, 0.04001716524362564, 0.07659038156270981, 0.03245966508984566, -0.04548272117972374, 0.021792598068714142, -0.02129196934401989, -0.019904427230358124, 0.007433905266225338, -0.07704583555459976, 0.051522109657526016, 0.03330284729599953, 0.042472805827856064, -0.034753456711769104, -0.03471599146723747, 0.010400369763374329, 0.0020785389933735132, -0.037717606872320175, 0.022492391988635063, 0.005754564888775349, 0.03934738039970398, -0.03536492958664894, 0.0010633703786879778, 0.0003904011391568929, -0.02287561073899269, -0.018275229260325432, -0.001092783291824162, -0.028466489166021347, -0.06915844231843948, 0.07872363924980164, 0.026931578293442726, 0.007792955730110407, -0.04485456645488739, -0.07210894674062729, -0.009005023166537285, -0.06706103682518005, -0.008246554993093014, -0.016479548066854477, 0.023362787440419197, -0.009828978218138218, 0.03203032910823822, -0.012627056799829006, 0.006959777325391769, 0.03207435831427574, -0.008741469122469425, -0.03647034615278244, 0.014807101339101791, 0.03340253233909607, -0.0010966722620651126, -0.024845317006111145, -0.033248964697122574, -0.010935458354651928, -0.022128084674477577, 0.011594234965741634, -0.01815243810415268, -0.05602747201919556, -0.04189138486981392, 0.025946225970983505, -0.05916905775666237, -0.0020570876076817513, 0.03500641509890556, -0.047373801469802856, 0.0014431950403377414, -0.029692867770791054, 0.059148676693439484, 0.010579382069408894, 0.02426166646182537, -0.016939006745815277, 0.022093724459409714, 0.02223828248679638, 0.024169225245714188, 0.01650853641331196, 0.014117524027824402, -0.019108083099126816, -0.06637207418680191, 0.012015757150948048, -0.007543847896158695, -0.05601579695940018, 0.061477113515138626, 0.04958419129252434, 0.0284173171967268, 0.07172920554876328, 0.05846467986702919, 0.053523723036050797, -0.00561069929972291, -0.059512194246053696, 0.023503558710217476, -0.014663655310869217, -0.015224137343466282, -0.0781734362244606, -0.017326027154922485, 0.007443469949066639, 0.002064049942418933, 0.022281598299741745, 0.059764035046100616, -0.044200390577316284, -0.027206318452954292, -0.0618247464299202, 0.03617332875728607, 0.024382848292589188, -0.033020004630088806, -0.040567245334386826, 0.049034181982278824, -0.014278212562203407, 0.0018557878211140633, -0.07152313739061356, -0.045078981667757034, -0.022005323320627213, 0.04808788746595383, -0.007546162698417902, 0.006282472983002663, 0.015401686541736126, -0.05559759959578514, -0.04395170137286186, 0.033193349838256836, 0.0013793042162433267, 0.03920542821288109, -0.013902987353503704, 0.010370142757892609, 0.010051490738987923, -0.008068844676017761, 0.018893837928771973, -0.0173784289509058, -0.0068067158572375774, -0.041488777846097946, -0.06575468927621841, 0.043449338525533676, -0.00319890258833766, 0.04085535183548927, 0.04836870729923248, -0.0007499185157939792, -0.007916828617453575, -0.03453543409705162, -0.0013580054510384798, 0.056522686034440994, -0.04338991641998291, -0.020525699481368065, 0.048450030386447906, 0.04357604682445526, 0.030170241370797157, -0.013196948915719986, 0.021038401871919632, -0.030155574902892113, -0.01222928799688816, 0.022151872515678406, -0.07479073107242584, -0.014542657881975174, 0.04548090696334839, -0.04510233551263809, -0.003139220643788576, 0.01748443767428398, 0.03292805701494217, 0.004803576972335577, 0.02577982470393181, 0.007773508783429861, 0.03463224694132805, 0.04337455332279205, -0.03676828742027283, -0.025096187368035316, 0.04196701943874359, -0.03818117082118988, -0.04125134274363518, -0.057679202407598495, -0.005112029612064362, 0.08586438000202179, 0.006999552715569735, 0.031136084347963333, 0.07969129085540771, -0.03539154306054115, 0.006996659561991692, 0.015656279399991035, -0.03730104863643646, -0.004364075139164925, -0.016027390956878662, 0.06067492812871933, 0.04732556268572807, -0.031510498374700546, -0.05086705461144447, -0.10712042450904846, 0.021517174318432808, -0.040484469383955, -0.08089789748191833, -0.02191578969359398, -0.018200529739260674, -0.026538852602243423, 0.03360055759549141, 0.014761199243366718, 0.05619298294186592, 0.031125612556934357, -0.013170608319342136, -0.022994590923190117, 0.008877696469426155, 0.04165066033601761, -0.021765505895018578, 0.06366375833749771, -0.041265927255153656, -0.002107932697981596, -0.026174940168857574, 0.012839937582612038, -0.049014315009117126, -0.056277092546224594, -0.0025177837815135717, -0.019481709226965904, -0.025837654247879982, 0.0014626935590058565, 0.04802490398287773, 0.03203514963388443, 0.05140703171491623, -0.08258575946092606, -0.02642909064888954, 0.025292685255408287, -0.0019283617148175836, 0.05087888240814209, 0.0793035700917244, 0.01742653362452984, 0.03014259599149227, -0.014726396650075912, -0.026218747720122337, -0.0020171625073999166, 0.03343794867396355, -0.02169746346771717, -0.017223088070750237, -0.013238045386970043, -0.020134957507252693, -0.04520257189869881, -0.08861996233463287, -0.020599860697984695, 0.029286352917551994, -0.0026354771107435226, 0.0008216374553740025, 0.013443350791931152, -0.041374072432518005, -0.013932934030890465, 0.005036037880927324, -0.06751009821891785, -0.021697169169783592, 0.0030199314933270216, 0.03944893181324005, -0.008108491078019142, -0.037611447274684906, -0.03933333605527878, 0.031626053154468536, 0.01356243435293436, -0.08931799978017807, 0.04730549827218056, 0.06589263677597046, -0.011151081882417202, -0.0010583531111478806, -0.03390965983271599, -0.02915135957300663, 0.002091384492814541, 0.07541149854660034, -0.0036630546674132347, -0.007397782523185015, 0.007582988124340773, -0.020635413005948067, -0.02022596076130867, 0.040597036480903625, 0.00019178101501893252, -0.05258253589272499, -0.020061315968632698, -0.0016149342991411686, 0.011275962926447392, 0.02661593072116375, -0.03492960333824158, 0.07242754101753235, 0.0037789226043969393, -0.009947194717824459, 0.023852551355957985, -0.009813354350626469, -0.0267977062612772, 0.014360192231833935, -0.03135291859507561, -0.022390464320778847, -0.008913775905966759, 0.03983147442340851, 0.026610946282744408 ]
<p>I'm wondering if there is more than the empty theory (no local fields, identically vanishing stress energy tensor) that can have central charge $c$ equals to $0$?</p> <p>My intuition tells me no, the stress energy tensor would transform as a primary field and so would only contain primary fields but there are none except for the identity operator. So there could only be (topological) degrees of freedom on the boundary. Is this reasoning wrong?</p> <p>ps: I'm only thinking at unitary theories, otherwise, sure it could be possible to combine in a balanced way fields carrying positive and negative central charge.</p>
g1569
[ 0.0827099159359932, 0.017130646854639053, -0.011712317354977131, 0.0027779133524745703, 0.06741970032453537, -0.004830582533031702, -0.02388370782136917, 0.014739184640347958, -0.003169638104736805, 0.014171136543154716, -0.03595198690891266, -0.023552747443318367, -0.037485718727111816, -0.06220731884241104, -0.04007373005151749, -0.02529907412827015, 0.03748108074069023, 0.01945955865085125, 0.03468046709895134, 0.02814530022442341, -0.02977421134710312, -0.003664421383291483, 0.05671035498380661, 0.012345025315880775, -0.03736400604248047, 0.04184247553348541, 0.02247021533548832, 0.053173501044511795, 0.003469819901511073, -0.05631168186664581, 0.05305347964167595, 0.013166616670787334, 0.014541307464241982, -0.030140476301312447, -0.01657022535800934, 0.023718902841210365, 0.007768143899738789, 0.034539297223091125, -0.002452027751132846, 0.007450539618730545, -0.026953300461173058, -0.030898939818143845, -0.00738349137827754, -0.02815399505198002, -0.0482814721763134, -0.0029477179050445557, -0.013046500273048878, 0.06040925532579422, -0.0022182269021868706, -0.0016925723757594824, -0.014194752089679241, -0.01671442948281765, 0.013021215796470642, 0.0034310189075767994, 0.03723205253481865, -0.01560905110090971, 0.00288540031760931, -0.0018055468099191785, 0.03916691988706589, 0.029059475287795067, -0.03365469351410866, 0.05658822879195213, -0.008802532218396664, 0.06911833584308624, -0.004010503645986319, -0.01014770194888115, -0.0380246639251709, 0.004214159678667784, -0.007725459989160299, 0.0038075828924775124, -0.001064491574652493, -0.07099542766809464, -0.022537505254149437, -0.0016066816169768572, 0.005808087065815926, 0.026928257197141647, 0.012486984021961689, -0.05224119871854782, 0.06537128239870071, -0.06075592711567879, -0.05009743571281433, -0.056126829236745834, 0.01160603016614914, 0.006269451230764389, 0.09372195601463318, -0.0813937857747078, 0.03357122093439102, 0.007952120155096054, -0.006753791589289904, 0.025312770158052444, -0.005053120665252209, 0.04957788437604904, 0.03915328159928322, -0.0034923460334539413, 0.03137863054871559, -0.020178623497486115, 0.04854365810751915, 0.056400831788778305, -0.029146425426006317, -0.09482105076313019, -0.03188498318195343, 0.024661965668201447, 0.015133264474570751, 0.019471457228064537, -0.0034863590262830257, -0.01597767136991024, -0.04428250342607498, -0.042412132024765015, 0.023321079090237617, 0.03606587275862694, -0.014005892910063267, 0.013708139769732952, -0.021295541897416115, 0.010480509139597416, -0.042245302349328995, 0.0018921346636489034, 0.06613654643297195, -0.08119374513626099, -0.018027830868959427, -0.010561552830040455, 0.0009140945039689541, 0.01663191244006157, 0.040847182273864746, 0.04982275143265724, 0.0015230224234983325, 0.041022177785634995, 0.014817125163972378, 0.0076792254112660885, 0.023365620523691177, -0.010273300111293793, 0.0076510170474648476, 0.015344936400651932, -0.03361507132649422, -0.04804586246609688, 0.07130852341651917, 0.024130068719387054, -0.04822326824069023, -0.003036008682101965, -0.007479394786059856, 0.005173956975340843, -0.006741311401128769, -0.031504373997449875, -0.0076082805171608925, -0.0031316950917243958, 0.04906471446156502, -0.060295332223176956, 0.0498882494866848, 0.009618321433663368, 0.024752812460064888, 0.013288564048707485, 0.01636006310582161, 0.03608959540724754, 0.017122047021985054, 0.008652577176690102, -0.02122471109032631, 0.027720799669623375, 0.044060397893190384, -0.05149885639548302, 0.019617043435573578, -0.06242531165480614, 0.00913142692297697, 0.004700676072388887, 0.11746256053447723, 0.0011453874176368117, -0.015862738713622093, -0.07057370990514755, 0.0164791252464056, 0.038168031722307205, 0.023068392649292946, 0.003250264562666416, -0.04212769865989685, -0.0003248016000725329, -0.005647057201713324, 0.05364044010639191, 0.005606558173894882, -0.017919065430760384, -0.05613218620419502, -0.013320371508598328, 0.05792732164263725, 0.01566506363451481, -0.09789194911718369, 0.007899058051407337, 0.047444455325603485, 0.002434795256704092, 0.040521349757909775, 0.03623322769999504, -0.05215159058570862, 0.07682810723781586, -0.030609238892793655, 0.05222480371594429, -0.03467119112610817, 0.042574916034936905, -0.00832442194223404, 0.04758142679929733, -0.028521377593278885, -0.022079041227698326, 0.02377992309629917, -0.007429112214595079, -0.009800810366868973, -0.0428609699010849, 0.03515102341771126, 0.02393948845565319, -0.009090056642889977, -0.04293312504887581, 0.01214547548443079, 0.03875737264752388, -0.06150123104453087, 0.009907763451337814, 0.04006025567650795, -0.06049090623855591, 0.010789092630147934, -0.022456660866737366, -0.024980677291750908, 0.10893693566322327, -0.04489648714661598, -0.041690122336149216, 0.003405932802706957, -0.02594059333205223, -0.030435387045145035, 0.02127652056515217, -0.010124445892870426, 0.014738684520125389, 0.058199506253004074, 0.03411540389060974, 0.006212056614458561, -0.002376082120463252, 0.034802112728357315, 0.002343459753319621, -0.05915924906730652, -0.05424501374363899, -0.05290282890200615, -0.027247529476881027, 0.04966837167739868, -0.020099762827157974, 0.03511036932468414, 0.03124307282269001, -0.009031238034367561, -0.005203531589359045, 0.0057312012650072575, 0.0027307758573442698, 0.01084316149353981, -0.012434066273272038, -0.03342314437031746, 0.012657545506954193, 0.006309757474809885, 0.018159974366426468, 0.020852314308285713, 0.009938503615558147, 0.00951844546943903, 0.01171716209501028, 0.027698855847120285, -0.03799579292535782, -0.033750977367162704, 0.03534587472677231, 0.004718800541013479, -0.0023074194323271513, 0.00800409447401762, -0.012474751099944115, -0.023630838841199875, -0.08873093873262405, 0.031364910304546356, 0.02143782377243042, 0.03222833201289177, 0.010688716545701027, -0.06296320259571075, -0.012954412028193474, -0.02705676481127739, -0.010860616341233253, -0.007898704148828983, 0.03972272947430611, -0.04620855674147606, 0.11625746637582779, 0.0016812599496915936, 0.04948277771472931, 0.012665529735386372, -0.012336759828031063, -0.023525748401880264, 0.006184983067214489, -0.013943006284534931, -0.0231725312769413, -0.009769356809556484, 0.06019947677850723, 0.028739457949995995, 0.06824681162834167, -0.009286602959036827, -0.021257810294628143, -0.030386505648493767, -0.005594303365796804, 0.015163934789597988, -0.0012254664907231927, 0.044947825372219086, 0.02783367782831192, 0.09620833396911621, 0.035145971924066544, -0.016029678285121918, -0.022046634927392006, 0.04541761428117752, -0.05796446278691292, -0.032511916011571884, 0.06284011155366898, -0.01685427688062191, -0.03415188193321228, 0.01020959485322237, 0.04292534291744232, 0.015121650882065296, 0.01204434409737587, -0.06962612271308899, -0.01947840116918087, 0.026492292061448097, -0.01978771761059761, -0.030943213030695915, 0.049727167934179306, 0.02363721653819084, -0.014120283536612988, -0.014436222612857819, 0.010327867232263088, -0.007245659828186035, -0.009831849485635757, 0.002871827455237508, -0.0209045447409153, -0.015279767103493214, -0.0008332855068147182, 0.011901050806045532, 0.023923326283693314, 0.0072751399129629135, 0.08132068812847137, -0.08083385229110718, 0.031173737719655037, -0.06005190312862396, -0.043016467243433, 0.018533965572714806, -0.019883880391716957, 0.0009129452519118786, 0.030918963253498077, -0.0028452971018850803, -0.011352167464792728, -0.0189447570592165, 0.027785466983914375, 0.0664154514670372, 0.06104970723390579, -0.03829126060009003, -0.026021597906947136, -0.03959465026855469, -0.056750088930130005, 0.011915059760212898, -0.01909507066011429, -0.03163442388176918, -0.008175542578101158, -0.009797302074730396, -0.0068921297788619995, 0.014069212600588799, -0.029843932017683983, -0.003429916687309742, -0.00408431701362133, -0.016179658472537994, -0.010360834188759327, 0.04087330028414726, 0.06775052845478058, -0.07870195806026459, 0.03368160501122475, 0.009527860209345818, -0.01251223124563694, 0.051438093185424805, -0.01760871149599552, 0.027984580025076866, 0.00884465966373682, -0.06263937056064606, -0.016915829852223396, -0.03174586594104767, -0.04023899510502815, 0.040063805878162384, 0.0014764070510864258, -0.014182847924530506, -0.034837499260902405, 0.030392758548259735, -0.06518492847681046, 0.032708972692489624, 0.022429758682847023, -0.01087910681962967, 0.010063950903713703, 0.04196665808558464, -0.01885128580033779, 0.033382534980773926, 0.00015872660151217133, -0.005955549422651529, 0.03804604336619377, -0.019012851640582085, -0.005124683026224375, 0.015088713727891445, 0.04901396110653877, -0.05726820230484009, -0.03504325821995735, -0.0028424328193068504, 0.0024849288165569305, 0.007711539976298809, -0.047923654317855835, 0.003317262278869748, -0.11531159281730652, -0.0154305100440979, 0.0008125831955112517, 0.07151496410369873, 0.003973501734435558, 0.01106488611549139, -0.06439023464918137, 0.016498995944857597, -0.019489815458655357, 0.05279633030295372, -0.01871107518672943, -0.007755296304821968, -0.060679201036691666, -0.027822641655802727, -0.03163941949605942, 0.016010120511054993, -0.04846233129501343, 0.065620057284832, -0.06671949476003647, -0.016889983788132668, -0.01776977814733982, 0.022693771868944168, 0.01799592562019825, 0.04752212390303612, 0.039464954286813736, -0.01817586086690426, -0.030231673270463943, -0.007452588062733412, 0.053119659423828125, -0.005197669379413128, -0.0006795406225137413, -0.02562638930976391, -0.008014065213501453, -0.009316334500908852, 0.03198238089680672, -0.01891700178384781, -0.0006517962319776416, -0.010866315104067326, -0.010332856327295303, -0.03164183720946312, 0.029114888980984688, -0.045875996351242065, -0.013129343278706074, 0.020258914679288864, 0.0471675805747509, 0.016565408557653427, -0.022515393793582916, -0.04470617324113846, -0.003979354165494442, 0.02130311354994774, -0.05792797729372978, -0.025523919612169266, -0.04722602665424347, -0.009028760716319084, 0.024346349760890007, -0.06498152017593384, 0.021605292335152626, 0.0037669860757887363, -0.01871281862258911, -0.02810053341090679, 0.026223013177514076, -0.04692655801773071, 0.008561225607991219, -0.04833126813173294, -0.006310862023383379, 0.05269940569996834, 0.0044254218228161335, 0.09442372620105743, -0.025102198123931885, -0.06433450430631638, 0.020097583532333374, -0.067966990172863, -0.04677436873316765, 0.057940199971199036, 0.08542612195014954, 0.030274121090769768, -0.07445894926786423, -0.01466699130833149, -0.02859182097017765, 0.0100835170596838, 0.006139147095382214, -0.04494231566786766, -0.0630960538983345, 0.01334306225180626, 0.01494826190173626, -0.04739534854888916, 0.07781940698623657, 0.014351706951856613, 0.02753099426627159, -0.02516629733145237, 0.05469895526766777, -0.054695479571819305, -0.014590729027986526, -0.0015691452426835895, 0.0039625754579901695, -0.015981076285243034, -0.012620040215551853, 0.035171687602996826, 0.042150892317295074, -0.020145056769251823, -0.04263049364089966, -0.04555649310350418, -0.021471155807375908, -0.023840930312871933, -0.0015577311860397458, -0.009025187231600285, 0.02473161555826664, -0.012813365086913109, 0.021507808938622475, 0.0466020293533802, -0.0005546504980884492, -0.013221596367657185, 0.03522752597928047, -0.017367135733366013, -0.01227125059813261, 0.0014955836813896894, -0.0177786722779274, 0.01838798262178898, 0.05898471176624298, -0.08356461673974991, -0.038905948400497437, -0.0480228029191494, 0.021754557266831398, 0.02954709529876709, -0.021454758942127228, 0.06775198131799698, -0.009103717282414436, 0.023719703778624535, 0.04013137146830559, 0.025556087493896484, -0.04873738810420036, 0.018098214641213417, 0.014552575536072254, -0.038436196744441986, -0.02095271274447441, -0.03183427453041077, 0.02404196560382843, 0.006776655092835426, -0.007055878173559904, -0.018394704908132553, 0.07712937891483307, 0.013196776621043682, 0.025369925424456596, 0.0008452387410216033, -0.049149040132761, -0.03244366869330406, 0.024973541498184204, 0.02030172012746334, 0.053928911685943604, -0.07201775908470154, 0.013599012978374958, 0.024800579994916916, -0.07895929366350174, -0.015027499757707119, 0.02579907700419426, -0.07811860740184784, 0.017021186649799347, -0.012593907304108143, -0.007437088061124086, -0.02836054004728794, -0.018850550055503845, -0.017115052789449692, 0.0032150722108781338, 0.021602751687169075, 0.020437708124518394, 0.016185404732823372, 0.03182421997189522, -0.009976344183087349, 0.010679266415536404, -0.018455075100064278, -0.03103923611342907, 0.07112560421228409, -0.054446615278720856, 0.051365818828344345, 0.010445015504956245, 0.029967788606882095, 0.004431401379406452, 0.06879128515720367, -0.05092224106192589, 0.02686409465968609, 0.02940959855914116, -0.008608999662101269, -0.017265701666474342, -0.0014667697250843048, 0.005192350596189499, 0.0358528308570385, -0.057731930166482925, 0.038258351385593414, 0.05156390741467476, -0.012104791589081287, -0.021765075623989105, -0.003024052130058408, 0.07177021354436874, 0.013356505893170834, 0.01915847510099411, 0.011184677481651306, -0.017444653436541557, 0.000004476064077607589, -0.013373322784900665, 0.022616565227508545, 0.0008441007230430841, -0.0156839732080698, 0.037969425320625305, 0.038782235234975815, 0.0053211417980492115, 0.008002703078091145, 0.01956043764948845, 0.06536972522735596, 0.10718406736850739, 0.01341362576931715, -0.027564875781536102, -0.07000430673360825, 0.047777414321899414, -0.059842564165592194, -0.007919875904917717, 0.0043092770501971245, -0.0012137708254158497, -0.00914877187460661, -0.026754230260849, -0.02935248613357544, -0.02782333828508854, 0.0015532249817624688, 0.014680524356663227, 0.038773998618125916, -0.020968040451407433, -0.04591526463627815, 0.01734268292784691, 0.014823222532868385, -0.002906734822317958, -0.01785609871149063, 0.012981781736016273, 0.06856363266706467, 0.00005023434277973138, -0.026661941781640053, 0.03601400554180145, 0.00040089202229864895, 0.04829980805516243, 0.0229320228099823, 0.012881258502602577, -0.05173104628920555, -0.04537702724337578, 0.02773616649210453, -0.03854871541261673, -0.055692873895168304, -0.0006681115482933819, 0.019998200237751007, 0.044948507100343704, -0.046231795102357864, 0.0002995663380715996, 0.02641301602125168, -0.028833672404289246, -0.0477132573723793, -0.004760622978210449, 0.049161646515131, 0.05354592204093933, -0.0016474457224830985, -0.0273636132478714, -0.07085277885198593, -0.02608526311814785, 0.03964102268218994, -0.004708964843302965, -0.003210692200809717, -0.04159388691186905, 0.009718772955238819, 0.03200075030326843, -0.006818793714046478, -0.040368542075157166, 0.01528916135430336, 0.07651477307081223, 0.060576535761356354, -0.015252416022121906, 0.003822397207841277, -0.04780710116028786, -0.00003297944203950465, -0.003206984605640173, -0.0772441029548645, 0.01912945695221424, -0.02414570190012455, -0.016741223633289337, -0.026942260563373566, 0.0878671184182167, 0.017111103981733322, 0.005205050576478243, 0.0027267304249107838, 0.027378791943192482, 0.024872222915291786, 0.01651318185031414, -0.008411422371864319, -0.00472074281424284, 0.05320015549659729, 0.045899197459220886, -0.02843165211379528, 0.009334108792245388, 0.02263576351106167, -0.0497264489531517, 0.0721256360411644, 0.023130444809794426, -0.029741410166025162, 0.00770026259124279, 0.03132123872637749, 0.05887848883867264, 0.019549382850527763, -0.053863197565078735, -0.02535620518028736, -0.037306610494852066, -0.060497481375932693, -0.023190930485725403, 0.04867251589894295, -0.005900432355701923, -0.039483800530433655, -0.025025051087141037, -0.06131255626678467, 0.03802633658051491, 0.018645480275154114, 0.0069540562108159065, -0.048230890184640884, 0.019165465608239174, 0.03865073621273041, 0.02103777974843979, -0.04865284636616707, 0.02080501802265644, -0.00862373411655426, 0.018717361614108086, -0.011227202601730824, 0.0010019280016422272, -0.020316310226917267, -0.010250754654407501, -0.045300163328647614, 0.015262864530086517, -0.0008308766991831362, 0.01614447683095932, -0.008999060839414597, -0.014285527169704437, -0.02700078673660755, -0.035548917949199677, -0.05091998726129532, -0.0491877980530262, -0.0258514154702425, -0.013280260376632214, -0.027682580053806305, -0.029850827530026436, 0.05755600333213806, -0.05718136206269264, -0.015273334458470345, -0.03415071219205856, -0.0026401286013424397, -0.10187218338251114, -0.06764090806245804, 0.06635846197605133, -0.03496035560965538, -0.018146144226193428, 0.06418105959892273, 0.02936401218175888, 0.05539599806070328, -0.013295523822307587, 0.02284902334213257, 0.016247814521193504, 0.06448721885681152, -0.014443227089941502, 0.017006151378154755, 0.022068575024604797, -0.04504766687750816, 0.009820747189223766, 0.008356600999832153, -0.008983059786260128, 0.03886127471923828, -0.02805125154554844, 0.015208760276436806, -0.028004556894302368, 0.016381079331040382, -0.006665334105491638 ]
<p>Why does production of white light using a LED require combining a short wavelength LED such as blue or UV, and a yellow phosphor coating?</p> <p>Why can't a single LED produce pure white light?</p>
g1570
[ 0.013699952512979507, 0.07757251709699631, -0.01292360294610262, 0.03401477634906769, 0.027097640559077263, 0.0006664033862762153, 0.04024272412061691, 0.030825920403003693, 0.00338163785636425, -0.06662458181381226, 0.03249775245785713, 0.05740269646048546, 0.0028599724173545837, 0.03342698514461517, -0.06569105386734009, -0.0261301938444376, -0.013023573905229568, 0.007178247906267643, 0.041265618056058884, 0.0644475594162941, -0.0602370910346508, -0.023402921855449677, -0.02351337857544422, -0.08460962772369385, 0.03164496645331383, 0.02630724012851715, -0.02168961428105831, -0.018597491085529327, -0.040463887155056, -0.022669102996587753, 0.004266838543117046, 0.029800960794091225, 0.04412345588207245, 0.04739825055003166, 0.03477342426776886, 0.002852421021088958, 0.00602662144228816, -0.05630176514387131, 0.003322293283417821, 0.017358925193548203, -0.020480554550886154, 0.1516750603914261, 0.02790760062634945, 0.013914508745074272, -0.02008187770843506, -0.0358528308570385, 0.025592342019081116, -0.032196272164583206, -0.03319079801440239, -0.007828492671251297, -0.0028199765365570784, -0.03359662741422653, -0.015453365631401539, -0.035767119377851486, 0.08706704527139664, -0.04354389011859894, -0.003051973646506667, -0.0487053357064724, 0.006907627452164888, 0.05820932984352112, -0.018271392211318016, -0.017332730814814568, 0.033421460539102554, 0.03311632201075554, 0.04098797217011452, -0.08741509914398193, 0.06445163488388062, -0.01524442620575428, 0.01945689134299755, 0.03622390702366829, -0.011681572534143925, -0.0050635733641684055, 0.007789491675794125, 0.00950562208890915, 0.06035623699426651, 0.04454047977924347, 0.022001929581165314, 0.011169316247105598, 0.008762110956013203, 0.027836084365844727, 0.034818001091480255, 0.0345657542347908, -0.023873716592788696, 0.030317548662424088, -0.03507265821099281, -0.034801334142684937, -0.040952425450086594, -0.06570154428482056, -0.0077037806622684, 0.00675605284050107, 0.016729986295104027, 0.0023296561557799578, 0.033391304314136505, 0.0028075650334358215, -0.006850776262581348, -0.06101158633828163, 0.009769859723746777, 0.026989631354808807, 0.0073967622593045235, 0.010777732357382774, -0.007065454963594675, -0.04260285571217537, -0.007144935894757509, -0.018731864169239998, 0.01823336072266102, -0.023434728384017944, 0.017343761399388313, 0.00738096097484231, -0.022150197997689247, 0.01576589234173298, -0.03778616338968277, 0.0011828382266685367, -0.07080642879009247, -0.04010321572422981, -0.030434085056185722, -0.006194165907800198, 0.05673997849225998, 0.02563832327723503, 0.028867453336715698, 0.05911237746477127, 0.05540427565574646, 0.010060465894639492, -0.015307651832699776, -0.0027169266249984503, 0.005827878136187792, -0.01833830587565899, 0.013655181974172592, -0.03232083097100258, -0.004989068489521742, -0.0006018799031153321, 0.023985549807548523, -0.005998170934617519, -0.03950505331158638, 0.05873262882232666, 0.07392265647649765, -0.016885023564100266, 0.0132652772590518, 0.04939790442585945, -0.03289233148097992, 0.008382030762732029, -0.03798309713602066, 0.008758153766393661, -0.024374358355998993, -0.02057579904794693, 0.016385342925786972, 0.0528988391160965, -0.03395965322852135, 0.04507320001721382, 0.022589288651943207, 0.051010895520448685, -0.015314762480556965, 0.009921517223119736, 0.031205609440803528, 0.008459850214421749, 0.000791342870797962, 0.001042479183524847, 0.030114032328128815, 0.0026620151475071907, -0.036348141729831696, -0.07892532646656036, 0.0772717148065567, 0.010504580102860928, -0.00015197663742583245, -0.057708751410245895, -0.020402565598487854, 0.06074390932917595, 0.004262756556272507, -0.07330576330423355, -0.07014797627925873, -0.029843216761946678, -0.045953378081321716, -0.022562427446246147, -0.0076002017594873905, 0.07479903101921082, 0.03446798399090767, 0.037523142993450165, 0.06413540244102478, -0.007352401502430439, -0.03779560700058937, 0.018000958487391472, -0.03825363144278526, -0.07359308004379272, -0.05468752235174179, -0.06101563200354576, 0.018534759059548378, 0.014270621351897717, 0.010465987958014011, -0.03626134991645813, -0.010579990223050117, 0.05638976767659187, -0.03142019361257553, -0.05082085728645325, 0.0757024884223938, 0.0012144908541813493, -0.04861844331026077, -0.033463284373283386, -0.009691016748547554, -0.010297944769263268, -0.028103629127144814, -0.03322243317961693, -0.06042776256799698, 0.03527957573533058, -0.008786175400018692, -0.021246835589408875, 0.016568593680858612, 0.04869215935468674, -0.027841374278068542, -0.010781369172036648, 0.03611070662736893, 0.003467034315690398, -0.005073690786957741, -0.007480366621166468, 0.006987352389842272, 0.014548348262906075, 0.02695837803184986, -0.04665515199303627, -0.03764185309410095, 0.013099011965095997, -0.056886035948991776, -0.027774441987276077, 0.014428694732487202, 0.019326092675328255, 0.007473426405340433, -0.009985857643187046, -0.007280247285962105, 0.04979178309440613, -0.09863150119781494, 0.048338014632463455, 0.005715123377740383, -0.02924582175910473, -0.014300435781478882, -0.029894065111875534, -0.024602454155683517, -0.014090525917708874, 0.010983872227370739, 0.011139038018882275, -0.008804352022707462, -0.009936357848346233, -0.03921586647629738, 0.026009533554315567, -0.015633856877684593, -0.04693390429019928, -0.012755273841321468, 0.0026381483767181635, -0.005825422238558531, -0.03288447856903076, 0.028558388352394104, -0.0010549657745286822, -0.030346570536494255, 0.027977410703897476, -0.06682351976633072, 0.0033314453903585672, 0.01539626345038414, -0.01485870499163866, -0.009983780793845654, -0.04984531179070473, 0.023648027330636978, 0.058000992983579636, 0.013796158134937286, -0.03546024486422539, -0.054519087076187134, -0.026470696553587914, -0.0003728207084350288, 0.018533781170845032, 0.007357834372669458, 0.004838691558688879, -0.04387036710977554, -0.022245030850172043, -0.002236691303551197, -0.03650203347206116, -0.019366251304745674, 0.020792584866285324, -0.05599696934223175, -0.06843402236700058, 0.01840839721262455, -0.03651542589068413, 0.030751926824450493, 0.006760935299098492, 0.01523957122117281, 0.03408318758010864, -0.01283502858132124, 0.011046263389289379, 0.0050419089384377, -0.029902419075369835, 0.04337302967905998, -0.025119280442595482, -0.02329184114933014, -0.031463123857975006, -0.008644849993288517, 0.10258237272500992, -0.015603619627654552, -0.0031610140576958656, 0.003219821723178029, -0.045736875385046005, 0.004948628135025501, -0.0076662590727210045, 0.017592385411262512, 0.014862093143165112, -0.03979383781552315, 0.04621322825551033, 0.018392853438854218, 0.01159935537725687, 0.027750836685299873, -0.018484875559806824, 0.060623422265052795, -0.015922803431749344, -0.05031074956059456, -0.03904300928115845, -0.02910342440009117, 0.004736098926514387, 0.037817709147930145, 0.035564128309488297, -0.046190664172172546, 0.04197666794061661, -0.005994855891913176, 0.04846420884132385, -0.04173242673277855, -0.04920242726802826, -0.002360840793699026, -0.05668254196643829, -0.030122185125947, 0.002392769558355212, -0.026110615581274033, -0.031070467084646225, -0.025220578536391258, -0.02434924989938736, 0.05634497478604317, -0.002360178856179118, 0.04872177541255951, 0.05112587288022041, 0.06879578530788422, 0.04256729036569595, -0.04141652584075928, 0.02030237764120102, 0.008852507919073105, -0.05319206416606903, 0.028257545083761215, -0.015816813334822655, -0.009353048168122768, -0.006255142390727997, 0.024185337126255035, -0.046128880232572556, -0.0866757482290268, -0.028160570189356804, 0.021170902997255325, -0.00886535830795765, -0.014075115323066711, 0.0030778199434280396, 0.01039070449769497, 0.017545370385050774, 0.07440683245658875, 0.004132590722292662, -0.055738288909196854, -0.04435032233595848, -0.05176542326807976, 0.06883186846971512, -0.018153628334403038, 0.08825385570526123, 0.05373191833496094, -0.04696119576692581, 0.05906808376312256, 0.01012609712779522, 0.015904754400253296, -0.048699136823415756, -0.01940707303583622, 0.016489924862980843, -0.011560852639377117, 0.019370390102267265, 0.007256592158228159, -0.012439708225429058, -0.028088340535759926, 0.057314589619636536, -0.035607513040304184, -0.011995643377304077, 0.020271917805075645, -0.0685911625623703, 0.002137094968929887, 0.04178846627473831, -0.028908371925354004, 0.0360456146299839, 0.011349665932357311, 0.039336878806352615, -0.03281028941273689, 0.0067104496993124485, -0.016842909157276154, -0.0013213006313890219, -0.07878704369068146, -0.0016061239875853062, -0.03756196051836014, -0.04193555936217308, -0.020921777933835983, -0.0013896515592932701, 0.02279551699757576, 0.0037073162384331226, 0.03539665788412094, -0.021398499608039856, 0.00906277820467949, -0.03053654544055462, 0.019273122772574425, 0.02156982384622097, -0.04471442475914955, 0.0307629257440567, 0.05361146107316017, -0.03988860920071602, -0.03812761977314949, -0.00484107481315732, 0.037127215415239334, -0.003059220500290394, 0.0733826756477356, 0.016962675377726555, 0.017378810793161392, -0.03789569064974785, -0.005608947481960058, -0.004858695901930332, 0.011244897730648518, 0.024652471765875816, 0.047769296914339066, -0.02257838286459446, 0.038632843643426895, 0.0539395734667778, 0.04885095730423927, 0.0050224256701767445, -0.016604101285338402, -0.07011798024177551, 0.01858854480087757, 0.04374081268906593, -0.03817665949463844, -0.007894347421824932, 0.010805085301399231, -0.0200762078166008, 0.05253356695175171, 0.005176426377147436, -0.0021840601693838835, -0.03877836465835571, -0.020260082557797432, 0.021486980840563774, 0.015690481290221214, 0.031118789687752724, 0.02596542052924633, 0.016539771109819412, 0.026829881593585014, -0.07262564450502396, 0.06383215636014938, -0.014929691329598427, -0.027794374153017998, 0.034898336976766586, -0.055826153606176376, -0.026005541905760765, -0.04352951422333717, -0.02145443856716156, -0.06071794405579567, 0.030771462246775627, -0.020579662173986435, -0.06055209040641785, 0.03893847391009331, -0.005377407651394606, -0.019612543284893036, 0.04476691037416458, 0.06041146069765091, 0.05385514721274376, -0.010436228476464748, -0.04839923605322838, 0.0063055469654500484, -0.03356929495930672, 0.0728488489985466, -0.017805298790335655, -0.03519503399729729, 0.02652633562684059, -0.07728742063045502, 0.0014976259553804994, -0.0532698854804039, 0.039352625608444214, 0.006105473730713129, 0.09676060825586319, 0.03134145960211754, -0.017457280308008194, -0.0064422753639519215, -0.058379124850034714, 0.030287431553006172, 0.014363611117005348, 0.051553912460803986, -0.03880569711327553, -0.025051571428775787, -0.028238920494914055, 0.009778467006981373, 0.023822221904993057, -0.0416678860783577, 0.03884641453623772, 0.017175432294607162, -0.05248156189918518, 0.025982368737459183, -0.01396951824426651, 0.0038258640561252832, -0.01978595368564129, -0.07820520550012589, -0.004126621410250664, 0.0006334480713121593, 0.03584263101220131, -0.038093335926532745, 0.019422875717282295, -0.004691991489380598, -0.04996275529265404, -0.032748911529779434, -0.006559702567756176, -0.017810702323913574, -0.040775980800390244, 0.025319034233689308, -0.024562561884522438, 0.05269048735499382, 0.02074427716434002, -0.0093458890914917, -0.07256168872117996, 0.07859478890895844, -0.023374108597636223, -0.01950703375041485, -0.03338081017136574, -0.04415138065814972, -0.03926139697432518, -0.011123890057206154, 0.03227335587143898, -0.016432246193289757, 0.029348507523536682, -0.035197362303733826, 0.004270780365914106, 0.0195769052952528, 0.05540049821138382, -0.0468277707695961, 0.034335214644670486, 0.005706250201910734, 0.004713363945484161, 0.047129642218351364, -0.00987548939883709, 0.07108229398727417, -0.0019658575765788555, -0.004540866706520319, -0.05326516926288605, 0.023721877485513687, 0.008479352109134197, -0.024158595129847527, 0.026501432061195374, -0.013871424831449986, -0.009228517301380634, -0.022720828652381897, 0.10162772983312607, 0.06372340023517609, -0.04395412281155586, 0.05754241347312927, 0.0029822292272001505, -0.006964066065847874, 0.034848179668188095, 0.018575847148895264, 0.06805969774723053, -0.04987448453903198, 0.03257828205823898, 0.04640955477952957, 0.03325144574046135, 0.021128928288817406, -0.03287845849990845, -0.020023055374622345, -0.04084761440753937, 0.0076060183346271515, 0.0166331734508276, -0.04845341667532921, 0.01705450937151909, 0.012973131611943245, 0.005406292621046305, 0.00513607868924737, 0.013759498484432697, -0.02214527316391468, 0.07057352364063263, 0.026975257322192192, 0.005805361084640026, 0.000950791290961206, -0.010029105469584465, -0.028527775779366493, 0.06595737487077713, 0.007359764538705349, -0.014202093705534935, -0.033241596072912216, -0.029786741361021996, 0.04213349521160126, -0.02064100280404091, -0.029914135113358498, -0.02171282097697258, -0.0070825787261128426, -0.005102126393467188, -0.0052560665644705296, -0.07474275678396225, 0.02192976325750351, 0.008096839301288128, 0.002037948463112116, 0.004406224470585585, 0.0014136723475530744, -0.007458618842065334, 0.029546519741415977, 0.019493332132697105, -0.035023320466279984, 0.04900122806429863, -0.02991395629942417, -0.012676196172833443, -0.002617905382066965, -0.005691411904990673, 0.02204791083931923, -0.001977045787498355, 0.010755086317658424, 0.01295363437384367, -0.04409382492303848, -0.01594030298292637, 0.05406811088323593, 0.003558837343007326, -0.05420880392193794, -0.0023471128661185503, -0.004784321412444115, -0.015157983638346195, -0.04548320919275284, -0.06615453958511353, -0.04386178031563759, 0.013650067150592804, -0.025252653285861015, -0.014465236105024815, -0.03186509385704994, -0.043808143585920334, 0.046545930206775665, -0.05298779159784317, -0.006825068034231663, 0.05935077741742134, -0.0058815269730985165, 0.005240072961896658, 0.03595251590013504, 0.02983640320599079, 0.00035749317612499, 0.015539403073489666, 0.011006121523678303, 0.038857609033584595, 0.008252200670540333, -0.016724539920687675, -0.021875135600566864, -0.02358955331146717, -0.05276744067668915, 0.02072906121611595, -0.015429525636136532, 0.012246886268258095, 0.033968690782785416, 0.10862612724304199, -0.038406532257795334, 0.05977530777454376, 0.026283329352736473, -0.047348394989967346, -0.004727293737232685, 0.06117970123887062, -0.014324158430099487, 0.019642800092697144, -0.027668798342347145, 0.016689851880073547, 0.02290751039981842, 0.030353400856256485, -0.04307098686695099, 0.02626769058406353, -0.013192648999392986, 0.013211456127464771, -0.0034047537483274937, 0.06123201549053192, -0.0500769279897213, 0.06954988092184067, 0.048253439366817474, -0.0021377119701355696, -0.010127159766852856, -0.029188506305217743, -0.020220836624503136, -0.024398429319262505, 0.020280079916119576, -0.005896365735679865, 0.03338008373975754, -0.015795383602380753, 0.018655570223927498, 0.011214742437005043, -0.03655873239040375, 0.060085028409957886, 0.037134800106287, -0.003127420786768198, -0.06206612288951874, -0.0015787670854479074, -0.05691811442375183, -0.023931263014674187, -0.0023848426062613726, 0.006701748352497816, 0.003348157973960042, -0.032585788518190384, 0.057400234043598175, 0.03702593594789505, 0.026860717684030533, -0.03561749681830406, 0.004944712854921818, -0.03161070495843887, 0.016155598685145378, 0.052935630083084106, -0.004807211924344301, -0.028232216835021973, 0.0071184649132192135, 0.11927847564220428, 0.06257959455251694, -0.08893268555402756, -0.01740362122654915, -0.04261597618460655, -0.003928470425307751, 0.02438553050160408, -0.015476016327738762, 0.04955228790640831, -0.0017468563746660948, -0.04690578579902649, 0.027292771264910698, 0.060699235647916794, 0.012072889134287834, 0.028968634083867073, -0.04894409328699112, 0.032310161739587784, -0.056296102702617645, 0.06169251725077629, 0.024327604100108147, 0.041551895439624786, 0.0026359674520790577, -0.010505576618015766, 0.006243925075978041, 0.02421814389526844, 0.023886529728770256, 0.018741732463240623, 0.07159885764122009, -0.014257445931434631, 0.021408000960946083, 0.00046164015657268465, -0.01695343665778637, -0.014455819502472878, -0.018698779866099358, 0.01474576722830534, -0.06205391883850098, 0.045946769416332245, 0.0018491036025807261, 0.014255556277930737, -0.05046495050191879, 0.017862971872091293, 0.0005478193634189665, 0.019175870344042778, -0.050833165645599365, -0.05064782127737999, 0.026809947565197945, -0.014835371635854244, -0.014619364403188229, 0.0490608848631382, 0.03138844296336174, -0.021766385063529015, -0.04723323881626129, 0.010686233639717102, -0.02500739134848118, 0.023319194093346596, 0.07774203270673752, -0.04136580973863602, 0.02149208076298237, -0.008754047565162182, -0.03545195236802101, -0.0030395567882806063, -0.0289062038064003, 0.0313018299639225, -0.018685946241021156, -0.0360349602997303, 0.004092965740710497, 0.037101585417985916, -0.02162983827292919, -0.03486756235361099 ]
<p>Suppose you have a U tube filled with a liquid. The height of the liquid column in both the arms of the U tube is not the same. Will the pressure be the same at two points in the two arms of the U tube which are at the same height from the base of the U tube or will it vary depending on height of liquid column above these two points?</p>
g1571
[ 0.0416855588555336, -0.021524127572774887, 0.007668443024158478, 0.008631114847958088, 0.03412283957004547, 0.05274862423539162, 0.014047370292246342, 0.011367865838110447, -0.07274163514375687, 0.0025331333745270967, -0.04330487921833992, 0.04291541874408722, -0.016105283051729202, -0.04933633282780647, 0.014789184555411339, -0.006826687138527632, 0.07876098901033401, -0.06554751098155975, -0.02180136926472187, 0.013419119641184807, -0.04303251579403877, 0.04328920692205429, 0.00765229994431138, -0.07638691365718842, -0.0469127781689167, -0.04616648703813553, 0.005426987074315548, 0.0035629631020128727, -0.04588700830936432, 0.035053182393312454, -0.041685063391923904, 0.02437293529510498, 0.06100542098283768, -0.04588566720485687, 0.001938022905960679, -0.01657644473016262, 0.07284843921661377, 0.012048745527863503, -0.0031036650761961937, -0.037159137427806854, 0.03758655861020088, 0.053173135966062546, -0.027553556486964226, -0.024536453187465668, -0.06282460689544678, -0.02708926796913147, -0.04560859128832817, -0.022779781371355057, -0.036932509392499924, 0.015778088942170143, 0.028823912143707275, 0.08206640928983688, -0.12034415453672409, -0.01923787221312523, -0.023813635110855103, 0.04995281249284744, 0.02537834458053112, -0.0007761589949950576, 0.01223826501518488, 0.07924173772335052, -0.005412125959992409, 0.021038571372628212, 0.01403575949370861, 0.05557238683104515, 0.032104089856147766, 0.005835157819092274, -0.01315977331250906, 0.007935851812362671, -0.05246003717184067, 0.03570222482085228, -0.008501646108925343, -0.04054049402475357, -0.045518290251493454, -0.02814091183245182, -0.09780952334403992, 0.01470466610044241, -0.018842371180653572, -0.008571987971663475, 0.027943015098571777, -0.0024311935994774103, -0.017786527052521706, 0.009591092355549335, 0.07547561824321747, 0.026717111468315125, -0.0031573837623000145, -0.000346808839822188, 0.01324636023491621, 0.0023061286192387342, -0.044037047773599625, 0.03894698619842529, -0.02084345556795597, 0.011319040320813656, 0.026300817728042603, -0.03227674588561058, -0.009448051452636719, -0.03630697727203369, 0.016381995752453804, 0.04448319599032402, 0.031529270112514496, 0.0005840497324243188, -0.03891749680042267, 0.008616991341114044, 0.038328010588884354, 0.030526261776685715, -0.04940282553434372, -0.02356809563934803, 0.04985694959759712, 0.05422694981098175, 0.017104584723711014, -0.03673102334141731, -0.02013484761118889, -0.03414520248770714, -0.013827229849994183, 0.017352214083075523, -0.035495102405548096, -0.05223051831126213, 0.034872863441705704, 0.018628358840942383, -0.0315140001475811, -0.013821653090417385, 0.01588250696659088, 0.02796131558716297, 0.015172857791185379, 0.061398863792419434, 0.001367273391224444, -0.027134910225868225, -0.027166882529854774, 0.017719216644763947, 0.016915464773774147, 0.006369824055582285, 0.047140300273895264, 0.012387975119054317, -0.09689442813396454, -0.016405519098043442, 0.08544232696294785, -0.0033438382670283318, -0.04139617457985878, 0.022210190072655678, 0.02904682047665119, -0.003091973951086402, 0.034199800342321396, 0.028147678822278976, -0.02671290561556816, 0.0036168748047202826, 0.011382682248950005, -0.03727046400308609, 0.02993348054587841, -0.020270628854632378, 0.007770310156047344, -0.017173128202557564, -0.032467540353536606, 0.03354312479496002, 0.03643304109573364, 0.004756456706672907, -0.05839589238166809, 0.043084658682346344, -0.03887975215911865, 0.022230513393878937, 0.04748082533478737, 0.021765822544693947, -0.00096795306308195, -0.0343342088162899, 0.09334457665681839, 0.021578473970294, -0.0903177261352539, 0.008113880641758442, -0.02889285422861576, -0.017465339973568916, 0.005344947800040245, -0.011562068946659565, -0.03750850260257721, 0.01572890765964985, -0.01973784528672695, 0.013641142286360264, 0.028746318072080612, 0.0023182884324342012, 0.012570226565003395, -0.033317677676677704, 0.026349669322371483, 0.0017641508020460606, -0.028936633840203285, -0.03133896738290787, 0.0015882914885878563, -0.07470051199197769, 0.010095317848026752, 0.029956039041280746, 0.05115494132041931, -0.033136166632175446, -0.03127264603972435, 0.0073694270104169846, -0.023361854255199432, -0.033392392098903656, -0.04981832951307297, 0.014362109825015068, -0.027697674930095673, -0.01818130351603031, 0.014833704568445683, -0.02140013687312603, -0.0654011070728302, 0.04048657417297363, 0.012200472876429558, 0.03019801340997219, 0.05629274621605873, 0.013968127779662609, -0.01775357313454151, 0.052126914262771606, -0.014302879571914673, 0.026069508865475655, 0.03256160765886307, 0.03601963445544243, -0.018251026049256325, 0.027404582127928734, 0.012270728126168251, 0.03917894884943962, -0.023975050076842308, 0.003856482682749629, 0.02921745553612709, -0.01614806428551674, -0.019687943160533905, 0.021884970366954803, 0.010158681310713291, 0.005236438009887934, -0.013898590579628944, 0.02216673456132412, -0.035810478031635284, -0.05074738711118698, 0.03981901332736015, -0.007429932244122028, 0.022896360605955124, -0.012983615510165691, 0.021056655794382095, 0.005194647237658501, 0.04740122705698013, -0.06378646194934845, 0.020835313946008682, -0.03052595630288124, -0.0030036852695047855, 0.030869241803884506, 0.028427094221115112, -0.03750859200954437, 0.006553188432008028, -0.03090623766183853, -0.0402672253549099, 0.057722099125385284, -0.001209466252475977, -0.017653346061706543, 0.0240046177059412, -0.02935088984668255, 0.029200555756688118, 0.06647717952728271, -0.05371956154704094, 0.018294043838977814, -0.01715770922601223, 0.06501615047454834, -0.04128856211900711, -0.011075485497713089, 0.016481144353747368, 0.016499372199177742, -0.05760781094431877, -0.05742289125919342, -0.002302030799910426, -0.02153022587299347, 0.030160708352923393, 0.05072114244103432, -0.054858870804309845, 0.0666268989443779, -0.00838681310415268, 0.008611414581537247, 0.03138178586959839, 0.07051249593496323, 0.009819733910262585, 0.030144039541482925, 0.010924157686531544, 0.05577084422111511, 0.008992526680231094, -0.004483941476792097, -0.010257036425173283, -0.009612295776605606, -0.028540050610899925, -0.015082007274031639, -0.0033424997236579657, 0.004711939953267574, -0.06330204755067825, 0.017682962119579315, 0.019098330289125443, -0.00001983688707696274, -0.02035474218428135, -0.01857798919081688, -0.013533378019928932, 0.03967500478029251, 0.0407390221953392, 0.001168835791759193, 0.03885822743177414, 0.0141157116740942, 0.055590640753507614, 0.0427437499165535, 0.0008951456402428448, 0.006449969485402107, -0.11397741734981537, -0.02185004949569702, -0.062402043491601944, -0.02244332805275917, -0.005029096733778715, 0.11176224052906036, 0.04413813725113869, 0.027736453339457512, -0.07207835465669632, 0.015124759636819363, -0.013615217991173267, 0.017026394605636597, -0.08797239512205124, 0.018308276310563087, 0.01675470359623432, -0.021374953910708427, -0.0435580350458622, 0.003999714273959398, 0.038320209830999374, 0.009855608455836773, -0.03826498985290527, 0.012645765207707882, -0.07812470942735672, -0.07941944897174835, -0.026657715439796448, 0.038703884929418564, -0.035310789942741394, 0.025746146216988564, -0.00015350217290688306, 0.05743645504117012, -0.043924108147621155, 0.01636391505599022, -0.004084500018507242, 0.05284871160984039, -0.012297570705413818, -0.009503481909632683, 0.038439225405454636, 0.010094554163515568, -0.021945277228951454, 0.01766178384423256, 0.028958046808838844, 0.013639140874147415, 0.00788135640323162, 0.018734320998191833, 0.04874473810195923, -0.019437147304415703, -0.01112642977386713, 0.011357958428561687, 0.027771124616265297, -0.004166893195360899, -0.01851583458483219, 0.03762677311897278, 0.05672670528292656, 0.007296372205018997, 0.009007303044199944, 0.030433712527155876, 0.012352656573057175, -0.023007238283753395, -0.008821116760373116, 0.0099455825984478, -0.008683853782713413, 0.003979031462222338, 0.04792361333966255, -0.07064472883939743, 0.039154741913080215, 0.05741500481963158, -0.04975290969014168, -0.04893295094370842, 0.07436571270227432, -0.009893447160720825, -0.02358461357653141, 0.02031797543168068, 0.025724735110998154, 0.01833117939531803, 0.011973747983574867, -0.04435520991683006, -0.0010628896998241544, -0.048160370439291, 0.016827885061502457, 0.023261182010173798, -0.04948551580309868, 0.05026721954345703, 0.0566394217312336, -0.03883224353194237, -0.03435641899704933, 0.01700008101761341, -0.03654944524168968, -0.029197933152318, -0.017210835590958595, 0.028439978137612343, 0.07262540608644485, -0.060639385133981705, 0.012322899885475636, -0.035433489829301834, -0.043489761650562286, 0.04378226771950722, 0.020414141938090324, -0.024798192083835602, 0.07099059224128723, 0.010223792865872383, -0.011405951343476772, -0.03944173455238342, -0.015681331977248192, -0.0210882555693388, 0.012608867138624191, -0.012557362206280231, -0.05422721430659294, 0.012559423223137856, 0.07408172637224197, -0.006738455034792423, -0.018224943429231644, 0.0009219119674526155, 0.05785485729575157, -0.0027497601695358753, 0.005785459652543068, -0.007158637512475252, -0.022702373564243317, 0.013270698487758636, -0.008305152878165245, 0.028002453967928886, 0.026024779304862022, 0.04389026388525963, 0.035371869802474976, 0.035745229572057724, 0.0035689526703208685, 0.00016696997045073658, -0.03406808525323868, -0.04183482378721237, 0.0069782729260623455, 0.02350812405347824, 0.014484280720353127, -0.07119569927453995, -0.027507565915584564, -0.014301247894763947, 0.005512612406164408, -0.011944340541958809, -0.02959800325334072, -0.0012330238241702318, 0.042508140206336975, -0.05599014833569527, -0.02834891900420189, -0.006630225572735071, 0.019766366109251976, 0.019509928300976753, 0.016808945685625076, 0.007527538575232029, 0.030185719951987267, 0.03672675043344498, 0.009807716123759747, -0.0020746695809066296, -0.01892434060573578, -0.015824900940060616, -0.07650408148765564, 0.04231635108590126, 0.0223960243165493, -0.075070321559906, -0.04649639502167702, -0.014965150505304337, 0.029757751151919365, -0.0028798573184758425, 0.011712099425494671, -0.022510064765810966, 0.012801630422472954, -0.03854236379265785, -0.022909054532647133, 0.0044326335191726685, 0.007279314566403627, -0.07713118195533752, -0.08465249836444855, -0.039769191294908524, -0.023560121655464172, 0.055765002965927124, 0.055555250495672226, 0.004335116595029831, 0.05277019366621971, 0.09743290394544601, 0.06297468394041061, 0.05216537043452263, 0.011095326393842697, 0.02475772239267826, 0.03075837530195713, -0.07645085453987122, 0.0002251798432553187, 0.0327092669904232, 0.03549513220787048, 0.04141286015510559, 0.043514855206012726, -0.01957889273762703, -0.039919305592775345, 0.022605830803513527, 0.057491615414619446, -0.020058225840330124, 0.031192634254693985, 0.037601254880428314, 0.01939920336008072, 0.02507159300148487, -0.03563917428255081, -0.06626427918672562, -0.006397276651114225, 0.007971461862325668, 0.01653817482292652, 0.018584804609417915, -0.06617212295532227, -0.00567786255851388, 0.044476743787527084, 0.0181136317551136, -0.016174621880054474, 0.005670981016010046, -0.009497289545834064, 0.0038834388833492994, -0.010004466399550438, 0.04385786131024361, 0.02846476249396801, -0.0015635235467925668, 0.01212379988282919, 0.02478836290538311, -0.019808294251561165, -0.00038933128234930336, -0.03496621921658516, -0.02272060699760914, -0.005889496766030788, -0.001313405460678041, 0.027573488652706146, 0.021597787737846375, 0.06484322994947433, 0.03577131778001785, -0.048148948699235916, 0.004742913879454136, -0.035062916576862335, 0.028786178678274155, 0.011427504941821098, 0.03251639008522034, -0.0266555342823267, 0.0018760357052087784, 0.00584925152361393, -0.028874773532152176, -0.06962517648935318, 0.018500570207834244, -0.01134998444467783, 0.010271592997014523, 0.04193286597728729, 0.024384763091802597, 0.01106185745447874, -0.04624882712960243, 0.020887065678834915, 0.03194012865424156, -0.010839816182851791, 0.010067068971693516, -0.08903729915618896, 0.000859535881318152, 0.020501835271716118, -0.035292234271764755, -0.014888618141412735, 0.04775451496243477, -0.05808883532881737, 0.037418562918901443, -0.0004423396021593362, 0.002021346241235733, 0.03544764593243599, -0.005935624707490206, 0.0651501715183258, -0.04063892364501953, -0.001523863524198532, -0.042670756578445435, -0.05735204741358757, 0.011914553120732307, 0.016998711973428726, -0.06659751385450363, -0.049675557762384415, 0.0051080333068966866, 0.036315955221652985, 0.004168861545622349, 0.058912817388772964, -0.06079608201980591, -0.014891308732330799, -0.0689026266336441, 0.007382387761026621, 0.023260140791535378, -0.05672062933444977, 0.05311059579253197, 0.015462272800505161, 0.006942277308553457, -0.004956492688506842, 0.033187802881002426, 0.004688870161771774, 0.033804599195718765, -0.02516847290098667, 0.0433669239282608, 0.013452471233904362, 0.0228420477360487, 0.08133241534233093, 0.00013121233496349305, -0.03176223114132881, -0.045080844312906265, -0.024729136377573013, 0.01768455095589161, -0.013146822340786457, -0.03032715618610382, -0.022224074229598045, 0.020434005185961723, 0.01590229757130146, 0.05216977372765541, 0.04009949415922165, 0.04109584912657738, 0.02417013607919216, -0.042483288794755936, -0.009297915734350681, 0.004657575394958258, 0.029541341587901115, 0.007973614148795605, 0.01719868741929531, -0.031112689524888992, 0.02262783609330654, 0.042254284024238586, 0.046800967305898666, -0.021585524082183838, -0.02210729941725731, -0.05892806872725487, 0.033930227160453796, 0.01657281443476677, -0.00634802458807826, 0.02888771891593933, 0.003989450167864561, -0.039247602224349976, 0.006561146583408117, -0.08111096173524857, 0.03857654333114624, -0.0034550607670098543, -0.025867467746138573, -0.028830086812376976, 0.01813288778066635, 0.005606318823993206, 0.042239412665367126, -0.040002480149269104, 0.026779120787978172, -0.010506154038012028, -0.051044922322034836, 0.04151660576462746, -0.016189392656087875, -0.005309696309268475, 0.023048540577292442, 0.056018102914094925, 0.058947596698999405, 0.015959488227963448, 0.030125267803668976, 0.04894975572824478, 0.02207418903708458, 0.03936714679002762, 0.047615304589271545, -0.0025242113042622805, -0.05848359316587448, 0.020667441189289093, 0.016718534752726555, -0.027160577476024628, -0.04354101046919823, 0.06251706182956696, -0.026791272684931755, 0.011071799322962761, -0.01949683204293251, 0.008365608751773834, -0.014169825240969658, -0.007239112630486488, 0.02514447271823883, -0.009120726026594639, -0.05996153503656387, 0.03728991374373436, -0.055064622312784195, 0.012629415839910507, 0.040677476674318314, -0.07200809568166733, -0.01054990291595459, 0.02476615086197853, 0.038780540227890015, -0.018653810024261475, -0.057947855442762375, -0.009828697890043259, 0.010930248536169529, -0.030969973653554916, -0.024516340345144272, 0.015626534819602966, -0.022350698709487915, 0.03890053555369377, -0.003378538182005286, -0.04642457515001297, -0.0091834282502532, -0.058321479707956314, -0.04940668120980263, -0.036891303956508636, 0.0008736363961361349, -0.05589451268315315, 0.06924446672201157, -0.05754168704152107, 0.0341445729136467, 0.003858881536871195, 0.043652359396219254, 0.0018865991150960326, -0.013990686275064945, 0.023184480145573616, -0.010390195064246655, 0.03163352608680725, -0.022081192582845688, -0.03660854697227478, -0.0009155874140560627, -0.009904523380100727, -0.07240135967731476, 0.005128353368490934, -0.01556191872805357, -0.03863838315010071, 0.0018905135802924633, 0.08206187188625336, -0.06216610223054886, -0.04140942171216011, 0.010803933255374432, 0.0013068898115307093, 0.005336903966963291, -0.015776144340634346, 0.04082075506448746, -0.013778314925730228, -0.07571591436862946, -0.04654407128691673, -0.02380504086613655, 0.02117171511054039, -0.07132816314697266, -0.07672414928674698, -0.0121191730722785, -0.04375479370355606, -0.03215685486793518, 0.018786443397402763, 0.00413758959621191, 0.026106074452400208, -0.03213684260845184, -0.022887587547302246, 0.014092459343373775, 0.012992401607334614, -0.01218466553837061, 0.024923207238316536, 0.010900336317718029, -0.012723277322947979, 0.006930431351065636, 0.02680567093193531, 0.004457583650946617, -0.03262431547045708, -0.01806764118373394, -0.00018831835768651217, 0.02389383129775524, -0.008296423591673374, -0.031686440110206604, -0.02706579864025116, -0.037664614617824554, 0.013332621194422245, 0.03917460888624191, -0.05336301773786545, -0.042007606476545334, 0.03593214601278305, 0.04874122887849808, 0.03054426610469818, -0.02030074968934059, -0.06885933876037598, -0.0718650221824646, 0.020810239017009735, -0.06550652533769608, -0.028861703351140022, -0.023983735591173172, 0.06996120512485504, 0.017663953825831413, -0.08447058498859406, 0.004549840465188026, 0.0426170751452446, -0.007761288434267044, 0.04147469624876976 ]
