question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>If a spring is cut up into n pieces, does the spring constant also change for these cut pieces?
I know spring constant is inversely proportional to deformation but is the same true for even the true length of the spring?</p> | g194 | [
0.0693577229976654,
-0.029526324942708015,
0.002952889772132039,
-0.01174753438681364,
0.006711889989674091,
0.00791073776781559,
-0.02235925942659378,
0.027899131178855896,
-0.03242366388440132,
0.026904534548521042,
-0.06527101248502731,
-0.022592198103666306,
-0.006896921433508396,
-0.04717292636632919,
0.018805429339408875,
-0.017571138218045235,
0.024659600108861923,
-0.02774284966289997,
0.018935326486825943,
0.022106889635324478,
0.036489978432655334,
-0.03444916382431984,
0.02198091149330139,
-0.036978673189878464,
0.00359911541454494,
-0.01253669522702694,
0.05841357260942459,
0.006205218378454447,
-0.07214820384979248,
0.01922391913831234,
0.06112345680594444,
-0.01121998019516468,
0.004173332825303078,
-0.04799521341919899,
-0.07955127209424973,
-0.010817118920385838,
0.02881159819662571,
0.02709697000682354,
0.05325859785079956,
-0.002550882287323475,
0.0335783027112484,
-0.049850430339574814,
-0.026960069313645363,
0.0562940277159214,
0.012920025736093521,
-0.0038304845802485943,
0.07316439598798752,
0.02717280574142933,
-0.0044651213102042675,
-0.01693480648100376,
0.006322385277599096,
0.02632669359445572,
-0.013586430810391903,
0.006673445925116539,
-0.018292594701051712,
-0.007681773975491524,
0.01627960056066513,
0.01607757806777954,
0.04230816662311554,
0.0519704706966877,
-0.01875700056552887,
-0.023562762886285782,
-0.02512870356440544,
-0.0474274642765522,
0.009819884784519672,
0.03973541781306267,
0.010534795932471752,
-0.042206231504678726,
0.0013339028228074312,
0.01615746319293976,
-0.03746439516544342,
0.00010832529369508848,
-0.011775309219956398,
-0.027702737599611282,
-0.035049717873334885,
0.028891105204820633,
0.031831033527851105,
0.017221590504050255,
-0.05711820721626282,
-0.013578389771282673,
-0.04619191959500313,
-0.0011341118952259421,
0.014446261338889599,
0.028575602918863297,
0.014284887351095676,
-0.04840264469385147,
0.0576835460960865,
0.02883254736661911,
-0.04603542760014534,
0.030963687226176262,
-0.026417892426252365,
-0.0639907568693161,
0.0009138448513112962,
0.008977174758911133,
-0.042872097343206406,
-0.014799518510699272,
-0.01543060876429081,
0.06531266123056412,
-0.0007163766422308981,
0.012626000680029392,
0.004572682548314333,
0.05291789397597313,
0.01839081011712551,
-0.009748738259077072,
-0.07018321752548218,
0.022526931017637253,
0.1011529341340065,
-0.04549931362271309,
0.014408916234970093,
-0.04758452624082565,
-0.0052502816542983055,
-0.008265824057161808,
-0.040780823677778244,
0.015312080271542072,
-0.02096567489206791,
-0.05987684056162834,
0.014201724901795387,
-0.046290259808301926,
0.010665484704077244,
0.038230568170547485,
0.029301535338163376,
-0.03294343128800392,
0.018735574558377266,
0.040980152785778046,
-0.04367947205901146,
-0.02109651453793049,
-0.03006005473434925,
0.071959488093853,
-0.0036941836588084698,
-0.027232611551880836,
0.04544173181056976,
0.011929827742278576,
-0.009420186281204224,
0.034574344754219055,
-0.02345890924334526,
0.05559426173567772,
0.013904242776334286,
-0.006804617587476969,
-0.01760762743651867,
0.08671001344919205,
0.02063128910958767,
-0.008568448014557362,
-0.020092204213142395,
-0.05719740316271782,
0.025748269632458687,
0.07190021872520447,
-0.017359808087348938,
-0.008757960051298141,
-0.005250683054327965,
0.0003879810974467546,
0.03353838622570038,
0.039966970682144165,
0.004786437842994928,
-0.01476147212088108,
0.011804582551121712,
-0.003957327920943499,
-0.0060465168207883835,
-0.020407646894454956,
0.02171330340206623,
0.038821179419755936,
-0.02652847021818161,
-0.01727902702987194,
-0.02257896028459072,
0.016252540051937103,
-0.05788642168045044,
0.011326565407216549,
-0.05256769806146622,
0.015301896259188652,
-0.028668008744716644,
-0.03873402252793312,
-0.06524685770273209,
0.03391589596867561,
-0.0008938021492213011,
0.06395310163497925,
-0.030720552429556847,
-0.0688842386007309,
0.06180109456181526,
0.03009716421365738,
0.026941770687699318,
0.022816428914666176,
-0.028324579820036888,
0.07270605862140656,
0.002145117614418268,
-0.03118174709379673,
-0.02797711081802845,
0.08762581646442413,
0.021580159664154053,
0.0039101107977330685,
-0.013687791302800179,
-0.05539116635918617,
0.008894410915672779,
-0.01677251234650612,
-0.04498402401804924,
0.0531456358730793,
0.04871663451194763,
-0.07054031640291214,
-0.06673698127269745,
-0.008589460514485836,
-0.00739414943382144,
0.0041502127423882484,
0.030944541096687317,
0.06923769414424896,
0.04706701636314392,
0.0031362678855657578,
0.0167160052806139,
0.05111084505915642,
-0.011991200037300587,
-0.01206665113568306,
0.007682995870709419,
-0.003737821476534009,
0.025066036731004715,
0.0181058868765831,
0.0121663399040699,
0.01364700123667717,
0.009407204575836658,
-0.029256509616971016,
0.03544012829661369,
0.0009236392215825617,
0.03068900667130947,
0.0013962042285129428,
-0.006344840861856937,
-0.0017201448790729046,
0.05097416043281555,
-0.05490203946828842,
-0.02552085556089878,
-0.005823146086186171,
0.04533476009964943,
-0.016949323937296867,
0.0401824526488781,
-0.021928925067186356,
-0.019914140924811363,
0.005194496363401413,
-0.0011029061861336231,
0.06087445467710495,
-0.009088275954127312,
0.040062885731458664,
-0.027979517355561256,
0.009358992800116539,
0.0002745106758084148,
-0.05253511294722557,
0.03446720540523529,
-0.0575348362326622,
-0.016429251059889793,
0.0009163605282083154,
0.007287034299224615,
0.016133097931742668,
0.005746598355472088,
0.014792848378419876,
-0.019652385264635086,
0.008395158685743809,
0.007180970627814531,
0.011188006959855556,
-0.04842493310570717,
0.046503063291311264,
-0.009606090374290943,
0.010876853950321674,
0.02207360975444317,
0.03674134984612465,
0.013017764315009117,
0.0059645636938512325,
-0.012506221421062946,
-0.023874882608652115,
0.021053997799754143,
-0.029430000111460686,
-0.03056754171848297,
-0.062214914709329605,
-0.00034566724207252264,
-0.02930999919772148,
0.016663115471601486,
0.05711352825164795,
0.02246669866144657,
0.06102433055639267,
0.016305765137076378,
0.05511265993118286,
-0.0281384140253067,
0.012613211758434772,
0.023701073601841927,
-0.032293785363435745,
-0.0424346961081028,
-0.008357018232345581,
0.027111820876598358,
0.05241900682449341,
-0.08888377249240875,
-0.013031291775405407,
0.040212057530879974,
0.016570335254073143,
0.0003489742230158299,
-0.07982023805379868,
-0.10029236227273941,
0.051942694932222366,
-0.014140890911221504,
-0.002777951071038842,
0.04881436750292778,
-0.0339074581861496,
-0.004849538207054138,
0.06552498042583466,
0.018022745847702026,
-0.05261559039354324,
-0.06589117646217346,
0.03929021954536438,
-0.07803711295127869,
-0.06314720958471298,
0.008008158765733242,
0.011153646744787693,
0.009289506822824478,
0.032960787415504456,
0.03924831002950668,
-0.013771799392998219,
0.007267729379236698,
0.02895941399037838,
-0.05206901207566261,
0.02860395610332489,
0.05582338944077492,
0.0037380338180810213,
-0.10425794124603271,
-0.011234679259359837,
-0.04340178519487381,
-0.049652278423309326,
-0.028960995376110077,
-0.03088594786822796,
0.006548854056745768,
-0.015367334708571434,
0.04012734442949295,
-0.011069669388234615,
-0.028167270123958588,
0.0009217743645422161,
0.004679294768720865,
-0.0024120607413351536,
-0.03320511057972908,
-0.02705417573451996,
-0.025364451110363007,
-0.05578307434916496,
-0.037064310163259506,
0.008237476460635662,
0.04119791090488434,
-0.025641361251473427,
-0.01936628296971321,
-0.036656077951192856,
0.03831510618329048,
0.06268993020057678,
-0.039793625473976135,
-0.011660939082503319,
-0.039926934987306595,
0.013576420024037361,
0.03152851760387421,
0.02870054356753826,
-0.010585248470306396,
-0.014630059711635113,
0.016136525198817253,
0.015252943150699139,
0.022800832986831665,
-0.037149298936128616,
-0.02766747586429119,
-0.04002371430397034,
0.033204782754182816,
0.011555088683962822,
0.02127240225672722,
0.07416817545890808,
-0.08719249069690704,
-0.022763807326555252,
0.07076076418161392,
-0.08159765601158142,
0.02933606319129467,
0.00800818856805563,
-0.015031500719487667,
0.0005262662889435887,
0.03499852493405342,
0.012801900506019592,
0.01570342294871807,
-0.013821315951645374,
-0.007833492942154408,
-0.031756166368722916,
0.03829333558678627,
0.036475520581007004,
-0.028600584715604782,
0.029021158814430237,
-0.01605338044464588,
0.12199979275465012,
0.022572370246052742,
0.01112282183021307,
0.08655296266078949,
0.026457320898771286,
0.028034882619976997,
-0.02251790091395378,
-0.059294119477272034,
0.03511267900466919,
0.01829967088997364,
-0.08402331173419952,
-0.0005894546629860997,
-0.04775681346654892,
0.0010852232808247209,
-0.051568690687417984,
-0.05889558047056198,
-0.019513769075274467,
0.02338286116719246,
0.006864774972200394,
-0.021477337926626205,
-0.04332558065652847,
-0.007550773210823536,
0.028696727007627487,
-0.026158342137932777,
0.0021211327984929085,
-0.01126678567379713,
-0.022636931389570236,
0.048197295516729355,
0.013912651687860489,
0.02841337025165558,
-0.03197957202792168,
-0.008558579720556736,
-0.0030208746902644634,
-0.0359642431139946,
-0.018044861033558846,
-0.0008100057602860034,
-0.025251735001802444,
0.05000821128487587,
-0.01874508522450924,
-0.0053930385038256645,
0.0037453167606145144,
0.015963289886713028,
0.00008599455759394914,
0.03816182166337967,
0.039764292538166046,
-0.016363542526960373,
0.013422098010778427,
0.01799336075782776,
0.07234323769807816,
-0.03917542099952698,
-0.05669337138533592,
-0.011084451340138912,
-0.06296832114458084,
-0.012858186848461628,
-0.02113526687026024,
0.04561186209321022,
0.005296988878399134,
-0.03756498172879219,
0.053956057876348495,
-0.01549945492297411,
0.03203902766108513,
-0.07596750557422638,
-0.045519374310970306,
-0.044118572026491165,
0.0678471252322197,
0.04614841938018799,
0.00041870339191518724,
0.004241981077939272,
-0.02422924153506756,
-0.050911251455545425,
0.015154493972659111,
-0.027836527675390244,
0.0333603210747242,
-0.04236048832535744,
-0.05202855169773102,
0.0037692920304834843,
-0.0313103012740612,
0.020531892776489258,
0.02574203535914421,
-0.020235329866409302,
-0.020776018500328064,
-0.013860569335520267,
0.006905157584697008,
-0.04160556569695473,
-0.0669095441699028,
0.02546587400138378,
0.057112693786621094,
-0.04935125261545181,
-0.023507097736001015,
-0.0672331154346466,
-0.023082317784428596,
0.010510235093533993,
0.08257181942462921,
0.06256840378046036,
0.005762532819062471,
-0.05286003649234772,
0.03508419543504715,
0.02823212929069996,
-0.025125570595264435,
0.008863952942192554,
0.01751542091369629,
0.026941481977701187,
-0.02285550907254219,
-0.0009762133122421801,
-0.04166853055357933,
0.0011411940213292837,
-0.03724227845668793,
0.03908378258347511,
0.031708985567092896,
-0.030091026797890663,
-0.01390462089329958,
0.029547736048698425,
-0.02156703919172287,
0.05831245332956314,
0.03138066828250885,
0.015562056563794613,
0.06273915618658066,
-0.029588686302304268,
0.02348492108285427,
-0.03162754327058792,
-0.05930077284574509,
0.035367388278245926,
0.021776672452688217,
-0.00008078107930487022,
0.024803096428513527,
0.0491592139005661,
0.03662540391087532,
-0.052044812589883804,
0.07812045514583588,
-0.002964133396744728,
0.04652199521660805,
-0.09516473859548569,
0.002946488792076707,
0.047768108546733856,
-0.013052600435912609,
0.03497656434774399,
-0.026430713012814522,
-0.017934449017047882,
0.03832646831870079,
-0.001136228209361434,
-0.029238779097795486,
-0.03574514016509056,
0.015237564221024513,
0.018540257588028908,
0.002846762537956238,
-0.0010641728295013309,
0.02430020086467266,
0.026514092460274696,
0.00832971092313528,
-0.022961070761084557,
-0.02189367264509201,
-0.010006492026150227,
0.056262921541929245,
0.043068401515483856,
-0.001443154294975102,
-0.02262616902589798,
-0.028165973722934723,
-0.030671851709485054,
0.05873487889766693,
0.03824298828840256,
0.031087582930922508,
-0.008648285642266273,
-0.03581230714917183,
-0.023532241582870483,
0.012683781795203686,
0.025094715878367424,
0.09071346372365952,
-0.046642519533634186,
-0.06173622980713844,
-0.004477613605558872,
-0.06311138719320297,
0.030694283545017242,
0.005882417783141136,
-0.02638426423072815,
0.07831913977861404,
-0.022189823910593987,
0.029862098395824432,
-0.015546833164989948,
0.052380017936229706,
-0.0034579001367092133,
-0.04110949859023094,
-0.00662661949172616,
-0.03481130674481392,
0.00557425944134593,
-0.02738562785089016,
-0.02765943482518196,
-0.05073505640029907,
-0.0046530188992619514,
-0.09708268940448761,
0.014237872324883938,
-0.04476361721754074,
0.009303501807153225,
0.010442111641168594,
0.02129138447344303,
-0.05477774515748024,
0.0484764389693737,
0.021325401961803436,
-0.047800518572330475,
0.03028867021203041,
-0.09687483310699463,
-0.08358635008335114,
-0.04949957877397537,
0.02741277404129505,
0.005557600874453783,
-0.059297386556863785,
-0.03887764364480972,
0.011856678873300552,
-0.010416998527944088,
0.0633658915758133,
-0.002386962529271841,
-0.004134511575102806,
-0.004785508383065462,
-0.0009766282746568322,
-0.08141633868217468,
-0.027217328548431396,
-0.023513300344347954,
0.027797454968094826,
0.06719967722892761,
0.01110558956861496,
0.012970522977411747,
0.00880860723555088,
0.008176125586032867,
0.011517058126628399,
0.011186777614057064,
0.049515336751937866,
0.09036711603403091,
0.019807077944278717,
0.00901887472718954,
-0.0015853301156312227,
-0.03155846521258354,
0.023484373465180397,
0.004909552168101072,
0.022117238491773605,
-0.0105277793481946,
0.07070772349834442,
-0.00979804527014494,
-0.005051334388554096,
-0.004869317170232534,
0.026617273688316345,
0.005270248744636774,
-0.027578778564929962,
-0.030405117198824883,
0.0029415530152618885,
0.036496639251708984,
0.014015384018421173,
-0.04795202240347862,
-0.030153213068842888,
-0.007166902534663677,
0.06700447201728821,
-0.026978207752108574,
0.015800349414348602,
-0.02685699239373207,
0.00704340822994709,
-0.06983565539121628,
0.04460975527763367,
-0.04912770539522171,
0.04333161935210228,
0.010804971680045128,
0.03392450511455536,
-0.05744697153568268,
0.04106197506189346,
0.025850417092442513,
0.04699575528502464,
0.05818398669362068,
-0.010834304615855217,
-0.0023062366526573896,
0.03646300733089447,
-0.030858779326081276,
0.03165755048394203,
0.009734537452459335,
0.015389733016490936,
-0.04595567286014557,
-0.01060487050563097,
0.01583148166537285,
0.049459051340818405,
-0.030846940353512764,
0.017153238877654076,
0.053935706615448,
0.019029196351766586,
-0.00453730346634984,
-0.026176579296588898,
0.024413425475358963,
-0.08213251829147339,
-0.05612548813223839,
-0.04214567691087723,
0.07597627490758896,
-0.04364849999547005,
-0.01622387394309044,
0.00956022646278143,
0.05987616628408432,
-0.004002616740763187,
-0.012177492491900921,
0.019928336143493652,
-0.004206523299217224,
-0.023254327476024628,
0.09764096140861511,
0.05208892002701759,
0.03255048766732216,
0.016952089965343475,
0.018151147291064262,
-0.030873434618115425,
0.039145875722169876,
0.024419676512479782,
0.05849104002118111,
0.025401582941412926,
0.019633673131465912,
-0.039771825075149536,
-0.044847484678030014,
0.037927839905023575,
-0.07064364105463028,
-0.03238574042916298,
0.015603580512106419,
-0.004931928589940071,
-0.01872178539633751,
0.02109418623149395,
-0.03228763863444328,
0.018312513828277588,
0.0005736250896006823,
-0.0185763631016016,
0.03593042492866516,
-0.0010542686795815825,
0.0049424683675169945,
-0.03626285493373871,
0.034841302782297134,
0.02003435045480728,
0.010878408327698708,
-0.0056818220764398575,
0.026560408994555473,
0.07692396640777588,
-0.0636112317442894,
0.01849738322198391,
0.001579758245497942,
0.023779597133398056,
0.009913494810461998,
0.020920393988490105,
0.00837691966444254,
-0.015514272265136242,
-0.013311821967363358,
0.021772073581814766,
-0.023887546733021736,
-0.028360692784190178,
0.016177203506231308,
-0.03054334782063961,
-0.06047585979104042,
-0.028081653639674187,
0.008412030525505543,
-0.0412939228117466,
-0.023211494088172913,
-0.023030593991279602,
-0.03077281080186367,
0.0354156494140625,
-0.03556457534432411,
0.041119400411844254,
0.02042336016893387,
-0.004443289712071419,
-0.007028383668512106,
0.012157661840319633,
-0.003048412036150694,
0.02913559228181839,
0.00966733694076538,
0.003850556444376707,
-0.02749698981642723,
-0.012699843384325504,
-0.010331186465919018,
-0.03137228265404701,
0.014298456721007824,
-0.018683763220906258,
0.008327824994921684,
-0.026025952771306038,
-0.0296919085085392,
0.05512668937444687,
0.027238011360168457,
0.015328891575336456,
-0.009858211502432823,
-0.018185710534453392,
0.037900660187006,
0.03023291938006878,
-0.051858264952898026,
-0.013738106936216354,
-0.050670452415943146,
0.01470055989921093,
-0.0594194121658802,
0.019791224971413612,
-0.013765398412942886,
-0.015720559284090996,
-0.001110666780732572,
0.0485982745885849,
-0.013099290430545807,
0.008633156307041645,
-0.005701314192265272,
0.017367979511618614
] |
<p>Suppose we have a finite , discrete set of orthonormal states $|k\rangle $</p>
<p>We can construct raising and lowering operators intuitively, for example $$a_+ =\sum_{k=1}^nC_{k+1}|k+1\rangle \langle k|$$</p>
<p>However most textbooks begin by defining ladders in terms of the linear combinations of hermitian operators. </p>
<p>How do we get from the above construction to showing that such ladder operators have the form $$a_\pm = \frac{\alpha\pm i\beta}{\sqrt{2}}$$ where $\alpha,\beta$ are hermitian?</p> | g5466 | [
0.02710874192416668,
-0.006666910834610462,
-0.0408981591463089,
-0.0014280240284278989,
0.03592846542596817,
-0.06619289517402649,
-0.00484936498105526,
0.010146524757146835,
0.025556450709700584,
0.023117566481232643,
-0.05079755559563637,
-0.003039885312318802,
0.009784002788364887,
0.02038814127445221,
-0.006209388840943575,
0.0016822952311486006,
0.0009638100164011121,
0.051879603415727615,
0.008369863033294678,
-0.04356381669640541,
-0.060360997915267944,
0.0495712049305439,
0.03560032323002815,
-0.0074285524897277355,
0.05723889544606209,
-0.02787139266729355,
0.030722087249159813,
0.04732057452201843,
-0.020251791924238205,
-0.031530555337667465,
-0.03697054460644722,
-0.04629455879330635,
0.04965989664196968,
0.0561322346329689,
0.009941867552697659,
0.03033597208559513,
0.09398648887872696,
-0.03454642742872238,
0.03805607557296753,
-0.10080182552337646,
-0.003477575723081827,
-0.03553830459713936,
0.02363937348127365,
-0.009778426960110664,
-0.046120110899209976,
-0.033013761043548584,
0.003778628772124648,
0.021526839584112167,
0.004121070262044668,
0.05033107101917267,
0.05285526067018509,
0.018046241253614426,
0.0036010693293064833,
-0.014501955360174179,
-0.01773037388920784,
0.008666325360536575,
-0.0017746114172041416,
-0.02062852680683136,
0.027547406032681465,
-0.0028935798909515142,
-0.003299084957689047,
-0.08871181309223175,
0.009219412691891193,
0.0018754282500594854,
0.03160174936056137,
0.03443684056401253,
0.0010649202158674598,
0.004806759767234325,
-0.0006217975751496851,
-0.006908212788403034,
0.004779329989105463,
-0.07213448733091354,
0.03434832766652107,
-0.05906250700354576,
-0.04457583650946617,
-0.008300534449517727,
0.02304415963590145,
-0.04418335109949112,
0.033895526081323624,
0.0414607934653759,
0.0077919852919876575,
0.013121119700372219,
0.029246404767036438,
0.02990635298192501,
-0.040740542113780975,
0.01595928892493248,
0.02300621010363102,
0.02636365033686161,
-0.0006504140910692513,
0.02842380478978157,
-0.0685400739312172,
-0.027659369632601738,
-0.009374295361340046,
0.04643367975950241,
-0.03658173978328705,
-0.056195326149463654,
-0.072671078145504,
0.018622102215886116,
0.04909072071313858,
0.007089370395988226,
-0.0015720499213784933,
0.02791650779545307,
0.046570777893066406,
-0.0591435432434082,
-0.040185846388339996,
0.02465664967894554,
0.06491740047931671,
-0.060594573616981506,
0.0258343406021595,
0.018889285624027252,
-0.07840397208929062,
0.033699825406074524,
-0.024841859936714172,
-0.052421778440475464,
0.03827570006251335,
0.02781984768807888,
-0.015293639153242111,
0.0025272732600569725,
0.03550395369529724,
0.0006389344343915582,
0.03504316136240959,
0.010682557709515095,
-0.00753499660640955,
0.0902320146560669,
0.032609205693006516,
0.0976024940609932,
-0.03128870204091072,
0.043848223984241486,
0.06814582645893097,
-0.028537863865494728,
0.07042735815048218,
0.024524524807929993,
-0.02568412758409977,
0.005672544240951538,
0.030759261921048164,
0.04610196501016617,
-0.0712951123714447,
-0.022462833672761917,
0.0060506402514874935,
-0.03432708606123924,
-0.021514790132641792,
0.0005624331533908844,
-0.014328908175230026,
0.008996137417852879,
0.041799984872341156,
0.03392582759261131,
0.021993126720190048,
-0.02742326818406582,
-0.021402740851044655,
0.035040657967329025,
0.02153376117348671,
0.056119777262210846,
0.05920138210058212,
-0.017382750287652016,
0.006448641885071993,
-0.02701275609433651,
0.055373985320329666,
-0.012203211896121502,
-0.02808932401239872,
-0.0188397578895092,
0.046760234981775284,
-0.024667037650942802,
0.013648034073412418,
0.0018693585880100727,
0.007404273841530085,
-0.0037865927442908287,
0.003388010198250413,
-0.022178879007697105,
0.011733091436326504,
-0.012322734110057354,
0.06222623586654663,
0.06372962146997452,
0.013924621045589447,
0.08039145916700363,
0.04602262005209923,
0.054612454026937485,
-0.032700542360544205,
-0.03499151021242142,
-0.00505009526386857,
-0.016676029190421104,
0.02915504388511181,
0.004613976459950209,
0.011570187285542488,
0.041220925748348236,
-0.008172099478542805,
0.007845059968531132,
-0.018806302919983864,
-0.03042534925043583,
-0.011040355078876019,
-0.043574780225753784,
0.010279186069965363,
-0.002255939180031419,
0.051671240478754044,
-0.0190444178879261,
0.00805178564041853,
-0.027092482894659042,
0.003591574262827635,
-0.0460689403116703,
-0.007696370128542185,
-0.02069723792374134,
0.027995027601718903,
0.014477142132818699,
0.020125078037381172,
0.005512670148164034,
-0.020450713112950325,
0.10682804882526398,
-0.02474338561296463,
-0.007836687378585339,
-0.025954680517315865,
-0.020609742030501366,
-0.06545393913984299,
-0.07630275189876556,
0.005355248227715492,
-0.006370385643094778,
-0.012427444569766521,
-0.002459123032167554,
0.046288494020700455,
-0.03628550097346306,
-0.0064603304490447044,
-0.034128010272979736,
-0.059043604880571365,
-0.023794420063495636,
-0.02642124518752098,
-0.004363538231700659,
-0.014331336133182049,
-0.001876611146144569,
-0.030897866934537888,
-0.0002339699276490137,
0.02626071497797966,
-0.03559252247214317,
-0.04324117675423622,
-0.04552536457777023,
-0.02174716629087925,
-0.07288387417793274,
-0.002134846057742834,
0.018222831189632416,
0.011707911267876625,
0.0372169129550457,
-0.0027019900735467672,
0.020757945254445076,
0.016034461557865143,
-0.004926315043121576,
0.022475628182291985,
-0.0031323477160185575,
0.02407984621822834,
0.024457581341266632,
0.006026493851095438,
0.06300142407417297,
-0.051736317574977875,
0.08025093376636505,
-0.002480258932337165,
0.048478152602910995,
-0.022260023280978203,
0.04021042212843895,
-0.03170379623770714,
0.012559756636619568,
0.01818721368908882,
0.024419179186224937,
0.04990096390247345,
0.011292765848338604,
-0.003557869466021657,
0.0020871683955192566,
-0.07662908732891083,
-0.008699011988937855,
-0.013195177540183067,
-0.00008545546006644145,
-0.06666100025177002,
-0.023842304944992065,
0.0030257049947977066,
0.05911102145910263,
0.005952924489974976,
-0.003491366049274802,
0.022865038365125656,
0.007209073752164841,
-0.030256927013397217,
-0.06621870398521423,
0.00016620599490124732,
-0.017312757670879364,
0.03006664663553238,
-0.008706603199243546,
-0.01629706658422947,
-0.012331566773355007,
-0.043780263513326645,
-0.0012291260063648224,
-0.02996908128261566,
-0.02619890123605728,
0.035197965800762177,
-0.03353435546159744,
-0.012886236421763897,
0.05125299468636513,
0.0009712427854537964,
0.014305882155895233,
-0.007601822726428509,
-0.017819605767726898,
-0.0424903929233551,
0.017514927312731743,
-0.007981522008776665,
-0.004938915837556124,
-0.030080700293183327,
0.05668581277132034,
-0.014544558711349964,
-0.008053797297179699,
0.008414224721491337,
-0.03835615888237953,
0.026481181383132935,
0.021911775693297386,
-0.012532267719507217,
-0.008751998655498028,
-0.03781876713037491,
0.03423246368765831,
0.05049867182970047,
0.01591610535979271,
-0.01750628650188446,
-0.04160887002944946,
0.02493719942867756,
-0.00023306858201976866,
-0.025978708639740944,
0.008893554098904133,
0.024538272991776466,
0.026082249358296394,
-0.07130495458841324,
-0.05489884689450264,
-0.03969913348555565,
-0.019556380808353424,
0.029881447553634644,
-0.011056553572416306,
-0.061639513820409775,
0.106923907995224,
-0.03213198482990265,
-0.07078198343515396,
0.05523001775145531,
-0.018146472051739693,
0.056223273277282715,
0.017270930111408234,
-0.04958892613649368,
-0.04238024353981018,
-0.027711721137166023,
-0.041231755167245865,
0.04021644592285156,
0.005531917326152325,
-0.015229973942041397,
0.012312005273997784,
-0.0661659762263298,
0.006013502832502127,
-0.014183558523654938,
0.018344471231102943,
-0.03172453120350838,
0.05268564820289612,
-0.01296922005712986,
-0.057484231889247894,
-0.036015480756759644,
-0.01261468417942524,
0.03143765404820442,
-0.019712259992957115,
-0.047083284705877304,
0.045337628573179245,
0.036661297082901,
0.04800822213292122,
-0.02493477426469326,
-0.0009211084106937051,
0.020369483157992363,
-0.014204093255102634,
0.022115617990493774,
-0.03685452416539192,
0.029805531725287437,
0.014560073614120483,
0.014189603738486767,
0.10285684466362,
-0.006197555921971798,
0.04788951575756073,
0.0094926618039608,
0.011645626276731491,
0.06047926843166351,
0.0429399199783802,
-0.00042838696390390396,
-0.013625881634652615,
0.004744094796478748,
-0.01698971539735794,
0.007116856053471565,
0.05479876324534416,
0.02368728071451187,
-0.02261013351380825,
0.00906122475862503,
-0.0010193639900535345,
0.06327881664037704,
0.030131366103887558,
0.003356931498274207,
0.01124768890440464,
0.0000510596510139294,
-0.036002449691295624,
-0.051803965121507645,
-0.06971699744462967,
0.0577579066157341,
0.0083931190893054,
0.008116665296256542,
0.02744484320282936,
0.03537506237626076,
0.02359146997332573,
-0.03323085606098175,
0.08013122528791428,
-0.06595342606306076,
-0.018253657966852188,
0.005255328956991434,
-0.01978624239563942,
0.029750755056738853,
0.06276728212833405,
0.039815496653318405,
-0.008552531711757183,
0.03397621959447861,
-0.03330274298787117,
-0.02007579430937767,
0.007817677222192287,
0.0016698711551725864,
0.009822043590247631,
0.007891414687037468,
0.013343174941837788,
0.09629810601472855,
-0.06926775723695755,
-0.032221317291259766,
0.002998023759573698,
-0.013263082131743431,
0.048618149012327194,
0.003388075390830636,
-0.032605674117803574,
0.04988463222980499,
0.018552793189883232,
-0.022585514932870865,
-0.013683554716408253,
-0.0017365155508741736,
-0.040963247418403625,
-0.004785110242664814,
0.010597746819257736,
-0.008689100854098797,
0.006841349881142378,
0.003918673377484083,
-0.02815246395766735,
-0.000060945934819756076,
-0.0008848878787830472,
-0.03623773157596588,
-0.012566106393933296,
-0.007802922744303942,
-0.014338662847876549,
-0.03205036371946335,
0.018119266256690025,
0.055728182196617126,
0.030824391171336174,
-0.023428328335285187,
-0.05296667292714119,
-0.019161926582455635,
0.04465904459357262,
-0.022158049046993256,
0.044609591364860535,
0.0416598804295063,
-0.08185906708240509,
0.06311982125043869,
-0.030391167849302292,
-0.03393390774726868,
0.00867000874131918,
-0.0004796455323230475,
-0.008563020266592503,
-0.0035120458342134953,
-0.026657117530703545,
0.010663735680282116,
-0.05291800573468208,
0.010399872437119484,
0.030701851472258568,
-0.04467618465423584,
0.07449832558631897,
-0.002649524714797735,
-0.05381859466433525,
-0.004037736915051937,
-0.01121609564870596,
-0.030233582481741905,
-0.03545935079455376,
-0.03110242821276188,
-0.01729569025337696,
0.04996722564101219,
-0.018249865621328354,
-0.012071417644619942,
0.0004718074924312532,
-0.0018251687288284302,
-0.026740266010165215,
-0.05297663435339928,
-0.011235521174967289,
-0.03775527700781822,
0.056598205119371414,
-0.00015428882034029812,
-0.08630123734474182,
-0.04606661573052406,
0.016920238733291626,
-0.0075873020105063915,
0.0314968042075634,
0.01895391009747982,
0.02874097228050232,
-0.07967909425497055,
-0.019927164539694786,
0.015419412404298782,
0.010113301686942577,
0.06150472164154053,
0.04323068633675575,
-0.03852584585547447,
-0.021397557109594345,
0.020238464698195457,
0.022165536880493164,
0.02230328693985939,
-0.022413616999983788,
0.0637412890791893,
0.026554759591817856,
0.020650479942560196,
0.0020266929641366005,
0.0036959454882889986,
-0.03762016445398331,
-0.007053890731185675,
-0.02942541427910328,
0.011430102400481701,
-0.045305728912353516,
-0.004762954078614712,
-0.01604091003537178,
-0.02080083265900612,
-0.028190841898322105,
-0.002910301322117448,
-0.04200940951704979,
0.013978257775306702,
-0.061580244451761246,
-0.02851833961904049,
0.08630126714706421,
-0.029938383027911186,
-0.014009295031428337,
-0.01591188833117485,
0.03227975592017174,
0.002403365448117256,
-0.003718462772667408,
-0.04853014275431633,
-0.062164463102817535,
-0.007170748431235552,
0.03635254502296448,
-0.01172246690839529,
0.004633480217307806,
-0.015890903770923615,
0.020968468859791756,
-0.04951779544353485,
-0.005450730212032795,
-0.01113237626850605,
0.09597215056419373,
0.013592447154223919,
-0.04434965178370476,
0.0018176578450948,
-0.05233302712440491,
0.030248526483774185,
0.04916136711835861,
-0.06529426574707031,
0.02553390897810459,
-0.07669366896152496,
-0.027372941374778748,
-0.05047944560647011,
-0.03859318792819977,
0.04451746121048927,
-0.010340549051761627,
-0.03341691568493843,
0.03079562447965145,
0.06846064329147339,
-0.00769526232033968,
0.013773098587989807,
-0.0010360459564253688,
0.04372537508606911,
0.01827249862253666,
0.003710836172103882,
0.0890144482254982,
0.02857733517885208,
0.034839991480112076,
0.021920543164014816,
0.02636328712105751,
0.01051388494670391,
0.03476528823375702,
-0.018233777955174446,
0.03675539046525955,
-0.0694957748055458,
-0.07647909969091415,
0.016123691573739052,
-0.03870779275894165,
-0.0019455200526863337,
0.01782909408211708,
-0.0010767611674964428,
0.04377361759543419,
-0.04259837791323662,
-0.006946181412786245,
-0.043761756271123886,
-0.041662588715553284,
0.008816908113658428,
0.06275659054517746,
-0.01713518239557743,
0.07196702063083649,
-0.0714874416589737,
-0.028802456334233284,
0.005848105996847153,
0.033051829785108566,
0.045528262853622437,
0.02810518443584442,
0.045675404369831085,
0.03002258762717247,
0.013739106245338917,
-0.034025173634290695,
0.0071707433089613914,
0.01962902583181858,
-0.0350753590464592,
0.06595977395772934,
-0.01696820743381977,
0.004349973052740097,
0.03121311031281948,
-0.005830509588122368,
0.04063815250992775,
0.01231150608509779,
0.018176734447479248,
0.020488664507865906,
-0.008838225156068802,
-0.08073348551988602,
-0.04442115128040314,
0.09497098624706268,
-0.036299798637628555,
0.006884530186653137,
0.023722602054476738,
0.00042817139183171093,
0.015309007838368416,
-0.042854875326156616,
-0.011560041457414627,
-0.009720067493617535,
0.02681766264140606,
-0.03843988478183746,
0.02004489302635193,
0.023982346057891846,
-0.009559527039527893,
0.025575773790478706,
-0.032797954976558685,
-0.001626953948289156,
-0.024142161011695862,
0.038560714572668076,
-0.057758793234825134,
0.05033133551478386,
-0.043695054948329926,
0.06212297081947327,
0.017379898577928543,
0.05196206271648407,
0.01892407052218914,
0.010401143692433834,
0.012247578240931034,
-0.008012779988348484,
0.001584867131896317,
0.028795868158340454,
-0.09287290275096893,
0.03157736361026764,
0.04801285266876221,
-0.025422783568501472,
-0.0375434011220932,
-0.017947359010577202,
-0.056724000722169876,
-0.05821533128619194,
0.036083463579416275,
-0.013230087235569954,
-0.04318445920944214,
-0.04693024605512619,
0.021714426577091217,
-0.019220639020204544,
-0.007211592048406601,
-0.017217930406332016,
-0.0044965557754039764,
0.03592352941632271,
-0.05385268107056618,
-0.021865932270884514,
0.00983410980552435,
0.0006781915435567498,
0.008578845299780369,
-0.053063079714775085,
-0.020895665511488914,
-0.0137991514056921,
-0.00008773371519055218,
-0.0007206934969872236,
0.018701232969760895,
0.06152685731649399,
-0.07312645763158798,
-0.028787247836589813,
0.04451199993491173,
0.020287802442908287,
0.03153475001454353,
-0.09320677816867828,
0.0425778292119503,
0.012824362143874168,
0.028668789193034172,
0.005616528447717428,
0.03860701620578766,
-0.024223772808909416,
0.027940426021814346,
-0.036694854497909546,
-0.017963435500860214,
0.010330988094210625,
-0.012582124210894108,
-0.013237839564681053,
-0.011162023060023785,
0.0074136508628726006,
-0.05141301080584526,
-0.009347818791866302,
0.02370813488960266,
-0.04585963487625122,
-0.04734763503074646,
0.010668902657926083,
0.01785765215754509,
-0.028989125043153763,
0.005548832472413778,
-0.0025589626748114824,
-0.005123477894812822,
-0.040697742253541946,
0.00563972070813179,
-0.027381377294659615,
-0.003394774394109845,
0.05610308796167374,
0.06587260961532593,
-0.023597978055477142,
-0.05962212383747101,
0.0558108426630497,
0.03060954622924328,
-0.03653382137417793,
0.023384273052215576,
-0.020104793831706047,
0.019314436241984367,
-0.053041934967041016,
-0.04278431832790375,
0.04430556297302246,
-0.026135968044400215,
0.03739272430539131,
-0.07671250402927399,
0.04606612026691437,
-0.039051029831171036,
-0.041781000792980194,
-0.066155344247818,
0.02355397492647171,
-0.028667133301496506,
0.01520560309290886,
-0.008127443492412567,
0.0033859831746667624,
0.06938902288675308,
0.006000084802508354,
-0.03725283965468407,
0.008781567215919495,
0.010655270889401436,
0.030054669827222824,
0.047213561832904816,
-0.002335786586627364,
-0.0479196272790432,
-0.0020942874252796173,
0.021313754841685295,
0.009806782007217407,
-0.04881149157881737,
0.04770369082689285,
0.05682094022631645,
0.011299483478069305,
0.04063982889056206,
0.005117436870932579,
0.037817347794771194,
0.027863750234246254,
0.02161351405084133,
0.04678655043244362,
-0.0290786512196064,
-0.022021345794200897,
-0.040804944932460785,
0.0028595151379704475,
-0.051491878926754,
0.010258535854518414,
-0.048060886561870575,
-0.023586474359035492
] |
<p>What equation would give me the answer to the question, "If i have a cup of water at a tempature of say boiling, how long would that cup of water take to cool off compared to say half that size of a cup of water." So the volume is in half. Its a general question I am just looking for where to start.</p> | g5467 | [
0.0734567791223526,
0.00012279785005375743,
0.02728218212723732,
-0.014757698401808739,
-0.016621802002191544,
-0.051140572875738144,
0.059385862201452255,
-0.00855990219861269,
-0.028954418376088142,
-0.011962242424488068,
-0.05171069875359535,
0.014136345125734806,
0.014674917794764042,
0.031123720109462738,
0.06619150191545486,
-0.03686251863837242,
-0.021722208708524704,
-0.049909140914678574,
-0.04006032273173332,
0.04847261682152748,
0.00018890683713834733,
-0.03136550635099411,
0.0011411779560148716,
-0.03781283274292946,
-0.08518524467945099,
-0.08259300887584686,
-0.007804548367857933,
0.06224141642451286,
-0.037261269986629486,
0.008454677648842335,
-0.0989018976688385,
0.04308587685227394,
0.024754369631409645,
0.026850614696741104,
-0.042534876614809036,
-0.03186865150928497,
0.06881822645664215,
0.0008246336947195232,
0.027254505082964897,
-0.02864411100745201,
0.010040661320090294,
-0.02903200313448906,
0.008200041018426418,
0.020428666844964027,
0.08561813831329346,
0.025948496535420418,
-0.05238686874508858,
0.02774638868868351,
-0.06859204918146133,
-0.00638402858749032,
0.005325829144567251,
0.04176665470004082,
0.01187458448112011,
-0.035272810608148575,
-0.11848174780607224,
-0.0027012445498257875,
0.014179222285747528,
-0.012342832051217556,
0.008349903859198093,
0.053533416241407394,
0.0024928958155214787,
-0.031670812517404556,
-0.03875155374407768,
0.0025105150416493416,
0.03991946950554848,
-0.023539477959275246,
-0.010498705320060253,
-0.036527954041957855,
-0.006238049827516079,
0.06432445347309113,
-0.01579257845878601,
-0.04051433503627777,
0.006966612301766872,
-0.03944636508822441,
-0.07691343873739243,
-0.04719360172748566,
0.03096082992851734,
-0.004314732272177935,
0.010827509686350822,
0.012975298799574375,
-0.06296909600496292,
-0.0023164963349699974,
0.04304235428571701,
0.0008536702953279018,
0.05928708240389824,
-0.007602772209793329,
0.006168777123093605,
-0.0029571368359029293,
-0.06794454902410507,
0.022711291909217834,
-0.05489831045269966,
-0.005054043140262365,
0.044411011040210724,
-0.00020973329083062708,
0.05236168950796127,
-0.03222222998738289,
-0.013043277896940708,
-0.028466615825891495,
-0.019366584718227386,
0.07714111357927322,
0.04450170323252678,
-0.007217611186206341,
0.02162916027009487,
-0.026080815121531487,
-0.00284929433837533,
-0.011829356662929058,
-0.0505201518535614,
-0.010028754360973835,
-0.03272801265120506,
0.00006351510819513351,
-0.03110690973699093,
-0.04792676866054535,
-0.049031492322683334,
0.027325449511408806,
-0.02572583593428135,
-0.030527474358677864,
0.01331411488354206,
-0.005986287258565426,
-0.005089143291115761,
-0.0403195321559906,
0.01574750617146492,
0.03754885122179985,
-0.03175181522965431,
0.02084212191402912,
0.0730338990688324,
-0.038207706063985825,
-0.04468405619263649,
0.04613790661096573,
0.01370805874466896,
0.05465482920408249,
0.02779489755630493,
0.025955772027373314,
-0.010622578673064709,
0.0003483208129182458,
0.05137810856103897,
0.07360102236270905,
-0.008214815519750118,
0.030010489746928215,
-0.018814804032444954,
-0.01859038509428501,
0.012265749275684357,
-0.007810002192854881,
-0.022271189838647842,
-0.01361208874732256,
-0.04673623666167259,
0.03966812789440155,
0.005638331174850464,
-0.047466475516557693,
0.012022435665130615,
-0.013193602673709393,
-0.03587121516466141,
0.0192714836448431,
0.05460616201162338,
-0.019775358960032463,
0.009261013939976692,
-0.01746051199734211,
0.02254454791545868,
-0.05592396482825279,
0.07197297364473343,
-0.00928746722638607,
-0.022870464250445366,
0.02909807302057743,
0.009022191166877747,
0.06948964297771454,
-0.08727850019931793,
0.06551459431648254,
-0.017455823719501495,
-0.02171318791806698,
0.0006915913545526564,
-0.07765501737594604,
-0.046060655266046524,
0.053778380155563354,
-0.004967099521309137,
0.04905158281326294,
0.05302279815077782,
0.007885636761784554,
0.06629486382007599,
0.011726009659469128,
0.0002701499324757606,
0.007887362502515316,
0.006199794355779886,
0.025173703208565712,
0.01805420033633709,
-0.03519221767783165,
0.017529752105474472,
0.028687285259366035,
0.06739261001348495,
0.011976233683526516,
-0.020290818065404892,
0.008134945295751095,
-0.022662097588181496,
-0.03715602681040764,
0.005651567596942186,
-0.00024360328097827733,
-0.03173370286822319,
-0.05274175852537155,
0.012686376459896564,
0.010155212134122849,
-0.001818526303395629,
0.008833043277263641,
-0.008208602666854858,
-0.04845445975661278,
0.03357979655265808,
0.0034038820303976536,
0.018392901867628098,
0.018876049667596817,
-0.001053080428391695,
0.027115173637866974,
0.047316983342170715,
-0.030132999643683434,
0.023614339530467987,
0.003429635427892208,
0.010775742121040821,
0.04507360979914665,
-0.04169507324695587,
0.03906987980008125,
0.00020091708574909717,
0.022976145148277283,
-0.042515285313129425,
0.03896503150463104,
0.008011986501514912,
0.04898744821548462,
-0.035600610077381134,
-0.0099275978282094,
-0.04203125089406967,
-0.01825588569045067,
-0.003145003691315651,
-0.047697894275188446,
-0.07603570073843002,
0.049275945872068405,
-0.02154964581131935,
0.04845743626356125,
0.03739246353507042,
-0.047179676592350006,
0.01811334490776062,
0.06143749877810478,
0.013904908671975136,
0.03391597047448158,
-0.005700279958546162,
0.02434934861958027,
0.02288164757192135,
0.060868777334690094,
-0.02956765703856945,
0.05730155110359192,
0.013347194530069828,
-0.0198541097342968,
-0.011242176406085491,
-0.07513581216335297,
0.0659639984369278,
0.0667463093996048,
-0.04924280196428299,
-0.01676863431930542,
-0.026240261271595955,
0.0012552393600344658,
-0.03249002620577812,
-0.027448369190096855,
-0.04097327962517738,
-0.019387466832995415,
-0.0314115546643734,
-0.0017766691744327545,
-0.017671238631010056,
0.007248694077134132,
0.03799677640199661,
-0.0003294924972578883,
-0.04019860550761223,
-0.027337728068232536,
-0.03567409887909889,
0.019939996302127838,
0.05078369751572609,
0.07497376203536987,
0.06035228446125984,
0.027492884546518326,
-0.013366460800170898,
0.04372931644320488,
-0.003622286254540086,
-0.05280611291527748,
0.008761104196310043,
-0.03335263207554817,
0.032810959964990616,
0.01879015751183033,
-0.005234910640865564,
-0.018468942493200302,
-0.05449063330888748,
0.10692501068115234,
0.03524871543049812,
-0.05949749797582626,
0.06210483983159065,
0.040760401636362076,
0.041612908244132996,
-0.01217113807797432,
-0.01181266363710165,
0.02709794230759144,
0.006164310034364462,
0.006518029607832432,
0.05740397050976753,
0.031643323600292206,
0.018720092251896858,
-0.03579314053058624,
0.006042126566171646,
-0.030290668830275536,
-0.004818314220756292,
-0.03846731409430504,
-0.020947828888893127,
0.008603585883975029,
-0.00751010375097394,
-0.003724088193848729,
-0.014718914404511452,
-0.022612029686570168,
-0.04135339334607124,
-0.011210495606064796,
-0.015968136489391327,
0.0178946852684021,
0.02550949715077877,
-0.027671080082654953,
-0.0178187545388937,
-0.008439789526164532,
-0.0102920550853014,
-0.027378130704164505,
0.036186203360557556,
-0.012051478959619999,
-0.03302517160773277,
-0.03650832176208496,
0.03851603716611862,
0.02442450448870659,
-0.02329256944358349,
-0.026497967541217804,
-0.005229990929365158,
-0.00923288892954588,
-0.013866487890481949,
-0.006199423223733902,
-0.006645962595939636,
0.035347677767276764,
-0.07876469194889069,
0.0072259134612977505,
0.0055604903027415276,
-0.014558698050677776,
-0.008328399620950222,
0.02306780405342579,
-0.016512930393218994,
0.034768473356962204,
-0.0011242041364312172,
-0.05840461701154709,
-0.02154535800218582,
0.02879142388701439,
-0.02930772490799427,
-0.02905021794140339,
-0.014600032940506935,
0.011237356811761856,
-0.02516668662428856,
-0.02795359492301941,
-0.019809992983937263,
-0.04819792881608009,
0.002914313692599535,
-0.038786880671978,
0.02756386250257492,
0.009963911026716232,
0.09070732444524765,
-0.01875227317214012,
0.007158447988331318,
0.031174302101135254,
0.01349718775600195,
-0.016543524339795113,
0.03500771149992943,
0.018293943256139755,
-0.04443036764860153,
-0.037730176001787186,
-0.00508288387209177,
0.058771949261426926,
-0.04566899687051773,
-0.0010806359350681305,
0.009580018930137157,
-0.028277406468987465,
-0.0019670098554342985,
-0.0076146540232002735,
0.02214491181075573,
0.03574894741177559,
-0.006001794710755348,
-0.0030651616398245096,
-0.056925006210803986,
0.04301130399107933,
0.03168269246816635,
0.004875206388533115,
0.03950872644782066,
-0.0131267374381423,
-0.041461218148469925,
-0.069757841527462,
-0.004387410823255777,
0.004064430948346853,
0.06264625489711761,
-0.02816011570394039,
0.06331692636013031,
-0.011439815163612366,
-0.003222975879907608,
0.02737382985651493,
0.01789393648505211,
0.03683479130268097,
-0.0032783704809844494,
0.014658020809292793,
-0.04522518441081047,
-0.04222164675593376,
-0.020900284871459007,
-0.01714862883090973,
0.030073529109358788,
-0.025347163900732994,
-0.03759632632136345,
0.010611500591039658,
0.03718523681163788,
-0.05546785518527031,
0.03146189823746681,
-0.03049345687031746,
0.023372821509838104,
0.05063214525580406,
-0.0027248261030763388,
-0.013419557362794876,
-0.03356869891285896,
-0.014618865214288235,
-0.02250511571764946,
-0.01346991304308176,
0.047635771334171295,
0.017561841756105423,
-0.04327401891350746,
-0.018328258767724037,
-0.04531018063426018,
0.0429314523935318,
-0.007260140497237444,
0.033974163234233856,
0.02878836914896965,
-0.04230215772986412,
-0.018104124814271927,
-0.045670002698898315,
0.02583356387913227,
-0.026872970163822174,
-0.019324500113725662,
0.06607203930616379,
-0.0217242781072855,
0.003583252429962158,
0.007234577089548111,
0.040530089288949966,
-0.04739495739340782,
-0.019460493698716164,
-0.04549624025821686,
0.015329016372561455,
-0.037984449416399,
0.03411421552300453,
-0.008895587176084518,
0.04354498162865639,
0.04006074368953705,
-0.05285497009754181,
-0.03323812782764435,
-0.04945419356226921,
-0.015811778604984283,
0.07135914266109467,
-0.06654449552297592,
-0.0345781147480011,
-0.06406809389591217,
0.03159112483263016,
0.01303134672343731,
0.01149276364594698,
-0.022722318768501282,
0.04417301341891289,
0.012558148242533207,
-0.03473999723792076,
-0.039837226271629333,
0.01297434326261282,
-0.005286272615194321,
-0.13306739926338196,
0.04442810267210007,
-0.031795352697372437,
-0.08436271548271179,
0.06107720360159874,
-0.024441616609692574,
0.05467360094189644,
-0.008675630204379559,
0.06992493569850922,
0.038409266620874405,
0.02185932733118534,
0.016185369342565536,
0.01593904383480549,
0.062088411301374435,
0.025954658165574074,
-0.012381342239677906,
0.014996428042650223,
-0.009917551651597023,
0.039358530193567276,
0.031024329364299774,
0.05099017545580864,
-0.002105653053149581,
0.040914785116910934,
0.034184906631708145,
-0.021041106432676315,
0.00836204644292593,
0.0015492028323933482,
0.04650292545557022,
0.010723219253122807,
-0.018286433070898056,
-0.02793971821665764,
-0.023654071614146233,
-0.055588942021131516,
0.04574048891663551,
0.02258237451314926,
0.027852943167090416,
0.06331689655780792,
-0.045697376132011414,
-0.026436245068907738,
-0.008750093169510365,
0.026443898677825928,
-0.028171971440315247,
0.014544326812028885,
-0.0016772920498624444,
0.06544941663742065,
0.08773967623710632,
0.026018112897872925,
0.07438512146472931,
0.057199981063604355,
0.04346119984984398,
-0.046629488468170166,
0.024395206943154335,
0.0027745112311095,
0.02012796327471733,
0.041536275297403336,
0.05480147525668144,
-0.035704903304576874,
0.0005021782126277685,
0.021382737904787064,
0.0015389235923066735,
-0.0016514919698238373,
-0.06649929285049438,
0.0006064372137188911,
0.037475068122148514,
-0.06114355847239494,
-0.010773111134767532,
0.03059282712638378,
0.01731766387820244,
-0.0012906990014016628,
-0.08139288425445557,
0.019553547725081444,
-0.05398166924715042,
-0.010895323008298874,
0.022840747609734535,
-0.018678121268749237,
0.01422270480543375,
0.007905096746981144,
0.0211928877979517,
0.04758504033088684,
0.0066963182762265205,
-0.004000535700470209,
-0.04861104488372803,
-0.010895046405494213,
0.005015640985220671,
0.04107839614152908,
0.020220253616571426,
0.009157009422779083,
0.0418115109205246,
0.018736768513917923,
0.05664323270320892,
-0.042938653379678726,
0.014932709746062756,
-0.002588799223303795,
0.009959539398550987,
0.01543927937746048,
0.01836106926202774,
0.006383970845490694,
0.03145722672343254,
0.005216620862483978,
-0.03792213648557663,
-0.10132776945829391,
-0.0174159687012434,
-0.005573940929025412,
0.03419532626867294,
-0.006881633773446083,
-0.023443050682544708,
-0.007997770793735981,
0.02050452120602131,
-0.0840349942445755,
-0.011135793291032314,
0.029441092163324356,
0.04085530340671539,
-0.05566616728901863,
0.01783168688416481,
0.04373141750693321,
-0.022959953173995018,
0.028819400817155838,
-0.05061497911810875,
0.007077966816723347,
0.02439352683722973,
0.005947418976575136,
-0.0011538127437233925,
0.027054719626903534,
-0.01937984861433506,
0.00959787517786026,
-0.0096582667902112,
0.0019817145075649023,
-0.041092317551374435,
-0.042697980999946594,
0.018267763778567314,
0.0020455007907003164,
0.01654951088130474,
0.017036138102412224,
0.007369792554527521,
-0.00018936880223918706,
0.03599470108747482,
0.022149180993437767,
0.028002195060253143,
-0.024766823276877403,
0.038465213030576706,
0.040196359157562256,
0.010878819972276688,
-0.014641780406236649,
-0.020872611552476883,
-0.07071826606988907,
-0.013479653745889664,
-0.01922994665801525,
0.0458274744451046,
-0.0019114024471491575,
-0.013840696774423122,
-0.012133555486798286,
0.002880035899579525,
0.017812825739383698,
0.04757610708475113,
-0.03416839614510536,
0.009780867025256157,
-0.08719335496425629,
0.008971989154815674,
-0.039957739412784576,
0.08942494541406631,
0.03812780603766441,
-0.007409145124256611,
0.03966759517788887,
0.02749551087617874,
-0.002245236886665225,
0.04077094420790672,
-0.05168095976114273,
-0.01115808542817831,
0.008738324046134949,
-0.028800837695598602,
0.036335378885269165,
-0.015118954703211784,
0.037368856370449066,
0.018257776275277138,
0.06157052889466286,
-0.03269949182868004,
-0.04783447086811066,
0.030906593427062035,
0.01727631501853466,
-0.016292307525873184,
-0.0004164724668953568,
0.004608203656971455,
-0.007754091173410416,
-0.08230214565992355,
-0.020232774317264557,
0.0050140563398599625,
0.003947307821363211,
-0.03888837620615959,
0.03498294949531555,
-0.029850104823708534,
0.014654782600700855,
-0.02615957334637642,
-0.02188555896282196,
-0.013931069523096085,
0.03694805130362511,
-0.022249266505241394,
0.00034069098182953894,
0.01886841654777527,
0.03379540517926216,
0.013522199355065823,
0.007592430338263512,
0.02493676356971264,
-0.05882110446691513,
0.05707661062479019,
-0.07570628821849823,
-0.017294788733124733,
-0.03501049429178238,
-0.0373048335313797,
-0.00776962423697114,
0.028072381392121315,
0.06833095848560333,
0.0281878300011158,
-0.024772120639681816,
0.045363351702690125,
-0.01343032531440258,
-0.025042230263352394,
0.0021632888820022345,
-0.02699645794928074,
-0.10263721644878387,
-0.0014172467635944486,
-0.0031793194357305765,
-0.02759638801217079,
0.0256252009421587,
0.06700797379016876,
-0.01850801147520542,
0.005160884466022253,
-0.004804447293281555,
0.016874443739652634,
0.005900043062865734,
-0.013519598171114922,
0.053536273539066315,
0.03221433609724045,
0.00468083843588829,
0.0336296521127224,
-0.014411586336791515,
0.08152355998754501,
0.028307946398854256,
0.06475167721509933,
-0.014858142472803593,
-0.038767896592617035,
0.04901503399014473,
-0.020183639600872993,
-0.0005284943617880344,
-0.021614203229546547,
0.0019627949222922325,
-0.011018479242920876,
0.002047494985163212,
0.053402625024318695,
-0.010169715620577335,
0.002659300807863474,
-0.037092484533786774,
-0.057588640600442886,
-0.04472591355443001,
0.025258367881178856,
-0.06945647299289703,
-0.06948109716176987,
-0.04186377301812172,
0.0018950247904285789,
-0.07698935270309448,
0.011877135373651981,
-0.028580866754055023,
-0.06693969666957855,
0.003916338086128235,
-0.019925542175769806,
0.004523991607129574,
0.006337826605886221,
0.020003998652100563,
0.0012011229991912842,
0.027322640642523766,
0.06401076167821884,
0.03131430223584175,
0.05623307451605797,
-0.0028056022711098194,
-0.0027317903004586697,
0.028459753841161728,
-0.000581147673074156,
-0.008610628545284271,
0.019729137420654297,
-0.021815482527017593,
0.007243351079523563,
-0.026166612282395363,
-0.035896800458431244,
0.048840202391147614,
0.00839989073574543,
-0.0757732018828392,
-0.03273019567131996,
0.02084863930940628,
-0.007357354275882244,
-0.0008683225023560226,
0.021045684814453125,
-0.02414463460445404,
-0.02785210683941841,
0.0017838113708421588,
-0.05832255631685257,
-0.011032059788703918,
-0.052176397293806076,
0.06508676707744598,
0.035349197685718536,
0.050011295825242996,
0.01729111187160015,
-0.006174726411700249,
-0.040389128029346466,
-0.04877817630767822
] |
<p>I've read the definition of the electromagnetic field tensor to be
\begin{equation}F^{\mu\nu}\equiv\begin{pmatrix}0&E_x&E_y&E_z\\-E_x&0&B_z&-B_y\\-E_y&-B_z&0&B_x\\-E_z&B_y&-B_x&0\end{pmatrix}\hspace{0.5in}(\dagger)\end{equation}
in <em>Introduction to Electrodynamics</em> by David Griffiths, or as
$$F_{\mu\nu}\equiv\begin{pmatrix}0&-E_x&-E_y&-E_z\\E_x&0&B_z&-B_y\\E_y&-B_z&0&B_x\\E_z&B_y&-B_x&0\end{pmatrix}$$
on the <em><a href="http://arxiv.org/abs/gr-qc/9712019" rel="nofollow">Lecture Notes on GR</a></em> by Sean Carroll, which I know to be consistent via ${F_{\mu\nu}=\eta_{\mu\alpha}F^{\alpha\beta}\eta_{\beta\nu}}$ where the metric $\eta_{\rho\sigma}$ has a (-+++) signature.</p>
<p>However <a href="http://en.wikipedia.org/wiki/Electromagnetic_tensor" rel="nofollow">on Wikipedia</a> and other sources (sorry I can't remember) they use a (+---) signature and they define the EM tensor to be the negative of ${(\dagger)}$.</p>
<p>These are my thoughts about it:
The antisymmetry $F^{\mu\nu}=-F^{\nu\mu}$ may point out that it's just an unfortunate mix of index letters and that for the sources notation to be consistent, either the first two or Wikipedia should change $\mu\nu$ to $\nu\mu$. If not the case, the properties seem to be the same; at first I thought the inner product would pop out a minus sign of difference, but it of course didn't happen, and as for other entities I've worked with, e. g. the 4-velocity, though the metric signature can change, the contravariant vector is the same in either case. However again, I've read the stress-energy tensor does change sign depending on the signature.</p>
<p>So is the signature of the metric involved in the definition of ${F^{\mu\nu}}$ or any tensor whatsoever? If so, how can I know what signature is involved? or if not, what's the matter with the minus sign difference on the definitions?</p> | g5468 | [
-0.0002279041218571365,
-0.0159731674939394,
-0.020980268716812134,
0.022711871191859245,
0.07194314152002335,
0.01521308533847332,
0.08511155843734741,
-0.002564388792961836,
-0.044562775641679764,
-0.04867124557495117,
-0.00014068666496314108,
0.0010428096866235137,
0.045446280390024185,
-0.08310496807098389,
0.026676476001739502,
-0.025631776079535484,
0.06436678022146225,
-0.04281938076019287,
0.0588577464222908,
-0.006101054139435291,
-0.05235084891319275,
0.08144428580999374,
0.010358523577451706,
-0.023358052596449852,
0.005147532559931278,
-0.007259777281433344,
0.06497222185134888,
-0.02948685921728611,
-0.04019508138298988,
-0.04448122903704643,
0.06338333338499069,
0.01472451537847519,
0.07484924793243408,
-0.09112933278083801,
-0.04973338544368744,
-0.003060703631490469,
0.05139230936765671,
0.10101132094860077,
0.016335373744368553,
0.05983542278409004,
0.0520741306245327,
0.0019780704751610756,
0.013353747315704823,
0.011983565054833889,
0.001853516441769898,
-0.0037986417300999165,
-0.025016941130161285,
0.02232317626476288,
-0.05030294135212898,
0.03633348271250725,
0.050273455679416656,
0.025661777704954147,
0.048241063952445984,
0.00036410472239367664,
0.01948472671210766,
0.05491776019334793,
0.031236445531249046,
-0.003434543265029788,
0.008131434209644794,
-0.0044074952602386475,
0.00028735038358718157,
-0.033701930195093155,
-0.02140715904533863,
0.00888003222644329,
0.009532484225928783,
-0.053181979805231094,
-0.05048047751188278,
-0.027668405324220657,
0.049750808626413345,
0.02766198106110096,
0.029246656224131584,
-0.04200274497270584,
0.021227994933724403,
-0.02242339216172695,
0.055629368871450424,
-0.023297801613807678,
-0.0016938357148319483,
-0.011965630576014519,
0.044448770582675934,
-0.061759427189826965,
0.02342667616903782,
0.01897640898823738,
0.04782393202185631,
0.01564483344554901,
0.07574755698442459,
0.004603036213666201,
-0.012774288654327393,
0.00722139235585928,
0.013487533666193485,
0.003258037380874157,
0.009766150265932083,
-0.0036656821612268686,
0.011540519073605537,
-0.014330192469060421,
0.0475420244038105,
-0.037557169795036316,
-0.012387475930154324,
0.032410603016614914,
-0.05560724064707756,
-0.048623956739902496,
-0.0059991455636918545,
0.028189387172460556,
0.016460545361042023,
0.011976915411651134,
0.0024180591572076082,
0.03409229964017868,
-0.02467835135757923,
-0.0204110536724329,
-0.013849068433046341,
0.020176690071821213,
-0.06256565451622009,
0.015861935913562775,
-0.05475838854908943,
-0.036749497056007385,
-0.04564812034368515,
-0.0377434678375721,
-0.0021911964286118746,
-0.07442907243967056,
-0.031195353716611862,
0.05455366522073746,
-0.07155143469572067,
-0.03522389754652977,
-0.011426125653088093,
0.06440990418195724,
-0.060354869812726974,
-0.033804137259721756,
0.03509031981229782,
0.023588214069604874,
0.017953673377633095,
-0.06114925444126129,
0.02968757599592209,
-0.024199098348617554,
0.021467402577400208,
0.014449408277869225,
-0.0002745147794485092,
0.03673581779003143,
-0.02274192124605179,
0.03101237863302231,
-0.016730645671486855,
0.01547524519264698,
-0.03444636985659599,
0.0149854626506567,
0.002295563230291009,
-0.07053107768297195,
-0.03428239747881889,
0.02606472745537758,
0.006965145468711853,
-0.03432995826005936,
0.03962478041648865,
0.014586634002625942,
0.006209933198988438,
0.09894177317619324,
-0.040894538164138794,
0.007078289985656738,
-0.037748537957668304,
-0.021404780447483063,
-0.025695500895380974,
-0.034822046756744385,
-0.05454060062766075,
0.02559516206383705,
0.06567888706922531,
-0.032304998487234116,
0.0875556692481041,
0.06812369078397751,
-0.017391040921211243,
-0.005646281410008669,
-0.01830154098570347,
0.03332841396331787,
0.0036296870093792677,
-0.07097727060317993,
-0.008122648112475872,
-0.010213957168161869,
0.03414224833250046,
0.017639284953475,
-0.02204548381268978,
0.013921298086643219,
-0.0027814155910164118,
0.024686457589268684,
0.028380658477544785,
0.0030667316168546677,
-0.07808569073677063,
0.011306761763989925,
0.050518698990345,
-0.023334914818406105,
-0.003328652586787939,
-0.0029333489947021008,
-0.024777259677648544,
0.019951973110437393,
-0.04062771052122116,
0.052984483540058136,
-0.02223447896540165,
-0.001417771214619279,
-0.0434015691280365,
0.09709661453962326,
0.037839218974113464,
0.009725741110742092,
-0.0487930066883564,
-0.03887749835848808,
-0.008110817521810532,
0.0385243184864521,
-0.03745131567120552,
0.024892939254641533,
0.03810419514775276,
0.007012888323515654,
-0.01510471198707819,
-0.02441064454615116,
0.0007396009750664234,
-0.018074527382850647,
0.029101472347974777,
0.01970643736422062,
0.021892962977290154,
-0.0580480694770813,
0.007426667958498001,
-0.024684730917215347,
0.002711578970775008,
-0.006757655180990696,
0.05362779647111893,
0.06629306823015213,
-0.0384843535721302,
0.05616913363337517,
-0.023876244202256203,
0.006396630313247442,
0.017034605145454407,
-0.02076425775885582,
-0.0811859667301178,
-0.012230643071234226,
0.004199695307761431,
0.02046249434351921,
0.0029705469496548176,
-0.014476407319307327,
-0.05085092782974243,
0.03254086524248123,
0.014189144596457481,
-0.006390186492353678,
0.0026163242291659117,
-0.023251822218298912,
-0.0028745413292199373,
0.010964896529912949,
0.038574498146772385,
0.02700755186378956,
0.025869963690638542,
-0.027365898713469505,
-0.01991134136915207,
0.025927411392331123,
0.032923199236392975,
-0.02761043794453144,
0.04036761447787285,
-0.004164423327893019,
-0.04019182547926903,
-0.0028263935819268227,
0.004512482322752476,
-0.021443970501422882,
-0.011788061819970608,
0.0038443906232714653,
0.0342094711959362,
-0.0015321355313062668,
-0.032037198543548584,
-0.027895813807845116,
-0.0710802748799324,
0.05751216411590576,
0.02079915627837181,
0.004677946679294109,
0.03288792446255684,
0.04714469611644745,
-0.054680075496435165,
-0.0100301718339324,
-0.0199522003531456,
0.05901075527071953,
0.020493412390351295,
0.018040960654616356,
-0.010818506591022015,
0.06645483523607254,
-0.00033581251045688987,
0.010850758291780949,
-0.003359054448083043,
0.02529846876859665,
-0.03537026047706604,
-0.01036806870251894,
0.011489778757095337,
0.019276395440101624,
-0.049047742038965225,
0.04222109913825989,
-0.03202994540333748,
-0.031762003898620605,
-0.0010190916946157813,
-0.047094643115997314,
-0.023990722373127937,
0.020114639773964882,
-0.0295826718211174,
-0.015091989189386368,
0.01740087941288948,
0.01971362717449665,
-0.0007305603940039873,
-0.07003793865442276,
-0.022006362676620483,
0.025920506566762924,
-0.004692353308200836,
-0.07298467308282852,
-0.05027087405323982,
-0.014432849362492561,
0.017947284504771233,
0.0013907599495723844,
-0.024154070764780045,
-0.04012931138277054,
0.06319047510623932,
-0.02901163510978222,
-0.08271587640047073,
-0.09228076040744781,
0.049517448991537094,
0.02552022412419319,
-0.0413324274122715,
0.02396572008728981,
0.03037418983876705,
-0.04944001883268356,
-0.020438140258193016,
0.027228284627199173,
-0.047864802181720734,
0.02126895822584629,
-0.010414433665573597,
-0.007436532527208328,
-0.08579129725694656,
-0.07216888666152954,
0.049672532826662064,
0.022705230861902237,
0.028555145487189293,
-0.018122870475053787,
-0.018550215288996696,
0.03059322014451027,
-0.017109906300902367,
0.013858729042112827,
0.003962750546634197,
-0.030128225684165955,
-0.009848639369010925,
0.014812328852713108,
-0.08960030972957611,
-0.017417779192328453,
-0.02922128327190876,
0.05368344858288765,
0.00939260981976986,
-0.0010005052899941802,
0.034451924264431,
-0.0369945652782917,
0.00826223660260439,
-0.019592728465795517,
0.0043876818381249905,
-0.0085965096950531,
0.011904898099601269,
0.02661275677382946,
0.0324331596493721,
0.001977951731532812,
0.015013080090284348,
0.01918864995241165,
0.03823491930961609,
0.026268748566508293,
-0.006034073419868946,
-0.042866893112659454,
0.10656790435314178,
0.04437551647424698,
0.013662295415997505,
-0.009745699353516102,
0.005055208690464497,
-0.016040634363889694,
0.012452058494091034,
-0.0352751761674881,
-0.025567587465047836,
0.05993562564253807,
0.02008087933063507,
0.01514782290905714,
-0.01688474789261818,
-0.009723590686917305,
0.04441958665847778,
-0.013306734152138233,
-0.015503937378525734,
0.04627417027950287,
-0.026113344356417656,
-0.01364938821643591,
0.00520790321752429,
-0.005285002291202545,
0.0495513379573822,
0.022616203874349594,
-0.010165044106543064,
-0.00961802713572979,
0.005874268244951963,
-0.00977786909788847,
0.01676005870103836,
0.022401519119739532,
-0.05911492556333542,
-0.006522048264741898,
0.009551662020385265,
-0.0030595220159739256,
-0.022930078208446503,
0.05732077360153198,
-0.03723694756627083,
-0.005281428340822458,
0.019157273694872856,
-0.001047368161380291,
-0.02531931735575199,
-0.021452439948916435,
-0.058109793812036514,
0.08259177207946777,
0.015544302761554718,
0.032801929861307144,
0.04570585861802101,
0.00401263078674674,
-0.025733862072229385,
0.016767216846346855,
-0.0162852481007576,
0.01300026848912239,
0.029757874086499214,
-0.035928934812545776,
0.0094345323741436,
-0.021047893911600113,
0.04619482904672623,
-0.05319468304514885,
0.06052403151988983,
0.05853136256337166,
-0.03823870047926903,
-0.03106902353465557,
0.004207069985568523,
0.013530123978853226,
0.04680169001221657,
0.061662524938583374,
0.03413627669215202,
-0.031180091202259064,
0.016551608219742775,
0.03846545144915581,
0.07820099592208862,
0.05329449847340584,
-0.032580193132162094,
-0.0026773535646498203,
-0.002384113147854805,
0.0568375438451767,
-0.023299282416701317,
0.03988126292824745,
-0.03795580193400383,
0.07459113001823425,
-0.012257728725671768,
0.010421603918075562,
0.040843501687049866,
-0.0009687222773209214,
0.09585636109113693,
0.013027160428464413,
-0.018505137413740158,
-0.032171785831451416,
-0.04406912624835968,
0.020279938355088234,
-0.05573895201086998,
-0.03267595171928406,
-0.04235150292515755,
0.0016210945323109627,
-0.05854835361242294,
0.022037962451577187,
0.05365888401865959,
-0.035457778722047806,
0.021527821198105812,
0.009312440641224384,
0.007451567333191633,
-0.008713767863810062,
0.007118028588593006,
-0.030603129416704178,
-0.03601842001080513,
0.03526715561747551,
0.012934061698615551,
0.03579841926693916,
0.029634907841682434,
-0.018428340554237366,
-0.03829796984791756,
0.03657400608062744,
-0.026059988886117935,
0.01558214146643877,
0.0558868870139122,
0.04773077741265297,
-0.024714739993214607,
-0.02195024862885475,
0.0387473963201046,
0.035856280475854874,
-0.013084717094898224,
-0.027853714302182198,
-0.05796859413385391,
-0.037476297467947006,
0.03343282639980316,
0.009652979671955109,
-0.003835507435724139,
-0.02601441740989685,
0.010694584809243679,
0.04921548813581467,
-0.044339101761579514,
0.004491603467613459,
0.0034120199270546436,
-0.006834891624748707,
0.051324035972356796,
0.0304331686347723,
0.015525237657129765,
-0.035522881895303726,
-0.04486987739801407,
-0.010519097559154034,
0.05031190067529678,
-0.05056226998567581,
-0.016785990446805954,
-0.06332235038280487,
-0.09139061719179153,
0.005176187958568335,
0.005629940889775753,
-0.004618141334503889,
0.04997045546770096,
-0.017997799441218376,
0.045940618962049484,
0.02738838456571102,
0.03262147679924965,
0.023205313831567764,
-0.009620072320103645,
0.016348140314221382,
0.0496351420879364,
-0.02284822054207325,
-0.033690717071294785,
-0.021496059373021126,
-0.008300384506583214,
0.027704279869794846,
0.021340247243642807,
-0.012915660627186298,
-0.004174618050456047,
-0.0473642461001873,
0.04200578108429909,
-0.0384361706674099,
0.05920904502272606,
0.037696368992328644,
-0.02768276073038578,
-0.027005355805158615,
-0.02159014903008938,
0.02405288629233837,
-0.0037747593596577644,
0.03688981384038925,
0.005641045980155468,
0.029002729803323746,
0.03883874788880348,
-0.06780862808227539,
0.02629798837006092,
-0.04455651342868805,
0.05484187975525856,
0.027498137205839157,
-0.02629000134766102,
-0.07512269169092178,
0.009611939080059528,
0.05532721430063248,
-0.06127351522445679,
-0.005181964486837387,
0.040622610598802567,
0.004821839276701212,
0.02371133305132389,
-0.0758192166686058,
0.023828573524951935,
-0.02959340251982212,
-0.006304525304585695,
-0.046518683433532715,
-0.04325592890381813,
0.038187578320503235,
0.036282677203416824,
-0.00009080980089493096,
-0.03953109309077263,
-0.025588514283299446,
0.009509675204753876,
-0.030132515355944633,
-0.030014658346772194,
0.055685319006443024,
0.029095320031046867,
-0.033729515969753265,
-0.02597939595580101,
-0.004476684145629406,
0.011504714377224445,
-0.01929684542119503,
0.0008689977694302797,
0.05950339138507843,
-0.007833595387637615,
-0.02796722948551178,
0.026437563821673393,
0.03848638758063316,
0.004810828249901533,
-0.000992997083812952,
-0.06660877168178558,
0.015066184103488922,
0.062297120690345764,
0.00019224260176997632,
0.046975694596767426,
-0.06368985772132874,
-0.024442225694656372,
-0.0019505458185449243,
-0.04278922826051712,
-0.021142300218343735,
0.003969889599829912,
-0.02203236147761345,
-0.014678580686450005,
-0.037406016141176224,
-0.010901948437094688,
0.06160357594490051,
-0.0347447395324707,
-0.03022967465221882,
-0.036529652774333954,
0.03111420013010502,
0.01765768975019455,
0.0317997969686985,
0.01784769631922245,
0.0010197310475632548,
-0.0002400921075604856,
-0.054976217448711395,
0.044531647115945816,
-0.013117401860654354,
0.011340238153934479,
0.03759036958217621,
-0.0535525381565094,
-0.029612762853503227,
0.004373501054942608,
0.03811364620923996,
-0.04935922101140022,
0.04645077884197235,
-0.028611525893211365,
-0.015276150777935982,
-0.05078057572245598,
0.03890269249677658,
-0.057679615914821625,
-0.008405439555644989,
0.007983666844666004,
-0.012550584971904755,
-0.007026506122201681,
0.003528051311150193,
0.00788854993879795,
0.03730341047048569,
0.009266271255910397,
0.02883916348218918,
-0.016684960573911667,
-0.025207243859767914,
-0.01238148845732212,
0.006779360584914684,
-0.05486400052905083,
0.02814035303890705,
-0.02562662959098816,
-0.014210935682058334,
-0.012390605174005032,
0.06103906407952309,
0.09239012002944946,
0.021517861634492874,
-0.019424308091402054,
0.02502436190843582,
0.09393878281116486,
-0.03238929435610771,
-0.035039715468883514,
0.0039105964824557304,
0.01831568032503128,
-0.034119922667741776,
-0.06759919226169586,
0.017922373488545418,
0.00018057954730466008,
-0.0463506281375885,
-0.018707744777202606,
0.04681524261832237,
-0.07290684431791306,
0.09174178540706635,
-0.006606957875192165,
0.04353827238082886,
0.016181984916329384,
-0.060275252908468246,
0.011336203664541245,
-0.024935003370046616,
-0.01757371798157692,
0.03108726069331169,
-0.013155901804566383,
-0.008124811574816704,
0.022492241114377975,
-0.057026974856853485,
0.05229797959327698,
-0.016722287982702255,
-0.028701523318886757,
0.02066739834845066,
-0.011290309019386768,
0.0166610237210989,
0.015516194514930248,
0.018311092630028725,
-0.01957748271524906,
0.042606502771377563,
-0.044718846678733826,
-0.014935358427464962,
-0.061599891632795334,
-0.008040832355618477,
-0.012183207087218761,
-0.0018814621726050973,
-0.06134222075343132,
0.05250333622097969,
-0.07351437211036682,
0.025896351784467697,
-0.0027721154037863016,
-0.0021976465359330177,
-0.004339955281466246,
-0.0072604333981871605,
-0.019160689786076546,
0.03789472579956055,
-0.009893841110169888,
-0.004531038925051689,
0.023067791014909744,
0.017898647114634514,
0.0027370655443519354,
-0.004594271071255207,
0.011080487631261349,
-0.03136400878429413,
-0.07540374994277954,
0.04276161268353462,
-0.04610617458820343,
0.01735401526093483,
0.006340058986097574,
0.015410569496452808,
-0.02103726752102375,
-0.01490701176226139,
0.032903749495744705,
-0.03695082664489746,
-0.014324016869068146,
0.01685606874525547,
0.027865814045071602,
0.03671941161155701,
-0.020823193714022636,
-0.06310681253671646,
-0.0020685261115431786,
-0.019190015271306038,
-0.0034920526668429375,
0.009956049732863903,
0.0033454210497438908,
-0.09151826053857803,
-0.047167763113975525,
0.01545054279267788,
-0.015551171265542507,
0.04907049611210823,
0.01645423099398613,
0.014233419671654701,
-0.04817534238100052,
-0.023655416443943977,
-0.015475782565772533,
0.0069011808373034,
-0.03729269281029701,
0.01675814762711525,
0.01542654912918806,
-0.0043106055818498135,
0.010684593580663204,
-0.07377669215202332,
0.021532272920012474,
-0.04597073420882225,
-0.06039084121584892,
0.007516369689255953,
-0.046296752989292145,
-0.057367708534002304,
-0.009690288454294205,
0.03884400799870491,
-0.00874498300254345,
-0.014820120297372341,
0.0362805500626564,
0.03902515769004822,
0.013047339394688606,
0.0722665786743164,
0.014096783474087715,
-0.03481133282184601,
0.03150439262390137,
0.018967948853969574,
0.07138946652412415,
-0.005836991127580404,
0.04019809514284134,
-0.05832541733980179,
-0.029119769111275673,
-0.0029016637708991766,
-0.06856007128953934,
-0.007488626055419445,
0.004008029121905565,
0.008449986577033997
] |
<p>The expression $\int | \Psi\left(x\right)|^2dx$ gives the probability of finding a particle at a given position. </p>
<p>If wave function gives the probabilities of positions, why do we calculate "expectation value of position"?</p>
<p>I don't understand the conceptual difference, we already have a wave function of a position. Expectation value is related to probabilities. </p>
<p>So what is the differences between them? And why do we calculate expectation value for position, although we have a function for probability of finding a particle at a given position?</p> | g5469 | [
0.01607886701822281,
-0.007631517481058836,
-0.01141854003071785,
-0.023930788040161133,
0.04330656677484512,
0.031937673687934875,
0.0369085855782032,
-0.00031168098212219775,
-0.1089983731508255,
-0.07480338960886002,
0.029976123943924904,
0.05039268359541893,
0.009736604057252407,
0.009841700084507465,
0.01829693280160427,
-0.012456725351512432,
0.0397966168820858,
-0.0051689413376152515,
-0.01997080259025097,
-0.02428053691983223,
-0.0011933683417737484,
-0.02228454500436783,
-0.06610321998596191,
-0.0015942312311381102,
-0.01782143861055374,
-0.02835308015346527,
-0.006847450975328684,
-0.0347176119685173,
0.002623419975861907,
0.031555987894535065,
0.030030757188796997,
0.002851558616384864,
0.0775049552321434,
-0.03668266907334328,
-0.03651416674256325,
-0.04615120589733124,
0.07871092855930328,
-0.023828580975532532,
-0.0036540692672133446,
-0.004040848929435015,
0.004594595171511173,
-0.0037136822938919067,
0.0115693099796772,
-0.03131308779120445,
0.005593445617705584,
-0.013442188501358032,
-0.057392362505197525,
0.03153596445918083,
-0.029126107692718506,
-0.0495261624455452,
0.01078011654317379,
0.01702304556965828,
0.047693174332380295,
0.06034256890416145,
0.0560729093849659,
0.07819247245788574,
0.032045911997556686,
0.014357917942106724,
0.027663154527544975,
0.0486709363758564,
0.03589438274502754,
0.060614265501499176,
0.0034427247010171413,
-0.021650712937116623,
0.051947060972452164,
-0.026760192587971687,
-0.035979703068733215,
0.0359613262116909,
-0.032136090099811554,
-0.007638053502887487,
-0.010266589932143688,
-0.038380686193704605,
-0.023954439908266068,
-0.020852426066994667,
-0.06091775372624397,
-0.03253667801618576,
-0.002983533311635256,
-0.019946767017245293,
-0.015223032794892788,
0.043367136269807816,
0.007920567877590656,
-0.03961111232638359,
0.017415817826986313,
0.001982372719794512,
0.02604878507554531,
0.03209613263607025,
-0.0010392711265012622,
0.025370128452777863,
-0.012397518381476402,
0.025128914043307304,
0.013269946910440922,
0.0013229065807536244,
0.07898504287004471,
0.049325764179229736,
-0.054720424115657806,
0.0015418489929288626,
-0.05796774849295616,
0.02412421442568302,
-0.012159901671111584,
0.02484273537993431,
0.011946234852075577,
0.00825030542910099,
0.04052506014704704,
0.03541145101189613,
-0.006853889673948288,
-0.02232687920331955,
0.009015286341309547,
0.04717276990413666,
-0.004389007110148668,
-0.015144169330596924,
0.017631804570555687,
0.04367154836654663,
0.003332719672471285,
-0.03736669570207596,
-0.10313443839550018,
0.006608264055103064,
0.07931186258792877,
-0.012923670001327991,
0.010028297081589699,
0.0428791381418705,
0.035263076424598694,
0.0617489293217659,
0.04723620042204857,
0.05564851313829422,
0.03812446445226669,
-0.012567589059472084,
-0.027795445173978806,
0.015995150431990623,
-0.001593895605765283,
0.021398423239588737,
0.06695542484521866,
-0.002051837509498,
-0.044653162360191345,
0.01477919053286314,
-0.011603710241615772,
-0.007255270145833492,
-0.00712211150676012,
-0.012897365726530552,
0.04371876269578934,
-0.02544292062520981,
0.015017419122159481,
0.01579674519598484,
0.03398384898900986,
-0.020650714635849,
-0.04308762401342392,
-0.029267506673932076,
-0.03704547509551048,
-0.0028820529114454985,
-0.02479453571140766,
0.019326213747262955,
-0.03873470798134804,
0.011768403463065624,
-0.027786457911133766,
0.005775608588010073,
0.0034836477134376764,
-0.0023936547804623842,
0.005268825683742762,
0.0589984729886055,
-0.04223575070500374,
0.025584347546100616,
0.04301345348358154,
0.009953038766980171,
0.034426528960466385,
0.008831314742565155,
-0.03831111267209053,
-0.04483409225940704,
0.04909032583236694,
-0.07580938190221786,
-0.048692867159843445,
-0.06270811706781387,
0.04722699150443077,
-0.02834467589855194,
-0.007682402152568102,
-0.007505385205149651,
-0.009668434038758278,
0.09532850235700607,
-0.05100364238023758,
-0.03633412346243858,
-0.004636563826352358,
0.022710243239998817,
-0.0140773244202137,
-0.015243102796375751,
-0.022354338318109512,
-0.05592915415763855,
-0.04934625327587128,
-0.025928249582648277,
0.009527076035737991,
0.01228481624275446,
-0.06913574784994125,
0.02803601138293743,
-0.043926604092121124,
-0.05860478803515434,
-0.014457168988883495,
0.09830893576145172,
-0.023966247215867043,
0.04602658748626709,
-0.00514608807861805,
-0.01190979965031147,
-0.04545062407851219,
0.03753466531634331,
-0.017237655818462372,
0.036107417196035385,
0.04966677725315094,
-0.019406486302614212,
0.041011180728673935,
0.06055665761232376,
-0.010361689142882824,
0.017046689987182617,
-0.0001311885571340099,
-0.042914018034935,
0.003378058783710003,
-0.01655210182070732,
0.011955155991017818,
-0.000876197125762701,
0.03598110377788544,
0.0006381328566931188,
-0.0019203552510589361,
0.00492912158370018,
0.009492728859186172,
-0.024484893307089806,
-0.022657522931694984,
-0.08203433454036713,
0.061288267374038696,
0.031328897923231125,
-0.02567579783499241,
0.08045771718025208,
-0.04853065311908722,
-0.034976162016391754,
-0.02316216006875038,
0.058946508914232254,
-0.08352424204349518,
-0.00820795726031065,
-0.02695353329181671,
0.04601629823446274,
0.05685462802648544,
0.03772561997175217,
0.00789676047861576,
0.012071199715137482,
0.07997124642133713,
0.016050994396209717,
-0.040499068796634674,
0.00776070449501276,
-0.016749568283557892,
0.03072812780737877,
0.02484852261841297,
-0.02435079589486122,
-0.005126796662807465,
-0.0045079695992171764,
-0.026375722140073776,
0.045149099081754684,
-0.01732696034014225,
-0.006714963354170322,
-0.0688440352678299,
-0.03593132644891739,
0.04564593732357025,
-0.03974268212914467,
-0.025761157274246216,
-0.02674010396003723,
-0.027358727529644966,
-0.034937784075737,
-0.02735435776412487,
0.03171257674694061,
-0.010071787051856518,
0.02818780392408371,
-0.020633462816476822,
0.004496977664530277,
0.014586950652301311,
0.04245421290397644,
-0.003409523982554674,
-0.025550881400704384,
0.06486906111240387,
0.06520051509141922,
-0.01732892543077469,
0.002701415913179517,
-0.00036032439675182104,
-0.07070843875408173,
0.002347263740375638,
-0.013632383197546005,
0.01926600933074951,
-0.04910098388791084,
-0.002677885117009282,
-0.009000287391245365,
-0.010273574851453304,
0.07492073625326157,
-0.007861495949327946,
-0.10479748994112015,
0.013600987382233143,
0.0032658500131219625,
0.021855860948562622,
-0.05592317879199982,
0.016779080033302307,
0.02803277224302292,
-0.030176950618624687,
-0.009777025319635868,
0.013990318402647972,
0.004236878361552954,
0.012132678180932999,
-0.02896028570830822,
0.01198092196136713,
-0.002058956539258361,
-0.0387720949947834,
0.028724223375320435,
-0.0005153949023224413,
-0.04690587520599365,
0.03849302977323532,
0.02873874641954899,
-0.01344947051256895,
-0.019644467160105705,
-0.06956358999013901,
-0.02360088936984539,
0.02037687785923481,
0.07034905254840851,
-0.009851927869021893,
-0.018827522173523903,
-0.04001546651124954,
0.012658295221626759,
-0.013582833111286163,
-0.012905888259410858,
-0.008881322108209133,
-0.0017511001788079739,
-0.036444585770368576,
-0.03567594289779663,
-0.029466575011610985,
0.001536237308755517,
0.04714793711900711,
0.0402517169713974,
-0.05239083617925644,
0.08241579681634903,
-0.01776242069900036,
-0.03466840088367462,
0.03314024955034256,
0.022266646847128868,
-0.0036126598715782166,
0.004389696288853884,
0.015013703145086765,
-0.03866351768374443,
0.016316689550876617,
0.00845359731465578,
0.004061593208462,
0.019018102437257767,
0.03823380917310715,
0.0016739288112148643,
-0.06881721317768097,
0.03282545506954193,
0.008266222663223743,
-0.04482464864850044,
0.01458427682518959,
-0.01656794175505638,
0.041983433067798615,
-0.030391601845622063,
-0.03102424554526806,
-0.05407889932394028,
0.017988264560699463,
0.07408632338047028,
-0.007813777774572372,
0.00046182223013602197,
0.03698744997382164,
0.011824099346995354,
0.03608724847435951,
0.03396785259246826,
0.00785314291715622,
-0.05341198667883873,
0.04208835959434509,
0.007858448661863804,
-0.019854774698615074,
-0.05581498518586159,
-0.008898652158677578,
-0.016241544857621193,
-0.0011235701385885477,
-0.05354006960988045,
-0.00006481947639258578,
0.0072277383878827095,
0.021701369434595108,
0.002667380729690194,
0.03646988421678543,
-0.05549146607518196,
-0.023699549958109856,
-0.041015055030584335,
-0.022963041439652443,
-0.03590245544910431,
0.004336564801633358,
0.03251852095127106,
0.060780033469200134,
-0.0045058163814246655,
0.018119223415851593,
-0.06470228731632233,
-0.03661070391535759,
0.03607707470655441,
-0.024001847952604294,
-0.04915669560432434,
0.009405306540429592,
-0.0013165764976292849,
-0.07095613330602646,
0.04384339973330498,
-0.0023614533711224794,
0.01843424141407013,
0.024817170575261116,
-0.011857941746711731,
0.034587081521749496,
0.01838603988289833,
-0.04602901265025139,
-0.05498487502336502,
0.008307848125696182,
-0.00024247044348157942,
-0.002099198754876852,
-0.02578899636864662,
0.10085225105285645,
-0.03981437906622887,
-0.014253816567361355,
-0.022851428017020226,
0.011440213769674301,
0.017854349687695503,
0.05999598652124405,
-0.039780281484127045,
-0.028522532433271408,
-0.008268877863883972,
0.021142667159438133,
-0.059265583753585815,
0.03772300109267235,
0.045835379511117935,
0.012093784287571907,
0.0030960405711084604,
0.039038270711898804,
-0.02571149356663227,
-0.010661778971552849,
0.04203033074736595,
0.06842520087957382,
0.039690159261226654,
-0.018225891515612602,
-0.0594816654920578,
0.005487250164151192,
0.06373269110918045,
0.05284241586923599,
0.020799998193979263,
-0.0315982811152935,
-0.026704922318458557,
-0.012532366439700127,
0.011698754504323006,
0.0001331532548647374,
0.03314226493239403,
0.007948257960379124,
0.04925558343529701,
-0.017641102895140648,
0.023679396137595177,
0.01724233105778694,
-0.0025200892705470324,
-0.02442832477390766,
-0.06436916440725327,
-0.00034690366010181606,
0.015206893905997276,
0.013743189163506031,
0.054658301174640656,
-0.03452829644083977,
-0.06308728456497192,
0.057916946709156036,
-0.05168036371469498,
-0.020831244066357613,
0.01634029857814312,
0.006124350242316723,
0.015931986272335052,
-0.03672328591346741,
-0.002377338707447052,
-0.03287124261260033,
-0.03491365537047386,
0.03242678567767143,
0.03375289589166641,
-0.1311417669057846,
-0.03614548221230507,
-0.07479581236839294,
0.040312886238098145,
-0.00717677129432559,
-0.030589217320084572,
0.03194089233875275,
-0.0031755086965858936,
0.024646557867527008,
-0.0065816896967589855,
-0.011312947608530521,
-0.07189884781837463,
0.023949986323714256,
-0.030902987346053123,
-0.03974661976099014,
-0.01780475303530693,
0.041356079280376434,
0.006357154808938503,
-0.03426414355635643,
-0.03352941572666168,
-0.03229432925581932,
-0.04158351197838783,
-0.02299143187701702,
0.005013694055378437,
0.07558529824018478,
0.0068856277503073215,
0.018863240256905556,
-0.04756435751914978,
-0.0041516972705721855,
-0.012420949526131153,
-0.0028817104175686836,
0.011579333804547787,
0.008273511193692684,
0.021879160776734352,
-0.034265875816345215,
-0.007396897301077843,
0.004722995217889547,
-0.00008536066161468625,
-0.026946216821670532,
0.0431332066655159,
0.08132775872945786,
-0.03551282733678818,
-0.020047517493367195,
0.01573266088962555,
0.08493360131978989,
0.00814771093428135,
-0.02525557391345501,
-0.008470436558127403,
-0.0011122950818389654,
-0.007115261163562536,
-0.0007313922978937626,
0.02462783455848694,
-0.032631803303956985,
0.03638041391968727,
0.04448288679122925,
0.04161401838064194,
0.027824541553854942,
-0.0514291413128376,
0.03639332950115204,
-0.006596366874873638,
-0.04133036732673645,
-0.032044246792793274,
-0.0220553670078516,
0.020087171345949173,
0.015769006684422493,
0.019149906933307648,
0.024504467844963074,
0.03821767494082451,
-0.026657981798052788,
-0.012264225631952286,
-0.02402953989803791,
-0.013079484924674034,
0.06019911170005798,
-0.013719362206757069,
-0.03277338668704033,
-0.02977002039551735,
-0.023660507053136826,
0.007760507054626942,
-0.00285623362287879,
0.028515182435512543,
0.017641570419073105,
-0.0029865719843655825,
0.006690870970487595,
-0.04931170493364334,
0.015590893104672432,
-0.014615854248404503,
-0.05530518665909767,
-0.05581328272819519,
0.021778574213385582,
0.028341475874185562,
-0.017379259690642357,
-0.02198803797364235,
-0.002510678954422474,
-0.01693367399275303,
0.010310091078281403,
-0.03540145978331566,
0.004372047260403633,
0.021130923181772232,
0.04489107057452202,
0.02188055031001568,
-0.03155455365777016,
0.01622142270207405,
0.014935730956494808,
0.030460499227046967,
0.0002188493381254375,
0.003509246977046132,
-0.024740947410464287,
0.027445616200566292,
0.063672736287117,
0.01035197451710701,
0.026544472202658653,
-0.02820734493434429,
-0.008567165583372116,
0.00354326656088233,
-0.026351286098361015,
0.010578908026218414,
-0.02501181699335575,
-0.02094443514943123,
-0.053596023470163345,
0.05412150174379349,
0.016567233949899673,
-0.044240884482860565,
0.09823774546384811,
0.01275065541267395,
-0.0077205318957567215,
-0.005900304298847914,
-0.014067509211599827,
0.03829999268054962,
-0.0441458560526371,
-0.024482471868395805,
0.00011092110798927024,
-0.02072523906826973,
0.0029207870829850435,
-0.01078114565461874,
0.02016112394630909,
-0.0032811008859425783,
0.04818835109472275,
-0.02138473279774189,
0.05454206094145775,
-0.007468835916370153,
-0.05597517266869545,
0.014122862368822098,
0.002633816795423627,
0.055442359298467636,
-0.04227253049612045,
0.0003860148135572672,
0.0031918685417622328,
-0.016421373933553696,
0.019662247970700264,
-0.05285276100039482,
0.011204333044588566,
0.06036408990621567,
-0.0277413260191679,
-0.014078119769692421,
0.041704777628183365,
0.049198899418115616,
-0.05434296652674675,
-0.022909238934516907,
0.06198732554912567,
0.00046934475540183485,
-0.046327996999025345,
-0.01627928391098976,
0.062106285244226456,
0.029965301975607872,
0.036833226680755615,
-0.029761141166090965,
0.029066186398267746,
0.08412707597017288,
-0.09237140417098999,
-0.03465128690004349,
-0.06590405106544495,
0.006066990550607443,
0.04361938312649727,
0.05609168857336044,
-0.03338129445910454,
-0.002278473461046815,
0.06160347908735275,
-0.05286838486790657,
-0.055109087377786636,
-0.0014103096909821033,
0.0684303566813469,
-0.024695392698049545,
-0.07763370871543884,
0.0011778241023421288,
-0.025280741974711418,
0.02042444422841072,
-0.0030138485599309206,
-0.016436077654361725,
0.009129212237894535,
0.032785024493932724,
0.06808192282915115,
-0.014256566762924194,
0.0016075969906523824,
-0.05546390265226364,
-0.020660344511270523,
-0.05849854648113251,
-0.07295308262109756,
0.03215053305029869,
-0.009575915522873402,
0.020590990781784058,
-0.010397015139460564,
-0.0037982454523444176,
-0.01114591583609581,
-0.011613822542130947,
-0.015580723993480206,
-0.03494052216410637,
-0.08719421923160553,
-0.017242025583982468,
-0.021278496831655502,
0.02372804656624794,
-0.01244332268834114,
0.013948140665888786,
-0.071587935090065,
0.013060529716312885,
0.018024533987045288,
0.024383770301938057,
-0.005636695306748152,
-0.011985289864242077,
-0.02335376851260662,
0.03361792117357254,
-0.038101356476545334,
-0.016791412606835365,
-0.014883950352668762,
-0.009768045507371426,
0.019723039120435715,
-0.02245597541332245,
0.03383858874440193,
-0.06281784921884537,
-0.05356310307979584,
-0.022289296612143517,
0.039782870560884476,
0.05342499911785126,
0.05845378711819649,
0.06583867967128754,
0.00764861423522234,
-0.07705147564411163,
0.0005145232426002622,
0.019919153302907944,
0.051136039197444916,
-0.042712368071079254,
0.008763516321778297,
0.009618468582630157,
-0.04081619530916214,
-0.04403365030884743,
0.06697080284357071,
-0.03435671702027321,
0.026919329538941383,
0.04412785917520523,
-0.014499030075967312,
0.003636898472905159,
0.004095754586160183,
0.04572831466794014,
0.02628609724342823,
-0.044929374009370804,
0.056268129497766495,
-0.023747088387608528,
-0.035882849246263504,
-0.017887815833091736,
-0.00016988144489005208,
0.03175577521324158,
0.0028555335011333227,
-0.028148947283625603,
0.02133004739880562,
0.02005319856107235,
-0.0029327278025448322,
0.04218168929219246,
-0.013104211539030075,
0.04232150688767433,
-0.0070252674631774426,
0.007283368613570929,
0.051690515130758286,
0.04547949135303497,
-0.04782227799296379,
-0.010864071547985077,
0.029589373618364334,
0.01066772174090147,
0.005478707142174244,
-0.021591465920209885,
-0.06019428372383118,
0.013658856973052025,
0.02642778493463993,
0.015320890583097935,
0.06674166023731232,
-0.023983798921108246,
-0.02343759685754776,
0.040751781314611435,
-0.043926991522312164,
0.11306182295084,
0.00721865426748991,
-0.07540013641119003,
0.011363349854946136,
0.013976005837321281,
0.014310367405414581,
-0.010221634991466999,
0.04870385304093361,
0.038611941039562225,
0.002540912013500929,
-0.049992918968200684,
0.00487516587600112,
0.022324156016111374,
0.02062968909740448,
0.05749994143843651
] |
<p>I've understood that the Cosmic Background Radiation(CBR) is an electromagnetic wave that originated from the big bang. However, we now live on a planet which that is also originating from the big bang.</p>
<p>Why does that Cosmic Background Radiation reaches us now? Why does CBR reaches us now, and not a couple of billion years earlier?</p> | g5470 | [
0.06122763082385063,
0.02380191534757614,
0.017352057620882988,
0.027565183117985725,
0.001598368980921805,
0.08185254782438278,
0.04243350028991699,
0.03284963592886925,
-0.04292767494916916,
-0.0722435712814331,
0.0337454229593277,
0.05140742287039757,
0.021042773500084877,
0.027176562696695328,
0.03077416494488716,
-0.06142565980553627,
-0.023048529401421547,
0.011648944579064846,
0.02580493688583374,
0.04262940585613251,
-0.029089294373989105,
-0.026640992611646652,
0.04766776040196419,
-0.028802568092942238,
-0.0636921375989914,
-0.052434418350458145,
0.01449576672166586,
0.0036477360408753157,
-0.000648893357720226,
-0.011186490766704082,
0.05227641016244888,
0.004507069941610098,
0.058562058955430984,
-0.016553519293665886,
0.01821153424680233,
-0.04840501397848129,
-0.05504465848207474,
0.01911359280347824,
0.003535698400810361,
-0.0004936427576467395,
0.02768411487340927,
-0.01192435808479786,
0.01696081832051277,
-0.014975486323237419,
0.01236698031425476,
-0.017017388716340065,
-0.017531778663396835,
-0.003924598451703787,
0.029702452942728996,
-0.04894780367612839,
-0.0854501947760582,
-0.011056928895413876,
0.04254329204559326,
0.036971088498830795,
0.01301036961376667,
-0.023491045460104942,
-0.01662464067339897,
-0.015418845228850842,
0.04722404107451439,
-0.05105180665850639,
0.022210214287042618,
0.034951865673065186,
0.0700962096452713,
0.04715908691287041,
0.01853536255657673,
-0.008843645453453064,
-0.013657760806381702,
0.0524715855717659,
-0.022865626960992813,
0.03720158711075783,
0.03210464492440224,
-0.05116317421197891,
-0.05778531730175018,
0.023897837847471237,
0.016452612355351448,
-0.03404652699828148,
-0.03145759552717209,
0.0037850025109946728,
0.010044516995549202,
0.08590558916330338,
-0.00498361187055707,
0.004155915230512619,
-0.06417524814605713,
-0.029447391629219055,
0.049212418496608734,
-0.0177201759070158,
-0.0372229665517807,
-0.03808803856372833,
-0.009353776462376118,
-0.07911211252212524,
0.043797414749860764,
-0.02298779785633087,
0.003803733503445983,
0.061933163553476334,
-0.003284251084551215,
-0.05556504800915718,
-0.020686713978648186,
-0.01638733223080635,
-0.009729957208037376,
0.016233712434768677,
-0.029841918498277664,
-0.0356900654733181,
0.022978950291872025,
0.03733009472489357,
-0.0033916593529284,
0.06575244665145874,
0.01577371545135975,
-0.02440907061100006,
-0.08731533586978912,
-0.013401878997683525,
0.0024350793100893497,
-0.03158141300082207,
0.05245675519108772,
0.015225601382553577,
-0.06948769092559814,
0.030220896005630493,
0.04792194813489914,
0.0026415979955345392,
0.02169390767812729,
0.05011724680662155,
0.022411946207284927,
0.014890654012560844,
-0.04212760925292969,
-0.01560771930962801,
-0.06478226184844971,
0.01121485698968172,
0.020566629245877266,
0.009737871587276459,
0.08312010765075684,
0.013850371353328228,
-0.024002032354474068,
0.052518703043460846,
-0.025442134588956833,
0.015432952903211117,
0.03862760588526726,
-0.04446990415453911,
0.025343365967273712,
0.004933720454573631,
0.015575113706290722,
0.061679042875766754,
0.006479095201939344,
-0.010063550435006618,
0.044121503829956055,
-0.03555707260966301,
-0.05211474746465683,
0.050073593854904175,
-0.03191983699798584,
0.000601236883085221,
0.014281127601861954,
-0.015130487270653248,
0.0036377401556819677,
0.04404359683394432,
0.020271392539143562,
-0.01772143505513668,
0.01737346313893795,
-0.004998546093702316,
0.016442131251096725,
0.006768901366740465,
0.010750931687653065,
0.011732064187526703,
0.035740695893764496,
-0.002122051315382123,
-0.06203646585345268,
-0.006093726493418217,
-0.029685677960515022,
0.008839836344122887,
-0.038754530251026154,
-0.08821779489517212,
0.007038076873868704,
0.01754932478070259,
-0.019318198785185814,
0.0027719822246581316,
0.017971176654100418,
-0.02552255243062973,
0.01969798654317856,
0.11338766664266586,
0.08311488479375839,
-0.020011525601148605,
-0.016603099182248116,
-0.030812712386250496,
-0.04212047904729843,
-0.04059301316738129,
0.022628335282206535,
0.002582294400781393,
0.011753617785871029,
-0.0504031665623188,
-0.05313645303249359,
-0.020250247791409492,
0.008362296037375927,
-0.028740767389535904,
-0.012005079537630081,
-0.05145908519625664,
-0.020464230328798294,
0.01071125827729702,
-0.026544567197561264,
-0.01171315647661686,
-0.0417318269610405,
-0.004790172446519136,
0.004512265790253878,
0.03782046586275101,
0.032606225460767746,
0.0602443553507328,
0.02471400983631611,
0.006404681131243706,
0.03357710316777229,
0.027110116556286812,
0.019532306119799614,
0.015690047293901443,
0.06122147664427757,
-0.021635141223669052,
-0.056511856615543365,
-0.04755786806344986,
-0.021713141351938248,
-0.019898567348718643,
-0.061829593032598495,
0.031469497829675674,
-0.0006005654577165842,
0.05288403853774071,
0.004587544593960047,
0.033274464309215546,
-0.01874273084104061,
0.01994156837463379,
0.027889996767044067,
0.03377194330096245,
0.009040437638759613,
0.035134702920913696,
-0.022421104833483696,
-0.031913239508867264,
0.0239320769906044,
0.01719784177839756,
-0.029670730233192444,
0.07530870288610458,
-0.04874110594391823,
0.023292498663067818,
0.014991565607488155,
0.006726265884935856,
0.03189081326127052,
-0.08678799867630005,
-0.032936062663793564,
0.01179241668432951,
-0.00500907190144062,
-0.013726265169680119,
0.008205612190067768,
0.039973948150873184,
0.039332564920186996,
-0.029431821778416634,
0.03251222148537636,
-0.04954009875655174,
-0.05264882370829582,
-0.016149379312992096,
0.05165678635239601,
-0.027302123606204987,
0.002248036675155163,
-0.015649978071451187,
-0.010180149227380753,
-0.05205092206597328,
-0.008760864846408367,
0.06062254682183266,
-0.09995389729738235,
-0.04628853127360344,
0.0034681144170463085,
0.017144041135907173,
0.03369449824094772,
0.054969966411590576,
-0.037951480597257614,
0.003850094974040985,
-0.026104625314474106,
0.05656510964035988,
-0.03836599737405777,
-0.0617452897131443,
0.004391943570226431,
0.06284311413764954,
0.013490135781466961,
-0.024105526506900787,
0.0046301777474582195,
-0.018220605328679085,
0.0230703204870224,
-0.03634827211499214,
0.039335742592811584,
0.012306855991482735,
-0.024119345471262932,
0.006569855380803347,
0.002648383378982544,
-0.05700899288058281,
-0.023056963458657265,
-0.05296742543578148,
-0.08114214986562729,
0.01029017474502325,
0.09638447314500809,
-0.0641380324959755,
-0.0016323052113875747,
-0.023066934198141098,
0.025001827627420425,
0.019074667245149612,
0.04513350874185562,
0.032824087888002396,
0.011880191043019295,
0.01659291237592697,
-0.021080562844872475,
0.013774105347692966,
0.03061332181096077,
-0.0484948456287384,
0.033737778663635254,
-0.07032405585050583,
-0.07318796962499619,
-0.015679333359003067,
-0.02477147802710533,
-0.016732649877667427,
-0.015103206969797611,
0.007634008303284645,
-0.0018960089655593038,
-0.0014864455442875624,
-0.002242310671135783,
0.08917749673128128,
0.030794598162174225,
-0.011321282014250755,
-0.02427363023161888,
0.04706774279475212,
0.016757182776927948,
0.008094693534076214,
0.01469696220010519,
0.03924982622265816,
-0.06495222449302673,
-0.010754003189504147,
0.022202294319868088,
0.014747925102710724,
-0.06137249246239662,
-0.02553608827292919,
-0.006607939023524523,
-0.030620377510786057,
-0.02851160801947117,
-0.00751079898327589,
-0.022002365440130234,
0.026591867208480835,
-0.03856173902750015,
-0.06950452923774719,
0.00718671502545476,
0.07087619602680206,
0.011034424416720867,
0.045111265033483505,
0.008130795322358608,
0.011407601647078991,
-0.07020614296197891,
0.016134055331349373,
-0.026555582880973816,
0.052541334182024,
0.048544492572546005,
-0.01781407929956913,
-0.056669969111680984,
0.03657326102256775,
0.0051019503735005856,
0.05712226405739784,
-0.0549452118575573,
-0.03804120421409607,
-0.031155919656157494,
-0.02775563672184944,
-0.006326730363070965,
0.028406677767634392,
0.08498601615428925,
-0.03427983820438385,
0.011581452563405037,
0.027844948694109917,
0.04212142154574394,
0.03666010499000549,
-0.014382771216332912,
-0.040249068289995193,
0.01630248688161373,
-0.02179567702114582,
0.055915914475917816,
0.04943925514817238,
-0.004282521549612284,
-0.01756189949810505,
0.0013537548948079348,
0.027616312727332115,
0.047655969858169556,
-0.03403490036725998,
0.00689702806994319,
0.018608907237648964,
-0.025784388184547424,
-0.004816682543605566,
-0.017300762236118317,
0.015643160790205002,
0.009836728684604168,
0.029825914651155472,
0.015375186689198017,
0.000012985742614546325,
-0.05198449641466141,
-0.0296822227537632,
-0.05336078628897667,
-0.041785966604948044,
0.025083722546696663,
-0.033279720693826675,
0.04560874402523041,
-0.01944466307759285,
0.004193396307528019,
-0.032226838171482086,
0.0006461633602157235,
0.009666748344898224,
0.0639168918132782,
0.006136258598417044,
-0.02363218367099762,
0.02685653604567051,
0.026884285733103752,
0.02149876207113266,
0.0061619943007826805,
0.06085202097892761,
0.00030560625600628555,
-0.02993420511484146,
-0.037180762737989426,
-0.002333298558369279,
0.006395174656063318,
-0.0005400999798439443,
-0.062427692115306854,
-0.05295458808541298,
0.06464701145887375,
-0.015683112666010857,
0.043353646993637085,
-0.029244951903820038,
0.05010753497481346,
0.018796980381011963,
-0.052043620496988297,
0.0015779889654368162,
0.0007530332077294588,
-0.041157614439725876,
0.00746579747647047,
0.0793909952044487,
0.005207312759011984,
-0.05613616481423378,
0.031113237142562866,
0.03959944099187851,
-0.01049885991960764,
0.05116187408566475,
-0.024242760613560677,
0.030247975140810013,
0.03118581511080265,
0.024932509288191795,
-0.039740342646837234,
0.020849959924817085,
0.04631790146231651,
-0.03341776877641678,
0.10396407544612885,
-0.02102624624967575,
-0.02187706157565117,
0.01787501387298107,
-0.027227181941270828,
0.07278513163328171,
0.016025325283408165,
0.01214845385402441,
-0.02911519818007946,
-0.01893751695752144,
-0.034192539751529694,
-0.007452103774994612,
-0.026917360723018646,
0.009680695831775665,
0.0056229643523693085,
-0.04565868154168129,
0.012370370328426361,
-0.02919434756040573,
0.021626804023981094,
0.06365084648132324,
-0.05239257961511612,
0.030388349667191505,
0.04467340186238289,
-0.02449408546090126,
-0.030775027349591255,
-0.054106052964925766,
-0.03405033051967621,
-0.025480052456259727,
-0.019380608573555946,
0.03873901441693306,
-0.037830810993909836,
0.0035720006562769413,
0.05449618026614189,
-0.0012775255599990487,
-0.01622115820646286,
0.032030537724494934,
0.01322519313544035,
-0.02848135307431221,
0.014490244910120964,
-0.048003848642110825,
-0.01385496649891138,
0.03277136757969856,
-0.019869055598974228,
0.04685842618346214,
-0.06239016726613045,
0.058206360787153244,
-0.023028628900647163,
0.010588176548480988,
0.025232963263988495,
-0.039323896169662476,
0.004561808425933123,
-0.008086846210062504,
-0.012232678011059761,
-0.014579693786799908,
0.004575035069137812,
-0.027705302461981773,
-0.04166826605796814,
-0.03250567242503166,
0.023875679820775986,
-0.005693456623703241,
-0.004131560679525137,
0.03546324372291565,
-0.045374080538749695,
0.0060844761319458485,
-0.014531798660755157,
0.06996139138936996,
0.013618451543152332,
0.0033410675823688507,
-0.013892012648284435,
0.0266736913472414,
0.024994932115077972,
0.0021506056655198336,
0.0015306443674489856,
-0.009380011819303036,
-0.015984952449798584,
-0.0034857813734561205,
-0.007661289535462856,
-0.07133432477712631,
0.027462638914585114,
0.04514866694808006,
-0.0636480525135994,
0.056663576513528824,
0.04814690724015236,
0.04076226428151131,
-0.02336260676383972,
-0.01549610961228609,
0.009314223192632198,
0.029650894924998283,
-0.004580761771649122,
0.006844398099929094,
-0.07648186385631561,
0.05708060786128044,
0.056821275502443314,
0.03847868740558624,
-0.003547669854015112,
0.039018966257572174,
0.0003655061009339988,
0.020515291020274162,
-0.0433090515434742,
-0.018152890726923943,
0.027809565886855125,
-0.062291666865348816,
0.008128410205245018,
0.026626653969287872,
0.051631949841976166,
0.037586238235235214,
0.011919943615794182,
0.012380742467939854,
0.023874999955296516,
-0.025617022067308426,
0.01539143268018961,
-0.007743357680737972,
0.034495383501052856,
0.027750082314014435,
-0.01029734406620264,
0.07116466760635376,
-0.00017905267304740846,
0.014333447441458702,
-0.01631254516541958,
-0.01969565637409687,
-0.0307296235114336,
0.0050197564996778965,
-0.013250187039375305,
-0.07081975042819977,
0.021440068259835243,
0.02704492397606373,
-0.03145366907119751,
-0.032387807965278625,
0.059525016695261,
0.008672312833368778,
-0.02965402789413929,
-0.032102469354867935,
-0.00038508782745338976,
-0.017229130491614342,
-0.029909715056419373,
0.03504806011915207,
-0.019366266205906868,
-0.03184397518634796,
-0.08945893496274948,
0.0244381632655859,
0.0017679600277915597,
-0.022806251421570778,
0.030256671831011772,
-0.0007138185319490731,
0.021376023069024086,
0.01817280985414982,
-0.04397181421518326,
-0.012677788734436035,
0.1139790490269661,
-0.005891145672649145,
0.01916434057056904,
-0.05542328953742981,
0.061398763209581375,
-0.05122998356819153,
-0.05922232195734978,
-0.048572905361652374,
0.03214229270815849,
-0.005922943353652954,
-0.020983057096600533,
-0.06052936613559723,
-0.011518824845552444,
-0.04437115043401718,
0.02765340358018875,
-0.0034451147075742483,
0.07642821222543716,
0.004036628175526857,
0.004625567700713873,
-0.06815573573112488,
0.06091711297631264,
0.02487521804869175,
-0.05024208500981331,
-0.024419520050287247,
-0.007935643196105957,
0.006579411681741476,
0.009702168405056,
-0.038614146411418915,
-0.026586394757032394,
0.006464896257966757,
-0.000212984174140729,
0.022305352613329887,
-0.012258953414857388,
0.02214241959154606,
-0.02184242568910122,
0.04449044540524483,
-0.019942816346883774,
0.03690515086054802,
-0.058293893933296204,
0.0253125112503767,
0.06669290363788605,
0.038763828575611115,
-0.020020075142383575,
-0.019389642402529716,
-0.03902650251984596,
0.06260945647954941,
0.011120827868580818,
-0.01731991209089756,
0.023305127397179604,
-0.018405349925160408,
-0.06408797204494476,
-0.007185125723481178,
-0.039303261786699295,
0.00677240826189518,
-0.010261885821819305,
-0.01749052293598652,
-0.032181691378355026,
-0.01942111924290657,
0.06302011758089066,
-0.016165345907211304,
-0.056687794625759125,
-0.008070150390267372,
-0.004073521587997675,
-0.05929404869675636,
-0.012195958755910397,
-0.012431852519512177,
0.010836678557097912,
-0.009845798835158348,
-0.008102825842797756,
0.017598574981093407,
-0.01731245405972004,
-0.09934037923812866,
0.031667884439229965,
-0.0368608795106411,
-0.07689455896615982,
0.05391959100961685,
0.041028160601854324,
0.03210210055112839,
0.02689777873456478,
-0.031149394810199738,
0.05106813833117485,
0.002311971038579941,
0.0022029101382941008,
-0.01930285058915615,
-0.05161729082465172,
-0.007126897573471069,
-0.030686337500810623,
-0.002427580999210477,
-0.04446415230631828,
-0.05655187740921974,
0.017852462828159332,
0.028883880004286766,
0.031769707798957825,
0.02387131378054619,
-0.003015118418261409,
0.00949046853929758,
0.006721988786011934,
0.05969464033842087,
-0.05994251370429993,
-0.02590883895754814,
-0.00819556973874569,
-0.051019564270973206,
0.0043211267329752445,
-0.009444871917366982,
0.0012462864397093654,
-0.019596252590417862,
0.03501802310347557,
-0.05738910287618637,
-0.013480478897690773,
-0.012368245050311089,
0.053033094853162766,
0.00719873420894146,
0.01988878659904003,
-0.04609273001551628,
0.01148986630141735,
-0.04630466178059578,
0.05706796795129776,
-0.012695007026195526,
0.016324935480952263,
0.02055605873465538,
-0.05524381995201111,
0.011447169817984104,
-0.024280810728669167,
0.01828763261437416,
0.05804266408085823,
0.04985670745372772,
-0.011980211362242699,
0.06235218420624733,
0.01029490027576685,
0.08242963999509811,
0.005256312433630228,
-0.058676280081272125,
0.007448536343872547,
0.011645468883216381,
-0.015428864397108555,
-0.028271682560443878,
-0.0036092251539230347,
0.02500569261610508,
0.00380293489433825,
-0.054318927228450775,
-0.025096403434872627,
0.006372304167598486,
0.04268169030547142,
0.03404023498296738,
-0.026399780064821243,
-0.0031959814950823784,
0.004715876188129187,
0.028358617797493935,
-0.04841297119855881,
-0.02561739832162857,
0.025214314460754395,
0.0004680721031036228,
0.0105616245418787,
0.03453635051846504,
-0.04309549182653427,
-0.001658049295656383,
-0.011552199721336365,
0.02013850025832653,
0.0030667744576931,
-0.00852338969707489,
-0.010563983581960201,
-0.0315120667219162,
0.01676066964864731,
-0.03696681186556816,
-0.022146565839648247,
0.05284276232123375,
0.00432377215474844,
-0.07157552242279053,
0.054347820580005646,
0.03617892414331436,
-0.013429633341729641,
-0.0015083389589563012,
0.026910368353128433,
0.033648934215307236,
0.03393469750881195,
-0.036455534398555756,
-0.002895766170695424,
0.016061754897236824,
-0.046844564378261566,
-0.0507192462682724
] |
<p>It's well known that the planets don't orbit the sun in perfect circles and the characteristics of the elliptical orbits which serve as better approximations to their motion have been calculated fairly accurately.</p>
<p>How accurately do elliptical orbits model their actual paths?</p> | g5471 | [
-0.05603684484958649,
0.05045601353049278,
0.012405527755618095,
0.053987257182598114,
0.06752165406942368,
0.02046930231153965,
0.030765382573008537,
-0.03923329710960388,
0.011114810593426228,
0.0358823761343956,
0.0037417474668473005,
-0.031044676899909973,
0.08964865654706955,
-0.030394399538636208,
0.038527101278305054,
-0.03455484285950661,
-0.013150101527571678,
0.005098740570247173,
0.06680833548307419,
0.027460584416985512,
0.07373712956905365,
-0.01750686764717102,
0.02848576195538044,
0.009106500074267387,
-0.10975942760705948,
0.0207115039229393,
-0.015398316085338593,
-0.04556844010949135,
-0.0062806433998048306,
-0.01063449028879404,
0.07195079326629639,
-0.03402417153120041,
0.04055128991603851,
-0.05043576657772064,
-0.05012190341949463,
0.008547038771212101,
0.020013194531202316,
0.044507887214422226,
-0.00294893397949636,
-0.02967153675854206,
0.0555717758834362,
0.0044078282080590725,
0.016652455553412437,
0.07979333400726318,
0.03466951847076416,
-0.04033900797367096,
-0.025515103712677956,
-0.0031615635380148888,
0.01867644675076008,
-0.020460955798625946,
-0.035895880311727524,
0.060776881873607635,
0.04281199723482132,
0.000867457187268883,
-0.002335389843210578,
0.05832423269748688,
0.03516209498047829,
-0.026803528890013695,
0.02666112594306469,
0.006290806457400322,
0.021751748397946358,
-0.0006330636679194868,
-0.013467928394675255,
-0.034589096903800964,
-0.022499922662973404,
0.015557991340756416,
-0.00410539610311389,
0.016310524195432663,
0.017522558569908142,
-0.03300076723098755,
0.024764979258179665,
0.02490164339542389,
-0.020616883412003517,
-0.07770012319087982,
-0.059557948261499405,
0.03360692784190178,
0.033452510833740234,
-0.030114399269223213,
0.026843247935175896,
0.04790014401078224,
0.006860977038741112,
0.03749512881040573,
-0.03652982413768768,
-0.0012617961037904024,
0.05288121476769447,
-0.019706718623638153,
0.020470820367336273,
0.01356158684939146,
0.0022375215776264668,
-0.006030313204973936,
-0.006688117980957031,
-0.04499970003962517,
0.04780890792608261,
0.022728588432073593,
0.008111951872706413,
-0.009327378123998642,
-0.08379978686571121,
0.051094815135002136,
0.06323640048503876,
0.03417487442493439,
-0.01801224797964096,
0.01775423251092434,
-0.00347071117721498,
-0.0205253753811121,
0.020989039912819862,
0.00039017200469970703,
0.048594940453767776,
0.026795951649546623,
0.04851936176419258,
-0.03260580450296402,
-0.020917559042572975,
-0.05001853033900261,
0.022174542769789696,
-0.005958734080195427,
-0.041819870471954346,
0.006048188079148531,
-0.021373596042394638,
-0.04492494463920593,
0.07976473867893219,
0.0575677864253521,
0.06882698088884354,
0.01236085407435894,
-0.025106512010097504,
0.03339579328894615,
0.0631830096244812,
-0.04283994808793068,
-0.011995513923466206,
-0.06128963455557823,
0.020649272948503494,
0.01953275501728058,
0.011989464983344078,
0.0022962598595768213,
-0.028139643371105194,
0.002902381820604205,
0.03742627799510956,
-0.02115177921950817,
0.033671580255031586,
-0.02551998384296894,
-0.03721572458744049,
-0.02838875912129879,
0.042514629662036896,
0.01929229125380516,
0.03486816957592964,
-0.024434693157672882,
-0.08790989220142365,
0.02110729180276394,
-0.00011112247739220038,
0.02675018645823002,
0.04079601541161537,
0.026897111907601357,
-0.014564900659024715,
0.051740217953920364,
0.03335724025964737,
-0.015672503039240837,
-0.028101950883865356,
0.0003881404409185052,
-0.014458652585744858,
0.027110623195767403,
0.00215060799382627,
0.012763992883265018,
0.06019144505262375,
-0.0331217385828495,
0.0503850057721138,
-0.009958598762750626,
-0.04253518581390381,
0.004537888336926699,
0.024490326642990112,
-0.03886786475777626,
-0.008036764338612556,
0.023836921900510788,
-0.00791403278708458,
-0.013689888641238213,
-0.006229058373719454,
0.06693322956562042,
-0.07535106688737869,
0.01138586550951004,
0.017108459025621414,
-0.015298927202820778,
-0.001838908763602376,
-0.018497880548238754,
0.06768158823251724,
0.03363598510622978,
-0.012674946337938309,
0.0038094939664006233,
-0.03242380917072296,
-0.020073074847459793,
0.00039909480256028473,
-0.05934106931090355,
-0.005758863873779774,
-0.05871686339378357,
0.02698586694896221,
0.023875080049037933,
0.04686163365840912,
-0.02268589660525322,
0.03826607018709183,
0.030426662415266037,
-0.027639951556921005,
-0.0022487426176667213,
-0.017839541658759117,
0.08385360985994339,
0.027956228703260422,
0.01292479783296585,
0.017224667593836784,
0.0029067869763821363,
-0.027133358642458916,
-0.00635626632720232,
-0.00583660276606679,
-0.012944797053933144,
0.03506730869412422,
0.0008638131548650563,
0.0017265032511204481,
0.04335229843854904,
0.002403577556833625,
0.022062646225094795,
-0.033829156309366226,
-0.0002882380795199424,
-0.025587692856788635,
0.03261682018637657,
-0.0002972827642224729,
-0.012521852739155293,
-0.00860535353422165,
-0.01478044968098402,
0.04731354862451553,
-0.0248413123190403,
0.03904961422085762,
0.012454166077077389,
-0.05943436175584793,
0.014464542269706726,
-0.026876868680119514,
0.08231509476900101,
-0.04451458901166916,
-0.06928402930498123,
0.01512768305838108,
0.010552841238677502,
0.00007079142233124003,
-0.050050243735313416,
0.01763061061501503,
-0.054304033517837524,
0.055294912308454514,
0.019366620108485222,
0.05429786816239357,
-0.02646990492939949,
-0.012790605425834656,
0.005205988418310881,
0.02658517099916935,
-0.04576745256781578,
0.04516765847802162,
0.05083468556404114,
-0.05259047821164131,
0.03788973391056061,
0.048792511224746704,
0.005556281190365553,
-0.03856119513511658,
-0.0004929227870889008,
0.012625610455870628,
-0.013589434325695038,
0.007498686667531729,
-0.0020428630523383617,
-0.01367297861725092,
0.05625898391008377,
0.0026289247907698154,
-0.033121999353170395,
0.02047298289835453,
0.008503695018589497,
0.01735108718276024,
-0.024030327796936035,
0.04587080702185631,
-0.06527291983366013,
-0.014126046560704708,
-0.01907498575747013,
0.004605796653777361,
0.056352656334638596,
0.002011961303651333,
0.043591514229774475,
-0.03713109344244003,
-0.02577115409076214,
-0.03448095545172691,
-0.0074681444093585014,
-0.05765876546502113,
0.014562913216650486,
0.010196389630436897,
-0.013744954019784927,
-0.006764707155525684,
-0.005625108256936073,
0.0642448216676712,
-0.05725939944386482,
-0.022705845534801483,
0.07640025019645691,
0.005773796234279871,
-0.026195650920271873,
0.016350572928786278,
0.004268369637429714,
0.03381358087062836,
0.05470062792301178,
-0.03725519776344299,
0.01939035765826702,
-0.013647333718836308,
-0.028476782143115997,
0.009300035424530506,
0.009828486479818821,
-0.002662257757037878,
0.08012279123067856,
-0.06276380270719528,
0.062204211950302124,
-0.033558961004018784,
0.0423353835940361,
0.02448526956140995,
-0.033628933131694794,
0.026060624048113823,
-0.021903982385993004,
-0.012101327069103718,
0.032658740878105164,
-0.0210211630910635,
0.028380053117871284,
0.03691857308149338,
-0.03225438669323921,
-0.052384670823812485,
-0.024022836238145828,
0.012516315095126629,
0.03324924409389496,
-0.03463362157344818,
-0.06080104038119316,
-0.04334767162799835,
0.03484080731868744,
0.028699658811092377,
0.06566108018159866,
-0.0021968635264784098,
-0.11183417588472366,
-0.003842355916276574,
-0.0032758209854364395,
0.003467387054115534,
0.02512826956808567,
-0.06497961282730103,
0.07309688627719879,
-0.012452010065317154,
-0.025548558682203293,
-0.03934624046087265,
-0.002915620803833008,
-0.007666024845093489,
-0.011090174317359924,
-0.009554699063301086,
0.0009758161031641066,
0.011310944333672523,
-0.06275587528944016,
-0.02496323175728321,
0.004715315997600555,
-0.016687318682670593,
-0.04011349007487297,
0.007820059545338154,
-0.0578848235309124,
0.08144953846931458,
-0.036639321595430374,
-0.02435024082660675,
-0.031454455107450485,
0.017491227015852928,
0.024340448901057243,
0.02938682772219181,
0.020463263615965843,
0.03562776744365692,
0.06884763389825821,
0.022901389747858047,
0.05218195915222168,
-0.024143435060977936,
-0.006504732184112072,
0.04159320890903473,
-0.04687139019370079,
-0.023200983181595802,
0.008108307607471943,
0.02429177798330784,
0.03905937075614929,
-0.03249645233154297,
0.06134572625160217,
0.057795774191617966,
-0.04108623415231705,
0.07209670543670654,
-0.007795530371367931,
0.028458280488848686,
0.045757029205560684,
-0.026474660262465477,
-0.022674107924103737,
-0.027415422722697258,
0.020403092727065086,
0.011638323776423931,
-0.012317324988543987,
0.024853527545928955,
-0.006583480630069971,
0.010327950119972229,
-0.03523401543498039,
-0.038476597517728806,
0.013954329304397106,
0.030013225972652435,
-0.06850593537092209,
0.015427550300955772,
-0.01731284335255623,
0.055434804409742355,
-0.06089038401842117,
0.01316349022090435,
-0.025274140760302544,
-0.035892896354198456,
-0.021667908877134323,
0.018503375351428986,
-0.01661957986652851,
0.01047089695930481,
-0.009989556856453419,
-0.03922150656580925,
0.014367473311722279,
-0.08015520870685577,
-0.0016128283459693193,
-0.01672150008380413,
-0.010898569598793983,
0.01816580630838871,
0.05807642638683319,
0.0030908009503036737,
0.023814130574464798,
0.04037512466311455,
0.04649519920349121,
-0.09911080449819565,
-0.037694886326789856,
0.027543993666768074,
0.03128017112612724,
-0.040918998420238495,
0.022361814975738525,
-0.03852619230747223,
-0.04281497746706009,
0.006046979688107967,
0.10080376267433167,
0.06323383748531342,
-0.05237875506281853,
0.023512225598096848,
-0.039999593049287796,
0.013242579065263271,
-0.007020661141723394,
0.025003183633089066,
0.02616584300994873,
-0.033731814473867416,
0.03471504524350166,
0.02446046844124794,
0.031512800604104996,
-0.009444969706237316,
0.0005204618209972978,
-0.0022944905795156956,
0.07799995690584183,
-0.0004252437793184072,
0.006032672710716724,
-0.042442336678504944,
-0.01668594405055046,
-0.012864998541772366,
0.015572533011436462,
0.0024407550226897,
-0.02025238610804081,
-0.05596475675702095,
0.0035554252099245787,
0.04467432573437691,
0.050359711050987244,
-0.03659456595778465,
0.002430608030408621,
-0.0581219308078289,
0.07555647194385529,
0.015360320918262005,
0.009694424457848072,
-0.035159241408109665,
0.00013882805069442838,
0.030002983286976814,
0.03608641400933266,
-0.0013133147731423378,
-0.03434431552886963,
-0.005397206638008356,
0.010800906457006931,
-0.027443554252386093,
-0.006389763206243515,
-0.011741315945982933,
0.02021820843219757,
0.023751532658934593,
0.0024071303196251392,
0.006455288268625736,
-0.07123345136642456,
-0.029808005318045616,
-0.015671072527766228,
0.0032609214540570974,
-0.000826069968752563,
-0.0015258772764354944,
-0.035900913178920746,
0.022481264546513557,
0.03801623731851578,
-0.042764339596033096,
0.020548393949866295,
-0.006746807135641575,
-0.05365655943751335,
0.011583919636905193,
-0.015055288560688496,
0.005758014973253012,
0.027797970920801163,
-0.041990965604782104,
-0.07930045574903488,
-0.04140938073396683,
-0.0022137421183288097,
0.033670831471681595,
-0.04153672233223915,
0.03095649741590023,
0.05426141992211342,
-0.10810405761003494,
0.08653959631919861,
-0.03141360357403755,
-0.027704862877726555,
0.01666356436908245,
0.03367695212364197,
0.021944480016827583,
-0.06021106243133545,
-0.03139391168951988,
-0.037746597081422806,
0.03673567622900009,
0.003340827999636531,
-0.07251667231321335,
0.03279706463217735,
-0.019012749195098877,
-0.04791197553277016,
-0.06199372187256813,
0.03012320026755333,
0.00676010362803936,
-0.00863032415509224,
0.017605606466531754,
0.03884126618504524,
0.048615939915180206,
-0.03816493600606918,
0.08306355029344559,
-0.029047587886452675,
0.009165025316178799,
-0.013679301366209984,
0.018953772261738777,
-0.016711441799998283,
-0.007574965711683035,
-0.036248136311769485,
-0.04079113155603409,
-0.006481134332716465,
-0.02963506057858467,
-0.05198775231838226,
0.014644530601799488,
-0.028698567301034927,
0.03144505247473717,
-0.005328976083546877,
-0.012886671349406242,
0.05462866276502609,
0.024820471182465553,
0.020027214661240578,
-0.015823211520910263,
-0.02389279007911682,
0.017156457528471947,
0.07843749225139618,
0.012079589068889618,
-0.035999976098537445,
-0.05822724476456642,
0.00991698820143938,
-0.009840906597673893,
-0.02933681011199951,
-0.03825979679822922,
0.0444125272333622,
-0.014623943716287613,
-0.018919123336672783,
-0.007932827807962894,
-0.06070614606142044,
-0.019424835219979286,
0.003172684460878372,
0.023479122668504715,
0.03423711657524109,
-0.040511347353458405,
0.01980149932205677,
0.013543224893510342,
-0.02579418197274208,
0.002862051362171769,
0.0117283184081316,
-0.007279949262738228,
-0.05803988501429558,
0.017180370166897774,
0.01709485426545143,
-0.0127651272341609,
-0.015710923820734024,
-0.030836163088679314,
0.00683983601629734,
-0.02166144922375679,
-0.015144788660109043,
-0.004089031834155321,
-0.00863429345190525,
0.019905922934412956,
0.024434639140963554,
-0.013087132945656776,
0.06396269798278809,
-0.012530560605227947,
0.053653642535209656,
-0.006530513521283865,
-0.0288302693516016,
-0.017499137669801712,
-0.0059127043932676315,
0.017420032992959023,
0.0313766673207283,
-0.002809705678373575,
-0.005889646243304014,
-0.01793747767806053,
0.03923758491873741,
0.004141419660300016,
-0.004656933713704348,
-0.00015830669144634157,
0.02162724733352661,
0.028855198994278908,
-0.025332104414701462,
0.04003531113266945,
-0.01124489214271307,
0.04138210788369179,
0.07607237994670868,
0.014404896646738052,
-0.020311851054430008,
0.02222725749015808,
0.048424992710351944,
0.0340612530708313,
0.026342852041125298,
-0.07177120447158813,
-0.020388459786772728,
0.022456593811511993,
-0.0332411453127861,
0.02582637593150139,
-0.03615140914916992,
0.0019353419775143266,
-0.006433762609958649,
0.0021951659582555294,
-0.05909959599375725,
-0.027221594005823135,
0.008061780594289303,
-0.022493651136755943,
0.0038887010887265205,
-0.04110383987426758,
-0.047919973731040955,
-0.001615464105270803,
-0.023820091038942337,
-0.0033668125979602337,
0.06752301752567291,
0.06600227952003479,
0.025470193475484848,
-0.015467870980501175,
0.004710651934146881,
0.00016459680045954883,
0.04514547437429428,
-0.027717415243387222,
-0.0354316383600235,
0.005871756002306938,
0.005596790928393602,
-0.08404403179883957,
-0.01202025730162859,
-0.0197896808385849,
-0.003930539358407259,
-0.01583763398230076,
0.0213290024548769,
-0.01658523641526699,
-0.07294486463069916,
0.01640772819519043,
-0.019254649057984352,
0.03824683651328087,
0.031366314738988876,
-0.03253715857863426,
0.03258848935365677,
0.027171896770596504,
-0.035668034106492996,
0.03304864466190338,
0.03272756189107895,
-0.02331000752747059,
-0.02504711225628853,
0.032998520880937576,
-0.072267547249794,
-0.028193913400173187,
0.008054327219724655,
-0.07841354608535767,
0.023507459089159966,
0.031069258227944374,
0.02925715781748295,
-0.03451289236545563,
0.0409860834479332,
0.007415540982037783,
-0.020455852150917053,
-0.0205086562782526,
-0.11185748875141144,
-0.019555212929844856,
0.002733012894168496,
-0.023133397102355957,
0.0006012687226757407,
0.04463765397667885,
0.0424589067697525,
0.0017888502916321158,
0.03086567297577858,
0.020341239869594574,
-0.04074055701494217,
-0.05677042528986931,
-0.037725936621427536,
-0.024198343977332115,
0.07718288898468018,
-0.02338043600320816,
-0.05175500735640526,
0.018991732969880104,
0.028984524309635162,
-0.0062683988362550735,
0.00008892008190741763,
0.021383225917816162,
-0.00046971754636615515,
0.021285004913806915,
-0.019417552277445793,
0.03899327665567398,
-0.00038409430999308825,
0.054288942366838455,
-0.01419177558273077,
-0.07335451245307922,
0.09960713237524033,
-0.029303545132279396,
0.012663922272622585,
0.08901840448379517,
0.029119452461600304,
-0.05635470524430275,
0.008725992403924465,
-0.029186472296714783,
-0.020272905007004738,
-0.027336513623595238,
-0.028044836595654488,
-0.015387454070150852,
-0.026776373386383057,
0.004978020675480366,
-0.05214959755539894,
0.02384471334517002,
0.0008035687496885657,
0.03443906456232071,
-0.045535583049058914,
-0.03390555828809738,
-0.03597453609108925,
0.04096592962741852,
-0.03935673087835312,
0.017509084194898605,
0.03413951024413109,
-0.009094237349927425,
0.016422763466835022,
-0.03225763514637947,
-0.013703756034374237,
-0.06872484087944031,
-0.0694969892501831,
-0.025418652221560478,
-0.006869264878332615,
-0.019863732159137726,
-0.05978721007704735,
0.015992343425750732,
-0.03689804673194885,
-0.0004731727240141481,
-0.02451680600643158,
-0.026319511234760284,
-0.030212145298719406,
-0.057636115700006485,
0.010480422526597977,
-0.012839637696743011,
0.03835706412792206,
-0.01768450252711773,
-0.0048409728333354,
-0.05098913237452507,
0.060804061591625214,
0.02595558948814869,
-0.07924046367406845,
-0.04999009892344475,
0.03218017891049385,
0.009973425418138504,
-0.05412067845463753,
0.06690583378076553,
-0.010491995140910149,
-0.0026962398551404476,
0.0005478900275193155,
0.002270469442009926,
0.028550634160637856
] |
<p>What is meant with the fact that Super Yang-Mills flows to a conformal field theory in the infrared? Also, is this a general fact or does this depend on the fact of considering a certain class of theories (such as $N=4$, $d=3$ for example)?</p>
<p>I have seen this statement numerous times in various articles such as</p>
<p><a href="http://arxiv.org/abs/hep-th/0207074">http://arxiv.org/abs/hep-th/0207074</a></p>
<p><a href="http://arxiv.org/abs/hep-th/0206054">http://arxiv.org/abs/hep-th/0206054</a></p>
<p>Every time this fact is stated by some author it is given as a known thing, and it is not explained.