<p>If I try to add up neutrino masses (let's assume 1 eV rest mass equivalent each) to count as DM, do I use the rest mass or relativistic mass?</p>
g1572
[ -0.007170498371124268, -0.014861277304589748, 0.02321632020175457, 0.01773637905716896, 0.081158846616745, 0.026835182681679726, 0.003167480695992708, 0.03884905204176903, -0.0018856730312108994, -0.03777124360203743, -0.018147174268960953, -0.05952344089746475, -0.03452172130346298, 0.01806461438536644, -0.049575936049222946, 0.022492580115795135, 0.06517018377780914, 0.01938871666789055, -0.007970897480845451, 0.0036913391668349504, 0.029975546523928642, -0.0490679033100605, 0.021808834746479988, -0.024424605071544647, 0.026270348578691483, 0.0032863093074411154, 0.002303940709680319, 0.034023139625787735, -0.048437509685754776, 0.019697602838277817, 0.03231845796108246, 0.0435844324529171, 0.01394539512693882, -0.0013436548179015517, -0.000756169087253511, -0.0214144978672266, -0.0320102758705616, 0.0663253515958786, 0.00655660405755043, -0.013988691382110119, 0.011823071166872978, -0.0230865441262722, 0.0011508483439683914, -0.011858649551868439, -0.009390571154654026, 0.05309445783495903, -0.06374818831682205, -0.05040600895881653, -0.01899188570678234, 0.017014801502227783, 0.05616864934563637, -0.011777782812714577, 0.03304635360836983, 0.04166095331311226, 0.0758684054017067, 0.060215674340724945, -0.03158978000283241, -0.061607908457517624, 0.05529133975505829, 0.05848689004778862, 0.0545547679066658, -0.025652511045336723, -0.0015765660209581256, -0.03504321724176407, 0.03401826322078705, 0.0436764620244503, -0.0026285829953849316, 0.02237233705818653, 0.015407308004796505, 0.0022336156107485294, -0.02058042399585247, 0.001136617618612945, 0.021826284006237984, -0.037920910865068436, -0.005709099117666483, 0.001759522594511509, -0.0048674787394702435, -0.025410279631614685, -0.0037919641472399235, -0.06242537125945091, -0.01690119132399559, -0.034140195697546005, 0.0870976448059082, -0.005988752469420433, 0.08027813583612442, 0.01601046323776245, -0.047979388386011124, 0.027025975286960602, 0.01903243362903595, 0.025585878640413284, 0.062301453202962875, -0.02908836491405964, 0.08091487735509872, 0.041483987122774124, 0.05788353830575943, -0.03203852102160454, -0.006154353730380535, 0.039584361016750336, 0.024622533470392227, -0.005028920713812113, -0.011478863656520844, 0.02273300662636757, -0.009802470915019512, -0.04372347891330719, -0.008911910466849804, -0.005589474458247423, 0.02570895105600357, -0.05596804991364479, -0.010185298509895802, -0.04909185320138931, -0.03873303160071373, -0.08345723897218704, -0.031173773109912872, 0.024108517915010452, -0.05787697806954384, -0.038825877010822296, 0.06614156812429428, -0.05235981196165085, -0.0261934082955122, 0.010984723456203938, 0.060023460537195206, 0.03646376356482506, 0.011043230071663857, 0.037570346146821976, -0.027895644307136536, -0.051877573132514954, 0.0021386747248470783, 0.029231799766421318, 0.003078491659834981, -0.00055985915241763, 0.017190566286444664, 0.005022295285016298, 0.007269158028066158, -0.025589121505618095, 0.02028844505548477, -0.0006797994137741625, 0.07109569013118744, 0.0010669571347534657, -0.030934318900108337, -0.02628815360367298, 0.03145572915673256, -0.018325960263609886, 0.005911773536354303, 0.004782804287970066, -0.039648137986660004, 0.013282009400427341, -0.022558823227882385, -0.021934127435088158, -0.03148512542247772, 0.1057647094130516, -0.0077913664281368256, 0.02594335377216339, -0.020678624510765076, -0.024506734684109688, 0.03928634151816368, -0.004559341352432966, -0.028111347928643227, -0.00015364390856120735, 0.0041847010143101215, 0.001368932193145156, 0.017544981092214584, -0.0355573408305645, 0.015032933093607426, -0.07809780538082123, 0.02933049574494362, -0.007605063728988171, 0.08615799248218536, -0.05592700093984604, -0.015494463965296745, -0.09351056069135666, -0.009391059167683125, 0.011574223637580872, -0.048619937151670456, 0.02870982512831688, 0.030326075851917267, 0.04216044023633003, -0.024630926549434662, -0.040839701890945435, 0.0068513876758515835, -0.01328963041305542, 0.024665240198373795, -0.017308376729488373, 0.05972568318247795, -0.0021836627274751663, -0.0405544675886631, -0.02539069578051567, 0.0384407714009285, 0.018266959115862846, -0.017770972102880478, 0.013454563915729523, 0.013153879903256893, 0.06004372984170914, 0.03830011934041977, 0.0708719789981842, 0.031615860760211945, -0.023701906204223633, -0.003669292898848653, 0.019792446866631508, -0.029734862968325615, 0.04982743784785271, -0.014296636916697025, 0.019588902592658997, -0.008245722390711308, -0.027330804616212845, 0.04625890776515007, 0.004322344902902842, 0.02906639315187931, 0.0026751691475510597, 0.07117470353841782, -0.004603282082825899, 0.08730452507734299, 0.024130985140800476, -0.012477261014282703, -0.0033775672782212496, -0.0731770321726799, 0.04153262451291084, -0.005393253173679113, -0.007936757057905197, 0.05246887356042862, -0.0023501822724938393, -0.11708379536867142, -0.050221998244524, 0.004862738773226738, -0.009549293667078018, -0.023015547543764114, 0.03638109192252159, -0.029157288372516632, 0.024809455499053, -0.000043311098124831915, 0.03998764976859093, -0.025737930089235306, -0.0008474316564388573, -0.03392738103866577, -0.0038512612227350473, 0.052973851561546326, 0.01680571772158146, -0.01603979803621769, 0.02419317699968815, 0.023617293685674667, -0.04383436217904091, 0.014975426718592644, -0.032482121139764786, 0.04877060279250145, 0.03791860118508339, 0.0007861682097427547, -0.004319550469517708, 0.038354333490133286, 0.010707281529903412, -0.0661776065826416, 0.08205600082874298, -0.06226355955004692, -0.011627336964011192, -0.05629090592265129, -0.05152088776230812, 0.06362736970186234, 0.007978051900863647, -0.04276864603161812, -0.016273006796836853, -0.023059828206896782, 0.049140963703393936, 0.02490285225212574, -0.05997369438409805, -0.04337725788354874, 0.02933109924197197, -0.02079029195010662, -0.045468442142009735, -0.0259939506649971, -0.01009389478713274, 0.03191520273685455, 0.018110331147909164, -0.03178567811846733, 0.03792383149266243, 0.012035018764436245, -0.0014487128937616944, 0.019247038289904594, -0.06392457336187363, 0.03646344691514969, -0.03508686274290085, -0.00907175987958908, 0.0036217987071722746, 0.007944149896502495, -0.007051263935863972, -0.010860374197363853, -0.015474206767976284, 0.03834342211484909, -0.08558597415685654, -0.031095242127776146, -0.056070927530527115, -0.06520572304725647, -0.0014103687135502696, 0.027413470670580864, 0.02560443803668022, -0.0033247272949665785, 0.016375968232750893, 0.031603310257196426, 0.015057736076414585, 0.05104374140501022, 0.052556104958057404, 0.044950421899557114, 0.028363892808556557, -0.0015692225424572825, 0.0008515609079040587, -0.020436177030205727, -0.03771214559674263, 0.01206495426595211, 0.04320114850997925, -0.012775772251188755, 0.014496052637696266, 0.043248336762189865, -0.03898976370692253, -0.011184406466782093, 0.015306043438613415, -0.0029328055679798126, -0.002875855192542076, -0.007043125573545694, -0.014754185453057289, 0.04120286926627159, -0.01916467770934105, -0.026293782517313957, -0.05054040253162384, -0.004605554509907961, -0.047090522944927216, 0.08948473632335663, 0.006833078805357218, -0.003693233011290431, 0.03679550066590309, 0.025808868929743767, 0.07246658951044083, -0.07424522936344147, 0.00029746899963356555, 0.0433712862432003, 0.01746486872434616, -0.040662121027708054, 0.03507833927869797, -0.01491220947355032, 0.043765515089035034, 0.0016557149356231093, -0.023890553042292595, 0.03284522145986557, -0.0040307724848389626, -0.02764776721596718, 0.009191201999783516, 0.006506076082587242, 0.006733127404004335, -0.0196104496717453, -0.003839796409010887, -0.02179912105202675, -0.045738980174064636, 0.01489059254527092, -0.024457836523652077, -0.015851901844143867, 0.03597809374332428, -0.03553716093301773, 0.044091399759054184, -0.0039308457635343075, -0.006985667627304792, -0.015923315659165382, 0.03540698438882828, 0.01891862042248249, 0.03285668417811394, 0.054343003779649734, 0.01883518509566784, -0.052043359726667404, -0.007466609124094248, -0.022563545033335686, -0.023707561194896698, -0.03636275231838226, 0.019621679559350014, 0.03219279646873474, -0.04051807522773743, -0.03662444278597832, 0.006599687039852142, -0.0040309615433216095, -0.05864403396844864, 0.0078031150624156, -0.018240531906485558, 0.03626582771539688, 0.038409724831581116, -0.02796602062880993, 0.022759879007935524, -0.0009323754347860813, 0.017236927524209023, -0.03276248648762703, -0.061493609100580215, -0.06077324599027634, -0.0045557040721178055, -0.01248105801641941, 0.002271468983963132, -0.003717468585819006, -0.028645580634474754, -0.04526548087596893, -0.026494864374399185, -0.08670290559530258, 0.03095202147960663, 0.046625733375549316, -0.0716065764427185, 0.0746707171201706, 0.02114475518465042, 0.06166389584541321, 0.04244178161025047, -0.06154780834913254, 0.02086765691637993, 0.029160482808947563, -0.024954115971922874, 0.0033237766474485397, 0.04267822206020355, 0.0011891600443050265, 0.01839127391576767, 0.010740051977336407, 0.004353916272521019, -0.040160004049539566, -0.027298638597130775, 0.013282966800034046, -0.012488258071243763, 0.05639476701617241, -0.014388618990778923, 0.011157041415572166, -0.04193064197897911, -0.001109516597352922, 0.021817432716488838, -0.013217258267104626, -0.015144863165915012, -0.061216458678245544, -0.03721781447529793, -0.05384867265820503, 0.06300070136785507, 0.05889417976140976, -0.009056410752236843, -0.0049686371348798275, -0.007785737048834562, 0.01463350560516119, -0.017314303666353226, 0.00806038174778223, 0.053810011595487595, -0.035087719559669495, 0.04376932606101036, 0.011762799695134163, 0.04633546248078346, 0.03139669820666313, -0.002459037583321333, 0.030971083790063858, -0.0015116962604224682, -0.0041878377087414265, -0.014471816830337048, -0.025795534253120422, 0.04812417924404144, -0.04254323989152908, -0.007589614484459162, -0.025394275784492493, 0.06240737810730934, -0.04651186242699623, 0.008795046247541904, -0.026913562789559364, 0.010336038656532764, 0.01655317284166813, 0.022981340065598488, 0.03345268592238426, 0.06700044125318527, 0.0470961257815361, 0.02089936099946499, -0.04753889888525009, -0.025614755228161812, 0.04464512690901756, -0.02897810935974121, 0.03542797267436981, -0.041583385318517685, -0.012657703831791878, 0.006420773454010487, -0.04749594256281853, 0.005518035963177681, 0.04612348601222038, -0.03199568763375282, -0.0153938177973032, -0.02224045805633068, -0.004073109477758408, -0.04985804110765457, 0.009445770643651485, -0.019051071256399155, 0.015211987309157848, -0.023610670119524002, -0.03893950954079628, 0.012460136786103249, -0.008415325544774532, -0.0009588793618604541, -0.0357481949031353, 0.0456424281001091, -0.03400208428502083, -0.013791394419968128, 0.03613049164414406, -0.008963515050709248, 0.0026112967170774937, 0.057220906019210815, 0.012677899561822414, -0.0007656642119400203, 0.009252737276256084, 0.0443546324968338, -0.0351162925362587, -0.08230596780776978, -0.02994772605597973, -0.01197983417659998, -0.011256498284637928, 0.04838813468813896, -0.0025127162225544453, -0.016936566680669785, -0.026232214644551277, 0.02658255584537983, -0.013921452686190605, -0.008957145735621452, -0.004007737617939711, -0.06027977913618088, 0.0455784872174263, 0.033865369856357574, 0.02362174727022648, 0.020190609619021416, -0.001121228444389999, 0.015420248731970787, -0.0020528193563222885, 0.004712711088359356, -0.01503074076026678, -0.007240247912704945, 0.08232052624225616, -0.017690060660243034, 0.0449804812669754, -0.0054638260044157505, 0.016343992203474045, -0.13857416808605194, -0.00810619629919529, -0.060223113745450974, 0.010568610392510891, -0.0030512716621160507, 0.05285288766026497, -0.07664947211742401, 0.05224529281258583, 0.008007748052477837, -0.03006240352988243, -0.030337736010551453, -0.028256982564926147, -0.005528200417757034, 0.05329989269375801, 0.03603677079081535, -0.008668548427522182, 0.022511888295412064, 0.006400889717042446, 0.07926178723573685, -0.0008101690327748656, -0.029593894258141518, 0.07025066018104553, -0.015803320333361626, 0.00990862213075161, -0.021509673446416855, -0.06528852880001068, 0.007563508115708828, -0.003772081807255745, -0.07342100888490677, -0.008952575735747814, 0.013604613952338696, -0.004454730544239283, 0.03970259428024292, 0.019889725372195244, 0.03284284844994545, -0.02401837892830372, -0.040437158197164536, 0.03331994265317917, 0.02118823677301407, -0.04048343002796173, -0.08590196073055267, -0.04399215430021286, -0.03095996379852295, 0.010808542370796204, -0.07002417743206024, 0.028484832495450974, 0.022503117099404335, -0.056282687932252884, -0.04421272873878479, 0.013920617289841175, 0.037258174270391464, -0.050748467445373535, -0.014106024987995625, -0.008436186239123344, -0.016527948901057243, 0.024205759167671204, -0.012090496718883514, 0.025767695158720016, -0.03355562686920166, -0.013287005014717579, 0.049927737563848495, -0.023409122601151466, -0.06247534230351448, -0.023150261491537094, 0.043973542749881744, -0.029920369386672974, -0.024540361016988754, -0.07036572694778442, -0.001417015097104013, -0.08724290132522583, 0.022786665707826614, -0.012023924849927425, -0.020427992567420006, 0.016197266057133675, 0.06505093723535538, 0.03150618448853493, 0.008094419725239277, 0.06612147390842438, 0.0066676754504442215, 0.04488936811685562, -0.0257333405315876, -0.040100112557411194, 0.015519151464104652, -0.02707858383655548, -0.017023902386426926, -0.02902219444513321, 0.011350302025675774, -0.027765698730945587, -0.02905677817761898, -0.020228665322065353, -0.02953079529106617, -0.07293019443750381, 0.04806949198246002, 0.00221863086335361, 0.03734215348958969, 0.0067895520478487015, -0.013243257068097591, 0.04395904019474983, 0.0021881815046072006, 0.019267389550805092, 0.017440464347600937, 0.01246463879942894, -0.0010732951341196895, 0.028792399913072586, -0.00956137478351593, -0.030364977195858955, 0.0032203008886426687, -0.030120491981506348, 0.003733839141204953, 0.04862029477953911, 0.07099681347608566, 0.015470750629901886, -0.027127208188176155, 0.011196210980415344, 0.007078453432768583, -0.024603210389614105, 0.021855581551790237, -0.03803078085184097, 0.03373171389102936, -0.042015258222818375, -0.021356524899601936, 0.024192264303565025, 0.023813826963305473, 0.0007114546024240553, -0.03278084471821785, -0.02157220058143139, 0.05014900863170624, -0.03480609878897667, -0.0399198904633522, -0.07452764362096786, 0.05379180237650871, 0.039805080741643906, -0.01065526157617569, 0.055440276861190796, 0.00802852213382721, -0.027835318818688393, -0.03273793309926987, -0.0033898637630045414, -0.04252992197871208, 0.02529897913336754, 0.008302401751279831, 0.006891561672091484, 0.019278567284345627, 0.016578735783696175, -0.03445220738649368, -0.02461862750351429, -0.04600106179714203, -0.038942959159612656, -0.013235099613666534, -0.0019195855129510164, -0.048076849430799484, -0.01783779077231884, -0.05986611917614937, -0.013450213707983494, 0.01921222172677517, 0.012455941177904606, -0.023345353081822395, -0.05970877781510353, 0.003349523525685072, -0.005210606846958399, 0.0882185772061348, 0.0434592179954052, -0.027201581746339798, 0.06792546808719635, 0.040822308510541916, 0.032205577939748764, 0.02548258751630783, 0.053613319993019104, 0.004855255130678415, -0.09556066989898682, 0.0142308184877038, 0.02909640036523342, 0.031233321875333786, 0.05305875837802887, -0.006324042100459337, 0.002847048221156001, -0.007926910184323788, 0.054885752499103546, 0.018927209079265594, 0.02255239523947239, -0.0072587039321660995, -0.04080493003129959, -0.020091630518436432, 0.024384427815675735, 0.01699078269302845, 0.04735901951789856, 0.007319353520870209, -0.004968366120010614, 0.02684524841606617, -0.04618661850690842, -0.007212220225483179, -0.08653853833675385, 0.0032643198501318693, 0.061686523258686066, -0.03419697284698486, 0.00955470185726881, -0.007025639060884714, 0.01918741688132286, -0.04847293347120285, -0.01987590081989765, -0.08619248867034912, 0.002341225277632475, 0.07014962285757065, -0.002445173216983676, 0.0104747349396348, -0.0029168378096073866, -0.011071356013417244, -0.063975989818573, 0.01966491900384426, 0.016494328156113625, -0.011390624567866325, 0.02459781989455223, 0.012180301360785961, -0.016258057206869125, 0.020850300788879395, -0.00900640431791544, -0.08059437572956085, 0.021977704018354416, 0.05692952126264572, -0.024981731548905373, -0.04440930485725403, 0.010622525587677956, 0.023384269326925278, 0.057182688266038895, -0.01804342307150364, -0.022863266989588737, -0.021670615300536156, -0.00440193759277463, 0.012478755787014961, 0.06484498828649521, -0.016872115433216095, 0.06495404243469238, -0.04885547608137131, -0.04643793776631355, 0.005781429819762707, 0.0503196194767952, -0.02166634052991867, 0.02217470109462738, -0.005462470464408398, 0.0063688368536531925, -0.006342171225696802, -0.005666422192007303, -0.06363623589277267 ]
<p>About the meta questions <a href="http://meta.physics.stackexchange.com/questions/1193/full-migration-of-theoretical-physics-se-questions-to-physics-se">1193</a> and <a href="http://meta.physics.stackexchange.com/questions/2609/why-theoretical-physics-has-been-closed">2609</a>, I've heard parallelly, that the complete branch <a href="http://en.wikipedia.org/wiki/Theoretical_physics" rel="nofollow">theoretical physics</a> is already done and that there isn't any thing else to do in this field, how true is it?</p>
g1573
[ 0.013907715678215027, 0.03753039985895157, 0.004368233028799295, 0.003164422931149602, 0.02674727514386177, -0.04136437177658081, 0.0254230797290802, 0.013726414181292057, 0.030514732003211975, -0.062187373638153076, 0.04238934442400932, -0.04979061335325241, 0.03488234430551529, 0.003203487955033779, -0.0330670103430748, -0.0580732487142086, 0.04738658666610718, -0.05705263465642929, 0.025303194299340248, 0.006300711072981358, 0.017175424844026566, -0.038949936628341675, 0.052452120929956436, -0.07422193139791489, -0.006781802047044039, -0.04261813312768936, -0.026297491043806076, -0.04759959876537323, -0.004024443216621876, -0.07173149287700653, 0.05264841020107269, -0.00407709926366806, 0.07310408353805542, 0.01171061396598816, -0.06472937017679214, -0.07043981552124023, 0.017681322991847992, 0.009681252762675285, 0.027692239731550217, 0.022518230602145195, 0.021921228617429733, 0.007356622256338596, -0.006895042490214109, -0.09110929816961288, 0.023223716765642166, -0.03465870022773743, -0.011128267273306847, 0.023338962346315384, -0.02944512479007244, -0.032620351761579514, 0.033449940383434296, 0.02959536947309971, -0.00414304481819272, 0.09376780688762665, 0.0570400208234787, -0.014617571607232094, 0.026370827108621597, -0.000772764440625906, 0.031921762973070145, -0.06641452014446259, -0.04379434511065483, -0.003794710384681821, -0.05299769714474678, 0.03784804791212082, 0.03038216568529606, -0.0029170226771384478, -0.016332486644387245, -0.006955376360565424, 0.04854879900813103, -0.004508419893682003, 0.02781377173960209, -0.06164126843214035, 0.013033408671617508, 0.04467307776212692, -0.03061566688120365, 0.0518823117017746, -0.02429506741464138, -0.04012380167841911, -0.017331799492239952, 0.04354953393340111, -0.09796580672264099, -0.06685984879732132, 0.01987784169614315, -0.022350268438458443, 0.007515627425163984, 0.007239443715661764, -0.04081841558218002, 0.049508415162563324, -0.00016821848112158477, 0.02459281124174595, -0.038604483008384705, -0.014246192760765553, 0.03516222909092903, -0.03379332646727562, -0.016619881615042686, -0.009969708509743214, -0.020911967381834984, 0.0061477432027459145, 0.04898206889629364, 0.024700868874788284, -0.013307720422744751, -0.004839221015572548, 0.026020025834441185, 0.034280937165021896, 0.030602749437093735, -0.0010782419703900814, -0.00902292039245367, -0.021812804043293, 0.0011895314091816545, 0.05720071122050285, -0.038936637341976166, 0.0019058723701164126, 0.016354667022824287, 0.02733173780143261, -0.046673841774463654, 0.03859247639775276, 0.03974049538373947, -0.02457594871520996, 0.012793107889592648, 0.017915135249495506, -0.010704313404858112, 0.03967655077576637, 0.05185359716415405, 0.037381984293460846, -0.08325278759002686, -0.026820367202162743, -0.0035810607951134443, -0.012525930069386959, -0.038885511457920074, -0.023864373564720154, -0.009813020005822182, -0.04476006701588631, -0.03873933479189873, 0.008165528066456318, 0.0177898146212101, 0.009709810838103294, 0.012555991299450397, 0.019395286217331886, 0.06972964107990265, -0.000825071067083627, 0.018509432673454285, 0.012016876600682735, -0.014139408245682716, -0.022262798622250557, 0.0400957353413105, 0.009026529267430305, -0.01342722401022911, 0.03288900479674339, -0.00758112920448184, 0.07319855690002441, -0.008092418313026428, 0.03805951774120331, 0.035563062876462936, -0.022911472246050835, 0.014463867992162704, -0.03453188017010689, 0.020972687751054764, -0.029476018622517586, 0.03417208045721054, -0.016177119687199593, 0.020103974267840385, -0.016974851489067078, 0.014847518876194954, -0.0017100638942793012, 0.03010525554418564, -0.009904243052005768, -0.021307436749339104, -0.04064334183931351, -0.012777566909790039, -0.03496750444173813, -0.0658964142203331, 0.03090129978954792, 0.06821314245462418, 0.05811610817909241, 0.05898623540997505, 0.06717285513877869, -0.00020669435616582632, -0.019838187843561172, -0.02978775091469288, 0.03439713642001152, -0.017894702032208443, -0.023781420662999153, 0.0525805689394474, 0.0038534177001565695, -0.0369386188685894, 0.006848023273050785, -0.06947240978479385, 0.035035327076911926, -0.04150336608290672, -0.015370906330645084, 0.003639278933405876, -0.0030322291422635317, -0.05050353705883026, 0.0014360947534441948, 0.02638133615255356, -0.026066282764077187, -0.03205941990017891, 0.01284252293407917, -0.008110865950584412, -0.04100235924124718, 0.029107918962836266, 0.06575442850589752, -0.010862129740417004, -0.023370536044239998, 0.02690989524126053, 0.019741572439670563, -0.020276442170143127, -0.02143140323460102, 0.02394118905067444, 0.014630074612796307, 0.0355440154671669, -0.036183618009090424, 0.04025740548968315, 0.05753695219755173, -0.011381050571799278, -0.034813396632671356, 0.0040389238856732845, -0.007021550089120865, 0.0033094605896621943, 0.057938698679208755, -0.03113398887217045, -0.020890481770038605, -0.028501657769083977, 0.027563832700252533, 0.017293980345129967, -0.0020503608975559473, -0.028790868818759918, -0.03865469992160797, -0.011675595305860043, 0.05036310851573944, -0.04105278477072716, -0.03307925537228584, -0.015995031222701073, -0.057068269699811935, 0.03272315859794617, 0.01744353212416172, -0.004022346809506416, -0.0032634653616696596, 0.00840686447918415, 0.006168006919324398, 0.09210523962974548, 0.009016362950205803, 0.00499196071177721, -0.004796783905476332, 0.058050304651260376, -0.09602013975381851, 0.035609833896160126, -0.007780787069350481, 0.024788888171315193, -0.006240278482437134, 0.07889824360609055, -0.046881698071956635, -0.018640069290995598, 0.041497234255075455, 0.0175075251609087, 0.005392436869442463, 0.04299766570329666, 0.05128038674592972, 0.03635942190885544, -0.017346175387501717, -0.003627290017902851, -0.027394631877541542, 0.009740782901644707, -0.02306889370083809, -0.03551796078681946, 0.020552927628159523, -0.06693892180919647, 0.01166955754160881, -0.02494325116276741, -0.010054033249616623, 0.03881063684821129, 0.013472562655806541, 0.027234209701418877, 0.0495416522026062, 0.019734373316168785, 0.02539992332458496, 0.018173454329371452, -0.0010976268677040935, 0.03155050426721573, -0.03782320022583008, -0.028445575386285782, -0.006925030145794153, 0.003294649999588728, 0.031022517010569572, -0.027038343250751495, -0.001903035561554134, 0.022681208327412605, -0.0805024802684784, -0.017656201496720314, 0.01856425777077675, 0.006518225185573101, -0.07473570853471756, 0.08692682534456253, 0.026516782119870186, -0.05606455355882645, 0.026275478303432465, 0.010391703806817532, -0.08486367762088776, -0.06556480377912521, 0.002940698526799679, -0.0706891342997551, 0.019154997542500496, 0.05088801681995392, 0.03094550035893917, 0.12242835760116577, 0.040147583931684494, -0.04733863100409508, -0.02887747995555401, -0.007440573535859585, 0.02353580854833126, -0.028271814808249474, 0.07033997774124146, 0.01362277939915657, -0.00779159227386117, 0.02964736334979534, -0.008578687906265259, -0.002636086428537965, 0.06229909881949425, 0.03673902153968811, 0.01329998392611742, 0.000858783139847219, 0.053387369960546494, 0.06637701392173767, -0.0052016377449035645, 0.0587615929543972, 0.04667980596423149, -0.013894475065171719, 0.011711339466273785, -0.015104547142982483, -0.0031219404190778732, 0.024808024987578392, 0.003592389402911067, -0.015176535584032536, -0.06083570420742035, -0.033314283937215805, -0.008109942078590393, -0.01523786410689354, 0.030044574290513992, 0.017016064375638962, -0.0022955124732106924, -0.0460049994289875, -0.09572145342826843, 0.04129409417510033, 0.05627522990107536, 0.007180612999945879, 0.02878216840326786, -0.031730618327856064, 0.010395246557891369, 0.01846408285200596, 0.0009482260793447495, 0.010632066056132317, 0.025104861706495285, -0.02003633789718151, 0.06971070170402527, -0.03762460872530937, 0.038769904524087906, 0.007287042681127787, 0.007044547703117132, 0.028066108003258705, 0.004385647363960743, -0.015215717256069183, -0.036972448229789734, 0.08870025724172592, -0.017132669687271118, -0.048097603023052216, -0.0047123245894908905, -0.018004916608333588, -0.027466246858239174, -0.019910898059606552, -0.039813362061977386, 0.028753699734807014, -0.014900697395205498, -0.03167175501585007, 0.03151850029826164, 0.00674064178019762, -0.0558975450694561, 0.013550772331655025, -0.010630068369209766, -0.021783355623483658, -0.00617616344243288, 0.08505254238843918, 0.028162993490695953, 0.017555130645632744, -0.016053829342126846, -0.006296505220234394, 0.024004975333809853, -0.06830551475286484, -0.007712668739259243, -0.030812865123152733, -0.0028498417232185602, -0.00985908042639494, -0.010882415808737278, 0.00692052161321044, 0.012049173004925251, -0.02650565281510353, 0.0019837261643260717, 0.0005665679345838726, -0.05945383012294769, 0.0042490530759096146, 0.024638613685965538, 0.016774311661720276, 0.027955370023846626, 0.014793343842029572, -0.013155247084796429, 0.0009925371268764138, -0.018223652616143227, 0.026733824983239174, 0.004979114513844252, 0.028163064271211624, -0.08823864907026291, 0.026781076565384865, 0.018485618755221367, -0.00863522570580244, -0.015743542462587357, 0.055462948977947235, -0.07653503865003586, -0.02119097113609314, -0.07863082736730576, -0.02392672188580036, 0.0043016416020691395, 0.027992894873023033, -0.01590319164097309, 0.018789412453770638, -0.05527828261256218, 0.04566457122564316, 0.05609593540430069, 0.02703465335071087, -0.03747556358575821, -0.019141606986522675, -0.019962787628173828, 0.03364971652626991, 0.014700774103403091, 0.03726506233215332, 0.022890491411089897, -0.06683742254972458, 0.021390940994024277, -0.03650333359837532, 0.06118505075573921, -0.04656147584319115, -0.011767725460231304, -0.012171966955065727, -0.047276031225919724, 0.021640712395310402, 0.03487401083111763, -0.010620747692883015, -0.034246813505887985, -0.10313372313976288, -0.0398707240819931, -0.059942446649074554, -0.020911075174808502, 0.0072936005890369415, 0.04290112107992172, -0.01814502850174904, -0.006016221828758717, -0.07693925499916077, -0.06040587276220322, -0.008426902815699577, 0.0372430682182312, -0.036982838064432144, 0.04533948749303818, -0.05354170873761177, -0.06850779801607132, 0.021921219304203987, 0.040220797061920166, 0.048859115689992905, 0.036472663283348083, -0.02516314387321472, -0.020984070375561714, -0.07673721015453339, -0.05304354429244995, -0.01025331486016512, 0.008826679550111294, 0.051961008459329605, -0.018310412764549255, 0.0045057255774736404, -0.03347131237387657, -0.007080556824803352, 0.038407329469919205, -0.0005187171045690775, -0.03549669682979584, 0.00769007345661521, -0.02396768517792225, -0.014029720798134804, -0.028480738401412964, -0.041185855865478516, 0.016753878444433212, -0.0338151678442955, -0.001787360175512731, -0.03259463980793953, -0.031446654349565506, 0.037974365055561066, -0.011558995582163334, 0.023143718019127846, -0.06877488642930984, -0.019123030826449394, -0.03963792324066162, -0.0037936794105917215, 0.028450608253479004, -0.06321784108877182, 0.012883644551038742, 0.006588044110685587, -0.020071271806955338, 0.034373167902231216, 0.00715849082916975, -0.013570000417530537, 0.04789549112319946, 0.03935981169342995, 0.03032068721950054, -0.028015492483973503, -0.028362007811665535, 0.03679996356368065, 0.021575013175606728, -0.029786907136440277, 0.06005557253956795, 0.0423700250685215, 0.028099991381168365, 0.005353996064513922, 0.007923955097794533, -0.0614289864897728, -0.08531838655471802, -0.037822119891643524, -0.02390480786561966, -0.02854747511446476, 0.012619337998330593, 0.0020750679541379213, 0.005698089022189379, -0.029834389686584473, -0.0076227192766964436, 0.005262818653136492, 0.04978786036372185, 0.01985383778810501, 0.007970568723976612, 0.06028598174452782, 0.0809243842959404, -0.02152574434876442, -0.03916338458657265, -0.05556474253535271, -0.03633855655789375, -0.019821593537926674, 0.05863816291093826, -0.017568927258253098, 0.007240509148687124, 0.03273400664329529, 0.05641218647360802, -0.004180966876447201, 0.00031559812487103045, 0.04241974279284477, 0.011595411226153374, 0.02032245136797428, -0.09774598479270935, -0.04520363360643387, -0.00422700634226203, -0.013966449536383152, -0.04977988079190254, -0.0025037878658622503, -0.006734000984579325, -0.018320199102163315, -0.03711985424160957, 0.028813505545258522, -0.011139820329844952, -0.08050037920475006, 0.038511972874403, -0.004842319525778294, -0.013297110795974731, 0.010738265700638294, -0.04562711715698242, -0.04350769892334938, -0.03917801380157471, 0.026803407818078995, -0.023592308163642883, -0.036962952464818954, 0.00941126886755228, 0.011699844151735306, 0.03623255342245102, 0.022884653881192207, 0.007062889635562897, 0.02886132523417473, 0.04432316869497299, 0.0020936063956469297, 0.022373581305146217, 0.04370446875691414, -0.037507977336645126, 0.029270483180880547, -0.045225054025650024, 0.04385873302817345, 0.04410681128501892, -0.025231285020709038, -0.03145695850253105, -0.022255808115005493, 0.00008526816964149475, -0.06923052668571472, 0.01598726026713848, 0.013344448991119862, 0.04035647213459015, -0.017112744972109795, 0.03236555680632591, 0.05522163212299347, 0.027106251567602158, -0.018479138612747192, 0.04689323902130127, -0.01256126444786787, -0.04220814257860184, 0.041452206671237946, 0.002765329321846366, 0.05422860383987427, 0.06689314544200897, -0.00558484299108386, 0.024603575468063354, -0.05424199625849724, -0.009101004339754581, -0.01776769571006298, -0.03826681151986122, -0.03459131717681885, 0.009405105374753475, 0.0002248693344881758, -0.04317264258861542, -0.023121941834688187, 0.026137355715036392, -0.007898041978478432, 0.03941406309604645, -0.008218737319111824, -0.033473096787929535, -0.020077338442206383, -0.03309892490506172, -0.07372283190488815, -0.0034564402885735035, 0.010166734457015991, 0.007830047979950905, 0.06699007004499435, -0.00501899654045701, 0.050233107060194016, 0.018472276628017426, 0.00336629431694746, -0.014215962961316109, -0.022460710257291794, 0.10961534082889557, 0.026027118787169456, -0.008906126022338867, -0.029055451974272728, -0.013491297140717506, -0.009558944962918758, 0.016196830198168755, 0.026786236092448235, -0.007403574418276548, 0.0011717085726559162, -0.045536864548921585, 0.01964225433766842, -0.02540060505270958, -0.07540062069892883, 0.016150446608662605, -0.005301446653902531, 0.05517882481217384, -0.03376680240035057, 0.013858171179890633, -0.03782021999359131, 0.04021469131112099, 0.01650521531701088, -0.005816873628646135, 0.01278810203075409, -0.035056255757808685, 0.0027713582385331392, 0.01776639185845852, 0.03425872325897217, -0.026026630774140358, -0.005080407485365868, 0.04565051943063736, 0.012668441981077194, -0.06327854841947556, 0.05834595859050751, -0.030135398730635643, 0.012881001457571983, 0.026639169082045555, -0.025882620364427567, 0.04719448834657669, 0.04759636148810387, -0.01780025288462639, 0.00885455310344696, 0.009838415309786797, -0.004162630531936884, -0.0449175164103508, 0.0011764459777623415, 0.06607618927955627, 0.01462774071842432, 0.009006861597299576, -0.04208323732018471, 0.0036947575863450766, -0.03441024571657181, -0.00855577178299427, -0.02257070690393448, -0.018041107803583145, 0.035561878234148026, -0.02205921709537506, 0.022520750761032104, 0.0058402749709784985, 0.03255315497517586, 0.010252011008560658, 0.01938123069703579, -0.0039421748369932175, 0.026020217686891556, 0.012068916112184525, -0.023870276287198067, 0.05344377085566521, -0.04624132066965103, -0.048554226756095886, 0.04626171290874481, 0.017659280449151993, 0.05602661892771721, 0.040807951241731644, -0.021312464028596878, -0.05054795369505882, -0.038781747221946716, 0.01428044680505991, 0.08045981079339981, 0.021255269646644592, -0.001974866958335042, -0.02037515863776207, 0.0032773467246443033, -0.03577423840761185, 0.024136554449796677, 0.0014007044956088066, 0.01115549448877573, -0.019139094278216362, -0.03736649081110954, 0.016635837033391, -0.044397737830877304, 0.04252105578780174, -0.033257827162742615, 0.02702787145972252, 0.009569041430950165, -0.015941470861434937, -0.056373901665210724, -0.01815751940011978, -0.006189251318573952, 0.04087993875145912, -0.05556723102927208, 0.017872657626867294, 0.07281061261892319, -0.06217800825834274, 0.009266122244298458, -0.0007586817955598235, -0.013578450307250023, -0.006962375249713659, 0.04737784340977669, -0.03405153378844261, -0.016634497791528702, -0.05025271698832512, -0.009527355432510376, 0.000027972122552455403, -0.02979726903140545, 0.006867620628327131, -0.012255857698619366, 0.0796121284365654, -0.02827414870262146, 0.09475097060203552, -0.0031540950294584036, -0.047039445489645004, -0.002945893444120884, 0.008789044804871082, 0.04637393727898598, 0.04668685421347618, -0.011408246122300625, 0.031031019985675812, 0.06310397386550903, 0.007382386829704046, -0.04459958150982857, -0.0259317047894001, 0.006018389947712421, 0.03821607306599617 ]
<p><strong>The Setup</strong>: Let's say we want to study a Euclidean $\mathrm{CFT}_2$ on $\mathbb R^2$ with coordinates $\sigma^1$ and $\sigma^2$ and metric </p> <p>$ds^2 = (d\sigma^1)^2+(d\sigma^2)^2$. </p> <p>It seems to me that in the usual discussion (e.g. di Francesco, Ginsparg, Polchinski), one proceeds to consider an analytic continuation of the CFT to $\mathbb C^2$ with coordinates $z^1, z^2$ and complex metric</p> <p>$ds^2 = (dz^1)^2+(dz^2)^2$</p> <p>and then, one performs the coordinate transformation $z = z^1+iz^2$ and $\bar z = z^1-iz^2$. In this way the coordinates $z$ and $\bar z$ can be considered "independent" because they are coordinates on a complex two-dimensional manifold. Also, in these coordinates the metric becomes</p> <p>$ds^2 = dz\,d\bar z$</p> <p>and it becomes clear that conformal mappings consist of mappings: $(z, \bar z)\to (f(z), g(\bar z))$.</p> <p><strong>My confusion is this</strong>: Since our original theory was on $\mathbb R^2$, books say that when we do calculations, we should consider the physical theory as living on the copy of $\mathbb R^2$ embedded in $\mathbb C^2$ given by the condition $\bar z = z^*$. But consider the mapping $(z, \bar z)\to (z^2, \bar z)$. This is a conformal mapping on $\mathbb C^2$, but it does not map the surface $\bar z = z^*$ to itself; for example the point $(z, \bar z)=(2,2)$ gets mapped to the point $(z^2, \bar z) =(4,2)$ and $2$ is clearly not equal to $4^*$. In particular, it seems to me that analytic continuation to a CFT on $\mathbb C^2$ enlarges the set of mappings one can have, so what relevance does it really have to the original CFT on $\mathbb R^2$? (my apologies for the long post)</p>
g1574
[ 0.012224148958921432, -0.013747907243669033, -0.007264118641614914, 0.018926555290818214, 0.012388189323246479, -0.010875200852751732, 0.0630047544836998, -0.005357711110264063, -0.04955022782087326, -0.04166136309504509, 0.023901015520095825, 0.004798812326043844, 0.05491616576910019, -0.03162439540028572, -0.030328666791319847, -0.02495012804865837, 0.016671031713485718, 0.015204111114144325, 0.03947838023304939, 0.00018077097774948925, -0.001347250072285533, 0.009387324564158916, 0.09323938190937042, -0.031138649210333824, -0.03420594707131386, -0.053896356374025345, 0.0762186124920845, -0.004395548719912767, 0.009815455414354801, -0.045806024223566055, 0.043226804584264755, 0.0508875735104084, 0.07789698243141174, 0.020132720470428467, -0.06936698406934738, -0.01241000834852457, 0.042777083814144135, 0.022710010409355164, 0.056145381182432175, -0.01413803268224001, 0.01133378129452467, 0.00807951670140028, 0.002257280983030796, -0.023472152650356293, -0.05966649949550629, -0.014959907159209251, -0.061712414026260376, 0.021634990349411964, -0.01089965458959341, 0.012664391659200191, -0.01633724570274353, 0.03315960243344307, -0.009899245575070381, 0.015310632064938545, -0.005481387488543987, 0.06439556926488876, 0.03200235217809677, 0.0032439902424812317, 0.06009724363684654, 0.006107200402766466, -0.017493324354290962, -0.007524971384555101, 0.02246960811316967, 0.015901492908596992, 0.03230298310518265, -0.07429865002632141, -0.05038531869649887, -0.006131842266768217, -0.03937258943915367, -0.03398919105529785, -0.008256386034190655, -0.10723293572664261, 0.09079448878765106, 0.0017792846774682403, -0.016336528584361076, 0.00924440287053585, 0.04370785132050514, -0.08979691565036774, 0.010073534213006496, -0.04165952652692795, 0.006632709875702858, -0.023322928696870804, 0.010016982443630695, -0.012043752707540989, 0.0767979770898819, 0.010882874950766563, 0.002611540025100112, 0.05291033536195755, 0.005871917586773634, 0.034503333270549774, -0.011366431601345539, 0.039381738752126694, 0.02121228165924549, -0.012942234985530376, 0.0011852307943627238, -0.029749084264039993, 0.0002187428472097963, 0.009880057536065578, 0.012862016446888447, -0.0022583508398383856, -0.03875451162457466, 0.014845880679786205, 0.0484679639339447, 0.05501289293169975, 0.04387199133634567, -0.05287407711148262, 0.02728194184601307, 0.0741356834769249, -0.0018304585246369243, -0.02777017652988434, -0.045630015432834625, 0.016799258068203926, 0.0027824407443404198, 0.03237582743167877, -0.054399505257606506, 0.02191445417702198, -0.024933598935604095, 0.01944131776690483, 0.030679496005177498, 0.02150106057524681, 0.012976785190403461, -0.006427437998354435, 0.07369576394557953, 0.023526402190327644, 0.005354548338800669, -0.010221903212368488, -0.011131756007671356, -0.06121515855193138, 0.06105447933077812, -0.022390026599168777, 0.04124538227915764, 0.0226899366825819, 0.052948638796806335, -0.029560429975390434, -0.01894647441804409, -0.05069749057292938, 0.010925877839326859, -0.023782093077898026, 0.043042637407779694, -0.007707457523792982, -0.01385264191776514, -0.04572509229183197, 0.034670647233724594, -0.040957771241664886, -0.019978826865553856, 0.028494160622358322, 0.0332808718085289, -0.04326465353369713, 0.02330796606838703, -0.020710792392492294, 0.05205792188644409, 0.023445479571819305, -0.011912710964679718, -0.009711607359349728, 0.046856723725795746, 0.028738725930452347, -0.01347085926681757, -0.0730811208486557, 0.0388062447309494, 0.03887691721320152, 0.08623629808425903, -0.002285580150783062, -0.028504379093647003, 0.009047256782650948, -0.013876112177968025, 0.030514677986502647, 0.018910808488726616, -0.0652863159775734, 0.005310214590281248, -0.044061195105314255, -0.0669451653957367, 0.04517744854092598, 0.000970803142990917, 0.01602334901690483, 0.03311977535486221, 0.009105917066335678, -0.08345500379800797, -0.011233819648623466, 0.028197068721055984, -0.015536061488091946, -0.026431215927004814, 0.021887442097067833, -0.032786205410957336, 0.00415465421974659, -0.02292633056640625, 0.04222015291452408, -0.019272809848189354, -0.062226802110672, -0.03140415623784065, 0.015706628561019897, -0.0066241053864359856, 0.01561589166522026, 0.017207622528076172, 0.08065211772918701, -0.009638688527047634, 0.013271626085042953, 0.029513824731111526, 0.03478666767477989, 0.028064684942364693, 0.02462218701839447, 0.03613397851586342, 0.033153582364320755, 0.04914207383990288, 0.0077351899817585945, -0.010347564704716206, -0.02398892492055893, -0.0640740618109703, -0.09749183803796768, -0.009150243364274502, 0.027963440865278244, -0.02129296027123928, 0.02140706777572632, -0.0018979661399498582, -0.03693624958395958, 0.0035836887545883656, -0.044925954192876816, -0.040163490921258926, -0.04379028081893921, -0.02087390422821045, 0.06878410279750824, -0.03158697113394737, 0.017442062497138977, 0.07329703122377396, -0.007484590634703636, -0.059488099068403244, 0.006277491804212332, -0.0914689227938652, -0.0027883120346814394, 0.020602241158485413, 0.03469246253371239, -0.012430288828909397, -0.03788416460156441, 0.034279584884643555, -0.020787669345736504, 0.020349878817796707, -0.009548269212245941, -0.0724525973200798, 0.011302316561341286, 0.06423615664243698, 0.02987227961421013, 0.017945492640137672, -0.06452755630016327, -0.008029045537114143, -0.029832804575562477, 0.006877312436699867, -0.036648429930210114, 0.07169917970895767, 0.02658984065055847, 0.02397659420967102, -0.006531831342726946, 0.04223468527197838, -0.01843990758061409, -0.020289987325668335, -0.021692374721169472, 0.008442346937954426, -0.007607050705701113, -0.00009962446347344667, -0.0018854389199987054, -0.07797899842262268, -0.06878357380628586, -0.033175401389598846, -0.029227575287222862, -0.012078988365828991, -0.0019394401460886002, -0.03532934933900833, 0.06373747438192368, -0.03615777567028999, 0.003950581420212984, 0.005892041604965925, -0.015645170584321022, 0.016530180349946022, 0.03359183296561241, 0.007703976705670357, 0.11613501608371735, -0.033884745091199875, -0.019526461139321327, -0.03531883656978607, -0.008123625069856644, -0.03207682818174362, 0.032205596566200256, -0.009268974885344505, -0.022373272106051445, -0.04182824119925499, -0.002489667385816574, -0.014649566262960434, -0.07561179995536804, 0.00588833075016737, 0.019827717915177345, -0.023404909297823906, 0.039283301681280136, 0.05060243234038353, 0.006415225565433502, -0.02308916486799717, 0.00207290961407125, -0.0010062922956421971, 0.023364121094346046, -0.023875093087553978, 0.012493632733821869, 0.014165441505610943, 0.042012784630060196, 0.026128480210900307, 0.026690183207392693, 0.052035924047231674, 0.03030572086572647, 0.06563729047775269, 0.028973771259188652, -0.09410100430250168, -0.07907100766897202, 0.015445683151483536, 0.011714354157447815, 0.02838590182363987, -0.024547012522816658, 0.010068775154650211, -0.014536112546920776, 0.01758245937526226, -0.015172838233411312, 0.005293589551001787, -0.015957636758685112, -0.0028450866229832172, 0.010761606507003307, -0.03520306944847107, 0.02121768891811371, -0.0480211116373539, -0.01593906059861183, 0.08371598273515701, 0.07437217235565186, -0.06019287183880806, 0.035563889890909195, 0.021022984758019447, -0.02116793394088745, 0.030158044770359993, 0.06947740167379379, -0.04145070165395737, -0.006998345255851746, -0.033293962478637695, -0.0465921126306057, -0.032547373324632645, 0.05063274875283241, 0.0552317313849926, -0.026790538802742958, 0.012968986295163631, -0.02231031097471714, 0.03341328352689743, -0.03925102576613426, 0.020990882068872452, 0.05583737790584564, -0.0017814678139984608, 0.02324221469461918, -0.062106069177389145, -0.038242824375629425, 0.01425991766154766, -0.03229706734418869, 0.014488929882645607, -0.03695150092244148, -0.00500749284401536, 0.06680168211460114, 0.036794744431972504, 0.04957640543580055, -0.010852294974029064, 0.02419937588274479, 0.04985301196575165, -0.0018337712390348315, -0.01305774413049221, 0.02384975180029869, -0.01679377630352974, -0.01275733020156622, 0.01043006032705307, -0.035492852330207825, -0.05362705886363983, 0.007446116302162409, -0.01756279356777668, 0.012226643040776253, -0.006872593890875578, 0.06786029040813446, 0.030253661796450615, -0.06623372435569763, 0.0047628674656152725, 0.027508622035384178, -0.041190255433321, -0.011026068590581417, 0.009402420371770859, 0.03391535207629204, 0.004816601984202862, 0.02935333177447319, -0.029744425788521767, -0.012696309946477413, -0.030570395290851593, -0.015052550472319126, -0.012442132458090782, 0.0004883227520622313, 0.00204581581056118, 0.021487941965460777, -0.002982955425977707, -0.013062505051493645, 0.03323712199926376, -0.02531115710735321, 0.054956648498773575, 0.03323904052376747, 0.0019233296625316143, 0.006810714956372976, -0.0030928472988307476, -0.008351492695510387, -0.07282458245754242, -0.03836912661790848, -0.10559558868408203, -0.020856689661741257, -0.0027119279839098454, 0.0059338705614209175, 0.06144777685403824, -0.02875172160565853, 0.00271352706477046, -0.07153104245662689, 0.0007019179756753147, -0.10466692596673965, 0.05666634067893028, -0.029062457382678986, 0.002435947535559535, -0.019550785422325134, -0.000816268497146666, -0.020646393299102783, -0.006405855529010296, 0.030823364853858948, 0.04291243478655815, -0.016779981553554535, 0.04283539205789566, 0.05269588157534599, 0.02283340133726597, -0.0092780701816082, -0.030342506244778633, -0.027319809421896935, 0.031936489045619965, 0.03440298140048981, 0.04408206418156624, -0.005728570744395256, -0.06079937145113945, 0.01845441944897175, 0.01964542455971241, 0.02868630737066269, -0.02059205248951912, 0.028872041031718254, 0.02176281064748764, -0.024533838033676147, -0.006084101274609566, -0.0335150882601738, -0.028908254578709602, -0.006655705161392689, -0.03109654039144516, -0.00521133141592145, -0.046039123088121414, 0.0038916850462555885, -0.05576162040233612, 0.0578719787299633, 0.09119351208209991, 0.0014127489412203431, -0.0384562723338604, -0.01369381882250309, 0.01236123126000166, -0.009380586445331573, 0.011213867925107479, 0.03141773119568825, -0.01162537932395935, -0.02150239609181881, 0.03302040323615074, -0.012686989270150661, 0.011636128649115562, 0.020366409793496132, -0.0679447129368782, 0.002225879579782486, -0.06391894817352295, 0.004043355584144592, -0.008968508802354336, 0.0605175644159317, 0.010031632147729397, -0.041475292295217514, -0.011928838677704334, 0.03301822766661644, 0.010951249860227108, 0.010666686110198498, 0.01697356626391411, -0.07154977321624756, 0.02711675316095352, 0.01431623101234436, -0.006156881805509329, 0.026740662753582, 0.00195664307102561, -0.014578530564904213, -0.01632309891283512, -0.026511123403906822, -0.05818991735577583, 0.010933537036180496, 0.023816587403416634, -0.022747736424207687, 0.003799708094447851, -0.0033062277361750603, -0.051662661135196686, -0.005197993945330381, -0.00008489735046168789, -0.07446315884590149, -0.014840579591691494, -0.03617612272500992, -0.003747218055650592, 0.054239556193351746, -0.005268275737762451, 0.03848618268966675, -0.013156015425920486, 0.08454068750143051, 0.1270325481891632, -0.02231932431459427, -0.005161907523870468, 0.01591259427368641, 0.01378414686769247, 0.03786375746130943, -0.006774846464395523, -0.021714115515351295, 0.02293158322572708, -0.00020157550170551986, -0.051264435052871704, -0.012333192862570286, 0.031948186457157135, -0.03577781841158867, 0.005600736942142248, 0.018306100741028786, 0.03348947688937187, -0.019213426858186722, 0.025021253153681755, 0.04955824464559555, -0.02917528711259365, 0.0021050937939435244, 0.02189241163432598, 0.026704950258135796, 0.015582817606627941, -0.034637145698070526, -0.032126788049936295, 0.01009733509272337, -0.019097164273262024, -0.0036839416716247797, -0.04840894415974617, -0.024597646668553352, 0.008878222666680813, 0.01741061918437481, -0.039789117872714996, -0.0030416648369282484, -0.01894422248005867, 0.048613641411066055, -0.014862100593745708, 0.012090703472495079, 0.06301600486040115, 0.009900806471705437, 0.045106738805770874, -0.05968542769551277, -0.04927831515669823, -0.03552970662713051, -0.04776846244931221, -0.06458387523889542, 0.06358988583087921, -0.011707162484526634, 0.0028309014160186052, -0.024759860709309578, -0.0012050002114847302, -0.029286475852131844, -0.039332110434770584, -0.037263255566358566, 0.0022568281274288893, 0.012164871208369732, 0.010940181091427803, -0.037915728986263275, -0.02659352868795395, 0.055263079702854156, 0.05243615433573723, 0.01002296432852745, -0.01750074326992035, -0.004094915930181742, 0.03818412870168686, 0.0039592888206243515, 0.004781520459800959, 0.04633619636297226, -0.03534163534641266, 0.07667314261198044, 0.012895531952381134, -0.03632568567991257, 0.006350135430693626, 0.049833230674266815, 0.0596710704267025, -0.05553508922457695, -0.0390230230987072, 0.006477343384176493, -0.05762883648276329, -0.010550050996243954, 0.017076993361115456, 0.00398646853864193, 0.0015713375760242343, 0.02700875885784626, -0.055586811155080795, -0.01280470471829176, 0.014060516841709614, -0.06474003195762634, 0.018270282074809074, -0.0026146413292735815, 0.01097268145531416, 0.0226959977298975, -0.003980516921728849, 0.03364168852567673, 0.07686614990234375, -0.02878352627158165, -0.017870768904685974, -0.024630948901176453, 0.0014729147078469396, -0.05683800205588341, 0.028276151046156883, -0.02891717478632927, 0.012238528579473495, 0.05423086881637573, -0.01767939142882824, 0.04381704330444336, 0.02970411442220211, 0.0003907460195478052, -0.007313212379813194, 0.01441890001296997, -0.03346250578761101, -0.01376249548047781, 0.10068843513727188, 0.0017980355769395828, 0.01107160747051239, -0.04065097123384476, -0.03375420346856117, -0.03317352384328842, 0.03739824891090393, 0.00918289553374052, 0.06857999414205551, 0.0415036603808403, -0.019114013761281967, 0.026300696656107903, -0.04979247227311134, 0.026415714994072914, -0.004078109748661518, 0.0008483200217597187, -0.0028588329441845417, -0.0126128438860178, -0.007502449210733175, -0.007713089231401682, -0.0313371978700161, -0.01767636090517044, 0.009587422013282776, -0.05608999356627464, -0.08220840245485306, 0.0027941432781517506, -0.010116437450051308, -0.026852235198020935, -0.0982237160205841, 0.06693178415298462, 0.003121857764199376, -0.005504971370100975, -0.07958561182022095, 0.0029466734267771244, -0.08467873185873032, -0.041983675211668015, -0.006938382051885128, 0.02896256372332573, 0.013696522451937199, -0.04260364919900894, 0.02795640006661415, -0.0034405160695314407, -0.0414213091135025, 0.031792037189006805, -0.009248333983123302, 0.06122204661369324, -0.011378557421267033, -0.017399022355675697, 0.04594273492693901, -0.004515156615525484, 0.031076954677700996, 0.028262445703148842, -0.03228205814957619, 0.01000291109085083, 0.05112025886774063, -0.010147223249077797, 0.04113500565290451, 0.004694636911153793, -0.004394538700580597, 0.028253117576241493, 0.017488259822130203, -0.005816784221678972, 0.004289151635020971, -0.002725728554651141, -0.029868898913264275, 0.03347653150558472, -0.027837693691253662, -0.02333591692149639, -0.04504089802503586, -0.004006723407655954, 0.036807913333177567, -0.004860887303948402, -0.0034536162856966257, 0.06538338214159012, 0.029738696292042732, -0.00854081567376852, -0.023503664880990982, 0.028332529589533806, -0.00031949463300406933, -0.000652132264804095, 0.040751539170742035, -0.0424862764775753, -0.019104087725281715, -0.02570449933409691, 0.024572866037487984, -0.019985267892479897, -0.049193739891052246, -0.02806057408452034, 0.05630470812320709, 0.0076530855149030685, -0.00418503163382411, -0.009563233703374863, 0.019757067784667015, 0.018296580761671066, 0.023365724831819534, -0.005040689371526241, -0.013010294176638126, -0.00522008677944541, 0.03977572172880173, -0.022423142567276955, -0.060290172696113586, -0.018906138837337494, -0.043476443737745285, 0.02242445945739746, -0.007232919335365295, 0.005668079014867544, -0.031664974987506866, -0.05069580301642418, 0.024190528318285942, 0.012669172137975693, -0.03818459063768387, -0.0014318145113065839, -0.0020530561450868845, -0.015155172906816006, 0.01376284658908844, -0.029113830998539925, 0.008379156701266766, -0.02908182330429554, 0.02635735645890236, -0.0716795101761818, 0.025045545771718025, 0.031031114980578423, 0.021961916238069534, -0.0258386991918087, -0.0743284821510315, -0.03147237375378609, -0.01403573527932167, 0.009294204413890839, 0.05487522855401039, 0.025402309373021126, 0.031305667012929916, 0.08236192166805267, 0.028504488989710808, 0.011590703390538692, 0.06396770477294922, -0.03713670372962952, -0.03349045664072037, -0.032030895352363586, 0.09998401254415512, -0.027753548696637154, 0.008351493626832962, 0.01549324207007885, 0.002046378329396248, 0.0136822909116745, -0.012079347856342793, -0.046054594218730927, -0.031119151040911674, 0.010093992576003075 ]