With an online research I could not make sense of this.</p>
<p>Could someone please explain?</p> | g5472 | [
0.06248589977622032,
0.0424179770052433,
-0.02973904460668564,
0.02429068833589554,
0.03593394532799721,
0.07611390203237534,
0.03738461062312126,
0.011095358058810234,
0.021297531202435493,
-0.030789200216531754,
-0.00930520799010992,
0.013439529575407505,
0.034139614552259445,
-0.008029267191886902,
-0.05712069943547249,
-0.05130818486213684,
-0.004428863991051912,
0.029191622510552406,
0.015081463381648064,
0.01833656057715416,
-0.05329970270395279,
-0.04667019471526146,
0.05509296804666519,
-0.04790382459759712,
-0.00023491831962019205,
-0.004310183692723513,
0.04641372710466385,
-0.10009288042783737,
0.06828628480434418,
-0.03262684494256973,
0.043349094688892365,
0.028746649622917175,
0.08522475510835648,
-0.055120717734098434,
-0.026206299662590027,
0.02972976490855217,
0.0565897673368454,
0.0031899847090244293,
0.04225010424852371,
-0.004417290911078453,
-0.021467432379722595,
0.04238590970635414,
0.02444508485496044,
-0.005425353068858385,
-0.03101487085223198,
-0.0130912559106946,
0.0009279553778469563,
0.01143509242683649,
-0.04335113242268562,
0.03029075264930725,
0.0327962227165699,
0.043453648686409,
0.03143695369362831,
0.03258823975920677,
-0.009739669039845467,
0.03828908130526543,
-0.0003106717485934496,
0.031553205102682114,
0.010183457285165787,
0.011203734204173088,
0.0054918392561376095,
-0.0552806593477726,
0.04329800605773926,
0.02356998808681965,
0.03871898725628853,
-0.01541720051318407,
-0.05441303178668022,
-0.044001199305057526,
0.05549245700240135,
-0.0055558402091264725,
0.005933190695941448,
-0.007063782308250666,
0.011830530129373074,
-0.00887860357761383,
-0.02371053211390972,
0.03692420572042465,
0.014822282828390598,
-0.032737430185079575,
-0.03925864398479462,
0.0011917806696146727,
-0.0448443777859211,
-0.04348289221525192,
0.059839725494384766,
0.005173642188310623,
0.03470101207494736,
-0.011156124994158745,
-0.020440109074115753,
0.03437075763940811,
0.007309171371161938,
-0.021643366664648056,
0.010838323272764683,
0.00008717455057194456,
-0.01752338372170925,
0.01864687167108059,
0.0344255231320858,
0.012669345363974571,
-0.00851532630622387,
0.021281030029058456,
0.01824912428855896,
-0.00470507750287652,
-0.047601595520973206,
0.03237636759877205,
0.051280613988637924,
0.029379503801465034,
-0.009481741115450859,
0.0014047255972400308,
-0.023791633546352386,
0.01452912949025631,
0.03045688383281231,
-0.0301483403891325,
-0.06161351874470711,
0.03490429371595383,
-0.03778446093201637,
0.0023557862732559443,
-0.0063482834957540035,
0.016276594251394272,
0.027237489819526672,
0.0016124509274959564,
-0.0033838339149951935,
0.0425865463912487,
0.024112898856401443,
-0.0246333759278059,
0.006292590405791998,
0.035240404307842255,
-0.06980011612176895,
-0.02330910973250866,
0.00724839000031352,
0.020384106785058975,
-0.030705584213137627,
-0.03293526917695999,
0.03904031217098236,
0.002092160517349839,
-0.0009741866961121559,
-0.018928969278931618,
0.032791703939437866,
-0.019412130117416382,
0.009852692484855652,
-0.05813430994749069,
0.026226025074720383,
0.014642606489360332,
0.014973878860473633,
0.0029340237379074097,
0.022965041920542717,
-0.016781019046902657,
-0.039818163961172104,
-0.022835537791252136,
-0.020634524524211884,
-0.01724301464855671,
0.0035814852453768253,
0.01547360047698021,
0.031298913061618805,
0.10536377131938934,
-0.006947478279471397,
-0.09401793032884598,
0.03211997076869011,
-0.012525324709713459,
-0.02314574643969536,
-0.04020518437027931,
0.017157312482595444,
-0.043113164603710175,
-0.00578576885163784,
-0.0034383749589323997,
0.026425587013363838,
0.05900083854794502,
-0.08917476236820221,
-0.019538961350917816,
0.004563536960631609,
-0.0075541408732533455,
-0.06877878308296204,
-0.058045774698257446,
-0.04348808899521828,
0.03868391364812851,
-0.019282326102256775,
0.007780850399285555,
0.02478235960006714,
0.023917129263281822,
-0.01646290346980095,
-0.025465862825512886,
0.05415373295545578,
-0.02893282100558281,
-0.058759454637765884,
-0.029346225783228874,
0.0037070203106850386,
-0.06961863487958908,
0.0054907724261283875,
0.031418073922395706,
-0.017584459856152534,
0.03515142202377319,
-0.006275500636547804,
0.022328734397888184,
-0.03972531110048294,
0.040854066610336304,
0.002661212580278516,
0.015435856766998768,
0.0005989988567307591,
0.009933081455528736,
-0.014170276001095772,
-0.040335964411497116,
-0.010417824611067772,
-0.02582523785531521,
0.012513665482401848,
-0.021526413038372993,
-0.005311422049999237,
-0.01924269087612629,
0.0300894882529974,
0.04900849610567093,
-0.032789021730422974,
0.014454999007284641,
0.013395569287240505,
0.005401423200964928,
0.012782436795532703,
-0.00030257331673055887,
0.01778886653482914,
-0.049217212945222855,
-0.03714104741811752,
-0.038220182061195374,
0.02495627850294113,
-0.025464937090873718,
-0.07520455121994019,
0.02562987245619297,
0.026022756472229958,
0.004235588014125824,
0.06264730542898178,
-0.018028948456048965,
-0.018002357333898544,
-0.01949218660593033,
-0.05965171381831169,
-0.041602835059165955,
0.00039004653808660805,
-0.00518513098359108,
-0.09013854712247849,
-0.053602200001478195,
0.0010767732746899128,
-0.029910380020737648,
-0.010256530717015266,
0.03999468684196472,
-0.010438526049256325,
-0.02115330472588539,
0.04365680739283562,
0.02321489341557026,
0.02915710210800171,
0.031323544681072235,
0.035058584064245224,
-0.04942527785897255,
0.003156928811222315,
0.07023436576128006,
0.03896478936076164,
-0.028591925278306007,
-0.011402850039303303,
-0.005911503918468952,
0.014507140964269638,
-0.04284771904349327,
-0.019382905215024948,
0.001573283807374537,
0.0008957040263339877,
-0.01920349895954132,
0.006629981566220522,
0.036840662360191345,
-0.011013067327439785,
-0.016639407724142075,
0.06165432184934616,
0.00546296825632453,
0.009804166853427887,
0.02211681939661503,
-0.018805155530571938,
-0.010893230326473713,
-0.011899687349796295,
0.00040843035094439983,
-0.0231767687946558,
-0.06708347797393799,
-0.04402405023574829,
0.034612905234098434,
-0.02461918070912361,
-0.016067806631326675,
-0.039023011922836304,
-0.007639076095074415,
-0.010029822587966919,
0.030926000326871872,
0.007143338676542044,
0.003174461657181382,
-0.058646902441978455,
-0.07836702466011047,
-0.032262638211250305,
-0.022897355258464813,
-0.0038493392057716846,
-0.08979105204343796,
0.0038633104413747787,
-0.04358392208814621,
-0.027054255828261375,
0.018209341913461685,
-0.0012489337241277099,
-0.029503323137760162,
0.0010676365345716476,
0.0521925650537014,
-0.022926824167370796,
0.017782283946871758,
0.02171538583934307,
0.0086179468780756,
0.0026137731038033962,
0.0752682313323021,
-0.010522400960326195,
0.06617868691682816,
0.009188767522573471,
0.05148354545235634,
0.056034572422504425,
0.013586333952844143,
-0.07439965754747391,
-0.01795409806072712,
-0.02831924706697464,
-0.03637850657105446,
0.015388868749141693,
0.014351013116538525,
-0.009316051378846169,
0.042651500552892685,
-0.021200722083449364,
-0.0024170968681573868,
-0.019026750698685646,
0.03455864638090134,
0.037204910069704056,
0.005338401533663273,
-0.05059841275215149,
-0.01956101693212986,
0.03207891806960106,
0.0049770730547606945,
0.0268924031406641,
0.010969221591949463,
-0.04065997526049614,
0.0008684839704073966,
0.00432603107765317,
0.010047423653304577,
-0.026068853214383125,
-0.00788890477269888,
-0.008887658827006817,
0.014080114662647247,
-0.03957207128405571,
-0.002258745487779379,
-0.06602144241333008,
0.029055265709757805,
0.024241158738732338,
-0.011329742148518562,
0.026816120371222496,
-0.027773717418313026,
-0.05594507232308388,
-0.001290510524995625,
0.06149725243449211,
0.04400245472788811,
-0.04158017784357071,
-0.025318030267953873,
0.03183022513985634,
-0.03326563164591789,
0.018750140443444252,
-0.00939923245459795,
0.07277194410562515,
-0.04364938661456108,
0.0038739051669836044,
0.01457489375025034,
-0.010059738531708717,
0.05265219137072563,
0.040464241057634354,
0.011961769312620163,
-0.020407313480973244,
0.013673384673893452,
0.03546421602368355,
0.01462575327605009,
-0.00754179572686553,
0.019202206283807755,
-0.024071067571640015,
-0.052214380353689194,
0.03284011781215668,
0.05327408015727997,
0.021092968061566353,
-0.034752946346998215,
-0.032263487577438354,
0.0510849803686142,
0.02159956470131874,
-0.05478934943675995,
0.007013671565800905,
0.04675307124853134,
-0.04992303252220154,
0.033433325588703156,
0.02947843261063099,
0.09115804731845856,
-0.007271008100360632,
0.030321529135107994,
-0.002356352284550667,
0.007246430031955242,
-0.045404449105262756,
0.02041465975344181,
-0.041117534041404724,
0.013943481259047985,
-0.020048467442393303,
0.011908612214028835,
-0.011157449334859848,
-0.03715924546122551,
-0.0055895294062793255,
0.028318017721176147,
0.021311789751052856,
-0.018856674432754517,
-0.01125192828476429,
-0.003709241980686784,
0.07802192866802216,
0.018107715994119644,
-0.017903367057442665,
-0.017392387613654137,
-0.059237219393253326,
-0.0060255322605371475,
0.014465359970927238,
0.02157316356897354,
0.022330675274133682,
-0.051808129996061325,
-0.0262917447835207,
0.04396336153149605,
0.013736366294324398,
-0.07507895678281784,
0.05010373517870903,
0.03257974237203598,
0.03279160335659981,
-0.03866233676671982,
0.0008597433916293085,
-0.04330127686262131,
0.054739683866500854,
-0.04861210659146309,
0.024893078953027725,
-0.026539435610175133,
0.04463515058159828,
0.07116570323705673,
0.060238659381866455,
0.017062246799468994,
-0.01572570763528347,
-0.05345546826720238,
0.024493444710969925,
0.025432655587792397,
-0.01096572820097208,
0.02352455072104931,
-0.0335814394056797,
0.0779305025935173,
0.02663329988718033,
0.030156834051012993,
-0.018197670578956604,
0.07257580757141113,
0.08501628786325455,
-0.008219345472753048,
0.09279535710811615,
-0.03592251241207123,
0.021056869998574257,
-0.006382186431437731,
-0.06255482882261276,
-0.036160875111818314,
-0.03937321901321411,
-0.06650509685277939,
-0.046444740146398544,
0.012293169274926186,
-0.010121461935341358,
0.026412371546030045,
-0.007361206226050854,
-0.06337042897939682,
-0.011467528529465199,
0.017786134034395218,
0.014630751684308052,
-0.006924530491232872,
-0.03435350954532623,
-0.035955894738435745,
0.011887979693710804,
-0.012661464512348175,
0.03198098763823509,
0.030597103759646416,
-0.01189070288091898,
-0.03501906245946884,
-0.11489036679267883,
-0.07894212007522583,
0.07254315912723541,
0.007057227659970522,
-0.0019908915273845196,
-0.016980301588773727,
0.014020903035998344,
0.011482832953333855,
0.02661411464214325,
-0.026781532913446426,
0.025081191211938858,
-0.034264110028743744,
-0.002068118192255497,
-0.014069980941712856,
0.07502798736095428,
0.049774039536714554,
0.021674219518899918,
-0.012330267578363419,
-0.033051297068595886,
-0.027341296896338463,
-0.012508015148341656,
-0.06402240693569183,
-0.030226897448301315,
-0.0013291548239067197,
-0.03653211146593094,
0.04940059036016464,
-0.06253467500209808,
0.023742886260151863,
0.012480470351874828,
-0.0007617122610099614,
-0.064365915954113,
0.02613825723528862,
-0.07056183367967606,
0.013220035471022129,
0.014036382548511028,
0.015171593055129051,
-0.011339404620230198,
0.09156566113233566,
0.07919451594352722,
0.017857646569609642,
-0.0023409626446664333,
-0.04758335277438164,
0.0173180028796196,
-0.05970613285899162,
0.005337684880942106,
0.03437093272805214,
0.08170370012521744,
-0.00524391932412982,
-0.02340123802423477,
-0.00014956798986531794,
0.01315959170460701,
-0.018757499754428864,
0.024326985701918602,
0.009860193356871605,
0.01938517577946186,
0.01866615191102028,
0.004216160625219345,
0.06777193397283554,
-0.08063724637031555,
-0.032511938363313675,
0.06627431511878967,
0.07119175791740417,
0.051610030233860016,
-0.047123298048973083,
0.1084882840514183,
0.05570882931351662,
0.041531987488269806,
-0.0033939252607524395,
0.022976061329245567,
0.018715571612119675,
0.0433051697909832,
0.05872294679284096,
-0.0195454228669405,
0.021464422345161438,
0.02161821536719799,
-0.015563677996397018,
-0.009942279197275639,
-0.0022368619684129953,
0.025096509605646133,
-0.029322156682610512,
0.04353136941790581,
-0.03206227347254753,
-0.04377215728163719,
0.03291758894920349,
-0.04445255547761917,
-0.026076748967170715,
0.050583723932504654,
0.018017278984189034,
-0.0035239874850958586,
-0.022488724440336227,
-0.04658505693078041,
0.011222443543374538,
-0.040448352694511414,
-0.002271363278850913,
0.010444145649671555,
-0.04175432026386261,
0.029112420976161957,
-0.00453916983678937,
-0.030420461669564247,
-0.013340488076210022,
0.025320833548903465,
0.04148273542523384,
-0.033046431839466095,
0.05410418659448624,
0.04436799883842468,
-0.002523713745176792,
-0.020608291029930115,
0.016324572265148163,
-0.015260021202266216,
-0.03634515777230263,
-0.03820236772298813,
-0.028870146721601486,
0.060726288706064224,
-0.021312158554792404,
-0.027410045266151428,
-0.10230465978384018,
-0.012129724025726318,
0.04460270702838898,
-0.03254186734557152,
0.008899318985641003,
0.04347153380513191,
0.015940586104989052,
-0.0071251713670790195,
-0.02965482510626316,
0.023654652759432793,
0.031107179820537567,
0.032863229513168335,
-0.003963553346693516,
-0.06615855544805527,
0.038582079112529755,
-0.009339460171759129,
-0.032958984375,
0.0046394686214625835,
0.0024936189875006676,
0.03566385805606842,
-0.008966895751655102,
-0.01946670189499855,
0.046392105519771576,
-0.017851650714874268,
0.023800337687134743,
0.030090272426605225,
0.050894707441329956,
-0.031562138348817825,
0.0010398111771792173,
0.0625934898853302,
0.0072953482158482075,
-0.0030957944691181183,
-0.032524146139621735,
-0.05401238799095154,
0.011362138204276562,
-0.028408711776137352,
-0.0031029810197651386,
0.06796250492334366,
0.0305506382137537,
0.024718347936868668,
-0.015565544366836548,
0.01856955885887146,
0.02564810961484909,
-0.01037992537021637,
0.017933908849954605,
0.03252951428294182,
0.03861250728368759,
-0.05353017523884773,
0.010990834794938564,
-0.033519890159368515,
0.06819712370634079,
-0.01817293092608452,
-0.018362872302532196,
-0.06983771920204163,
-0.02595817670226097,
0.05469826981425285,
0.02171097695827484,
-0.043218690901994705,
-0.00843482930213213,
0.0177325326949358,
-0.010512021370232105,
-0.03766544908285141,
0.02703174389898777,
-0.0012235118774697185,
-0.047089360654354095,
-0.05559074506163597,
-0.05671566724777222,
0.004449857398867607,
-0.028796158730983734,
-0.037265606224536896,
0.0247670765966177,
-0.07255270332098007,
-0.03334785997867584,
-0.04327079653739929,
0.03512699902057648,
-0.008273485116660595,
-0.022994322702288628,
0.0038699007127434015,
-0.05138656124472618,
0.03205938637256622,
0.04320886358618736,
-0.011778751388192177,
0.019996190443634987,
-0.02207331173121929,
-0.05606371536850929,
0.0015610912814736366,
-0.019266966730356216,
-0.02338855154812336,
0.005180647596716881,
0.010269849561154842,
-0.024869946762919426,
-0.03606206923723221,
-0.028133574873209,
-0.0088419821113348,
0.041903406381607056,
0.0073181865736842155,
-0.002051144139841199,
0.012760373763740063,
0.07529308646917343,
0.047452643513679504,
-0.048495497554540634,
-0.05303400382399559,
-0.0069812280125916,
0.019735395908355713,
-0.05702443793416023,
0.001213114825077355,
0.015552988275885582,
0.03042895346879959,
-0.021493852138519287,
0.03040279820561409,
0.013822860084474087,
0.004540107678622007,
0.06896570324897766,
0.007131955120712519,
0.017688503488898277,
0.012123978696763515,
0.07327340543270111,
-0.010684516280889511,
-0.05132457986474037,
-0.07885847240686417,
-0.011712128296494484,
0.05689045414328575,
0.04422368109226227,
-0.008033382706344128,
0.018918536603450775,
-0.06389573216438293,
-0.05783004313707352,
0.004863365553319454,
-0.011548686772584915,
0.031804438680410385,
0.02869638055562973,
0.01930856890976429,
0.009661752730607986,
-0.03822896257042885,
-0.014126433990895748,
-0.024256998673081398,
-0.044150736182928085,
0.019572673365473747,
0.028731705620884895,
-0.04130903258919716,
0.0077156671322882175,
-0.0037828858476132154,
-0.00823194719851017,
-0.04323761910200119,
-0.03998212143778801,
0.036026280373334885,
-0.03731934353709221,
-0.04466286301612854,
0.0075297169387340546,
-0.03180082514882088,
-0.007964407093822956,
-0.07859395444393158,
0.05892793834209442,
-0.008031380362808704,
0.013986652716994286,
-0.0015571226831525564,
-0.030619340017437935,
0.04146163910627365,
0.024828916415572166,
0.024234984070062637,
-0.04408196359872818,
-0.06707637757062912,
-0.061320580542087555,
0.0003072910476475954,
0.013112572953104973,
-0.07006687670946121,
0.02456238679587841,
0.019230199977755547,
0.05472978949546814,
-0.005057178437709808,
0.07043201476335526,
0.08773979544639587,
-0.011780922301113605,
-0.033369872719049454,
0.0092687476426363,
-0.017315493896603584,
0.031813085079193115,
-0.0012911314843222499,
-0.011638473719358444,
0.012486595660448074,
0.04824597015976906,
0.023699497804045677,
-0.056070275604724884,
-0.009388493373990059,
0.01761467009782791
] |
<p>How would I calculate the uncertainty for the average of this set?</p>
<p>$32.5 \pm 0.1$</p>
<p>$32.0 \pm 0.1$</p>
<p>$32.3 \pm 0.1$</p> | g5473 | [
0.0019165632547810674,
0.008699765428900719,
-0.0016189670423045754,
0.007674846798181534,
0.01328772958368063,
0.013359752483665943,
-0.036687981337308884,
-0.0430573970079422,
-0.09297767281532288,
0.0006353092030622065,
0.00943142082542181,
0.05889254808425903,
-0.04192506894469261,
-0.05240051820874214,
-0.028633348643779755,
0.039328545331954956,
0.005923185031861067,
0.006451749708503485,
0.06096353754401207,
0.04553138464689255,
0.009190770797431469,
-0.03266330063343048,
-0.03729019686579704,
-0.06544063985347748,
0.05281525105237961,
-0.012592071667313576,
-0.015128284692764282,
0.032968174666166306,
-0.09460484236478806,
0.002909415867179632,
-0.009268224239349365,
-0.031021276488900185,
0.07965955883264542,
0.01570804975926876,
-0.023604480549693108,
-0.03762587532401085,
0.04945822060108185,
0.04351644590497017,
0.002223383169621229,
0.0248683150857687,
-0.04842695593833923,
0.003488742047920823,
0.0844583734869957,
0.011202690191566944,
-0.01261000707745552,
0.02966996468603611,
-0.040109943598508835,
0.05337217450141907,
-0.02161274664103985,
-0.01923556998372078,
0.009895089082419872,
0.020003706216812134,
0.0406457781791687,
0.04251406714320183,
-0.010647416114807129,
0.07422692328691483,
0.0818924754858017,
-0.05065630003809929,
0.00715817091986537,
0.00820937380194664,
0.014000515453517437,
-0.027852842584252357,
0.008927319198846817,
-0.023307429626584053,
-0.03762359544634819,
0.0017953895730897784,
-0.03163643926382065,
-0.021817350760102272,
0.02663150057196617,
-0.004720982164144516,
0.01589353196322918,
0.006974129006266594,
0.024930376559495926,
0.011163986288011074,
-0.09390311688184738,
0.016101492568850517,
-0.010887852869927883,
0.010803603567183018,
0.0008363479282706976,
0.037456490099430084,
-0.003763669403269887,
0.00785673875361681,
-0.01029781624674797,
-0.07075070589780807,
-0.03794065862894058,
-0.016513610258698463,
0.03743482381105423,
-0.04022830352187157,
-0.046888988465070724,
-0.002520574489608407,
-0.014546007849276066,
-0.027531389147043228,
0.004759741947054863,
0.07030213624238968,
0.0884459987282753,
0.013684063218533993,
-0.048036377876996994,
0.03903933987021446,
-0.028952084481716156,
0.05199576914310455,
0.00044345599599182606,
0.034615520387887955,
0.02407260239124298,
-0.0585455596446991,
-0.0573287270963192,
0.02113856002688408,
-0.002439932432025671,
0.012708979658782482,
0.0035752991680055857,
0.04524562880396843,
0.008373851887881756,
-0.012449867092072964,
-0.006486459635198116,
-0.05219630151987076,
0.0006778382230550051,
-0.01954299584031105,
-0.025111552327871323,
0.0007949908613227308,
0.022806184366345406,
-0.03959080949425697,
0.0611712746322155,
0.006621222477406263,
0.023330487310886383,
0.10293193906545639,
-0.008062761276960373,
-0.017080673947930336,
-0.021080566570162773,
-0.03246757388114929,
0.07945067435503006,
-0.003744708141312003,
0.027296055108308792,
-0.05893799290060997,
-0.009614437818527222,
-0.0103849396109581,
-0.03302337974309921,
-0.025566603988409042,
-0.006582566536962986,
-0.00617101090028882,
-0.0011006939457729459,
0.026156701147556305,
-0.03701697662472725,
0.03230218216776848,
0.03265506774187088,
-0.08508819341659546,
-0.046610765159130096,
-0.02479846403002739,
0.030200334265828133,
-0.09986187517642975,
-0.008115003816783428,
-0.025608541443943977,
0.06232377886772156,
0.055546533316373825,
0.039760999381542206,
0.040418174117803574,
-0.023974884301424026,
-0.019063228741288185,
-0.027903825044631958,
0.0362369641661644,
-0.04123283177614212,
0.01704033650457859,
0.010772659443318844,
0.02776087075471878,
0.026581015437841415,
0.012640309520065784,
0.009700712747871876,
0.02600293979048729,
0.08502541482448578,
0.021528182551264763,
-0.033123698085546494,
-0.01594032533466816,
0.05668068304657936,
-0.040287867188453674,
0.030069837346673012,
-0.046977441757917404,
0.025017255917191505,
-0.0206929761916399,
-0.007083679549396038,
-0.02762235701084137,
0.06434320658445358,
0.06076453626155853,
0.02555564045906067,
0.030802255496382713,
0.04832726716995239,
-0.032363202422857285,
-0.03528611734509468,
0.015195845626294613,
-0.003349154256284237,
-0.03619471192359924,
-0.04600154608488083,
-0.022885985672473907,
0.005878060590475798,
-0.027529655024409294,
-0.04408389329910278,
-0.005308079067617655,
0.02922164648771286,
0.0022579010110348463,
0.08328159153461456,
0.019286224618554115,
0.009033352136611938,
0.002843767637386918,
0.06105727702379227,
0.03127390518784523,
0.016307106241583824,
-0.0188261978328228,
0.008550708182156086,
-0.005716156214475632,
0.0014718597522005439,
-0.02310185879468918,
-0.07190891355276108,
0.03662847355008125,
-0.002026170725002885,
-0.013227091170847416,
0.02209377847611904,
0.03415115177631378,
0.052179913967847824,
0.03190021961927414,
0.059382662177085876,
-0.038055669516325,
0.05424550175666809,
-0.0009541057515889406,
-0.04491434618830681,
0.009568811394274235,
0.011034706607460976,
0.07018542289733887,
-0.011188690550625324,
0.0731261819601059,
0.04398416727781296,
0.04508943483233452,
0.016839250922203064,
0.04868069663643837,
-0.03852776437997818,
-0.06450586020946503,
-0.0588209331035614,
0.05957946926355362,
0.02906740829348564,
0.019138529896736145,
0.006896663457155228,
-0.03948282450437546,
0.013072961941361427,
0.05588889867067337,
0.024993887171149254,
0.05788877233862877,
0.010769393295049667,
-0.014639082364737988,
-0.008850197307765484,
-0.04592784494161606,
0.012063353322446346,
0.01415273454040289,
-0.05308692902326584,
0.0506310909986496,
0.0025117089971899986,
0.012810740619897842,
0.044846367090940475,
-0.011788574978709221,
-0.001573942368850112,
-0.06383904069662094,
-0.038160309195518494,
0.007378184236586094,
0.0053748684003949165,
0.0031911174301058054,
0.0174118485301733,
-0.029708558693528175,
-0.018509529531002045,
0.01157288160175085,
0.03143220767378807,
-0.04157108813524246,
0.02658189833164215,
-0.012430333532392979,
0.005280604586005211,
-0.0001437855971744284,
0.011392541229724884,
0.013780334033071995,
0.04191849008202553,
0.0992131307721138,
-0.013890160247683525,
-0.013013157993555069,
0.0422053337097168,
-0.006769358180463314,
-0.04005355387926102,
0.0021032269578427076,
-0.007201224099844694,
-0.005924546625465155,
-0.013308724388480186,
0.021140748634934425,
-0.015271411277353764,
-0.056551944464445114,
0.05481798201799393,
0.018424691632390022,
0.007931993342936039,
0.01335820835083723,
0.005206036847084761,
-0.008912911638617516,
-0.011939370073378086,
0.006473271641880274,
-0.04286016523838043,
-0.004667364526540041,
0.04238072410225868,
-0.03976564481854439,
-0.008178104646503925,
-0.013926053419709206,
0.0199124775826931,
0.045102838426828384,
-0.07204616069793701,
-0.02857985533773899,
0.018900124356150627,
-0.039021700620651245,
0.05023176223039627,
-0.04255218803882599,
-0.008735905401408672,
0.007390190847218037,
0.005955493077635765,
0.051826439797878265,
0.010081659071147442,
0.019109493121504784,
-0.010005936957895756,
0.04425785318017006,
-0.0014749827096238732,
0.03667866066098213,
-0.015458926558494568,
-0.019687477499246597,
0.01769169047474861,
-0.058478500694036484,
0.013479079119861126,
0.02182258665561676,
-0.026974648237228394,
-0.017828302457928658,
-0.023040562868118286,
0.02569202333688736,
-0.029625261202454567,
-0.0008471118635497987,
0.04484701529145241,
0.008067255839705467,
-0.006238526199012995,
0.01237455103546381,
-0.05592009425163269,
-0.06976241618394852,
0.05686110258102417,
0.03656759113073349,
-0.012320656329393387,
-0.0017012916505336761,
-0.048688143491744995,
-0.0320846363902092,
-0.01574162393808365,
-0.05907544121146202,
-0.043471258133649826,
-0.01080461498349905,
0.009648826904594898,
-0.05197935551404953,
0.030702535063028336,
-0.005135820247232914,
-0.007746151182800531,
0.00035781768383458257,
0.0025959487538784742,
0.04155515506863594,
0.014001457951962948,
0.028617890551686287,
-0.04537496343255043,
-0.05499232932925224,
0.006606696173548698,
0.050666648894548416,
-0.03781828284263611,
-0.07637164741754532,
-0.03418348357081413,
-0.021110882982611656,
0.038943514227867126,
0.007332398556172848,
-0.053361404687166214,
0.11756175756454468,
0.043094612658023834,
-0.03554721176624298,
-0.06880050152540207,
0.04515479877591133,
0.04347774386405945,
-0.04096074402332306,
-0.007945396937429905,
-0.017588401213288307,
0.022240638732910156,
-0.06036900356411934,
0.009221374057233334,
0.03289283066987991,
0.04591599106788635,
0.03298452869057655,
-0.017354412004351616,
-0.025814658030867577,
0.020465029403567314,
0.03488842025399208,
-0.08246960490942001,
-0.020920131355524063,
-0.013949991203844547,
-0.06913445144891739,
-0.017710722982883453,
0.0011807059636339545,
-0.04279729351401329,
0.06413626670837402,
0.030052803456783295,
-0.06938986480236053,
0.01104799471795559,
0.059688277542591095,
0.0023178886622190475,
0.0385400764644146,
-0.02289641834795475,
-0.03103582188487053,
-0.0003823309380095452,
0.02903112582862377,
0.024034086614847183,
-0.010367338545620441,
-0.03200222924351692,
0.008551623672246933,
0.0012579573085531592,
-0.0014343839138746262,
-0.03281416371464729,
-0.014265832491219044,
0.020288240164518356,
0.012991425581276417,
0.002016498940065503,
0.03792504593729973,
0.03789199888706207,
-0.03581531345844269,
-0.03282468020915985,
0.0020251921378076077,
-0.04092295467853546,
0.03027133271098137,
-0.005614400375634432,
-0.002812893595546484,
0.02383529022336006,
-0.02641296572983265,
0.022963793948292732,
-0.02771591953933239,
0.004463975317776203,
-0.0010865699732676148,
0.027158647775650024,
0.047125138342380524,
0.04491123929619789,
0.0324719212949276,
0.025456147268414497,
-0.009408911690115929,
0.024857202544808388,
-0.018547460436820984,
-0.038522861897945404,
0.021639227867126465,
-0.05065686255693436,
0.011437523178756237,
0.0053079924546182156,
-0.003752379911020398,
0.03510211035609245,
0.025131501257419586,
-0.011231118813157082,
-0.020304597914218903,
0.039343543350696564,
0.048231080174446106,
-0.0010730110807344317,
-0.044489797204732895,
-0.06337986141443253,
0.01333738025277853,
0.03931882977485657,
-0.010463052429258823,
-0.03636905550956726,
0.04346198961138725,
0.020976215600967407,
0.013605707325041294,
-0.01989506185054779,
-0.018045790493488312,
-0.03584492579102516,
0.019813846796751022,
-0.02419632486999035,
0.006527844350785017,
-0.042819131165742874,
0.017786839976906776,
0.0007852789713069797,
0.01100414153188467,
0.008741375058889389,
-0.028060300275683403,
0.03132077679038048,
-0.0015482420567423105,
-0.02277720905840397,
0.024623243138194084,
-0.007546266075223684,
-0.02799626998603344,
0.028335759416222572,
0.023504991084337234,
-0.037272144109010696,
0.01023914571851492,
-0.015633907169103622,
0.0580587200820446,
0.014913412742316723,
0.0018005681922659278,
0.008314299397170544,
-0.03473122417926788,
-0.015941016376018524,
-0.03712514042854309,
-0.022021213546395302,
-0.009410806000232697,
0.09367793798446655,
0.010134725831449032,
-0.019955437630414963,
-0.03347288817167282,
-0.01591578498482704,
0.05068955197930336,
0.021776296198368073,
-0.00596002209931612,
-0.023655548691749573,
0.01980891078710556,
-0.053320206701755524,
-0.046069033443927765,
-0.04514801502227783,
0.003377488348633051,
-0.0025339031126350164,
0.02773604542016983,
0.017727481201291084,
-0.030550746247172356,
0.04428982734680176,
-0.004486557096242905,
0.03349955752491951,
0.007508355192840099,
0.0038650045171380043,
0.011022843420505524,
-0.03238238766789436,
0.005054947454482317,
-0.07710127532482147,
0.007219509221613407,
0.04672086983919144,
-0.01852581650018692,
0.05591288208961487,
-0.021852217614650726,
0.018859142437577248,
-0.0059594581834971905,
0.008056656457483768,
-0.04982539638876915,
-0.011500410735607147,
-0.03562375530600548,
0.027653787285089493,
-0.00046704409760423005,
-0.007881967350840569,
-0.07057136297225952,
0.03643523156642914,
0.04127058386802673,
0.013477351516485214,
-0.03974508121609688,
0.03824315592646599,
-0.024842314422130585,
-0.030430415645241737,
0.033980727195739746,
0.001416610088199377,
0.03557693213224411,
0.004284000024199486,
0.017380064353346825,
0.014940980821847916,
0.030384456738829613,
0.029171697795391083,
-0.025869589298963547,
0.07515425980091095,
0.04497695714235306,
0.02036510407924652,
-0.08148317784070969,
-0.0016820259625092149,
0.0398203544318676,
-0.012807611376047134,
0.008585118688642979,
0.042978107929229736,
-0.01563148759305477,
0.04235529527068138,
-0.07051277905702591,
-0.02309420518577099,
-0.003598094917833805,
-0.02062520943582058,
0.05012453719973564,
0.01631501317024231,
0.01409450825303793,
-0.06145818904042244,
0.025936929509043694,
-0.0005669410456903279,
0.0367722287774086,
-0.027146968990564346,
0.021938618272542953,
0.001804765430279076,
0.05233541876077652,
-0.00512347836047411,
-0.03877504914999008,
0.004774823319166899,
-0.05855303630232811,
-0.028621850535273552,
0.037814486771821976,
-0.00039040661067701876,
-0.013696609996259212,
-0.025138065218925476,
-0.0023194407112896442,
-0.01916608400642872,
-0.02866309881210327,
-0.0602579340338707,
-0.03164646774530411,
0.00038187336758710444,
0.011082300916314125,
-0.010641698725521564,
-0.00368167064152658,
0.021530192345380783,
-0.010976175777614117,
0.005330041982233524,
0.0032511723693460226,
-0.03246289864182472,
-0.015871185809373856,
0.01504079531878233,
0.035561639815568924,
0.06263004243373871,
-0.01351143978536129,
0.006719409953802824,
-0.07033140957355499,
0.004185257479548454,
-0.022964132949709892,
-0.06915105879306793,
0.0625218078494072,
0.008531661704182625,
-0.007602748926728964,
0.005735909566283226,
0.04526607692241669,
0.031127503141760826,
0.020191678777337074,
0.0024712064769119024,
0.03645653277635574,
-0.042733579874038696,
0.02831711247563362,
0.04867834597826004,
0.048640236258506775,
-0.039136387407779694,
-0.011824769899249077,
0.014215126633644104,
0.04026971757411957,
-0.016134662553668022,
-0.05291295796632767,
0.0006634891615249217,
-0.024083826690912247,
-0.014038282446563244,
-0.04789281636476517,
0.06707988679409027,
0.04176922142505646,
-0.0442684106528759,
0.062291283160448074,
-0.051004037261009216,
0.07221032679080963,
-0.027445632964372635,
0.05716143921017647,
0.038030609488487244,
0.025082750245928764,
0.029909489676356316,
0.01728132739663124,
-0.02292945235967636,
-0.0034767051693052053,
0.04028600454330444,
-0.04470648244023323,
0.013709921389818192,
0.007753870449960232,
-0.017119107767939568,
-0.025338707491755486,
-0.014719149097800255,
-0.01898297853767872,
0.009428747929632664,
0.00759142218157649,
0.030489183962345123,
-0.0006416779942810535,
-0.01095567736774683,
-0.04601796343922615,
-0.01668108068406582,
-0.06437815725803375,
-0.04392976686358452,
-0.03157278522849083,
0.05096518248319626,
0.010369551368057728,
-0.00223445612937212,
-0.05737455189228058,
-0.05815506353974342,
-0.0427670031785965,
-0.03282150998711586,
0.007434451952576637,
-0.07342267036437988,
0.013118458911776543,
0.020992731675505638,
-0.02181689813733101,
0.0457528680562973,
0.03315191715955734,
-0.02917494811117649,
0.006496706046164036,
-0.013595625758171082,
-0.012014634907245636,
-0.016969265416264534,
-0.030026385560631752,
0.01986992172896862,
0.07862690836191177,
0.052550360560417175,
0.026688281446695328,
-0.0012592802522704005,
-0.018638744950294495,
-0.027247337624430656,
-0.08206343650817871,
0.05424408242106438,
0.019450807943940163,
-0.039226386696100235,
0.007704326882958412,
-0.04967807978391647,
-0.0032674609683454037,
0.04510631412267685,
-0.08260540664196014,
-0.02778269164264202,
-0.002700335346162319,
-0.023642128333449364,
0.013891366310417652,
-0.0915818139910698,
-0.03559563308954239,
-0.013715289533138275,
0.00394852738827467,
-0.01757546328008175,
-0.06171445548534393,
0.0375019833445549,
0.016464300453662872,
-0.0032691331580281258,
-0.04537663608789444,
0.01760292984545231,
-0.008959915488958359,
-0.019464774057269096,
-0.06385845690965652,
-0.057413842529058456,
0.014602066949009895,
0.02685389295220375,
-0.03306295722723007,
-0.0026624989695847034,
-0.011509103700518608,
-0.040964145213365555,
-0.0824478268623352,
-0.052313610911369324,
0.017473269253969193,
-0.00044878627522848547,
-0.014760470017790794,
-0.04940325394272804,
-0.026566743850708008,
-0.10060933232307434,
0.051078666001558304,
0.006844362709671259,
0.06864812970161438,
0.05223575979471207,
0.031406838446855545,
0.05143046751618385,
0.027844984084367752,
-0.05899132043123245,
-0.03805777430534363,
0.010661453939974308,
0.01299825869500637,
0.017840730026364326,
0.03144150227308273,
-0.060424741357564926,
0.019332675263285637,
0.064278244972229,
-0.011853870935738087,
-0.045461129397153854,
0.031221112236380577,
-0.044955819845199585,
0.12492410838603973,
0.04326309636235237,
-0.01611640676856041,
0.013325541280210018,
0.01261916570365429,
-0.013214271515607834,
-0.014996510930359364,
-0.012889690697193146,
-0.017446167767047882,
-0.04600394889712334,
0.06661418080329895,
0.02372620441019535,
0.007652399130165577,
-0.028621414676308632,
-0.018514085561037064
] |
<p>Is there a real difference between <a href="http://en.wikipedia.org/wiki/Eternal_inflation" rel="nofollow">eternal inflation</a> and "chaotic inflation" theories? </p> | g5474 | [
0.022845441475510597,
0.02553163655102253,
0.015256395563483238,
0.017562400549650192,
0.008099156431853771,
-0.03554181754589081,
-0.010408979840576649,
-0.01042177900671959,
-0.0389113612473011,
0.0026151540223509073,
0.04681864008307457,
-0.016114287078380585,
0.06150731444358826,
-0.00485985167324543,
-0.0040489379316568375,
0.02102985978126526,
0.03336706757545471,
0.0572609007358551,
0.016843292862176895,
0.02225317992269993,
-0.0016045515658333898,
0.0014414762845262885,
0.040226202458143234,
0.036420788615942,
-0.013128126971423626,
-0.0734398290514946,
-0.06353920698165894,
0.003751351498067379,
-0.031414393335580826,
-0.056799162179231644,
0.053260065615177155,
0.006307474337518215,
0.025190161541104317,
-0.012231186032295227,
-0.01625865139067173,
-0.00318384962156415,
0.07067741453647614,
0.03482769802212715,
0.03887956216931343,
-0.0047744750045239925,
0.018095968291163445,
0.06001760810613632,
0.021953100338578224,
-0.01631968654692173,
-0.09812652319669724,
-0.0011388200800865889,
-0.05499189719557762,
0.017920849844813347,
-0.0045165433548390865,
-0.032096754759550095,
0.04850665479898453,
0.030003657564520836,
-0.00045302920625545084,
0.06142733618617058,
0.03366363048553467,
0.020038019865751266,
0.0237185787409544,
0.027902772650122643,
0.03636108711361885,
0.02397051826119423,
0.00479041738435626,
0.013777953572571278,
0.042097728699445724,
-0.02339627780020237,
-0.020916776731610298,
0.014882083982229233,
0.0026100454851984978,
-0.005702170077711344,
0.0005537630058825016,
-0.05407300218939781,
0.00013301466242410243,
-0.02827504090964794,
-0.016712136566638947,
-0.007455084007233381,
-0.014714665710926056,
0.07545340806245804,
0.010999343357980251,
-0.08679551631212234,
0.06950917840003967,
-0.008315238170325756,
-0.005164013709872961,
-0.012097318656742573,
0.03953321650624275,
0.002852801699191332,
0.08588343113660812,
0.026364218443632126,
-0.018140453845262527,
-0.020008843392133713,
0.044358838349580765,
-0.04034993797540665,
-0.013310886919498444,
-0.043858807533979416,
0.003649005200713873,
0.03157197684049606,
-0.007232846692204475,
0.05613530054688454,
-0.02922562137246132,
0.08661539107561111,
-0.01345058809965849,
0.019797854125499725,
-0.061517585068941116,
0.021467896178364754,
0.01887618377804756,
0.027752013877034187,
-0.012959254905581474,
-0.052369896322488785,
0.020203866064548492,
-0.055702243000268936,
-0.013323098421096802,
-0.001340049784630537,
-0.02722972258925438,
-0.003947091288864613,
-0.003386564552783966,
0.004901516251266003,
0.027733124792575836,
-0.005040662828832865,
-0.027645209804177284,
0.02889246866106987,
0.02037064917385578,
0.03978206217288971,
0.004967669025063515,
-0.05189499631524086,
0.05904293432831764,
0.04952702298760414,
-0.027968190610408783,
0.02710864134132862,
0.05044941231608391,
0.006169809028506279,
0.0018113936530426145,
0.002646767534315586,
0.005520904902368784,
0.029290802776813507,
-0.02244298718869686,
-0.007304734084755182,
0.003585735335946083,
0.0074866884388029575,
0.03424733504652977,
0.012799595482647419,
-0.025597795844078064,
0.056697778403759,
0.03409912809729576,
-0.07122542709112167,
0.011831485666334629,
-0.002100006677210331,
-0.0434609018266201,
-0.001865653321146965,
-0.002524419454857707,
0.015905633568763733,
0.0030197715386748314,
0.05003737658262253,
-0.06280165165662766,
0.04486141726374626,
0.038583483546972275,
0.019921544939279556,
-0.026389796286821365,
0.026985719799995422,
0.023237770423293114,
0.02458191104233265,
-0.04732794687151909,
0.0021475960966199636,
-0.07285865396261215,
-0.0618022121489048,
0.11118747293949127,
-0.022908320650458336,
-0.023311525583267212,
-0.027200067415833473,
0.014707299880683422,
0.014912818558514118,
-0.05598866567015648,
0.001443695742636919,
0.007213575765490532,
0.013667215593159199,
-0.0460355207324028,
0.009161676280200481,
0.11223465949296951,
0.01651408150792122,
-0.01173383928835392,
0.05664103478193283,
-0.003539454657584429,
-0.10606640577316284,
-0.0005737968604080379,
0.02901529148221016,
0.02630423754453659,
0.0420149564743042,
0.05867895483970642,
0.01718248799443245,
0.0017380781937390566,
0.001548819593153894,
-0.03952091187238693,
0.028609486296772957,
0.02036864124238491,
-0.02105245366692543,
-0.009776263497769833,
0.05154076963663101,
-0.005731587298214436,
0.006998563650995493,
-0.03575115650892258,
0.005038422532379627,
-0.07508927583694458,
-0.04592495411634445,
0.035207897424697876,
0.035200413316488266,
0.04509083554148674,
-0.08297606557607651,
-0.04193532094359398,
-0.011785601265728474,
-0.016720453277230263,
-0.06283748149871826,
-0.02792702242732048,
0.00458881538361311,
0.007769368123263121,
-0.04270249605178833,
0.01895500160753727,
0.07956728339195251,
0.02506786584854126,
0.015541298314929008,
0.0006591108394786716,
-0.02266640216112137,
0.030929038301110268,
0.04414425045251846,
-0.006424658466130495,
0.026875460520386696,
0.06398662179708481,
-0.019848857074975967,
0.04201488569378853,
-0.046377867460250854,
0.031153090298175812,
-0.050305988639593124,
0.001867224695160985,
0.02924381196498871,
-0.012237131595611572,
-0.0422181561589241,
-0.01728689856827259,
-0.003907383885234594,
-0.005475203972309828,
0.005016520619392395,
0.033548757433891296,
0.023295849561691284,
0.009773511439561844,
0.025788800790905952,
-0.021965688094496727,
-0.04146978259086609,
-0.016444891691207886,
-0.008009867742657661,
0.008624504320323467,
-0.03637611120939255,
0.009929285384714603,
-0.03954613581299782,
-0.007473778445273638,
0.02155962586402893,
-0.01437701378017664,
-0.04223628342151642,
-0.023572266101837158,
-0.04941998049616814,
0.0717257708311081,
-0.008605435490608215,
0.011678620241582394,
-0.0038576226215809584,
-0.022779138758778572,
0.007199357729405165,
0.06495355814695358,
-0.026130404323339462,
0.015811674296855927,
-0.0028344171587377787,
-0.06694624572992325,
-0.034862760454416275,
-0.0161490049213171,
0.02868872508406639,
-0.06723685562610626,
0.014164520427584648,
-0.011840167455375195,
0.00865233689546585,
0.023107705637812614,
-0.020475296303629875,
-0.022908451035618782,
0.03900188207626343,
-0.0026236926205456257,
0.008521526120603085,
-0.0027006801683455706,
-0.04234259948134422,
0.05195463448762894,
0.012408092617988586,
-0.05204203352332115,
-0.034851524978876114,
-0.03760027512907982,
-0.05564546585083008,
-0.04633249714970589,
0.03781541436910629,
-0.00004414256181917153,
-0.02993658557534218,
0.0030347390566021204,
0.024684656411409378,
-0.0026338184252381325,
0.0791788175702095,
-0.0427841953933239,
0.032147761434316635,
0.007108589634299278,
-0.025288216769695282,
-0.0013599643716588616,
-0.0014647202333435416,
0.042465973645448685,
-0.021256547421216965,
-0.017678728327155113,
0.034384239464998245,
0.03573109582066536,
0.046643324196338654,
-0.005647287238389254,
-0.019706668332219124,
0.0048581380397081375,
-0.08590872585773468,
0.0054611340165138245,
0.08408095687627792,
0.005406392738223076,
0.030038854107260704,
0.08284114301204681,
-0.003542293794453144,
-0.028158241882920265,
0.0625234991312027,
0.07518595457077026,
0.017952071502804756,
-0.08254023641347885,
-0.007349471561610699,
0.011053823865950108,
0.00044325535418465734,
-0.0016249290201812983,
0.004365305881947279,
-0.03308255597949028,
-0.06341128796339035,
-0.052372045814991,
0.020474549382925034,
-0.00667957216501236,
-0.036696191877126694,
-0.023566845804452896,
-0.05555503070354462,
-0.008494415320456028,
-0.0348481759428978,
-0.06056637689471245,
0.03025892749428749,
0.03184166178107262,
0.035416554659605026,
-0.02513899840414524,
0.01196590717881918,
-0.002180658048018813,
0.022967912256717682,
-0.01305325422435999,
0.009631292894482613,
-0.03135459125041962,
-0.04204810783267021,
-0.0087523078545928,
-0.022552181035280228,
0.023653285577893257,
-0.059566691517829895,
0.05108891800045967,
-0.03161042183637619,
0.014248542487621307,
-0.045442141592502594,
0.004629726521670818,
0.021493854001164436,
0.016678957268595695,
-0.0146851921454072,
-0.018148837611079216,
-0.005683830939233303,
0.026931723579764366,
0.07356233894824982,
-0.02677512727677822,
0.04787910357117653,
-0.06758804619312286,
0.00900948140770197,
-0.029384486377239227,
-0.025893718004226685,
-0.01091860979795456,
0.008258185349404812,
0.01780303753912449,
0.036496683955192566,
0.043285176157951355,
0.004393479321151972,
0.06402670592069626,
0.02919502556324005,
-0.03502646088600159,
0.03007654659450054,
0.03625369817018509,
-0.008601942099630833,
0.00774781359359622,
0.008754373528063297,
-0.012048724107444286,
-0.02578502520918846,
-0.03546818718314171,
-0.03808928653597832,
-0.01622898317873478,
-0.09715895354747772,
0.024426469579339027,
0.02470894530415535,
-0.0010018895845860243,
0.005359317176043987,
0.0026728843804448843,
0.020454436540603638,
-0.026399673894047737,
-0.06283356249332428,
0.025635110214352608,
-0.0436565987765789,
0.048622194677591324,
-0.03972263261675835,
-0.029230529442429543,
0.03014468215405941,
0.015431969426572323,
0.00944328773766756,
0.029346618801355362,
-0.0342133529484272,
-0.015268450602889061,
-0.022606467828154564,
0.032651111483573914,
0.013296501711010933,
0.031530849635601044,
0.011562696658074856,
0.046026140451431274,
-0.010171214118599892,
0.011300927959382534,
-0.0325515978038311,
0.07050842046737671,
0.026814527809619904,
-0.033534642308950424,
0.017462655901908875,
-0.06414077430963516,
-0.056144583970308304,
-0.055345308035612106,
0.06730727851390839,
-0.016954340040683746,
0.04425809159874916,
-0.023172695189714432,
0.0010376680875197053,
0.043703898787498474,
-0.004974198993295431,
-0.04876377433538437,
0.01864900067448616,
-0.03270084783434868,
-0.006100369151681662,
-0.012389568611979485,
0.06372477859258652,
0.026789043098688126,
-0.06027599051594734,
0.08871926367282867,
0.022131185978651047,
0.014674820937216282,
-0.002948570530861616,
0.01043797843158245,
0.04795260354876518,
0.03783312812447548,
-0.0038123936392366886,
-0.02836148627102375,
-0.010361595079302788,
-0.027566835284233093,
0.03352560102939606,
0.012589672580361366,
0.0034596368204802275,
0.008574159815907478,
-0.04475429654121399,
0.0265683401376009,
0.05466359853744507,
-0.0187261700630188,
0.014937637373805046,
-0.07540007680654526,
0.010781764052808285,
-0.003166400594636798,
-0.0008711659465916455,
0.015833215788006783,
0.016386911273002625,
-0.07286825776100159,
-0.050737109035253525,
-0.04406437277793884,
-0.02706078812479973,
0.016919976100325584,
-0.04395781084895134,
0.038305941969156265,
0.044235359877347946,
0.02589457668364048,
-0.07997637987136841,
0.06817243993282318,
-0.03540307655930519,
-0.013392025604844093,
0.010682431049644947,
0.026477422565221786,
-0.02387728914618492,
0.05960846319794655,
0.03222639113664627,
0.08927015960216522,
-0.013852009549736977,
-0.03189791738986969,
0.033832062035799026,
0.023213250562548637,
0.026093827560544014,
0.032460253685712814,
-0.02575790323317051,
-0.002441773423925042,
-0.030489645898342133,
-0.06559653580188751,
-0.01310478150844574,
0.0040617771446704865,
-0.03646429255604744,
-0.004687882028520107,
-0.016347773373126984,
-0.04480542987585068,
0.029927659779787064,
0.011419213376939297,
0.007150798570364714,
-0.0027276678010821342,
0.011361288838088512,
0.05623419210314751,
0.0012844545999541879,
-0.0024733892641961575,
0.029017578810453415,
-0.00990780908614397,
-0.031437914818525314,
-0.018717952072620392,
0.037487637251615524,
0.03819078952074051,
0.011765762232244015,
0.010366616770625114,
-0.021367782726883888,
0.018527310341596603,
-0.06680403649806976,
0.016751611605286598,
-0.006204654462635517,
-0.0015136158326640725,
0.045375168323516846,
0.0852213203907013,
-0.03961688280105591,
0.054194021970033646,
-0.03660653159022331,
0.016131006181240082,
-0.036389004439115524,
-0.005829783622175455,
-0.04724075645208359,
0.06301857531070709,
0.006029447074979544,
0.012364010326564312,
0.02842724323272705,
0.03568476065993309,
0.0407438687980175,
-0.012010354548692703,
-0.038041189312934875,
-0.02384090982377529,
0.029026439413428307,
-0.014372516423463821,
0.009669839404523373,
-0.04161887988448143,
-0.006617845967411995,
-0.052175428718328476,
0.019316790625452995,
0.02268124558031559,
-0.07355576008558273,
-0.03293674811720848,
0.01123417355120182,
0.002342390827834606,
0.03462028130888939,
0.008913476951420307,
0.04541854187846184,
0.01605314016342163,
0.026995718479156494,
-0.031316012144088745,
-0.01514620240777731,
-0.03421270474791527,
0.02834346704185009,
0.010223968885838985,
0.0019034681608900428,
0.00721715297549963,
-0.011154111474752426,
0.021051205694675446,
-0.032748159021139145,
0.06888993829488754,
0.015760043635964394,
0.06285744160413742,
0.028350597247481346,
-0.01726350001990795,
0.013413089327514172,
0.0006851389189250767,
-0.0393366701900959,
-0.02454206719994545,
-0.004822955001145601,
-0.02225738950073719,
0.06856557726860046,
-0.04417245835065842,
-0.047996919602155685,
0.08159399032592773,
0.039613042026758194,
0.05042733624577522,
-0.032806672155857086,
-0.058982424437999725,
-0.013253518380224705,
-0.014254093170166016,
0.03251784294843674,
-0.030320217832922935,
-0.021204164251685143,
-0.01211177185177803,
-0.0058606574311852455,
-0.05426937714219093,
0.014156773686408997,
-0.023542672395706177,
-0.020671136677265167,
-0.026474427431821823,
-0.006813463289290667,
-0.0021998006850481033,
-0.03341147303581238,
0.07526693493127823,
-0.028603246435523033,
0.027552856132388115,
0.012563792057335377,
0.02287980541586876,
0.062094394117593765,
-0.05831628665328026,
0.019724786281585693,
-0.09635177999734879,
0.056258149445056915,
0.06504476815462112,
-0.011760408990085125,
-0.0022192865144461393,
0.004574186634272337,
-0.03806253895163536,
-0.012744072824716568,
-0.004592824261635542,
0.00216737505979836,
0.007846349850296974,
-0.007283464539796114,
-0.004117720294743776,
-0.0019586256239563227,
0.06111539900302887,
0.02413974702358246,
-0.013125973753631115,
0.027024440467357635,
-0.02854209765791893,
-0.010579995810985565,
-0.016688235104084015,
-0.012533864937722683,
0.030768295750021935,
0.040341150015592575,
-0.0195537731051445,
0.0070940409786999226,
-0.05182229354977608,
0.005010692402720451,
0.006257639266550541,
0.023007526993751526,
-0.0446041002869606,
0.015225360170006752,
0.0980614423751831,
0.023479929193854332,
-0.02062915824353695,
0.005186794325709343,
-0.06903650611639023,
-0.005749697331339121,
-0.03951043263077736,
0.011694222688674927,
-0.04445186257362366,
-0.04673982039093971,
-0.04069145768880844,
0.021079739555716515,
-0.011792842298746109,
0.050634436309337616,
-0.01611482724547386,
0.018425213173031807,
0.0030249026603996754,
-0.05774896219372749,
-0.005139021668583155,
0.024372072890400887,
0.013179797679185867,
-0.03193961828947067,
-0.027871740981936455,
-0.033889852464199066,
-0.02585916593670845,
-0.06377129256725311,
-0.01300868671387434,
-0.016705989837646484,
0.06624341011047363,
0.0020165308378636837,
-0.05856608226895332,
-0.0777016133069992,
-0.031093068420886993,
-0.05704937130212784,
-0.04092516005039215,
-0.023431621491909027,
0.022452672943472862,
0.02707003802061081,
0.00425763102248311,
-0.027486467733979225,
0.0382920540869236,
-0.019023491069674492,
-0.06560300290584564,
0.02559417486190796,
-0.0397680401802063,
-0.0030689984560012817,
0.022400645539164543,
-0.0020158591214567423,
0.025687692686915398,
0.006019619293510914,
0.001615104149095714,
-0.016963902860879898,
0.0044279699213802814,
0.042979370802640915,
-0.05175282806158066,
-0.015096179209649563,
0.01037309318780899,
-0.025855593383312225,
0.06043278053402901,
-0.004458071198314428,
0.01715019904077053,
-0.032421816140413284,
0.06283653527498245,
-0.00002727707578742411,
0.04352660849690437,
0.015617757104337215,
-0.023692386224865913,
0.05320603400468826,
-0.03264305740594864,
-0.04217447340488434,
0.005455047823488712,
-0.013858785852789879,
0.033690180629491806,
-0.025120284408330917,
0.028976354748010635,
-0.09183792769908905,
-0.001942237140610814,
0.02753756381571293,
-0.0191042460501194,
-0.08095448464155197,
-0.0989961251616478,
-0.03395255282521248,
-0.011741328053176403,
0.09982491284608841,
-0.0260099358856678,
-0.036403972655534744,
-0.04381709173321724,
-0.0055297985672950745,
-0.028748013079166412,
0.024615289643406868,
0.030907806009054184,
0.07010060548782349,
-0.02503977157175541,
-0.004287763498723507,
-0.005956198088824749,
0.045300647616386414,
0.03181041404604912,
-0.049952615052461624,
0.051940273493528366,
-0.0055954596027731895,
0.0362231582403183,
-0.01708967052400112,
-0.03760765492916107,
-0.018468469381332397,
-0.04776102304458618,
0.013204552233219147,
0.0007620779215358198,
-0.03958816081285477,
0.028762254863977432,
0.02696203999221325,
-0.04319394379854202,
-0.028201790526509285,
-0.013056705705821514,
0.027812089771032333,
-0.07395821064710617,
-0.008489452302455902,
0.02295594848692417,
0.003440051106736064,
0.020037753507494926,
-0.011562835425138474,
0.05338260531425476,
-0.0046967677772045135,
-0.016757629811763763,
-0.013730165548622608,
0.02394813857972622,
-0.03672187775373459
] |
<p>I'm trying to come up with an expression for the partition function of a system of spin-1/2 ideal gas particles on a line of length $L$. The total number of particles $N$ is fixed, with $N = N_\uparrow + N_\downarrow$. Here, $N_\uparrow$ is the number of spin-up particles and $N_\downarrow$ is the number of spin-down particles in a particular microstate.</p>
<p>I have the following Hamiltonian for the particles of mass $m$.</p>
<p>$$H = \sum_{i=1}^{N}{\frac{(p_i + \beta s_i)^2}{2m} -b s_i} $$</p>
<p>Here, $s_i = 1$ for the spin-up $N_\uparrow$ particles and $s_i = -1$ for the spin-down $N_\uparrow$ particles. $\beta$ and $b$ are constants.</p>
<p>I'm trying to use the Hamiltonian to write down the energy for the spin-up and spin-down particles so I can write down the partition function. If I expand the Hamiltonian, I get:</p>
<p>$$H = \sum_{i=1}^{N}{\frac{p_i^2}{2m} + \frac{p_i \beta s_i}{m} - b s_i + \beta^2} $$</p>
<p>How do I find the energy of the two sets of spin particles from this and use it to come up with the partition function? Is the energy of the particles just?</p>
<p>$$E_\uparrow = \frac{p_i^2}{2m} + \frac{p_i \beta}{m} - b + \beta^2$$
$$E_\downarrow = \frac{p_i^2}{2m} + \frac{-p_i \beta}{m} + b + \beta^2$$</p>
<p>How would one evaluate this in the canonical partition function:</p>
<p>$$Z = \sum_{\mu_s}e^{-\beta H}$$</p>
<p>where $\mu_s$ is the summing over all microstates. I'm not sure how to evaluate this.</p> | g5475 | [
-0.007945309393107891,
-0.03221840038895607,
-0.037591710686683655,
-0.0662081241607666,
0.010354778729379177,
-0.02565116435289383,
0.03897342458367348,
0.03419050574302673,
-0.02660113200545311,
0.021262047812342644,
-0.01659352146089077,
0.02857651188969612,
0.012253201566636562,
-0.009791713207960129,
0.0027876337990164757,
0.0018268092535436153,
0.012007337994873524,
0.0047232843935489655,
-0.03363480791449547,
0.0026680417358875275,
0.017550615593791008,
-0.02067158743739128,
-0.016188625246286392,
-0.009485677815973759,
0.053023844957351685,
-0.01705167442560196,
0.014637032523751259,
0.01101358700543642,
-0.0460793562233448,
0.038625188171863556,
-0.03866254538297653,
0.019201628863811493,
-0.0018515511183068156,
-0.05895800516009331,
0.0180426687002182,
0.009607107378542423,
0.095504030585289,
0.00121417420450598,
0.01342995185405016,
-0.06420857459306717,
0.0030758818611502647,
-0.04610679671168327,
0.041356876492500305,
0.017816539853811264,
0.039372555911540985,
0.006073327269405127,
0.030745478346943855,
-0.017484573647379875,
-0.06665349006652832,
0.009734894149005413,
0.020626479759812355,
0.04031066969037056,
0.015018360689282417,
-0.005834608338773251,
0.0027973935939371586,
0.0616423524916172,
-0.003059798153117299,
-0.024866091087460518,
0.05564795434474945,
0.06955458223819733,
0.03720329329371452,
-0.036260947585105896,
-0.013696650043129921,
-0.015422952361404896,
0.04759567975997925,
0.011285707354545593,
-0.026486536487936974,
0.005873932968825102,
0.008100461214780807,
-0.0015193679137155414,
0.03318836912512779,
-0.04205732047557831,
0.03716931492090225,
-0.07856513559818268,
-0.06830368936061859,
-0.02564627304673195,
0.00542354304343462,
0.012909178622066975,
-0.004191773012280464,
0.02389748953282833,
-0.015232374891638756,
-0.01535690575838089,
0.037351638078689575,
0.017193898558616638,
0.026730256155133247,
-0.018167095258831978,
-0.007847459055483341,
-0.03976774588227272,
-0.01217641867697239,
0.047675300389528275,
0.02001647651195526,
0.06524346023797989,
0.0337514765560627,
0.017684757709503174,
-0.04613901302218437,
-0.0225799810141325,
-0.012483229860663414,
-0.03773261606693268,
-0.03449986129999161,
0.04400942847132683,
-0.03044401854276657,
-0.01344180479645729,
0.04896805062890053,
-0.07692361623048782,
0.019542917609214783,
-0.015626996755599976,
0.023835236206650734,
0.04171700030565262,
0.021238787099719048,
0.01963183283805847,
0.007499131374061108,
0.032612353563308716,
-0.04474397376179695,
-0.01626552641391754,
-0.05629969388246536,
-0.016364987939596176,
0.045659687370061874,
-0.020269064232707024,
-0.03375015780329704,
0.07020498067140579,
0.05496576428413391,
0.010286632925271988,
-0.016891537234187126,
0.06680959463119507,
-0.01755177229642868,
0.02901642955839634,
-0.0347132533788681,
0.011693982407450676,
0.010223683901131153,
-0.0014628333738073707,
0.012795784510672092,
-0.05776001513004303,
0.01765868440270424,
-0.018486451357603073,
0.004225288052111864,
0.019953260198235512,
-0.0033260234631597996,
-0.003728687297552824,
-0.04232274368405342,
0.012294006533920765,
0.0024540990125387907,
-0.06877312809228897,
-0.012284474447369576,
-0.003066553268581629,
-0.029835516586899757,
0.04542645066976547,
0.003644255455583334,
-0.06695348024368286,
-0.046953678131103516,
0.06768250465393066,
-0.008825655095279217,
0.1270965337753296,
-0.027292102575302124,
-0.005958396475762129,
0.025773271918296814,
-0.011463779956102371,
0.04196982458233833,
-0.045569680631160736,
-0.005833655130118132,
-0.026135530322790146,
0.029571618884801865,
-0.02374013140797615,
0.04484935849905014,
-0.037645094096660614,
-0.08060936629772186,
0.09609275311231613,
0.003960094880312681,
-0.018960880115628242,
0.022843964397907257,
-0.01909797266125679,
0.0035537651274353266,
0.04868864268064499,
0.007898833602666855,
0.015372131019830704,
0.006835261359810829,
0.06305531412363052,
0.009713114239275455,
0.03255419433116913,
0.004435833543539047,
-0.010473179630935192,
0.03908607363700867,
-0.03756386414170265,
0.06448815762996674,
-0.027591919526457787,
-0.021068399772047997,
-0.016476357355713844,
0.030047418549656868,
-0.013314164243638515,
-0.03642182797193527,
-0.015421600081026554,
0.026745503768324852,
0.10066214948892593,
0.013479305431246758,
-0.029546989127993584,
0.008115850389003754,
0.006703623570501804,
0.04325224459171295,
-0.07812879234552383,
0.0005498339305631816,
-0.03397532179951668,
-0.02225538156926632,
0.07037278264760971,
0.06790559738874435,
-0.025609858334064484,
0.04649043083190918,
-0.024132147431373596,
0.026062896475195885,
0.018707770854234695,
0.002124818740412593,
0.022383367642760277,
-0.011332407593727112,
-0.05197850242257118,
-0.015883389860391617,
0.008835792541503906,
0.03775104507803917,
0.015336356125772,
0.02430781163275242,
-0.0030958340503275394,
0.030740153044462204,
-0.03947024419903755,
-0.04695328325033188,
-0.00785586703568697,
0.056956782937049866,
-0.014980005100369453,
0.006171240471303463,
0.020251713693141937,
-0.004672322887927294,
0.038275834172964096,
-0.040532633662223816,
0.034190308302640915,
-0.029654862359166145,
-0.03272321820259094,
-0.005754593759775162,
-0.025275154039263725,
0.03927690163254738,
0.021218817681074142,
-0.042877912521362305,
0.034893281757831573,
0.04953433573246002,
0.012011812068521976,
-0.023544955998659134,
-0.0323699489235878,
-0.01285702083259821,
0.0518898069858551,
0.0126974917948246,
0.018166298046708107,
-0.03696872293949127,
-0.008966227993369102,
-0.02958597056567669,
-0.033334143459796906,
0.007222951855510473,
0.011211277917027473,
0.004514560103416443,
0.006048629060387611,
0.010669240728020668,
-0.044859472662210464,
-0.004069790709763765,
0.025029446929693222,
-0.04867666959762573,
-0.014439864084124565,
0.011143160052597523,
-0.0007883802172727883,
-0.02450486272573471,
0.040320832282304764,
0.019801216199994087,
-0.035491399466991425,
-0.008276697248220444,
-0.05457692965865135,
0.03395744785666466,
0.003461538814008236,
-0.0282878577709198,
0.06904493272304535,
-0.011914175935089588,
0.04824860021471977,
0.04946461692452431,
-0.044872649013996124,
0.05930635705590248,
0.014318984001874924,
0.04544800519943237,
-0.01728792116045952,
-0.06316955387592316,
0.008811031468212605,
-0.02832122892141342,
0.029632393270730972,
0.03448282554745674,
-0.08935204893350601,
-0.010610762983560562,
-0.03434200584888458,
0.015763990581035614,
-0.001373882289044559,
0.006493125110864639,
0.07464125007390976,
0.03347783163189888,
-0.04276592656970024,
-0.001322926371358335,
0.005435829050838947,
0.015151116997003555,
-0.04138714447617531,
0.04022955149412155,
0.08930959552526474,
-0.004840358160436153,
-0.008881469257175922,
-0.014306137338280678,
-0.024363359436392784,
-0.0283353328704834,
0.011994682252407074,
-0.026224277913570404,
-0.01923554763197899,
0.005391203332692385,
-0.023853570222854614,
-0.05317208543419838,
0.05363021418452263,
0.06189153343439102,
-0.03658764809370041,
-0.020218463614583015,
-0.007765676360577345,
0.03292643651366234,
-0.025879856199026108,
0.07471849024295807,
-0.0493302121758461,
-0.021444035694003105,
-0.032604657113552094,
0.03825626149773598,
-0.0020708232186734676,
-0.03821547329425812,
-0.03123047575354576,
-0.02603825554251671,
-0.07489238679409027,
-0.04244360327720642,
0.04921134561300278,
0.0009174388833343983,
-0.004330842290073633,
-0.0035982662811875343,
0.028769787400960922,
-0.0241325031965971,
0.003717489307746291,
-0.0550803579390049,
-0.05191449820995331,
-0.00302839744836092,
0.005216328427195549,
-0.08736920356750488,
0.031631212681531906,
-0.04104591906070709,
0.0293766800314188,
-0.03275257349014282,
-0.05343710258603096,
-0.021108703687787056,
0.03225463628768921,
0.0026110834442079067,
-0.015654662624001503,
-0.051887232810258865,
0.0374642051756382,
0.05789345130324364,
0.03548899292945862,
0.019825853407382965,
-0.0362987145781517,
0.04861754924058914,
-0.029051469638943672,
0.005052441265434027,
0.05909248813986778,
0.05288827419281006,
-0.05736131593585014,
0.03706701099872589,
0.05679505690932274,
-0.01864054799079895,
-0.042156416922807693,
-0.03390061482787132,
0.007760134059935808,
0.03579701855778694,
-0.05119700729846954,
0.00640615401789546,
-0.006675622425973415,
0.06392645835876465,
-0.04465723782777786,
0.02973814867436886,
-0.03282466530799866,
0.005751624237746,
-0.04079762473702431,
-0.03855735436081886,
-0.030121102929115295,
-0.00044488563435152173,
-0.031043726950883865,
0.00917887780815363,
0.052751947194337845,
-0.01668086275458336,
0.04551250487565994,
-0.021979685872793198,
-0.01014132983982563,
0.014312468469142914,
-0.0007565301493741572,
0.0028631691820919514,
-0.0707562267780304,
-0.0782289206981659,
0.03362935781478882,
0.04733438417315483,
-0.016581835225224495,
0.0046722847037017345,
-0.05712905153632164,
-0.016420824453234673,
0.04597858339548111,
-0.06913483887910843,
-0.04094386100769043,
-0.006069188937544823,
-0.03238712251186371,
0.029923999682068825,
-0.032977182418107986,
-0.01026294194161892,
-0.00622320082038641,
0.01308530755341053,
-0.007309628650546074,
0.01263867411762476,
0.003095218911767006,
0.03721495345234871,
-0.02488786354660988,
-0.02066858485341072,
-0.006156432908028364,
0.02214723639190197,
-0.04053734987974167,
-0.005466403439640999,
-0.0012860160786658525,
-0.05812495946884155,
-0.029273809865117073,
-0.04047195240855217,
-0.05117683485150337,
-0.006923700217157602,
0.06611578166484833,
-0.02857816033065319,
-0.015512690879404545,
-0.020782455801963806,
0.0038237411063164473,
-0.0034788271877914667,
0.044473204761743546,
-0.0007162301335483789,
-0.022837262600660324,
-0.023174531757831573,
-0.0038955037016421556,
-0.03485624119639397,
-0.05083555728197098,
-0.02990950271487236,
0.04001028835773468,
0.013611193746328354,
-0.0000984048965619877,
-0.013963987119495869,
0.002441268414258957,
0.025993304327130318,
0.0032918904908001423,
-0.05118506774306297,
-0.05498627573251724,
-0.024083884432911873,
-0.024920867756009102,
0.03365563601255417,
-0.0057512689381837845,
0.0038335963618010283,
-0.008848079480230808,
0.018205486238002777,
-0.011040844954550266,
-0.051930394023656845,
0.014765139669179916,
0.03484170511364937,
0.017535710707306862,
-0.040648624300956726,
0.032666441053152084,
-0.010421408340334892,
-0.04206519573926926,
-0.01731147989630699,
0.03933751583099365,
-0.07379865646362305,
0.05650705471634865,
0.020602723583579063,
0.01091983262449503,
0.044663798063993454,
-0.03205401822924614,
0.03838355839252472,
-0.07694973051548004,
0.0050315335392951965,
-0.0002547941985540092,
-0.06961388885974884,
0.004709654953330755,
0.0294804647564888,
0.003253351664170623,
-0.007410061080008745,
0.021007219329476357,
-0.026510514318943024,
0.028054116293787956,
-0.007372373249381781,
0.005035129841417074,
0.03363335132598877,
-0.04476141929626465,
0.0065969666466116905,
0.02919881045818329,
0.027818171307444572,
0.05470661818981171,
0.010460155084729195,
0.012600365094840527,
0.0553082600235939,
-0.028197336941957474,
0.03388619050383568,
-0.06331178545951843,
-0.024005353450775146,
0.004893486388027668,
0.0026408967096358538,
0.008037632331252098,
-0.013813840225338936,
0.03193483501672745,
-0.0009694259497337043,
0.04295002296566963,
0.025648323819041252,
0.02922595664858818,
-0.027482429519295692,
0.012638821266591549,
0.016730990260839462,
-0.02490364946424961,
0.05181346833705902,
-0.005136056337505579,
-0.011943805031478405,
0.0029616665560752153,
0.063034787774086,
0.040968675166368484,
-0.0007709884084761143,
-0.03742086887359619,
0.009795986115932465,
-0.04569631814956665,
0.03413636237382889,
-0.04200482368469238,
0.03355205059051514,
0.016442766413092613,
-0.04021839797496796,
-0.009788901545107365,
0.03987441956996918,
0.04607096686959267,
0.003473823657259345,
0.009064408019185066,
-0.07888331264257431,
0.047688812017440796,
-0.0047931368462741375,
-0.018754148855805397,
-0.050975922495126724,
0.028126118704676628,
0.018493717536330223,
0.019436733797192574,
-0.017107363790273666,
-0.05115235969424248,
-0.02572840079665184,
-0.01390173938125372,
-0.0270814411342144,
0.003255177289247513,
-0.03795398026704788,
0.00433719577267766,
0.04898252338171005,
-0.0066469707526266575,
-0.04446366801857948,
0.0033791030291467905,
-0.02464146539568901,
-0.047446172684431076,
0.03578568622469902,
0.0448404960334301,
0.006684320978820324,
0.009206188842654228,
0.0420411191880703,
0.07940436899662018,
-0.03303273394703865,
-0.1087682694196701,
0.014384817332029343,
-0.006886743474751711,
-0.017860298976302147,
-0.05151043459773064,
-0.010994120500981808,
-0.02994770184159279,
-0.045921046286821365,
-0.028121287003159523,
0.004804552532732487,
0.018802732229232788,
0.02992466278374195,
0.03273671492934227,
0.02228366769850254,
0.021941710263490677,
-0.04473559558391571,
0.029980996623635292,
-0.03032262809574604,
0.0072354506701231,
-0.016758674755692482,
0.005769072100520134,
-0.01092308945953846,
0.09309465438127518,
-0.004496591165661812,
0.05760036036372185,
-0.021528523415327072,
-0.06931863725185394,
0.0037007764913141727,
0.01279476284980774,
0.024499880149960518,
-0.035908155143260956,
-0.04273108020424843,
-0.03518034890294075,
0.017733249813318253,
-0.055812008678913116,
-0.013286574743688107,
-0.06424321979284286,
-0.012477352283895016,
-0.007716171443462372,
0.01699228212237358,
-0.001268173335120082,
-0.03547101095318794,
-0.09425170719623566,
-0.016805745661258698,
0.00005402189344749786,
-0.0727987289428711,
0.011105911806225777,
0.009772272780537605,
0.016552522778511047,
0.00046531468979083,
0.01443095225840807,
0.022830983623862267,
0.05640394613146782,
0.01871073991060257,
-0.021060680970549583,
0.053480274975299835,
0.06470396369695663,
-0.0025776985567063093,
0.07172822952270508,
0.02266661264002323,
0.018740398809313774,
0.007100266870111227,
-0.09527075290679932,
0.07559322565793991,
0.006298935040831566,
-0.0018158782040700316,
0.022719519212841988,
0.028772808611392975,
0.013988287188112736,
0.01127263717353344,
0.027979619801044464,
-0.04405703395605087,
0.00022539733618032187,
-0.00961982924491167,
0.002153533510863781,
-0.023843811824917793,
-0.026481008157134056,
-0.0026500634849071503,
0.07262992113828659,
-0.0043868739157915115,
0.011432388797402382,
0.057453788816928864,
-0.016208771616220474,
-0.07180626690387726,
0.00451468862593174,
-0.007502193097025156,
0.026964319869875908,
-0.037338804453611374,
0.023500466719269753,
0.016536112874746323,
-0.03616085648536682,
0.008053557947278023,
0.007266110274940729,
-0.0028907270170748234,
0.022848252207040787,
0.056296855211257935,
-0.02529538981616497,
0.06771735846996307,
-0.027125399559736252,
0.0005970596102997661,
-0.04283531382679939,
-0.0009000042919069529,
-0.03918077424168587,
0.02637840248644352,
0.0850052461028099,
-0.007120923604816198,
0.03987520560622215,
0.06104638800024986,
-0.06996331363916397,
0.0027180530596524477,
-0.08102689683437347,
-0.0969487726688385,
0.09201014041900635,
0.01727336458861828,
-0.02576981671154499,
-0.01167426910251379,
0.029350414872169495,
-0.01954573392868042,
-0.07167739421129227,
-0.0007396139553748071,
-0.04227229207754135,
-0.04855310916900635,
-0.016345052048563957,
0.01821068301796913,
-0.015943529084324837,
-0.006241426337510347,
0.012838711030781269,
0.05169904604554176,
0.0432547964155674,
-0.021942704916000366,
0.021278448402881622,
0.03318709507584572,
-0.014319997280836105,
-0.02801651321351528,
-0.008576354943215847,
0.042676620185375214,
0.034814585000276566,
0.0685834288597107,
0.007380684372037649,
0.061911098659038544,
0.004844742361456156,
0.03836726024746895,
-0.0259317047894001,
0.012925975024700165,
0.014282154850661755,
0.054036594927310944,
-0.03654669597744942,
0.00682862801477313,
-0.05786888301372528,
-0.005116737447679043,
0.010160752572119236,
-0.018688693642616272,
0.034437358379364014,
0.055252742022275925,
0.019833633676171303,
-0.05141338333487511,
0.03609907999634743,
0.026265639811754227,
-0.004637753590941429,
-0.030324017629027367,
-0.020359449088573456,
0.019827669486403465,
-0.031065616756677628,
0.02904648892581463,
-0.07365620881319046,
-0.02481335960328579,
0.04486687853932381,
0.040841538459062576,
-0.006307187955826521,
-0.022802529856562614,
0.014812549576163292,
-0.015715256333351135,
0.02590503729879856,
-0.004336867015808821,
0.03289051726460457,
-0.006477418355643749,
-0.02229362539947033,
0.021845100447535515,
0.008752726018428802,
-0.03623421490192413,
-0.0540849007666111,
0.07622583210468292,
-0.031421028077602386,
-0.008886403404176235,
0.034554436802864075,
-0.06336671113967896,
0.015339336358010769,
0.07441597431898117,
0.05004778876900673,
0.028281331062316895,
-0.001568746054545045,
0.017713630571961403,
0.013619942590594292,
0.0636461079120636,
-0.07241825014352798,
0.08879251033067703,
0.028923610225319862,
-0.027355575934052467,
0.027443639934062958,
-0.03962556645274162,
-0.03923269733786583,
-0.024986157193779945,
-0.012919394299387932,
-0.009332585148513317,
-0.01920454017817974,
0.023722952231764793,
0.04708006605505943
] |
<p>According to the Newtons gravity we can write,
$$\vec F = \frac{\hat r_{12} G m_1 m_2 }{r_{12}^2}$$ and we are well known that this law satisfies the planetary motions. What changes will we see if we rewrite the law in this way,
$$\vec F = \frac{\hat r_{12} G m_1 m_2 }{r_{12}^{2+p}}$$ where p is a positive number. I mean shape of the arbit, angular and linear momentum etc. </p> | g5476 | [
-0.00695730559527874,
0.04482106491923332,
-0.03063485026359558,
0.010685552842915058,
0.060781169682741165,
0.023486103862524033,
0.030961574986577034,
-0.01487058401107788,
-0.04569767042994499,
-0.02916250191628933,
-0.008864646777510643,
-0.009435391053557396,
0.06621737033128738,
-0.011082937940955162,
0.038486018776893616,
0.017256969586014748,
0.038229696452617645,
0.019924785941839218,
0.0043387641198933125,
-0.01030336320400238,
-0.006622095126658678,
-0.009035280905663967,
-0.02952691726386547,
-0.023852050304412842,
-0.02027977630496025,
0.02432095818221569,
0.02831536903977394,
0.019899392500519753,
-0.04344373196363449,
0.011954296380281448,
0.09101375937461853,
-0.029627658426761627,
0.004108574707061052,
-0.08912914246320724,
-0.03142420947551727,
0.014962621964514256,
0.04962436482310295,
0.050566576421260834,
0.041833799332380295,
-0.05362103879451752,
0.024124976247549057,
-0.07625418156385422,
-0.00996342021971941,
0.01759718731045723,
0.020399177446961403,
-0.012918160296976566,
0.037588298320770264,
-0.05475320294499397,
-0.0161716528236866,
0.03875024616718292,
0.004121578764170408,
0.06536853313446045,
-0.043489228934049606,
-0.055951569229364395,
-0.013094933703541756,
0.05386849865317345,
0.009536544792354107,
-0.037919171154499054,
0.0052136084996163845,
0.026320671662688255,
-0.013369468040764332,
-0.02527562715113163,
0.0018288909923285246,
0.023625321686267853,
0.01784471422433853,
0.016956698149442673,
-0.030474741011857986,
-0.003142440924420953,
-0.010983946733176708,
-0.014789791777729988,
0.0375286228954792,
-0.0012395954690873623,
0.02768147550523281,
-0.019700320437550545,
-0.020722484216094017,
0.006562761962413788,
0.0036696805618703365,
0.0025332216173410416,
-0.03345685452222824,
0.0012252642773091793,
-0.0001621156116016209,
-0.0161582063883543,
0.0029344966169446707,
0.014390439726412296,
0.047379132360219955,
-0.039759375154972076,
0.06046541780233383,
0.04682633653283119,
-0.046440865844488144,
0.028196601197123528,
0.018283549696207047,
-0.11288910359144211,
0.004190254490822554,
0.028474202379584312,
-0.022414853796362877,
-0.025584392249584198,
-0.030857963487505913,
0.00876542367041111,
-0.03318467363715172,
0.0011736549204215407,
-0.0024573467671871185,
0.02560228295624256,
-0.011569753289222717,
-0.024298284202814102,
0.011521782726049423,
-0.025105902925133705,
0.016906525939702988,
-0.004374575335532427,
0.042084310203790665,
-0.049992144107818604,
0.01886298879981041,
-0.010317604057490826,
0.02405521459877491,
-0.039919205009937286,
-0.0459483303129673,
-0.019235892221331596,
0.0777752473950386,
-0.005765761248767376,
-0.00869088526815176,
0.11510852724313736,
0.004941282793879509,
-0.0016001325566321611,
0.004457712173461914,
0.07657342404127121,
-0.019081974402070045,
-0.05699724704027176,
-0.010440956801176071,
-0.018301434814929962,
0.12252414971590042,
-0.057611916214227676,
-0.014207800850272179,
0.004645418841391802,
-0.019251396879553795,
0.03666962683200836,
-0.016567407175898552,
0.0015790644101798534,
-0.03334377333521843,
0.044708795845508575,
-0.043232232332229614,
-0.09722510725259781,
-0.0196841973811388,
-0.04332045838236809,
0.05885772407054901,
-0.02193516492843628,
-0.00938220601528883,
-0.008229757659137249,
0.03533320128917694,
-0.03254208713769913,
0.05466259643435478,
-0.014476774260401726,
-0.006988495588302612,
0.027397431433200836,
0.03170422464609146,
0.005584300961345434,
0.01957296021282673,
-0.06975791603326797,
0.015316850505769253,
0.029757602140307426,
-0.041652195155620575,
-0.016246438026428223,
0.0682157576084137,
-0.06176437810063362,
0.029646996408700943,
0.03689879924058914,
-0.06301577389240265,
0.07994069904088974,
-0.03339266777038574,
-0.00024912424851208925,
-0.013571173883974552,
-0.03785235062241554,
-0.04082530364394188,
0.001179186045192182,
-0.0055243754759430885,
0.04088323563337326,
-0.026470627635717392,
-0.023604024201631546,
-0.06965425610542297,
-0.06592914462089539,
0.021491628140211105,
0.04027976468205452,
0.028446581214666367,
-0.018881844356656075,
-0.0003772449854295701,
0.010785792022943497,
0.029942288994789124,
0.046705055981874466,
0.01057604793459177,
-0.021441711112856865,
-0.04985201731324196,
-0.012419532053172588,
-0.032517507672309875,
0.06657708436250687,
-0.02030397392809391,
0.10343574732542038,
0.04015791043639183,
0.0057539986446499825,
-0.052459314465522766,
-0.016891533508896828,
-0.05380794778466225,
0.15247437357902527,
0.022297585383057594,
0.018033096566796303,
0.0224298108369112,
-0.009602648206055164,
0.0021515502594411373,
-0.0248754620552063,
0.03667725622653961,
0.01872328855097294,
-0.015858519822359085,
0.040347278118133545,
0.08446509391069412,
-0.061139948666095734,
0.006118060555309057,
0.006650745868682861,
-0.048730503767728806,
-0.026229050010442734,
0.03919113427400589,
0.004981921520084143,
-0.0065744309686124325,
-0.00488143740221858,
-0.018229074776172638,
0.04015209898352623,
-0.011837945319712162,
0.05428338795900345,
0.03449030965566635,
-0.04140831530094147,
-0.038772571831941605,
-0.03419887274503708,
0.009285339154303074,
0.0347553975880146,
-0.03160984814167023,
-0.0042943465523421764,
-0.03701416403055191,
-0.005642823874950409,
-0.014518899843096733,
0.005600778851658106,
0.04941743239760399,
0.0320129431784153,
0.02343680150806904,
0.01722722500562668,
0.01745736598968506,
-0.005242327693849802,
-0.025963982567191124,
-0.05678822845220566,
0.044525012373924255,
0.04642779752612114,
0.055498216301202774,
0.06807614117860794,
0.0005221618339419365,
0.08399471640586853,
0.008951487019658089,
-0.03408876061439514,
-0.03557500243186951,
0.05092518404126167,
0.005459126550704241,
0.040171068161726,
-0.03014100342988968,
0.011745866388082504,
-0.024179136380553246,
0.02839636243879795,
0.0033123274333775043,
-0.017461813986301422,
-0.021504439413547516,
0.03180874511599541,
-0.056305065751075745,
0.009647136554121971,
-0.007433638907968998,
0.06072588637471199,
-0.01597198098897934,
0.03323077782988548,
-0.0018495332915335894,
0.055651262402534485,
-0.00039867739542387426,
0.09455707669258118,
-0.03389734774827957,
-0.022196641191840172,
0.025009000673890114,
-0.059863850474357605,
-0.055090975016355515,
0.02008417807519436,
-0.02152060903608799,
-0.015472985804080963,
-0.038345035165548325,
-0.007541891653090715,
0.03348702937364578,
-0.06418129056692123,
-0.012015239335596561,
0.02941013313829899,
-0.03507130965590477,
0.03317079320549965,
0.002268520649522543,
0.06478720158338547,
0.04979474097490311,
-0.012615981511771679,
-0.007706528063863516,
0.05672391876578331,
-0.03388013690710068,
0.026514023542404175,
0.03715597465634346,
-0.014056050218641758,
0.015515685081481934,
0.0028350346256047487,
-0.0808214619755745,
0.0570848286151886,
0.02486277185380459,
0.0022302973084151745,
0.005413280799984932,
-0.029270077124238014,
-0.008365338668227196,
-0.010155033320188522,
-0.016426261514425278,
0.10570063441991806,
0.008797635324299335,
-0.01082912739366293,
-0.060903698205947876,
-0.030245361849665642,
-0.008127947337925434,
0.05216551199555397,
-0.023895440623164177,
0.023667538538575172,
-0.044102124869823456,
-0.07699836790561676,
0.02524876967072487,
-0.024101462215185165,
-0.005169554613530636,
0.03669017180800438,
-0.05839300528168678,
-0.0315178819000721,
-0.04822121188044548,
0.014460601843893528,
-0.007592946756631136,
0.06627965718507767,
0.012998603284358978,
-0.009343457408249378,
0.008951811119914055,
0.04602543264627457,
-0.016082290560007095,
0.017515195533633232,
0.07205379754304886,
0.017110388725996017,
0.005134700331836939,
-0.015934068709611893,
-0.036943934857845306,
-0.0525980144739151,
0.0014780823839828372,
0.006101540755480528,
0.00980924628674984,
0.030121520161628723,
0.003605024656280875,
0.001415812293998897,
-0.02292049676179886,
-0.008439501747488976,
0.04573119059205055,
-0.0015216117026284337,
0.05851836875081062,
0.0658869743347168,
0.029344597831368446,
0.03006421960890293,
0.000038347112422343343,
0.0067130266688764095,
-0.033486124128103256,
-0.03254273533821106,
-0.04287741333246231,
0.0578387975692749,
0.014063275419175625,
0.06910078972578049,
0.02094648778438568,
-0.03146390616893768,
-0.03520473837852478,
-0.02918468788266182,
-0.009657240472733974,
-0.03661702200770378,
0.026045268401503563,
-0.01910409890115261,
0.006143906153738499,
0.019266601651906967,
0.029740624129772186,
-0.001576826092787087,
0.01590031571686268,
0.025259705260396004,
0.04097529500722885,
0.002937805373221636,
-0.0208937656134367,
-0.010290408506989479,
-0.018228894099593163,
0.02680598571896553,
-0.059301260858774185,
-0.037152379751205444,
0.05006422474980354,
-0.020629866048693657,
0.01566057838499546,
-0.02953305095434189,
0.03444097563624382,
0.009906207211315632,
0.03729384392499924,
-0.023458752781152725,
0.01940891146659851,
-0.03963664546608925,
-0.0443388968706131,
0.03933903947472572,
-0.008596424013376236,
0.034658271819353104,
0.009461837820708752,
0.033579010516405106,
-0.01726885885000229,
-0.03601593151688576,
0.03558161109685898,
-0.0100862430408597,
-0.03307048976421356,
-0.023433711379766464,
-0.006378578022122383,
-0.006495550740510225,
0.012183606624603271,
-0.027714960277080536,
0.01760466955602169,
0.046822331845760345,
-0.02995852380990982,
-0.0054140714928507805,
0.020710762590169907,
-0.04718803986907005,
0.045716989785432816,
0.06719441711902618,
0.023675553500652313,
-0.02455538511276245,
0.014645947143435478,
-0.009763329289853573,
0.03630091995000839,
-0.04197276383638382,
-0.0038859678898006678,
-0.031820256263017654,
-0.04117811471223831,
-0.006997005548328161,
0.01438138261437416,
-0.03962969407439232,
-0.0749269425868988,
0.01969517208635807,
-0.015688711777329445,
-0.016965463757514954,
-0.04644288495182991,
0.04529818147420883,
0.009770967997610569,
0.006274096667766571,
-0.055128615349531174,
0.024672625586390495,
0.01734478399157524,
0.06460066884756088,
-0.03605584055185318,
-0.010670664720237255,
0.025829369202256203,
0.04140168055891991,
-0.02658151462674141,
-0.005019171163439751,
0.04446304216980934,
0.0017150903586298227,
0.03917939215898514,
0.001096347812563181,
-0.041062530130147934,
-0.0019480325281620026,
0.002768254140391946,
-0.0183640755712986,
-0.0629114955663681,
0.02412426844239235,
0.0232227835804224,
0.0068772402592003345,
0.01659199222922325,
-0.01676587574183941,
-0.060697950422763824,
-0.0000035339173791726353,
-0.024749083444476128,
0.02317238040268421,
-0.01757162995636463,
-0.020746594294905663,
-0.017903203144669533,
0.00161098747048527,
-0.012753850780427456,
-0.01606139913201332,
0.05362865328788757,
-0.021779675036668777,
0.03171594813466072,
-0.027157027274370193,
-0.041410915553569794,
0.0003460761217866093,
0.04725559428334236,
-0.0523105226457119,
0.015576884150505066,
0.005542994476854801,
-0.03705248609185219,
-0.051745735108852386,
-0.03383634239435196,
-0.081633560359478,
-0.010385483503341675,
0.019200915470719337,
0.008047731593251228,
-0.016743188723921776,
0.020797746255993843,
0.047746505588293076,
-0.05514003336429596,
-0.05915917456150055,
0.07032462954521179,
-0.0019634063355624676,
-0.0660477802157402,
0.023271756246685982,
0.031457237899303436,
0.012904012575745583,
0.011332264170050621,
0.029400425031781197,
-0.0011529176263138652,
-0.006581176072359085,
-0.019051451236009598,
0.016967976465821266,
0.01920475997030735,
-0.013888035900890827,
0.01806991547346115,
-0.017527414485812187,
0.04661351069808006,
-0.03519508242607117,
0.004537036642432213,
-0.024011796340346336,
-0.04152383282780647,
-0.03531274199485779,
0.026604661718010902,
-0.035557180643081665,
0.10238628834486008,
-0.02511599101126194,
0.0628570094704628,
0.02213738113641739,
-0.04610162973403931,
-0.04132990166544914,
0.04886486753821373,
0.029699647799134254,
-0.0012789997272193432,
-0.04684078320860863,
0.02977488934993744,
0.007177215069532394,
-0.036914922297000885,
-0.015986217185854912,
0.03412611410021782,
0.022389555349946022,
0.07478085905313492,
-0.0017403318779543042,
-0.016701936721801758,
0.02126936800777912,
0.006165136117488146,
0.044055864214897156,
-0.02122020348906517,
-0.0168753694742918,
-0.025749431923031807,
0.06230518966913223,
-0.013257825747132301,
-0.06656115502119064,
-0.04890923947095871,
0.009737505577504635,
-0.004072314128279686,
-0.02063075825572014,
-0.04051040858030319,
0.0343489870429039,
-0.010226080194115639,
-0.033660877496004105,
0.05553894117474556,
-0.007331497967243195,
-0.04379837214946747,
0.012581423856317997,
-0.0012664060341194272,
0.006651928182691336,
-0.02147727645933628,
-0.03253205865621567,
0.04920090734958649,
0.01743091456592083,
0.0553133450448513,
-0.013721824623644352,
-0.06994661688804626,
0.010453556664288044,
-0.035668712109327316,
0.009768793359398842,
0.0739593654870987,
0.00585951516404748,
-0.021698541939258575,
-0.016680346801877022,
-0.018203653395175934,
-0.024014567956328392,
-0.010860741138458252,
0.0016861289041116834,
-0.0006165067316032946,
-0.0017019431106746197,
-0.05635957047343254,
0.04156599938869476,
-0.03141138330101967,
0.012508457526564598,
0.0038511701859533787,
-0.03710062429308891,
0.019915761426091194,
-0.027440905570983887,
-0.02162567712366581,
-0.02334900200366974,
-0.03334301337599754,
0.0561530627310276,
-0.015549841336905956,
-0.009349800646305084,
0.04193276911973953,
0.0036342404782772064,
0.07004822790622711,
0.046322960406541824,
0.038915928453207016,
-0.05219763517379761,
0.009015003219246864,
0.009460813365876675,
-0.050308167934417725,
0.037747617810964584,
0.027352632954716682,
0.036125365644693375,
0.028978317975997925,
0.02136451192200184,
0.009264013729989529,
-0.023845193907618523,
0.03924328088760376,
0.021309198811650276,
0.0618237666785717,
0.0362621545791626,
0.022446269169449806,
-0.02945466712117195,
0.057874664664268494,
-0.02080399915575981,
-0.0042268261313438416,
-0.019315829500555992,
-0.009535226039588451,
0.015537013299763203,
0.028893139213323593,
0.019632186740636826,
0.009554293937981129,
-0.0431634895503521,
0.012930147349834442,
0.04149378836154938,
-0.055989064276218414,
0.017776841297745705,
0.04357784241437912,
0.03636877238750458,
-0.05775804445147514,
0.023845234885811806,
-0.012975752353668213,
0.024121565744280815,
-0.015521571971476078,
0.042426202446222305,
0.03918415307998657,
-0.048251137137413025,
-0.02173907868564129,
-0.0374591238796711,
0.05176708474755287,
-0.07614228129386902,
-0.06905275583267212,
-0.015110855922102928,
-0.027078162878751755,
-0.037830889225006104,
-0.015222197398543358,
0.0456807017326355,
-0.03526454046368599,
0.013188723474740982,
-0.03251219168305397,
0.026604939252138138,
0.02517903409898281,
-0.05263598635792732,
-0.0010169710731133819,
-0.014150602743029594,
0.03256313502788544,
-0.031918350607156754,
-0.04612904042005539,
0.00925940740853548,
0.051254622638225555,
-0.0029834886081516743,
0.029837748035788536,
-0.014616422355175018,
0.02699943445622921,
-0.026372285559773445,
-0.01631314307451248,
0.07169990241527557,
0.008088480681180954,
0.05335212126374245,
-0.019775811582803726,
0.010579807683825493,
-0.013671702705323696,
0.011855725198984146,
0.005521099548786879,
0.015871107578277588,
0.020155657082796097,
0.00598542857915163,
-0.045210592448711395,
-0.0007571097230538726,
-0.0068800137378275394,
0.029167551547288895,
-0.07381140440702438,
-0.024259358644485474,
0.050934065133333206,
0.025335710495710373,
0.02065250836312771,
0.013450204394757748,
-0.016574978828430176,
-0.0562426820397377,
-0.027126256376504898,
0.021448364481329918,
-0.029958121478557587,
-0.05008245259523392,
0.033336181193590164,
0.010827885940670967,
-0.03467041999101639,
-0.005178685765713453,
0.018105531111359596,
0.008075748570263386,
-0.05798351764678955,
-0.01958206482231617,
-0.07257026433944702,
-0.041509419679641724,
-0.008554689586162567,
-0.00561255170032382,
0.007708803750574589,
0.020939841866493225,
0.066386878490448,
-0.00757315568625927,
0.022146306931972504,
0.0006735751521773636,
0.007446705363690853,
-0.020104363560676575,
-0.04520973935723305,
-0.03457605838775635,
-0.019908159971237183,
-0.12773825228214264,
-0.048883482813835144,
-0.025948816910386086,
-0.04479706287384033,
-0.00012731259630527347,
0.01234698947519064,
-0.06250573694705963,
-0.0023707104846835136,
0.01012648269534111,
-0.030233504250645638,
0.02629275619983673,
0.008102566003799438,
0.03564197197556496,
-0.02981577068567276,
-0.07666192203760147,
-0.041303765028715134,
0.022523246705532074,
-0.028046542778611183,
-0.04808978736400604,
0.03115888126194477,
-0.0101206349208951,
-0.002406287705525756,
0.02095351368188858,
-0.018039243295788765,
0.0009332197951152921,
-0.005557207856327295,
-0.017244353890419006,
0.03728151693940163,
0.011017187498509884,
-0.042131394147872925,
-0.011013197712600231,
-0.02097276598215103,
-0.000484114745631814,
0.0217750146985054,
0.042191654443740845,
-0.054775774478912354,
-0.07135426998138428,
0.053988952189683914,
0.02657882496714592,
-0.007905874401330948,
0.011470817029476166,
-0.0007093226886354387,
-0.0459388792514801,
0.029084378853440285,
0.06887160241603851
] |
<p>According to Einstein's theory of relativity, the more speed something has the slower that time passes for it; and presumably when traveling at the speed of light, time stops entirely. So this means that when a photon is created, the rest of existence virtually pauses until the photon ceases to exist, and then the rest of existence begins again. If time is stopped while the photon exists, then what are we measuring when we measure light? In order to measure the actual photon, we would need to take the measurement while time was standing still. Speed requires time, so why do we say that light travels at a speed?</p> | g195 | [
0.02259199693799019,
0.022298339754343033,
0.013104279525578022,
0.027968626469373703,
0.04870029166340828,
0.025910120457410812,
0.07126234471797943,
0.03504052013158798,
-0.03619464114308357,
0.022388769313693047,
0.01145384181290865,
-0.02976253814995289,
0.0021704554092139006,
0.047780923545360565,
-0.02221040427684784,
-0.02542383410036564,
0.09456848353147507,
-0.036062922328710556,
0.0016690926859155297,
0.029326090589165688,
0.04878190532326698,
0.0052037667483091354,
0.006984461098909378,
-0.03756250813603401,
-0.005102967843413353,
-0.03079698234796524,
0.016321424394845963,
-0.030570538714528084,
-0.01067042350769043,
-0.035887960344552994,
0.04888632521033287,
-0.01277199573814869,
0.006423120386898518,
0.012450693175196648,
0.05494280532002449,
-0.07159283012151718,
0.020150460302829742,
0.05461692810058594,
0.03955618664622307,
0.008469977416098118,
-0.02190920151770115,
-0.010034359991550446,
-0.028638316318392754,
-0.03277112543582916,
0.07896459847688675,
0.03176504746079445,
0.019367869943380356,
0.04606691375374794,
-0.0069216517731547356,
0.013052438385784626,
-0.01298139151185751,
0.030509192496538162,
0.020012643188238144,
0.022047119215130806,
0.0491827018558979,
-0.028862731531262398,
-0.0026661434676498175,
0.02093004435300827,
0.025221465155482292,
0.015232699923217297,
-0.017218077555298805,
-0.04707346484065056,
0.06651701033115387,
0.04757886379957199,
0.04825437813997269,
-0.0019073854200541973,
0.01761236973106861,
-0.05318295583128929,
0.027536951005458832,
-0.007517440244555473,
0.018016282469034195,
-0.017879880964756012,
-0.015960682183504105,
0.02136215940117836,
0.04031478613615036,
0.031829070299863815,
0.04266643896698952,
-0.009461764246225357,
-0.02678118832409382,
0.005339433904737234,
-0.0067010303027927876,
-0.037243008613586426,
-0.007226620335131884,
-0.01152744423598051,
0.06058615818619728,
-0.008953405544161797,
-0.06700962036848068,
-0.034819893538951874,
-0.04260842502117157,
0.03075256198644638,
0.025231439620256424,
-0.023205524310469627,
0.10870939493179321,
0.011052229441702366,
-0.04932589828968048,
-0.0574883297085762,
-0.00469770934432745,
0.039813410490751266,
-0.014510832726955414,
0.017755629494786263,
-0.04969051852822304,
-0.0116110285744071,
-0.02715425007045269,
0.028043346479535103,
0.027968229725956917,
-0.013030310161411762,
-0.04028278589248657,
-0.05543947592377663,
-0.03226523846387863,
-0.04469960182905197,
0.020381955429911613,
-0.023605432361364365,
-0.03377402946352959,
-0.028850629925727844,
-0.020144576206803322,
-0.050043441355228424,
0.02585010603070259,
0.01319856196641922,
-0.023737719282507896,
0.03897787630558014,
0.0074592879973351955,
0.021571097895503044,
-0.028126593679189682,
0.005598881281912327,
-0.004988509230315685,
0.03593885526061058,
0.03129926323890686,
0.0026500762905925512,
0.0005812934832647443,
0.06294001638889313,
-0.005438718944787979,
0.07398718595504761,
-0.028065020218491554,
0.03664397820830345,
-0.03219937905669212,
-0.0019786052871495485,
0.05814991891384125,
0.000585733272600919,
0.014531927183270454,
0.03678792342543602,
-0.03214965760707855,
-0.0002926283923443407,
0.02078111097216606,
-0.010457227937877178,
-0.02333894744515419,
0.06134786829352379,
0.0051427255384624004,
0.01110482681542635,
-0.01423086877912283,
0.0208826195448637,
0.0251361895352602,
0.05807463452219963,
0.0010265876771882176,
-0.019314387813210487,
0.010897854343056679,
-0.05199067294597626,
0.0135877076536417,
0.014668174088001251,
-0.02487548068165779,
0.03315509110689163,
0.08718640357255936,
-0.0008549668127670884,
-0.01775018684566021,
0.004672950133681297,
-0.036834657192230225,
0.04555678367614746,
-0.04001498222351074,
-0.04959351196885109,
-0.0021430293563753366,
-0.07864793390035629,
-0.044808126986026764,
0.0024297062773257494,
-0.00030709494603797793,
-0.015643641352653503,
0.007613364141434431,
0.004928484559059143,
0.04337194189429283,
0.003819317789748311,
-0.07132094353437424,
-0.02128669060766697,
-0.004110998008400202,
-0.03887590765953064,
0.019880130887031555,
-0.02008461020886898,
-0.007271890994161367,
0.012644661590456963,
-0.01016748882830143,
-0.08662934601306915,
-0.0799301341176033,
0.009901138953864574,
0.025493554770946503,
-0.06097779422998428,
-0.012998881749808788,
0.0518852137029171,
0.0053239138796925545,
-0.018231414258480072,
0.005314770620316267,
-0.04531293362379074,
-0.008534719236195087,
0.021698668599128723,
-0.0439155139029026,
0.025496559217572212,
-0.034235402941703796,
-0.0560542494058609,
-0.003810025053098798,
-0.029658742249011993,
-0.07658977061510086,
-0.01421389076858759,
0.007851982489228249,
0.07214777171611786,
0.07941395044326782,
-0.0028459765017032623,
0.00774697121232748,
-0.009044257923960686,
-0.010911257937550545,
0.010512049309909344,
-0.014382346533238888,
0.01255819108337164,
0.02026681788265705,
0.0621691532433033,
0.012843090109527111,
-0.002086702035740018,
-0.04500194638967514,