<p>I'm trying to learn how to apply WKB. I asked a <a href="http://physics.stackexchange.com/questions/90157/how-to-apply-the-wkb-approximation-in-this-case">similar question</a> already, but that question was related to finding the energies. Here, I would like to understand how to find the wave functions using WKB.</p> <blockquote> <p><em>An electron, say, in the nuclear potential</em> $$U(r)=\begin{cases} &amp; -U_{0} \;\;\;\;\;\;\text{ if } r &lt; r_{0} \\ &amp; k/r \;\;\;\;\;\;\;\;\text{ if } r &gt; r_{0} \end{cases}$$ <em>What is the wave function inside the barrier region ($r_{0} &lt; r &lt; k/E$)?</em></p> </blockquote> <p>Shouldn't the wave function have the following form?</p> <p>$$\psi(r)=\frac{A}{\sqrt{2m(E-U(r))}}e^{\phi(r)}+\frac{B}{\sqrt{2m(E-U(r))}}e^{-\phi(r)}$$ where $$\phi(r)=\frac{1}{\hbar}\int_{0}^{r} \sqrt{2m(E-U(r))} dr'$$</p>
g1575
[ -0.0040938640013337135, 0.0031081971246749163, 0.004160798620432615, -0.017800597473978996, 0.02066623978316784, 0.002410388085991144, 0.006434171460568905, 0.05481594055891037, -0.0250378530472517, -0.022755492478609085, -0.0025368828792124987, 0.04387553408741951, 0.01022664736956358, 0.04478299990296364, -0.0101545425131917, -0.06313983350992203, 0.025642964988946915, 0.019273312762379646, 0.0027899923734366894, 0.0148463761433959, -0.03291623294353485, 0.029760653153061867, -0.030242739245295525, 0.012530782260000706, 0.004949331283569336, 0.012179260142147541, 0.009968896396458149, -0.020673345774412155, -0.030008241534233093, 0.016088858246803284, -0.04487112909555435, 0.0296369306743145, 0.06349349021911621, -0.0625939667224884, -0.022119948640465736, 0.0627349466085434, 0.04751615226268768, 0.01571531593799591, -0.007447239011526108, -0.01712653413414955, -0.053666744381189346, 0.009054047986865044, -0.00540086580440402, 0.037020985037088394, 0.02755795419216156, -0.019523780792951584, -0.05411070957779884, -0.0028443061746656895, -0.0003514725831337273, -0.026232179254293442, -0.02926551178097725, 0.06066984310746193, 0.0730263888835907, 0.03043375350534916, 0.010985680855810642, -0.024367231875658035, -0.0024712670128792524, 0.05033392459154129, 0.0767374336719513, 0.015521813184022903, 0.06732553988695145, -0.007521516177803278, 0.021547088399529457, -0.08448579162359238, 0.049107909202575684, 0.02500947192311287, 0.00186544144526124, 0.07801327854394913, -0.011196860112249851, -0.017092151567339897, 0.057901158928871155, -0.033953916281461716, -0.0468159094452858, -0.008520679548382759, 0.0027333342004567385, -0.006252873223274946, 0.00027323010726831853, 0.011178151704370975, 0.061912354081869125, 0.04953618720173836, -0.011312664486467838, 0.01926121488213539, 0.03868580609560013, -0.002430821768939495, -0.0012529134983196855, -0.025301871821284294, -0.004458801820874214, 0.0356542207300663, -0.010313563048839569, 0.007534915115684271, -0.01425801869481802, -0.007393610663712025, -0.006834884639829397, -0.003361743874847889, 0.02944980561733246, -0.007685488555580378, -0.027638746425509453, 0.026732802391052246, 0.031114522367715836, 0.01454741507768631, 0.022181876003742218, -0.0017993398942053318, 0.002348195295780897, 0.0079279700294137, -0.05131570249795914, 0.00078785908408463, -0.011547968722879887, -0.0254390649497509, 0.023832617327570915, -0.0051531074568629265, -0.04992862790822983, -0.04107334837317467, -0.009331932291388512, 0.014179253950715065, -0.07016975432634354, 0.04622497037053108, -0.003557705320417881, -0.05818639695644379, -0.04431048035621643, 0.04381623491644859, 0.010962538421154022, 0.06044691801071167, -0.05734557285904884, 0.03386896476149559, 0.025536732748150826, 0.026545077562332153, -0.06402374804019928, -0.036257434636354446, 0.005127090960741043, -0.005648230668157339, 0.08120303601026535, -0.009791738353669643, -0.020593946799635887, -0.018212758004665375, 0.06238877400755882, 0.010496375150978565, 0.01775605045258999, 0.05198550596833229, -0.037984732538461685, -0.0383903831243515, -0.005746480077505112, -0.009088005870580673, 0.032914623618125916, -0.0360867902636528, -0.04487202316522598, -0.015352810733020306, -0.031851429492235184, -0.025002464652061462, 0.024010280147194862, 0.023206640034914017, -0.0633382797241211, 0.06398040801286697, -0.016552144661545753, -0.0388215146958828, 0.07506832480430603, -0.02484000101685524, 0.054513588547706604, -0.01381834875792265, 0.01657005399465561, 0.05051042139530182, 0.03875294327735901, 0.021601077169179916, 0.06491454690694809, 0.05518967658281326, 0.008202101103961468, -0.0021774033084511757, 0.07331368327140808, -0.05949605256319046, 0.03728005290031433, -0.0224921852350235, 0.0014681146712973714, -0.051507916301488876, -0.00987483561038971, 0.009514185599982738, -0.034260351210832596, 0.10371148586273193, 0.02759723924100399, -0.04252765327692032, -0.006902419030666351, 0.06060599908232689, -0.017668116837739944, -0.026052847504615784, 0.05783610790967941, 0.023428795859217644, 0.0028644297271966934, -0.00796584878116846, -0.024112218990921974, 0.07713324576616287, -0.004104841034859419, -0.008812382817268372, 0.019177597016096115, 0.0009901991579681635, 0.027185164391994476, -0.03292597457766533, -0.03084835223853588, 0.035800788551568985, 0.0216408371925354, -0.04920927435159683, -0.016223840415477753, -0.06099589169025421, 0.033204302191734314, 0.07279693335294724, 0.0325019545853138, 0.05190392583608627, 0.08249343186616898, 0.019150948151946068, 0.031590785831213, 0.00751484977081418, 0.03352580592036247, -0.03466325253248215, -0.014467529021203518, -0.03597268462181091, -0.00609974330291152, 0.02169317565858364, 0.01783972978591919, 0.0017674061236903071, -0.054875269532203674, 0.01282313372939825, -0.04115002602338791, 0.03461833670735359, -0.01796458102762699, -0.00561321759596467, 0.007551365066319704, 0.09397529065608978, 0.0012464248575270176, 0.04761229828000069, -0.07971131801605225, -0.0016853257548063993, -0.06111888214945793, -0.0025118477642536163, -0.10190607607364655, -0.00707643385976553, -0.0322008915245533, -0.013454439118504524, 0.00877146702259779, 0.04564117640256882, -0.04300485551357269, -0.04701853543519974, 0.002528238808736205, -0.003924666438251734, -0.007776506245136261, 0.014120795764029026, 0.02665221132338047, 0.06942041218280792, 0.008292662911117077, 0.004906953778117895, 0.01763678528368473, -0.006117847748100758, -0.05342639610171318, 0.02634909749031067, -0.0280216746032238, 0.039007849991321564, -0.08485729992389679, 0.03629522770643234, 0.006055227480828762, -0.028749514371156693, -0.024561520665884018, -0.02200762927532196, 0.011463960632681847, -0.04137632995843887, 0.026037221774458885, 0.0487246960401535, 0.027248701080679893, 0.001699519925750792, -0.022055169567465782, -0.025951480492949486, -0.035486213862895966, -0.0032638751436024904, 0.04507189989089966, -0.024190017953515053, -0.032849881798028946, 0.05634171515703201, 0.008169264532625675, -0.007798183709383011, 0.03906479850411415, -0.10185781866312027, 0.01605074107646942, -0.009913635440170765, 0.004812014754861593, -0.008628914132714272, -0.0456087701022625, -0.03725093975663185, 0.04083408787846565, 0.02497236244380474, -0.04421567544341087, -0.07110341638326645, 0.07008004188537598, 0.010180962271988392, 0.012001289054751396, -0.029964720830321312, -0.037318598479032516, 0.019203364849090576, -0.017794262617826462, 0.00533352792263031, -0.04216563701629639, 0.0007977079367265105, 0.04568760097026825, -0.03429471701383591, -0.03945273533463478, 0.03925648331642151, -0.004621397238224745, -0.01844152994453907, -0.03658942133188248, -0.033540915697813034, -0.013401015661656857, -0.02088310942053795, 0.016789603978395462, 0.00238512409850955, -0.04310142621397972, 0.029164355248212814, 0.005541698075830936, 0.047142066061496735, -0.004983088467270136, 0.005555195268243551, 0.0019236658699810505, -0.027549181133508682, 0.007164097391068935, 0.004680122714489698, 0.022127343341708183, -0.05462893471121788, -0.03540630266070366, -0.038324128836393356, 0.06295789778232574, 0.022999681532382965, 0.022274097427725792, 0.06430430710315704, -0.01754174940288067, -0.026652997359633446, -0.009399747475981712, -0.020077627152204514, 0.006469658575952053, 0.012488031759858131, 0.032662443816661835, 0.01880870759487152, -0.050084188580513, -0.019967269152402878, 0.0020055421628057957, 0.004150030203163624, 0.000026539413738646545, -0.002250890014693141, 0.030147943645715714, -0.047240085899829865, -0.03763148933649063, 0.03558071702718735, 0.0012306601274758577, 0.003230297239497304, -0.04103025794029236, 0.04208992421627045, -0.015054688788950443, -0.017382405698299408, -0.04991788789629936, 0.01429850235581398, -0.0037785463500767946, 0.024123867973685265, -0.0771990716457367, -0.03068174608051777, 0.03858538344502449, -0.025442371144890785, 0.029525674879550934, 0.036981116980314255, -0.014454195275902748, -0.03159285709261894, 0.039998650550842285, -0.039120908826589584, -0.07433988153934479, -0.027147287502884865, 0.030582059174776077, 0.016680248081684113, -0.03645525500178337, -0.03499595448374748, -0.011654376052320004, -0.011993191204965115, 0.04232235997915268, -0.02057790383696556, -0.045739784836769104, -0.031523097306489944, -0.014039003290235996, 0.01811368763446808, -0.01387648656964302, -0.017018385231494904, -0.014374405145645142, -0.02806270308792591, 0.089528888463974, 0.029039844870567322, 0.03352013975381851, -0.05686818063259125, -0.056581344455480576, -0.0013643010752275586, 0.05039236322045326, 0.013398264534771442, 0.011597138829529285, -0.04728620499372482, -0.056293126195669174, 0.05961829051375389, -0.017151884734630585, -0.022250598296523094, 0.011632326059043407, -0.025879789143800735, 0.003608678700402379, 0.07976754754781723, -0.002577169332653284, -0.016587311401963234, -0.02085031569004059, -0.023309973999857903, 0.012664835900068283, -0.021165253594517708, 0.07313244789838791, -0.027943890541791916, -0.029506271705031395, -0.04993365332484245, 0.00003098158413195051, -0.04909747466444969, 0.026300981640815735, -0.07805660367012024, -0.023252315819263458, -0.05037229508161545, 0.053077589720487595, -0.041394639760255814, -0.03243852034211159, 0.006268851459026337, -0.01274404302239418, -0.014940227381885052, -0.03446682170033455, -0.019944217056035995, -0.03595331311225891, 0.06803932785987854, 0.03944621980190277, -0.00968882068991661, 0.062072284519672394, 0.006110161542892456, 0.017215512692928314, 0.004271392710506916, -0.01827230490744114, 0.058662597090005875, -0.04764007404446602, -0.027897946536540985, -0.015677912160754204, -0.05395141616463661, -0.015595948323607445, -0.03845001384615898, 0.04384027048945427, 0.017741672694683075, -0.011836393736302853, 0.07496503740549088, -0.00526113947853446, 0.034058503806591034, -0.0483885332942009, -0.0006076193531043828, 0.02282489649951458, -0.03217858076095581, -0.0281976405531168, -0.030883587896823883, 0.01425476185977459, -0.031365107744932175, 0.011686165817081928, -0.04096110910177231, 0.04572403430938721, 0.020229849964380264, 0.04776310548186302, 0.06733463704586029, 0.005153734236955643, -0.008220254443585873, -0.036694712936878204, -0.052813805639743805, -0.020144136622548103, 0.030484221875667572, -0.030848579481244087, 0.035281937569379807, -0.1130511537194252, -0.032434333115816116, 0.0768885463476181, -0.000887373520527035, 0.02862424962222576, -0.03845438361167908, 0.00925509724766016, 0.011795242317020893, 0.001370284124277532, -0.036817554384469986, 0.03570585325360298, -0.01751961000263691, -0.02299145981669426, -0.012056662701070309, -0.024664385244250298, 0.07606132328510284, -0.0499119833111763, -0.009182478301227093, 0.05088328570127487, 0.024289967492222786, 0.003880764590576291, 0.018241126090288162, 0.08253507316112518, 0.029747067019343376, 0.02261565811932087, -0.05032998323440552, 0.05530614033341408, 0.01308275293558836, 0.03756050765514374, 0.031472284346818924, 0.04511919617652893, 0.05228477716445923, 0.009992008097469807, -0.039693038910627365, -0.07146468758583069, 0.04490799456834793, 0.025325465947389603, 0.07356621325016022, 0.06527279317378998, 0.004892969503998756, -0.03746632859110832, -0.021357176825404167, 0.030316583812236786, -0.04022740572690964, -0.018979592248797417, -0.023896245285868645, 0.043295200914144516, 0.00690750265493989, -0.09617893397808075, 0.017070604488253593, -0.09077505767345428, -0.0075437454506754875, 0.08449199050664902, 0.044392555952072144, 0.03763595595955849, -0.022769471630454063, 0.04042886942625046, -0.013310343027114868, 0.021851778030395508, -0.06077640876173973, 0.011674436740577221, 0.06084257736802101, -0.0260984655469656, -0.005081871058791876, -0.03183504194021225, 0.05708271265029907, 0.007772506680339575, -0.048580724745988846, 0.007753543555736542, 0.02439109981060028, 0.006825579330325127, 0.017131341621279716, 0.08267240226268768, 0.021820517256855965, -0.027004607021808624, -0.024086548015475273, -0.02046988345682621, 0.01303067710250616, 0.03152303770184517, -0.004707891959697008, -0.006027917377650738, -0.04686029255390167, -0.05411281809210777, -0.0003810859052464366, -0.040605973452329636, -0.050375133752822876, 0.028021976351737976, -0.027705591171979904, 0.021724959835410118, -0.0559796504676342, -0.02003146894276142, -0.022010257467627525, 0.0460306853055954, 0.030425770208239555, 0.013951645232737064, -0.006790872663259506, 0.09356553107500076, -0.010135599412024021, 0.004517028108239174, -0.003521790960803628, -0.006782932672649622, -0.01859312877058983, -0.04663979262113571, -0.03460865467786789, 0.01895071007311344, -0.02657627873122692, 0.02217676304280758, 0.0400804802775383, 0.049295857548713684, -0.00459249084815383, -0.032087888568639755, -0.012875624001026154, -0.015478274784982204, -0.004546867683529854, -0.0006138181779533625, -0.02522438019514084, -0.0039186738431453705, 0.032428525388240814, 0.014462023973464966, -0.06852511316537857, 0.0538676418364048, 0.014519475400447845, -0.02877258136868477, 0.0020728502422571182, 0.019144203513860703, 0.023821383714675903, -0.020309748128056526, 0.01010194793343544, 0.019140228629112244, 0.027081212028861046, -0.03130650147795677, 0.025072943419218063, -0.013520101085305214, 0.028176220133900642, -0.0012445892207324505, -0.02850218676030636, 0.03884606063365936, -0.024029888212680817, -0.02277546562254429, -0.014628848060965538, -0.0803200826048851, 0.00593587476760149, 0.011481785215437412, 0.018609875813126564, 0.04555780068039894, -0.018203336745500565, 0.004803614690899849, -0.03828498721122742, 0.017488153651356697, 0.03461379185318947, -0.006480784621089697, -0.006253744009882212, 0.05335201695561409, 0.0018939238507300615, -0.0032417236361652613, -0.020282451063394547, 0.018559863790869713, 0.004178653471171856, -0.05107729136943817, -0.02556759864091873, 0.008309180848300457, -0.02218823879957199, 0.005057632457464933, 0.012401752173900604, 0.015588815324008465, 0.035815127193927765, -0.05721835047006607, 0.010005975142121315, 0.0004807962104678154, -0.005464512854814529, 0.011011946946382523, 0.028629718348383904, -0.04696408286690712, -0.014085792936384678, 0.07330803573131561, 0.01546752080321312, -0.06923440098762512, -0.012597184628248215, 0.05798889324069023, 0.01708107255399227, -0.07385534048080444, -0.016693249344825745, 0.034075092524290085, 0.0056678070686757565, -0.005987234879285097, -0.010448669083416462, -0.013616017065942287, 0.01710030622780323, 0.007823444902896881, -0.03268604725599289, 0.004101351369172335, -0.012269416823983192, 0.0015198838664218783, -0.02721586264669895, -0.009981963783502579, 0.00145737174898386, 0.029642002657055855, 0.04528781771659851, -0.023239493370056152, -0.0005185076734051108, 0.007555140182375908, -0.02550313249230385, 0.017467422410845757, -0.008011979050934315, -0.010311407037079334, 0.004158006981015205, -0.004626308102160692, -0.029767654836177826, 0.01541788037866354, 0.017444178462028503, -0.025089750066399574, -0.024427345022559166, -0.005109538324177265, 0.04697945713996887, -0.0331660732626915, 0.012696604244410992, -0.017964057624340057, -0.02371910959482193, -0.003050548955798149, -0.06935735791921616, -0.018684763461351395, 0.06636705249547958, -0.024583620950579643, 0.05773022770881653, 0.04529381915926933, -0.05537257716059685, -0.0061050839722156525, 0.06984338909387589, -0.007710923440754414, -0.03652925789356232, 0.01423500943928957, 0.052532173693180084, -0.01234055869281292, -0.04613066464662552, 0.026481110602617264, -0.03874910995364189, 0.00645621120929718, -0.024775074794888496, -0.04656306654214859, -0.05866324156522751, -0.04468579962849617, -0.058533262461423874, 0.05119016021490097, -0.006734753493219614, -0.00009114551357924938, -0.053347039967775345, -0.001996137434616685, 0.05127454921603203, -0.0039589013904333115, 0.0616593137383461, 0.04420352727174759, -0.04509217292070389, 0.027657927945256233, 0.019779015332460403, 0.017385661602020264, -0.009851373732089996, 0.05208384245634079, -0.027249008417129517, -0.026770805940032005, -0.013579989783465862, -0.020572038367390633, 0.023417532444000244, -0.07470718771219254, 0.01741013303399086, -0.035073794424533844, -0.021000664681196213, -0.03625832125544548, -0.033524204045534134, -0.005065509118139744, -0.009983358904719353, 0.09027435630559921, 0.033599335700273514, -0.0013959616189822555, -0.014260465279221535, -0.015340370126068592, -0.018576795235276222, -0.029397767037153244, -0.05571644380688667, -0.011806118302047253, -0.01660817116498947, 0.056237172335386276, -0.019229315221309662, -0.005023713689297438, -0.01788749359548092, -0.021725451573729515, 0.08507978916168213, 0.025232167914509773, -0.07675033807754517, 0.017706720158457756, -0.026140226051211357, 0.03539394587278366, 0.04934556782245636, 0.02177921123802662, -0.019608626142144203, -0.03497092425823212, 0.026788828894495964, 0.07646022737026215, -0.04475502297282219, 0.009967201389372349, -0.010190833359956741 ]
<p>Is there any temperature dependence of relaxation time in impurity scattering of conducting electrons? It seems to me that there is none. But, some people claim that there is.</p> <p>So if you could explain, how temperature dependence comes into play if it does at all?</p>
g827
[ 0.027307387441396713, 0.02824956364929676, 0.02319273166358471, 0.008225880563259125, 0.016495143994688988, 0.05544167757034302, -0.025935107842087746, 0.01609024591743946, 0.01059300359338522, 0.05002094432711601, -0.04799336940050125, 0.04113402217626572, -0.03432828187942505, -0.03393704444169998, -0.002832900732755661, 0.023801399394869804, 0.08571527153253555, -0.037247296422719955, -0.005728893913328648, 0.043003108352422714, -0.03708317503333092, 0.000750838196836412, -0.0031590485014021397, -0.031763847917318344, 0.0070456392131745815, 0.0810244083404541, -0.0519629567861557, -0.006212601438164711, 0.026522835716605186, -0.037832848727703094, -0.01110922172665596, 0.017233557999134064, 0.007231995929032564, 0.04459279775619507, -0.0006218018243089318, -0.015946028754115105, 0.0050716944970190525, -0.005970893427729607, 0.03043949417769909, 0.0065001980401575565, -0.011074136011302471, -0.03725098446011543, 0.021866941824555397, -0.0015479588182643056, 0.014410083182156086, 0.019561907276511192, -0.04030804708600044, 0.0528060682117939, -0.049356333911418915, -0.048500027507543564, 0.008988629095256329, 0.061220694333314896, -0.009137940593063831, 0.00032560486579313874, 0.00931972824037075, -0.07365136593580246, 0.020226988941431046, 0.046448495239019394, 0.015561116859316826, 0.021653512492775917, 0.04449919983744621, 0.038945380598306656, -0.027022114023566246, -0.004560699220746756, 0.07150902599096298, 0.0077108717523515224, -0.011067429557442665, 0.017850033938884735, 0.019926300272345543, 0.02807777374982834, 0.0005803212989121675, -0.01091696135699749, -0.10318535566329956, -0.033426087349653244, 0.03628388047218323, -0.0408242903649807, -0.010821063071489334, -0.02187361940741539, 0.021609393879771233, 0.006054678466171026, -0.04139290750026703, 0.03297044336795807, -0.013446046970784664, 0.037808556109666824, -0.007550321985036135, -0.008965644985437393, 0.05604251101613045, 0.0004888185067102313, 0.02582465671002865, 0.0015595206059515476, -0.020181383937597275, -0.06199444457888603, 0.01730639860033989, 0.004209001548588276, 0.05496580898761749, 0.007138638757169247, -0.009576613083481789, 0.04276883974671364, -0.039845965802669525, 0.04872794449329376, -0.03371882811188698, -0.008817397989332676, 0.021295111626386642, 0.02258840762078762, -0.011287098750472069, 0.028025425970554352, -0.027029626071453094, -0.012558113783597946, 0.0018086497439071536, 0.017753444612026215, -0.02096189558506012, -0.041959114372730255, -0.03300198167562485, 0.01999904401600361, -0.024344639852643013, 0.05777730420231819, -0.04890427365899086, -0.07005823403596878, 0.029702402651309967, -0.05942627042531967, 0.027805432677268982, 0.011370600201189518, -0.01473985705524683, 0.007208231370896101, 0.009677990339696407, 0.014756573364138603, 0.008187348954379559, -0.002083282684907317, 0.007333723362535238, 0.0789063423871994, -0.044488634914159775, 0.022926997393369675, -0.047682952135801315, 0.02588229812681675, -0.042424723505973816, -0.021104777231812477, 0.04553191363811493, -0.02183103933930397, -0.012298135086894035, 0.016751041635870934, 0.027352001518011093, -0.039527636021375656, 0.006899837404489517, -0.04632946103811264, 0.0009223871165886521, -0.02344280108809471, -0.06677203625440598, -0.03312263265252113, 0.029702307656407356, 0.045201029628515244, -0.005792140960693359, 0.0017182460287585855, 0.07585298269987106, -0.07862195372581482, -0.027663985267281532, -0.04561663046479225, 0.03084011748433113, -0.022263964638113976, 0.05670842528343201, -0.002426769584417343, -0.018693674355745316, -0.02164708636701107, -0.016118744388222694, -0.024930136278271675, 0.010490871034562588, 0.011773984879255295, -0.00491182878613472, 0.043258726596832275, -0.003923298791050911, -0.05063319578766823, -0.04231337830424309, 0.0030951201915740967, 0.046775754541158676, -0.003566524712368846, -0.0025760161224752665, -0.0047867572866380215, 0.036569271236658096, 0.006306276191025972, 0.02134927548468113, -0.029786041006445885, -0.06527407467365265, 0.009709973819553852, -0.029381100088357925, -0.06282331049442291, 0.018221935257315636, 0.022779028862714767, -0.012362758629024029, -0.0008522903663106263, -0.032293688505887985, -0.041608959436416626, -0.026710547506809235, -0.10812682658433914, -0.017024267464876175, -0.01297830417752266, 0.018458297476172447, -0.020768992602825165, 0.037454988807439804, -0.019362809136509895, -0.06457605212926865, -0.000878856226336211, -0.049004632979631424, -0.04030107334256172, -0.0037279664538800716, -0.03551354631781578, 0.06224516034126282, 0.024406736716628075, -0.06978476047515869, -0.02265021577477455, 0.01659516431391239, -0.0004183315031696111, 0.013103964738547802, 0.03697163984179497, 0.06656203418970108, 0.03259385749697685, 0.04099449887871742, 0.026576964184641838, -0.008828219957649708, 0.010200757533311844, 0.0047142961993813515, 0.034034308046102524, 0.013340254314243793, -0.04037991911172867, 0.011601407080888748, -0.020101143047213554, -0.032289642840623856, -0.0010165348649024963, -0.0454937182366848, 0.0177649836987257, -0.04489455744624138, 0.048247288912534714, -0.03775430843234062, 0.0327264778316021, -0.06574563682079315, 0.013129313476383686, -0.004276889376342297, 0.053847283124923706, -0.012099129147827625, -0.05057814344763756, -0.029753731563687325, -0.004268850199878216, -0.05101902782917023, 0.057484615594148636, -0.01005952525883913, 0.09397555887699127, 0.022487595677375793, -0.07666248083114624, -0.015023506246507168, -0.026478003710508347, 0.01475613098591566, -0.05525434389710426, -0.010983533225953579, -0.011864817701280117, 0.015590319409966469, 0.005986609496176243, -0.04861826077103615, -0.028276527300477028, -0.023149168118834496, 0.008324116468429565, -0.007809107657521963, -0.026099056005477905, 0.012248072773218155, 0.060600075870752335, 0.00006250994192669168, -0.0000060646507336059585, -0.03752340003848076, 0.013927854597568512, -0.021410299465060234, 0.02200712263584137, -0.011144857853651047, 0.024408498778939247, -0.04183952510356903, 0.003777222242206335, 0.009578716941177845, 0.002052825875580311, 0.0018650287529453635, -0.04761442169547081, -0.026198718696832657, -0.007435068022459745, 0.0011490724282339215, -0.015279736369848251, 0.03606827184557915, -0.0411844477057457, -0.023398812860250473, 0.011486691422760487, 0.006235904525965452, -0.05074027553200722, 0.03143047168850899, 0.017287524417042732, -0.008192130364477634, -0.027266042307019234, 0.007241329178214073, -0.023196300491690636, 0.01477823406457901, -0.000036723828088724986, 0.0025343066081404686, 0.04886997118592262, 0.05791109427809715, -0.021605586633086205, -0.0313093475997448, 0.035089991986751556, 0.05618898570537567, -0.00010286787437507883, -0.0697098895907402, 0.0327671580016613, 0.08509737998247147, 0.051049571484327316, -0.0275435708463192, -0.023095082491636276, -0.05177268385887146, -0.04805087298154831, 0.012585502117872238, 0.05709477886557579, 0.04077425226569176, 0.0415910929441452, -0.02244502119719982, 0.023351548239588737, -0.10065336525440216, 0.028945043683052063, 0.049838338047266006, -0.07625415921211243, -0.01567440666258335, -0.006733604706823826, 0.033377476036548615, -0.025616686791181564, 0.008127194829285145, 0.02547597326338291, -0.010006731376051903, -0.008436440490186214, -0.04275168851017952, 0.01680948957800865, -0.0684472844004631, -0.018030740320682526, -0.03803688660264015, -0.013267213478684425, -0.01193239912390709, -0.00941170658916235, 0.06858772784471512, 0.03149932250380516, 0.02969815582036972, 0.06472030282020569, 0.01966315321624279, 0.007946014404296875, -0.06851766258478165, 0.07671023160219193, 0.019238067790865898, 0.022403432056307793, 0.012300578877329826, -0.036381758749485016, 0.04098010063171387, 0.008361064828932285, 0.053896255791187286, 0.05951177701354027, 0.011418810114264488, -0.002824686700478196, -0.08302176743745804, 0.05275104567408562, -0.059583038091659546, -0.018452024087309837, -0.03233440965414047, 0.02220763824880123, 0.01312932837754488, -0.012456627562642097, 0.02723948284983635, -0.06772740185260773, 0.014413844794034958, 0.04317847639322281, 0.0004960966762155294, 0.03148498758673668, 0.07540664821863174, -0.04876609146595001, -0.0698695257306099, 0.02358277700841427, -0.014267765916883945, 0.08422897011041641, 0.026797562837600708, 0.019437603652477264, 0.03919509798288345, 0.07584752887487411, 0.012246871367096901, 0.0072903260588645935, -0.07818564772605896, 0.0021455402020365, -0.010436643846333027, 0.044114213436841965, 0.0074550677090883255, -0.07342533767223358, -0.026800034567713737, -0.04036184027791023, -0.06892520189285278, -0.10370182245969772, 0.03972462937235832, 0.026320280507206917, 0.02121092937886715, 0.04044756293296814, 0.03910403326153755, -0.049574222415685654, 0.01956360600888729, -0.004148737993091345, 0.09140980243682861, -0.07403537631034851, -0.03161035105586052, -0.005868079606443644, 0.022337142378091812, -0.019682494923472404, -0.00858344230800867, 0.041644465178251266, 0.041572537273168564, -0.02183537185192108, -0.05037081614136696, -0.05628592148423195, -0.11336909234523773, -0.005189131014049053, -0.03925679996609688, 0.0318395160138607, 0.05580317974090576, -0.035934239625930786, -0.0015384092694148421, -0.029752353206276894, -0.03823944553732872, 0.004454851150512695, -0.007458094507455826, -0.007927007041871548, 0.026933031156659126, -0.04807179048657417, 0.011648338288068771, -0.003792255651205778, -0.0025763490702956915, 0.038089435547590256, -0.0037515254225581884, 0.00617219740524888, -0.006142605561763048, 0.005686857271939516, -0.05689886212348938, -0.039529960602521896, -0.030606407672166824, 0.0048413630574941635, 0.018770910799503326, 0.012985030189156532, -0.025801461189985275, 0.008168214932084084, 0.02091415971517563, -0.019555406644940376, 0.04901108518242836, 0.019207609817385674, -0.005810457747429609, -0.013188100419938564, -0.03535972535610199, 0.004924894776195288, 0.005420491565018892, -0.021718041971325874, -0.024888984858989716, 0.008893623948097229, -0.043347641825675964, -0.0525362528860569, -0.001959813991561532, -0.06472853571176529, 0.019793188199400902, 0.0650930404663086, 0.038642607629299164, 0.04294817894697189, -0.0657147765159607, -0.04343748837709427, 0.006930014584213495, 0.011040707118809223, -0.03566193953156471, -0.023494290187954903, 0.0690687894821167, 0.00853011291474104, -0.01882721669971943, 0.05277010798454285, -0.0056043965741992, 0.022734863683581352, 0.050324760377407074, 0.05320293828845024, 0.0785616934299469, -0.02246769517660141, -0.029874349012970924, -0.002523107221350074, -0.008190284483134747, -0.053509943187236786, -0.03602989763021469, -0.040073830634355545, 0.020778564736247063, -0.015558802522718906, -0.005914841778576374, 0.009445665404200554, -0.0038094106130301952, 0.008408323861658573, 0.030466735363006592, -0.06827645748853683, 0.025319337844848633, -0.03912468999624252, 0.04915337264537811, 0.001843306585215032, -0.02200116589665413, -0.007569003850221634, 0.02406136691570282, 0.033354729413986206, -0.018730582669377327, 0.03676849231123924, 0.07222621142864227, -0.0022665702272206545, 0.018899310380220413, 0.00916663184762001, -0.030275214463472366, 0.023486725986003876, 0.02687087655067444, -0.08785630762577057, -0.07054801285266876, -0.026696521788835526, -0.015515374951064587, 0.03301771357655525, 0.04056383669376373, 0.014976522885262966, 0.025825856253504753, -0.013693410903215408, -0.06941801309585571, -0.01514420099556446, 0.0051987068727612495, 0.03294109180569649, 0.02850162424147129, 0.011948605999350548, -0.0061441645957529545, 0.03203413262963295, 0.000912435061763972, 0.02360798418521881, -0.02523009106516838, -0.04512501507997513, 0.07022381573915482, -0.025655332952737808, 0.05795035511255264, 0.01730409637093544, 0.002385280793532729, -0.0342186763882637, -0.014435057528316975, -0.011156847700476646, -0.008681880310177803, 0.026636341586709023, -0.06123966723680496, 0.030772633850574493, 0.007344708312302828, 0.020883016288280487, 0.05953408405184746, -0.004534794483333826, 0.03695464879274368, -0.02344607003033161, -0.005047199781984091, -0.035493869334459305, 0.04630830138921738, 0.009014674462378025, -0.0200253427028656, -0.01772555708885193, -0.028462357819080353, -0.03447350859642029, 0.04166112095117569, 0.04997938871383667, 0.029615214094519615, 0.03185785561800003, -0.019391978159546852, 0.027095166966319084, 0.014670225791633129, 0.017937593162059784, -0.04563141241669655, 0.03238863870501518, 0.028887953609228134, 0.01646873541176319, -0.036808911710977554, 0.054352857172489166, 0.02760358713567257, 0.0004368589143268764, -0.015742534771561623, 0.00328471465036273, -0.010207030922174454, -0.044378116726875305, -0.013548163697123528, 0.009830198250710964, -0.0018910894868895411, -0.08126114308834076, -0.016008762642741203, -0.06455130130052567, 0.014511274173855782, 0.0032068302389234304, 0.024274734780192375, 0.05295438691973686, 0.004756671376526356, 0.03524719551205635, 0.040058303624391556, -0.01961536332964897, 0.05929303541779518, -0.016404980793595314, -0.02930191531777382, 0.02548605389893055, 0.06494122743606567, -0.0483926385641098, -0.01370741706341505, 0.0032581679988652468, -0.025155672803521156, -0.008154713548719883, -0.042684804648160934, 0.04064733162522316, 0.04063821956515312, -0.0011861183447763324, -0.0031348371412605047, 0.03248364478349686, 0.0281778983771801, 0.012822538614273071, 0.04868798330426216, 0.022287320345640182, 0.05507617071270943, 0.07657641172409058, 0.009784193709492683, 0.0047211782075464725, 0.030725080519914627, -0.008073640987277031, -0.025028424337506294, -0.031752459704875946, -0.030208416283130646, 0.0872817412018776, -0.04580919072031975, -0.018871041014790535, -0.03109040856361389, -0.006379995495080948, -0.05181393027305603, 0.022513272240757942, -0.06245715543627739, 0.039864711463451385, -0.011467867530882359, -0.020540079101920128, 0.03581155836582184, -0.04929136112332344, -0.009010914713144302, -0.004118815530091524, 0.00922907330095768, 0.0329764261841774, 0.03253835067152977, -0.056373871862888336, -0.0034285350702703, -0.007027890533208847, -0.04323585703969002, 0.036817047744989395, 0.01715376228094101, -0.028487730771303177, 0.004278016742318869, -0.0031122290529310703, -0.029058940708637238, -0.00028281882987357676, 0.02508699521422386, 0.042885225266218185, -0.05460553988814354, -0.006898551248013973, 0.025098517537117004, 0.026110563427209854, 0.0038559087552130222, 0.01484241895377636, 0.07094324380159378, -0.07966302335262299, -0.023101845756173134, 0.01004072930663824, -0.013416928239166737, 0.022897515445947647, -0.06659869104623795, -0.014284834265708923, -0.03116564080119133, 0.04845047369599342, 0.06390418857336044, 0.0239059180021286, -0.005126843694597483, -0.06810854375362396, -0.0182171817868948, -0.00010081766231451184, -0.0072949850000441074, -0.049716606736183167, 0.05252714455127716, -0.049626290798187256, 0.010301339440047741, -0.009621135890483856, -0.02157382294535637, -0.0016597582725808024, -0.024617092683911324, 0.026680322363972664, -0.005394575651735067, 0.008960818871855736, 0.0017513837665319443, -0.011817515827715397, -0.011749076656997204, 0.06372105330228806, -0.020215721800923347, -0.06063398718833923, 0.039327386766672134, -0.03195396810770035, 0.0008871706668287516, 0.01614624820649624, 0.025413012132048607, 0.013943509198725224, -0.001361348549835384, 0.010627523064613342, 0.058787956833839417, 0.0004632197960745543, 0.06037410721182823, -0.02718711458146572, 0.026512788608670235, -0.019065776839852333, 0.06769488751888275, -0.009202321991324425, 0.021979695186018944, -0.045332975685596466, -0.0262345802038908, -0.04341236501932144, -0.0667252391576767, -0.027443571016192436, 0.07031217217445374, 0.008555631153285503, 0.010829634964466095, 0.008243858814239502, 0.001256804447621107, -0.04615456983447075, 0.003953360486775637, 0.0024445566814392805, 0.012955714017152786, 0.031195832416415215, 0.09263180196285248, -0.025354593992233276, 0.08584968745708466, -0.019963612779974937, 0.019439538940787315, -0.023023128509521484, 0.028229130432009697, -0.0014528633328154683, 0.05517054721713066, -0.0219944529235363, 0.05531136319041252, 0.005713991820812225, 0.0016538914060220122, 0.0028288117609918118, 0.02212178148329258, 0.04430714249610901, 0.038338057696819305, 0.00007996319618541747, 0.05820753797888756, 0.0010098026832565665, 0.020340830087661743, 0.009270742535591125, -0.03009091131389141, -0.0033165928907692432, -0.03356699272990227, -0.028380440548062325, -0.02976062521338463, -0.008013958111405373, 0.014921997673809528, 0.024470223113894463, -0.06950359791517258, -0.030248070135712624, -0.07723985612392426, 0.06024303287267685, -0.006615196820348501, -0.042422376573085785, 0.02467370219528675, 0.00031496098381467164, 0.009491238743066788, 0.03069344162940979, -0.027722693979740143, -0.004317741375416517, 0.006878141779452562, 0.03505953028798103, -0.014215326867997646, -0.058260418474674225, 0.005537594202905893, -0.033507850021123886 ]
<p>The problem I am working on is:</p> <blockquote> <p><em>Big Ben, the Parliament tower clock in London, has an hour hand 2.70 m long with a mass of 300 kg, and a minute hand 4.20 m long with a mass of 100 kg (see figure below). Calculate the total rotational kinetic energy of the two hands about the axis of rotation. (You may model the hands as long, thin rods rotated about one end. Assume the hour and minute hands are rotating at a constant rate of one revolution per 12 hours and 60 minutes, respectively.)</em></p> </blockquote> <p>(Converted) Angular Speed of Clock Hands:</p> <p>Hour Hand $1.45\cdot10^{-4}~rad/s$</p> <p>Minute Hand $1.75\cdot10^{-3}~rad/s$</p> <p>Rotational Moment of Inertia:</p> <p>Hour Hand $I=1/3(300~kg)(2.70~m)^2=729~kg\cdot m^2$</p> <p>Minute Hand $I=1/3(100~kg)(4.20~m)^2=243~kg\cdot m^2$</p> <p>Rotational Kinetic Energy:</p> <p>$K_{rot}=1/2(729~kg\cdot m^2)(1.45\cdot10^{-4}~rad/s)^2+1/2(243~kg\cdot m^2)(1.75\cdot10^{-3}~rad/s)^2$</p> <p>When I calculate this, it comes out incorrect, what has happened?</p>
g1576
[ 0.0799107551574707, -0.00448117358610034, -0.00014612531231250614, -0.03567558154463768, 0.02701607532799244, -0.004383025225251913, 0.040722060948610306, 0.042208217084407806, -0.04917534068226814, 0.019267244264483452, 0.012900498695671558, 0.023659465834498405, -0.038126666098833084, -0.05035965517163277, 0.0646321251988411, -0.0006008090567775071, 0.1040143147110939, 0.023922132328152657, 0.024467067793011665, 0.09578674286603928, 0.007544333580881357, 0.010810468345880508, -0.04908006638288498, -0.04484880343079567, 0.027361225336790085, -0.04083653911948204, -0.025427130982279778, 0.0042235273867845535, -0.07230010628700256, -0.01679958961904049, -0.024027051404118538, 0.04213050380349159, -0.014618500135838985, -0.035888154059648514, 0.016128674149513245, -0.007116558495908976, 0.032263919711112976, -0.035369761288166046, -0.026615817099809647, -0.019953841343522072, 0.022872405126690865, 0.0047919792123138905, 0.002338916528970003, 0.00564022408798337, -0.006841533351689577, -0.01781887374818325, 0.036429643630981445, 0.05203043296933174, -0.01784713752567768, 0.01742308959364891, 0.004754167515784502, 0.01952425017952919, 0.0515531562268734, -0.016523482277989388, -0.0386701375246048, 0.07128444314002991, 0.01228972990065813, -0.033052731305360794, 0.046717576682567596, 0.10896466672420502, 0.035103876143693924, -0.09668295830488205, -0.018760133534669876, -0.013349375687539577, -0.004816373810172081, -0.03194768354296684, 0.04483037441968918, -0.013071293942630291, 0.00244475738145411, -0.025986002758145332, -0.015773380175232887, -0.05248568579554558, 0.04773604869842529, -0.0007390485843643546, -0.02973899245262146, 0.003534403396770358, 0.01636148802936077, -0.02300606295466423, -0.04678148031234741, 0.004589574411511421, -0.08993888646364212, 0.04960814490914345, 0.027778731659054756, 0.021025244146585464, 0.02483706921339035, -0.0031566000543534756, -0.020504668354988098, 0.050817593932151794, -0.00848254095762968, 0.04842451214790344, 0.04624057561159134, -0.020213250070810318, 0.08619039505720139, -0.005425161216408014, -0.011587509885430336, -0.009042412042617798, -0.06933323293924332, 0.09594845026731491, 0.010268989019095898, 0.023836182430386543, -0.018194880336523056, -0.0015768171288073063, -0.0210124421864748, -0.0033601289615035057, 0.052468303591012955, -0.003053383668884635, -0.007857254706323147, -0.015226170420646667, -0.12607647478580475, -0.024246646091341972, 0.0019056436140090227, -0.07148310542106628, 0.004026297014206648, -0.04916374012827873, -0.008951209485530853, -0.03087126463651657, 0.09582162648439407, -0.018920885398983955, 0.02146090753376484, 0.004840823821723461, -0.014799637719988823, -0.020732641220092773, -0.048092782497406006, 0.038659971207380295, -0.0359705351293087, -0.01050009299069643, -0.04152148589491844, -0.008795478381216526, 0.0860695093870163, -0.03762992098927498, -0.001587822218425572, 0.0319775752723217, 0.024826694279909134, 0.002356930635869503, 0.018561571836471558, 0.011125587858259678, -0.039313096553087234, -0.025294657796621323, 0.020824585109949112, 0.016206061467528343, 0.0063285231590271, -0.05056077614426613, 0.04082528501749039, 0.0160770695656538, -0.010937241837382317, 0.06155865266919136, 0.00818219780921936, -0.03301653638482094, 0.03100758232176304, 0.045001182705163956, -0.01267711166292429, 0.04123556986451149, -0.014646284282207489, -0.02608383260667324, 0.05243181437253952, 0.02343153767287731, 0.018548738211393356, 0.006026749964803457, 0.001218529068864882, 0.03169604390859604, 0.045561473816633224, -0.014754395000636578, 0.04629049077630043, -0.019297076389193535, 0.015348928049206734, 0.0358477458357811, 0.013910084031522274, -0.04425903782248497, -0.018051540479063988, -0.01261433120816946, -0.045482784509658813, -0.027666587382555008, 0.04444045200943947, -0.003996682818979025, -0.005504559725522995, 0.0699564516544342, 0.03815717250108719, -0.013639084994792938, -0.041360631585121155, -0.0368538498878479, 0.03285234794020653, -0.02176988683640957, 0.03581373393535614, -0.024946628138422966, 0.0013791319215670228, -0.013943295925855637, 0.0315859280526638, 0.027627989649772644, -0.08746637403964996, -0.03060927614569664, -0.011266623623669147, 0.028098614886403084, 0.011096584610641003, -0.014826793223619461, -0.019194746389985085, 0.07123535871505737, 0.04517751187086105, -0.039973579347133636, 0.0025110961869359016, 0.06455198675394058, 0.006132768467068672, -0.011439500376582146, 0.0646376982331276, 0.0033271340653300285, 0.0023823080118745565, 0.0028307742904871702, 0.003206922672688961, -0.006066203583031893, 0.01913478597998619, -0.019064728170633316, -0.016186608001589775, 0.048414360731840134, -0.05200847610831261, 0.03315114602446556, 0.00688658794388175, 0.0021923789754509926, 0.007288714405149221, -0.003931841813027859, -0.07772128283977509, -0.00863397866487503, -0.002414196263998747, -0.015326390042901039, -0.0036121471785008907, -0.001966827316209674, 0.012276466004550457, -0.006115023046731949, -0.0376269668340683, 0.026455307379364967, -0.005932978820055723, -0.015434499830007553, -0.020488662645220757, 0.06502850353717804, -0.05353269726037979, 0.026906348764896393, 0.050454992800951004, 0.04263772815465927, -0.03418530896306038, 0.019248589873313904, 0.034802697598934174, 0.009771814569830894, 0.036207444965839386, 0.03248104453086853, -0.009459360502660275, -0.04489453509449959, 0.011875963769853115, 0.003692477010190487, 0.060771241784095764, -0.030018262565135956, 0.03520435467362404, 0.04363275691866875, -0.01790650561451912, -0.011784563772380352, -0.052021708339452744, -0.022664621472358704, -0.003365551121532917, 0.016301337629556656, -0.044950369745492935, 0.0217302143573761, -0.05433210730552673, -0.009695680812001228, -0.0051553500816226006, 0.028347047045826912, 0.019503135234117508, 0.03245220705866814, -0.045514918863773346, -0.043825600296258926, -0.04609529301524162, 0.03720324859023094, 0.0308037381619215, 0.007538138423115015, -0.014572246931493282, 0.06952253729104996, 0.016464725136756897, 0.07795829325914383, 0.0006475465488620102, -0.09131529927253723, 0.013904684223234653, -0.025273052975535393, -0.008615023456513882, 0.01053945068269968, 0.0072951908223330975, -0.012997354380786419, -0.055832065641880035, 0.04300647974014282, 0.03911890462040901, -0.026158345863223076, -0.05009341612458229, 0.04776414483785629, 0.011876523494720459, -0.002290656790137291, -0.0389576256275177, 0.10103755444288254, 0.045289963483810425, -0.03087521158158779, -0.009342316538095474, 0.06473326683044434, 0.03718721121549606, -0.06446211040019989, -0.041322972625494, -0.008465774357318878, 0.023847144097089767, -0.060515422374010086, 0.006423209328204393, 0.07301146537065506, -0.00562042323872447, 0.007278783712536097, -0.03551618382334709, -0.05215618014335632, 0.023831689730286598, -0.008221867494285107, -0.05215573310852051, 0.01353253424167633, -0.01979728229343891, -0.0075312103144824505, -0.006284345407038927, -0.0012325552524998784, -0.02730010449886322, -0.01345200277864933, 0.0028717268723994493, 0.04480234906077385, -0.008524301461875439, -0.021045973524451256, 0.007749502547085285, -0.012846571393311024, 0.024941112846136093, -0.01926174759864807, -0.04932854697108269, -0.008125925436615944, -0.0045014931820333, -0.03723383694887161, -0.011577922850847244, 0.07014808803796768, 0.00990124698728323, -0.0015478378627449274, -0.027561787515878677, -0.02974916249513626, -0.03494687378406525, 0.029439721256494522, 0.03462826460599899, 0.009471348486840725, -0.02802756056189537, 0.01060057245194912, -0.0591517798602581, -0.033622369170188904, 0.014270187355577946, 0.006966899614781141, -0.028780179098248482, -0.010286903008818626, 0.01161970105022192, -0.009431520476937294, 0.009344945661723614, 0.019746994599699974, -0.004800329450517893, -0.025792550295591354, 0.03063332848250866, 0.025501713156700134, -0.02791374921798706, 0.044862933456897736, -0.007635076995939016, 0.010324721224606037, 0.010891043581068516, -0.0044087739661335945, -0.012712092138826847, 0.00778561644256115, -0.026172678917646408, 0.030423631891608238, -0.0021703646052628756, 0.03272630646824837, 0.015562186017632484, -0.06074099987745285, -0.031504109501838684, 0.067580945789814, 0.013252059929072857, -0.08546087145805359, 0.06524769216775894, -0.05679445341229439, 0.037507519125938416, -0.01662234403192997, -0.02515009604394436, 0.019255921244621277, -0.01978633739054203, -0.03821854665875435, -0.06449443101882935, 0.002943249884992838, 0.02688366174697876, 0.019112946465611458, -0.025758501142263412, -0.009597690775990486, 0.053170476108789444, -0.02909165807068348, 0.04702049121260643, -0.013290038332343102, 0.00951378047466278, -0.04606108367443085, 0.013051698915660381, -0.06631500273942947, 0.047819096595048904, 0.014101407490670681, -0.007398147601634264, 0.0031208929140120745, -0.02668013982474804, 0.01930605247616768, -0.026232291013002396, -0.018798358738422394, 0.04405369237065315, 0.0710025504231453, 0.015439136885106564, -0.0008079041726887226, -0.015965912491083145, 0.04352361708879471, 0.00013597832003142685, 0.007250071037560701, 0.004998866934329271, -0.0909183993935585, 0.03264208137989044, 0.03134677931666374, 0.003937401343137026, -0.04069052264094353, 0.015198973938822746, 0.031112246215343475, -0.03787869215011597, 0.0640733540058136, 0.02730514667928219, -0.0523717999458313, 0.012860605493187904, 0.06676354259252548, 0.08247384428977966, 0.03229454532265663, 0.022268883883953094, -0.01766914315521717, 0.02498805522918701, 0.013241409324109554, -0.01653195172548294, -0.031139103695750237, -0.009741418063640594, 0.013759108260273933, 0.020088177174329758, 0.01846826635301113, 0.0383840948343277, 0.031098613515496254, 0.02586970292031765, 0.01726835034787655, 0.006190768908709288, 0.013623731210827827, -0.02821400761604309, 0.08855129033327103, -0.04871290177106857, -0.07687054574489594, -0.027533408254384995, -0.023416731506586075, -0.0094622652977705, 0.01119180303066969, -0.006961931008845568, 0.02755947969853878, -0.00916279386729002, -0.014316783286631107, -0.04840349778532982, 0.04276913031935692, -0.014618486166000366, 0.04603549465537071, -0.07242903113365173, 0.04167572781443596, -0.021110540255904198, -0.006610341370105743, -0.023561522364616394, -0.015165776945650578, 0.027429241687059402, 0.0014314706204459071, -0.023935649544000626, -0.037026092410087585, 0.00825774297118187, -0.025693697854876518, -0.010234944522380829, -0.000494760402943939, -0.022595280781388283, 0.03399120643734932, -0.005973747465759516, 0.03823691979050636, 0.03415742143988609, -0.03340039774775505, -0.05384525656700134, 0.002785701537504792, -0.02838624082505703, 0.08505331724882126, 0.0464293546974659, -0.017468055710196495, -0.012289467267692089, 0.014191457070410252, 0.04849489778280258, -0.020645931363105774, 0.029176907613873482, 0.03719170391559601, -0.01894790306687355, -0.06393628567457199, 0.00832116324454546, 0.05162687599658966, 0.03457113355398178, 0.012279825285077095, 0.009127090685069561, 0.006001460365951061, -0.052556112408638, 0.018025998026132584, -0.06103960797190666, 0.01563783548772335, -0.003296211361885071, 0.026870060712099075, -0.019020847976207733, 0.05512513965368271, -0.018287960439920425, 0.07408072054386139, -0.024663880467414856, 0.014212570153176785, 0.01608872599899769, 0.03440992906689644, -0.019795957952737808, -0.02742701955139637, 0.008113180287182331, -0.047955501824617386, 0.03835684061050415, -0.07240138947963715, 0.06147331744432449, 0.03804304078221321, 0.036143261939287186, -0.052986130118370056, -0.02824992872774601, 0.015357977710664272, -0.007753149140626192, -0.011621462181210518, -0.04784216731786728, 0.03921632841229439, -0.04168495908379555, -0.03578631952404976, -0.023189008235931396, -0.011210668832063675, -0.014058301225304604, 0.018466748297214508, 0.0004619500832632184, -0.07724037021398544, 0.008075821213424206, 0.022141074761748314, 0.025887466967105865, -0.006733486894518137, 0.013413684442639351, -0.0101454583927989, -0.02689949795603752, 0.004998598247766495, 0.010044356808066368, -0.022021977230906487, 0.04236001893877983, 0.03425068035721779, 0.03520633652806282, 0.06447416543960571, 0.044073741883039474, -0.028518961742520332, 0.0005732777644880116, 0.026158716529607773, 0.01040751114487648, -0.027349207550287247, -0.02363845333456993, 0.004194178618490696, 0.07910335063934326, 0.008146665059030056, 0.04935673996806145, 0.01740333065390587, 0.02829633466899395, -0.057170525193214417, -0.028469596058130264, -0.02339392527937889, 0.009784373454749584, -0.012415604665875435, -0.012211856432259083, 0.018070295453071594, -0.05230778083205223, -0.015356834977865219, 0.008879442699253559, 0.019396547228097916, -0.04955238848924637, -0.04564299434423447, -0.05637500807642937, -0.05352073162794113, -0.023078972473740578, 0.012858349829912186, -0.004720581695437431, -0.025215866044163704, -0.03376501798629761, -0.04282094165682793, 0.02020527608692646, -0.04164670407772064, 0.017883487045764923, 0.0015969506930559874, -0.029332170262932777, 0.012217340059578419, -0.05139955133199692, -0.06366944313049316, -0.03549335524439812, -0.06112924963235855, -0.009481659159064293, -0.025660503655672073, 0.008630265481770039, 0.0157203059643507, -0.0649079903960228, -0.03435533866286278, 0.06550988554954529, -0.02861960232257843, 0.019083697348833084, 0.014970104210078716, -0.049290210008621216, 0.018588965758681297, 0.007805480621755123, 0.06609920412302017, -0.03207679092884064, 0.00008948847971623763, -0.0157052930444479, 0.04548325017094612, -0.00792758259922266, 0.014451868832111359, 0.057760197669267654, 0.06883814930915833, -0.0052632964216172695, -0.0184797253459692, 0.03729918226599693, -0.024315956979990005, -0.023162677884101868, -0.06370861083269119, 0.015169622376561165, 0.021174738183617592, -0.1070316955447197, 0.03491995111107826, 0.03145229071378708, -0.04679933190345764, 0.04540063068270683, -0.044932808727025986, -0.018453003838658333, 0.06998928636312485, 0.03639096021652222, 0.04519510641694069, -0.06489884108304977, 0.04158477485179901, -0.023569650948047638, 0.04455031454563141, 0.02416752278804779, 0.0371372289955616, 0.013446700759232044, 0.02264169231057167, -0.04269766807556152, -0.061255235224962234, 0.05031130835413933, -0.015226487070322037, -0.04059327021241188, -0.023447901010513306, 0.024826042354106903, -0.04060191288590431, 0.014504920691251755, 0.04091028496623039, -0.05334973335266113, -0.06737713515758514, -0.00776910362765193, -0.0010071141878142953, 0.03585304692387581, -0.03426264226436615, -0.014101781882345676, -0.03185266628861427, -0.022145472466945648, -0.010790185071527958, -0.023649554699659348, 0.02235344983637333, -0.03155302256345749, -0.009456152096390724, 0.02578212320804596, -0.08341946452856064, -0.007001339457929134, 0.032639238983392715, -0.04596707224845886, 0.030055800452828407, 0.0075196451507508755, 0.03141990676522255, 0.014951398596167564, -0.03841368481516838, -0.010376153513789177, -0.05495152249932289, 0.010168042033910751, 0.05815478041768074, -0.06001989543437958, 0.04621068015694618, 0.007136923260986805, 0.02621225267648697, -0.024615725502371788, -0.006179946940392256, -0.006151678506284952, 0.03164265677332878, -0.007080940529704094, 0.09943107515573502, 0.04152027517557144, 0.004665990825742483, -0.03341399505734444, 0.011123198084533215, 0.04153518006205559, 0.018766093999147415, 0.04224667325615883, 0.019602790474891663, 0.02721666358411312, -0.007167842239141464, -0.0006220127106644213, 0.04247881472110748, 0.009135577827692032, 0.06666230410337448, 0.019595887511968613, -0.02838439866900444, -0.007667935453355312, 0.005389830097556114, 0.0039366018027067184, 0.009811495430767536, -0.003587398212403059, -0.05384339764714241, 0.03590273857116699, -0.027934672310948372, -0.09548555314540863, 0.002073541283607483, 0.05601665377616882, 0.018252087756991386, -0.04153001308441162, 0.009156865067780018, 0.025992680341005325, -0.07045187056064606, -0.035289421677589417, -0.034364692866802216, -0.002158698858693242, -0.030447201803326607, -0.037614524364471436, 0.00016174954362213612, -0.035955723375082016, 0.014286203309893608, -0.05713341012597084, 0.009193851612508297, -0.014495808631181717, -0.0083860969170928, 0.009966103360056877, -0.018339861184358597, 0.025421885773539543, 0.025222862139344215, 0.004200491588562727, -0.04046760872006416, -0.036275412887334824, -0.024861514568328857, -0.007839452475309372, -0.026026500388979912, -0.04821839928627014, -0.002326433779671788, 0.06299352645874023, 0.006886460352689028, 0.016078712418675423, 0.011087534949183464, -0.08461757749319077, -0.0027871967758983374, 0.03803177550435066, -0.01025468297302723, 0.038145460188388824, 0.021649658679962158, -0.031912580132484436, -0.017592541873455048, -0.030782056972384453, -0.0368063747882843, -0.0039778100326657295, -0.05698446184396744, 0.022424843162298203, -0.03636782988905907, -0.01966957375407219, 0.03270020708441734 ]