-0.047611743211746216,
-0.024441102519631386,
-0.030900822952389717,
-0.10625241696834564,
-0.04008564352989197,
-0.010336804203689098,
0.04268743097782135,
-0.018695330247282982,
0.016059884801506996,
-0.039974916726350784,
-0.018683863803744316,
0.016369057819247246,
0.030105456709861755,
-0.010009423829615116,
0.0083553995937109,
0.022147076204419136,
-0.05328802391886711,
-0.012474226765334606,
-0.026181504130363464,
0.004261131398379803,
0.003799400757998228,
-0.028849707916378975,
-0.024654192849993706,
0.0008301819325424731,
-0.05952726677060127,
0.010599670931696892,
0.03321952372789383,
0.05399814620614052,
-0.05154109001159668,
-0.014716398902237415,
-0.023722929880023003,
0.034800946712493896,
-0.04666467383503914,
0.053500592708587646,
0.057839203625917435,
-0.09921301901340485,
-0.009263957850635052,
-0.023916302248835564,
0.0027257984038442373,
-0.008005179464817047,
-0.02463320642709732,
-0.016065098345279694,
-0.025165362283587456,
-0.057221610099077225,
0.03838779032230377,
0.022430581972002983,
0.009498600848019123,
-0.06017407402396202,
0.02652345970273018,
0.05890784412622452,
-0.046201109886169434,
0.04755859076976776,
-0.04874499514698982,
0.019037088379263878,
-0.033688388764858246,
0.021303702145814896,
0.025772081688046455,
0.01575976051390171,
0.016689440235495567,
-0.032780539244413376,
-0.05972632020711899,
-0.0011487153824418783,
-0.10073701292276382,
0.04695212095975876,
-0.01741185411810875,
-0.024032751098275185,
-0.0030697251204401255,
0.007267523556947708,
0.026153022423386574,
-0.0019514914602041245,
0.02341362088918686,
0.005686468910425901,
0.08220763504505157,
-0.017723072320222855,
-0.057110100984573364,
-0.026935242116451263,
-0.061782509088516235,
0.028882727026939392,
-0.02920185960829258,
0.02661091461777687,
-0.018896745517849922,
-0.007056143134832382,
-0.0013178595108911395,
-0.03205005079507828,
-0.032000232487916946,
-0.06534997373819351,
-0.009623060934245586,
0.05811033397912979,
0.029709666967391968,
-0.015029053203761578,
0.033001143485307693,
-0.006016146391630173,
0.021655308082699776,
-0.054048117250204086,
0.04337909072637558,
0.026207810267806053,
-0.017526889219880104,
0.03385133296251297,
0.02967369183897972,
-0.011372199282050133,
-0.010436313226819038,
0.02105644717812538,
-0.010970213450491428,
0.031097382307052612,
-0.019883038476109505,
-0.050031863152980804,
0.00288360845297575,
0.0016240719705820084,
-0.030449578538537025,
-0.04069865867495537,
0.030128303915262222,
0.015462566167116165,
-0.04586467146873474,
0.014002983458340168,
0.05069626495242119,
0.0444612056016922,
0.01565249264240265,
0.01582099311053753,
0.025192031636834145,
-0.03390449285507202,
0.07096309214830399,
0.0026368179824203253,
-0.05123819783329964,
-0.040285371243953705,
-0.03874843195080757,
-0.02225598134100437,
-0.025877010077238083,
0.05779207497835159,
0.010929004289209843,
-0.04045400768518448,
-0.07517830282449722,
-0.06890276819467545,
0.09780724346637726,
0.006043385248631239,
0.04103304445743561,
0.05321144685149193,
-0.062333445996046066,
0.03651842102408409,
0.020695935934782028,
0.03954637795686722,
-0.004986737389117479,
-0.013906052336096764,
0.011241386644542217,
-0.02116929553449154,
-0.019342748448252678,
0.025234680622816086,
0.040070608258247375,
0.015022847801446915,
0.021252339705824852,
-0.014239843934774399,
0.041357215493917465,
0.034873418509960175,
-0.029368305578827858,
0.028064077720046043,
0.03061266429722309,
0.011797260493040085,
0.024490902200341225,
0.0006427076295949519,
0.01823725365102291,
0.0327005572617054,
-0.058703891932964325,
0.017920982092618942,
0.018115557730197906,
-0.06102926656603813,
-0.065188467502594,
-0.006222461815923452,
-0.015170680359005928,
0.03616996482014656,
-0.0515470989048481,
-0.015160935930907726,
-0.037605151534080505,
0.02860337868332863,
0.025542106479406357,
0.009092113934457302,
-0.013976766727864742,
0.03571714460849762,
-0.016105975955724716,
0.023433931171894073,
0.047217682003974915,
-0.026462959125638008,
0.016090966761112213,
-0.003430870594456792,
-0.00807432271540165,
0.07106829434633255,
-0.04259592294692993,
0.03634465113282204,
0.03756093978881836,
-0.030129995197057724,
0.02647813782095909,
-0.016858242452144623,
-0.02525300905108452,
0.00024986258358694613,
0.032655980437994,
0.0014435293851420283,
-0.05018283799290657,
0.033057764172554016,
0.024222390726208687,
0.05009710416197777,
0.005982060916721821,
0.03591710701584816,
-0.022259339690208435,
0.009600752033293247,
0.02693820558488369,
0.013423425145447254,
0.0534265860915184,
-0.0443730391561985,
0.013120648451149464,
0.0028693024069070816,
-0.014995129778981209,
0.026258457452058792,
0.03550202399492264,
0.03964075446128845,
0.04897686839103699,
0.0004875826998613775,
0.05599246546626091,
0.04789054021239281,
0.01409586425870657,
0.027588648721575737,
-0.0012199559714645147,
0.044791098684072495,
0.00892774946987629,
-0.042513955384492874,
0.01328338123857975,
-0.022196073085069656,
-0.045703157782554626,
-0.01220646034926176,
-0.019852787256240845,
-0.06516779959201813,
0.08242783695459366,
-0.018559282645583153,
0.014379600062966347,
-0.04304710775613785,
-0.014964505098760128,
-0.016433972865343094,
0.0103676188737154,
0.03595293313264847,
0.083772674202919,
-0.04632198065519333,
0.038064874708652496,
0.07425693422555923,
-0.005786424968391657,
0.0504266619682312,
0.021314339712262154,
-0.010936451144516468,
-0.05336339399218559,
-0.04520135372877121,
-0.008520676754415035,
-0.033686086535453796,
0.011694299057126045,
0.006817531306296587,
0.05599158629775047,
0.022327018901705742,
-0.02143874205648899,
-0.04620404914021492,
0.003064157674089074,
-0.03557871654629707,
-0.03199368715286255,
-0.014558120630681515,
-0.04083727300167084,
0.02841510996222496,
-0.06303181499242783,
0.00585626857355237,
-0.0032396200112998486,
-0.03694935515522957,
0.014739073812961578,
-0.012602907605469227,
-0.0347517728805542,
0.03282701596617699,
0.008597551845014095,
0.030590010806918144,
-0.02412932738661766,
-0.015293235890567303,
-0.00263805384747684,
0.02128998562693596,
-0.00021309853764250875,
-0.045284658670425415,
-0.010797536000609398,
-0.001974723534658551,
0.050801921635866165,
0.0031192272435873747,
-0.07559437304735184,
-0.040637772530317307,
0.019403377547860146,
-0.01932375505566597,
0.02921236865222454,
-0.04039783775806427,
0.05502377077937126,
0.021917689591646194,
0.07176264375448227,
-0.01143028773367405,
0.0021692116279155016,
0.01837860979139805,
-0.0030777379870414734,
0.04188445210456848,
-0.036773525178432465,
0.024776512756943703,
-0.0007118322537280619,
-0.06147129461169243,
0.017322108149528503,
0.021733492612838745,
-0.03156307712197304,
0.1121864840388298,
0.0036963745951652527,
-0.037408195436000824,
-0.002128651598468423,
0.03247963637113571,
-0.022593704983592033,
0.05899086594581604,
-0.017530815675854683,
0.05129142105579376,
-0.04945999011397362,
-0.016964862123131752,
-0.0172007754445076,
0.01768569089472294,
-0.05979418382048607,
0.028478030115365982,
-0.011876513250172138,
-0.09977094829082489,
-0.029907774180173874,
-0.0020203266758471727,
0.09286157041788101,
0.04845604673027992,
0.00047120696399360895,
0.01868657022714615,
-0.03482009097933769,
0.014651392586529255,
-0.032980769872665405,
-0.013223744928836823,
-0.014978853985667229,
-0.04409348964691162,
0.03529362753033638,
-0.03513196110725403,
0.026091869920492172,
0.005785270594060421,
0.0362478606402874,
-0.04482204094529152,
-0.04443131387233734,
0.04192707687616348,
0.047402381896972656,
-0.00019973544112872332,
-0.021838409826159477,
-0.022543730214238167,
-0.0634172335267067,
0.027930952608585358,
-0.019170468673110008,
-0.005388269200921059,
-0.03585293889045715,
0.03359844908118248,
0.036590348929166794,
0.013215486891567707,
-0.012603157199919224,
-0.024194274097681046,
0.07022962719202042,
-0.001437148661352694,
-0.02781003713607788,
-0.07280892133712769,
0.011998550035059452,
0.003637096844613552,
0.013573071919381618,
0.0427350215613842,
-0.013110458850860596,
-0.0018497081473469734,
-0.005368467886000872,
0.023339377716183662,
-0.008894659578800201,
0.10285729914903641,
0.004504744429141283,
0.0474759116768837,
0.01387141551822424,
-0.05857691913843155,
-0.02420138753950596,
-0.039017755538225174,
-0.019061248749494553,
-0.016426831483840942,
-0.06207507103681564,
-0.022976087406277657,
0.02860003150999546,
-0.05546159669756889,
-0.07207204401493073,
0.04413432627916336,
-0.04526440426707268,
0.023105105385184288,
0.04941585287451744,
-0.02099529653787613,
-0.04583778232336044,
0.05244581401348114,
0.0018489668145775795,
-0.007572648581117392,
0.07203894108533859,
0.005420379806309938,
0.03357818350195885,
-0.0351627953350544,
-0.0023558821994811296,
-0.017756231129169464,
-0.019497999921441078,
-0.03288334608078003,
0.035891126841306686,
-0.003488079411908984,
-0.03715830296278,
0.06898926943540573,
0.02867392636835575,
0.029783960431814194,
0.04943017661571503,
0.01899544894695282,
0.05050838366150856,
-0.02970600314438343,
0.01652882806956768,
0.009711225517094135,
-0.013052001595497131,
-0.00419464660808444,
0.04986605793237686,
0.027013372629880905,
0.01630116067826748,
-0.013392212800681591,
0.011885091662406921,
0.04478614404797554,
-0.011581937782466412,
0.022281715646386147,
0.007820540107786655,
0.02284172549843788,
-0.006844342220574617,
-0.042739950120449066,
-0.003927369602024555,
0.04994329437613487,
-0.035055119544267654,
-0.05813963711261749,
-0.011180572211742401,
-0.017808621749281883,
0.02527008205652237,
-0.042251307517290115,
0.008703782223165035,
-0.02404986135661602,
0.02868446335196495,
0.0007084783865138888,
-0.00047085608821362257,
-0.014176271855831146,
-0.08778303116559982,
0.003128075273707509,
-0.053466737270355225,
-0.03458418324589729,
0.028147432953119278,
-0.0394066758453846,
0.019566360861063004,
-0.012308134697377682,
-0.09269286692142487,
0.021932020783424377,
-0.004144520498812199,
-0.0001681508292676881,
-0.003864019177854061,
-0.001372997066937387,
-0.045257341116666794,
-0.017147140577435493,
0.03068665787577629,
-0.00785552803426981,
0.018144527450203896,
-0.037373632192611694,
-0.030032668262720108,
-0.02339766174554825,
0.07730010896921158,
-0.0357905738055706,
-0.03034750185906887,
-0.023760102689266205,
0.033392056822776794,
-0.013537317514419556,
-0.04615184664726257,
0.027687860652804375,
-0.011711696162819862,
0.04801715165376663,
-0.012596579268574715,
-0.015535677783191204,
0.0002080454141832888,
0.019230984151363373,
-0.046844299882650375,
0.03780832886695862,
-0.033589981496334076,
-0.041112691164016724,
0.006725028157234192,
-0.06926476210355759,
-0.027653226628899574,
0.04366612061858177,
0.012322487309575081,
0.004225193522870541,
0.025337181985378265,
-0.024566365405917168,
0.026577817276120186,
-0.017446253448724747,
-0.028948599472641945,
-0.011016408912837505,
0.06249259039759636,
-0.013622330501675606,
0.010986031033098698,
-0.0547185018658638,
-0.052141111344099045,
-0.037564717233181,
-0.023609500378370285,
0.025783207267522812,
-0.07093878090381622,
0.013106059283018112,
-0.0643782690167427,
-0.02008996345102787,
-0.02599438466131687,
-0.040853582322597504,
0.007877340540289879,
0.05135178565979004,
0.007530927658081055,
0.003665435593575239,
-0.01375039666891098,
0.010467547923326492,
0.032948657870292664,
-0.010378189384937286,
0.05818618834018707,
-0.03739631175994873,
0.07158075273036957,
0.006078692153096199,
-0.02835262566804886,
-0.03706115856766701,
-0.005263661965727806,
-0.0061729964800179005,
-0.07799482345581055,
0.007736360188573599,
0.02116963267326355,
0.050626326352357864,
-0.06689267605543137,
0.03123585693538189,
0.03816249221563339,
0.0847773477435112,
-0.010338111780583858,
-0.027781212702393532,
0.07362708449363708,
0.02546464465558529,
0.0389653705060482,
0.06265285611152649,
-0.03270741179585457,
0.021670017391443253,
-0.015538278967142105,
-0.005302491132169962,
0.013523762114346027,
0.016643190756440163,
-0.01166206318885088,
-0.008527384139597416,
0.029550479725003242,
-0.02110273763537407,
-0.04221131652593613,
0.04253305867314339,
-0.033068642020225525
] |
<p>We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's principle) and even General Relativity (we get Einstein's equation from the Einstein-Hilbert action). However, how do we explain this very principle, i.e., more mathematically, I want to ask the following: <br/></p>
<blockquote>
<p><em>If I am given a set of generalized positions and velocities, say, $\{q_{i}, \dot{q}_{i}\}$, which describes a classical system with known dynamics (equations of motion), then, how do I rigorously show that there always <em><strong>exists</strong></em> an action functional $A$, where</em>
$$A ~=~ \int L(q_{i}, \dot{q}_{i})dt,$$
<em>such that $\delta A = 0$ gives the correct equations of motion and trajectory of the system?</em> <br/></p>
</blockquote>
<p>I presume historically, the motivation came from Optics: i.e., light rays travel along a path where $S = \int_{A}^{B} n ds$ is minimized (or at least stationary). (Here, $ds$ is the differential element along the path). I don't mind some symplectic geometry talk if that is needed at all.</p> | g5477 | [
0.034856077283620834,
0.026238571852445602,
-0.017172928899526596,
0.08473823219537735,
0.06978639960289001,
-0.01971215382218361,
0.03996492922306061,
-0.016039086505770683,
0.03249639272689819,
-0.002605913672596216,
-0.04687560349702835,
0.022386813536286354,
0.04824483022093773,
0.04448937252163887,
-0.03411061689257622,
-0.02072315476834774,
0.047316793352365494,
-0.03266099467873573,
0.036357346922159195,
0.03423100337386131,
-0.0003768260939978063,
0.009517927654087543,
0.026218632236123085,
-0.02649216167628765,
0.04131302982568741,
-0.0019452357664704323,
0.06311547011137009,
-0.04562815651297569,
-0.057941146194934845,
0.014254306443035603,
0.028280068188905716,
-0.06031766161322594,
0.033378198742866516,
-0.03396626189351082,
0.03406835347414017,
0.0052258954383432865,
0.032842542976140976,
0.00008736172458156943,
0.0254913792014122,
-0.016840500757098198,
0.02048778347671032,
-0.020829346030950546,
0.04175602272152901,
-0.00019116491603199393,
0.01832982711493969,
-0.023677092045545578,
-0.017161183059215546,
-0.03765963017940521,
-0.0820954442024231,
-0.0051925587467849255,
-0.0045759049244225025,
0.06947877258062363,
0.030160432681441307,
-0.04300672560930252,
0.02406933344900608,
0.06469698250293732,
0.017284013330936432,
0.049153007566928864,
-0.026768680661916733,
0.005218379199504852,
-0.008174377493560314,
-0.020349036902189255,
0.046920254826545715,
-0.0007850277470424771,
0.08905506879091263,
-0.02348443679511547,
-0.0635179802775383,
-0.02286759950220585,
0.050731513649225235,
-0.012203667312860489,
-0.00520213833078742,
0.012108619324862957,
-0.05091327801346779,
-0.03300567716360092,
-0.00552657013759017,
-0.04523983970284462,
0.015595192089676857,
0.012090368196368217,
0.004164333920925856,
-0.005375695414841175,
-0.07056085020303726,
-0.02818947657942772,
0.046506933867931366,
-0.003334642620757222,
0.03888864442706108,
0.03748377412557602,
0.08605329692363739,
0.019060907885432243,
0.008121322840452194,
0.03713184967637062,
0.0185227207839489,
-0.023184144869446754,
0.09577691555023193,
0.03238114342093468,
-0.030679423362016678,
-0.0184320155531168,
-0.0020953428465873003,
0.04412815719842911,
0.027321232482790947,
-0.014317352324724197,
0.0029324456118047237,
-0.0022261138074100018,
0.005983125418424606,
0.02047746628522873,
-0.011362964287400246,
-0.02544364519417286,
0.04335053265094757,
0.016206787899136543,
0.0269419364631176,
0.014216510578989983,
0.0141143174842,
-0.040080729871988297,
-0.041702743619680405,
-0.014963474124670029,
-0.012647721916437149,
0.010692013427615166,
0.013323069550096989,
0.01289826724678278,
-0.01769511215388775,
0.04108886048197746,
-0.039735544472932816,
0.05878902226686478,
0.022494034841656685,
0.04945949837565422,
-0.0010140312369912863,
0.051095910370349884,
-0.0031084546353667974,
-0.011174124665558338,
-0.0171367060393095,
0.027075789868831635,
0.06534573435783386,
0.01907171495258808,
0.012874685227870941,
-0.009644032455980778,
-0.0031666946597397327,
0.03919220715761185,
-0.000925414205994457,
-0.01488280575722456,
0.03193284571170807,
0.023766733705997467,
-0.031467705965042114,
-0.04236702248454094,
-0.04029345139861107,
-0.025242848321795464,
0.0025193034671247005,
0.019437862560153008,
-0.023381181061267853,
0.016199646517634392,
0.010584304109215736,
-0.019026923924684525,
-0.021713264286518097,
0.12113499641418457,
0.005039438605308533,
-0.03242935240268707,
0.06999168545007706,
-0.05005551874637604,
0.0243073757737875,
-0.017600754275918007,
-0.03000520169734955,
-0.08343905210494995,
0.07472733408212662,
-0.011465031653642654,
0.0375412255525589,
-0.014516249299049377,
-0.04764671251177788,
0.000685215403791517,
-0.013898149132728577,
-0.02206560969352722,
0.06807015091180801,
-0.05709481239318848,
-0.02885432168841362,
-0.008258357644081116,
0.025477679446339607,
0.0610077828168869,
-0.017454514279961586,
0.04920872673392296,
-0.018916474655270576,
-0.0408482626080513,
-0.007876020856201649,
-0.02646920643746853,
-0.06702646613121033,
-0.004808901343494654,
0.014871329069137573,
-0.025223931297659874,
-0.04907090589404106,
0.03177360072731972,
-0.017883237451314926,
-0.04303402081131935,
-0.0828961506485939,
0.010204064659774303,
-0.017124298959970474,
-0.05064026638865471,
0.019604695960879326,
0.0341159850358963,
0.0028454712592065334,
0.02853800728917122,
0.016396017745137215,
-0.06242668628692627,
-0.06835903972387314,
0.015764174982905388,
0.020476482808589935,
0.058928076177835464,
0.005106351338326931,
-0.0060946149751544,
-0.0015367941232398152,
0.003107838798314333,
0.0018235546303912997,
-0.016760945320129395,
0.041986968368291855,
0.013837159611284733,
0.044636234641075134,
-0.03795613348484039,
-0.03673264756798744,
-0.012670598924160004,
-0.04315217584371567,
-0.06829071044921875,
-0.006649489980190992,
-0.010171078145503998,
0.02149645797908306,
0.0210107509046793,
-0.058176103979349136,
0.008347496390342712,
-0.03394569084048271,
0.04446251317858696,
-0.02205008454620838,
-0.007397450506687164,
-0.027575677260756493,
-0.001481671817600727,
0.03220219910144806,
0.06593339145183563,
-0.09945046156644821,
0.048310425132513046,
0.022526388987898827,
-0.03900352492928505,
0.08326325565576553,
0.003684976138174534,
0.0009150152909569442,
-0.03922261297702789,
0.07983753085136414,
0.06191062554717064,
0.03368073329329491,
-0.014751795679330826,
-0.0119680380448699,
-0.03018207848072052,
0.045016951858997345,
-0.0048275720328092575,
0.017396779730916023,
0.012048664502799511,
0.01192451175302267,
0.0253103356808424,
-0.03941459208726883,
-0.07215458154678345,
0.01155948732048273,
-0.06758034974336624,
-0.03770006448030472,
-0.0013186442665755749,
-0.032900191843509674,
0.041614048182964325,
0.0016610572347417474,
-0.013626087456941605,
-0.023107878863811493,
0.05517639219760895,
-0.02216547727584839,
0.04229055717587471,
-0.000404501857701689,
0.005149046890437603,
0.027127020061016083,
-0.0019376204581931233,
-0.0028331915382295847,
-0.007124262861907482,
-0.0011191071243956685,
0.05071534961462021,
0.001210073591209948,
0.021894482895731926,
-0.030321653932332993,
-0.04407983645796776,
0.009369449689984322,
0.011236951686441898,
-0.00004611023541656323,
0.038545288145542145,
0.008492214605212212,
-0.04877603426575661,
-0.029715532436966896,
-0.052370451390743256,
0.05254518985748291,
-0.06126699224114418,
0.04356700927019119,
0.06083732843399048,
-0.01838003471493721,
-0.01022923830896616,
-0.031195202842354774,
0.007191572804003954,
0.03231881558895111,
-0.006623799446970224,
-0.05320954695343971,
0.002503468655049801,
-0.029527442529797554,
-0.02519344538450241,
-0.05237335339188576,
-0.01568733900785446,
-0.03569028526544571,
-0.0012905282201245427,
0.009818656370043755,
0.059374723583459854,
0.01198300626128912,
0.003414756152778864,
-0.015928268432617188,
-0.09984410554170609,
0.01769191212952137,
0.012069806456565857,
0.033650852739810944,
0.03448117896914482,
-0.01470292266458273,
-0.0362139455974102,
-0.016758620738983154,
0.007073167711496353,
-0.03562147170305252,
-0.019425857812166214,
0.03347961977124214,
-0.017015568912029266,
-0.03387446701526642,
-0.07380971312522888,
-0.018060658127069473,
-0.02995292656123638,
0.07809142768383026,
-0.007856495678424835,
-0.056722331792116165,
-0.001348521327599883,
-0.02612348087131977,
-0.0066246348433196545,
-0.003018117044121027,
-0.0007700511487200856,
-0.02337927371263504,
0.012950186617672443,
-0.02544054575264454,
-0.051131539046764374,
-0.033881496638059616,
-0.013005027547478676,
0.09311795979738235,
-0.012596170417964458,
-0.016494372859597206,
-0.01320983562618494,
-0.07178187370300293,
0.03703317791223526,
-0.0033072112128138542,
-0.022777622565627098,
0.0003373720101080835,
0.04785112291574478,
0.013438384979963303,
-0.04103422537446022,
-0.0013450157130137086,
-0.07354306429624557,
0.021294401958584785,
0.013559178449213505,
-0.008646856062114239,
-0.014773036353290081,
0.042476773262023926,
0.049488365650177,
0.0712456926703453,
-0.03924023360013962,
-0.021341361105442047,
0.042170051485300064,
-0.03920966386795044,
0.05485557019710541,
0.040284037590026855,
-0.01929272897541523,
0.005360034294426441,
-0.019838780164718628,
-0.0107268076390028,
0.015326643362641335,
0.0651615560054779,
-0.03495737910270691,
0.008498279377818108,
0.010271192528307438,
0.016042757779359818,
0.006247560027986765,
0.0031151543371379375,
0.015938958153128624,
-0.09575330466032028,
-0.03251064196228981,
0.02602342888712883,
0.03400004655122757,
0.06572942435741425,
0.03802395239472389,
0.02593223936855793,
0.012805379927158356,
-0.07142296433448792,
0.030643582344055176,
0.005278019700199366,
-0.0015821700217202306,
0.006528358906507492,
0.0003652595914900303,
0.0046899993903934956,
-0.010426389053463936,
0.016607707366347313,
0.03034955821931362,
0.06065131351351738,
-0.014960240572690964,
-0.04718118533492088,
-0.014600743539631367,
-0.017627432942390442,
0.0012066590134054422,
0.0024468828924000263,
0.01615387760102749,
-0.03210877627134323,
-0.020811624825000763,
0.0005207026842981577,
-0.03647111728787422,
0.04477933421730995,
0.004675626289099455,
0.008379236795008183,
-0.09995667636394501,
0.008213161490857601,
-0.039006464183330536,
0.029702208936214447,
0.05009482800960541,
-0.01677505299448967,
-0.05488868057727814,
-0.0026649432256817818,
-0.011801719665527344,
0.029452096670866013,
0.05607789754867554,
0.04807816818356514,
-0.031146302819252014,
0.02975129336118698,
0.0806412547826767,
0.03797873109579086,
-0.00003525083957356401,
0.009131323546171188,
-0.06984595209360123,
-0.031451717019081116,
-0.007347576320171356,
0.01417404692620039,
0.01925380527973175,
-0.052406370639801025,
0.04544851556420326,
-0.009020620957016945,
0.03085276670753956,
0.016059383749961853,
0.11154844611883163,
0.03208596259355545,
0.012075376696884632,
0.03520992770791054,
-0.04890477657318115,
-0.012836097739636898,
0.051588673144578934,
-0.06537258625030518,
0.0050947037525475025,
-0.0205782949924469,
-0.055962301790714264,
0.00248826015740633,
-0.00678587332367897,
0.00035751055111177266,
0.02608805149793625,
-0.03078870289027691,
-0.020229052752256393,
-0.05096568539738655,
-0.003888759994879365,
0.04853370040655136,
-0.038974829018116,
-0.004795853979885578,
-0.03101394698023796,
0.0459754504263401,
0.015627045184373856,
0.06765422224998474,
0.020136931911110878,
-0.04584357142448425,
0.04409194737672806,
-0.061783742159605026,
-0.044527240097522736,
0.011933472007513046,
0.017830120399594307,
0.03660554811358452,
-0.028037186712026596,
-0.020841967314481735,
-0.03326240926980972,
-0.02381974458694458,
0.02851227857172489,
0.021022919565439224,
0.006157769355922937,
-0.03268437832593918,
-0.0009580403566360474,
-0.0337730273604393,
0.01611463539302349,
0.005577591247856617,
-0.0365951731801033,
-0.04672076925635338,
0.0038108299486339092,
-0.018614880740642548,
-0.06619853526353836,
-0.017670098692178726,
-0.020177891477942467,
0.012124004773795605,
-0.005671439226716757,
-0.0627087876200676,
-0.026973111554980278,
0.031182534992694855,
0.021261829882860184,
-0.002508140867576003,
0.005558677949011326,
-0.10000933706760406,
-0.0010404555359855294,
-0.007114999927580357,
0.027733271941542625,
0.026682263240218163,
0.03622215986251831,
0.06090646982192993,
-0.015032531693577766,
-0.06160140410065651,
0.014433730393648148,
0.031876955181360245,
0.034173037856817245,
-0.05120784044265747,
0.04846271127462387,
-0.002057878766208887,
-0.04352378845214844,
-0.029146544635295868,
-0.0038413014262914658,
-0.004156932234764099,
-0.030445275828242302,
-0.02301684394478798,
-0.014085889793932438,
0.05860624089837074,
-0.04609737545251846,
0.07386546581983566,
-0.0029370251577347517,
-0.03697837144136429,
-0.03782806545495987,
0.027991821989417076,
0.042336683720350266,
0.009011722169816494,
0.006932464428246021,
0.006456885952502489,
0.005378867499530315,
-0.033601175993680954,
0.0017500517424196005,
0.01807612180709839,
-0.02703305333852768,
-0.03579983115196228,
-0.012256952933967113,
-0.05565108731389046,
-0.02047019824385643,
0.04793110489845276,
0.022972745820879936,
-0.02926168590784073,
-0.034611426293849945,
-0.023590704426169395,
-0.03175106272101402,
0.03388380631804466,
-0.03318408131599426,
-0.0680762454867363,
0.0037966049276292324,
-0.039763640612363815,
-0.042501047253608704,
-0.07273170351982117,
0.055008407682180405,
-0.048619747161865234,
-0.023717641830444336,
-0.0381091944873333,
-0.008611226454377174,
0.059728290885686874,
-0.036400772631168365,
0.01601753942668438,
-0.01836540363729,
0.010319290682673454,
-0.0546543262898922,
0.01584767736494541,
0.015860887244343758,
0.0742407813668251,
0.08798252046108246,
-0.04774853214621544,
0.04655299335718155,
0.028617942705750465,
0.006775820627808571,
0.01891322247684002,
0.0013002778869122267,
-0.03952229768037796,
-0.04570097476243973,
-0.09508927911520004,
0.026993462815880775,
-0.038067299872636795,
0.012979029677808285,
0.048315271735191345,
-0.04083697497844696,
-0.04872610792517662,
0.02766617015004158,
-0.009853419847786427,
-0.020311277359724045,
0.001234750496223569,
0.07136119902133942,
0.03215913102030754,
0.015246930532157421,
-0.05927061289548874,
0.031126894056797028,
-0.025798065587878227,
-0.02573982998728752,
0.04331744462251663,
0.030501941218972206,
0.01763521507382393,
0.02313375659286976,
0.024875912815332413,
0.017888670787215233,
0.03749620169401169,
-0.03691320866346359,
-0.003092609578743577,
0.03555695712566376,
-0.032728709280490875,
-0.02021150477230549,
0.04158095270395279,
0.007516033481806517,
-0.00043498445302248,
0.02566329762339592,
0.019340379163622856,
0.06637851893901825,
-0.028869185596704483,
-0.013429144397377968,
0.004432988818734884,
0.008974028751254082,
-0.01768760196864605,
0.003943940158933401,
0.0016864720964804292,
-0.012830236926674843,
0.032542433589696884,
-0.049225661903619766,
0.02223111130297184,
-0.004968535620719194,
-0.05295025557279587,
-0.005106460303068161,
0.02961176447570324,
0.02598605491220951,
0.04403793066740036,
0.040051527321338654,
-0.02243817038834095,
0.04396302253007889,
-0.005848818924278021,
0.030047688633203506,
-0.007887063547968864,
0.06665720790624619,
0.038735970854759216,
-0.0072361016646027565,
-0.04009620472788811,
0.06731902807950974,
0.04231453686952591,
-0.039314378052949905,
-0.06697742640972137,
-0.021301433444023132,
0.02313881367444992,
0.009318497963249683,
-0.056230805814266205,
-0.025971801951527596,
0.027769552543759346,
-0.03263889625668526,
-0.0037052074912935495,
-0.0047615463845431805,
-0.003286282066255808,
0.0044288127683103085,
-0.018025077879428864,
0.010267199017107487,
-0.009198316372931004,
-0.08617507666349411,
-0.011148354038596153,
0.0013083000667393208,
-0.014968390576541424,
-0.029494453221559525,
-0.005469315219670534,
0.05242990329861641,
-0.0312839113175869,
-0.022087357938289642,
-0.0441284142434597,
0.012952698394656181,
0.02394273690879345,
0.01663372665643692,
-0.03491929545998573,
0.039406247437000275,
-0.019315063953399658,
-0.019779307767748833,
0.007123220711946487,
0.043449096381664276,
0.026026321575045586,
-0.020418602973222733,
0.05348098278045654,
0.04885730519890785,
0.00686667812988162,
-0.04037398844957352,
-0.043139539659023285,
-0.026317959651350975,
-0.013625008054077625,
-0.0049123079515993595,
-0.03574904426932335,
-0.03405676782131195,
0.010502221994102001,
-0.015940196812152863,
-0.006119678262621164,
-0.026557059958577156,
-0.002226094016805291,
0.013318673707544804,
0.04087185114622116,
0.01868494600057602,
0.010785352438688278,
0.0164113100618124,
-0.029262181371450424,
-0.003846500301733613,
-0.02600955031812191,
0.04736056178808212,
0.040874119848012924,
-0.0030571110546588898,
-0.04285754635930061,
-0.024059439077973366,
-0.00508681358769536,
0.009863382205367088,
0.007597208023071289,
0.004316443577408791,
-0.031284622848033905,
0.005769600160419941,
0.009069799445569515,
0.02305322326719761,
-0.02100328914821148,
0.05825606361031532,
0.026908285915851593,
0.021589571610093117,
0.013783673755824566,
-0.03139565512537956,
-0.029300110414624214,
-0.09333851933479309,
0.010636073537170887,
-0.02196299284696579,
-0.0028525807429105043,
-0.09979341179132462,
0.011166305281221867,
0.0063311439007520676,
-0.003070665057748556,
-0.04514298960566521,
-0.026072321459650993,
0.05761659890413284,
-0.02079099230468273,
0.02291133441030979,
-0.07561087608337402,
-0.017850017175078392,
0.00322326784953475,
0.033156417310237885,
0.043890807777643204,
-0.0834190621972084,
-0.011265240609645844,
0.014440665021538734,
0.022125178948044777,
-0.021695667877793312,
0.07323866337537766,
0.016112959012389183,
0.014316757209599018,
0.007986446842551231,
0.03984834998846054,
0.07907143235206604,
-0.00038009596755728126,
0.02384091727435589,
0.0058412072248756886,
-0.020600222051143646,
0.031731270253658295,
0.010526754893362522,
0.014569761231541634,
0.061954252421855927,
-0.014883491210639477,
-0.04270198941230774,
0.038959480822086334,
-0.01675359532237053,
-0.03145914524793625,
-0.01964523456990719,
-0.00876668281853199,
0.010057643055915833
] |
<p>A bucket is filled with water and a handful of sand. The water is then spun. Why and what forces are in play which cause the sand particles to congregate in the centre of the bucket?</p> | g196 | [
0.06476177275180817,
0.04283927008509636,
-0.004585010465234518,
-0.04292195290327072,
0.06702416390180588,
0.04131430760025978,
0.0837707668542862,
-0.025586368516087532,
-0.022325800731778145,
-0.04823490232229233,
-0.030072515830397606,
-0.01093212142586708,
0.023512430489063263,
0.009076776914298534,
-0.0006561618065461516,
0.05336184427142143,
-0.006964799948036671,
0.033512894064188004,
-0.04215020313858986,
0.025363080203533173,
-0.010316669009625912,
0.001007196493446827,
0.003448928240686655,
-0.0014265273930504918,
-0.062119632959365845,
-0.017118560150265694,
0.005135110579431057,
0.0015772857004776597,
0.010940522886812687,
0.03589669242501259,
0.06578468531370163,
0.05461805686354637,
-0.07089436799287796,
-0.055832188576459885,
-0.04008708521723747,
-0.06995564699172974,
-0.02179594896733761,
-0.0365494079887867,
-0.008322684094309807,
0.008188187144696712,
-0.010693646967411041,
0.008459523320198059,
0.018593313172459602,
0.0167889054864645,
-0.035160571336746216,
-0.005085067357867956,
0.04974725842475891,
0.02141481265425682,
-0.008057503029704094,
-0.015306183136999607,
-0.030783914029598236,
-0.033069171011447906,
-0.0007147627184167504,
0.03290041163563728,
0.0447249561548233,
0.023880206048488617,
0.03700025752186775,
0.021448669955134392,
-0.001553767709992826,
0.03947588428854942,
-0.01939702406525612,
0.022663539275527,
-0.06786192208528519,
0.03277967870235443,
0.006078457459807396,
-0.00583369517698884,
0.04440939426422119,
0.004174431785941124,
0.046515628695487976,
0.03610263019800186,
0.033489566296339035,
-0.047298040241003036,
-0.026542948558926582,
-0.027478057891130447,
-0.041430335491895676,
0.030045967549085617,
-0.016978813335299492,
0.055890824645757675,
-0.024965770542621613,
-0.047996070235967636,
0.031706154346466064,
0.0670066550374031,
-0.08388374745845795,
-0.002418458228930831,
0.030584009364247322,
-0.017166050150990486,
-0.04634872451424599,
-0.015634534880518913,
-0.0035272727254778147,
-0.06028241291642189,
-0.0027396571822464466,
-0.012944964691996574,
0.06327170878648758,
0.02871009334921837,
-0.07208822667598724,
-0.07379218935966492,
-0.019133666530251503,
0.060598187148571014,
-0.025729000568389893,
0.03452788665890694,
0.0022466096561402082,
-0.021244699135422707,
0.02669122815132141,
-0.0706154853105545,
-0.008030040189623833,
-0.026373786851763725,
-0.009399582631886005,
0.06391327828168869,
-0.004783562384545803,
-0.0231633260846138,
0.006135144736617804,
-0.006270978134125471,
-0.03659263998270035,
-0.025847600772976875,
0.0395062156021595,
-0.011428936384618282,
0.06163249909877777,
0.05911754071712494,
0.05592137947678566,
0.003444869304075837,
-0.0005822250968776643,
-0.04872572794556618,
-0.017284365370869637,
0.04592736065387726,
-0.023680325597524643,
-0.007383570075035095,
0.02117125503718853,
0.012194276787340641,
0.007770679425448179,
0.0380309633910656,
0.01277474220842123,
-0.02361801266670227,
0.0072615179233253,
-0.013166137039661407,
-0.0077792322263121605,
0.054503049701452255,
-0.03695165738463402,
-0.0033203610219061375,
0.02005966566503048,
-0.0427866205573082,
0.031915053725242615,
0.04046408459544182,
0.040247123688459396,
-0.021023934707045555,
0.049783024936914444,
0.03302288427948952,
0.02271815948188305,
0.010652470402419567,
-0.00850484799593687,
0.029951607808470726,
-0.03590822219848633,
0.03199030086398125,
0.018326139077544212,
-0.059258878231048584,
0.061947837471961975,
0.023640071973204613,
0.07214456796646118,
-0.017937887459993362,
0.03734995052218437,
0.011293767020106316,
0.09388303756713867,
-0.009228259325027466,
0.0033849983010441065,
0.046787720173597336,
-0.05692090466618538,
0.01980290375649929,
0.025733010843396187,
-0.03404083102941513,
-0.006649646908044815,
0.006792673375457525,
-0.022302748635411263,
-0.03864993527531624,
-0.03827821835875511,
0.0565091073513031,
-0.013721466064453125,
0.05300483480095863,
0.012598162516951561,
-0.029618313536047935,
0.026939736679196358,
0.034888479858636856,
-0.003904943820089102,
-0.06356142461299896,
0.01381700113415718,
0.029829612001776695,
0.013530544936656952,
-0.009310144931077957,
0.010062295943498611,
0.017604852095246315,
-0.05123097822070122,
-0.012727106921374798,
-0.03609989583492279,
-0.05143945664167404,
-0.039258379489183426,
-0.01445102971047163,
0.017909444868564606,
-0.027760688215494156,
0.00824351143091917,
-0.06932495534420013,
-0.020743083208799362,
-0.0028238301165401936,
-0.023951755836606026,
-0.006750888656824827,
0.02037823013961315,
0.020888080820441246,
-0.03528724983334541,
0.0027472330257296562,
0.0030063006561249495,
0.03282853960990906,
0.022589636966586113,
-0.002685421146452427,
-0.011624591425061226,
0.04781696945428848,
-0.045237693935632706,
-0.0002068385510938242,
-0.10110369324684143,
0.004649577662348747,
0.032865338027477264,
0.05088222026824951,
-0.006239765323698521,
0.03480331972241402,
-0.0754360556602478,
-0.0758824273943901,
-0.047804996371269226,
0.008832319639623165,
-0.005148967728018761,
0.014382986351847649,
-0.012649682350456715,
-0.03231421113014221,
-0.015793917700648308,
0.03457397222518921,
0.003195660188794136,
-0.037468571215867996,
0.029227137565612793,
0.006420683115720749,
0.0760951042175293,
0.0011563758598640561,
0.022751830518245697,
0.03090851381421089,
0.027336720377206802,
-0.07808417081832886,
-0.02696550451219082,
0.04144586622714996,
0.004004867747426033,
-0.057485610246658325,
0.029722275212407112,
0.0018732290482148528,
0.06328678876161575,
-0.06801166385412216,
0.06734402477741241,
0.03391772136092186,
0.03443282097578049,
-0.08288082480430603,
-0.025021273642778397,
0.050459109246730804,
0.0058552855625748634,
-0.0013385363854467869,
-0.03074108064174652,
0.04789092764258385,
-0.06827335804700851,
-0.02150101400911808,
-0.029170827940106392,
-0.002657567150890827,
0.009543156251311302,
-0.012485937215387821,
-0.03791790083050728,
-0.014574477449059486,
-0.047694507986307144,
-0.01879657432436943,
0.03191833943128586,
0.024302590638399124,
-0.031390417367219925,
0.013760979287326336,
0.023964298889040947,
-0.012309844605624676,
-0.020175358280539513,
-0.024414319545030594,
-0.02572283148765564,
-0.049329448491334915,
-0.03549924120306969,
-0.023261360824108124,
-0.011403693817555904,
-0.005835354328155518,
-0.023179806768894196,
0.010987622663378716,
0.011480206623673439,
0.031759876757860184,
-0.01170202624052763,
0.029667148366570473,
-0.06703518331050873,
0.02056192047894001,
0.029804060235619545,
0.07259240001440048,
0.061349716037511826,
-0.000352969131199643,
0.07690350711345673,
0.031773459166288376,
0.014692823402583599,
0.029248682782053947,
0.007366953883320093,
0.09143254905939102,
0.020719945430755615,
-0.03271055221557617,
0.019980892539024353,
-0.001077830558642745,
-0.05672869458794594,
0.04036097601056099,
0.028512200340628624,
-0.03611348196864128,
-0.04600183665752411,
0.015280134044587612,
-0.05832773819565773,
-0.0032789474353194237,
-0.03040168620646,
0.01743192784488201,
-0.0635862797498703,
-0.0244422797113657,
-0.02453601360321045,
0.038794104009866714,
0.07185414433479309,
-0.05382983386516571,
-0.07319042086601257,
-0.022070804610848427,
0.0033341634552925825,
-0.0156928151845932,
0.03098120726644993,
0.04914799705147743,
-0.0147366588935256,
-0.007897419854998589,
-0.002708214335143566,
-0.02667304500937462,
-0.012886911630630493,
-0.0268437210470438,
-0.05338618904352188,
-0.03953912854194641,
-0.08719132840633392,
-0.04471971467137337,
0.028818361461162567,
0.025332113727927208,
-0.003172897268086672,
-0.012423323467373848,
-0.032356999814510345,
0.030099380761384964,
-0.0228620283305645,
-0.050380196422338486,
-0.0584762841463089,
0.050354696810245514,
0.05196373909711838,
-0.02005203627049923,
0.07615819573402405,
0.009531466290354729,
0.019226476550102234,
-0.00008859860827215016,
0.005350136198103428,
-0.03960394859313965,
-0.005433705635368824,
0.033589981496334076,
-0.02069748379290104,
-0.01142948679625988,
-0.003828297834843397,
-0.021082613617181778,
0.003378496505320072,
-0.04741373658180237,
-0.026990365236997604,
-0.0010851022088900208,
-0.04238567501306534,
0.02037985809147358,
0.006737302523106337,
0.03415863588452339,
-0.03932254761457443,
-0.005118233151733875,
0.06499899923801422,
-0.019013991579413414,
-0.07353876531124115,
0.034491926431655884,
0.037530068308115005,
0.01829158142209053,
0.04949433356523514,
0.0024074772372841835,
-0.027668621391057968,
-0.04143567383289337,
0.0626707375049591,
0.04086495190858841,
-0.011142048053443432,
0.03419644013047218,
-0.04768810048699379,
0.005509399808943272,
0.04022208973765373,
-0.02228214591741562,
0.02843298949301243,
-0.027618451043963432,
0.06963455677032471,
0.026018792763352394,
0.0500364676117897,
-0.046159859746694565,
0.02594546414911747,
-0.00047813329729251564,
-0.041137050837278366,
-0.0010033563012257218,
-0.027168793603777885,
-0.004409699235111475,
0.002919526072219014,
0.019113963469862938,
-0.06525932997465134,
-0.048281002789735794,
0.0409432053565979,
0.012665214017033577,
0.034484732896089554,
-0.040488310158252716,
-0.021315287798643112,
-0.04982278496026993,
0.026715492829680443,
0.042032863944768906,
-0.006006411276757717,
-0.03640550747513771,
0.03344450891017914,
0.01248141098767519,
0.013436194509267807,
0.08807839453220367,
-0.030424989759922028,
-0.02300972118973732,
0.010993780568242073,
0.009471814148128033,
-0.004838792607188225,
-0.013118003495037556,
-0.04051829129457474,
-0.036243971437215805,
-0.031330656260252,
-0.01409237366169691,
-0.01072736643254757,
-0.015414179302752018,
-0.046354688704013824,
0.054340068250894547,
-0.008486298844218254,
0.016400832682847977,
0.01480046845972538,
0.0008137266850098968,
-0.013108545914292336,
-0.036173015832901,
0.006854661274701357,
0.018364382907748222,
0.02449674718081951,
0.04199260100722313,
-0.0009219541097991168,
-0.019003765657544136,
0.044162169098854065,
0.08098923414945602,
0.00500998692587018,
-0.037108007818460464,
0.020808516070246696,
-0.011508285067975521,
-0.009982696734368801,
0.017845872789621353,
-0.02618488296866417,
-0.027835683897137642,
-0.006297674961388111,
0.07981908321380615,
-0.03613271191716194,
0.020521633327007294,
-0.04418782517313957,
0.0075766341760754585,
-0.0499241016805172,
-0.018397727981209755,
-0.005785629618912935,
-0.014827431179583073,
0.015123534947633743,
-0.003006268758326769,
0.08687441051006317,
-0.012157106772065163,
-0.025963502004742622,
-0.01020327489823103,
0.022930750623345375,
0.01431840006262064,
0.04342331737279892,
0.0024520668666809797,
0.03249959647655487,
0.011716448701918125,
0.012169956229627132,
0.004762830678373575,
0.08894549310207367,
-0.023480577394366264,
0.021349303424358368,
0.048237886279821396,
-0.011212140321731567,
0.0037099174223840237,
-0.016445057466626167,
-0.03632974997162819,
0.012469346635043621,
-0.04039075970649719,
-0.014479859732091427,
0.029691357165575027,
0.018497416749596596,
-0.05894820764660835,
0.03147096931934357,
-0.027458876371383667,
0.004915589466691017,
-0.002493135631084442,
-0.004596085287630558,
0.014398746192455292,
0.050540998578071594,
-0.01085333339869976,
0.019256943836808205,
-0.06966974586248398,
0.004821839742362499,
0.015231260098516941,
0.007647813763469458,
0.005772830918431282,
-0.01579618640244007,
-0.028025731444358826,
0.0072153490036726,
0.05404830351471901,
0.03048652969300747,
-0.014883026480674744,
0.01911761984229088,
-0.01884486898779869,
0.002358990954235196,
0.01668795756995678,
0.008305950090289116,
0.0036500010173767805,
0.029100485146045685,
0.06648392975330353,
-0.015254399739205837,
0.028621869161725044,
-0.004295411519706249,
-0.011427178978919983,
-0.057956352829933167,
0.007279249373823404,
-0.06165007874369621,
0.041754886507987976,
0.02264266647398472,
-0.015079914592206478,
-0.02573723904788494,
0.005211689043790102,
0.09157109260559082,
-0.009315506555140018,
0.025756528601050377,
-0.035699307918548584,
0.046217769384384155,
0.04930606111884117,
0.08069347590208054,
0.03185879439115524,
-0.013457111082971096,
-0.005072041414678097,
0.04592502862215042,
-0.005520990584045649,
-0.001031564432196319,
0.03252927213907242,
-0.02553587220609188,
-0.0347546823322773,
0.0677996352314949,
-0.02648301236331463,
0.025732196867465973,
0.0984145924448967,
-0.022205540910363197,
-0.056029945611953735,
-0.04180775210261345,
0.005583003628998995,
-0.05269212648272514,
-0.04028376191854477,
-0.0005453405319713056,
-0.05765247717499733,
0.0018633666913956404,
-0.0018891984364017844,
-0.0029654190875589848,
-0.003710603341460228,
0.000008641225576866418,
-0.054304588586091995,
-0.025227952748537064,
0.044184986501932144,
0.011710715480148792,
0.012960429303348064,
-0.028689401224255562,
0.020973866805434227,
0.03957095742225647,
-0.017840970307588577,
0.06875072419643402,
0.036307111382484436,
-0.04139406606554985,
-0.02546144835650921,
-0.04662550613284111,
0.026922136545181274,
0.04728958010673523,
0.032502759248018265,
0.06329946964979172,
-0.011096886359155178,
0.05097442865371704,
0.017195992171764374,
-0.03161691501736641,
0.020757121965289116,
0.02568857930600643,
-0.04128147289156914,
-0.04669756442308426,
0.01820620335638523,
0.008233848959207535,
-0.020503653213381767,
0.0015153505373746157,
-0.02056366764008999,
0.015583550557494164,
0.019055718556046486,
-0.04103856161236763,
-0.02762630768120289,
-0.025056522339582443,
-0.012719790451228619,
0.07021962851285934,
0.02832477167248726,
-0.015599124133586884,
-0.09323043376207352,
-0.002166994847357273,
-0.06628328561782837,
0.005405206233263016,
0.038069430738687515,
0.027398161590099335,
0.005315845832228661,
0.0099112493917346,
0.017646780237555504,
-0.017143746837973595,
-0.002232540166005492,
-0.017374230548739433,
-0.021909603849053383,
0.0583372488617897,
-0.0705370232462883,
-0.05616453289985657,
0.007551334798336029,
0.032791607081890106,
-0.07837732881307602,
-0.029042866080999374,
-0.027201484888792038,
-0.07998234778642654,
0.03938665613532066,
0.0342220664024353,
0.004014755133539438,
0.04693190008401871,
0.02978741191327572,
0.0024632441345602274,
-0.03326348587870598,
0.0011865620035678148,
0.02703043445944786,
-0.03228207677602768,
0.04037957265973091,
-0.0040665278211236,
0.061432648450136185,
0.02081061713397503,
0.049879640340805054,
-0.0156643558293581,
0.02468610741198063,
-0.0035090181045234203,
0.024158865213394165,
0.03768486529588699,
-0.039154183119535446,
-0.021632814779877663,
0.015208938159048557,
0.00895682256668806,
-0.003684417111799121,
0.014086322858929634,
-0.009389827959239483,
0.002580673899501562,
0.03056580387055874,
0.014538636431097984,
0.029941832646727562,
0.08386766910552979,
0.017265258356928825,
-0.07325409352779388,
0.029295891523361206,
-0.04794032499194145,
-0.030341358855366707,
-0.03984440490603447,
0.07938303798437119,
0.03260258212685585,
0.02806743234395981,
0.029653724282979965,
0.013934437185525894,
-0.021958226338028908,
-0.00740704033523798,
-0.04666273668408394,
0.006791948340833187,
-0.005038868635892868,
-0.011552726849913597,
-0.010134538635611534,
0.0012632367433980107,
0.03441556543111801,
0.02905498817563057,
0.03758934512734413,
0.0032018180936574936,
0.006624702364206314,
-0.013860180974006653,
-0.04156193882226944,
-0.02387908101081848,
0.046791840344667435,
-0.0003563071368262172,
0.021165693178772926,
-0.09074036031961441,
0.03481944650411606,
0.061617814004421234,
-0.017149418592453003,
-0.03774195909500122,
0.010976024903357029,
-0.008642110973596573,
0.04963923618197441,
-0.019752956926822662,
0.04802877455949783,
-0.016909455880522728,
-0.04419918358325958,
-0.0467192716896534,
-0.017140790820121765,
0.018881533294916153,
0.006968252826482058,
-0.03540531173348427,
-0.034164320677518845,
0.04474344104528427,
-0.05550180748105049,
-0.05642670392990112,
-0.04156825318932533,
-0.027976030483841896,
0.006521276663988829,
-0.04884020611643791,
-0.03770333528518677,
0.015904631465673447,
-0.023645849898457527,
0.057149749249219894,
-0.012515264563262463,
0.010476258583366871,
-0.017296021804213524,
0.024346521124243736,
-0.0068969749845564365,
-0.014062175527215004,
-0.07738271355628967,
-0.057160913944244385,
0.0028547311667352915,
-0.032172754406929016,
-0.027043115347623825,
0.052979402244091034,
-0.05133023113012314,
-0.010717892087996006,
-0.019763514399528503,
0.02379225753247738,
0.0005026390426792204,
-0.04108506813645363,
-0.011194339022040367,
-0.010856738314032555,
-0.04253219813108444,
0.024142934009432793,
0.017989065498113632,
-0.002377750352025032,
-0.0038288889918476343,
-0.05145417898893356,
-0.03578150272369385,
-0.0023100378457456827,
-0.028525447472929955,
0.016007855534553528,
-0.0040621068328619,
-0.04257749766111374,
0.051365822553634644,
-0.0654214471578598,
0.004824486561119556,
-0.0024883844889700413,
0.039334964007139206,
-0.06519656628370285,
-0.04857116565108299,
0.09503728151321411,
-0.014965049922466278,
-0.054532717913389206,
-0.002553256694227457,
0.01693485677242279,
-0.043411046266555786,
0.03475060313940048,
0.002777949208393693,
0.00822878535836935,
-0.03477213531732559,
0.031153444200754166
] |
<p>When walking, if I apply a force of 2N on the earth, the earth applies a force of 2N back on my feet due to Newtons 3rd Law of Motion. These 2 forces are equal in magnitude but opposite in direction, so they negate each other and add up to zero. So how can we move then if the net force adds up to zero? </p> | g197 | [
0.026310615241527557,
0.03794616460800171,
0.0040714372880756855,
0.019240224733948708,
0.0645490437746048,
0.06925731897354126,
0.004925312474370003,
0.045733001083135605,
-0.02970454841852188,
-0.055947598069906235,
-0.03809662535786629,
-0.03612971678376198,
-0.001124003785662353,
-0.011365768499672413,
-0.02139344811439514,
0.05994699150323868,
0.055326588451862335,
-0.008788912557065487,
0.026636872440576553,
0.005836228374391794,
0.013879443518817425,
0.026653442531824112,
-0.03680294752120972,
-0.047428231686353683,
-0.06676056981086731,
-0.02621915191411972,
0.0487658753991127,
0.005233610048890114,
-0.04396146535873413,
-0.008667737245559692,
0.038583457469940186,
0.0029752759728580713,
0.012116091325879097,
-0.050052765756845474,
-0.04260551184415817,
0.04210115596652031,
0.011383523233234882,
0.016520995646715164,
-0.02533837780356407,
-0.011418623849749565,
0.030250156298279762,
-0.053862378001213074,
0.029736768454313278,
0.01604628562927246,
-0.010677505284547806,
-0.04065180569887161,
0.025071242824196815,
-0.012650811113417149,
0.014353495091199875,
0.022203078493475914,
-0.05898794159293175,
0.011447392404079437,
-0.036223649978637695,
-0.01377872470766306,
0.015930572524666786,
0.044788263738155365,
0.04182087257504463,
-0.09550195932388306,
0.0009149053948931396,
0.025314737111330032,
-0.020175842568278313,
-0.024856654927134514,
0.05970414727926254,
0.02236808091402054,
0.006947129033505917,
-0.007064439821988344,
-0.057081930339336395,
0.07234308123588562,
0.07821281999349594,
-0.008168388158082962,
0.015547864139080048,
0.02548426017165184,
-0.02744544856250286,
-0.011006851680576801,
0.002325915265828371,
0.019062316045165062,
0.02264922857284546,
0.03168945014476776,
-0.005877177231013775,
0.038773152977228165,
-0.026143258437514305,
0.03198955953121185,
0.019198475405573845,
0.017705289646983147,
0.05146687477827072,
-0.01214544102549553,
0.031177762895822525,
0.012691383250057697,
-0.017480403184890747,
0.04661969840526581,
0.01704075001180172,
0.021583471447229385,
0.07696202397346497,
0.06646442413330078,
-0.005951493047177792,
-0.0840875431895256,
0.03915303573012352,
0.045138824731111526,
0.017776988446712494,
-0.04392837733030319,
-0.024995941668748856,
0.03396296128630638,
0.038326065987348557,
-0.026589078828692436,
0.012568836100399494,
0.0037938610184937716,
0.09713494777679443,
0.0248020701110363,
-0.014664621092379093,
-0.0325746051967144,
-0.010270629078149796,
-0.03008822537958622,
0.009201884269714355,
-0.03659175708889961,
0.0011502832639962435,
0.005260711070150137,
0.054698437452316284,
-0.04360971972346306,
0.037259940057992935,
0.06691888719797134,
0.025242744013667107,
0.04093501344323158,
0.011372663080692291,
0.028842337429523468,
-0.040407247841358185,
-0.04998357966542244,
-0.011701013892889023,
0.002876082668080926,
-0.001166900503449142,
-0.055019717663526535,
0.052192412316799164,
0.04246768355369568,
0.023509306833148003,
-0.011953838169574738,
0.005371740087866783,
-0.00030121911549940705,
-0.051104556769132614,
0.005587323568761349,
-0.028505653142929077,
0.03754616901278496,
-0.027669932693243027,
-0.014779197983443737,
0.05232942849397659,
-0.004707645624876022,
-0.005563739687204361,
0.02800755575299263,
-0.003759178565815091,
-0.01641148515045643,
0.027748528867959976,
0.016111670061945915,
-0.007198147475719452,
0.0891803726553917,
0.02428913116455078,
-0.06666097044944763,
0.07354190200567245,
-0.0811929777264595,
0.023431651294231415,
0.019770262762904167,
-0.05891800299286842,
-0.033673129975795746,
0.06961420178413391,
0.0002334070741198957,
0.029743749648332596,
0.035883646458387375,
0.013184129260480404,
0.035895708948373795,
-0.04483642801642418,
-0.01759326457977295,
0.019616052508354187,
0.022916201502084732,
-0.034448325634002686,
0.009239702485501766,
0.005011684726923704,
0.010344034992158413,
-0.028561662882566452,
0.037383198738098145,
-0.052115339785814285,
0.007227221503853798,
-0.025642817839980125,
-0.0018343047704547644,
0.014862710610032082,
0.027431229129433632,
-0.002147355116903782,
0.06540357321500778,
-0.04500286281108856,
-0.04441064968705177,
-0.022162094712257385,
0.03037371300160885,
-0.0322214774787426,
-0.0006137428572401404,
-0.05006880685687065,
-0.005765847396105528,
0.003881340380758047,
-0.01838955283164978,
-0.007262037601321936,
-0.008847986347973347,
-0.04663900285959244,
-0.039497941732406616,
0.0161866657435894,
-0.06107240170240402,
0.03174971416592598,
0.03125718981027603,
0.0236586295068264,
-0.01464843936264515,
0.010276036337018013,
-0.007329815533012152,
0.030147550627589226,
0.008160305209457874,
0.07054591923952103,
0.013669291511178017,
0.01454618014395237,
0.013384291902184486,
-0.027440577745437622,
0.048618465662002563,
-0.03038395568728447,
0.0228729248046875,
-0.01361105591058731,
-0.012700493447482586,
-0.06150076910853386,
-0.04194897040724754,
-0.029657354578375816,
-0.01006352435797453,
0.0429387167096138,
0.023551106452941895,
-0.0277019664645195,
-0.03911123424768448,
-0.04338571056723595,
-0.0071233902126550674,
-0.006537649780511856,
0.048517730087041855,
0.010197916999459267,
-0.009515488520264626,
-0.002237739274278283,
0.00028779133572243154,
0.05453302711248398,
0.06048097088932991,
0.049462370574474335,
0.06982137262821198,
0.009939650073647499,
0.011732527054846287,
0.009880049154162407,
-0.005717455875128508,
-0.018237300217151642,
0.017505008727312088,
0.05317346006631851,
-0.013833760283887386,
0.011467300355434418,
0.025877155363559723,
-0.07794832438230515,
0.05792360007762909,
0.008256779052317142,
-0.025170257315039635,
-0.039879441261291504,
0.06063862890005112,
0.0442691333591938,
0.045485157519578934,
-0.051672711968421936,
0.009599803015589714,
-0.060651566833257675,
-0.060226406902074814,
0.028882114216685295,
-0.040533848106861115,
0.062447305768728256,
0.08636181801557541,
0.005571112968027592,
-0.02912413701415062,
-0.025893844664096832,
0.015421273186802864,
0.024050699546933174,
0.04025767743587494,
0.027267543599009514,
-0.005329669453203678,
-0.019539905712008476,
0.008209193125367165,
-0.010073966346681118,
0.017338018864393234,
0.06957685947418213,
-0.04631569981575012,
-0.016084492206573486,
0.02164299413561821,
-0.046793024986982346,
0.07841586321592331,
-0.022496994584798813,
0.007786118425428867,
0.05025835335254669,
-0.05144599825143814,
0.0022622416727244854,
-0.03201495110988617,
-0.03743993490934372,
-0.006058485247194767,
-0.042290907353162766,
0.04252655431628227,
0.06947986036539078,
-0.011613557115197182,
0.05318679288029671,
-0.004163113888353109,
-0.010744983330368996,
-0.061147671192884445,
-0.02666938491165638,
0.04394623264670372,
0.0012483980972319841,
-0.012083013541996479,
0.02656964771449566,
-0.007675998378545046,
-0.016827020794153214,
-0.023559682071208954,
0.000582920853048563,
-0.05738415941596031,
0.006222094874829054,
0.00454675080254674,
-0.09949932247400284,
0.059476517140865326,
-0.015526856295764446,
-0.061419159173965454,
-0.014400279149413109,
0.02492152899503708,
0.02127004973590374,
0.013652665540575981,
0.034013375639915466,
0.00623431708663702,
-0.044037289917469025,
-0.08809279650449753,
0.001182019361294806,
0.0005300513003021479,
-0.0026303406339138746,
0.07337465137243271,
-0.07343320548534393,
0.04588237404823303,
-0.0613836944103241,
-0.004461296368390322,
0.014771901071071625,
0.02320769801735878,
-0.027457714080810547,
-0.0139093529433012,
-0.026406649500131607,
0.00447371881455183,
0.031550318002700806,
-0.048109881579875946,
0.021852323785424232,
0.09280087053775787,
-0.011102080345153809,
-0.02053547464311123,
-0.09385447949171066,
-0.02364835888147354,
-0.026723217219114304,
0.08954256772994995,
0.00014791323337703943,
0.04897456243634224,
-0.05324016511440277,
-0.02822416089475155,
0.05500493943691254,
-0.03672187402844429,
-0.02312389202415943,
-0.02125300094485283,
0.03645568713545799,
0.014095666818320751,
0.03855036199092865,
0.010212153196334839,
-0.025881657376885414,
0.03807063400745392,
-0.00840737298130989,
0.01973382569849491,
0.0013311558868736029,
0.0106469402089715,
0.005733757745474577,
0.011256958357989788,
0.0014531814958900213,
0.03400494530797005,
0.011973243206739426,
0.006349562667310238,
0.0442948080599308,
-0.07458873093128204,
-0.02178218401968479,
-0.0005244174390099943,
0.000587093411013484,
-0.041658855974674225,
0.03308945521712303,
-0.019033150747418404,
0.015025990083813667,
0.05440389737486839,
0.044226571917533875,
0.07773692905902863,
-0.010458491742610931,
0.015417356044054031,
-0.0012702315580099821,
0.002249399432912469,
-0.02140490710735321,
-0.042794011533260345,
0.05040235072374344,
0.013166561722755432,
-0.01632894016802311,
-0.021478775888681412,
0.003666284028440714,
-0.051122359931468964,
0.028478926047682762,
-0.025108005851507187,
-0.02299916185438633,
-0.003931931219995022,
-0.0332653634250164,
0.010012366808950901,
0.014817583374679089,
0.04186699539422989,
-0.023740757256746292,
0.01919419877231121,
-0.06041707098484039,
0.05227045342326164,
0.012762744911015034,
-0.0020642471499741077,
-0.017104877158999443,
0.0061863139271736145,
-0.014042586088180542,
0.021620886400341988,
-0.021870547905564308,
-0.10259094834327698,
0.029815830290317535,
0.013407322578132153,
0.016209209337830544,
0.029042406007647514,
0.008575714193284512,
-0.01735282875597477,
0.003789464943110943,
0.08634132891893387,
0.012659371830523014,
-0.05433230102062225,
-0.022766685113310814,
0.06865069270133972,
0.04949085786938667,
-0.01818510703742504,
0.022553449496626854,
-0.016509754583239555,
-0.07678506523370743,
0.035336196422576904,
0.03378886356949806,
0.049789976328611374,
-0.05423672869801521,
0.035061199218034744,
0.02669871598482132,
0.04389632120728493,
0.0066840932704508305,
0.01994408294558525,
0.04090418294072151,
0.06021398678421974,
-0.0039453767240047455,
0.024863114580512047,
-0.023441705852746964,
0.07295317202806473,
-0.04459642991423607,
-0.08917610347270966,
0.009047468192875385,
0.003538405289873481,
0.03293735161423683,
-0.033605366945266724,
-0.05566582456231117,
0.005367812234908342,
-0.025975855067372322,
0.05715858191251755,
-0.03980966657400131,
0.0707964077591896,
-0.041207920759916306,
-0.010100018233060837,
-0.032616447657346725,
0.001039526192471385,
-0.039819300174713135,
0.030113819986581802,
0.015874940901994705,
-0.0012437873519957066,
-0.013079576194286346,
0.02525101974606514,
-0.05451865494251251,
0.0047689746133983135,
0.05468121916055679,
0.009472014382481575,
0.00836120918393135,
0.041532840579748154,
-0.01535860262811184,
-0.020347127690911293,
0.061579156666994095,
0.022064095363020897,
0.047512054443359375,
-0.054008081555366516,
-0.03847665339708328,
-0.032751165330410004,
-0.005442794878035784,
-0.033161286264657974,
-0.011828797869384289,
-0.03774070367217064,
-0.03918537124991417,
-0.018703550100326538,
0.01934233121573925,
-0.0586446113884449,
0.03842265158891678,
0.02028764970600605,
0.010901647619903088,
-0.025516396388411522,
-0.07039997726678848,
0.042560115456581116,
-0.06308598071336746,
-0.028520507737994194,
0.027576472610235214,
0.011763427406549454,
-0.03603922203183174,
0.0323924794793129,
-0.04201707988977432,
-0.001559503492899239,
0.04613996297121048,
0.025683075189590454,
0.018479786813259125,
-0.015135086141526699,
-0.04535390064120293,
-0.025852063670754433,
-0.03511296957731247,
0.035874705761671066,
-0.00781301036477089,
0.014165673404932022,
0.03598931059241295,
0.041458647698163986,
0.05541682988405228,
-0.020002156496047974,
-0.055678367614746094,
0.05585957318544388,
0.0013019335456192493,
0.004191006999462843,
0.04052509739995003,
-0.039693355560302734,
-0.006687263026833534,
-0.04285208880901337,
-0.02116096392273903,
-0.014610213227570057,
-0.01250672247260809,
0.03305542469024658,
-0.01844678446650505,
0.015979081392288208,
0.040681999176740646,
-0.01334385946393013,
0.00291260052472353,
-0.020172612741589546,
0.061868663877248764,
-0.012012721970677376,
0.03748941421508789,
-0.020123405382037163,
-0.0046717580407857895,
-0.05386113375425339,
0.03747420012950897,
0.052964359521865845,
-0.0421292819082737,
-0.0053691319189965725,
-0.032361164689064026,
-0.012395602650940418,
0.015518652275204659,
-0.043825551867485046,
-0.03520972281694412,
0.043788280338048935,
-0.04536808654665947,
-0.034975066781044006,
-0.040765341371297836,
-0.013311038725078106,
-0.02793182246387005,
-0.026380326598882675,
0.009127168916165829,
-0.019354021176695824,
0.04520375654101372,
0.008988426998257637,
-0.01220551785081625,
-0.03151847422122955,
-0.028530990704894066,
-0.06519067287445068,
-0.0008935145451687276,
0.03482000157237053,
0.005880951415747404,
-0.015111824497580528,
0.003776692086830735,
0.018630970269441605,
-0.003956174943596125,
0.03647876903414726,
-0.0024048849008977413,
-0.0021960348822176456,
-0.005712899379432201,
-0.04602152481675148,
-0.08348456770181656,
0.00048043232527561486,
-0.017618466168642044,
0.014341799542307854,
-0.00012031196820316836,
-0.04430572688579559,
-0.05889706686139107,
0.06083055958151817,
-0.050524577498435974,
-0.003576569026336074,
0.07321063429117203,
-0.029900887981057167,
-0.027620675042271614,
-0.017827190458774567,
-0.03812655806541443,
-0.02394269034266472,
0.005407898221164942,
-0.05344226211309433,
-0.009468247182667255,
0.006413642317056656,
0.020704401656985283,
0.09888162463903427,
-0.007907156832516193,
0.0421987920999527,
0.0586543083190918,
-0.042864665389060974,
0.039811886847019196,
0.004246840253472328,
-0.02908909134566784,
-0.0031839129514992237,
-0.015581974759697914,
0.00009764176502358168,
-0.031649067997932434,
-0.008994251489639282,
0.03841225430369377,
-0.00022956542670726776,
0.06248902156949043,
-0.021686216816306114,
0.008417257107794285,
-0.013233356177806854,
-0.014957724139094353,
0.019896864891052246,
-0.039515912532806396,
-0.10114574432373047,
-0.01549267303198576,
-0.008251871913671494,
0.03459978476166725,
-0.045159582048654556,
-0.020077025517821312,
0.032220300287008286,
0.023498818278312683,
0.013810520991683006,
-0.012901388108730316,
0.0029740342870354652,
-0.0010300057474523783,
0.057461854070425034,
0.013414456509053707,
-0.0010667690075933933,
0.01139941718429327,
-0.03179348260164261,
0.014436236582696438,
0.06589149683713913,
-0.040019210427999496,
0.02880294807255268,
-0.016135450452566147,
-0.04192066937685013,
-0.004712366033345461,
0.07101991772651672,
-0.006718166172504425,
-0.05648886784911156,
-0.008033613674342632,
0.01083578635007143,
0.03810271993279457,
-0.04122043401002884,
0.003753588767722249,
0.0078157102689147,
-0.065789595246315,
0.048173971474170685,
-0.012498986907303333,
0.0015032258816063404,
0.0019802451133728027,
0.003122384427115321,
-0.006838413421064615,
-0.036395516246557236,
-0.004652647767215967,
0.022655285894870758,
-0.02221791073679924,
0.03978116065263748,
-0.014695840887725353,
-0.017786787822842598,
-0.04592248052358627,
0.022887617349624634,
0.005380450747907162,
-0.044865164905786514,
-0.020273752510547638,
0.05586617439985275,
-0.026235200464725494,
0.025186320766806602,
-0.002896066987887025,
-0.017692893743515015,
0.02381914108991623,
-0.03160611540079117,
0.03122183121740818,
0.03763614967465401,
0.0038283299654722214,
-0.02597677707672119,
-0.018678350374102592,
-0.011770322918891907,
0.03312283381819725,
0.03870847821235657,
-0.026479903608560562,
-0.03793434798717499,
0.0675332322716713,
0.027331016957759857,
-0.037735436111688614,
-0.010579906404018402,
-0.019558200612664223,
0.02415662445127964,
0.039138633757829666,
0.003764806082472205,
0.01602770760655403,
0.011497534811496735,
-0.03156139701604843,
-0.09711994230747223,
-0.05944826453924179,
-0.017928259447216988,
0.005820858292281628,
-0.030938154086470604,
-0.02352706529200077,
-0.003395624225959182,
-0.03233638405799866,
-0.022412890568375587,
0.011026132851839066,
0.03608889505267143,
0.03874879330396652,
0.042366404086351395,
0.05471135303378105,
0.05421082675457001,
-0.006270933896303177,
0.032155394554138184,
0.02443827874958515,
-0.04751953110098839,
-0.01901346445083618,
0.012181561440229416,
0.00908677652478218,
-0.060880474746227264,
-0.11858578771352768,
-0.010168669745326042,
-0.05161236226558685,
-0.0113397017121315,
0.026204196736216545,
0.008635111153125763,
-0.023332634940743446,
-0.034048840403556824,
-0.02968931570649147,
-0.019303280860185623,
-0.026567962020635605,
0.0309261716902256,
-0.037656500935554504,
-0.03829788416624069,
-0.054937928915023804,
0.016946066170930862,
-0.03561599552631378,
-0.0012024365132674575,
-0.041551120579242706,
-0.030602196231484413,
0.04255194589495659,
-0.01783863827586174,
-0.012838912196457386,
0.058472905308008194,
-0.008131638169288635,
-0.01633993163704872,
0.017543476074934006,
-0.0004325363552197814,
0.0007790980744175613,
-0.014504917897284031,
0.027598591521382332,
-0.0064140986651182175,
-0.07960645854473114,
-0.023529918864369392,
0.01123952679336071,
-0.01007686648517847,
-0.022858496755361557,
-0.02844734862446785,
-0.02050882950425148,
-0.007780479267239571,
0.016229234635829926,
-0.03001275472342968,
-0.043717361986637115,
0.010980078019201756
] |
<p><em>For topological insulators</em>
<strong>Is there any way to define <a href="http://www.google.com/search?as_q=order+parameter+topological+phase+transition" rel="nofollow">order parameter for topological phase transitions</a>?</strong></p> | g5478 | [
-0.03727590665221214,
0.02328135259449482,
0.005910729989409447,
0.004258149303495884,
0.08851445466279984,
-0.014344303868710995,
-0.023211020976305008,
0.012764046899974346,
-0.020959561690688133,
0.02590234950184822,
-0.012446201406419277,
-0.013334016315639019,
0.04776454344391823,
0.0006737183430232108,
-0.04912082850933075,
0.0025775774847716093,
0.041798897087574005,
0.06069953367114067,
0.0450378879904747,
-0.043649084866046906,
-0.015646683052182198,
0.01270759291946888,
-0.02189542166888714,
-0.06729111820459366,
-0.03073716349899769,
0.05622612684965134,
0.004622372332960367,
-0.025049325078725815,
-0.023378858342766762,
0.016260048374533653,
0.015160903334617615,
0.0019504823721945286,
0.06080981343984604,
0.043687451630830765,
-0.02443264238536358,
-0.02187981642782688,
0.06257171183824539,
0.06291838735342026,
0.05228610709309578,
-0.0032533102203160524,
0.03147964924573898,
0.033366598188877106,
0.05317066237330437,
-0.04209214821457863,
-0.0026484238915145397,
0.006234088446944952,
-0.05796698108315468,
0.038790736347436905,
-0.0022539969068020582,
-0.04134922847151756,
0.04402953386306763,
0.0818585529923439,
0.006052895449101925,
-0.014142434112727642,
0.003934934735298157,
0.02251109480857849,
0.002138994401320815,
0.014293280430138111,
0.10931815207004547,
0.041037458926439285,
-0.04583694785833359,
0.030510928481817245,
0.08573061972856522,
-0.0067795198410749435,
0.06703655421733856,
0.037396810948848724,
-0.02064882591366768,
-0.03641121834516525,
-0.02924026921391487,
-0.02126016840338707,
-0.04447730630636215,
0.05852513015270233,
0.014734743162989616,
-0.0010140727972611785,
-0.02417360246181488,
0.03514021262526512,
-0.013150220736861229,
-0.05327502265572548,
0.008783512748777866,
-0.000350637681549415,
-0.05500396341085434,
-0.0074651786126196384,
0.01083560660481453,
0.0598926916718483,
-0.05699741467833519,
-0.004707189276814461,
0.05549078434705734,
-0.023529410362243652,
0.04625852406024933,
0.0004245759919285774,
0.0067610410042107105,
0.02422914281487465,
-0.06655117869377136,
0.006409408524632454,
0.02547208033502102,
-0.03393397480249405,
0.01897135190665722,
0.01764254830777645,
0.06738625466823578,
-0.06152243912220001,
-0.038075316697359085,
0.004165733698755503,
-0.05066058039665222,
-0.07083117961883545,
-0.017822209745645523,
-0.009267663583159447,
0.0066772145219147205,
-0.02295595593750477,
0.03906219080090523,
0.01319622341543436,
0.003542477497830987,
0.009637389332056046,
0.0075017842464149,
0.030098721385002136,
-0.013929717242717743,
0.02139013074338436,
0.0808500349521637,
-0.05396946892142296,
-0.029388073831796646,
0.03388051688671112,
0.02590326778590679,
-0.023912949487566948,
0.06415318697690964,
0.10480846464633942,
-0.022435206919908524,
0.005915768910199404,
0.050004418939352036,
-0.008259018883109093,
0.033297330141067505,
-0.0015799986431375146,
-0.03981306031346321,
-0.04223436489701271,
0.016697052866220474,
0.009007503278553486,
-0.03080791048705578,
0.03505811095237732,
0.05431417375802994,
0.021099373698234558,
0.019837452098727226,
0.014202273450791836,
0.005303526297211647,
-0.048179272562265396,
-0.003101618494838476,
-0.06468233466148376,
-0.0006332569173537195,
0.008298460394144058,
0.044228263199329376,
0.01577012985944748,
0.010187195613980293,
0.0028928436804562807,
-0.008745790459215641,
0.04764697328209877,
0.021457822993397713,
-0.011252044700086117,
0.003077651606872678,
-0.026719238609075546,
0.04508097469806671,
0.01016518659889698,
0.03480377793312073,
-0.03829231858253479,
-0.003466515801846981,
-0.02361956425011158,
-0.0027096925769001245,
-0.018420441076159477,
-0.039799079298973083,
-0.05102207511663437,
0.03131890296936035,
0.022349169477820396,
0.009627784602344036,
-0.053830936551094055,
-0.011451666243374348,
0.013677248731255531,
0.06596044450998306,
0.0387616902589798,
0.03248080611228943,
0.045523423701524734,
-0.011342165991663933,
0.07365106791257858,
0.04592984542250633,
-0.0033412203192710876,
0.02469104528427124,
-0.025944888591766357,
0.03506138175725937,
0.02060866542160511,
-0.01711498759686947,
0.004833736922591925,
-0.026764383539557457,
0.0357792042195797,
-0.032354068011045456,
0.0410422682762146,
-0.02513367123901844,
0.007715740241110325,
-0.0033691220451146364,
-0.0059358817525208,
0.043057769536972046,
-0.010304264724254608,
0.03261539340019226,
-0.0019238772802054882,
-0.06437738239765167,
-0.029692037031054497,
0.017156483605504036,
0.038758933544158936,
0.056322433054447174,
0.032982151955366135,
-0.034081220626831055,
-0.01571858674287796,
0.0010140326339751482,
0.035299550741910934,
-0.009510275907814503,
0.015919962897896767,
0.007575133349746466,
0.01690102182328701,
-0.01747303269803524,
0.05851641297340393,
-0.05572443827986717,
0.030464116483926773,
-0.01628691330552101,
-0.015742428600788116,
-0.011796860955655575,
0.06715508550405502,
-0.04334742948412895,
0.001945311320014298,
0.015623004175722599,
-0.0065696663223207,
-0.03296050801873207,
-0.07647266238927841,
0.055207960307598114,
-0.009244582615792751,
0.06841230392456055,
-0.029089488089084625,
-0.04670087620615959,
-0.03362804651260376,
-0.05283716320991516,
-0.03419273719191551,
0.058980878442525864,
0.008355021476745605,
-0.049431849271059036,
-0.03385317698121071,
0.010112530551850796,
0.02098602056503296,
-0.022021718323230743,
-0.05896801874041557,
0.018196560442447662,
-0.001592242275364697,
-0.06567710638046265,
-0.013650905340909958,
0.01393849216401577,
-0.010903160087764263,
-0.03316819295287132,
0.016933124512434006,
0.023558221757411957,
-0.030110323801636696,
-0.021863173693418503,
-0.043394334614276886,
-0.05317993834614754,
-0.044472843408584595,
0.03719903156161308,
0.02174556814134121,
-0.03252888098359108,
-0.04172787815332413,
0.014404638670384884,
0.004452643450349569,
0.0752742812037468,
0.0011399842333048582,
0.015981338918209076,
0.01219660509377718,
-0.01754164882004261,
-0.004881680011749268,
0.00541846826672554,
0.03095804899930954,
0.012159742414951324,
-0.00628991425037384,
-0.006980710197240114,
0.028457513079047203,
0.04033338278532028,
0.012750024907290936,
-0.008061856962740421,
-0.0002620359300635755,
0.013340584002435207,
0.01926405355334282,
0.004384854342788458,
-0.01567717082798481,
0.00015021544822957367,
0.030914895236492157,
-0.0027986285276710987,
-0.04136316478252411,
0.05944698303937912,
0.018609626218676567,
-0.057995639741420746,
0.01019610371440649,
0.04394042119383812,
0.024903368204832077,
0.03548065945506096,
0.08600951731204987,
-0.029856858775019646,
-0.03927037864923477,
-0.03891099616885185,
-0.03773966059088707,
0.046884991228580475,
0.03379134088754654,
0.07000242918729782,
-0.012294044718146324,
-0.03519444540143013,
0.003547647502273321,
0.014953911304473877,
-0.013319491408765316,
-0.012219858355820179,
-0.030659986659884453,
0.001797764329239726,
-0.042469412088394165,
0.05335797742009163,
0.06351622939109802,
0.025294478982686996,
0.055680662393569946,
0.019206048920750618,
0.048851847648620605,
0.003540471661835909,
0.06165386363863945,
0.02448323927819729,
-0.0678504928946495,
-0.022816162556409836,
-0.018404271453619003,
-0.007632318418473005,
0.001636763452552259,
-0.012162873521447182,
0.015181376598775387,
-0.04343283176422119,
0.027007361873984337,
-0.019429713487625122,
-0.06807008385658264,
-0.009088944643735886,
-0.036176249384880066,
0.06641534715890884,
-0.02407034859061241,
-0.04003417119383812,
0.013941279612481594,
-0.04225899651646614,
-0.023305486887693405,
0.005598111543804407,
-0.040732041001319885,
0.04002280905842781,
-0.04675544425845146,
-0.012335114181041718,
0.09515092521905899,
-0.03526635468006134,
-0.005160438362509012,
0.006558293476700783,
0.02299276739358902,
-0.009585043415427208,
-0.005149945616722107,
0.030515465885400772,
-0.008595265448093414,
0.0009358695824630558,
-0.0036993389949202538,
-0.015579333528876305,
0.0001783313200576231,
0.04606029763817787,
-0.005384859163314104,
0.017514051869511604,
0.0018986499635502696,
0.07887434959411621,
-0.04314832389354706,
0.0015984941273927689,
-0.00032678325078450143,
-0.03530653193593025,
0.05090353265404701,
0.0061429766938090324,
0.09428305923938751,
-0.03956723213195801,
0.008577684871852398,
0.009502911940217018,
-0.04829505458474159,
0.020278919488191605,
-0.024593103677034378,
0.027639368548989296,
-0.025233455002307892,
-0.024032602086663246,
0.0019262558780610561,
-0.021070053800940514,
0.013571164570748806,
0.000241315588937141,
-0.018316034227609634,
0.015362035483121872,
-0.04650868847966194,
0.006895634811371565,
-0.02431933581829071,
-0.039227116852998734,
-0.07038003951311111,
0.02573803812265396,
-0.09018190950155258,
-0.0066543337889015675,
-0.03076503798365593,
-0.018610233440995216,
-0.01763180084526539,
0.02838747203350067,
0.0038323504850268364,
0.029528634622693062,
-0.031122341752052307,
-0.03810213878750801,
-0.011088656261563301,
-0.02382075786590576,
-0.07375601679086685,
0.00762090552598238,
-0.019303154200315475,
0.041743434965610504,
-0.034492142498493195,
-0.029844122007489204,
-0.006628273520618677,
0.012435870245099068,
-0.057612236589193344,
-0.03904211148619652,
-0.06012502312660217,
-0.032841674983501434,
-0.05547943711280823,
0.004762942437082529,
-0.01634986139833927,
-0.0024448588956147432,
-0.08126568794250488,
0.010553271509706974,
-0.007068697363138199,
-0.001723986817523837,
-0.02328594960272312,
-0.007484983652830124,
-0.07977625727653503,
-0.05685114115476608,
0.05790123715996742,
0.014443979598581791,
0.021946541965007782,
-0.01379868108779192,
0.02556653693318367,
-0.02780475653707981,
0.04324522614479065,
0.012928951531648636,
0.06762329488992691,
-0.027444889768958092,
-0.012993589974939823,
-0.04870939254760742,
-0.007295365445315838,
0.016425451263785362,
-0.03665618598461151,
0.010083228349685669,
-0.019016200676560402,
0.023106113076210022,
-0.007902225479483604,
-0.019660810008645058,
0.016488002613186836,
0.011288384906947613,
0.025752460584044456,
-0.03849576786160469,
-0.023543577641248703,
-0.061784643679857254,
-0.01671093888580799,
-0.025243889540433884,
0.0016848962986841798,
0.03285389766097069,
-0.014887682162225246,
0.046622391790151596,
-0.004954643547534943,
-0.0440082810819149,
0.056028541177511215,
-0.024285076186060905,
-0.054259419441223145,
-0.007608041632920504,
0.021451467648148537,
0.04263002425432205,
0.027264833450317383,
-0.07368969917297363,
-0.0060785189270973206,
-0.02381078712642193,
-0.0033846411388367414,
-0.03284356743097305,
0.01832290180027485,
0.05001508444547653,
0.05908799171447754,
0.060370516031980515,
0.04088466987013817,
-0.010713590309023857,
0.0022088494151830673,
-0.03099753148853779,
-0.035559043288230896,
-0.05480460822582245,
0.01205158419907093,
0.050172384828329086,
-0.031050769612193108,
0.023670505732297897,
0.016579972580075264,
-0.038146838545799255,
0.03380836173892021,
0.04190560057759285,
0.02928907796740532,
-0.0018872023792937398,
0.04108921438455582,
0.0035356804728507996,
-0.002178857335820794,
0.033794254064559937,
-0.07766838371753693,
0.06263738125562668,
0.008760342374444008,
-0.04895685240626335,
0.04222433269023895,
-0.02425275184214115,
-0.013494416140019894,
0.046174488961696625,
0.048567596822977066,
-0.023015983402729034,
0.08765318244695663,
0.03927719593048096,
-0.01956484280526638,
-0.02018774300813675,
-0.041737642139196396,
0.002938766498118639,
0.06520063430070877,
-0.024472635239362717,
0.013506908901035786,
-0.004343951586633921,
0.045135218650102615,
0.006338214967399836,
0.0295838862657547,
-0.06022288277745247,
-0.0106891468167305,
0.015689382329583168,
0.030429314821958542,
0.05746037885546684,
-0.048459433019161224,
-0.030778950080275536,
-0.045615557581186295,
-0.028609201312065125,
-0.07173026353120804,
0.08355174958705902,
-0.014191975817084312,
-0.021768813952803612,
0.02475052885711193,
-0.023797208443284035,
-0.037731338292360306,
0.0009625832899473608,
-0.06940124183893204,
0.008876323699951172,
0.02871791645884514,
-0.039303477853536606,
-0.020619358867406845,
-0.0716274231672287,
0.0820627361536026,
0.020777832716703415,
-0.0013369414955377579,
0.05614146590232849,
-0.02008536271750927,
-0.019265834242105484,
-0.020328346639871597,
-0.013528217561542988,
-0.025219151750206947,
-0.022246284410357475,
-0.026184720918536186,
0.017816102132201195,
-0.01622132398188114,
-0.0011129694757983088,
0.06905142217874527,
-0.024498458951711655,
0.0250663124024868,
-0.015990789979696274,
-0.012860926799476147,
0.0003382478025741875,
-0.0040695760399103165,
0.017853111028671265,
0.014472533948719501,
-0.042971134185791016,
-0.05384702607989311,
-0.0038164544384926558,
0.019707469269633293,
0.007152709178626537,
0.02099892497062683,
0.05283782258629799,
-0.0023000913206487894,
0.0032635931856930256,
-0.017003461718559265,
-0.03940282016992569,
-0.014000033028423786,
-0.03874674811959267,
-0.015710772946476936,
0.033599965274333954,
0.004404261242598295,
-0.08514406532049179,
0.024732166901230812,
0.019399696961045265,
-0.0066127716563642025,
-0.03385557979345322,
-0.003952970262616873,
-0.02748318575322628,
-0.007016179617494345,
0.010192101821303368,
0.04406427592039108,
0.029672585427761078,
0.011476258747279644,
-0.11754252016544342,
-0.005705606192350388,
0.009463924914598465,
0.058892447501420975,
-0.02198955975472927,
0.001578667899593711,
-0.02019932121038437,
0.10253241658210754,
0.009929735213518143,
-0.021038126200437546,
0.0204812902957201,
0.03018062189221382,
-0.014172558672726154,
0.03635149449110031,
-0.005775212775915861,
0.0913625955581665,
0.016468465328216553,
-0.030639832839369774,
-0.027710411697626114,
0.004816399421542883,
-0.009766291826963425,
-0.00014060959802009165,
0.009324001148343086,
-0.04140574485063553,
-0.03431689739227295,
0.002209688303992152,
0.020691797137260437,
0.0086626335978508,
-0.06248512119054794,
-0.07503357529640198,
-0.04395325109362602,
0.03239251300692558,
0.028889838606119156,
0.051734670996665955,
0.02356213703751564,
0.009688814170658588,
-0.03570149466395378,
-0.016381429508328438,
-0.004781506955623627,
-0.052406154572963715,
-0.04879453778266907,
-0.008374813012778759,
0.026738177984952927,
0.010409457609057426,
-0.05362006649374962,
-0.053474243730306625,
0.01206718385219574,
0.0354129932820797,
0.04462447017431259,
0.024918781593441963,
0.02680322341620922,
-0.010657917708158493,
-0.06510353088378906,
-0.007968706078827381,
-0.01689509116113186,
-0.005079772789031267,
0.007376537192612886,
0.041503455489873886,
0.013263029046356678,
0.022454723715782166,
-0.09479788690805435,
0.005727226845920086,
0.01111967395991087,
0.035093966871500015,
0.010052754543721676,
0.014887070283293724,
0.009494736790657043,
0.03243060037493706,
-0.024700650945305824,
0.027108365669846535,
-0.01502931397408247,
-0.0319555327296257,
0.006537461653351784,
0.03615797683596611,
-0.029765157029032707,
-0.03762683644890785,
-0.02195003256201744,
-0.0276273675262928,
-0.06916080415248871,
0.006645985413342714,
-0.043819040060043335,
-0.029232436791062355,
0.013112730346620083,
-0.08096364885568619,
-0.007224856410175562,
0.012331737205386162,
0.03295139595866203,
0.019165940582752228,
0.038800232112407684,
0.007920176722109318,
-0.002124918857589364,
-0.06754835695028305,
-0.0037963194772601128,
0.0909406840801239,
-0.05732475593686104,
0.07447456568479538,
0.07848964631557465,
-0.0017529405886307359,
-0.007047112099826336,
0.04447481408715248,
-0.0401754267513752,
-0.06705617159605026,
0.0005171572556719184,
-0.0008901660912670195,
-0.024471264332532883,
-0.036710791289806366,
-0.024223048239946365,
-0.011621205136179924,
0.02028363198041916,
0.04895449057221413,
-0.057994160801172256,
-0.02950320765376091,
-0.0033343054819852114,
0.009943482466042042,
-0.009817062877118587,
-0.05429471284151077,
0.007990526035428047,
0.044733621180057526,
-0.012854808941483498,
-0.011884934268891811,
0.04310757294297218,
0.03333238884806633,
0.003424377180635929,
-0.00946096796542406,
-0.004600627347826958,
0.02716764435172081,
0.00245438190177083,
0.010248126462101936,
-0.05847170576453209,
-0.08104096353054047,
0.010232956148684025,
-0.0027838721871376038,
-0.047853294759988785,
0.03902355954051018,
-0.02247142232954502,
0.013079669326543808,
0.012091587297618389,
0.004089250694960356,
0.0187529306858778,
-0.05112258344888687,
0.01176535990089178,
0.06306707859039307,
-0.02953461930155754,
0.0376543253660202,
0.015191812999546528,
0.0151272127404809,
0.04464621841907501,
0.0055537838488817215,
-0.006541259121149778,
-0.0024406579323112965,
0.03755619749426842,
-0.014677407220005989,
0.04561683163046837,
0.001980268396437168,
0.016537224873900414,
0.043624017387628555,
0.042373888194561005,
-0.05928361415863037,
0.016829434782266617,
-0.02500566653907299,
0.06541887670755386,
-0.015485609881579876,
-0.09091104567050934,
0.01077625434845686,
-0.01127275638282299,
-0.03145834431052208,
-0.002442459110170603,
-0.028869932517409325,
-0.02707020752131939,
0.015790695324540138,
-0.023375602439045906,
0.014655186794698238,
-0.024661298841238022,
0.0012103209737688303,
-0.015479900874197483,
-0.028592802584171295
] |
<p>In an arbitrary number of dimensions, one can naturally define two tensors, Kronecker delta and Levi-Civita epsilon tensor. However, why isn't it advantageous to define some totally symmetric tensor as well? Is there an intuitive reason for that or is it basically related to differential forms?</p> | g5479 | [
0.023009847849607468,
0.05563025176525116,
-0.0035969428718090057,
0.010675023309886456,
0.06257135421037674,
0.0189435426145792,
0.0388934426009655,
0.00753525085747242,
-0.07648122310638428,
-0.07368331402540207,
-0.03282207250595093,
-0.010378027334809303,
0.08239465951919556,
0.01932823657989502,
0.02884572744369507,
-0.05753140151500702,
0.024189291521906853,
-0.025363920256495476,
0.04681481048464775,
-0.009097320027649403,
-0.04793775454163551,
0.03219572827219963,
-0.018103264272212982,
-0.026734471321105957,
0.05251375213265419,
0.0025834552943706512,
0.08034450560808182,
-0.0401829369366169,
-0.04059932753443718,
-0.0165100060403347,
0.06361187994480133,
0.029470421373844147,
0.04979127272963524,
0.06320086121559143,
0.03580828756093979,
-0.0033927340991795063,
0.011740204878151417,
0.046832866966724396,
0.02766387350857258,
-0.03704187273979187,
0.04710758104920387,
-0.013340202160179615,
-0.007688697427511215,
-0.018199091777205467,
-0.02891506813466549,
0.05566210672259331,
-0.02628103271126747,
0.01742645353078842,
0.0004343213513493538,
-0.04105367884039879,
0.06477448344230652,
-0.01002801675349474,
0.02285422384738922,
-0.005392902065068483,
0.025015927851200104,
-0.07702063024044037,
0.021532708778977394,
-0.04038934409618378,
-0.016349267214536667,
-0.021590685471892357,
-0.034917403012514114,
0.025285666808485985,
-0.016137370839715004,
0.005146034061908722,
0.04237448424100876,
0.00497492915019393,
-0.021979810670018196,
-0.01056644506752491,
0.06453506648540497,
0.04711538925766945,
0.018402814865112305,
-0.03266420215368271,
0.11255252361297607,
0.0023518118541687727,
0.01631946489214897,
0.0031583153177052736,
0.008871300145983696,
-0.038349658250808716,
0.025546832010149956,
-0.016529805958271027,
-0.03269529715180397,
-0.006900067441165447,
0.07100760191679001,
0.017741022631525993,
0.05518665537238121,
0.008618170395493507,
0.02563159540295601,
-0.024747762829065323,
0.01782277412712574,
0.035151317715644836,
-0.0027742611709982157,
-0.015540660358965397,
0.02045404724776745,
0.05930706113576889,
-0.015763774514198303,
-0.07411511987447739,
-0.005939490627497435,
0.03959224745631218,
-0.011620745062828064,
0.001085001858882606,
0.030169777572155,
0.06880942732095718,
0.013904938474297523,
-0.035098135471343994,
0.05711425095796585,
-0.007964244112372398,
0.045372191816568375,
-0.0015745180426165462,
0.03192159906029701,
-0.026119200512766838,
-0.009914104826748371,
0.03628852963447571,
-0.07280038297176361,
0.002737959148362279,
0.011052906513214111,
0.060831762850284576,
0.043902866542339325,
-0.04244653880596161,
-0.022999994456768036,
0.060179173946380615,
-0.0013801028253510594,
0.0035729219671338797,
0.015599589794874191,
0.03376675397157669,
0.007047788705676794,
0.038243360817432404,
0.04923757165670395,
0.020538339391350746,
0.0460258424282074,
-0.07367239892482758,
0.03246099129319191,
0.028147418051958084,
0.004932032432407141,
0.00034210365265607834,
0.051609087735414505,
0.03422049805521965,
-0.04998442530632019,
-0.026043979451060295,
-0.014472825452685356,
-0.040325507521629333,
-0.011346223764121532,
-0.000048990812501870096,
-0.09049206972122192,
0.02616807632148266,
0.013126357458531857,
-0.05491506680846214,
-0.01936587318778038,
-0.015733933076262474,
-0.006310328375548124,
0.03669070079922676,
0.003153082448989153,
0.03740043193101883,
-0.022350164130330086,
0.021917838603258133,
0.0023320785257965326,
-0.032314445823431015,
0.037121597677469254,
-0.015827210620045662,
-0.0419648140668869,
-0.026824751868844032,
0.015041732229292393,
0.04514503851532936,
0.026017459109425545,
-0.06384279578924179,
0.009967917576432228,
0.03982284665107727,
-0.019453927874565125,
-0.05120569467544556,
-0.019498588517308235,
-0.05397533252835274,
-0.02740008756518364,
0.0655190497636795,
0.0020698162261396646,
0.03113248199224472,
0.011961730197072029,
0.015048571862280369,
-0.04632604867219925,
0.017203517258167267,
0.019444113597273827,
0.04161577671766281,
-0.08293076604604721,
-0.009498877450823784,
0.01304446067661047,
-0.017668765038251877,
0.010776620358228683,
0.005714514758437872,
-0.015884095802903175,
-0.027432844042778015,
-0.05240916088223457,
0.03777698054909706,
0.02113700844347477,
-0.006596533115953207,
0.03442590683698654,
0.05408557876944542,
-0.007679637521505356,
0.06107072904706001,
0.003078385256230831,
-0.010556710883975029,
-0.06620054692029953,
0.09063122421503067,
-0.05383693426847458,
0.04192674905061722,
-0.016729608178138733,
-0.010166632011532784,
-0.10541322082281113,
0.013191144913434982,
-0.02055423893034458,
0.030444804579019547,
0.03963075578212738,
-0.016368327662348747,
0.02473774179816246,
-0.08262442797422409,
0.06217625364661217,
-0.01797117479145527,
0.02446826733648777,
-0.03255225718021393,
0.0029268485959619284,
0.0230251532047987,
-0.035534560680389404,
0.002650792244821787,
0.03966663405299187,
-0.050741929560899734,
0.05115264281630516,
0.03310888633131981,
-0.060543905943632126,
-0.01835208386182785,
0.0008839219226501882,
0.0019810188096016645,
0.008301366120576859,
-0.008767925202846527,
-0.06912683695554733,
-0.04473942145705223,
0.0541769415140152,
0.04977104440331459,
-0.0030669430270791054,
0.05643334612250328,
-0.008556178770959377,
0.007090776693075895,
0.031176088377833366,
0.04773453250527382,
0.09154004603624344,
-0.005152767524123192,
0.020998282358050346,
0.05919717252254486,
0.009034435264766216,
-0.0282286424189806,
-0.005775980651378632,
0.0038843760266900063,
-0.013898845762014389,
0.05060454085469246,
-0.07023867219686508,
0.005645716097205877,
-0.03902241215109825,
-0.07444662600755692,
0.03312159702181816,
-0.02981528639793396,
0.006267470773309469,
-0.02951114811003208,
-0.04357139766216278,
0.010730655863881111,
-0.04791957885026932,
0.03395739942789078,
0.026752958074212074,
0.02258419618010521,
-0.043176133185625076,
0.04528680071234703,
0.011055133305490017,
0.021274320781230927,
0.027726583182811737,
-0.023219186812639236,
-0.045337289571762085,
0.03827870264649391,
0.02729603834450245,
0.03396949544548988,
-0.06271245330572128,
-0.027541786432266235,
-0.03992261365056038,
0.019315896555781364,
0.018324367702007294,
0.010244796052575111,
0.008980987593531609,
0.03439294546842575,
-0.01293436624109745,
0.012114250101149082,
0.12609189748764038,
-0.032977499067783356,
0.004693520255386829,
0.0084647536277771,
-0.029254889115691185,
-0.0056804330088198185,
0.039849814027547836,
0.07003237307071686,
0.0037785330787301064,
-0.08041611313819885,
0.004423759412020445,
0.010482944548130035,
-0.011259220540523529,
-0.053435035049915314,
-0.031093530356884003,
0.011000515893101692,
0.03952720761299133,
-0.02026580646634102,
0.037010155618190765,
-0.009980504401028156,
0.016590643674135208,
-0.008927494287490845,
-0.021299228072166443,
-0.008888053707778454,
-0.004790949635207653,
0.0204450786113739,
-0.02321045473217964,
0.007143628783524036,
-0.017425166442990303,
0.02052239142358303,
-0.01141790859401226,
-0.026555374264717102,
0.06561175733804703,
-0.0086006885394454,
-0.05048853158950806,
-0.010805178433656693,
-0.040832195430994034,
-0.007878784090280533,
0.063359834253788,
0.0676947757601738,
0.04745929315686226,
0.03416198119521141,
-0.08483125269412994,
0.013573854230344296,
0.0012463367311283946,
0.0036752596497535706,
-0.04088728502392769,
-0.03105894848704338,
0.0234551802277565,
0.012410315684974194,
-0.05624730512499809,
-0.013307411223649979,
-0.08541292697191238,
-0.07037245482206345,
-0.01897398941218853,
-0.038846809417009354,
-0.06155640259385109,
-0.0014269431121647358,
-0.06532525271177292,
0.01610017567873001,
-0.020966224372386932,
-0.023413458839058876,
-0.006281187757849693,
0.0023569208569824696,
0.019773215055465698,
0.005154660437256098,
-0.010227604769170284,
0.03421302139759064,
0.03219021484255791,
0.013577654957771301,
0.025770418345928192,
-0.003666909411549568,
0.07873612642288208,
0.0550781674683094,
-0.048110201954841614,
-0.0038264920003712177,
0.012291587889194489,
0.030603626742959023,
-0.029481608420610428,
-0.000983523903414607,
0.02173883281648159,
0.013438230380415916,
0.027728253975510597,
-0.06986308842897415,
-0.014922545291483402,
0.07729325443506241,
0.03585650771856308,
0.007929610088467598,
-0.019934210926294327,
-0.04241080954670906,
0.03073011338710785,
-0.030956851318478584,
-0.004747839644551277,
-0.05870726704597473,
0.0054741413332521915,
-0.01030038669705391,
0.015795109793543816,
-0.025666028261184692,
0.006672699004411697,
-0.028907733038067818,
-0.005569869186729193,
0.00833688210695982,
-0.07049985229969025,
0.02758706361055374,
-0.011088390834629536,
-0.00947213638573885,
0.04895555227994919,
0.02815569005906582,
-0.02814144268631935,
-0.03272493556141853,
-0.03312723711133003,
-0.024531865492463112,
0.029017416760325432,
0.004960025195032358,
-0.07938513159751892,
0.01520461030304432,
-0.017250442877411842,
-0.018464267253875732,
0.0016367475036531687,
-0.016691308468580246,
-0.01786687597632408,
-0.03292740881443024,
-0.0029347087256610394,
-0.02141493186354637,
-0.0004518032365012914,
-0.014174005948007107,
0.0273845624178648,
-0.03955452889204025,
0.01994669809937477,
-0.0475199893116951,
0.07409263402223587,
0.010778635740280151,
-0.03911402076482773,
-0.03297936171293259,
0.018042191863059998,
0.01869979128241539,
0.007922863587737083,
-0.02787553146481514,
0.023484906181693077,
0.021856199949979782,
0.01584240235388279,
0.08566577732563019,
0.039620913565158844,
0.021310338750481606,
-0.03603935241699219,
-0.022694112733006477,
0.007087760139256716,
0.007042125333100557,
0.01076603401452303,
-0.019133180379867554,
0.012874791398644447,
-0.004910923074930906,
-0.027093572542071342,
0.08910917490720749,
-0.02442445605993271,
0.03073686733841896,
0.05906984582543373,
0.021099744364619255,
-0.001689824042841792,
-0.07709244638681412,
0.0001097609056159854,
-0.017920812591910362,
-0.02673865668475628,
-0.04155607894062996,
-0.017287837341427803,
-0.012980499304831028,
-0.06711792945861816,
-0.01676730439066887,
-0.019237378612160683,
-0.03915957733988762,
-0.0008663233602419496,
-0.02271723747253418,
0.008761455304920673,
-0.009532966651022434,
0.007579318713396788,
0.019278952851891518,
-0.009984970092773438,
-0.02217557467520237,
0.031070956960320473,
-0.01277611032128334,
0.0019426927901804447,
-0.01589655876159668,
-0.03787528723478317,
0.04243055731058121,
-0.028209907934069633,
-0.019993659108877182,
0.030314365401864052,
0.08686316758394241,
-0.007178692612797022,
-0.029574066400527954,
0.011428792029619217,
-0.0058452594093978405,
0.017334086820483208,
0.017732838168740273,
-0.028167469426989555,