<p>I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable (self-adjoint operator) in quantum mechanics? </p> <p>E.g. an operator $A$ with the Hamiltonian $H$?</p>
g651
[ -0.01803760789334774, 0.009309487417340279, -0.002664918312802911, 0.016259774565696716, 0.05100636184215546, -0.015780486166477203, 0.01007404737174511, 0.021277502179145813, 0.0033444873988628387, 0.030980069190263748, -0.046681880950927734, 0.012001329101622105, 0.01471671275794506, 0.026054564863443375, -0.0004603572597261518, -0.0027413133066147566, 0.019303271546959877, 0.02165864408016205, 0.002924003405496478, -0.04742223769426346, -0.03024817630648613, 0.024132827296853065, 0.01963341422379017, -0.025847507640719414, 0.008143923245370388, -0.05349212512373924, 0.05894584581255913, -0.06059412285685539, -0.002709493972361088, -0.029238441959023476, 0.0717722624540329, -0.016166193410754204, 0.06667879968881607, -0.049992725253105164, -0.048058491200208664, -0.04405134171247482, 0.03370071202516556, -0.02898416481912136, 0.03832201659679413, 0.019994698464870453, 0.0285794660449028, 0.017631638795137405, 0.03151005506515503, -0.04116866737604141, 0.04035278037190437, -0.02966805174946785, 0.015870345756411552, 0.027358831837773323, 0.020925315096974373, -0.016778361052274704, 0.015603735111653805, 0.030481144785881042, 0.07320085167884827, 0.06448738276958466, 0.11199375987052917, -0.0010055695893242955, 0.06032079458236694, 0.04486854374408722, 0.02744084782898426, 0.016715358942747116, -0.013791249133646488, 0.031207116320729256, 0.030337171629071236, 0.07121653109788895, 0.07140093296766281, -0.00034285502624697983, 0.0031794984824955463, -0.020981190726161003, 0.009095690213143826, 0.04501457139849663, 0.00895681045949459, -0.017771480605006218, 0.012400195933878422, 0.012829262763261795, 0.03842340409755707, -0.014851505868136883, 0.05250336602330208, -0.028515631332993507, 0.039184048771858215, -0.033796340227127075, -0.03858325630426407, -0.05139971524477005, 0.04465547576546669, -0.01583969034254551, 0.038284532725811005, -0.045289427042007446, -0.031768616288900375, -0.0010045479284599423, -0.03138875961303711, 0.015392167493700981, 0.01552347932010889, 0.009304124861955643, 0.045065898448228836, 0.027111416682600975, -0.037238504737615585, -0.05532680079340935, -0.021238131448626518, 0.03858533129096031, -0.05539536848664284, -0.008971602655947208, -0.027342066168785095, 0.025415172800421715, 0.03512971103191376, -0.04078652337193489, 0.02801324613392353, 0.03115035593509674, -0.014944165013730526, -0.01561034470796585, -0.01982458308339119, 0.022064799442887306, -0.024915391579270363, 0.00840037502348423, -0.007531259208917618, -0.035861507058143616, 0.03391116484999657, -0.033979836851358414, -0.0021386942826211452, 0.020225459709763527, -0.007141198962926865, 0.006492573767900467, 0.03389221802353859, 0.05460754781961441, -0.024208614602684975, 0.04055415093898773, -0.025130076333880424, 0.005949206650257111, -0.013873054645955563, -0.029729507863521576, 0.014799707569181919, -0.013748198747634888, 0.05452772602438927, -0.02923133596777916, 0.01096740085631609, 0.03739864379167557, -0.02835579216480255, -0.018364092335104942, 0.022841254249215126, -0.026722321286797523, 0.03931437060236931, -0.0797688215970993, 0.06310348212718964, -0.021834049373865128, -0.02913055196404457, 0.007169461343437433, 0.040607765316963196, -0.04832012578845024, 0.02102670446038246, -0.03371081501245499, 0.03713642433285713, -0.0030628496315330267, 0.019068382680416107, 0.005375253036618233, 0.0001405321672791615, -0.04175829887390137, 0.0416715070605278, -0.01893068663775921, -0.02654184028506279, 0.014122694730758667, -0.0028598636854439974, -0.021268991753458977, 0.033008452504873276, 0.004737704526633024, 0.006315995007753372, 0.0009660432115197182, -0.029183631762862206, -0.03526097163558006, -0.016945861279964447, -0.026962805539369583, 0.0005645257188007236, -0.0015386217273771763, 0.004203389398753643, 0.006246617995202541, -0.022101808339357376, 0.037701211869716644, 0.026913262903690338, 0.05923609435558319, -0.01710343547165394, -0.01369605865329504, -0.05720479041337967, 0.0526573620736599, -0.04211800545454025, -0.012216768227517605, 0.012699127197265625, -0.05309973657131195, -0.0009417975670658052, 0.01781131699681282, -0.0009031337685883045, 0.0021021312568336725, -0.08689660578966141, 0.016890954226255417, -0.01039995439350605, -0.054082512855529785, 0.0031445911154150963, 0.020344076678156853, -0.02600613422691822, -0.004071196541190147, -0.06438582390546799, 0.0040387799963355064, 0.03207354247570038, -0.048419564962387085, 0.04029020667076111, 0.018327077850699425, 0.046492207795381546, 0.022197918966412544, 0.030383797362446785, 0.048980917781591415, -0.010405076667666435, 0.009591980837285519, 0.04093793407082558, -0.0025869649834930897, 0.05226302146911621, -0.020700884982943535, 0.06682495772838593, -0.05733786150813103, -0.009035530500113964, 0.008804515935480595, 0.03416621685028076, 0.02379414811730385, -0.03411296755075455, 0.016020826995372772, 0.06246424838900566, -0.024906599894165993, 0.03320680558681488, -0.02433423511683941, -0.05146302282810211, 0.01998010464012623, -0.053449563682079315, -0.028554152697324753, -0.01787503808736801, -0.01900409162044525, -0.001545655308291316, 0.015518018044531345, -0.008505325764417648, 0.011494720354676247, -0.027094533666968346, 0.08894744515419006, 0.03262195363640785, 0.05892452970147133, 0.012123001739382744, 0.014740088023245335, 0.009704732336103916, 0.010124375112354755, -0.02148546651005745, -0.004703217186033726, 0.06531013548374176, -0.001960748340934515, 0.05570890009403229, 0.022823328152298927, 0.004680574405938387, 0.01292582880705595, 0.020351648330688477, -0.04641179367899895, -0.0684945285320282, -0.0350668802857399, -0.02300385758280754, -0.02122490480542183, -0.01476368959993124, -0.015746021643280983, -0.0015159163158386946, 0.003382403403520584, 0.02885739877820015, -0.031180204823613167, 0.013107480481266975, 0.0251618679612875, -0.04116036742925644, -0.06691565364599228, -0.03965839743614197, 0.016255782917141914, 0.014393993653357029, -0.021871356293559074, -0.04879213497042656, 0.03137589991092682, -0.010533719323575497, -0.028701353818178177, -0.012946253642439842, -0.07325077056884766, -0.01899229921400547, -0.092253178358078, -0.0022975204046815634, -0.010147424414753914, -0.012013087049126625, 0.0741303414106369, -0.06728413701057434, 0.04400473088026047, 0.01135807204991579, -0.06636004894971848, 0.020426001399755478, 0.02614906057715416, -0.019998326897621155, -0.011786063201725483, 0.025002991780638695, 0.014244859106838703, 0.023285139352083206, 0.0649065151810646, -0.03731519728899002, 0.06857603043317795, 0.04822704941034317, 0.020937809720635414, 0.003992598969489336, 0.04886075109243393, -0.049789026379585266, 0.05158518627285957, 0.006755502428859472, 0.03062690608203411, 0.04329682141542435, 0.05244538187980652, -0.03852482885122299, -0.009147181175649166, -0.0707196369767189, 0.02420235611498356, -0.05227775126695633, -0.0008043205016292632, -0.006948612630367279, -0.04723169654607773, 0.05935991182923317, -0.01953251287341118, -0.07650554180145264, -0.02641797810792923, -0.005267868749797344, -0.09285525977611542, -0.055964089930057526, -0.014451398514211178, 0.003222138388082385, -0.016873814165592194, 0.041076816618442535, 0.018625089898705482, -0.0554451085627079, 0.036343079060316086, -0.02059873752295971, -0.061868708580732346, -0.03435068577528, -0.011194471269845963, -0.03928321972489357, 0.0015997268492355943, -0.07538231462240219, -0.030619895085692406, 0.027544669806957245, -0.021364783868193626, -0.025943724438548088, -0.006060290150344372, 0.03643173351883888, 0.02334430441260338, 0.005403772462159395, 0.032372042536735535, -0.005230139009654522, 0.0370950885117054, 0.01255208719521761, 0.020918194204568863, 0.02217239886522293, -0.023972144350409508, 0.02504042163491249, -0.002133772475644946, 0.09833201766014099, 0.011319968849420547, -0.02080557309091091, -0.025163082405924797, -0.014629477635025978, -0.007955080829560757, 0.024923047050833702, 0.019944090396165848, -0.059061892330646515, -0.023255959153175354, 0.03797614574432373, 0.04822881147265434, -0.03320017457008362, -0.014376813545823097, -0.03858710080385208, -0.0059200795367360115, 0.054979439824819565, -0.06061449646949768, -0.019656969234347343, -0.014564676210284233, -0.017851559445261955, -0.005707381758838892, 0.006378904450684786, -0.04385833442211151, 0.05682351440191269, 0.020842140540480614, 0.017255226150155067, 0.01165736373513937, 0.0049462891183793545, 0.12008621543645859, 0.017059391364455223, -0.02088300511240959, 0.07545538991689682, -0.011995545588433743, 0.019955525174736977, 0.013207533396780491, -0.025164559483528137, -0.07976513355970383, 0.021505126729607582, 0.02737453393638134, 0.0239412784576416, 0.002618196187540889, 0.05690019577741623, 0.016363482922315598, -0.003733985358849168, 0.02777026779949665, 0.07332763075828552, 0.03597036004066467, -0.0037125656381249428, 0.009211456403136253, -0.015607070177793503, 0.010325086303055286, -0.006697081029415131, -0.060834065079689026, 0.05737326294183731, 0.018614988774061203, -0.007894091308116913, -0.0076561588793993, -0.04722875729203224, 0.024957356974482536, -0.02540421113371849, -0.0314483642578125, -0.04743165895342827, 0.055871009826660156, -0.048530153930187225, -0.009067125618457794, -0.011218104511499405, -0.007882906123995781, -0.029019270092248917, 0.0239900890737772, 0.06677798181772232, 0.005300511606037617, -0.036000169813632965, 0.015821736305952072, 0.03387293219566345, -0.031972289085388184, -0.05615566298365593, -0.06655429303646088, -0.0052209412679076195, 0.031164074316620827, -0.011195301078259945, -0.010774020105600357, -0.03546277806162834, -0.003039797767996788, -0.03402460366487503, 0.03983180597424507, -0.013572867959737778, 0.005032384768128395, 0.06366398185491562, -0.019129257649183273, -0.015564581379294395, 0.004833178129047155, 0.022819465026259422, 0.01567739062011242, -0.04878434166312218, -0.05026749521493912, -0.04740920290350914, -0.025908183306455612, -0.010147479362785816, 0.05304386094212532, 0.004557210020720959, -0.0665632113814354, -0.060157660394907, -0.05171347036957741, -0.01775326579809189, 0.001853780122473836, -0.015456429682672024, -0.02406330220401287, -0.03563794866204262, -0.035323187708854675, 0.06436554342508316, -0.008985091000795364, -0.012688249349594116, -0.000633260584436357, -0.0914732962846756, 0.02773093618452549, -0.08763570338487625, 0.009848320856690407, -0.016048578545451164, 0.022155137732625008, -0.002490451093763113, 0.03878949210047722, 0.011149845086038113, -0.047435034066438675, 0.010489466600120068, -0.052552394568920135, -0.017132673412561417, -0.013250289484858513, -0.016042374074459076, 0.020517131313681602, 0.020941108465194702, 0.011044071055948734, -0.027324430644512177, 0.025828562676906586, 0.01623758301138878, -0.010915789753198624, -0.026586005464196205, -0.0011795111931860447, 0.05527857318520546, 0.02506236359477043, 0.04118965193629265, 0.027138665318489075, -0.06270306557416916, 0.011990685947239399, 0.006612282246351242, 0.026132358238101006, 0.004293444100767374, -0.022123757749795914, -0.06527673453092575, 0.014630400575697422, 0.009664598852396011, -0.010553570464253426, -0.01417639758437872, 0.028465278446674347, 0.05609551817178726, -0.052941177040338516, 0.0125328553840518, -0.05353314056992531, -0.01624937728047371, -0.04258138686418533, -0.03001350164413452, 0.045137159526348114, 0.04291338473558426, 0.06595718115568161, -0.018361816182732582, -0.06838762760162354, -0.05341273918747902, -0.08519146591424942, -0.014179075136780739, -0.0016374537954106927, 0.011041359975934029, -0.006051827687770128, -0.006448457483202219, -0.0016098784981295466, -0.029854705557227135, 0.022795068100094795, 0.024854276329278946, 0.0778130516409874, 0.04704511538147926, 0.058780737221241, 0.055547356605529785, 0.006022145040333271, -0.023683520033955574, -0.05111778900027275, -0.0313999317586422, 0.026925576850771904, 0.04161326587200165, 0.10323208570480347, -0.035573624074459076, 0.000455661938758567, 0.015153189189732075, 0.032163459807634354, 0.017267588526010513, -0.0293083805590868, -0.05602743849158287, 0.000056614091590745375, 0.004175588022917509, 0.048073120415210724, -0.06984903663396835, -0.019120045006275177, -0.03253675997257233, -0.016969799995422363, 0.09254539012908936, -0.01913345418870449, -0.01863839104771614, 0.07321986556053162, -0.006288489326834679, 0.038137879222631454, 0.08739110827445984, 0.04703035578131676, 0.006134897004812956, -0.021190181374549866, 0.001052521402016282, -0.00959834549576044, -0.010052397847175598, -0.017808949574828148, 0.0360853374004364, 0.05279159173369408, 0.030855519697070122, 0.01417464017868042, 0.007496878504753113, 0.01798316463828087, -0.009232594631612301, 0.027365176007151604, -0.025659602135419846, -0.07105337828397751, -0.057551417499780655, 0.0003509947855491191, 0.02596459724009037, -0.035069625824689865, -0.043311748653650284, -0.036057643592357635, -0.06990361958742142, 0.07863769680261612, 0.01934097521007061, 0.009282814338803291, 0.05259691923856735, 0.07518965750932693, -0.06024819239974022, -0.03347401320934296, -0.027947986498475075, -0.011614922434091568, 0.03799311816692352, 0.03914164751768112, 0.010281271301209927, 0.018694184720516205, -0.0183548666536808, -0.0064485156908631325, 0.04595787450671196, -0.03631848841905594, 0.0619904026389122, 0.002546281786635518, -0.03220166265964508, 0.08125944435596466, -0.05312127619981766, 0.013173061423003674, -0.004460720345377922, -0.012138593941926956, -0.028687987476587296, 0.0020859926007688046, 0.039639607071876526, 0.026356495916843414, -0.0006088771624490619, 0.023256897926330566, -0.030790984630584717, 0.03314472362399101, -0.05570405349135399, 0.027937021106481552, 0.0076127685606479645, 0.028531616553664207, -0.036631014198064804, 0.0169387087225914, -0.03195726126432419, 0.01776966266334057, 0.018128780648112297, 0.020118942484259605, 0.06366118043661118, -0.009035118855535984, -0.032836735248565674, -0.0003977143787778914, 0.025300540030002594, -0.014753499999642372, 0.012148077599704266, -0.008797232992947102, -0.05271834135055542, -0.036222051829099655, -0.009899153374135494, 0.02457740157842636, -0.03547290340065956, 0.0473068431019783, 0.022435445338487625, -0.010642449371516705, -0.019573692232370377, -0.027484547346830368, 0.003494496922940016, -0.07456693798303604, -0.06477189064025879, 0.010986178182065487, -0.0018307656282559037, -0.02058516815304756, -0.08030164241790771, 0.03645111620426178, -0.015681857243180275, -0.004313551355153322, 0.026903698220849037, 0.037970252335071564, 0.030067257583141327, -0.011723636649549007, -0.057620011270046234, -0.05317511409521103, -0.04661194235086441, -0.005137494299560785, 0.025012167170643806, 0.013387010432779789, 0.002133995061740279, -0.03481806814670563, 0.028174089267849922, -0.010744255036115646, -0.03945314139127731, -0.020089711993932724, -0.010324973613023758, 0.011756657622754574, -0.022009365260601044, -0.016378086060285568, 0.031465254724025726, 0.03595733642578125, -0.06185700371861458, -0.040870413184165955, 0.024862373247742653, 0.03882673755288124, 0.031577639281749725, 0.015402940101921558, -0.017078541219234467, 0.04007629677653313, -0.020687483251094818, -0.013749397359788418, 0.0018199071055278182, -0.023879079148173332, 0.007371017709374428, -0.0949435606598854, -0.015245577320456505, -0.0014084149152040482, 0.00023519435490015894, 0.032053880393505096, 0.003908053506165743, 0.03698490932583809, 0.016659149900078773, 0.03368356451392174, 0.0006496352725662291, -0.0344274677336216, -0.04801950603723526, -0.005419677589088678, -0.01194024458527565, -0.03453255817294121, 0.02761789970099926, -0.05510837584733963, -0.05358625203371048, 0.021291205659508705, -0.009017921052873135, -0.02426467277109623, 0.07195224612951279, -0.06993993371725082, 0.026514029130339622, -0.028092510998249054, -0.01505313254892826, 0.03638556972146034, 0.017072441056370735, -0.030932920053601265, 0.039749547839164734, 0.02245410718023777, 0.0053938268683850765, -0.03196650743484497, -0.04825964942574501, -0.007182322908192873, 0.0223519429564476, -0.006782780401408672, -0.0002937855606433004, 0.037129927426576614, 0.006333481520414352, 0.020695893093943596, 0.0006597720785066485, 0.06488342583179474, -0.028345897793769836, 0.024359093979001045, 0.06600726395845413, -0.007110724225640297, -0.04842856898903847, 0.0075265406630933285, 0.05601317808032036, -0.03732439875602722, 0.03242895379662514, -0.005614534020423889, 0.03736770898103714, -0.050695884972810745, 0.01415137480944395, -0.02375055104494095, 0.03780599310994148, -0.05013129487633705, 0.01250505167990923, 0.04190995171666145, 0.00911339744925499, 0.0020275802817195654, 0.07609093934297562, -0.05775178223848343, -0.05549369379878044, -0.017854170873761177, -0.004923107102513313, 0.0540006086230278, 0.011615331284701824, 0.010578400455415249, -0.03761555999517441, -0.025324054062366486, -0.01520110759884119, -0.017111647874116898, -0.0652843564748764, 0.01899239793419838 ]
<p>Please can anyone explain the concepts of <a href="http://en.wikipedia.org/wiki/Electromagnetically_induced_transparency" rel="nofollow">electromagnetic induced transparency</a>? I am having problem with the technicality of the explanation on wikipedia. Please I am an engineer with a physics background though and would love if this can be explained with little to no jargons . I am working on optical buffers and studying recent technologies and would love and explanation on this.</p>
g1577
[ 0.04417850449681282, 0.029377801343798637, -0.012115773744881153, -0.049867451190948486, 0.057438887655735016, 0.054082322865724564, 0.09260646998882294, 0.06457611173391342, -0.007286861538887024, -0.012290630489587784, -0.014347766526043415, 0.028827572241425514, 0.03258611261844635, 0.030521932989358902, 0.027049660682678223, 0.03508787974715233, 0.0837634727358818, 0.03241553530097008, 0.0038679952267557383, 0.019358476623892784, -0.005965337157249451, 0.04832374304533005, -0.04543660581111908, -0.04509025812149048, -0.023015057668089867, 0.017037758603692055, 0.002301954897120595, -0.0678965225815773, 0.022329559549689293, -0.06528822332620621, -0.031660296022892, -0.009624503552913666, 0.027891669422388077, 0.003368905046954751, 0.01655072532594204, -0.011443120427429676, -0.013851989060640335, 0.0644942969083786, 0.039561010897159576, 0.06940987706184387, 0.02295796386897564, 0.03153158724308014, -0.029230711981654167, -0.06841345131397247, -0.021865621209144592, 0.010459741577506065, -0.046864982694387436, 0.015553774312138557, 0.011539939790964127, -0.04484424740076065, -0.010637754574418068, -0.006167954299598932, 0.019673865288496017, 0.029345031827688217, 0.00027579531888477504, -0.01913575269281864, -0.0010467370739206672, 0.011169119738042355, 0.0826675146818161, -0.009981945157051086, -0.02360326610505581, 0.01435531210154295, -0.037272561341524124, -0.0006587589741684496, 0.002003128407523036, -0.01683180034160614, 0.0036513975355774164, -0.04827825725078583, 0.04025871306657791, 0.025115497410297394, -0.050287745893001556, -0.012679193168878555, -0.09808473289012909, -0.0426793210208416, 0.048141855746507645, -0.017055239528417587, -0.007217132020741701, 0.03158380091190338, 0.03610268607735634, 0.0491931214928627, 0.004378444980829954, 0.0065018548630177975, 0.011528889648616314, 0.024719955399632454, 0.0490078330039978, 0.0022590975277125835, -0.029420142993330956, -0.028900835663080215, -0.025555729866027832, -0.03352080285549164, 0.022627858445048332, -0.017983395606279373, 0.01928216964006424, 0.022710032761096954, 0.006458824034780264, 0.014613171108067036, 0.01836434379220009, 0.0413348525762558, -0.03136881813406944, 0.026441652327775955, 0.001171679818071425, -0.04178418964147568, 0.07377301156520844, 0.016176527366042137, 0.03707251697778702, 0.03428974747657776, -0.019002098590135574, 0.03208377957344055, -0.011454479768872261, 0.031462475657463074, -0.08197426795959473, 0.04473870247602463, -0.06108992546796799, -0.02430259808897972, -0.02719365619122982, -0.017418209463357925, 0.06221368908882141, 0.025737792253494263, -0.011850859969854355, 0.06116102263331413, 0.04810579493641853, 0.07130775600671768, 0.007591933012008667, 0.04762999713420868, 0.01371231209486723, -0.009759551845490932, -0.003177072387188673, 0.0005759211489930749, 0.042242828756570816, -0.041320815682411194, 0.02333165518939495, -0.015116793103516102, -0.019208582118153572, 0.016679761931300163, 0.02735665999352932, -0.0034514826256781816, 0.03403045982122421, -0.05387153849005699, 0.025574663653969765, -0.025458192452788353, -0.011477727442979813, -0.023227093741297722, -0.02731761895120144, -0.028689580038189888, -0.014553888700902462, 0.02666671946644783, -0.01842574030160904, 0.02648238092660904, 0.09403270483016968, -0.032058343291282654, 0.04095418006181717, 0.05121836066246033, -0.006528213620185852, -0.0510738268494606, 0.019729899242520332, 0.0020340224727988243, 0.022798364982008934, -0.016808131709694862, -0.006841807160526514, 0.0347965732216835, 0.05492014437913895, 0.01971280761063099, -0.029692044481635094, -0.037034809589385986, -0.07658281922340393, 0.008690797723829746, 0.0065695797093212605, -0.08175339549779892, -0.011053023859858513, -0.06718975305557251, -0.03357395902276039, 0.014707068912684917, 0.03484561666846275, 0.032140668481588364, -0.025542965158820152, 0.07699842751026154, 0.06563755869865417, -0.012526344507932663, 0.02007470652461052, -0.023793110623955727, -0.06034636124968529, -0.01138030644506216, 0.011997436173260212, -0.056102775037288666, -0.013109280727803707, -0.07244125753641129, -0.018083836883306503, -0.010493025183677673, -0.06733835488557816, 0.02948797680437565, -0.05610893294215202, -0.04965594783425331, -0.01950777694582939, -0.006169899366796017, -0.027789367362856865, -0.007057812996208668, 0.04921852797269821, -0.006530513521283865, -0.015028068795800209, -0.014570246450603008, -0.018580414354801178, -0.03075677901506424, 0.0439036563038826, 0.006041856482625008, 0.01618186943233013, 0.00834196712821722, 0.006641055457293987, -0.011223494075238705, -0.011557839810848236, 0.018975157290697098, 0.014618098735809326, -0.02741936221718788, 0.07498466223478317, -0.03981279581785202, 0.0236173365265131, 0.04794807359576225, -0.015133066102862358, -0.005148284137248993, -0.034803375601768494, -0.023426728323101997, 0.04047618806362152, -0.051739633083343506, 0.01360586192458868, 0.013012855313718319, -0.0458378829061985, -0.02351994439959526, -0.032405558973550797, -0.014019190333783627, -0.028575053438544273, 0.00904869195073843, -0.027934864163398743, 0.01801467128098011, -0.0863080769777298, 0.007454917300492525, 0.030371028929948807, 0.013114885427057743, -0.05199604853987694, 0.0014403843088075519, -0.007202533073723316, -0.001958354376256466, 0.010581656359136105, -0.017716770991683006, -0.0543040856719017, -0.016173474490642548, -0.022731319069862366, -0.09194061160087585, 0.019115764647722244, -0.023606449365615845, 0.013256070204079151, -0.0024288357235491276, -0.027633266523480415, -0.062010813504457474, 0.05766836553812027, 0.007119559217244387, 0.014533604495227337, -0.010611104778945446, -0.015550276264548302, 0.04209345579147339, -0.050363872200250626, 0.05880450829863548, 0.02599107287824154, 0.018861616030335426, -0.037387460470199585, -0.02794593945145607, -0.04398592561483383, 0.027748066931962967, -0.05438899248838425, 0.000863561755977571, -0.002556907245889306, 0.01790425181388855, -0.02226467803120613, 0.046276435256004333, 0.004595318343490362, -0.043623246252536774, 0.0632571280002594, 0.04581506550312042, 0.025002436712384224, 0.018860530108213425, 0.044954683631658554, 0.0027604904025793076, -0.05077770724892616, -0.03841268643736839, -0.048736218363046646, -0.003574132453650236, 0.014102968387305737, -0.03008657693862915, -0.031863074749708176, -0.016998570412397385, -0.02474011294543743, 0.02775232121348381, -0.059270162135362625, -0.009939237497746944, -0.0034531818237155676, -0.000004569450538838282, -0.05062919482588768, -0.01304760854691267, 0.002774282591417432, -0.011791525408625603, -0.05739752575755119, 0.024398941546678543, -0.04148203879594803, 0.019844921305775642, 0.00981055200099945, -0.0335167832672596, 0.035327281802892685, 0.04199330881237984, -0.017186427488923073, -0.07760430872440338, -0.011846219189465046, 0.062205687165260315, -0.035314302891492844, 0.03491591662168503, 0.022592555731534958, 0.07061197608709335, -0.011834980919957161, 0.028980961069464684, -0.011977244168519974, 0.02867875061929226, 0.013926813378930092, -0.0005520175327546895, -0.012409922666847706, -0.02237841486930847, 0.007743818685412407, -0.0323951318860054, 0.039416275918483734, -0.018400954082608223, 0.052108246833086014, -0.052645493298769, -0.009552659466862679, -0.05325665697455406, 0.0817892774939537, -0.03800471872091293, -0.026738381013274193, -0.0440671406686306, -0.008727739565074444, -0.028974713757634163, -0.06912083178758621, 0.030984697863459587, -0.023942898958921432, -0.01998952589929104, 0.05575781315565109, -0.039450157433748245, -0.06522161513566971, -0.025918876752257347, -0.005804682150483131, 0.018152959644794464, 0.00906448159366846, 0.004091974347829819, -0.005972052458673716, 0.025750918313860893, 0.08288556337356567, 0.031774893403053284, -0.019215213134884834, -0.07217422127723694, -0.06282947212457657, 0.007862568832933903, 0.02292509563267231, 0.0367727056145668, 0.057937536388635635, -0.028177835047245026, 0.004270663484930992, -0.04301679506897926, -0.004389861132949591, -0.02648230269551277, -0.055169835686683655, 0.006684121675789356, 0.025517603382468224, 0.0003972497070208192, -0.022978607565164566, -0.00422710832208395, -0.03999410942196846, -0.020053686574101448, -0.020747583359479904, 0.048795413225889206, 0.005952667910605669, -0.03208823502063751, 0.04682118818163872, 0.032442573457956314, -0.03359409049153328, 0.06424447894096375, -0.02645265869796276, 0.05344383046030998, 0.03166547417640686, 0.006850496865808964, 0.04599512368440628, -0.06572327762842178, -0.0052689746953547, 0.03490743786096573, -0.02255779504776001, -0.05834100767970085, 0.007319277618080378, 0.017989827319979668, -0.009875655174255371, -0.03556501865386963, -0.009931111708283424, -0.04941697046160698, -0.05173324793577194, -0.03675902634859085, 0.0705755278468132, 0.012134460732340813, 0.03763827309012413, -0.003851386019960046, 0.015358764678239822, 0.034643590450286865, -0.021448537707328796, -0.045488160103559494, 0.06526400148868561, 0.0029818492475897074, -0.02493865042924881, -0.02730502001941204, 0.016042908653616905, -0.030729878693819046, -0.03468417003750801, -0.01793558895587921, 0.04648098722100258, 0.059257470071315765, 0.0522821806371212, -0.024585334584116936, 0.010540447197854519, 0.00778152234852314, -0.023465510457754135, 0.018590332940220833, -0.023504743352532387, -0.028052976354956627, 0.0006290384917519987, 0.054499320685863495, 0.03710949793457985, -0.01607559435069561, 0.02568371221423149, 0.014069482684135437, 0.02292001247406006, 0.031666483730077744, -0.01582234352827072, 0.01646450161933899, -0.008309819735586643, 0.044664572924375534, -0.03251161798834801, 0.10717438906431198, 0.02851819433271885, -0.010312517173588276, 0.06517535448074341, -0.04207692667841911, -0.0031415054108947515, -0.0148442592471838, 0.0134437782689929, 0.039769530296325684, -0.0041983965784311295, -0.041012849658727646, -0.0180773064494133, 0.01856980286538601, -0.0174470953643322, 0.019309725612401962, -0.03558631241321564, 0.003282982623204589, -0.006588946096599102, 0.0007011670968495309, -0.05502515658736229, 0.0021263642702251673, 0.030252527445554733, -0.01988137885928154, -0.06975150853395462, 0.008866255171597004, -0.009209559299051762, -0.02853175438940525, 0.023715976625680923, -0.021990008652210236, 0.02536473423242569, 0.0021724046673625708, -0.05807651951909065, -0.027216587215662003, 0.01595148630440235, 0.016720304265618324, 0.019522516056895256, 0.03839573264122009, 0.06801696866750717, -0.03234120458364487, 0.011886853724718094, 0.02935149520635605, -0.009085049852728844, 0.00006718533404637128, -0.013673229143023491, -0.0005296741146594286, 0.089411661028862, -0.014857474714517593, 0.04811091721057892, 0.018115781247615814, -0.01114415843039751, 0.07956448197364807, 0.016564158722758293, -0.027790414169430733, 0.040745120495557785, 0.01949252560734749, -0.03171386197209358, -0.013052177615463734, -0.03161807730793953, -0.05612843111157417, 0.01393344160169363, 0.05021205171942711, -0.044514164328575134, -0.03929073363542557, 0.03524221107363701, -0.01476757787168026, 0.018128307536244392, 0.011354660615324974, 0.004244909156113863, 0.008475860580801964, -0.02256828173995018, -0.030828075483441353, 0.04811393842101097, -0.024571172893047333, -0.05645408108830452, -0.016308505088090897, -0.07410328835248947, -0.0027980529703199863, 0.026865560561418533, 0.01366241555660963, -0.03767316788434982, -0.009799876250326633, -0.03540491685271263, -0.012769016437232494, -0.003515866119414568, 0.001207802095450461, 0.015404454432427883, 0.02119404636323452, 0.016590001061558723, -0.021588552743196487, -0.013281823135912418, 0.037689220160245895, 0.037920162081718445, 0.016644641757011414, -0.04576743021607399, 0.05128015577793121, 0.0543053075671196, 0.019939694553613663, 0.0020933288615196943, -0.06314456462860107, 0.05097173526883125, 0.01557683851569891, 0.028246251866221428, 0.05566702410578728, -0.031061649322509766, 0.00030990131199359894, 0.0012656881008297205, 0.08599570393562317, -0.004946927074342966, -0.01888786256313324, 0.023981289938092232, 0.0008069410105235875, 0.033782895654439926, -0.057281214743852615, 0.029771726578474045, -0.046973370015621185, 0.09606347978115082, -0.03771607205271721, 0.03154611587524414, 0.03880614787340164, 0.006862110923975706, -0.0212139543145895, -0.018038753420114517, -0.0275117140263319, 0.04531070217490196, 0.07610713690519333, -0.009347986429929733, 0.02339671179652214, 0.02939555048942566, -0.013370880857110023, 0.026188364252448082, -0.0017417045310139656, 0.0676676332950592, -0.00039488787297159433, 0.01736265979707241, -0.015011652372777462, -0.04028007760643959, -0.018818732351064682, 0.00881722941994667, 0.035672981292009354, 0.015453469939529896, -0.04830504208803177, -0.0670468732714653, 0.031493861228227615, 0.04973457008600235, 0.026683397591114044, 0.06433866173028946, -0.022398144006729126, -0.03672698140144348, -0.07922500371932983, -0.07508627325296402, -0.017074570059776306, 0.028759006410837173, -0.040032707154750824, -0.04856270179152489, -0.0506453737616539, 0.02035118080675602, -0.010426193475723267, -0.016101360321044922, -0.039647433906793594, -0.038444891571998596, 0.027684921398758888, 0.02176658622920513, 0.03447091951966286, -0.018119364976882935, -0.04226355627179146, 0.014971748925745487, 0.021575644612312317, 0.02034616842865944, -0.009303818456828594, -0.012902706861495972, -0.03980555385351181, -0.020513879135251045, 0.032446976751089096, -0.006193340755999088, -0.020174529403448105, -0.07262615859508514, -0.04269718751311302, -0.08984483778476715, -0.05573369190096855, -0.047286394983530045, -0.0581282414495945, 0.00011301621998427436, 0.01948738656938076, -0.02998877502977848, -0.06962274760007858, 0.07794162631034851, 0.036694180220365524, 0.036541249603033066, 0.07550326734781265, -0.012589582242071629, -0.00017745012883096933, -0.00936291366815567, 0.01572696678340435, -0.026928098872303963, -0.048962440341711044, 0.03934234008193016, 0.04146229475736618, 0.03616657853126526, 0.0443602055311203, 0.02340538427233696, -0.01870582066476345, 0.06582003086805344, 0.03006579354405403, 0.0011018066434189677, 0.004282648209482431, 0.07407685369253159, 0.056988246738910675, -0.017923403531312943, 0.02680276334285736, -0.05119125917553902, -0.01352675724774599, -0.05806347727775574, 0.010421781800687313, -0.030883794650435448, -0.011687480844557285, -0.02154403366148472, 0.06754773110151291, -0.05315093323588371, 0.03798537701368332, -0.06989668309688568, 0.009134218096733093, 0.00029170766356401145, -0.013391000218689442, -0.014293466694653034, -0.01712271198630333, -0.021854696795344353, -0.014971297234296799, 0.0117386095225811, -0.012599842622876167, 0.05444567650556564, -0.060193900018930435, -0.027873888611793518, 0.05165034905076027, 0.008167910389602184, -0.05285300314426422, 0.024291209876537323, 0.03456532955169678, 0.007375709246844053, -0.062340639531612396, 0.0017386680701747537, 0.03848192095756531, -0.027543995529413223, -0.005661877803504467, -0.04206617921590805, 0.03956718370318413, 0.0632171779870987, -0.0516362339258194, -0.049023378640413284, -0.011138183996081352, -0.02630624733865261, 0.006262516137212515, -0.02504250779747963, -0.05421064794063568, 0.0021033906377851963, -0.02684498205780983, -0.015313472598791122, -0.031182220205664635, 0.051474232226610184, 0.013192163780331612, 0.04714823514223099, 0.03661944717168808, 0.021577509120106697, 0.021183069795370102, -0.009630284272134304, -0.044718217104673386, -0.03247181326150894, -0.021898148581385612, 0.0336722768843174, 0.0328172966837883, 0.0234177615493536, 0.016587737947702408, 0.01567559503018856, -0.00874033011496067, -0.0029018609784543514, 0.0010483530350029469, 0.0694502666592598, 0.054280783981084824, -0.01022224873304367, -0.018887605518102646, -0.006282424554228783, 0.0031541697680950165, -0.04960494861006737, 0.012420649640262127, 0.036593854427337646, 0.028357120230793953, -0.05095701292157173, 0.016443567350506783, -0.0022415430285036564, 0.025632785633206367, -0.023019321262836456, -0.021667031571269035, -0.030736088752746582, -0.012486538849771023, 0.05234132707118988, 0.0008691931143403053, 0.006790587678551674, -0.019882122054696083, -0.04100341349840164, 0.0006285266135819256, 0.024070240557193756, 0.006321251858025789, 0.020320607349276543, 0.010024269111454487, 0.05063343048095703, -0.04797498136758804, -0.05163455754518509, -0.03007642738521099, 0.0009665656834840775, 0.0037745514418929815, -0.01681855507194996, 0.019878434017300606, -0.014427143149077892, -0.02795199491083622, -0.006604813039302826, 0.02720067836344242, 0.009991113096475601, 0.03819805383682251, 0.08643064647912979, -0.04178788140416145, -0.015347681939601898, 0.03418595343828201, 0.06810873001813889, 0.03291481360793114, -0.006436211057007313, -0.00949163269251585, 0.008724660612642765, -0.043766677379608154, -0.0620262436568737, 0.023764273151755333, 0.0003278166404925287, -0.014428989961743355 ]
<p>Photons have no mass but they can push things, as evidenced by <a href="https://en.wikipedia.org/wiki/Laser_propulsion">laser propulsion</a>. </p> <p>Can photons push the source which is emitting them? If yes, will a more intense flashlight accelerate me more? Does the wavelength of the light matter? Is this practical for space propulsion? Doesn't it defy the law of momentum conservation?</p> <p><em>Note: As John Rennie mentioned, all in all the wavelength doesn't matter, but for a more accurate answer regarding that, see the comments in <a href="http://physics.stackexchange.com/a/112870/46604">DavePhD's answer</a> .</em></p> <p><em>Related Wikipedia articles: <a href="https://en.wikipedia.org/wiki/Ion_thruster">Ion thruster</a>, <a href="https://en.wikipedia.org/wiki/Spacecraft_propulsion">Space propulsion</a></em></p>
g483
[ -0.012586710043251514, 0.09608747810125351, 0.01746736839413643, 0.04079699516296387, 0.018256748095154762, 0.015997080132365227, -0.04040488973259926, 0.006017390172928572, -0.02002730965614319, -0.02482541650533676, 0.09806899726390839, 0.038357749581336975, -0.031143536791205406, -0.02837563492357731, -0.020215721800923347, 0.01870325393974781, 0.0946282297372818, -0.004477301146835089, 0.03279813379049301, 0.08007965981960297, -0.021225249394774437, -0.018258506432175636, -0.0317532904446125, -0.06828782707452774, -0.021263184025883675, 0.03479520231485367, -0.005903166718780994, -0.07093582302331924, -0.0011388324201107025, -0.01946544647216797, 0.022339509800076485, -0.046190060675144196, 0.042661961168050766, -0.013498019427061081, -0.05826123431324959, -0.026687420904636383, 0.016109120100736618, -0.023125050589442253, -0.025532785803079605, 0.03668791055679321, -0.0323401615023613, -0.01717207580804825, 0.008069850504398346, 0.0363534614443779, -0.0020131024066358805, 0.0067442129366099834, 0.0329604409635067, -0.020739469677209854, 0.017414558678865433, -0.031233731657266617, -0.011919948272407055, -0.008866935037076473, -0.06548258662223816, 0.0018633146537467837, 0.03962704539299011, -0.005165318958461285, -0.043141208589076996, -0.022172145545482635, 0.055221837013959885, 0.003215455450117588, -0.03204609081149101, -0.016407161951065063, 0.04875294491648674, -0.00833651702851057, -0.008015234023332596, -0.060917891561985016, -0.029780203476548195, -0.046633291989564896, 0.025103263556957245, -0.0021894716192036867, 0.06512083858251572, 0.02385530434548855, -0.013748318888247013, -0.04835040122270584, 0.02529810182750225, -0.017410576343536377, 0.010660200379788876, 0.02793261781334877, -0.054449111223220825, 0.03891042619943619, 0.03036789782345295, -0.03886094689369202, 0.018215041607618332, -0.06613530218601227, 0.031123878434300423, -0.017932163551449776, -0.03319995477795601, -0.009139039553701878, 0.011602412909269333, 0.008258574642241001, 0.07955898344516754, 0.03753059357404709, 0.0670904591679573, 0.011664104647934437, 0.016193093731999397, 0.01885836012661457, 0.06052793562412262, 0.05578261986374855, 0.01736222580075264, -0.012544902972877026, -0.013692384585738182, -0.015734290704131126, -0.003043274162337184, 0.01798865757882595, 0.031393203884363174, -0.02948633022606373, 0.028443118557333946, -0.010522959753870964, 0.00040602911030873656, -0.020087407901883125, -0.026623668149113655, -0.019292695447802544, -0.029030296951532364, -0.00997231900691986, -0.07805319130420685, -0.03324833884835243, 0.03440002724528313, -0.05341938138008118, -0.0024209199473261833, 0.09209499508142471, 0.06582678109407425, 0.013865962624549866, -0.022755777463316917, 0.032147862017154694, 0.0437779501080513, -0.03907090798020363, 0.02579881250858307, -0.019079696387052536, -0.02271328680217266, -0.0009812318021431565, -0.055023740977048874, 0.03520723432302475, -0.030449962243437767, -0.010340850800275803, 0.018389228731393814, -0.015844466164708138, -0.008278188295662403, 0.024427363649010658, 0.04658111557364464, 0.011433820240199566, 0.04577948898077011, -0.024218395352363586, -0.02005366049706936, 0.028466779738664627, -0.01610383577644825, 0.03407302126288414, -0.05098572000861168, 0.04359133169054985, -0.0036847859155386686, 0.049805738031864166, 0.03758455812931061, 0.033560387790203094, 0.05595614016056061, -0.02914022095501423, 0.020737428218126297, -0.0041702077724039555, 0.03251907229423523, 0.044965654611587524, -0.0701548382639885, -0.01737852767109871, 0.021186020225286484, 0.026889754459261894, 0.018108772113919258, -0.019173897802829742, -0.04902747645974159, -0.03569354861974716, -0.028274202719330788, -0.09110920131206512, -0.03086780197918415, -0.013888377696275711, -0.009084436111152172, 0.018914923071861267, 0.022474858909845352, 0.05089492350816727, 0.011234335601329803, -0.000341534148901701, 0.03543373942375183, 0.008983848616480827, 0.016576312482357025, -0.04398386552929878, -0.03479909151792526, -0.028511589393019676, 0.010416626930236816, -0.06562554836273193, -0.035245202481746674, -0.06448614597320557, -0.040993526577949524, 0.0345630869269371, -0.023928355425596237, 0.015389356762170792, -0.010219505056738853, 0.01887482963502407, 0.036112334579229355, 0.03774576634168625, -0.03808613121509552, -0.04537427797913551, -0.022151490673422813, -0.05240827053785324, -0.03321928158402443, 0.030045149847865105, -0.02741820178925991, 0.03433799743652344, -0.022944172844290733, -0.005003825295716524, 0.00950508564710617, 0.020865844562649727, -0.03809910640120506, -0.009241988882422447, 0.04014008119702339, -0.03696025535464287, 0.09839320927858353, -0.00908451247960329, 0.05346902459859848, 0.04969481751322746, -0.03395083174109459, -0.018160855397582054, -0.08291471749544144, 0.045493122190237045, 0.000763517979066819, -0.040747661143541336, -0.04567160829901695, -0.0351453572511673, 0.05739578977227211, -0.010478079319000244, -0.05854104831814766, -0.012800733558833599, -0.04494704678654671, -0.011348667554557323, 0.0070481267757713795, 0.0323583222925663, -0.002385874278843403, -0.006955687887966633, -0.006104199215769768, -0.03502964600920677, 0.07206915318965912, 0.014363261871039867, -0.012137356214225292, 0.010272886604070663, 0.0063932472839951515, 0.04656704142689705, 0.03425903618335724, -0.034011662006378174, 0.006465590093284845, -0.011725622229278088, 0.009523151442408562, -0.09444732964038849, -0.0007122056558728218, -0.029255319386720657, -0.009357495233416557, -0.057393427938222885, 0.012967728078365326, -0.0053769685328006744, 0.0012521720491349697, 0.0286602471023798, -0.059881169348955154, 0.0048005362041294575, -0.0468793548643589, 0.058748867362737656, -0.08195227384567261, -0.000013927618965681177, 0.027002999559044838, -0.00580517016351223, -0.07119051367044449, 0.018707236275076866, -0.01649930328130722, -0.003424885915592313, -0.012874686159193516, -0.010777304880321026, 0.01639614626765251, 0.0015913263196125627, -0.004500422161072493, 0.02220090851187706, -0.022958608344197273, 0.00761766592040658, 0.005007204599678516, 0.04438791051506996, 0.01535031758248806, 0.013803467154502869, 0.026262156665325165, -0.05570274218916893, 0.0015393546782433987, -0.006026837043464184, -0.06382454931735992, -0.007609499618411064, -0.010728608816862106, -0.06308633089065552, -0.007028666790574789, 0.003937663976103067, -0.0021861721761524677, 0.002165504964068532, -0.0168276596814394, 0.005871262867003679, 0.04528987780213356, -0.020160404965281487, 0.035173043608665466, 0.025038329884409904, 0.029709739610552788, -0.000015304067346733063, -0.018873533234000206, -0.016591191291809082, 0.04641750827431679, -0.023459473624825478, -0.010432826355099678, -0.006644680164754391, 0.004430726170539856, -0.011733654886484146, -0.09957700967788696, -0.03710860759019852, 0.007429100107401609, 0.04980762302875519, 0.016348209232091904, 0.06931190192699432, -0.03256310895085335, 0.1288871169090271, -0.01927877962589264, -0.04728437587618828, -0.017492562532424927, -0.026808373630046844, -0.020591339096426964, 0.020498139783740044, -0.006712379865348339, -0.055302150547504425, -0.013259965926408768, -0.022088326513767242, 0.04690427705645561, 0.0005674443673342466, 0.04099048674106598, -0.021846171468496323, -0.032849956303834915, 0.011977323330938816, 0.03244728967547417, 0.038574375212192535, -0.034274905920028687, 0.00776233384385705, -0.009407452307641506, 0.014583094976842403, 0.03958003968000412, 0.04343872144818306, 0.020839735865592957, 0.037185586988925934, 0.01717456988990307, 0.018673228099942207, -0.04614795744419098, 0.04322865232825279, 0.016599860042333603, 0.033819593489170074, -0.005777211859822273, -0.01280850637704134, 0.016317125409841537, -0.018062898889183998, 0.05337132513523102, -0.0026554015930742025, 0.001476336969062686, -0.009629856795072556, -0.0059700473211705685, 0.0005993549129925668, 0.00040273391641676426, 0.07582861185073853, 0.05025758594274521, -0.04109819233417511, -0.023458169773221016, 0.034005340188741684, 0.03521908447146416, -0.047923918813467026, -0.018201984465122223, 0.024286171421408653, 0.028590882197022438, 0.006430755835026503, -0.00977296568453312, 0.06373703479766846, -0.0005641641328111291, -0.053955528885126114, -0.004311966244131327, -0.004890101961791515, 0.005595345050096512, -0.029495425522327423, 0.05307737737894058, -0.023813117295503616, -0.01069470401853323, 0.0347784087061882, -0.006552461069077253, 0.05878226459026337, 0.04891877621412277, -0.028887491673231125, 0.014180363155901432, 0.031619563698768616, -0.00986875407397747, 0.04895313084125519, 0.0034508497919887304, -0.053821876645088196, 0.012914614751935005, -0.02131666988134384, -0.018927061930298805, -0.034888025373220444, 0.00040283557609654963, 0.020813362672924995, -0.02928701788187027, -0.059196893125772476, 0.0005691424594260752, -0.01527714729309082, 0.011402112431824207, 0.0624292716383934, 0.0209745354950428, 0.021634778007864952, -0.03732464835047722, 0.023256372660398483, 0.046791546046733856, -0.009127025492489338, -0.030003122985363007, -0.02257559821009636, 0.02131379395723343, 0.022986017167568207, -0.040894340723752975, -0.015038044191896915, -0.015592633746564388, 0.02516586147248745, -0.021129289641976357, -0.02279340662062168, 0.01507728360593319, 0.04054053872823715, 0.0030270416755229235, 0.01651945151388645, 0.03871333599090576, -0.006386831868439913, 0.0410439558327198, 0.05328045040369034, 0.08474627882242203, -0.02766592800617218, 0.04929462447762489, -0.007237906102091074, 0.043907277286052704, 0.0008341674110852182, 0.02851521223783493, 0.040502309799194336, 0.03702018782496452, 0.05707768350839615, 0.007360980845987797, 0.03922085091471672, 0.08480624109506607, 0.039784025400877, 0.05830581113696098, 0.010478902608156204, 0.057862650603055954, 0.03143828734755516, 0.020332712680101395, 0.029637429863214493, -0.006930706091225147, -0.023127585649490356, -0.062269505113363266, -0.01025710254907608, -0.022719023749232292, -0.06862813234329224, 0.010860037989914417, -0.041628677397966385, 0.008928335271775723, 0.04009623825550079, -0.018106818199157715, 0.013002470135688782, 0.02793264016509056, 0.035551153123378754, -0.04722680523991585, -0.0019516784232109785, 0.0959622785449028, -0.015353959053754807, 0.09272225946187973, 0.0053987642750144005, -0.05921859294176102, -0.007306106388568878, -0.048021167516708374, -0.058708738535642624, 0.05164318159222603, -0.026415036991238594, -0.02320607379078865, 0.016303159296512604, 0.019575759768486023, -0.07254085689783096, -0.014592495746910572, -0.029550058767199516, -0.07092663645744324, -0.009681707248091698, 0.014403549954295158, -0.044712163507938385, 0.016899365931749344, -0.03560618683695793, -0.014138873666524887, 0.053394269198179245, -0.017906589433550835, 0.03615259751677513, -0.01706274226307869, -0.037440575659275055, -0.03601648285984993, 0.0029949992895126343, -0.09122493118047714, -0.03418150171637535, -0.054142601788043976, 0.08719591796398163, 0.054359063506126404, 0.004089624620974064, -0.02366236038506031, 0.03444186970591545, -0.005622402299195528, -0.04306872934103012, 0.020426154136657715, 0.01661248505115509, -0.060705676674842834, -0.048100829124450684, 0.0020364432130008936, -0.017947610467672348, -0.014769736677408218, -0.006955391727387905, -0.02092604525387287, 0.0145657267421484, -0.04996194317936897, 0.011880115605890751, 0.04752697795629501, -0.042415179312229156, -0.03965824842453003, 0.059132903814315796, 0.05120271071791649, -0.05002831295132637, -0.016850357875227928, -0.02048339881002903, 0.02741975337266922, 0.025530656799674034, 0.03359753265976906, 0.018780969083309174, -0.03358658775687218, 0.01736965961754322, 0.014383346773684025, 0.004519644659012556, 0.040050260722637177, 0.020065583288669586, 0.043099936097860336, -0.03887943923473358, -0.007305380422621965, -0.053950194269418716, 0.08383723348379135, 0.018023092299699783, -0.014897807501256466, -0.027695486322045326, -0.07677441835403442, 0.002070450456812978, -0.024759827181696892, 0.08139725774526596, 0.031172338873147964, 0.014943188056349754, 0.001587654696777463, -0.02382740192115307, 0.00601390702649951, -0.06680145859718323, -0.020410597324371338, 0.03290024399757385, -0.020598825067281723, -0.03125596046447754, -0.006211163941770792, 0.0377805233001709, -0.011898393742740154, 0.005081519018858671, 0.010453367605805397, -0.09131075441837311, 0.024444041773676872, 0.04351475089788437, -0.0006709725712426007, -0.03241470456123352, 0.010715795680880547, -0.046905238181352615, 0.021948285400867462, -0.07850784063339233, 0.0061865756288170815, 0.03812151402235031, -0.01975327357649803, 0.04016997292637825, -0.021822556853294373, -0.0023192900698632, 0.013164243660867214, -0.057706184685230255, -0.004271183628588915, -0.00854397565126419, -0.08824226260185242, 0.008146927691996098, 0.041067712008953094, 0.0676448866724968, 0.00764246191829443, -0.03195880725979805, -0.02724144235253334, -0.011138230562210083, -0.049675170332193375, 0.012474424205720425, 0.0652458518743515, -0.02600502409040928, -0.00425257533788681, -0.0021981901954859495, 0.009582885541021824, 0.016785990446805954, -0.08948388695716858, -0.004630235955119133, 0.0002578044368419796, 0.013103628531098366, 0.006872445810586214, -0.007569422945380211, 0.05051717534661293, 0.0306868776679039, 0.03997127339243889, 0.0686778575181961, -0.002468364080414176, -0.0066066947765648365, -0.02556879259645939, -0.019659405574202538, 0.05290910601615906, 0.013726840727031231, -0.07951551675796509, 0.05069555342197418, -0.041460998356342316, -0.018678002059459686, -0.010100316256284714, -0.01861657202243805, -0.013979107141494751, -0.026895631104707718, 0.057226620614528656, 0.013554556295275688, -0.004752527456730604, -0.05728275328874588, 0.009510660544037819, -0.026032205671072006, -0.017140664160251617, 0.008062753826379776, 0.0011506574228405952, 0.015774136409163475, 0.0053993575274944305, 0.014288988895714283, 0.007882870733737946, -0.04593757912516594, 0.004586855880916119, 0.017804672941565514, 0.021110184490680695, -0.008556205779314041, -0.037783604115247726, -0.00933019444346428, -0.005022608209401369, -0.0458315946161747, 0.01938152313232422, -0.04549282789230347, -0.029094576835632324, 0.03826316446065903, -0.05204859748482704, 0.02704768255352974, 0.002472799737006426, -0.03623529151082039, 0.013433489948511124, -0.03283734619617462, -0.01626083254814148, -0.052631717175245285, -0.049712054431438446, -0.0005609971121884882, -0.013988114893436432, 0.03590172156691551, -0.06062932685017586, 0.043238766491413116, -0.027395017445087433, -0.05359626188874245, 0.03526634722948074, -0.002866505878046155, -0.01504939328879118, 0.054238513112068176, 0.009348982013761997, 0.0297115296125412, -0.030331702902913094, 0.003131957957521081, -0.015143472701311111, 0.038106225430965424, 0.04018881544470787, -0.02131991647183895, -0.041726283729076385, -0.028041595593094826, 0.08431456983089447, 0.033673204481601715, -0.0806194618344307, 0.012833505868911743, 0.003954611718654633, 0.015814989805221558, 0.028836166486144066, -0.004325579851865768, -0.01888597570359707, -0.0014771699206903577, -0.012459452264010906, 0.013995930552482605, -0.02444216050207615, 0.023129064589738846, -0.017964700236916542, -0.04284035041928291, -0.02537645399570465, -0.05060838907957077, 0.0344216525554657, 0.03067302517592907, 0.017576638609170914, 0.022440211847424507, 0.013974050059914589, 0.06672471016645432, -0.029495105147361755, 0.02467171661555767, -0.07524364441633224, -0.01520246360450983, 0.04322970286011696, -0.006149528082460165, -0.010340491309762001, 0.012003849260509014, 0.018861981108784676, 0.03637803718447685, -0.03380013629794121, -0.0743865817785263, 0.02286471053957939, -0.02979733608663082, -0.048567138612270355, -0.007375997491180897, 0.03202275559306145, 0.00020865834085270762, 0.02191498503088951, 0.04358284920454025, -0.007664686534553766, 0.010241237469017506, 0.0381341278553009, 0.03994246572256088, -0.008983863517642021, 0.01606234721839428, -0.02681892365217209, -0.01563877798616886, 0.03763185441493988, -0.02952517382800579, -0.022623339667916298, -0.0453009270131588, 0.050356704741716385, -0.04002309963107109, -0.006202902644872665, -0.07759729027748108, -0.020093707367777824, -0.010355937294661999, -0.02034829743206501, 0.03572658821940422, 0.023791536688804626, 0.03864461928606033, 0.017069919034838676, -0.0017208452336490154, -0.06183697655797005, 0.023178432136774063, 0.0241318978369236, -0.01560672465711832, -0.027624167501926422, 0.043845128268003464, 0.04407857730984688, 0.007944582961499691, 0.0769161656498909, 0.07896377891302109, -0.00788191519677639, 0.04093453288078308, 0.037382058799266815, -0.01852821744978428, -0.0456436425447464, 0.043556611984968185, -0.014036808162927628, -0.012047664262354374, 0.01932249590754509, 0.0255295280367136, 0.020282546058297157, -0.038457296788692474, -0.032876450568437576, -0.06627757102251053, -0.005521515384316444, 0.0013330550864338875 ]