-0.06287290155887604,
-0.029412047937512398,
-0.009638136252760887,
0.0337476022541523,
0.018979202955961227,
0.041339192539453506,
0.0078915199264884,
-0.04525899887084961,
-0.034795600920915604,
-0.06540769338607788,
-0.012894523330032825,
0.020022915676236153,
-0.0068735601380467415,
0.023315031081438065,
0.000593577220570296,
-0.010835210792720318,
-0.004499489441514015,
-0.011179774068295956,
-0.06145865470170975,
-0.022995958104729652,
-0.041867271065711975,
-0.008484558202326298,
-0.008590513840317726,
0.02825414016842842,
-0.05413002148270607,
0.02839820086956024,
0.024856669828295708,
0.0643758475780487,
-0.004476801957935095,
-0.013405947014689445,
0.05723763629794121,
-0.05519036203622818,
-0.07427283376455307,
-0.020503506064414978,
0.014851078391075134,
-0.004547800403088331,
-0.01320965588092804,
-0.006766697857528925,
-0.01571861281991005,
0.013432006351649761,
-0.008249419741332531,
0.03331945091485977,
-0.02437456138432026,
0.03388608619570732,
-0.007115752436220646,
0.036489665508270264,
0.019741244614124298,
-0.049735408276319504,
-0.01343911699950695,
-0.003934450447559357,
-0.0002536677639000118,
0.032840993255376816,
-0.002679175231605768,
0.028177928179502487,
-0.017255820333957672,
-0.033165354281663895,
-0.0600770004093647,
-0.012610859237611294,
0.03826896473765373,
0.030269812792539597,
-0.007431229576468468,
-0.01775270141661167,
-0.026319537311792374,
-0.046537794172763824,
0.03720354661345482,
0.015424749813973904,
-0.057500969618558884,
0.028111832216382027,
-0.003048812737688422,
-0.06453507393598557,
-0.0484091155230999,
-0.062433723360300064,
0.03456985950469971,
0.00010064207162940875,
-0.02344270795583725,
-0.05239661782979965,
0.014499480836093426,
-0.0007591726607643068,
-0.015835769474506378,
-0.024426599964499474,
-0.029390523210167885,
0.003420670982450247,
-0.006332730874419212,
0.02104918658733368,
0.014935486949980259,
-0.10253174602985382,
-0.030872099101543427,
0.0209922157227993,
-0.004043704830110073,
0.050911519676446915,
0.06766164302825928,
0.026601849123835564,
0.057361289858818054,
0.05132248252630234,
0.027973122894763947,
0.04171466454863548,
-0.011734356172382832,
0.029012629762291908,
-0.030052179470658302,
-0.002162837190553546,
-0.0048292456194758415,
0.01811503805220127,
-0.03488115221261978,
0.003123739967122674,
-0.05239855498075485,
-0.033716924488544464,
0.019210971891880035,
0.017682362347841263,
-0.0748467817902565,
0.056598860770463943,
0.003783461870625615,
-0.0019082718063145876,
-0.05811847746372223,
-0.0285246130079031,
-0.006783172953873873,
0.006525469943881035,
0.01565948687493801,
0.014284705743193626,
0.07388521730899811,
-0.02476789802312851,
-0.04708779603242874,
0.02550945058465004,
0.042085450142621994,
0.02528514713048935,
0.07518032938241959,
-0.03402286767959595,
0.021898984909057617,
-0.03477010875940323,
-0.013885987922549248,
0.016452541574835777,
0.029339324682950974,
0.015716465190052986,
0.011773298494517803,
-0.06749899685382843,
-0.01062055118381977,
-0.026053668931126595,
-0.011106006801128387,
-0.014880688861012459,
-0.009736471809446812,
0.003708516014739871,
0.058253705501556396,
0.03817499428987503,
-0.00501064769923687,
0.010939660482108593,
0.002316389698535204,
0.0168817937374115,
0.04311947897076607,
-0.04836708679795265,
0.04432757943868637,
0.005198104307055473,
0.0571882389485836,
-0.00015155818255152553,
0.02096284180879593,
-0.023025983944535255,
0.07147915661334991,
-0.030269218608736992,
-0.04077126458287239,
-0.0509280301630497,
0.0015601355116814375,
0.10216275602579117,
-0.0225905142724514,
-0.020816106349229813,
0.02815345861017704,
0.07816212624311447,
-0.0032066628336906433,
0.019792703911662102,
0.028785139322280884,
0.055423106998205185,
-0.00279629766009748,
-0.10264020413160324,
0.014210132881999016,
0.04911826178431511,
0.0037167570553719997,
-0.002257161308079958,
-0.06049450859427452,
-0.038009874522686005,
-0.0054380749352276325,
-0.022731678560376167,
0.0001484512904426083,
-0.004295338876545429,
-0.018480129539966583,
0.001910942723043263,
0.042351461946964264,
-0.023822641000151634,
0.011036733165383339,
-0.031532663851976395,
0.019712351262569427,
0.03394618257880211,
-0.008866221643984318,
0.029791997745633125,
0.018269874155521393,
-0.010252307169139385,
0.009075039066374302,
-0.004179465118795633,
-0.0031237804796546698,
0.03735321760177612,
0.03255874291062355,
-0.015200615860521793,
-0.019199132919311523,
0.011830784380435944,
-0.0172877199947834,
0.000581510306801647,
0.021755078807473183,
-0.027333343401551247,
-0.05117195472121239,
-0.08004510402679443,
0.012049665674567223,
0.037720926105976105,
0.0090244235470891,
0.0040452308021485806,
-0.012337756343185902,
0.05439462140202522,
-0.0037876989226788282,
-0.04535296559333801,
0.017999621108174324,
-0.0311726164072752,
0.0352967269718647,
0.010771520435810089,
0.03830930218100548,
-0.005097195040434599,
-0.004436951596289873,
0.010842832736670971,
-0.017510216683149338,
-0.022750435397028923,
0.000546636525541544,
0.004038582090288401,
-0.0021926509216427803,
0.011727928183972836,
-0.03521840646862984,
-0.02982405014336109,
-0.008268055506050587,
0.03467724472284317,
-0.0030331448651850224,
0.03087903931736946,
0.005525106564164162,
-0.029610440135002136,
0.049002137035131454,
-0.08468867838382721,
-0.015657959505915642,
0.05304934084415436,
-0.07296264171600342,
0.038678139448165894,
-0.02609545737504959,
0.003066436154767871,
-0.08346659690141678,
-0.04481571540236473,
-0.026721103116869926,
-0.0171077698469162,
-0.008678956888616085,
-0.0169233288615942,
0.025154151022434235,
-0.0512147918343544,
0.01828758232295513,
0.010879780165851116,
0.008933605626225471,
-0.016544824466109276,
0.061281967908144,
0.006833534222096205,
-0.016769805923104286,
-0.016818242147564888,
0.027621136978268623,
-0.0039689186960458755,
-0.03826672211289406,
-0.02308397740125656,
0.02066710777580738,
0.020773492753505707,
-0.0075351702980697155,
0.0203358456492424,
-0.011289278045296669,
-0.03900165483355522,
0.004354921169579029,
-0.0528603233397007,
0.009027700871229172,
-0.036465685814619064,
0.07362327724695206,
0.07281161844730377,
0.008835877291858196,
0.05817026272416115,
-0.06934674084186554,
-0.008516120724380016,
0.03376815840601921,
-0.04683341458439827,
-0.009771669283509254,
-0.031151341274380684,
0.02719653584063053,
0.003907950595021248,
-0.06731096655130386,
-0.010631561279296875,
0.04621654003858566
] |
<p>I read that Wu's experiment illustrates that parity violation is possible for weak processes. In that experiment, when Co-60 undergoes beta decay, the emitted electrons come out opposite to the direction of nuclear spin. The mirror image process does not occur.</p>
<p>I also read that parity is conserved for EM and strong processes. But consider the following from EM. Say I have a positively-charged particle moving to the right, and the magnetic field is into the page. Then force on the particle is up (i.e. the particle is accelerated upwards initially). And here, the mirror image also does not occur! The mirror image (the mirror I am thinking of lies in the plane that cuts your head between the eyes) would be moving left, magnetic field into page, acceleration still pwards - but EM would predict that the acceleration is supposed to be downwards!!</p>
<p>Why isn't this an example of parity violation?</p> | g5480 | [
0.0442020483314991,
0.019468987360596657,
0.010312321595847607,
0.0008144283201545477,
0.0661853775382042,
0.0406537689268589,
0.031187642365694046,
0.08673960715532303,
0.027471227571368217,
-0.04783381149172783,
0.01141980942338705,
0.039667561650276184,
0.00015731049643363804,
-0.011808856390416622,
0.02041008695960045,
0.012578804045915604,
0.05225032940506935,
-0.0268290713429451,
0.03535287082195282,
0.03853471949696541,
-0.05983113870024681,
0.02214668318629265,
0.011173667386174202,
-0.017988435924053192,
0.03399626165628433,
0.009046855382621288,
0.009543998166918755,
-0.07915081083774567,
-0.03280731290578842,
-0.017831867560744286,
0.067478246986866,
-0.020108481869101524,
0.03999797999858856,
-0.06536952406167984,
-0.006885949522256851,
-0.040172044187784195,
0.036546047776937485,
-0.03951575234532356,
0.0377332903444767,
0.05328566953539848,
0.027028517797589302,
-0.042163386940956116,
0.0460728257894516,
-0.006279490422457457,
0.041600439697504044,
-0.007444161456078291,
-0.028585385531187057,
-0.012684988789260387,
0.0013898896286264062,
-0.05068035423755646,
-0.03363853320479393,
-0.013872713781893253,
0.04513447731733322,
-0.023765429854393005,
0.0124821737408638,
-0.007053122390061617,
-0.018284128978848457,
0.006346916314214468,
0.03914980962872505,
0.0035022234078496695,
0.011620214208960533,
0.000056025466619757935,
0.046695638447999954,
0.012422961182892323,
0.04896366596221924,
-0.005905184894800186,
-0.08245237171649933,
0.033964455127716064,
0.08324995636940002,
0.06490771472454071,
0.030091799795627594,
0.025104384869337082,
-0.07123950868844986,
-0.052179671823978424,
0.02914065308868885,
-0.028250304982066154,
0.017862578853964806,
-0.02888362854719162,
-0.01954132877290249,
0.004232270643115044,
-0.06919949501752853,
0.0019267040770500898,
0.004608575254678726,
0.06635037064552307,
0.06805991381406784,
-0.021991638466715813,
-0.0034266645088791847,
0.04076547175645828,
0.00472271628677845,
0.023822953924536705,
0.06026078760623932,
-0.014723798260092735,
0.02300790697336197,
0.007576343137770891,
-0.012714113108813763,
-0.003335339715704322,
-0.02575770393013954,
0.06938900798559189,
-0.06500215828418732,
0.035181090235710144,
-0.042827676981687546,
0.029725227504968643,
-0.03274400904774666,
0.017566878348588943,
0.04655234143137932,
0.017353279516100883,
0.002677403623238206,
0.06126798689365387,
-0.05036621540784836,
-0.024982329457998276,
0.02030491642653942,
-0.0370514951646328,
-0.03573004901409149,
0.012648165225982666,
0.02364247292280197,
-0.022407693788409233,
0.09979505836963654,
-0.0463867224752903,
0.03261043131351471,
0.04630320146679878,
0.028830884024500847,
0.02030298300087452,
-0.019920680671930313,
0.035120826214551926,
-0.03345339000225067,
-0.02298315241932869,
-0.026058584451675415,
0.0013854644494131207,
-0.00026624335441738367,
0.0020845597609877586,
-0.011073355562984943,
0.03421831130981445,
0.012337204068899155,
0.054446782916784286,
0.03497794270515442,
-0.010942055843770504,
0.031655099242925644,
-0.004174248781055212,
0.03020605817437172,
-0.09567482769489288,
-0.03229987993836403,
-0.011678186245262623,
0.03324775770306587,
-0.013923409394919872,
-0.029324296861886978,
-0.025389619171619415,
-0.031642042100429535,
0.022281495854258537,
0.056858889758586884,
0.05213882401585579,
-0.010435194708406925,
0.05960688367486,
0.017345866188406944,
-0.0381435863673687,
0.021694142371416092,
-0.051949597895145416,
0.06014129891991615,
0.000572750112041831,
0.037127282470464706,
0.0452493280172348,
0.07824227958917618,
0.017276296392083168,
-0.04824887216091156,
0.05946312099695206,
-0.04039682075381279,
-0.050890807062387466,
0.013940840028226376,
-0.002400381024926901,
0.014780878089368343,
-0.021078143268823624,
-0.08888609707355499,
0.024801788851618767,
0.01894119754433632,
0.04220670089125633,
-0.04971606656908989,
0.010592550970613956,
-0.037839774042367935,
-0.03404425457119942,
-0.027826007455587387,
0.01489525567740202,
-0.0294992346316576,
-0.04320298135280609,
-0.05423326790332794,
-0.05273381620645523,
0.016092875972390175,
-0.07443799078464508,
-0.043159935623407364,
0.04551341384649277,
-0.031804848462343216,
0.02601495198905468,
0.013990717008709908,
0.007395051885396242,
-0.015751950442790985,
0.025152891874313354,
-0.02887951210141182,
-0.0624537467956543,
0.0011753648286685348,
-0.04589115455746651,
-0.01826523058116436,
0.01936212182044983,
-0.03802008554339409,
0.04609344154596329,
0.0007262857398018241,
0.022934377193450928,
-0.018166381865739822,
-0.020355988293886185,
-0.018989086151123047,
-0.03677736967802048,
0.001542719779536128,
-0.03624532371759415,
-0.011011974886059761,
0.08257634192705154,
-0.017397146672010422,
-0.0560833215713501,
0.03208274766802788,
0.029340794309973717,
0.006995602045208216,
0.032521672546863556,
-0.06929119676351547,
0.038222651928663254,
-0.05896328389644623,
-0.03929794207215309,
0.031128032132983208,
-0.01145950611680746,
-0.008248787373304367,
0.017388923093676567,
-0.06247115135192871,
-0.004397508222609758,
-0.01842363178730011,
0.015756456181406975,
-0.08392619341611862,
0.046115484088659286,
-0.005415973719209433,
0.016377918422222137,
0.04118699952960014,
0.04278164356946945,
0.0217922180891037,
0.04628439620137215,
0.001306420424953103,
-0.006796898320317268,
-0.037791214883327484,
0.012412195093929768,
-0.052022211253643036,
0.03543895110487938,
0.029959745705127716,
-0.01718171499669552,
0.007512394804507494,
-0.027568558230996132,
-0.011116107925772667,
-0.06075536459684372,
0.04019446671009064,
-0.04784982278943062,
0.019443340599536896,
0.004184985999017954,
0.012510884553194046,
-0.02229170687496662,
0.024106008931994438,
0.0341569148004055,
0.005374351516366005,
-0.031208179891109467,
0.01634078472852707,
-0.03548956289887428,
0.042919956147670746,
0.0196547731757164,
-0.0220965426415205,
-0.025386493653059006,
-0.01086096465587616,
-0.004595993086695671,
-0.007699811365455389,
-0.001184989814646542,
-0.054156772792339325,
0.09068579971790314,
-0.026467816904187202,
0.015848005190491676,
0.012237418442964554,
0.0006538510788232088,
-0.004425658378750086,
0.010583559982478619,
-0.013343282975256443,
0.02835812047123909,
-0.08817585557699203,
0.009663887321949005,
-0.005830071400851011,
-0.054545190185308456,
0.033240608870983124,
-0.04519180580973625,
-0.005136641673743725,
-0.04599085450172424,
0.028900722041726112,
0.02507675439119339,
-0.10453298687934875,
0.03404217213392258,
0.0734521821141243,
-0.008005336858332157,
-0.02246367186307907,
0.004258919041603804,
0.039625972509384155,
-0.04663138464093208,
-0.041797418147325516,
0.025328712537884712,
0.008107808418571949,
-0.007810007315129042,
-0.020375218242406845,
0.003279555356130004,
0.05568031966686249,
0.02188790962100029,
0.006359959486871958,
-0.03519827872514725,
-0.019841859117150307,
-0.011714915744960308,
-0.010322678834199905,
-0.013005692511796951,
-0.0417555533349514,
-0.011479553766548634,
0.009227915666997433,
-0.02254343032836914,
-0.0330548994243145,
0.01813332736492157,
0.06388955563306808,
-0.017901288345456123,
-0.03578634187579155,
0.006835409440100193,
0.022694189101457596,
-0.014014506712555885,
-0.022997986525297165,
0.02215970866382122,
-0.025222159922122955,
0.006556886248290539,
0.002163331024348736,
0.021497756242752075,
0.045035216957330704,
0.009341289289295673,
0.046323005110025406,
0.003547236556187272,
0.0027499960269778967,
-0.020529260858893394,
-0.018263770267367363,
0.048432327806949615,
0.049612704664468765,
-0.04813247546553612,
-0.008074731566011906,
-0.06222143769264221,
-0.011186354793608189,
-0.026154903694987297,
0.04389513283967972,
0.03551345691084862,
-0.02310463972389698,
0.019640116021037102,
0.01775505021214485,
0.013175735250115395,
0.06244989112019539,
-0.004639496561139822,
0.025667818263173103,
-0.028722401708364487,
-0.05123114958405495,
0.005699360743165016,
0.029602041468024254,
0.022917775437235832,
0.032791536301374435,
0.011793909594416618,
-0.010712431743741035,
0.016316412016749382,
-0.03260691091418266,
-0.03807947784662247,
-0.05097516253590584,
0.04586859047412872,
-0.011694816872477531,
0.059768833220005035,
0.029455620795488358,
-0.027618078514933586,
-0.06080470606684685,
-0.02631732076406479,
-0.013485044240951538,
-0.01379677839577198,
0.0500134713947773,
-0.017302611842751503,
0.04510281980037689,
0.07354764640331268,
-0.024162739515304565,
0.013664258643984795,
0.031947314739227295,
-0.010537661612033844,
-0.035524990409612656,
0.04165639728307724,
0.02191011607646942,
0.003711095778271556,
-0.009991093538701534,
-0.012554388493299484,
-0.03410400450229645,
0.00595879228785634,
0.060461945831775665,
-0.01591741107404232,
-0.02723875269293785,
-0.029633769765496254,
-0.024545419961214066,
-0.007679327391088009,
-0.0057023935951292515,
-0.08643832802772522,
0.01225784607231617,
-0.0198518019169569,
-0.06006947532296181,
-0.007137890439480543,
-0.03174642473459244,
0.028005875647068024,
-0.060749638825654984,
0.02010936476290226,
-0.021233346313238144,
0.049157362431287766,
0.0048282574862241745,
0.0457112118601799,
0.02576413005590439,
-0.007895875722169876,
-0.016747964546084404,
-0.014093456789851189,
0.015583792701363564,
-0.01766621693968773,
-0.04173954203724861,
0.03274523466825485,
0.05464283376932144,
-0.05106954649090767,
0.07826647907495499,
0.10207629203796387,
0.007235036697238684,
-0.007262371946126223,
0.057964593172073364,
0.048280563205480576,
-0.006144380196928978,
0.01686466857790947,
0.0204318780452013,
-0.008500340394675732,
-0.003147565759718418,
0.036073777824640274,
-0.04421680420637131,
-0.015741709619760513,
-0.06504188477993011,
-0.011542556807398796,
0.0009133674902841449,
0.01738593727350235,
0.0228503979742527,
0.09737876802682877,
0.08487088978290558,
0.005165402777493,
0.08704321086406708,
0.00038399125332944095,
0.0018297713249921799,
0.03783174976706505,
-0.004476485308259726,
-0.02484901063144207,
0.06016494706273079,
-0.060944367200136185,
-0.04055442288517952,
0.02839616872370243,
-0.05632825940847397,
0.03353980928659439,
0.03347807377576828,
-0.044185422360897064,
0.023203229531645775,
-0.009846076369285583,
0.016048435121774673,
0.006085818167775869,
-0.003151031443849206,
-0.015062365680932999,
0.00019116744806524366,
-0.010528814047574997,
-0.01299401093274355,
0.02722737193107605,
-0.04016350582242012,
-0.021417945623397827,
-0.053597770631313324,
-0.022830922156572342,
-0.01320710964500904,
0.013967152684926987,
-0.001524062710814178,
0.030651560053229332,
-0.027581587433815002,
0.0632956326007843,
-0.029149627313017845,
-0.02067161351442337,
0.02620222419500351,
0.01986531913280487,
-0.032355234026908875,
-0.04285659268498421,
0.08087793737649918,
-0.03162611648440361,
-0.03967900574207306,
-0.0012241554213687778,
-0.04996960610151291,
0.0026697481516748667,
-0.05400518700480461,
-0.04419875517487526,
-0.025546662509441376,
0.028688427060842514,
0.00754761416465044,
-0.006558744236826897,
0.04063758999109268,
0.04058344289660454,
0.022894851863384247,
0.04828966408967972,
-0.013756228610873222,
-0.010409441776573658,
-0.0533641055226326,
-0.0663762092590332,
-0.02030549757182598,
-0.0010862128110602498,
0.03668496757745743,
0.034134652465581894,
0.030918797478079796,
-0.03476587310433388,
0.01766832359135151,
0.0020593577064573765,
0.010904856957495213,
-0.004178420640528202,
0.03408098593354225,
-0.045655425637960434,
-0.024766355752944946,
0.007792928721755743,
0.028827998787164688,
0.047683484852313995,
0.006789826788008213,
-0.05576660856604576,
0.051231782883405685,
0.020204346626996994,
0.05007150024175644,
-0.018245184794068336,
-0.009564905427396297,
-0.04105781391263008,
-0.004305942915380001,
0.05006878823041916,
0.023151053115725517,
0.05273944139480591,
0.030078193172812462,
-0.032246820628643036,
-0.011635561473667622,
0.014915325678884983,
0.020807946100831032,
-0.09528294205665588,
-0.0002474695793353021,
0.00800691545009613,
0.021459773182868958,
0.040292415767908096,
-0.00444570928812027,
-0.038023222237825394,
0.0693412721157074,
0.004117380362004042,
-0.03718998283147812,
0.00946077611297369,
-0.04690074920654297,
-0.016321195289492607,
0.010716812685132027,
-0.05938437581062317,
-0.028807472437620163,
0.013721410185098648,
-0.019637901335954666,
-0.005933236796408892,
0.003169080475345254,
0.059952251613140106,
-0.01815139316022396,
-0.018403533846139908,
-0.034578874707221985,
-0.031421177089214325,
0.0355694405734539,
-0.0644455999135971,
0.020656855776906013,
0.010911020450294018,
0.04501384496688843,
-0.04238109663128853,
-0.011121111921966076,
-0.01626935973763466,
-0.0008001332171261311,
0.04556829854846001,
-0.06093912199139595,
0.05844661593437195,
-0.04111919179558754,
0.024108577519655228,
-0.025202998891472816,
-0.011489283293485641,
-0.013105017133057117,
0.05343974754214287,
-0.04585234448313713,
-0.022551828995347023,
0.025030842050909996,
-0.001478682504966855,
0.0008542679133825004,
-0.021096181124448776,
-0.03892044350504875,
0.0030882679857313633,
-0.023801017552614212,
0.0155946621671319,
0.04799073934555054,
0.03316321596503258,
-0.0962551161646843,
0.003985161427408457,
0.00959981419146061,
-0.0011532659409567714,
0.028943773359060287,
-0.03927072882652283,
-0.0785137414932251,
-0.023120488971471786,
-0.11635524034500122,
0.04147607088088989,
-0.001680627465248108,
-0.025737641379237175,
-0.02208520658314228,
-0.017135832458734512,
0.039359305053949356,
0.01573125272989273,
-0.013998851180076599,
0.04719403013586998,
-0.022508051246404648,
0.044245265424251556,
-0.020343275740742683,
0.03518306463956833,
-0.028428558260202408,
0.025531768798828125,
-0.07608173787593842,
-0.027538960799574852,
0.004435697104781866,
-0.04860106110572815,
-0.03915350139141083,
0.01467335969209671,
0.010539057664573193,
-0.016098061576485634,
-0.03258686140179634,
-0.0037934407591819763,
0.020619869232177734,
-0.011126643046736717,
-0.02262159064412117,
0.06487301737070084,
0.01351380068808794,
0.0756545439362526,
-0.06081761047244072,
-0.002909589558839798,
-0.018198994919657707,
0.04325813055038452,
-0.015760043635964394,
0.016362953931093216,
0.003348506288602948,
-0.021882249042391777,
0.0038558964151889086,
-0.047347184270620346,
-0.010291364043951035,
0.01562037505209446,
0.00027190690161660314,
-0.010893036611378193,
-0.026061126962304115,
0.08624428510665894,
-0.003302541561424732,
0.04349914565682411,
-0.037919823080301285,
-0.04283487796783447,
0.033983271569013596,
0.011534440331161022,
0.028683798387646675,
-0.015501280315220356,
-0.017017817124724388,
0.007170615717768669,
0.03522355481982231,
-0.017499670386314392,
0.0015121164033189416,
-0.028659574687480927,
-0.005288776941597462,
0.00937074888497591,
-0.014293016865849495,
-0.0018608631798997521,
0.0026400391943752766,
-0.05110076814889908,
-0.04419560730457306,
-0.028717221692204475,
0.022971833124756813,
-0.052277255803346634,
-0.010749025270342827,
-0.04806293547153473,
-0.01594182662665844,
0.02072685770690441,
0.015610156580805779,
-0.013077909126877785,
0.0010384400375187397,
-0.018098335713148117,
0.0030581941828131676,
0.0472492016851902,
-0.07009626924991608,
0.012953626923263073,
0.009149331599473953,
0.008721093647181988,
-0.0004024039371870458,
-0.002302601234987378,
-0.027202019467949867,
0.031888533383607864,
0.020257815718650818,
-0.015309982933104038,
-0.03361429274082184,
0.029221350327134132,
0.08576278388500214,
-0.03416261821985245,
-0.010468391701579094,
0.0010082104708999395,
-0.007238907739520073,
0.012789743021130562,
-0.04968218877911568,
-0.01715310849249363,
0.05163804441690445,
-0.00944691151380539,
-0.005636192858219147,
-0.023718809708952904,
0.08121658861637115,
-0.0016006999649107456,
0.009784527122974396,
-0.02310599386692047,
-0.02855663187801838,
-0.0497400164604187,
-0.00870839785784483,
0.08248051255941391,
-0.025661850348114967,
-0.0029156289529055357,
0.10689020156860352,
-0.022906078025698662,
-0.015139935538172722,
-0.04668208584189415,
0.05853218957781792,
0.027012042701244354,
0.018215402960777283,
0.005295884795486927,
-0.025847144424915314,
-0.06574077904224396,
-0.005456395912915468,
-0.04387582838535309,
0.013903203420341015,
0.004967348650097847,
-0.012035135179758072,
0.018021369352936745,
0.00948227196931839,
0.010876530781388283,
-0.03083828277885914,
-0.011900232173502445,
0.007137910928577185,
0.021639270707964897,
0.0347607396543026,
0.02520461566746235,
-0.017038429155945778,
-0.05495623126626015,
0.008520037867128849,
0.005231973249465227,
0.024582920596003532,
-0.06243783235549927,
-0.04393504187464714,
-0.0022791875526309013,
-0.0095966262742877,
-0.01643107831478119,
-0.022733716294169426,
-0.026259222999215126,
0.016561416909098625,
0.043769095093011856,
-0.033250730484724045,
0.0852050855755806,
0.02241351269185543,
-0.013875316828489304,
0.013872804120182991,
0.013214398175477982,
0.04178781062364578,
0.021432489156723022,
-0.0472315214574337,
0.005075288936495781,
0.006969565525650978,
-0.017154261469841003,
-0.01563395746052265,
-0.027841391041874886,
-0.07345131039619446,
0.07766418904066086
] |
<p>I'm interested in designing and building a Stirling engine which uses air that has been heated, which expands and then acts upon a piston producing power. </p>
<p>There is a fixed amount of air inside the sealed 2" cylinder, and a relatively stable heat supply. The piston compresses cool air and is powered by the expanding, heated air.</p>
<p>Two questions here:</p>
<ol>
<li><p>How to find the power needed to compress air inside the 2" diameter cylinder to different depths?</p></li>
<li><p>Depending on the amount of compression produced by the piston, how does that affect the rate of expansion of the heated air?</p></li>
</ol>
<p>If the power needed to compress the air to a certain pressure exceeds the net power output of the expanding air, then the engine won't function. So, I need to calculate the stroke of the piston inside the cylinder to a depth that the engine can use efficiently. </p>
<p>Thanks.</p> | g5481 | [
0.013393647968769073,
0.014927806332707405,
-0.0026382592041045427,
0.026222525164484978,
-0.021826177835464478,
-0.033178891986608505,
0.02262081392109394,
0.0014427915448322892,
-0.09111355990171432,
-0.023869900032877922,
-0.010862588882446289,
0.023216117173433304,
0.044307392090559006,
0.012917070649564266,
0.06544721871614456,
0.04597720503807068,
0.03643422573804855,
-0.03520340099930763,
0.014194678515195847,
0.021306172013282776,
0.007893763482570648,
0.028496813029050827,
-0.010232091881334782,
-0.022386344149708748,
0.019636165350675583,
-0.05330094322562218,
0.037399355322122574,
-0.03620806336402893,
-0.027616558596491814,
-0.09212476760149002,
0.00750724645331502,
0.03560071066021919,
0.03575571998953819,
-0.017360152676701546,
-0.0503157414495945,
0.042341187596321106,
0.05807879567146301,
0.018109748139977455,
0.0035313693806529045,
-0.003839569864794612,
0.01644306071102619,
-0.07095053046941757,
0.015648486092686653,
0.04119586572051048,
0.0063035027123987675,
-0.06033916398882866,
-0.04103560000658035,
0.006839687004685402,
-0.04373221471905708,
0.02212553471326828,
0.044148754328489304,
-0.007175199221819639,
-0.050536323338747025,
-0.05376323685050011,
-0.027663657441735268,
0.0070666056126356125,
-0.06044758856296539,
-0.024879947304725647,
0.03641403838992119,
0.015152987092733383,
-0.05757454037666321,
-0.0028752884827554226,
0.014212044887244701,
-0.001367695163935423,
0.014156877994537354,
-0.030427852645516396,
-0.03161702677607536,
-0.05629231035709381,
-0.003951203543692827,
0.05860399827361107,
-0.010136614553630352,
-0.06122523546218872,
0.0016205408610403538,
-0.04955156520009041,
0.006125930696725845,
-0.03377063199877739,
0.019655615091323853,
-0.011400915682315826,
0.020429551601409912,
0.0048012943007051945,
-0.013000969775021076,
-0.010952969081699848,
0.0526316799223423,
-0.031864576041698456,
0.04622771590948105,
0.005555180832743645,
-0.018056366592645645,
0.029388651251792908,
0.0006634396268054843,
0.011293345130980015,
-0.02872372232377529,
0.06064361706376076,
0.08026622235774994,
0.011484638787806034,
0.04088465869426727,
-0.003723472822457552,
-0.015453214757144451,
-0.012298881076276302,
0.015408851206302643,
0.010278967209160328,
0.005658369045704603,
-0.03652516379952431,
-0.004324272740632296,
-0.010972577147185802,
-0.041702188551425934,
0.02915084920823574,
-0.03580702841281891,
0.01686418056488037,
-0.013857413083314896,
-0.0037258549127727747,
-0.01148931123316288,
-0.028307011350989342,
-0.02975192293524742,
0.0018780197715386748,
-0.06254355609416962,
-0.03849772736430168,
0.007649329956620932,
0.05620235204696655,
-0.002323707565665245,
-0.011953724548220634,
0.05240008607506752,
0.03684351220726967,
0.012331575155258179,
-0.012585139833390713,
0.059121761471033096,
0.030194366350769997,
-0.022748025134205818,
-0.007972302846610546,
-0.0317656509578228,
0.026954831555485725,
0.041321635246276855,
0.018986431881785393,
-0.01046514417976141,
0.05061280354857445,
0.06886377185583115,
0.02823278121650219,
-0.06934888660907745,
0.01833230070769787,
-0.011965716257691383,
0.04710683226585388,
-0.04966350644826889,
0.0015669044805690646,
-0.033461056649684906,
0.009373974986374378,
-0.00034810035140253603,
-0.013054528273642063,
-0.029627203941345215,
-0.07646520435810089,
-0.028856215998530388,
0.006664651911705732,
-0.001040975796058774,
0.031282875686883926,
0.019784385338425636,
-0.034537602216005325,
0.04178014025092125,
0.03440208360552788,
-0.03347135707736015,
0.020931968465447426,
0.013243320398032665,
0.017200909554958344,
0.07542932033538818,
-0.007819597609341145,
0.005710001103579998,
0.023114319890737534,
-0.05105045065283775,
0.08469731360673904,
-0.05828734114766121,
-0.019872799515724182,
-0.012751629576086998,
0.0046721869148314,
-0.024404581636190414,
-0.020195653662085533,
-0.008967808447778225,
-0.0013557331403717399,
0.023741504177451134,
0.02440100535750389,
0.14265969395637512,
0.004986831918358803,
-0.016388671472668648,
-0.026665065437555313,
-0.06834428757429123,
-0.02207145094871521,
0.013946782797574997,
-0.03520630672574043,
-0.01300039142370224,
-0.015500640496611595,
0.05963805690407753,
-0.04340290650725365,
-0.08620712906122208,
0.01563759706914425,
-0.03813754767179489,
0.005518379155546427,
0.08426447212696075,
0.008469012565910816,
-0.06857020407915115,
-0.00183112605009228,
0.04619520902633667,
-0.04882749915122986,
-0.03821904584765434,
-0.03842362016439438,
0.015451894141733646,
0.030989879742264748,
0.04448476806282997,
0.017089644446969032,
0.02665141224861145,
0.02461746521294117,
-0.011785331182181835,
0.04914551600813866,
0.014917886815965176,
0.015161892399191856,
0.018188372254371643,
-0.050215624272823334,
0.02483365871012211,
0.06269843131303787,
0.02069779299199581,
0.06596051901578903,
-0.0294682364910841,
-0.011430791579186916,
-0.024255918338894844,
-0.024797411635518074,
0.07219737768173218,
0.013507083058357239,
-0.00046200930955819786,
-0.017175806686282158,
-0.06903979927301407,
-0.014366800896823406,
0.02858678065240383,
0.016510816290974617,
-0.007927803322672844,
0.04856753349304199,
-0.0423361212015152,
0.014290575869381428,
0.01237411703914404,
-0.00022093103325460106,
0.004514576401561499,
0.023718280717730522,
-0.05635727196931839,
0.06596709787845612,
0.027064403519034386,
0.047542717307806015,
0.02447625994682312,
-0.007645510137081146,
-0.020239204168319702,
-0.03734017536044121,
0.010729094967246056,
-0.03420574590563774,
-0.011665408499538898,
0.0024489068891853094,
-0.015814345329999924,
0.014006639830768108,
-0.054722703993320465,
0.04025303199887276,
-0.00363578787073493,
-0.009569183923304081,
-0.11347202211618423,
-0.02821882627904415,
-0.050125375390052795,
-0.009003901854157448,
-0.05201340466737747,
-0.0048542688600718975,
0.04577859491109848,
0.01967887207865715,
-0.00497417850419879,
-0.0235088262706995,
-0.051965922117233276,
-0.022272592410445213,
0.0047909957356750965,
-0.04094061627984047,
0.06955448538064957,
0.020454078912734985,
-0.020542455837130547,
-0.009717634879052639,
-0.0017481374088674784,
-0.004376496188342571,
0.043576277792453766,
-0.03366280719637871,
0.008443913422524929,
-0.016797078773379326,
0.056767694652080536,
-0.01370193436741829,
0.012300738133490086,
0.006904457695782185,
-0.03266197443008423,
0.026802418753504753,
0.050588659942150116,
-0.04586467891931534,
-0.007479877211153507,
0.07655763626098633,
0.042991332709789276,
-0.012436846271157265,
-0.003427700838074088,
-0.011137363500893116,
-0.021807560697197914,
0.022199179977178574,
0.051340844482183456,
0.06022518128156662,
0.005318667273968458,
0.002656845608726144,
-0.022674592211842537,
-0.009522686712443829,
-0.029305657371878624,
-0.08919861912727356,
-0.01914014294743538,
-0.020510071888566017,
0.0040246229618787766,
0.03372624143958092,
-0.042396824806928635,
0.03531418368220329,
-0.007916823029518127,
0.02571822516620159,
-0.10687240213155746,
-0.038021933287382126,
0.06845367699861526,
-0.08112374693155289,
-0.02442745491862297,
-0.04649711400270462,
-0.014245104044675827,
-0.05576751381158829,
0.014303878881037235,
0.023199496790766716,
-0.008574043400585651,
-0.03913642838597298,
-0.021568721160292625,
-0.02909519337117672,
0.00473436526954174,
0.042943019419908524,
0.02173539064824581,
-0.026796752586960793,
-0.03806788846850395,
-0.012410241179168224,
-0.03348126262426376,
0.04500812664628029,
-0.042264919728040695,
-0.016401831060647964,
-0.016012009233236313,
0.005226298235356808,
-0.029863979667425156,
0.008070211857557297,
0.00019130113651044667,
-0.011505300179123878,
0.015674158930778503,
0.034091148525476456,
0.021296996623277664,
0.015994472429156303,
-0.006300883833318949,
-0.03469472378492355,
-0.04176563397049904,
0.020109714940190315,
-0.03342039883136749,
-0.023764390498399734,
0.06872051954269409,
-0.04176926985383034,
0.007950388826429844,
0.01591605693101883,
0.03186513110995293,
0.037467144429683685,
0.023125698789954185,
0.0073181684128940105,
-0.08310044556856155,
0.013461299240589142,
-0.025519629940390587,
-0.058694418519735336,
-0.06011377274990082,
0.03207459673285484,
-0.02707441709935665,
-0.04316097870469093,
0.045793406665325165,
0.01448176708072424,
0.034261614084243774,
-0.022403808310627937,
0.02982162870466709,
0.0391373410820961,
-0.007596992421895266,
0.004283074289560318,
-0.006471109576523304,
-0.02698645554482937,
0.016224035993218422,
-0.006647393107414246,
-0.038006290793418884,
0.019954049959778786,
-0.02820225991308689,
0.041825395077466965,
0.0010094507597386837,
-0.025296708568930626,
0.0002058093814412132,
-0.021638935431838036,
0.0011519116815179586,
0.0339752733707428,
0.004404168110340834,
-0.00017823587404564023,
-0.06334976851940155,
-0.03702075406908989,
-0.11773966252803802,
0.012252612970769405,
-0.012598225846886635,
-0.009052780456840992,
-0.004085420165210962,
0.01691223680973053,
-0.0036625820212066174,
-0.009487295523285866,
0.031090762466192245,
0.026186954230070114,
0.07994826883077621,
0.036536745727062225,
-0.06677651405334473,
0.00823583360761404,
0.06663009524345398,
0.0316944420337677,
0.053465861827135086,
0.015490110963582993,
0.006931481882929802,
0.026902370154857635,
0.023649659007787704,
-0.002161311451345682,
0.048133574426174164,
-0.07845928519964218,
0.029169732704758644,
-0.023329593241214752,
0.02459292858839035,
0.053783152252435684,
-0.030323969200253487,
-0.010673788376152515,
0.015592969954013824,
0.005257651675492525,
-0.009015674702823162,
0.02510220743715763,
0.028362572193145752,
-0.0912126749753952,
0.026647087186574936,
-0.01458357647061348,
-0.02205464616417885,
-0.011486560106277466,
0.012196366675198078,
0.015802927315235138,
0.0436960831284523,
-0.00694113178178668,
-0.002245901385322213,
0.051661621779203415,
-0.024201542139053345,
0.007255686912685633,
-0.0037965145893394947,
-0.032838303595781326,
-0.00459107244387269,
0.00006194303568918258,
0.040703121572732925,
-0.020406104624271393,
-0.06508340686559677,
-0.06713452190160751,
0.005894315894693136,
0.004538329783827066,
-0.009515619836747646,
0.007764367386698723,
0.005165575072169304,
-0.02979784831404686,
-0.0049903858453035355,
0.037358034402132034,
-0.05887037143111229,
0.03306323662400246,
0.03779752179980278,
-0.02829812467098236,
0.008234364911913872,
0.00819793064147234,
-0.08780386298894882,
-0.008220445364713669,
-0.0031036678701639175,
-0.06524341553449631,
-0.014603164978325367,
0.01261228509247303,
-0.0282592810690403,
-0.03279830887913704,
0.07191228121519089,
-0.0053245131857693195,
0.0045201643370091915,
0.02591310814023018,
-0.010835920460522175,
0.027938058599829674,
-0.006470691412687302,
-0.020623330026865005,
0.044695910066366196,
0.020941969007253647,
0.027176475152373314,
-0.011228146031498909,
0.005669101607054472,
0.04711436107754707,
0.057074110954999924,
0.030483976006507874,
-0.019915547221899033,
-0.03204531595110893,
-0.030209610238671303,
0.03873145580291748,
0.0027819161769002676,
0.03559333086013794,
-0.019183699041604996,
0.033994413912296295,
-0.038448870182037354,
0.026292845606803894,
0.0648554340004921,
-0.00588349299505353,
-0.007464412599802017,
0.037167564034461975,
-0.010438011027872562,
0.016897613182663918,
-0.04196847602725029,
0.006700198631733656,
-0.005290601868182421,
-0.01068868488073349,
0.023830249905586243,
0.004527626559138298,
0.052484240382909775,
0.028034579008817673,
0.0232203658670187,
0.03601277992129326,
0.008420312777161598,
-0.00646461034193635,
0.02129938267171383,
-0.05651725456118584,
0.03782220929861069,
0.011689011938869953,
0.01455042976886034,
-0.01678485982120037,
0.08954154700040817,
-0.03496328368782997,
0.07414574921131134,
0.0023905320558696985,
-0.02328815869987011,
0.02281738631427288,
-0.021593453362584114,
-0.0380634143948555,
0.05342362821102142,
-0.010456179268658161,
-0.05628906190395355,
0.008552676066756248,
0.021030539646744728,
-0.05886080488562584,
-0.019681023433804512,
0.006224081385880709,
0.015300956554710865,
-0.0075702909380197525,
0.009361819364130497,
-0.04246416315436363,
-0.024789003655314445,
-0.008569827303290367,
-0.037974294275045395,
0.04702798277139664,
-0.011877157725393772,
-0.01789753884077072,
-0.06503504514694214,
0.025185788050293922,
-0.005702786147594452,
-0.026698347181081772,
0.03702408820390701,
0.054465215653181076,
-0.02116265520453453,
0.0046547758392989635,
0.003089067293331027,
-0.042327139526605606,
0.06038360670208931,
-0.00008875722414813936,
0.005400859285145998,
0.0083558214828372,
-0.014536242932081223,
0.014449057169258595,
0.020298277959227562,
0.01435580663383007,
-0.010388721711933613,
-0.027670618146657944,
-0.04431693255901337,
0.0016090646386146545,
0.03468717634677887,
0.020634589716792107,
0.03247138112783432,
-0.04524373263120651,
0.02342846803367138,
-0.04800357297062874,
0.09861442446708679,
-0.01635603979229927,
-0.020589476451277733,
0.008812633343040943,
0.0216537993401289,
-0.0019370318623259664,
0.013266699388623238,
0.05578649789094925,
0.032028574496507645,
0.00021877822291571647,
0.017236612737178802,
-0.013279387727379799,
0.0393497496843338,
0.010814148001372814,
0.0862160176038742,
0.026626691222190857,
-0.0042220186442136765,
-0.010357318446040154,
0.03342064097523689,
-0.03947526216506958,
0.00915786437690258,
-0.04532959312200546,
-0.029766762629151344,
0.021172603592276573,
0.05930548161268234,
-0.02107791230082512,
0.04533305764198303,
0.0722653716802597,
0.07402127236127853,
-0.041727181524038315,
-0.03167453780770302,
0.022869516164064407,
0.008704015985131264,
-0.013067224994301796,
0.005926122888922691,
0.008148393593728542,
-0.05473926290869713,
-0.012184924446046352,
0.05971452221274376,
-0.03676151484251022,
0.02271142043173313,
-0.010448196902871132,
0.04544198885560036,
0.022901274263858795,
0.0162470992654562,
-0.035877078771591187,
0.06174841895699501,
-0.009138712659478188,
0.024476340040564537,
-0.07042344659566879,
0.0572088286280632,
0.02149408683180809,
-0.057951878756284714,
-0.012384035624563694,
0.0719563290476799,
-0.020251009613275528,
0.020302819088101387,
-0.019680574536323547,
-0.015554895624518394,
0.03358297049999237,
-0.0193864144384861,
0.020590998232364655,
-0.031105784699320793,
0.08040980249643326,
0.030706193298101425,
0.05925527587532997,
-0.017989283427596092,
-0.0023213443346321583,
-0.05303848907351494,
0.08999915421009064,
-0.029636068269610405,
-0.04529496654868126,
0.05037801340222359,
-0.04902986064553261,
-0.05485587194561958,
0.013448777608573437,
-0.06694384664297104,
-0.02287527173757553,
-0.0695110559463501,
-0.026597104966640472,
-0.0009722948307171464,
0.0350848063826561,
0.0391777902841568,
-0.09308011829853058,
-0.010255640372633934,
-0.011146876029670238,
0.04528942331671715,
-0.01563517190515995,
0.023018857464194298,
0.030870560556650162,
-0.014547686092555523,
0.040808744728565216,
-0.034547410905361176,
-0.018513096496462822,
0.037591591477394104,
-0.03474225476384163,
-0.009778469800949097,
0.03523769974708557,
-0.04649301618337631,
-0.0014461497776210308,
-0.004610369447618723,
0.029590049758553505,
-0.005642653908580542,
0.030070921406149864,
-0.0038944617845118046,
-0.039343755692243576,
0.010300052352249622,
-0.07759904861450195,
-0.07033713161945343,
-0.040811069309711456,
-0.014427141286432743,
0.03311978280544281,
0.002352581126615405,
-0.023573938757181168,
0.025170285254716873,
-0.024040590971708298,
-0.04396399110555649,
0.04371928796172142,
0.06643697619438171,
0.01609859988093376,
-0.0003674351901281625,
0.04283116012811661,
-0.02477278932929039,
0.034366901963949203,
0.011905381456017494,
0.029252395033836365,
0.016085771843791008,
0.02217121422290802,
0.03628150001168251,
0.029156940057873726,
-0.004059416241943836,
-0.014375937171280384,
0.001006577629595995,
0.0020529276225715876,
-0.04116218164563179,
0.013819624669849873,
0.05456400662660599,
-0.034129828214645386,
-0.02266395464539528,
-0.0425008200109005,
0.04158955067396164,
0.00016357607091777027,
-0.0272318497300148,
-0.012606114149093628,
0.014565362595021725,
0.00956494826823473,
0.0013914962764829397,
-0.018170146271586418,
0.0010077315382659435,
0.0017762286588549614,
-0.0026052307803183794,
-0.06442811340093613,
-0.029022159054875374,
0.02177984081208706,
-0.050015758723020554,
0.03899816796183586,
-0.04144390672445297,
-0.026066020131111145,
0.06396540999412537,
0.004653591196984053,
-0.027291491627693176,
-0.024983035400509834,
-0.0031612792517989874,
0.0251621101051569,
-0.0019395285053178668,
0.0710604339838028,
-0.009337794966995716,
-0.03850051760673523,
0.015368692576885223,
-0.05112734064459801,
-0.006138817872852087,
-0.04902525618672371,
-0.045534368604421616,
0.0890311747789383,
0.06460054963827133,
0.009170028381049633,
0.025944950059056282,
-0.019988572224974632,
-0.02011016570031643,
-0.005627034697681665,
0.012613961473107338,
-0.017485423013567924,
-0.009348250925540924,
0.09980569034814835,
-0.05436663702130318,
-0.04636554419994354,
-0.026025520637631416,
0.03626791760325432,
-0.06510772556066513,
-0.006011570803821087,
-0.0041139572858810425,
-0.018931007012724876,
-0.057384952902793884,
-0.01287007611244917
] |
<p><img src="http://i.stack.imgur.com/h8s8B.png" alt="enter image description here">
Consider a cell containing Rubidium and enlight it with a laser. Connect the system with an oscilloscope and give a triangular wave as input (so you can know when the Rubidium is resonant). This is the signal that you see downward. You can see the output in the upper signal. It is given by the difference between input signal and the signal received by the photodiode... Looking at the spectral line relative to D2 rubidium transition, the oscilloscope gives me this picture. </p>
<p>I need a pragmatic hint. I have to measure the Doppler broadening so I need to convert time scale to frequency scale. </p>
<p>How can I do that?
Thanks a lot!</p> | g5482 | [
-0.008444374427199364,
0.01214794535189867,
-0.009194022975862026,
-0.06377850472927094,
0.06779070943593979,
0.009387845173478127,
0.00831447634845972,
-0.01886056549847126,
0.003939823247492313,
0.016801686957478523,
-0.020267250016331673,
0.06736626476049423,
0.03405020758509636,
0.04556799307465553,
0.03414347767829895,
-0.03316307067871094,
0.09246479719877243,
0.004876951687037945,
0.08007843047380447,
0.020934222266077995,
0.006786737125366926,
0.015857746824622154,
-0.033942271023988724,
-0.08053917437791824,
0.0027130325324833393,
0.006664100103080273,
0.016712989658117294,
0.012642329558730125,
-0.055719856172800064,
0.026460867375135422,
-0.004112322349101305,
0.00230353488586843,
0.027857068926095963,
0.08619769662618637,
0.046062812209129333,
0.016980895772576332,
0.02124989964067936,
0.019601961597800255,
-0.015291314572095871,
0.047664664685726166,
0.027742143720388412,
0.013864594511687756,
0.02503388188779354,
0.010219434276223183,
0.05138447508215904,
-0.07222072035074234,
-0.023725753650069237,
-0.018710706382989883,
-0.039825182408094406,
0.060890134423971176,
-0.013859902508556843,
0.04558045417070389,
0.015625983476638794,
-0.004139892291277647,
-0.017452215775847435,
0.008955853059887886,
-0.03805066645145416,
-0.013881059363484383,
0.04890986531972885,
0.041573915630578995,
-0.010813558474183083,
-0.04356703162193298,
0.023149438202381134,
-0.0035403824876993895,
0.041395194828510284,
0.03477782756090164,
0.041362911462783813,
-0.016956007108092308,
-0.022862110286951065,
0.01654217578470707,
0.01725388877093792,
-0.03767947852611542,
-0.02153809182345867,
-0.011490992270410061,
-0.006275376304984093,
0.013356608338654041,
-0.0030970724765211344,
-0.02793058753013611,
0.018298141658306122,
0.006292362231761217,
-0.047508735209703445,
-0.033158816397190094,
0.026377005502581596,
0.04192264750599861,
0.03152502700686455,
0.005356380715966225,
-0.00891230721026659,
0.014927360229194164,
0.007152771111577749,
0.006082220934331417,
0.004561383742839098,
-0.018349528312683105,
0.06085261330008507,
-0.005518029909580946,
0.05486997589468956,
-0.002592472592368722,
-0.033099088817834854,
0.061642494052648544,
0.021113581955432892,
-0.016067981719970703,
-0.00682690879330039,
-0.012970276176929474,
-0.07479415088891983,
-0.05110212415456772,
-0.07402956485748291,
-0.020183248445391655,
0.007891670800745487,
-0.035838350653648376,
-0.0067973667755723,
-0.03274814411997795,
-0.0363604761660099,
-0.10365470498800278,
-0.01128140278160572,
0.0032096130307763815,
0.0001821901969378814,
-0.018962183967232704,
0.008571047335863113,
0.025094419717788696,
-0.08225007355213165,
0.006017184816300869,
0.06539466232061386,
-0.09910634905099869,
0.028863798826932907,
0.07038614898920059,
0.02709341049194336,
0.08576824516057968,
-0.019592341035604477,
-0.010388839058578014,
-0.0007770495722070336,
0.035674817860126495,
0.016995910555124283,
0.043224185705184937,
0.009043525904417038,
0.05838107690215111,
0.024363232776522636,
0.07364056259393692,
0.04907609149813652,
-0.03428278863430023,
-0.03272299841046333,
0.0016488502733409405,
0.01025596633553505,
-0.023328427225351334,
0.027918290346860886,
-0.006015324499458075,
0.013415449298918247,
0.011880582198500633,
-0.01475894171744585,
-0.007977919653058052,
0.0868910700082779,
0.0015418396797031164,
0.0402626097202301,
0.06786861270666122,
0.03418813645839691,
-0.029027510434389114,
-0.03941269963979721,
0.015118452720344067,
0.02147521637380123,
-0.003935055807232857,
-0.03704257309436798,
0.015125871635973454,
0.029123779386281967,
-0.0033390980679541826,
-0.050656940788030624,
0.0035057158675044775,
-0.005190051160752773,
0.025289099663496017,
0.017781205475330353,
-0.013313030824065208,
-0.031876783818006516,
-0.027745341882109642,
-0.025824587792158127,
0.02528947778046131,
-0.017778640612959862,
-0.04893174394965172,
-0.01670054718852043,
0.10465554147958755,
-0.003979755099862814,
0.020004041492938995,
0.06527858227491379,
0.018310032784938812,
-0.038459207862615585,
-0.0238781850785017,
0.027317428961396217,
-0.06499140709638596,
-0.026803992688655853,
0.006364309694617987,
0.013710585422813892,
-0.04666941240429878,
-0.046442389488220215,
0.05864125117659569,
0.004845898598432541,
-0.03223240002989769,
-0.005195673555135727,
0.0028258038219064474,
-0.03489993140101433,
-0.00304243341088295,
-0.03344649448990822,
-0.04373782128095627,
-0.02345656044781208,
-0.052806708961725235,
-0.01409529522061348,
0.01768527925014496,
0.032972194254398346,
0.022944355383515358,
0.031861115247011185,
-0.03075282834470272,
-0.00675860745832324,
-0.0161467082798481,
-0.030899323523044586,
0.038813453167676926,
0.0016266992315649986,
0.04630443826317787,
-0.039379045367240906,
-0.011723431758582592,
-0.00038787993253208697,
0.0709799975156784,
0.0031098925974220037,
-0.006609080825001001,
-0.024671467021107674,
0.09138468652963638,
-0.03559950739145279,
0.005104116164147854,
0.027578992769122124,
0.0029324369970709085,
0.033971887081861496,
-0.007500975392758846,
-0.012864516116678715,
0.06677063554525375,
0.020023085176944733,
-0.013099604286253452,
-0.004456962924450636,
0.008846649900078773,
-0.050033848732709885,
-0.04334742948412895,
-0.020240962505340576,
0.019913379102945328,
-0.0013293565716594458,
0.010434900410473347,
-0.019916856661438942,
0.028433850035071373,
-0.00953440647572279,
-0.048030756413936615,
0.0030028442852199078,
-0.021782631054520607,
-0.004363688640296459,
-0.005077805370092392,
-0.003450667252764106,
0.04405277594923973,
-0.03214659169316292,
-0.0616271011531353,
0.05623675137758255,
0.00555209768936038,
-0.0023524134885519743,
-0.0003428872732911259,
-0.05612384155392647,
0.006803953554481268,
0.006136889103800058,
0.012484968639910221,
-0.09658902883529663,
-0.02568301185965538,
-0.025397390127182007,
0.018196789547801018,
0.006199376657605171,
0.005476220976561308,
-0.03550771623849869,
-0.04721774533390999,
-0.003918734844774008,
0.00018737028585746884,
0.010061097331345081,
-0.03675501421093941,
0.0021093955729156733,
-0.003061115276068449,
0.04391036555171013,
-0.008525322191417217,
0.0030123372562229633,
-0.020672710612416267,
0.022637395188212395,
-0.010257234796881676,
0.02897622622549534,
-0.003493553027510643,
-0.040399469435214996,
-0.011055797338485718,
-0.05859183147549629,
0.021595962345600128,
0.008079985156655312,
-0.004887412302196026,
0.026627155020833015,
0.015890242531895638,
-0.013899827376008034,
0.04214692860841751,
-0.05872111767530441,
0.010514344088733196,
-0.0130942827090621,
0.022309059277176857,
-0.0263789314776659,
-0.014963856898248196,
0.09436212480068207,
0.0015753639163449407,
0.120295949280262,
0.061473965644836426,
0.009597786702215672,
-0.05672747641801834,
0.00643236143514514,
0.010822510346770287,
0.014144699089229107,
-0.018750665709376335,
-0.018312884494662285,
-0.0019497170578688383,
0.013069480657577515,
0.014478234574198723,
-0.001654118183068931,
-0.0525260791182518,
-0.011876935139298439,
-0.04356469586491585,
0.007618145551532507,
-0.08677168935537338,
-0.03073478676378727,
-0.01809777319431305,
0.01964792050421238,
0.045113515108823776,
-0.006455030292272568,
-0.03751973807811737,
-0.017936768010258675,
-0.016977941617369652,
-0.0033434422221034765,
-0.03993145748972893,
0.03126498684287071,
0.019108673557639122,
-0.05151081085205078,
0.0274107176810503,
-0.02023492567241192,
0.01539059542119503,
-0.03882066160440445,
-0.020720813423395157,
-0.006466079503297806,
-0.0551435686647892,
-0.047529127448797226,
0.0390431247651577,
-0.015495135448873043,
-0.0029085767455399036,
-0.05285351350903511,
0.013980427756905556,
-0.060198698192834854,
-0.039582427591085434,
-0.01953965239226818,
-0.005239805672317743,
-0.028452137485146523,
0.019540851935744286,
-0.05233440920710564,
-0.060908909887075424,
-0.016303077340126038,
0.0270429365336895,
-0.00886427704244852,
-0.029329316690564156,
0.01771426945924759,
0.036470361053943634,
0.04630504548549652,
0.026132218539714813,
-0.01731528341770172,
-0.013530159369111061,
-0.04143591597676277,
-0.022626718506217003,
0.0025863826740533113,
-0.021942073479294777,
-0.02446509338915348,
0.015564865432679653,
-0.010300230234861374,
0.06671735644340515,
0.010822673328220844,
0.047937773168087006,
-0.01450812816619873,
-0.09623786807060242,
0.012411645613610744,
0.024401666596531868,
0.0038954559713602066,
-0.01166248507797718,
0.03415011987090111,
-0.006373126991093159,
0.0473945215344429,
0.0881114974617958,
-0.06077112630009651,
0.005094519816339016,
0.03486783057451248,
-0.07300277799367905,
0.03380599245429039,
0.004200213588774204,
-0.009460831992328167,
-0.017331581562757492,
0.026269560679793358,
0.0076684351079165936,
-0.04755245894193649,
-0.008497007191181183,
0.008301408030092716,
-0.029539451003074646,
-0.01814015954732895,
-0.04403079301118851,
0.03319460526108742,
0.030966389924287796,
-0.05948773771524429,
-0.0030122417956590652,
-0.013455813750624657,
-0.016637282446026802,
-0.026198701933026314,
0.018856072798371315,
-0.04647764936089516,
0.05418754741549492,
0.03717304766178131,
-0.01499859057366848,
-0.01876930519938469,
0.04838643595576286,
-0.06698156893253326,
-0.017017938196659088,
0.03631215915083885,
-0.009171519428491592,
-0.022896459326148033,
0.05651307478547096,
0.07302945107221603,
-0.01590067893266678,
0.03394933417439461,
0.021190134808421135,
-0.02340668812394142,
0.06767512857913971,
0.014257253147661686,
0.013664400205016136,
-0.0299049261957407,
0.044869016855955124,
0.03974590077996254,
0.019533459097146988,
0.05388019233942032,
-0.013629949651658535,
-0.002313526812940836,
-0.003284962149336934,
-0.002428124425932765,
0.030232371762394905,
-0.04726323112845421,
-0.03531120344996452,
-0.004844881594181061,
-0.007789486087858677,
-0.004740558564662933,
0.050120849162340164,
-0.02937828190624714,
-0.02066906914114952,
-0.031205937266349792,
-0.032093487679958344,
-0.03913319110870361,
0.06445765495300293,
-0.027256594970822334,
-0.052897859364748,
-0.027506999671459198,
-0.019662633538246155,
-0.019491571933031082,
0.05160167068243027,
-0.06337714940309525,
-0.005267216358333826,
-0.021616004407405853,
-0.023055657744407654,
-0.0075732143595814705,
0.01661291904747486,
-0.007836874574422836,
0.0058809127658605576,
-0.06132306158542633,
0.02032819762825966,
-0.041169438511133194,
-0.02783079817891121,
0.020454933866858482,
-0.067860446870327,
-0.057525571435689926,
0.006185511127114296,
0.009106621146202087,
-0.06233362853527069,
0.02627388760447502,
-0.083556167781353,
0.04199964925646782,
0.019675491377711296,
0.01199246197938919,
-0.02904672734439373,
-0.016639621928334236,
-0.013617678545415401,
0.05240800604224205,
-0.03207625448703766,
-0.02446601912379265,
0.009738992899656296,
0.0782649964094162,
-0.0069580236449837685,
0.0017224340699613094,
0.056499164551496506,
-0.016200603917241096,
0.017886817455291748,
-0.015198102220892906,
-0.027154292911291122,
-0.036378856748342514,
0.03932902216911316,
0.003907231613993645,
-0.012887783348560333,
-0.02836565114557743,
0.050776150077581406,
0.040949150919914246,
-0.04706089198589325,
-0.020842110738158226,
-0.048564258962869644,
-0.03819639980792999,
0.05697005242109299,
-0.009138986468315125,
0.049777138978242874,
-0.00588691933080554,
0.0010144701227545738,
-0.024275589734315872,
0.009101351723074913,
0.025357559323310852,
0.056261882185935974,
-0.05925731733441353,
0.003478678874671459,
-0.0006906056660227478,
0.023927515372633934,
-0.002496554749086499,
-0.053746264427900314,
0.00784886721521616,
0.05292261764407158,
-0.017913581803441048,
-0.039990417659282684,
-0.023760955780744553,
-0.05788981541991234,
0.03176174685359001,
-0.0220298171043396,
0.016042212024331093,
0.022383471950888634,
-0.04777717590332031,
0.009937366470694542,
0.0401492677628994,
-0.03218036890029907,
0.05398799479007721,
-0.01158940326422453,
0.01815931685268879,
-0.025492040440440178,
0.018314234912395477,
0.020912447944283485,
0.042607665061950684,
0.05898011848330498,
-0.052686646580696106,
-0.029706010594964027,
0.015362179838120937,
0.03205908089876175,
0.008686715736985207,
-0.017008746042847633,
-0.02844574861228466,
0.013148456811904907,
0.0016104989917948842,
0.018819931894540787,
-0.012465174309909344,
0.04625558853149414,
0.058598265051841736,
0.002991038840264082,
0.030850527808070183,
-0.006744293961673975,
-0.01774977333843708,
-0.018078137189149857,
-0.010393832810223103,
-0.024159912019968033,
-0.00864278245717287,
-0.01589529775083065,
0.07064522057771683,
0.03177610784769058,
0.005976064596325159,
0.02311881072819233,
0.0062747616320848465,
-0.055761951953172684,
-0.027442021295428276,
0.06717642396688461,
0.06800439953804016,
0.001957549713551998,
-0.05438472330570221,
-0.02814115211367607,
0.045031800866127014,
0.013267415575683117,
0.025740105658769608,
0.043337635695934296,
0.005855040159076452,
-0.012328511103987694,
0.05374058708548546,
-0.014895075932145119,
-0.05179528146982193,
0.05370530113577843,
-0.027139419689774513,
0.03727715089917183,
-0.04006950557231903,
-0.006059768609702587,
0.0057589225471019745,
-0.003548074048012495,
-0.037370383739471436,
0.002152060391381383,
0.009265613742172718,
-0.023881444707512856,
-0.007310135290026665,
-0.01168062724173069,
-0.04691684991121292,
-0.03727276995778084,
-0.059493158012628555,
0.01543864794075489,
0.06303493678569794,
0.08730299025774002,
-0.003630155697464943,
-0.019009899348020554,
0.013239884749054909,
-0.027726830914616585,
-0.015803905203938484,
-0.015179265290498734,
-0.029227351769804955,
-0.042144108563661575,
0.09165088832378387,
-0.036445703357458115,
-0.0019452106207609177,
0.05251088738441467,
0.046983376145362854,
0.012738341465592384,
0.02183408848941326,
-0.000551987555809319,
0.08482532203197479,
0.02272326499223709,
0.004382803104817867,
0.03526529297232628,
0.009856871329247952,
0.005203654523938894,
0.025459779426455498,
-0.008977181278169155,
0.03448115661740303,
0.0676926001906395,
-0.02861197479069233,
0.01452347356826067,
0.024893201887607574,
-0.029969491064548492,
0.017087137326598167,
-0.02376769483089447,
-0.035703495144844055,
0.021635876968503,
0.027403855696320534,
0.006836978252977133,
0.0057429722510278225,
-0.033464983105659485,
0.09038001298904419,
0.03870671987533569,
0.010198710486292839,
0.06852791458368301,
0.0247828159481287,
0.007898949086666107,
-0.052298542112112045,
0.030304916203022003,
0.06401102989912033,
0.032056521624326706,
-0.05518180876970291,
0.042699024081230164,
-0.014887162484228611,
-0.03179441764950752,
0.017005734145641327,
0.054625995457172394,
-0.0077072614803910255,
0.061675187200307846,
0.04863325506448746,
0.010759735479950905,
0.02097167819738388,
-0.04165797680616379,
-0.0010632430203258991,
-0.12354689836502075,
-0.026327215135097504,
-0.01430569402873516,
0.003937289118766785,
0.06615159660577774,
-0.03934317082166672,
-0.04631669074296951,
-0.02458658628165722,
-0.1102822795510292,
-0.03531644493341446,
-0.023295743390917778,
0.031658563762903214,
0.021281583234667778,
-0.016475418582558632,
0.040392231196165085,
-0.01914866268634796,
0.023773670196533203,
-0.030811898410320282,
-0.03669307008385658,
-0.03536815196275711,
-0.07113294303417206,
-0.001522529753856361,
-0.04214876890182495,
0.01273293700069189,
0.0015843259170651436,
-0.02987128123641014,
-0.01573227345943451,
0.04377109184861183,
-0.031159033998847008,
-0.082028828561306,
0.030481284484267235,
-0.026531055569648743,
-0.0009098536102101207,
0.04722437262535095,
-0.022646455094218254,
-0.0011271104449406266,
-0.00899982638657093,
-0.000001892134378067567,
-0.02779865451157093,
0.045638903975486755,
0.03639383986592293,
-0.014209235087037086,
0.028004908934235573,
0.004828477278351784,
0.012229550629854202,
-0.008463561534881592,
-0.06577369570732117,
-0.026598628610372543,
-0.02892950177192688,
-0.026408785954117775,
-0.0009777338709682226,
0.007265901658684015,
-0.043485891073942184,
0.0259084552526474,
0.04494448006153107,
-0.024433234706521034,
-0.007590313907712698,
-0.03936799243092537,
-0.04404602572321892,
0.0021446740720421076,
-0.03215207904577255,
-0.03926289454102516,
-0.01911674439907074,
0.006961108185350895,
-0.049005988985300064,
-0.014778191223740578,
-0.04412626847624779,
0.027956601232290268,
-0.0684167668223381,
-0.007939288392663002,
0.05848283693194389,
0.019265562295913696,
-0.008465355262160301,
-0.003779187798500061,
0.05552451312541962,
-0.04095342010259628,
0.0651877224445343,
-0.04305770620703697,
0.028495123609900475,
0.010560845024883747,
0.021051637828350067,
-0.019354628399014473,
0.06486327946186066,
0.0038268330972641706,
-0.019052671268582344,
-0.021281421184539795,
0.043371982872486115,
0.07509303838014603,
-0.05820789933204651,
-0.01844300702214241,
0.04275882989168167,
0.006503882352262735,
0.011566328816115856,
0.03248196095228195,
0.002077703597024083,
0.038850609213113785,
-0.0060556563548743725,
0.01750290021300316,
-0.05415213853120804,
0.005504783242940903,
-0.008477922528982162,
-0.026540324091911316,
0.07580889761447906,
-0.04680850729346275,
-0.001667071832343936,
-0.05412713438272476,
0.025142818689346313
] |
<p>Suppose I would like to have maximally physical image format. Which quantities should I store in the pixel? Obviously, it should be frequency spectrum, i.e. table with frequency vs. WHAT?</p>
<p>How to convert RGB values to any sort of physical quantities and vise versa?</p> | g5483 | [
0.010727857239544392,
-0.0016902663046494126,
0.00032224159804172814,
-0.05023188889026642,
0.04128798097372055,
-0.01370502170175314,
-0.0315592959523201,
-0.0175496656447649,
-0.08374680578708649,
-0.01385420747101307,
0.0674685537815094,
-0.00286653614602983,
0.051096461713314056,
0.02288224548101425,
-0.00821224320679903,
0.02864936552941799,
0.009230826050043106,
-0.005689865443855524,
0.04151025041937828,
0.054824233055114746,
-0.017988862469792366,
0.004526912700384855,
-0.033603180199861526,
-0.01128375343978405,
-0.029132870957255363,
-0.00484941340982914,
0.07773786038160324,
0.04876743257045746,
-0.014452905394136906,
-0.012948073446750641,
0.006398661993443966,
-0.0011104440782219172,
-0.018123436719179153,
0.015146159566938877,
-0.02059643156826496,
-0.009377853944897652,
0.016871009021997452,
0.008633057586848736,
0.034364357590675354,
0.07168401032686234,
0.02032744511961937,
-0.0022783009335398674,
0.020534362643957138,
-0.001825045794248581,
-0.010588605888187885,
-0.01075405441224575,
-0.015488836914300919,
-0.02390868216753006,
-0.05054590851068497,
0.024075835943222046,
-0.07994434237480164,
0.04863917455077171,
-0.018697531893849373,
-0.00011429539881646633,
0.007622655015438795,
0.008634415455162525,
0.019584523513913155,
0.0033753325697034597,
0.00684595201164484,
0.014109980314970016,
0.023083962500095367,
-0.06685876101255417,
-0.03617378696799278,
-0.026292696595191956,
0.007530256174504757,
0.05987689271569252,
-0.05201737582683563,
-0.00617018761113286,
0.014857983216643333,
-0.004208169877529144,
0.024567238986492157,
0.02617538347840309,
0.08807690441608429,
-0.00004870577686233446,
-0.0006161268684081733,
-0.08393055945634842,
-0.009179585613310337,
-0.012417790479958057,
0.01604662463068962,
0.057511091232299805,
-0.009627701714634895,
-0.0005461173714138567,
0.09998339414596558,
-0.002718329196795821,
0.01808329112827778,
0.025592489168047905,
0.03847061097621918,
-0.002506702207028866,
-0.005306745879352093,
0.03364138305187225,
0.013490256853401661,
-0.023017197847366333,
0.08330356329679489,
0.02201579324901104,
0.00828114990144968,
-0.0009379854309372604,
0.00465818215161562,
0.08649032562971115,
-0.026141410693526268,
-0.000603720371145755,
0.03170961141586304,
0.005566646344959736,
0.03636610507965088,
-0.02216755971312523,
-0.024322962388396263,
-0.04348156601190567,
0.035437457263469696,
0.029001742601394653,
-0.05878080055117607,
-0.012342655099928379,
-0.04598233103752136,
-0.020817797631025314,
-0.023975806310772896,
-0.03574766591191292,
-0.002699663396924734,
0.017933262512087822,
0.035340916365385056,
0.004967073909938335,
0.00604161387309432,
0.06614436209201813,
0.05332862213253975,
-0.014963287860155106,
0.07777106016874313,
0.03802898898720741,
-0.004925501998513937,
-0.013762439601123333,
0.012662695720791817,
-0.016940098255872726,
0.026841821148991585,
0.007762530352920294,
0.05609496682882309,
-0.027682827785611153,
-0.015406045131385326,
-0.005453130230307579,
-0.04742167517542839,
0.03085341490805149,
0.04194742441177368,
0.013888572342693806,
0.009942618198692799,
-0.051980044692754745,
-0.04201803728938103,
-0.004447046667337418,
-0.05705465376377106,
0.006179281044751406,
0.0027711321599781513,
-0.04542157053947449,
-0.015916945412755013,
-0.007726049982011318,
0.052391715347766876,
0.0014096125960350037,
-0.014281006529927254,
0.04438290745019913,
-0.002476789290085435,
0.002588757313787937,
0.03471006453037262,
-0.03166436776518822,
0.06656316667795181,
0.04555754363536835,
-0.027292797341942787,
0.034923046827316284,
0.028677169233560562,
0.006305579096078873,
0.010133413597941399,
-0.0026680459268391132,
-0.007762019522488117,
-0.09210497885942459,
0.015218338929116726,
-0.08546629548072815,
-0.007298649754375219,
-0.0706573948264122,
0.022340046241879463,
0.03893493488430977,
-0.034664276987314224,
-0.022955402731895447,
0.037766147404909134,
0.023308785632252693,
0.012777443043887615,
0.030705539509654045,
0.05991934612393379,
-0.032746609300374985,
-0.03283991292119026,
-0.020025527104735374,
0.02295910380780697,
-0.0020166467875242233,
0.04063930734992027,
-0.07564540207386017,
-0.004641675390303135,
0.0038720208685845137,
-0.06194736808538437,
0.08574481308460236,
-0.006442319136112928,
0.021872403100132942,
0.017550943419337273,
0.040670741349458694,
-0.02201593667268753,
-0.05098903179168701,
-0.032120633870363235,
0.033494431525468826,
-0.05616172030568123,
0.014718614518642426,
0.05040339007973671,
-0.03493155911564827,
0.011629311367869377,
0.09170054644346237,
0.0072596375830471516,
-0.004861670080572367,
-0.05446958169341087,
-0.04611881822347641,
-0.043281786143779755,
0.00009066034544957802,
0.01978141814470291,
0.012473614886403084,
-0.03730187937617302,
0.0091072553768754,
0.02913578972220421,
0.04010195657610893,
-0.04548918083310127,
-0.06912539154291153,
0.012264231219887733,
0.0576193705201149,
-0.03916357085108757,
-0.052565641701221466,
0.003030908526852727,
-0.031062250956892967,
0.0375467911362648,
0.00704573467373848,
0.043073177337646484,
0.03520054742693901,
0.04667837172746658,
0.00792669877409935,
-0.048238519579172134,
0.02591615729033947,
0.009451931342482567,
0.04206661880016327,
-0.05423182621598244,
0.07126521319150925,
-0.08817407488822937,
0.07605990022420883,
-0.004108763299882412,
-0.03151426836848259,
0.0730309784412384,
0.04943240061402321,
0.0388699546456337,
0.011586806736886501,
-0.06841015815734863,
0.009759832173585892,
-0.023729829117655754,
-0.012924187816679478,
0.007459277752786875,
0.08413095772266388,
-0.03564845025539398,
-0.0305903572589159,
0.021129125729203224,
-0.002231704071164131,
-0.04803658276796341,
0.020753812044858932,
-0.00035488620051182806,
-0.001000730786472559,
-0.07330480962991714,
0.0028470808174461126,
-0.010649129748344421,
0.0071680848486721516,
-0.060553088784217834,
0.003201791550964117,
-0.027824364602565765,
0.030149267986416817,
-0.017429139465093613,
0.03882020339369774,
0.018241100013256073,
0.04021614044904709,
0.0347026064991951,
-0.017034556716680527,
0.0405186228454113,
-0.042064420878887177,
0.03688548877835274,
0.019466150552034378,
0.019756875932216644,
-0.002499024849385023,
0.040441278368234634,
-0.0032981294207274914,
0.03626548498868942,
-0.027167700231075287,
-0.049986571073532104,
-0.002647871384397149,
-0.011774956248700619,
-0.03322106972336769,
0.050320081412792206,
0.015624352730810642,
-0.03780939429998398,
0.05198929086327553,
-0.052174098789691925,
0.01613720878958702,
-0.016395436599850655,
-0.016822276636958122,
-0.061315733939409256,
-0.04634837433695793,
0.03855910524725914,
-0.01577656902372837,
0.09029713273048401,
0.03755524754524231,
-0.02993130497634411,
0.017103489488363266,
0.03904951363801956,
-0.0014824389945715666,
0.006253478582948446,
0.07445234805345535,
-0.032574981451034546,
0.005808279849588871,
0.004938765894621611,
-0.007729381322860718,
-0.023577777668833733,
-0.017975712195038795,
-0.03731217235326767,
0.018044477328658104,
-0.02547522448003292,
-0.03854317218065262,
0.027758896350860596,
-0.0008158156415447593,
-0.056664761155843735,
-0.046989455819129944,
-0.01896047778427601,
-0.040292512625455856,
0.029744474217295647,
-0.030365638434886932,
-0.007430793717503548,
0.021571537479758263,
-0.038270480930805206,
-0.0006634513847529888,
-0.010777934454381466,
0.01449671108275652,
-0.003801904618740082,
0.03893722966313362,
-0.052406005561351776,
0.016982408240437508,
-0.032904382795095444,
0.03368563950061798,
-0.015983954071998596,
-0.0350651741027832,
0.019841765984892845,
-0.050398409366607666,
0.023912321776151657,
-0.02252906560897827,
-0.04184733331203461,
-0.054999180138111115,
0.029896849766373634,
-0.028041454032063484,
-0.01364423893392086,
-0.009506721049547195,
0.011137500405311584,
-0.05263657867908478,
-0.019174307584762573,
-0.00985603965818882,
0.02013063244521618,
-0.035619329661130905,
0.021569881588220596,
0.05715728551149368,
-0.011850259266793728,
0.045930374413728714,
-0.02137628011405468,
-0.002778521040454507,
-0.007225609850138426,
-0.05338265374302864,
-0.003993541933596134,
-0.02652088925242424,
-0.04635873809456825,
0.031185351312160492,
-0.037006255239248276,
0.04787115380167961,
-0.04373461753129959,
-0.013388922438025475,
-0.04259748011827469,
-0.022769324481487274,
0.02173748053610325,
0.011791019700467587,
-0.037785161286592484,
-0.05799416825175285,
-0.006180877331644297,
-0.08488883823156357,
-0.004618732258677483,
0.03139382600784302,
-0.008980263024568558,
-0.02602224238216877,
0.036494676023721695,
-0.01652262918651104,
0.012947470881044865,
-0.06327114254236221,
-0.005362999625504017,
0.0515638142824173,
0.045501403510570526,
0.0017410889267921448,
0.017612427473068237,
-0.08842263370752335,
-0.03349444642663002,
-0.011300086043775082,
-0.02012455090880394,
-0.02958759106695652,
0.010076271370053291,
-0.016207385808229446,
-0.0031680564861744642,
0.045088279992341995,
0.010233955457806587,
-0.007652446161955595,
-0.03914711996912956,
0.02358289621770382,
-0.04308108612895012,
0.015458490699529648,
0.06980451941490173,
-0.05696733668446541,
0.027810586616396904,
0.008807064034044743,
-0.04650542885065079,
-0.05547100305557251,
0.04888731986284256,
-0.015389792621135712,
-0.0018962440080940723,
0.05526147410273552,
-0.008360784500837326,
-0.015399244613945484,
0.08425682038068771,
0.008215826004743576,
0.014886883087456226,
0.03944006562232971,
-0.00253391289152205,
-0.01568998582661152,
0.031098296865820885,
0.051819268614053726,
0.02576485276222229,
0.00751346442848444,
0.029687581583857536,
0.02246204949915409,
0.047663189470767975,
-0.009895914234220982,
0.049647919833660126,
0.05305013433098793,
-0.06307107210159302,
-0.011346187442541122,
-0.05002851039171219,
0.011687949299812317,
-0.008822415955364704,
-0.04405561462044716,
0.0016213388880714774,
-0.014057685621082783,
0.015940655022859573,
-0.011680882424116135,
-0.03440454229712486,
0.06940800696611404,
-0.012721654959022999,
-0.009046095423400402,
-0.06548737734556198,
-0.010653666220605373,
0.0190129391849041,
0.009053057059645653,
-0.0783323422074318,
-0.03894128277897835,
0.0018507079221308231,
0.020070068538188934,
-0.023496024310588837,
0.03163907304406166,
0.0781416967511177,
0.003269872162491083,
-0.007318039890378714,
0.03821422904729843,
-0.07512824982404709,
-0.015884490683674812,
-0.010465490631759167,
0.05297262594103813,
-0.07319176942110062,
-0.032423608005046844,
-0.028978992253541946,
-0.0267755426466465,
-0.0016815264243632555,
-0.08017507940530777,
0.06789152324199677,
0.009085147641599178,
0.07151079922914505,
0.019961971789598465,
-0.01656368188560009,
-0.039028458297252655,
-0.02795165777206421,
-0.053797900676727295,
-0.08858701586723328,
0.012139644473791122,
0.058678582310676575,
0.01852784864604473,
-0.014760746620595455,
0.05188285559415817,
-0.04381217807531357,
-0.021486032754182816,
0.02383902110159397,
0.011782522313296795,
-0.03662576898932457,
0.03429926186800003,
0.07303033769130707,
0.012853843159973621,
0.0422053262591362,
-0.026614172384142876,
0.019442414864897728,
-0.008704275824129581,
-0.05680515617132187,
0.03144598379731178,
0.002224598079919815,
-0.0050723012536764145,
0.012028397992253304,
0.020161110907793045,
0.04226420819759369,
-0.015181072056293488,
0.040756549686193466,
0.014024176634848118,
-0.013982800766825676,
0.00988723710179329,
0.03489468991756439,
-0.03821758180856705,
0.009085677564144135,
0.003952255006879568,
-0.0233810655772686,
-0.04901416599750519,
0.04638152942061424,
0.05173373967409134,
-0.017466461285948753,
-0.06965186446905136,
0.011278574354946613,
-0.04955073073506355,
0.04598734900355339,
0.0028499308973550797,
-0.02041737549006939,
0.00023739671451039612,
0.00740358280017972,
-0.02100016362965107,
0.09549950063228607,
-0.024068281054496765,
0.033459316939115524,
0.01755352132022381,
-0.05810951814055443,
-0.027605080977082253,
-0.058455388993024826,
-0.028200164437294006,
-0.026083864271640778,
0.028232574462890625,
0.021103795617818832,
0.02670520730316639,
-0.04073968529701233,
0.05270569026470184,
-0.023834984749555588,
0.016032112762331963,
-0.02174442447721958,
-0.046960700303316116,
-0.026401350274682045,
0.0024109664373099804,
-0.020291553810238838,
0.06351465731859207,
0.0222703255712986,
0.03875380754470825,
-0.003307702485471964,
-0.0054498896934092045,
0.051013413816690445,
-0.026683207601308823,
-0.0033240001648664474,
0.00746623519808054,
0.004670098889619112,
0.013414266519248486,
-0.0017886601854115725,
0.07167632132768631,
0.0009722687536850572,
0.04118628054857254,
-0.012729313224554062,
-0.017872361466288567,
0.05839688330888748,
-0.00023339971085079014,
0.06673643738031387,
0.02635890804231167,
-0.0655263215303421,
-0.030760949477553368,
0.05361273139715195,
0.00431018928065896,
-0.0036675564479082823,
-0.016204973682761192,
0.011221230030059814,
-0.02123137190937996,
0.03166070207953453,
0.00690906448289752,
-0.017244452610611916,
0.0006300116656348109,
-0.05551787093281746,
0.01982581615447998,
-0.051633499562740326,
0.006869764998555183,
-0.011488473042845726,
-0.013870966620743275,
-0.04012994095683098,
-0.05457910895347595,
-0.004401282407343388,
-0.01714337430894375,
0.01821674406528473,
0.006912834011018276,
0.03551493212580681,
-0.04663768410682678,
-0.038888268172740936,
-0.029476383700966835,
-0.004756041802465916,
-0.01903674192726612,
0.0024396092630922794,
0.025698883458971977,
0.06364331394433975,
-0.05053260922431946,
-0.05065653473138809,
-0.07271261513233185,
-0.020756011828780174,
-0.00021692416339647025,
-0.016380568966269493,
-0.009645778685808182,
-0.03821771964430809,
0.011018922552466393,
0.01051692757755518,
-0.007409927435219288,
0.025227408856153488,
0.02759888768196106,
0.06223991513252258,
0.015901582315564156,
0.006330219563096762,
0.0009540070313960314,
-0.024065334349870682,
-0.041949313133955,
-0.003740373533219099,
-0.06723709404468536,
0.06108858436346054,
0.01795932464301586,
0.014732121489942074,
0.08205878734588623,
0.07751038670539856,
-0.014751856215298176,
0.021464895457029343,
0.010448219254612923,
0.00876625720411539,
0.015031066723167896,
0.0028732384089380503,
0.039680980145931244,
-0.0697825625538826,
0.0017534311627969146,
0.04044642299413681,
0.017463495954871178,
0.035259075462818146,
0.03537464514374733,
0.05461111664772034,
-0.000014965278751333244,
-0.012739797122776508,
0.029704855754971504,
0.011369312182068825,
-0.028473656624555588,
-0.016902271658182144,
-0.03379455953836441,
0.020898383110761642,
-0.04939639940857887,
-0.031339142471551895,
0.016782451421022415,
-0.04976406693458557,
0.039084214717149734,
0.028993865475058556,
-0.0010869178222492337,
-0.00797185953706503,
0.0027551772072911263,
-0.036137353628873825,
-0.05232417210936546,
-0.0000868418428581208,
-0.0070488001219928265,
0.002785877324640751,
0.007246894296258688,
-0.01608499325811863,
-0.07074293494224548,
0.0372837595641613,
-0.06051533669233322,
-0.009389307349920273,
-0.004677676595747471,
-0.003645329736173153,
-0.01676223799586296,
0.03936483711004257,
-0.004877176135778427,
-0.039596013724803925,
0.02842818573117256,
-0.07429064065217972,
0.019645817577838898,
-0.005342309363186359,
0.035128749907016754,
0.023406008258461952,
-0.011074933223426342,
-0.024145586416125298,
-0.013176478445529938,
-0.07694267481565475,
0.0454004667699337,
0.051340289413928986,
-0.06979838758707047,
0.003591847838833928,
-0.019214319065213203,
-0.016162831336259842,
0.012633808888494968,
-0.027817759662866592,
-0.015960948541760445,
-0.07729988545179367,
0.006674263626337051,
0.0606469064950943,
0.02662770263850689,
0.032150764018297195,
-0.0143350875005126,
0.01141126174479723,
0.033753443509340286,
-0.0005270875990390778,
0.00112844945397228,
0.03189794346690178,
0.030735550448298454,
0.01561079639941454,
-0.026655539870262146,
-0.014082200825214386,
-0.0020377535838633776,
0.023579373955726624,
0.024425316601991653,
0.07548113167285919,
-0.0071273320354521275,
-0.00419207476079464,
-0.02432609722018242,
-0.03642687201499939,
-0.010991403833031654,
0.012136359699070454,
-0.01316281408071518,
-0.051026955246925354,
0.022566458210349083,
-0.013716175220906734,
0.020067615434527397,
0.0027067039627581835,
-0.02791205234825611,
0.015332892537117004,
-0.02998950704932213,
-0.03239309415221214,
-0.02016058750450611,
-0.004965031985193491,
0.058245182037353516,
0.00873525533825159,
0.03467083349823952,
-0.040545668452978134,
0.01615596003830433,
-0.010217932984232903,
0.021920742467045784,
-0.00776043813675642,
-0.0012488701613619924,
-0.04871911555528641,
0.018667573109269142,
-0.043268267065286636,
0.031847432255744934,
-0.0575510635972023,
0.012937239371240139,
0.03556220978498459,
-0.025304801762104034,
-0.06616339087486267,
0.01617354527115822,
0.02715425007045269,
0.06300543248653412,
0.02657516673207283,
-0.014836735092103481,
0.08166051656007767,
-0.04429664835333824,
0.10112624615430832,
-0.011617720127105713,
0.04335299879312515,
0.02385377511382103,
0.012464501895010471,
0.04225843772292137,
0.00007347012433456257,
-0.04724692553281784,
-0.0019515877356752753,
-0.02489691786468029
] |
<p>A charge is at rest in an inertial reference frame. </p>
<p>Consider this situation from the point of view of an observer who is accelerating relative to the charge. Would the observer observe electromagnetic waves generated by the charge?</p> | g5484 | [
0.035266268998384476,
0.01346793957054615,
0.029620999470353127,
0.016215132549405098,
0.0760481134057045,
0.033281486481428146,
0.031357575207948685,
0.027948904782533646,
-0.029281282797455788,
-0.007160239387303591,
0.0011557377874851227,
0.002517738612368703,
-0.009775056503713131,
0.012096734717488289,
0.00015100825112313032,
-0.012368951924145222,
0.10441804677248001,
-0.020693568512797356,
-0.055802974849939346,
-0.016717756167054176,
0.052152618765830994,
-0.0015400283737108111,
-0.005609577987343073,
-0.0023706613574177027,
-0.0338628776371479,
0.02617393061518669,
0.019968891516327858,
-0.014755676500499249,
-0.024407505989074707,
-0.03598720580339432,
0.036396510899066925,
0.014086896553635597,
-0.027752459049224854,
0.014412538148462772,
0.009088185615837574,
-0.040155958384275436,
0.027723990380764008,
0.10492368042469025,
-0.02308676578104496,
0.026715626940131187,
-0.003737999126315117,
-0.009247475303709507,
-0.0224279947578907,
-0.022928766906261444,
0.06962002068758011,
0.025586340576410294,
0.049018494784832,
0.05838907137513161,
0.0011506823357194662,
-0.04364094138145447,
-0.04062800854444504,
0.044545728713274,
0.011556653305888176,
0.018991658464074135,
0.02623841166496277,
0.06586891412734985,
-0.03405469283461571,
-0.030970288440585136,
0.050305698066949844,
0.04536527022719383,
-0.011970043182373047,
-0.05679033324122429,
0.004886923357844353,
-0.019934911280870438,
0.021110298112034798,
-0.02200232446193695,
-0.06270629912614822,
-0.01138710230588913,
-0.008608079515397549,
-0.016224125400185585,
0.01499964389950037,
-0.03145795688033104,
-0.11521712690591812,
0.009913820773363113,
-0.005698753520846367,
0.031911905854940414,
0.013232705183327198,
-0.026026194915175438,
-0.005043646786361933,
-0.014845463447272778,
-0.046764764934778214,
-0.013758937828242779,
0.05200045183300972,
0.03551504388451576,
0.07260735332965851,
-0.06341653317213058,
0.05217776447534561,
0.004238958936184645,
-0.00019701151177287102,
-0.03194168582558632,
0.043756306171417236,
0.02738320827484131,
0.09308885037899017,
-0.037929438054561615,
0.008975193835794926,
-0.035257626324892044,
-0.09404052048921585,
0.03097374364733696,
0.0696074590086937,
0.035292308777570724,
-0.05986867845058441,
-0.04785407707095146,
-0.005590136628597975,
-0.023144103586673737,
0.034215547144412994,
-0.016341809183359146,
-0.049510594457387924,
-0.004088376183062792,
0.0020152064971625805,
-0.05648099631071091,
0.04785450920462608,
-0.08991663157939911,
0.0014315209118649364,
-0.011455737054347992,
-0.0827781930565834,
-0.027148213237524033,
0.022382717579603195,
-0.018304813653230667,
-0.01751098409295082,
0.04996180534362793,
-0.011030561290681362,
0.004668384790420532,
-0.05118198320269585,
0.06774074584245682,
0.027319544926285744,
0.02957540936768055,
-0.06136399134993553,
-0.011060678400099277,
0.01604888215661049,
0.05079437419772148,
0.013813457451760769,
0.026990791782736778,
0.014967268332839012,
-0.040929533541202545,
-0.01188584417104721,
-0.0034733377397060394,
0.04351843148469925,
-0.028882799670100212,
0.014750921167433262,
-0.01299334317445755,
0.040859404951334,
-0.04775484651327133,
0.024568721652030945,
-0.04938248544931412,
-0.008177797310054302,
0.019405173137784004,
-0.01996171474456787,
-0.005595242604613304,
0.07689481228590012,
0.08428774029016495,
-0.04660974442958832,
0.04833157733082771,
0.0013243143912404776,
0.01207982748746872,
0.1001792624592781,
-0.010143937543034554,
0.03254343569278717,
-0.01054694689810276,
-0.014796029776334763,
-0.011665300466120243,
0.07316599786281586,
0.0201479010283947,
-0.025900887325406075,
0.003870151937007904,
-0.010405908338725567,
-0.05823805183172226,
0.019178980961441994,
-0.04199560359120369,
0.056611061096191406,
-0.07812245935201645,
-0.029611725360155106,
-0.01482564676553011,
0.03458715230226517,
0.017228608950972557,
0.034690726548433304,
0.059906117618083954,
-0.040296830236911774,
-0.020415659993886948,
0.05821726843714714,
-0.024503638967871666,
-0.05677642673254013,
-0.018095437437295914,
0.003107069991528988,
-0.026767628267407417,
0.008292566984891891,
0.00844363123178482,
-0.02937072515487671,
-0.02505006454885006,
-0.05228358879685402,
-0.006326852831989527,
0.011309634894132614,
-0.04696277529001236,
-0.06900734454393387,
0.04459059238433838,
-0.03224429488182068,
0.011715451255440712,
0.032142024487257004,
0.011320985853672028,
0.025345802307128906,
0.011489424854516983,
-0.021396448835730553,
0.058240167796611786,
-0.010018112137913704,
0.010359653271734715,
0.015631455928087234,
-0.04664212092757225,
-0.02455887198448181,
-0.07138396799564362,
-0.0136113865301013,
-0.004440230317413807,
0.034423090517520905,
0.017642898485064507,
0.01315268874168396,
0.02522404119372368,
-0.040587689727544785,
0.01127831544727087,
0.010145297273993492,
0.010890240781009197,
-0.027271244674921036,
0.06874432414770126,
-0.04540476202964783,
0.010710707865655422,
-0.004619303159415722,
-0.04347287863492966,
-0.02332371659576893,
-0.058024562895298004,
-0.059599488973617554,
-0.007874859496951103,
-0.010503197088837624,
-0.024439670145511627,
-0.002427127445116639,
0.07312143594026566,
-0.015825798735022545,
0.0028673517517745495,
0.05450017750263214,
0.07715695351362228,
-0.06258983165025711,
0.013033878058195114,
0.03275144100189209,
-0.07474646717309952,
-0.013495034538209438,
0.029462695121765137,
0.018886839970946312,
-0.04958631470799446,
-0.017936009913682938,
-0.015541777946054935,
0.04242477938532829,
0.06752536445856094,
0.01596946269273758,
-0.002713070949539542,
0.06159587204456329,
-0.013012089766561985,
0.014517745934426785,
-0.014085804112255573,
0.000060042195400455967,
-0.03722182288765907,
-0.030552096664905548,
0.03648047521710396,
-0.026708846911787987,
-0.026929961517453194,
0.007810926530510187,
-0.03292981907725334,
-0.030924860388040543,
-0.04267105460166931,
-0.06782255321741104,
0.011486143805086613,
0.016294585540890694,
0.028096459805965424,
-0.01668880507349968,
-0.009850820526480675,
-0.035955607891082764,
0.06845582276582718,
0.0128202298656106,
0.04159850999712944,
-0.024974990636110306,
0.013226604089140892,
0.0016401293687522411,
-0.046975214034318924,
0.02281540259718895,
-0.07310536503791809,
-0.046535689383745193,
-0.00802441593259573,
-0.03330032154917717,
0.04710695892572403,
0.011568011716008186,
-0.07778876274824142,
-0.012266281992197037,
-0.017623864114284515,
0.046309541910886765,
-0.00849092099815607,
-0.050728511065244675,
-0.006214230787009001,
0.03488382697105408,
-0.004061520099639893,
-0.00807498674839735,
0.009612057358026505,
0.017669912427663803,
-0.020170964300632477,
-0.010372019372880459,
0.04845130816102028,
0.012213516980409622,
-0.07047740370035172,
0.02917422540485859,
-0.01781993918120861,
0.04077174887061119,
0.009139728732407093,
0.00022205339337233454,
-0.00813780166208744,
0.02920285053551197,
0.008832652121782303,
-0.04858247935771942,
-0.012664826586842537,
-0.00894739106297493,
-0.034759726375341415,
-0.007232570089399815,
0.0014167793560773134,
-0.03787051886320114,
-0.06085300073027611,
-0.03809996694326401,
-0.017382198944687843,
0.0026319557800889015,
0.03342900797724724,
0.0014908346347510815,
-0.026123706251382828,
0.04651324450969696,
0.06879211962223053,
0.034476056694984436,
-0.013949540443718433,
-0.03315509110689163,
-0.03818579018115997,
-0.030573580414056778,
-0.017118407413363457,
0.0028545460663735867,
-0.029937831684947014,
0.06445354968309402,
-0.05851292610168457,
0.011386674828827381,
0.0603332445025444,
0.03276826813817024,
0.0030692219734191895,
0.05938638001680374,
0.05168593302369118,
-0.06327807903289795,
-0.05812293291091919,
0.029138078913092613,
-0.009129633195698261,
-0.03709592670202255,
-0.04746218025684357,
0.01832846738398075,
-0.056499265134334564,
0.027218502014875412,
-0.022987589240074158,
0.007153310347348452,
-0.03629051521420479,
-0.020460691303014755,
0.018305575475096703,
0.04687622934579849,
-0.03006691299378872,
-0.014451987110078335,
-0.038446128368377686,
-0.02344490773975849,
0.021628975868225098,
-0.0029199563432484865,
-0.03490162268280983,
0.024414807558059692,
0.032927826046943665,
-0.04456218332052231,
0.028291132301092148,
0.04721314460039139,
-0.047648970037698746,
0.004180395044386387,
-0.012419288977980614,
0.020605232566595078,
0.0032517805229872465,
-0.027313727885484695,
-0.018720006570219994,
0.03847312554717064,
-0.009723647497594357,
-0.011185931973159313,
0.0030687619000673294,
-0.024472802877426147,
0.010801238007843494,
-0.011568678542971611,
-0.05843527242541313,
0.035733018070459366,
0.015382837504148483,
0.021435009315609932,
0.013995668850839138,
0.006945128086954355,
-0.007523983251303434,
0.012198563665151596,
-0.04273350164294243,
-0.053043704479932785,
-0.0003935813729185611,
0.0000014379900221683783,
-0.029383251443505287,
0.023725830018520355,
-0.03702240437269211,
0.02911241538822651,
0.007004865445196629,
0.038488708436489105,
0.07190776616334915,
-0.012754443101584911,
0.008875813335180283,
-0.01518229953944683,
0.026895420625805855,
0.03573784977197647,
-0.0058771600015461445,
-0.05665140971541405,
-0.005663416348397732,
-0.05789672210812569,
-0.004778584465384483,
-0.011555451899766922,
-0.030229730531573296,
0.026561608538031578,
0.03577839210629463,
0.055238690227270126,
0.008338731713593006,
0.016076307743787766,
0.029167847707867622,
0.040569406002759933,
0.01936338096857071,
0.059913795441389084,
-0.026955312117934227,
-0.051201555877923965,
0.09870894998311996,
0.08381268382072449,
-0.03632892295718193,
-0.015577017329633236,
0.017182115465402603,
-0.04960810765624046,
-0.002672039670869708,
-0.0006050709052942693,
0.010832562111318111,
-0.0653117373585701,
-0.01923443377017975,
-0.0007484325906261802,
0.00699018407613039,
0.030428927391767502,
0.016445910558104515,
0.02224130742251873,
0.01766185648739338,
0.010128547437489033,
-0.061770960688591,
-0.015558815561234951,
0.09335849434137344,
0.041895635426044464,
-0.030374309048056602,
0.030919713899493217,
-0.002456564223393798,
-0.049781639128923416,
0.001372518832795322,
-0.06381895393133163,
-0.014136006124317646,
0.055606238543987274,
-0.04298514500260353,
-0.043342433869838715,
-0.048370666801929474,
-0.015290678478777409,
0.03349698334932327,
0.0014446014538407326,
-0.005362064577639103,
0.016968758776783943,
-0.0002357800112804398,
0.019898224622011185,
-0.019655892625451088,
-0.03133241459727287,
-0.04106452688574791,
-0.049776047468185425,
0.013375293463468552,
-0.010182023979723454,
0.015857189893722534,
-0.003507792018353939,
-0.002595936181023717,
-0.00017903326079249382,
0.0075228032656013966,
0.0264006108045578,
0.00680984603241086,
-0.0017073561903089285,
-0.03531702607870102,
-0.02293393760919571,
0.005507383029907942,
-0.015457229688763618,
-0.01770513877272606,
-0.0012679373612627387,
0.031116819009184837,
-0.004041313659399748,
0.039540596306324005,
-0.06667377799749374,
-0.07501546293497086,
0.03793040290474892,
-0.03140900656580925,
0.0011044961865991354,
-0.011898323893547058,
0.0018420742126181722,
0.059935327619314194,
-0.006703340448439121,
0.017491241917014122,
-0.005506687797605991,
0.017300952225923538,
-0.02821914665400982,
-0.046831268817186356,
-0.01593775488436222,
0.012292485684156418,
-0.04193144664168358,
0.030342981219291687,
0.020977528765797615,
-0.013866716995835304,
-0.0017313185380771756,
0.019520077854394913,
-0.02432718127965927,
0.07732182741165161,
-0.013706094585359097,
0.05862366780638695,
-0.0026404643431305885,
-0.022068394348025322,
-0.03911447525024414,
-0.016806814819574356,
-0.017260359600186348,
-0.03485060855746269,
0.07563230395317078,
-0.044345200061798096,
0.04352943226695061,
-0.011102396063506603,
-0.004769430961459875,
0.0033380426466464996,
0.025198262184858322,
0.00013519800268113613,
0.005350423511117697,
-0.011896575801074505,
0.033490270376205444,
-0.006301751360297203,
-0.016821876168251038,
-0.03306690603494644,
0.05185573548078537,
0.004761670716106892,
0.02421807497739792,
-0.024195153266191483,
-0.013317122124135494,
0.022952500730752945,
-0.043177057057619095,
-0.04543468356132507,
0.06383678317070007,
0.03903108090162277,
0.007289532106369734,
-0.034325215965509415,
-0.019160166382789612,
0.021181346848607063,
0.07193561643362045,
-0.062106840312480927,
-0.0469205267727375,
0.049108367413282394,
-0.012126880697906017,
0.022699957713484764,
0.01844862289726734,
0.03437335789203644,
-0.023712091147899628,
0.012667028233408928,
-0.05899655446410179,
-0.07823978364467621,
0.09763367474079132,
0.01574818603694439,
0.045450739562511444,
0.029518961906433105,
0.0027771370951086283,
0.012705346569418907,
0.006350216921418905,
-0.021830294281244278,
0.00628452654927969,
-0.002988192718476057,
-0.0025199302472174168,
-0.03742436319589615,
-0.0065789595246315,
-0.02884630300104618,
0.05432681366801262,
0.007223754655569792,
-0.010038566775619984,
0.048680443316698074,
-0.08479141443967819,
-0.0011519313557073474,
0.019123954698443413,
-0.000015033293493615929,
0.05998022109270096,
-0.00014848590944893658,
-0.0011687559308484197,
0.0019014071440324187,
0.01196221448481083,
0.014409366995096207,
0.018387826159596443,
-0.010912628844380379,
-0.028684252873063087,
-0.060306284576654434,
0.010073083452880383,
-0.009480959735810757,
-0.07650235295295715,
0.023392360657453537,
-0.014045597054064274,
-0.05224777013063431,
-0.015742750838398933,
0.07589392364025116,
0.04743007943034172,
-0.019114874303340912,
-0.02785821259021759,
0.0020556633826345205,
0.041984766721725464,
0.017897166311740875,
-0.01305204164236784,
0.01299485843628645,
0.017136910930275917,
-0.026189371943473816,
-0.04432394728064537,
-0.02460586465895176,
0.04475116357207298,
0.022029172629117966,
-0.011823338456451893,
0.03640159219503403,
-0.005234359297901392,
-0.01640928164124489,
-0.03139718994498253,
0.0029034800827503204,
0.046436529606580734,
-0.012693741358816624,
-0.037659283727407455,
0.022582953795790672,
0.014943540096282959,
0.0247469674795866,
-0.05201033875346184,
0.0294041745364666,
0.07704979181289673,
-0.019217930734157562,
0.001376535976305604,
0.05248238146305084,
-0.01302928477525711,
-0.005704034585505724,
0.05735619738698006,
-0.0009629111154936254,
0.09709098190069199,
-0.01513252779841423,
0.012037279084324837,
-0.011839600279927254,
0.021488774567842484,
0.039990074932575226,
-0.0010725654428824782,
-0.021241359412670135,
-0.08153925836086273,
-0.005675357300788164,
0.06354811787605286,
-0.026921626180410385,
-0.022632254287600517,
0.012109681032598019,
-0.04983730614185333,
-0.004065504763275385,
0.03835707902908325,
0.0013511449797078967,
-0.03698190301656723,
-0.013587097637355328,
0.033364567905664444,
-0.013138558715581894,
0.027529263868927956,
-0.05800555273890495,
-0.01574341394007206,
-0.008156927302479744,
-0.02579500339925289,
-0.028027301654219627,
-0.01944364421069622,
-0.03315374627709389,
-0.04290030524134636,
-0.11062484234571457,
-0.0823979377746582,
0.0439847931265831,
0.0010002435883507133,
-0.06958773732185364,
0.016445353627204895,
0.02161746844649315,
0.018805500119924545,
0.009479538537561893,
-0.03375885635614395,
0.025319494307041168,
-0.004762642551213503,
0.0035849043633788824,
-0.022893665358424187,
0.04106856510043144,
0.026987716555595398,
0.012437868863344193,