<p>I'm reading that general relativity let's us describe physics from the point of view of both inertial and accelerated observers. What does that actually mean in terms of doing actual physics? For example, say a physicist performed Millikan's oil drop experiment or Young's double slit experiment or decomposed white light with a prism: (1) in deep space, far from any gravitational field, (2) on Earth, (3) near a black hole. I'm assuming she would get different results, and I'm assuming that in some way this is near the heart of what's important regarding GTR, but how exactly? In other words, what are the implications of GTR for understanding these experiments?</p> <p>Thank you</p>
g1578
[ -0.01181933842599392, 0.0663016214966774, -0.006348263472318649, -0.00434140907600522, 0.04265289753675461, 0.04559219256043434, 0.06408495455980301, 0.01711498387157917, -0.03933356702327728, -0.018712753430008888, 0.06644360721111298, -0.04198552668094635, 0.014800497330725193, -0.04617708921432495, 0.019206225872039795, -0.0694827139377594, 0.032282933592796326, -0.008701952174305916, -0.03885773941874504, -0.009976479224860668, 0.029021969065070152, -0.016923047602176666, 0.008238413371145725, 0.0009536793804727495, -0.049089398235082626, -0.01952523924410343, -0.006215566303580999, -0.02184096723794937, -0.04882325232028961, 0.0011307781096547842, -0.014499001204967499, -0.05325157195329666, -0.04206809028983116, -0.01905485987663269, -0.0006632154691033065, -0.05275927484035492, 0.015101110562682152, 0.027922386303544044, -0.022537650540471077, -0.02881184220314026, -0.017615675926208496, -0.0208366047590971, 0.010899517685174942, -0.029020322486758232, 0.07450597733259201, 0.07257939875125885, -0.01685182750225067, 0.00223461608402431, 0.04509780928492546, -0.026742644608020782, 0.008700880222022533, 0.04109621047973633, 0.038733720779418945, 0.09722988307476044, 0.05069665610790253, 0.03733576089143753, -0.03973142430186272, 0.04048134386539459, 0.10557997226715088, -0.04397027939558029, 0.0048625413328409195, -0.05505641922354698, -0.012633790262043476, -0.018692297860980034, 0.00010738825949374586, -0.02478351630270481, -0.035339582711458206, -0.052955493330955505, 0.022204115986824036, -0.00645368592813611, 0.0369640477001667, -0.0032832203432917595, 0.002793835708871484, -0.00046217042836360633, -0.01695670746266842, 0.00911572203040123, -0.006018038373440504, 0.023604148998856544, 0.026837190613150597, 0.059798359870910645, -0.0511949248611927, -0.001141063403338194, 0.0011604083701968193, 0.024010224267840385, 0.0757683515548706, 0.02291499637067318, -0.018354536965489388, 0.03245863318443298, -0.0005247761146165431, 0.07225407660007477, 0.10013562440872192, 0.00029388099210336804, 0.06888007372617722, 0.07083212584257126, -0.05810803547501564, -0.005092881619930267, -0.012182614766061306, 0.04614976420998573, 0.04415840283036232, 0.06369717419147491, -0.060812823474407196, 0.005775881465524435, 0.0674290731549263, -0.00336501095443964, 0.013661352917551994, -0.03746247664093971, 0.014550034888088703, 0.030105166137218475, 0.004063731990754604, 0.01706012524664402, -0.03272392973303795, 0.02439550682902336, 0.034385066479444504, -0.021011995151638985, -0.024481479078531265, -0.026503589004278183, 0.01858043484389782, 0.021941281855106354, 0.038304898887872696, 0.029998045414686203, 0.047690942883491516, 0.11182213574647903, -0.03175061196088791, 0.05104074999690056, -0.05447554960846901, -0.0256960391998291, 0.00313443411141634, -0.05904252082109451, 0.004004061687737703, 0.020472440868616104, 0.011228435672819614, -0.03544565290212631, 0.002488408936187625, 0.051302310079336166, -0.03996436297893524, -0.011398361064493656, 0.02431560307741165, 0.01886749267578125, 0.035993847995996475, 0.014629793353378773, -0.046956777572631836, -0.004073214717209339, -0.014618763700127602, -0.007028116378933191, 0.015630319714546204, 0.037559304386377335, 0.0032912823371589184, 0.04429296404123306, 0.01048245932906866, -0.00673086429014802, 0.028414098545908928, 0.058598365634679794, 0.014179532416164875, -0.06408922374248505, 0.08602126687765121, 0.024555804207921028, -0.07169383764266968, -0.018144851550459862, 0.033352840691804886, 0.026371177285909653, 0.07131358981132507, -0.006017810665071011, -0.0312601663172245, 0.07236344367265701, -0.07754933089017868, 0.0375857800245285, -0.015376297757029533, -0.11509362608194351, 0.003388682845979929, -0.02549107000231743, -0.027982152998447418, 0.025709670037031174, 0.034752946346998215, 0.05789494141936302, 0.0012529917294159532, 0.05825261026620865, 0.010106070898473263, -0.004321345593780279, -0.03965100273489952, 0.0263084564357996, -0.012938004918396473, -0.07314877212047577, -0.013228862546384335, -0.07314898073673248, -0.0003283762198407203, -0.052986085414886475, -0.00034462244366295636, 0.0028516408056020737, -0.02705417387187481, 0.03753598406910896, 0.023126734420657158, -0.0522335059940815, -0.01683858595788479, 0.045226454734802246, -0.05281471461057663, 0.019787857308983803, 0.027684228494763374, -0.009126619435846806, -0.0012935767881572247, 0.06386858224868774, -0.073653444647789, 0.016346432268619537, 0.01939522847533226, 0.006647864356637001, 0.021946212276816368, 0.0169814620167017, -0.028923122212290764, 0.005176427774131298, 0.03591348975896835, -0.005884811747819185, 0.06295503675937653, -0.01972920261323452, 0.04633312299847603, 0.0036070249043405056, -0.022618789225816727, -0.06773769110441208, 0.023563550785183907, 0.0019392501562833786, 0.048963502049446106, 0.016459085047245026, -0.009603858925402164, 0.017737533897161484, -0.008408425375819206, -0.0019129280699416995, -0.000953876122366637, -0.010243643075227737, -0.05918009579181671, -0.03714809939265251, 0.02494841441512108, 0.001256698975339532, -0.04888611286878586, 0.056555915623903275, -0.07085061073303223, -0.00896454881876707, 0.06816651672124863, 0.005226139910519123, -0.022397315129637718, -0.024778390303254128, 0.06429305672645569, -0.008717252872884274, -0.019614705815911293, -0.020524272695183754, -0.035781312733888626, -0.02462601289153099, 0.0026970321778208017, -0.026166528463363647, 0.07376725226640701, -0.001475028577260673, -0.039329059422016144, -0.03020489774644375, 0.0009692137246020138, 0.043101634830236435, -0.05831991508603096, -0.02509581297636032, 0.017800472676753998, 0.035315826535224915, -0.03046027570962906, 0.004291621036827564, -0.05932624638080597, -0.02573280781507492, 0.03416857868432999, -0.03513001650571823, -0.01484422292560339, 0.025967979803681374, -0.010685243643820286, -0.01436475571244955, -0.019093824550509453, 0.039377301931381226, 0.005897984374314547, 0.015458961948752403, -0.03970308229327202, -0.01474816258996725, -0.030491745099425316, -0.02969571202993393, -0.0021733855828642845, -0.037809859961271286, 0.008507340215146542, -0.056264620274305344, -0.00013298384146764874, -0.03138221055269241, -0.061712123453617096, -0.03973746672272682, -0.0388157032430172, -0.02706603705883026, 0.03911621496081352, -0.05576330050826073, 0.026730669662356377, 0.042985815554857254, 0.03567690774798393, 0.010808093473315239, -0.000050199945690110326, -0.011514781042933464, 0.04270227253437042, -0.04218520596623421, -0.06470632553100586, 0.043460018932819366, -0.009389366954565048, 0.03057597018778324, -0.016118433326482773, 0.006003305781632662, -0.009021086618304253, -0.05531318485736847, 0.021159036085009575, 0.05486473813652992, -0.06995847076177597, -0.0036062344443053007, -0.02978518232703209, -0.018603438511490822, -0.012467564083635807, -0.02525007352232933, -0.005307316780090332, 0.045537665486335754, -0.002748509170487523, -0.01321104820817709, 0.005887581966817379, 0.0012451211223378778, -0.05075329542160034, -0.017895758152008057, -0.04688848555088043, -0.012007239274680614, 0.01244172640144825, 0.009527995251119137, -0.005518755875527859, -0.023497337475419044, 0.00017989211482927203, 0.047390226274728775, 0.025232233107089996, -0.07232112437486649, 0.00017148189363069832, -0.027115797623991966, -0.00043396628461778164, 0.022978264838457108, -0.05242510139942169, 0.009431784972548485, -0.01588159240782261, -0.0004182466655038297, -0.02915424481034279, 0.009452493861317635, 0.07805882394313812, -0.030710579827427864, 0.0512809082865715, -0.0018877304391935468, -0.09609852731227875, 0.05176056548953056, 0.0504300594329834, 0.02780046872794628, 0.012191644869744778, 0.00968706514686346, 0.005056372378021479, 0.005715959705412388, -0.003220210550352931, -0.008415480144321918, -0.024533113464713097, -0.04467044770717621, -0.05631937459111214, 0.004424505867063999, -0.006211337633430958, 0.026403946802020073, -0.02078929729759693, -0.06025191396474838, -0.0057000527158379555, -0.0025232655461877584, -0.0031758768018335104, 0.04543560743331909, -0.019800467416644096, -0.020818201825022697, 0.011281928978860378, -0.07590196281671524, -0.04023535177111626, -0.01257648691534996, -0.005259551107883453, 0.04247753694653511, -0.018077902495861053, -0.03477668762207031, 0.02640903927385807, -0.07336722314357758, 0.013921724632382393, -0.027803471311926842, -0.00977769959717989, -0.02480778470635414, -0.0007773934630677104, 0.06830230355262756, -0.023222891613841057, -0.008940215222537518, 0.038587260991334915, -0.03678629547357559, -0.038754623383283615, -0.017337152734398842, -0.03414314612746239, -0.02666224166750908, -0.028579555451869965, 0.006608275696635246, -0.037871893495321274, 0.0014589829370379448, -0.01377907581627369, -0.019979773089289665, 0.0149989053606987, -0.013678722083568573, 0.02880246937274933, 0.03140309080481529, -0.0690799131989479, 0.05539686977863312, 0.053553495556116104, -0.009320618584752083, -0.023069189861416817, -0.05710413306951523, 0.015964899212121964, -0.027608690783381462, -0.05571075156331062, 0.028066912665963173, 0.011271058581769466, -0.005156882107257843, -0.05525640770792961, -0.04310910403728485, 0.0688861832022667, -0.010394291020929813, 0.00994452927261591, -0.0545378103852272, -0.004745955113321543, -0.010042289271950722, 0.052262187004089355, 0.046614859253168106, 0.0974566712975502, -0.03218694031238556, -0.016844311729073524, 0.05268793925642967, 0.06549811363220215, 0.011123478412628174, -0.005077236331999302, -0.02417338453233242, 0.09380211681127548, -0.001292747794650495, 0.021063311025500298, 0.009714726358652115, -0.0327044315636158, 0.07296964526176453, -0.003318688366562128, 0.024960948154330254, 0.039569541811943054, 0.032014958560466766, 0.07175801694393158, 0.032772500067949295, 0.019596964120864868, 0.03226938471198082, -0.03850964829325676, 0.04344707727432251, -0.009763620793819427, 0.001717179431580007, -0.03697005286812782, -0.0006441246368922293, -0.05403755605220795, 0.016252942383289337, -0.028295723721385002, -0.017338784411549568, 0.04554085433483124, 0.029468758031725883, -0.009341632016003132, -0.020502038300037384, -0.012043511494994164, 0.03568887338042259, -0.024983031675219536, -0.026530617848038673, 0.00484529510140419, -0.01344413124024868, 0.012847294099628925, 0.011719025671482086, -0.07391031831502914, -0.0405380055308342, -0.07576680928468704, -0.03434641286730766, -0.04654448479413986, -0.002933046082034707, -0.02174108475446701, -0.013779879547655582, 0.02409297227859497, 0.008589585311710835, -0.0065511357970535755, 0.012478957884013653, 0.01776966080069542, -0.018860233947634697, -0.051723066717386246, 0.007825439795851707, 0.027806591242551804, -0.06647049635648727, -0.023856259882450104, 0.04578971862792969, -0.02686208300292492, 0.0015571742551401258, 0.022955210879445076, -0.026305241510272026, 0.0141165005043149, -0.0229211263358593, 0.02356221340596676, 0.013665094040334225, -0.05862262845039368, -0.019079403951764107, 0.04375568404793739, -0.014073116704821587, -0.04041951522231102, -0.01660371944308281, -0.031333934515714645, 0.0017293962882831693, 0.03798139467835426, 0.01051398180425167, -0.036339495331048965, 0.05348736792802811, 0.05669384077191353, -0.019716180860996246, -0.026612283661961555, 0.02034480683505535, -0.006182963028550148, 0.023286527022719383, -0.02284231036901474, 0.01957745850086212, 0.02681734599173069, -0.02196878008544445, 0.002672493690624833, -0.017308436334133148, -0.009513800963759422, -0.021717211231589317, -0.017769688740372658, 0.04806392639875412, 0.014434011653065681, -0.01002032682299614, 0.018571967259049416, 0.018690552562475204, -0.016172334551811218, 0.057919152081012726, 0.018485374748706818, 0.008686572313308716, 0.03627656772732735, -0.00520327128469944, 0.07217929512262344, 0.03872021660208702, -0.001820715726353228, -0.02787083201110363, 0.0031343516893684864, -0.034189432859420776, 0.0738416388630867, -0.019206499680876732, -0.0462309755384922, 0.042122118175029755, -0.014391674660146236, 0.06089542806148529, 0.0031912776175886393, -0.013268782757222652, -0.015712901949882507, -0.016303788870573044, 0.06434265524148941, -0.024120207875967026, -0.07236281782388687, -0.07085316628217697, -0.00705857016146183, 0.0327724814414978, 0.0008273155544884503, 0.042083799839019775, -0.02391696162521839, -0.04277626425027847, -0.05086703225970268, -0.006583039183169603, -0.014967692084610462, -0.004031991586089134, -0.0015885778702795506, -0.028896883130073547, 0.04550272598862648, -0.02509816735982895, -0.00936231017112732, -0.06828711926937103, 0.0740528404712677, -0.01965712197124958, -0.007112888153642416, -0.010585527867078781, 0.035534702241420746, 0.01318761520087719, -0.02138705737888813, 0.01253011729568243, 0.012546791695058346, -0.011806611903011799, -0.06910806149244308, 0.006777225527912378, 0.017444392666220665, 0.008725687861442566, 0.06350868940353394, -0.03674918785691261, 0.01531883142888546, 0.06401601433753967, -0.0484621524810791, -0.004929320886731148, 0.003629434620961547, -0.004324157256633043, -0.007543493062257767, -0.029490290209650993, -0.04154684767127037, 0.01577545702457428, -0.06484074890613556, -0.0021113399416208267, 0.0025024390779435635, -0.02889455296099186, 0.0007566983695141971, -0.005544358864426613, -0.03470873460173607, -0.022599415853619576, 0.03176337480545044, 0.010198231786489487, 0.02404998056590557, -0.037538934499025345, -0.057344332337379456, -0.02463134564459324, 0.033158671110868454, -0.01898884028196335, -0.017513027414679527, 0.05446023866534233, 0.033671386539936066, 0.029560960829257965, -0.013565339148044586, 0.026060255244374275, 0.016853397712111473, -0.026311147958040237, 0.02126232348382473, -0.04231918603181839, 0.014546304941177368, 0.0288409274071455, 0.045148804783821106, 0.0011758973123505712, 0.027348192408680916, 0.043816614896059036, -0.05599735304713249, 0.048957519233226776, 0.024085266515612602, -0.012376844882965088, -0.010522052645683289, 0.01991444081068039, -0.012292260304093361, 0.007319134194403887, 0.03998652845621109, 0.04019365832209587, 0.0034202777314931154, 0.020732183009386063, 0.016751037910580635, 0.028541818261146545, 0.023516345769166946, -0.005193702876567841, 0.00042842014227062464, -0.037457507103681564, -0.05402291566133499, 0.00036036132951267064, 0.025734752416610718, -0.0536956824362278, -0.015834486111998558, 0.048688117414712906, -0.04500842094421387, -0.11304585635662079, 0.024486441165208817, 0.01425947155803442, 0.0057679819874465466, 0.04627818986773491, 0.01999340020120144, 0.01793665625154972, 0.020121397450566292, -0.09490092098712921, 0.006967057473957539, 0.027491727843880653, -0.03725855052471161, 0.06574743241071701, -0.030693626031279564, 0.005488332360982895, 0.001772930845618248, -0.07227503508329391, -0.043982669711112976, 0.018483148887753487, -0.01940511353313923, -0.037657689303159714, -0.009257066063582897, 0.0018917276756837964, 0.01592210680246353, -0.013952747918665409, -0.05477802827954292, -0.04186121001839638, -0.04037768766283989, -0.02161596156656742, -0.030082223936915398, 0.11003448069095612, 0.05931423604488373, 0.047108691185712814, -0.012020058929920197, 0.08625119179487228, 0.016717351973056793, -0.05863455682992935, -0.0581376850605011, -0.05082634463906288, -0.05596604570746422, -0.013460196554660797, 0.012150698341429234, -0.009368617087602615, 0.035061657428741455, -0.007618557661771774, 0.024789532646536827, 0.06554768979549408, 0.001345297321677208, -0.006016093771904707, -0.02159741334617138, -0.03263196721673012, -0.03257711976766586, -0.0029810538981109858, 0.0004967011045664549, 0.02898014709353447, 0.030831312760710716, -0.03767217695713043, 0.009253510273993015, 0.03652970865368843, -0.04202035814523697, -0.015031549148261547, 0.013065271079540253, -0.013842371292412281, 0.01212687324732542, 0.020944152027368546, -0.044885583221912384, -0.051568660885095596, 0.014086185023188591, -0.018699701875448227, 0.033379796892404556, 0.03288879245519638, 0.038586001843214035, -0.014272636733949184, 0.00924371276050806, 0.027828732505440712, -0.005461842752993107, -0.026922833174467087, 0.012810388579964638, 0.013388129882514477, -0.034243181347846985, -0.00982298981398344, -0.01613810658454895, 0.050043925642967224, -0.03369859606027603, 0.0655413493514061, 0.047131262719631195, -0.02385583519935608, -0.02203715778887272, 0.06022533401846886, 0.04480123892426491, -0.002988433698192239, -0.012199614197015762, 0.009750492870807648, -0.01583794131875038, -0.0055948104709386826, 0.00753424409776926, 0.046277835965156555, 0.019710898399353027, 0.00033544233883731067, -0.015192822553217411, 0.05034136772155762, 0.014478631317615509, 0.03616013377904892, 0.015555004589259624, -0.04368731379508972, 0.001012644381262362, 0.013797919265925884, -0.010213331319391727, 0.025960860773921013, 0.021300798282027245, 0.05243848264217377, -0.032101504504680634, -0.0317913293838501, -0.0429530069231987, -0.009328564628958702, -0.006872218567878008, 0.03514345735311508 ]
<p>The anthropic principle has become a very popular explanation among theoretical physicists lately. Life is unlikely, but only life can observe, so we find ourselves in an unlikely position, so to speak. What I would like to ask is just how unlikely is life? Is the evolution of life generic for most laws of physics, or extremely unlikely with extreme fine-tuning? What is so controversial about the anthropic principle? No one is surprised to find themselves on an Earth-like planet orbiting a long lived star at just about the right distance from the star with plenty of liquid water, a thick atmosphere and plenty of carbon amidst the sterile antiseptic reaches of space. What are the major pros and cons? String theory conveniently provides a multiverse and a landscape.</p>
g1579
[ -0.005482934415340424, 0.05277606099843979, 0.013424577191472054, -0.014758282341063023, -0.005195124540477991, 0.04334408789873123, -0.014489766210317612, -0.032965973019599915, 0.016126291826367378, 0.026612602174282074, 0.01819787360727787, -0.012551071122288704, 0.0330539271235466, -0.02054605819284916, -0.019335215911269188, -0.03937201946973801, 0.037554994225502014, -0.00823624525219202, 0.07069557905197144, -0.007199176121503115, -0.019669344648718834, -0.0057268464006483555, 0.02768825925886631, 0.01714150421321392, -0.03520934283733368, -0.031042220070958138, -0.017363086342811584, -0.022294266149401665, 0.04487970843911171, -0.009179783053696156, 0.03668578714132309, 0.020084166899323463, 0.05824293568730354, -0.04907607287168503, 0.005827808286994696, -0.047558754682540894, 0.0013221539556980133, 0.02234296314418316, 0.0690162405371666, 0.005598961841315031, -0.08056119829416275, -0.014578799717128277, 0.031029794365167618, 0.0227999035269022, 0.015307579189538956, 0.04036588966846466, -0.07108787447214127, -0.01838056556880474, 0.03278074786067009, -0.05606238543987274, 0.010428840294480324, 0.03863859921693802, 0.03706798329949379, 0.011735215783119202, 0.09151555597782135, 0.015018454752862453, 0.010312248952686787, 0.02501234970986843, -0.04061052203178406, -0.029358817264437675, 0.0010091104777529836, 0.07209353148937225, -0.04042275622487068, 0.05011001229286194, 0.03211917728185654, 0.0016267099417746067, 0.012607206590473652, 0.010805238038301468, 0.061746250838041306, -0.009598728269338608, 0.017905134707689285, -0.11041507124900818, -0.055472977459430695, -0.018481433391571045, -0.016696184873580933, 0.045858584344387054, -0.047354694455862045, 0.033876169472932816, 0.02094048447906971, 0.05521736294031143, -0.001302551245316863, -0.006214823108166456, -0.043327998369932175, 0.032151155173778534, -0.008220313116908073, -0.05949484929442406, 0.03763769194483757, -0.012256034649908543, -0.03677190840244293, 0.00869534071534872, 0.06214156001806259, -0.0030690862331539392, 0.016983620822429657, -0.012097413651645184, -0.043111883103847504, 0.005934306886047125, -0.01065434142947197, 0.013323171995580196, -0.05148053169250488, -0.02243143878877163, -0.028712546452879906, 0.020281516015529633, 0.042134083807468414, 0.03865295276045799, -0.053650327026844025, -0.030846470966935158, 0.003329105908051133, 0.02590213343501091, 0.006917839404195547, 0.0010192964691668749, -0.027514293789863586, 0.08425098657608032, 0.0017306082881987095, -0.04867255687713623, -0.0216095931828022, -0.009732868522405624, 0.007864751853048801, 0.028416840359568596, 0.021768109872937202, 0.04308955743908882, 0.048735473304986954, 0.04947435110807419, 0.06917238980531693, -0.009266642853617668, -0.09775210171937943, 0.0069837248884141445, -0.04083404317498207, -0.04458146542310715, 0.014794455841183662, 0.0039547341875731945, 0.02128182165324688, 0.02802174538373947, -0.06773567199707031, -0.009544463828206062, -0.025853972882032394, -0.005950661841779947, -0.024363504722714424, -0.015635864809155464, -0.011750916950404644, -0.021237818524241447, 0.020053094252943993, -0.03553323820233345, 0.041011810302734375, 0.01576320268213749, -0.04977595433592796, 0.032029371708631516, 0.0031069363467395306, -0.015478315763175488, 0.04073828086256981, -0.0003747519222088158, -0.04517323896288872, 0.0573766753077507, 0.05449094623327255, 0.0027988844085484743, -0.00046705896966159344, 0.040535107254981995, 0.0004474408633541316, 0.02256264165043831, -0.004926932975649834, -0.023067262023687363, 0.045873045921325684, 0.040373917669057846, -0.006164727732539177, -0.02125312015414238, 0.0058492147363722324, 0.02981417253613472, -0.032206639647483826, -0.07411321252584457, 0.03693044185638428, 0.07084353268146515, -0.027091262862086296, -0.05252779647707939, 0.08206304162740707, 0.013456578366458416, -0.05176303908228874, -0.06217078119516373, -0.013936887495219707, -0.0037206222768872976, -0.1019161194562912, -0.03505534306168556, -0.001624631229788065, -0.035052258521318436, -0.05935215577483177, 0.04789896309375763, 0.024454763159155846, 0.0076737310737371445, 0.026069562882184982, -0.0008738497272133827, -0.037627849727869034, -0.014166679233312607, 0.008955108933150768, -0.027142608538269997, 0.01760745607316494, -0.030100757256150246, 0.05553600564599037, -0.03333102911710739, -0.006315511651337147, 0.015993839129805565, 0.03015872836112976, -0.02364467829465866, 0.03866330161690712, 0.03623291477560997, -0.00002949450572486967, -0.028891541063785553, -0.03971050679683685, 0.009711015969514847, -0.04881991446018219, 0.0010637296363711357, -0.01150257233530283, -0.022438276559114456, 0.06718861311674118, -0.03246616944670677, -0.025638606399297714, 0.046401023864746094, -0.034030113369226456, -0.03070477955043316, -0.016324669122695923, 0.0014335802989080548, -0.03439659625291824, 0.012596551328897476, 0.08456601947546005, -0.027945037931203842, 0.02934359945356846, 0.05820545181632042, 0.021132031455636024, -0.0009388339822180569, -0.09633428603410721, -0.02139413356781006, 0.010960583575069904, 0.007037549279630184, -0.03595314547419548, 0.025219891220331192, 0.012959402985870838, -0.0034604493994265795, -0.013399052433669567, 0.022463740780949593, 0.021120021119713783, -0.0357576385140419, 0.03226335719227791, 0.0367017537355423, 0.0007973205065354705, -0.028296345844864845, -0.02642686665058136, 0.029362453147768974, 0.07133133709430695, -0.022025657817721367, 0.008072653785347939, -0.049431294202804565, -0.011721414513885975, -0.009061741642653942, 0.03190922364592552, 0.0006957982550375164, 0.006999189034104347, 0.015763472765684128, -0.007445781026035547, 0.00939839705824852, 0.0214985441416502, 0.034299418330192566, -0.04864501953125, 0.013417934067547321, 0.010299316607415676, 0.0461856871843338, -0.05900029465556145, -0.01970307156443596, -0.0641702339053154, 0.02589409239590168, -0.026253415271639824, 0.018689654767513275, -0.06306979060173035, 0.022719072178006172, 0.06037693843245506, 0.04978473484516144, -0.020812684670090675, 0.0055693075992167, 0.025940442457795143, 0.01975170150399208, -0.0830693244934082, -0.01682647503912449, 0.0423310361802578, -0.02311890758574009, 0.007172520272433758, -0.029210232198238373, -0.011006662622094154, 0.012859282083809376, 0.07750430703163147, 0.00006948960071895272, 0.017742566764354706, 0.016186509281396866, 0.011208939366042614, 0.052011508494615555, -0.01603851281106472, -0.024117199704051018, -0.023587364703416824, 0.004904004279524088, 0.011980111710727215, -0.011055530980229378, 0.042057573795318604, 0.018560368567705154, -0.10426332801580429, 0.018242336809635162, 0.01753721386194229, -0.0229457076638937, 0.052510250359773636, 0.06587877124547958, -0.014309119433164597, 0.013953262008726597, -0.05836412310600281, -0.02615668810904026, -0.003265634411945939, -0.05407852306962013, 0.011996806599199772, 0.040669381618499756, 0.016632959246635437, 0.008359557949006557, 0.005399479530751705, 0.02966334857046604, -0.026842201128602028, 0.010966663248836994, 0.07735203951597214, -0.04252595826983452, -0.021022306755185127, -0.02753790281713009, -0.034893281757831573, 0.02293824777007103, 0.0837411880493164, -0.029182521626353264, -0.06945590674877167, -0.02606142684817314, -0.057613205164670944, 0.0012043608585372567, 0.0010835396824404597, 0.010321379639208317, -0.044129736721515656, -0.04715103283524513, -0.08696252852678299, -0.01887817308306694, -0.017671314999461174, -0.009699095971882343, -0.02195845916867256, 0.016164500266313553, 0.003430399112403393, 0.0018329828744754195, 0.05769657716155052, -0.02026519924402237, 0.019394056871533394, 0.013870734721422195, 0.019165482372045517, -0.041190918534994125, 0.059532999992370605, 0.03817025199532509, 0.013515389524400234, -0.05566571652889252, 0.040808022022247314, 0.06805509328842163, -0.02145284228026867, 0.056613944470882416, 0.04886018857359886, 0.026226529851555824, 0.022009801119565964, -0.02125008963048458, -0.02398861013352871, -0.030188968405127525, 0.013286076486110687, -0.01040391344577074, 0.014101373963057995, -0.04164872691035271, -0.01354455016553402, -0.0054466258734464645, 0.04839028790593147, 0.0028494989965111017, 0.008112507872283459, -0.008746369741857052, -0.06399095803499222, 0.04740052670240402, 0.03872167691588402, 0.04967961832880974, -0.003653481602668762, 0.0038538933731615543, -0.011592379771173, 0.00577120715752244, 0.03625737875699997, 0.0054011219181120396, 0.0153385940939188, -0.019387388601899147, 0.011528565548360348, -0.013605457730591297, -0.05568305775523186, 0.00971620250493288, 0.014309117570519447, 0.02667379193007946, -0.05896119028329849, -0.011345462873578072, -0.03555678203701973, -0.044200729578733444, 0.020234905183315277, -0.00287619442678988, -0.0015821600100025535, -0.029657205566763878, 0.01697525382041931, -0.012180738151073456, 0.012473296374082565, 0.026271160691976547, 0.004438369069248438, -0.02443796768784523, -0.015133034437894821, -0.03803081810474396, 0.019494248554110527, -0.0629810243844986, -0.009857500903308392, -0.05279894173145294, 0.01276136003434658, 0.10771991312503815, 0.01126497145742178, -0.05773235857486725, -0.002082275692373514, 0.002876098034903407, -0.018572526052594185, -0.0821169912815094, 0.028248075395822525, -0.008358125574886799, 0.02077462524175644, 0.01747114211320877, 0.00132102076895535, -0.015959449112415314, -0.07791104912757874, 0.06753363460302353, 0.024211976677179337, 0.008786877617239952, -0.04749312996864319, 0.012824599631130695, 0.014186406508088112, -0.009140496142208576, -0.0064938860014081, 0.03736594319343567, -0.0214866790920496, 0.0015805648872628808, -0.005305466707795858, -0.030928835272789, 0.033455438911914825, 0.025539806112647057, 0.03835258632898331, -0.01288791373372078, 0.0899617150425911, 0.013745239935815334, 0.005390099715441465, 0.04859723523259163, 0.01853107661008835, -0.03170229494571686, 0.012419459410011768, 0.05466429144144058, 0.033185407519340515, -0.0017402354860678315, -0.030293280258774757, 0.02687407284975052, 0.00675611337646842, -0.027375228703022003, 0.0073502808809280396, 0.025632550939917564, 0.026830265298485756, -0.0001779816229827702, -0.03934330865740776, -0.001365312491543591, -0.0008849199512042105, 0.05891504883766174, 0.03955880180001259, 0.04963960126042366, -0.023532437160611153, -0.013416380621492863, 0.0419120118021965, 0.010615312494337559, -0.05032781511545181, -0.0048424056731164455, 0.017127513885498047, 0.017529165372252464, -0.05099575221538544, -0.04258173331618309, -0.00482450146228075, -0.01980244182050228, -0.02055220864713192, 0.0011867855209857225, -0.02132249064743519, -0.05129395052790642, -0.00006010121796862222, -0.000013219214451964945, 0.008604311384260654, -0.013411153107881546, -0.04619928449392319, 0.007144839037209749, -0.06277266144752502, -0.024915123358368874, -0.03325290605425835, -0.047259099781513214, 0.025281531736254692, 0.003723375964909792, -0.02700677141547203, -0.006123741623014212, 0.021710023283958435, -0.019341405481100082, -0.033522870391607285, 0.0028024676721543074, -0.028602540493011475, 0.01329182367771864, -0.015990043058991432, -0.03698611631989479, -0.020187124609947205, 0.01917736418545246, 0.03135151416063309, -0.03596789762377739, 0.00702674500644207, -0.01640505902469158, 0.019232172518968582, 0.005123602692037821, -0.061494164168834686, 0.04172488674521446, 0.020269732922315598, -0.029187656939029694, -0.03319058194756508, -0.03659369796514511, 0.06796754151582718, -0.0279216505587101, 0.0020213709212839603, 0.005165455862879753, 0.020423853769898415, -0.03188316896557808, 0.0077934893779456615, 0.032792843878269196, -0.06092727184295654, 0.035829126834869385, -0.014709520153701305, -0.018546033650636673, -0.06116548925638199, 0.010854498483240604, 0.044394802302122116, -0.058574359863996506, -0.06528103351593018, -0.002320382511243224, -0.024661850184202194, 0.006274355575442314, 0.051103658974170685, -0.01313320454210043, 0.01247377134859562, 0.0028983294032514095, 0.005283616483211517, 0.008709723129868507, -0.013522075489163399, 0.012557120993733406, -0.06583327800035477, 0.03695812076330185, 0.02263583056628704, 0.003311200998723507, -0.09613072872161865, 0.0032227179035544395, 0.006247104611247778, 0.03982388973236084, -0.000707156490534544, 0.03149178624153137, -0.00899207592010498, 0.019154468551278114, 0.008436542004346848, 0.0521870031952858, 0.003455791622400284, 0.07725077122449875, -0.015257099643349648, -0.01915169134736061, -0.06302677094936371, -0.01343249436467886, 0.02132168412208557, -0.054245829582214355, 0.04266463220119476, 0.06391511112451553, 0.01422949880361557, 0.07608017325401306, -0.019388874992728233, 0.024825194850564003, 0.01995317079126835, -0.027180446311831474, 0.0011153564555570483, -0.04295846447348595, -0.022760488092899323, -0.06642226874828339, -0.03321303054690361, 0.02571173757314682, 0.03136906772851944, -0.00812250841408968, -0.018741272389888763, 0.04709009826183319, 0.009221416898071766, -0.02179580181837082, 0.019762985408306122, 0.007569575682282448, 0.05104455351829529, 0.00027817056979984045, 0.025539033114910126, 0.03435569629073143, -0.04989633709192276, -0.08860380202531815, 0.00009310485620517284, 0.024505741894245148, -0.03162001073360443, -0.02466304786503315, 0.02618684247136116, 0.0508066825568676, 0.007800048217177391, 0.028312889859080315, 0.011536960490047932, 0.04369121789932251, -0.0026963897980749607, 0.04159224405884743, 0.03633124381303787, -0.014964362606406212, 0.020196396857500076, 0.014592420309782028, -0.005092809908092022, 0.04536157101392746, -0.03322560712695122, -0.033570002764463425, 0.024237992241978645, -0.019230153411626816, -0.05048359930515289, 0.05200642719864845, -0.02184304967522621, 0.015492917038500309, 0.01524793729186058, 0.008955495432019234, -0.02149667777121067, 0.022326607257127762, 0.02496829256415367, 0.061577871441841125, 0.04762496054172516, -0.008610446006059647, -0.03540893271565437, -0.01582218147814274, 0.07760632038116455, 0.06350818276405334, 0.01369477715343237, 0.04897003248333931, -0.05122341960668564, -0.021047446876764297, -0.009344877675175667, 0.022748254239559174, -0.013503442518413067, 0.026539525017142296, 0.07297801971435547, 0.011480382643640041, -0.028339345008134842, 0.06000601127743721, 0.04146454855799675, -0.05623898282647133, -0.01464940421283245, -0.045634523034095764, 0.01963360607624054, -0.07005103677511215, -0.022994713857769966, 0.04084598645567894, 0.0518760085105896, 0.041720952838659286, -0.026275910437107086, -0.0397956557571888, -0.012074144557118416, -0.09072702378034592, -0.05208784341812134, 0.029033957049250603, 0.00539097934961319, -0.04587695002555847, -0.014007260091602802, -0.0010490892454981804, 0.06818205863237381, -0.05388525128364563, -0.050611600279808044, -0.00395210413262248, -0.019897565245628357, 0.015017292462289333, -0.03878934681415558, -0.027282504364848137, 0.039101891219615936, -0.032564032822847366, -0.041038043797016144, -0.027021879330277443, 0.015068236738443375, 0.021132692694664, 0.027474360540509224, 0.04707009717822075, -0.007895618677139282, -0.009033545851707458, -0.02240985631942749, -0.012613841332495213, 0.009240405634045601, -0.019441820681095123, -0.03099888190627098, -0.047924481332302094, -0.0448649525642395, -0.024634061381220818, -0.028742874041199684, -0.09150318801403046, 0.05203082039952278, 0.015147450380027294, 0.010094469413161278, 0.03820387274026871, 0.09216480702161789, 0.04991883412003517, -0.002174453344196081, -0.010942063294351101, -0.062281981110572815, -0.01719975471496582, 0.06986778974533081, -0.004920190665870905, -0.029490875080227852, 0.023154212161898613, -0.06280629336833954, 0.0028521898202598095, 0.003888673847541213, 0.07462786883115768, 0.00007421304326271638, 0.03793995827436447, 0.041477520018815994, -0.022639112547039986, 0.007869209162890911, -0.003215468255802989, -0.04520620033144951, 0.0003622561926022172, 0.05738234892487526, -0.007917976006865501, 0.011286568827927113, 0.03278414532542229, -0.052932992577552795, 0.04447679594159126, -0.005847272928804159, -0.04865596443414688, 0.001031807973049581, -0.07416482269763947, -0.014883973635733128, -0.008493042550981045, -0.013062145560979843, -0.0027611039113253355, -0.07644272595643997, 0.0350821278989315, -0.06924278289079666, 0.06787344813346863, -0.05884226784110069, -0.05249609425663948, 0.028423083946108818, 0.04427949711680412, 0.04003289341926575, 0.017822761088609695, -0.036198683083057404, -0.0035654986277222633, -0.053258802741765976, 0.03092501126229763, -0.005758976563811302, 0.05404750257730484, 0.0020263222977519035, -0.017192242667078972, -0.057325150817632675, 0.03695819899439812, 0.07581187784671783, -0.01203152071684599, 0.032018646597862244, 0.027568859979510307, -0.012249348685145378, -0.018758835271000862, 0.02088826149702072, -0.016083650290966034, 0.007163160014897585, -0.00029081531101837754, -0.04187657684087753, 0.02472676709294319, -0.03373056650161743, -0.008526798337697983 ]
<p>I was recently reading <a href="http://en.wikipedia.org/wiki/Siphon#Explanation_using_Bernoulli.27s_equation" rel="nofollow">the explanation for the behaviour of a siphon</a> on Wikipedia, which uses Bernoulli's equation in its proof. The argument is generally pretty easy to follow, except for one key point: how can we assume that the velocity of the water is constant at all points throughout its flow through the tube? This tacit assumption is made at various point, not least in the terming of "the siphon velocity" (implying there's only one). I would be grateful if someone could clarify this.</p> <p>Note: I've done a hefty amount of classical mechanics in my time, but barely any fluid mechanics I'm afraid. First principles explanations would be appreciated.</p>
g1580
[ 0.029282227158546448, 0.02296474762260914, -0.01085873693227768, -0.01711815409362316, 0.07305548340082169, 0.01571948453783989, 0.058054011315107346, 0.022481407970190048, -0.043893590569496155, -0.03402683138847351, -0.024309024214744568, -0.014226574450731277, -0.02717389166355133, 0.040061838924884796, -0.01816033385694027, -0.03631449490785599, -0.037455443292856216, -0.02537965029478073, 0.014877223409712315, 0.033836688846349716, 0.0018199440091848373, 0.022220907732844353, 0.012666204012930393, -0.002404592465609312, 0.0155238201841712, -0.014547845348715782, 0.03575233370065689, -0.03706275299191475, 0.014829830266535282, -0.04834676533937454, 0.011043769307434559, -0.017034875229001045, 0.03611825779080391, -0.03714174032211304, -0.02815358340740204, -0.019622985273599625, 0.0017689551459625363, -0.023510485887527466, 0.025387071073055267, -0.0326092503964901, 0.01684398017823696, 0.03358740359544754, -0.06702183187007904, 0.07667003571987152, 0.00675585912540555, -0.010527485981583595, 0.010195056907832623, -0.04124035686254501, -0.05645477771759033, 0.0005516804521903396, 0.012345555238425732, 0.026378847658634186, 0.0028868208173662424, 0.009581385180354118, -0.05545254796743393, 0.07636038959026337, 0.04620323330163956, 0.01121983490884304, -0.02172688953578472, -0.0022935832384973764, 0.001860130811110139, -0.012954759411513805, 0.017235733568668365, 0.011831462383270264, 0.02065829187631607, -0.03103865683078766, -0.02050338312983513, -0.059327781200408936, 0.002518598921597004, 0.03936289995908737, -0.05199248343706131, -0.0829923003911972, -0.009049979038536549, -0.0314575619995594, -0.03635210916399956, 0.014738417230546474, -0.05444010719656944, 0.019177762791514397, 0.010934351943433285, -0.05834116414189339, -0.01193840242922306, 0.03411971777677536, 0.037696726620197296, 0.0115603506565094, 0.011945974081754684, 0.0023084688000380993, 0.03509777411818504, -0.036359310150146484, -0.022833073511719704, -0.03324143588542938, -0.10461491346359253, -0.06368547677993774, 0.0022591855376958847, -0.0012631601421162486, -0.01743001863360405, -0.07580406218767166, -0.061417851597070694, 0.05596350133419037, 0.004401240963488817, 0.06991004943847656, -0.07916013151407242, 0.042347826063632965, 0.024529973044991493, 0.00027819734532386065, 0.0018677815096452832, -0.034083060920238495, 0.02080378867685795, 0.05959535390138626, -0.016022950410842896, -0.04592779651284218, 0.012997006997466087, -0.06363407522439957, 0.01880311779677868, 0.04177931323647499, -0.015466460026800632, 0.0068083275109529495, 0.03110048919916153, 0.03416389226913452, 0.03073284775018692, 0.05965325981378555, -0.05833621695637703, 0.051940951496362686, -0.035979922860860825, 0.011508692055940628, -0.051427748054265976, 0.047914743423461914, -0.013042162172496319, 0.01055295579135418, 0.008055011741816998, 0.051079168915748596, 0.084136001765728, 0.0118987075984478, -0.0301887895911932, -0.00252424250356853, 0.04206744208931923, 0.012434802949428558, -0.012384424917399883, -0.003404999151825905, 0.007135236170142889, 0.025256304070353508, 0.05158095806837082, -0.03482460975646973, 0.06192832440137863, -0.00044329676893539727, -0.03610316663980484, -0.01281171478331089, -0.029618678614497185, 0.010946341790258884, 0.0029245917685329914, 0.021339699625968933, -0.013760237023234367, 0.08813825994729996, 0.03961347043514252, 0.021951092407107353, -0.014728820882737637, 0.007921691983938217, 0.028657209128141403, 0.025038674473762512, 0.0035146011505275965, 0.03025112673640251, 0.010653795674443245, -0.02185067906975746, 0.06846883893013, -0.005561062600463629, -0.12728381156921387, 0.02953856810927391, 0.00568460812792182, -0.039034802466630936, -0.01831304095685482, -0.028902661055326462, -0.025019848719239235, -0.035067182034254074, -0.04126571863889694, 0.01828761026263237, -0.031968891620635986, -0.01644318737089634, 0.033243101090192795, 0.015623978339135647, -0.038021743297576904, -0.0073011512868106365, 0.010927679017186165, 0.005581011530011892, -0.009496044367551804, -0.06370475888252258, -0.012083644978702068, 0.02500739134848118, -0.0068181962706148624, 0.009809279814362526, -0.009248320013284683, 0.007505268789827824, 0.038194235414266586, -0.025765659287571907, -0.0355406291782856, 0.04231434315443039, -0.007021001540124416, -0.04486290365457535, -0.017395252361893654, -0.07511218637228012, 0.0014501521363854408, 0.017515214160084724, -0.04634128138422966, 0.030024994164705276, 0.04187343269586563, 0.036344293504953384, 0.006872397847473621, -0.01846444420516491, 0.0007894280715845525, 0.02370682917535305, -0.017511533573269844, 0.02131507731974125, 0.0406746082007885, 0.01854686439037323, -0.010674686171114445, 0.048523448407649994, -0.004419229459017515, -0.0036302211228758097, -0.006065045017749071, 0.012565933167934418, 0.005275093950331211, 0.017410041764378548, -0.01394666824489832, -0.027339309453964233, -0.05503520742058754, 0.005141390487551689, -0.07760103791952133, -0.019429629668593407, -0.012262535281479359, -0.03602287918329239, 0.00480516254901886, 0.03611551225185394, -0.0194254070520401, 0.013294268399477005, -0.029156332835555077, 0.014265580102801323, 0.033405717462301254, 0.03986001014709473, 0.008642174303531647, 0.012287347577512264, -0.005768819246441126, 0.0009519654558971524, 0.029263127595186234, -0.024487042799592018, -0.05834204703569412, -0.008311956189572811, -0.00694133760407567, -0.022867370396852493, 0.04006614908576012, -0.07146043330430984, 0.05791286751627922, 0.021045086905360222, -0.022967321798205376, -0.050868380814790726, 0.04624300077557564, 0.015138667076826096, 0.010806683450937271, 0.01026746816933155, 0.019555415958166122, 0.04404598847031593, -0.04412687197327614, -0.03728844225406647, 0.03476143255829811, 0.01572183519601822, 0.018123270943760872, 0.0330779142677784, -0.04274218901991844, 0.013496617786586285, -0.025109846144914627, 0.040221091359853745, 0.03341900184750557, 0.0009179436601698399, 0.006182233802974224, 0.022395558655261993, -0.011652321554720402, 0.03811655193567276, -0.024560900405049324, -0.027670197188854218, 0.018349334597587585, -0.0014300912152975798, -0.02010718733072281, 0.019342293962836266, -0.007182780187577009, -0.07935778051614761, -0.06253544241189957, 0.012427915818989277, 0.04079030454158783, -0.05214283987879753, 0.023756081238389015, -0.03692691773176193, 0.028738632798194885, -0.012846885249018669, 0.04260561242699623, 0.044300079345703125, -0.041464462876319885, 0.0230012945830822, 0.036210644990205765, 0.06229683384299278, 0.04361848533153534, -0.021917691454291344, -0.04059547930955887, -0.030008884146809578, -0.06849157065153122, 0.04021606221795082, -0.0420699268579483, -0.009783808141946793, -0.008592828176915646, 0.06849896162748337, -0.02740422822535038, -0.05626301467418671, 0.012290043756365776, -0.01816762238740921, 0.034164439886808395, 0.029030058532953262, -0.033931754529476166, 0.001523077255114913, -0.031343813985586166, 0.016434967517852783, -0.005130333360284567, 0.025432948023080826, 0.007314399816095829, 0.057401143014431, -0.042122725397348404, -0.036933619529008865, 0.024416308850049973, 0.00782841444015503, 0.016462238505482674, -0.015552259050309658, -0.01969631388783455, 0.00667970348149538, -0.09130988270044327, -0.028871288523077965, 0.02580028958618641, -0.0020009949803352356, 0.013744151219725609, -0.03306867927312851, 0.015122966840863228, -0.02084139548242092, 0.030280277132987976, 0.08281668275594711, 0.07428773492574692, 0.003540939185768366, 0.037934429943561554, -0.008660325780510902, -0.06810491532087326, 0.013263188302516937, -0.004175134468823671, -0.027428744360804558, 0.011358501389622688, 0.020600395277142525, 0.045685552060604095, -0.01795162260532379, 0.06794998794794083, 0.05273350700736046, -0.00040031885146163404, -0.027132339775562286, -0.051738008856773376, -0.0027430346235632896, 0.019669415429234505, 0.03728696331381798, -0.03699284419417381, 0.019283071160316467, 0.07250510156154633, -0.026971235871315002, -0.03928692638874054, 0.027480807155370712, 0.01023072563111782, -0.010584025643765926, -0.028514940291643143, 0.031008465215563774, -0.015986740589141846, -0.02866840921342373, -0.03128765895962715, -0.06693686544895172, -0.012065598741173744, 0.013628528453409672, 0.015910634770989418, -0.023010119795799255, 0.04922637343406677, 0.03597777709364891, -0.04600008949637413, 0.06487281620502472, 0.06281566619873047, 0.02951132319867611, -0.02897767722606659, 0.06386925280094147, -0.024468431249260902, -0.022799089550971985, -0.09135503321886063, 0.03263469040393829, 0.06467010825872421, -0.011767865158617496, 0.054904043674468994, -0.014892937615513802, -0.009915283881127834, 0.00008547353354515508, 0.057101864367723465, 0.011598311364650726, -0.023068517446517944, -0.0601176954805851, -0.003205494023859501, 0.011695901863276958, 0.014176647178828716, -0.020425910130143166, -0.03821442648768425, -0.0053820740431547165, -0.0016816881252452731, -0.005762297660112381, 0.07463792711496353, -0.00445218663662672, 0.04841446131467819, -0.01278635486960411, 0.01671123504638672, 0.024316899478435516, 0.0275927372276783, 0.028570637106895447, -0.0014265661593526602, 0.021297376602888107, -0.024332432076334953, -0.0694163590669632, -0.0315687470138073, 0.018162205815315247, 0.01744375005364418, -0.015102468430995941, -0.022301457822322845, -0.06388209760189056, 0.004249792080372572, -0.027958953753113747, 0.040135350078344345, 0.0850284993648529, -0.012116219848394394, -0.059898629784584045, -0.009590004570782185, 0.004427285399287939, 0.038008466362953186, 0.046656034886837006, 0.005766024347394705, 0.05722104758024216, 0.009759520180523396, -0.008978559635579586, -0.046066366136074066, 0.028718631714582443, -0.0143744433298707, 0.006299209780991077, 0.04407026991248131, -0.0060987877659499645, 0.011691626161336899, 0.003780180588364601, 0.023719996213912964, -0.016547707840800285, 0.04825017601251602, 0.011432564817368984, -0.0053704967722296715, 0.10114802420139313, -0.058146122843027115, 0.007740094792097807, -0.02236188016831875, -0.008584636263549328, -0.06040918454527855, 0.014855788089334965, -0.05157719925045967, -0.00811636634171009, -0.05402064323425293, 0.07192628085613251, 0.01675100065767765, 0.04951876401901245, 0.03679509833455086, -0.00834459438920021, 0.02954818122088909, -0.03226865082979202, -0.022710449993610382, -0.023503070697188377, 0.006894522346556187, 0.011041566729545593, 0.04946766048669815, -0.009827636182308197, 0.033127833157777786, -0.01835034042596817, -0.0394795723259449, 0.024797018617391586, -0.03999215364456177, -0.03207824379205704, 0.001981006935238838, -0.0017638860736042261, 0.04407324269413948, 0.04422043263912201, -0.008357618935406208, -0.023919163271784782, -0.041931718587875366, -0.00404323311522603, -0.04725297540426254, 0.021506691351532936, -0.010923168621957302, -0.00809909962117672, 0.05691581219434738, -0.01580553501844406, -0.054088495671749115, -0.06945959478616714, 0.052592046558856964, 0.004088185727596283, 0.02654416859149933, 0.043681610375642776, -0.08989419043064117, -0.04176946356892586, 0.00398703757673502, -0.007007848005741835, 0.06882209330797195, 0.021627211943268776, 0.044863902032375336, -0.01466781459748745, -0.022160205990076065, 0.026889633387327194, 0.09322784096002579, 0.035838738083839417, -0.03925512731075287, 0.021388374269008636, 0.03991721197962761, -0.00029829476261511445, 0.013567166402935982, -0.0534321628510952, -0.008582986891269684, 0.03797254338860512, 0.01951722428202629, 0.039362143725156784, -0.022878006100654602, 0.0043448940850794315, -0.05528789013624191, 0.04465257376432419, -0.06823695451021194, 0.015512112528085709, 0.024093102663755417, -0.0024616580922156572, 0.025531966239213943, -0.013967144303023815, 0.015334323048591614, -0.0038719044532626867, -0.01266464963555336, -0.018957942724227905, 0.0009406855097040534, 0.003052064450457692, 0.03081861138343811, -0.0032870920840650797, 0.035810746252536774, -0.01304550375789404, 0.04190699756145477, 0.06752044707536697, -0.016781035810709, 0.03128216043114662, -0.006512885447591543, -0.01418506819754839, 0.018668271601200104, -0.042742013931274414, -0.02401365339756012, 0.07432868331670761, 0.006409371271729469, 0.0471012257039547, -0.008059528656303883, 0.024949951097369194, 0.009494307450950146, -0.020383840426802635, 0.008126514963805676, -0.0484173409640789, -0.006423334125429392, 0.009263993240892887, 0.02938465215265751, 0.040525104850530624, 0.04685460403561592, -0.027279440313577652, -0.03760002553462982, -0.006584335584193468, 0.0793742686510086, 0.07875407487154007, -0.012842615135014057, -0.01673424057662487, -0.03252699226140976, -0.06249592825770378, 0.01427531335502863, 0.03101523593068123, -0.060851212590932846, 0.008815927430987358, -0.02170967124402523, 0.019795004278421402, 0.022268252447247505, 0.00539044663310051, -0.0021511774975806475, -0.030979299917817116, -0.009997188113629818, 0.023278290405869484, -0.01134863868355751, -0.012012619525194168, -0.01740667223930359, 0.03130817785859108, 0.0020047954749315977, -0.047076206654310226, -0.0542193204164505, -0.04245384410023689, 0.007097549736499786, -0.05906589701771736, 0.007133960723876953, -0.007178290281444788, 0.022392064332962036, 0.020439937710762024, -0.018923362717032433, 0.03287991136312485, 0.03640549257397652, -0.05235632508993149, -0.02449610084295273, -0.00040728168096393347, 0.04225378483533859, 0.013576874509453773, -0.005817986559122801, 0.010942072607576847, -0.01078103482723236, 0.051403503865003586, 0.018725354224443436, -0.026080019772052765, -0.03845794126391411, -0.039830949157476425, -0.07574710994958878, 0.007475037593394518, -0.01793917827308178, 0.012352876365184784, -0.0045420099049806595, -0.03460785374045372, -0.03290853276848793, 0.013994988054037094, 0.05471113324165344, 0.00839082058519125, -0.08389227092266083, 0.02512313239276409, 0.0561118982732296, -0.04118530824780464, 0.030875958502292633, 0.043288279324769974, 0.0033364815171808004, 0.03609592095017433, -0.012361151166260242, 0.02200922928750515, -0.002856501145288348, 0.01238119788467884, 0.03850284963846207, 0.020012037828564644, 0.03964358940720558, 0.007116732187569141, 0.09922276437282562, 0.06472743302583694, -0.05332616716623306, 0.015989072620868683, -0.01835157908499241, 0.04149091616272926, -0.07056379318237305, -0.026951801031827927, -0.009919896721839905, -0.07651966065168381, -0.0226444061845541, 0.07572989165782928, -0.02888575568795204, 0.0032048174180090427, -0.005700316280126572, -0.011073223315179348, 0.053214505314826965, -0.03409351408481598, 0.00794928427785635, 0.018559252843260765, 0.0396479032933712, -0.050407953560352325, 0.012251329608261585, -0.020968452095985413, -0.01443325262516737, -0.06751611828804016, 0.04282686486840248, -0.03704068064689636, 0.017658492550253868, 0.04540608823299408, 0.011598002165555954, 0.04771219193935394, -0.01950819231569767, 0.006030689924955368, 0.03647330775856972, 0.04936954006552696, -0.02017534337937832, 0.019301073625683784, -0.012837355956435204, 0.0057847220450639725, 0.036026738584041595, -0.041759856045246124, -0.06400757282972336, -0.06089543551206589, -0.0442948192358017, -0.061279453337192535, 0.005756678059697151, -0.028248487040400505, -0.016835954040288925, -0.010087077505886555, 0.07683327794075012, -0.037994373589754105, 0.021843256428837776, 0.053252995014190674, 0.045535821467638016, -0.01570512168109417, 0.010357958264648914, -0.019135139882564545, -0.002453429391607642, -0.061147887259721756, -0.020863818004727364, 0.029093967750668526, 0.03041149117052555, -0.00923366378992796, -0.0034407416824251413, 0.021132610738277435, -0.05592919886112213, -0.029265373945236206, 0.004378036130219698, -0.030111096799373627, -0.008352391421794891, 0.0012560226023197174, 0.03831595554947853, -0.03338814899325371, -0.05252832919359207, -0.017331790179014206, -0.04766581580042839, -0.007124872412532568, 0.005533040035516024, -0.034386325627565384, 0.03379412740468979, -0.06651422381401062, -0.02754049561917782, -0.04248538613319397, -0.007513844408094883, -0.005599826108664274, -0.08141906559467316, -0.004455179441720247, -0.048145879060029984, 0.012854272499680519, -0.004385343752801418, 0.018143413588404655, -0.022726288065314293, 0.02388838306069374, 0.0377189964056015, -0.02514227293431759, -0.05022439733147621, -0.0013150072190910578, 0.004753004759550095, 0.050378959625959396, 0.002815498039126396, 0.022380637004971504, -0.03268634155392647, -0.059365928173065186, -0.01200112421065569, 0.007973531261086464, 0.03586757928133011, -0.006984869483858347, 0.10239027440547943, -0.012346098199486732, 0.03680332377552986, 0.020178332924842834, 0.00012791123299393803, -0.09056612849235535, -0.06354828923940659, 0.09710809588432312, -0.034536365419626236, -0.02348707802593708, -0.02668781951069832, 0.0030104208271950483, 0.042661599814891815, -0.01481905858963728, -0.025458136573433876, -0.06157141551375389, -0.04211072996258736, 0.012961920350790024 ]