0.02699151448905468,
0.0032221756409853697,
0.028863022103905678,
-0.06210103631019592,
0.016075467690825462,
-0.04632954299449921,
-0.04120729863643646,
0.0413074865937233,
0.05880235508084297,
-0.004801973234862089,
-0.027818411588668823,
0.007044357713311911,
0.05755290016531944,
0.03190145641565323,
0.0021156577859073877,
-0.011595037765800953,
0.00786193460226059,
0.028779679909348488,
0.07095924764871597,
0.012717928737401962,
0.023242199793457985,
-0.03071730025112629,
0.0018092031823471189,
-0.08510962873697281,
-0.016655992716550827,
0.03859667852520943,
0.05180663615465164,
0.03304031491279602,
-0.00902702659368515,
0.006103808991611004,
0.02793656289577484,
-0.008401313796639442,
-0.040070150047540665,
0.03975417837500572,
0.05431264266371727,
0.025768663734197617,
0.005134011618793011,
0.03556918352842331,
0.04552266746759415,
0.015100275166332722,
0.05790669843554497,
-0.002467229263857007,
0.022859178483486176,
0.03538111224770546,
0.017407801002264023,
-0.06244082748889923,
-0.008928870782256126,
0.025002023205161095,
-0.035459235310554504,
0.02294345386326313,
0.008855554275214672,
-0.0034324536100029945,
0.005030942615121603,
-0.011340780183672905,
0.024542996659874916,
0.002853123238310218,
0.02880040742456913,
-0.04856743663549423,
-0.012945740483701229,
-0.06024112552404404,
0.017524508759379387,
0.02372855879366398,
0.04974515736103058,
-0.012755549512803555,
0.03123699128627777,
-0.014774804003536701,
0.022641729563474655,
-0.004160391632467508,
-0.06035701930522919,
0.011413772590458393,
0.08306838572025299,
-0.0331200510263443,
-0.00023346635862253606,
-0.0036892849020659924,
-0.025407390668988228,
0.038355518132448196,
-0.010771743021905422,
0.004821880254894495,
-0.022226205095648766,
-0.03326297551393509,
-0.025722946971654892,
-0.056747693568468094,
-0.014066905714571476,
0.021301250904798508
] |
<p>I found this explanation somewhere:
Since wavelength=c/freq so in a AC power line of 50 Hz, wavelength=(3*10^8)/50 = 6000 Km, so voltage phase reverses after 6000 Km in a ac Power line.</p>
<p>Now this would have been correct if it was a 50 Hz E.M. Transmission line, but does the same occur in metal wire with A.C. ? Clearly the power transmission through the wire would not be through E.M. waves. I am also confused if a wave phenomenon does occur in a AC wire or not. If it occurs then how (in terms of flow of electrons) and at what speed/wavelength ?</p> | g5485 | [
0.10899718850851059,
-0.00019986517145298421,
-0.002310893964022398,
-0.0059257387183606625,
0.09424080699682236,
0.0010093461023643613,
-0.010237980633974075,
0.003471979172900319,
-0.04847678542137146,
0.016398200765252113,
0.03464782238006592,
0.046049077063798904,
-0.02224651351571083,
0.004569403361529112,
0.021975720301270485,
-0.03551756218075752,
0.029537800699472427,
-0.033967189490795135,
0.049328092485666275,
0.049861181527376175,
0.01152985543012619,
-0.004983966238796711,
-0.025239555165171623,
-0.03160529211163521,
-0.0049812523648142815,
0.03872662037611008,
0.004097937140613794,
-0.057159990072250366,
-0.032664548605680466,
-0.0504206083714962,
0.02052329108119011,
-0.014634753577411175,
0.06924423575401306,
-0.03703860938549042,
-0.07181736081838608,
0.026463132351636887,
0.020952288061380386,
0.0012578339083120227,
0.008514822460711002,
0.03639478608965874,
0.019359739497303963,
0.009536098688840866,
0.06982582062482834,
0.028659762814641,
0.04115506634116173,
-0.033808544278144836,
-0.06641346961259842,
0.00330214761197567,
-0.042684659361839294,
-0.044324543327093124,
-0.016676900908350945,
0.0027104890905320644,
0.03844382241368294,
0.045759499073028564,
-0.026848485693335533,
0.0005919469404034317,
0.029518386349081993,
-0.021060332655906677,
0.03868311643600464,
0.03194847330451012,
0.022441014647483826,
0.022218996658921242,
0.03504595160484314,
0.014678246341645718,
-0.011703141033649445,
0.01327875442802906,
-0.026943325996398926,
-0.05368959158658981,
0.020185722038149834,
0.006190564949065447,
-0.015692327171564102,
-0.07728035002946854,
-0.01872306689620018,
-0.03233308345079422,
0.05705632269382477,
-0.009192043915390968,
0.027140634134411812,
-0.003439749125391245,
0.022125789895653725,
-0.000844719703309238,
-0.05329090356826782,
0.0014683700865134597,
-0.03633231297135353,
0.09304359555244446,
0.026992356404662132,
0.0004851866397075355,
0.02656273916363716,
0.0020564147271215916,
0.004173074383288622,
-0.005701570305973291,
0.008175184950232506,
0.003387095406651497,
0.043785713613033295,
-0.002228605793789029,
-0.03196851164102554,
-0.017693495377898216,
-0.033471010625362396,
0.04161582514643669,
-0.004052836913615465,
0.015295005403459072,
-0.06621497869491577,
-0.05344902351498604,
0.002042364561930299,
-0.0034053700510412455,
-0.047289565205574036,
0.010067084804177284,
0.014332269318401814,
-0.007792563643306494,
0.002996213501319289,
0.036158569157123566,
-0.024398913607001305,
-0.07521600276231766,
-0.04724346846342087,
0.0446975938975811,
-0.04125070944428444,
-0.011024141684174538,
-0.0034155738539993763,
0.036232225596904755,
0.009306631982326508,
0.017083579674363136,
0.017207935452461243,
-0.002134443260729313,
0.008655906654894352,
-0.026435375213623047,
-0.03534771874547005,
0.022935617715120316,
0.013752099126577377,
0.0065394858829677105,
0.08307220041751862,
0.04159821197390556,
-0.010021098889410496,
0.04733561724424362,
-0.04604968801140785,
0.021822050213813782,
0.02943061850965023,
-0.04006921499967575,
0.05444946140050888,
-0.027813099324703217,
0.01788971573114395,
0.0091044707223773,
0.025018319487571716,
-0.08508481085300446,
0.08618839830160141,
-0.04978200048208237,
-0.04440174624323845,
0.03602141514420509,
-0.02429772913455963,
-0.019179651513695717,
0.0784699097275734,
-0.03430280461907387,
0.0072230505757033825,
0.06904322654008865,
-0.012721454724669456,
-0.014720001257956028,
0.00603060144931078,
0.005460863932967186,
-0.012870695441961288,
-0.044244688004255295,
-0.007752806413918734,
-0.01875239424407482,
0.012730238027870655,
0.0015299798687919974,
-0.022097233682870865,
0.017719805240631104,
0.016262827441096306,
-0.025241252034902573,
-0.042176127433776855,
-0.0018943444592878222,
0.020581770688295364,
-0.044318363070487976,
-0.06580453366041183,
0.007448932621628046,
-0.0007948726415634155,
0.07052487134933472,
0.04006724804639816,
0.007965545170009136,
0.05526897311210632,
0.004411950241774321,
0.04535621777176857,
-0.03212137892842293,
-0.04556136950850487,
-0.03234940394759178,
-0.002689155749976635,
-0.008086426183581352,
0.038748469203710556,
0.0005754523444920778,
-0.010331721976399422,
-0.005659433081746101,
-0.06927715241909027,
0.02844175510108471,
-0.029306750744581223,
0.019075686112046242,
-0.06882860511541367,
0.013687015511095524,
0.0021991743706166744,
-0.021174494177103043,
-0.03383030369877815,
0.0012212656438350677,
-0.025543181225657463,
0.02560533955693245,
0.09169933199882507,
0.0058208368718624115,
0.01782042346894741,
-0.015231763944029808,
0.030889781191945076,
0.027956536039710045,
-0.07087665796279907,
-0.0365639366209507,
0.0560896098613739,
0.014739331789314747,
0.035537008196115494,
0.02050855942070484,
-0.013556187972426414,
0.0029668668285012245,
-0.03823457658290863,
0.0368562750518322,
-0.004711447283625603,
0.01986459270119667,
-0.035393234342336655,
0.032315995544195175,
0.01420609187334776,
-0.02115556038916111,
0.0021980106830596924,
-0.006945093162357807,
-0.047757383435964584,
0.022949613630771637,
-0.052556637674570084,
-0.05869756639003754,
-0.022344470024108887,
-0.03995649516582489,
-0.020551882684230804,
0.04232015833258629,
-0.01761723682284355,
-0.06837353110313416,
-0.008349934592843056,
0.010027618147432804,
0.028887221589684486,
-0.01824062503874302,
0.017870888113975525,
-0.04244128242135048,
-0.0003912287938874215,
-0.0270267054438591,
-0.02075406163930893,
-0.010270087979733944,
0.016325879842042923,
0.010638154111802578,
0.0008936097729019821,
0.01823841594159603,
-0.01841665804386139,
-0.02249869331717491,
0.07694564759731293,
-0.00036302386433817446,
0.012656557373702526,
0.06393527239561081,
-0.011385426856577396,
-0.039504650980234146,
0.00017330086848232895,
0.10978768020868301,
-0.049615222960710526,
-0.004056990146636963,
-0.014768796041607857,
0.009220840409398079,
0.01073781680315733,
-0.03303425759077072,
-0.002925512148067355,
0.00476907379925251,
0.005106236785650253,
0.01932526007294655,
-0.00902186706662178,
-0.01709279604256153,
-0.014820600859820843,
0.06634514778852463,
-0.0726470798254013,
-0.02400616742670536,
-0.019554361701011658,
-0.07939331978559494,
0.08065234869718552,
-0.06812704354524612,
0.06411749124526978,
-0.020123470574617386,
-0.039024483412504196,
-0.02435293421149254,
0.015937425196170807,
0.03450066223740578,
-0.0040404582396149635,
-0.065635085105896,
-0.007575805298984051,
0.005042294971644878,
0.017876209691166878,
0.05649810656905174,
-0.03249194845557213,
-0.009396843612194061,
0.01041635312139988,
0.007507846690714359,
0.005142375361174345,
0.03637704625725746,
0.0704101175069809,
-0.039481379091739655,
-0.060318827629089355,
-0.021443979814648628,
-0.011513740755617619,
-0.04705077037215233,
-0.05526598542928696,
-0.005479109473526478,
0.03021089918911457,
0.00012845209857914597,
0.01347355917096138,
-0.04340995103120804,
0.06644809246063232,
0.0009438027045689523,
0.00452893553301692,
0.02126685343682766,
0.013501888141036034,
-0.06341687589883804,
-0.056941863149404526,
0.00734831765294075,
0.006716087460517883,
-0.007823540829122066,
0.016221998259425163,
0.012060659006237984,
-0.03677040711045265,
-0.04519451782107353,
0.018727151677012444,
-0.0031203636899590492,
-0.014903785660862923,
0.026304073631763458,
0.028216613456606865,
0.09714527428150177,
-0.04812544584274292,
-0.03163541480898857,
-0.07627991586923599,
-0.015015605837106705,
-0.019068937748670578,
-0.06655261665582657,
0.020121963694691658,
-0.016802571713924408,
-0.006804682780057192,
0.09727417677640915,
-0.008272294886410236,
0.054189860820770264,
0.01612149178981781,
0.00998962577432394,
-0.008725866675376892,
0.00762123754248023,
0.024465711787343025,
0.06730971485376358,
-0.006292751524597406,
-0.016779299825429916,
-0.01581811159849167,
0.0025864620693027973,
0.060144588351249695,
-0.02297183871269226,
0.05563223361968994,
-0.05917198583483696,
-0.03229158744215965,
0.01486098300665617,
0.01727401837706566,
-0.0032295347191393375,
0.035139430314302444,
-0.03884604573249817,
0.033197399228811264,
-0.024717187508940697,
0.052510667592287064,
-0.0283647533506155,
-0.00637426320463419,
0.01438888069242239,
0.018454859033226967,
0.05729135125875473,
0.01291636098176241,
-0.06619065999984741,
-0.003637158079072833,
-0.06055745482444763,
-0.0009554850403219461,
-0.009423908777534962,
0.019579477608203888,
-0.0303029827773571,
0.011547388508915901,
0.038538429886102676,
-0.039539676159620285,
0.05998668447136879,
-0.018498286604881287,
-0.024949021637439728,
-0.026699010282754898,
-0.049227025359869,
0.0006312968325801194,
-0.0006293659680522978,
-0.01507798582315445,
0.010614989325404167,
-0.058173540979623795,
-0.06521070748567581,
-0.03968709707260132,
0.009075254201889038,
0.038618043065071106,
0.0053472984582185745,
-0.04604170098900795,
0.011338750831782818,
-0.011442732065916061,
-0.01682940684258938,
0.01686824858188629,
0.019829533994197845,
-0.016532691195607185,
0.01692558079957962,
-0.00551672512665391,
0.05572904646396637,
0.02663874253630638,
0.0031401729211211205,
0.04640697315335274,
-0.08211115747690201,
0.0026810462586581707,
0.00006677604687865824,
-0.03880976140499115,
0.0034415745176374912,
-0.0339227095246315,
-0.09290852397680283,
-0.00913916528224945,
0.02239171788096428,
0.04837741330265999,
-0.0023156884126365185,
0.04788302630186081,
0.027387965470552444,
0.020379727706313133,
0.03938274830579758,
0.036174532026052475,
0.06300734728574753,
-0.00442185765132308,
0.01664038747549057,
0.028405431658029556,
0.0008626431226730347,
-0.0158698633313179,
0.0324009470641613,
-0.019406579434871674,
-0.009280006401240826,
-0.05884780362248421,
-0.05105806142091751,
-0.0383133664727211,
0.05416277423501015,
0.0029484231490641832,
0.024293484166264534,
0.03540099039673805,
0.045397158712148666,
0.08293027430772781,
-0.011624506674706936,
-0.00003191843279637396,
-0.02934110350906849,
-0.040497615933418274,
0.006665172521024942,
-0.023804914206266403,
-0.01728787086904049,
-0.01202515047043562,
-0.037047721445560455,
0.007869251072406769,
0.041599780321121216,
-0.0511539950966835,
-0.05169370025396347,
-0.010955939069390297,
-0.04815227910876274,
-0.02819015644490719,
0.003550928784534335,
0.03446543589234352,
-0.026190243661403656,
-0.03272407501935959,
0.04087800160050392,
-0.053687259554862976,
-0.003686877666041255,
-0.00027688161935657263,
0.023146620020270348,
0.04708254337310791,
-0.036749280989170074,
-0.06979893893003464,
0.014179619960486889,
-0.030288485810160637,
-0.009531120769679546,
0.007393603678792715,
0.04710845649242401,
0.06624617427587509,
0.025570789352059364,
0.010287158191204071,
0.005549626424908638,
-0.050797540694475174,
-0.004141038283705711,
-0.01880878582596779,
-0.017433777451515198,
0.0031542566139250994,
0.014330985955893993,
-0.037449371069669724,
0.005019931588321924,
-0.015399973839521408,
0.10788702219724655,
0.011024599894881248,
-0.056661419570446014,
-0.006290363147854805,
0.012484955601394176,
-0.03424816206097603,
0.0017156857065856457,
-0.018213216215372086,
-0.00048061361303552985,
-0.01138029433786869,
0.01945497840642929,
0.00457985233515501,
-0.03043370135128498,
-0.035637225955724716,
-0.003199765458703041,
0.004585165064781904,
-0.0296834334731102,
-0.03456142544746399,
0.05013183876872063,
0.03467379882931709,
0.030549924820661545,
-0.026604488492012024,
-0.0018904682947322726,
-0.007491506636142731,
-0.0254671610891819,
0.01376858539879322,
0.05662562698125839,
0.09930527210235596,
-0.05457565560936928,
-0.0898505449295044,
-0.01718529872596264,
-0.029051896184682846,
0.01006834115833044,
0.000353476993041113,
-0.006754097528755665,
-0.02024650201201439,
0.022564057260751724,
-0.029778681695461273,
0.03661399707198143,
-0.034864261746406555,
0.029797609895467758,
0.08422329276800156,
0.009881565347313881,
-0.028466667979955673,
0.05681116133928299,
0.045983318239450455,
-0.037683822214603424,
-0.0021754298359155655,
-0.006633533630520105,
0.045459091663360596,
-0.051705215126276016,
-0.0014529101317748427,
0.03505178913474083,
0.010966879315674305,
-0.029207929968833923,
0.01559868548065424,
0.06232582405209541,
0.011789955198764801,
-0.005063438322395086,
0.03312261775135994,
-0.05365312099456787,
0.02344677969813347,
-0.015250511467456818,
0.04508693516254425,
0.018605081364512444,
-0.024175509810447693,
0.039143215864896774,
-0.0413079634308815,
0.05019819363951683,
0.042991962283849716,
-0.007655251305550337,
-0.006284965667873621,
-0.06368447095155716,
0.09084951132535934,
0.05559784173965454,
0.023303132504224777,
-0.011886600404977798,
0.013315623626112938,
-0.025584347546100616,
0.010872541926801205,
0.09629689157009125,
0.06599140912294388,
0.07033046334981918,
0.03196500986814499,
-0.02244945988059044,
-0.034266259521245956,
-0.02754584699869156,
0.03609367087483406,
0.023465722799301147,
-0.015032006427645683,
-0.06099535524845123,
-0.013044442981481552,
-0.051746468991041183,
0.029510080814361572,
-0.016037816181778908,
-0.00804463867098093,
0.04138309508562088,
-0.030947184190154076,
-0.05953406170010567,
0.02528868056833744,
0.03431218862533569,
0.10931745916604996,
0.019122280180454254,
-0.020230988040566444,
0.018894437700510025,
0.01827828586101532,
0.010506191290915012,
0.030002649873495102,
-0.0010788593208417296,
0.01432704459875822,
0.0077473754063248634,
0.03208358213305473,
0.06468504667282104,
0.00842781737446785,
0.02894388884305954,
0.008547747507691383,
-0.0021284965332597494,
0.03904490917921066,
0.005681909155100584,
0.04522314667701721,
0.023606663569808006,
-0.024041438475251198,
0.04817487671971321,
0.054167669266462326,
-0.009371253661811352,
0.015115807764232159,
-0.012882230803370476,
-0.025311768054962158,
0.022723523899912834,
-0.04256900027394295,
-0.008584332652390003,
-0.03972594439983368,
0.029114659875631332,
0.0012030390789732337,
0.0034435621928423643,
-0.03350865840911865,
0.05040106922388077,
0.012952855788171291,
0.009021926671266556,
-0.0162978395819664,
0.02636951208114624,
0.09519720077514648,
-0.02999439463019371,
-0.00898273941129446,
-0.0023920023813843727,
-0.03796713054180145,
0.005438728723675013,
0.00799238495528698,
-0.015355625189840794,
0.004144249949604273,
-0.01557617075741291,
0.07821240276098251,
-0.03419627621769905,
0.011618931777775288,
0.06195025518536568,
-0.04164450988173485,
0.0245309229940176,
-0.034524593502283096,
-0.017182933166623116,
0.03509550541639328,
-0.008480105549097061,
-0.04951132833957672,
-0.01860234886407852,
-0.01219046302139759,
-0.018584903329610825,
-0.05121272802352905,
0.03964439034461975,
0.009371149353682995,
0.013026098720729351,
-0.0060752215795218945,
0.04807816445827484,
0.010811294429004192,
-0.04297172278165817,
-0.041197601705789566,
-0.0042379479855299,
0.015503446571528912,
0.04519040882587433,
0.05625798553228378,
-0.01658332161605358,
-0.008567878045141697,
-0.07946566492319107,
-0.027694331482052803,
-0.005074294749647379,
-0.006273084320127964,
-0.046033959835767746,
0.04800775647163391,
-0.023014789447188377,
-0.009563745930790901,
-0.008560892194509506,
-0.04916839301586151,
0.011649956926703453,
0.015088570304214954,
0.015873214229941368,
-0.016890855506062508,
0.030340760946273804,
-0.0032476531341671944,
-0.06615032255649567,
0.011061769910156727,
-0.003413585713133216,
-0.05983292683959007,
0.04185812920331955,
-0.04963846877217293,
-0.04196390509605408,
-0.028547877445816994,
-0.05426757410168648,
-0.005250969436019659,
-0.024594774469733238,
0.05461496114730835,
0.02640562318265438,
0.025188080966472626,
0.03106296807527542,
-0.005218645092099905,
-0.017275476828217506,
0.012217944487929344,
0.03408762067556381,
-0.01807643659412861,
0.03979010507464409,
0.0021628495305776596,
-0.0026699977461248636,
-0.02215835638344288,
-0.03529025986790657,
-0.051782093942165375,
0.03271211311221123,
-0.022806711494922638,
0.040987808257341385,
-0.0036170778330415487,
0.015030305832624435,
0.05704956129193306,
-0.02888859622180462,
-0.04080844670534134,
-0.017749080434441566,
-0.00003276898496551439,
-0.022101230919361115,
-0.03260656073689461,
-0.007751080673187971,
0.04153146967291832,
-0.0452711321413517,
-0.013752119615674019,
0.00041840545600280166,
0.0068491073325276375,
0.0005657516303472221,
-0.01867719180881977,
-0.05986080318689346,
0.008050215430557728,
0.004682326223701239,
0.005034244619309902,
-0.08059029281139374,
-0.003936157561838627,
-0.005112926010042429,
0.005488126538693905,
0.028307801112532616,
-0.0017168308841064572,
-0.015688110142946243,
0.12192085385322571,
0.05655189976096153,
-0.012162288650870323,
0.005856850650161505,
0.0035749967209994793,
-0.0066032432951033115,
-0.023306509479880333,
0.014657271094620228,
0.0006053923862054944,
-0.08700840920209885,
0.02400539256632328,
0.010336928069591522,
-0.0770162045955658,
0.004859809298068285,
-0.01995004154741764,
0.00246041058562696,
0.0047949557192623615,
0.008689289912581444,
-0.06957248598337173,
-0.035906970500946045,
-0.0449051596224308,
-0.024112265557050705,
-0.02428669109940529,
0.017015621066093445,
0.019229058176279068,
-0.0370020754635334,
-0.0426408089697361,
-0.029715806245803833
] |
<p>Suppose we have a capacitor of capacitance $C$ and a cell of emf $E$, why is the maximum energy stored in a capacitor equal to $\tfrac{1}{2}CE^2$? I feel confused because, the potential difference against the capacitor will be less than the emf of the cell because of the potential drop across the resistor. What is the flaw in my thinking?</p> | g5486 | [
0.043363306671381,
0.014650270342826843,
-0.012072023935616016,
0.019632333889603615,
0.07213008403778076,
0.003613451961427927,
0.04704562947154045,
0.0198593121021986,
-0.061749447137117386,
-0.02371840737760067,
-0.029330909252166748,
0.000016046893506427296,
0.02462487481534481,
0.00894009880721569,
0.03920998424291611,
0.028542425483465195,
0.10286824405193329,
-0.01970573328435421,
-0.009577191434800625,
0.03307507932186127,
-0.05183396860957146,
-0.03749079629778862,
-0.006501760799437761,
0.011930218897759914,
-0.010336628183722496,
0.019626356661319733,
0.03286341205239296,
-0.019382966682314873,
-0.10292286425828934,
0.01162159163504839,
0.01618386059999466,
0.024003250524401665,
0.06471740454435349,
-0.01264193095266819,
-0.026319844648241997,
-0.021410813555121422,
0.06373388320207596,
0.06307704746723175,
0.04211646690964699,
-0.0023223047610372305,
0.012140142731368542,
0.02863507717847824,
0.030002037063241005,
-0.002004925161600113,
-0.008150911889970303,
-0.04350123926997185,
-0.018147310242056847,
-0.021674130111932755,
-0.040379561483860016,
-0.07584122568368912,
-0.0014792145229876041,
-0.00412380788475275,
0.04114918038249016,
0.03383374959230423,
0.04865122586488724,
-0.039039384573698044,
0.005397092085331678,
0.025964096188545227,
0.039013855159282684,
0.022606337442994118,
0.04874700307846069,
0.02591833844780922,
-0.052935246378183365,
0.03526885062456131,
-0.0013025671942159534,
0.004937624558806419,
-0.011323239654302597,
0.03976229205727577,
0.025290418416261673,
-0.02309156395494938,
0.03299655020236969,
-0.046052832156419754,
-0.01809488981962204,
-0.033218078315258026,
0.04042613506317139,
-0.03587184101343155,
0.0356287956237793,
-0.039626628160476685,
0.01595444045960903,
-0.061158858239650726,
-0.00015284134133253247,
-0.02666311152279377,
0.043516386300325394,
0.006153170485049486,
0.07132688164710999,
0.050628311932086945,
0.014120831154286861,
0.07214289158582687,
-0.052403975278139114,
0.05778003856539726,
-0.01126536913216114,
-0.05265715718269348,
0.07369821518659592,
-0.012639003805816174,
0.014589929021894932,
0.018052736297249794,
0.011200358159840107,
0.001155039295554161,
-0.011689899489283562,
0.01692277006804943,
0.01584375649690628,
-0.017078951001167297,
0.023228714242577553,
0.01622416451573372,
-0.012119571678340435,
0.0257414523512125,
0.062378957867622375,
-0.020870117470622063,
0.003274607239291072,
-0.03282492235302925,
0.00651509128510952,
-0.037375930696725845,
-0.03473588451743126,
-0.017631184309720993,
-0.03856964036822319,
0.02114010602235794,
0.05045139417052269,
-0.0494137778878212,
0.007175895851105452,
0.0344151109457016,
-0.010349566116929054,
0.068047434091568,
0.0075317258015275,
0.05269349366426468,
0.015440475195646286,
0.058216214179992676,
0.055967509746551514,
0.010638847015798092,
0.0539192333817482,
-0.00039956060936674476,
0.03228351101279259,
-0.02029101364314556,
-0.009796260856091976,
-0.04150819405913353,
0.028592146933078766,
0.034382179379463196,
-0.03923078998923302,
0.014554084278643131,
-0.0062145995907485485,
-0.010289041325449944,
-0.010069641284644604,
-0.00666916836053133,
0.031298037618398666,
-0.005343599710613489,
-0.0286279134452343,
-0.004942204803228378,
-0.02270713821053505,
0.01104688923805952,
0.007408669218420982,
0.010255502536892891,
0.06493213027715683,
0.025841951370239258,
-0.03934868052601814,
-0.03722596913576126,
0.05027148127555847,
0.017639394849538803,
0.05113108083605766,
0.00025531850405968726,
-0.024668950587511063,
0.048244934529066086,
0.04234791919589043,
0.05835041403770447,
0.032329630106687546,
-0.007326027844101191,
-0.07513880729675293,
-0.0030404054559767246,
-0.0031201899982988834,
0.0021324942354112864,
-0.005786202847957611,
-0.038716211915016174,
-0.00533552560955286,
-0.050130054354667664,
0.04153253883123398,
0.015911346301436424,
0.0005192175158299506,
0.05894169583916664,
0.0437033586204052,
0.018519779667258263,
0.03762275353074074,
0.012672157026827335,
-0.024094708263874054,
0.012769002467393875,
0.0194228645414114,
-0.033705320209264755,
0.02225407026708126,
0.031276553869247437,
-0.02066170796751976,
0.048168446868658066,
-0.04526229202747345,
0.011894427239894867,
-0.060489457100629807,
-0.0052389297634363174,
-0.029401026666164398,
0.06793440878391266,
-0.03311208263039589,
0.025418799370527267,
0.020258715376257896,
-0.044610392302274704,
-0.022163212299346924,
-0.013480406254529953,
-0.009685610421001911,
0.005249052308499813,
0.05842382833361626,
0.021082738414406776,
0.02715439908206463,
0.001345513854175806,
-0.004769823048263788,
-0.02224772237241268,
0.07168736308813095,
-0.03595602139830589,
-0.0354447066783905,
0.018646201118826866,
-0.038832295686006546,
0.01705777831375599,
0.01426409836858511,
-0.030986320227384567,
0.012235136702656746,
-0.0018774190684780478,
-0.07244735211133957,
0.018818847835063934,
-0.039114926010370255,
-0.032157376408576965,
0.03394952043890953,
-0.004465038888156414,
-0.04939848929643631,
0.004209556616842747,
-0.03402869030833244,
-0.016440795734524727,
-0.04958684742450714,
-0.005573099013417959,
-0.07187880575656891,
0.06568208336830139,
-0.0034362541045993567,
0.003419665852561593,
-0.043635014444589615,
0.01347113773226738,
-0.020199058577418327,
0.017663322389125824,
-0.016754934564232826,
-0.050647154450416565,
0.005349435843527317,
-0.04143115133047104,
-0.01379311177879572,
0.01971639133989811,
-0.02101672627031803,
-0.035768527537584305,
0.005669168196618557,
-0.005875010974705219,
-0.014007204212248325,
0.0014632121892645955,
0.018533771857619286,
-0.013501682318747044,
-0.06279576569795609,
0.0004326554189901799,
0.03004813939332962,
-0.05299775302410126,
-0.04244185984134674,
0.0031607686541974545,
-0.04695960506796837,
-0.01804358884692192,
-0.006117551121860743,
0.03900613635778427,
-0.015404836274683475,
0.02845066599547863,
-0.049940261989831924,
0.05253829434514046,
-0.059411000460386276,
-0.013806076720356941,
0.006590364500880241,
-0.015278433449566364,
-0.03268597647547722,
0.08378573507070541,
-0.01042009238153696,
-0.004643636755645275,
-0.006381232291460037,
-0.042358338832855225,
0.021841594949364662,
-0.04101280868053436,
0.04337530955672264,
-0.02423749677836895,
-0.07349845767021179,
-0.013175521977245808,
-0.053297173231840134,
-0.014353790320456028,
-0.037635572254657745,
-0.05707306042313576,
-0.006646784953773022,
-0.047525838017463684,
-0.0035240831784904003,
-0.009507912211120129,
-0.02612324059009552,
0.05187500640749931,
0.01697138138115406,
-0.06458324939012527,
0.045404914766550064,
0.012863575480878353,
0.030663589015603065,
-0.033133380115032196,
-0.08315428346395493,
0.05764830857515335,
-0.03935395926237106,
0.02801598608493805,
-0.04273252189159393,
-0.0219402052462101,
0.02721952274441719,
0.05322033539414406,
-0.011682400479912758,
-0.05534970387816429,
0.028754500672221184,
0.054385099560022354,
-0.035010796040296555,
0.04109779745340347,
-0.014339510351419449,
-0.055290285497903824,
-0.0581313893198967,
0.01876010000705719,
0.020392345264554024,
-0.016838738694787025,
-0.039627157151699066,
-0.10954213887453079,
-0.0031810947693884373,
-0.031777121126651764,
-0.008187728002667427,
0.019557971507310867,
0.025287574157118797,
-0.00226874859072268,
-0.06941352784633636,
0.045816682279109955,
-0.030992690473794937,
-0.004086134489625692,
0.0355440229177475,
0.04322041571140289,
0.021920332685112953,
0.0022588218562304974,
-0.00957131665199995,
-0.03977466747164726,
-0.0051446715369820595,
0.07082155346870422,
0.02734687551856041,
-0.04795924946665764,
0.011708011850714684,
0.016893800348043442,
0.0020480556413531303,
-0.046771880239248276,
0.027881642803549767,
0.04431803524494171,
-0.01751508004963398,
0.040321484208106995,
-0.008023389615118504,
-0.019237235188484192,
0.029966549947857857,
-0.04889198765158653,
-0.004933700896799564,
0.03908339887857437,
-0.025682659819722176,
-0.015769112855196,
-0.031592678278684616,
0.020505473017692566,
-0.00631314143538475,
0.04930592328310013,
0.055114973336458206,
-0.03082975000143051,
0.05990593880414963,
-0.022402610629796982,
-0.04823685809969902,
-0.016219161450862885,
-0.019928937777876854,
0.05341501533985138,
-0.04844076931476593,
-0.041379161179065704,
-0.014277906157076359,
-0.014625628478825092,
-0.010537808761000633,
0.0514812171459198,
0.05466809123754501,
-0.07784673571586609,
-0.07145681977272034,
-0.02617787942290306,
0.005931617226451635,
0.03912557289004326,
0.03203964978456497,
-0.035378288477659225,
-0.02211669646203518,
-0.04753555357456207,
0.013843819499015808,
-0.0057516698725521564,
0.030994892120361328,
0.04257714003324509,
-0.035686034709215164,
-0.028724754229187965,
-0.011540887877345085,
-0.008908580988645554,
-0.012248928658664227,
0.042737897485494614,
-0.024931946769356728,
-0.026477785781025887,
0.030166318640112877,
-0.007210397627204657,
0.028606627136468887,
0.06773583590984344,
0.041888777166604996,
-0.02440999448299408,
0.0031877292785793543,
-0.03435857594013214,
0.026297004893422127,
-0.000311498501105234,
0.06867310404777527,
-0.01639280840754509,
-0.01330755278468132,
-0.04074810445308685,
0.02050466649234295,
0.017704294994473457,
0.03151528164744377,
-0.0798872709274292,
-0.015693452209234238,
-0.025659574195742607,
0.025863485410809517,
0.05296209827065468,
0.09610319137573242,
-0.02628474496304989,
0.04791522026062012,
-0.019212666898965836,
-0.033737342804670334,
-0.017650673165917397,
0.0317496731877327,
0.014444275759160519,
0.040089577436447144,
-0.022082863375544548,
0.015803175047039986,
-0.006543864496052265,
-0.00254156906157732,
0.05746154859662056,
-0.023414282128214836,
0.039501555263996124,
-0.03393091261386871,
0.070590078830719,
0.014375729486346245,
0.008878588676452637,
-0.007678097113966942,
0.05396410450339317,
0.10850268602371216,
-0.07662051916122437,
-0.03293774649500847,
0.02506098523736,
-0.020407583564519882,
0.012949489988386631,
-0.011146027594804764,
-0.06118038296699524,
-0.05438903346657753,
-0.04462325572967529,
-0.0017134693916887045,
-0.01257704570889473,
-0.02622237429022789,
-0.011303825303912163,
0.011637847870588303,
-0.03584204614162445,
0.011748147197067738,
-0.022379392758011818,
0.03521670773625374,
0.04950898885726929,
-0.0024709273129701614,
-0.030780749395489693,
0.0007208151509985328,
0.021128438413143158,
0.05472623184323311,
0.022928589954972267,
-0.016019804403185844,
-0.04707544296979904,
-0.05186247080564499,
0.02101222798228264,
0.016997966915369034,
0.043205853551626205,
0.009816184639930725,
0.04784097895026207,
0.05799431353807449,
-0.010459856130182743,
0.006756986025720835,
-0.0003818167024292052,
-0.0973500907421112,
-0.034303851425647736,
-0.04085993766784668,
0.002620335668325424,
-0.03242674097418785,
0.04258440434932709,
-0.008881323039531708,
0.005790223367512226,
-0.06752073019742966,
-0.021121200174093246,
0.016468701884150505,
-0.001389173325151205,
0.053142085671424866,
0.06668847799301147,
-0.00836810190230608,
-0.0061430255882442,
0.021715182811021805,
-0.006971040740609169,
0.04715917259454727,
-0.015114564448595047,
-0.03752752020955086,
-0.010848652571439743,
-0.02623932622373104,
0.021193964406847954,
-0.028085920959711075,
0.05352030694484711,
-0.01889168471097946,
0.03350489214062691,
0.03590891510248184,
-0.0033701136708259583,
-0.014061841182410717,
0.001615538727492094,
-0.046978265047073364,
0.024176746606826782,
0.02315603941679001,
0.021962717175483704,
0.018939245492219925,
0.06088777631521225,
-0.031691234558820724,
0.005350205581635237,
-0.04230661690235138,
-0.014564254321157932,
0.05912149325013161,
0.033975452184677124,
0.06287665665149689,
-0.03825743496417999,
-0.022157369181513786,
0.032278843224048615,
-0.024397794157266617,
-0.04124162718653679,
0.041251927614212036,
0.040533315390348434,
0.029347538948059082,
0.05740518867969513,
-0.006429234519600868,
-0.00921066664159298,
-0.031768761575222015,
0.008957559242844582,
-0.021678676828742027,
-0.03521954268217087,
0.0189815741032362,
-0.011311903595924377,
0.00836336612701416,
-0.052186012268066406,
-0.006895195227116346,
0.07400021702051163,
-0.004677318502217531,
-0.023842230439186096,
-0.06676234304904938,
-0.02054543048143387,
0.040500517934560776,
-0.007871796377003193,
0.03499918803572655,
-0.036701250821352005,
-0.04524201899766922,
0.005313911009579897,
0.10628726333379745,
0.005843275226652622,
0.014425793662667274,
-0.04673875868320465,
0.0035487038549035788,
-0.02493082731962204,
0.0029529582243412733,
0.02411774732172489,
-0.004476300440728664,
-0.0009163824724964797,
0.04247967526316643,
-0.01750882714986801,
0.001931531005539,
0.048216842114925385,
0.03935309872031212,
-0.005318869836628437,
0.03239138796925545,
0.04173365980386734,
0.04442023113369942,
0.0005681333714164793,
-0.007285118568688631,
-0.010050562210381031,
-0.010252346284687519,
0.019230779260396957,
0.002172580687329173,
-0.02782618999481201,
-0.049565065652132034,
-0.06339079141616821,
0.024021556600928307,
-0.04122451692819595,
0.01735731028020382,
0.024450669065117836,
0.030346456915140152,
-0.04639991372823715,
0.09363027662038803,
-0.0036190396640449762,
-0.000057330831623403355,
-0.028364896774291992,
0.07165701687335968,
0.016321035102009773,
0.00536895589902997,
0.003710511839017272,
-0.051002927124500275,
-0.043379370123147964,
0.02857276052236557,
0.041889920830726624,
0.0780315101146698,
0.011448707431554794,
-0.011163711547851562,
-0.027389537543058395,
0.016318367794156075,
-0.005807557608932257,
-0.010637323372066021,
0.026603003963828087,
-0.07479429244995117,
0.022859983146190643,
0.0007632584893144667,
-0.021084031090140343,
0.00767906429246068,
-0.0027040208224207163,
-0.06113648787140846,
-0.04276101291179657,
0.040572941303253174,
0.00843871384859085,
-0.049510810524225235,
-0.000510027224663645,
0.008348888717591763,
0.022621603682637215,
0.012068231590092182,
0.005722709000110626,
0.0409868024289608,
0.035782136023044586,
-0.035290930420160294,
0.03921128436923027,
0.07117624580860138,
-0.04174112156033516,
-0.014950096607208252,
0.05216243490576744,
0.009728501550853252,
0.06121319904923439,
0.037005819380283356,
-0.028790734708309174,
-0.039216890931129456,
-0.023834584280848503,
-0.05087471008300781,
-0.021824391558766365,
-0.058245714753866196,
0.07744139432907104,
0.027422426268458366,
0.030268412083387375,
-0.03126076981425285,
0.029835311695933342,
0.05091870203614235,
-0.0033827878069132566,
-0.036652036011219025,
-0.017994945868849754,
-0.0073774391785264015,
0.008694556541740894,
-0.013843201100826263,
-0.023231955245137215,
-0.04887494444847107,
-0.03222699835896492,
0.02967623434960842,
-0.022916117683053017,
0.03237110376358032,
-0.023617994040250778,
0.010712538845837116,
-0.024295508861541748,
-0.035332273691892624,
0.02304975874722004,
0.04016386717557907,
0.04343898221850395,
0.005189420655369759,
-0.0794873908162117,
0.010825827717781067,
-0.08583773672580719,
-0.005058689508587122,
-0.0750933513045311,
-0.04154767096042633,
-0.010865946300327778,
-0.027262812480330467,
0.004082725383341312,
0.011152667924761772,
-0.03546416386961937,
-0.054231081157922745,
-0.0017581398133188486,
-0.026487743481993675,
-0.04630116745829582,
0.019270967692136765,
-0.03248485550284386,
-0.02956121787428856,
0.03745372220873833,
-0.040340449661016464,
-0.010473362170159817,
-0.0011905906721949577,
-0.00995981227606535,
0.018856020644307137,
-0.011760219931602478,
0.0541892945766449,
0.029221361503005028,
-0.03841792792081833,
0.019005414098501205,
-0.01380224246531725,
0.011381153017282486,
0.010080941021442413,
-0.022535046562552452,
0.03621920943260193,
-0.08608879894018173,
0.007098014000803232,
-0.0028732784558087587,
0.0033174387644976377,
0.012282775714993477,
0.028377803042531013,
-0.012015266343951225,
-0.05203735828399658,
0.004337686114013195,
0.0159666258841753,
0.02787889540195465,
0.031354889273643494,
-0.008443639613687992,
0.0472850538790226,
0.012972505763173103,
-0.028756875544786453,
0.05397767946124077,
0.008468682877719402,
-0.013333036564290524,
-0.015677230432629585,
-0.023786500096321106,
-0.04945995286107063,
-0.07110411673784256,
-0.013780351728200912,
-0.03578079119324684,
-0.008716910146176815,
-0.032016776502132416,
0.013766785152256489,
0.002707237843424082,
0.0026581392157822847,
-0.00031610202859155834,
0.011006479151546955,
-0.040589507669210434,
-0.0004477480542846024,
-0.009191813878715038,
0.03279696777462959,
0.07202890515327454,
0.017833663150668144,
-0.0011058469535782933,
-0.055930182337760925,
-0.03564969822764397,
-0.05905327573418617,
-0.04568634182214737,
-0.014557898044586182,
-0.00908717978745699,
-0.05658779665827751,
-0.038074806332588196,
0.05623435229063034,
-0.01587965525686741,
-0.015709904953837395,
-0.026698166504502296,
-0.057664062827825546,
0.07910879701375961,
0.09714498370885849,
-0.04818001016974449,
0.04987041652202606,
-0.003606495913118124,
0.008190955966711044,
-0.015833821147680283,
-0.03700627014040947,
-0.027594519779086113,
-0.023855267092585564,
-0.024104135110974312,
0.03060223162174225,
0.0069336132146418095,
0.032888952642679214,
0.01657218672335148
] |
<p>How to prove the identity
$$
\tilde {\sigma}_{\alpha}\sigma_{\beta}\tilde {\sigma}_{\gamma} = g_{\alpha \beta}\tilde {\sigma}_{\gamma} + g_{\alpha \gamma}\tilde {\sigma}_{\beta} - g_{\beta \gamma} \tilde {\sigma}_{\alpha} + i\varepsilon_{\alpha \beta \gamma \delta}\tilde {\sigma}^{\delta}, \qquad (1)
$$
where
$$
\sigma_{\alpha} = (\hat {\mathbf E}, \sigma ), \quad \tilde {\sigma}_{\beta} = (\hat {\mathbf E}, -\sigma ), \quad \varepsilon_{\alpha \beta \gamma \delta } = -\varepsilon_{\beta \alpha \gamma \delta} = ..., \quad \varepsilon_{0123} = 1, \quad g_{\alpha \beta} = diag(1, -1, -1, -1)?
$$
I tried to do this by constructing the relation
$$
\sigma_{\alpha}\tilde {\sigma}_{\beta} = g_{\alpha \beta}\sigma_{0} + i\varepsilon_{0\alpha \beta \gamma}\sigma^{\gamma} - \delta^{0}_{\alpha}(\delta^{0}_{\beta}\sigma_{0} - \tilde {\sigma}_{\beta}) - \delta^{0}_{\beta}(\delta^{0}_{\alpha}\sigma_{0} - \sigma_{\alpha}),
$$
where first summand corresponds to $\alpha = \beta$, the second - to $\alpha , \beta \neq 0$, the third - to $\alpha = 0, \beta \neq 0$, the last - to $\beta = 0, \alpha \neq 0$, and $\sigma^{\mu} = g^{\mu \nu}\sigma_{\nu}$.</p>
<p>But I can't get the answer in a compact form of $(1)$ by using my construction. In particular, I don't understand how $\varepsilon_{\alpha \beta \gamma \delta}$ is appeared in the final answer. </p>
<p>An edit.</p>
<p>I proved it, but the proof is terrible.</p> | g5487 | [
0.030430277809500694,
-0.02598380297422409,
-0.0074043916538357735,
-0.04526996612548828,
0.09021644294261932,
-0.0032603361178189516,
0.1004692018032074,
-0.05045245215296745,
-0.050208739936351776,
-0.007182753644883633,
-0.03756721317768097,
0.04253409802913666,
-0.02109503000974655,
0.006388823036104441,
0.047807477414608,
0.023566508665680885,
0.017650064080953598,
-0.02111276425421238,
0.02580145187675953,
0.022729147225618362,
0.008402824401855469,
0.024337487295269966,
0.049393534660339355,
-0.04392514005303383,
0.056656405329704285,
0.002781390445306897,
-0.03113323077559471,
0.060719579458236694,
0.03196512907743454,
-0.05229772627353668,
-0.002287487266585231,
0.0406109094619751,
0.08347540348768234,
0.037179507315158844,
0.0064072879031300545,
0.018955595791339874,
0.034397318959236145,
-0.04074813798069954,
0.034113962203264236,
-0.03993647173047066,
-0.040011558681726456,
0.01889818347990513,
-0.021225541830062866,
0.03355885669589043,
0.008010377176105976,
0.025389201939105988,
0.02601506933569908,
0.011829190887510777,
0.008263290859758854,
-0.01102676521986723,
-0.01390669122338295,
-0.003531557973474264,
0.01734023727476597,
-0.06761961430311203,
-0.059152714908123016,
0.007326105609536171,
0.060512688010931015,
-0.06893639266490936,
0.03626125678420067,
0.020828843116760254,
-0.02051723375916481,
-0.04249159246683121,
0.0383378304541111,
0.009527093730866909,
0.06624853610992432,
-0.07157904654741287,
0.027943968772888184,
-0.030091026797890663,
0.03007509745657444,
0.004418920259922743,
0.0013993047177791595,
-0.024225037544965744,
0.07267902046442032,
-0.005809667520225048,
0.024447215721011162,
0.011285346001386642,
0.034763555973768234,
0.004439057316631079,
-0.09047006815671921,
-0.008021911606192589,
0.03660695627331734,
-0.015056534670293331,
0.028829161077737808,
0.0313558392226696,
0.03789200633764267,
-0.053552787750959396,
-0.014728141017258167,
-0.0036248445976525545,
-0.04264049604535103,
-0.012808904983103275,
0.014565318822860718,
-0.04241739958524704,
-0.008661146275699139,
0.10434684157371521,
-0.052804384380578995,
-0.05569986626505852,
0.02000213973224163,
0.007597034331411123,
-0.0017321441555395722,
0.02028828114271164,
0.03531293198466301,
0.006928292568773031,
-0.013928219676017761,
0.020092587918043137,
-0.013187826611101627,
0.019052207469940186,
-0.01686503365635872,
-0.003124120645225048,
-0.04241003841161728,
-0.00843015220016241,
-0.09088662266731262,
-0.013085871934890747,
-0.003201994812116027,
-0.06545241922140121,
0.01766113005578518,
-0.0023636319674551487,
-0.015047646127641201,
-0.023506317287683487,
0.023376258090138435,
-0.03919157758355141,
-0.043820708990097046,
-0.014679967425763607,
-0.03641918674111366,
-0.030534790828824043,
-0.03151407092809677,
-0.010029873810708523,
-0.036536671221256256,
0.023655327036976814,
0.07722267508506775,
-0.009558790363371372,
0.02434852533042431,
0.025231974199414253,
0.03600076958537102,
0.03227813169360161,
0.013442275114357471,
0.0295052919536829,
-0.02795987017452717,
0.01518850214779377,
-0.013059943914413452,
-0.020637480542063713,
-0.09111128002405167,
0.018661757931113243,
-0.0027434099465608597,
0.004027076065540314,
0.02321447804570198,
0.06163540855050087,
0.011097623966634274,
-0.0503825880587101,
-0.006187213119119406,
0.02016475796699524,
0.03285850211977959,
0.05780384689569473,
-0.03315512835979462,
-0.03171256184577942,
0.02046826481819153,
-0.037658289074897766,
0.02363898791372776,
0.028196869418025017,
-0.0653754472732544,
-0.03347616642713547,
0.011552640236914158,
-0.009689020924270153,
0.02079596556723118,
-0.0588424950838089,
-0.0442340187728405,
0.020355574786663055,
0.03434290364384651,
-0.020394615828990936,
-0.006777362897992134,
-0.05676950886845589,
-0.011767076328396797,
0.026416245847940445,
0.05498110130429268,
-0.03067610412836075,
0.03301675617694855,
0.02006634511053562,
-0.08400291949510574,
-0.029282836243510246,
0.013419661670923233,
-0.04113203287124634,
-0.030665040016174316,
0.008406417444348335,
0.008451136760413647,
0.005487003363668919,
-0.07655306905508041,
-0.020038465037941933,
0.04372303932905197,
0.026591043919324875,
0.02384124882519245,
0.05452710762619972,
-0.01887493208050728,
0.017445199191570282,
0.0038544833660125732,
-0.018922992050647736,
0.021111546084284782,
0.048818524926900864,
0.017989689484238625,
-0.0799676924943924,
-0.02567439340054989,
0.0054277218878269196,
-0.09336861222982407,
0.026858633384108543,
0.031944792717695236,
-0.02066931687295437,
0.02623710222542286,
0.0050308131612837315,
-0.019427580758929253,
-0.03493921458721161,
0.028348449617624283,
-0.006222775671631098,
-0.03504987061023712,
-0.07973843067884445,
-0.010072542354464531,
-0.03180178254842758,
0.037404995411634445,
-0.05153918266296387,
0.0289996899664402,
0.002863834612071514,
-0.023856336250901222,
0.009599690325558186,
-0.01760098896920681,
-0.01963711902499199,
0.014752781018614769,
-0.021103452891111374,
-0.009257582947611809,
0.08991093188524246,
-0.03808717802166939,
-0.009030664339661598,
-0.06092369183897972,
0.0008329621632583439,
-0.022498827427625656,
-0.005008268635720015,
-0.07528840750455856,
-0.01520074438303709,
0.00047887806431390345,
0.004666028544306755,
-0.039426881819963455,
0.014627187512814999,
0.04192613065242767,
0.03497063368558884,
-0.01974194496870041,
-0.01023076381534338,
0.005048766266554594,
0.035803087055683136,
0.002260899171233177,
0.00673909205943346,
0.05146125331521034,
0.03991817310452461,
-0.002011469565331936,
-0.017242230474948883,
0.0077647739090025425,
-0.010003512725234032,
0.03181075304746628,
0.044165268540382385,
0.029467443004250526,
-0.03523935750126839,
0.05515378341078758,
0.00296269659884274,
0.02458469569683075,
0.0360226072371006,
-0.0389837808907032,
-0.08774082362651825,
-0.025443682447075844,
-0.009420536458492279,
-0.021813802421092987,
0.019135598093271255,
-0.06346762925386429,
-0.013552996329963207,
-0.006215137895196676,
-0.0021942409221082926,
-0.03793617710471153,
0.005309741478413343,
0.03922202065587044,
0.01382798608392477,
-0.06560827791690826,
0.0019192863255739212,
-0.0014343662187457085,
0.031312745064496994,
0.06467768549919128,
0.026901524513959885,
0.01999424770474434,
-0.007943017408251762,
-0.031728725880384445,
0.037416744977235794,
-0.00871118251234293,
-0.041961390525102615,
0.03453530743718147,
0.026812702417373657,
0.025380119681358337,
0.010973191820085049,
0.027001522481441498,
0.019830452278256416,
0.016686050221323967,
-0.013656694442033768,
-0.01298875454813242,
0.04102412611246109,
-0.010442289523780346,
-0.014251330867409706,
0.01520029827952385,
-0.0343187041580677,
-0.01911165565252304,
0.028235865756869316,
-0.03681635111570358,
-0.039033275097608566,
0.0621761716902256,
-0.01237428281456232,
-0.01081619132310152,
-0.03424800932407379,
-0.016043439507484436,
0.06522256135940552,
0.005132304970175028,
-0.015018955804407597,
-0.030041055753827095,
-0.08091561496257782,
0.004190361127257347,
0.06297758966684341,
0.016899950802326202,
-0.041088204830884933,
0.0022671669721603394,
0.031895458698272705,
-0.019755126908421516,
-0.06344791501760483,
-0.03788484260439873,
-0.0032589975744485855,
0.03243669867515564,
-0.046337030827999115,
-0.01996840164065361,
0.008726543746888638,
-0.022295035421848297,
-0.01970423012971878,
-0.009784173220396042,
-0.01529684104025364,
0.03584901988506317,
0.022261876612901688,
-0.007657983340322971,
0.007067565806210041,
-0.023425422608852386,
0.0714225098490715,
0.01499844342470169,
-0.003930834587663412,
-0.035293594002723694,
-0.029806461185216904,
-0.025985434651374817,
-0.006604373455047607,
0.017017072066664696,
-0.05964530259370804,
0.04589353874325752,
0.057191163301467896,
0.027816234156489372,
0.034533873200416565,
-0.005225188098847866,
0.0006861041183583438,
0.02087489701807499,
0.028254831209778786,
0.022364165633916855,
0.08383501321077347,
-0.0038988441228866577,
0.020243460312485695,
0.03704730421304703,
-0.09101280570030212,
-0.017949508503079414,
-0.032111674547195435,
-0.02600076049566269,
0.0031037195585668087,
0.03575938567519188,
0.0005158766871318221,
0.03693089634180069,
-0.031385522335767746,
-0.05286477133631706,
0.007286741863936186,
0.039684634655714035,
0.06512458622455597,
0.05514002963900566,
0.05467903986573219,
-0.0012695854529738426,
-0.10488623380661011,
-0.02461608313024044,
0.008526196703314781,
-0.041186150163412094,
0.021513216197490692,
0.024574773386120796,
0.030759984627366066,
0.06298186630010605,
0.017455752938985825,
0.04432922974228859,
0.00706294784322381,
0.04929954186081886,
-0.04552064463496208,
0.05806568264961243,
-0.022525547072291374,
-0.000649463792797178,
0.036368630826473236,
-0.013796894811093807,
-0.017987936735153198,
-0.04333978518843651,
-0.02112942934036255,
-0.02601679041981697,
0.003532838774845004,
-0.08041340112686157,
-0.009578223340213299,
-0.02965574897825718,
0.022833973169326782,
0.04960186779499054,
0.016038382425904274,
-0.023365722969174385,
0.013327271677553654,
-0.026179498061537743,
0.007989315316081047,
0.07176097482442856,
-0.06315600126981735,
-0.003920095972716808,
-0.02815118618309498,
0.03562154248356819,
-0.024901172146201134,
0.027760224416851997,
0.03690788522362709,
-0.0023942659609019756,
-0.06527309119701385,
0.03139624744653702,
-0.014181225560605526,
0.004357513971626759,
-0.03901847079396248,
-0.021041816100478172,
-0.02271798439323902,
0.06294462829828262,
0.0355326309800148,
0.038830213248729706,
0.04286498576402664,
-0.01935724727809429,
-0.04011065140366554,
-0.007453263271600008,
0.030903030186891556,
-0.04493892192840576,
0.024350179359316826,
-0.07447800785303116,
0.011546873487532139,
-0.06629698723554611,
0.03545762225985527,
0.0015423527220264077,
-0.062322381883859634,
0.021144233644008636,
-0.0030328542925417423,
0.007722106762230396,
-0.036307379603385925,
0.023968730121850967,
0.0034364040475338697,
-0.026110270991921425,
-0.08034783601760864,
0.04227472469210625,
0.007055926136672497,
-0.01575239934027195,
0.010748667642474174,
0.013299243524670601,
-0.02576753869652748,
-0.002590634860098362,
-0.0053394269198179245,
-0.019926855340600014,
0.008913317695260048,
0.0043368227779865265,
0.027197545394301414,
-0.053356148302555084,
-0.0077612437307834625,
0.063597172498703,
0.008785716257989407,
0.10567866265773773,
0.02157902531325817,
-0.003366632852703333,
0.04878669232130051,
0.02053854614496231,
-0.07338234782218933,
-0.025296790525317192,
0.04572897404432297,
-0.0193681251257658,
-0.03541354835033417,
-0.01311727799475193,
0.029703788459300995,
-0.06220301613211632,
-0.004359268583357334,
-0.05748335272073746,
0.009378310292959213,
-0.01938014104962349,
-0.045614488422870636,
-0.03653435409069061,
0.00038953128387220204,
0.00977134145796299,
0.010654257610440254,
0.03855644538998604,
-0.02019648067653179,
0.029621781781315804,
0.001398481777869165,
0.006776395719498396,
-0.009054862894117832,
0.004877039697021246,
-0.02872990444302559,
-0.046762287616729736,
-0.05362789332866669,
0.019057638943195343,
-0.017149994149804115,
0.01095650065690279,
0.07583536207675934,
-0.052261631935834885,
0.01621243916451931,
-0.02077385224401951,
-0.03668178990483284,
0.07488282769918442,
0.0499466136097908,
-0.004478273447602987,
0.04776953160762787,
-0.014332733117043972,
-0.01425924338400364,
-0.005023397505283356,
-0.04416469484567642,
-0.03853778913617134,
-0.030733468011021614,
-0.016243139281868935,
0.03888190910220146,
-0.024401899427175522,
-0.04615071415901184,
-0.007650654297322035,
-0.036127373576164246,
0.03218354657292366,
0.025284746661782265,
-0.026292182505130768,
-0.03156313672661781,
0.0042121936567127705,
0.015918150544166565,
-0.04690006375312805,
-0.08537744730710983,
0.06963369250297546,
0.012039936147630215,
0.004597064107656479,
-0.009522506035864353,
-0.04103713110089302,
-0.022801311686635017,
0.04552551731467247,
0.0019862207118421793,
-0.033388301730155945,
0.011122439056634903,
0.015277637168765068,
0.03691999241709709,
-0.04416827857494354,
-0.010306106880307198,
0.0077269794419407845,
0.04281482473015785,
-0.006688615307211876,
0.009269311092793941,
-0.030521763488650322,
-0.013251220807433128,
0.014617878943681717,
0.05476482957601547,
0.004752029664814472,
-0.028639204800128937,
0.016230953857302666,
0.02841443009674549,
0.0034732280764728785,
0.006178951822221279,
0.015057488344609737,
-0.002685125218704343,
-0.030465852469205856,
0.00546633917838335,
0.024124186486005783,
-0.024579202756285667,
-0.032996322959661484,
0.010393287055194378,
-0.03665384277701378,
-0.11052895337343216,
0.04028655216097832,
-0.034775570034980774,
-0.03674197196960449,
0.018943848088383675,
0.05535443499684334,
0.006796487141400576,
0.04267958179116249,
0.02444412186741829,
0.025079838931560516,
0.07905905693769455,
-0.04129879176616669,
-0.031229455024003983,
-0.05263322964310646,
0.029556207358837128,
-0.02115647867321968,
0.0384976901113987,
-0.010625109076499939,
0.006880910135805607,
0.017868373543024063,
0.07497114688158035,
-0.02544580027461052,
-0.027052270248532295,
-0.02528553642332554,
-0.009924016892910004,
0.008705904707312584,
0.000996903982013464,
-0.022103626281023026,
-0.009237496182322502,
-0.00042616325663402677,
-0.000516984611749649,
0.06618254631757736,
0.03312679007649422,
0.05697708576917648,
0.0021151446271687746,
0.03549594804644585,
0.010831153951585293,
0.01168166846036911,
0.00689004035666585,
-0.023464595898985863,
0.06036811321973801,
0.03591487184166908,
0.0020370713900774717,
0.026061641052365303,
-0.05890815705060959,
0.04380613937973976,
0.029758887365460396,
-0.027612850069999695,
0.02529158629477024,
0.025202540680766106,
-0.02390521764755249,
-0.007881179451942444,
0.05356139317154884,
-0.04322434961795807,
0.06519711017608643,
0.06397470831871033,
0.017768235877156258,
-0.022928917780518532,
0.03902381286025047,
0.051812831312417984,
0.006705257575958967,
0.013776574283838272,
-0.03194304183125496,
0.009485765360295773,
0.016411328688263893,
0.0003948491648770869,
-0.0016374699771404266,
-0.02041751705110073,
0.029787763953208923,
-0.015231066383421421,
-0.010090085677802563,
-0.02708696387708187,
0.021365221589803696,
-0.061684440821409225,
0.11320959031581879,
-0.021353553980588913,
0.045458585023880005,
0.005597129464149475,
-0.02313707210123539,
-0.02562965452671051,
0.010691092349588871,
-0.024372806772589684,
0.010585295967757702,
-0.08429939299821854,
0.0041365292854607105,
0.08695979416370392,
0.03996046259999275,
0.012365755625069141,
0.007196451537311077,
-0.007737546693533659,
-0.022915810346603394,
0.04358852282166481,
0.005395916290581226,
-0.02792237140238285,
0.0007170106400735676,
-0.02297685109078884,
-0.013975602574646473,
0.022612981498241425,
0.044222764670848846,
0.024671731516718864,
0.03412172943353653,
0.023338472470641136,
-0.03309594839811325,
0.029951103031635284,
-0.01342331524938345,
0.013797820545732975,
-0.007855353876948357,
0.03009730391204357,
-0.012891671620309353,
-0.007280528545379639,
0.003920719958841801,
0.060733940452337265,
-0.00762044545263052,
-0.0008969106711447239,
0.035513512790203094,
-0.053711146116256714,
-0.00484361220151186,
-0.0048822215758264065,
0.03802018612623215,
0.004057019017636776,
0.0415816605091095,
0.026957934722304344,
0.02311382256448269,
0.012273685075342655,
0.02358981966972351,
-0.0773395523428917,
0.020875059068202972,
-0.03458227217197418,
-0.030457735061645508,
0.0316036082804203,
0.02567986771464348,
-0.020504597574472427,
0.03888576105237007,
-0.028658289462327957,
0.028252651914954185,
0.01116760540753603,
-0.046929579228162766,
-0.0374024361371994,
-0.03456946089863777,
-0.011579838581383228,
0.026878735050559044,
-0.0038838947657495737,
0.0267535001039505,
-0.060717564076185226,
-0.0273728184401989,
0.07927490025758743,
-0.06813368946313858,
-0.006697273347526789,
0.004759812727570534,
0.06705813109874725,
0.04443543776869774,
-0.04113224893808365,
0.02814752422273159,
-0.03379904478788376,
0.003997946158051491,
0.07396775484085083,
-0.019233819097280502,
-0.03880823403596878,
-0.05378167703747749,
-0.06784806400537491,
-0.049925148487091064,
0.025306817144155502,
-0.07169262319803238,
0.03362283483147621,
-0.021628085523843765,
-0.05431888625025749,
-0.0009697138448245823,
-0.030942343175411224,
0.0001771320530679077,
-0.04355046898126602,
0.008750657550990582,
0.020323997363448143,
-0.09984755516052246,
0.03865715488791466,
0.01506984792649746,
-0.012142553925514221,
-0.03831067308783531,
0.011914900504052639,
0.004207523074001074,
0.011768327094614506,
-0.0255722776055336,
-0.016821738332509995,
0.03386989235877991,
0.009961741045117378,
-0.01175023801624775,
-0.03445345163345337,
0.03518851473927498,
0.02443854883313179,
0.006780658382922411,
0.05088142305612564,
0.011364552192389965,
0.036378346383571625,
-0.04413409158587456,
-0.0018646143143996596,
0.04263671487569809,
-0.05739552900195122,
-0.020368626341223717,
-0.03366086259484291,
0.04893050715327263,
-0.03205591440200806,
-0.05385829508304596,
-0.0033887496683746576,
-0.020436229184269905
] |
<p>I am solving a Hamiltonian including a term $(x\cdot S)^2$.
The Hamiltonian is like this form:
\begin{equation}
H=L\cdot S+(x\cdot S)^2
\end{equation}
where $L$ is angular momentum operator and $S$ is spin operator. The eigenvalue for $L^2$ and $S^2$ are $l(l+1)$ and $s(s+1)$. </p>
<p>If the Hamiltonian only has the first term, it is just spin orbital coupling and it is easy to solve. The total $J=L+S$, $L^2$ and $S^2$ are quantum number. However, when we consider the second term position and spin coupling $(x\cdot S)^2$, it becomes much harder. The total $J$ is still a quantum number. We have $[(x\cdot S)^2, J]=0$. However, $[(x\cdot S)^2,L^2]≠0$, $L$ is not a quantum number anymore.</p>
<p>Anybody have ideas on how to solve this Hamiltonian?</p> | g5488 | [
0.05389158055186272,
-0.008156458847224712,
-0.005400029942393303,
-0.06133200228214264,
-0.00908433273434639,
-0.03518340364098549,
0.03563870117068291,
0.014183402061462402,
0.07061680406332016,
0.014370260760188103,
-0.04126473888754845,
0.03926970064640045,
-0.005657465197145939,
0.011020595207810402,
0.0642675906419754,
0.031827546656131744,
0.03148417919874191,
0.02404293231666088,
-0.01999826356768608,
-0.028749532997608185,
-0.009811745025217533,
0.0005105144227854908,
-0.008820013143122196,
-0.04937320947647095,
-0.03400197625160217,
-0.04222928732633591,
-0.03716486319899559,
0.03322375565767288,
0.013831942342221737,
0.027864761650562286,
-0.018045609816908836,
-0.022108102217316628,
0.03975934162735939,
-0.006439882796257734,
0.019377483054995537,
0.041351862251758575,
0.03413751348853111,
0.010706284083425999,
-0.007377867586910725,
0.003219550708308816,
0.04073486477136612,
-0.09340367466211319,
0.021487310528755188,
0.03383656218647957,
-0.0021294818725436926,
-0.001093622064217925,
-0.005662181414663792,
0.04515797644853592,
-0.03060811385512352,
0.02796384133398533,
-0.015241594985127449,
0.03645032271742821,
0.0010288009652867913,
-0.020808961242437363,
0.042314205318689346,
0.03126225993037224,
-0.03178809583187103,
0.021716976538300514,
-0.003594330046325922,
0.08531167358160019,
0.07186920195817947,
-0.01124323159456253,
0.0004949570866301656,
0.02476944401860237,
0.05320851877331734,
-0.0006074982229620218,
-0.0016498531913384795,
0.019522806629538536,
-0.059867627918720245,
-0.005728604272007942,
-0.01420863438397646,
-0.04723237827420235,
0.08046936988830566,
-0.024098210036754608,
0.003678202163428068,
-0.01030043326318264,
0.01706096902489662,
-0.016863973811268806,
-0.025953544303774834,
0.04017619043588638,
-0.027243388816714287,
-0.032603465020656586,
0.003754987148568034,
-0.014080042019486427,
0.03905262053012848,
0.0536772757768631,
-0.024643810465931892,
0.01111909095197916,
-0.024588415399193764,
0.04951930046081543,
0.016619542613625526,
0.011417748406529427,
0.04187014326453209,
-0.026949068531394005,
0.011080959811806679,
0.0000631560615147464,
0.0009438677225261927,
-0.01195620372891426,
-0.023147309198975563,
-0.013552792370319366,
-0.0647343248128891,
0.0077592297457158566,
0.009667626582086086,
-0.001615582499653101,
0.030518192797899246,
0.03120627999305725,
0.014628304168581963,
0.007009498309344053,
0.003370902733877301,
0.047462690621614456,
-0.005608344450592995,
0.011462697759270668,
0.020786438137292862,
-0.047561999410390854,
-0.03852378576993942,
0.016112979501485825,
0.03445352613925934,
-0.04310121387243271,
-0.028462881222367287,
-0.0008599507855251431,
0.006564597599208355,
0.04870547726750374,
0.037178896367549896,
0.10740833729505539,
0.050523534417152405,
-0.016239797696471214,
-0.013641968369483948,
-0.0020556114614009857,
0.10793641954660416,
-0.003511215792968869,
-0.07744403183460236,
-0.041768524795770645,
0.05908413231372833,
0.07011792063713074,
0.019048156216740608,
0.03770503029227257,
-0.02757408656179905,
0.006792970933020115,
0.029160238802433014,
0.019272636622190475,
-0.005822590086609125,
-0.06682207435369492,
0.03601190447807312,
-0.010871119797229767,
-0.03042348101735115,
-0.011369850486516953,
0.0673830583691597,
-0.05440513789653778,
-0.040202584117650986,
-0.02528534084558487,
0.031004754826426506,
0.01566939987242222,
0.015910953283309937,
0.011492195539176464,
0.025798475369811058,
-0.03853267431259155,
0.064951591193676,
0.002576594240963459,
0.017951788380742073,
-0.013422026298940182,
0.05552469193935394,
-0.021122068166732788,
0.027185967192053795,
-0.019774960353970528,
-0.025057919323444366,
0.08119772374629974,
-0.0385364405810833,
-0.026153504848480225,
-0.008429464884102345,
0.004843736533075571,
-0.019129209220409393,
-0.0014988671755418181,
0.008048798888921738,
0.0702407956123352,
0.049917276948690414,
0.06095420569181442,
-0.03274141624569893,
0.009206741116940975,
-0.026296747848391533,
0.041913941502571106,
0.04727662354707718,
-0.029538366943597794,
-0.011232376098632812,
-0.009245323948562145,
-0.010038638487458229,
0.02762788161635399,
0.026175368577241898,
0.014076103456318378,
-0.018729317933321,
-0.034733351320028305,
0.03624298423528671,
0.029971109703183174,
0.061702974140644073,
0.03145546093583107,
-0.07814143598079681,
0.029243437573313713,
0.045084718614816666,
-0.030888259410858154,
-0.02359165996313095,
0.02451569400727749,
-0.012683840468525887,
0.028569288551807404,
0.027127955108880997,
0.006779845338314772,
0.017871476709842682,
-0.012829143553972244,
0.008474564179778099,
0.010816716589033604,
-0.016973836347460747,
-0.0032049384899437428,
0.0060927071608603,
0.001027898397296667,
-0.02542167156934738,
0.07239974290132523,
-0.03486181050539017,
0.019293172284960747,
0.02636551856994629,
-0.0027537804562598467,
-0.09182462096214294,
0.03887730836868286,
-0.02184799499809742,
0.005725617986172438,
0.08508019894361496,
0.03293048217892647,
0.006397872697561979,
0.012132523581385612,
-0.05373470112681389,
0.044301100075244904,
-0.03564513847231865,
0.0021695131435990334,
0.011970828287303448,
-0.018403109163045883,
-0.051070649176836014,
-0.04203282296657562,
0.062280163168907166,
0.01078796572983265,
-0.017314624041318893,
0.026160361245274544,
0.007912847213447094,
0.05443772301077843,
-0.03210442513227463,
0.05645617097616196,
-0.032219987362623215,
-0.03291786089539528,
0.07652972638607025,
0.04626313969492912,
-0.023191146552562714,
0.03674273192882538,
-0.026704709976911545,
0.058667976409196854,
-0.017206935212016106,
-0.029332397505640984,
-0.04847143962979317,
0.00517072482034564,
0.0035052995663136244,
-0.008650763891637325,
-0.023326296359300613,
0.02314772456884384,
-0.006940060295164585,
-0.027830906212329865,
-0.022425223141908646,
0.012766028754413128,
0.03437555208802223,
0.009786711074411869,
0.014152579009532928,
0.017398258671164513,
0.00436992896720767,
-0.03949711471796036,
0.03421952947974205,
-0.025974731892347336,
-0.04068569839000702,
0.05556531250476837,
-0.06430710852146149,
0.05918969213962555,
0.00009711697202874348,
-0.08453671634197235,
-0.011883256956934929,
0.019216159358620644,
-0.015432748943567276,
-0.031141597777605057,
-0.02354396879673004,
0.00695040775462985,
-0.006075309123843908,
0.028014643117785454,
0.0627242848277092,
-0.057889796793460846,
-0.015805834904313087,
0.05524362996220589,
0.037185344845056534,
-0.02564997225999832,
0.03880006819963455,
0.03527924045920372,
0.03037598729133606,
-0.009057202376425266,
0.005965218413621187,
-0.03605787083506584,
0.024017056450247765,
-0.009140709415078163,
0.0464111752808094,
0.0747528225183487,
0.04078279435634613,
0.019751206040382385,
0.00623369961977005,
-0.02215188927948475,
0.011596821248531342,
-0.034538011997938156,
-0.039265818893909454,
0.019569825381040573,
0.003073327708989382,
-0.042410727590322495,
-0.009153755381703377,
0.04172077029943466,
0.03935634717345238,
-0.060260023921728134,
0.04562730714678764,
0.0005304522928781807,
-0.027078118175268173,
-0.037639226764440536,
0.02596461772918701,
-0.05609193444252014,
-0.060753535479307175,
-0.04248930513858795,
0.01918533444404602,
0.03340919688344002,
0.0002064129221253097,
0.05772082135081291,
-0.0886346846818924,
0.010713107883930206,
-0.04430759698152542,
-0.006028398871421814,
0.010821684263646603,
-0.02353883907198906,
-0.0245092511177063,
0.028224194422364235,
-0.04531218484044075,
0.022753311321139336,
-0.017827190458774567,
-0.02028741128742695,
0.014598964713513851,
0.020517872646450996,
-0.020441558212041855,
-0.034551553428173065,
-0.05393446981906891,
0.023702433332800865,
-0.03880304470658302,
-0.04013998061418533,
-0.04550565034151077,
-0.025264078751206398,
-0.052236929535865784,
-0.021145746111869812,
-0.04081019014120102,
0.007496383972465992,
0.010282667353749275,
0.06356823444366455,
-0.03193323686718941,
0.004409364424645901,
-0.014271203428506851,
0.06543535739183426,
-0.006303556729108095,
0.04097200185060501,
0.031104031950235367,
-0.023253990337252617,
0.01960238814353943,
0.038695819675922394,
0.0003342067648191005,
-0.01084719505161047,
-0.03258050978183746,
-0.034097518771886826,
0.012976701371371746,
-0.06739781051874161,
0.0075860414654016495,
-0.027519213035702705,
0.05633443221449852,
-0.0979408398270607,
0.051866233348846436,
-0.0010196985676884651,
-0.05408782884478569,
-0.024996787309646606,
-0.02869754657149315,
0.011170562356710434,
-0.03463856130838394,
0.009880796074867249,
-0.024917257949709892,
0.033240336924791336,
0.043370623141527176,
0.024168046191334724,
0.047764942049980164,
-0.007268606219440699,
0.012293200008571148,
-0.01631154492497444,
-0.005073796026408672,
-0.015883522108197212,
-0.02253521978855133,
0.022679243236780167,
0.02896743081510067,
0.01984357461333275,
-0.011194957420229912,
-0.023105185478925705,
-0.031010281294584274,
0.006808015517890453,
-0.059234555810689926,
-0.06942195445299149,
0.006283929105848074,
-0.011256489902734756,
0.0008914663922041655,
0.08037938177585602,
0.05751877278089523,
0.0056039500050246716,
0.03277571499347687,
-0.018345631659030914,
-0.03923962637782097,
0.014470042660832405,
-0.04009081795811653,
-0.005374678410589695,
-0.04542304947972298,
0.0012043605092912912,
0.01810383051633835,
-0.001695328624919057,
-0.06931157410144806,
-0.007307472173124552,
-0.02953951247036457,
0.11082404106855392,
0.0014199453871697187,
-0.032523028552532196,
-0.014711245894432068,
-0.06303863227367401,
0.04481421038508415,
-0.006285775452852249,
-0.003950163722038269,
0.020862266421318054,
-0.00042019906686618924,
0.011086959391832352,
0.008724658749997616,
-0.030820120126008987,
-0.05891304090619087,
0.008127710781991482,
0.012021792121231556,
-0.04839804023504257,
-0.025456877425312996,
0.02563932165503502,
0.04393592104315758,
0.04575091600418091,
-0.03258127719163895,
0.05480651557445526,
-0.002383273560553789,
-0.019762497395277023,
-0.051895249634981155,
-0.07506375759840012,
-0.014933641999959946,
-0.017744794487953186,
0.00814130064100027,
-0.013414960354566574,
-0.020404716953635216,
-0.01592114008963108,
-0.0007701823487877846,
-0.03686503693461418,
-0.09898066520690918,
0.011642176657915115,
-0.0071779158897697926,
0.024255286902189255,
-0.03153907135128975,
-0.03160689026117325,
-0.0047712186351418495,
-0.018341654911637306,
0.005146860610693693,
-0.015742316842079163,
-0.039371687918901443,
0.04383685067296028,
-0.06437361240386963,
0.0037771868519484997,
-0.015584453009068966,
0.001219667145051062,
0.043797578662633896,
-0.02361144684255123,
0.0007300968281924725,
-0.018658185377717018,
0.040854524821043015,
0.00575780775398016,
0.06583315134048462,
-0.01082533784210682,
0.017305521294474602,
0.03011438436806202,
-0.025623532012104988,
0.043123889714479446,
-0.006709767039865255,
-0.0165132824331522,
0.011849405243992805,
-0.00581597862765193,
0.012656578794121742,
-0.01691242679953575,
0.04588122293353081,
-0.002573836361989379,
-0.0394342802464962,
0.012292709201574326,
0.02852492779493332,
0.03538351505994797,
0.021239737048745155,
-0.0672164112329483,
0.05202333629131317,
0.00043290614848956466,
-0.045626815408468246,
-0.00468540471047163,
-0.07043583691120148,
0.03137022629380226,
-0.004568381700664759,
-0.018650099635124207,
0.04401338845491409,
-0.007986882701516151,
0.045823708176612854,
0.01517940778285265,
-0.029886538162827492,
-0.04368751496076584,
0.015867970883846283,
-0.02313520573079586,
0.019580919295549393,
-0.014288755133748055,
0.002318547572940588,
0.01893574558198452,
0.01946512795984745,
-0.03952421993017197,
0.006181112956255674,
0.001181803410872817,
-0.024011895060539246,
-0.0470639169216156,
0.032329756766557693,
0.014131259173154831,
-0.021061599254608154,
-0.013076328672468662,
-0.01621190272271633,
0.07139264047145844,
0.020851602777838707,
0.018679818138480186,
0.03729963302612305,
-0.03781397268176079,
0.0005007214494980872,
-0.03188537433743477,
-0.01743769459426403,
-0.044773977249860764,
-0.034480463713407516,
0.038018252700567245,
-0.021787023171782494,
-0.04236093536019325,
0.025261150673031807,
0.01771857589483261,
-0.051619868725538254,
-0.03693496435880661,
0.014697099104523659,
-0.036673981696367264,
-0.0029680151492357254,
-0.008870217949151993,
-0.06172453612089157,
0.014677397906780243,
-0.03338780254125595,
0.006735943257808685,
0.02978784590959549,
-0.032777220010757446,
-0.014237281866371632,
0.03308999165892601,
0.07106099277734756,
0.03614598885178566,
0.0022430934477597475,
-0.0433746799826622,
-0.013047611340880394,
0.060913342982530594,
0.03129936382174492,
0.03401672840118408,
0.01055277418345213,
0.015667619183659554,
0.018709970638155937,
-0.019536640495061874,
-0.07601556926965714,
0.014194413088262081,
-0.027583450078964233,
0.042347170412540436,
0.07196526229381561,
0.0028093510773032904,
0.01818743906915188,
0.006185117177665234,
-0.02045738324522972,
-0.020454561337828636,
-0.05729498714208603,
0.08284332603216171,
-0.008505046367645264,
-0.02899779938161373,
-0.052548639476299286,
0.029352763667702675,
-0.030942510813474655,
-0.05378131568431854,
0.03652559220790863,
0.0526571124792099,
0.020342687144875526,
0.023367207497358322,
-0.08735671639442444,
-0.04196740314364433,
0.007792851887643337,
-0.0007641493575647473,
0.0561949722468853,
-0.008954024873673916,
-0.027214843779802322,
0.030422616750001907,
0.07773926854133606,
-0.028192415833473206,
0.03992987051606178,
0.07368575036525726,
-0.0033054621890187263,
0.00849140528589487,
-0.0513780377805233,
-0.027505075559020042,
0.035639915615320206,
0.016085831448435783,
-0.016754604876041412,
-0.0018691514851525426,
0.008214732632040977,
0.045815423130989075,
-0.040485553443431854,
-0.030197976157069206,
0.025905439630150795,
0.09632116556167603,
-0.019101863726973534,
-0.013862992636859417,
0.04113428294658661,
0.042820148169994354,
-0.027476675808429718,
-0.000446992926299572,
0.06564445793628693,
-0.03897911310195923,
0.03308276832103729,
-0.0031740833073854446,
0.036409929394721985,
-0.0396992452442646,
0.035633135586977005,
0.019601844251155853,
-0.024705853313207626,
0.01735682226717472,
0.011039754375815392,
-0.04575176537036896,
-0.05588763952255249,
-0.003168813418596983,
0.0025944605004042387,
0.07303465902805328,
-0.009867629036307335,
-0.019351860508322716,
0.0193275548517704,
0.009729760698974133,
-0.021975910291075706,
-0.011526748538017273,
0.02524648606777191,
-0.043962810188531876,
-0.08262399584054947,
-0.004831345286220312,
0.021534496918320656,
0.005573873408138752,
-0.05769534036517143,
0.019744286313652992,
-0.010968702845275402,
-0.03430657833814621,
0.06423662602901459,
0.011951117776334286,
0.02095896191895008,
0.00694404449313879,
-0.005611566826701164,
-0.0035268773790448904,
-0.03208919242024422,
-0.014684110879898071,
-0.02960115671157837,
0.04342145472764969,
-0.02247595228254795,
0.03611525520682335,
0.011229717172682285,
-0.05488703399896622,
-0.007345506921410561,
-0.05100685730576515,
-0.08521768450737,
0.05084008723497391,
-0.012412941083312035,
0.0708145946264267,
0.0048873270861804485,
0.02069810777902603,
-0.030692243948578835,
-0.0358465239405632,
0.010906911455094814,
0.036346435546875,
-0.059670768678188324,
-0.03934947028756142,
0.009017802774906158,
0.0534871444106102,
-0.01991550624370575,
0.020878484472632408,
-0.0075205652974545956,
0.04789508506655693,
0.06261475384235382,
0.00537882000207901,
-0.0066457814536988735,
0.022203415632247925,
-0.004455342888832092,
-0.013897962868213654,
-0.04023663327097893,
0.04552111029624939,
0.05859535187482834,
0.010234126821160316,
0.0029683602042496204,
-0.05838047340512276,
-0.017075106501579285,
-0.001962224952876568,
-0.024657810106873512,
-0.04220813512802124,
0.01937791518867016,
-0.05776289105415344,
-0.04058587923645973,
0.018538257107138634,
-0.012799671851098537,
0.012340851128101349,
-0.023780805990099907,
-0.007234680000692606,
0.04100120812654495,
0.008906020782887936,
-0.02715456299483776,
0.05983193591237068,
0.017018122598528862,
0.016084739938378334,
-0.016038795933127403,
0.01934708282351494,
-0.0002380421501584351,
-0.0051450286991894245,
0.01472637988626957,
-0.06786414980888367,
-0.0064290668815374374,
-0.026816777884960175,
0.00024077435955405235,
-0.023809274658560753,
0.006537461653351784,
0.01681467518210411,
-0.030848590657114983,
0.056643642485141754,
-0.007614918984472752,
0.022401776164770126,
-0.07414352148771286,
-0.09660522639751434,
-0.00880187377333641,
-0.015068764798343182,
-0.052279531955718994,
-0.10038917511701584,
0.04554017633199692,
0.00376463052816689,
0.01814958266913891,
-0.021944398060441017,
-0.0041077835485339165,
-0.006491865962743759,
0.038331516087055206,
0.005449377931654453,
-0.0164653230458498,
0.03513617813587189,
-0.03850603103637695,
0.024331841617822647,
0.0387859009206295,
-0.06560739874839783,
-0.02552708052098751,
0.0027473443187773228,
-0.0653558298945427,
0.005952155217528343,
-0.059420377016067505,
-0.0015752280596643686,
-0.0351962111890316,
-0.017424749210476875,
0.02293904684484005,
-0.14554229378700256,
-0.015666205435991287,
0.0260357353836298
] |
<p>Whenever I have seen Venus described, its high surface temperature is attributed to an intense greenhouse effect. This seems to make sense, as its atmosphere is roughly 96% CO<sub>2</sub>. But on Earth, the greenhouse effect works because the atmosphere is (mostly) transparent to sunlight, but (somewhat) opaque to longer wavelength light radiated back from the surface.</p>
<p>The atmosphere of Venus would be very opaque to longer wavelength light from the surface, just like Earth (at least around the CO<sub>2</sub> absorption bands). But isn't Venus also very cloudy and largely opaque to visible light? If the solar radiation that reaches the surface is limited, wouldn't this also limit the ability of the CO<sub>2</sub> to "trap" heat?</p>
<p>The atmospheric pressure at the surface of Venus is much higher than it is at the surface of Earth. Isn't this a more straight-forward explanation for much of the high temperature?</p> | g5489 | [
0.0441807359457016,
0.01687854342162609,
0.0033573773689568043,
0.07412610948085785,
0.005218220874667168,
0.10083900392055511,
0.03887249156832695,
0.02684558555483818,
-0.03233399614691734,
-0.0010450572008267045,
0.012600802816450596,
0.021955540403723717,
0.06292205303907394,
0.006149983499199152,
0.0021667410619556904,
0.037025053054094315,
0.05372073873877525,
-0.022374290972948074,
0.01123984158039093,
0.027635453268885612,
-0.016334732994437218,
-0.05686473473906517,
0.043403446674346924,
-0.008195506408810616,
-0.09607737511396408,
0.038365766406059265,
0.01593727245926857,
0.008235340006649494,
0.05344710871577263,
-0.006299037951976061,
-0.02853044867515564,
0.022970050573349,
0.04856396093964577,
-0.01608135551214218,
0.004264358896762133,
0.0038195326924324036,
-0.0014371686847880483,
0.005330487620085478,
0.02904585748910904,
-0.02223772555589676,
-0.02725241333246231,
-0.03547198325395584,
0.022766320034861565,
0.018132803961634636,
-0.0445236936211586,
-0.024174828082323074,
-0.04043307527899742,
-0.020388340577483177,
-0.0016147438436746597,
-0.04599012807011604,
-0.015762999653816223,
0.01309832464903593,
-0.03018021211028099,
-0.037352267652750015,
0.028387470170855522,
0.012061730958521366,
0.02315044216811657,
0.03733937814831734,
0.07726119458675385,
0.025369539856910706,
0.0015832160133868456,
-0.01222781091928482,
-0.010923338122665882,
0.05894676595926285,
-0.0037288987077772617,
-0.007843095809221268,
-0.05197325721383095,
-0.007570852525532246,
0.040984611958265305,
-0.0022117826156318188,
-0.010648678988218307,
-0.03638919070363045,
-0.03885255381464958,
-0.07960830628871918,
0.00451534241437912,
-0.015489268116652966,
-0.052491020411252975,
-0.004191149026155472,
0.018240012228488922,
0.0004659171390812844,
0.03171726316213608,
-0.009767004288733006,
-0.037516552954912186,
0.030253099277615547,
0.0824524536728859,
-0.052019257098436356,
0.0007873952854424715,
-0.02825446054339409,
-0.0003486576024442911,
0.008448207750916481,
0.027940204367041588,
0.00007137520151445642,
0.05802127718925476,
0.028309451416134834,
-0.026475772261619568,
-0.017795749008655548,
0.03831421583890915,
-0.03386438265442848,
-0.015216989442706108,
0.0033946128096431494,
-0.01862710900604725,
-0.04197842255234718,
0.046487897634506226,
0.06539102643728256,
0.013489790260791779,
-0.01229992974549532,
0.00792840775102377,
-0.0031441550236195326,
-0.030625376850366592,
-0.0001867712417151779,
-0.006540256552398205,
0.008601722307503223,
-0.055075980722904205,
-0.026972254738211632,
-0.038765255361795425,
-0.008065154775977135,
0.049389779567718506,
-0.034513819962739944,
0.058812882751226425,
0.029929623007774353,
0.04805681109428406,
0.14651107788085938,
0.02159978449344635,
0.0035039654467254877,
0.0035867164842784405,
-0.014954589307308197,
-0.0323299914598465,
-0.041486892849206924,
0.03496972471475601,
-0.07711419463157654,
-0.03227372467517853,
0.06317415833473206,
-0.04494604468345642,
0.03754783421754837,
0.036493558436632156,
-0.008884494192898273,
-0.06742321699857712,
-0.01691431738436222,
0.004706185311079025,
0.060005199164152145,
0.041882943361997604,
0.02418534830212593,
0.050779711455106735,
0.039469268172979355,
-0.061495423316955566,
0.05093269422650337,
-0.002856035018339753,
0.026809021830558777,
0.0592665821313858,
-0.0011291287373751402,
-0.003796506440266967,
0.036674462258815765,
0.05911897122859955,
-0.01720549538731575,
0.0029179449193179607,
-0.009820226579904556,
0.04484153166413307,
-0.05491434782743454,
0.022789880633354187,
0.034679558128118515,
0.0440744124352932,
0.013707769103348255,
0.009641625918447971,
-0.027599312365055084,
-0.11491367965936661,
0.016825277358293533,
-0.04378308728337288,
-0.04052828252315521,
-0.07582150399684906,
0.002044946188107133,
-0.05024755746126175,
0.032151300460100174,
0.037371888756752014,
0.06798502057790756,
-0.0295886043459177,
-0.02517291158437729,
0.1105685904622078,
0.00002973108166770544,
0.021452225744724274,
-0.027140945196151733,
0.016956767067313194,
-0.027050592005252838,
-0.011682418175041676,
-0.06008220091462135,
-0.01601368933916092,
-0.003250635229051113,
0.021697621792554855,
-0.05587689206004143,
-0.0032054828479886055,
0.0752183049917221,
-0.03446182981133461,
-0.022234268486499786,
0.019865522161126137,
0.011698572896420956,
0.05393889918923378,
-0.08546030521392822,
-0.023842018097639084,
0.0024067580234259367,
-0.07340133190155029,
0.037571001797914505,
-0.06266642361879349,
0.04657783359289169,
0.03243451565504074,
-0.016712382435798645,
0.00203621294349432,
0.04104781523346901,
-0.02715010568499565,
0.028837284073233604,
0.01990324817597866,
0.019039718434214592,
-0.0030824600253254175,
-0.06313131004571915,
0.09911144524812698,
0.021047087386250496,
0.04214257746934891,
0.01981969177722931,
-0.03942666947841644,
-0.017893565818667412,
-0.03268473222851753,
-0.044378940016031265,
0.0706685483455658,
-0.03797384724020958,
0.02317827381193638,
-0.0005672990228049457,
-0.037573378533124924,
0.020225489512085915,
-0.08795038610696793,
-0.002553348196670413,
0.026181500405073166,
0.06325706839561462,
0.008800342679023743,
0.025767691433429718,
-0.0318097360432148,
-0.00012966396752744913,
-0.06229391321539879,
-0.007522466592490673,
0.011237316764891148,
-0.040234193205833435,
-0.0008928499883040786,
0.014152349904179573,
-0.03568445146083832,
-0.0995461493730545,
-0.07306075841188431,
0.02152780257165432,
0.030335690826177597,
0.0010287517216056585,
-0.027668209746479988,
0.02729363553225994,
-0.03800974041223526,
-0.01710771769285202,
-0.015656905248761177,
0.03972562029957771,
-0.008150249719619751,
-0.01426872331649065,
0.029502926394343376,
-0.04023224860429764,
-0.05396190285682678,
0.029101314023137093,
-0.006487166043370962,
-0.07266047596931458,
-0.015628507360816002,
-0.04981885105371475,
0.04196649789810181,
0.04660971462726593,
0.022951001301407814,
0.031566012650728226,
-0.03585341200232506,
-0.0007584468694403768,
0.016347847878932953,
-0.03958794102072716,
0.0022074126172810793,
0.0848584994673729,
-0.0042772674933075905,
0.017024386674165726,
-0.01827642321586609,
0.05682989954948425,
-0.030499348416924477,
0.0016823792830109596,
-0.003386307740584016,
-0.03952913358807564,
0.05383189767599106,
0.004007039126008749,
-0.009474695660173893,
-0.004609914496541023,
0.027562033385038376,
-0.11827229708433151,
-0.027118170633912086,
-0.00278555229306221,
0.023263495415449142,
-0.030393455177545547,
0.0571027435362339,
0.0038264263421297073,
0.012990470975637436,
0.03191584721207619,
-0.011728227138519287,
-0.030669862404465675,
0.021378768607974052,
0.03237443044781685,
-0.07980313152074814,
0.03371085599064827,
0.005367441568523645,
-0.04393010959029198,
0.004734116606414318,
0.017313741147518158,
-0.007042842451483011,
0.01573094166815281,
-0.05719504505395889,
-0.011032141745090485,
-0.011691219173371792,
-0.010341735556721687,
-0.0069596292451024055,
0.01196261402219534,
-0.05398298427462578,
0.009653938934206963,
-0.05282710865139961,
-0.0028941468335688114,
-0.039829593151807785,
-0.016211112961173058,
0.06012820079922676,
0.048166751861572266,
-0.0009643489611335099,
-0.01206888910382986,
-0.01586955040693283,
0.005990751087665558,
-0.014238184317946434,
-0.021487075835466385,
-0.032349057495594025,
-0.050939034670591354,
-0.029954830184578896,
-0.05955866724252701,
0.05384458601474762,
0.059735748916864395,
0.0032647615298628807,
0.0075478097423911095,
-0.003064240561798215,
0.0455179288983345,
-0.036146193742752075,
0.008257443085312843,
0.0385688915848732,
-0.008115997537970543,
-0.028225304558873177,
-0.013137700967490673,
-0.07615713775157928,
-0.04845014587044716,
0.018380485475063324,
0.0008390052244067192,
0.016825485974550247,
-0.04871884360909462,
-0.0437401682138443,
0.032149288803339005,
0.0033331981394439936,
0.018215684220194817,
0.007535478100180626,
0.019450124353170395,
-0.02331838570535183,
0.021710466593503952,
0.028174376115202904,
0.0357283279299736,
-0.049693915992975235,
-0.016683191061019897,
0.037665512412786484,
0.015450727194547653,
-0.04489017650485039,
-0.041847631335258484,
0.004251631908118725,
-0.025161996483802795,
0.0021829591132700443,
-0.00114060181658715,
-0.00700311129912734,
0.023296182975172997,
-0.021234501153230667,
-0.002227237680926919,
-0.004172261338680983,
0.05705086514353752,
0.07466351240873337,
-0.0573938824236393,
-0.019647778943181038,
0.04102298244833946,
0.020626209676265717,
0.019614914432168007,
0.03846229612827301,
0.01703767664730549,
0.004998153541237116,
0.05887928232550621,
0.03344079852104187,
-0.039058297872543335,
-0.02361711487174034,
0.03941335529088974,
-0.032783519476652145,
-0.044261857867240906,
-0.016863448545336723,
-0.07924053072929382,
0.03230184689164162,
0.050014201551675797,
-0.011661208234727383,
-0.040413640439510345,
0.045036621391773224,
0.04860702157020569,
0.01439081970602274,
-0.029046066105365753,
0.013288600370287895,
-0.011793501675128937,
0.038843750953674316,
-0.02661345712840557,
-0.056553471833467484,
0.032080285251140594,
0.003560942830517888,
0.019936297088861465,
-0.013092130422592163,
0.0663532242178917,
0.04140673205256462,
0.010491929948329926,
-0.03907136991620064,
-0.011021972633898258,
0.013262207619845867,
0.010402816347777843,
-0.01558435894548893,
-0.029910629615187645,
0.01673802174627781,
-0.02685180865228176,
-0.04253989830613136,
-0.010147396475076675,
0.005701103713363409,
0.0021431196946650743,
0.015814563259482384,
0.07609368115663528,
0.0381886325776577,
-0.028294777497649193,
-0.052760377526283264,
-0.028449933975934982,
0.040786758065223694,
-0.004895858000963926,
-0.07253451645374298,
-0.0006906203925609589,
-0.005273381248116493,
0.05559401959180832,
0.021832119673490524,
-0.019015107303857803,
0.001541191479191184,
0.021390628069639206,
0.03335068002343178,
-0.002230125479400158,
0.02512226440012455,
-0.03030405193567276,
-0.02684168703854084,
0.05707274377346039,
0.08325380831956863,
-0.006130973808467388,
0.004046035930514336,
-0.015942508354783058,
-0.04097284376621246,
-0.014060196466743946,
-0.01490702573210001,
0.0526333823800087,
-0.004262683447450399,
-0.05917573720216751,
-0.01893029175698757,
0.01734171248972416,
-0.02835150808095932,
0.02568596787750721,
-0.035216014832258224,
0.007629035040736198,
0.006545423064380884,
0.046872496604919434,
0.04014331474900246,
-0.015068723820149899,
-0.06300220638513565,
-0.016743894666433334,
-0.0004842435009777546,
0.009966001845896244,
-0.037370532751083374,
0.044060152024030685,
0.05349480360746384,
0.0739022046327591,
0.020211607217788696,
0.03511182591319084,
0.0029102852568030357,
0.003181842854246497,
-0.013851114548742771,
-0.028850236907601357,
0.0005800182116217911,
0.02036355994641781,
0.06547429412603378,
0.05042548105120659,
-0.03845427185297012,
0.017308935523033142,
-0.012069064192473888,
0.022497570142149925,
-0.0015634145820513368,
-0.010946007445454597,
-0.01730145514011383,
0.03391879051923752,
-0.03472837805747986,
0.027004150673747063,
-0.01130245253443718,
-0.03218267485499382,
0.034530073404312134,
-0.04436572641134262,
-0.021901750937104225,
0.013339598663151264,
-0.03433426097035408,
-0.012664020992815495,
-0.013047825545072556,
0.02478673867881298,
0.04815332964062691,
-0.030815672129392624,
0.02434731461107731,
-0.017206614837050438,
0.09475764632225037,
0.02202851139008999,
-0.04375492036342621,
-0.0032601067796349525,
-0.03687693923711777,
0.020672649145126343,
0.03014562278985977,
-0.0047824205830693245,
-0.0338699109852314,
0.004832609090954065,
0.01663322187960148,
-0.0019419158343225718,
-0.006329894997179508,
-0.015998486429452896,
-0.011872119270265102,
0.0025565302930772305,
0.03644365444779396,
-0.006213621702045202,
-0.01734866015613079,
0.003891443833708763,
-0.006867082789540291,
-0.01238664984703064,
-0.013271110132336617,
0.06202307343482971,
0.011027475818991661,
-0.024238986894488335,
-0.00668389443308115,
-0.0370912067592144,
-0.033308204263448715,
0.03819497674703598,
0.026182251051068306,
-0.01024805661290884,
0.016740502789616585,
-0.029286446049809456,
0.00334218330681324,
0.0367271788418293,
0.06784455478191376,
0.03441974148154259,
0.03937812149524689,
-0.004381099250167608,
0.028036728501319885,
0.04053772985935211,
-0.019379694014787674,
-0.01564151607453823,
0.0025053450372070074,
-0.02228747494518757,
-0.003483895678073168,
0.04525448754429817,
0.0038152143824845552,
0.04659423604607582,
-0.0007874468574300408,
0.005709846969693899,
0.052127957344055176,
0.07357625663280487,
-0.016411591321229935,
0.01995314657688141,
-0.03274926170706749,
0.02876528725028038,
-0.025768272578716278,
0.0070197065360844135,
0.022588951513171196,
0.02574417181313038,
0.0610162690281868,
-0.022891508415341377,
0.02334597148001194,
-0.04669782519340515,
-0.05720309540629387,
0.039598919451236725,
-0.027815883979201317,
-0.004621352534741163,
-0.0694088488817215,
-0.026815831661224365,
-0.04835127666592598,
-0.04650602117180824,
-0.0053671193309128284,
0.04993686452507973,
0.015831274911761284,
0.028986385092139244,
-0.05564534291625023,
-0.0022266937885433435,
0.019722744822502136,
-0.06581785529851913,
0.017062576487660408,
-0.0025469146203249693,
0.0133016686886549,
-0.041512563824653625,
0.012508473359048367,
-0.047415975481271744,
-0.053238555788993835,
0.03368024900555611,
-0.05296079441905022,
-0.0234015304595232,
0.05943607911467552,
-0.009812995791435242,
0.04264760762453079,
-0.008258718065917492,
0.033297523856163025,
0.009723135270178318,
0.044601649045944214,
-0.013089202344417572,
0.02831249125301838,
0.000011852464922412764,
-0.07142698019742966,
0.04701101407408714,
0.018022872507572174,
-0.012620970606803894,
-0.049874622374773026,
-0.08508315682411194,
-0.05515144020318985,
0.037747934460639954,
-0.02382054179906845,
0.015253051184117794,
-0.02809370681643486,
-0.01846877671778202,
0.025233183056116104,
-0.019327104091644287,
0.044029898941516876,
-0.005117983557283878,
0.015194231644272804,
0.01511914748698473,
0.0677499771118164,
0.009892579168081284,
-0.012896616011857986,
-0.04286874085664749,
-0.009942503646016121,
0.029632296413183212,
0.020005587488412857,
0.00460045738145709,
0.014280249364674091,
-0.05342889204621315,
0.02818545326590538,
-0.001329423626884818,
-0.08972436189651489,
-0.011483103968203068,
0.0195157527923584,
0.04780653491616249,
0.011844519525766373,
0.032034922391176224,
0.002710983157157898,
-0.024915898218750954,
-0.01897415891289711,
-0.009068346582353115,
-0.00042849231977015734,
-0.0656704381108284,
-0.04913461580872536,
-0.019841235131025314,
0.023394059389829636,
0.005018906202167273,
-0.013345267623662949,
0.00290853762999177,
0.034239962697029114,
-0.05754680559039116,
-0.00012741271348204464,
0.002307888586074114,
-0.04660855233669281,
0.04099058732390404,
0.027260955423116684,
0.05183019861578941,
0.06276813894510269,
-0.004147262312471867,
0.012657752260565758,
0.022498492151498795,
0.03420816361904144,
-0.03608941659331322,
-0.0010645485017448664,
-0.015099924057722092,
-0.02269837073981762,
-0.03833044692873955,
-0.018375493586063385,
-0.010914013721048832,
-0.010770516470074654,
-0.004674338269978762,
0.026858927682042122,
-0.01607908494770527,
0.017134983092546463,
0.009630869142711163,
0.019663391634821892,
-0.0734696313738823,
-0.011897371150553226,
0.006813254207372665,
0.04738062620162964,
-0.03931475803256035,
-0.03452369570732117,
-0.022033922374248505,
-0.038193024694919586,
-0.028709255158901215,
0.006770787760615349,
-0.0014311914565041661,
0.04052475094795227,
0.02515469305217266,
-0.0017635755939409137,
-0.010469160974025726,
-0.004742225166410208,
-0.010315896943211555,
0.009071100503206253,
-0.07554369419813156,
0.08470376580953598,
0.05724003538489342,
-0.012454459443688393,
0.004053929820656776,
-0.04169193655252457,
-0.02378380112349987,
-0.0010155257768929005,
0.048666540533304214,
-0.0018160862382501364,
0.03227570280432701,
0.03679914399981499,
-0.01388646475970745,
-0.039188142865896225,
-0.010077053681015968,
-0.021869376301765442,
-0.008003787137567997,
-0.052499860525131226,
-0.06698167324066162,
0.0316118560731411,
-0.05344682186841965,
-0.01814780756831169,
0.03942500427365303,
0.0445941686630249,
-0.05934373661875725,
0.01634559966623783,
-0.0638887882232666,
0.019042646512389183,
0.11910546571016312,
-0.0065223099663853645,
-0.01778865046799183,
-0.0465165413916111,
-0.023006850853562355,
0.04025067016482353,
-0.03854561224579811,
-0.003453826764598489,
0.02165483683347702,
0.004766183905303478,
0.008880771696567535,
0.0027948333881795406,
-0.0030836176592856646,
0.008703488856554031,
0.0019891236443072557,
-0.02522176504135132,
0.009397360496222973,
0.0034902598708868027,
-0.030921511352062225,
-0.035863328725099564,
0.030240973457694054,
0.021637797355651855,
-0.03846079856157303,
-0.004581288900226355,
-0.0019912542775273323,
-0.015241316519677639,
-0.03643787279725075,
0.030654538422822952,
-0.029228560626506805,
-0.022162452340126038,
0.0016488691326230764,
0.04980742931365967,
-0.04513733088970184,
-0.0005803349195048213,
-0.06043460592627525,
-0.011082588694989681,
-0.0355195514857769
] |
<p>I'm having a hard time understanding the deal with <a href="http://en.wikipedia.org/wiki/Self-adjoint_operator" rel="nofollow">self-adjoint differential opertors </a> used to solve a set of two coupled 2nd order PDEs.</p>
<p>The thing is, that the solution of the PDEs becomes numerically unstable and I've heared that this is due to the fact, that the used operators were not self-adjoint and the energy is not preserved in this case.</p>
<p>The two coupled 2nd order PDEs are:</p>
<p>$$\frac{\partial ^2p}{\partial t^2}=V_{px}^2 {H_2} p + \alpha V_{pz}^2 {H_1} q + V_{sz}^2{H_1}(p - \alpha q) + S\tag{1}$$</p>
<p>$$\frac{\partial ^2q}{\partial t^2}=\frac{V_{pn}^2}{\alpha}{H_2} p + V_{pz}^2 {H_1} q - V_{sz}^2{H_2} \left(\frac{1}{\alpha}p - q \right) + S\tag{2}$$</p>
<p>where p is the pressure wave field and q is an auxiliary wave field, $S$ is the Source term $V_{px}$ and $V_{sz}$ are seismic velocities into the x - or z-direction respectively, $\alpha = 1$ and $H_1$ and $H_2$ are the rotated differential operators:
\begin{eqnarray}
{H_1}& =& \sin ^2 \theta \cos ^2 \phi \frac{\partial ^2}{\partial x ^2}+\sin ^2 \theta \sin ^2 \phi \frac{\partial ^2}{\partial y ^2} + \cos ^2 \theta \frac{\partial ^2}{\partial z ^2}+\\ &&\sin ^2 \theta \sin 2 \phi \frac{\partial ^2}{\partial x \partial z} + \sin 2 \theta \sin \phi \frac{\partial ^2}{\partial x \partial y}+ \sin 2 \theta \cos \phi \frac{\partial ^2}{\partial x \partial y}\end{eqnarray}</p>
<p>$$
{H_2} = \frac{\partial ^2}{\partial x ^2}+\frac{\partial ^2}{\partial y ^2}+\frac{\partial ^2}{\partial z ^2} - {H_1}.
$$</p>
<p>where $\phi$ is an azimuth angle and $\theta$ is a tilt angle.</p>
<p>In this case I am solving for the solution of a pressure wavefield.</p>
<p><strong>EDIT</strong>
Is there a physical explanation for self-adjoint operators?
The paper I am referring to can be found <a href="http://www.cgg.com/technicalDocuments/cggv_0000009953.pdf" rel="nofollow">here</a> were equation 14 and 15 resemble my postet equations.</p> | g5490 | [
0.05015519633889198,
0.007873378694057465,
-0.029461568221449852,
0.0163616631180048,
0.08286264538764954,
-0.06691177934408188,
0.05982263386249542,
-0.025884028524160385,
-0.037918973714113235,
0.009365481324493885,
-0.010105838067829609,
0.04615345969796181,
-0.01722184754908085,
0.045254845172166824,
0.009774647653102875,
-0.03837070241570473,
0.08009297400712967,
0.035260993987321854,
0.016381816938519478,
-0.04259445145726204,
-0.07512935996055603,
-0.0142102325335145,
0.045221418142318726,
-0.027456391602754593,
-0.0018300466472283006,
-0.07353812456130981,
0.049415115267038345,
-0.04667685180902481,
-0.006719685159623623,
-0.03605104610323906,
0.02331702783703804,
0.00947213638573885,
0.07988155633211136,
0.01494491659104824,
-0.029970930889248848,
-0.021031884476542473,
0.0406617633998394,
-0.02772759273648262,
0.01514563150703907,
-0.010009247809648514,
0.018786536529660225,
-0.045423828065395355,
0.05733076110482216,
-0.028781834989786148,
-0.01504592690616846,
-0.05057043954730034,
-0.08854580670595169,
-0.007480738218873739,
-0.0035720248706638813,
0.03787698969244957,
0.04915474355220795,
0.019174426794052124,
0.05410236492753029,
-0.02101624198257923,
0.0031334792729467154,
0.016150381416082382,
0.022678948938846588,
0.03339052572846413,
0.043518614023923874,
0.0061373417265713215,
-0.03219931200146675,
-0.012315457686781883,
0.054546259343624115,
0.03238615021109581,
0.0010559677612036467,
-0.05401118844747543,
-0.026614774018526077,
-0.028665678575634956,
0.05748891830444336,
0.036819685250520706,
-0.02987693063914776,
0.00533446716144681,
0.0096534239128232,
-0.0049924422055482864,
0.032756026834249496,
-0.023467065766453743,
0.024098487570881844,
-0.04563676193356514,
-0.010334547609090805,
-0.027027186006307602,
-0.0011852936586365104,
0.001671519479714334,
0.0010102603118866682,
0.002742972457781434,
0.013111443258821964,
-0.044157836586236954,
0.01283775083720684,
-0.010597358457744122,
-0.005000273697078228,
-0.030488979071378708,
-0.011893878690898418,
-0.011707202531397343,
0.015744399279356003,
0.032654013484716415,
0.01799456775188446,
0.019898546859622,
-0.02085809037089348,
0.0717240571975708,
-0.006148547865450382,
-0.06396299600601196,
-0.012023800052702427,
0.030273394659161568,
-0.01909969002008438,
0.007254750467836857,
0.015704438090324402,
0.0020778838079422712,
-0.0037354803644120693,
0.03678641840815544,
0.008497508242726326,
0.03422508016228676,
0.007114763837307692,
0.044869981706142426,
-0.0033833193592727184,
-0.05436624959111214,
-0.0010318439453840256,
-0.024763494729995728,
-0.011977197602391243,
-0.015960989519953728,
-0.011783424764871597,
0.05546233057975769,
0.023936500772833824,
0.02120397984981537,
0.0434608981013298,
0.050743456929922104,
0.037772078067064285,
-0.0034983763471245766,
-0.009146870113909245,
-0.05400983616709709,
0.029862679541110992,
-0.037879571318626404,
0.01305298414081335,
-0.03816358000040054,
0.049470216035842896,
0.017377108335494995,
0.009488921612501144,
0.020503951236605644,
-0.022824855521321297,
0.0027306382544338703,
0.028360148891806602,
-0.036900170147418976,
0.0515437088906765,
-0.04868768900632858,
0.007784437388181686,
0.007769356481730938,
0.006818321533501148,
0.013237600214779377,
0.06754082441329956,
-0.04062663018703461,
0.023223955184221268,
0.02352055348455906,
-0.021553101018071175,
0.04185425490140915,
0.021038560196757317,
0.020351115614175797,
0.0639796331524849,
0.048574987798929214,
-0.029347525909543037,
-0.02899654023349285,
-0.003571432549506426,
-0.038592129945755005,
0.09609244763851166,
0.011871064081788063,
-0.005925944074988365,
0.04281134903430939,
-0.030718237161636353,
0.010576135478913784,
0.016473762691020966,
-0.04884473979473114,
-0.03942330181598663,
-0.04863257333636284,
-0.016338642686605453,
0.048546165227890015,
0.0649430900812149,
0.08844971656799316,
0.04463570937514305,
0.030273476615548134,
0.0030957714188843966,
-0.007967740297317505,
-0.04010937735438347,
0.061335183680057526,
-0.021304378286004066,
0.004467033315449953,
-0.023991284891963005,
-0.05641523376107216,
0.08229152858257294,
0.013491236604750156,
-0.01929360069334507,
0.023453377187252045,
-0.06701009720563889,
-0.0011239702580496669,
0.060082606971263885,
0.007173324469476938,
-0.003565167775377631,
0.11077750474214554,
-0.04131646081805229,
0.04310833290219307,
-0.0019489653641358018,
-0.044648345559835434,
-0.06152179464697838,
0.048970550298690796,
0.001095241284929216,
0.011119413189589977,
0.13717423379421234,
0.010831918567419052,
-0.002461836440488696,
-0.015225226990878582,
-0.026245221495628357,
-0.02819080278277397,
0.014680144377052784,
-0.020357059314846992,
-0.007732097525149584,
-0.06336329877376556,
0.00022659703972749412,
0.02144639566540718,
-0.026683259755373,
-0.05292458087205887,
0.006961998995393515,
0.011915137991309166,
-0.07210814207792282,
-0.024456864222884178,
-0.016235604882240295,
-0.016730953007936478,
0.05182182043790817,
0.023806121200323105,
-0.045399848371744156,
0.03041909821331501,
-0.005181711632758379,
0.03671658784151077,
-0.031915582716464996,
-0.016635818406939507,
-0.03695948049426079,
-0.008586307056248188,
0.005371659528464079,
0.03287028893828392,
0.04270762577652931,
-0.010198312811553478,
0.03398103266954422,
0.02616659365594387,
0.005148590542376041,
0.05832752585411072,
0.05259963124990463,
-0.025676338002085686,
0.03510098531842232,
-0.011365608312189579,
0.051728036254644394,
0.02808663621544838,
0.07671411335468292,
0.054311905056238174,
0.03409843519330025,
0.011468881741166115,
0.029230335727334023,
-0.04342354089021683,
-0.09023366123437881,
-0.005318557843565941,
-0.021404918283224106,
-0.019479693844914436,
-0.004882200621068478,
0.05289918929338455,
0.00487677613273263,
-0.00287416810169816,
-0.001970604993402958,
0.05422220751643181,
-0.03167765587568283,
0.0057744961231946945,
-0.021112734451889992,
0.009987273253500462,
-0.010215398855507374,
-0.02072220668196678,
0.046757977455854416,
-0.00632056687027216,
0.02940414845943451,
0.055425167083740234,
0.02269098348915577,
0.044775307178497314,
-0.004344271961599588,
-0.0051044258289039135,
-0.016545657068490982,
-0.03338799625635147,
-0.09260313212871552,
0.007142544724047184,
0.03092106245458126,
-0.004380237311124802,
0.007306746672838926,
0.04186009615659714,
-0.01345272921025753,
-0.042005058377981186,
0.037872880697250366,
0.08089959621429443,
-0.02595689706504345,
-0.010524985380470753,
0.007330112159252167,
0.03654993325471878,
-0.01757954992353916,
0.007192652206867933,
-0.012665227055549622,
-0.003871489781886339,
-0.018216433003544807,
-0.07505322992801666,
0.019453108310699463,
0.031673118472099304,
0.024894321337342262,
0.053785089403390884,
-0.022508226335048676,
-0.003437585663050413,
0.032223332673311234,
-0.045780859887599945,
-0.05101476237177849,
-0.06882607936859131,
-0.06031620502471924,
0.05725911259651184,
0.011999761685729027,
-0.016313618049025536,
-0.02893912047147751,
-0.015079081989824772,
0.011264815926551819,
0.029113316908478737,
-0.0692831426858902,
-0.0770772397518158,
-0.014752654358744621,
-0.02749866247177124,
-0.06978906691074371,
-0.0519179068505764,
-0.026514288038015366,
-0.0004918079939670861,
-0.013816158287227154,
0.03492124006152153,
-0.06751738488674164,
0.0643400251865387,
-0.002442038618028164,
-0.06130446121096611,
0.015191846527159214,
0.008903075940907001,
-0.013600552454590797,
-0.023757727816700935,
0.014551076106727123,
-0.039633676409721375,
-0.00820140354335308,
0.04444827511906624,
0.055636368691921234,
0.0353362150490284,
0.019127322360873222,
-0.0016157240606844425,
-0.04803682118654251,
-0.030880630016326904,
-0.05629007890820503,
0.03866095095872879,
0.06463067978620529,
0.012605812400579453,
-0.03588194400072098,
-0.0016627587610855699,
0.02949417568743229,
0.019439661875367165,
0.04424215480685234,
0.04782465845346451,
-0.07087972015142441,
-0.028457822278141975,
-0.007639376446604729,
0.009006667882204056,
-0.012246706523001194,
0.031790874898433685,
-0.00970927719026804,
-0.02257046103477478,
-0.043759535998106,
0.033272456377744675,
0.010062795132398605,
-0.013724084943532944,
-0.03975984454154968,
0.004091579932719469,
-0.08848501741886139,
-0.04787971079349518,
0.016230473294854164,
-0.011033477261662483,
0.0060305409133434296,
0.01388383749872446,
-0.038393259048461914,
-0.10107266902923584,
-0.011514265090227127,
-0.041092030704021454,
-0.044591937214136124,
0.012421299703419209,
0.049129750579595566,
0.020942559465765953,
0.008011778816580772,
0.07646243274211884,
0.05744442343711853,
-0.019328854978084564,
-0.02400834858417511,
-0.01499601174145937,
0.030444471165537834,
-0.012176393531262875,
0.047308389097452164,
-0.001211908063851297,
-0.017470208927989006,
-0.029374713078141212,
0.041885536164045334,
-0.03462688624858856,
-0.02616777829825878,
0.03368540108203888,
0.010475590825080872,
-0.009477662853896618,
-0.08643023669719696,
0.000923686835449189,
-0.03465764969587326,
-0.015492242760956287,
-0.022480959072709084,
0.004702363163232803,
-0.06212882325053215,
-0.03692644089460373,
-0.019778216257691383,
-0.0014347245451062918,
0.016739901155233383,
0.019504277035593987,
-0.01967606134712696,
-0.042095523327589035,
0.036788925528526306,
-0.028998805209994316,
0.04099022597074509,
0.00643501291051507,
0.04250103980302811,
-0.009110662154853344,
-0.024557804688811302,
-0.0010838084854185581,
0.010889068245887756,
-0.05002252385020256,
0.010918214917182922,
0.020099034532904625,
0.009323024190962315,
-0.014440604485571384,
-0.01727193035185337,
0.020101651549339294,
0.04464410990476608,
0.010135217569768429,
0.03097110241651535,
-0.016367295756936073,
-0.059682879596948624,
0.027595313265919685,
0.028403867036104202,
-0.003351234830915928,
0.01059769093990326,
0.0237849373370409,
0.018592074513435364,
0.012731360271573067,
0.01216994971036911,
0.027166733518242836,
0.008075674995779991,
0.04868309199810028,
-0.003446342423558235,
-0.047783657908439636,
0.06562062352895737,
-0.03933825343847275,
-0.016251185908913612,
0.006835735868662596,
0.07187595218420029,
-0.042730022221803665,
-0.011626207269728184,
0.0037754748482257128,
-0.024789676070213318,
0.057282280176877975,
-0.10845641046762466,
0.002546138595789671,
-0.020688842982053757,
0.0032334360294044018,
-0.01939288154244423,
-0.0052131409756839275,
0.017037127166986465,
-0.006046330090612173,
-0.03742070496082306,
-0.05529281124472618,
-0.06185612455010414,
0.013346569612622261,
0.008609551005065441,
-0.04441579803824425,
-0.013022984378039837,
-0.0524493046104908,
-0.0008503747521899641,
-0.014470494352281094,
0.016797954216599464,
0.002212358172982931,
-0.02940109372138977,
-0.031094465404748917,
0.002427334664389491,
0.041690289974212646,
0.02087106555700302,
0.05952936038374901,
0.04322439059615135,
-0.011677754111588001,
0.0042490772902965546,
-0.027064310386776924,
-0.005599453579634428,
-0.007880894467234612,
0.0172710157930851,
0.06747909635305405,
-0.042424239218235016,
-0.013328462839126587,
-0.022158779203891754,
0.002273700898513198,
0.0015813845675438643,
-0.0003851174551527947,
-0.0002965870371554047,
-0.01800709404051304,
-0.03721761703491211,
-0.001232418930158019,
-0.037313174456357956,
-0.04300209879875183,
0.012952015735208988,
0.016104286536574364,
0.06640700995922089,
-0.0220418069511652,
0.04857758432626724,
0.003753728000447154,
0.020012766122817993,
-0.06292426586151123,
0.09763209521770477,
0.02647910639643669,
0.028252432122826576,
-0.008770018815994263,
0.022266684100031853,
0.00040589444688521326,
-0.04561370238661766,
-0.045706961303949356,
0.07217534631490707,
0.014150399714708328,
0.040063176304101944,
-0.002303870627656579,
0.012659095227718353,
0.04127595201134682,
-0.05752642825245857,
-0.02770690992474556,
0.009885412640869617,
0.05723906680941582,
0.0030194660648703575,
-0.035973235964775085,
-0.010077794082462788,
0.024826472625136375,
0.03126448392868042,
-0.10867439955472946,
-0.042875420302152634,
-0.01450816635042429,
0.01649746112525463,
-0.0039108507335186005,
-0.024844616651535034,
-0.013132437132298946,
0.0014417674392461777,
0.018377607688307762,
-0.05368383973836899,
0.01673859916627407,
0.007844529114663601,
-0.03488646447658539,
0.017600202932953835,
-0.028003746643662453,
-0.06985948979854584,
0.0017870865995064378,
-0.022918395698070526,
-0.0209539532661438,
0.0449044443666935,
-0.051748476922512054,
0.032955847680568695,
-0.007779351435601711,
-0.030256938189268112,
-0.026866519823670387,
0.036590736359357834,
0.004847537260502577,
-0.05136018991470337,
0.044228244572877884,
-0.012336143292486668,
0.020986301824450493,
0.02122398279607296,
0.0011067289160564542,
-0.022090891376137733,
-0.027207210659980774,
-0.03556082770228386,
0.03869566693902016,
0.0003718109510373324,
0.0012130285613238811,
0.0135189862921834,
0.021752027794718742,
-0.03859659284353256,
-0.011589881032705307,
-0.03152644261717796,
-0.03494024649262428,
-0.003335914807394147,
0.061123427003622055,
0.006399460602551699,
-0.03209945186972618,
-0.017929738387465477,
-0.02247140184044838,
-0.041491854935884476,
-0.026516709476709366,
0.06684078276157379,
-0.016638025641441345,
-0.005241502076387405,
0.026834091171622276,
-0.019766466692090034,
-0.022431369870901108,
0.008027808740735054,
0.03546749800443649,
0.061106808483600616,
0.08673549443483353,
-0.013118254952132702,
0.027243204414844513,
0.008563284762203693,
0.03901824727654457,
0.06472278386354446,
0.0345023088157177,
0.029676180332899094,
-0.004839843139052391,
0.0018047781195491552,
0.03969605639576912,
-0.02307606302201748,
0.04177341237664223,
-0.036236513406038284,
0.05868493393063545,
-0.004754060413688421,
-0.0029962584376335144,
-0.015274656936526299,
0.02137238159775734,
-0.03252638131380081,
0.05864054337143898,
-0.013887304812669754,
0.0006196334143169224,
0.07468738406896591,
0.033974941819906235,
-0.023189695551991463,
0.0014236138667911291,
0.005366968922317028,
-0.028206823393702507,
-0.021745366975665092,
0.018330208957195282,
0.041934140026569366,
0.01031556911766529,
0.018116191029548645,
-0.03609619662165642,
-0.019245285540819168,
-0.035864539444446564,
0.037844572216272354,
0.016354313120245934,
-0.04661043360829353,
0.052754130214452744,
0.05560609698295593,
0.028104612603783607,
0.010307216085493565,
0.0709102675318718,
0.008131762035191059,
-0.019154584035277367,
-0.05163899064064026,
0.012875732965767384,
0.00995932798832655,
0.011799664236605167,
-0.11502069979906082,
0.032266080379486084,
0.05091378465294838,
-0.001667521893978119,
-0.0710580050945282,
-0.010009944438934326,
-0.04411498084664345,
0.035941243171691895,
0.0020045312121510506,
0.01016007550060749,
-0.0036664993967860937,
0.02161359041929245,
0.039293669164180756,
0.020268317312002182,
-0.03003595396876335,
0.0214404109865427,
0.014377526007592678,
0.05329933762550354,
-0.01377080474048853,
-0.03690889850258827,
0.004632204305380583,
0.06511680781841278,
0.0229346863925457,
0.014460787177085876,
-0.04714154452085495,
-0.040567848831415176,
-0.026185983791947365,
0.020250173285603523,
0.039457689970731735,
-0.02775222808122635,
0.013013925403356552,
-0.01641586609184742,
0.05928431451320648,
0.005046935752034187,
-0.008126926608383656,
-0.04802414029836655,
-0.013493877835571766,
-0.009109427221119404,
0.023407327011227608,
-0.01794010028243065,
-0.0025356276892125607,
0.0495644137263298,
-0.008168531581759453,
0.04844655841588974,
-0.04357582703232765,
0.04334146901965141,
-0.03657139837741852,
-0.021415332332253456,
-0.05092579126358032,
0.08269347250461578,
-0.02639608457684517,
0.0076498002745211124,
0.023607108741998672,
-0.044530488550662994,
0.00015139629249460995,
0.03363591432571411,
-0.01528595108538866,
-0.057319000363349915,
0.005189999938011169,
-0.04392331838607788,
0.00660028075799346,
0.008405931293964386,
-0.011085402220487595,
-0.041399065405130386,
-0.006599262822419405,
-0.02603789046406746,
0.03464013338088989,
-0.013848778791725636,
-0.057484470307826996,
0.0036847065202891827,
-0.027511855587363243,
-0.02816302701830864,
0.013850447721779346,
-0.021379128098487854,
-0.020676013082265854,
-0.05117322504520416,
0.02765134535729885,
0.027707519009709358,
0.0029896884225308895,
-0.03058115765452385,
0.019483208656311035,
-0.0010941928485408425,
-0.03898214176297188,
0.01421806588768959,
-0.06984753906726837,
0.00891455914825201,
-0.035292137414216995,
-0.01082147192209959,
0.02455717697739601,
-0.04518556594848633,
0.016393234953284264,
-0.007984163239598274,
0.0533190593123436,
-0.06848111748695374,
0.01247347891330719,
-0.006427241954952478,
0.0335715189576149,
-0.025766387581825256,
-0.00006404868327081203,
-0.011823756620287895,
0.004314098507165909,
-0.01348880585283041,
0.06776931136846542,
0.015639225021004677,
0.010889681056141853,
-0.006252567749470472,
0.0024092933163046837,
-0.0459638349711895,
-0.027859525755047798,
-0.03922614827752113,
-0.0554456003010273,
0.010851186700165272,
-0.046698540449142456,
0.0018986174836754799,
0.033386193215847015,
-0.07768971472978592,
0.015411742962896824,
-0.0556342750787735,
-0.05599908158183098,
-0.04101857170462608
] |
<p>So, I have a couple questions about transfer orbits.</p>
<p>As I understand it, an object's, say a satellite, orbit is basically tied to it velocity relative to the object, the planet, that it is orbiting.</p>
<p>The basic premise is that you have the satellite in a circular orbit of X radius, going speed v. Now, if the satellite decelerates, it reduces its velocity.</p>
<p>Since the new velocity is not enough to maintain its original orbit, the satellite will "fall" towards the planet. Now, even though the satellite was (say) originally at the proper velocity for the new lower orbit due to the deceleration, by the time it actually arrives at the new orbit, its velocity likely changed, due to the different acceleration vector of the planet, the vector causing the actual fall. Even if it was at the proper velocity, it's actual vector would like be wrong, it would no longer be tangential to the planet, it would likely be steeper. This would effectively cause the satellite to fall right through the lower orbit and keep accelerating toward the planet. Minimally it would not be in the stable orbit desired.</p>
<p>So, this is why there is a second acceleration/deceleration necessary to correct the satellites velocity and perhaps it vector once it reaches the new orbit.</p>
<p>Of course, the opposite all applies if trying to get to a higher orbit.</p>
<p>My question is during the initial deceleration, is that simply applied opposite the current orbital velocity vector? And when the satellite arrives at the new orbit, what direction is the correctional acceleration/deceleration made? Is it the difference of the desired tangential direction that it wants to go and the current direction it is going? or simply opposite its current vector?</p>
<p>I understand that the point of the Hohmann transfer orbits is to use as little velocity change (and thus fuel) as possible, but can an orbital transfer be faster or slower if you're willing to burn more fuel to affect the velocity change? Will a slower satellite "fall faster" than a faster one? Intuitively that makes sense to me, but at the same time there's the concept that no matter how fast the bullet, it hits the ground at the same time, it just travels farther. So I'm not sure.</p>
<p>On the other hand, if you apply more thrust and you're trying to lift to a higher orbit, that seems directly related to the amount of thrust you're willing to use.</p>
<p>Is this how the transfer orbits work? There's the math and formulas to calculate the delta v necessary on both ends of the transfer, but I'm just trying to visualize the process.</p>
<p>Finally, if you had unlimited fuel, and time was more a consideration, would you even bother with this process versus something more "point and shoot, turn and burn"?</p> | g5491 | [
0.022632943466305733,
-0.01197983231395483,
0.011607296764850616,
0.05721431225538254,
0.06608784198760986,
0.011115624569356441,
0.008789361454546452,
0.006231626030057669,
-0.04620454087853432,
-0.014956443570554256,
0.0014218479627743363,
0.05158494785428047,
0.09299919009208679,
0.006143889855593443,
-0.012639766559004784,
-0.04640398919582367,
0.0850546583533287,
-0.009961025789380074,
-0.002643282525241375,
0.05854058638215065,
0.04153271019458771,
-0.008117702789604664,
-0.03271329402923584,
-0.015586448833346367,
-0.020814871415495872,
-0.0031416907440871,
-0.01422527339309454,
-0.02446999028325081,
-0.0055762422271072865,
0.041822489351034164,
-0.006725903134793043,
-0.05224400758743286,
-0.012143910862505436,
-0.001511343172751367,
-0.06422221660614014,
0.0008356116013601422,
-0.014637036249041557,
0.002496065106242895,
0.042155105620622635,
0.001614871434867382,
-0.015105707570910454,
-0.08203115314245224,
-0.024239446967840195,
0.0032263316679745913,
0.01347443088889122,
-0.012139036320149899,
-0.027054032310843468,
-0.02854260802268982,
0.050442080944776535,
-0.008701828308403492,
0.0007506376714445651,
0.05633492022752762,
-0.03623545914888382,
0.026828063651919365,
-0.0442606545984745,
0.011375321075320244,
0.02818170376121998,
-0.012163901701569557,
0.021720686927437782,
0.016133805736899376,
-0.07110615074634552,
0.00932706892490387,
-0.006508289370685816,
-0.04455915093421936,
0.03885137289762497,
-0.008641584776341915,
-0.039705291390419006,
0.04806588217616081,
0.030229538679122925,
0.028256600722670555,
0.022893015295267105,
0.023645693436264992,
-0.04465147480368614,
-0.0725613459944725,
-0.029583442956209183,
-0.020487472414970398,
0.0016587696736678481,
-0.06674350053071976,
0.03939621523022652,
0.010458325035870075,
-0.018535472452640533,
0.07292727380990982,
-0.006471386644989252,
0.029403092339634895,
0.02595563791692257,
0.040875792503356934,
-0.008785013109445572,
0.06326910853385925,
-0.020062671974301338,
0.02032768726348877,
0.03825431317090988,
-0.05658990144729614,
0.027204999700188637,
0.03208548575639725,
-0.01903814636170864,
-0.025138691067695618,
-0.044157475233078,
0.040403813123703,
0.029082603752613068,
-0.02158844843506813,
0.04204479232430458,
-0.04926754906773567,
0.036160871386528015,
-0.037079308182001114,
-0.012934407219290733,
0.021369578316807747,
0.08675742149353027,
0.05208860710263252,
0.02384353242814541,
-0.00668295519426465,
-0.06698872148990631,
-0.08916215598583221,
0.013096805661916733,
-0.030466854572296143,
-0.045944515615701675,
-0.04706045240163803,
0.015406608581542969,
0.016328489407896996,
0.006895684637129307,
-0.008984159678220749,
0.036042388528585434,
0.024143418297171593,
0.001388146192766726,
0.08650097250938416,
0.06809534877538681,
0.011299793608486652,
-0.03540898859500885,
-0.02823648788034916,
0.001006871578283608,
0.035465531051158905,
-0.04888639971613884,
-0.02964053675532341,
-0.0074927625246346,
0.015874169766902924,
-0.002575336489826441,
-0.04169458523392677,
-0.008441989310085773,
-0.020798882469534874,
-0.03629820793867111,
-0.036303214728832245,
0.054796744138002396,
-0.019751466810703278,
0.00642818957567215,
-0.028995532542467117,
-0.10012456774711609,
0.06453169882297516,
-0.02577418088912964,
0.0358901210129261,
0.07662644237279892,
-0.0314306765794754,
-0.040813688188791275,
-0.015384234488010406,
0.007237316574901342,
-0.03710684925317764,
0.01009008102118969,
0.021596509963274002,
0.037287965416908264,
0.019224032759666443,
0.019598713144659996,
-0.005447329021990299,
0.08054795116186142,
0.009610184468328953,
0.024987464770674706,
0.004219226539134979,
-0.06415396183729172,
0.0007373784901574254,
-0.010740276426076889,
-0.02868788130581379,
0.00007592576730530709,
-0.027006836608052254,
-0.007380613125860691,
-0.04348231479525566,
0.03915053978562355,
0.06996981799602509,
-0.009454757906496525,
0.048929329961538315,
0.07377806305885315,
0.024624193087220192,
-0.0388953723013401,
0.010098268277943134,
-0.013655462302267551,
0.003323094453662634,
0.03301743417978287,
0.043821461498737335,
0.03408540412783623,
-0.06370065361261368,
-0.003685514209792018,
-0.04523816332221031,
-0.02682369016110897,
-0.0023711540270596743,
-0.013879644684493542,
-0.03550758212804794,
0.051304347813129425,
-0.0010627394076436758,
0.0027694753371179104,
-0.0038403382059186697,
-0.0162869393825531,
-0.004063156433403492,
-0.07282618433237076,
-0.00818180013448,
0.042792923748493195,
-0.029531659558415413,
0.06502817571163177,
0.022859621793031693,
0.09224792569875717,
0.012423057109117508,
-0.023922786116600037,
0.02218260057270527,
0.023235032334923744,
-0.012789345346391201,
0.028021380305290222,
0.012508888728916645,
-0.0026476900093257427,
-0.005070446990430355,
-0.015798797830939293,
0.044878922402858734,
0.004675745032727718,
0.01667589694261551,
0.022081324830651283,
-0.03183497115969658,
0.004496647045016289,
-0.045539699494838715,
0.026251498609781265,
-0.00495225889608264,
-0.020813612267374992,
0.007026845123618841,
-0.04815207049250603,
-0.05916079878807068,
0.04083317890763283,
0.028475897386670113,
-0.03210288658738136,
0.013272174634039402,
0.018689779564738274,
-0.07565019279718399,
0.010646591894328594,
-0.04140382632613182,
0.035003237426280975,
0.022871265187859535,
0.010768442414700985,
0.04806556552648544,
0.041552502661943436,
-0.031257499009370804,
-0.049106400460004807,
-0.0023952617775648832,
0.02596399560570717,
-0.1118486151099205,
0.06455370038747787,
-0.008393513970077038,
-0.061511196196079254,
-0.051691457629203796,
-0.034418780356645584,
-0.005118145141750574,
-0.07628349959850311,
0.00952960830181837,
-0.025791266933083534,
0.022387735545635223,
-0.04658941924571991,
0.02619006298482418,
-0.06809799373149872,
0.005710851401090622,
-0.01288872491568327,
0.008318399079144001,
0.023329591378569603,
-0.009671219624578953,
-0.04171440005302429,
0.0043570417910814285,
-0.04861714318394661,
-0.0276420209556818,
-0.03437859192490578,
0.030286995694041252,
-0.05307440832257271,
-0.022550467401742935,
0.008652254939079285,
0.04463779181241989,
-0.027108056470751762,
0.036771759390830994,
-0.02079344354569912,
-0.05014234781265259,
-0.0046120574697852135,
-0.029559588059782982,
-0.009133435785770416,
-0.011620679870247841,
-0.04800038039684296,
0.015208286233246326,
-0.00018313560576643795,
-0.008794965222477913,
-0.004937584977596998,
0.05861542001366615,
-0.05944032594561577,
-0.06047847121953964,
-0.018084505572915077,
0.003350666491314769,
0.06481140106916428,
0.01558440551161766,
0.012059350498020649,
0.032833926379680634,
0.05647659674286842,
-0.02200756035745144,
-0.050655756145715714,
-0.028458261862397194,
0.029173092916607857,
-0.0211439561098814,
0.024052634835243225,
0.037250492721796036,
0.05063862353563309,
0.04143914580345154,
-0.05810118839144707,
0.01617193967103958,
-0.07553714513778687,
0.026515407487750053,
-0.034279804676771164,
-0.009078359231352806,
-0.0434286929666996,
0.0008954302757047117,
-0.003139820881187916,
-0.04531830921769142,
-0.029813747853040695,
0.013720440678298473,
0.002293527824804187,
0.013980699703097343,
-0.047039639204740524,
-0.059866998344659805,
-0.05450190603733063,
0.029402941465377808,
0.014361229725182056,
0.03533831611275673,
-0.04937227442860603,
-0.033115945756435394,
-0.02421995811164379,
-0.018700111657381058,
0.03638068586587906,
0.06192999333143234,
-0.03455260396003723,
-0.030683694407343864,
-0.018667371943593025,
0.05926523357629776,
0.004548737779259682,
0.02979295328259468,
0.03390762209892273,
0.03694906458258629,
0.036822620779275894,
0.017763659358024597,
-0.01052991021424532,
-0.00008231453830376267,
0.01425211876630783,
0.006694228388369083,
0.02100006677210331,
0.027181420475244522,
-0.03415682166814804,
-0.07583577930927277,
0.03780480846762657,
-0.046577125787734985,
-0.007924220524728298,
0.007352204993367195,
-0.01280421856790781,
-0.004129704553633928,
-0.02274489775300026,
0.00027396046789363027,
-0.004045806359499693,
0.027664320543408394,
-0.0030948235653340816,
-0.0009000894497148693,
-0.057179030030965805,
0.10522077232599258,
0.022423675283789635,
0.011712864972651005,
-0.03937391936779022,
-0.0034913821145892143,
-0.06045415624976158,
-0.025794150307774544,
0.02573612704873085,
-0.025053128600120544,
-0.051220815628767014,
-0.020167702808976173,
0.012802250683307648,
-0.027981143444776535,
0.0065335920080542564,
0.021194463595747948,
0.030625557526946068,
0.006169599015265703,
0.006225237622857094,
-0.03701811283826828,
-0.00680093327537179,
-0.01061555277556181,
0.053016722202301025,
0.03290751576423645,
-0.03718779608607292,
-0.0235491581261158,
-0.0008880430250428617,
0.04919002205133438,
0.009268068708479404,
-0.026657741516828537,
0.028093622997403145,
-0.03865983337163925,
0.0828576311469078,
0.08415720611810684,
-0.01624530553817749,
0.027792012318968773,
-0.009183363988995552,
0.010458351112902164,
0.024326076731085777,
0.011434939689934254,
-0.027567977085709572,
-0.05362774804234505,
-0.06705772131681442,
0.03506425395607948,
0.008061963133513927,
0.05918531492352486,
-0.059038061648607254,
-0.047495387494564056,
0.02729698270559311,
-0.002716508461162448,
-0.02612771838903427,
-0.013583355583250523,
-0.021975548937916756,
-0.0030518213752657175,
-0.019387800246477127,
0.07154438644647598,
0.0046415976248681545,
0.00007964987162267789,
-0.02601982094347477,
0.06707216799259186,
-0.007196545135229826,
-0.0014565952587872744,
0.031145954504609108,
0.026374047622084618,
0.055734455585479736,
-0.021645229309797287,
0.08766284584999084,
0.03546568378806114,
0.03636088967323303,
0.05574720352888107,
0.052983880043029785,
0.06064758822321892,
-0.05292855575680733,
0.03678389638662338,
0.009301135316491127,
0.0837831050157547,
0.033461794257164,
0.013047855347394943,
0.04227706417441368,
0.03062584437429905,
-0.043520502746105194,
-0.008715379051864147,
-0.037249717861413956,
-0.010802244767546654,
0.014412234537303448,
-0.0023283592890948057,
-0.012670489959418774,
-0.0348861888051033,
-0.019269529730081558,
0.0656537339091301,
0.0422155000269413,
-0.016880536451935768,
-0.02697395347058773,
-0.003457828890532255,
0.039213381707668304,
-0.018580565229058266,
0.011341337114572525,
-0.039996180683374405,
-0.015449723228812218,
0.0429132841527462,
0.03237610682845116,
-0.03706261143088341,
0.07220564037561417,
-0.015140733681619167,
0.0019265924347564578,
0.015078439377248287,
-0.03183411806821823,
-0.011066345497965813,
-0.004973622504621744,
0.005629595834761858,
-0.03501412644982338,
-0.005764446221292019,
0.05630142614245415,
-0.044964056462049484,
-0.004729372449219227,
-0.0432632751762867,
0.02587231993675232,
-0.023160729557275772,
-0.045965615659952164,
-0.022455774247646332,
0.03553586080670357,
-0.022930361330509186,
-0.046213097870349884,
-0.018806306645274162,
-0.020867954939603806,
-0.046373892575502396,
0.11244495958089828,
-0.03993500396609306,
0.011348305270075798,
0.0009151836857199669,
-0.05569304898381233,
-0.040850959718227386,
0.005154888145625591,
0.012702923268079758,
-0.0027233355212956667,
-0.01681225560605526,
-0.02392997033894062,
-0.00861978530883789,
-0.02676129713654518,
0.08506190031766891,
-0.030796125531196594,
-0.02527078054845333,
0.0007507101399824023,
0.005886496044695377,
0.05961519107222557,
-0.000314663426252082,
-0.0014486738946288824,
0.005046529695391655,
0.014114455319941044,
0.08554014563560486,
-0.05218161642551422,
-0.02328817918896675,
-0.03853273764252663,
-0.061979763209819794,
-0.006882778834551573,
-0.012949693016707897,
0.022437771782279015,
0.004121026024222374,
0.020351091399788857,
0.02262466959655285,
0.017231890931725502,
-0.000015010896277090069,
0.02911313809454441,
0.018587984144687653,
-0.030911194160580635,
-0.028852377086877823,
-0.03468557819724083,
0.018076125532388687,
-0.024224361404776573,
0.04820508882403374,
-0.024445505812764168,
0.053285833448171616,
-0.06726400554180145,
-0.025749199092388153,
-0.018716134130954742,
-0.009259102866053581,
0.02916526049375534,
-0.052364494651556015,
-0.0557435005903244,
0.01829027384519577,
-0.0063233766704797745,
0.09253111481666565,
0.008130816742777824,
-0.028907455503940582,
-0.015793826431035995,
-0.022421307861804962,
0.005467060022056103,
-0.00677858479321003,
-0.08380761742591858,
-0.001001712866127491,
-0.022178353741765022,
-0.04226246476173401,
-0.03760877251625061,
-0.01946284808218479,
-0.0009210817515850067,
0.047612618654966354,
0.02609061822295189,
-0.008257116191089153,
0.013376417569816113,
0.02857080288231373,
0.05236352980136871,
-0.0027381840627640486,
0.04499305412173271,
-0.030206957831978798,
-0.006164215505123138,
-0.026323897764086723,
0.06695156544446945,
-0.0017021459061652422,
0.013184758834540844,
-0.06357167661190033,
-0.05408157408237457,
0.012072395533323288,
0.03249261528253555,
-0.018910229206085205,
-0.05712408572435379,
-0.0035472330637276173,
-0.07481174916028976,
0.02804964780807495,
-0.0033040684647858143,
-0.03188998997211456,
0.019551288336515427,
0.01370485220104456,
-0.07245286554098129,
0.05089085176587105,
-0.010886902920901775,
-0.053524360060691833,
0.009676102548837662,
-0.01735284924507141,
-0.039957817643880844,
0.015806477516889572,
0.004704992286860943,
-0.024153055623173714,
-0.04515431076288223,
0.04997149854898453,
0.0012735198251903057,
0.026169121265411377,
-0.013056043535470963,
0.017114367336034775,
-0.009685095399618149,
-0.008277174085378647,
0.08070411533117294,
-0.018736062571406364,
0.006327353417873383,
0.0626029446721077,
0.016366228461265564,
0.04008501023054123,
0.07411185652017593,
0.014720833860337734,
0.10259407758712769,
-0.01794235035777092,
0.022620750591158867,
0.030171312391757965,
-0.010155526921153069,
0.062462229281663895,
-0.022944288328289986,
-0.03743887320160866,
-0.006384826265275478,
0.00023835818865336478,
0.004823644179850817,
-0.015911966562271118,
0.019562212750315666,
-0.015142981894314289,
0.03157004714012146,
0.04222124069929123,
0.014220792800188065,
0.01142034213989973,
0.008135456591844559,
0.022365402430295944,
0.033229805529117584,
-0.007828890345990658,
-0.04101216420531273,
0.027907032519578934,
0.03869357332587242,
0.06670451909303665,
-0.015671681612730026,
0.07266601175069809,
-0.06143302097916603,
-0.0009497171267867088,
0.009670287370681763,
-0.020395560190081596,
-0.038446974009275436,
-0.014355097897350788,
-0.0597456693649292,
-0.017194828018546104,
-0.0029706889763474464,
0.009206561371684074,
0.0004297381092328578,
0.0015711589949205518,
-0.037249911576509476,
-0.05968032032251358,
-0.02289101853966713,
-0.02972574345767498,
0.02838953211903572,
0.02567732147872448,
-0.0016092367004603148,
0.06716862320899963,
0.0058389101177453995,
-0.014369651675224304,
0.026457302272319794,
0.03365779668092728,
0.008094020187854767,
0.07868572324514389,
0.03597120940685272,
0.0044278595596551895,
0.02716328203678131,
-0.0023760346230119467,
-0.006627811584621668,
0.044065870344638824,
0.051536183804273605,
0.03168990835547447,
-0.04068884253501892,
0.03685147687792778,
-0.003499821526929736,
0.019500479102134705,
-0.003110635792836547,
0.0011695866705849767,
-0.009521013125777245,
0.009048241190612316,
-0.010585526935756207,
-0.013278520666062832,
0.06618001312017441,
0.04245869442820549,
-0.029559290036559105,
0.030955800786614418,
-0.021216245368123055,
0.023507412523031235,
-0.03288504481315613,
-0.06215813383460045,
-0.009951514191925526,
0.0817694291472435,
0.0486181378364563,
0.04726642370223999,
-0.002344108186662197,
0.012126338668167591,
0.027915824204683304,
0.02020547352731228,
-0.007714440114796162,
0.015097378753125668,
0.05686825141310692,
-0.03180500119924545,
0.04137430340051651,
0.015450420789420605,
0.025625621899962425,
-0.008517319336533546,
0.017502887174487114,
0.019685592502355576,
-0.03161118924617767,
-0.0017999151023104787,
0.0135331517085433,
-0.0318433977663517,
-0.01558983325958252,
-0.01091253012418747,
0.005241383798420429,
-0.018851470202207565,
-0.006527763791382313,
-0.011344380676746368,
-0.043755076825618744,
0.018872572109103203,
0.024593576788902283,
0.005678044632077217,
-0.009142454713582993,
-0.045609232038259506,
0.01041016448289156,
-0.0015537863364443183,
-0.025133686140179634,
-0.04464224353432655,
-0.018370771780610085,
-0.026959074661135674,
-0.007381107192486525,
-0.00682689668610692,
-0.024464014917612076,
-0.010423465631902218,
-0.032011572271585464,
-0.017860936000943184,
-0.04009305685758591,
-0.06191195547580719,
-0.03956266865134239,
0.008290644735097885,
0.0057535902597010136,
-0.017092110589146614,
-0.041468292474746704,
0.024379903450608253,
0.00857367180287838,
-0.015069523826241493,
0.0067964219488203526,
0.05970621481537819,
0.02143029496073723,
-0.06027374044060707,
0.029124636203050613,
0.0359872542321682,
0.02011776529252529,
-0.018502425402402878,
-0.07040786743164062,
0.008950837887823582,
-0.018245583400130272,
-0.014875774271786213,
-0.012479945085942745,
-0.039478667080402374,
-0.01624654419720173,
0.04579896107316017,
0.02321474254131317,
-0.07063575088977814,
-0.05685516819357872,
-0.041779883205890656,
-0.04359721392393112,
-0.005574734881520271
] |
<p>Does the axis of Time point into a black hole or away from?</p>
<p>Can you give a reference paper?</p> | g5492 | [
0.030833756551146507,
0.011389981023967266,
0.014831192791461945,
-0.015728894621133804,
0.0366193912923336,
0.006694451905786991,
0.03856253623962402,
-0.01718662865459919,
-0.018933715298771858,
0.04228801280260086,
0.024657338857650757,
0.029196221381425858,
0.03962196782231331,
-0.06876756250858307,
0.038781650364398956,
-0.03965405374765396,
0.013218685053288937,
0.020296894013881683,
-0.00840995367616415,
-0.013615290634334087,
0.06431092321872711,
-0.070211261510849,
0.03307892754673958,
-0.041290730237960815,
-0.013539652340114117,
0.007041840814054012,
0.023091131821274757,
-0.04994700476527214,
-0.10360492765903473,
-0.015503284521400928,
0.06775724142789841,
0.0241985060274601,
0.022974936291575432,
-0.010714691132307053,
0.03037380240857601,
-0.019848566502332687,
-0.031253211200237274,
-0.018448829650878906,
0.0596887469291687,
-0.006370780523866415,
0.03532623499631882,
-0.011410309001803398,
-0.046587299555540085,
-0.03405560925602913,
0.019667673856019974,
0.018529660999774933,
0.008447364903986454,
0.020366644486784935,
-0.02537824772298336,
-0.023076726123690605,
-0.02686247229576111,
0.04384027421474457,
0.09513267874717712,
0.04164998605847359,
-0.020813578739762306,
0.03588123247027397,
-0.007662605494260788,
0.011291365139186382,
0.03303137049078941,
0.029039960354566574,
-0.08268844336271286,
-0.015804408118128777,
-0.011317886412143707,
-0.002752414671704173,
0.05086341127753258,
-0.023979205638170242,
-0.07852516323328018,
-0.01136665977537632,
-0.09167502820491791,
0.0031573367305099964,
0.038194749504327774,
-0.02413766272366047,
0.0014892194885760546,
0.027596836909651756,
-0.06315355002880096,
0.056947920471429825,
-0.014552515000104904,
-0.012158524245023727,
-0.006114611402153969,
0.020006466656923294,
-0.0038053253665566444,
-0.003514002077281475,
0.0017751214327290654,
-0.007561876438558102,
0.10857105255126953,
0.0007635510992258787,
0.04959939047694206,
0.019417909905314445,
-0.027264468371868134,
-0.01755768433213234,
0.03646222874522209,
-0.006238245405256748,
0.0511215440928936,
-0.004624176304787397,
0.04460576921701431,
0.03304068744182587,
-0.01766929216682911,
0.034697677940130234,
0.034906018525362015,
0.04256674274802208,
-0.10122191160917282,
0.022718243300914764,
-0.03142145648598671,
0.004806698765605688,
0.06967075169086456,
-0.0396060086786747,
0.03319606930017471,
0.014735158532857895,
-0.03119659423828125,
-0.03359367325901985,
-0.01676533930003643,
-0.07957258075475693,
-0.03467670455574989,
0.0037602372467517853,
-0.002831347519531846,
-0.004559522494673729,
0.026757817715406418,
-0.05245312675833702,
0.06574354320764542,
0.04043343663215637,
-0.004193615633994341,
0.0005238258745521307,
0.02038627676665783,
0.05438263341784477,
0.011530398391187191,
-0.04983919858932495,
-0.03800235688686371,
-0.03365013748407364,
-0.021416857838630676,
0.02928849682211876,
-0.04564560949802399,
-0.0005876274663023651,
0.0023578365799039602,
0.02235403284430504,
-0.07371766120195389,
0.01616823486983776,
0.01274837926030159,
-0.045560214668512344,
-0.0026802753563970327,
0.04237896949052811,
0.023547029122710228,
-0.033438075333833694,
-0.00105880422051996,
-0.03806977719068527,
0.035560961812734604,
0.022712059319019318,
-0.002788676181808114,
-0.04990624263882637,
0.057582780718803406,
0.042459163814783096,
-0.0027927954215556383,
0.08627185225486755,
-0.05192248523235321,
0.030714910477399826,
0.007778529543429613,
0.016960464417934418,
-0.01768564060330391,
0.009037592448294163,
0.0316178984940052,
-0.023965978994965553,
0.018572384491562843,
-0.04533511400222778,
-0.013538272120058537,
0.06001422926783562,
-0.020538143813610077,
-0.05424890294671059,
-0.0025333762168884277,
-0.05063502490520477,
0.026435906067490578,
0.012712499126791954,
-0.02254835143685341,
0.024042392149567604,
0.002181075280532241,
-0.002760261530056596,
0.023016689345240593,
0.04522984102368355,
-0.023713402450084686,
0.03500475734472275,
0.03594584763050079,
0.025128530338406563,
0.058327361941337585,
-0.02335510030388832,
-0.026458105072379112,
-0.02147093042731285,
-0.0026979614049196243,
-0.018128423020243645,
0.009888270869851112,
0.03502220660448074,
0.011183002963662148,
0.0034494204446673393,
-0.017919836565852165,
-0.003441272536292672,
-0.014295735396444798,
0.010868014767765999,
-0.019211508333683014,
0.04087609797716141,
0.017913203686475754,
-0.04437383636832237,
0.0022192748729139566,
0.08285032957792282,
0.01136151421815157,
0.01575513370335102,
-0.010627382434904575,
0.0665559396147728,
-0.0027842018753290176,
-0.023170510306954384,
-0.00039537285920232534,
0.03638012334704399,
0.009119870141148567,
0.018905647099018097,
0.007729158736765385,
0.058992110192775726,
0.037061601877212524,
0.030330197885632515,
-0.07385411858558655,
0.012737114913761616,
-0.03916943073272705,
0.06567289680242538,
0.008829322643578053,
0.0508902408182621,
-0.062680184841156,
-0.02523156628012657,
0.06350624561309814,
-0.022450264543294907,
-0.009730249643325806,
0.029133766889572144,
-0.0009567493107169867,
-0.05216331407427788,
0.03437228873372078,
-0.0303902979940176,
-0.12631911039352417,
-0.04099471867084503,
0.007032177876681089,
-0.039219219237565994,
0.05021805688738823,
-0.03638094291090965,
-0.0026868751738220453,
-0.03787565231323242,
-0.014306318014860153,
0.0015446956967934966,
0.008974638767540455,
0.009659580886363983,
-0.02654311992228031,
-0.005280207842588425,
-0.0040703024715185165,
0.019384805113077164,
0.06832953542470932,
-0.010034515522420406,
0.01893593743443489,
0.026629293337464333,
0.04023988917469978,
-0.009718108922243118,
0.0016751689836382866,
0.012037725187838078,
-0.005233040079474449,
-0.006792436353862286,
0.02769298665225506,
0.0279933400452137,
-0.11278091371059418,
-0.004871962126344442,
0.015714125707745552,
0.012343183159828186,
0.005863652564585209,
-0.02237986959517002,
-0.036989059299230576,
0.00439635431393981,
-0.03806925192475319,
0.025972291827201843,
0.03357396647334099,
-0.0035467837005853653,
-0.01678447797894478,
0.0519973449409008,
0.08014463633298874,
0.059772931039333344,
-0.00352963013574481,
-0.0016361135058104992,
-0.024719417095184326,
0.007374223787337542,
0.002980182645842433,
-0.04435358941555023,
-0.03323483467102051,
-0.028236154466867447,
-0.05291365087032318,
0.031860969960689545,
-0.026545654982328415,
-0.02378280833363533,
-0.015964070335030556,
0.03158789500594139,
-0.07790638506412506,
-0.04793122410774231,
-0.07319486886262894,
0.034987181425094604,
-0.007509505841881037,
0.04897603392601013,
0.060363300144672394,
0.04038356617093086,
0.04973427206277847,
-0.050328414887189865,
0.009588327258825302,
0.03697749227285385,
-0.014901957474648952,
0.011777163483202457,
-0.02837534435093403,
0.006384167820215225,
0.04399535059928894,
0.0011506169103085995,
0.03138948231935501,
-0.06360779702663422,
0.03247363865375519,
0.02471342124044895,
0.0064707971177995205,
0.0008037453517317772,
0.040018752217292786,
0.009080409072339535,
-0.002842577174305916,
0.012140446342527866,
0.013184311799705029,
-0.0176507867872715,
-0.0020367042161524296,
0.03341073915362358,
0.006307277828454971,
-0.011890033259987831,
-0.06268659979104996,
0.049586668610572815,
0.03908037021756172,
-0.0009396592504344881,
0.04921184107661247,
-0.02009543590247631,
-0.04321988672018051,
0.02414293959736824,
-0.06502152234315872,
-0.020625468343496323,
0.0217980295419693,
0.04317255690693855,
-0.00891001708805561,
-0.010534253902733326,
-0.02497638575732708,
-0.010907678864896297,
0.04649913311004639,
-0.0033119653817266226,
0.030954968184232712,
-0.04342341423034668,
0.004008133430033922,
0.00021412217756733298,
0.056884583085775375,
-0.013944492675364017,
-0.00004761421587318182,
0.026722397655248642,
0.041051313281059265,
-0.025222010910511017,
0.0474492646753788,
-0.030596338212490082,
-0.02431917004287243,
-0.05890747904777527,
0.06277681887149811,
-0.009858530014753342,
-0.010034157894551754,
0.021223267540335655,
0.019985252991318703,
0.0004947537090629339,
-0.02664048597216606,
0.021718448027968407,
0.050105202943086624,
-0.00434121023863554,
0.004730312153697014,
-0.033196307718753815,
0.016639022156596184,
0.04556922987103462,
0.04484257474541664,
0.004583884030580521,
0.008092875592410564,
0.05689626932144165,
0.004871547222137451,
0.040223173797130585,
-0.01173133123666048,
-0.039395663887262344,
-0.023078706115484238,
-0.004124252125620842,
-0.02295786142349243,
0.056601569056510925,
0.001317487796768546,
-0.01304110698401928,
-0.023861944675445557,
-0.022789446637034416,
0.016718989238142967,
0.0009819116676226258,
-0.021262681111693382,
-0.027785614132881165,
-0.007032972294837236,
-0.0573284775018692,
0.03458134084939957,
-0.046729717403650284,
-0.03251657262444496,
-0.07682105153799057,
-0.010646057315170765,
0.005117940716445446,
-0.01580693945288658,
0.08970116078853607,
-0.01253154594451189,
-0.015471188351511955,
0.03610594943165779,
-0.008542842231690884,
-0.005662428215146065,
0.041574783623218536,
0.015746772289276123,
0.04924389347434044,
0.03480854630470276,
0.005306266713887453,
-0.013582377694547176,
-0.0026178956031799316,
-0.0036683958023786545,
-0.029705870896577835,
-0.05146493762731552,
-0.026058105751872063,
0.09813984483480453,
-0.02999759279191494,
0.05787935107946396,
-0.0085305105894804,
-0.04320279136300087,
-0.010194492526352406,
0.027591530233621597,
-0.025260092690587044,
0.0011719187023118138,
0.0030456404201686382,
-0.026554690673947334,
0.03357512503862381,
0.011797216720879078,
0.00676494836807251,
-0.029771871864795685,
0.06914102286100388,
0.010448655113577843,
-0.0177365280687809,
-0.03941402956843376,
0.009732980281114578,
-0.0659513846039772,
0.062297653406858444,
0.023407381027936935,
0.030240993946790695,
-0.02031734772026539,
0.0020028455182909966,
0.044101208448410034,
-0.022291110828518867,
0.040113456547260284,
-0.052224524319171906,
-0.019474998116493225,
0.028832856565713882,
-0.02914365939795971,
0.0091887591406703,
-0.001315161120146513,
-0.02831585332751274,
-0.0457206554710865,
-0.019780153408646584,
0.0035982143599539995,
-0.03780507668852806,
-0.027242010459303856,
-0.03286566585302353,
-0.017912041395902634,
0.019984250888228416,
-0.020018195733428,
0.016008727252483368,
-0.017812777310609818,
-0.08686519414186478,
-0.0014145479071885347,
0.0017349900444969535,
-0.015577875077724457,
-0.05376886948943138,
-0.05293925106525421,
-0.0529528371989727,
-0.023657264187932014,
0.04415667802095413,
-0.06868340075016022,
0.04484396055340767,
0.022953657433390617,
0.015434260480105877,
-0.008533231914043427,
0.102568119764328,
-0.03011341206729412,
-0.0317799374461174,
0.017931928858160973,
-0.06952749192714691,
-0.02046452835202217,
-0.004012213554233313,
0.057064980268478394,
0.015655862167477608,
0.03191263601183891,
0.03247728571295738,
-0.04741724953055382,
-0.0033532206434756517,
0.06531758606433868,
-0.009348627179861069,
-0.015402081422507763,
-0.02484574168920517,
0.008314509876072407,
-0.03363032266497612,
-0.05726509168744087,
-0.004205617588013411,
-0.0023844134993851185,
-0.03095305897295475,
0.012803428806364536,
0.010902893729507923,
-0.07659716159105301,
0.06345999985933304,
0.00019384623738005757,
0.04028211161494255,
-0.008717503398656845,
0.03991544246673584,
0.051071569323539734,
0.01457179244607687,
-0.019805675372481346,
0.07343804836273193,
0.02504848875105381,
-0.016676830127835274,
-0.014295949600636959,
0.023360170423984528,
0.007087097503244877,
-0.062086787074804306,
0.01604020968079567,
0.02284153364598751,
-0.012321722693741322,
0.007461488246917725,
-0.05477789789438248,
-0.011870237998664379,
0.04272953048348427,
0.0041396403685212135,
0.039331916719675064,
0.034903451800346375,
-0.03632907196879387,
0.030087828636169434,
0.014033177867531776,
-0.045345548540353775,
-0.008876092731952667,
-0.009610897861421108,
0.045547302812337875,
0.0024056746624410152,
0.00685565359890461,
-0.03017299808561802,
-0.03739912807941437,
-0.03935238718986511,
0.0933060273528099,
-0.0700141116976738,
-0.04423488304018974,
-0.0368797741830349,
-0.003983782138675451,
0.019792204722762108,
-0.0016398443840444088,
0.028455697000026703,
-0.06965026259422302,
0.043162163347005844,
0.014813190326094627,
-0.04113831743597984,
-0.023490678519010544,
0.054566238075494766,
-0.04236701875925064,
0.027765579521656036,
-0.04956508055329323,
0.026601405814290047,
0.014781014062464237,
-0.03862803801894188,
-0.02927885763347149,
-0.029682299122214317,
-0.01991727203130722,
-0.024833081290125847,
-0.01226616557687521,
0.004206264857202768,
-0.04188007116317749,
-0.05818747356534004,
0.012741249985992908,
-0.019750216975808144,
0.024638377130031586,
-0.010918540880084038,
-0.02432110719382763,
-0.022068003192543983,
-0.05214426666498184,
0.029537705704569817,
-0.005858963821083307,
0.01145156566053629,
0.029900114983320236,
0.02629544585943222,
-0.04249081760644913,
-0.023301176726818085,
-0.04171324521303177,
-0.0004860186018049717,
0.0662558525800705,
-0.026623602956533432,
0.02503242902457714,
0.006426363252103329,
0.007860017009079456,
0.07524648308753967,
-0.025857364758849144,
0.0013318454148247838,
-0.004415289964526892,
0.00884932465851307,
0.047536518424749374,
-0.05167807266116142,
-0.06144082173705101,
0.02119194157421589,
-0.025026960298419,
-0.02540009841322899,
-0.016883501783013344,
-0.05793200060725212,
-0.03401261195540428,
0.0490088127553463,
-0.04161367565393448,
-0.030317747965455055,
0.015146133489906788,
0.01915775053203106,
-0.01499679870903492,
-0.03163042664527893,
0.054139990359544754,
-0.03075508587062359,
0.023563828319311142,
0.04335601627826691,
0.001111363060772419,
0.02930404804646969,
-0.0029570830520242453,
0.03137943148612976,
0.01335331704467535,
-0.009602583013474941,
-0.02149823307991028,
-0.005707824137061834,
0.09089131653308868,
0.01543507818132639,
-0.058012161403894424,
-0.03274357691407204,
-0.010124661028385162,
0.041295550763607025,
-0.043318361043930054,
0.023766756057739258,
-0.02865288220345974,
0.02339441142976284,
0.05135954171419144,
0.027687521651387215,
-0.052096012979745865,
0.000057101104175671935,
-0.0034245948772877455,
0.010822300799190998,
-0.05128874629735947,
0.016472103074193,
-0.010162645019590855,
0.027722176164388657,
0.02872285433113575,
-0.011222194880247116,
-0.053301502019166946,
0.009506833739578724,
-0.0264812633395195,
0.05080632492899895,
0.022230176255106926,
0.0069558387622237206,
-0.06973683834075928,
0.036774586886167526,
0.043557584285736084,
-0.049564093351364136,
-0.022850148379802704,
0.008478098548948765,
-0.03197569400072098,
-0.02116178162395954,
-0.03717941418290138,
0.035979993641376495,
0.0019994599279016256,
-0.06738895922899246,
-0.005038351286202669,
0.006406125612556934,
-0.10821419954299927,
-0.024396153166890144,
-0.06433693319559097,
0.03493209555745125,
0.03292357921600342,
0.0010228062747046351,
0.011354207061231136,
-0.032913412898778915,
0.007315369322896004,
-0.010670959949493408,
-0.05795777589082718,
0.02222946658730507,
-0.09178190678358078,
-0.02457370236515999,
-0.015852322801947594,
0.040329426527023315,
-0.015205039642751217,
0.046824291348457336,
0.03716607391834259,
0.03527218475937843,
-0.024990400299429893,
0.011839729733765125,
-0.06415941566228867,
0.008210568688809872,
-0.031186887994408607,
0.014604330994188786,
0.006027834489941597,
0.04687076061964035,
-0.009612036868929863,
0.03188715875148773,
-0.02907515875995159,
-0.09266552329063416,
0.06937399506568909,
-0.031009159982204437,
-0.0006017660489305854,
0.047054290771484375,
-0.044450514018535614,
0.018825076520442963,
0.044294241815805435,
0.014813598245382309,
-0.00835869088768959,
0.018101539462804794,
-0.04200426861643791,
0.045407120138406754,
0.04514574632048607,
0.032341767102479935,
-0.04136708751320839,
0.02121843211352825,
0.04344445466995239,
-0.00010053269943455234,
-0.007067258469760418,
-0.048209045082330704,
-0.022472109645605087,
0.011719432659447193,
-0.020548462867736816,
0.004386846907436848,
-0.031014423817396164,
-0.017083963379263878,
-0.002347988309338689,
0.03208542615175247,
-0.022284334525465965,
-0.024427972733974457,
0.01079501211643219,
0.025776546448469162,
0.0034383386373519897,
0.004795023240149021,
-0.02675819583237171,
-0.07494821399450302,
-0.03095783293247223,
0.02815411426126957,
-0.041583046317100525,
0.11907528340816498,
0.004144629929214716,
0.01988128572702408,
-0.012367429211735725,
0.03339675813913345,
0.05902376398444176,
0.008232970722019672,
0.023663656786084175,
-0.04004941135644913,
-0.01060031820088625,
-0.009595964103937149,
-0.018698619678616524,
-0.04174351692199707,
0.04248563572764397,
-0.007565182168036699,
0.054004427045583725,
0.01191383134573698,
0.013143245130777359,
0.012746036984026432,
-0.005050536245107651,
0.0059943897649645805,
0.03791453689336777,
-0.06774452328681946,
-0.012589801102876663,
-0.042572930455207825,
-0.045698802918195724,
0.017178334295749664,
-0.0018735745688900352,
0.004487090744078159,
0.035404421389102936,
-0.011991999112069607,
0.01483918260782957,
-0.028143752366304398,
-0.0026956521905958652,
0.04357575252652168
] |
<blockquote>
<p>The wheel of a car has a radius of 20 cm. It initially rotates at 120
rpm. In the next minute it makes 90 revolutions. What is the angular
acceleration?</p>
</blockquote>
<p>So the answer is solved by using one of the angular kinematic equations. More specifically delta theta. The problem I am having trouble understanding is the answer which probably stems from my poor fundamentals. </p>
<p>The answer is: (90x2pi) = 4pi(60) + 1/2 (alpha) (60)^2</p>
<p>So where does 90x2pi come from?</p> | g5493 | [
0.05924593284726143,
0.06971763074398041,
0.007855917327105999,
-0.0062101553194224834,
0.046445105224847794,
-0.028513262048363686,
0.07259001582860947,
0.03501570597290993,
-0.034509625285863876,
0.002934388117864728,
-0.04567084461450577,
0.05142519250512123,
0.05025104433298111,
-0.04841269180178642,
0.08003907650709152,
-0.03628144785761833,
-0.023402072489261627,
0.0007879612967371941,
0.01234289538115263,
-0.01668231189250946,
0.01714360900223255,
-0.02368093654513359,
-0.01841823197901249,
-0.05075696110725403,
0.049736082553863525,
-0.00034795168903656304,
0.011825064197182655,
0.009873402304947376,
-0.06307901442050934,
0.019883953034877777,
-0.006110905669629574,
0.00911226961761713,
0.020883478224277496,
-0.03101060912013054,
-0.042888619005680084,
-0.011778844520449638,
0.0022199093364179134,
0.018896616995334625,
0.00998033955693245,
-0.005166696384549141,
0.013295460492372513,
0.0006893883692100644,
0.0859966054558754,
0.004835361149162054,
0.06271974742412567,
-0.018246158957481384,
-0.009809505194425583,
0.022188222035765648,
-0.03374394029378891,
0.05125439167022705,
-0.04574313759803772,
-0.03522307053208351,
0.02904166653752327,
-0.01179807074368,
-0.01598847471177578,
0.06015974283218384,
0.046220168471336365,
-0.04129111394286156,
0.04465670883655548,
0.05462659150362015,
-0.048141155391931534,
-0.06500460207462311,
0.038175005465745926,
-0.021864434704184532,
0.06759504228830338,
-0.03228796645998955,
0.03197137638926506,
0.02944021299481392,
0.03745812922716141,
0.01799842156469822,
0.012427750043570995,
-0.03992871567606926,
0.025207804515957832,
-0.06733928620815277,
-0.07616572082042694,
0.0215904600918293,
0.019631722941994667,
-0.036237627267837524,
0.0022381048183888197,
-0.00017894990742206573,
-0.04181788116693497,
0.01080557331442833,
-0.012761144898831844,
0.05148673802614212,
0.04205286130309105,
-0.029953602701425552,
0.00008757643081480637,
0.03966725245118141,
-0.010808315128087997,
0.010223201476037502,
0.07774985581636429,
-0.052613165229558945,
0.023161755874753,
-0.023663882166147232,
-0.01414468977600336,
-0.040150512009859085,
-0.05930718034505844,
0.07984673231840134,
-0.0075591267086565495,
0.03461579605937004,
0.03324590250849724,
-0.0009466168121434748,
0.004498004447668791,
-0.03779980540275574,
0.06752966344356537,
0.03017742745578289,
0.015443224459886551,
-0.0008365906542167068,
0.01228603720664978,
0.0016379696317017078,
0.00245493883267045,
-0.04247292876243591,
-0.02326398901641369,
-0.07901585847139359,
-0.030017558485269547,
0.01839207112789154,
0.08549080789089203,
0.02281990833580494,
0.030066072940826416,
0.07182836532592773,
-0.005401014816015959,
0.028384605422616005,
-0.01756352186203003,
0.0708533301949501,
0.04431852698326111,
-0.015292078256607056,
-0.036480069160461426,
-0.009355665184557438,
0.03222058340907097,
0.0120059410110116,
-0.009840164333581924,
0.054993435740470886,
0.02491608075797558,
-0.0006620351923629642,
0.03397590294480324,
0.04118073359131813,
-0.043932076543569565,
0.0037385928444564342,
0.019772391766309738,
0.015347081236541271,
-0.011464434675872326,
-0.03252658620476723,
0.03226354718208313,
0.040896423161029816,
-0.0577448345720768,
-0.002907409332692623,
0.022571304813027382,
0.0017285427311435342,
-0.012386664748191833,
0.03887325897812843,
-0.04950539395213127,
0.03216603398323059,
-0.0006797115784138441,
-0.06399359554052353,
0.06989367306232452,
0.007226328831166029,
0.05328961834311485,
-0.0133915850892663,
-0.005870805587619543,
0.05176860839128494,
0.1074119359254837,
-0.040180400013923645,
-0.018579155206680298,
-0.0019858316518366337,
-0.055430568754673004,
-0.013939677737653255,
-0.008612385019659996,
-0.016606483608484268,
-0.01895320415496826,
-0.04305832460522652,
-0.04534612596035004,
0.019154652953147888,
0.029633425176143646,
0.040212370455265045,
-0.049737442284822464,
0.02755114436149597,
0.033292919397354126,
-0.02081625536084175,
0.02135288529098034,
0.0037023178301751614,
-0.004523164592683315,
-0.031350381672382355,
-0.0008631501696072519,
0.012196935713291168,
0.019168829545378685,
-0.027624597772955894,
0.04832186549901962,
0.06892897933721542,
-0.07779542356729507,
0.01607566699385643,
0.055051740258932114,
-0.01186752412468195,
0.008181697688996792,
0.020407792180776596,
0.006838771048933268,
-0.023665275424718857,
-0.008173701353371143,
-0.07051990926265717,
-0.03677570819854736,
0.019459551200270653,
0.0186281967908144,
-0.004680967424064875,
0.03641326352953911,
0.04335707053542137,
0.03304624557495117,
-0.018483823165297508,
0.003944926895201206,
-0.057567048817873,
0.037101928144693375,
0.03438028693199158,
0.006774724926799536,
0.020446257665753365,
-0.050682272762060165,
0.0548553504049778,
-0.044401589781045914,
-0.034049637615680695,
0.03502754494547844,
-0.006262463051825762,
-0.011997268535196781,
0.04029999300837517,
0.04820598289370537,
-0.08818076550960541,
0.0032533486373722553,
-0.03518778085708618,
-0.04262172058224678,
-0.009485036134719849,
-0.033735040575265884,
-0.0765366181731224,
-0.01005559228360653,
0.08670736104249954,
-0.031445786356925964,
-0.05373389273881912,
-0.01113183330744505,
-0.02113998867571354,
0.012131629511713982,
0.02350483648478985,
-0.0074322461150586605,
0.03215128928422928,
-0.0008272780105471611,
-0.030690232291817665,
0.015953170135617256,
0.009818955324590206,
0.0056142318062484264,
-0.001992247300222516,
-0.015285525470972061,
-0.04380165413022041,
0.11707732826471329,
-0.0033457763493061066,
-0.011523991823196411,
-0.00002659405981830787,
-0.004321365151554346,
-0.04030757024884224,
-0.03328278660774231,
0.02307533100247383,
-0.031169425696134567,
-0.03669416531920433,
-0.014743396081030369,
0.013010991737246513,
-0.026441816240549088,
-0.024414170533418655,
-0.03662263602018356,
-0.020036092028021812,
0.0037430597003549337,
0.026097776368260384,
-0.03437957167625427,
0.012890929356217384,
-0.0246153362095356,
-0.01709132269024849,
0.0038393563590943813,
0.012332585640251637,
-0.08111207187175751,
0.03652208298444748,
-0.006226539611816406,
0.021312810480594635,
-0.04749784618616104,
-0.02567877806723118,
0.005411920603364706,
-0.00035916161141358316,
-0.04919354245066643,
0.024797862395644188,
0.009307320229709148,
0.005232838913798332,
-0.006422482896596193,
0.03497372195124626,
0.006289915647357702,
-0.023972896859049797,
0.01199665479362011,
0.0362868495285511,
-0.028800999745726585,
-0.04509172588586807,
-0.08075383305549622,
0.04231985658407211,
0.035698842257261276,
-0.022752933204174042,
0.018106095492839813,
0.0564352311193943,
-0.00030713347950950265,
0.008589453995227814,
0.02851657010614872,
-0.013529892079532146,
-0.003439013846218586,
-0.016055189073085785,
0.024397313594818115,
-0.0025893854908645153,
0.01575394533574581,
0.014842042699456215,
0.032382212579250336,
-0.05882520601153374,
-0.04620002582669258,
0.08988494426012039,
-0.035729214549064636,
-0.05505165457725525,
-0.028002213686704636,
-0.018923839554190636,
-0.04266088828444481,
-0.007897578179836273,
-0.03928147256374359,
-0.01395286526530981,
0.05201775208115578,
0.05485899746417999,
-0.04864584654569626,
-0.13571642339229584,
-0.03361476585268974,
-0.008711128495633602,
0.05521569773554802,
0.027233578264713287,
-0.050830718129873276,
0.04243653640151024,
0.029139971360564232,
-0.046264417469501495,
0.005290595814585686,
0.029578518122434616,
-0.025494081899523735,
-0.008202111348509789,
0.00009780914115253836,
-0.03679843246936798,
-0.04872480034828186,
0.05273488909006119,
0.0008219490991905332,
-0.011092695407569408,
-0.023571614176034927,
-0.016210436820983887,
-0.03275555372238159,
-0.04198693111538887,
0.024946406483650208,
0.02048155851662159,
-0.007882178761065006,
-0.0015716379275545478,
0.0212543997913599,
-0.004953091032803059,
-0.02265375480055809,
-0.006288481410592794,
-0.008917639032006264,
-0.0048845624551177025,
-0.0071690380573272705,
0.01477423682808876,
-0.005110418424010277,
0.005834637675434351,
0.005734310485422611,
0.009218105114996433,
0.012916252948343754,
-0.035812944173812866,
-0.02835405245423317,
0.03737381845712662,
0.03130825608968735,
-0.017040498554706573,
-0.017872510477900505,
0.029936589300632477,
-0.03730970621109009,
-0.006153848022222519,
-0.00639572087675333,
-0.05811607092618942,
0.026966391131281853,
-0.022120671346783638,
0.04258013144135475,
-0.009711259044706821,
-0.05648079887032509,
0.020919285714626312,
-0.03187448903918266,
0.048175834119319916,
0.019633231684565544,
0.043948251754045486,
-0.0313236378133297,
-0.01123259961605072,
-0.012630566023290157,
0.03507639840245247,
-0.017768383026123047,
-0.009566637687385082,
0.006746669299900532,
-0.015341819263994694,
0.03045240044593811,
-0.035514574497938156,
0.009957469068467617,
-0.05130866914987564,
-0.013935457915067673,
-0.057475361973047256,
0.0031113605946302414,
-0.018397312611341476,
-0.05632689595222473,
0.03214770182967186,
-0.038732048124074936,
-0.016655974090099335,
0.012478655204176903,
0.02011221833527088,
-0.018586130812764168,
0.08086221665143967,
0.0040811593644320965,
0.04577924683690071,
0.07306576520204544,
0.03384879231452942,
-0.010602627880871296,
0.08131041377782822,
-0.012565831653773785,
-0.05406618118286133,
0.07587136328220367,
0.021634414792060852,
0.031241144984960556,
-0.010434930212795734,
-0.007210167590528727,
0.024025747552514076,
-0.07502614706754684,
0.03763023018836975,
-0.0023152546491473913,
-0.006067001726478338,
0.05881693959236145,
0.06790570914745331,
0.034325651824474335,
0.016928842291235924,
0.0006514030392281711,
-0.02636571228504181,
-0.013368931598961353,
0.0051282490603625774,
-0.04411504790186882,
0.020333686843514442,
-0.07275547087192535,
0.01722133159637451,
-0.01160468440502882,
0.043363288044929504,
0.04699469357728958,
0.0018894700333476067,
0.011124704033136368,
0.0007033515721559525,
0.02377108857035637,
-0.009982283227145672,
-0.03717150539159775,
0.05770622566342354,
0.009209387935698032,
-0.011740648187696934,
0.035836536437273026,
0.006755542010068893,
-0.02758754789829254,
-0.027209488674998283,
0.00429182406514883,
-0.012320959940552711,
0.009707380086183548,
0.010298330336809158,
-0.06803519278764725,
-0.007997943088412285,
-0.02286168374121189,
0.027141304686665535,
-0.009966326877474785,
-0.005888417363166809,
-0.003948665224015713,
0.03407740220427513,
0.03298493102192879,
-0.03724392503499985,
-0.028087614104151726,
0.012798771262168884,
-0.03239740431308746,
0.021182607859373093,
-0.014784982427954674,
-0.026350555941462517,
0.0071927644312381744,
0.013317116536200047,
-0.024879898875951767,
0.011186610907316208,
-0.019711516797542572,
0.07591076195240021,
0.025477848947048187,
-0.05377659201622009,
-0.03295707330107689,
-0.039521895349025726,
0.03162389248609543,
-0.008267552591860294,
0.013254925608634949,
0.0025875179562717676,
-0.03628215193748474,
-0.0381888784468174,
0.07677002996206284,
-0.025031987577676773,
0.003503113752231002,
0.09041911363601685,
-0.03170201927423477,
-0.01592349074780941,
0.0009666102705523372,
-0.009986752644181252,
0.0010014149593189359,
-0.03056556172668934,
-0.04415174201130867,
0.006157515570521355,
-0.06602761149406433,
-0.010696731507778168,
-0.015683306381106377,
0.008587140589952469,
-0.012758287601172924,
0.0680730864405632,
0.036269284784793854,
-0.0046352967619895935,
0.03344472870230675,
0.02335204742848873,
0.057541392743587494,
0.06831511110067368,
0.03600126877427101,
0.005799159407615662,
0.003443025518208742,
-0.040756843984127045,
0.013506647199392319,
-0.0029929771553725004,
-0.005836037453263998,
0.02548113465309143,
-0.012819547206163406,
-0.0063148383051157,
0.003324206219986081,
-0.041985634714365005,
-0.019111214205622673,
-0.03163091838359833,
-0.0007832833216525614,
-0.018101489171385765,
-0.009006202220916748,
-0.006301018409430981,
0.03923420235514641,
-0.03977251797914505,
-0.0025540681090205908,
-0.03544171527028084,
-0.030336197465658188,
0.0035995792131870985,
0.033575303852558136,
-0.04981408640742302,
0.028435448184609413,
-0.03869646415114403,
-0.07561376690864563,
-0.00168809003662318,
0.029833542183041573,
-0.0038821210619062185,
-0.062081124633550644,
0.02899280935525894,
-0.0017333078430965543,
0.04292506352066994,
0.016712000593543053,
-0.020706187933683395,
-0.023639792576432228,
0.05775182694196701,
0.042122919112443924,
-0.05844472721219063,
-0.0661323145031929,
0.024234889075160027,
0.01870810054242611,
-0.0210191048681736,
-0.043347880244255066,
-0.06792735308408737,
0.043083034455776215,
-0.011422940529882908,
0.06046021357178688,
0.04120408743619919,
-0.019890883937478065,
0.016918472945690155,
0.02397170662879944,
0.012595629319548607,
0.05087586119771004,
0.0007964378455653787,
0.03163380175828934,
0.011431175284087658,
0.0025530816055834293,
0.037500858306884766,
0.036603279411792755,
-0.015535234473645687,
-0.03597417101264,
0.031918372958898544,
-0.016846507787704468,
0.05853262543678284,
-0.012990047223865986,
0.03611074015498161,
0.05083167552947998,
0.0019664266146719456,
0.01537618413567543,
0.01785130985081196,
-0.04785593971610069,
0.03085697814822197,
-0.03060222789645195,
-0.05568712204694748,
-0.055043917149305344,
0.027546310797333717,
-0.03559713065624237,
-0.012907152995467186,
-0.023104606196284294,
-0.03588264808058739,
0.009141549468040466,
0.022894151508808136,
0.0019038320751860738,
-0.059077609330415726,
0.02889820747077465,
0.029867563396692276,
0.032290246337652206,
0.0062935370951890945,
0.004122075624763966,
-0.06594517827033997,
-0.0291257556527853,
-0.031690772622823715,
-0.01636996492743492,
0.012911077588796616,
0.03842249512672424,
0.05915382504463196,
0.0008938579703681171,
0.07022647559642792,
-0.018942084163427353,
0.05948209390044212,
0.03848728910088539,
0.005142447538673878,
-0.0045151859521865845,
-0.022470366209745407,
0.03858521953225136,
0.005419501103460789,
0.010205878876149654,
-0.04365835338830948,
0.026303449645638466,
0.013605940155684948,
-0.0029599175322800875,
0.010762643069028854,
0.0480181947350502,
0.020418914034962654,
0.016812456771731377,
-0.08273879438638687,
-0.050876859575510025,
0.07949095964431763,
0.022697826847434044,
-0.001722126267850399,
-0.03832044079899788,
0.040523409843444824,
0.06285903602838516,
0.10398298501968384,
0.025802871212363243,
0.027314014732837677,
-0.046577539294958115,
-0.014777719974517822,
-0.0657891258597374,
-0.019170571118593216,
0.020033985376358032,
0.056577667593955994,
-0.043284036219120026,
-0.026687752455472946,
0.04974379390478134,
0.01736893132328987,
-0.024489648640155792,
0.0133452033624053,
-0.06009574234485626,
-0.025257015600800514,
0.008015585131943226,
0.023183900862932205,
-0.005949656944721937,
-0.03389117494225502,
-0.04082563519477844,
-0.00852349866181612,
-0.007081625051796436,
0.001743415603414178,
-0.025283079594373703,
0.0064332629553973675,
-0.011141559109091759,
0.022338883951306343,
0.04902835935354233,
-0.03548431023955345,
-0.03218206390738487,
-0.020278993993997574,
-0.06859765946865082,
-0.006348868366330862,
-0.012209039181470871,
0.008984328247606754,
0.0036440992262214422,
-0.03357119858264923,
-0.010891580022871494,
-0.002227567136287689,
-0.012126179412007332,
-0.030651887878775597,
-0.01759941317141056,
-0.008748946711421013,
0.004515094216912985,
0.02188009023666382,
-0.00945079792290926,
-0.010025585070252419,
0.02363733761012554,
-0.02459905855357647,
-0.01566246896982193,
0.051753148436546326,
0.005685035139322281,
-0.030340490862727165,
-0.006000364664942026,
0.03571450337767601,
0.022952338680624962,
0.02373410575091839,
-0.024727948009967804,
-0.001044696313329041,
0.036338694393634796,
-0.010170498862862587,
0.0407847985625267,
0.08871110528707504,
0.014863472431898117,
0.00257720029912889,
-0.006112892180681229,
0.024981200695037842,
-0.07779964804649353,
0.029808558523654938,
0.020440660417079926,
-0.04742308333516121,
-0.0227200947701931,
-0.047548554837703705,
-0.022110726684331894,
0.026515770703554153,
-0.007803590502589941,
0.058917153626680374,
-0.015766067430377007,
-0.015086271800100803,
-0.011476024053990841,
-0.04456246644258499,
0.03256063535809517,
-0.10330342501401901,
-0.04574723541736603,
-0.05125297233462334,
-0.029453188180923462,
-0.049842238426208496,
0.0025743592996150255,
-0.02342529408633709,
0.007899371907114983,
0.03728397190570831,
-0.045446332544088364,
0.07884389162063599,
-0.0366540290415287,
-0.007517512422055006,
0.011399861425161362,
-0.046861644834280014,
-0.03091282956302166,
0.029479598626494408,
0.054259590804576874,
-0.04612104222178459,
-0.007215996738523245,
0.016778409481048584,
-0.04028112813830376,
0.009347619488835335,
-0.004454928915947676,
0.054151009768247604,
0.06624269485473633,
-0.010663868859410286,
-0.0098858792334795,
0.026892833411693573,
-0.07548263669013977,
-0.035164833068847656,
0.032149430364370346,
-0.05669451504945755,
-0.01809101738035679,
0.057127002626657486,
-0.008235392160713673,
-0.03691312298178673,
-0.001115963445045054,
0.033258337527513504,
0.010331385768949986,
0.012558319605886936,
0.04456465318799019,
-0.04681691899895668,
-0.10064549744129181,
-0.017940465360879898
] |
<p><em>I have encountered this claim while searching for sources answering " <a href="http://skeptics.stackexchange.com/questions/5310/can-we-see-the-curvature-of-earth-from-the-top-of-worlds-tallest-building">Can we see the curvature of earth from the top of world's tallest building?</a> ".</em></p>
<p>Wikipedia <a href="http://en.wikipedia.org/wiki/Horizon#Curvature_of_the_horizon" rel="nofollow">article on horizon</a> claims (with no references), that compared to a geometrical model, the the apparent curvature of Earth is less than expected due to refraction of light in the atmosphere.</p>
<p>Thinking about the problem, I fail to see why this could be so. It is easy to see the refraction affects a distance of the apparent horizont, but I fail to see how it could affect its curvature, as the refraction seems to have the same effect in all directions, because your distance to horizon is the same in all directions. </p>
<p>Is that claim just bogus and there is no such effect, or is the effect real?</p> | g980 | [
0.03322063758969307,
0.03685333579778671,
-0.005388766992837191,
0.055367641150951385,
-0.016353540122509003,
0.0654490515589714,
0.05747055262327194,
0.03948042169213295,
0.007409883197396994,
0.010259725153446198,
0.07525120675563812,
0.01622888445854187,
0.06982602924108505,
0.016150198876857758,
0.0007053178851492703,
0.045986443758010864,
0.06973619014024734,
-0.058742184191942215,
0.00618209270760417,
-0.04271511361002922,
0.01715490221977234,
-0.06984223425388336,
0.00038162642158567905,
0.01817423664033413,
-0.1065523698925972,
0.02626655623316765,
0.004025888163596392,
-0.012976334430277348,
-0.01266916748136282,
0.011238318867981434,
0.023002300411462784,
0.037267740815877914,
0.028545625507831573,
-0.04449709132313728,
0.000058573503338266164,
-0.04471597820520401,
0.043793439865112305,
0.03592374175786972,
0.021039342507719994,
-0.018436042591929436,
0.006424538791179657,
-0.012602534145116806,
-0.03215385228395462,
0.016509393230080605,
-0.0019991351291537285,
0.02708575502038002,
-0.007444336079061031,
0.08490978181362152,
0.033137641847133636,
-0.05195845291018486,
-0.030421609058976173,
0.004315211903303862,
-0.0007553512114100158,
0.03761627525091171,
0.03817838057875633,
0.0026055779308080673,
-0.01904895342886448,
-0.009973355568945408,
0.09165031462907791,
0.0036408910527825356,
-0.0035147692542523146,
0.07396971434354782,
0.017186729237437248,
0.0022852406837046146,
-0.005274210125207901,
-0.013428627513349056,
-0.06823332607746124,
-0.012692083604633808,
0.03881044685840607,
-0.025921879336237907,
0.028414176777005196,
-0.028983013704419136,
-0.06037072837352753,
0.0038886077236384153,
-0.02480306662619114,
-0.0004385281354188919,
-0.00714838458225131,
-0.015134559012949467,
0.025473197922110558,
0.040826547890901566,
0.04003376141190529,
-0.011010220274329185,
-0.013262373395264149,
0.022587023675441742,
0.04549267888069153,
0.014794234186410904,
0.038600604981184006,
0.023415224626660347,
-0.0290208887308836,
0.008106912486255169,
-0.0071263969875872135,
-0.024322353303432465,
0.03493862226605415,
0.06241626664996147,
-0.02770617976784706,
-0.008579904213547707,
-0.04183727502822876,
-0.006794946733862162,
-0.0025866718497127295,
0.032408978790044785,
-0.0671442374587059,
0.04356472194194794,
0.06094289571046829,
0.03343553841114044,
0.03593921661376953,
0.05226058140397072,
0.013521842658519745,
0.02583981677889824,
0.02912142314016819,
-0.07590911537408829,
-0.012622463516891003,
-0.06836622208356857,
-0.032015059143304825,
-0.04035390540957451,
-0.08935102075338364,
-0.04849432781338692,
0.10202379524707794,
-0.030244557186961174,
0.004274692386388779,
0.046193040907382965,
0.027722565457224846,
0.03550765663385391,
0.06979544460773468,
0.07755941152572632,
-0.04275495558977127,
0.00996161624789238,
-0.012887251563370228,
-0.027591640129685402,
0.08454254269599915,
-0.017866037786006927,
0.006496903952211142,
0.031890083104372025,
-0.008391915820538998,
0.011490995064377785,
-0.013554694131016731,
0.024007240310311317,
0.00627770135179162,
-0.005890670232474804,
-0.018628474324941635,
0.019309362396597862,
-0.0026444762479513884,
0.04169837012887001,
0.06732020527124405,
-0.033429428935050964,
-0.06217627972364426,
-0.03343756124377251,
0.04091181233525276,
0.025067219510674477,
0.03823119029402733,
0.0022354573011398315,
-0.017287274822592735,
0.020149506628513336,
-0.027585774660110474,
-0.03610793128609657,
-0.031039077788591385,
-0.024772290140390396,
0.03151288256049156,
0.03801599144935608,
0.019836876541376114,
-0.02593613974750042,
0.004480174742639065,
-0.002635813085362315,
0.06504130363464355,
-0.027659622952342033,
-0.04788283631205559,
-0.05839002504944801,
-0.01282233465462923,
-0.018181653693318367,
-0.014310549013316631,
-0.07169190794229507,
-0.09007815271615982,
0.00651609618216753,
0.027090152725577354,
-0.0008986223256215453,
-0.05249787122011185,
-0.008575547486543655,
0.05637643113732338,
-0.0056743077002465725,
-0.0910901129245758,
-0.004375144839286804,
-0.03382037580013275,
-0.0017005805857479572,
0.016137678176164627,
-0.033826183527708054,
-0.029221683740615845,
-0.005382699891924858,
-0.02483397163450718,
0.01383582130074501,
0.03195196017622948,
-0.014818763360381126,
-0.04044125974178314,
-0.02326536551117897,
0.011932320892810822,
0.031473591923713684,
0.057299405336380005,
-0.01342620886862278,
0.026034602895379066,
0.020052112638950348,
-0.029238006100058556,
0.04158589243888855,
-0.016525859013199806,
0.014051849022507668,
0.08693324774503708,
-0.015518146567046642,
0.00875820592045784,
0.02092282474040985,
-0.01139588002115488,
0.007484563160687685,
0.02610355243086815,
-0.026272855699062347,
-0.01158223394304514,
-0.028621338307857513,
0.06623739004135132,
-0.011524850502610207,
0.05815492570400238,
0.04756837338209152,
-0.021706055849790573,
0.01536020077764988,
-0.014296924695372581,
0.03294692933559418,
0.017743080854415894,
-0.0007216000813059509,
0.007813604548573494,
0.007097142282873392,
0.03092358447611332,
-0.02714158594608307,
-0.03112536109983921,
-0.024943264201283455,
-0.005096659064292908,
0.010505528189241886,
0.010359343141317368,
-0.032740261405706406,
0.002014094265177846,
-0.004180425312370062,
0.035569362342357635,
0.0010630039032548666,
0.0036223847419023514,
0.013971204869449139,
0.014390163123607635,
0.021837573498487473,
-0.008603040128946304,
-0.08107838779687881,
-0.10500776767730713,
-0.010652530938386917,
0.05176865682005882,
-0.028997119516134262,
0.00660804333165288,
0.00014631655358243734,
0.01886063627898693,
0.0021791798062622547,
0.05271057412028313,
0.02796589769423008,
-0.006877601146697998,
0.020603258162736893,
0.04409072920680046,
0.016171270981431007,
-0.001865153550170362,
0.02902383543550968,
-0.026432767510414124,
-0.03375221788883209,
-0.03566225618124008,
-0.014285411685705185,
0.037236690521240234,
0.04719984903931618,
-0.10315319150686264,
-0.005045255180448294,
-0.000969650165643543,
0.046842098236083984,
-0.010534756816923618,
0.004879745189100504,
0.02595151774585247,
0.056078240275382996,
-0.017806723713874817,
0.03495439514517784,
-0.03214220702648163,
0.05068870261311531,
-0.014921571128070354,
0.021753421053290367,
0.03438539803028107,
-0.0005443168338388205,
-0.031093958765268326,
0.008326816372573376,
-0.06460481882095337,
0.03042319230735302,
0.07667068392038345,
-0.017007745802402496,
-0.06948019564151764,
-0.008883753791451454,
0.047487761825323105,
0.028773276135325432,
-0.015407368540763855,
0.009781152941286564,
0.0746041089296341,
0.007562491111457348,
-0.01800725981593132,
-0.0191129669547081,
-0.027375301346182823,
0.005891027394682169,
-0.012282051146030426,
-0.004322834312915802,
0.013567047193646431,
-0.0034985675010830164,
-0.02007123827934265,
0.06413345783948898,
-0.04166676104068756,
-0.013126752339303493,
0.0031957323662936687,
-0.04549546539783478,
0.011333483271300793,
-0.04720323905348778,
-0.030304474756121635,
0.024243421852588654,
-0.011728725396096706,
0.0020166535396128893,
-0.0023006463889032602,
0.014541271142661572,
-0.06840851157903671,
0.027458062395453453,
0.006941909436136484,
0.02154032327234745,
-0.003302608150988817,
-0.013614618219435215,
-0.096828892827034,
-0.01311284676194191,
-0.008794218301773071,
-0.010856096632778645,
-0.009774861857295036,
0.0020372490398585796,
0.007188231218606234,
-0.05839594826102257,
0.004155334550887346,
0.02216990664601326,
-0.03455303981900215,
0.0015111105749383569,
-0.04172738268971443,
-0.0266337338835001,
-0.01701970584690571,
0.03650876507163048,
0.05023478344082832,
-0.012222541496157646,
-0.002750919433310628,
0.05090281739830971,
-0.03331688418984413,
-0.0413808710873127,
0.0010513849556446075,
0.04039844870567322,
-0.033682215958833694,
-0.007217055652290583,
-0.0305799413472414,
0.008621098473668098,
0.07950770109891891,
-0.03389886021614075,
0.01549128070473671,
-0.008248208090662956,
0.02347126230597496,
0.02625032514333725,
0.04308955743908882,
0.029296865686774254,
0.02932014688849449,
-0.05129682272672653,
0.049177225679159164,
-0.016454041004180908,
0.034119777381420135,
-0.069733165204525,
0.0034709894098341465,
-0.030172696337103844,
0.00993814691901207,
0.049584828317165375,
0.023901715874671936,
0.002588160103186965,
-0.009872390888631344,
-0.022647147998213768,
-0.026767197996377945,
0.05310923978686333,
0.025372959673404694,
0.06585663557052612,
0.02391863986849785,
0.015091001987457275,
-0.033348433673381805,
0.006557126995176077,
0.031117461621761322,
0.017586009576916695,
0.005073885433375835,
-0.014922978356480598,
-0.02301773987710476,
-0.06736201792955399,
-0.03187543898820877,
-0.09172913432121277,
-0.023672495037317276,
-0.02481873333454132,
-0.007273288909345865,
-0.03382057324051857,
0.003855540417134762,
0.049066491425037384,
-0.02478223294019699,
0.022434646263718605,
-0.0009386692545376718,
0.02865394577383995,
0.012628558091819286,
0.001426330883987248,
0.029821034520864487,
-0.0023885820992290974,
0.008507308550179005,
0.0803227648139,
-0.0014110441552475095,
-0.09220779687166214,
0.022956036031246185,
-0.0010295150568708777,
-0.08365774899721146,
-0.01804298907518387,
0.022200293838977814,
0.024958550930023193,
-0.03883473575115204,
-0.06352673470973969,
0.06729906797409058,
0.026781819760799408,
-0.005162399262189865,
-0.0349288135766983,
0.03994143381714821,
0.009024097584187984,
-0.006593179889023304,
0.049030039459466934,
-0.023754149675369263,
-0.031714364886283875,
-0.011916425079107285,
0.05431637167930603,
-0.027752472087740898,
-0.04684433341026306,
-0.10094983130693436,
0.013835127465426922,
-0.004012689925730228,
0.018239108845591545,
-0.02919166348874569,
-0.00214814068749547,
-0.010398926213383675,
0.028273718431591988,
-0.016277631744742393,
0.09269428253173828,
-0.017240528017282486,
-0.04945485666394234,
0.005997459404170513,
0.0007086407276801765,
0.04758134111762047,
-0.03055071271955967,
-0.003493581200018525,
0.010226866230368614,
-0.070518359541893,
-0.03424918279051781,
-0.06256284564733505,
-0.0036494042724370956,
-0.023042988032102585,
-0.042912181466817856,
0.004936114884912968,
0.03856511414051056,
-0.012800564058125019,
-0.04556964337825775,
-0.055623751133680344,
0.020087186247110367,
-0.023090699687600136,
0.01849784143269062,
-0.03774867206811905,
0.023333873599767685,
0.02855985052883625,
0.02676636353135109,
0.03022211417555809,
-0.025499377399683,
-0.05786220729351044,
-0.0383797325193882,
-0.032682474702596664,
-0.0005133881350047886,
-0.04288802668452263,
0.02587716467678547,
0.004594838246703148,
-0.017642194405198097,
0.029080208390951157,
0.07912139594554901,
-0.0044920663349330425,
0.011906715109944344,
-0.029066620394587517,
-0.018262729048728943,
-0.018217645585536957,
0.01993141882121563,
0.03006518818438053,
-0.042697396129369736,
-0.022348064929246902,
0.05225639045238495,
0.007732135709375143,
0.024390945211052895,
-0.009551508352160454,
-0.017168700695037842,
0.023221615701913834,
-0.03558232635259628,
-0.05153790861368179,
-0.006135090719908476,
-0.05160432681441307,
-0.014200553297996521,
0.023564357310533524,
-0.021360298618674278,
0.006264060270041227,
0.013821122236549854,
-0.02606542967259884,
0.010532058775424957,
0.01399839948862791,
-0.016813823953270912,
-0.044997770339250565,
0.017845774069428444,
0.0642484724521637,
0.013119594193994999,
0.018797777593135834,
0.034863851964473724,
0.011263764463365078,
-0.06457572430372238,
-0.042091768234968185,
0.04068973660469055,
0.034751616418361664,
-0.05081305280327797,
-0.06653885543346405,
-0.00013697294343728572,
0.04115387424826622,
-0.04094855487346649,
0.05312558263540268,
-0.005982235539704561,
-0.007347245700657368,
-0.04941386356949806,
0.033480267971754074,
-0.013639343902468681,
0.01649230159819126,
-0.022636115550994873,
0.03554556146264076,
0.013291678391397,
0.005423098336905241,
0.06825613975524902,
0.01185915619134903,
-0.016918016597628593,
0.03628532215952873,
0.042064279317855835,
0.05550302565097809,
-0.012325404211878777,
0.07262293249368668,
-0.011024851351976395,
-0.051742471754550934,
-0.04553680866956711,
0.026161402463912964,
0.07831628620624542,
0.02025975100696087,
0.0035569972824305296,
-0.04830083250999451,
0.033414218574762344,
0.08494078367948532,
0.017809497192502022,
-0.02257252298295498,
-0.009011967107653618,
0.021633045747876167,
-0.007991602644324303,
0.014970161020755768,
-0.002161407610401511,
0.015706121921539307,
-0.012143364176154137,
0.0006291705067269504,
-0.04169900342822075,
0.09142754971981049,
0.0056137158535420895,
-0.007869608700275421,
-0.02519015595316887,
-0.03893160820007324,
-0.009005796164274216,
0.011252165772020817,
0.044288087636232376,
0.035985324531793594,
-0.03481917083263397,
0.021369919180870056,
-0.027129273861646652,
-0.01568984054028988,
0.013210700824856758,
-0.014334862120449543,
-0.028413034975528717,
-0.010265461169183254,
-0.04004829376935959,
0.003286914201453328,
-0.0524895004928112,
0.03337479382753372,
-0.03430807217955589,
0.04378700628876686,
-0.07836445420980453,
0.008980597369372845,
0.021173596382141113,
-0.025222396478056908,
0.014968649484217167,
-0.010826602578163147,
-0.011074930429458618,
-0.021880915388464928,
-0.031665246933698654,
-0.0027007972821593285,
-0.0035425624810159206,
-0.032240837812423706,
-0.09376994520425797,
-0.021605774760246277,
0.02112702839076519,
-0.07545120269060135,
0.006778808776289225,
0.018195318058133125,
-0.05917959287762642,
0.03114694356918335,
-0.00011867722059832886,
0.06000182032585144,
-0.017776472494006157,
0.010521932505071163,
0.024284565821290016,
0.09095314145088196,
0.005352554842829704,
0.003983441740274429,
0.0716518685221672,
-0.0090821897611022,
-0.011097772046923637,
-0.05655119940638542,
-0.08969902992248535,
-0.04151534289121628,
-0.04364614561200142,
-0.005062164273113012,
-0.0851883590221405,
0.014674530364573002,
0.012180604971945286,
0.03327365964651108,
0.0038014445453882217,
0.01909749209880829,
0.04556803032755852,
-0.02361493930220604,
-0.020221369341015816,
0.013495847582817078,
0.05054048076272011,
-0.022028153762221336,
0.05326331406831741,
-0.020028969272971153,
0.039395783096551895,
0.03615296259522438,
0.03407956659793854,
0.02258480153977871,
-0.02050616778433323,
-0.006152180954813957,
0.01935364492237568,
-0.009213503450155258,
-0.06959667801856995,
0.01831008493900299,
0.0013462037313729525,
-0.05521341413259506,
-0.07035201787948608,
0.028824368491768837,
-0.0025760710705071688,
-0.04115942493081093,
0.016889246180653572,
0.006034567952156067,
0.005640655290335417,
-0.02118324302136898,
0.02000236138701439,
0.02622470073401928,
0.007786932401359081,
-0.06439722329378128,
0.013814273290336132,
-0.028132928535342216,
-0.0839623361825943,
-0.02944510616362095,
-0.022526094689965248,
-0.02239738032221794,
-0.006709182634949684,
-0.0201267097145319,
0.026882050558924675,
0.002264860551804304,
-0.03201476112008095,
-0.06176082044839859,
0.0667305663228035,
0.04323878511786461,
-0.02262943796813488,
-0.010858985595405102,
-0.007538129109889269,
-0.05308353900909424,
-0.03332158178091049,
-0.03993789106607437,
-0.01776210032403469,
0.0016021679621189833,
0.009630695916712284,
0.05706840008497238,
0.09464983642101288,
0.02049061842262745,
-0.024520443752408028,
0.006704052910208702,
-0.008971630595624447,
-0.012881970964372158,
-0.0018268608255311847,
0.0019092524889856577,
-0.07421714067459106,
-0.02253279648721218,
0.03251909464597702,
-0.029986893758177757,
-0.019655605778098106,
-0.024864455685019493,
0.028476309031248093,
0.08231531083583832,
0.01150888204574585,
0.0028430765960365534,
-0.05075547844171524,
-0.04454077035188675,
-0.003943508956581354,
-0.02117730677127838,
-0.005912377033382654,
0.05001002550125122,
0.021118270233273506,
-0.031900133937597275,
0.04945407807826996,
-0.03832137957215309,
0.03168535232543945,
0.08046974986791611,
-0.0028656618669629097,
0.02768126130104065,
0.011095634661614895,
-0.01558177825063467,
0.01956588588654995,
-0.005232829600572586,
0.01050771214067936,
-0.01728937029838562,
-0.056913651525974274,
-0.049211535602808,
0.0013754800893366337,
0.03737640753388405,
-0.051582131534814835,
-0.029758233577013016,
0.04804108664393425,
0.04728347808122635,
-0.06524179875850677,
-0.03465840592980385,
0.00300394999794662,
0.07062312960624695,
0.042351897805929184,
-0.03745967894792557,
-0.004110276233404875,
-0.009153669700026512,
0.01176371518522501,
0.007650233339518309,
-0.015197004191577435,
-0.013481764122843742,
-0.036336347460746765,
-0.034939419478178024,
0.005293500609695911,
0.022556500509381294,
-0.025391412898898125,
0.0019639418460428715,
0.04268159717321396,
0.012354721315205097,
-0.019434118643403053,
-0.03050067648291588,
-0.00011202030873391777,
-0.0198389682918787,
0.04739435389637947,
0.004363991320133209,
-0.00866328552365303,
0.021192848682403564,
-0.02626572735607624,
0.0029114841017872095,
0.001276065013371408,
-0.00716901570558548,
0.0038476395420730114,
-0.0032818587496876717,
-0.0398939773440361,
0.016636423766613007,
-0.03213351592421532,
0.011560714803636074,
0.006712459027767181,
0.010067926719784737,
0.025067709386348724
] |
<p>I want to create a soap blaster using:</p>
<ol>
<li>a 1" hose with 8 bar compressed air</li>
<li>a non pressured container of soap and water mix</li>
<li><strong>without</strong> the use a pressurized tank</li>
</ol>
<p>I.e. something like this <a href="http://www.biltema.no/no/Verktoy/Trykkluft/Verktoy/Sandblasing/Sandblasepistol-17355/" rel="nofollow">sand blaster</a>:
<img src="http://i.stack.imgur.com/khJu3.jpg" alt="enter image description here"></p>
<p>where the sand is picked up from the vacuum of the air flow.