<p>Amorphous metals are often referred to as metallic glasses due to their quenched atomic disorder. Do they fracture in the same fashion as silicate glasses? If not, what failure mode(s) do they have?</p>
g1581
[ 0.0009036808623932302, 0.012160953134298325, -0.013137717731297016, 0.01928722858428955, 0.013818660750985146, -0.002368635730817914, -0.009097104892134666, -0.010764595121145248, 0.06146639585494995, -0.018762700259685516, 0.05760962516069412, 0.048754218965768814, 0.01873437501490116, -0.029434598982334137, -0.0027827357407659292, 0.0022622058168053627, -0.0205256175249815, 0.006863131653517485, -0.002641713945195079, 0.06058923155069351, -0.05229980871081352, -0.04972191900014877, 0.02313085086643696, 0.023423144593834877, -0.0010733623057603836, -0.0009385902085341513, -0.046697307378053665, -0.028370214626193047, -0.00811370275914669, 0.02328062802553177, 0.08186247944831848, 0.00598224438726902, 0.032254260033369064, -0.09061461687088013, 0.018284929916262627, 0.044676292687654495, 0.0046032569371163845, 0.0005653698462992907, 0.011967379599809647, -0.032885633409023285, -0.015256987884640694, -0.015242391265928745, 0.03275000676512718, -0.08596022427082062, -0.00017762649804353714, 0.02924983762204647, -0.05014456808567047, -0.0037598644848912954, -0.045455850660800934, 0.039787158370018005, 0.038627590984106064, 0.056105852127075195, 0.07501216977834702, -0.04685597121715546, -0.00559360021725297, -0.010490535758435726, -0.055658143013715744, 0.03809712454676628, 0.0781533271074295, -0.03681183233857155, -0.01553249265998602, 0.05165949463844299, 0.002945219399407506, -0.05311773717403412, 0.027825739234685898, -0.0033488261979073286, -0.03642474114894867, 0.026773814111948013, 0.03529966622591019, -0.031627118587493896, 0.03490433096885681, -0.029261739924550056, -0.048710908740758896, -0.07518412172794342, -0.019265197217464447, 0.04178256914019585, -0.03448360040783882, 0.03429839387536049, 0.005656696390360594, 0.021931594237685204, 0.0687011107802391, -0.009174884296953678, 0.01214506383985281, -0.02181297540664673, -0.01794346608221531, 0.004636711906641722, -0.036314595490694046, 0.013257565908133984, 0.02257583476603031, -0.03533947095274925, -0.018136106431484222, -0.009382431395351887, 0.03503437712788582, -0.0021519900765269995, -0.002754118060693145, 0.04006348177790642, -0.06707460433244705, -0.012691357173025608, -0.05876665189862251, -0.0011831491719931364, 0.011937782168388367, -0.02586929313838482, 0.04516126587986946, -0.03341066837310791, -0.02766498364508152, -0.053003523498773575, 0.030041923746466637, 0.022371184080839157, 0.018986480310559273, 0.03907984122633934, 0.021558478474617004, 0.06754991412162781, -0.04688841849565506, 0.04234801605343819, 0.009348299354314804, 0.03497236594557762, 0.054088108241558075, -0.049479108303785324, 0.016892479732632637, -0.0005533969961106777, 0.0330459363758564, -0.030504988506436348, 0.040756940841674805, -0.009650670923292637, -0.039419177919626236, 0.015863433480262756, 0.026060396805405617, -0.0055199963971972466, 0.0029725348576903343, -0.006415970623493195, -0.037235699594020844, -0.011669245548546314, -0.030448272824287415, -0.06134159490466118, -0.0376923605799675, 0.050423383712768555, 0.004843232221901417, -0.037448327988386154, -0.034710101783275604, 0.008607150055468082, -0.0393221452832222, -0.007197865284979343, -0.004390242975205183, 0.004648914095014334, -0.012864193879067898, -0.0091319615021348, -0.014606790617108345, 0.02828117646276951, 0.006609233561903238, 0.01763196475803852, -0.07749194651842117, 0.04444856196641922, -0.025808943435549736, -0.05111687630414963, 0.0005923722055740654, -0.023207809776067734, 0.052989307790994644, -0.03716452419757843, 0.005370377562940121, 0.02335299365222454, 0.017569590359926224, -0.07152309268712997, -0.06063627824187279, 0.032081253826618195, -0.03161465749144554, -0.024720339104533195, 0.05092426389455795, 0.028726952150464058, 0.05983499437570572, -0.03472119942307472, -0.015268857590854168, -0.016228370368480682, 0.024634553119540215, 0.04329543560743332, 0.003425701055675745, 0.02301660366356373, -0.04254456236958504, 0.03881492465734482, 0.08213966339826584, 0.009523865766823292, 0.005808756686747074, 0.003546728752553463, -0.017925286665558815, -0.03786175698041916, 0.03809170797467232, -0.057392023503780365, 0.035731665790081024, 0.058390822261571884, 0.012557224370539188, -0.0015008705668151379, -0.025336310267448425, 0.027469076216220856, 0.0041353446431458, -0.0038087009452283382, -0.0076154121197760105, -0.09363245964050293, 0.04148359224200249, -0.053296398371458054, 0.03855965659022331, 0.02840787172317505, 0.015234386548399925, 0.011578821577131748, -0.06268439441919327, 0.004135370720177889, 0.025807596743106842, 0.0005747498944401741, -0.08560653030872345, -0.018468938767910004, -0.016616815701127052, 0.06962069123983383, 0.017106840386986732, -0.017416201531887054, -0.02353198453783989, -0.023809228092432022, -0.01975267380475998, 0.012417522259056568, 0.04206578806042671, -0.02545361965894699, 0.027866419404745102, 0.0673968642950058, 0.018566258251667023, 0.02405199222266674, -0.04606664553284645, -0.060087550431489944, 0.009460950270295143, 0.00853402353823185, -0.03156479448080063, 0.003770100185647607, 0.0860012099146843, -0.05051874741911888, -0.024590501561760902, -0.003534783376380801, 0.021271387115120888, -0.0003437062550801784, -0.046529173851013184, 0.01145828515291214, -0.0006076785502955317, 0.04101947322487831, -0.0010244738077744842, -0.01947096921503544, 0.020219283178448677, -0.014372484758496284, 0.0034689041785895824, 0.00535862660035491, -0.03244815394282341, -0.04641088843345642, -0.06392014771699905, 0.0007577586802653968, 0.04552064836025238, 0.05179012939333916, 0.05950982868671417, -0.010710370726883411, -0.005041314754635096, -0.018313564360141754, -0.008441461250185966, -0.06812164932489395, 0.032393939793109894, 0.03141913190484047, -0.020946737378835678, 0.026469236239790916, 0.02630903571844101, -0.015771957114338875, 0.0023001532536000013, 0.000010787532119138632, 0.001890073879621923, -0.009869091212749481, 0.040976084768772125, 0.049429140985012054, -0.07383061200380325, 0.007188154850155115, 0.031514041125774384, 0.017924008890986443, 0.01068556122481823, -0.028071409091353416, 0.022461196407675743, 0.0010013836435973644, -0.0021549263037741184, -0.00771836144849658, -0.010564284399151802, -0.03595300763845444, -0.04064955562353134, 0.03232147917151451, -0.049473464488983154, -0.06549687683582306, 0.008041491732001305, -0.06429268419742584, 0.04633533954620361, 0.0671735480427742, -0.004386271350085735, 0.06315997242927551, -0.029433229938149452, 0.021594742313027382, 0.008271553553640842, -0.04210028424859047, -0.0029099879320710897, 0.05275755375623703, 0.017712097615003586, 0.023302922025322914, -0.051200829446315765, 0.03142625465989113, -0.045562222599983215, -0.03875171020627022, -0.04707518592476845, -0.05330219119787216, -0.01733432151377201, 0.061055660247802734, -0.07023999094963074, 0.019103623926639557, -0.01819573901593685, -0.07269079238176346, 0.08132848143577576, 0.03954998031258583, 0.022351359948515892, 0.04207852482795715, -0.08147723972797394, 0.03229543939232826, -0.06740594655275345, -0.006416651885956526, -0.032697342336177826, -0.014506425708532333, -0.08180065453052521, 0.02597866952419281, 0.03280094638466835, 0.010974986478686333, -0.02282746694982052, -0.017448805272579193, 0.01003638282418251, -0.022958237677812576, -0.034886039793491364, 0.01957601308822632, -0.04939836263656616, 0.00930212251842022, -0.03377297520637512, -0.038597412407398224, -0.020421216264367104, 0.015119556337594986, -0.00022698270913679153, 0.020303063094615936, 0.06078372895717621, 0.027592381462454796, 0.049500688910484314, 0.04468720778822899, 0.023150581866502762, 0.016621913760900497, 0.015767594799399376, 0.02112480439245701, 0.029431328177452087, 0.03392113745212555, 0.08956611901521683, -0.038840003311634064, 0.023646783083677292, -0.013049912638962269, -0.022112010046839714, -0.07380808889865875, -0.022382192313671112, 0.030171431601047516, -0.007556921802461147, -0.0010793792316690087, 0.0216392632573843, -0.007779404055327177, 0.03503839299082756, -0.013237292878329754, 0.023490790277719498, -0.026654275134205818, -0.04063115268945694, 0.0013980731600895524, 0.023391731083393097, -0.006217030342668295, 0.02174392156302929, -0.03960413858294487, 0.017225895076990128, -0.013753103092312813, -0.01164746843278408, -0.014146731235086918, 0.04629277065396309, 0.009490033611655235, 0.032705213874578476, -0.0043689715676009655, -0.030263811349868774, 0.006848134100437164, -0.019511748105287552, 0.03163769841194153, 0.043800123035907745, 0.044923316687345505, -0.0274373609572649, -0.03845588490366936, -0.008441116660833359, -0.02890494093298912, -0.08500301837921143, -0.028440212830901146, -0.030042679980397224, -0.007718787528574467, 0.03508082032203674, -0.002351389266550541, -0.014477566815912724, -0.02928767539560795, 0.0075551788322627544, 0.07800454646348953, 0.018007807433605194, 0.017091449350118637, -0.02434050850570202, 0.026227546855807304, -0.047164980322122574, 0.0002938502002507448, 0.040275219827890396, 0.024497224017977715, -0.004138325806707144, -0.028335602954030037, -0.038874369114637375, -0.0354604534804821, -0.00818965956568718, -0.011296437121927738, -0.025044523179531097, -0.06889422237873077, 0.06717900186777115, 0.052873868495225906, 0.02731819823384285, -0.00954426545649767, 0.04409283399581909, 0.0032734659034758806, -0.041003890335559845, -0.04205922782421112, -0.0015735256019979715, 0.020493440330028534, 0.013692716136574745, -0.0036283941008150578, -0.006869456265121698, -0.020891573280096054, 0.01157253049314022, 0.007723604328930378, -0.0019755547400563955, 0.019220244139432907, -0.034469109028577805, 0.0008255527354776859, -0.010390070267021656, -0.011875227093696594, 0.022829927504062653, -0.006527958903461695, 0.0432719886302948, 0.01705324836075306, 0.021358534693717957, 0.07626920938491821, 0.027079831808805466, 0.0353972427546978, 0.07502251118421555, -0.010886099189519882, 0.06252606958150864, 0.04906512796878815, -0.05377815291285515, 0.03926698490977287, -0.043087419122457504, -0.004465125035494566, -0.03181077167391777, -0.018785938620567322, -0.014651288278400898, 0.0002926369779743254, -0.02972312457859516, 0.058790601789951324, -0.0629410520195961, 0.06947985291481018, 0.012980794534087181, -0.0721171498298645, 0.032929155975580215, 0.01752571016550064, -0.027524715289473534, -0.03226597607135773, 0.052630890160799026, -0.06498108059167862, -0.0636453777551651, -0.03302205353975296, 0.007557650562375784, 0.00017092860070988536, 0.03348536044359207, 0.03951543942093849, 0.06742371618747711, -0.03542696684598923, -0.033820297569036484, -0.004414146766066551, 0.02302435413002968, -0.012380793690681458, 0.019543593749403954, 0.04464567080140114, 0.01865447871387005, 0.004082963336259127, -0.05179715156555176, 0.015927571803331375, -0.011908037588000298, -0.0013967902632430196, 0.033091675490140915, -0.04351596161723137, 0.02212839014828205, -0.0033273117151111364, 0.01899372786283493, -0.04137922078371048, -0.024701258167624474, -0.042452841997146606, 0.017582999542355537, 0.041224922984838486, -0.013079270720481873, 0.008200009353458881, -0.05984563007950783, 0.009692403487861156, -0.023880500346422195, -0.06390410661697388, 0.04371398687362671, 0.02584649622440338, 0.04671156778931618, -0.03589970991015434, 0.05439308285713196, -0.043779123574495316, 0.001814932213164866, -0.012656730599701405, 0.010720420628786087, 0.05040319263935089, 0.10410653054714203, 0.022510940209031105, -0.06365186721086502, 0.0027863956056535244, 0.009954544715583324, -0.01383911445736885, -0.09136838465929031, 0.030675390735268593, -0.08552728593349457, -0.059641238301992416, 0.030189843848347664, 0.024990947917103767, -0.003869858104735613, -0.04029608145356178, 0.0030487840995192528, 0.006013901904225349, -0.001488911104388535, 0.0027134574484080076, 0.03110414184629917, -0.013254710473120213, 0.005778190214186907, -0.011625177226960659, -0.0001485004904679954, 0.004050928633660078, -0.03219754993915558, 0.09272587299346924, -0.008317227475345135, -0.0005278092576190829, 0.021665720269083977, 0.0193171463906765, 0.0513078048825264, -0.013277783058583736, 0.04342980310320854, 0.06680703163146973, 0.029752682894468307, 0.034424569457769394, -0.025721443817019463, 0.04411068558692932, -0.008619115687906742, 0.049919724464416504, 0.007484971079975367, 0.04274347051978111, -0.01679009571671486, -0.04673110693693161, -0.016694584861397743, -0.041618477553129196, 0.018964769318699837, 0.009085499681532383, 0.02782372757792473, -0.06853856891393661, 0.057771001011133194, -0.0855046883225441, -0.04234014078974724, 0.006439290940761566, 0.07317569851875305, -0.05061141774058342, -0.037993770092725754, 0.005406009964644909, 0.007600217591971159, -0.011849510483443737, -0.03623945638537407, -0.010599156841635704, -0.031215522438287735, -0.045156121253967285, 0.03345118835568428, -0.056933216750621796, 0.00948365405201912, -0.013319786638021469, -0.013692284002900124, 0.1328008770942688, -0.0061350055038928986, -0.021962963044643402, 0.009531560353934765, 0.002743409713730216, 0.02626645751297474, -0.04760248586535454, 0.0281918253749609, 0.014025498181581497, 0.01888374425470829, -0.007189258933067322, -0.025809206068515778, 0.044250812381505966, 0.012175992131233215, 0.03300352394580841, -0.07535076886415482, 0.056566476821899414, 0.0315885990858078, 0.049003325402736664, -0.005885496269911528, -0.011642972007393837, 0.029584482312202454, 0.032390471547842026, 0.026321297511458397, 0.045439399778842926, 0.015157556161284447, 0.024761751294136047, -0.025395378470420837, -0.0024564003106206656, 0.05623132735490799, 0.06701251119375229, 0.006874542683362961, -0.024084068834781647, -0.01892496645450592, -0.014062980189919472, -0.06618382781744003, -0.0015994291752576828, -0.00984486285597086, -0.054528605192899704, -0.010176547802984715, -0.013200074434280396, 0.0716412141919136, 0.01745641604065895, -0.005912197753787041, -0.002976836636662483, 0.01091095618903637, -0.026015754789114, -0.044464774429798126, -0.04015231877565384, -0.008967329747974873, 0.021669812500476837, -0.022360194474458694, 0.04673467203974724, -0.02105395309627056, -0.0030542209278792143, 0.051485326141119, -0.03962916508316994, 0.021005282178521156, -0.013559309765696526, 0.025517882779240608, 0.03525953367352486, -0.03616873174905777, 0.045276518911123276, -0.025281233713030815, 0.014271420426666737, 0.018310729414224625, -0.0045755780301988125, 0.009735540486872196, -0.057726144790649414, 0.04356662184000015, -0.013459568843245506, -0.025287214666604996, -0.005933090578764677, -0.035899870097637177, 0.06024947762489319, 0.005687593016773462, 0.002046623732894659, -0.019773468375205994, 0.05781347304582596, 0.035642072558403015, 0.018903696909546852, 0.021348465234041214, 0.059183888137340546, 0.03418011590838432, -0.07337653636932373, -0.012548158876597881, 0.01210868638008833, -0.004366666544228792, 0.00930178165435791, 0.0045120990835130215, -0.02447636052966118, -0.004616898484528065, 0.01884276419878006, -0.04808840528130531, 0.022108644247055054, 0.03895052894949913, 0.006054652854800224, 0.017725562676787376, 0.012533496133983135, 0.022535599768161774, -0.06184716522693634, 0.00004075741526321508, 0.02034604363143444, -0.015112041495740414, 0.04540927708148956, 0.02912886254489422, -0.0023647411726415157, -0.06405886262655258, -0.03145505487918854, 0.04364435002207756, 0.0261786337941885, -0.035635486245155334, -0.01661120355129242, 0.050325680524110794, 0.011038036085665226, -0.029241781681776047, -0.01033129170536995, -0.059773970395326614, 0.010630013421177864, 0.011319934390485287, 0.0016380716115236282, -0.013523058034479618, 0.04513568431138992, -0.0042780363000929356, -0.006746307946741581, -0.010790216736495495, 0.006979943718761206, 0.0587625689804554, 0.05199671536684036, 0.0038528377190232277, -0.08944909274578094, 0.002098735887557268, -0.10855796933174133, -0.012858430854976177, -0.0308492761105299, 0.012996536679565907, 0.014340875670313835, 0.0019209214951843023, -0.00515070790424943, 0.04805217310786247, -0.0341961532831192, -0.008238499984145164, 0.01752830669283867, 0.04531075805425644, -0.023391498252749443, -0.07178588211536407, -0.06632016599178314, -0.03871139883995056, -0.03572682663798332, 0.014516319148242474, 0.007414627820253372, 0.005097533110529184, -0.026946663856506348, 0.05722493678331375, -0.01377315353602171, -0.0076061272993683815, 0.009231583215296268, -0.010301926173269749, 0.02013244666159153, -0.020996475592255592, 0.0006256536580622196, 0.014413897879421711, 0.00259510544128716, -0.028753692284226418, -0.04388201981782913, 0.02636454813182354, 0.000734736502636224, -0.08104775100946426, 0.04389170557260513, 0.041423406451940536, -0.01967914029955864, 0.02351091057062149, -0.03167715668678284, -0.005351390689611435, 0.01583273708820343, 0.03770952299237251, -0.0511975921690464, 0.03737731650471687, -0.009255874902009964, -0.03823065385222435, -0.008618070743978024, -0.030820118263363838, -0.027449727058410645, -0.016137195751070976, -0.01131416019052267 ]
<p>When comparing two light sources, for example, a light bulb at 20W and a light bulb at 100W, what is it about the incoming light that makes the latter look brighter than the former? Are there different reasons why different light sources looks different in brightness (High five for cramming three instances of "different" in the same sentence)? For example, in <a href="http://physics.stackexchange.com/questions/3145/sensitivity-of-eye">this</a> thread, it is stated that the human eye is most sensitive around 555nm, something that I guess translates to meaning that given a light of the same intensity (whatever that means, hence my question), it is going to be perceived as most bright when hitting 555nm. Does this question have different answers depending on if you're seeing light as a particle vs a wave?</p>
g1582
[ 0.04089341685175896, 0.0003787150781136006, 0.004961040336638689, -0.02576463669538498, 0.03544709458947182, -0.035586073994636536, 0.028324289247393608, 0.00471058115363121, -0.01883869245648384, -0.02173062227666378, 0.04193172603845596, 0.010794829577207565, 0.04053682088851929, 0.029894160106778145, 0.01422728318721056, -0.03689057379961014, 0.042382750660181046, -0.03942001610994339, 0.03735673427581787, -0.01405369397252798, -0.006386276800185442, -0.006561984773725271, -0.026202697306871414, -0.05555034428834915, -0.04946247115731239, 0.00013883996871300042, -0.016376744955778122, -0.03827622905373573, -0.0011625797487795353, 0.010287737473845482, 0.01393880881369114, -0.03133802115917206, 0.06321575492620468, -0.012063175439834595, -0.02839585393667221, -0.023045865818858147, -0.0061789145693182945, 0.010834813117980957, -0.009485134854912758, 0.019229207187891006, 0.03458993881940842, 0.029381103813648224, -0.0060600037686526775, -0.04518644139170647, 0.04477247968316078, -0.005883711855858564, 0.0006436610128730536, 0.052374936640262604, 0.02125571295619011, -0.01886916719377041, -0.03646090254187584, 0.009100186638534069, -0.010966068133711815, 0.015301691368222237, 0.09420820325613022, -0.04257095605134964, 0.002473134081810713, 0.030237404629588127, 0.08824343979358673, 0.06950674951076508, 0.0221774410456419, 0.001544544822536409, 0.0270305834710598, 0.014788425527513027, 0.01160090509802103, -0.021944046020507812, 0.025474732741713524, -0.0033811575267463923, 0.0500880591571331, 0.01670088991522789, -0.02655707485973835, 0.002294887788593769, -0.09624770283699036, -0.012272956781089306, 0.01621650904417038, -0.05478974059224129, -0.008740529417991638, 0.0023280284367501736, 0.0020637770649045706, 0.04967351630330086, 0.03437141329050064, -0.029484223574399948, 0.009105255827307701, 0.05629321560263634, -0.015575248748064041, 0.03378325328230858, -0.001858353614807129, -0.011759093962609768, -0.015363061800599098, -0.02703838050365448, 0.09112919121980667, -0.006780074443668127, 0.09291964769363403, 0.033698562532663345, -0.10353231430053711, 0.021704817190766335, 0.0076492419466376305, 0.030207976698875427, 0.025467589497566223, 0.015736596658825874, 0.01858026161789894, -0.01689828932285309, -0.012235286645591259, 0.0328584723174572, -0.009347443468868732, -0.014594980515539646, -0.01067879144102335, 0.014941498637199402, -0.10422571748495102, -0.011770996265113354, -0.08323324471712112, -0.07018550485372543, -0.014264076948165894, -0.019051263108849525, -0.11246997863054276, -0.025360628962516785, 0.06107344105839729, -0.006397050805389881, -0.03652742877602577, 0.053530316799879074, 0.024006854742765427, -0.006637141574174166, -0.0559048056602478, 0.014347493648529053, 0.028414404019713402, 0.012635269202291965, 0.034176506102085114, -0.005369066726416349, 0.03971206769347191, 0.005744374822825193, 0.04167556017637253, -0.016939928755164146, 0.00487259728834033, -0.0026663339231163263, 0.024845516309142113, 0.0322687141597271, 0.07417664676904678, -0.03365754336118698, 0.04418208822607994, 0.07791506499052048, 0.02594044618308544, -0.05275349318981171, 0.002619427163153887, -0.029090113937854767, -0.015345430001616478, 0.04568653181195259, -0.04918338358402252, -0.0045688883401453495, 0.04523308202624321, 0.05848728120326996, 0.0508204884827137, 0.017777757719159126, 0.05153009295463562, -0.0830099880695343, 0.03158926963806152, -0.034847699105739594, -0.025662900879979134, -0.029535789042711258, -0.0942201316356659, 0.03338858485221863, 0.04498063772916794, 0.0017875268822535872, 0.019410206004977226, 0.0131424181163311, -0.006254526320844889, -0.020857103168964386, 0.0018901355797424912, -0.0669541135430336, 0.029935969039797783, -0.03990323096513748, -0.005364007782191038, 0.036131080240011215, 0.004305145237594843, -0.002959339413791895, 0.047047801315784454, 0.0005677465815097094, 0.09390369802713394, -0.045874256640672684, -0.011644759215414524, 0.017819060012698174, -0.07580845057964325, -0.031853087246418, -0.017074232921004295, -0.043971672654151917, -0.016213353723287582, -0.06319621205329895, -0.021047338843345642, -0.06365720182657242, -0.039111144840717316, 0.04747404530644417, -0.013568858616054058, -0.0738377720117569, -0.020091058686375618, 0.03384656831622124, -0.0027348564472049475, -0.01825275830924511, -0.09143872559070587, -0.00017495722568128258, -0.027921942993998528, -0.0033759979996830225, -0.03473339602351189, 0.01956619881093502, 0.026521362364292145, 0.02041741833090782, 0.01855343207716942, 0.09352551400661469, -0.0387226827442646, 0.008991341106593609, 0.023249102756381035, -0.03934808075428009, -0.012201724573969841, -0.007457016967236996, 0.006222706753760576, -0.01899297721683979, 0.002042744541540742, 0.03783857077360153, -0.02210480533540249, 0.018853599205613136, 0.009964038617908955, -0.019238349050283432, -0.016013622283935547, -0.012774202041327953, 0.09130963683128357, -0.024848192930221558, -0.04600005969405174, 0.03653443604707718, -0.04538615420460701, -0.004307654686272144, 0.012669378891587257, 0.08473069220781326, -0.025433432310819626, 0.014255674555897713, -0.021923216059803963, 0.026858605444431305, 0.014280622825026512, -0.01878896914422512, 0.01640583947300911, -0.0038743605837225914, 0.04432966187596321, -0.016981860622763634, -0.035943567752838135, -0.028995903208851814, -0.02895454689860344, 0.027051327750086784, -0.014682600274682045, -0.09468797594308853, 0.029104556888341904, -0.027537265792489052, -0.03207811340689659, 0.0469183512032032, 0.0071917688474059105, 0.033639293164014816, -0.050598785281181335, 0.007303666789084673, 0.011731603182852268, -0.039437372237443924, 0.01392434909939766, 0.04224269464612007, -0.05906238406896591, 0.023739637807011604, 0.005154341924935579, -0.060513950884342194, 0.019040333107113838, 0.0299352016299963, 0.010457738302648067, 0.02303379960358143, 0.03100816160440445, -0.03944985195994377, -0.016084449365735054, -0.040774792432785034, 0.025337522849440575, 0.06690678000450134, -0.04194504767656326, -0.017018822953104973, 0.0029722237959504128, 0.009871892631053925, -0.019958583638072014, 0.0017236160347238183, 0.017930490896105766, -0.020809948444366455, -0.024178611114621162, 0.0015606586821377277, -0.09288188070058823, -0.011056694202125072, 0.07501374185085297, -0.06540831923484802, 0.03556825965642929, 0.010530566796660423, 0.015308232977986336, -0.013929166831076145, -0.05423919856548309, 0.037101492285728455, -0.006592265330255032, -0.021658847108483315, -0.007977078668773174, 0.014100675471127033, 0.01018115971237421, -0.008218285627663136, 0.012849303893744946, -0.0009368160390295088, -0.03477581962943077, 0.0291330236941576, -0.000026861711376113817, 0.017606468871235847, 0.030554790049791336, 0.08038251101970673, -0.07464513927698135, -0.028679419308900833, -0.031182911247015, 0.05624626949429512, -0.06241394206881523, -0.0009607732645235956, -0.018741726875305176, 0.002710950095206499, 0.011264633387327194, -0.015064491890370846, -0.008853098377585411, 0.031122544780373573, -0.007010943256318569, -0.018640875816345215, -0.020393282175064087, 0.026511680334806442, 0.03788749501109123, -0.026882464066147804, -0.0388043038547039, -0.02539774961769581, 0.05835679918527603, 0.022000495344400406, -0.06670468300580978, -0.03695651516318321, 0.028499934822320938, -0.01915169134736061, -0.06504135578870773, 0.022818397730588913, 0.009341666474938393, -0.033380571752786636, -0.03895530104637146, -0.0037664880510419607, 0.04001924768090248, 0.009126931428909302, 0.060864418745040894, 0.041773710399866104, -0.09709546715021133, -0.010254431515932083, 0.013436767272651196, -0.005848847795277834, -0.0014495899667963386, -0.028097977861762047, 0.0009161523776128888, -0.04708772152662277, 0.04533783718943596, 0.03990708664059639, -0.009046796709299088, -0.0020203327294439077, -0.004141423385590315, -0.04027973860502243, 0.003031535306945443, 0.0028750700876116753, 0.03725786507129669, -0.03312627971172333, 0.03540581837296486, 0.010206615552306175, 0.03884909674525261, 0.00013455138832796365, -0.048287663608789444, -0.009146638214588165, 0.0387386791408062, 0.007569835986942053, 0.016640357673168182, -0.03322175145149231, 0.0017503062263131142, -0.011066652834415436, -0.006149113178253174, 0.034580059349536896, -0.0052795386873185635, -0.02369474619626999, 0.02123011276125908, 0.01492930669337511, -0.007048320025205612, 0.0061115482822060585, -0.010442487895488739, 0.05205294489860535, -0.010806410573422909, -0.022473743185400963, 0.06358341127634048, -0.00838945060968399, -0.02812393382191658, -0.03203705698251724, 0.010456914082169533, -0.06502576917409897, 0.015271266922354698, 0.017035644501447678, -0.02914188988506794, 0.021474916487932205, 0.013565844856202602, 0.04458080977201462, 0.03544244170188904, 0.050461988896131516, 0.006615183316171169, 0.023675736039876938, -0.047551292926073074, -0.001334089902229607, -0.0008257510489784181, -0.04776015132665634, -0.03598131611943245, -0.018590165302157402, 0.013625890016555786, -0.011272243224084377, -0.03424187749624252, -0.0306568443775177, 0.06401075422763824, 0.05936242267489433, 0.015880517661571503, -0.04031915217638016, -0.04224863648414612, 0.016228700056672096, -0.020059989765286446, -0.011511865071952343, 0.08669068664312363, 0.023732535541057587, -0.018859917297959328, -0.03433966636657715, -0.07064200937747955, 0.0005316250026226044, 0.003567453008145094, 0.04729568213224411, 0.06364118307828903, 0.03654351457953453, -0.0053092436864972115, -0.03614107146859169, 0.04067448526620865, 0.05997811630368233, -0.016571544110774994, 0.043363768607378006, 0.01345810480415821, 0.08846723288297653, 0.024755895137786865, 0.020762227475643158, 0.020708467811346054, -0.061315760016441345, 0.0928627997636795, 0.03132224082946777, -0.010057550854980946, -0.029466012492775917, 0.03429702669382095, 0.03682023659348488, -0.03755727782845497, 0.029915351420640945, -0.03514932841062546, -0.0208656657487154, -0.017934735864400864, -0.008443565107882023, 0.01185944490134716, -0.10302150994539261, -0.017436513677239418, -0.030865605920553207, 0.012571189552545547, 0.0023097360972315073, -0.024837732315063477, 0.030867377296090126, -0.02826535888016224, 0.02714833989739418, -0.0021412651985883713, -0.03578510507941246, 0.0605885311961174, 0.02240903303027153, -0.08617750555276871, -0.031894512474536896, -0.06044856086373329, 0.0019425763748586178, -0.0151357501745224, -0.030413731932640076, 0.009969569742679596, 0.017529675737023354, 0.05910824239253998, 0.004005144815891981, 0.009277886711061, -0.06949076056480408, -0.04826187342405319, -0.03964872658252716, -0.05024375021457672, -0.048166077584028244, 0.03284965083003044, 0.0393325611948967, -0.0038056797347962856, 0.015491648577153683, -0.007076231762766838, 0.05828999727964401, -0.003750306088477373, -0.0428793728351593, 0.03329933062195778, -0.013157384470105171, -0.01183957327157259, -0.0330728217959404, 0.006151068024337292, 0.04679534584283829, 0.0508936382830143, -0.00362748047336936, -0.022056426852941513, 0.010167714208364487, -0.04618018493056297, -0.0025718421675264835, 0.009145035408437252, -0.02616013213992119, -0.0003810203343164176, 0.053108274936676025, 0.037429578602313995, -0.07371485233306885, 0.07734676450490952, 0.022290579974651337, -0.012774461880326271, -0.03188638016581535, -0.031019628047943115, 0.04922476410865784, 0.033714309334754944, 0.0023439181968569756, -0.024785593152046204, 0.05351822450757027, 0.021343713626265526, -0.05207391455769539, -0.046531300991773605, 0.015531813725829124, -0.00879992637783289, 0.02678767777979374, 0.022449448704719543, 0.015363809652626514, -0.0075526791624724865, 0.009827734902501106, 0.05863332748413086, -0.011371318250894547, 0.03193366527557373, 0.08041387051343918, 0.03424690291285515, 0.007081903051584959, -0.00017103529535233974, -0.0309439804404974, 0.004744481761008501, 0.0033751155715435743, -0.017417512834072113, 0.05214693769812584, -0.04443757236003876, -0.0018645889358595014, 0.01696842350065708, 0.0342031829059124, 0.013109461404383183, -0.015589690767228603, -0.012880463153123856, -0.0375983901321888, -0.0366852730512619, 0.03584105521440506, -0.01527000218629837, 0.027519583702087402, 0.034120187163352966, 0.00423644483089447, 0.04128776118159294, 0.03623536229133606, 0.038945067673921585, 0.036728955805301666, -0.0291600301861763, -0.026722555980086327, 0.05740726366639137, -0.015937713906168938, -0.008300756104290485, -0.057753145694732666, 0.05722975730895996, -0.05215722694993019, -0.04522668942809105, -0.015578655526041985, 0.0013429904356598854, 0.02119353413581848, 0.03850267454981804, -0.04039637744426727, 0.04097558930516243, -0.037460554391145706, 0.007457773666828871, -0.0021908667404204607, -0.011308564804494381, -0.057445645332336426, -0.024978632107377052, -0.007666430901736021, 0.027798175811767578, -0.026934821158647537, 0.018604839220643044, -0.004150239750742912, 0.0008279802859760821, 0.015408934094011784, -0.019183510914444923, 0.013492756523191929, 0.03136053308844566, -0.03324079141020775, 0.01698940433561802, -0.07498294860124588, 0.04031534120440483, -0.05516016110777855, -0.012138857506215572, -0.01680215261876583, -0.039554983377456665, 0.013576667755842209, -0.037229787558317184, 0.011270769871771336, 0.01590573601424694, 0.000808205280918628, 0.06114456057548523, 0.0493750125169754, 0.07517050206661224, 0.03407784923911095, -0.01119239255785942, -0.019654372707009315, 0.037855587899684906, -0.007707009557634592, 0.0119936503469944, 0.02844618819653988, -0.015506891533732414, -0.026476532220840454, -0.0236344076693058, -0.035326793789863586, -0.014001279138028622, -0.02166793681681156, 0.01735939085483551, -0.013273796997964382, -0.00710641872137785, -0.032932866364717484, 0.051110975444316864, -0.01663813181221485, 0.03700976073741913, 0.045592863112688065, -0.05096685141324997, -0.0001673057267908007, -0.007399316877126694, -0.005185037385672331, -0.0021659918129444122, -0.04065403714776039, 0.025933261960744858, 0.0767085999250412, -0.03543031960725784, 0.002293164609000087, -0.0035172177013009787, -0.04644143953919411, -0.03866758197546005, -0.0001230647903867066, 0.022338934242725372, 0.05914454907178879, -0.02069283090531826, -0.001721879467368126, 0.020023969933390617, 0.01738532818853855, 0.01498707477003336, -0.04896850883960724, -0.0167137011885643, -0.01689193584024906, -0.0322677418589592, -0.0034090036060661077, -0.0014313204446807504, -0.029770417138934135, 0.034102361649274826, 0.09285178035497665, -0.026508376002311707, 0.045664090663194656, 0.021790970116853714, -0.06154495105147362, -0.011419101618230343, 0.01494990848004818, -0.04274561256170273, 0.03828387334942818, -0.03891099989414215, 0.020632775500416756, 0.009178838692605495, -0.04225362837314606, -0.030232297256588936, 0.02853318303823471, 0.03186419978737831, -0.05064986273646355, -0.05316466838121414, -0.006530147045850754, 0.017497673630714417, -0.009532633237540722, -0.08510421961545944, 0.04909294843673706, 0.03322561830282211, -0.014497686177492142, 0.028805388137698174, 0.012616381980478764, -0.0026184041053056717, 0.007803075946867466, -0.00562382023781538, 0.029871758073568344, -0.060236167162656784, -0.03747469186782837, 0.039187997579574585, -0.016869226470589638, -0.056155309081077576, -0.04204438254237175, -0.019006237387657166, -0.01886260323226452, -0.0376448780298233, 0.03447593003511429, 0.06170522794127464, 0.014271472580730915, 0.03734830766916275, -0.024293923750519753, 0.0284891277551651, -0.021104371175169945, 0.026253171265125275, -0.022808538749814034, 0.01942555420100689, 0.02111070230603218, 0.01565513014793396, 0.02316495217382908, -0.014148881658911705, -0.005499906837940216, 0.060188502073287964, 0.036253198981285095, 0.018496785312891006, 0.009320242330431938, -0.04903391748666763, 0.006480306852608919, -0.016129646450281143, -0.004733702167868614, -0.022763952612876892, -0.014796702191233635, -0.022843483835458755, 0.0067014447413384914, -0.010311992838978767, -0.03748854249715805, 0.04255383089184761, -0.020858118310570717, 0.05158267915248871, -0.0036452647764235735, -0.0025616728235036135, 0.017927952110767365, 0.029335621744394302, 0.006262816023081541, -0.020912613719701767, -0.01356470212340355, -0.07470862567424774, 0.03704433888196945, 0.010872073471546173, 0.024470774456858635, 0.002503048162907362, 0.022572539746761322, -0.008650442585349083, 0.0010403551859781146, -0.016237454488873482, -0.03950602933764458, -0.008734636008739471, -0.06118078529834747, 0.007432292215526104, 0.03007284551858902, 0.025112491101026535, -0.07111961394548416, -0.03212357684969902, 0.017850017175078392, -0.07240664958953857, 0.08718013763427734, 0.08184952288866043, -0.012376043014228344, -0.06248592585325241, 0.01361030526459217, -0.05142071098089218, -0.007540825288742781, -0.002769829472526908, 0.03355693072080612, 0.00016402985784225166, -0.0024620203766971827, 0.010021088644862175, 0.04743451625108719, -0.058551937341690063, 0.004830782301723957 ]
<p>Does the internal structure of a neutron star resemble anything like that of an atomic nucleus? I.e., are the neutrons arranged in a shell like structure with different energy levels, and without a distinct location for each neutron?</p> <p>I know that the force holding a neutron star is gravity, compared to the strong interaction inside atomic nuclei, but does this matter?</p>
g1583
[ -0.045049071311950684, 0.057941172271966934, 0.023473113775253296, -0.0404575876891613, -0.0053189592435956, -0.0036604544147849083, -0.0478174202144146, -0.024223187938332558, 0.0049900091253221035, -0.06836217641830444, -0.011515301652252674, -0.01250416785478592, -0.038025908172130585, -0.06464164704084396, 0.03399687260389328, -0.022639131173491478, 0.03977642580866814, 0.0019983926322311163, -0.006443918216973543, 0.012022691778838634, 0.02317669987678528, 0.06432037800550461, -0.029813021421432495, 0.020966261625289917, -0.001439166022464633, -0.0019305918831378222, 0.02562328800559044, -0.061990682035684586, -0.03197450935840607, -0.010493976064026356, 0.03405681625008583, -0.04901726543903351, 0.04643995314836502, -0.02755647525191307, -0.050376612693071365, -0.04847411438822746, -0.005546871107071638, 0.021965276449918747, 0.00022733355581294745, 0.009712280705571175, 0.006178945302963257, 0.007358903530985117, -0.006377215031534433, -0.046141307801008224, -0.06640733033418655, 0.007170455995947123, -0.010426009073853493, -0.057059530168771744, -0.008473571389913559, 0.0012475744588300586, -0.01459738239645958, 0.024699604138731956, -0.018819445744156837, 0.0709129050374031, 0.030251825228333473, -0.021622221916913986, 0.03153742849826813, 0.028411993756890297, 0.08918105810880661, -0.004489833023399115, -0.005902406759560108, 0.0045671663247048855, -0.006669563706964254, -0.01645214483141899, -0.01328991074115038, 0.011427201330661774, -0.08604959398508072, 0.03526365011930466, 0.02043256163597107, -0.00483731459826231, 0.0013961276272311807, 0.0016166968271136284, -0.0581943541765213, -0.06325526535511017, 0.000044537031499203295, 0.026236170902848244, -0.018105139955878258, -0.011820345185697079, 0.01941898837685585, 0.08525987714529037, 0.07272820919752121, -0.021503284573554993, 0.0012791788903996348, 0.039412081241607666, 0.054336294531822205, 0.02745697647333145, -0.02510089986026287, 0.026569392532110214, 0.012418505735695362, 0.08002811670303345, 0.020456189289689064, 0.039199165999889374, 0.010928035713732243, -0.016802897676825523, -0.0049760290421545506, -0.06371526420116425, 0.025579821318387985, 0.04680735245347023, -0.007448654621839523, 0.04135210067033768, -0.022227074950933456, -0.0049385190941393375, 0.04936720058321953, 0.006368694826960564, -0.017286019399762154, 0.021245064213871956, 0.007360813207924366, -0.0065574245527386665, 0.01724439300596714, 0.027231493964791298, -0.03904123231768608, -0.04590675234794617, 0.08173436671495438, 0.0016573992324993014, -0.0282837375998497, -0.006727565545588732, 0.06877508759498596, 0.009053768590092659, -0.015580689534544945, 0.07964393496513367, 0.053702596575021744, 0.0649891123175621, -0.018994910642504692, -0.0052352407947182655, -0.02797124907374382, -0.03686993569135666, 0.02416859194636345, 0.016258353367447853, -0.016405262053012848, -0.03214673325419426, -0.005080897826701403, -0.022054359316825867, -0.037272561341524124, -0.003539206925779581, -0.011306442320346832, 0.014613982290029526, -0.006830953527241945, -0.06441809982061386, -0.005232230760157108, -0.025114350020885468, -0.005543050821870565, 0.05561358109116554, -0.041013576090335846, -0.004755022935569286, 0.018822936341166496, -0.011755417101085186, 0.018023744225502014, 0.021085374057292938, -0.01956852152943611, 0.005083019845187664, 0.050481945276260376, 0.0002551809011492878, 0.031624216586351395, -0.0473371297121048, 0.00906912051141262, -0.026807747781276703, 0.03384900838136673, 0.01030567567795515, -0.017224350944161415, 0.011700673028826714, 0.06783679127693176, 0.026334689930081367, 0.07571253180503845, 0.02180252969264984, -0.030052967369556427, -0.003123794449493289, 0.015969356521964073, -0.01113667618483305, 0.017736684530973434, -0.022735146805644035, -0.02263074368238449, -0.03676634654402733, -0.015882698819041252, 0.07441629469394684, 0.008938274346292019, -0.07832065224647522, 0.031185641884803772, -0.02371763065457344, 0.019613251090049744, 0.039242085069417953, -0.03983720391988754, 0.03419946879148483, -0.03144948557019234, 0.00032529488089494407, -0.013401213102042675, -0.00950584840029478, 0.012047143653035164, -0.0075583490543067455, 0.03962941840291023, 0.05806978791952133, 0.04764543101191521, 0.005129493307322264, 0.06580659747123718, 0.011475695297122002, 0.01267407275736332, -0.02650202251970768, -0.019229436293244362, -0.04728575795888901, 0.022935746237635612, 0.018941091373562813, -0.01449737697839737, -0.013179163448512554, -0.03239666298031807, -0.0045005762949585915, 0.04272002726793289, 0.011476438492536545, -0.03162678703665733, 0.043032027781009674, 0.010769179090857506, 0.018818946555256844, 0.001273458357900381, 0.03251463547348976, -0.04151909798383713, -0.007386131677776575, -0.028032271191477776, 0.03267020732164383, -0.004805502016097307, -0.006488332990556955, -0.031293440610170364, 0.0554211251437664, -0.04178820177912712, -0.027172468602657318, 0.029029516503214836, -0.070954330265522, -0.05942510440945625, -0.04432317987084389, -0.009236814454197884, 0.011397616006433964, 0.05167851969599724, -0.001739536295644939, -0.10436110943555832, 0.02805154211819172, -0.007819779217243195, -0.00044881130452267826, 0.03299962356686592, 0.014391609467566013, -0.0017162681324407458, -0.023919422179460526, 0.0006491459207609296, -0.03832404315471649, -0.02125570923089981, -0.04081697762012482, -0.0527736134827137, 0.004031755030155182, 0.032859548926353455, -0.017888683825731277, 0.011455321684479713, -0.02911682426929474, -0.021217698231339455, 0.006050216034054756, 0.02899903431534767, 0.012293864041566849, -0.06729897111654282, 0.03667699545621872, -0.002920768456533551, 0.0346372127532959, -0.01749986968934536, -0.01855696551501751, -0.06819740682840347, -0.05650719627737999, 0.014894223771989346, -0.06438985466957092, -0.04611419886350632, 0.021181635558605194, -0.02306467480957508, 0.006913142744451761, 0.012682328000664711, -0.009496192447841167, 0.06212234124541283, 0.03863627463579178, -0.05341583490371704, 0.06325716525316238, -0.022981930524110794, -0.022365789860486984, -0.039311885833740234, -0.052476052194833755, -0.07435432076454163, 0.026687519624829292, -0.014847494661808014, -0.0027593004051595926, 0.03960590809583664, 0.018290523439645767, -0.058136049658060074, -0.04169311746954918, -0.01907653547823429, 0.029190821573138237, 0.009533080272376537, 0.008553213439881802, -0.01453336514532566, -0.003753898898139596, 0.012731156311929226, -0.016357343643903732, 0.013561053201556206, -0.013713812455534935, 0.015409077517688274, 0.06336942315101624, 0.03589874133467674, 0.011834360659122467, -0.04233816638588905, 0.08759015053510666, 0.010298595763742924, 0.02339976653456688, 0.009795285761356354, -0.00820374395698309, -0.018735112622380257, 0.027116961777210236, -0.07306292653083801, 0.0029416431207209826, -0.042416151612997055, -0.045848995447158813, -0.06010005995631218, 0.04572131112217903, 0.01720665954053402, 0.03981063887476921, -0.016235869377851486, 0.00952730979770422, -0.06611673533916473, 0.03475084528326988, 0.02904256246984005, -0.02115684747695923, -0.03232971578836441, 0.017234522849321365, 0.02089712955057621, 0.002760567469522357, 0.0009841843275353312, 0.0703553780913353, -0.02743157558143139, 0.01686064340174198, -0.006109156180173159, -0.0660809576511383, -0.014114226214587688, -0.04714475944638252, -0.032454658299684525, 0.01682388223707676, -0.0773286521434784, 0.022714676335453987, -0.006067491136491299, -0.013812250457704067, 0.036743275821208954, -0.015030237846076488, 0.05376853048801422, -0.0039558918215334415, 0.019499478861689568, -0.004611896816641092, 0.019916651770472527, 0.05819050222635269, -0.030489899218082428, -0.06595007330179214, -0.014962575398385525, -0.02572534792125225, -0.0006655119941569865, -0.05204663798213005, -0.012743107974529266, -0.026955047622323036, 0.026531782001256943, -0.060016922652721405, -0.008277802728116512, 0.00973487552255392, -0.02102208137512207, 0.04179162532091141, 0.021305281668901443, -0.037742432206869125, 0.06754101067781448, 0.0588986836373806, -0.07927294820547104, -0.013132881373167038, 0.027177320793271065, -0.009242569096386433, 0.03190016746520996, 0.025548674166202545, -0.014930232428014278, 0.04503526911139488, 0.01464146189391613, -0.06079084426164627, 0.06298622488975525, -0.0454142726957798, 0.0691390335559845, -0.0030857836827635765, -0.015519494190812111, -0.01201794296503067, 0.0016968229319900274, -0.029673101380467415, -0.008229220286011696, 0.05091777816414833, 0.0724916011095047, -0.007598609197884798, 0.023533077910542488, -0.015484122559428215, 0.02920638583600521, -0.023681607097387314, -0.0018738929647952318, -0.07870613783597946, -0.01698128692805767, 0.009122352115809917, 0.029795585200190544, -0.020634928718209267, -0.012294787913560867, 0.04671737179160118, -0.06333576887845993, -0.009634257294237614, -0.03845330327749252, 0.01839093118906021, -0.01283192727714777, -0.05009917914867401, 0.03452790528535843, 0.0561726950109005, -0.003494584234431386, -0.07595519721508026, -0.09787946194410324, -0.07281583547592163, 0.014216611161828041, 0.04627187177538872, 0.004164684098213911, 0.015949832275509834, -0.022990131750702858, -0.08626449853181839, -0.017108647152781487, 0.041333217173814774, 0.012965532019734383, 0.01962456665933132, 0.004839051514863968, 0.08640298247337341, -0.0020615921821445227, 0.04352695494890213, 0.032879576086997986, 0.02634413167834282, 0.035039015114307404, 0.0015994870336726308, -0.009409492835402489, 0.016458706930279732, 0.0458679124712944, -0.005481362342834473, 0.07089678943157196, 0.04005115106701851, -0.06499721109867096, 0.024488572031259537, -0.04287901520729065, -0.02338186837732792, 0.04770934209227562, -0.01741698570549488, 0.03423186391592026, 0.05012638866901398, 0.01551862433552742, 0.04117046669125557, 0.007362435571849346, 0.028567595407366753, -0.027714425697922707, 0.05053193122148514, -0.0563485361635685, -0.025309331715106964, 0.016544433310627937, -0.0007703673327341676, -0.06778917461633682, -0.05804818123579025, -0.05461907014250755, -0.005332073662430048, -0.03542039543390274, -0.045402053743600845, -0.0057412851601839066, -0.016415536403656006, 0.031055616214871407, -0.0052597420290112495, 0.025316651910543442, 0.053771696984767914, 0.01623832806944847, -0.011306592263281345, -0.039663489907979965, 0.007120893336832523, -0.0287764985114336, 0.019435053691267967, 0.05065026134252548, 0.034162260591983795, 0.02103217877447605, -0.039297740906476974, 0.0738426074385643, -0.019904693588614464, -0.01794845424592495, -0.05200733616948128, 0.03061571530997753, -0.03371585160493851, -0.0005073267966508865, -0.0033723595552146435, -0.01144396048039198, 0.014219910837709904, -0.030804498121142387, -0.0015343842096626759, -0.014717712998390198, 0.01896520145237446, -0.006039823405444622, 0.027003666386008263, -0.043557990342378616, -0.038784097880125046, 0.02735958807170391, 0.006974590476602316, 0.021218711510300636, -0.05349652096629143, -0.009197880513966084, 0.020562568679451942, 0.07967793941497803, 0.03128260001540184, -0.029284344986081123, 0.029716262593865395, 0.007223296444863081, 0.006126908119767904, -0.0281661469489336, 0.03693486750125885, 0.028725653886795044, -0.037337835878133774, -0.02029947005212307, -0.0057520498521625996, 0.0017783648800104856, 0.024505170062184334, -0.045828938484191895, 0.007992043159902096, -0.012081602588295937, 0.008815394714474678, -0.02394000254571438, 0.010216038674116135, 0.0510813444852829, 0.011477275751531124, -0.07922477275133133, 0.013315815478563309, -0.00018344628915656358, -0.010401603765785694, 0.00242815469391644, 0.05489085242152214, 0.03006731905043125, 0.00015006345347501338, -0.024512602016329765, -0.012362939305603504, -0.002974712522700429, 0.0003865451435558498, 0.04030235856771469, 0.010414715856313705, -0.04002056270837784, -0.023899508640170097, 0.00013437373854685575, 0.0002470007457304746, 0.02990645170211792, -0.010270250961184502, 0.016596069559454918, -0.008778790012001991, 0.006094804499298334, -0.018202517181634903, -0.025492001324892044, -0.0031600126530975103, -0.006891262251883745, 0.02817084640264511, 0.04136271774768829, 0.02459684945642948, -0.05219826102256775, 0.042931847274303436, -0.07218654453754425, 0.03694761171936989, -0.006744919344782829, 0.004436148330569267, 0.034028034657239914, -0.019278118386864662, 0.021345453336834908, -0.06027577444911003, -0.05650675669312477, 0.02013571187853813, -0.007438233587890863, 0.02414272353053093, 0.04377878084778786, 0.02982957474887371, -0.04780067503452301, -0.021866127848625183, 0.047318972647190094, -0.014031383208930492, 0.05553892254829407, 0.012987579219043255, -0.008951784111559391, 0.018986964598298073, 0.008586783893406391, -0.03271244093775749, 0.019382329657673836, 0.013662154786288738, 0.02309788390994072, 0.0019141231896355748, 0.08926301449537277, 0.04006417468190193, 0.03178223595023155, 0.029631320387125015, 0.02688557095825672, 0.06860724091529846, 0.029943814501166344, 0.08227626979351044, 0.023788228631019592, -0.08390025794506073, 0.026312723755836487, -0.032347533851861954, -0.019076352939009666, 0.019927164539694786, -0.0354633666574955, 0.013278757221996784, -0.005933176726102829, 0.052799422293901443, -0.010105212219059467, 0.02082776464521885, 0.03286341577768326, 0.011413203552365303, 0.025155790150165558, 0.024491460993885994, -0.011195399798452854, -0.014920762740075588, 0.00815852452069521, 0.006353397388011217, -0.05460632964968681, 0.030312174931168556, -0.005800710525363684, 0.027591638267040253, 0.042962487787008286, -0.02541760541498661, -0.010552434250712395, -0.06662485748529434, 0.01010431069880724, 0.006854549050331116, 0.005222888197749853, 0.001962791197001934, -0.04958965629339218, -0.012964214198291302, 0.03252691403031349, -0.08914898335933685, 0.040735166519880295, -0.002360572339966893, -0.05785321071743965, 0.050768956542015076, 0.018302658572793007, -0.05470237508416176, -0.014299632981419563, 0.022955793887376785, 0.042865365743637085, 0.03488706424832344, -0.010033509694039822, 0.03745703026652336, -0.0009903464233502746, 0.061155322939157486, 0.05966899171471596, -0.012340285815298557, -0.040931038558483124, -0.007893003523349762, 0.02661139704287052, 0.02279006503522396, -0.04473176226019859, 0.06869720667600632, 0.022163255140185356, -0.016374925151467323, -0.02713817171752453, 0.03701905533671379, 0.029974302276968956, -0.019520994275808334, -0.006396404467523098, -0.006570038851350546, -0.0573735237121582, 0.004600738640874624, 0.004727536346763372, 0.013329937122762203, -0.03429321572184563, -0.031660664826631546, -0.058793991804122925, 0.039064452052116394, -0.023550184443593025, -0.02022434026002884, 0.0021057857666164637, -0.004461054690182209, 0.09738985449075699, 0.012552500702440739, -0.04360996559262276, 0.041345495730638504, -0.011946852318942547, -0.017155703157186508, -0.03546154126524925, -0.013785034418106079, -0.015598871745169163, 0.0017063029808923602, -0.0653541088104248, -0.040631864219903946, 0.04112643748521805, -0.03339724242687225, 0.043516047298908234, 0.04778750613331795, 0.0613347627222538, 0.004793484229594469, -0.02109362743794918, 0.08125188946723938, -0.06328703463077545, -0.0525619201362133, 0.05754009261727333, -0.009921497665345669, 0.006116750184446573, 0.04559364914894104, -0.00440629618242383, -0.008468826301395893, -0.043049171566963196, -0.02457350865006447, -0.020005622878670692, 0.06744615733623505, 0.003965792246162891, -0.03106619603931904, 0.032182373106479645, 0.043687496334314346, 0.02603558637201786, -0.06570812314748764, 0.03882833942770958, -0.02018650993704796, -0.08841221034526825, 0.0369400829076767, -0.0519983246922493, -0.04255878925323486, 0.06900381296873093, -0.020337950438261032, 0.08813649415969849, -0.06787343323230743, 0.0473756268620491, 0.007930080406367779, -0.03492588922381401, -0.008729428052902222, 0.012553566135466099, 0.020824791863560677, -0.04231735318899155, -0.04106302559375763, 0.02435273490846157, 0.0342026948928833, 0.020639466121792793, 0.03831574320793152, -0.0023725538048893213, -0.0221076812595129, 0.009655406698584557, -0.005000052507966757, -0.03929687663912773, -0.036627717316150665, -0.017649421468377113, 0.038379453122615814, -0.027889376506209373, -0.016599692404270172, -0.01678394339978695, -0.056107256561517715, -0.04173138737678528, -0.083901546895504, 0.000807200325652957, 0.002379747573286295, 0.015294365584850311, -0.044873327016830444, -0.01853034645318985, -0.041138406842947006, -0.03504679724574089, 0.018003646284341812, 0.024528853595256805, 0.007679792586714029, -0.01905922405421734, -0.003438927000388503, 0.014504097402095795, 0.08096276968717575, 0.03882720693945885, 0.006101362872868776, -0.0657973363995552, 0.018164437264204025, -0.0424184575676918, -0.022890321910381317, -0.030983816832304, 0.08992933481931686, 0.004253670573234558, 0.0028113587759435177, 0.005800346378237009, 0.01548893190920353, 0.0005911508924327791, -0.03918983414769173 ]