The question is really which laws of physics apply in this creation and how can I calculate the dimensions for my soap blaster with the maximum allowed pickup of soap mixture at the lowest noise level?</p> | g5494 | [
0.036357440054416656,
0.003190074348822236,
-0.0031872058752924204,
0.01186198927462101,
0.034413211047649384,
0.07509168237447739,
0.006449466571211815,
0.009790748357772827,
-0.03835422918200493,
-0.041712552309036255,
0.004120460711419582,
-0.02864851802587509,
0.04422096163034439,
0.03118717297911644,
0.029382042586803436,
-0.02363513968884945,
0.044385284185409546,
-0.05587498098611832,
0.020717447623610497,
-0.020302053540945053,
-0.006882981862872839,
-0.0616353303194046,
0.006553409155458212,
-0.14322982728481293,
-0.014507269486784935,
-0.02722742035984993,
-0.008642501197755337,
0.057564832270145416,
-0.062351860105991364,
0.0013316308613866568,
0.013078153133392334,
-0.017712922766804695,
-0.03470321372151375,
-0.030916213989257812,
-0.05705473572015762,
-0.05701659619808197,
-0.00812954269349575,
-0.014757893979549408,
-0.02533537521958351,
0.0004118062206543982,
-0.008570961654186249,
-0.05142781883478165,
0.008787265978753567,
0.014175078831613064,
-0.022833412513136864,
0.030612599104642868,
-0.006014576181769371,
0.016141101717948914,
0.0017722980119287968,
-0.008589264005422592,
-0.0596102736890316,
-0.02305954322218895,
-0.05003982409834862,
-0.0032482841052114964,
0.013131539337337017,
0.0067665427923202515,
-0.019124027341604233,
-0.042859286069869995,
0.017876682803034782,
-0.010439048521220684,
-0.045968350023031235,
0.0494253933429718,
-0.0419321209192276,
0.07657346874475479,
-0.001899437396787107,
0.040329623967409134,
-0.0674077719449997,
-0.08952238410711288,
0.015344168990850449,
0.001541478675790131,
0.04502096772193909,
-0.012771159410476685,
-0.0020895604975521564,
-0.08261917531490326,
-0.02070077322423458,
0.051704902201890945,
0.0074776699766516685,
0.018409648910164833,
-0.0017282033804804087,
0.03736650571227074,
0.021346278488636017,
0.02755560912191868,
-0.0013639968819916248,
-0.0749463140964508,
0.09944979101419449,
0.0012386891758069396,
-0.024680983275175095,
0.028691131621599197,
-0.009890527464449406,
0.014543362893164158,
-0.01602480746805668,
-0.0069642942398786545,
0.06394141912460327,
0.011452091857790947,
0.0019979565404355526,
-0.008588206954300404,
-0.012778605334460735,
0.06242838874459267,
-0.022657521069049835,
-0.01436995342373848,
0.025909649208188057,
0.012055840343236923,
0.03967868909239769,
-0.006984591018408537,
-0.07374544441699982,
0.018632909283041954,
0.01401012297719717,
0.014071415178477764,
-0.027471227571368217,
-0.05090701952576637,
-0.03661743924021721,
-0.06869353353977203,
-0.05742911249399185,
-0.012108903378248215,
-0.003677722765132785,
-0.0317772701382637,
-0.008027641102671623,
0.010535296984016895,
0.0251935962587595,
0.06557270884513855,
0.06992679834365845,
0.011617982760071754,
0.022420261055231094,
-0.03355150669813156,
0.008769983425736427,
-0.033901650458574295,
0.0023708967491984367,
0.02169155143201351,
0.05568339303135872,
-0.04175196588039398,
0.01598440296947956,
-0.025615036487579346,
-0.010449845343828201,
-0.04393235966563225,
-0.0025748214684426785,
0.02118101716041565,
-0.02685559168457985,
-0.002738522132858634,
0.023121895268559456,
-0.009615875780582428,
0.0022464198991656303,
0.02503020130097866,
-0.025345372036099434,
-0.0024425482843071222,
0.007989940233528614,
-0.02084825001657009,
0.016400286927819252,
0.03335060551762581,
-0.03129441663622856,
-0.03754374384880066,
-0.020853426307439804,
0.006872853264212608,
0.01824566349387169,
-0.00019192634499631822,
-0.002778072142973542,
0.004062389489263296,
0.03632364794611931,
0.02130056917667389,
0.045042186975479126,
0.006452362984418869,
0.0008215329144150019,
-0.011816595681011677,
0.021460387855768204,
0.0047125425189733505,
-0.10460038483142853,
-0.05289142206311226,
-0.03195379301905632,
-0.05213424190878868,
0.04855401813983917,
-0.022695833817124367,
-0.034005772322416306,
-0.05293593183159828,
0.007037526927888393,
-0.023973733186721802,
-0.051349613815546036,
0.057257652282714844,
0.04004467651247978,
-0.10034513473510742,
0.018123460933566093,
-0.005630581174045801,
0.017198525369167328,
-0.02279031276702881,
0.04942065477371216,
0.004068462178111076,
0.003267676802352071,
0.015070523135364056,
0.02066856063902378,
-0.048005733639001846,
-0.037968046963214874,
-0.012642402201890945,
-0.03673696517944336,
0.009437642991542816,
-0.0424109511077404,
-0.0025468231178820133,
-0.06959007680416107,
-0.027295401319861412,
0.04130347818136215,
-0.04610428214073181,
0.002440578071400523,
-0.019513852894306183,
0.0018625874072313309,
0.06847204267978668,
0.03455513343214989,
0.017265167087316513,
0.03778070956468582,
-0.046927932649850845,
-0.06929165869951248,
0.005588226485997438,
-0.007467879913747311,
0.02738116681575775,
0.01614636369049549,
0.01152748055756092,
-0.015182007104158401,
-0.023634567856788635,
-0.005944548640400171,
0.015950797125697136,
-0.01355966180562973,
0.01941290684044361,
-0.0370120108127594,
0.014667893759906292,
-0.010984008200466633,
0.01844947598874569,
0.033842720091342926,
0.05293493717908859,
0.03764485940337181,
-0.03781191632151604,
-0.012851675972342491,
0.01866137981414795,
0.028774019330739975,
0.005019755102694035,
-0.018396150320768356,
0.0225686002522707,
0.01922282762825489,
-0.03360358253121376,
0.03182026743888855,
0.0443539135158062,
0.012939883396029472,
0.03307129442691803,
-0.010765375569462776,
0.015490232035517693,
0.0589120127260685,
0.02272794581949711,
0.013010804541409016,
0.0008630089578218758,
-0.02648875303566456,
-0.06037987023591995,
-0.016582448035478592,
-0.034077003598213196,
0.02569715492427349,
-0.0001437644095858559,
-0.00360964541323483,
-0.012348474934697151,
0.0009672996238805354,
0.00468798540532589,
-0.01890813186764717,
0.018847474828362465,
0.018571853637695312,
0.014566166326403618,
-0.044083110988140106,
-0.07059706747531891,
0.0248833317309618,
0.006008862517774105,
0.026091961190104485,
0.018257277086377144,
-0.07708843797445297,
0.014115768484771252,
-0.044189244508743286,
0.006805929820984602,
-0.017071757465600967,
0.014920033514499664,
-0.00969066470861435,
0.006437125150114298,
0.025616517290472984,
-0.00886564701795578,
0.04019980877637863,
-0.007626006379723549,
0.024320553988218307,
-0.0401432029902935,
-0.0018948044162243605,
0.037933092564344406,
-0.028666706755757332,
0.027042962610721588,
-0.018617672845721245,
0.014869765378534794,
0.026140842586755753,
-0.0186558086425066,
0.05549635738134384,
0.03149872645735741,
-0.02857297658920288,
0.07085546851158142,
-0.01416679285466671,
0.020759550854563713,
0.004205198958516121,
0.014877879992127419,
0.02862589992582798,
0.10390286147594452,
0.006618332117795944,
-0.049756478518247604,
0.018810946494340897,
0.0499885194003582,
-0.003979158122092485,
-0.04386212304234505,
0.015287662856280804,
-0.03187629207968712,
-0.0794878825545311,
0.015103723853826523,
-0.010974603705108166,
-0.03059566393494606,
-0.00985637679696083,
0.029927972704172134,
-0.003627188503742218,
0.01962711289525032,
0.03827810660004616,
-0.005766562186181545,
-0.05024879425764084,
-0.025938961654901505,
0.0385698601603508,
-0.01653888449072838,
0.017020899802446365,
0.01498871948570013,
-0.035143449902534485,
-0.07987256348133087,
-0.014289799146354198,
-0.027663256973028183,
0.003620268078520894,
0.005340128671377897,
0.022887811064720154,
-0.001548759755678475,
0.012223955243825912,
0.023980023339390755,
0.04029101878404617,
0.030720124021172523,
-0.019102374091744423,
-0.009617404080927372,
-0.07721710205078125,
-0.022482186555862427,
-0.024799495935440063,
0.007913336157798767,
0.029365308582782745,
0.00842888280749321,
-0.011149399913847446,
-0.018671737983822823,
0.0003569133987184614,
-0.08476032316684723,
-0.044256649911403656,
0.07130555063486099,
-0.000325211847666651,
0.021668272092938423,
0.03279031813144684,
-0.005748121999204159,
0.07233570516109467,
0.02090221270918846,
-0.055244080722332,
-0.0042735133320093155,
0.015791459009051323,
0.05868950113654137,
0.03647725656628609,
0.0678977519273758,
0.019300665706396103,
-0.045256610959768295,
-0.006471709813922644,
-0.00764037761837244,
-0.00013275213132146746,
-0.03468417376279831,
-0.003296277951449156,
-0.015713924542069435,
0.02185099571943283,
0.04193154722452164,
-0.04778634011745453,
0.03364555165171623,
-0.04041106626391411,
-0.048549115657806396,
-0.014051446691155434,
0.0004717753326985985,
0.03484708443284035,
-0.008013063110411167,
0.05217130482196808,
-0.009036002680659294,
-0.0074899946339428425,
0.031018786132335663,
0.04062390699982643,
0.052157048135995865,
0.009355173446238041,
-0.009496270678937435,
-0.0057762800715863705,
-0.015118896961212158,
0.001914900611154735,
0.032183416187763214,
0.019053446128964424,
-0.1037144735455513,
0.004664983134716749,
-0.05251377448439598,
-0.025628594681620598,
-0.013765337876975536,
0.024362713098526,
0.0046289777383208275,
0.006525299046188593,
0.0023429871071130037,
-0.09905748814344406,
0.008054154925048351,
0.07808876782655716,
0.04863860458135605,
0.010433316230773926,
-0.06412360817193985,
-0.018685810267925262,
-0.04278874024748802,
0.04938465729355812,
0.019798416644334793,
-0.026067767292261124,
-0.015118326991796494,
-0.025785379111766815,
-0.012389647774398327,
-0.001987899886444211,
-0.06401106715202332,
0.01825769431889057,
-0.02290942892432213,
-0.015119686722755432,
0.044320251792669296,
-0.03372078388929367,
0.005116698332130909,
0.051795706152915955,
0.007034267298877239,
0.0029349643737077713,
-0.009449372068047523,
-0.03351673483848572,
0.020434383302927017,
0.06842735409736633,
0.03466619551181793,
0.03134230896830559,
-0.006794121116399765,
-0.033013392239809036,
-0.03355515003204346,
-0.035275962203741074,
0.03481826186180115,
-0.03964114561676979,
0.022771261632442474,
0.010980411432683468,
0.006644558627158403,
0.010969397611916065,
0.02149258926510811,
0.0015484236646443605,
-0.03026418946683407,
0.013854192569851875,
0.056350380182266235,
0.05450769513845444,
0.07673949748277664,
-0.027185242623090744,
-0.08654729276895523,
-0.05469541251659393,
0.04976034536957741,
0.001601899741217494,
-0.004011907149106264,
-0.003777963574975729,
-0.04379042610526085,
-0.016261951997876167,
0.07074490189552307,
-0.035092681646347046,
-0.0018097672145813704,
-0.005345336627215147,
0.007283804006874561,
-0.029313649982213974,
-0.010640237480401993,
-0.014446765184402466,
-0.005951460916548967,
-0.010695177130401134,
-0.05704941228032112,
-0.007497250568121672,
-0.019086187705397606,
-0.08201153576374054,
0.03064444102346897,
0.034323159605264664,
-0.000848781259264797,
0.03281736001372337,
0.10402907431125641,
-0.015363309532403946,
-0.006610156502574682,
0.03803678974509239,
-0.01536728348582983,
-0.01607527583837509,
-0.025048885494470596,
0.0447751022875309,
0.010176902636885643,
-0.037259481847286224,
0.021525109186768532,
0.026261039078235626,
0.06444840878248215,
-0.02038409188389778,
0.002215985208749771,
0.006724390666931868,
-0.009173166006803513,
0.006492716260254383,
0.04167575016617775,
-0.019936712458729744,
-0.012389322742819786,
-0.06395434588193893,
0.02717571333050728,
-0.009958673268556595,
-0.039789602160453796,
-0.042694367468357086,
0.02613195776939392,
-0.013788999989628792,
-0.06784307211637497,
0.016523294150829315,
0.00019183900440111756,
0.006660823244601488,
-0.050664547830820084,
-0.012266423553228378,
0.06190003082156181,
0.04686281085014343,
0.03961670398712158,
0.017952831462025642,
0.025023212656378746,
0.06274775415658951,
-0.04623328894376755,
-0.007999524474143982,
-0.06805218011140823,
0.00019495667947921902,
0.041596945375204086,
-0.03758784383535385,
0.015686672180891037,
0.03282508999109268,
-0.014949226751923561,
0.04854593425989151,
-0.023601049557328224,
-0.07133343815803528,
0.040164124220609665,
0.007428413722664118,
0.011827514506876469,
0.03333134576678276,
0.026697266846895218,
0.01084781251847744,
-0.002264050766825676,
0.058594558387994766,
-0.031113356351852417,
0.006387695670127869,
-0.0418117456138134,
0.07027709484100342,
0.09196586161851883,
-0.02313891611993313,
-0.03678309917449951,
-0.00476043950766325,
0.010265100747346878,
-0.030639031901955605,
0.06870155781507492,
0.028776902705430984,
0.015077284537255764,
-0.02947968989610672,
0.03597186133265495,
0.04430616647005081,
0.01413794420659542,
-0.009383874014019966,
0.04638240113854408,
0.03446882590651512,
-0.0036338032223284245,
0.04557397961616516,
-0.00885052140802145,
-0.06150094419717789,
0.046660132706165314,
-0.044647540897130966,
-0.056512486189603806,
0.03981861472129822,
0.06458551436662674,
0.03609709069132805,
0.04493872821331024,
-0.0006746273138560355,
-0.054727062582969666,
-0.017630327492952347,
0.022482190281152725,
0.031861208379268646,
0.10611750930547714,
-0.07211394608020782,
0.014875322580337524,
0.022490445524454117,
-0.03659532964229584,
0.057702772319316864,
-0.05254939943552017,
0.014090976677834988,
-0.012511122040450573,
-0.01956377550959587,
0.06291075050830841,
0.019651589915156364,
0.06288346648216248,
0.03114735335111618,
-0.012783060781657696,
0.0025523046497255564,
-0.01559493225067854,
-0.009539073333144188,
0.002798588713631034,
-0.07296496629714966,
-0.04750688746571541,
-0.00392921781167388,
-0.029505016282200813,
0.005087988916784525,
0.024709392338991165,
0.010832949541509151,
-0.03443329781293869,
-0.01546761766076088,
-0.00527919689193368,
0.005246439017355442,
-0.022502876818180084,
0.020565645769238472,
0.03778940066695213,
-0.043321605771780014,
-0.012946664355695248,
-0.042360350489616394,
-0.013757198117673397,
-0.04785998910665512,
0.0031484023202210665,
-0.05272885039448738,
0.021351266652345657,
-0.03770165517926216,
0.04651184380054474,
-0.016132604330778122,
0.014172441326081753,
0.003803983563557267,
-0.012047696858644485,
0.053577203303575516,
-0.019077572971582413,
0.08362098783254623,
0.00473374268040061,
-0.010504237376153469,
0.0004124629485886544,
0.03550168126821518,
-0.013251900672912598,
0.022674039006233215,
0.018025143072009087,
-0.054350100457668304,
0.004027550108730793,
0.005885978229343891,
0.017333460971713066,
0.04341477155685425,
0.0031177373602986336,
0.0000040601412365504075,
0.027079718187451363,
-0.014814073219895363,
0.11050275713205338,
-0.013785429298877716,
0.04774261638522148,
0.034488409757614136,
0.036603137850761414,
-0.034193623811006546,
0.02030758187174797,
0.03290237858891487,
0.1071712002158165,
-0.00617642980068922,
0.02228320576250553,
-0.028540458530187607,
-0.009131482802331448,
-0.048712894320487976,
-0.003752931719645858,
-0.010043168440461159,
-0.09404551982879639,
0.009886964224278927,
0.0507003590464592,
-0.07093752175569534,
0.052303530275821686,
-0.00905322190374136,
-0.007270862348377705,
0.031235063448548317,
-0.02229541353881359,
-0.0022378487046808004,
-0.05886082351207733,
0.043151672929525375,
-0.035701852291822433,
0.05070628970861435,
0.06444457918405533,
-0.001752555021084845,
0.013697627931833267,
0.02279517985880375,
-0.027472330257296562,
0.0030592945404350758,
-0.014011248014867306,
-0.04769308120012283,
0.03184378519654274,
0.03206527233123779,
-0.04555497318506241,
0.02152280882000923,
0.027226634323596954,
0.008518604561686516,
-0.04142696037888527,
-0.02224101312458515,
0.03181854635477066,
-0.03422718122601509,
-0.00536767765879631,
-0.038758788257837296,
-0.016259480267763138,
-0.002081720856949687,
0.03328694403171539,
0.03799910470843315,
-0.03297380730509758,
0.0081350551918149,
-0.0002833183389157057,
0.04917917400598526,
-0.005211529787629843,
-0.02512751892209053,
0.0446351133286953,
0.044113218784332275,
-0.0175247211009264,
0.022430822253227234,
-0.027652639895677567,
0.025439150631427765,
0.031212732195854187,
-0.051834944635629654,
0.016792958602309227,
-0.03792733699083328,
0.006599010434001684,
0.02493765950202942,
0.0015361023833975196,
-0.017326034605503082,
-0.027641678228974342,
0.010866689495742321,
0.011364923790097237,
-0.03876122832298279,
0.014992127195000648,
0.001032814267091453,
-0.007564488332718611,
-0.07787025719881058,
0.05536143481731415,
0.07810813188552856,
0.013608856126666069,
0.0044610206969082355,
0.009493551217019558,
0.020156407728791237,
-0.0005202910397201777,
0.033572278916835785,
-0.035775355994701385,
-0.015210798010230064,
0.07344163209199905,
-0.06211629882454872,
0.04498114809393883,
-0.044315509498119354,
-0.046110060065984726,
-0.025101765990257263,
-0.011865871027112007,
0.006930074188858271,
-0.03768753260374069,
0.011661985889077187,
0.048672255128622055,
-0.016788458451628685,
0.003464405657723546,
-0.012576756998896599,
-0.012846583500504494,
0.000636923243291676,
-0.002868033479899168,
0.008566359989345074,
-0.08973681181669235,
-0.07703401148319244,
0.0561973936855793,
0.011593278497457504,
-0.05966955050826073,
0.023211052641272545,
0.01320482324808836,
0.06241677328944206,
0.023569729179143906,
-0.0049004266038537025,
-0.07620687037706375,
0.04067651554942131,
0.002827787073329091,
-0.008242045529186726,
-0.0469854399561882,
0.03004043735563755,
0.003121446818113327,
-0.0018696492770686746,
-0.002305631060153246,
0.0376163087785244,
-0.018133100122213364,
0.012974732555449009,
-0.04266596958041191
] |
<p>Noether's Theorem is used to related the invariance under certain continuous transformations to conserved currents. A common example is that translations in spacetime correspond to the conservation of four-momentum.</p>
<p>In the case of angular momentum, the tensor (in special relativity) has 3 independent components for the classical angular momentum, but 3 more independent components that, as far as I know, represent Lorentz boosts. So, what conservation law corresponds to invariance under Lorentz boosts?</p> | g252 | [
0.003855211893096566,
-0.024884816259145737,
-0.029535917565226555,
-0.0561172291636467,
-0.057300642132759094,
0.03999257832765579,
0.00016243025311268866,
0.03252511844038963,
-0.008347575552761555,
0.055033836513757706,
-0.049536556005477905,
-0.0250528696924448,
-0.03567875176668167,
-0.018661536276340485,
0.006186280865222216,
0.012769426219165325,
0.06761524081230164,
0.03381060063838959,
0.08538545668125153,
-0.048257458955049515,
0.0516338087618351,
-0.012684048153460026,
-0.013393002562224865,
-0.05622325837612152,
0.01313764601945877,
0.023582061752676964,
0.021189024671912193,
-0.019040901213884354,
-0.0995810329914093,
-0.042803265154361725,
0.05516071617603302,
-0.004639270715415478,
0.030950965359807014,
-0.029660994186997414,
-0.00040217844070866704,
-0.04540148004889488,
0.0432460755109787,
0.04267111420631409,
0.04575780779123306,
-0.0027149964589625597,
0.028084538877010345,
0.07284817844629288,
-0.004398936405777931,
0.0022206970024853945,
-0.008932647295296192,
-0.03472110629081726,
-0.0376923494040966,
-0.049003615975379944,
-0.015505635179579258,
-0.01219437550753355,
-0.0114507544785738,
0.023456348106265068,
0.02693808451294899,
-0.025551291182637215,
-0.014514382928609848,
-0.013618224300444126,
0.03516852483153343,
-0.017026063054800034,
-0.053749311715364456,
0.05042976886034012,
0.009785709902644157,
-0.03677612543106079,
-0.00517768831923604,
-0.0046727778390049934,
0.07266858965158463,
-0.02572743594646454,
-0.023212164640426636,
0.011038809083402157,
-0.005423299502581358,
-0.017981261014938354,
0.03403075784444809,
0.014888757839798927,
0.01713971234858036,
-0.012536237947642803,
-0.017006583511829376,
0.04628833010792732,
-0.005562696605920792,
0.029131174087524414,
0.009231049567461014,
-0.012911101803183556,
-0.040993377566337585,
-0.000411948625696823,
0.05803844705224037,
-0.010389840230345726,
0.08449526131153107,
0.030680818483233452,
-0.03498601168394089,
0.003751118667423725,
-0.05861646682024002,
-0.024256324395537376,
0.056380316615104675,
-0.021636933088302612,
0.0070714098401367664,
-0.0271934624761343,
0.011926892213523388,
-0.009119526483118534,
0.010214864276349545,
0.015228476375341415,
0.032757312059402466,
-0.06635414808988571,
-0.02950521744787693,
0.01151068415492773,
-0.062299229204654694,
-0.03241420164704323,
0.06473115086555481,
0.04838060960173607,
0.028344033285975456,
0.02429393120110035,
-0.013383219949901104,
0.011130576953291893,
-0.053555119782686234,
-0.1368541568517685,
0.004282565321773291,
0.038030996918678284,
-0.05878866836428642,
-0.015442440286278725,
0.037728969007730484,
-0.054791875183582306,
0.06107192113995552,
0.0767662525177002,
0.010466326959431171,
0.04137628152966499,
0.024206748232245445,
0.04737458378076553,
-0.01876397803425789,
0.05153266340494156,
-0.010726840235292912,
0.02570832148194313,
0.036486104130744934,
-0.05800102278590202,
0.03389539197087288,
-0.035334814339876175,
-0.00427889171987772,
-0.01728089340031147,
-0.007571456488221884,
-0.009098761714994907,
0.027418795973062515,
0.0015036833938211203,
0.009656671434640884,
0.006834843195974827,
0.02077457681298256,
-0.012594814412295818,
0.03894057124853134,
-0.01155178528279066,
-0.0052407835610210896,
-0.04608435556292534,
-0.03158740699291229,
0.004890586715191603,
0.01420910656452179,
-0.01181220542639494,
-0.001129477983340621,
0.09171213954687119,
0.012050459161400795,
-0.03567661717534065,
0.07358991354703903,
-0.02023727260529995,
0.011659716255962849,
-0.06357203423976898,
-0.005948785226792097,
0.01756230555474758,
0.02652149833738804,
-0.0442623496055603,
0.005697840359061956,
0.022942574694752693,
-0.054749928414821625,
-0.0058415550738573074,
0.018411440774798393,
-0.0662868469953537,
-0.020784487947821617,
-0.01975318230688572,
-0.03823181614279747,
-0.015610657632350922,
0.011713430285453796,
0.015439770184457302,
0.022517194971442223,
0.03308640792965889,
-0.028480179607868195,
-0.03745759278535843,
0.012474668212234974,
-0.03669458627700806,
-0.026117447763681412,
0.00904127862304449,
0.0537089928984642,
0.015903212130069733,
0.02754325605928898,
0.08655355870723724,
0.007626377046108246,
-0.014760011807084084,
-0.08198404312133789,
0.02425621636211872,
0.020495017990469933,
-0.02077929675579071,
-0.038585733622312546,
0.055434450507164,
0.03773302212357521,
0.01528596505522728,
-0.019044170156121254,
-0.038294728845357895,
-0.03399486094713211,
0.04890110343694687,
-0.0020442656241357327,
0.027498725801706314,
0.06042982265353203,
-0.027471015229821205,
0.021472953259944916,
-0.000834361300803721,
-0.030245956033468246,
-0.004330931231379509,
0.058278944343328476,
-0.047739189118146896,
0.026958171278238297,
-0.04502694681286812,
-0.008099597878754139,
-0.05296541750431061,
-0.029297249391674995,
-0.006580940913408995,
-0.005938786547631025,
0.04691595956683159,
-0.07656130194664001,
0.0387832336127758,
-0.012673948891460896,
-0.019085077568888664,
0.03919428959488869,
0.006021989043802023,
-0.050283223390579224,
0.01958087831735611,
-0.024818601086735725,
-0.0206112340092659,
0.04411785677075386,
0.047148872166872025,
-0.039760246872901917,
-0.0017643935279920697,
-0.02052760124206543,
0.029252318665385246,
0.03105008229613304,
0.05921194702386856,
-0.0024311337620019913,
0.024215616285800934,
0.008209235034883022,
0.06031953915953636,
0.0340653657913208,
0.006670875009149313,
-0.013564340770244598,
-0.011970729567110538,
0.07205319404602051,
0.05623926594853401,
0.02391979843378067,
-0.009579525329172611,
-0.023663043975830078,
-0.008528967387974262,
-0.023511668667197227,
-0.028341375291347504,
-0.015098103322088718,
0.0019757074769586325,
0.01185110118240118,
0.04087274894118309,
0.0018607490928843617,
0.03592629358172417,
-0.06710536032915115,
0.00635708961635828,
-0.008533189073204994,
-0.05393971875309944,
0.037938281893730164,
0.019141824916005135,
-0.036626335233449936,
0.004220862407237291,
0.014248503372073174,
0.04144798219203949,
0.00381459086202085,
0.0066354963928461075,
-0.05214231088757515,
0.06628962606191635,
-0.03171784058213234,
0.021916858851909637,
0.010703585110604763,
0.020770953968167305,
-0.009418574161827564,
-0.0009199426858685911,
-0.058179568499326706,
-0.014760514721274376,
-0.0063166203908622265,
0.034395765513181686,
-0.021697454154491425,
0.010770016349852085,
0.006341941654682159,
-0.009097988717257977,
-0.002696190495043993,
0.03567327558994293,
-0.03601289913058281,
0.03526124730706215,
-0.029582461342215538,
0.027425825595855713,
0.04923608899116516,
-0.028134360909461975,
0.01219070702791214,
-0.012609812431037426,
0.0017366153188049793,
-0.05804448947310448,
-0.03728816658258438,
0.10215119272470474,
-0.026589663699269295,
-0.03972224146127701,
0.04634455591440201,
-0.008768168278038502,
0.005172803532332182,
0.011555112898349762,
-0.03041495941579342,
-0.007951771840453148,
0.021913394331932068,
0.017719486728310585,
-0.05214808136224747,
0.03194565698504448,
-0.043051328510046005,
0.039603762328624725,
-0.0723765566945076,
-0.022820277139544487,
-0.020989643409848213,
-0.0017205077456310391,
0.016826923936605453,
-0.021380120888352394,
-0.03700670599937439,
-0.011952701024711132,
0.0021982358302921057,
-0.01993756927549839,
0.05765535682439804,
0.0003131935081910342,
-0.08731492608785629,
0.008713390678167343,
-0.02227921225130558,
-0.018204815685749054,
-0.008683789521455765,
-0.0026122131384909153,
0.03802276775240898,
-0.014699035324156284,
-0.007182864937931299,
-0.019603269174695015,
-0.05175448954105377,
0.028565779328346252,
0.003314422909170389,
-0.057245682924985886,
0.06408343464136124,
-0.01766798086464405,
-0.06778845936059952,
-0.011469115503132343,
-0.021652519702911377,
0.04414965584874153,
0.022806614637374878,
0.007269741501659155,
0.018059244379401207,
-0.0025703199207782745,
0.023337887600064278,
-0.0050719911232590675,
0.035814449191093445,
-0.03327355161309242,
0.050985708832740784,
-0.025326242670416832,
0.04196634888648987,
0.033253613859415054,
-0.019447006285190582,
0.025478241965174675,
0.013893849216401577,
0.046317506581544876,
-0.0062894974835217,
0.0398293100297451,
-0.01702660694718361,
-0.00041273573879152536,
0.016177376732230186,
-0.005413636099547148,
-0.004501450806856155,
0.04643169790506363,
0.049001701176166534,
-0.03054879978299141,
-0.02874629758298397,
0.009409992024302483,
-0.0410301499068737,
-0.0526956208050251,
0.017492201179265976,
0.07213221490383148,
0.005200384650379419,
-0.019300557672977448,
0.020487571135163307,
0.05087351053953171,
0.01686803065240383,
-0.00422376673668623,
0.015193833038210869,
-0.0031286219600588083,
0.010040180757641792,
0.058495983481407166,
0.017985260114073753,
-0.04330061748623848,
0.012585610151290894,
0.026142120361328125,
0.03747956082224846,
-0.07788734138011932,
0.006750296801328659,
-0.017720401287078857,
0.03210531920194626,
-0.009419884532690048,
0.042227644473314285,
0.010374951176345348,
-0.029893355444073677,
0.04931829869747162,
-0.02910328283905983,
-0.06629189103841782,
0.018170392140746117,
0.07609445601701736,
0.056930363178253174,
-0.010861990042030811,
-0.027958404272794724,
0.00412644911557436,
-0.02000989206135273,
-0.002287427196279168,
0.022365620359778404,
-0.04726509377360344,
0.037303198128938675,
0.009004795923829079,
-0.015453030355274677,
-0.1055535078048706,
-0.023116104304790497,
-0.006231839768588543,
0.033301692456007004,
0.012264087796211243,
0.036842815577983856,
-0.05697965249419212,
0.032872430980205536,
0.0014788026455789804,
0.07027259469032288,
-0.014413163997232914,
-0.025734759867191315,
0.02197994850575924,
0.031077580526471138,
0.0027744092512875795,
0.07080408930778503,
-0.021975677460432053,
-0.039522286504507065,
-0.011447000317275524,
-0.026831505820155144,
0.04866918921470642,
-0.026088831946253777,
-0.02300141751766205,
0.1034599244594574,
0.03128300607204437,
0.033930495381355286,
-0.03504883870482445,
-0.05538449063897133,
0.09037332236766815,
0.03460041433572769,
0.012455398216843605,
0.01684766262769699,
-0.010023469105362892,
-0.05471690744161606,
-0.026287123560905457,
-0.009507494047284126,
-0.01641976088285446,
0.027468176558613777,
0.03962842747569084,
-0.005703879054635763,
0.00010783712059492245,
0.007838110439479351,
0.0673518255352974,
-0.018924539908766747,
0.024458125233650208,
0.0217895545065403,
0.009883773513138294,
0.03819916397333145,
-0.014993234537541866,
-0.05246664956212044,
0.042419154196977615,
-0.044012464582920074,
-0.028273914009332657,
0.04356887564063072,
-0.021652061492204666,
-0.034012265503406525,
-0.01342254038900137,
0.024784307926893234,
-0.018261194229125977,
0.06148252263665199,
0.01046660915017128,
-0.026078730821609497,
-0.05868581682443619,
-0.008456851355731487,
0.002316331258043647,
0.020719636231660843,
0.016524484381079674,
-0.00245284684933722,
0.003919380716979504,
-0.009261978790163994,
-0.0003409210476092994,
0.033656977117061615,
-0.04815588891506195,
-0.022939903661608696,
0.07144927978515625,
0.02577820047736168,
-0.019498448818922043,
-0.0414622500538826,
0.047143224626779556,
-0.012993319891393185,
-0.05868420749902725,
-0.02883164957165718,
-0.02636799030005932,
-0.04671550914645195,
-0.009581669233739376,
0.06346724927425385,
0.021092072129249573,
-0.003560593817383051,
0.01692936010658741,
0.012227865867316723,
0.07457100600004196,
-0.06794285774230957,
0.032080765813589096,
0.03466959297657013,
0.026268906891345978,
-0.01611236110329628,
-0.06065734103322029,
-0.01987534575164318,
0.04397089406847954,
-0.014150350354611874,
-0.0372014045715332,
-0.003983668517321348,
0.01036884542554617,
0.00921095721423626,
0.02101479470729828,
0.04254108667373657,
-0.026346378028392792,
0.012768825516104698,
0.047607146203517914,
-0.007449259050190449,
-0.04508381336927414,
0.012751064263284206,
-0.0029310265090316534,
0.01871040277183056,
-0.04007358476519585,
0.019622543826699257,
-0.009511854499578476,
0.10075860470533371,
-0.012276770547032356,
-0.00002678749297047034,
0.027293862774968147,
0.020093131810426712,
0.023184025660157204,
-0.03436068445444107,
-0.024612396955490112,
0.0009242820087820292,
0.011453483253717422,
-0.05041057989001274,
0.00810894463211298,
-0.0145256407558918,
0.026419028639793396,
0.050362251698970795,
-0.031853578984737396,
-0.0536353662610054,
-0.03377852961421013,
-0.011187300086021423,
-0.023132238537073135,
-0.0027619870379567146,
-0.027685590088367462,
0.025513382628560066,
-0.009816475212574005,
-0.020119009539484978,
-0.016119588166475296,
0.014932204969227314,
0.03087664395570755,
0.06532173603773117,
0.015812948346138,
-0.016956359148025513,
-0.0040434375405311584,
-0.017299683764576912,
-0.014581236988306046,
0.047818250954151154,
0.03819096460938454,
-0.04991684854030609,
0.02459609881043434,
-0.010899800807237625,
0.04074666649103165,
-0.04639188200235367,
-0.03677215054631233,
-0.03697969764471054,
0.011758149601519108,
-0.06938247382640839,
0.010830276645720005,
-0.00558765372261405,
0.01195063628256321,
0.047199033200740814,
-0.058721646666526794,
-0.0744129940867424,
-0.00884993840008974,
-0.08172164857387543,
-0.011445083655416965,
0.03519082069396973,
0.05025649070739746,
-0.00843128189444542,
0.007096423301845789,
-0.011921430937945843,
-0.00967174582183361,
-0.007531775627285242,
0.011677943170070648,
0.006114885676652193,
0.014060486108064651,
-0.021195249632000923,
0.02663702704012394,
0.01726572774350643,
0.017133662477135658,
0.050581734627485275,
0.03521351516246796,
0.05649769306182861,
0.03347775340080261,
-0.02783583663403988,
-0.029714519158005714,
-0.021380983293056488,
0.007554893847554922,
0.017226895317435265,
0.02872839756309986,
-0.027358317747712135,
-0.011422760784626007,
-0.013212926685810089,
0.038648974150419235,
-0.03669874742627144,
-0.02667570486664772,
-0.05623979866504669,
-0.011517981067299843,
0.05355969816446304,
-0.018345916643738747,
-0.039020031690597534,
0.06197170540690422,
0.04931224510073662,
0.0371706560254097,
-0.01961168460547924,
0.009417933411896229,
-0.04256318137049675,
0.0015492980601266026,
-0.05317246913909912,
-0.01774773932993412,
-0.019389161840081215,
0.04326298460364342,
-0.013214376755058765,
-0.026163486763834953,
0.002702991710975766,
-0.013580933213233948,
0.09582427144050598,
0.03364637866616249,
-0.02262943610548973,
0.010631658136844635,
0.04599233716726303,
0.0300925113260746,
-0.04761739447712898,
0.008384870365262032,
0.04938795790076256,
-0.049527108669281006,
-0.09866742044687271,
-0.009355447255074978,
0.03803570941090584,
-0.010547833517193794,
0.005140105728060007,
-0.019791405647993088,
-0.08407960087060928,
-0.028106089681386948,
0.00856310036033392,
0.04082197695970535,
0.0054187411442399025,
-0.042983707040548325,
-0.017707612365484238,
-0.045483484864234924,
0.03455808013677597,
-0.009411030448973179,
0.03319322317838669,
0.04870699718594551,
-0.00792892836034298,
-0.05789009854197502,
0.05553283914923668,
0.017200211063027382,
-0.03986362740397453,
-0.006930993404239416,
-0.01695874147117138,
-0.00875520333647728,
0.00022392906248569489,
-0.001621328410692513,
0.03550052270293236,
0.03028128109872341,
-0.040534645318984985,
-0.04794604331254959,
-0.06554371118545532,
0.023031726479530334,
-0.06113152951002121,
-0.0044158631935715675,
-0.06882456690073013,
0.023777704685926437,
0.0049248309805989265,
-0.013749200850725174,
-0.0037380398716777563,
0.01120442058891058,
-0.0008225784404203296,
0.016256805509328842,
-0.00445531727746129,
-0.051914725452661514,
-0.055285483598709106,
0.002242809860035777,
0.0679246187210083,
0.0011764713563024998,
-0.08784900605678558,
-0.0133907999843359,
-0.02667022868990898,
-0.0299785528331995,
0.02052668295800686,
0.062156882137060165,
0.05304212123155594,
-0.039620839059352875,
-0.0042831795290112495,
-0.051852717995643616,
0.010761922225356102,
0.02441926673054695,
-0.05538023263216019,
-0.04015178233385086,
0.0037010498344898224,
-0.006427758373320103,
0.05299753695726395,
0.035189393907785416,
0.05044436454772949,
-0.014656459912657738,
-0.013802546076476574,
0.034612469375133514,
0.010424695909023285,
0.038697484880685806,
-0.028080936521291733,
-0.043650344014167786,
-0.015184322372078896,
0.006775050889700651,
0.014779338613152504,
0.003262487705796957,
-0.011745440773665905,
-0.03458566963672638,
-0.04120427370071411,
0.00214887922629714,
-0.07159150391817093,
0.11228104680776596,
-0.016934577375650406,
-0.020462438464164734,
0.07630605250597,
0.0035381873603910208,
-0.009035451337695122,
0.06480569392442703,
0.04332798346877098,
-0.05032134801149368,
-0.0175044946372509,
-0.042201656848192215,
-0.06728927046060562,
0.008160481229424477,
0.0028440256137400866,
-0.005054953973740339,
-0.02471797540783882,
-0.014149024151265621,
0.028595665469765663,
0.004961972590535879,
0.02363296039402485,
-0.0329156257212162,
-0.010127674788236618,
-0.03962159529328346,
-0.020010409876704216,
0.010312851518392563,
0.06095480918884277,
0.04297812655568123,
-0.03752822056412697,
0.01264007855206728,
-0.023336490616202354,
-0.03555256128311157,
-0.051542267203330994,
-0.03653779253363609,
-0.05542583763599396,
0.03635171428322792
] |
<p>I'm not a current student at any school, but I am learning a new profession, and some of it is a basic understanding of elecrticity. I have some knowledge, but definitely not enough, and I have had to self teach most of what I know using old textbooks that I have found added to some military experience in ths subject. anyways I'm trying to teach myself how to calculate current through resistors, but I'm having trouble setting up and working through word problems. I know this may seem simple to most people on here, and I apologize for that, but sucking at something is the first step at being sorta good at something.</p>
<p>Examples</p>
<p>A 242Ω resistor is in parallel with a 180Ω resistor, and a 240Ω resistor is in series with the combination. A current of 22mA flows through the 242Ω resistor. The current through the 180Ω resistor is <em>_</em>_mA.</p>
<p>Two 24Ω resistors are in parallel, and a 43Ω resistor is in series with the combination. When 78V is applied to the three resistors, the voltage drop across the 24Ω resistor is___volts.</p> | g5495 | [
0.033216916024684906,
0.00660146027803421,
-0.031881798058748245,
-0.051003970205783844,
0.06541721522808075,
-0.040390744805336,
0.041385531425476074,
0.028292959555983543,
-0.04407370090484619,
0.07003160566091537,
-0.04623981937766075,
0.0683508962392807,
-0.02838921546936035,
0.006804864853620529,
0.0011976819951087236,
0.004151821136474609,
0.0608542338013649,
0.023659057915210724,
0.004710728302598,
-0.019280564039945602,
0.054118938744068146,
-0.010583033785223961,
-0.054526809602975845,
0.017160840332508087,
-0.0396752767264843,
-0.020105155184864998,
-0.05702480301260948,
-0.00913982093334198,
-0.07641566544771194,
-0.03968650847673416,
-0.039136648178100586,
0.002063985913991928,
0.06905597448348999,
0.007179673295468092,
-0.01754174195230007,
-0.013343444094061852,
0.007454637438058853,
0.06482931226491928,
0.0006224330281838775,
0.021147815510630608,
0.03310106322169304,
-0.007237071171402931,
0.02438521571457386,
0.02692871168255806,
0.013269055634737015,
-0.03845951333642006,
-0.031028032302856445,
-0.0012663599336519837,
-0.011594343930482864,
-0.04247352108359337,
0.024927692487835884,
-0.014550616033375263,
0.02792016789317131,
0.02230355516076088,
-0.03663345053792,
-0.027323776856064796,
0.011996525339782238,
-0.0439283549785614,
0.04050583764910698,
-0.028891226276755333,
0.05057929828763008,
0.0066719986498355865,
0.0064758299849927425,
-0.007909856736660004,
0.04328543320298195,
0.020673029124736786,
-0.01804012432694435,
0.03384235501289368,
0.019214816391468048,
0.06690764427185059,
-0.042558006942272186,
-0.043674319982528687,
-0.008807031437754631,
-0.039234332740306854,
0.007673067506402731,
0.006120010279119015,
0.02283330447971821,
0.028282875195145607,
0.008486599661409855,
0.002411454450339079,
0.005096415523439646,
-0.04623223468661308,
0.03185426816344261,
0.05326900631189346,
0.11192204058170319,
-0.015331272035837173,
-0.037497665733098984,
0.055424872785806656,
-0.07013007998466492,
-0.05484633520245552,
-0.011955097317695618,
0.015240772627294064,
0.021330488845705986,
-0.0032702486496418715,
0.03475480526685715,
-0.0495266355574131,
-0.05896470695734024,
0.04767683520913124,
0.027103882282972336,
0.03775305300951004,
-0.018261335790157318,
0.02113565430045128,
-0.02664978802204132,
-0.0700748935341835,
-0.06044503673911095,
0.03738218918442726,
0.08994247019290924,
0.025950385257601738,
-0.03981095924973488,
-0.0164801012724638,
-0.05186029151082039,
-0.03312169015407562,
-0.013339457102119923,
-0.025988919660449028,
-0.005822146777063608,
-0.002895468147471547,
-0.009000440128147602,
0.020630495622754097,
0.03119453601539135,
-0.001704432419501245,
-0.0008715696749277413,
-0.00023286005307454616,
0.05127155780792236,
-0.0061187599785625935,
-0.008859212510287762,
0.010853676125407219,
0.0027996834833174944,
0.00545114791020751,
0.08669306337833405,
0.008151150308549404,
0.001238003489561379,
-0.03070847876369953,
-0.02696158178150654,
0.0004014567530248314,
0.00477223563939333,
-0.028449097648262978,
0.013208801858127117,
-0.020795032382011414,
-0.019852962344884872,
0.011708269827067852,
0.017568351700901985,
-0.02759133279323578,
0.028815697878599167,
-0.05534043535590172,
-0.018977981060743332,
0.018478795886039734,
-0.06977128237485886,
-0.0726267546415329,
0.0591786690056324,
-0.04026280343532562,
-0.002275128848850727,
0.08489082008600235,
-0.01346472930163145,
-0.036258332431316376,
0.02498214691877365,
0.044082898646593094,
0.02811688929796219,
-0.0547715499997139,
0.023749619722366333,
0.01723541133105755,
0.008455086499452591,
0.03370191901922226,
-0.006369196809828281,
-0.004984269384294748,
-0.02156580612063408,
-0.006173750851303339,
0.041446756571531296,
-0.008501325733959675,
-0.008270448073744774,
-0.013028065674006939,
-0.021635405719280243,
-0.03063824400305748,
0.025502463802695274,
-0.007073334883898497,
0.005868059583008289,
0.09280680119991302,
0.12717661261558533,
-0.008904590271413326,
0.05034186318516731,
-0.005347725469619036,
-0.02201964519917965,
-0.019219322130084038,
0.05464191362261772,
0.02756633423268795,
-0.00730382464826107,
0.02312152273952961,
-0.011464986950159073,
0.027227051556110382,
-0.08477047830820084,
-0.04441855475306511,
-0.04924662038683891,
0.011671334505081177,
0.01689288206398487,
-0.0012775965733453631,
-0.01840512827038765,
-0.022421129047870636,
0.04465330392122269,
-0.06175139546394348,
-0.011394758708775043,
-0.030248623341321945,
0.010810918174684048,
-0.009997550398111343,
0.11398803442716599,
0.061703409999608994,
0.04067961499094963,
0.056250154972076416,
-0.06246093660593033,
-0.05330681428313255,
0.005606477148830891,
-0.014040970243513584,
-0.008367354981601238,
-0.0004932574811391532,
0.0212806835770607,
-0.0221870094537735,
-0.013557210564613342,
-0.026198221370577812,
0.00339932506904006,
-0.044786736369132996,
-0.0704667940735817,
0.05821109190583229,
0.03978961333632469,
-0.05715503543615341,
0.047130946069955826,
-0.00364883616566658,
-0.05042332410812378,
0.0291580893099308,
0.008102456107735634,
-0.019843081012368202,
-0.004348019137978554,
-0.04940131679177284,
-0.04901382327079773,
0.048124637454748154,
-0.0064221834763884544,
-0.030711794272065163,
-0.03362646326422691,
-0.013216322287917137,
-0.007078561466187239,
-0.005287611857056618,
-0.04363328590989113,
0.03896994888782501,
0.04178820922970772,
-0.008642430417239666,
0.02712131291627884,
-0.0015795924700796604,
-0.001160874031484127,
-0.008220079354941845,
0.07633902132511139,
0.06043336167931557,
-0.048330157995224,
0.019548488780856133,
-0.017586667090654373,
-0.06723962724208832,
-0.036855679005384445,
0.07169786095619202,
-0.016455380246043205,
-0.0002520863199606538,
-0.018665112555027008,
0.017244862392544746,
0.03519156202673912,
0.03528811037540436,
-0.005389781203120947,
0.011512692086398602,
0.056891441345214844,
0.0715404525399208,
-0.07203704863786697,
-0.015421761199831963,
-0.0044398135505616665,
-0.0010625360300764441,
0.046923477202653885,
0.031975019723176956,
-0.04131489247083664,
-0.019638339057564735,
0.03206697851419449,
-0.04246377944946289,
-0.026524914428591728,
-0.07088374346494675,
0.0575280636548996,
-0.031174033880233765,
0.0388210266828537,
0.07272258400917053,
-0.004501633811742067,
-0.020887497812509537,
-0.006707685999572277,
-0.03476566821336746,
0.017587091773748398,
-0.053191736340522766,
0.012998641468584538,
0.012300947681069374,
0.03996054083108902,
0.00040015412378124893,
-0.044817060232162476,
-0.017688922584056854,
0.020366011187434196,
-0.02423250488936901,
0.014951673336327076,
0.014017807319760323,
-0.008104871027171612,
-0.055285338312387466,
-0.04031937196850777,
0.04771724343299866,
-0.04523744061589241,
-0.016910476610064507,
0.028738565742969513,
-0.02398834191262722,
-0.020947320386767387,
0.014490876346826553,
-0.00742771802470088,
-0.014031089842319489,
0.04749000817537308,
-0.0022831715177744627,
-0.04292339086532593,
-0.01488995086401701,
0.03135863319039345,
-0.05880022048950195,
0.010235604830086231,
0.0198543518781662,
0.04816353693604469,
0.034516606479883194,
-0.018770618364214897,
-0.03161507844924927,
-0.01174185425043106,
-0.014385038055479527,
0.03439905121922493,
-0.04122333228588104,
-0.0035136330407112837,
0.059998419135808945,
0.02218754217028618,
0.010779348202049732,
-0.010853507556021214,
0.02860046736896038,
-0.06967094540596008,
0.02044983021914959,
0.011365311220288277,
0.04202088713645935,
0.029491355642676353,
-0.03441758081316948,
0.009209657087922096,
0.0012406158493831754,
-0.022777698934078217,
0.03815907984972,
0.031172718852758408,
-0.04987187311053276,
-0.05758463591337204,
-0.008521096780896187,
-0.038913894444704056,
-0.01941240392625332,
-0.015335270203649998,
0.03075958974659443,
0.0052122571505606174,
-0.03250671178102493,
0.059807151556015015,
-0.0020724914502352476,
-0.026427695527672768,
-0.017449278384447098,
-0.05497092381119728,
-0.01650458574295044,
0.012809530831873417,
0.057520683854818344,
0.03209869936108589,
0.029280800372362137,
0.001023649238049984,
-0.0383634977042675,
-0.038919657468795776,
-0.01311431173235178,
0.00532524986192584,
-0.00025687695597298443,
0.0003380296693649143,
0.058616749942302704,
-0.017965562641620636,
-0.08119762688875198,
0.022704152390360832,
0.037026241421699524,
-0.010553180240094662,
0.006672973744571209,
0.019351176917552948,
-0.01534347515553236,
-0.009537107311189175,
0.024669870734214783,
-0.07855292409658432,
0.047093525528907776,
-0.005875323433429003,
0.017500553280115128,
0.009355046786367893,
-0.014437714591622353,
0.02150573953986168,
-0.03530201315879822,
0.03464338183403015,
0.03597063571214676,
-0.029606681317090988,
-0.022408554330468178,
-0.038096316158771515,
-0.0003331272164359689,
-0.05920253321528435,
-0.022715220227837563,
-0.0022731877397745848,
-0.021432673558592796,
0.05139024183154106,
-0.002083991887047887,
-0.03889104723930359,
0.021024273708462715,
-0.014290246181190014,
0.02636534348130226,
0.07569839060306549,
0.0028746018651872873,
-0.029295723885297775,
-0.011863994412124157,
-0.020368123427033424,
-0.016112493351101875,
0.04880024120211601,
0.0601218119263649,
-0.04243296757340431,
0.01634484902024269,
-0.017798548564314842,
-0.032554131001234055,
-0.016497893258929253,
0.030549747869372368,
0.050749655812978745,
0.015588559210300446,
0.043489523231983185,
0.03544121980667114,
0.006342622451484203,
0.01586810313165188,
-0.032229676842689514,
-0.08284196257591248,
-0.0003325740108266473,
0.013318420387804508,
0.03453319892287254,
0.00652055349200964,
0.07675173133611679,
0.026180557906627655,
0.032534874975681305,
0.0693148598074913,
-0.03831912577152252,
0.022128380835056305,
-0.016831357032060623,
-0.0009765079012140632,
-0.009575546719133854,
-0.005268644541501999,
0.03389028087258339,
0.050507232546806335,
-0.002547299023717642,
-0.013047067448496819,
-0.06660802662372589,
-0.039295196533203125,
-0.025277910754084587,
0.04558444768190384,
-0.09052516520023346,
-0.04627398028969765,
0.004774180706590414,
-0.007732562720775604,
0.009764905087649822,
-0.0017889124574139714,
-0.022651400417089462,
-0.01841742731630802,
-0.006042683497071266,
0.032498687505722046,
0.013673405162990093,
0.017317362129688263,
0.034484654664993286,
0.06312234699726105,
0.0008704338106326759,
0.016755860298871994,
-0.04438479617238045,
0.011171679943799973,
-0.03349357098340988,
-0.03594757616519928,
0.028019621968269348,
-0.012274821288883686,
-0.03040998801589012,
-0.0027232361026108265,
-0.008133521303534508,
-0.027831610292196274,
-0.03435636684298515,
0.022337261587381363,
0.013120999559760094,
-0.04013283923268318,
0.035797495394945145,
-0.039338331669569016,
-0.056542932987213135,
0.017220882698893547,
-0.027378151193261147,
-0.04854524880647659,
-0.024700647220015526,
0.033871255815029144,
-0.022759584710001945,
0.022472646087408066,
-0.03008522093296051,
0.06358614563941956,
0.03998492285609245,
0.015914978459477425,
0.04049047827720642,
0.09661358594894409,
0.006130685098469257,
-0.05103091895580292,
-0.0785326138138771,
-0.034715428948402405,
0.020990723744034767,
0.0326463021337986,
-0.014297270216047764,
-0.016359766945242882,
-0.004416962619870901,
0.019234083592891693,
-0.05094307288527489,
-0.006021130830049515,
-0.0012427211040630937,
0.020772406831383705,
0.03482712060213089,
0.01617705635726452,
0.00583249656483531,
0.002035666024312377,
0.07923165708780289,
0.05615601688623428,
0.00039189905510284007,
-0.03317185863852501,
-0.034625861793756485,
0.016995951533317566,
-0.0771385133266449,
0.003656254382804036,
-0.028736799955368042,
0.018701251596212387,
0.05414726212620735,
0.03735662251710892,
0.009393821470439434,
0.006519067566841841,
-0.04012232646346092,
-0.011737869121134281,
-0.07995908707380295,
0.03482384607195854,
0.055525001138448715,
-0.021052435040473938,
0.04581184685230255,
-0.02146437205374241,
-0.011057031340897083,
-0.0654345154762268,
-0.04441217705607414,
-0.012732542119920254,
0.05591443181037903,
-0.05346280336380005,
0.03370300680398941,
0.023664819076657295,
-0.01432493794709444,
-0.009745042771100998,
0.015256322920322418,
0.05133847892284393,
-0.05497584119439125,
-0.015142962336540222,
-0.012912308797240257,
-0.060482729226350784,
0.01732611656188965,
0.0475502572953701,
-0.040784064680337906,
0.02369353361427784,
0.005870332475751638,
0.01814134418964386,
-0.001723557710647583,
0.012400208041071892,
-0.026058625429868698,
-0.0757216364145279,
-0.021716371178627014,
0.030145572498440742,
0.03145291656255722,
-0.06466761231422424,
-0.009501204825937748,
0.018470000475645065,
0.013015169650316238,
-0.03529655560851097,
-0.010714031755924225,
0.0480516143143177,
-0.008185946382582188,
0.05937895178794861,
0.03088669292628765,
-0.03718779981136322,
-0.02473929524421692,
0.031836651265621185,
0.042420800775289536,
0.015621419064700603,
-0.051075421273708344,
0.0033433884382247925,
0.04469018056988716,
0.00779716344550252,
-0.0033877212554216385,
0.007828586734831333,
-0.03597685694694519,
-0.015652038156986237,
0.004246645141392946,
0.023455679416656494,
-0.031268827617168427,
-0.02302294410765171,
-0.04360942170023918,
0.01434173621237278,
-0.03645593672990799,
0.009911656379699707,
0.006814781576395035,
-0.05317606404423714,
0.043723758310079575,
0.041068583726882935,
0.014643127098679543,
0.01847611367702484,
0.019902896136045456,
0.03976360708475113,
0.02453865110874176,
-0.02202964946627617,
0.06845684349536896,
-0.007654350716620684,
0.01658506877720356,
0.00674179382622242,
-0.07233574986457825,
0.04175140708684921,
-0.040718842297792435,
0.019397597759962082,
0.038038551807403564,
0.015280629508197308,
0.024212732911109924,
0.03408694267272949,
0.025122713297605515,
-0.0024483974557369947,
0.028559524565935135,
0.0499943383038044,
0.0038212521467357874,
0.03497694805264473,
0.0023568461183458567,
-0.007206030655652285,
0.02377084083855152,
-0.02283835969865322,
0.04240517318248749,
0.035303957760334015,
0.012004661373794079,
0.00560396071523428,
0.07651473581790924,
-0.02979680523276329,
-0.022777164354920387,
-0.042473677545785904,
0.01683168113231659,
0.0006444991449825466,
0.05115765333175659,
0.03308180347084999,
-0.01559195015579462,
0.011999513953924179,
-0.04070771485567093,
0.09761883318424225,
0.042398396879434586,
-0.03523271903395653,
-0.03066517971456051,
0.07943425327539444,
-0.003628750331699848,
-0.049246788024902344,
0.048843737691640854,
0.06296180933713913,
-0.03550053387880325,
-0.009776630438864231,
0.01931743696331978,
-0.04473986476659775,
0.014271276071667671,
0.044603630900382996,
-0.03573214262723923,
0.06029465049505234,
0.051251474767923355,
0.010412752628326416,
-0.014928650110960007,
0.027138380333781242,
0.04167628288269043,
-0.010382095351815224,
-0.056253716349601746,
-0.03598172962665558,
0.025310512632131577,
0.02240855060517788,
0.0016971378354355693,
-0.11079326272010803,
-0.01980740576982498,
-0.06593341380357742,
-0.039221327751874924,
-0.014881862327456474,
-0.016359172761440277,
0.04020174220204353,
0.008455771021544933,
-0.028308330103754997,
-0.008004243485629559,
-0.023896273225545883,
-0.015473338775336742,
-0.024037329480051994,
-0.05156758055090904,
-0.01675802655518055,
0.009537884965538979,
-0.050662849098443985,
0.008308131247758865,
0.032439224421978,
-0.025133255869150162,
0.005225061904639006,
0.011390477418899536,
0.007443029899150133,
0.012012188322842121,
-0.0070898886770009995,
0.05002390220761299,
-0.024222357198596,
-0.05537232756614685,
0.05388179048895836,
0.024321958422660828,
-0.041619233787059784,
0.10047321766614914,
0.008183130994439125,
0.06455200165510178,
-0.04342346638441086,
0.04178797826170921,
-0.0076422239653766155,
-0.01375526562333107,
-0.005174970254302025,
-0.03710607439279556,
-0.04020098224282265,
-0.006820029113441706,
-0.015153639018535614,
-0.002378858160227537,
0.04739007353782654,
0.04008026793599129,
-0.010256743989884853,
-0.059888578951358795,
-0.04219076409935951,
-0.009905758313834667,
0.03536299243569374,
-0.024868382140994072,
0.004230957943946123,
0.005348284263163805,
0.026210732758045197,
-0.0018972427351400256,
-0.018609434366226196,
-0.01743692345917225,
-0.01982766017317772,
-0.009644626639783382,
-0.025353554636240005,
0.0035368723329156637,
-0.01431908831000328,
0.003040896961465478,
-0.04429887235164642,
-0.027565209195017815,
0.02858244813978672,
0.04006181284785271,
0.02998809702694416,
0.00795984547585249,
-0.02006998471915722,
0.03090757317841053,
0.005688514094799757,
0.007058452814817429,
-0.07829009741544724,
-0.037087589502334595,
-0.03524412587285042,
-0.00430715549737215,
-0.028528383001685143,
-0.04194354638457298,
0.043627358973026276,
0.012281466275453568,
-0.02653154358267784,
0.004876899998635054,
0.029509088024497032,
-0.03698339685797691,
-0.0502949059009552,
0.023946333676576614,
-0.0298128891736269,
-0.01585196703672409,
-0.002335999393835664,
0.01369426678866148,
0.006665648892521858,
-0.00417513819411397,
-0.02208896540105343,
-0.02770158089697361,
0.013239827007055283,
0.031091725453734398,
-0.005365095101296902,
-0.048131149262189865,
-0.0795736163854599
] |
<p>I learned that neutrinos have a much lower energy than electrons. Pair production of electrons occurs when the photon energy is above 2 times the energy of an electron. So I am wondering if pair production of neutrinos wouldn't be even more common and occur at much lower energy levels?</p> | g5496 | [
0.00461001880466938,
0.05153768137097359,
0.03765477240085602,
0.05774044990539551,
-0.009077069349586964,
0.0175273846834898,
-0.06618942320346832,
0.033057358115911484,
-0.01852353848516941,
-0.022494135424494743,
0.008832532912492752,
-0.011661207303404808,
-0.018473587930202484,
-0.025602782145142555,
-0.05193223059177399,
0.019917262718081474,
0.0423380546271801,
-0.028760042041540146,
0.0014691698597744107,
0.04717624559998512,
-0.022242026403546333,
-0.029725924134254456,
0.049319181591272354,
-0.011472638696432114,
-0.03667372092604637,
0.03886710852384567,
-0.03555130213499069,
-0.015764782205224037,
-0.055369459092617035,
0.0022541771177202463,
0.02476619742810726,
0.005626115016639233,
0.0968024805188179,
-0.033538561314344406,
-0.05631463602185249,
-0.04967115446925163,
0.037091419100761414,
-0.00927166361361742,
0.04307921230792999,
0.008381414227187634,
0.023031052201986313,
0.0391310453414917,
-0.04120781645178795,
-0.015052405185997486,
-0.012369431555271149,
-0.010378411039710045,
-0.017875339835882187,
0.04334722459316254,
-0.023909907788038254,
-0.0320187471807003,
0.031372204422950745,
-0.004443258047103882,
0.012292691506445408,
0.0467618927359581,
0.11853871494531631,
0.01519795786589384,
-0.045829061418771744,
-0.014635073021054268,
0.05455151945352554,
0.0014593967935070395,
0.002940843114629388,
0.017546875402331352,
0.015878090634942055,
-0.003435649676248431,
0.02658601850271225,
0.02242698147892952,
-0.025922603905200958,
0.0013736020773649216,
0.08985346555709839,
0.04168776795268059,
-0.0371646024286747,
-0.003588408697396517,
-0.02457115612924099,
-0.021261990070343018,
0.059988971799612045,
-0.022679252550005913,
-0.001321714837104082,
-0.0058487216010689735,
-0.0039687310345470905,
-0.0058924295008182526,
0.0071068513207137585,
-0.012762822210788727,
0.0020445031113922596,
-0.001047763740643859,
0.08726975321769714,
-0.04756847769021988,
-0.020119741559028625,
0.01544906198978424,
0.03526243939995766,
0.03203565999865532,
0.06796254962682724,
-0.01864321529865265,
0.08476158231496811,
-0.01267943624407053,
0.010091576725244522,
-0.014704418368637562,
0.017489321529865265,
0.004669758025556803,
-0.013553963042795658,
-0.05102159455418587,
-0.05267972871661186,
0.016110394150018692,
0.032388944178819656,
-0.015378068201243877,
-0.006442327052354813,
-0.011034767143428326,
0.04477250948548317,
-0.030566738918423653,
-0.049198348075151443,
0.00023262118338607252,
0.006118922494351864,
-0.013759330846369267,
-0.06367061287164688,
-0.0003531966358423233,
-0.021493861451745033,
0.014546043239533901,
-0.03903639689087868,
-0.04090047627687454,
-0.020802563056349754,
0.11644262820482254,
0.03133183717727661,
0.011849756352603436,
-0.006350348237901926,
0.013920809142291546,
-0.03815661743283272,
-0.039194099605083466,
-0.0074396864511072636,
0.047684747725725174,
0.03146903216838837,
0.028139054775238037,
0.03293667733669281,
-0.05772646516561508,
-0.014179468154907227,
-0.024489762261509895,
0.07389383018016815,
0.050957877188920975,
0.03687345236539841,
0.048335716128349304,
0.06311812251806259,
-0.016195692121982574,
0.0037520993500947952,
0.023538732901215553,
-0.014662555418908596,
-0.06826944649219513,
0.01418166235089302,
-0.009113099426031113,
-0.03622973710298538,
0.030091160908341408,
-0.08269073814153671,
0.0673641562461853,
-0.01755072921514511,
-0.0019421778852120042,
-0.014513377100229263,
-0.03529703989624977,
0.009449164383113384,
0.02927708812057972,
-0.016195321455597878,
0.00048815293121151626,
0.017834998667240143,
0.00621872628107667,
0.048795126378536224,
-0.013497955165803432,
0.07030455768108368,
-0.026367856189608574,
0.022980419918894768,
-0.005770652089267969,
0.0224798284471035,
-0.016292518004775047,
-0.009098561480641365,
-0.0036827747244387865,
-0.035553138703107834,
-0.05070681497454643,
-0.02374962344765663,
0.01630440540611744,
-0.010399932973086834,
0.03462781384587288,
0.00012053425598423928,
-0.05144278332591057,
-0.03966103494167328,
-0.0012355683138594031,
-0.015836017206311226,
0.01019413024187088,
-0.0008661539177410305,
0.01700950413942337,
0.047605250030756,
0.01035099197179079,
-0.009076098911464214,
0.04325910657644272,
-0.01603037118911743,
0.016363997012376785,
-0.015797190368175507,
0.007302304729819298,
0.003928461577743292,
-0.030279098078608513,
0.005459943786263466,
0.021439194679260254,
-0.02893604151904583,
-0.025374868884682655,
0.029711322858929634,
-0.004217213951051235,
-0.03593418747186661,
0.03371364250779152,
0.002843160880729556,
-0.007959388196468353,
-0.0031933244317770004,
0.033343229442834854,
-0.034645043313503265,
-0.055339306592941284,
0.05193202942609787,
-0.0425691232085228,
-0.052934784442186356,
-0.04072868078947067,
-0.023433316498994827,
0.03394584357738495,
-0.039165712893009186,
-0.048829592764377594,
-0.019216755405068398,
0.00571438716724515,
-0.027733640745282173,
0.012204673141241074,
-0.03422829136252403,
-0.018011322245001793,
0.016561292111873627,
0.0032215327955782413,
-0.017001640051603317,
0.05687377601861954,
-0.014127121306955814,
-0.017877861857414246,
-0.04139941558241844,
0.03831692785024643,
-0.048528559505939484,
0.11525537818670273,
-0.009237151592969894,
-0.10056847333908081,
-0.035618726164102554,
-0.005588495172560215,
0.02074453793466091,
-0.00918232649564743,
0.009584140963852406,
-0.009937461465597153,
-0.05068305507302284,
-0.05421915650367737,
0.012213257141411304,
0.07338107377290726,
0.034951258450746536,
-0.058856260031461716,
0.03262260556221008,
-0.02066551148891449,
-0.0022431956604123116,
-0.0015581996412947774,
0.02474515326321125,
-0.007972347550094128,
-0.02135259471833706,
0.045995596796274185,
-0.010142889805138111,
0.01626134291291237,
-0.004098278470337391,
0.04583997651934624,
-0.018060481175780296,
-0.006974990479648113,
0.005970415659248829,
-0.02708679810166359,
-0.014233249239623547,
-0.012164819985628128,
0.00160671875346452,
-0.0060264659114181995,
0.02993917651474476,
-0.034412093460559845,
-0.007770659867674112,
0.06006883457303047,
-0.034959826618433,
0.06590881943702698,
-0.07088490575551987,
-0.030142223462462425,
0.025242578238248825,
-0.08613239973783493,
0.02259695529937744,
0.00017069349996745586,
-0.02304965630173683,
-0.055939771234989166,
0.002714521950110793,
-0.012964531779289246,
0.028519868850708008,
-0.02393767237663269,
0.052538398653268814,
-0.06972545385360718,
-0.05069459602236748,
-0.07892942428588867,
0.011018086224794388,
0.07856651395559311,
-0.041450873017311096,
-0.016050267964601517,
0.01181932631880045,
-0.05246705934405327,
0.018900876864790916,
0.008840030990540981,
0.03004065714776516,
-0.0009879788849502802,
-0.09060531109571457,
0.057867590337991714,
0.016930483281612396,
-0.06682075560092926,
0.005698478315025568,
-0.010908185504376888,
0.028029024600982666,
-0.02220527082681656,
-0.007159113883972168,
0.015237677842378616,
-0.06067885085940361,
0.005578711163252592,
-0.04652828350663185,
0.04466882720589638,
-0.004634604789316654,
0.08667875826358795,
-0.024071862921118736,
0.021148931235074997,
0.02857089228928089,
0.04180023446679115,
-0.039099231362342834,
-0.047030240297317505,
0.016129666939377785,
-0.0538279227912426,
-0.015429167076945305,
0.007892580702900887,
0.03426685556769371,
0.05180683732032776,
-0.018996063619852066,
0.025935804471373558,
0.0031190214212983847,
0.0504009909927845,
0.05063150078058243,
-0.011539651080965996,
-0.04599970951676369,
0.051506027579307556,
-0.03179866448044777,
0.02097262069582939,
-0.024431008845567703,
-0.014595643617212772,
0.04413211718201637,
0.03265345096588135,
-0.00511776190251112,
0.07358328998088837,
-0.037347350269556046,
-0.00827096588909626,
0.018892966210842133,
0.031100302934646606,
-0.09277397394180298,
0.009087140671908855,
-0.016127588227391243,
-0.03227385878562927,
0.036351148039102554,
-0.03908776119351387,
0.03231850266456604,
0.011794438585639,
-0.002726159757003188,
-0.030195672065019608,
-0.03242523968219757,
-0.02482886239886284,
0.030288880690932274,
-0.0009365765145048499,
0.04819178953766823,
0.01006421260535717,
0.026827141642570496,
-0.014299541711807251,
-0.06324255466461182,
-0.03739028796553612,
-0.035042114555835724,
0.030048804357647896,
0.07642487436532974,
-0.013537494465708733,
-0.06457872688770294,
-0.03167083114385605,
0.01897321082651615,
-0.01356042455881834,
0.011508939787745476,
0.007853140123188496,
0.026773802936077118,
0.046532463282346725,
0.0067740208469331264,
0.012369043193757534,
0.0006758186500519514,
-0.03354271873831749,
0.022045651450753212,
-0.00861138291656971,
0.022637616842985153,
0.012380287051200867,
-0.046044621616601944,
0.0025949254631996155,
0.0254365261644125,
-0.03774216026067734,
-0.07467105984687805,
-0.04014302417635918,
-0.049331773072481155,
0.057360731065273285,
0.03370528295636177,
0.015554194338619709,
0.06117478385567665,
-0.025893043726682663,
0.06449635326862335,
0.057355187833309174,
-0.04144812747836113,
-0.0479327030479908,
-0.01437925174832344,
-0.02523905783891678,
-0.01220385916531086,
0.03805261850357056,
0.013497631065547466,
0.06645405292510986,
0.008013315498828888,
-0.03983168303966522,
0.030888553708791733,
0.04733303561806679,
-0.009884754195809364,
-0.019635850563645363,
-0.045822374522686005,
0.0040479316376149654,
-0.023486411198973656,
-0.000508263532537967,
-0.013386588543653488,
0.04328655079007149,
-0.012407482601702213,
0.05235718935728073,
-0.045257627964019775,
0.037279389798641205,
0.02069210074841976,
0.13326695561408997,
-0.003907524049282074,
-0.017717789858579636,
-0.07062570005655289,
-0.009994645603001118,
0.09099303185939789,
0.0075529953464865685,
-0.020003562793135643,
-0.01447365339845419,
0.0012355867074802518,
0.003874952672049403,
0.019791023805737495,
-0.051597144454717636,
0.026068901643157005,
0.033165741711854935,
0.0492648184299469,
-0.04046238213777542,
0.03779426962137222,
0.04320931062102318,
-0.0264250710606575,
0.030048467218875885,
-0.022422323003411293,
-0.0013284176820889115,
-0.02913137711584568,
-0.016495628282427788,
0.002761161420494318,
-0.008859658613801003,
0.013031300157308578,
-0.010594092309474945,
0.017956020310521126,
-0.02994055300951004,
0.017689598724246025,
0.014121828600764275,
-0.015294184908270836,
0.06180950254201889,
-0.0715569332242012,
-0.0028307901229709387,
0.02849557437002659,
0.01262285653501749,
0.03441314399242401,
-0.012642505578696728,
-0.08599662780761719,
-0.02091999724507332,
-0.015782052651047707,
-0.05389270931482315,
-0.014937427826225758,
0.013218422420322895,
0.03329465165734291,
-0.004179035313427448,
0.022563572973012924,
-0.056132152676582336,
-0.027155080810189247,
0.0044057490304112434,
0.008981584571301937,
0.03954704478383064,
0.009675425477325916,
-0.011617913842201233,
-0.040997155010700226,
-0.005205259192734957,
-0.054542891681194305,
0.026372456923127174,
-0.053444135934114456,
0.06971009075641632,
0.06580042839050293,
-0.07200712710618973,
0.019748827442526817,
0.0010386145440861583,
0.017960574477910995,
0.043819766491651535,
-0.08209043741226196,
-0.018430940806865692,
0.0031310576014220715,
0.011440460570156574,
0.014900614507496357,
0.00807400606572628,
-0.10177318006753922,
-0.024318885058164597,
-0.006503492593765259,
-0.039599351584911346,
0.0003908362123183906,
0.01017253752797842,
0.03925682604312897,
-0.029408494010567665,
0.025462843477725983,
0.002209909027442336,
-0.04228239133954048,
-0.01477139163762331,
-0.00214779214002192,
-0.03645938262343407,
-0.007302498444914818,
0.020440800115466118,
-0.013670469634234905,
0.006474084686487913,
0.004105492495000362,
0.01804477348923683,
0.07243318110704422,
-0.02522144466638565,
0.024166472256183624,
0.05197334289550781,
0.053895387798547745,
-0.03371648117899895,
-0.031278129667043686,
0.06623976677656174,
0.038011983036994934,
0.010883479379117489,
0.05055314302444458,
-0.021598568186163902,
0.025681085884571075,
0.035578541457653046,
0.018147151917219162,
-0.02309381030499935,
0.005281161516904831,
0.006658469792455435,
-0.015861336141824722,
0.022444460541009903,
-0.0024553616531193256,
-0.05202581360936165,
0.0007833671988919377,
0.08017545193433762,
-0.0009074034751392901,
-0.04324883967638016,
-0.007037651725113392,
-0.020434673875570297,
0.02156287431716919,
0.022099871188402176,
-0.05321209505200386,
0.06307845562696457,
0.0017630324000492692,
-0.008391973562538624,
-0.030075443908572197,
0.023351922631263733,
-0.012706144712865353,
0.04322890192270279,
0.0009657073533162475,
-0.009791377931833267,
0.042346708476543427,
0.029926706105470657,
0.02311871014535427,
0.04758043214678764,
0.003284809645265341,
-0.07531341165304184,
-0.04401107877492905,
-0.01291225478053093,
-0.011725843884050846,
0.02482755109667778,
0.040567245334386826,
0.021648544818162918,
-0.07111664861440659,
-0.008422713726758957,
0.013569013215601444,
-0.003938595298677683,
0.034073613584041595,
0.012097499333322048,
-0.08974450826644897,
-0.028143974021077156,
0.027777569368481636,
-0.001089151599444449,
-0.06291453540325165,
0.035500504076480865,
-0.05015144869685173,
0.07527367025613785,
0.03025345876812935,
0.05018189176917076,
-0.001882733078673482,
0.02127010188996792,
0.013898912817239761,
-0.020551256835460663,
-0.0009695658809505403,
0.07823117077350616,
-0.025378083810210228,
-0.02096533589065075,
-0.0038288391660898924,
-0.00876008253544569,
-0.05335008352994919,
0.01843816414475441,
0.01084070559591055,
0.006299939937889576,
0.028774160891771317,
0.019839348271489143,
-0.0016880983021110296,
0.010362357832491398,
0.004408936016261578,
0.09336618334054947,
-0.031810931861400604,
0.022735722362995148,
-0.04542766883969307,
-0.0035851069260388613,
-0.02906082756817341,
0.016215629875659943,
-0.015079681761562824,
-0.030051378533244133,
0.00697088660672307,
0.009628930129110813,
-0.02145186811685562,
0.022116145119071007,
-0.02305414155125618,
-0.03228655084967613,
-0.04373680427670479,
0.004922875668853521,
0.010454115457832813,
0.059893835335969925,
-0.014232310466468334,
0.04237029328942299,
0.08197873085737228,
-0.05234184116125107,
-0.02117396518588066,
-0.00888275820761919,
-0.015059537254273891,
0.07475727051496506,
-0.020606182515621185,
-0.004856928251683712,
0.009910326451063156,
-0.03536754101514816,
-0.04204964265227318,
0.0011101121781393886,
0.004011253360658884,
-0.03041278012096882,
0.07666638493537903,
-0.004342386499047279,
-0.008366680704057217,
-0.0012452618684619665,
0.011607524938881397,
0.029119087383151054,
-0.006571970880031586,
-0.03915417939424515,
0.0038116101641207933,
-0.016680438071489334,
-0.03593159839510918,
-0.04423213750123978,
0.023425418883562088,
0.00902129989117384,
0.004274358507245779,
0.017601268365979195,
0.004608175251632929,
-0.050593052059412,
0.018316447734832764,
0.024055615067481995,
-0.005602159537374973,
0.06982067227363586,
0.03247862681746483,
-0.007837245240807533,
-0.042412061244249344,
-0.05140088126063347,
-0.01726112700998783,
-0.02872518077492714,
0.030034884810447693,
-0.06074695289134979,
-0.045834608376026154,
-0.012165146879851818,
-0.06731261312961578,
-0.04120167717337608,
-0.019301854074001312,
-0.022177185863256454,
-0.026736008003354073,
-0.030482884496450424,
0.016439668834209442,
-0.05542726069688797,
-0.00756416330114007,
-0.010367417708039284,
0.031125517562031746,
0.023693757131695747,
-0.07172956317663193,
-0.050837136805057526,
0.026048842817544937,
-0.009154479950666428,
-0.013686683028936386,
-0.021347960457205772,
0.04506973922252655,
-0.030211275443434715,
-0.016657648608088493,
0.012583086267113686,
0.01801411621272564,
0.010317528620362282,
0.022263839840888977,
0.0320185087621212,
0.00330335577018559,
-0.017723096534609795,
-0.015284567140042782,
-0.00732704671099782,
-0.00547049893066287,
-0.001548592234030366,
0.03714343532919884,
0.023694325238466263,
-0.045214198529720306,
-0.0010591993341222405,
0.015115270391106606,
0.018227264285087585,
-0.007292578462511301,
0.06286639720201492,
-0.030587127432227135,
-0.036655668169260025,
-0.028030257672071457,
0.011260687373578548,
-0.026873359456658363,
0.02876492589712143,
0.034210991114377975,
-0.04080428555607796,
0.019402150064706802,
0.02617081254720688,
-0.023058265447616577,
0.013088801875710487,
0.0873974934220314,
-0.014368128031492233,
0.0339944027364254,
0.0073580206371843815,
0.0006688491557724774,
-0.004202848765999079,
-0.027750862762331963,
0.006260685157030821,
0.03592626005411148,
-0.029587972909212112,
-0.023814069107174873,
0.09613031893968582,
-0.021398372948169708,
-0.005500186234712601,
-0.004328441806137562,
-0.038485560566186905,
0.005627784878015518,
0.025596920400857925,
0.02285033091902733,
-0.044706303626298904,
0.017918847501277924,
0.014378724619746208,
0.000596894882619381,
0.026502110064029694,
-0.0277769323438406,
-0.02871541865170002,
-0.03282066434621811,
0.03763572871685028,
0.10646816343069077,
-0.010835511609911919,
0.05495975539088249,
-0.010763506405055523,
-0.04356681555509567,
0.009309557266533375,
-0.032690152525901794,
0.011831996962428093,
0.025202319025993347,
-0.0823596715927124,
-0.002007674425840378,
-0.012959187850356102,
0.0013517377665266395,
-0.04054449498653412
] |
<p>Given d(slit separation)= $0.158\:\rm{mm}$, $\lambda _{red}= 665\:\rm{nm}$, $\lambda _{g/y}= 565nm$, L(distance from screen)= $2.24\:\rm{m}$</p>
<p>What is the distance between the third order red and green/yellow fringes? </p>
<p>I am using the equation $X _{3}= \frac{m \lambda L}{d}$ (just to find the distance to the third red fringe). My teacher told me this equation is approximate, but I think this is beyond simple approximation error... I keep getting the answer $2.8284 \times 10^{7}\:\rm{m}$. This seems unreasonable; what am I doing wrong? </p>
<p>$\:\rm{m} = \:\rm{mm}\times10^{-13}, \:\rm{m}= \:\rm{nm}\times10^{-9}$, right? </p> | g5497 | [
0.016994260251522064,
0.008469665423035622,
-0.020076580345630646,
-0.07377656549215317,
0.015332860872149467,
0.014835136011242867,
-0.011203440837562084,
0.0005151715013198555,
-0.010752583853900433,
-0.007125141564756632,
-0.0021238946355879307,
0.002555958926677704,
-0.024836210533976555,
-0.013944041915237904,
0.017080364748835564,
0.002397860400378704,
-0.0010510485153645277,
-0.03677189722657204,
0.026023710146546364,
-0.006223252043128014,
-0.02164779044687748,
0.03116157278418541,
-0.045049238950014114,
-0.09272392839193344,
0.015235241502523422,
-0.02696297876536846,
-0.0013940628850832582,
-0.008294117636978626,
-0.023725250735878944,
0.0437876358628273,
-0.03491571918129921,
0.08128227293491364,
0.035869698971509933,
-0.010480455122888088,
-0.006297917105257511,
0.0329219214618206,
0.0016525727696716785,
0.06407883018255234,
-0.00006218927592271939,
0.02738611213862896,
0.027226297184824944,
-0.017636870965361595,
-0.021560242399573326,
-0.04385191947221756,
0.030561594292521477,
-0.01764223724603653,
-0.04257292300462723,
-0.04044140875339508,
0.03876907378435135,
-0.01426044199615717,
-0.010987924411892891,
0.12772917747497559,
0.005869261454790831,
0.060495588928461075,
-0.01565786451101303,
0.019464559853076935,
0.049129143357276917,
-0.04473721981048584,
0.03708994388580322,
0.021467629820108414,
0.018114348873496056,
-0.03133315220475197,
-0.016581233590841293,
-0.03366130590438843,
0.0014908640878275037,
-0.0051923030987381935,
-0.01121875923126936,
0.01490606740117073,
-0.02912178449332714,
-0.03535616025328636,
0.007532333489507437,
-0.03943149000406265,
0.03968026116490364,
0.017369503155350685,
-0.09305290877819061,
-0.006411624141037464,
-0.022952545434236526,
0.014784217812120914,
0.012535938993096352,
0.050433721393346786,
-0.03169400244951248,
-0.00009029034845298156,
-0.02140071988105774,
0.04436049237847328,
-0.018944084644317627,
0.023941947147250175,
-0.020718764513731003,
-0.008632220327854156,
0.032408006489276886,
0.07918557524681091,
-0.00043605477549135685,
-0.0056515284813940525,
0.013165340758860111,
-0.02709314599633217,
0.037337351590394974,
0.012738670222461224,
-0.01666981168091297,
0.06026178598403931,
0.017855964601039886,
-0.022368615493178368,
-0.02613937109708786,
-0.008766676299273968,
0.09237022697925568,
-0.009581607766449451,
-0.03712982311844826,
-0.01577945239841938,
0.050609052181243896,
0.020663918927311897,
0.06798503547906876,
0.019967274740338326,
-0.03173775598406792,
-0.008772492408752441,
-0.06316311657428741,
-0.07529541850090027,
0.04727062210440636,
-0.034240201115608215,
0.03309997543692589,
-0.032647427171468735,
0.026652786880731583,
0.02352563664317131,
0.042550958693027496,
0.03072669543325901,
0.05053028464317322,
0.0530044250190258,
0.026605479419231415,
-0.0405883714556694,
0.0016798757715150714,
-0.03199313208460808,
0.06397652626037598,
0.03192855045199394,
-0.009355537593364716,
-0.044481534510850906,
0.03556983917951584,
0.002061839448288083,
0.009622205048799515,
0.007794555742293596,
0.009514984674751759,
-0.0018759198719635606,
-0.06299924105405807,
0.04605736583471298,
0.02425396628677845,
-0.055861011147499084,
0.01577671244740486,
-0.07370245456695557,
-0.06780967116355896,
-0.0026551890186965466,
0.007909493520855904,
-0.03024335391819477,
0.041283018887043,
-0.031232625246047974,
0.04676284268498421,
0.05809066444635391,
-0.032998938113451004,
0.018016690388321877,
-0.029421541839838028,
-0.014444803819060326,
0.034450504928827286,
-0.0048056431114673615,
0.00832490622997284,
0.012943034060299397,
0.0359228141605854,
-0.023432984948158264,
0.016766725108027458,
0.06025247275829315,
0.016679946333169937,
-0.005485268775373697,
0.07999740540981293,
-0.08860668540000916,
-0.0218771081417799,
-0.06249389424920082,
-0.045966073870658875,
-0.006200556177645922,
0.014304202049970627,
-0.013361133635044098,
-0.0486639179289341,
0.07324866205453873,
0.00915423221886158,
-0.05198564752936363,
-0.04489991068840027,
0.07977878302335739,
0.01709935814142227,
-0.007838805206120014,
0.02210809849202633,
-0.03375093266367912,
0.032261647284030914,
-0.010790792293846607,
0.03523276001214981,
-0.016899265348911285,
-0.020852280780673027,
0.00747836846858263,
-0.03745153173804283,
0.06994740664958954,
0.046662718057632446,
0.009118892252445221,
-0.02960222214460373,
0.05395263433456421,
0.009645650163292885,
-0.016064399853348732,
-0.024724291637539864,
0.009309192188084126,
-0.02211693301796913,
0.011239358223974705,
0.021057410165667534,
-0.006137085612863302,
0.015015970915555954,
0.014066305942833424,
0.0342499203979969,
-0.006627869326621294,
0.012835262343287468,
0.05311821028590202,
-0.06916869431734085,
-0.03467795252799988,
-0.002738515380769968,
0.05198292061686516,
0.006674197036772966,
-0.06266778707504272,
0.033209431916475296,
-0.02645891159772873,
-0.0002920213155448437,
0.041202250868082047,
-0.06459315866231918,
-0.04127625375986099,
0.05778319761157036,
-0.05363193154335022,
0.05635184049606323,
0.0000937036020332016,
-0.009475193917751312,
0.04067673906683922,
0.020193232223391533,
0.012388302013278008,
-0.07483751326799393,
-0.02484099380671978,
-0.014869951643049717,
-0.015025511384010315,
0.04154101759195328,
0.0023955393116921186,
-0.010237903334200382,
0.005368273705244064,
-0.0361190028488636,
-0.008979971520602703,
0.03877096623182297,
0.026066854596138,
-0.04729435592889786,
0.07613495737314224,
0.020012909546494484,
0.021980702877044678,
0.0563594289124012,
0.034088555723428726,
-0.0349927693605423,
0.0001887338876258582,
0.05651970952749252,
0.07333263754844666,
0.06430979073047638,
0.07269977778196335,
-0.011222786270081997,
-0.049499496817588806,
-0.03813796490430832,
0.02351786568760872,
-0.02173111028969288,
-0.044036250561475754,
-0.0480978898704052,
-0.005195160862058401,
0.06827092170715332,
-0.0369098000228405,
-0.03898453712463379,
0.019499866291880608,
-0.054993584752082825,
0.023531639948487282,
0.020922843366861343,
-0.013901522383093834,
0.003827084554359317,
0.004454439040273428,
0.057670675218105316,
-0.008770735003054142,
0.02635333314538002,
-0.07409118860960007,
0.007478818763047457,
-0.014497981406748295,
-0.004099230747669935,
0.0018206509994342923,
0.01412621047347784,
-0.038797877728939056,
0.006567647214978933,
0.0312727652490139,
0.02092866413295269,
-0.07143249362707138,
0.045603636652231216,
0.06618738919496536,
0.015726644545793533,
-0.011808639392256737,
-0.02435527741909027,
0.0124083636328578,
-0.0036319762002676725,
0.03643615543842316,
-0.04099287465214729,
-0.03742147982120514,
0.016262611374258995,
0.014857294969260693,
0.019512731581926346,
-0.006512332707643509,
0.02656541019678116,
0.027681713923811913,
-0.03995702415704727,
0.02286766842007637,
0.05756310001015663,
-0.02806810662150383,
0.02449255809187889,
0.014486859552562237,
0.01696043647825718,
-0.015284877270460129,
0.017451701685786247,
0.0022584935650229454,
0.0017421826487407088,
-0.027348164469003677,
-0.01143742073327303,
-0.0142001798376441,
0.0007563216495327652,
-0.008596999570727348,
-0.03222166374325752,
0.0679280087351799,
-0.014994887635111809,
-0.039906181395053864,
-0.04481599107384682,
-0.06096241623163223,
-0.003708099713549018,
0.0070520080626010895,
-0.001433485304005444,
0.008136915042996407,
-0.038541030138731,
-0.004619516897946596,
0.02233043499290943,
-0.0438290536403656,
-0.013594378717243671,
-0.06033257395029068,
0.0446939617395401,
-0.04124230891466141,
0.051320984959602356,
0.014608830213546753,
0.007634433917701244,
0.010533864609897137,
0.01275405753403902,
-0.035352855920791626,
-0.05876090005040169,
-0.029655946418642998,
-0.007370061241090298,
-0.03799445182085037,
-0.034831464290618896,
0.09293212741613388,
-0.019298475235700607,
0.003907944541424513,
0.005559975281357765,
-0.03634152188897133,
-0.0028575132600963116,
-0.03528479114174843,
-0.024343358352780342,
0.003535544965416193,
-0.06014377996325493,
-0.00691039627417922,
0.0563054159283638,
-0.03761356696486473,
0.03665900230407715,
-0.0022070445120334625,
-0.024306349456310272,
-0.04199939966201782,
0.013381406664848328,
-0.09107021987438202,
0.03607860580086708,
0.050234075635671616,
-0.0023383768275380135,
-0.043917566537857056,
-0.03870150074362755,
0.0022969951387494802,
-0.036425042897462845,
0.005841616075485945,
-0.0040594590827822685,
-0.051237788051366806,
-0.0202348530292511,
0.0008760556811466813,
-0.024746807292103767,
0.058118872344493866,
-0.005634436849504709,
-0.00549528282135725,
-0.001395752071402967,
0.0026602300349622965,
0.01838134042918682,
-0.015466731041669846,
0.011935356073081493,
-0.08069508522748947,
0.00637461245059967,
-0.05991686135530472,
-0.03712623938918114,
-0.03683063015341759,
-0.039984263479709625,
-0.015148582868278027,
0.03199124336242676,
-0.03800175338983536,
0.03644466772675514,
0.05620333179831505,
-0.026744704693555832,
0.031488969922065735,
0.020108327269554138,
-0.05510430783033371,
-0.00427465233951807,
0.04830876737833023,
-0.0609443224966526,
-0.03539453446865082,
0.032873425632715225,
-0.008278990164399147,
-0.017279312014579773,
0.02551933377981186,
-0.015853276476264,
-0.018104834482073784,
0.007071216590702534,
-0.04061306267976761,
0.01795635186135769,
-0.044419847428798676,
0.0836370512843132,
0.0005456741782836616,
-0.06757216900587082,
0.031601790338754654,
0.008943663910031319,
0.02481020800769329,
0.03362628072500229,
-0.034092795103788376,
-0.04253590479493141,
0.05903271213173866,
0.03132244944572449,
0.018969854339957237,
0.008131266571581364,
-0.013336601667106152,
0.027533527463674545,
0.053184136748313904,
-0.03386612981557846,
0.07634768635034561,
-0.007406353950500488,
0.03032975271344185,
-0.031557269394397736,
0.009078806266188622,
-0.02223546989262104,
0.01971544697880745,
0.02535923570394516,
-0.006550880614668131,
0.009756765328347683,
-0.01424015685915947,
0.004133317619562149,
-0.02635950967669487,
-0.050461817532777786,
-0.02549596317112446,
0.02893776074051857,
0.020286396145820618,
0.05173710733652115,
0.028044912964105606,
-0.04869677871465683,
0.0402611568570137,
-0.010670110583305359,
0.01045606005936861,
-0.04596596956253052,
-0.008173431269824505,
0.03930392861366272,
0.0064634280279278755,
0.00400796253234148,
0.08168066293001175,
-0.0834718868136406,
-0.024039719253778458,
0.058708637952804565,
0.03964901342988014,
-0.0424010194838047,
-0.0014202510938048363,
-0.008632778190076351,
0.024697260931134224,
0.004020437598228455,
0.046123605221509933,
0.002447886858135462,
-0.04062015190720558,
-0.022196253761649132,
0.015104318037629128,
-0.046111442148685455,
0.024765154346823692,
0.010086417198181152,
0.0020614315290004015,
-0.041373539716005325,
-0.03857940435409546,
0.005000024102628231,
0.0297034103423357,
0.03206978365778923,
0.03133060038089752,
-0.004867744632065296,
-0.0034554176963865757,
0.01742534153163433,
-0.0028519430197775364,
0.03892052173614502,
-0.022938024252653122,
-0.05442497506737709,
0.03589697927236557,
0.0030302186496555805,
-0.04449903219938278,
0.03379053249955177,
0.017145751044154167,
-0.015427231788635254,
0.03316131979227066,
-0.0035111180040985346,
0.011334657669067383,
-0.014159570448100567,
-0.03873227536678314,
-0.03766512870788574,
0.041564300656318665,
0.06247592717409134,
-0.0071959663182497025,
-0.0024598061572760344,
0.03049854002892971,
-0.01065101195126772,
-0.06360241025686264,
0.01279208343476057,
-0.004130054265260696,
-0.03851325437426567,
-0.02917972393333912,
0.0038045106921344995,
0.0709042027592659,
-0.028394902125000954,
0.01968332566320896,
0.08458006381988525,
0.024246780201792717,
0.015593243762850761,
-0.014083664864301682,
0.02048179879784584,
0.0017258221050724387,
-0.04089324548840523,
-0.02068208158016205,
-0.06158735975623131,
-0.06332691013813019,
-0.027318434789776802,
-0.01197952963411808,
-0.021838504821062088,
-0.014510910958051682,
-0.0006694879266433418,
-0.008955682627856731,
0.012461762875318527,
-0.014687040820717812,
0.024900957942008972,
-0.04035862535238266,
0.00055268983123824,
-0.012052306905388832,
-0.006182538811117411,
0.08093356341123581,
-0.042040854692459106,
0.014468029141426086,
0.048884861171245575,
-0.011165534146130085,
0.023777220398187637,
-0.0032976011279970407,
-0.002926347777247429,
-0.04811614379286766,
-0.07266626507043839,
0.008236812427639961,
0.0272193793207407,
-0.01280630100518465,
0.019953368231654167,
-0.07066235691308975,
-0.049948759377002716,
-0.027075733989477158,
-0.008992858231067657,
-0.04446462541818619,
-0.05924158915877342,
0.03354809433221817,
-0.03496250510215759,
-0.054416436702013016,
-0.014600970782339573,
0.006652606185525656,
0.011737726628780365,
0.016090571880340576,
-0.006796692498028278,
-0.06150147318840027,
-0.015960557386279106,
0.0625239685177803,
0.02885456196963787,
-0.004256438463926315,
0.024044670164585114,
-0.04826251417398453,
-0.02545567788183689,
-0.015362451784312725,
-0.014558104798197746,
0.04432470351457596,
0.012936782091856003,
-0.06822873651981354,
-0.05083485692739487,
0.08525317162275314,
-0.03414780646562576,
-0.05910972133278847,
0.057451020926237106,
-0.029830506071448326,
-0.0009322216501459479,
-0.009786074049770832,
0.01943756453692913,
-0.043051864951848984,
0.07819019258022308,
-0.022728331387043,
0.03918319195508957,
0.03260860964655876,
0.035971030592918396,
0.05467973276972771,
0.030915116891264915,
-0.009324663318693638,
0.05766738951206207,
0.0013012642739340663,
0.09414027631282806,
0.019383559003472328,
-0.019525425508618355,
0.015147523023188114,
0.004272045101970434,
0.02033623680472374,
0.027458002790808678,
0.016706448048353195,
-0.0007091923034749925,
0.04820675402879715,
-0.018078718334436417,
0.015048840083181858,
-0.02707332745194435,
0.012852414511144161,
-0.014582264237105846,
0.026342235505580902,
0.0013184880372136831,
-0.01189105212688446,
-0.04337543621659279,
0.006387340370565653,
0.00485403835773468,
0.04383914917707443,
-0.01612435095012188,
-0.04291895031929016,
0.0008167139603756368,
-0.012365275993943214,
0.054489053785800934,
-0.1082896888256073,
0.007380056660622358,
0.015859631821513176,
0.0006087527144700289,
0.04022199660539627,
-0.07476989179849625,
-0.006822055671364069,
-0.013899076730012894,
0.06058370694518089,
-0.0055417162366211414,
0.007350841537117958,
0.0618186891078949,
-0.0520450584590435,
0.0025982316583395004,
0.004799720831215382,
0.04562181979417801,
0.023615028709173203,
-0.013592726550996304,
-0.008391773328185081,
0.025206711143255234,
-0.016329696401953697,
0.011600279249250889,
0.0668138936161995,
0.01589955948293209,
0.019092468544840813,
-0.04279046505689621,
-0.00623812573030591,
-0.008409821428358555,
-0.03529351204633713,
-0.03625683858990669,
-0.05371815338730812,
-0.03697321191430092,
-0.03235918655991554,
-0.019734175875782967,
0.05229783058166504,
-0.010070043615996838,
-0.04022518917918205,
-0.07243870943784714,
-0.060018811374902725,
0.024084752425551414,
-0.04831205680966377,
-0.040610093623399734,
0.004382333252578974,
-0.03212946653366089,
0.006159836892038584,
0.026846904307603836,
0.01168652530759573,
-0.002468190621584654,
-0.04281611368060112,
0.01329278014600277,
0.018665939569473267,
0.015140937641263008,
-0.022606905549764633,
-0.039054229855537415,
0.0610186904668808,
0.02624390460550785,
-0.024120386689901352,
0.007175531703978777,
0.03894716501235962,
0.017771365121006966,
0.05550717934966087,
-0.0242121834307909,
-0.036396827548742294,
0.018757620826363564,
0.02755196951329708,
0.06560014188289642,
0.036252666264772415,
0.06289436668157578,
0.008814089931547642,
-0.027172919362783432,
-0.03573612868785858,
-0.04526242986321449,
-0.021328868344426155,
0.06334615498781204,
0.01710693910717964,
-0.06298594921827316,
0.020769178867340088,
0.02118847891688347,
0.030599413439631462,
-0.009746464900672436,
0.014913160353899002,
-0.016603752970695496,
0.03347193822264671,
0.04338809475302696,
-0.014385120943188667,
-0.025643862783908844,
0.026428021490573883,
-0.05289978161454201,
-0.024377785623073578,
0.04172807186841965,
-0.015756919980049133,
-0.009342692792415619,
-0.043771788477897644,
-0.0195709727704525,
-0.014177149161696434,
-0.003772446420043707,
-0.030704954639077187,
0.07286227494478226,
0.015127153135836124,
-0.03059358522295952,
-0.04152520000934601,
-0.029688434675335884,
0.011745937168598175,
-0.05432424321770668,
0.013792232610285282,
0.06307706236839294,
-0.027346394956111908,
0.025748535990715027,
0.015903910622000694,
0.01671518012881279,
-0.043305039405822754,
0.013745827600359917,
-0.004505779128521681,
0.06634345650672913,
0.009152115322649479,
-0.013566294685006142,
0.009636916220188141,
0.05669441446661949,
-0.013453245162963867,
-0.003241671249270439,
0.036686643958091736,
-0.006165784318000078,
0.048814255744218826,
0.08827637881040573,
-0.07604324072599411,
0.042886752635240555,
-0.029471969231963158,
-0.014008810743689537,
-0.02688082680106163,
-0.05605362355709076,
-0.0522286556661129,
-0.03407394513487816,
0.031811125576496124,
0.026914360001683235,
-0.01237945631146431,
0.010851806960999966,
0.02649851143360138
] |
<p>I know that in quantum mechanics there is no "time operator", so such a question is ill-posed. Anyway if the tunneling is instantaneous, this would imply an information transmission faster than $c$. On the other hand, how could someone define such a "time"?</p> | g5498 | [
0.06807330250740051,
0.05789029598236084,
0.001980283297598362,
0.021088091656565666,
0.06609727442264557,
-0.0008194483816623688,
0.016292832791805267,
-0.024244576692581177,
-0.042902979999780655,
0.03282740339636803,
-0.07820209115743637,
-0.004656956065446138,
-0.008369345217943192,
0.01834649220108986,
0.017433172091841698,
-0.016573550179600716,
0.05269044265151024,
-0.01621115952730179,
0.047345247119665146,
0.008228876627981663,
0.003224386600777507,
-0.00516801793128252,
0.008060045540332794,
-0.0225934237241745,
0.0034741749987006187,
-0.07869935035705566,
0.012055720202624798,
-0.08248062431812286,
-0.029529668390750885,
-0.0005693537532351911,
0.05429408699274063,
-0.06231521815061569,
0.006387746427208185,
-0.05749573931097984,
-0.041884202510118484,
-0.04763153940439224,
0.0055910563096404076,
-0.023352637887001038,
0.07314243912696838,
0.013013768009841442,
0.037565380334854126,
0.006291452795267105,
-0.008537011221051216,
-0.06586277484893799,
-0.03128966689109802,
0.007294058799743652,
0.04860680550336838,
0.03417208790779114,
0.006316342391073704,
-0.06404903531074524,
-0.05178247392177582,
0.02035064995288849,
0.03750817850232124,
0.06721380352973938,
0.019296014681458473,
-0.036092545837163925,
0.024807706475257874,
-0.01638025790452957,
0.03799505904316902,
0.026200519874691963,
0.044714294373989105,
-0.024900557473301888,
0.053236573934555054,
0.0035178863909095526,
0.04149702191352844,
0.0572853721678257,
-0.0033789456356316805,
0.0021031321957707405,
-0.00923738069832325,
0.020798252895474434,
0.028677355498075485,
-0.01876833289861679,
-0.03445256128907204,
-0.004731006920337677,
0.03125717118382454,
0.006844057701528072,
0.07078626751899719,
-0.028507862240076065,
0.013240212574601173,
0.021454356610774994,
-0.09092826396226883,
-0.0018820601981133223,
-0.0927162617444992,
-0.05819585174322128,
0.039822325110435486,
0.03242868185043335,
0.01447033416479826,
-0.005407196935266256,
0.030296290293335915,
0.03985552117228508,
-0.05154640972614288,
-0.05637134239077568,
0.03771384432911873,
-0.011051871813833714,
0.00008287998934974894,
-0.0005036587826907635,
-0.044469356536865234,
0.026722922921180725,
-0.07581300288438797,
0.0792618840932846,
-0.030117178335785866,
-0.06766699254512787,
0.0039532058872282505,
-0.015648560598492622,
-0.020275741815567017,
-0.021356990560889244,
-0.025434402748942375,
-0.07664892822504044,
-0.00534992478787899,
0.0474756583571434,
0.016320334747433662,
-0.002771189669147134,
0.0028567607514560223,
0.04252380132675171,
-0.0003425783070269972,
-0.03558750078082085,
0.016393350437283516,
-0.024051714688539505,
-0.05660189688205719,
-0.005825353320688009,
-0.007639070972800255,
0.011321625672280788,
-0.015440260991454124,
0.02803080715239048,
0.041254788637161255,
0.04864024743437767,
-0.02632443606853485,
0.028883500024676323,
0.035893917083740234,
0.030994942411780357,
-0.02325971983373165,
0.03824916109442711,
0.035817522555589676,
0.049123406410217285,
-0.039513472467660904,
0.013832397758960724,
-0.0003829245106317103,
-0.00042939820559695363,
-0.005693180952221155,
0.025006746873259544,
0.0031899521127343178,
-0.05237514525651932,
0.010947083123028278,
-0.007421824615448713,
-0.035226717591285706,
-0.009554524905979633,
-0.021901965141296387,
0.028074784204363823,
0.008401386439800262,
-0.048260290175676346,
-0.02259819209575653,
0.09406612813472748,
0.025739597156643867,
-0.016714395955204964,
0.03492395207285881,
0.038290005177259445,
0.06355088204145432,
-0.04665740579366684,
0.024387972429394722,
0.05152058228850365,
0.0575944222509861,
0.04024167358875275,
-0.02329063042998314,
-0.007854139432311058,
-0.02949938178062439,
0.018495535477995872,
0.036622900515794754,
-0.016918011009693146,
0.03442952781915665,
-0.0884782001376152,
-0.0520300455391407,
0.05228017643094063,
-0.0038555117789655924,
0.056808434426784515,
0.007611998822540045,
0.02902434952557087,
0.023149827495217323,
-0.023693112656474113,
-0.028779849410057068,
0.02963043563067913,
-0.037145230919122696,
-0.008310054428875446,
-0.009375314228236675,
-0.04600795730948448,
-0.010845922864973545,
-0.0038163280114531517,
0.017036817967891693,
-0.05701214447617531,
-0.06335558742284775,
-0.010101285763084888,
-0.020526593551039696,
-0.05589238926768303,
0.0041845375671982765,
0.05638523027300835,
-0.04509422183036804,
-0.010542859323322773,
0.0793190449476242,
-0.022359497845172882,
0.012813269160687923,
-0.013707169331610203,
0.039207857102155685,
0.021366391330957413,
0.031164519488811493,
-0.011441702954471111,
0.07198688387870789,
0.025006061419844627,
-0.032577939331531525,
-0.03000200167298317,
0.02908340096473694,
-0.021648813039064407,
0.07703863829374313,
-0.02068846859037876,
0.022708430886268616,
0.022641625255346298,
-0.009518870152533054,
-0.05051378905773163,
0.025975771248340607,
0.04783529043197632,
0.040468811988830566,
-0.014046227559447289,
-0.011174925602972507,
-0.003736649639904499,
0.06600378453731537,
-0.04741373658180237,
-0.00819497648626566,
-0.02266567200422287,
-0.050691086798906326,
-0.040663931518793106,
-0.058900848031044006,
0.03522824868559837,
-0.03386945277452469,
0.026774492114782333,
-0.04952940344810486,
0.0044718049466609955,
-0.0008040224201977253,
0.10942717641592026,
0.03234081342816353,
0.011534100398421288,
0.04223567247390747,
0.017025642096996307,
0.038273051381111145,
-0.018995989114046097,
-0.06491448730230331,
0.028797905892133713,
-0.045633163303136826,
0.016675768420100212,
0.0377255417406559,
-0.04744481295347214,
-0.027378175407648087,
0.00033187505323439837,
-0.03375726938247681,
-0.03764568269252777,
-0.02723126858472824,
-0.006041290238499641,
-0.0034168781712651253,
-0.01239226758480072,
0.04981844127178192,
0.0024050825741142035,
-0.09525585174560547,
-0.015977274626493454,
-0.021868500858545303,
0.00035760554601438344,
0.05829595401883125,
-0.061071913689374924,
-0.03814885392785072,
-0.053930025547742844,
0.017857175320386887,
0.04157811403274536,
-0.017477935180068016,
-0.033515527844429016,
-0.03431980684399605,
0.021675385534763336,
0.0033523556776344776,
0.024683628231287003,
-0.029099877923727036,
-0.05880432203412056,
0.0016744991298764944,
-0.05631810426712036,
-0.012979662045836449,
-0.05718882754445076,
-0.05799034237861633,
-0.008083946071565151,
-0.036057088524103165,
0.04862238094210625,
-0.014769157394766808,
-0.09572956711053848,
0.035875968635082245,
0.025274720042943954,
0.0121952248737216,
0.016775505617260933,
-0.011367114260792732,
0.03553853556513786,
0.012004798278212547,
0.08834271878004074,
-0.010462350212037563,
0.05163617059588432,
0.07212326675653458,
-0.032276760786771774,
0.02128390036523342,
0.016914667561650276,
-0.038560155779123306,
0.010712391696870327,
0.01874437928199768,
0.019222650676965714,
0.04452403634786606,
-0.07786306738853455,
0.0048599690198898315,
-0.03561282902956009,
-0.01724223978817463,
-0.05326415225863457,
0.02686186321079731,
0.032781023532152176,
0.0031308126635849476,
-0.0046766516752541065,
0.0038375298026949167,
-0.02612408623099327,
-0.04710825905203819,
0.03911428898572922,
-0.012272432446479797,
-0.041441746056079865,
-0.0147929722443223,
-0.036168985068798065,
-0.030877768993377686,
-0.005332707427442074,
0.004899490159004927,
-0.014878415502607822,
-0.05369635671377182,
-0.014399807900190353,
-0.024159878492355347,
-0.03913576528429985,
0.0020555516239255667,
-0.03735332190990448,
-0.0066149295307695866,
-0.013174484483897686,
-0.05310691148042679,
-0.07919073104858398,
0.01666794717311859,
0.0897059366106987,
-0.006506658624857664,
0.0033526066690683365,
-0.009301600977778435,
0.02768687717616558,
-0.1061118021607399,
0.051011912524700165,
0.01922338269650936,
0.004631723742932081,
0.01161183975636959,
0.03010532446205616,
-0.01105585042387247,
-0.007754611782729626,
-0.002164869336411357,
0.020586781203746796,
-0.016826946288347244,
-0.044598158448934555,
-0.017713679000735283,
0.055893316864967346,
-0.038802556693553925,
0.03182031586766243,
0.018403446301817894,
-0.052200671285390854,
0.010930553078651428,
-0.032880231738090515,
0.05306124687194824,
0.08470464497804642,
-0.007232427131384611,
-0.011355732567608356,
0.011787540279328823,
0.026714878156781197,
0.04403459653258324,
0.06996670365333557,
0.020650548860430717,
0.03792819008231163,
0.016073008999228477,
0.04618484899401665,
0.03171588480472565,
-0.018016882240772247,
-0.011396423913538456,
-0.06049518287181854,
-0.0156139200553298,
-0.00548238679766655,
-0.05223296582698822,
-0.035028260201215744,
0.02774178981781006,
-0.02503683976829052,
0.014409190975129604,
0.022251447662711143,
-0.0224019605666399,
-0.055804044008255005,
0.000012525994861789513,
-0.04155830666422844,
0.01124417595565319,
0.006117822602391243,
-0.015110163018107414,
0.004099078476428986,
-0.007003078702837229,
-0.0033604023046791553,
0.002372165909036994,
-0.05606181174516678,
-0.007025280501693487,
-0.028207829222083092,
0.0019664266146719456,
0.02704339288175106,
-0.03034696914255619,
0.013192808255553246,
0.043349772691726685,
0.0326402448117733,
0.058510441333055496,
0.0016049782279878855,
-0.015270491130650043,
-0.01172273326665163,
-0.06043921038508415,
-0.05101027712225914,
-0.08193648606538773,
0.003709714161232114,
0.010364647023379803,
0.012546497397124767,
0.0624002143740654,
-0.08975300192832947,
0.005350269842892885,
0.03638409450650215,
0.03652677685022354,
0.016663817688822746,
0.05767466500401497,
-0.0161335077136755,
0.00501658022403717,
0.013353223912417889,
0.06914189457893372,
-0.014111971482634544,
-0.0375855453312397,
-0.04149571806192398,
0.04635012149810791,
0.012148293666541576,
-0.011788529343903065,
0.03393005579710007,
-0.02027907222509384,
0.037724316120147705,
0.024400565773248672,
0.0029960584361106157,
0.0463915690779686,
0.06663321703672409,
0.026867995038628578,
-0.019653307273983955,
0.02283705398440361,
0.01168471947312355,
0.0023149894550442696,
0.00004896179598290473,
-0.03585495054721832,
-0.061453595757484436,
-0.00014982801803853363,
-0.0019278802210465074,
-0.03825395181775093,
0.07699569314718246,
0.0038641991559416056,
-0.06355402618646622,
0.001552862930111587,
-0.06885487586259842,
-0.04704970493912697,
0.04240027815103531,
0.08066447079181671,
0.02031911537051201,
-0.062483884394168854,
0.04841777682304382,
-0.0163625068962574,
-0.01672295480966568,
0.01071279775351286,
0.005136098712682724,
-0.008297527208924294,
0.038217294961214066,
-0.05897245556116104,
-0.008866237476468086,
0.03230074420571327,
0.0025601729284971952,
0.006382348481565714,
0.06065722554922104,
0.05664381384849548,
0.007466913666576147,
0.007919181138277054,
0.025555770844221115,
-0.01962900720536709,
-0.001025877078063786,
0.018015867099165916,
0.0044911266304552555,
-0.003762194886803627,
-0.007051636464893818,
0.009972791187465191,
0.03760180622339249,
-0.051513005048036575,
0.02981993556022644,
-0.02330056019127369,
-0.04347100481390953,
0.0609242282807827,
0.009568613953888416,
-0.006209961604326963,
0.0031806165352463722,
-0.008541732095181942,
-0.10705447942018509,
0.036715950816869736,
0.03846462070941925,
-0.008909334428608418,
-0.01065507810562849,
-0.06066450476646423,
-0.0006233329768292606,
-0.038224004209041595,
-0.01097541581839323,
-0.006205209065228701,
0.01918153464794159,
0.05199729651212692,
0.02498946152627468,
-0.019494300708174706,
0.01217654813081026,
-0.03038770705461502,
-0.004707654006779194,
-0.031377680599689484,
-0.03905491530895233,
0.03435765579342842,
-0.028344430029392242,
-0.0644916445016861,
-0.0273174736648798,
-0.031239060685038567,
0.0070355418138206005,
-0.020731398835778236,
0.02321626991033554,
0.013383525423705578,
0.06627199798822403,
-0.027223248034715652,
-0.008733073249459267,
-0.07552032172679901,
-0.023374101147055626,
0.004105913918465376,
-0.024616476148366928,
0.04805104434490204,
0.0035461452789604664,
-0.008227551355957985,
-0.03458772599697113,
0.01830853521823883,
0.021990833804011345,
0.053781408816576004,
-0.02201874740421772,
-0.034865908324718475,
0.02409856952726841,
-0.06529814004898071,
-0.0659065917134285,
-0.006487454753369093,
0.08885550498962402,
-0.015025418251752853,
-0.02354569174349308,
-0.004265873227268457,
-0.0011804238893091679,
0.03345297649502754,
-0.01945275068283081,
-0.0026176581159234047,
-0.02832978591322899,
0.007611746899783611,
0.011273800395429134,
0.05098786950111389,
0.062086351215839386,
0.014699108898639679,
0.027302253991365433,
-0.017999393865466118,
0.0032095869537442923,
0.0630432590842247,
0.008152991533279419,
0.04160063713788986,
-0.004017371218651533,
0.0017782013164833188,
-0.02669510431587696,
-0.043991874903440475,
0.025667930021882057,
0.0598914809525013,
0.015317967161536217,
-0.039078276604413986,
0.023142069578170776,
0.005862889811396599,
0.013562018983066082,
-0.02552724815905094,
0.02052794024348259,
0.04693533480167389,
-0.05044572427868843,
-0.07132258266210556,
0.02180783450603485,
-0.05045124888420105,
0.025972997769713402,
0.01255706511437893,
0.013374139554798603,
0.014412849210202694,
0.05497429147362709,
-0.01405327208340168,
0.003704669186845422,
0.06873444467782974,
0.03756427764892578,
-0.017885232344269753,
0.001162004075013101,
-0.04499127343297005,
-0.05580833554267883,
-0.021091822534799576,
0.0024742537643760443,
0.0016558633651584387,
-0.0026944708079099655,
-0.012045281007885933,
0.04531412571668625,
0.007934578694403172,
0.013024535030126572,
0.03068798966705799,
-0.01877615787088871,
0.014458609744906425,
0.1058720275759697,
0.030786368995904922,
0.017966825515031815,
0.026685167104005814,
0.010344180278480053,
-0.017746996134519577,
-0.056129030883312225,
0.02147551439702511,
-0.002956950571388006,
-0.046217165887355804,
0.030320869758725166,
-0.03131221979856491,
-0.02100038342177868,
0.03228916600346565,
0.011073119007050991,
0.08013696223497391,
0.011186039075255394,
0.02156355232000351,
0.022830110043287277,
0.0014202260645106435,
0.022868050262331963,
-0.0200765710324049,
-0.020515793934464455,
-0.00608132453635335,
0.014771568588912487,
0.03339504823088646,
-0.008503280580043793,
0.003019596915692091,
0.033946625888347626,
0.02425049990415573,
0.018865663558244705,
-0.01635958068072796,
0.017211182042956352,
-0.0011136452667415142,
0.04195881262421608,
0.01933138258755207,
-0.026269152760505676,
-0.01054821815341711,
0.004960950929671526,
0.012127788737416267,
-0.05378478765487671,
0.013085747137665749,
0.04299238696694374,
-0.030675243586301804,
-0.06506811082363129,
0.023311901837587357,
0.037112366408109665,
-0.024441927671432495,
-0.003720463253557682,
0.013370784930884838,
-0.06017446890473366,
-0.005784978158771992,
0.05149291828274727,
-0.01674574613571167,
-0.03772733360528946,
-0.03241817280650139,
-0.014027123339474201,
-0.04813167080283165,
-0.005164629779756069,
0.041776176542043686,
0.0500088706612587,
-0.021570349112153053,
-0.07863222807645798,
-0.02515948750078678,
-0.05742872133851051,
0.013318636454641819,
-0.004564961418509483,
0.01891113817691803,
-0.038834910839796066,
-0.0062178573571145535,
-0.0047208466567099094,
-0.0296058040112257,
0.01541830413043499,
-0.04547705873847008,
0.015655159950256348,
0.015627389773726463,
0.006370545830577612,
0.09299119561910629,
-0.03908639773726463,
-0.012210406363010406,
0.05032314360141754,
-0.018242284655570984,
0.008925062604248524,
-0.040395233780145645,
-0.07389721274375916,
0.017599046230316162,
-0.05013955011963844,
-0.011729990132153034,
0.02249833382666111,
-0.00003534374991431832,
0.0033380340319126844,
0.026882296428084373,
0.025948025286197662,
0.024750517681241035,
0.02537602372467518,
-0.03987554460763931,
-0.037594590336084366,
0.03603126481175423,
0.03421581909060478,
0.02587117627263069,
-0.03305478021502495,
0.02500804327428341,
-0.019847257062792778,
-0.017477169632911682,
0.03411105275154114,
0.021052761003375053,
0.013650154694914818,
-0.01081489771604538,
-0.010787121951580048,
-0.02126391790807247,
-0.03311633691191673,
-0.02875819429755211,
0.029761014506220818,
-0.06078075245022774,
-0.010720954276621342,
0.03388670086860657,
0.004207531455904245,
-0.03212609887123108,
-0.018212679773569107,
-0.03709046170115471,
0.005282355006784201,
-0.030904561281204224,
-0.04432889074087143,
-0.013555959798395634,
0.022345958277583122,
0.04989597573876381,
-0.0011409847065806389,
-0.001606903737410903,
-0.02185579389333725,
-0.04148099571466446,
0.04627683013677597,
-0.009077630005776882,
0.05241648107767105,
0.0006713165785185993,
0.03600923717021942,
-0.038622207939624786,
0.02491873875260353,
-0.02974781207740307,
0.0025820783339440823,
0.018163034692406654,
-0.050041891634464264,
-0.021192774176597595,
-0.019051628187298775,
0.056983135640621185,
-0.0398743636906147,
0.024099215865135193,
0.04060531035065651,
-0.02022727206349373,
0.01763298735022545,
0.016708198934793472,
-0.03964512422680855,
-0.00632210960611701,
0.030003327876329422,
0.01641910895705223,
0.017175601795315742,
-0.025352658703923225,
-0.01977238617837429,
0.007726325653493404,
-0.009597606025636196,
0.02824796922504902,
0.0019355296390131116,
0.021235330030322075,
0.007393075153231621
] |
<p>One of the weirdest things about quantum mechanics (QM) is the exponential growth of the dimensions of Hilbert space with increasing number of particles.