<p>While watching the first 4 seconds of <a href="http://www.gizmodo.com.au/2011/11/driving-at-745kmh-is-ludicrous-from-any-angle/" rel="nofollow">driving at 745 km/h is ludicrous from any angle</a> wondered </p> <p>1)If we knew the curvature of the earth in a "flat" desert, what would be the speed of the car?</p> <p>2)Assuming we don't know the curvature of the earth, how long would it take for the car to go around the earth ( assuming a "flat" desert all the way travelling on a great arc)?</p> <p>Using my ninja pause skills it seemed it took 2 seconds from the time the car appeared ( as a dot ) in horizon to the time it passed by the camera, although 2 second window of observation seems to lead to a great error in overall estimates, using the 745 as the value for 1 and 2 the error of human observation could be calculated (?) </p>
g1584
[ 0.032667677849531174, 0.04105037823319435, -0.008069555275142193, -0.0188908614218235, 0.05871906131505966, 0.01936226710677147, 0.04163798689842224, -0.012575972825288773, -0.07783880829811096, -0.013210275210440159, 0.03614332526922226, 0.000028063965146429837, 0.10424784570932388, 0.014247003011405468, 0.0526491142809391, -0.016388989984989166, -0.020784035325050354, -0.006661207880824804, -0.02386004477739334, -0.011414271779358387, 0.04013562202453613, -0.03639881685376167, 0.013561385683715343, -0.005828016437590122, -0.061848822981119156, -0.03890179470181465, -0.005809576716274023, 0.01839485764503479, -0.05488435924053192, -0.041442714631557465, 0.01835637539625168, 0.004932795651257038, 0.0008826603880152106, -0.02419520914554596, -0.06955979764461517, -0.017657659947872162, 0.02229209989309311, 0.024233577772974968, 0.03638150542974472, 0.007482199929654598, -0.02327040582895279, -0.03432982414960861, 0.011442489922046661, 0.04623283073306084, 0.06386544555425644, 0.018832648172974586, -0.02978506311774254, 0.01680923067033291, 0.057454198598861694, 0.029391122981905937, -0.040309734642505646, 0.04039065167307854, 0.04417935013771057, 0.03903429955244064, -0.008941829204559326, -0.031147314235568047, -0.018597453832626343, -0.016462087631225586, 0.06496918946504593, -0.009120399132370949, -0.05392426997423172, -0.10243722051382065, 0.027595505118370056, 0.03076310269534588, 0.0044777244329452515, -0.017108259722590446, -0.010495557449758053, 0.015274870209395885, 0.04863164946436882, -0.028710033744573593, 0.043373629450798035, -0.011314638890326023, -0.03354434296488762, -0.0883689746260643, -0.036281801760196686, 0.004849149379879236, 0.031077446416020393, -0.027890590950846672, 0.0503946952521801, -0.009811249561607838, 0.014146249741315842, 0.031072158366441727, -0.07585735619068146, 0.05206476151943207, 0.02661149576306343, -0.01392010785639286, -0.024140385910868645, 0.004703166428953409, 0.03327324613928795, -0.03051566332578659, 0.032901179045438766, -0.06281308829784393, -0.029189137741923332, -0.009177048690617085, -0.019407451152801514, -0.05352471396327019, -0.02380356937646866, 0.0653131753206253, -0.044541750103235245, 0.09586617350578308, -0.030047472566366196, -0.01623392291367054, 0.027184899896383286, 0.054149288684129715, 0.010546481236815453, 0.014694906771183014, -0.07831142097711563, 0.010126421228051186, 0.027959810569882393, -0.12471460551023483, 0.060204293578863144, -0.03075842559337616, 0.021253986284136772, 0.027111494913697243, -0.044964250177145004, -0.054075777530670166, -0.008726008236408234, 0.002127690939232707, -0.005233248695731163, 0.0222765002399683, -0.025465376675128937, 0.05640996992588043, 0.025289468467235565, 0.05256753787398338, 0.04335927590727806, -0.007191396784037352, 0.0007583187543787062, -0.01419672928750515, 0.019669847562909126, 0.009761500172317028, -0.05682741105556488, 0.06300841271877289, 0.053974855691194534, 0.02245929464697838, -0.056479811668395996, 0.05920197069644928, -0.009253179654479027, 0.012565622106194496, -0.040100641548633575, 0.016895189881324768, 0.04373340681195259, 0.027474747970700264, 0.05402539297938347, -0.006033641751855612, -0.006375261582434177, -0.005366278812289238, -0.03214999660849571, 0.0015679853968322277, 0.020774569362401962, 0.00553255807608366, -0.025137508288025856, 0.007361754309386015, 0.028031261637806892, 0.019657380878925323, 0.007224055472761393, 0.014376320876181126, 0.04339304938912392, -0.00013604263949673623, -0.027651347219944, 0.029825301840901375, 0.048471029847860336, -0.009827958419919014, -0.021435145288705826, -0.01981855370104313, -0.032858170568943024, -0.011960005387663841, 0.0022631329484283924, -0.016234125941991806, 0.024342326447367668, -0.03274010121822357, -0.07414495944976807, -0.01688014157116413, 0.019367245957255363, -0.01218966580927372, -0.05586918443441391, -0.023327035829424858, 0.03155294433236122, -0.04293835163116455, -0.04006965085864067, -0.011382014490664005, 0.004531717859208584, -0.07116897404193878, 0.021255895495414734, 0.015139339491724968, -0.011153257451951504, -0.02300824224948883, 0.030486799776554108, -0.04170306399464607, -0.08224966377019882, 0.016209393739700317, 0.01131761446595192, -0.07655758410692215, 0.007769598625600338, 0.035925574600696564, -0.006620843429118395, -0.014004267752170563, 0.04881790280342102, -0.022976940497756004, 0.030529024079442024, 0.0033475118689239025, -0.010376088321208954, -0.01195614319294691, 0.04789113998413086, -0.00466467859223485, 0.007740804925560951, -0.030569763854146004, 0.015035310760140419, 0.023608746007084846, -0.04127214848995209, 0.04981720820069313, 0.06143578886985779, 0.03526032716035843, 0.005789265502244234, 0.015742631629109383, 0.04470212757587433, 0.02942340075969696, 0.005410306621342897, -0.019334731623530388, -0.007134873885661364, 0.005345575977116823, 0.07323095947504044, 0.004827515222132206, 0.019393190741539, -0.03248482197523117, 0.022637201473116875, 0.02028367854654789, -0.04524940997362137, -0.023902179673314095, -0.0121842660009861, 0.015511006116867065, 0.05710301548242569, -0.027644222602248192, -0.014878500252962112, 0.004758065566420555, 0.01983681693673134, 0.022447865456342697, 0.041434481739997864, -0.03207860887050629, 0.07649295777082443, -0.0017334551084786654, 0.015613886527717113, -0.009519117884337902, -0.05208488926291466, -0.03223071247339249, -0.020400064066052437, -0.045259542763233185, -0.01075323112308979, 0.02585756592452526, 0.012313059531152248, 0.0195121169090271, 0.0040260483510792255, -0.07235872000455856, -0.012674893252551556, 0.033252112567424774, 0.0508975088596344, 0.0024868410546332598, -0.010871980339288712, -0.010390784591436386, -0.05177188664674759, 0.01505180075764656, -0.02262691594660282, 0.017474940046668053, 0.009636095724999905, 0.009622808545827866, -0.044108834117650986, -0.02155221253633499, -0.013906766660511494, 0.0006284866249188781, -0.009905287064611912, -0.06822642683982849, -0.022784879431128502, -0.018391376361250877, -0.03917275741696358, 0.03941595181822777, -0.008069896139204502, -0.005574926268309355, -0.004410726483911276, -0.0521358959376812, -0.03456168249249458, -0.010225595906376839, -0.016222618520259857, -0.0005489559262059629, -0.04119241237640381, 0.057451341301202774, 0.044505905359983444, -0.029082536697387695, -0.020075831562280655, 0.0050995624624192715, -0.01990342140197754, 0.016339559108018875, -0.04678185656666756, 0.029570266604423523, 0.042504750192165375, 0.021464787423610687, 0.02284473553299904, 0.03167874366044998, 0.006717714946717024, -0.0037482113111764193, 0.021267054602503777, -0.07091938704252243, 0.052805714309215546, -0.04847080633044243, -0.004935058299452066, -0.006163311656564474, -0.007233232259750366, -0.025108594447374344, -0.012934388592839241, -0.013275787234306335, 0.025889847427606583, -0.03563692048192024, -0.008254185318946838, -0.0016860351897776127, -0.019793633371591568, 0.019816121086478233, 0.012384944595396519, -0.045127302408218384, -0.058216288685798645, 0.010833308100700378, 0.0281592458486557, 0.10246118903160095, 0.016796937212347984, -0.03597630187869072, -0.07233330607414246, 0.031634461134672165, 0.029020216315984726, 0.05310340225696564, 0.003034544875845313, -0.04240814223885536, 0.002790754893794656, -0.00045459414832293987, 0.0093287518247962, 0.04591554030776024, -0.010928741656243801, -0.03857967630028725, -0.02410508506000042, -0.021001439541578293, 0.02871892973780632, 0.03557124361395836, 0.0051645552739501, -0.007392069790512323, -0.028483137488365173, 0.03758973255753517, -0.03593023493885994, -0.03895638883113861, 0.014110096730291843, 0.0310787595808506, 0.027841124683618546, -0.04880634322762489, -0.07796186953783035, 0.04072826728224754, 0.05238600820302963, -0.0425775982439518, -0.05576210841536522, -0.04491718113422394, 0.015279592014849186, 0.04473106563091278, -0.03147517144680023, 0.0014039771631360054, -0.0015380370896309614, -0.06520646810531616, 0.05712787061929703, 0.039358802139759064, 0.026893887668848038, -0.044563911855220795, 0.01702479086816311, -0.035837072879076004, -0.0365825779736042, 0.002253201324492693, -0.01844692975282669, -0.0035223786253482103, 0.011088298633694649, -0.017166441306471825, -0.003153624478727579, 0.020898284390568733, 0.01208525337278843, 0.019325463101267815, 0.045503538101911545, -0.019454263150691986, -0.05482499673962593, 0.014782354235649109, -0.022461185231804848, 0.03539000079035759, 0.0677042305469513, -0.014790746383368969, -0.017862694337964058, -0.03688287362456322, -0.035224270075559616, -0.08073099702596664, 0.03156482055783272, -0.05098870024085045, 0.07078567892313004, -0.06261922419071198, 0.014404933899641037, -0.039775263518095016, -0.007395491469651461, -0.00877207051962614, 0.03766649216413498, 0.021751565858721733, -0.02271014265716076, 0.018692346289753914, 0.02411796525120735, 0.020508484914898872, 0.039087191224098206, 0.04588001221418381, -0.05941241607069969, -0.01324065774679184, -0.017433682456612587, -0.0381152369081974, 0.04054436460137367, -0.01601368933916092, -0.019693365320563316, 0.04207003861665726, -0.01489112339913845, -0.007160816807299852, 0.03929806128144264, 0.042411282658576965, -0.02186201699078083, -0.015243865549564362, -0.016892537474632263, -0.01202633697539568, -0.05704531446099281, 0.025007622316479683, -0.013951748609542847, -0.042859312146902084, 0.005406241398304701, 0.04023579880595207, 0.01467033289372921, 0.008994578383862972, -0.05127549171447754, 0.022825729101896286, 0.07660182565450668, 0.018903100863099098, -0.03934282064437866, 0.10080080479383469, -0.05080420896410942, 0.059296004474163055, 0.02262170985341072, 0.0487092100083828, 0.058968182653188705, -0.011485477909445763, -0.016771836206316948, 0.026792198419570923, 0.06349597871303558, -0.03729064762592316, -0.055929996073246, 0.04137496277689934, -0.019504442811012268, -0.054503023624420166, -0.018643492832779884, -0.00911092571914196, 0.01885724440217018, 0.06923370808362961, -0.052139755338430405, 0.060390885919332504, 0.004049294628202915, -0.052546609193086624, -0.07323971390724182, -0.011348219588398933, 0.024704599753022194, 0.0362277626991272, -0.051071565598249435, 0.05291655659675598, -0.031536877155303955, 0.060562483966350555, -0.018763845786452293, -0.005063941702246666, -0.0020310573745518923, -0.015910565853118896, -0.030269673094153404, -0.006528500933200121, -0.05402953922748566, 0.009719259105622768, 0.04307432472705841, -0.023256605491042137, -0.007494465447962284, 0.04567250609397888, -0.013572420924901962, 0.02094811573624611, -0.01771060936152935, -0.018886622041463852, -0.0877341777086258, 0.02640414424240589, 0.03485590219497681, -0.04290146753191948, 0.006284960079938173, 0.006507407873868942, -0.008811641484498978, -0.029621822759509087, -0.007372456602752209, -0.03554409742355347, 0.012576009146869183, -0.02152148261666298, -0.013781974092125893, -0.047340910881757736, -0.02404617890715599, 0.007909470237791538, 0.03082091361284256, -0.018928030505776405, -0.046857815235853195, 0.02562166005373001, -0.0716613158583641, 0.03467915952205658, 0.009077987633645535, -0.032011158764362335, 0.013601496815681458, 0.027282066643238068, 0.09384746849536896, -0.04833577573299408, 0.025329936295747757, 0.07738876342773438, 0.04743218794465065, 0.07596885412931442, 0.02337237261235714, -0.035117488354444504, 0.039104167371988297, -0.047377415001392365, -0.03039647452533245, 0.043988700956106186, -0.020739423111081123, 0.018642108887434006, 0.05830805003643036, 0.03673957288265228, 0.01918186992406845, 0.008713957853615284, 0.0026876728516072035, -0.02390163391828537, -0.0505669005215168, -0.011465748772025108, -0.03964301198720932, -0.03907965496182442, 0.025890665128827095, -0.009858260862529278, -0.044941987842321396, -0.037222642451524734, 0.014037931337952614, -0.010671484284102917, 0.0249512679874897, -0.04992995038628578, 0.09126069396734238, -0.052958033978939056, -0.07456934452056885, -0.016467662528157234, 0.023289017379283905, 0.04111909866333008, -0.01852712221443653, 0.005870114546269178, 0.012771831825375557, 0.028379185125231743, 0.024469012394547462, -0.03022252582013607, -0.009909730404615402, 0.011276151984930038, -0.021770447492599487, -0.01773729734122753, -0.04128239303827286, 0.047319985926151276, -0.021682074293494225, 0.025646669790148735, -0.006774509325623512, -0.06673623621463776, 0.05891736224293709, 0.010956687852740288, 0.02321755699813366, 0.03003324754536152, -0.0675308108329773, -0.0448550209403038, 0.0010340521112084389, 0.025217890739440918, 0.0597689189016819, 0.02146751433610916, 0.034789033234119415, -0.05422613024711609, 0.0009217889164574444, 0.008247798308730125, 0.03438252955675125, -0.035764142870903015, 0.01099726278334856, 0.010413709096610546, -0.05534049868583679, 0.028853490948677063, 0.004285986069589853, -0.025530915707349777, 0.051507607102394104, 0.005886373575776815, 0.040755659341812134, 0.07133527100086212, -0.048700831830501556, 0.004362545441836119, -0.033510103821754456, -0.028326138854026794, 0.005206997971981764, 0.005624293815344572, -0.02310725674033165, -0.01948418654501438, 0.002938677789643407, -0.0343623012304306, -0.008982561528682709, -0.04622216895222664, -0.05436631292104721, 0.03212931379675865, 0.01181909628212452, -0.03799152001738548, 0.015099989250302315, -0.0056911553256213665, 0.04352088272571564, -0.03975951299071312, -0.007450716104358435, 0.05479941889643669, 0.04084733501076698, -0.0501319020986557, 0.023432547226548195, 0.08427213877439499, 0.02841169387102127, 0.05967036634683609, -0.05808843672275543, 0.012780213728547096, -0.02608969621360302, -0.024421989917755127, 0.05106034129858017, -0.05586740002036095, -0.0021390258334577084, 0.053530797362327576, 0.002334796590730548, 0.016233226284384727, -0.007467811461538076, 0.01273133885115385, -0.01108824647963047, -0.012286907061934471, 0.016525784507393837, -0.016841916367411613, 0.06302260607481003, -0.07146013528108597, 0.018242063000798225, 0.026043986901640892, 0.03234434500336647, -0.04845896363258362, -0.011005335487425327, 0.03664837032556534, 0.016872422769665718, 0.027589572593569756, 0.020977430045604706, -0.05824832245707512, 0.014302266761660576, -0.023002326488494873, -0.06301797926425934, -0.04739091172814369, 0.0028665466234087944, -0.013825555332005024, -0.020600702613592148, -0.031621553003787994, 0.03405914083123207, -0.07014849781990051, 0.007355359848588705, 0.01775728538632393, -0.003927226644009352, 0.062472544610500336, -0.03563782572746277, 0.012774422764778137, 0.03632282465696335, -0.06122981756925583, -0.017315547913312912, -0.002725892933085561, 0.03722935914993286, -0.0061177536845207214, -0.014302616938948631, 0.01208132691681385, -0.013766693882644176, -0.03533054515719414, -0.061585523188114166, 0.02833748608827591, -0.008007370866835117, 0.019777873530983925, -0.019886231049895287, 0.00561191001906991, 0.030278218910098076, -0.005522894207388163, -0.06221066787838936, 0.05515466630458832, 0.02925904653966427, 0.02906099520623684, 0.037794146686792374, 0.01574523188173771, -0.016000445932149887, -0.005093819927424192, -0.015106051228940487, 0.024665875360369682, 0.009891868568956852, -0.023285159841179848, -0.021615268662571907, -0.052780404686927795, -0.012591538019478321, 0.029783962294459343, 0.028992004692554474, -0.05293896421790123, -0.02089032158255577, 0.023688344284892082, 0.04299444705247879, 0.004272898193448782, 0.010945805348455906, -0.0027141133323311806, -0.049505628645420074, 0.029317671433091164, 0.06055447459220886, 0.03941534459590912, 0.03186209872364998, -0.03548779711127281, -0.011146719567477703, -0.035979606211185455, -0.0520905926823616, 0.05315500497817993, 0.05617865175008774, 0.015436159446835518, 0.0057244328781962395, 0.04702406004071236, 0.03745599836111069, -0.033441267907619476, 0.004683273378759623, 0.004992664325982332, -0.005633308552205563, 0.02310221455991268, -0.006764162797480822, 0.0032937198411673307, 0.04880446568131447, -0.04768121987581253, -0.021174566820263863, -0.02649512328207493, 0.0006405607564374804, -0.08445344865322113, 0.05564112588763237, -0.061735495924949646, 0.023576930165290833, 0.08101921528577805, -0.005193009041249752, 0.022000625729560852, -0.007319290656596422, -0.0402231439948082, 0.002278711413964629, -0.0335475355386734, -0.03717781603336334, 0.03567521646618843, -0.023774558678269386, 0.03745277598500252, 0.04775073006749153, 0.009323617443442345, 0.011873441748321056, 0.007369777653366327, 0.0003537844750098884, 0.0799640640616417, -0.008119655773043633, -0.012291221879422665, 0.0262281633913517, -0.00008870393503457308, -0.035098109394311905, 0.005164859816431999, 0.020593393594026566, 0.008621838875114918, -0.009877081960439682, 0.006725057493895292, 0.02415275201201439, -0.0027748465072363615, -0.04050362482666969, 0.022791313007473946, 0.03689021244645119, -0.017070868983864784, -0.012741482816636562, -0.03736880421638489, -0.041735731065273285, 0.04059764742851257 ]
<p>The book I'm reading about optics says that an anti-reflective film applied on glass* makes the glass <em>more</em> transparent, because the air→film and film→glass reflected waves (originated from a <a href="http://en.wikipedia.org/wiki/Paraxial_approximation" rel="nofollow">paraxial</a> incoming wave) interfere destructively with each other, resulting on virtually no reflected light; therefore the "extra" light that would normally get reflected, gets transmitted instead (to honor the principle of conservation of energy, I suppose?).</p> <p>However, <a href="http://physics.stackexchange.com/questions/10410/why-dont-waves-erase-out-each-other-when-looking-onto-a-wall/10439#10439">this answer</a> states that <em>"Superposition is the principle that the amplitudes due to two waves incident on the same point in space at the same time can be naively added together, but the waves do not affect each other."</em></p> <p>So, how does this fit into this picture? If the reflected waves actually continue happily travelling back, where does the extra transmitted light come from?</p> <p><sub>* the film is described as (1) having an intermediate index of refraction between those of air and glass, so that both the air-film and film-glass reflections are "hard", i.e., produce a 180º inversion in the phase of the incoming wave, and (2) having a depth of 1/4 of the wavelength of the wave in the film, so that the film-glass reflection travels half its wavelength back and meets the air-film reflection in the opposite phase, thus cancelling it.</sub></p>
g1585
[ 0.042212825268507004, 0.02503502555191517, 0.0035168540198355913, 0.01381317526102066, 0.01653619483113289, 0.025798022747039795, 0.04102349281311035, 0.024733232334256172, -0.012367725372314453, -0.0281472597271204, -0.011272655799984932, 0.05897771567106247, 0.009908245876431465, 0.017593996599316597, 0.01934414729475975, -0.035484299063682556, 0.07250270992517471, -0.03983856365084648, 0.0170891173183918, -0.002682122867554426, -0.017849842086434364, -0.04641856253147125, 0.013531058095395565, -0.060795966535806656, -0.03476038575172424, 0.033321935683488846, 0.017723482102155685, -0.08431500196456909, -0.022961223497986794, -0.03802214190363884, 0.047486308962106705, -0.014151112176477909, 0.015422229655086994, -0.03178425878286362, 0.04690832644701004, -0.010777689516544342, 0.015858173370361328, 0.01614796742796898, 0.0352514274418354, -0.002673615701496601, -0.04660063982009888, 0.026948824524879456, -0.015473970212042332, 0.0005155983963049948, 0.020098453387618065, 0.0006257513305172324, -0.017966149374842644, -0.002342275343835354, 0.004385568201541901, -0.048377059400081635, -0.009210081771016121, 0.037837132811546326, 0.03106137551367283, 0.03827076032757759, 0.025855839252471924, -0.001924258773215115, -0.00835111178457737, -0.01060570776462555, 0.07618319988250732, -0.027147604152560234, -0.029118061065673828, -0.0024586827494204044, -0.010224703699350357, 0.040664833039045334, 0.08514872193336487, -0.010015499778091908, -0.03420202061533928, -0.007911736145615578, 0.051473211497068405, 0.010234065353870392, 0.034413598477840424, -0.008530119433999062, -0.0451461561024189, -0.02936159260571003, -0.02131638675928116, -0.012662990018725395, 0.007845023646950722, 0.012495486997067928, -0.00012625577801372856, 0.0026928335428237915, 0.02441142313182354, -0.03482605516910553, -0.04768168181180954, 0.025416070595383644, -0.010213606059551239, 0.009587099775671959, 0.04825276508927345, -0.0073008607141673565, -0.025501705706119537, -0.03759482130408287, 0.04727309197187424, 0.006743116304278374, 0.05005941167473793, 0.020924126729369164, 0.03709625080227852, 0.006257985252887011, -0.009507053531706333, -0.03790241479873657, -0.06216653063893318, 0.008724438026547432, -0.028270382434129715, -0.02411327324807644, 0.0403292290866375, 0.004793707747012377, 0.00046943555935285985, 0.020338937640190125, 0.029520662501454353, -0.008549055084586143, -0.06929617375135422, 0.01495618000626564, -0.05102110281586647, 0.002295616315677762, -0.06203063577413559, -0.01910802163183689, -0.0047924090176820755, -0.0064200484193861485, 0.06871184706687927, -0.02868863381445408, 0.042524006217718124, 0.06708396226167679, 0.05400027334690094, 0.06885334104299545, 0.010789102874696255, 0.029804028570652008, 0.0003860888828057796, 0.005242691840976477, 0.010698243044316769, -0.0131046362221241, 0.058150358498096466, -0.04222015663981438, 0.013060174882411957, 0.0025850466918200254, 0.01967078074812889, 0.01144403126090765, -0.026118868961930275, -0.014838111586868763, 0.03856479376554489, -0.022975774481892586, -0.018108541145920753, -0.0017543290741741657, -0.0026651525404304266, 0.016355348750948906, -0.01967046596109867, -0.003695825347676873, -0.016864793375134468, -0.029896996915340424, -0.013646816834807396, 0.01266907062381506, 0.012490816414356232, -0.022316256538033485, 0.02925872430205345, 0.0342596098780632, -0.030969804152846336, 0.020427469164133072, 0.03176924213767052, -0.041921090334653854, 0.0017142279539257288, -0.04253043979406357, 0.00032111542532220483, 0.00021864756126888096, 0.12245295941829681, -0.010084323585033417, 0.0007324677426367998, 0.011966302990913391, -0.03862517327070236, -0.026661137118935585, 0.004044718109071255, -0.034314803779125214, 0.0035084369592368603, -0.05528319999575615, -0.042456816881895065, 0.027334334328770638, 0.053365420550107956, 0.058297112584114075, 0.004499416798353195, 0.06889310479164124, 0.07741951197385788, -0.041487399488687515, 0.007055411580950022, 0.022923875600099564, -0.041211314499378204, -0.000031286475859815255, -0.057487279176712036, -0.052755407989025116, 0.03131788969039917, -0.051908887922763824, 0.038753632456064224, 0.004066973924636841, -0.053495053201913834, 0.01645745150744915, 0.015007242560386658, -0.004791614133864641, -0.030581703409552574, 0.029673101380467415, 0.025249386206269264, 0.049552880227565765, 0.04197372868657112, 0.0032182554714381695, -0.03149968013167381, 0.024839892983436584, -0.024527657777071, 0.007867760956287384, 0.06151088327169418, -0.032290782779455185, 0.03451535850763321, 0.06651923805475235, -0.0845659151673317, -0.012816962786018848, -0.03372086212038994, 0.03777026757597923, -0.04556070640683174, 0.04046085476875305, 0.05540144816040993, -0.04917728155851364, 0.03937448188662529, 0.01920386590063572, -0.002365940250456333, 0.006825271528214216, -0.03618689253926277, 0.005639297887682915, 0.03172336891293526, 0.050330307334661484, -0.03328234329819679, -0.014635715633630753, -0.020851457491517067, 0.013624628074467182, -0.04936718940734863, 0.009298230521380901, -0.004789744969457388, -0.014153728261590004, -0.011331094428896904, -0.05489902198314667, -0.012960026040673256, 0.007281971629709005, 0.06281805783510208, -0.04480917379260063, -0.014324614778161049, 0.034004371613264084, 0.00993060227483511, 0.029135702177882195, 0.030096227303147316, -0.017586711794137955, -0.04779386892914772, 0.03705582767724991, -0.0010574412299320102, 0.00731505686417222, -0.018373601138591766, 0.015892980620265007, 0.021750222891569138, 0.029883811250329018, 0.021744949743151665, 0.0055969590321183205, 0.02902340330183506, -0.009256208315491676, 0.023516247048974037, -0.03395546227693558, -0.0288645438849926, 0.016408778727054596, -0.027567943558096886, 0.049537476152181625, -0.006657032296061516, 0.010247645899653435, -0.0068880231119692326, -0.04076867923140526, -0.0627172440290451, -0.0016099294880405068, -0.0024182216729968786, 0.1060134768486023, 0.010471037589013577, -0.0010247936006635427, 0.033189307898283005, 0.09735710918903351, 0.003453615354374051, -0.007128655444830656, -0.0025441301986575127, -0.001054427120834589, 0.03503875434398651, -0.06751889735460281, 0.046770937740802765, 0.02103162370622158, -0.06045869365334511, -0.0027113875839859247, -0.08286309987306595, -0.0034517692402005196, 0.014035353437066078, -0.10039131343364716, 0.06122403219342232, 0.03758158162236214, 0.006393938325345516, 0.0326804555952549, -0.020488865673542023, -0.023967107757925987, -0.01654648408293724, 0.012535851448774338, -0.01503879763185978, 0.021032067015767097, 0.06475917249917984, -0.011596285738050938, -0.03954371437430382, -0.022665727883577347, -0.06893783807754517, 0.014555957168340683, 0.012412038631737232, 0.0017987708561122417, 0.013378845527768135, 0.04528997093439102, -0.06873519718647003, -0.061027079820632935, -0.03901340439915657, 0.033888354897499084, 0.020241858437657356, -0.0035629102494567633, -0.017277875915169716, 0.030819186940789223, -0.008340860716998577, 0.05394955724477768, -0.04631735011935234, -0.05105257406830788, -0.005645242054015398, 0.05748731270432472, -0.06564893573522568, 0.027088211849331856, 0.0273625236004591, 0.015413082204759121, 0.039582882076501846, -0.03840396925806999, 0.003812911454588175, 0.010200617834925652, -0.0020260673481971025, -0.02009335532784462, 0.04474708437919617, 0.02229435183107853, -0.030095286667346954, -0.04611051082611084, -0.013407599180936813, -0.026800470426678658, -0.05963515490293503, 0.006858362816274166, -0.01034617517143488, 0.07374191284179688, 0.034596700221300125, -0.007260404992848635, -0.012416140176355839, -0.02963295765221119, 0.03607206419110298, -0.002715112641453743, 0.019499007612466812, 0.018006736412644386, -0.007415272295475006, 0.018748896196484566, 0.0047434112057089806, 0.04486529901623726, 0.04863743484020233, -0.062052950263023376, -0.05572547763586044, 0.008149814791977406, 0.031220493838191032, 0.09324365854263306, 0.05074918270111084, -0.017527706921100616, 0.019845427945256233, -0.008997499942779541, 0.013663263991475105, -0.0582607239484787, 0.00830070674419403, -0.0407995767891407, -0.04536045342683792, -0.011673525907099247, -0.019820626825094223, 0.00021617223683279008, 0.0073445457965135574, -0.03145364299416542, 0.005782544147223234, 0.031949158757925034, -0.022603200748562813, -0.02450406365096569, 0.008956553414463997, 0.025714827701449394, 0.0016217689262703061, 0.02839651145040989, 0.03069409914314747, 0.03165841102600098, -0.01115583535283804, -0.015529023483395576, -0.0006703925901092589, 0.021486571058630943, -0.002676827134564519, -0.03581614047288895, -0.0349041149020195, -0.029681995511054993, 0.0011858063517138362, -0.005635111592710018, 0.012021178379654884, -0.03170827403664589, -0.013548946008086205, -0.0510094091296196, -0.022879362106323242, -0.016265204176306725, -0.02623801864683628, 0.015432866290211678, 0.04887590929865837, 0.014253079891204834, -0.03860638663172722, 0.058328449726104736, -0.07206141948699951, -0.019399933516979218, 0.08630232512950897, -0.029317112639546394, -0.06630251556634903, -0.015089936554431915, -0.037667643278837204, 0.02356906421482563, -0.05141967162489891, -0.13336005806922913, 0.046182338148355484, 0.10348068922758102, 0.04866451770067215, -0.03448687121272087, 0.01012217067182064, 0.03816604986786842, -0.02824084274470806, 0.024478401988744736, -0.024982940405607224, -0.008824734017252922, -0.00958144012838602, 0.09797845780849457, 0.016232013702392578, -0.0009589462424628437, -0.040955688804388046, -0.06723816692829132, -0.023445846512913704, -0.009424306452274323, -0.03878583386540413, 0.012013686820864677, -0.018391761928796768, 0.00862784031778574, 0.02083847112953663, 0.04066245257854462, 0.02957586944103241, 0.024740761145949364, 0.05738472193479538, -0.023760855197906494, 0.020857863128185272, -0.09485574066638947, 0.07403852045536041, 0.023045266047120094, -0.029968764632940292, 0.026397371664643288, -0.012615501880645752, 0.014059766195714474, -0.04817550256848335, 0.02968301810324192, 0.03400862589478493, -0.046339843422174454, -0.06762644648551941, -0.024764545261859894, -0.04114430025219917, 0.05283665657043457, -0.016191544011235237, -0.02521686628460884, -0.0363551564514637, 0.0339396670460701, 0.024870149791240692, 0.01383343618363142, 0.07258325815200806, 0.026626449078321457, 0.00500955106690526, -0.042525213211774826, -0.03827885538339615, -0.005980294197797775, 0.00469190115109086, 0.03385510668158531, 0.017636962234973907, 0.047051962465047836, 0.019525915384292603, -0.01628801040351391, -0.042250875383615494, 0.06614568084478378, 0.032276760786771774, -0.02833089791238308, -0.05065026134252548, 0.00822653528302908, 0.07312449812889099, -0.000028644606572925113, -0.03749455139040947, 0.001074025291018188, -0.038373932242393494, 0.062388304620981216, -0.012650402262806892, -0.06426235288381577, -0.030084898695349693, -0.02242487482726574, -0.03742239251732826, -0.05495414137840271, -0.006943979300558567, -0.01782769337296486, 0.039980698376894, 0.01838703826069832, -0.01860622875392437, 0.012048561125993729, -0.01142942439764738, 0.020675471052527428, -0.010373873636126518, -0.020719081163406372, 0.0008957221871241927, 0.03668590635061264, 0.04172009602189064, 0.010191129520535469, 0.02239849977195263, 0.056436724960803986, -0.0075654820539057255, -0.08947067707777023, -0.010784164071083069, -0.02168327197432518, 0.017497412860393524, -0.025057977065443993, -0.0828571617603302, -0.01814652793109417, -0.009621888399124146, 0.002294182311743498, 0.002892542164772749, 0.0488760769367218, -0.06593498587608337, -0.0251380056142807, 0.024595240131020546, -0.004558470565825701, -0.010855697095394135, -0.06907873600721359, 0.021943747997283936, -0.03936001658439636, 0.01923779398202896, 0.05624644458293915, 0.044797133654356, -0.0015657061012461782, 0.04214950650930405, -0.07066289335489273, -0.0019489278784021735, 0.017636137083172798, 0.0613592229783535, 0.04580913856625557, -0.061959099024534225, 0.014568690210580826, 0.017417864874005318, 0.1345551311969757, 0.044443123042583466, -0.015743637457489967, 0.0038116155192255974, 0.010657764971256256, 0.03152601420879364, 0.04107849672436714, 0.025479918345808983, 0.0017976452363654971, 0.007700922898948193, -0.005317734554409981, 0.015187556855380535, 0.018692895770072937, 0.01264845859259367, -0.047053344547748566, 0.025890741497278214, -0.04258376732468605, 0.03604960814118385, 0.02843070589005947, -0.03613218665122986, -0.035208187997341156, 0.041138965636491776, -0.06898248940706253, 0.00201714807190001, 0.01874150149524212, 0.02133261412382126, -0.0070171961560845375, -0.009446393698453903, 0.00888441689312458, -0.0372651033103466, 0.00424653384834528, -0.03832376375794411, 0.04681824892759323, -0.006983657367527485, -0.05071019381284714, -0.019823959097266197, 0.0015086403582245111, 0.007626234088093042, -0.02374473214149475, 0.04033254459500313, 0.008570194244384766, -0.011009413748979568, -0.0387209951877594, -0.043118786066770554, -0.01240622065961361, 0.03741288557648659, -0.022199800238013268, -0.011533639393746853, -0.03598165512084961, 0.045637622475624084, -0.026241013780236244, 0.05774107947945595, -0.027141764760017395, 0.01608162559568882, 0.07577812671661377, 0.003204191802069545, 0.02075962722301483, 0.013840051367878914, -0.03652709349989891, 0.06876852363348007, -0.049451444298028946, 0.0062583452090620995, 0.04072348400950432, 0.01280170027166605, -0.030412767082452774, 0.00753613468259573, -0.016338393092155457, -0.03012680448591709, 0.027912724763154984, -0.005730165634304285, 0.06259205937385559, -0.02459343895316124, -0.010531265288591385, -0.10162634402513504, -0.0013890584232285619, -0.027480794116854668, -0.04469938203692436, 0.01816515438258648, -0.04045993462204933, -0.005074186250567436, 0.01904144324362278, 0.02152862213551998, -0.009697817265987396, 0.00758452108129859, -0.01908653788268566, -0.01721574179828167, 0.08641261607408524, -0.03544066846370697, -0.04224551469087601, 0.06104453280568123, 0.024493958801031113, 0.02723037078976631, 0.04660793021321297, -0.035721711814403534, 0.028279418125748634, -0.04187518730759621, -0.026256591081619263, -0.011752588674426079, 0.029538311064243317, -0.0020928075537085533, 0.03538752719759941, -0.06474437564611435, 0.021006956696510315, -0.007278278935700655, -0.05040968209505081, -0.024402279406785965, -0.03426229581236839, -0.05106940492987633, -0.04293389990925789, -0.06605600565671921, 0.011106017976999283, -0.013516140170395374, 0.03688620775938034, -0.07215193659067154, 0.06692459434270859, 0.015779996290802956, -0.013294551521539688, -0.002694445662200451, -0.008860919624567032, -0.04867270588874817, 0.04260630905628204, -0.028648149222135544, 0.03807387873530388, 0.0318300798535347, -0.01516395341604948, -0.003958337940275669, 0.03589877858757973, 0.006639047525823116, -0.037937913089990616, -0.009792936965823174, -0.002689965069293976, 0.018516212701797485, -0.0169071052223444, -0.010068879462778568, -0.01837887242436409, -0.006291310302913189, 0.035079360008239746, -0.027835190296173096, 0.02701190859079361, 0.01680607907474041, -0.02677658386528492, -0.0264382716268301, -0.00007098326022969559, -0.028436550870537758, 0.020537100732326508, -0.011445969343185425, -0.06723503768444061, -0.034396667033433914, -0.009205646812915802, 0.009053339250385761, -0.018684137612581253, -0.0258029717952013, 0.00891233142465353, 0.07082733511924744, 0.05905189737677574, -0.000867524475324899, -0.0007889901753515005, -0.016793297603726387, -0.02979343943297863, -0.05664242431521416, -0.03857158496975899, 0.030756788328289986, 0.010429049842059612, 0.00813268218189478, -0.04419770464301109, 0.030271239578723907, -0.011972436681389809, 0.05250480771064758, 0.01798456534743309, 0.050548046827316284, -0.0024292445741593838, 0.006946770008653402, -0.015134455636143684, -0.026894282549619675, 0.0074442243203520775, -0.06277843564748764, 0.03184123709797859, 0.021092534065246582, 0.03355073183774948, -0.011800062842667103, -0.06861335039138794, -0.017881283536553383, 0.04037761315703392, 0.030321896076202393, -0.015710748732089996, -0.028556231409311295, 0.028061656281352043, -0.011721039190888405, 0.028293557465076447, -0.08920411765575409, 0.005006059538573027, -0.010684351436793804, -0.04526534676551819, 0.012757020071148872, 0.000403978192480281, 0.008320371620357037, -0.017518384382128716, 0.05437907949090004, -0.038478486239910126, -0.03306930512189865, -0.07043133676052094, 0.0006924658664502203, -0.006304547656327486, 0.026701681315898895, 0.0035447366535663605, -0.0062157949432730675, -0.046175260096788406, 0.016144175082445145, 0.0735270231962204, -0.0010757364798337221, -0.009977343492209911, 0.08927162736654282, -0.0359904021024704, 0.019250422716140747, -0.006428159307688475, 0.06695495545864105, -0.008208277635276318, -0.019237006083130836, -0.057716548442840576, -0.008403868414461613, -0.02226118929684162, -0.019935764372348785, -0.014552367851138115, -0.008244139142334461, -0.02041534148156643 ]
<p>For some electric devices, like a fan or air conditioner, I read about their power consumption in watts on their specification guide.</p> <p>Does it tell about the power at normal or full speed? or Does the speed even affect the power consumption? Can I find the consumption at different speeds?</p>
g1586
[ 0.0584874227643013, 0.049199748784303665, -0.000692899280693382, 0.02548268809914589, -0.0044368552044034, -0.0692439004778862, -0.020227832719683647, 0.02932414412498474, -0.060310736298561096, 0.021704718470573425, 0.00028108322294428945, -0.01143755204975605, -0.0036221379414200783, 0.027971845120191574, 0.010598772205412388, -0.00467731524258852, -0.0007656009984202683, -0.05680064484477043, 0.08394546806812286, 0.04027089849114418, 0.012672019191086292, -0.017536301165819168, -0.02872922085225582, 0.03266814723610878, -0.007095043081790209, 0.023639610037207603, -0.055239446461200714, -0.020418306812644005, -0.09161070734262466, -0.024010544642806053, -0.03493130952119827, 0.0405515618622303, 0.01565093919634819, -0.006331510376185179, -0.05189438536763191, 0.019230959936976433, 0.07857100665569305, 0.000035766337532550097, 0.005696013104170561, 0.026557015255093575, -0.02860083431005478, 0.009450704790651798, -0.03462556377053261, 0.011325112544000149, -0.02468724176287651, -0.024089401587843895, -0.03412839397788048, 0.004174754023551941, -0.0165543295443058, -0.023274516686797142, 0.005055929999798536, -0.0037117116153240204, 0.05314645916223526, -0.013287736102938652, 0.05710858851671219, -0.08674601465463638, -0.05110646039247513, -0.0057914406061172485, 0.004643624648451805, -0.0351102277636528, 0.00984445121139288, -0.0015569021925330162, -0.035906530916690826, 0.03522155061364174, 0.014951442368328571, -0.03014502301812172, 0.0754665806889534, -0.05542900413274765, -0.008864350616931915, -0.006931011565029621, -0.02563926763832569, 0.008297418244183064, -0.014235038310289383, -0.09500875324010849, -0.011030123569071293, -0.017167309299111366, 0.0432569719851017, -0.0022961765062063932, 0.009195537306368351, 0.056517574936151505, 0.018073901534080505, -0.02905665524303913, 0.06327643245458603, 0.008766775950789452, -0.000848617113661021, -0.002690628170967102, -0.030112585052847862, -0.00228539458476007, 0.05156134441494942, -0.004230076912790537, -0.014136547222733498, -0.0441475436091423, 0.03468558192253113, 0.003474281169474125, 0.018446650356054306, 0.012388356029987335, -0.025715172290802002, 0.041976749897003174, 0.03236088156700134, 0.04733516275882721, 0.010346424765884876, 0.012042849324643612, -0.031510621309280396, -0.005168017465621233, -0.01745353452861309, 0.05755026265978813, -0.018389089033007622, -0.04517967253923416, -0.022260617464780807, -0.021112903952598572, 0.05830482766032219, -0.04592052102088928, 0.0038094096817076206, 0.019623328000307083, -0.033120132982730865, -0.07932905852794647, -0.005653935018926859, -0.031221603974699974, 0.003026476362720132, 0.04733964428305626, -0.02385602332651615, 0.03480449318885803, -0.06714086979627609, -0.003630564548075199, 0.013975459150969982, 0.01386782992631197, 0.015279748477041721, -0.055714063346385956, -0.004178354982286692, 0.04452130198478699, 0.02763393335044384, 0.00744745135307312, -0.04581412672996521, 0.003273978130891919, 0.03485164791345596, 0.08386567234992981, 0.020071733742952347, -0.0352829247713089, 0.009032505564391613, 0.023323502391576767, 0.03608951345086098, 0.018963109701871872, 0.008460757322609425, 0.008910013362765312, -0.0034091193228960037, 0.01969587244093418, -0.0060134585946798325, -0.02083607017993927, 0.030217034742236137, 0.09228380769491196, 0.032062266021966934, 0.07428429275751114, -0.038029272109270096, -0.05846994370222092, 0.047006964683532715, 0.0004606959701050073, -0.030916329473257065, 0.01585959829390049, -0.030045531690120697, 0.07933584600687027, 0.028615528717637062, 0.036843281239271164, 0.00800629798322916, 0.05201016366481781, -0.013574166223406792, -0.0314159095287323, 0.021210351958870888, -0.016067223623394966, 0.009490740485489368, -0.021123556420207024, -0.04204622283577919, 0.07496362179517746, -0.010655359365046024, 0.02596127614378929, 0.015585927292704582, -0.008557136170566082, 0.03723308444023132, 0.010001428425312042, 0.05229886993765831, -0.026578612625598907, -0.055729638785123825, -0.004335046745836735, 0.004395630210638046, -0.05166706070303917, -0.051063764840364456, 0.006780537776648998, -0.027201659977436066, -0.006929691415280104, 0.0026905988343060017, 0.061776451766490936, -0.03621472790837288, 0.0004555339110083878, 0.016246264800429344, 0.010666010901331902, -0.043536797165870667, 0.007995677180588245, -0.01466455776244402, 0.003078349167481065, -0.022595403715968132, -0.03449739143252373, 0.041597750037908554, -0.009416121058166027, 0.0015070938970893621, -0.0020603747107088566, 0.013030690141022205, 0.013258984312415123, -0.00829991977661848, -0.023046260699629784, 0.02569647878408432, 0.0004283915041014552, 0.04742099344730377, -0.013517921790480614, 0.04185642674565315, 0.06481388956308365, 0.032975029200315475, 0.027971239760518074, -0.05449901521205902, 0.0032027261331677437, -0.010134228505194187, -0.01805022917687893, -0.022673044353723526, 0.04499824345111847, -0.0012727876892313361, -0.03922786936163902, -0.056748539209365845, 0.021049154922366142, -0.015905560925602913, -0.011426055803894997, -0.01028456725180149, 0.02162889577448368, -0.017055533826351166, -0.015091833658516407, 0.04802416265010834, 0.009657301008701324, -0.01068666111677885, 0.019403161481022835, 0.009199577383697033, -0.020059728994965553, 0.05000990256667137, -0.05509404093027115, 0.01775813288986683, -0.03337068110704422, 0.06284184008836746, 0.004616128280758858, -0.03842732310295105, -0.03953838348388672, 0.019272172823548317, -0.06994647532701492, -0.009329591877758503, 0.04960138350725174, 0.009303230792284012, 0.03255749121308327, 0.022358251735568047, 0.023166457191109657, -0.022121043875813484, -0.039296094328165054, 0.026103459298610687, -0.033849410712718964, -0.013373726047575474, -0.015646731480956078, -0.04667055979371071, 0.04244654253125191, -0.03136696293950081, 0.017337409779429436, 0.022889643907546997, -0.04329615458846092, 0.05117577314376831, -0.007781337480992079, 0.01445706281810999, 0.039803676307201385, 0.01770957000553608, 0.05391635745763779, -0.03512958064675331, -0.02632865309715271, 0.027264634147286415, -0.04000561684370041, 0.014648450538516045, -0.043762173503637314, 0.014478492550551891, -0.016290919855237007, 0.012156733311712742, 0.03853227570652962, -0.0551019161939621, -0.012837267480790615, 0.011799764819443226, -0.09193263947963715, -0.04313524812459946, 0.016297409310936928, -0.025281069800257683, -0.002485840115696192, -0.03865518420934677, -0.019775519147515297, 0.00042620309977792203, -0.06907492876052856, 0.03459231182932854, 0.021398324519395828, 0.010011243633925915, -0.040985412895679474, -0.009920946322381496, -0.05879826843738556, 0.05050848051905632, -0.054347965866327286, -0.045134566724300385, 0.048306018114089966, -0.017370255663990974, 0.06443874537944794, -0.04739651456475258, -0.04284258931875229, -0.01086855586618185, -0.013003919273614883, -0.0464855395257473, 0.02302190475165844, 0.007776000536978245, -0.016466587781906128, -0.042610008269548416, 0.006287547294050455, 0.02062317170202732, -0.04901192709803581, -0.010880809277296066, -0.002156301401555538, 0.04855085909366608, -0.03178563714027405, 0.024410024285316467, 0.004519616719335318, -0.0499919131398201, 0.01806604489684105, 0.017760535702109337, -0.059039484709501266, 0.05656103044748306, -0.04019123688340187, -0.010694677010178566, -0.046397410333156586, -0.026984868571162224, 0.012437638826668262, 0.020062055438756943, -0.020896270871162415, 0.007048432249575853, 0.030118679627776146, -0.02797347493469715, 0.029354438185691833, 0.07997281849384308, 0.023738449439406395, -0.04905281960964203, 0.002161538228392601, -0.007994786836206913, -0.04961373656988144, -0.050492580980062485, 0.026189398020505905, -0.011605797335505486, 0.012481057085096836, 0.07716374844312668, -0.04443599656224251, -0.048195939511060715, -0.014605548232793808, -0.027567263692617416, -0.04235270619392395, -0.018670283257961273, 0.0016506962710991502, -0.05022628232836723, -0.006123605649918318, 0.05296645686030388, 0.03774184361100197, 0.07079198211431503, 0.005289793945848942, -0.029391491785645485, 0.022422609850764275, 0.027720438316464424, 0.021732361987233162, 0.032438285648822784, -0.062912218272686, -0.00651398254558444, 0.056875426322221756, -0.027266548946499825, 0.04844091832637787, 0.004003542475402355, 0.03181954845786095, 0.05699501186609268, 0.013459224253892899, -0.03781697154045105, 0.03996840864419937, 0.004879096057265997, 0.01419711485505104, -0.05346066504716873, -0.010083057917654514, 0.02592378482222557, -0.030775807797908783, 0.004954172298312187, -0.005429435055702925, 0.0010674339719116688, -0.0687018632888794, -0.013284135609865189, -0.021736565977334976, -0.04102437570691109, 0.011827580630779266, -0.05927487835288048, 0.0008066878071986139, 0.015813549980521202, 0.03899799659848213, -0.013339311815798283, 0.0757543072104454, -0.02720712125301361, 0.004948675166815519, -0.0032395527232438326, 0.01819750666618347, 0.022245125845074654, -0.021297330036759377, 0.023744244128465652, -0.06038137525320053, 0.06864943355321884, -0.030192675068974495, -0.04415393993258476, 0.018244922161102295, -0.008359415456652641, 0.00831141509115696, -0.0065195392817258835, 0.037615396082401276, -0.019921109080314636, -0.0069976323284208775, 0.06425980478525162, 0.01152107771486044, -0.010925733484327793, -0.057754822075366974, -0.03912727162241936, -0.016871264204382896, -0.07152349501848221, 0.012919754721224308, 0.08414828032255173, 0.021765155717730522, -0.041199974715709686, -0.059781454503536224, 0.033629775047302246, 0.006859085988253355, -0.005696777254343033, -0.01993654854595661, -0.004707629326730967, 0.05484950542449951, 0.06023723632097244, 0.008244656957685947, 0.02847953327000141, -0.07476992905139923, 0.055176105350255966, 0.017217593267560005, -0.014561057090759277, -0.023762574419379234, -0.005628619343042374, 0.025527190417051315, -0.06654871255159378, 0.029316792264580727, -0.03581715002655983, 0.004788703750818968, -0.03473752364516258, 0.027669111266732216, -0.07567628473043442, -0.026204485446214676, -0.011099427007138729, 0.03059268556535244, -0.003673246130347252, -0.050386566668748856, 0.029520690441131592, 0.018750322982668877, -0.05026621371507645, -0.037898238748311996, 0.061043065041303635, -0.010446188971400261, -0.05097039043903351, 0.023244868963956833, -0.03493474796414375, -0.017246786504983902, -0.032305534929037094, -0.00849674642086029, 0.004212398547679186, -0.01303134672343731, -0.04440808668732643, 0.09198863059282303, -0.035636987537145615, -0.02896437793970108, -0.010493751615285873, -0.024914294481277466, -0.05498681589961052, 0.06509726494550705, -0.013186520896852016, -0.005515263415873051, 0.03601086884737015, 0.023859335109591484, 0.005591982044279575, -0.051180534064769745, -0.02346988581120968, 0.026569761335849762, 0.0494174063205719, -0.04962535947561264, -0.008117876015603542, 0.08136171847581863, -0.009488657116889954, -0.030726969242095947, -0.06552139669656754, 0.06021920219063759, 0.06661845743656158, -0.04560045897960663, -0.05738065391778946, 0.05487431213259697, 0.03149652108550072, 0.03375277295708656, 0.04126211628317833, -0.04184211790561676, 0.02133764699101448, 0.09167163074016571, 0.029528237879276276, -0.024249421432614326, 0.00984988547861576, 0.06730431318283081, 0.008044425398111343, 0.043340589851140976, -0.027489833533763885, 0.018232934176921844, 0.04755984991788864, -0.0013977503404021263, 0.00744841480627656, 0.019786423072218895, -0.019649749621748924, 0.04059155285358429, 0.04073304682970047, -0.013820264488458633, 0.04704665392637253, -0.010548843070864677, -0.001648123376071453, 0.03487333282828331, -0.07587304711341858, -0.009946110658347607, 0.04167450591921806, 0.028393579646945, 0.03201038017868996, 0.008415396325290203, -0.009934036992490292, -0.027617372572422028, -0.024294890463352203, -0.011556869372725487, -0.0038838968612253666, -0.053639788180589676, 0.032128963619470596, -0.002543962560594082, -0.05814634636044502, -0.00010357521387049928, 0.009771057404577732, -0.009825675748288631, 0.03527258336544037, -0.007668243255466223, 0.01940472237765789, -0.02635030448436737, -0.050098005682229996, 0.06003902107477188, 0.01127329096198082, 0.011981792747974396, 0.029108788818120956, -0.00976707972586155, -0.025931457057595253, 0.014512215740978718, 0.06543105840682983, 0.023321382701396942, 0.02772856317460537, -0.06570309400558472, -0.030415333807468414, 0.019590802490711212, 0.05926467478275299, -0.03640130162239075, -0.007647304330021143, -0.025943750515580177, 0.0193604938685894, 0.013864973559975624, 0.01448332704603672, 0.011300790123641491, 0.05488523468375206, -0.0009997113374993205, 0.01962997578084469, -0.030503593385219574, 0.0701955035328865, -0.032994937151670456, 0.009245609864592552, -0.05527673289179802, 0.02257842756807804, -0.04793212562799454, 0.05118751525878906, -0.06351829320192337, -0.023452742025256157, -0.020543469116091728, 0.06960141658782959, 0.027287306264042854, -0.005651745479553938, 0.051779855042696, 0.03117571957409382, 0.009961945936083794, 0.03636614978313446, 0.027097109705209732, 0.04885711520910263, -0.011485133320093155, 0.026800576597452164, 0.004705164115875959, -0.010302870534360409, 0.08017996698617935, 0.004818716552108526, 0.03159618750214577, 0.006116670090705156, -0.02838739939033985, 0.018357202410697937, -0.07497765123844147, 0.0424470454454422, -0.0021338772494345903, 0.05348784103989601, -0.016567669808864594, -0.04795379936695099, 0.008080124855041504, -0.04281576722860336, -0.022796237841248512, 0.03448385000228882, -0.04733787104487419, -0.01407735887914896, -0.04056960716843605, -0.04700876772403717, -0.024655893445014954, -0.0269609447568655, 0.013613691553473473, 0.051336027681827545, -0.07213377952575684, 0.027830589562654495, -0.023934360593557358, 0.12243141233921051, 0.0648212730884552, 0.0009277785429731011, 0.08661944419145584, 0.015354666858911514, -0.046387966722249985, -0.04728030413389206, 0.03909395635128021, -0.00535954674705863, 0.016231734305620193, 0.06548866629600525, 0.02664766274392605, -0.017899533733725548, -0.0014603278832510114, 0.02021278627216816, -0.0024630259722471237, 0.04000939801335335, -0.010904261842370033, -0.04810529574751854, 0.006990260444581509, -0.0246944110840559, -0.010367338545620441, -0.000544366892427206, 0.025914279744029045, 0.04181497544050217, -0.027690071612596512, -0.02962973341345787, -0.0004319357394706458, 0.029581870883703232, 0.029091637581586838, -0.0011038740631192923, 0.058107323944568634, -0.06904861330986023, 0.00874573364853859, -0.016931641846895218, -0.011186380870640278, 0.006232943385839462, -0.0035173469223082066, -0.01354956440627575, 0.04838341847062111, -0.0016800726298242807, -0.03930000960826874, -0.02152031473815441, -0.017617058008909225, -0.004095984157174826, -0.05585052818059921, -0.02829170599579811, -0.09281796962022781, -0.0116372499614954, 0.03705041855573654, 0.06180841848254204, -0.02118135429918766, -0.02937140129506588, -0.005694576073437929, -0.019543128088116646, -0.10964123904705048, 0.008962548337876797, -0.004581811372190714, -0.023947570472955704, -0.019952930510044098, -0.0027066378388553858, 0.017950015142560005, -0.04824214428663254, -0.03939370438456535, 0.01410495676100254, -0.022524088621139526, -0.05544303357601166, -0.07946871966123581, 0.06553780287504196, -0.0017411645967513323, -0.030097685754299164, 0.011139514856040478, -0.0021685324609279633, 0.023985667154192924, -0.0026550039183348417, 0.011809716001152992, 0.02489030547440052, 0.04511755704879761, 0.026167938485741615, 0.009968315251171589, -0.029992803931236267, 0.008361638523638248, -0.009164919145405293, -0.020572299137711525, -0.028118137270212173, 0.0421978160738945, -0.023083271458745003, -0.0028318592812865973, 0.07400611788034439, 0.00376829388551414, 0.04520297795534134, 0.007172068580985069, -0.02302057296037674, -0.04372479394078255, 0.027409765869379044, 0.024286314845085144, 0.0031336506363004446, 0.027776790782809258, -0.014634455554187298, -0.02357509545981884, 0.003961201291531324, -0.004516087472438812, -0.04168197885155678, 0.06053971126675606, -0.013197740539908409, 0.03698757290840149, -0.04467625543475151, 0.005055989604443312, 0.015117989853024483, 0.07203945517539978, -0.019065339118242264, -0.021099885925650597, 0.025607949122786522, -0.008227449841797352, 0.0472867451608181, 0.02976221963763237, 0.0003492861578706652, -0.0012152764247730374, 0.010914284735918045, 0.0020240608137100935, -0.007734717335551977, -0.03604394569993019, -0.02681560255587101, -0.011194287799298763, 0.04690966010093689, -0.013450871221721172, 0.035271283239126205, -0.0018482358427718282, -0.03794989362359047, 0.020800314843654633, -0.08590643852949142, 0.07854489237070084, 0.05191318690776825, -0.005770922638475895, -0.016641167923808098, 0.016177145764231682, -0.016863061115145683, -0.05637937784194946, -0.02166125550866127, 0.008719081059098244, -0.015844980254769325, -0.014062047936022282, -0.008967500180006027, -0.02978985570371151 ]
<p>Why is electricity not transmitted wirelessly such that we don't need to span cables on the earth's surface? As in: electricity is transmitted wirelessly from the power plant to the household.</p>
g1587
[ 0.04905476048588753, 0.0725574642419815, -0.005150196608155966, 0.03079758770763874, 0.0010703210718929768, 0.05575471743941307, 0.0177158135920763, 0.016762660816311836, -0.07992804795503616, -0.06077095493674278, 0.03281814604997635, -0.04340047389268875, -0.011796712875366211, 0.03338019549846649, -0.01136658526957035, 0.002605099929496646, -0.013094991445541382, -0.017223162576556206, 0.0502731017768383, 0.054703403264284134, 0.003213310381397605, -0.04484216868877411, 0.020489614456892014, -0.02939366176724434, -0.07620888203382492, -0.008565343916416168, -0.0008527222671546042, -0.0695667564868927, 0.03635776787996292, -0.03428773209452629, -0.02964218705892563, 0.01512027159333229, 0.030040515586733818, -0.05493536591529846, -0.0729953944683075, -0.02748776413500309, -0.02397485077381134, -0.04640965163707733, 0.006210835184901953, 0.0018929571378976107, -0.027616214007139206, 0.04404141753911972, -0.026963956654071808, 0.013128840364515781, 0.02481568232178688, -0.02972816303372383, -0.011084659025073051, 0.027664415538311005, 0.017516523599624634, -0.05350165069103241, -0.03539211302995682, -0.026799002662301064, 0.0117331612855196, 0.038120850920677185, 0.05533072352409363, -0.045469436794519424, 0.030696697533130646, -0.01671566069126129, 0.025204215198755264, -0.00881087314337492, 0.004051698371767998, 0.02928486466407776, 0.016246682032942772, 0.03353636711835861, 0.015725955367088318, -0.0173011627048254, -0.07089800387620926, -0.031380414962768555, 0.029096266254782677, 0.10265889018774033, 0.027557674795389175, -0.09753869473934174, -0.003363919211551547, -0.033126868307590485, 0.09935620427131653, 0.006853441707789898, -0.023123936727643013, 0.021970979869365692, -0.037377845495939255, 0.04145296290516853, -0.004014536738395691, -0.004602409433573484, -0.04430173337459564, -0.02631211094558239, 0.050734832882881165, -0.008238393813371658, 0.040819864720106125, -0.05266079679131508, 0.023403270170092583, -0.039948027580976486, -0.00158465257845819, 0.030856166034936905, 0.10608328133821487, 0.005419208202511072, -0.05000890791416168, -0.10253529995679855, -0.03441045805811882, 0.006767535116523504, 0.008320020511746407, 0.01793591119349003, -0.036953531205654144, -0.030475590378046036, 0.003920575603842735, 0.041601408272981644, 0.05089140683412552, 0.008724085055291653, 0.006827789358794689, 0.017311055213212967, 0.014558609575033188, -0.05571547523140907, 0.04567050188779831, -0.009842160157859325, 0.01507621631026268, 0.021625975146889687, -0.001294590882025659, -0.027897542342543602, 0.0713469535112381, -0.013255688361823559, 0.061312831938266754, 0.03556260094046593, -0.02024960145354271, -0.012131909839808941, -0.012268703430891037, 0.0035846729297190905, -0.01763295941054821, 0.010907256975769997, 0.038807813078165054, 0.006299158558249474, 0.019726866856217384, -0.006051930598914623, 0.0018212809227406979, 0.05397944152355194, -0.09548023343086243, 0.006078286096453667, 0.08142934739589691, 0.012163356877863407, 0.003472242970019579, -0.04719274863600731, 0.04880301654338837, 0.008344447240233421, -0.008030746132135391, 0.02721305377781391, -0.00011661811004159972, -0.051969654858112335, -0.021329063922166824, 0.054154008626937866, 0.00830790214240551, -0.0439552403986454, 0.024438010528683662, 0.006302991881966591, -0.02097608521580696, 0.016315188258886337, 0.06305288523435593, 0.0016857922310009599, 0.022998105734586716, -0.0383584089577198, 0.07528401911258698, -0.04841036722064018, 0.01993624120950699, -0.0012826446909457445, 0.046839747577905655, 0.00705083180218935, -0.03723709285259247, -0.0176746416836977, -0.0250990092754364, -0.02092236652970314, 0.017514390870928764, -0.023730657994747162, 0.042916055768728256, -0.020328614860773087, -0.061811663210392, -0.04094582796096802, 0.010218390263617039, 0.09609486162662506, -0.010292084887623787, 0.04134681820869446, 0.016109952703118324, -0.025345642119646072, -0.008611582219600677, -0.061719875782728195, -0.04145160689949989, -0.023889604955911636, -0.030743150040507317, -0.01899988017976284, -0.02602718025445938, -0.002555577550083399, -0.041679441928863525, -0.048702046275138855, -0.0063005536794662476, -0.009826007299125195, -0.012711336836218834, 0.0036715352907776833, -0.03458714112639427, -0.008074293844401836, 0.006169191095978022, 0.0060222879983484745, 0.044434014707803726, 0.002494958695024252, 0.030618907883763313, -0.019054630771279335, 0.05284729227423668, 0.028429051861166954, 0.0265645869076252, -0.03546634688973427, -0.016962576657533646, -0.03601204231381416, -0.039931245148181915, -0.0666845366358757, 0.044243354350328445, -0.06549832969903946, 0.030273377895355225, -0.09847760200500488, 0.022797273471951485, -0.03797779977321625, -0.0266763623803854, -0.039253681898117065, -0.05674368515610695, -0.0072667296044528484, -0.06612984091043472, 0.004509674850851297, 0.0018606892554089427, -0.07531091570854187, 0.029158281162381172, -0.002426866441965103, 0.00726653914898634, 0.002574020531028509, -0.06737688183784485, -0.07410707324743271, -0.022946584969758987, -0.02554127387702465, -0.019220862537622452, 0.0026927620638161898, -0.007634809240698814, 0.03264426067471504, -0.0005798595957458019, 0.015621650032699108, -0.025970477610826492, -0.015704240649938583, 0.0084563959389925, -0.04686141759157181, 0.004779779352247715, -0.05986851453781128, -0.011892303824424744, 0.026831205934286118, 0.046833526343107224, -0.0018838031683117151, 0.015071290545165539, -0.0025545861572027206, -0.0281089898198843, -0.041714269667863846, 0.08590985834598541, 0.006340804509818554, -0.03307958319783211, 0.008492116816341877, 0.0007834431016817689, -0.06917475908994675, 0.022998342290520668, 0.06774775683879852, -0.010039040818810463, -0.030054181814193726, -0.04274405539035797, -0.03001374751329422, 0.050666868686676025, -0.017809899523854256, -0.0028769890777766705, 0.06787198781967163, 0.01143721304833889, 0.0003046708588954061, -0.023584280163049698, -0.03786824643611908, 0.03992006182670593, 0.03947845846414566, -0.008904525078833103, -0.0020253241527825594, -0.01703273504972458, -0.07244107127189636, 0.012284290045499802, 0.010228125378489494, 0.01715896651148796, 0.029790842905640602, 0.024858009070158005, -0.018627099692821503, 0.03489500656723976, 0.000779132591560483, 0.022011926397681236, -0.061788227409124374, -0.02454409748315811, 0.012142333202064037, -0.016353091225028038, 0.003500751219689846, 0.03354869782924652, -0.03868844732642174, 0.03560879826545715, -0.02840881049633026, 0.007642957381904125, -0.00991849321871996, 0.023362889885902405, -0.018788179382681847, -0.10510896146297455, -0.02236708626151085, 0.016633009538054466, 0.06726831942796707, 0.012379019521176815, 0.034361399710178375, -0.03013983555138111, 0.042152516543865204, 0.006838261615484953, -0.02289552055299282, 0.04126279056072235, 0.0063405716791749, 0.07874768227338791, 0.08301776647567749, 0.026943586766719818, 0.04435731843113899, -0.06039048731327057, -0.07702304422855377, -0.046450044959783554, 0.03636396676301956, 0.003920501098036766, 0.03544732928276062, -0.03554752096533775, -0.03442270681262016, 0.001976524945348501, 0.0036238492466509342, -0.040601108223199844, 0.037565890699625015, -0.06822860240936279, 0.026136981323361397, -0.03408960625529289, -0.016027383506298065, -0.03921734169125557, -0.0014212997630238533, 0.04282938316464424, -0.04916507378220558, -0.08630595356225967, -0.00963040255010128, -0.01371211651712656, 0.04251808300614357, 0.004451546352356672, 0.02067730762064457, -0.03525950014591217, -0.018678609281778336, -0.08869031071662903, -0.01410931721329689, -0.019031492993235588, 0.013564609922468662, -0.014123257249593735, -0.05554935708642006, 0.0028059903997927904, -0.00973301101475954, 0.01773075759410858, 0.036955997347831726, 0.008743064478039742, 0.020670730620622635, -0.021519040688872337, 0.040242940187454224, -0.035250138491392136, 0.015491781756281853, 0.027667177841067314, -0.005826126784086227, 0.03374899923801422, 0.04582071676850319, 0.03055427223443985, 0.0042226556688547134, -0.006830642931163311, 0.00857030414044857, -0.014219989068806171, 0.07596273720264435, -0.010270927101373672, 0.0014667579671368003, 0.015344026498496532, -0.001544462633319199, -0.04194214567542076, 0.02343994937837124, 0.028572186827659607, -0.037548892199993134, 0.046210747212171555, 0.013900644145905972, -0.012085228227078915, 0.022574463859200478, -0.017814675346016884, -0.04335082322359085, -0.014209081418812275, -0.0016085802344605327, 0.008313952013850212, -0.027061160653829575, -0.07247039675712585, 0.045697540044784546, -0.06178813427686691, 0.010762879624962807, 0.00719753373414278, -0.0590858981013298, -0.020472388714551926, -0.027004117146134377, -0.007104726508259773, -0.03360419720411301, -0.003984760493040085, 0.0039766281843185425, 0.009852373041212559, 0.0772799625992775, 0.020163755863904953, 0.01560700312256813, 0.003982757683843374, 0.034108854830265045, 0.020997531712055206, 0.03896265849471092, -0.005562121514230967, -0.014567127451300621, -0.009196269325911999, 0.005020854528993368, 0.02467339299619198, -0.0081253657117486, -0.03914272412657738, -0.07171886414289474, 0.03336435928940773, -0.01597948744893074, 0.016128407791256905, -0.1002858504652977, 0.03352905437350273, 0.0122144166380167, -0.045452624559402466, 0.04053032025694847, 0.03791863098740578, -0.019985653460025787, 0.03041125275194645, 0.06828588247299194, 0.01362889725714922, -0.06929327547550201, -0.025894345715641975, 0.023964615538716316, -0.04220828413963318, 0.02491820976138115, -0.054438188672065735, -0.014179792255163193, 0.04234175756573677, -0.006742121186107397, 0.039852604269981384, 0.03948432579636574, 0.02897048182785511, 0.050924502313137054, 0.11367157101631165, -0.020578546449542046, 0.02759791538119316, -0.013349507935345173, 0.006277552340179682, 0.05638228356838226, -0.02241581492125988, 0.016634779050946236, 0.03647108003497124, 0.03172052279114723, -0.002762343268841505, -0.022286247462034225, 0.027179216966032982, 0.005018084775656462, -0.01356129627674818, -0.01508538518100977, -0.012883481569588184, -0.04437824338674545, 0.07323474436998367, 0.008597034960985184, -0.047770049422979355, 0.029152508825063705, -0.03674483299255371, 0.013232854194939137, 0.0008545647724531591, 0.03208010643720627, -0.060895904898643494, -0.00374390697106719, -0.0520348995923996, 0.011773715727031231, -0.016957545652985573, 0.04040483385324478, 0.06735613197088242, 0.11420214921236038, -0.05460771918296814, 0.034438587725162506, 0.0042282212525606155, 0.011184259317815304, -0.05621106177568436, -0.04483073577284813, 0.003970609046518803, 0.006536682136356831, -0.016555702313780785, 0.00870048813521862, -0.005467445123940706, 0.038393285125494, -0.05362479016184807, 0.025916626676917076, -0.03281056508421898, -0.0169048011302948, -0.0013777563581243157, -0.049920495599508286, -0.019376887008547783, 0.015688281506299973, -0.014735298231244087, -0.012824797071516514, -0.0053367819637060165, -0.0004869310068897903, 0.016387876123189926, -0.020383507013320923, 0.009064625948667526, -0.004983846098184586, -0.027719231322407722, 0.013480082154273987, 0.027146250009536743, 0.05421159788966179, 0.02872263453900814, -0.01309988833963871, 0.031199177727103233, 0.014768757857382298, 0.000561817258130759, -0.04553548991680145, -0.05704238638281822, 0.012991989962756634, 0.08914100378751755, -0.03590281307697296, -0.04797496646642685, -0.0292437132447958, 0.023443330079317093, 0.028458910062909126, 0.018186360597610474, -0.00674248905852437, 0.010735264979302883, 0.02704857848584652, -0.0031110355630517006, 0.005736839957535267, -0.08308009058237076, -0.0007117774803191423, 0.012677343562245369, 0.017288023605942726, 0.01405320130288601, 0.07844557613134384, -0.023996487259864807, -0.017056237906217575, -0.0006011057994328439, 0.008325130678713322, 0.007910802960395813, 0.00687252776697278, 0.024320026859641075, 0.009618429467082024, -0.008303900249302387, -0.006467497907578945, 0.0891093835234642, 0.0239938385784626, 0.05909469723701477, 0.0037365835160017014, 0.017226528376340866, 0.012253748252987862, -0.03684074059128761, 0.004739456344395876, 0.023034272715449333, 0.0010323520982638001, -0.011291817761957645, -0.011036803014576435, -0.027832254767417908, -0.03572360798716545, 0.034856367856264114, -0.017902888357639313, -0.032815948128700256, -0.06583210080862045, -0.006168148946017027, 0.031284134835004807, -0.03845939040184021, -0.0040390463545918465, 0.04254096373915672, -0.042804449796676636, 0.02905997633934021, 0.038626983761787415, -0.006715722382068634, 0.0638522058725357, 0.005867379251867533, 0.025474974885582924, 0.01534656435251236, 0.009637770242989063, -0.02033182978630066, -0.006177555304020643, -0.007981222122907639, 0.014414566569030285, -0.04409420117735863, -0.03588973730802536, 0.004410268273204565, 0.023132983595132828, -0.005933431442826986, 0.01294011902064085, 0.03896893560886383, 0.0064141154289245605, -0.020215293392539024, 0.010745792649686337, 0.05072663724422455, -0.01634100452065468, 0.011665728874504566, -0.00346702104434371, 0.010807270184159279, 0.004589491058140993, -0.011600683443248272, -0.07197127491235733, 0.027151206508278847, 0.09015115350484848, 0.012871173210442066, 0.004849577788263559, 0.01640651933848858, -0.004828636068850756, 0.06486684083938599, -0.024897417053580284, 0.05464427173137665, 0.04018297791481018, 0.052351221442222595, -0.017134349793195724, -0.002112670335918665, -0.033035121858119965, -0.0051213158294558525, 0.006824173964560032, 0.006879860069602728, -0.05093098804354668, -0.04781819134950638, -0.03512870892882347, -0.05238161236047745, -0.01908246986567974, -0.0017658440629020333, -0.006352499593049288, 0.024338090792298317, 0.04182597994804382, 0.028689594939351082, -0.005706558935344219, 0.007000562734901905, 0.008907144889235497, 0.0060051726177334785, 0.04534200206398964, 0.03503893315792084, 0.022834913805127144, -0.03210800141096115, 0.046676382422447205, -0.013506838120520115, 0.03809376060962677, -0.010097327642142773, 0.05052945017814636, -0.014687334187328815, -0.05506037548184395, 0.04062047228217125, 0.02745000086724758, -0.0363977774977684, 0.01761956699192524, 0.03064369037747383, 0.006352107040584087, -0.014225207269191742, 0.012521293945610523, 0.02193433605134487, -0.04853612929582596, -0.024870166555047035, -0.005544639192521572, -0.02061125822365284, 0.0034854812547564507, -0.031096654012799263, -0.011700237169861794, 0.019083499908447266, -0.04594201222062111, -0.03048723377287388, 0.0013877167366445065, -0.010299280285835266, 0.0034605402033776045, 0.003038322553038597, 0.007117078173905611, 0.043939195573329926, 0.04074816033244133, 0.03800884261727333, -0.014436583034694195, 0.0017044628039002419, -0.051712509244680405, -0.06931386888027191, 0.0770760253071785, -0.00991514977067709, -0.03361007198691368, 0.004626668058335781, 0.013370371423661709, 0.015038046054542065, -0.06845427304506302, 0.006540521048009396, -0.015516553074121475, -0.014895012602210045, -0.009472019970417023, 0.010432904586195946, -0.020792387425899506, -0.016543257981538773, 0.006667874753475189, 0.015429356135427952, -0.013355403207242489, 0.026089251041412354, 0.05057566240429878, 0.009340991266071796, 0.006962387822568417, 0.0321805477142334, 0.029894890263676643, 0.02434965968132019, -0.04358648508787155, 0.058254048228263855, 0.00863160565495491, 0.04839247092604637, -0.005875092931091785, 0.04108204320073128, 0.0011969121405854821, 0.04241258651018143, -0.07100089639425278, -0.020554516464471817, -0.025242147967219353, 0.05635293573141098, -0.001894505461677909, -0.00020731821132358164, 0.00009081105963559821, -0.0764244943857193, -0.007590204942971468, -0.004208098631352186, 0.053032051771879196, 0.005379296839237213, 0.0593036524951458, 0.03734629601240158, 0.026904068887233734, 0.030208991840481758, 0.08362266421318054, 0.0012831756612285972, -0.044716477394104004, 0.0027001225389540195, 0.01115481648594141, -0.019094470888376236, -0.01256521139293909, -0.05546772480010986, 0.061123862862586975, 0.053005706518888474, -0.05744335427880287, -0.031237252056598663, 0.007431476842612028, 0.03619060665369034, 0.04193834587931633, 0.05415036529302597, -0.034718163311481476, -0.07355624437332153, -0.02630668506026268, -0.009646736085414886, 0.051683828234672546, -0.029867390170693398, -0.020826002582907677, 0.04213433340191841, 0.03944987803697586, -0.04480377212166786, 0.0035111939068883657, 0.018860749900341034, -0.0202716663479805, 0.00023734175192657858, 0.026511140167713165, 0.03528529405593872, -0.02937692031264305, -0.02203112095594406, 0.007197067607194185, -0.07753079384565353, 0.004082050174474716, 0.017157597467303276, -0.0051107872277498245, 0.07068683207035065, -0.041620638221502304, -0.006511561572551727, 0.00922578014433384, -0.08353166282176971, 0.00037512811832129955, 0.013111266307532787, -0.007356693968176842, -0.025632165372371674, -0.028429627418518066, -0.016127848997712135, 0.01736726239323616 ]
<p>The book I'm reading about optics says at some point that "each color (wavelength) contained in the white light interferes only with itself". But why is this so?</p> <p>Edit: I moved the rest of the question <a href="http://physics.stackexchange.com/q/12208/4283">elsewhere</a>.</p>
g1588
[ -0.0015885491156950593, -0.003374921390786767, 0.024971237406134605, -0.026546992361545563, 0.06509457528591156, 0.026948025450110435, 0.005050617270171642, 0.024606794118881226, -0.004725878592580557, -0.003948582801967859, 0.06840592622756958, 0.009534571319818497, -0.0049329823814332485, 0.04926953837275505, -0.05012843757867813, -0.018165528774261475, -0.01736937090754509, 0.015177469700574875, 0.03646756336092949, 0.009029516018927097, -0.04326385632157326, -0.02923087403178215, -0.02393682301044464, -0.06843847781419754, -0.03738265857100487, 0.043591950088739395, 0.024372240528464317, -0.07698570936918259, -0.020221222192049026, -0.00018878361152019352, 0.0012818858958780766, 0.0066751581616699696, 0.045146793127059937, -0.016452400013804436, -0.024280065670609474, 0.006889713928103447, 0.002257570158690214, -0.00275811436586082, 0.00828794576227665, 0.0741337388753891, -0.016973212361335754, 0.0925159677863121, -0.00619205366820097, -0.028017232194542885, 0.010097063146531582, -0.021414892747998238, -0.013821464963257313, 0.007889903150498867, 0.00888625718653202, -0.01703455112874508, 0.0031757077667862177, 0.025387341156601906, -0.02680205926299095, 0.020709598436951637, 0.061421219259500504, -0.04094647988677025, 0.032646480947732925, 0.002171223983168602, 0.037245407700538635, 0.042285505682229996, 0.007553335279226303, -0.00810408964753151, -0.030042754486203194, 0.055867891758680344, 0.010583088733255863, -0.043027251958847046, -0.05913865566253662, -0.025980833917856216, 0.03061036206781864, 0.01072622463107109, -0.00843379832804203, -0.05013497546315193, -0.008862730115652084, -0.0017272558761760592, 0.011903682723641396, 0.03057628497481346, 0.05575102940201759, 0.07249253243207932, -0.005711710080504417, 0.0146097457036376, -0.06921187043190002, -0.016088688746094704, 0.0015320155071094632, -0.0002697663730941713, 0.018641378730535507, -0.0214961227029562, 0.002274478320032358, -0.05105169489979744, -0.04851415753364563, 0.024090535938739777, 0.0287692379206419, 0.00543044600635767, 0.02433708868920803, 0.05914626643061638, 0.030565543100237846, -0.06813842058181763, 0.02039439231157303, 0.0415269136428833, -0.018816569820046425, -0.007508938666433096, -0.029294487088918686, -0.009023712016642094, -0.03168268874287605, -0.0011993531370535493, -0.021411383524537086, -0.04148910567164421, 0.007655689027160406, -0.00565330358222127, -0.032194189727306366, 0.02892836555838585, -0.06830190867185593, -0.01723410002887249, -0.06935351341962814, -0.02184431068599224, -0.010278881527483463, 0.01943320222198963, 0.061059530824422836, -0.02456461265683174, 0.02069813385605812, 0.06334005296230316, 0.032805342227220535, 0.022268613800406456, -0.040359288454055786, -0.0017242487519979477, -0.013563225977122784, 0.0015980559401214123, 0.03996767848730087, -0.03331330418586731, 0.006206913385540247, -0.02109859324991703, -0.00817120261490345, -0.006135112140327692, -0.043977491557598114, 0.012694869190454483, 0.019991762936115265, -0.06281054764986038, 0.015378032810986042, 0.009819337166845798, 0.02528376504778862, 0.029037747532129288, 0.0072799865156412125, -0.0362732969224453, 0.01576508954167366, 0.003661187831312418, 0.008922995068132877, -0.015268753282725811, -0.002131994580850005, -0.030120614916086197, 0.023971255868673325, -0.0017439055955037475, -0.010729271918535233, 0.07004515826702118, 0.035052817314863205, -0.05356716364622116, -0.036136046051979065, 0.0012776650255545974, 0.0500289648771286, 0.028418654575943947, -0.004629479255527258, -0.010568523779511452, 0.04333514720201492, -0.007447589188814163, -0.006254822481423616, 0.06384076923131943, -0.03572260960936546, -0.01926543563604355, -0.029943518340587616, -0.11974373459815979, 0.004459254443645477, -0.04929867386817932, -0.007290296722203493, -0.009748478420078754, -0.035960011184215546, 0.04229862987995148, 0.05554255098104477, 0.088827945291996, 0.05712133273482323, -0.014983060769736767, -0.02838646061718464, 0.02111142687499523, -0.04198072850704193, -0.041437115520238876, 0.002813424915075302, -0.11428755521774292, 0.007999635301530361, -0.02329111285507679, -0.031115354970097542, -0.008366049267351627, -0.03165232390165329, 0.031108979135751724, 0.004151428118348122, -0.02795274183154106, 0.04508053511381149, -0.0023946466390043497, 0.0011375776957720518, -0.050399050116539, 0.002045087516307831, 0.010510323569178581, -0.042250316590070724, -0.0208751130849123, -0.01346997544169426, 0.04297790303826332, 0.015937024727463722, 0.03239559754729271, 0.041593022644519806, 0.019009336829185486, -0.03436380624771118, -0.016270043328404427, 0.025039400905370712, -0.014475731179118156, 0.03175612911581993, -0.03337302431464195, 0.046078797429800034, 0.04364609345793724, -0.00004797655128641054, -0.06357518583536148, -0.03007706068456173, 0.017137158662080765, -0.0034446290228515863, 0.013092337176203728, -0.021402956917881966, 0.014501731842756271, -0.022195331752300262, -0.03650407865643501, -0.028432225808501244, 0.00684005580842495, -0.07043804973363876, 0.029911844059824944, 0.0008061262196861207, 0.023522911593317986, -0.09185238182544708, -0.04194099083542824, -0.003190770512446761, -0.02686336636543274, 0.0674983412027359, 0.03656003996729851, -0.01730373315513134, -0.0005126937758177519, 0.025334566831588745, 0.004270366858690977, 0.048413317650556564, -0.01628195121884346, -0.012531543150544167, 0.018343009054660797, -0.00998727884143591, -0.026159822940826416, 0.007607437204569578, -0.04585632309317589, -0.07988949865102768, 0.007868699729442596, -0.014060594141483307, 0.033247143030166626, -0.0548207089304924, -0.020084461197257042, -0.00965052004903555, -0.010879000648856163, 0.013367992825806141, 0.059331536293029785, -0.051786188036203384, -0.033458683639764786, -0.04291008785367012, -0.029976774007081985, 0.05453356355428696, -0.05570896342396736, -0.011645651422441006, -0.04037392511963844, -0.018990112468600273, 0.049902331084012985, -0.0021466759499162436, -0.04778803512454033, -0.011798850260674953, 0.06570668518543243, 0.01769888587296009, -0.04629635810852051, 0.033402107656002045, 0.018576085567474365, -0.041410911828279495, -0.024694159626960754, 0.028538262471556664, 0.00024118786677718163, -0.054551973938941956, -0.004973684437572956, -0.033182721585035324, -0.05204638093709946, 0.046356115490198135, -0.04094541445374489, 0.04873030260205269, 0.020424317568540573, -0.012900575064122677, -0.0244144294410944, -0.028104158118367195, 0.027090424671769142, -0.024080893024802208, 0.02520841173827648, 0.04149901494383812, -0.009012171067297459, 0.027890395373106003, -0.01655655913054943, -0.04253675416111946, 0.06031027436256409, -0.06273035705089569, 0.0031188607681542635, 0.010459903627634048, -0.03961183503270149, 0.03830366209149361, -0.012765671126544476, -0.022707806900143623, 0.0024221630301326513, -0.007660821080207825, 0.02982233464717865, 0.027355855330824852, 0.0321696475148201, -0.06298784911632538, 0.0593605674803257, -0.006616611033678055, 0.035201556980609894, -0.033756792545318604, -0.018289215862751007, -0.01787751540541649, -0.01147785596549511, -0.08063013106584549, 0.06428756564855576, 0.016142331063747406, -0.05900849029421806, 0.0053551578894257545, -0.04495582729578018, 0.011777865700423717, -0.04515761882066727, 0.012026617303490639, 0.013382647186517715, 0.028216678649187088, -0.014368312433362007, 0.005719856824725866, -0.005068753845989704, 0.012662505730986595, -0.062002070248126984, -0.006242509000003338, -0.027362508699297905, 0.02474781684577465, 0.01821061782538891, -0.00821380503475666, -0.02421528659760952, -0.03704434260725975, -0.03541231155395508, 0.006076739635318518, -0.011815720237791538, 0.009727644734084606, 0.02864731289446354, 0.02337753027677536, 0.007901242934167385, 0.043354425579309464, 0.03592880815267563, -0.0052061909809708595, -0.05661420896649361, -0.06048541143536568, 0.035530876368284225, -0.024564331397414207, 0.13446521759033203, 0.050997041165828705, -0.028416836634278297, 0.038088440895080566, -0.009579971432685852, -0.010676904581487179, -0.10257118940353394, -0.03485158458352089, -0.01622391678392887, 0.01914011687040329, 0.022238807752728462, 0.03767384961247444, 0.037343814969062805, -0.010354031808674335, -0.0034236761275678873, -0.03799724206328392, 0.0008951556519605219, 0.03219986334443092, -0.04724936559796333, 0.039533983916044235, 0.07178724557161331, -0.014380574226379395, 0.022411324083805084, 0.005217490252107382, 0.03593806177377701, 0.009091311134397984, 0.026177508756518364, 0.009385357610881329, -0.01975867711007595, -0.07319070398807526, -0.026429466903209686, 0.010969895869493484, -0.07932448387145996, 0.038282256573438644, -0.04630693048238754, 0.019580688327550888, -0.03115278109908104, 0.019806962460279465, -0.00877193920314312, -0.0017873127944767475, -0.0027087246999144554, 0.025838004425168037, 0.041599091142416, 0.04429241269826889, 0.028609279543161392, -0.010538481175899506, -0.02638113871216774, -0.0026033848989754915, 0.04673895239830017, 0.033367373049259186, 0.007135909050703049, -0.014491780661046505, 0.0637822300195694, 0.008525249548256397, 0.003459385596215725, -0.019406208768486977, -0.05173325911164284, 0.026599803939461708, 0.028233172371983528, 0.03179667517542839, -0.03474104031920433, 0.021957362070679665, -0.00208468409255147, 0.03039565496146679, -0.016912702471017838, -0.059760451316833496, -0.009374459274113178, -0.019111722707748413, 0.004094505216926336, -0.031477391719818115, 0.0031527127139270306, -0.021947404369711876, 0.012024437077343464, 0.02123194746673107, 0.005384002346545458, -0.023092271760106087, 0.0012986698420718312, -0.0024434742517769337, 0.0038117982912808657, 0.04555809870362282, 0.05419699475169182, 0.05818382650613785, 0.03963594138622284, 0.07260482013225555, -0.0141762625426054, 0.05144152045249939, -0.02508433908224106, 0.039353545755147934, 0.03361789509654045, -0.044337477535009384, 0.0024357291404157877, -0.03858507424592972, 0.03489615395665169, -0.013537783175706863, -0.010549074970185757, -0.034409962594509125, -0.03964274004101753, -0.014135733246803284, -0.029980607330799103, -0.027192600071430206, 0.03944111242890358, 0.06424134224653244, 0.02471650205552578, -0.019356993958353996, -0.03494696691632271, -0.02102995291352272, 0.028149006888270378, 0.06420989334583282, 0.027092386037111282, -0.026518283411860466, 0.018519418314099312, -0.09211834520101547, 0.02387334406375885, -0.031594499945640564, 0.06178297474980354, 0.01716640219092369, 0.05843081325292587, 0.0698045939207077, -0.06988047808408737, -0.043275922536849976, -0.015438555739820004, -0.025688115507364273, 0.004561672452837229, -0.015476415865123272, -0.06420426070690155, 0.033355213701725006, 0.034389279782772064, -0.006063705775886774, 0.04615360498428345, -0.01848050393164158, 0.06476777791976929, 0.016244450584053993, -0.03599397838115692, 0.016624201089143753, -0.0011942473938688636, -0.003687414573505521, -0.023449355736374855, -0.04241465404629707, -0.0038984897546470165, 0.0450853556394577, -0.03099239058792591, -0.01252081897109747, -0.03479522466659546, 0.018844079226255417, -0.04537007585167885, -0.03312552347779274, -0.030954087153077126, -0.02910871058702469, -0.007739972788840532, 0.031200652942061424, -0.0035942383110523224, -0.031149329617619514, 0.009427144192159176, 0.03252224624156952, -0.05996314063668251, 0.053592290729284286, 0.03686278313398361, 0.006452418398112059, -0.037655286490917206, -0.02386740781366825, 0.017493795603513718, -0.0040625641122460365, -0.06573915481567383, -0.033927071839571, -0.015881609171628952, -0.06688819825649261, -0.021375687792897224, 0.015232103876769543, 0.03789639100432396, 0.003852008143439889, 0.0022997725754976273, 0.006283943075686693, -0.02654930204153061, 0.009010990150272846, 0.012359946966171265, 0.03428645804524422, 0.037269845604896545, 0.0370374359190464, -0.0997355580329895, 0.013218766078352928, -0.023283179849386215, -0.00038908576243557036, 0.04911474138498306, -0.026598824188113213, 0.04113044962286949, -0.01898043602705002, 0.0651485025882721, -0.013817905448377132, -0.01916833408176899, 0.0606372095644474, -0.0027507443446666002, 0.024913165718317032, 0.031606536358594894, -0.016416065394878387, 0.058338262140750885, 0.012634983286261559, 0.00050213688518852, 0.014311746694147587, 0.02219574712216854, -0.008959220722317696, 0.023855607956647873, -0.02203628048300743, -0.07442633807659149, 0.05138009786605835, 0.021422160789370537, 0.0016832519322633743, -0.018336370587348938, -0.0289015993475914, 0.013958783820271492, 0.010213914327323437, 0.02757163904607296, 0.01290823146700859, 0.07189128547906876, -0.004705711267888546, 0.05103765428066254, 0.015775591135025024, -0.013051561079919338, -0.003633836517110467, 0.036278605461120605, 0.0006533730193041265, -0.03434431552886963, -0.006773526314646006, -0.04417828842997551, 0.03892480581998825, -0.023165326565504074, -0.009111414663493633, -0.06522830575704575, -0.02793935500085354, 0.0061017307452857494, 0.020476412028074265, -0.023228080943226814, 0.11055132746696472, -0.045395705848932266, -0.05664525553584099, -0.022571824491024017, 0.027104372158646584, -0.0026750853285193443, 0.021103013306856155, -0.06857632100582123, -0.0006672085728496313, 0.073384590446949, -0.00901321042329073, -0.0050685470923781395, 0.04749707877635956, -0.06505372375249863, 0.058994315564632416, 0.019776079803705215, 0.0041234735399484634, 0.02148672565817833, -0.020785624161362648, -0.06802476197481155, 0.046639688313007355, 0.028592653572559357, -0.029585877433419228, 0.017311008647084236, 0.025479476898908615, -0.011289664544165134, -0.049247805029153824, -0.05993444845080376, -0.04378201812505722, -0.004020593594759703, -0.0345776230096817, 0.002209441037848592, -0.0008217066060751677, -0.020903408527374268, -0.017822833731770515, 0.0034227038267999887, 0.01776570826768875, 0.05808673053979874, -0.021008936688303947, -0.022670287638902664, 0.04588872566819191, -0.02395515702664852, 0.036645952612161636, -0.006345302332192659, 0.04275212064385414, 0.036689791828393936, 0.02261437103152275, 0.016960764303803444, -0.07338887453079224, -0.0584973581135273, 0.03355436027050018, -0.007850514724850655, 0.036618348211050034, 0.0224988404661417, 0.06557615101337433, 0.06950652599334717, 0.0233223345130682, 0.06737910211086273, 0.035558950155973434, -0.09071317315101624, -0.012166410684585571, 0.022864095866680145, 0.029592357575893402, 0.02094307541847229, 0.008597012609243393, 0.0442022979259491, -0.03283591568470001, 0.013042408972978592, -0.054634373635053635, 0.0003272609319537878, 0.00043147854739800096, -0.02082381770014763, -0.03886810690164566, 0.015735432505607605, -0.07387370616197586, 0.028755223378539085, -0.004787382669746876, 0.025472797453403473, 0.04789073392748833, -0.031100984662771225, -0.01586441695690155, 0.02215367555618286, 0.02987896278500557, -0.03243279084563255, 0.03922630101442337, -0.032826345413923264, 0.02204933948814869, -0.06850992888212204, -0.05742543190717697, 0.04789390787482262, 0.06783568859100342, 0.014291955158114433, 0.04674938693642616, 0.006843571551144123, 0.058310531079769135, 0.013695472851395607, -0.0729667916893959, 0.016034932807087898, 0.010364877991378307, 0.007107492070645094, 0.017076652497053146, 0.003957951441407204, -0.016529809683561325, -0.08093561232089996, 0.017454979941248894, -0.027007993310689926, 0.0235423780977726, -0.00002226097603852395, 0.015252605080604553, 0.0720263347029686, -0.027678444981575012, 0.06298469752073288, -0.036574289202690125, -0.01359367836266756, 0.012903046794235706, -0.08402065932750702, 0.049941375851631165, 0.007952343672513962, 0.002515195170417428, 0.012905384413897991, -0.023636572062969208, -0.023907680064439774, 0.00601313216611743, 0.05118177831172943, 0.0669180303812027, 0.014130204916000366, -0.021501628682017326, -0.035046838223934174, 0.008089225739240646, 0.011796637438237667, -0.023127613589167595, -0.0028417175635695457, -0.02428378164768219, 0.04598638415336609, -0.017756188288331032, -0.015339882113039494, -0.02101009525358677, -0.00563573744148016, 0.06487518548965454, -0.019875094294548035, 0.03070649690926075, 0.028026863932609558, -0.0430946871638298, -0.012192477472126484, -0.04451173171401024, -0.005120973102748394, -0.01344376988708973, 0.0874628946185112, -0.0025289803743362427, -0.011906985193490982, 0.0026057856157422066, 0.010040123015642166, 0.06267818063497543, 0.011568299494683743, -0.056443553417921066, -0.04508347064256668, -0.010501815937459469, -0.02274312824010849, 0.002879435196518898, -0.006767680868506432, 0.052100665867328644, 0.008729927241802216, -0.03054533340036869, 0.07245448231697083, 0.01015507709234953, 0.0571221262216568, 0.07585036009550095, -0.07143125683069229, -0.03755783289670944, -0.04047626629471779, 0.0034712462220340967, -0.009417262859642506, -0.009296300821006298, -0.009554543532431126, -0.008256365545094013, 0.03797907382249832, 0.025408713147044182, -0.03901609405875206, -0.03349582478404045, -0.03915083035826683 ]
<p>Could anyone suggest a recent review article or book on gas chromatography instrumentation? My interest is in the devices themselves, rather than using them for a particular application.</p> <p><a href="http://rsi.aip.org/resource/1/rsinak/v61/i11/p3317_s1" rel="nofollow">This article</a>, "Gas Chromatography" in Review of Scientific Instruments is the sort of thing I'm going for; I'm just checking to see if there's a more recent or superior introduction.</p>
g1589
[ -0.01728656142950058, -0.021445995196700096, 0.01908552646636963, -0.038706425577402115, -0.026377275586128235, -0.016651540994644165, 0.032207559794187546, 0.035401418805122375, -0.10088369995355606, -0.003820758778601885, 0.10605429112911224, 0.04095403105020523, 0.0021444172598421574, -0.03254919871687889, 0.049989670515060425, -0.06112140789628029, -0.03311474993824959, 0.02683083526790142, 0.03354179114103317, 0.045904144644737244, 0.019769052043557167, 0.030207380652427673, 0.001568455365486443, -0.020093247294425964, -0.016624432057142258, -0.0006283852271735668, -0.0030059190467000008, -0.027852816507220268, -0.011319485493004322, 0.040601372718811035, -0.08022180944681168, -0.009178336709737778, -0.031093226745724678, 0.027375243604183197, -0.03962855786085129, -0.0013956684852018952, 0.03178335726261139, 0.010482622310519218, -0.016222450882196426, -0.0455157607793808, 0.08017024397850037, 0.07008115202188492, -0.04178277775645256, -0.08214198797941208, 0.06434817612171173, 0.08017988502979279, -0.005926304496824741, 0.008821237832307816, 0.00211643660441041, -0.019410261884331703, -0.03420742228627205, 0.07859397679567337, 0.002909957431256771, -0.046434011310338974, 0.05354948341846466, 0.06093376874923706, -0.04143570363521576, 0.07174810767173767, -0.0234883651137352, -0.016888588666915894, -0.04275376349687576, 0.05507307127118111, -0.005984108429402113, -0.06682159006595612, 0.028898289427161217, -0.010927602648735046, 0.010788355022668839, -0.012309616431593895, 0.0024563150946050882, 0.03291170671582222, -0.010090911760926247, 0.0426308736205101, 0.09331546723842621, 0.046393122524023056, 0.003989099524915218, -0.06363851577043533, -0.03000638633966446, 0.021960126236081123, 0.014950728043913841, -0.01040821522474289, -0.004613346420228481, -0.014073830097913742, -0.04191625490784645, -0.002392275258898735, -0.004715436138212681, -0.04360895976424217, 0.012545434758067131, -0.04389475658535957, 0.019154297187924385, 0.010734294541180134, -0.003959305118769407, 0.03799827769398689, 0.022598760202527046, 0.0004558551881927997, -0.05006538704037666, 0.06661716103553772, -0.03736144304275513, -0.017672808840870857, -0.019575709477066994, 0.02426093816757202, 0.009997010231018066, -0.01687716133892536, 0.061732351779937744, 0.03814408555626869, -0.00951418373733759, -0.017116954550147057, -0.003706215647980571, 0.05922134220600128, -0.08163074404001236, -0.05903056636452675, 0.01288536936044693, 0.08109764009714127, -0.049387115985155106, -0.01689363643527031, 0.0001913421874633059, 0.042643677443265915, 0.040965721011161804, -0.01463857851922512, 0.009714939631521702, -0.00926685705780983, 0.003790532471612096, 0.0869520977139473, -0.018908144906163216, 0.000172118961927481, -0.04162576422095299, -0.030709335580468178, 0.008516686968505383, -0.010418511927127838, -0.02657081000506878, 0.027772953733801842, -0.0011157956905663013, -0.04117146134376526, -0.006054271478205919, -0.04255738854408264, 0.0061085280030965805, -0.025940489023923874, 0.04462171345949173, 0.0157318115234375, -0.013628163374960423, 0.0012788110179826617, 0.026366177946329117, 0.016798794269561768, -0.00008166329644154757, -0.021187998354434967, 0.06952928006649017, 0.05104229226708412, 0.012220166623592377, 0.01304157916456461, -0.015196221880614758, -0.019429391250014305, 0.04015733301639557, -0.027238687500357628, -0.005747959483414888, -0.0020591754000633955, -0.01748833619058132, -0.005565418861806393, -0.0426206961274147, 0.0007182921981438994, -0.015080759301781654, -0.01876874268054962, 0.01174758281558752, -0.0012606296222656965, -0.015447159297764301, 0.02576671540737152, -0.07331223040819168, 0.03998521342873573, 0.00732610747218132, -0.059469372034072876, 0.021017521619796753, -0.04230309650301933, -0.02319333516061306, -0.011910698376595974, -0.009118203073740005, 0.0025183679535984993, -0.005994514096528292, 0.0028402938041836023, 0.08360884338617325, -0.002453382359817624, -0.011152573861181736, -0.04320523142814636, 0.0006608659168705344, -0.03745926171541214, 0.005699776578694582, -0.04599529132246971, -0.06377221643924713, 0.012071467004716396, 0.010659409686923027, -0.0719699114561081, -0.022577300667762756, -0.014453749172389507, 0.026190439239144325, 0.07685379683971405, 0.030678316950798035, 0.017810577526688576, -0.08132997900247574, 0.01023581437766552, -0.02747506834566593, -0.005831549875438213, 0.05240945145487785, -0.01153597328811884, -0.08251175284385681, 0.02881675586104393, 0.019981829449534416, 0.08573907613754272, 0.03071911446750164, -0.05137772485613823, -0.028777964413166046, -0.061100028455257416, 0.02607506699860096, -0.03711158409714699, -0.052660755813121796, 0.03723594546318054, 0.06370773911476135, -0.02399393543601036, 0.057427145540714264, -0.005810868926346302, 0.0061863805167376995, -0.0007363804033957422, 0.06796087324619293, -0.006485142279416323, -0.005646045319736004, -0.00894226972013712, -0.022255195304751396, -0.0014107420574873686, 0.05818723887205124, -0.015441720373928547, 0.04534125328063965, 0.020925793796777725, -0.007811731658875942, -0.03147609159350395, -0.09436403959989548, 0.0064997379668056965, -0.0004682904982473701, -0.04465614631772041, 0.016155747696757317, -0.00846131332218647, -0.01693141832947731, -0.041513584554195404, -0.02288411371409893, 0.004719740245491266, -0.012325162068009377, -0.009691170416772366, -0.02284296043217182, -0.011184188537299633, -0.0028779932763427496, -0.04770642891526222, -0.0106364069506526, 0.016384337097406387, 0.02831602841615677, -0.034580860286951065, 0.002603774191811681, 0.00915859080851078, 0.005158792715519667, 0.054478079080581665, -0.011356237344443798, 0.033108726143836975, 0.07287470251321793, 0.029526032507419586, -0.013675452210009098, 0.009747919626533985, -0.013826356269419193, -0.031747929751873016, 0.011148747056722641, 0.0046080732718110085, -0.004219965077936649, -0.06027398630976677, -0.027458151802420616, 0.00937894731760025, 0.05247986689209938, -0.0369475856423378, 0.03431427478790283, -0.04961115121841431, 0.01635652594268322, -0.02087835967540741, 0.010554851032793522, -0.004276886582374573, 0.001026964164339006, -0.016349351033568382, 0.04560476914048195, -0.01910013146698475, 0.029622089117765427, -0.06470648944377899, 0.028797615319490433, -0.01525738276541233, -0.01566881500184536, 0.04000289738178253, 0.007493431679904461, -0.0047487844713032246, 0.02438136748969555, 0.02662741020321846, 0.005884693935513496, 0.01714114286005497, -0.035113539546728134, -0.03582334145903587, 0.007269587367773056, -0.011759205721318722, -0.03859735280275345, -0.027078300714492798, 0.07157132029533386, -0.011726128868758678, 0.006474093534052372, -0.084964819252491, -0.023014342412352562, 0.048919498920440674, -0.014921712689101696, 0.01907084882259369, -0.0019564200192689896, -0.017973292618989944, -0.06798217445611954, 0.012530660256743431, 0.06214847415685654, -0.028798716142773628, -0.052017007023096085, 0.007270623464137316, -0.009125752374529839, -0.020830225199460983, -0.003441889537498355, 0.019071128219366074, -0.056895095854997635, 0.04185770824551582, 0.02993099018931389, 0.010763224214315414, 0.024011151865124702, -0.02775494195520878, 0.010287856683135033, -0.005433395970612764, -0.01194294448941946, -0.002355578588321805, -0.024012042209506035, 0.0036610146053135395, 0.046503596007823944, 0.046685270965099335, 0.016521461308002472, 0.0022277336101979017, 0.03530149534344673, -0.033808086067438126, -0.03185426443815231, 0.00766638433560729, 0.009543937630951405, -0.011631252244114876, 0.012674350291490555, -0.03816966712474823, 0.012996602803468704, -0.03355008363723755, -0.046032220125198364, -0.009842198342084885, 0.016289209946990013, 0.07114706188440323, -0.02012508362531662, -0.04346955195069313, -0.0037368852645158768, 0.07794398814439774, 0.03444954380393028, -0.022971296682953835, -0.015096054412424564, 0.018519315868616104, 0.006021896842867136, 0.0008836250053718686, -0.02318565919995308, 0.026162132620811462, 0.00022732389334123582, 0.030536092817783356, 0.011990663595497608, 0.018149277195334435, 0.025562619790434837, -0.04537060484290123, -0.011025840416550636, 0.015481298789381981, 0.019537121057510376, -0.048942726105451584, -0.01653250865638256, 0.06606576591730118, 0.005580240860581398, 0.0584075041115284, -0.01864723674952984, -0.0772547721862793, 0.03330586105585098, 0.03432479500770569, 0.017314108088612556, -0.014720991253852844, -0.033057328313589096, -0.04066787660121918, 0.028132740408182144, 0.06353785842657089, 0.017369205132126808, -0.04701199755072594, 0.004978509154170752, 0.043886199593544006, -0.0572904497385025, -0.07055791467428207, -0.01693248562514782, -0.06437457352876663, -0.043681226670742035, 0.02986295148730278, -0.02949783019721508, 0.04666217416524887, 0.010617476888000965, 0.03733357787132263, 0.011502797715365887, 0.027221323922276497, -0.004755976144224405, -0.026894839480519295, -0.016885418444871902, -0.012663467787206173, -0.0362996868789196, 0.06409420073032379, -0.02956121601164341, -0.05576033890247345, -0.0866384282708168, 0.022997725754976273, -0.015651913359761238, -0.00750367809087038, -0.018290434032678604, 0.0395413339138031, 0.040412142872810364, 0.028018254786729813, -0.06585488468408585, -0.014056099578738213, 0.03286433219909668, 0.009784795343875885, 0.026593998074531555, 0.020485900342464447, -0.02369214966893196, 0.03033769130706787, -0.046683419495821, 0.010426742024719715, -0.001418087282218039, 0.05500931665301323, 0.026032181456685066, 0.06426781415939331, 0.025606593117117882, -0.04650791734457016, -0.0053561958484351635, 0.007166814524680376, -0.021015632897615433, 0.0025330453645437956, 0.00020168040646240115, -0.02430441603064537, 0.02920318953692913, -0.002479531802237034, 0.022840669378638268, 0.02926812320947647, 0.0010908960830420256, 0.010163304395973682, -0.0007563288672827184, 0.028582721948623657, -0.008044449612498283, 0.07428371161222458, -0.01769883930683136, 0.006570254452526569, -0.003694172017276287, 0.006901351734995842, 0.0041147759184241295, -0.0028939491603523493, -0.04981403425335884, -0.016561346128582954, 0.04135877266526222, 0.0019222790142521262, -0.01373563427478075, -0.0025802229065448046, -0.022667208686470985, 0.024078963324427605, -0.03824339807033539, 0.06246812269091606, -0.0299869105219841, 0.004432428628206253, -0.013516842387616634, -0.018741244450211525, 0.003903541946783662, -0.010484141297638416, -0.06107640638947487, -0.00023200070427265018, 0.0019824013579636812, -0.0014683414483442903, 0.015471364371478558, -0.012699773535132408, -0.0020182428415864706, 0.01748075522482395, -0.022745076566934586, -0.05065017566084862, -0.04540484398603439, 0.014303205534815788, 0.02562883496284485, 0.017795592546463013, 0.05220386013388634, -0.02332441695034504, -0.06477878242731094, -0.0030847792513668537, 0.01519582886248827, -0.008092755451798439, 0.010034164413809776, -0.018798092380166054, 0.025034651160240173, -0.041957657784223557, 0.03283395245671272, -0.014752980321645737, 0.07424561679363251, -0.03337211534380913, -0.05298354849219322, -0.02516438625752926, 0.015534639358520508, 0.02892501838505268, 0.022037602961063385, 0.020398998633027077, 0.00992884486913681, -0.007184204645454884, -0.015067932195961475, -0.04482610151171684, -0.0052983625791966915, 0.02153928205370903, -0.015008027665317059, 0.06959477066993713, -0.01912914589047432, 0.06582298129796982, -0.034553561359643936, 0.006510293576866388, 0.0019564644899219275, -0.006940785795450211, 0.004609755706042051, -0.08607661724090576, 0.011130799539387226, -0.06412920355796814, -0.004328740295022726, 0.04303790628910065, 0.015979930758476257, -0.029174238443374634, -0.005265567917376757, 0.03825518116354942, 0.031808771193027496, 0.006402668077498674, -0.025982549414038658, 0.012969798408448696, -0.00026099197566509247, 0.052367936819791794, -0.05205842852592468, -0.004772396292537451, -0.05033212527632713, 0.04061112925410271, 0.045127809047698975, -0.0015521837631240487, -0.00001672837242949754, 0.05583888664841652, -0.048113465309143066, 0.024171359837055206, 0.0014897179789841175, 0.020979437977075577, 0.055056098848581314, 0.00037691855686716735, 0.02443578839302063, -0.057739175856113434, 0.04151080921292305, 0.01685016229748726, 0.008497190661728382, -0.05535013973712921, 0.008260813541710377, 0.040719710290431976, 0.03474722430109978, 0.02866392396390438, 0.02789110317826271, -0.025252634659409523, -0.05232558399438858, -0.013213502243161201, 0.07355870306491852, 0.04219190776348114, 0.032887011766433716, -0.025108864530920982, -0.07268083840608597, -0.05170729011297226, -0.07032885402441025, 0.01198605913668871, -0.0341557115316391, 0.022928809747099876, -0.0237407423555851, -0.004563198424875736, 0.0004791565879713744, -0.05203915387392044, 0.01359119638800621, -0.03935539349913597, 0.0310230515897274, -0.0415693074464798, 0.026125947013497353, 0.035512182861566544, 0.03604940325021744, -0.030758466571569443, -0.02089708298444748, -0.021831046789884567, -0.048859816044569016, 0.05465542897582054, -0.045674294233322144, -0.017025532200932503, 0.02331504411995411, -0.012101668864488602, 0.00933641567826271, -0.004901528358459473, 0.02366197295486927, -0.06751661747694016, -0.011274629272520542, 0.0532885305583477, 0.05055158957839012, 0.014558187685906887, -0.036528706550598145, 0.013485576026141644, -0.019800454378128052, -0.06051613390445709, 0.01582312397658825, 0.007980628870427608, -0.003148032585158944, 0.015301048755645752, -0.0035191087517887354, -0.04890933260321617, 0.04256563261151314, -0.0565335676074028, 0.050732724368572235, -0.013545157387852669, 0.048365093767642975, -0.027456529438495636, 0.04222077503800392, -0.009573112241923809, -0.06731355935335159, 0.03207115828990936, 0.0016800209414213896, 0.029159775003790855, -0.015309703536331654, 0.01775422878563404, 0.020965345203876495, 0.05466827377676964, -0.023778114467859268, -0.03921752795577049, -0.015027246437966824, 0.028499476611614227, -0.023789791390299797, 0.013004356063902378, 0.016152121126651764, 0.00045168393990024924, -0.015474332496523857, 0.05419701337814331, -0.02339920401573181, -0.030683254823088646, 0.04536738246679306, -0.008034985512495041, 0.011961499229073524, -0.001235596020705998, 0.026404839009046555, -0.001379741937853396, 0.03173704445362091, -0.03751406818628311, 0.04054698720574379, 0.030072592198848724, 0.03742033615708351, -0.004231595899909735, -0.015675658360123634, -0.0645824745297432, 0.02338200993835926, 0.039679549634456635, -0.0639113336801529, 0.04790987819433212, 0.07942088693380356, 0.03198461979627609, 0.04008147865533829, -0.053537044674158096, -0.04181507229804993, 0.00788493175059557, 0.03129701316356659, 0.07472239434719086, -0.08347591757774353, 0.04393725469708443, -0.042750582098960876, 0.00578801054507494, 0.022886402904987335, -0.01104120071977377, 0.017344266176223755, -0.04838784039020538, 0.016308924183249474, -0.043930064886808395, 0.019970303401350975, 0.03160436823964119, 0.026353096589446068, -0.045086123049259186, -0.009194482117891312, -0.0322740413248539, -0.07601264864206314, -0.029159486293792725, -0.020363537594676018, -0.02604798600077629, -0.09835172444581985, -0.04318644106388092, -0.057546693831682205, 0.04966051131486893, 0.014030440710484982, 0.014170289039611816, -0.03917904198169708, -0.04371052607893944, -0.03506793454289436, -0.014736499637365341, 0.024943729862570763, -0.051530592143535614, -0.011983392760157585, 0.021056653931736946, 0.01613002084195614, 0.010174092836678028, 0.04363449662923813, 0.011406976729631424, -0.051017556339502335, 0.005227934569120407, 0.0024930883664637804, 0.01852315664291382, 0.027145186439156532, 0.012486525811254978, 0.049110837280750275, 0.028155073523521423, -0.022381920367479324, 0.012705202214419842, -0.007715953979641199, -0.04172942787408829, 0.01286927331238985, 0.0027438781689852476, -0.01472431980073452, -0.052238382399082184, 0.03261987864971161, -0.02607100084424019, 0.017470920458436012, -0.011122955940663815, 0.02433188259601593, -0.05080633610486984, -0.03821257874369621, 0.04390574246644974, 0.0044239298440515995, 0.050392717123031616, 0.0313168540596962, 0.004025598987936974, 0.01554284617304802, 0.00603867694735527, -0.023006528615951538, 0.11003745347261429, -0.0664002001285553, 0.04473986104130745, 0.07390659302473068, -0.023366620764136314, 0.020280616357922554, 0.04146740958094597, 0.061386533081531525, -0.008966131135821342, -0.04632679373025894, -0.007802688982337713, 0.023112017661333084, -0.09284168481826782, -0.026408987119793892, 0.026198988780379295, 0.0012195659801363945, -0.043271876871585846, 0.06833379715681076, 0.0119677959010005, 0.06767373532056808, -0.013747337274253368, -0.07524283975362778, -0.016814017668366432, 0.03486217185854912, 0.030450154095888138, 0.060317542403936386, 0.030145082622766495, 0.029186198487877846, 0.05811433121562004, 0.040685150772333145, -0.0282196756452322, -0.08012279123067856, -0.016610076650977135, 0.020336810499429703, -0.03256853297352791 ]