This was already discussed by Born and Schrodinger but here's a recent reference:</p>
<p><a href="http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.4770v2.pdf" rel="nofollow">http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.4770v2.pdf</a></p>
<p>and another one:</p>
<p><a href="http://www.scottaaronson.com/papers/are.pdf" rel="nofollow">http://www.scottaaronson.com/papers/are.pdf</a></p>
<p>Another difference between quantum mechanics and classical physics is that QM is discrete.<br>
A good example is the line spectrum of hydrogen.</p>
<p>Is there any good observational example which demonstrates the exponential growth of Hilbert space dimensions?<br>
Even for low numbers?<br>
(Does it perhaps show up in the line spectrum of a three or four valent atom?)</p> | g5499 | [
0.025032801553606987,
0.038092777132987976,
0.002334750024601817,
-0.079778753221035,
0.005337496753782034,
0.029405469074845314,
-0.04892248287796974,
-0.034523651003837585,
-0.023042801767587662,
-0.049349360167980194,
0.049856677651405334,
-0.02130657248198986,
0.07099301367998123,
0.025752564892172813,
-0.028512954711914062,
-0.0707508772611618,
0.02996235527098179,
-0.0066697257570922375,
-0.0223652645945549,
-0.05676915496587753,
0.025139952078461647,
0.014330265112221241,
-0.03069242089986801,
-0.04075957089662552,
0.0426376536488533,
0.04504302889108658,
0.01330909226089716,
-0.009349361062049866,
0.018729420378804207,
0.04970311000943184,
0.011311745271086693,
-0.021440520882606506,
0.03023499622941017,
-0.011814436875283718,
0.004824771545827389,
0.0007782395114190876,
0.04485082998871803,
0.03182923421263695,
0.049524370580911636,
-0.022826939821243286,
0.00021610190742649138,
-0.053759872913360596,
0.03979357331991196,
-0.005863338243216276,
0.01989407278597355,
-0.00016259821131825447,
0.004334880039095879,
0.03478548675775528,
-0.004958903416991234,
0.0445021353662014,
0.032043956220149994,
0.028353678062558174,
0.040041886270046234,
0.05457586795091629,
0.0434151291847229,
0.05435335636138916,
-0.050308454781770706,
-0.02983459271490574,
0.06359115988016129,
0.028958527371287346,
0.028203535825014114,
0.01943160407245159,
0.024982875213027,
0.014909712597727776,
0.05136962607502937,
0.011865128763020039,
-0.035239074379205704,
-0.02021951787173748,
0.020656131207942963,
-0.0033984901383519173,
0.0446530245244503,
-0.06926443427801132,
-0.04743828997015953,
-0.005599107127636671,
-0.007550247944891453,
0.03268330916762352,
0.003188297152519226,
0.001564179314300418,
-0.04625409096479416,
0.052672382444143295,
-0.04635383188724518,
-0.04813564941287041,
-0.0071700033731758595,
-0.02558661624789238,
0.07590259611606598,
0.06056708097457886,
0.04199590906500816,
0.0007155954372137785,
0.009003891609609127,
0.0219954214990139,
0.010991081595420837,
0.01958603411912918,
0.050362832844257355,
0.002959171077236533,
-0.04253658279776573,
-0.03190752863883972,
0.015988582745194435,
0.043364059180021286,
0.009491612203419209,
0.011216710321605206,
-0.005334076471626759,
0.050979968160390854,
0.07259393483400345,
-0.05015731602907181,
0.004443030338734388,
0.023639973253011703,
-0.015251737087965012,
-0.017535176128149033,
0.03717794641852379,
0.018849318847060204,
-0.046007875353097916,
-0.039372801780700684,
-0.06134020537137985,
-0.0490666963160038,
-0.00510256364941597,
-0.004052458330988884,
0.027748331427574158,
-0.041604816913604736,
-0.006401181221008301,
0.009316148236393929,
0.02700202912092209,
-0.013945027254521847,
0.09580165892839432,
0.013254926539957523,
-0.025431904941797256,
-0.004921842832118273,
0.028524160385131836,
0.002246236428618431,
0.025932352989912033,
-0.021703867241740227,
-0.015933973714709282,
0.02143002487719059,
-0.016858890652656555,
-0.021539386361837387,
-0.012882758863270283,
-0.0033595231361687183,
-0.029186535626649857,
-0.01409844309091568,
0.0169378612190485,
0.05012936145067215,
0.01866377890110016,
-0.05834854021668434,
0.008536930195987225,
-0.023758137598633766,
0.05168372392654419,
-0.03957577422261238,
0.019033407792448997,
-0.007448562420904636,
0.009506942704319954,
0.031021082773804665,
0.003276238450780511,
0.029751311987638474,
0.011963783763349056,
-0.028322391211986542,
-0.03657776117324829,
0.047942597419023514,
-0.03103014826774597,
-0.027729205787181854,
-0.006634236313402653,
-0.017764320597052574,
-0.01772039197385311,
0.02680344693362713,
-0.03821738436818123,
0.007420696783810854,
-0.012232192791998386,
0.05227398872375488,
0.021369174122810364,
-0.04133583977818489,
0.003575159702450037,
-0.02655210718512535,
0.013081744313240051,
-0.016173038631677628,
0.012316493317484856,
0.03605147451162338,
-0.026286138221621513,
0.04608062282204628,
0.01755720004439354,
-0.09134353697299957,
0.007320777978748083,
-0.021392980590462685,
0.0020460672676563263,
-0.016063803806900978,
0.007666402030736208,
-0.02995901368558407,
0.0053121428936719894,
0.046463027596473694,
0.023402933031320572,
-0.00780646363273263,
-0.04085858538746834,
-0.02594202198088169,
-0.024242253974080086,
-0.010202460922300816,
0.04675495997071266,
0.0024372623302042484,
0.022943850606679916,
-0.032255083322525024,
0.03134680911898613,
-0.07210028916597366,
-0.01936197653412819,
-0.04402082413434982,
0.017584137618541718,
0.029431438073515892,
0.008294354192912579,
0.006769365631043911,
0.02815030701458454,
-0.020940106362104416,
-0.014933371916413307,
-0.002522907452657819,
0.015993596985936165,
-0.029031919315457344,
0.02926371432840824,
0.04606591537594795,
-0.03383810445666313,
-0.026426605880260468,
-0.013415678404271603,
0.008408507332205772,
-0.020669834688305855,
-0.012992870062589645,
-0.007669483311474323,
0.03143177554011345,
-0.012365678325295448,
-0.037331730127334595,
-0.006768454797565937,
0.044535938650369644,
0.04511823132634163,
-0.04627528414130211,
0.024284007027745247,
0.000621894549112767,
-0.016296405345201492,
0.07439184188842773,
-0.12759406864643097,
0.004497447516769171,
0.03247600048780441,
-0.030580827966332436,
-0.004179480951279402,
0.031780581921339035,
-0.05752205476164818,
-0.030479444190859795,
0.08447720110416412,
0.0857711210846901,
0.08447623252868652,
-0.014847243204712868,
-0.07532991468906403,
-0.01830277219414711,
0.06823880225419998,
-0.03280864655971527,
-0.01574159413576126,
-0.009147235192358494,
-0.06159508600831032,
-0.0050431182608008385,
-0.001478299731388688,
-0.008547510020434856,
0.007045273203402758,
0.004212743602693081,
0.0051846797578036785,
0.007874753326177597,
0.04595377668738365,
0.0100484574213624,
-0.00694775115698576,
-0.08501320332288742,
-0.021331410855054855,
0.005036737769842148,
-0.0034254975616931915,
0.03209707513451576,
0.00041866154060699046,
-0.05695256218314171,
0.01247409824281931,
0.009697678498923779,
-0.06686164438724518,
0.0009266102570109069,
-0.00025719605037011206,
0.11453016102313995,
-0.003947888500988483,
0.024522319436073303,
-0.018707767128944397,
-0.05239524319767952,
0.019923124462366104,
-0.04293660819530487,
0.049927886575460434,
-0.052554573863744736,
-0.07757283747196198,
-0.010196685791015625,
-0.08777850866317749,
0.013895903714001179,
0.07138815522193909,
-0.05975579842925072,
-0.0016277051763609052,
-0.03301440179347992,
-0.043919824063777924,
-0.00023487067664973438,
-0.023437801748514175,
0.041789304465055466,
-0.01127948984503746,
0.006974312476813793,
-0.037563592195510864,
0.019516948610544205,
0.011166049167513847,
-0.04446284845471382,
-0.024628138169646263,
0.04775356873869896,
0.0007266549509949982,
-0.0608268603682518,
0.007509807590395212,
-0.022706318646669388,
0.03775518015027046,
-0.04794430360198021,
-0.03920956701040268,
-0.00970582477748394,
0.020584337413311005,
-0.0418042317032814,
0.021271076053380966,
-0.006386927794665098,
-0.04767833650112152,
0.001024220255203545,
-0.02578541450202465,
-0.045766402035951614,
-0.040075480937957764,
0.01764916628599167,
0.05030788108706474,
-0.04141389951109886,
-0.017915792763233185,
-0.0777924582362175,
0.01829265058040619,
-0.010984772816300392,
0.06385214626789093,
0.03841240331530571,
-0.01216166652739048,
-0.012955998070538044,
0.0043028914369642735,
0.0561264306306839,
0.02529546059668064,
-0.07361230999231339,
0.02922050654888153,
0.013414628803730011,
-0.034996237605810165,
-0.03247815743088722,
-0.04002299904823303,
-0.030556289479136467,
0.04152815043926239,
-0.015465226955711842,
-0.004150153137743473,
0.010614325292408466,
0.013383647426962852,
-0.0013711845967918634,
-0.0149961207062006,
-0.03098863549530506,
-0.009057080373167992,
0.00954918097704649,
-0.046212002635002136,
0.02724863402545452,
-0.04848774895071983,
-0.07096042484045029,
0.036639656871557236,
0.028539199382066727,
-0.02288922667503357,
0.014003623276948929,
-0.0010721326107159257,
0.005366561934351921,
0.061168123036623,
-0.07382028549909592,
-0.028494926169514656,
-0.039726823568344116,
0.01938813179731369,
0.01339017879217863,
-0.029338466003537178,
-0.007168181706219912,
-0.015979822725057602,
0.03979746624827385,
0.05655059218406677,
-0.015449444763362408,
-0.04718171805143356,
-0.005226979032158852,
0.009941764175891876,
-0.010448860004544258,
0.038576409220695496,
-0.0034772928338497877,
-0.011064033955335617,
-0.05502805486321449,
-0.0264365766197443,
-0.02563563361763954,
-0.014616664499044418,
-0.008271458558738232,
0.07737363874912262,
0.03766656666994095,
-0.016441121697425842,
0.010645637288689613,
-0.029872065410017967,
-0.021762095391750336,
-0.01984216459095478,
-0.04256073012948036,
0.023387964814901352,
0.00731254369020462,
0.006311357952654362,
-0.001954873325303197,
-0.04492461308836937,
0.005282912403345108,
0.08303506672382355,
0.00622387882322073,
-0.019928449764847755,
0.03869663178920746,
-0.050867967307567596,
-0.02123280055820942,
-0.007507035043090582,
0.06698108464479446,
-0.005057614296674728,
-0.003265172941610217,
0.056434664875268936,
0.012865935452282429,
-0.011639253236353397,
-0.044079892337322235,
0.019960729405283928,
-0.01090208999812603,
-0.001410448458045721,
-0.06588967889547348,
0.002519783331081271,
0.0004482956719584763,
0.009331394918262959,
-0.04112059995532036,
0.010091845877468586,
0.022573009133338928,
0.019433720037341118,
0.050794992595911026,
-0.039990101009607315,
0.02820909023284912,
0.0022397644352167845,
0.02827385999262333,
0.035990167409181595,
-0.019527528434991837,
-0.06736952811479568,
-0.043642714619636536,
0.0383392795920372,
0.0003076626162510365,
-0.003444428090006113,
0.05981479585170746,
-0.018877385184168816,
0.023660369217395782,
-0.035117872059345245,
0.03251911327242851,
-0.0014079295797273517,
0.00596585962921381,
0.10918816179037094,
0.05393354222178459,
0.0020935358479619026,
0.0013362762983888388,
0.034622009843587875,
0.05018874257802963,
-0.07073598355054855,
-0.001408941694535315,
-0.04793000966310501,
0.026036042720079422,
0.035634689033031464,
0.055521056056022644,
-0.03117351047694683,
-0.01972569152712822,
0.016623834148049355,
-0.09846309572458267,
-0.04156053438782692,
0.061420585960149765,
0.035717759281396866,
0.05495532602071762,
-0.060795094817876816,
-0.023138953372836113,
-0.05400903522968292,
0.029118292033672333,
-0.012269583530724049,
-0.03247281536459923,
-0.07238499820232391,
0.02122523821890354,
-0.02554113045334816,
0.004818690940737724,
0.030413953587412834,
-0.0027539501897990704,
0.00007189261668827385,
-0.04228606075048447,
-0.005676383152604103,
-0.0798221006989479,
-0.01356619130820036,
-0.010444068349897861,
-0.004828046541661024,
-0.07850047945976257,
0.03201046958565712,
-0.040840115398168564,
0.017629774287343025,
0.05407705530524254,
0.003218182362616062,
0.03054237924516201,
-0.01264857780188322,
0.02321120910346508,
-0.02204783260822296,
-0.009955122135579586,
0.03589819744229317,
-0.008694764226675034,
0.007820608094334602,
0.045946065336465836,
-0.0169784314930439,
-0.05618107318878174,
0.03772706165909767,
-0.049201976507902145,
-0.007669297978281975,
0.03227668255567551,
-0.04346473142504692,
0.029168935492634773,
0.026644526049494743,
-0.022745518013834953,
-0.010332455858588219,
0.013205775059759617,
0.06382975727319717,
0.0047469898127019405,
-0.0070532760582864285,
-0.01931397058069706,
-0.006972091738134623,
0.0056682550348341465,
0.02913937158882618,
0.00260330131277442,
0.054448287934064865,
-0.04073801264166832,
-0.048713959753513336,
0.03482768312096596,
0.005697456654161215,
-0.01567201502621174,
0.01688675582408905,
-0.023983057588338852,
0.022452957928180695,
-0.06505712866783142,
0.01813274249434471,
0.05114210397005081,
-0.019785184413194656,
-0.008703673258423805,
0.005845716688781977,
0.051666807383298874,
0.07602418959140778,
0.005751044489443302,
0.026264481246471405,
-0.025953231379389763,
-0.01917446032166481,
0.11002528667449951,
0.021148309111595154,
0.024913081899285316,
0.03127196803689003,
0.05612201616168022,
0.0024122914765030146,
-0.03456651419401169,
-0.038669653236866,
0.02953089401125908,
0.036799125373363495,
-0.010489781387150288,
-0.0779557004570961,
0.03114756941795349,
0.07377564907073975,
0.014035980217158794,
-0.052214156836271286,
-0.04811640828847885,
-0.06350509822368622,
-0.009869921952486038,
-0.01844804547727108,
0.01577582024037838,
-0.007259529083967209,
-0.03972594067454338,
-0.04961036518216133,
0.05194391310214996,
0.01225461158901453,
0.00474158488214016,
0.07986458390951157,
-0.053696535527706146,
0.0026827382389456034,
-0.013405379839241505,
0.01065644808113575,
0.009159773588180542,
0.06920570135116577,
0.06635955721139908,
-0.01346577238291502,
0.07932940870523453,
0.06837429106235504,
0.045746300369501114,
0.021469686180353165,
-0.0030071905348449945,
0.02555599994957447,
-0.058000512421131134,
-0.04917547106742859,
-0.005741715431213379,
0.009294847026467323,
0.05720359832048416,
0.012325982563197613,
-0.031833257526159286,
-0.025454076007008553,
0.021642979234457016,
0.00011609447392402217,
-0.002338123507797718,
0.029112301766872406,
0.02334863878786564,
-0.0454542301595211,
-0.031467415392398834,
-0.032584160566329956,
-0.049594633281230927,
0.0008634358528070152,
-0.025762472301721573,
-0.005117705557495356,
-0.03575301542878151,
-0.03289303556084633,
-0.01284614484757185,
0.0369827076792717,
-0.003789546899497509,
0.028236810117959976,
-0.033940985798835754,
0.0018563560442999005,
0.023872172459959984,
-0.04055618494749069,
-0.01415998488664627,
0.03700229525566101,
0.017249232158064842,
-0.024524657055735588,
-0.004565047565847635,
-0.009316794574260712,
0.025379719212651253,
-0.017966514453291893,
-0.10276782512664795,
0.06330377608537674,
0.026542693376541138,
0.016440268605947495,
0.06099938973784447,
0.04601307585835457,
-0.007097330875694752,
0.008645719848573208,
-0.047713976353406906,
0.037587326020002365,
0.06416913121938705,
-0.01737804524600506,
0.029141517356038094,
0.047626908868551254,
-0.056528180837631226,
-0.02901153266429901,
-0.06884511560201645,
0.02230411395430565,
0.05300479009747505,
-0.039895351976156235,
-0.03353004530072212,
-0.05376257002353668,
-0.0026504015550017357,
0.020716218277812004,
-0.013179938308894634,
0.029492361471056938,
-0.0032437429763376713,
0.025023283436894417,
-0.049320656806230545,
-0.0291437990963459,
0.032992515712976456,
0.011430305428802967,
0.05362401530146599,
-0.04738405719399452,
-0.0022232760675251484,
0.008037734776735306,
-0.004582239780575037,
0.002270773518830538,
-0.030211132019758224,
-0.032366957515478134,
0.03702079877257347,
0.02257215790450573,
-0.031209928914904594,
-0.0011695673456415534,
-0.06447992473840714,
-0.012590744532644749,
-0.006814226973801851,
-0.013523292727768421,
-0.015496903099119663,
-0.004917783197015524,
0.044070761650800705,
0.007001135498285294,
-0.03105865977704525,
-0.03194195404648781,
0.016577135771512985,
-0.013813694007694721,
-0.017830293625593185,
0.0010157112265005708,
0.007043428719043732,
0.003952753730118275,
0.005580522585660219,
-0.003762239357456565,
0.04058781638741493,
0.002631968352943659,
-0.028599506244063377,
0.03528423607349396,
0.04747580364346504,
0.02725563570857048,
-0.03215249627828598,
-0.018302710726857185,
0.006615030579268932,
-0.028916995972394943,
-0.035511426627635956,
0.0056372215040028095,
0.02818993851542473,
0.015211449936032295,
-0.043377842754125595,
-0.019143691286444664,
-0.08030805736780167,
0.021778129041194916,
0.019381728023290634,
0.031022923067212105,
0.002166111720725894,
-0.024206938222050667,
0.04526360705494881,
-0.024261334910988808,
0.025597337633371353,
-0.003026690101251006,
-0.040901679545640945,
0.030154772102832794,
-0.005613548681139946,
0.021529294550418854,
-0.03140748292207718,
-0.009780854918062687,
-0.03271578252315521,
-0.049517832696437836,
0.04652480408549309,
0.02265298180282116,
0.013051314279437065,
0.06132715195417404,
0.0006663628155365586,
0.013423207215964794,
0.0072277504950761795,
0.05458086356520653,
-0.005698977038264275,
-0.0008929999894462526,
-0.04485964775085449,
0.005808256566524506,
-0.0463557131588459,
-0.010473738424479961,
-0.05859456956386566,
0.02271738089621067,
0.02615080028772354,
0.027318241074681282,
0.05565652251243591,
-0.057139165699481964,
0.03332380950450897,
0.008962159976363182,
0.02134108915925026,
-0.022643733769655228,
0.03377591446042061,
-0.025760555639863014,
0.06495265662670135,
0.005280768033117056,
0.004608840681612492,
-0.007327719125896692,
0.0018275593174621463,
0.05519554391503334,
-0.024554215371608734,
-0.01909715123474598,
-0.06728307902812958,
-0.029383981600403786,
0.007868732325732708,
0.0719146654009819,
0.0264600683003664,
-0.04808042198419571,
-0.0021206580568104982,
-0.029829327017068863,
0.08872010558843613,
0.028788389638066292,
-0.06287045776844025,
0.01915343478322029,
0.057929836213588715,
-0.003057457273826003,
-0.025200609117746353,
0.04664072021842003,
-0.014416908845305443,
-0.015245195478200912,
-0.012562012299895287,
-0.037654563784599304,
-0.006960336118936539,
-0.021232906728982925,
0.03725847974419594
] |
<p>Does increasing the amount of electric charge on a conductor cause an increase in its <em>electric potential</em> to a point at which it becomes maximum; where it can hold no more extra charge?</p>
<p>Is it true? How?</p>
<p>I read it from a book while studying <em>capacitance</em>.</p>
<p>Does this idea sound <em>foolish</em>?</p> | g5500 | [
0.014658399857580662,
0.06554029136896133,
-0.0019069913541898131,
0.022006811574101448,
0.04442334547638893,
0.03807687759399414,
-0.0357394777238369,
0.00006211329309735447,
-0.012317398563027382,
0.044196274131536484,
-0.07298483699560165,
-0.004626409616321325,
0.04714169353246689,
0.015419712290167809,
0.035192035138607025,
0.0012752411421388388,
0.07275565713644028,
-0.04681479558348656,
0.010432936251163483,
0.005597073584794998,
-0.007807993795722723,
-0.03720731660723686,
0.05337071791291237,
0.014115589670836926,
-0.05603170767426491,
-0.005081210285425186,
-0.019562073051929474,
0.03978807106614113,
-0.04236365854740143,
-0.01820651814341545,
-0.013849565759301186,
0.03517395630478859,
0.016998426988720894,
0.028420208021998405,
-0.06912641227245331,
-0.05052860081195831,
0.06073025241494179,
0.02920188196003437,
-0.005592042114585638,
0.023747889325022697,
0.020766891539096832,
-0.01839292049407959,
0.008794156834483147,
0.009498202241957188,
-0.04877345636487007,
-0.07387514412403107,
0.019027264788746834,
0.004493079613894224,
-0.01446265634149313,
-0.05325166881084442,
-0.020028164610266685,
-0.019045855849981308,
0.06331136077642441,
0.03221047669649124,
0.0553397499024868,
-0.0033093916717916727,
-0.023288970813155174,
-0.043954379856586456,
0.049866072833538055,
0.0343686044216156,
0.020513158291578293,
0.025519177317619324,
0.0180053748190403,
0.032631997019052505,
0.006092027295380831,
-0.0107696782797575,
-0.019469330087304115,
-0.012473264709115028,
0.019192861393094063,
-0.005578105337917805,
-0.00038540069363079965,
-0.05257001146674156,
-0.08219587802886963,
-0.04339402914047241,
0.02596229501068592,
0.03567105531692505,
0.059554893523454666,
-0.0006187038961797953,
0.03995872288942337,
0.00803015660494566,
0.018258916214108467,
-0.046610042452812195,
-0.01630089432001114,
-0.022050531581044197,
0.029441554099321365,
-0.039617639034986496,
0.026611406356096268,
0.0279292743653059,
-0.023917149752378464,
-0.0002028062444878742,
0.014829142950475216,
-0.04145092889666557,
0.0347042977809906,
0.005138208158314228,
0.021754181012511253,
-0.010297689586877823,
0.010718433186411858,
0.0035468784626573324,
0.015792813152074814,
-0.02566833235323429,
-0.05299130454659462,
-0.019712159410119057,
0.06964349746704102,
0.030803104862570763,
-0.06260256469249725,
0.045904021710157394,
0.004355726297944784,
-0.01034254115074873,
0.02958783693611622,
-0.009576943702995777,
0.005709574557840824,
-0.03935011476278305,
-0.03664031997323036,
-0.017518725246191025,
-0.0262189581990242,
0.022574013099074364,
0.024065669625997543,
-0.015399659983813763,
0.010247265920042992,
0.050673551857471466,
-0.02267787605524063,
0.017984498292207718,
-0.019980715587735176,
0.013880507089197636,
-0.012462747283279896,
0.056331831961870193,
0.052949752658605576,
-0.009722939692437649,
0.01026126928627491,
-0.01982390508055687,
0.00857151672244072,
-0.0001557282084831968,
-0.003596115857362747,
-0.04863922297954559,
0.012740161269903183,
0.04623540863394737,
0.014154772274196148,
-0.012163599953055382,
0.02381671778857708,
0.014432063326239586,
0.01957808993756771,
-0.062327634543180466,
0.004136658273637295,
0.012945175170898438,
-0.010182221420109272,
0.00585021311417222,
-0.00009147237142315134,
0.04695263132452965,
0.015005921013653278,
0.04400743171572685,
0.02630479820072651,
0.03357118368148804,
-0.018040655180811882,
-0.07719003409147263,
0.044873107224702835,
-0.0011263941414654255,
0.05374296009540558,
0.027698064222931862,
0.0032048113644123077,
-0.013779724016785622,
0.040714994072914124,
0.021401215344667435,
0.009518957696855068,
0.026920050382614136,
-0.039060406386852264,
0.02851758897304535,
0.003412594785913825,
-0.01153256930410862,
-0.059737443923950195,
0.002844163915142417,
0.01356538850814104,
-0.043043818324804306,
0.04537148401141167,
0.06271222233772278,
0.0016010199906304479,
0.04808732494711876,
0.03957386687397957,
0.012421412393450737,
0.0680747851729393,
-0.02402760274708271,
-0.06255140900611877,
-0.0018794216448441148,
0.0013062615180388093,
-0.036565911024808884,
0.0045439982786774635,
-0.022005481645464897,
-0.03482358530163765,
0.051782168447971344,
-0.012468821369111538,
-0.014761872589588165,
-0.09681347012519836,
0.0053140101954340935,
0.026229333132505417,
0.08375098556280136,
-0.01807500794529915,
-0.006208707112818956,
0.01027563214302063,
-0.03883247449994087,
0.006614358630031347,
-0.027511822059750557,
-0.04307252913713455,
0.008971109054982662,
0.00797505583614111,
-0.007452190853655338,
0.010652800090610981,
-0.02919786423444748,
-0.008339167572557926,
-0.06868616491556168,
0.07953748106956482,
0.015311179682612419,
0.03721495345234871,
0.008354013785719872,
0.012860712595283985,
0.0036259121261537075,
-0.02629833295941353,
-0.027225332334637642,
-0.021841509267687798,
-0.007036861963570118,
-0.033002451062202454,
-0.03995736315846443,
0.002534592757001519,
-0.0032121120020747185,
0.03589571267366409,
0.054168667644262314,
-0.05994889885187149,
0.005605330690741539,
-0.01819385588169098,
-0.028319641947746277,
-0.013462723232805729,
-0.027027303352952003,
-0.0376833900809288,
0.0162322036921978,
-0.004298264626413584,
-0.016301237046718597,
-0.0013241193955764174,
0.038636960089206696,
-0.01778658665716648,
-0.013909857720136642,
-0.029865184798836708,
-0.05367502197623253,
0.0009565699729137123,
-0.027998661622405052,
-0.004460653755813837,
0.027500271797180176,
0.00005164296453585848,
-0.029270874336361885,
0.0047556315548717976,
0.003630580147728324,
-0.011987637728452682,
-0.004088376648724079,
0.03208857774734497,
-0.025779830291867256,
0.004502160474658012,
0.011760438792407513,
0.01818622462451458,
-0.008057582192122936,
-0.016055308282375336,
0.09657394886016846,
0.0024825306609272957,
-0.017897987738251686,
0.002968149958178401,
0.028176330029964447,
-0.008957039564847946,
0.0027026270981878042,
-0.08415669947862625,
0.018453050404787064,
-0.07149189710617065,
-0.08950230479240417,
0.03005828522145748,
0.009772563353180885,
-0.020724669098854065,
0.08824503421783447,
-0.039147596806287766,
0.014476150274276733,
0.03337416797876358,
-0.03583330288529396,
0.008313270285725594,
-0.015410332940518856,
0.06442490965127945,
-0.03682366758584976,
-0.026219045743346214,
0.004534968640655279,
-0.06370270997285843,
-0.021984616294503212,
0.0067678759805858135,
-0.014285365119576454,
0.0010086419060826302,
-0.07567468285560608,
-0.02036956511437893,
-0.04226848483085632,
-0.02338826283812523,
0.00035051742452196777,
0.11130192875862122,
-0.050058044493198395,
0.02356109395623207,
0.0009132566046901047,
0.038812555372714996,
-0.05215451493859291,
-0.031097810715436935,
0.004340813960880041,
0.00027882776339538395,
-0.014863820746541023,
-0.0660555437207222,
-0.013478865846991539,
0.06830689311027527,
0.1040358766913414,
-0.021580206230282784,
-0.02950868010520935,
0.06320218741893768,
-0.0004726434126496315,
-0.032550860196352005,
0.015789318829774857,
0.00012259943468961865,
-0.011847143061459064,
-0.04689011350274086,
0.005148646887391806,
0.001045140903443098,
0.013687552884221077,
0.0017605922184884548,
-0.07447921484708786,
-0.010207835584878922,
-0.04675609990954399,
-0.02564779482781887,
0.024844199419021606,
0.028585877269506454,
0.004925386980175972,
-0.039150454103946686,
-0.02551303431391716,
-0.024248477071523666,
0.04158793017268181,
0.030636033043265343,
0.009939819574356079,
-0.05011729151010513,
-0.019751746207475662,
-0.011498906649649143,
-0.036824654787778854,
0.02720354124903679,
0.08242753893136978,
0.0662262961268425,
0.007758516352623701,
0.012073518708348274,
-0.02645554021000862,
-0.09131107479333878,
-0.06685871630907059,
-0.012674499303102493,
0.05515044927597046,
0.03646009787917137,
-0.015466539189219475,
0.01324794627726078,
0.009711132384836674,
0.03697121515870094,
-0.0006300603272393346,
-0.007230042479932308,
0.042600419372320175,
-0.043125707656145096,
-0.017698174342513084,
-0.0040000504814088345,
0.06377339363098145,
-0.07344990223646164,
0.05011902377009392,
0.016995150595903397,
-0.034091826528310776,
0.02807079255580902,
0.015003307722508907,
0.00915021076798439,
0.01250444259494543,
0.012662467546761036,
0.038915395736694336,
-0.008846623823046684,
-0.04886897653341293,
-0.011271360330283642,
-0.006106141954660416,
0.008132480084896088,
0.09690085798501968,
0.05995115265250206,
-0.03495180234313011,
-0.006637989543378353,
0.007886865176260471,
0.012957284227013588,
0.0445573665201664,
0.0009936378337442875,
-0.0038768588565289974,
0.011235213838517666,
-0.02930210903286934,
-0.030067550018429756,
-0.026795051991939545,
0.007058665622025728,
0.007583552040159702,
0.00028156727785244584,
-0.027370963245630264,
-0.009360179305076599,
-0.013546080328524113,
-0.014760885387659073,
-0.009847777895629406,
-0.015310739167034626,
-0.03479642793536186,
-0.034115128219127655,
-0.050085317343473434,
0.04646942764520645,
0.018482988700270653,
0.0565708726644516,
0.044155240058898926,
-0.016123736277222633,
0.045303549617528915,
-0.019071485847234726,
-0.024881241843104362,
0.07796953618526459,
-0.0011187022319063544,
0.005776437930762768,
-0.043745093047618866,
0.025760771706700325,
-0.029375972226262093,
-0.009902975521981716,
-0.0602043941617012,
0.003049395279958844,
-0.008362088352441788,
0.047018129378557205,
0.0007095685577951372,
0.03206394612789154,
0.0174211785197258,
0.00491075636819005,
-0.035348933190107346,
-0.022517766803503036,
0.0017261655302718282,
0.02190406061708927,
0.015630710870027542,
0.005052228458225727,
-0.0638280063867569,
0.009236007928848267,
0.00677019078284502,
-0.05389833450317383,
0.04786990210413933,
-0.04513857513666153,
0.025346603244543076,
-0.0303663220256567,
0.055959269404411316,
-0.007233617827296257,
0.05298762395977974,
-0.0072873299941420555,
0.047647230327129364,
0.07614670693874359,
-0.004166748840361834,
0.026028603315353394,
-0.01830330677330494,
0.006370178423821926,
0.018332751467823982,
-0.05099625512957573,
0.0014282265910878778,
0.022865338250994682,
0.007050082553178072,
-0.06266391277313232,
0.021324332803487778,
0.016100171953439713,
0.016892138868570328,
-0.003203627420589328,
-0.08090098202228546,
0.0037601192016154528,
-0.03628058731555939,
-0.02351493015885353,
0.015263817273080349,
-0.06470611691474915,
-0.030025595799088478,
-0.029795976355671883,
0.04529330134391785,
0.04657120257616043,
-0.020013654604554176,
-0.005447851959615946,
-0.07563516497612,
-0.035575300455093384,
-0.025957534089684486,
-0.0129894083365798,
0.062676340341568,
0.05895734205842018,
0.03491589054465294,
0.044668179005384445,
-0.05101001635193825,
-0.022062310948967934,
0.04011203348636627,
-0.0954117700457573,
-0.05600043758749962,
-0.013379791751503944,
0.008987706154584885,
-0.035253867506980896,
-0.023647846654057503,
-0.050645481795072556,
-0.014904738403856754,
-0.04861973226070404,
0.02796788327395916,
0.021388327702879906,
-0.04399001970887184,
0.03754901513457298,
0.049281105399131775,
-0.004949027206748724,
0.04947396367788315,
-0.08632989227771759,
0.011091729626059532,
0.04958799108862877,
0.03850829228758812,
-0.04409203305840492,
0.0031889346428215504,
0.024842441082000732,
-0.01873796246945858,
-0.03232168033719063,
0.03359906002879143,
-0.009619573131203651,
-0.007412872742861509,
-0.04422659054398537,
-0.02241653762757778,
0.030998069792985916,
0.00013392728578764945,
-0.04267748445272446,
0.04968849569559097,
0.024713825434446335,
0.028798038139939308,
0.052975453436374664,
0.02606542780995369,
-0.08335532993078232,
-0.018317442387342453,
-0.04118478298187256,
0.009736712090671062,
0.07874995470046997,
0.005475193727761507,
0.028874430805444717,
-0.04758409783244133,
-0.024903204292058945,
0.01734755001962185,
-0.023946717381477356,
0.013772952370345592,
0.06205681338906288,
0.043112024664878845,
0.031194549053907394,
0.02120054140686989,
0.020952580496668816,
-0.02062893658876419,
-0.023053467273712158,
0.04317019134759903,
-0.0037660354282706976,
0.0026879720389842987,
-0.009349425323307514,
0.04645939916372299,
0.043095435947179794,
0.0014793018344789743,
0.017253447324037552,
0.13460351526737213,
0.0160241536796093,
-0.043095577508211136,
-0.1025678887963295,
0.0036687590181827545,
0.09894763678312302,
0.0035966874565929174,
-0.02041677199304104,
-0.03589467704296112,
-0.032785218209028244,
-0.019824018701910973,
0.020711123943328857,
0.029084371402859688,
0.03129439055919647,
-0.002992910798639059,
0.026016993448138237,
-0.05287535488605499,
0.048782311379909515,
-0.020523957908153534,
0.005286226514726877,
0.008091391064226627,
-0.0013639935059472919,
-0.04519934207201004,
-0.004166641738265753,
0.015781745314598083,
0.09974028170108795,
0.041006091982126236,
-0.0009420887217856944,
0.04138243943452835,
0.016706250607967377,
-0.014712614938616753,
-0.012707522138953209,
-0.017454439774155617,
-0.007181278429925442,
0.023032862693071365,
0.022969316691160202,
0.009094567969441414,
-0.05010870471596718,
-0.0064907982014119625,
0.027661481872200966,
-0.05644422024488449,
-0.024401845410466194,
0.07676567137241364,
-0.017475558444857597,
-0.01499621570110321,
0.054715320467948914,
-0.019942140206694603,
-0.030666958540678024,
-0.0053797997534275055,
0.05983858183026314,
-0.035736944526433945,
0.035372164100408554,
-0.021752409636974335,
-0.017581390216946602,
-0.009454408660531044,
0.06387999653816223,
0.05528396740555763,
0.04069826379418373,
-0.006243683863431215,
-0.007659292314201593,
0.022207504138350487,
0.04944677650928497,
0.014178536832332611,
0.015486449003219604,
-0.01745692268013954,
-0.04755501449108124,
0.01165471039712429,
-0.012926160357892513,
-0.042880088090896606,
0.04546672850847244,
-0.030231887474656105,
-0.03222571685910225,
-0.02393796481192112,
0.037235621362924576,
0.022860316559672356,
-0.028496015816926956,
0.04276524856686592,
0.00017010611190926284,
0.0017449251608923078,
0.04821040853857994,
0.021011080592870712,
-0.03354595601558685,
0.04370011016726494,
0.0326530784368515,
-0.03661028668284416,
0.050210531800985336,
-0.05677993223071098,
-0.04723131284117699,
0.032101791352033615,
-0.033188316971063614,
0.04635798931121826,
0.006714056711643934,
-0.009821432642638683,
0.002090627560392022,
-0.07106903195381165,
-0.004987410735338926,
0.017250506207346916,
-0.05641354247927666,
0.037816017866134644,
0.0191185399889946,
0.02515323832631111,
0.0019044078653678298,
-0.025974998250603676,
0.03086761385202408,
0.012866215780377388,
-0.035707417875528336,
0.022645926102995872,
0.027666820213198662,
-0.06145196035504341,
-0.007482065819203854,
0.06903716921806335,
-0.02899349294602871,
-0.023685568943619728,
-0.011223912239074707,
-0.005990918260067701,
0.058042727410793304,
0.010733840055763721,
-0.007456637918949127,
0.025176789611577988,
0.012493164278566837,
-0.015554426237940788,
0.040946487337350845,
0.011955853551626205,
0.0005662269541062415,
-0.04558511823415756,
-0.05094432830810547,
-0.09056952595710754,
0.02485811524093151,
-0.029615648090839386,
-0.01566140726208687,
-0.004491954576224089,
0.010136964730918407,
-0.009031719528138638,
-0.0394313707947731,
0.00327275600284338,
-0.007074765861034393,
0.0021437997929751873,
-0.022086692973971367,
-0.01412616390734911,
0.019835524260997772,
-0.07455715537071228,
-0.05060752108693123,
0.007131811231374741,
-0.08308383077383041,
-0.011263489723205566,
0.027535803616046906,
0.03702351078391075,
0.030936429277062416,
0.0012450520880520344,
-0.025828594341874123,
0.03746403008699417,
-0.029557853937149048,
0.016104426234960556,
-0.04278511926531792,
0.03386428579688072,
0.02135884389281273,
0.0038101463578641415,
-0.009258796460926533,
-0.0362078957259655,
-0.034890033304691315,
-0.02819502167403698,
-0.00005126640826347284,
0.022304171696305275,
-0.003802298801019788,
-0.007967023178935051,
-0.03991948440670967,
0.003613445209339261,
-0.004436922259628773,
0.010893144644796848,
0.025445880368351936,
-0.009824884124100208,
-0.0363638810813427,
0.04537981003522873,
0.0529664121568203,
0.04150800779461861,
0.038156747817993164,
0.03781173750758171,
-0.017150050029158592,
-0.0132602509111166,
0.014414883218705654,
-0.05732371285557747,
-0.051763396710157394,
-0.014005947858095169,
0.008150341920554638,
0.0035958015359938145,
0.011078858748078346,
-0.006443731486797333,
0.04739539325237274,
-0.0580090768635273,
0.007412397302687168,
-0.013327131047844887,
-0.022960325703024864,
0.0001680734276305884,
-0.025548670440912247,
0.09566032886505127,
0.034079428762197495,
-0.010073606856167316,
-0.04343723505735397,
-0.053174812346696854,
-0.03188866376876831,
-0.030389847233891487,
0.011690436862409115,
0.042615871876478195,
-0.052574533969163895,
0.05543535202741623,
0.08600647747516632,
0.011171284131705761,
-0.03331513702869415,
-0.0348823219537735,
-0.033606115728616714,
0.014214273542165756,
0.013361694291234016,
-0.035408906638622284,
-0.014108708128333092,
0.0008944791625253856,
0.027752093970775604,
0.007506947498768568,
-0.007726562209427357,
-0.030023977160453796,
-0.03210574761033058,
-0.0891152173280716,
-0.01616191491484642,
-0.03833374008536339,
0.020793719217181206,
-0.0806698352098465
] |
<p>One would say that $AdS_n$ satisfies the equations for the scalar curvature (R) and Ricci tensor ($R_{\mu \nu}$), $R = - \frac{n(n-1)}{L^2}$ and $R_{ab} = - \frac{n-1}{L^2}g_{ab}$. </p>
<ul>
<li>But do the signs in the above depend on the sign of the metric convention? </li>
</ul>
<hr>
<p>I am confused when I look at these two metrics,</p>
<ul>
<li><p>$ds_1^2 = \frac{r^2}{Q^2}dt^2 - \frac{Q^2}{r^2}dr^2$</p></li>
<li><p>$ds_2^2 = \left ( 1 - \frac{\Lambda r^2}{3} \right ) dt^2 - \frac{ dr^2 } { \left ( 1 - \frac{\Lambda r^2}{3} \right ) }$</p></li>
</ul>
<p>Are both the above valid metrics of $AdS_2$? (with what sign of $\Lambda$?)</p>
<p>For the first one has, $R = 2/Q^2$ and $R_{ab} = \frac{1}{Q^2}g_{ab}$ </p>
<p>For the second one has $R = - \frac{2\Lambda}{3}$ and $R_{ab} = -\frac{\Lambda}{3}g_{ab}$</p>
<p>Now I am not sure how to consistently define $L>0$ for these two metrics using the same formula for both!</p> | g5501 | [
-0.05263931304216385,
0.0032136524096131325,
-0.03559095039963722,
0.01634884811937809,
0.049278486520051956,
0.018157128244638443,
0.0663752481341362,
-0.021378450095653534,
-0.044477708637714386,
-0.011994700878858566,
-0.0024229739792644978,
0.08883045613765717,
0.08396169543266296,
-0.05666765198111534,
0.03278080001473427,
0.01329690869897604,
0.014407557435333729,
-0.03669963404536247,
0.019066233187913895,
-0.012892056256532669,
-0.07359203696250916,
0.021998420357704163,
0.028592579066753387,
-0.027210205793380737,
0.013435675762593746,
-0.039262548089027405,
0.049654290080070496,
0.01891065202653408,
-0.07080154865980148,
-0.04679902642965317,
0.044271357357501984,
0.09627155214548111,
0.0620572455227375,
-0.037146084010601044,
0.0077202171087265015,
-0.04939679428935051,
0.027321042492985725,
-0.008753539994359016,
0.0016933702863752842,
0.024069786071777344,
0.05122790485620499,
-0.018765004351735115,
0.034525174647569656,
0.010129145346581936,
0.019636409357190132,
-0.016206029802560806,
-0.03877789154648781,
0.04832049831748009,
0.03199797868728638,
-0.001236027106642723,
0.006113906856626272,
0.015129485167562962,
0.011704239062964916,
0.008591658435761929,
-0.05394554138183594,
0.05122985318303108,
0.018077582120895386,
-0.004296205472201109,
0.022578278556466103,
0.044147372245788574,
-0.03595731779932976,
-0.004061331041157246,
0.010003911331295967,
0.037720367312431335,
0.022709164768457413,
-0.010828672908246517,
0.020915096625685692,
-0.05251764506101608,
0.06858182698488235,
-0.051442380994558334,
-0.015418022871017456,
-0.022316616028547287,
0.08303868770599365,
-0.03307729586958885,
-0.011735878884792328,
0.036924585700035095,
0.034442149102687836,
0.0222014170140028,
-0.025492560118436813,
-0.005122943315654993,
0.012973331846296787,
-0.02163904905319214,
0.042369294911623,
0.04865245521068573,
0.004289258737117052,
0.012121695093810558,
-0.01742316223680973,
0.016565637663006783,
0.008888162672519684,
0.0677868202328682,
0.021826617419719696,
-0.050901126116514206,
-0.00914947222918272,
0.06267447024583817,
0.004439993295818567,
-0.003628121456131339,
-0.04548199474811554,
-0.02974948100745678,
-0.05832836404442787,
-0.008397108875215054,
-0.03160891681909561,
0.06123454123735428,
0.04129591956734657,
0.042439792305231094,
-0.0033587636426091194,
-0.017553433775901794,
0.017818065360188484,
0.019211476668715477,
-0.018877733498811722,
-0.07809863984584808,
-0.02998470515012741,
0.022522253915667534,
0.0058616530150175095,
-0.047725874930620193,
-0.028810668736696243,
-0.030889859423041344,
0.06102797016501427,
-0.019288113340735435,
-0.003910512663424015,
0.020647792145609856,
-0.012867436744272709,
0.01066572405397892,
0.08410828560590744,
0.024217018857598305,
0.01764732412993908,
-0.014737891033291817,
0.008606786839663982,
0.01937847025692463,
0.0481242761015892,
-0.044682689011096954,
0.06997611373662949,
0.00859428197145462,
0.008860132656991482,
0.01074809767305851,
-0.026044145226478577,
0.03684287145733833,
0.0012228448176756501,
0.0038009081035852432,
-0.02726888284087181,
-0.04119349271059036,
-0.02143249288201332,
0.00004386943328427151,
0.0013331405352801085,
-0.02767893299460411,
-0.10198406875133514,
-0.0006523645133711398,
0.010161740705370903,
-0.07329262048006058,
0.04854452610015869,
-0.00810249149799347,
0.023798706009984016,
0.06526060402393341,
-0.05590827390551567,
0.04312900826334953,
-0.02109929546713829,
0.028140544891357422,
-0.03761010617017746,
-0.010600363835692406,
0.024393919855356216,
0.020140381529927254,
0.058976203203201294,
0.003044488839805126,
0.05375174432992935,
0.041400324553251266,
-0.02649077959358692,
0.025216981768608093,
-0.006195880938321352,
0.008010005578398705,
0.011706098914146423,
-0.06714462488889694,
-0.04917699843645096,
0.0071138422936201096,
0.01699938252568245,
-0.005815101787447929,
0.04088803753256798,
0.013436411507427692,
-0.03311530873179436,
0.029865993186831474,
0.020805614069104195,
0.002992977388203144,
-0.057923175394535065,
-0.04264555871486664,
0.006076036486774683,
-0.013143469579517841,
-0.008304632268846035,
-0.013554456643760204,
-0.011298645287752151,
-0.011593741364777088,
-0.06662040948867798,
0.04163726791739464,
-0.04548314958810806,
0.024135597050189972,
0.020978061482310295,
0.06561890989542007,
-0.008451971225440502,
0.04945683106780052,
-0.018644267693161964,
-0.0822804644703865,
0.0025458154268562794,
0.07437659800052643,
0.011516142636537552,
-0.015764161944389343,
0.02347422204911709,
-0.008780631236732006,
-0.018677962943911552,
0.004499262664467096,
-0.01449668500572443,
-0.012683389708399773,
0.06904853135347366,
-0.015505412593483925,
0.01491645909845829,
-0.08922700583934784,
-0.003785810898989439,
-0.024706047028303146,
0.0144192511215806,
-0.05277667194604874,
-0.016534531489014626,
-0.0022494960576295853,
-0.020497631281614304,
0.022103166207671165,
-0.0005028221057727933,
0.014694073237478733,
0.048163626343011856,
-0.03701699897646904,
0.013519637286663055,
0.03908528760075569,
-0.020110664889216423,
-0.019564231857657433,
0.03645668923854828,
0.007968265563249588,
0.0032467495184391737,
-0.058493614196777344,
0.03374708816409111,
0.030314629897475243,
0.027105480432510376,
-0.05413224175572395,
0.011434787884354591,
0.009689558297395706,
0.0780002772808075,
0.0017760853515937924,
-0.02365056239068508,
0.032520219683647156,
-0.018868463113904,
0.026639271527528763,
0.041693322360515594,
0.03642599284648895,
0.011387340724468231,
0.005098240450024605,
-0.01562410593032837,
0.035691507160663605,
0.00560198025777936,
0.006958318408578634,
-0.0025100535713136196,
-0.02502291277050972,
0.013124668039381504,
-0.03187011182308197,
0.005553901195526123,
-0.012918932363390923,
-0.03672589361667633,
0.0059075728058815,
-0.0184326171875,
-0.026609349995851517,
0.008338878862559795,
0.05550865828990936,
-0.018332192674279213,
0.03020552545785904,
0.030924469232559204,
0.01748507097363472,
0.08928055316209793,
0.0079190069809556,
0.014645172283053398,
-0.0006792867789044976,
0.0109718581661582,
0.008652407675981522,
-0.05325157940387726,
-0.03777868673205376,
-0.04212797060608864,
-0.04135817661881447,
-0.0381413996219635,
0.019157059490680695,
0.04580899327993393,
0.0007349230581894517,
-0.029247893020510674,
-0.003998426254838705,
0.03259812667965889,
-0.02886113151907921,
-0.0376402921974659,
0.05760040134191513,
0.0017990072956308722,
0.05674389377236366,
-0.005044678691774607,
0.03250722587108612,
-0.024653755128383636,
-0.04429710656404495,
-0.04695556312799454,
-0.03692980110645294,
-0.08395525813102722,
0.008753707632422447,
-0.014375612139701843,
0.00449750991538167,
0.032711755484342575,
-0.0238084327429533,
0.024940524250268936,
-0.049093786627054214,
-0.015223917551338673,
-0.019057370722293854,
-0.02947441302239895,
-0.09902846813201904,
0.04005414992570877,
-0.013832349330186844,
-0.026404425501823425,
0.010015053674578667,
0.0015133358538150787,
-0.03799642249941826,
0.006857444532215595,
0.0018793640192598104,
-0.012754091992974281,
-0.05829661712050438,
-0.042086411267519,
-0.011345745995640755,
-0.017313027754426003,
-0.05376100540161133,
-0.04089561104774475,
0.040556930005550385,
0.004961952567100525,
0.012338240630924702,
-0.012550179846584797,
0.01252838782966137,
-0.04943999648094177,
-0.033529698848724365,
0.012827029451727867,
0.010999683290719986,
0.019533326849341393,
0.01815112866461277,
-0.004254176747053862,
-0.004122706595808268,
-0.042758941650390625,
0.042796894907951355,
0.03621525689959526,
-0.02883049286901951,
-0.02975630946457386,
0.03905196860432625,
0.016678744927048683,
0.02433422952890396,
0.009049358777701855,
0.009366902522742748,
0.030962584540247917,
0.054434407502412796,
-0.031370747834444046,
-0.014918248169124126,
-0.0403929241001606,
0.005382823292165995,
0.0004058819613419473,
-0.023702898994088173,
-0.017868222668766975,
0.0011950889602303505,
0.07240024209022522,
0.05350879207253456,
0.013920415192842484,
-0.04795530438423157,
0.00685889134183526,
0.00674394378438592,
0.005185125395655632,
-0.003264394123107195,
0.008012727834284306,
-0.047107357531785965,
0.03468502685427666,
0.00676559517160058,
-0.030384588986635208,
0.04004758596420288,
0.11106055974960327,
0.03641233593225479,
-0.010032442398369312,
0.04313565045595169,
-0.036767955869436264,
-0.0028917216695845127,
0.02787068858742714,
-0.05598802864551544,
0.0006382851279340684,
-0.0026582907885313034,
0.0032977676019072533,
-0.013679196126759052,
-0.019436795264482498,
-0.04825097694993019,
-0.030098270624876022,
-0.029833685606718063,
-0.0033958496060222387,
-0.01756904646754265,
-0.006479869596660137,
-0.06758995354175568,
-0.047310952097177505,
-0.023407330736517906,
-0.022513186559081078,
0.013105407357215881,
0.017333105206489563,
-0.0411088652908802,
0.06017240136861801,
0.06152740493416786,
-0.045288730412721634,
0.032462555915117264,
-0.05260099843144417,
0.03860611468553543,
0.029407914727926254,
-0.011921333149075508,
-0.0562991201877594,
-0.014032687060534954,
-0.0605340301990509,
-0.02087651565670967,
0.03754168748855591,
0.010083181783556938,
-0.004337966442108154,
0.0027333495672792196,
0.0637480616569519,
-0.04069195315241814,
0.05476711317896843,
0.010125714354217052,
-0.04012308269739151,
-0.02317376248538494,
-0.006354086101055145,
0.04651165381073952,
-0.018267042934894562,
-0.005707820411771536,
0.045558732002973557,
-0.04085379093885422,
0.010965300723910332,
0.039553407579660416,
0.07905647158622742,
0.01994355209171772,
-0.03896700218319893,
0.009024991653859615,
-0.023341741412878036,
-0.009819772094488144,
-0.03818943351507187,
0.0017865264089778066,
-0.03761371225118637,
0.07223418354988098,
-0.040873028337955475,
0.02346459962427616,
0.0042162565514445305,
-0.037164729088544846,
0.061223480850458145,
-0.013550003059208393,
0.024100616574287415,
-0.08810165524482727,
0.0005171385710127652,
0.021100761368870735,
0.006797826383262873,
-0.01572594977915287,
0.05441058799624443,
0.01669134944677353,
0.007467941846698523,
0.026231152936816216,
0.06705872714519501,
-0.06751619279384613,
0.02739466354250908,
-0.01795366406440735,
0.03809405490756035,
0.039752308279275894,
0.041191764175891876,
-0.04918564856052399,
-0.010312434285879135,
-0.016101444140076637,
0.049621351063251495,
-0.01096922904253006,
0.06258084625005722,
-0.03827276825904846,
0.024574311450123787,
0.03321448713541031,
-0.0033901967108249664,
-0.029793180525302887,
0.006716751493513584,
-0.0020031894091516733,
0.010218133218586445,
-0.029567401856184006,
0.006503441371023655,
0.03855390474200249,
-0.030254025012254715,
0.014345438219606876,
-0.04969135299324989,
-0.044100694358348846,
0.004516643937677145,
0.02854202128946781,
-0.03167584910988808,
-0.0000632304436294362,
0.02587270550429821,
-0.04965369403362274,
0.0013089339481666684,
-0.05716285482048988,
0.015593319199979305,
0.030957750976085663,
0.017398498952388763,
0.004550357349216938,
0.021656129509210587,
0.03446803241968155,
-0.06431498378515244,
0.1100902333855629,
-0.03176787868142128,
0.014296958222985268,
0.0057629989460110664,
-0.04276479035615921,
-0.0021729683503508568,
0.012629133649170399,
0.02711178921163082,
-0.053299691528081894,
-0.016489475965499878,
0.0504775270819664,
0.06570301204919815,
0.005347868427634239,
0.017939947545528412,
0.014946096576750278,
-0.016135061159729958,
-0.004385516978800297,
0.018190372735261917,
0.013535039499402046,
0.007425916381180286,
0.005889053922146559,
0.04872531071305275,
0.0640321895480156,
0.011618178337812424,
-0.012786638922989368,
-0.01826842688024044,
-0.06682848185300827,
0.0478893518447876,
-0.01807727850973606,
0.03635689243674278,
0.003317627590149641,
-0.02061321586370468,
-0.048958972096443176,
0.03891461715102196,
0.014726664870977402,
-0.021041175350546837,
0.02516169846057892,
-0.007744019851088524,
0.017455631867051125,
0.05239127576351166,
-0.03716100752353668,
0.004659807309508324,
0.00019972817972302437,
0.05502154678106308,
-0.019448623061180115,
-0.029815172776579857,
-0.00019537033222150058,
-0.014591928571462631,
0.07033120840787888,
-0.11253193020820618,
-0.03033728338778019,
0.07308728247880936,
-0.028875671327114105,
-0.04495470970869064,
-0.07025015354156494,
0.037090200930833817,
-0.0027911579236388206,
-0.01222039945423603,
0.01245599240064621,
0.008133956231176853,
0.023747257888317108,
0.03740837424993515,
-0.025301652029156685,
-0.020010439679026604,
-0.03039921075105667,
0.012218581512570381,
-0.0350923053920269,
0.008422642946243286,
-0.016588306054472923,
-0.017365755513310432,
-0.020425844937562943,
0.031133901327848434,
-0.058747757226228714,
0.046181876212358475,
0.007432849146425724,
0.012426228262484074,
0.014700244180858135,
0.00021950621157884598,
-0.04257366806268692,
0.05911710485816002,
0.06336825340986252,
-0.014368398115038872,
-0.0652133971452713,
-0.026564516127109528,
0.00822421070188284,
-0.0009687361307442188,
0.00428138067945838,
0.047902531921863556,
-0.06087145581841469,
-0.0415477529168129,
0.04525380581617355,
-0.015548854134976864,
-0.037663619965314865,
0.04361722618341446,
-0.045936133712530136,
-0.017613403499126434,
-0.03365828096866608,
-0.0525747574865818,
-0.03685161843895912,
-0.05963033810257912,
0.00014691977412439883,
-0.019412659108638763,
-0.036570481956005096,
-0.029302377253770828,
0.009079374372959137,
-0.003855072194710374,
0.039350561797618866,
-0.022748202085494995,
-0.024338675662875175,
0.037813764065504074,
-0.03404907509684563,
-0.030264252796769142,
-0.003655680688098073,
0.0037980142515152693,
0.027659498155117035,
-0.0418054461479187,
0.05049164220690727,
0.0008280977490358055,
0.06107071787118912,
0.016018131747841835,
-0.001973377075046301,
0.000734484288841486,
0.022298837080597878,
-0.05713650956749916,
-0.001896404311992228,
0.07812690734863281,
0.01002548262476921,
0.012029782868921757,
-0.015468709170818329,
-0.0001796231954358518,
0.031413283199071884,
0.035630885511636734,
0.011186240240931511,
-0.026489244773983955,
0.03485947102308273,
-0.006384354084730148,
-0.0038989402819424868,
-0.04316224530339241,
-0.05386929214000702,
0.018308373168110847,
-0.03728444501757622,
-0.018488314002752304,
0.04839428514242172,
0.058193862438201904,
0.012319433502852917,
0.02190299518406391,
0.03111557476222515,
0.05308140441775322,
-0.027809515595436096,
0.0007079550414346159,
0.0040306206792593,
0.01950324885547161,
0.03402740880846977,
-0.09770357608795166,
0.0626106709241867,
0.021015826612710953,
-0.03760513663291931,
0.009600257501006126,
0.00022134424943942577,
-0.03790418431162834,
-0.020145388320088387,
-0.09005019813776016,
0.05060458928346634,
-0.05379264056682587,
-0.054503850638866425,
0.02580288238823414,
-0.0214749313890934,
-0.005847068037837744,
0.027990344911813736,
-0.06454605609178543,
0.03719387575984001,
-0.0014282710617408156,
-0.006737000308930874,
0.02766716293990612,
0.015520657412707806,
0.01986073888838291,
0.004548300057649612,
-0.002149403328076005,
-0.016187358647584915,
0.029355641454458237,
0.003000780940055847,
-0.045424267649650574,
0.016065115109086037,
0.018324360251426697,
0.027396321296691895,
0.014935523271560669,
-0.03217856585979462,
0.0028345254249870777,
-0.026234107092022896,
-0.07065305858850479,
0.013856247067451477,
0.029498225077986717,
-0.08716762065887451,
0.008183499798178673,
0.0043511902913451195,
-0.011843547224998474,
0.0577143169939518,
-0.016450410708785057,
0.03402451425790787,
0.018535874783992767,
-0.07089745253324509,
-0.010514006949961185,
0.06856638938188553,
-0.0381317213177681,
-0.012514671310782433,
-0.012499971315264702,
-0.003288491629064083,
-0.052740372717380524,
0.035564783960580826,
-0.0002655792632140219,
0.02919333055615425,
-0.037418246269226074,
0.005112862214446068,
-0.00154836883302778,
-0.010290254838764668,
0.0643690675497055,
-0.035517618060112,
-0.021240435540676117,
-0.0017310406547039747,
0.01428565476089716,
-0.05433302000164986,
-0.03962530195713043,
-0.002329448703676462,
0.040694043040275574,
-0.04181439056992531,
-0.02694164775311947,
-0.045411840081214905,
0.024095920845866203,
-0.09631960839033127,
-0.0713687539100647,
-0.011635753326117992,
-0.03658967837691307,
-0.013676953501999378,
-0.023722656071186066,
0.0493399053812027,
-0.054263610392808914,
-0.006577629130333662,
-0.03269282728433609,
0.02281438373029232,
-0.015420576557517052,
0.11624790728092194,
-0.01779998652637005,
-0.023180995136499405,
0.048228684812784195,
-0.025586623698472977,
-0.012385670095682144,
-0.00981426052749157,
-0.006191545631736517,
0.06166814640164375,
-0.026167811825871468,
-0.03813651576638222,
0.019719863310456276,
0.00545224454253912,
0.03473123908042908,
-0.03282715752720833,
0.008341658860445023,
0.06531190872192383,
0.00733051635324955,
-0.0056444318033754826,
0.04893306642770767,
-0.007427034433931112,
-0.042214978486299515,
0.017776453867554665,
0.06996359676122665,
-0.02713867649435997,
-0.0026882458478212357,
-0.01740262284874916,
-0.05713548883795738,
0.006007976830005646,
0.02325189672410488,
-0.004410582594573498,
-0.04667520895600319,
0.044670265167951584
] |
<p>What's the conserved quantity corresponding to the generator of conformal transformations? </p> | g5502 | [
-0.0321386344730854,
0.03358784317970276,
-0.017995893955230713,
-0.041721172630786896,
0.06768693774938583,
0.0064496542327106,
0.018360629677772522,
0.05149981006979942,
-0.013657740317285061,
-0.02128499373793602,
-0.05715228617191315,
0.0034016708377748728,
0.029655171558260918,
-0.01983768120408058,
0.004265123978257179,
0.011606255546212196,
0.04162883013486862,
0.018509510904550552,
0.017337044700980186,
0.011037576012313366,
-0.07949800789356232,
-0.05633228272199631,
-0.015369068831205368,
-0.02598540671169758,
0.033983077853918076,
0.010460006073117256,
0.010938533581793308,
-0.02693348191678524,
-0.055392734706401825,
-0.0440656803548336,
0.06845531612634659,
0.04491274058818817,
0.07367191463708878,
-0.04681847244501114,
-0.03989650309085846,
0.0017156504327431321,
0.0034668759908527136,
-0.005069029051810503,
0.1176711767911911,
-0.0033127176575362682,
-0.0026585839223116636,
0.016960404813289642,
-0.009437899105250835,
0.007977114990353584,
-0.0008106420864351094,
0.01087636686861515,
-0.008230794221162796,
-0.015673108398914337,
-0.00636280607432127,
-0.04438150301575661,
0.02968592382967472,
0.052551474422216415,
0.02195809781551361,
0.030202900990843773,
-0.002072301460430026,
0.060272250324487686,
-0.05067507550120354,
-0.0560758151113987,
-0.004424809943884611,
0.05087672919034958,
-0.006100345402956009,
-0.035759586840867996,
0.006536444183439016,
0.016548728570342064,
0.07631233334541321,
-0.0543227382004261,
-0.054517630487680435,
0.05151517689228058,
-0.027826333418488503,
0.019252754747867584,
0.00013243569992482662,
0.010792568325996399,
0.022926809266209602,
0.050241488963365555,
-0.00031642199610359967,
0.02724694088101387,
0.035873014479875565,
-0.03169815242290497,
-0.02213059924542904,
-0.032885707914829254,
-0.06026024371385574,
-0.018549656495451927,
0.023708254098892212,
0.007266663946211338,
0.08715156465768814,
0.001278004259802401,
0.01830802671611309,
0.07657293975353241,
-0.037044819444417953,
-0.0018275005277246237,
0.023617984727025032,
-0.05657195299863815,
0.022425340488553047,
-0.0527014434337616,
0.024975255131721497,
-0.008912991732358932,
0.00827081874012947,
0.009208114817738533,
0.00851418636739254,
0.0035371154081076384,
-0.008342034183442593,
0.005751138553023338,
-0.021326441317796707,
0.026168063282966614,
0.03243996948003769,
0.03333190828561783,
0.052637021988630295,
-0.06382498890161514,
0.025985313579440117,
-0.05405999347567558,
0.020319048315286636,
0.011654822155833244,
-0.02142925001680851,
0.04287000373005867,
-0.07096315920352936,
-0.02936870977282524,
0.004202166572213173,
-0.008151233196258545,
0.05244114622473717,
0.04391973465681076,
0.027359051629900932,
-0.08156348764896393,
0.05240028724074364,
0.04603361710906029,
0.03694571927189827,
-0.00982634723186493,
-0.027166541665792465,
0.038119327276945114,
0.05792912095785141,
0.007017901632934809,
0.030871115624904633,
-0.03315192088484764,
-0.009726700372993946,
-0.03423919901251793,
0.013641768135130405,
-0.00624912278726697,
0.02107093669474125,
0.0259763915091753,
0.01730131171643734,
0.026768984273076057,
-0.06221309304237366,
-0.0454522967338562,
0.02406056970357895,
-0.04133513197302818,
-0.006030460353940725,
-0.054212458431720734,
0.049540918320417404,
-0.040630750358104706,
0.0645267441868782,
-0.03241267427802086,
0.03665417432785034,
0.03426889702677727,
0.03120717592537403,
-0.06340190023183823,
0.046399809420108795,
-0.01333562284708023,
0.030908433720469475,
-0.021275460720062256,
-0.06299909204244614,
0.026378776878118515,
0.05452701449394226,
-0.01643589697778225,
-0.04393642768263817,
0.0022741216234862804,
-0.03959670662879944,
-0.05515213683247566,
0.031970348209142685,
-0.04112221300601959,
-0.09131832420825958,
-0.004904475063085556,
-0.03525802120566368,
0.011945633217692375,
0.06696067005395889,
0.02694273553788662,
-0.015013208612799644,
0.02176610939204693,
-0.08439908176660538,
-0.022226296365261078,
0.06856807321310043,
-0.014768389984965324,
0.022128146141767502,
-0.034032877534627914,
0.02932346798479557,
0.021961765363812447,
0.017969869077205658,
-0.004530952777713537,
-0.02429409883916378,
-0.022647300735116005,
-0.06156885251402855,
-0.01227364782243967,
0.017351657152175903,
0.04656662791967392,
-0.033431876450777054,
-0.004685562569648027,
-0.03781886771321297,
0.047055281698703766,
0.016132622957229614,
-0.037773989140987396,
-0.03567041456699371,
0.015063810162246227,
0.008982490748167038,
-0.0026192935183644295,
0.06466249376535416,
-0.015537983737885952,
-0.02775382623076439,
0.02795972302556038,
0.012203320860862732,
-0.011814743280410767,
-0.018368028104305267,
-0.010980368591845036,
0.02117202803492546,
0.003938015084713697,
-0.012550965882837772,
-0.04811474680900574,
-0.008790654130280018,
-0.033697664737701416,
-0.030827069655060768,
0.02621396817266941,
-0.032081376761198044,
0.02456669509410858,
0.00043304034625180066,
0.003435551654547453,
0.031464628875255585,
0.04120387136936188,
-0.05340335890650749,
0.04797060787677765,
-0.01927047222852707,
-0.030505990609526634,
0.04055996239185333,
0.015351514331996441,
-0.027453400194644928,
0.04553240165114403,
-0.0399954691529274,
-0.0075493440963327885,
-0.03950493782758713,
0.04158418998122215,
-0.043016593903303146,
0.02475629560649395,
0.03015533648431301,
-0.009002468548715115,
0.060300491750240326,
0.03429128974676132,
-0.05814853683114052,
-0.009146188385784626,
0.02165277488529682,
0.030160222202539444,
0.013040532357990742,
0.0003852174268104136,
0.019367149099707603,
0.03712347149848938,
0.000052962997870054096,
-0.014808711595833302,
-0.020276403054594994,
-0.016052639111876488,
-0.021627437323331833,
-0.015185048803687096,
0.038916878402233124,
-0.012315463274717331,
-0.02430814690887928,
-0.017061758786439896,
0.036174144595861435,
-0.07250913977622986,
-0.014883605763316154,
0.029573945328593254,
-0.019826704636216164,
-0.04915574565529823,
0.034670375287532806,
0.008260704576969147,
0.009590777568519115,
-0.005946303252130747,
-0.05313751474022865,
0.08135588467121124,
-0.00841024424880743,
0.030914152041077614,
-0.061343368142843246,
-0.016396414488554,
-0.012170280329883099,
0.0007997071370482445,
-0.04625885188579559,
-0.009881659410893917,
0.03452247008681297,
0.03318646550178528,
0.007942122407257557,
-0.007456763181835413,
0.008480542339384556,
-0.02567369118332863,
-0.03685211017727852,
-0.040037404745817184,
-0.022448044270277023,
0.08024858683347702,
-0.04573088139295578,
-0.004711144138127565,
0.04000682756304741,
0.02557973377406597,
0.004322795197367668,
-0.016979679465293884,
0.00790159311145544,
-0.01495048962533474,
0.0066040619276463985,
0.02902095392346382,
0.030276678502559662,
-0.006009700242429972,
0.02496602199971676,
0.024459924548864365,
0.05080912634730339,
0.024948451668024063,
-0.019450021907687187,
-0.02357870526611805,
0.051933277398347855,
0.0641619935631752,
-0.08972682803869247,
-0.022135881707072258,
-0.02245352417230606,
-0.014260436408221722,
-0.012857607565820217,
-0.008523095399141312,
0.004291288089007139,
-0.029881494119763374,
-0.0369856096804142,
-0.047315891832113266,
0.02061159722507,
-0.05826874449849129,
0.0811082124710083,
-0.01158024650067091,
0.024988984689116478,
0.02043118141591549,
-0.05194184556603432,
0.02232762798666954,
0.016663892194628716,
-0.08052041381597519,
0.011695697903633118,
0.0015404662117362022,
0.015890296548604965,
0.005539232399314642,
-0.0425814650952816,
-0.038553547114133835,
-0.07264113426208496,
0.008701506070792675,
0.0708199217915535,
-0.07384195178747177,
-0.010463317856192589,
0.023547256365418434,
0.03836454451084137,
-0.01816641166806221,
0.027526970952749252,
0.02988775447010994,
-0.02442897856235504,
-0.03169029951095581,
0.014222747646272182,
-0.030804667621850967,
-0.03252134844660759,
-0.029220039024949074,
0.003655517240986228,
-0.0724291279911995,
0.0027214859146624804,
0.04324166104197502,
-0.047967374324798584,
0.021886184811592102,
-0.04684801399707794,
0.05363038554787636,
0.009521917439997196,
-0.054040633141994476,
0.0045389411970973015,
0.04545202478766441,
0.010971159674227238,
0.03793305158615112,
-0.09583532810211182,
-0.047975849360227585,
0.05171848461031914,
0.04135735705494881,
0.011206756345927715,
-0.002615307690575719,
-0.005099587608128786,
0.0037557485047727823,
-0.0125747574493289,
-0.023687396198511124,
-0.012711410410702229,
0.018200654536485672,
-0.07357639074325562,
-0.03176870569586754,
0.0015958405565470457,
-0.028120839968323708,
0.015833403915166855,
-0.012715020217001438,
0.014596299268305302,
0.018714308738708496,
-0.02600795216858387,
0.01760431006550789,
0.014728174544870853,
0.005328094121068716,
0.027497973293066025,
0.02861633151769638,
0.005075835157185793,
-0.06541110575199127,
0.0035483255051076412,
-0.012334893457591534,
0.0234865490347147,
0.028567010536789894,
0.006567976903170347,
0.005856132600456476,
-0.016464199870824814,
0.041012849658727646,
-0.049211982637643814,
-0.043483078479766846,
-0.026399167254567146,
-0.00669280206784606,
0.04464235156774521,
0.005666191224008799,
0.0642835795879364,
-0.029600979760289192,
-0.040961120277643204,
0.013412204571068287,
0.02937554195523262,
-0.02541825734078884,
-0.021608682349324226,
0.04710846766829491,
-0.04591745138168335,
-0.026517698541283607,
0.04162647947669029,
-0.02138162963092327,
0.024619337171316147,
0.000849774747621268,
0.0020367479883134365,
0.05224951356649399,
0.04379299283027649,
0.0819002017378807,
0.04863325133919716,
-0.03650643676519394,
-0.014396713115274906,
-0.08606082201004028,
0.025444215163588524,
0.061711836606264114,
0.02326338365674019,
0.031066376715898514,
-0.06345059722661972,
0.04816069081425667,
-0.060722507536411285,
0.02485581673681736,
-0.0249948650598526,
0.045649029314517975,
0.06313783675432205,
0.005431798752397299,
0.0311698280274868,
-0.016239406540989876,
-0.010532159358263016,
-0.005923373159021139,
0.0143237030133605,
-0.0709281712770462,
0.008730361238121986,
-0.09381396323442459,
-0.01694648154079914,
-0.0005771525902673602,
-0.010378124192357063,
0.008076301775872707,
0.04526284709572792,
0.07148910313844681,
-0.013423587195575237,
-0.019059238955378532,
0.012044740840792656,
0.015007087029516697,
-0.06340193748474121,
0.01291013415902853,
-0.030400391668081284,
0.018898941576480865,
-0.007839023135602474,
0.02417406626045704,
-0.010726077482104301,
0.05838334560394287,
0.017291836440563202,
-0.0008092772914096713,
0.055984046310186386,
-0.028982512652873993,
-0.04938875883817673,
-0.014826655387878418,
0.02910699136555195,
0.051408715546131134,
0.05367213860154152,
0.004493268672376871,
-0.04678650200366974,
-0.028282267972826958,
-0.05994061753153801,
0.05273648723959923,
-0.05145620182156563,
0.03056979551911354,
0.037271469831466675,
0.04681932553648949,
-0.007895308546721935,
-0.020221292972564697,
0.000030662802601000294,
-0.07856399565935135,
0.008671639487147331,
0.03137302026152611,
0.05260678380727768,
0.029390404000878334,
0.03886618837714195,
0.0015638266922906041,
-0.01404258981347084,
-0.02840244770050049,
0.004712734371423721,
-0.007327430881559849,
-0.039462048560380936,
0.06625276058912277,
0.002973609371110797,
0.039742838591337204,
-0.00997020211070776,
0.07511771470308304,
0.05946165323257446,
0.061831094324588776,
0.006106673739850521,
-0.03567405045032501,
-0.033000607043504715,
-0.031246600672602654,
-0.019749052822589874,
-0.02140752226114273,
0.022281024605035782,
0.03315836936235428,
-0.012559697031974792,
-0.028856638818979263,
-0.025547904893755913,
-0.04257582500576973,
0.025765690952539444,
0.012104923836886883,
0.01198552455753088,
-0.0026108534075319767,
-0.02917873114347458,
0.05063200742006302,
-0.047792986035346985,
-0.03414302319288254,
0.0498485192656517,
-0.002388062421232462,
0.06027291342616081,
-0.07793571054935455,
-0.055659789592027664,
0.0036681576166301966,
0.006021624431014061,
0.00932803563773632,
-0.04536917433142662,
0.0069643971510231495,
0.02806614525616169,
0.0006647377158515155,
-0.0333394892513752,
0.012742026709020138,
-0.002393210306763649,
0.025120334699749947,
0.001184762455523014,
0.007365264929831028,
-0.048733968287706375,
0.0025509821716696024,
-0.0315726064145565,
-0.01633324846625328,
0.0029060575179755688,
0.013719171285629272,
0.008224286139011383,
-0.04696481302380562,
0.05312039330601692,
0.03705424815416336,
0.02962154522538185,
-0.03735475614666939,
0.003961590584367514,
0.0013005418004468083,
-0.00800581555813551,
0.0363113097846508,
0.03312421590089798,
0.009653116576373577,
-0.016458244994282722,
-0.02327893115580082,
0.00946455355733633,
0.002971908077597618,
0.038767505437135696,
0.023670757189393044,
-0.011320836842060089,
0.043708380311727524,
0.011672177352011204,
0.016325389966368675,
-0.01430568564683199,
-0.030715199187397957,
-0.04369169846177101,
-0.05280349776148796,
-0.03203928843140602,
0.000388262327760458,
0.02691037207841873,
-0.03705747053027153,
0.007028880063444376,
-0.10579153895378113,
-0.10136587172746658,
0.000307668000459671,
-0.01784408837556839,
-0.06899109482765198,
0.00709550129249692,
0.04112511873245239,
-0.03356185182929039,
0.02639092691242695,
0.008837705478072166,
0.07638754695653915,
0.07070129364728928,
0.02721310220658779,
0.007632321212440729,
-0.013853509910404682,
0.011173047125339508,
-0.03941762074828148,
0.008455701172351837,
0.03518013283610344,
0.047398973256349564,
-0.050143759697675705,
0.018080443143844604,
0.05757227912545204,
-0.10192985832691193,
0.017495829612016678,
-0.002905908040702343,
0.04330082982778549,
-0.012159394100308418,
-0.014729867689311504,
-0.05148656293749809,
0.0006375009543262422,
-0.033875469118356705,
-0.03201554715633392,
0.024249225854873657,
0.051348283886909485,
-0.02672787569463253,
0.048448141664266586,
0.04115566238760948,
-0.0311704371124506,
-0.020313797518610954,
-0.026013869792222977,
0.039201103150844574,
0.018968800082802773,
-0.018030734732747078,
-0.022584594786167145,
0.03502213582396507,
-0.030378930270671844,
-0.0602414533495903,
0.0761263370513916,
-0.07132160663604736,
0.03581893816590309,
-0.0043957652524113655,
0.049406979233026505,
-0.08916106820106506,
0.02463889680802822,
0.057912927120923996,
0.02270822785794735,
0.013038953766226768,
-0.024455124512314796,
0.04433717951178551,
0.015953917056322098,
-0.055116645991802216,
0.007627988234162331,
-0.038111362606287,
-0.02648535557091236,
-0.05925753340125084,
0.0049515459686517715,
-0.011789582669734955,
0.05402909591794014,
-0.039851896464824677,
0.018047496676445007,
-0.03725719451904297,
-0.03969738632440567,
0.04963543638586998,
-0.00606575096026063,
-0.011450813151896,
-0.0024333717301487923,
0.010253692977130413,
-0.08719722926616669,
0.07122593373060226,
0.0003285151906311512,
-0.02838391624391079,
-0.001421082648448646,
-0.012627802789211273,
-0.03913789987564087,
0.0583113394677639,
-0.029069766402244568,
-0.020516514778137207,
-0.02425466850399971,
-0.02510126307606697,
0.013460169546306133,
-0.009164668619632721,
-0.023212388157844543,
0.03124435991048813,
0.011478956788778305,
0.020459145307540894,
0.03743276372551918,
-0.04524762183427811,
0.005061283707618713,
-0.015197958797216415,
-0.024451332166790962,
0.009475360624492168,
0.008926850743591785,
0.009288077242672443,
-0.0012531750835478306,
0.0503501296043396,
0.05876295641064644,
-0.01916453056037426,
0.029239604249596596,
-0.007445523049682379,
-0.00510669918730855,
-0.036187224090099335,
0.008795658126473427,
-0.007410399150103331,
-0.027744730934500694,
-0.0007032714784145355,
0.0015843004221096635,
0.06365946680307388,
-0.0028818880673497915,
0.02047410048544407,
0.007986684329807758,
0.019624048843979836,
0.000891361094545573,
-0.029533253982663155,
-0.06617021560668945,
0.010714840143918991,
0.0190396960824728,
0.006144816521555185,
-0.019695540890097618,
-0.021950285881757736,
-0.016127968207001686,
0.04264931380748749,
0.031262464821338654,
-0.012451523914933205,
-0.04042111709713936,
0.006534443236887455,
0.03215612471103668,
0.03913712501525879,
0.0011658272705972195,
-0.012564645148813725,
-0.027181917801499367,
0.007302272133529186,
-0.018619390204548836,
-0.018210148438811302,
0.029689976945519447,
-0.013731778599321842,
0.04492062330245972,
-0.07047867029905319,
-0.017490031197667122,
-0.03634919971227646,
0.015579869970679283,
-0.010532150976359844,
-0.01883656531572342,
-0.031126366928219795,
-0.008864871226251125,
-0.008868202567100525,
-0.010472742840647697,
-0.010784277692437172,
-0.02367776818573475,
0.022080207243561745,
-0.03719241917133331,
-0.05431662127375603,
0.0010874707950279117,
-0.004666336812078953,
0.05582476407289505,
0.05090358108282089,
-0.009415891952812672,
0.03370357304811478,
0.01512075774371624,
0.046741362661123276,
0.04884492605924606,
0.059166062623262405,
-0.016110563650727272,
-0.0033308586571365595,
0.048265907913446426,
-0.023240622133016586,
0.03124057874083519,
0.005555090494453907,
0.03519146889448166,
0.01731770485639572,
0.05068955197930336,
-0.060936421155929565,
-0.031143290922045708,
0.0015909118810668588,
0.001971944235265255
] |
<p><strong>Problem</strong>: For a $P,V,T$ system with constant mass,entropy can be considered a function of $U,V$, i.e. $S=S(U,V)$. The goal is to derive the rest of the thermodynamic functions via Legendre transformations.</p>
<p><strong>Attempted answer</strong>:</p>
<p>I start with the 1st law of thermodynamics $dU = TdS - PdV$, which I solve for $dS$: \begin{equation}dS=(1/T)dU+(P/T)dV\end{equation}</p>
<p>Let, $Y\equiv S,C_1\equiv 1/T,X_1\equiv U, C_2\equiv P/T, X_2\equiv V$.</p>
<p>The first Legendre transformation and the associated differential are:</p>
<p>\begin{equation}\widetilde{T1} = Y - C_1 X_1 = S - (1/T)U\end{equation}</p>
<p>\begin{equation}d\widetilde{T1} = dS - (1/T)dU + (1/T^2)UdT = (P/T)dV +(U/T^2)dT\end{equation}</p>
<p>Therefore $\widetilde{T1} = \widetilde{T1}(V,T)$.</p>
<p>Does this seem correct to you ?</p>
<ol>
<li>Do I stop here for $\widetilde{T_1}$ or is there more to do?</li>
<li>What are the natural variables for $\widetilde{T_1}$? I am a little concerned due to the fact that $T$ is intensive variable and if I recollect correctly, the natural variables are always extensive.</li>
</ol> | g5503 | [
-0.02032618597149849,
-0.024156974628567696,
-0.016373995691537857,
-0.03547785058617592,
-0.005107641685754061,
0.0016559651121497154,
0.006769828498363495,
0.03079148568212986,
-0.045672010630369186,
0.038536861538887024,
-0.04385334625840187,
0.008716071955859661,
0.008751505985856056,
-0.029191642999649048,
-0.014962281100451946,
0.03942197933793068,
0.06970446556806564,
0.02594289556145668,
0.057834871113300323,
-0.010573326610028744,
-0.0726047158241272,
0.012256915681064129,
0.014546453021466732,
-0.06036917865276337,
0.0510021448135376,
-0.03045794554054737,
-0.002924403641372919,
0.06539598107337952,
-0.04368048533797264,
0.009449873119592667,
0.005281870719045401,
0.011069835163652897,
0.061989445239305496,
-0.01823854073882103,
0.014608618803322315,
0.028539147228002548,
0.10254628211259842,
-0.042956169694662094,
0.04572857916355133,
-0.013816514052450657,
-0.02729766070842743,
0.040088701993227005,
0.0575583279132843,
0.027313029393553734,
-0.014830761589109898,
0.029059015214443207,
-0.02670004777610302,
-0.011405504308640957,
-0.052205003798007965,
-0.008904943242669106,
0.05615062639117241,
0.02126901037991047,
0.004989496897906065,
-0.010861674323678017,
-0.03238946571946144,
0.06316506117582321,
0.028227271512150764,
-0.016783175989985466,
0.0205011535435915,
0.016883306205272675,
-0.008038485422730446,
-0.05466100201010704,
-0.05878036841750145,
-0.043424125760793686,
0.038710497319698334,
-0.05003630369901657,
0.06582573056221008,
-0.012760406360030174,
0.01407993957400322,
-0.006450154818594456,
-0.039243340492248535,
-0.03467431664466858,
0.06352777779102325,
-0.03783656656742096,
0.0593860037624836,
0.014114731922745705,
0.04971471428871155,
-0.04399968683719635,
-0.008125510066747665,
-0.03260650113224983,
-0.044197067618370056,
0.014937871135771275,
0.05037666857242584,
-0.023529795929789543,
-0.008492166176438332,
-0.013260826468467712,
0.03768974915146828,
0.02462102472782135,
0.013774329796433449,
0.06444051116704941,
-0.00988791137933731,
0.047008439898490906,
0.060010600835084915,
-0.009705021046102047,
-0.0236828476190567,
-0.007911317050457,
-0.006270857993513346,
0.01774521730840206,
0.022269224748015404,
-0.03712109848856926,
-0.009093767032027245,
-0.060505036264657974,
-0.03261805698275566,
-0.014167304150760174,
0.012831568717956543,
-0.021873638033866882,
0.03792233392596245,
-0.028641512617468834,
-0.031243184581398964,
0.00468159094452858,
0.016672685742378235,
-0.08370541036128998,
0.03933890163898468,
0.01071608904749155,
-0.00724841607734561,
-0.019645361229777336,
0.03377021476626396,
-0.013820911757647991,
-0.07231100648641586,
0.01819375529885292,
-0.009418212808668613,
0.028356365859508514,
0.015920083969831467,
0.06410862505435944,
0.01969427429139614,
0.011143636889755726,
-0.019192978739738464,
0.0015187007375061512,
0.03759359195828438,
-0.03548812121152878,
-0.02954147197306156,
0.002768438309431076,
-0.02547609992325306,
-0.006949308793991804,
0.01980711705982685,
0.010625654831528664,
0.002322648884728551,
0.050703395158052444,
-0.00113317696377635,
0.024920806288719177,
0.014708977192640305,
-0.019579889252781868,
0.03277239203453064,
0.019403841346502304,
-0.04253154993057251,
0.019575921818614006,
-0.02024093084037304,
-0.06796476244926453,
-0.02971750684082508,
-0.006327332928776741,
-0.018190832808613777,
0.0374925322830677,
-0.006928616669028997,
-0.008740102872252464,
-0.05213121324777603,
0.0022686643060296774,
0.012780134566128254,
0.026238160207867622,
0.044415585696697235,
-0.02845277450978756,
-0.032756928354501724,
-0.0005484540015459061,
0.014637427404522896,
-0.01792033389210701,
0.02645253762602806,
-0.009627891704440117,
-0.001958772772923112,
-0.028737645596265793,
-0.03007953055202961,
-0.00584598770365119,
-0.07705925405025482,
-0.0007978143985383213,
-0.003832567948848009,
-0.014804498292505741,
-0.014070218428969383,
-0.01394240278750658,
-0.01641913317143917,
-0.008282276801764965,
0.014990968629717827,
-0.0343046560883522,
-0.009161015041172504,
-0.012212470173835754,
0.09801916033029556,
0.014062471687793732,
-0.0017449449514970183,
-0.00005543142469832674,
0.008710616268217564,
0.027548257261514664,
-0.07294707000255585,
0.02416491135954857,
-0.014771406538784504,
0.02699737623333931,
-0.020245930179953575,
0.03951994702219963,
-0.024060083553195,
-0.02771928533911705,
0.058137521147727966,
-0.060987986624240875,
-0.08776286244392395,
-0.04702017083764076,
-0.0060284980572760105,
0.02233232744038105,
0.04691872373223305,
0.020705515518784523,
-0.029913881793618202,
0.003324665129184723,
-0.029212087392807007,
-0.0048177968710660934,
-0.02912159636616707,
0.023145880550146103,
0.008533107116818428,
-0.0517304353415966,
-0.050163913518190384,
0.005044156685471535,
-0.0691361129283905,
-0.08045794814825058,
-0.014731321483850479,
0.049301739782094955,
0.017714908346533775,
0.02364068105816841,
-0.06459364295005798,
0.0477144755423069,
-0.0432828888297081,
0.04299793019890785,
-0.06601830571889877,
0.010867048054933548,
-0.0341460146009922,
-0.031946517527103424,
-0.010705155320465565,
-0.00012027498451061547,
-0.0012066527269780636,
0.05757277086377144,
0.05117492750287056,
-0.020789483562111855,
0.014389251358807087,
0.07056619971990585,
-0.010725628584623337,
-0.000660950317978859,
-0.023074936121702194,
0.022702716290950775,
0.007476295344531536,
-0.05617392435669899,
0.07399064302444458,
0.018065160140395164,
0.03170152008533478,
0.0004463394288904965,
0.004661889281123877,
-0.007064903620630503,
0.016938041895627975,
-0.0384175144135952,
-0.06673761457204819,
0.023056909441947937,
0.019241442903876305,
-0.005365695338696241,
-0.016820980235934258,
-0.026968108490109444,
-0.027853477746248245,
0.004340557847172022,
0.023844772949814796,
-0.04647228866815567,
0.019816352054476738,
0.022051939740777016,
-0.023664144799113274,
0.06822364777326584,
-0.05998548865318298,
0.006276251282542944,
-0.05746523663401604,
0.013910626992583275,
0.015990152955055237,
-0.028010496869683266,
0.02854856289923191,
0.063980333507061,
0.02867431938648224,
0.027825484052300453,
0.010822299867868423,
-0.06460152566432953,
-0.03794962167739868,
0.03171200677752495,
-0.00744756730273366,
-0.005230159964412451,
0.06922047585248947,
0.021040434017777443,
-0.05000834912061691,
-0.009108898229897022,
0.028626741841435432,
-0.05593162402510643,
-0.0009526789071969688,
-0.008847896941006184,
0.033300600945949554,
0.022741133347153664,
-0.0014449129812419415,
0.018477967008948326,
0.024178192019462585,
0.010896943509578705,
-0.04680479317903519,
0.03267795965075493,
0.005530824884772301,
-0.07596790790557861,
-0.011683962307870388,
-0.00834663026034832,
-0.017358403652906418,
-0.02717142179608345,
0.025715433061122894,
0.056005705147981644,
-0.027929214760661125,
-0.0033373197074979544,
-0.016036808490753174,
-0.015724491328001022,
-0.004673427902162075,
-0.008977053686976433,
-0.00850650854408741,
-0.005997461266815662,
-0.0021149078384041786,
-0.013321413658559322,
0.030789891257882118,
0.013311278074979782,
-0.011795654892921448,
-0.06581158190965652,
0.06366109848022461,
-0.0014103625435382128,
0.02478191629052162,
-0.08635018020868301,
0.04586053639650345,
-0.010817892849445343,
0.023892946541309357,
-0.04879341647028923,
-0.028575565665960312,
-0.008355433121323586,
-0.017634371295571327,
-0.06361628323793411,
0.005710008088499308,
0.0647689625620842,
0.015070118010044098,
-0.024013960734009743,
-0.01754732057452202,
0.05183350667357445,
-0.010280616581439972,
-0.018023908138275146,
0.0424916073679924,
-0.025956083089113235,
-0.023504149168729782,
-0.008707089349627495,
-0.033966246992349625,
0.06618408113718033,
0.011024135164916515,
-0.08688086271286011,
0.002035165671259165,
0.005023852456361055,
-0.0023959167301654816,
0.008053372614085674,
0.021311236545443535,
-0.009122786112129688,
0.041038043797016144,
0.011006421409547329,
-0.046029381453990936,
0.0194769985973835,
0.04113297536969185,
0.03167460486292839,
-0.009242099709808826,
-0.056337062269449234,
0.009457414969801903,
-0.034578654915094376,
0.026138853281736374,
0.05538571625947952,
0.0010437500895932317,
0.07948649674654007,
0.01118948869407177,
-0.01481554377824068,
-0.03560895845293999,
-0.0361986979842186,
0.04259312525391579,
-0.030312560498714447,
-0.0062818946316838264,
-0.00991895142942667,
-0.00008590196375735104,
-0.00732967397198081,
0.010414916090667248,
-0.005774207413196564,
-0.05863853171467781,
0.03313510864973068,
0.0567719005048275,
-0.01726073957979679,
0.018576255068182945,
0.010127539746463299,
0.09214259684085846,
-0.02201460301876068,
-0.06377668678760529,
-0.02399776130914688,
0.02520761825144291,
-0.044398292899131775,
0.03983443230390549,
0.022001946344971657,
-0.043847568333148956,
0.06912172585725784,
-0.0021716130431741476,
-0.04091886058449745,
0.09977847337722778,
-0.015590917319059372,
-0.06357893347740173,
-0.015324769541621208,
-0.018402308225631714,
-0.035111285746097565,
0.05070808157324791,
-0.08124519884586334,
-0.024369146674871445,
-0.027393609285354614,
0.028753912076354027,
-0.06109525263309479,
-0.04935934767127037,
-0.018628453835844994,
-0.005593432113528252,
-0.027730323374271393,
0.03566693887114525,
-0.02151660993695259,
-0.035432130098342896,
-0.021349534392356873,
-0.02189107984304428,
-0.07658305764198303,
-0.028342144563794136,
-0.026760734617710114,
-0.01720600388944149,
0.01679961569607258,
0.001998614054173231,
0.05755005404353142,
0.007264858577400446,
0.00736657902598381,
0.1076648160815239,
-0.027095317840576172,
0.0225555207580328,
-0.0766383558511734,
-0.04592699557542801,
0.026560869067907333,
0.055211469531059265,
0.002804658142849803,
0.04417353495955467,
0.046498142182826996,
-0.0005636903224512935,
0.02696695737540722,
-0.024365676566958427,
0.050988808274269104,
0.0636272057890892,
0.03072282485663891,
0.006911158561706543,
0.009977314621210098,
-0.016658565029501915,
0.0452716164290905,
0.049286868423223495,
-0.009941463358700275,
0.00559592479839921,
-0.022660674527287483,
-0.016788959503173828,
0.047934893518686295,
-0.01207074522972107,
0.017188971862196922,
0.01722942665219307,
0.012807974591851234,
-0.031177977100014687,
0.05512985587120056,
-0.03472789749503136,
-0.01820455491542816,
0.022977888584136963,
-0.054523762315511703,
0.03120640479028225,
-0.015232390724122524,
0.0365649089217186,
-0.02652214840054512,
-0.02054690197110176,
0.05523118004202843,
0.009309564717113972,
-0.06382378190755844,
0.0318133570253849,
0.030055884271860123,
-0.00839933380484581,
0.035099200904369354,
-0.025889547541737556,
-0.008935661986470222,
-0.03243887051939964,
-0.0458882711827755,
0.05927645415067673,
-0.02620898000895977,
0.006197195965796709,
0.0011910921894013882,
-0.025767982006072998,
0.04287507012486458,
0.02571423538029194,
-0.03768007829785347,
0.018585041165351868,
-0.003584305290132761,
0.0013301119906827807,
0.023816902190446854,
-0.08900178223848343,
0.0782998576760292,
0.05183595418930054,
0.026913322508335114,
-0.03184591606259346,
-0.03691963478922844,
-0.016770068556070328,
-0.03736935555934906,
-0.027513155713677406,
0.02895660325884819,
-0.0826929360628128,
0.016808168962597847,
-0.0072456058114767075,
0.07372992485761642,
-0.01877262443304062,
0.018222589045763016,
-0.02475789003074169,
0.05234304815530777,
-0.04596267640590668,
0.023286253213882446,
0.055724408477544785,
0.03819981962442398,
0.026951588690280914,
-0.0125542301684618,
-0.03873038291931152,
0.0023395109456032515,
-0.011952158994972706,
0.05672711133956909,
0.05445776879787445,
-0.03421594575047493,
0.09592261165380478,
-0.00340394233353436,
0.04489703103899956,
-0.028099996969103813,
0.0012724172556772828,
0.0047954777255654335,
-0.009549582377076149,
-0.09174606949090958,
-0.056413643062114716,
0.03968274965882301,
-0.02708672545850277,
-0.03809406980872154,
-0.00435522710904479,
0.028072664514183998,
0.010325399227440357,
0.012378176674246788,
0.00582475820556283,
0.033359136432409286,
-0.03209056332707405,
0.0019763356540352106,
0.03882869333028793,
-0.0479157380759716,
-0.01431210059672594,
0.04291430860757828,
-0.022881757467985153,
-0.0429978221654892,
0.010780194774270058,
-0.07819107919931412,
0.01284436509013176,
0.03872627764940262,
-0.0011594704119488597,
-0.01173233799636364,
-0.02533815987408161,
-0.007809416390955448,
0.03565070033073425,
-0.01999974250793457,
0.035692788660526276,
-0.023113103583455086,
0.023044100031256676,
-0.0005113590159453452,
0.0064654117450118065,
-0.00574919069185853,
-0.011088692583143711,
0.017181463539600372,
-0.04799068719148636,
-0.06290877610445023,
0.059707287698984146,
0.012531338259577751,
-0.022622209042310715,
0.10917695611715317,
0.06496485322713852,
0.02187390998005867,
0.04439759999513626,
-0.03436976298689842,
0.05365530028939247,
0.012352191843092442,
-0.05769071727991104,
-0.02309301123023033,
-0.022094467654824257,
-0.009022151120007038,
-0.07044427841901779,
-0.006788922473788261,
0.00086990772979334,
-0.06619924306869507,
-0.05061054229736328,
0.03466051444411278,
-0.019113529473543167,
-0.048872530460357666,
-0.018481524661183357,
0.018129123374819756,
-0.011348329484462738,
-0.00024846039013937116,
-0.07491722702980042,
0.04805764555931091,
-0.0004447333631105721,
0.0069229938089847565,
-0.011406375095248222,
-0.018783515319228172,
-0.008390669710934162,
0.0294665340334177,
0.010735823772847652,
0.03015749901533127,
0.048196595162153244,
-0.03939759358763695,
0.014981565997004509,
-0.027012130245566368,
-0.005012872163206339,
0.04333777725696564,
-0.022908154875040054,
0.030871056020259857,
0.042221423238515854,
-0.007365274243056774,
-0.03539777919650078,
-0.019408339634537697,
0.012425449676811695,
0.017699429765343666,
-0.03645375743508339,
0.09074345976114273,
-0.005717993713915348,
0.06111065298318863,
-0.008668663911521435,
-0.008005375042557716,
0.006583270151168108,
-0.020213669165968895,
-0.005857526324689388,
0.04944039508700371,
-0.038453880697488785,
0.0528140552341938,
0.042115382850170135,
0.03937733545899391,
0.052131641656160355,
0.02545551396906376,
0.02895480953156948,
-0.04795315861701965,
-0.017388392239809036,
0.019001564010977745,
-0.04389560967683792,
0.05089392885565758,
0.07731618732213974,
0.03360820934176445,
-0.0583411268889904,
0.001974191516637802,
0.014215707778930664,
-0.01102120615541935,
-0.03887385129928589,
0.015557526610791683,
0.044915322214365005,
0.0065470002591609955,
-0.03607678785920143,
0.023327486589550972,
0.00628245621919632,
-0.007419329136610031,
-0.0016455036820843816,
-0.01915724389255047,
0.0014035404892638326,
0.03167778253555298,
-0.0028560676146298647,
-0.00035412790020927787,
0.028763676062226295,
0.02845410443842411,
0.046930134296417236,
0.008560765534639359,
0.015326028689742088,
0.04904533922672272,
0.0193282812833786,
0.07981874793767929,
0.0315886065363884,
-0.04319692775607109,
0.011524120345711708,
-0.06876439601182938,
0.023127999156713486,
0.01049506664276123,
-0.002654150128364563,
-0.018486060202121735,
0.029440611600875854,
0.03616480529308319,
-0.008334779180586338,
-0.027713702991604805,
0.017088426277041435,
-0.013344375416636467,
-0.029611460864543915,
-0.021452290937304497,
-0.04501399025321007,
-0.010201789438724518,
0.011254568584263325,
0.03324954956769943,
-0.07294962555170059,
0.01817445456981659,
-0.002843572525307536,
0.07469803094863892,
-0.08243271708488464,
0.006158141884952784,
-0.006096159107983112,
0.006679882295429707,
0.010787870734930038,
0.030510181561112404,
0.029805587604641914,
0.02643825113773346,
0.05171716585755348,
0.0010035153245553374,
0.0370882973074913,
0.027439218014478683,
-0.05880928039550781,
0.007765735033899546,
0.02965441159904003,
0.00675525376573205,
-0.029606986790895462,
-0.07311206310987473,
0.0537930428981781,
0.03828360512852669,
-0.04149673506617546,
0.0255984328687191,
-0.009768795222043991,
-0.005850773770362139,
0.03091994859278202,
-0.0060155498795211315,
-0.021861230954527855,
-0.02882280759513378,
0.016988079994916916,
0.012070910073816776,
-0.02225450426340103,
-0.03626378998160362,
-0.06269743293523788,
-0.058198459446430206,
0.003112603910267353,
-0.03264261409640312,
-0.016569023951888084,
-0.056257400661706924,
-0.03819791227579117,
0.01914425566792488,
-0.062961645424366,
-0.006840123794972897,
-0.02797512710094452,
-0.0009114787681028247,
-0.037250664085149765,
-0.004606770817190409,
-0.012678219005465508,
-0.036553800106048584,
0.00791865773499012,
-0.010049259290099144,
-0.022180359810590744,
-0.06841856986284256,
0.04203891381621361,
-0.009894450195133686,
0.019932566210627556,
-0.015310253016650677,
-0.042464420199394226,
0.016322726383805275,
0.06375450640916824,
-0.04467162862420082,
0.0304573904722929,
-0.037551771849393845,
-0.007545160129666328,
0.007211536169052124,
0.0005719066830351949,
-0.03285437449812889,
-0.0032864767126739025,
0.01118723675608635,
0.023184780031442642,
0.05926445871591568,
-0.0461132675409317,
-0.032805923372507095,
0.00849459320306778,
0.031208761036396027,
0.015115777961909771,
0.024484917521476746,
-0.02307700924575329,
0.033066291362047195
] |
<p>On a <a href="https://en.wikipedia.org/wiki/Porkchop_plot" rel="nofollow">porkchop plot</a> for a given departure date (X axis), why are there two local energy minimums along the arrival date (Y-axis) for a transfer between Earth and Mars? The Hohmann transfer orbit seems to have one optimal solution, but the plot's two minimums seem fairly distinct in time but similar in energy; 15.0 to 15.5 and 15.5 to 16.0 in terms of C3L (something I only vaguely understand; KSP mostly deals in delta-V)</p>
<p><a href="https://en.wikipedia.org/wiki/File%3aPorkchop_plot.gif" rel="nofollow"><img src="http://i.stack.imgur.com/rer1W.png" alt="Earth to Mars porkchop plot"></a></p>
<p>A <a href="http://mars.jpl.nasa.gov/spotlight/porkchopAll.html" rel="nofollow">NASA page</a> about sending spacecraft to Mars refers to "Type 1" and "Type 2" transfer orbits, which clashes with a perhaps simple view that there should be a singular optimal Hohmann transfer orbit; the smallest ellipse tangent to two orbits. Granted, the planets' orbits are not perfectly circular, but the different transit times (red contours) for local minimums differ by almost a factor of two! (about 200 days and about 400 days) I'm not sure if I'm reading the plot correctly though, as there is a disconnect between the given Earth-Mars plot, and the prose on the page as well, which talks about 7 month (~200 day) or 10 month (~300 day) transfers.</p> | g5504 | [
0.023670118302106857,
0.01294977031648159,
0.007923292927443981,
0.0013516258914023638,
-0.031085658818483353,
0.02440054342150688,
-0.01958555355668068,
0.02629525400698185,
-0.10658513754606247,
0.025821996852755547,
0.05445028468966484,
0.051252152770757675,
0.05782780423760414,
-0.010220054537057877,
0.027652915567159653,
-0.015081960707902908,
0.04610553756356239,
-0.020009823143482208,
0.062043096870183945,
0.04246550425887108,
0.05005500838160515,
-0.02095249481499195,
0.00171927351038903,
-0.028184914961457253,
0.030709154903888702,
-0.07963687181472778,
-0.019291743636131287,
-0.010835562832653522,
-0.03751930221915245,
0.015931742265820503,
-0.003871405264362693,
-0.017939211800694466,
0.024363655596971512,
-0.09287494421005249,
-0.06536702811717987,
-0.0037964871153235435,
-0.04535147547721863,
0.02587546408176422,
0.007677382789552212,
0.013071984052658081,
-0.06760106235742569,
-0.05091337487101555,
0.02428670972585678,
-0.007176707033067942,
0.016049060970544815,
-0.0016733875963836908,
0.00022153816826175898,
-0.019234998151659966,
0.033343955874443054,
-0.06168410927057266,
-0.017188800498843193,
0.05697228014469147,
-0.040394704788923264,
0.010309410281479359,
-0.020848805084824562,
0.010072737000882626,
0.0513986274600029,
-0.00896535161882639,
0.025607867166399956,
0.031894247978925705,
-0.00942465104162693,
0.023079777136445045,
-0.0037403872702270746,
-0.005728535819798708,
0.0016183103434741497,
0.004872916731983423,
-0.04585302993655205,
0.05981718748807907,
-0.010599102824926376,
-0.016461782157421112,
0.03829158470034599,
-0.0020920834504067898,
-0.013143705204129219,
-0.055786121636629105,
-0.003134980797767639,
-0.015127276070415974,
0.0363474003970623,
-0.04523226246237755,
0.011364278383553028,
0.005738521926105022,
-0.030616067349910736,
0.08914528042078018,
-0.03239383548498154,
0.06515233963727951,
0.029427895322442055,
0.058543670922517776,
0.037030842155218124,
-0.010160633362829685,
0.019827743992209435,
0.019689403474330902,
-0.05607462301850319,
-0.011591305024921894,
0.023579049855470657,
0.0487150102853775,
-0.02838025614619255,
-0.014838744886219501,
-0.02580735646188259,
0.039059240370988846,
-0.033496055752038956,
-0.005808365996927023,
0.03232226148247719,
-0.001341335941106081,
0.010571126826107502,
0.02926221303641796,
0.014909186400473118,
-0.009333038702607155,
0.021331146359443665,
0.04513782262802124,
0.0015726479468867183,
-0.016320927068591118,
-0.065646693110466,
-0.03688925877213478,
-0.029908636584877968,
-0.009081664495170116,
0.03167314454913139,
-0.014544562436640263,
0.028126230463385582,
-0.08431816101074219,
0.04774469509720802,
-0.013066411018371582,
-0.024281883612275124,
-0.042873602360486984,
-0.03726749122142792,
0.091511569917202,
0.0005974998348392546,
0.010233206674456596,
-0.04590768367052078,
-0.04535999521613121,
-0.021220585331320763,
0.01294084545224905,
-0.06265751272439957,
-0.009013374336063862,
-0.029881853610277176,
0.02437770552933216,
0.01984439231455326,
-0.0868997573852539,
0.0029721534810960293,
0.016777489334344864,
0.024919673800468445,
-0.04433511942625046,
0.045688290148973465,
-0.08418884873390198,
-0.012918309308588505,
-0.04807101562619209,
-0.08260919898748398,
0.06359388679265976,
-0.009506672620773315,
0.05473709851503372,
0.08210967481136322,
-0.0018911220831796527,
-0.02343028411269188,
0.0411829948425293,
0.015264229848980904,
-0.0003249374567531049,
-0.038636330515146255,
0.010453171096742153,
0.02185203693807125,
-0.00918081309646368,
-0.01958620175719261,
0.017728259786963463,
0.035049084573984146,
-0.005778660532087088,
0.06610853970050812,
-0.0028972621075809,
-0.04027829319238663,
0.0017365553649142385,
-0.029155589640140533,
-0.03595484048128128,
0.041237447410821915,
-0.06564980000257492,
-0.01672298088669777,
-0.02336793765425682,
0.03219372034072876,
0.002284827409312129,
0.013400732539594173,
0.025529498234391212,
0.06166898086667061,
-0.015607952140271664,
-0.01690550521016121,
-0.018241195008158684,
0.008060220628976822,
-0.01175330113619566,
-0.0036525095347315073,
0.02156548574566841,
0.001169521943666041,
-0.10704342275857925,
0.039511412382125854,
-0.012876615859568119,
-0.05465856194496155,
0.010037215426564217,
-0.030812788754701614,
-0.031150447204709053,
0.008808590471744537,
-0.04251369461417198,
-0.029843376949429512,
0.02715677209198475,
0.031245483085513115,
-0.006397431716322899,
-0.11200614273548126,
0.020286014303565025,
0.038548581302165985,
0.002169210696592927,
0.03054937906563282,
-0.01812508888542652,
0.016708407551050186,
0.006914087105542421,
0.016557084396481514,
-0.004146722611039877,
0.03626877814531326,
-0.02401949092745781,
-0.009949359111487865,
-0.03352968394756317,
0.0019693621434271336,
0.01761423610150814,
-0.0020518365781754255,
0.017762809991836548,
-0.008645663037896156,
0.02476712130010128,
0.016822202131152153,
-0.038297154009342194,
-0.028871897608041763,
-0.030614446848630905,
0.02477707713842392,
0.011571524664759636,
0.05145459249615669,
-0.009199918247759342,
-0.005161894951015711,
-0.04203479364514351,
-0.03214520215988159,
-0.016180239617824554,
-0.08969000726938248,
0.04474973678588867,
-0.014114742167294025,
-0.0544312559068203,
0.023012034595012665,
-0.0447889119386673,
0.03876081109046936,
-0.023630084469914436,
-0.03290778398513794,
0.020314302295446396,
0.05349178612232208,
-0.03734413906931877,
-0.03410528600215912,
0.06538110226392746,
0.056066639721393585,
-0.00558057427406311,
0.0074952044524252415,
-0.028715817257761955,
-0.023363186046481133,
0.0008885512943379581,
-0.0032549791503697634,
0.026731524616479874,
-0.03093085251748562,
0.026248713955283165,
-0.008143116720020771,
-0.08739148825407028,
-0.03573887050151825,
0.03492932766675949,
-0.026026282459497452,
-0.048292126506567,
-0.008432281203567982,
-0.013817824423313141,
0.057386450469493866,
0.014484535902738571,
-0.039445143193006516,
0.004105052910745144,
-0.031183063983917236,
0.05774448812007904,
-0.03909114748239517,
-0.025466589257121086,
-0.03088575229048729,
0.03783942759037018,
0.031040215864777565,
0.06335210800170898,
-0.03643886744976044,
0.0007709154160693288,
-0.01353568583726883,
-0.033379003405570984,
-0.029496191069483757,
-0.008835501037538052,
-0.025993352755904198,
-0.06993799656629562,
-0.03375300019979477,
0.05383622646331787,
-0.023298216983675957,
-0.029692623764276505,
-0.03199814632534981,
0.04454992339015007,
-0.019281769171357155,
0.01412523165345192,
-0.03764186054468155,
0.03545822203159332,
0.02904636599123478,
0.028697289526462555,
0.026508303359150887,
-0.04685613140463829,
0.03618649020791054,
-0.03653305768966675,
-0.03196144104003906,
-0.020272256806492805,
0.014618807472288609,
-0.007456570863723755,
-0.012680786661803722,
0.03856893628835678,
-0.044651105999946594,
-0.012747273780405521,
-0.011475699953734875,
-0.043781425803899765,
-0.10144072026014328,
0.031311582773923874,
0.04956195503473282,
-0.01901322789490223,
0.009943974204361439,
0.01302790455520153,
0.0031769806519150734,
-0.025382298976182938,
-0.05791027098894119,
0.005088248290121555,
-0.006576318293809891,
-0.009480170905590057,
-0.07428673654794693,
0.01270954217761755,
-0.041955094784498215,
0.033095769584178925,
-0.050111740827560425,
0.028654756024479866,
-0.07014714181423187,
-0.06192657724022865,
-0.02394341118633747,
0.0683385580778122,
-0.003965840674936771,
0.07764468342065811,
-0.043244898319244385,
-0.04783855751156807,
-0.06490320712327957,
0.023289473727345467,
-0.05427397042512894,
0.062105704098939896,
0.009515883401036263,
0.08665241301059723,
-0.0382235161960125,
0.008721712976694107,
-0.011312096379697323,
-0.03630620986223221,
0.04171660915017128,
-0.025014132261276245,
-0.015013148076832294,
-0.0009413647348992527,
-0.0018589019309729338,
-0.08538244664669037,
0.015363899059593678,
-0.025935987010598183,
0.012253373861312866,
0.0007260289858095348,
-0.011265772394835949,
-0.04082018882036209,
-0.03687184676527977,
-0.00009075589332496747,
0.030374808236956596,
0.04063146933913231,
0.020032133907079697,
0.02810785360634327,
-0.02480759285390377,
0.0703149288892746,
0.04315834864974022,
-0.04113426432013512,
-0.044255513697862625,
0.03673776611685753,
0.005735021084547043,
-0.02101314812898636,
0.028456997126340866,
0.009068273939192295,
0.037746362388134,
0.005949158221483231,
0.028949568048119545,
-0.08074821531772614,
-0.03574426472187042,
-0.017576171085238457,
-0.0004211423802189529,
0.03559797257184982,
-0.009178738109767437,
0.009820224717259407,
-0.000057236713473685086,
0.047248851507902145,
0.039441585540771484,
0.046189893037080765,
-0.0423160083591938,
-0.022223811596632004,
-0.031431645154953,
-0.03547966480255127,
0.013264436274766922,
-0.030801398679614067,
0.0018275418551638722,
-0.024121791124343872,
0.08579366654157639,
0.03174803778529167,
0.030021224170923233,
0.051807794719934464,
-0.025972671806812286,
0.036681659519672394,
0.018525883555412292,
-0.0001798592711566016,
-0.04955075681209564,
-0.018759625032544136,
-0.02204374223947525,
0.018754631280899048,
-0.042304061353206635,
0.022558704018592834,
-0.01718546822667122,
0.004623993765562773,
0.0499996542930603,
-0.033418621867895126,
0.0017442000098526478,
0.023987770080566406,
0.019464625045657158,
-0.0318022295832634,
-0.0208923127502203,
0.006783169228583574,
0.01826627179980278,
0.008757823146879673,
-0.019194256514310837,
0.10071364045143127,
-0.009917818009853363,
-0.05167108029127121,
0.020563999190926552,
0.04511399194598198,
0.031962454319000244,
0.02292557805776596,
0.01948375627398491,
0.015134554356336594,
0.02704007737338543,
0.04841526597738266,
-0.0028792230878025293,
0.04159463569521904,
0.0008803881937637925,
0.04521714895963669,
-0.004388028755784035,
0.024783028289675713,
0.018108228221535683,
0.004387373570352793,
0.06199583038687706,
-0.018058691173791885,
-0.04400225356221199,
0.019717028364539146,
-0.025502800941467285,
0.04314366728067398,
0.03141460567712784,
-0.07000371813774109,
-0.005591492634266615,
-0.06102699413895607,
0.01847403310239315,
0.03783714398741722,
0.05039548873901367,
-0.0029123914428055286,
-0.012539830058813095,
-0.0013957733754068613,
-0.005108695477247238,
0.018735842779278755,
0.03930594399571419,
0.009291966445744038,
-0.029014484956860542,
0.06731349974870682,
-0.03706260398030281,
-0.04824770987033844,
0.04557649418711662,
0.024583743885159492,
-0.06855013221502304,
0.02478279173374176,
-0.05656282603740692,
0.013596965931355953,
0.0024117405992001295,
0.04472034052014351,
0.007773439399898052,
0.0048803105019032955,
-0.00971186812967062,
0.010635167360305786,
-0.017571207135915756,
-0.016705943271517754,
-0.003964423667639494,
-0.038866445422172546,
-0.004461046773940325,
-0.03503502905368805,
0.0604141429066658,
0.09872926026582718,
0.010066334158182144,
-0.0015766698634251952,
-0.03897438570857048,
-0.08168331533670425,
0.06292690336704254,
0.009802195243537426,
-0.009001322090625763,
-0.029732046648859978,
-0.025262068957090378,
0.005859090946614742,
0.010614089667797089,
0.016041060909628868,
0.010772528126835823,
-0.06291206181049347,
-0.007723201997578144,
-0.0146484961733222,
0.01699366606771946,
0.08668706566095352,
-0.0394299291074276,
-0.007880049757659435,
0.029622256755828857,
-0.02729065902531147,
0.08119052648544312,
-0.04361334443092346,
0.022654591128230095,
0.023885158821940422,
-0.003654801519587636,
0.026972338557243347,
-0.017496520653367043,
-0.02612481825053692,
-0.043892618268728256,
-0.04154480621218681,
0.023711204528808594,
0.02535976842045784,
0.018103627488017082,
-0.06448043137788773,
0.022697357460856438,
0.085904560983181,
0.02268967404961586,
0.03145220875740051,
0.043489836156368256,
-0.00023779348703101277,
-0.009848707355558872,
-0.04195338115096092,
-0.048988424241542816,
0.029476717114448547,
-0.03205057978630066,
0.04631033167243004,
-0.0019682717975229025,
0.09498035907745361,
-0.01486805360764265,
-0.04029450938105583,
-0.013478328473865986,
0.011629500426352024,
0.04551104083657265,
-0.07751072943210602,
-0.06358722597360611,
-0.013342577032744884,
-0.029744969680905342,
0.06247154623270035,
0.007695536129176617,
0.015031211078166962,
0.01442773174494505,
-0.014684317633509636,
-0.003273305483162403,
-0.0013605133863165975,
-0.05913706496357918,
-0.0500037781894207,
-0.009925397112965584,
-0.03633633628487587,
-0.023893587291240692,
-0.018957063555717468,
-0.0024180556647479534,
0.024926478043198586,
-0.05983920767903328,
0.005342136602848768,
0.015301081351935863,
0.057168763130903244,
0.030604960396885872,
0.05833129957318306,
-0.03805084154009819,
0.014815881848335266,
0.009678670205175877,
0.00037164476816542447,
0.02768978849053383,
0.0005737593164667487,
-0.0008004282717593014,
-0.02512194775044918,
-0.010898254811763763,
0.056270163506269455,
0.006047470029443502,
-0.02298993617296219,
-0.04961414262652397,
-0.021767286583781242,
-0.062438350170850754,
0.057672299444675446,
-0.014760579913854599,
-0.006850832607597113,
0.020172731950879097,
0.03343752399086952,
-0.03093627281486988,
0.052088864147663116,
-0.0126581946387887,
-0.036481812596321106,
0.010954909026622772,
-0.04036468267440796,
-0.007518910802900791,
-0.02056066505610943,
0.06943079829216003,
0.01136735174804926,
-0.017605958506464958,
-0.0036478377878665924,
-0.05350832641124725,
0.05033596232533455,
-0.008979178965091705,
-0.019259897992014885,
0.004071973729878664,
0.03248581662774086,
0.1116720512509346,
0.021164849400520325,
0.0378967747092247,
0.04766044393181801,
0.02860703505575657,
0.03956654295325279,
0.0001369865203741938,
0.05382945016026497,
0.0024308008141815662,
0.006061450578272343,
-0.03435255214571953,
0.04783777892589569,
0.04547134414315224,
0.04003153368830681,
-0.046446461230516434,
0.05440659448504448,
-0.03688432276248932,
-0.012452705763280392,
0.04132682457566261,
0.042413800954818726,
0.0046492707915604115,
0.012351247482001781,
-0.02875417098402977,
0.050267543643713,
-0.001406754832714796,
-0.010990113019943237,
0.033124279230833054,
0.0009295304189436138,
0.01447180937975645,
0.00796267855912447,
-0.036088086664676666,
0.07147890329360962,
-0.0046592517755925655,
0.038556043058633804,
-0.08816973119974136,
0.03274201229214668,
-0.03290402516722679,
0.0034881208557635546,
0.018276462331414223,
0.01429932750761509,
0.03302289918065071,
0.014025499112904072,
-0.03985598683357239,
0.006373214069753885,
0.03499729558825493,
0.017154628410935402,
-0.014376560226082802,
-0.014476833865046501,
0.008799309842288494,
-0.07534462958574295,
0.000166312835062854,
0.017975712195038795,
0.05678148195147514,
-0.02793477289378643,
-0.03874947875738144,
0.0624144971370697,
0.04835515841841698,
-0.0006959605379961431,
-0.000045317341573536396,
0.015063555911183357,
-0.007442050613462925,
0.026690443977713585,
0.043530818074941635,
0.030336888507008553,
-0.0073799616657197475,
-0.011866861023008823,
0.009645448997616768,
-0.047000952064991,
-0.004927462432533503,
0.01932677999138832,
-0.018468448892235756,
0.012059847824275494,
-0.012992886826395988,
-0.01586579717695713,
0.025308681651949883,
-0.04557846486568451,
0.0032298676669597626,
0.015239964239299297,
0.02389204315841198,
-0.031110256910324097,
0.03275008872151375,
0.03402675315737724,
-0.004916984587907791,
0.020188147202134132,
-0.03519951552152634,
-0.014088881202042103,
-0.019632212817668915,
0.021696629002690315,
0.05175049602985382,
0.03428686037659645,
0.023019732907414436,
0.04499911889433861,
-0.016951171681284904,
0.02010045386850834,
-0.0004046695539727807,
0.01988935098052025,
0.05826409161090851,
0.049955133348703384,
0.08134695142507553,
0.026434626430273056,
0.009887197986245155,
0.010499784722924232,
0.03499658405780792,
0.0115440022200346,
0.014910569414496422,
-0.007418257184326649,
-0.05605004355311394,
-0.018330974504351616,
0.03026694618165493,
0.019703904166817665,
-0.03794410824775696,
0.05859055370092392,
-0.0020395538304001093,
0.017826160416007042,
-0.004245688673108816,
-0.014652317389845848,
-0.02782438136637211,
0.02387211099267006,
0.01691894605755806,
-0.014559815637767315,
-0.005412808619439602,
-0.06110502406954765,
-0.0018273191526532173,
0.026485051959753036,
-0.01980794593691826,
-0.06695597618818283,
0.02988833375275135,
-0.016938669607043266,
0.016805818304419518,
0.013629094697535038,
-0.04175587743520737,
0.009841292165219784,
-0.05221417546272278,
-0.03137614205479622,
-0.07518110424280167,
-0.020791709423065186,
-0.030384495854377747,
0.005380719434469938,
-0.030047543346881866,
-0.07447359710931778,
-0.028090376406908035,
-0.007293245289474726,
-0.027089092880487442,
0.030264755710959435,
0.0159266609698534,
-0.00219453452154994,
0.023879414424300194,
-0.04477763548493385,
-0.011043732054531574,
-0.0031897020526230335,
-0.04688560962677002,
-0.010071062482893467,
-0.01017937995493412,
-0.033907100558280945,
0.006025293841958046,
0.015038978308439255,
-0.061481110751628876,
-0.019587479531764984,
0.024731826037168503,
0.010248693637549877,
0.009912138804793358,
-0.021194033324718475,
-0.01851675845682621,
0.022737698629498482,
0.02062315121293068,
-0.0003366364981047809
] |
<p>I think I remember a talk where a professor said that <a href="http://en.wikipedia.org/wiki/4_Vesta" rel="nofollow">Vesta</a> is a particularly important asteroid because its gravity is strong enough to perturb other asteroids.</p>
<p>In spite of Vesta's size, this effect might be so strong that some smaller asteroids might be kicked out of their orbits - making their way to Jupiter, or to the inner solar system.</p>
<p>Can Vesta dominate the orbits of other asteroids?</p>
<p>All related to the one question, there are particular points I'm interested in:</p>
<ul>
<li>if so, how often, presumably?</li>
<li>is there a preferred direction (inwards / outwards)? </li>
<li>has the perturbation rate been constant over geologic timescales?</li>
<li>do the "victims" stay in the plane of the ecliptic? </li>
<li>did someone model such processes?</li>
</ul>
<p>I currently think the whole process is chaotic - essentially unpredictable. </p> | g5505 | [
0.03343731909990311,
0.07246207445859909,
-0.005562487989664078,
-0.009598775766789913,
0.02965943142771721,
0.012856253422796726,
0.027439918369054794,
-0.02941150777041912,
0.012282351963222027,
-0.019053030759096146,
0.023074835538864136,
0.034117020666599274,
0.1214071586728096,
-0.033966727554798126,
0.05190436169505119,
-0.011489584110677242,
0.07937674969434738,
-0.009921401739120483,
0.05906242877244949,
0.051289916038513184,
-0.010558443143963814,
-0.019365541636943817,
-0.03250613063573837,
-0.0170790646225214,
-0.018487969413399696,
0.044036585837602615,
0.032952938228845596,
-0.03404240310192108,
0.026254041120409966,
0.0016955578466877341,
0.016516441479325294,
-0.025512970983982086,
0.03586088493466377,
-0.10247299075126648,
-0.06605362147092819,
0.01107007171958685,
0.03178824111819267,
0.014661929570138454,
-0.02737209014594555,
0.03833800554275513,
0.003112808335572481,
-0.06659761816263199,
-0.04684038460254669,
0.022596633061766624,
-0.04332799091935158,
0.004983848426491022,
0.001936627784743905,
-0.07761673629283905,
0.026278071105480194,
0.015244635753333569,
-0.04690670967102051,
0.02156279981136322,
0.024791307747364044,
-0.03717255964875221,
-0.030786830931901932,
0.05300956964492798,
0.057991549372673035,
0.011659149080514908,
0.03350544348359108,
0.022776002064347267,
0.01898174360394478,
-0.021213244646787643,
-0.03623659908771515,
-0.02838652767241001,
-0.006150146014988422,
-0.021613316610455513,
-0.0636972114443779,
0.021827707067131996,
0.024431569501757622,
-0.022780831903219223,
0.010359233245253563,
-0.0034369181375950575,
-0.03684265539050102,
-0.10575158149003983,
-0.03318621963262558,
0.04222453013062477,
0.014584517106413841,
0.0008775052265264094,
-0.006507762707769871,
-0.0015192206483334303,
-0.007999307475984097,
0.007032613269984722,
-0.00228407746180892,
0.007413627579808235,
0.040122680366039276,
0.025219906121492386,
0.027720659971237183,
0.025014933198690414,
-0.016733422875404358,
0.0023358087055385113,
0.07402649521827698,
-0.003210347844287753,
0.0016231485642492771,
-0.0103412214666605,
-0.05644696205854416,
-0.022769954055547714,
0.0071212477050721645,
0.06873542070388794,
-0.045298878103494644,
-0.006880016066133976,
-0.01630317233502865,
0.0019874272402375937,
0.0033743190579116344,
-0.01053000520914793,
0.009648477658629417,
-0.003324573626741767,
0.06358576565980911,
-0.02820010483264923,
0.06584706902503967,
-0.039863791316747665,
-0.0006987884407863021,
-0.02062072418630123,
0.03167622163891792,
0.0035118847154080868,
-0.0005055456422269344,
0.05569062381982803,
0.02070167101919651,
-0.028815871104598045,
0.02782285585999489,
-0.008266119286417961,
-0.021480249240994453,
0.024336252361536026,
-0.011554374359548092,
0.028705555945634842,
-0.05203830823302269,
-0.028686435893177986,
-0.0011540371924638748,
0.003232482587918639,
0.03201146796345711,
-0.009547112509608269,
-0.05408579111099243,
0.005008323583751917,
0.01280505396425724,
0.030155396088957787,
0.019689524546265602,
0.06709535419940948,
-0.019949808716773987,
0.012797310948371887,
-0.051449716091156006,
0.042399223893880844,
0.03276899829506874,
-0.03905550017952919,
-0.0049054441042244434,
0.01672394946217537,
-0.04284239560365677,
0.031482648104429245,
0.0217023566365242,
0.03563520684838295,
-0.010787888430058956,
0.03121333383023739,
0.020661093294620514,
0.0932018905878067,
-0.00390744348987937,
-0.058151975274086,
-0.01074392069131136,
0.02684970200061798,
-0.0036269233096390963,
0.022643158212304115,
-0.04315870255231857,
-0.005064248573035002,
0.03296070918440819,
0.011793767102062702,
0.062156543135643005,
0.035607051104307175,
-0.07848083972930908,
0.034118130803108215,
0.008900521323084831,
-0.027061816304922104,
-0.01671343483030796,
-0.013630164787173271,
-0.024154141545295715,
-0.05940396711230278,
0.017843281850218773,
0.07681058347225189,
0.0016428098315373063,
-0.0011470342287793756,
0.028835052624344826,
-0.03474986553192139,
-0.008136994205415249,
-0.009321772493422031,
0.025912277400493622,
-0.02797260880470276,
0.0001967753778444603,
0.016271667554974556,
0.021529274061322212,
-0.048617884516716,
0.03945291042327881,
0.04896280914545059,
0.00027642285567708313,
-0.03913253918290138,
-0.03060917928814888,
-0.029469547793269157,
0.004933855962008238,
0.03634186461567879,
-0.012899653986096382,
-0.023296289145946503,
0.017015112563967705,
-0.044200483709573746,
-0.055713117122650146,
-0.013797246851027012,
-0.034755438566207886,
0.00009571421833243221,
0.07087419182062149,
-0.019618360325694084,
0.006332744844257832,
-0.00047134741907939315,
-0.019026612862944603,
0.08499394357204437,
-0.019572218880057335,
0.002697599120438099,
-0.020169835537672043,
-0.027691924944519997,
0.007439520675688982,
0.10781405121088028,
-0.06357228010892868,
-0.016167402267456055,
-0.045987505465745926,
0.027033573016524315,
0.06599277257919312,
0.023797737434506416,
0.02034786157310009,
-0.02966703101992607,
0.0034190432634204626,
-0.004089782014489174,
0.00800286140292883,
0.000020958228560630232,
-0.02261374518275261,
0.009322261437773705,
0.02051215060055256,
0.009205661714076996,
-0.028427604585886,
-0.0020874745678156614,
0.023483021184802055,
-0.053896404802799225,
0.005219914484769106,
-0.03398044779896736,
0.07866538316011429,
-0.044870033860206604,
-0.006508472841233015,
0.02467084676027298,
0.01933269016444683,
-0.09224333614110947,
0.01961236633360386,
-0.015033373609185219,
0.06030181422829628,
-0.07228227704763412,
-0.0023043432738631964,
-0.03725449740886688,
-0.03652416542172432,
-0.04331599920988083,
-0.001473724259994924,
-0.05662277713418007,
-0.11127365380525589,
0.0689699649810791,
-0.06461108475923538,
-0.023718440905213356,
-0.05271286144852638,
0.0882379338145256,
-0.030989937484264374,
-0.009505094960331917,
0.005462678149342537,
0.022934773936867714,
0.05033903941512108,
-0.015418286435306072,
0.005165125243365765,
-0.04238065332174301,
0.014999965205788612,
-0.012990782037377357,
-0.00764060765504837,
0.000040553011785959825,
-0.019002975896000862,
0.06413739919662476,
0.004095980431884527,
0.035251401364803314,
0.010075314901769161,
0.028945215046405792,
-0.04932522401213646,
-0.033421557396650314,
-0.06455048173666,
0.0079455291852355,
0.040276940912008286,
-0.04227728024125099,
-0.02691684104502201,
-0.0012812662171199918,
0.057855308055877686,
0.03289034590125084,
-0.008749478496611118,
0.07278115302324295,
-0.032546985894441605,
0.009710032492876053,
-0.009043192490935326,
-0.024814482778310776,
0.040970560163259506,
0.05583031475543976,
-0.027736740186810493,
0.021501649171113968,
-0.032367363572120667,
0.0156568456441164,
-0.032378870993852615,
0.0029119006358087063,
0.027048416435718536,
0.021465040743350983,
-0.02604222670197487,
0.0705331414937973,
0.022522546350955963,
0.0006723665865138173,
-0.02152722142636776,
-0.02035604789853096,
0.006266182288527489,
-0.03621045500040054,
-0.04569513723254204,
0.027040567249059677,
-0.011156215332448483,
0.05599154531955719,
-0.06460004299879074,
-0.040200162678956985,
-0.03398939594626427,
0.07169076800346375,
0.026112966239452362,
-0.019186899065971375,
-0.0037360480055212975,
-0.05189568176865578,
0.00010698528058128431,
0.047782063484191895,
-0.015399622730910778,
0.01581428386271,
-0.04019106552004814,
-0.02936287224292755,
-0.06214515492320061,
0.021715492010116577,
0.010191718116402626,
-0.021198734641075134,
-0.028068263083696365,
-0.023625513538718224,
-0.04676372930407524,
0.0276726596057415,
0.06441690772771835,
0.03649130463600159,
0.06389999389648438,
0.02472856640815735,
-0.03945155814290047,
0.030594835057854652,
-0.006136162206530571,
-0.055569592863321304,
-0.021946433931589127,
0.05501028150320053,
0.02809731662273407,
0.028071511536836624,
-0.0055776312947273254,
-0.028784332796931267,
0.030273588374257088,
-0.06871666759252548,
0.03542949631810188,
-0.01250002346932888,
0.06475785374641418,
0.016906458884477615,
0.019686128944158554,
0.017857559025287628,
0.027242477983236313,
-0.0073570432141423225,
-0.006266409531235695,
0.000019713976143975742,
-0.02369806170463562,
-0.01522070076316595,
-0.0018347211880609393,
-0.0011236503487452865,
-0.0019419958116486669,
0.003146226517856121,
-0.014888860285282135,
-0.04200727865099907,
-0.015402202494442463,
0.03304458037018776,
0.009941688738763332,
-0.016830414533615112,
0.08795192837715149,
0.021452540531754494,
0.04107842594385147,
0.05493675917387009,
-0.021281853318214417,
0.02047288790345192,
0.02561705932021141,
0.008124170824885368,
0.0498802624642849,
-0.003972009755671024,
-0.00016802901518531144,
0.03402679041028023,
-0.044989924877882004,
0.01942135952413082,
-0.08226703852415085,
-0.12426010519266129,
0.04857579246163368,
-0.052509795874357224,
0.01806238852441311,
-0.05303983390331268,
0.051232535392045975,
0.006103293038904667,
-0.037204667925834656,
0.0034070408437401056,
0.05144764110445976,
-0.009898209944367409,
0.03358246013522148,
-0.025336015969514847,
0.006342506036162376,
-0.021770132705569267,
0.0031627670396119356,
-0.009364076890051365,
-0.02055937610566616,
0.001304571283981204,
-0.09775778651237488,
-0.06101620942354202,
0.018833769485354424,
0.023851225152611732,
-0.06771045923233032,
-0.03914472460746765,
0.004919588100165129,
0.0025786373298615217,
-0.03878135234117508,
0.04236351326107979,
0.05067272484302521,
-0.008949876762926579,
-0.023614278063178062,
0.060242682695388794,
0.01482363510876894,
-0.018571192398667336,
-0.0014770601410418749,
0.07229244709014893,
-0.010551568120718002,
-0.02017534151673317,
-0.008006134070456028,
0.023585068061947823,
0.021740363910794258,
0.03724798560142517,
0.027416009455919266,
0.002605428220704198,
-0.03013341687619686,
0.00974136870354414,
-0.03233162313699722,
0.060953300446271896,
0.0006259623332880437,
-0.0016339841531589627,
0.030069943517446518,
0.0017571463249623775,
-0.002957007847726345,
0.03368920460343361,
-0.010344743728637695,
0.04714158549904823,
0.02932305634021759,
0.02720632031559944,
0.032730039209127426,
-0.061170969158411026,
-0.017123354598879814,
-0.010810701176524162,
-0.0043783714063465595,
0.0184320155531168,
-0.019092857837677002,
0.012594625353813171,
-0.021361704915761948,
0.0465901717543602,
0.02774512954056263,
-0.016296153888106346,
-0.03320752829313278,
0.014037994667887688,
0.01887757144868374,
0.04082004353404045,
0.0467175617814064,
-0.06769382208585739,
0.026984086260199547,
-0.027765687555074692,
0.00453069107607007,
-0.054551783949136734,
-0.0009697513887658715,
-0.01584090292453766,
0.022862309589982033,
0.045607421547174454,
-0.04377587512135506,
-0.03217747062444687,
-0.016198262572288513,
-0.031283941119909286,
0.04531754180788994,
-0.01606091670691967,
-0.029491301625967026,
-0.06206030026078224,
0.02761032059788704,
0.01190788485109806,
-0.0109901437535882,
-0.03954757750034332,
-0.024730512872338295,
-0.08951354026794434,
0.006855221930891275,
0.027332592755556107,
0.0008078847313299775,
0.02762911468744278,
-0.025585195049643517,
-0.026954688131809235,
-0.02403991110622883,
-0.025982368737459183,
0.013484657742083073,
-0.031432103365659714,
-0.0063405423425138,
-0.019471947103738785,
-0.001665924210101366,
0.016238875687122345,
0.005048563238233328,
0.012796384282410145,
-0.008441462181508541,
0.004167039413005114,
-0.0010192134650424123,
-0.08947230875492096,
-0.0030377365183085203,
-0.06761251389980316,
-0.043235987424850464,
0.003984216600656509,
-0.0011359055060893297,
-0.005506983958184719,
-0.03941285237669945,
-0.06472501903772354,
-0.03186015412211418,
0.004070763476192951,
0.013942698948085308,
-0.024247273802757263,
-0.00144663464743644,
-0.02208811230957508,
-0.0015702306991443038,
-0.019761275500059128,
0.07764746993780136,
-0.00048621982568874955,
0.009704112075269222,
-0.05237751454114914,
-0.03651439771056175,
-0.015248040668666363,
0.011569091118872166,
-0.043574072420597076,
-0.0367865264415741,
0.04691995680332184,
0.01838388480246067,
-0.05055363476276398,
0.012347375974059105,
0.0780172348022461,
0.06468602269887924,
-0.06182379648089409,
-0.052608270198106766,
0.006115049589425325,
-0.005759169347584248,
0.04850783944129944,
-0.0058423904702067375,
-0.01677609607577324,
-0.02653508260846138,
0.050611428916454315,
0.04183247685432434,
0.013506727293133736,
-0.0025907857343554497,
0.01520884782075882,
0.04409405216574669,
0.001016524387523532,
-0.023772751912474632,
0.03361887112259865,
-0.03277171403169632,
0.006899732630699873,
-0.038946349173784256,
-0.03824484720826149,
0.020081965252757072,
-0.012814869172871113,
0.04534231126308441,
0.019653072580695152,
-0.00015087770589161664,
-0.0414118766784668,
-0.016829263418912888,
-0.03311653807759285,
0.059754952788352966,
0.10275661945343018,
0.06871648132801056,
-0.03565634414553642,
-0.04349090903997421,
0.033894091844558716,
0.03409719839692116,
-0.024347513914108276,
-0.03036956861615181,
-0.010599829256534576,
-0.015113916248083115,
-0.025070853531360626,
0.04666214436292648,
-0.027424046769738197,
0.002624920103698969,
0.00017320775077678263,
-0.05072694271802902,
0.07014178484678268,
0.02043294534087181,
0.03433258458971977,
0.005398019216954708,
-0.03960408270359039,
-0.04397278279066086,
0.0006105970242060721,
0.011012814939022064,
0.029311982914805412,
-0.07001981884241104,
0.024921473115682602,
-0.006967640947550535,
0.027127651497721672,
-0.007969625294208527,
0.001414406462572515,
-0.025586966425180435,
0.007774693425744772,
0.10376511514186859,
0.04858506843447685,
0.007362329866737127,
-0.021745651960372925,
0.01976308785378933,
0.029318664222955704,
0.016986962407827377,
0.04747769236564636,
0.014654425904154778,
0.02784864604473114,
0.029179109260439873,
-0.020126353949308395,
-0.035319194197654724,
-0.032102447003126144,
-0.0053137680515646935,
0.026035184040665627,
0.021213674917817116,
0.04373494163155556,
-0.017830321565270424,
-0.022142402827739716,
0.011352361179888248,
-0.05524817854166031,
-0.037162184715270996,
0.021615589037537575,
-0.011275619268417358,
-0.034399792551994324,
-0.007489053066819906,
0.011592087335884571,
-0.003999659791588783,
0.003972078673541546,
0.03467593714594841,
0.026640096679329872,
-0.026382677257061005,
-0.0016469493275508285,
-0.061763156205415726,
0.023165453225374222,
-0.014015687629580498,
-0.029618432745337486,
0.01008223369717598,
-0.031473495066165924,
-0.028379052877426147,
0.0279922466725111,
-0.0036385192070156336,
0.05435968562960625,
-0.009563096798956394,
0.0224419217556715,
0.034260351210832596,
-0.03188241645693779,
-0.002398382406681776,
-0.023372424766421318,
-0.007443073205649853,
-0.021253062412142754,
0.01889847218990326,
0.047660864889621735,
-0.0037205566186457872,
0.029488159343600273,
0.07678653299808502,
-0.014338692650198936,
-0.0160161592066288,
0.043756213039159775,
0.030009077861905098,
0.022261105477809906,
0.013746349141001701,
-0.03299826756119728,
0.01507855486124754,
0.01616687700152397,
0.013623681850731373,
0.005501496605575085,
0.0555165596306324,
0.0036771814338862896,
-0.04403486102819443,
0.02154489792883396,
0.0314582958817482,
-0.015838541090488434,
0.014992724172770977,
-0.04339936003088951,
0.06948582082986832,
0.06280037015676498,
0.06487269699573517,
-0.03496216610074043,
0.032853350043296814,
0.013461234979331493,
-0.03557682782411575,
0.03596588224172592,
-0.013183413073420525,
0.008776037953794003,
-0.03971468284726143,
-0.035891152918338776,
-0.017636273056268692,
0.05044351518154144,
0.003833680646494031,
-0.02343691699206829,
-0.00639713229611516,
0.00008858492219587788,
-0.02767280861735344,
0.05032949894666672,
-0.02009899914264679,
0.009308057837188244,
0.005055991932749748,
0.0702262744307518,
0.012048502452671528,
-0.04962144047021866,
0.11124541610479355,
-0.0468771792948246,
-0.0004406421212479472,
0.0022732578217983246,
-0.056496307253837585,
0.03941033408045769,
-0.01183013990521431,
-0.015371772460639477,
-0.006021099165081978,
-0.013952599838376045,
-0.010428765788674355,
-0.014546843245625496,
0.011454037390649319,
0.02624882571399212,
-0.034607045352458954,
0.07322753965854645,
-0.04689737409353256,
-0.025044437497854233,
-0.02303830161690712,
-0.01844148337841034,
0.0063923196867108345,
0.01601184532046318,
0.030672943219542503,
-0.07067260891199112,
0.04178516939282417,
-0.05468451976776123,
0.004174202214926481,
-0.010955678299069405,
-0.006995584815740585,
-0.06802798062562943,
-0.04915415868163109,
0.008126072585582733,
-0.034319326281547546,
-0.06226401403546333,
-0.03034043312072754,
-0.03842724859714508,
-0.03331688046455383,
-0.02905256114900112,
-0.0012837700778618455,
0.008235212415456772,
0.011755446903407574,
0.03141172230243683,
-0.04567212983965874,
0.0029035841580480337,
-0.02625424414873123,
-0.0065210238099098206,
0.01924945041537285,
0.06451398134231567,
-0.047949716448783875,
0.004893860314041376,
0.0001638811081647873,
0.0615692175924778,
-0.05098287761211395,
-0.03337925300002098,
-0.04764264076948166,
-0.014321097172796726,
-0.03705912455916405,
0.02748880535364151,
0.03730998560786247,
-0.06016819551587105,
-0.013302790932357311,
-0.037446875125169754,
0.016637297347187996,
0.03600378707051277
] |
<p>When trying to find the Fourier transform of the Coulomb potential</p>
<p>$$V(\mathbf{r})=-\frac{e^2}{r}$$</p>
<p>one is faced with the problem that the resulting integral is divergent. Usually, it is then argued to introduce a screening factor $e^{-\mu r}$ and take the limit $\lim_{\mu \to 0}$ at the end of the calculation.</p>
<p>This always seemed somewhat ad hoc to me, and I would like to know what the mathematical justification for this procedure is. I could imagine the answer to be along the lines of: well, the Coulomb potential doesn't have a <em>proper</em> FT, but it has a <em>weak</em> FT defined like this …</p>
<p>Edit: Let me try another formulation:</p>
<p>What would a mathematician (being unaware of any physical meanings) do when asked to find the Fourier transform of the Coulomb potential?</p> | g5506 | [
0.057565171271562576,
0.02541332319378853,
0.013956408947706223,
-0.08011607080698013,
0.07514414191246033,
-0.009535618126392365,
0.011584808118641376,
0.03534034267067909,
-0.03599373251199722,
0.005413350649178028,
-0.04231279343366623,
0.010161268524825573,
0.003988700918853283,
0.04448660463094711,
0.0015370489563792944,
-0.050671011209487915,
0.07039687037467957,
0.005488574970513582,
-0.015063480474054813,
0.008117441087961197,
-0.050127431750297546,
0.049655474722385406,
0.048726171255111694,
0.033622875809669495,
0.009866580367088318,
-0.027417480945587158,
0.036056045442819595,
0.0229794904589653,
-0.012814822606742382,
-0.0028844079934060574,
-0.010755660943686962,
0.05534825101494789,
0.04758840054273605,
-0.022822385653853416,
-0.01124307420104742,
-0.01556407567113638,
0.0549103319644928,
0.050940241664648056,
0.002127454150468111,
0.012848109006881714,
-0.02990633063018322,
0.03192300722002983,
0.030164573341608047,
0.031624749302864075,
-0.010371551848948002,
-0.022347507998347282,
-0.03815721720457077,
0.0018552558030933142,
-0.031509313732385635,
-0.011967536062002182,
-0.014801442623138428,
0.02999971993267536,
0.03175931051373482,
-0.05591955408453941,
0.002317497506737709,
-0.019371306523680687,
-0.0507049560546875,
0.021199505776166916,
-0.00585164874792099,
-0.0018674422753974795,
0.051090307533741,
-0.025444814935326576,
-0.010338296182453632,
0.0008616010891273618,
0.048758164048194885,
0.031987518072128296,
-0.03236375004053116,
-0.018568765372037888,
0.014926787465810776,
0.007497902028262615,
0.004253776744008064,
-0.05472474917769432,
-0.008013543672859669,
0.011193097569048405,
-0.014858254231512547,
-0.009227599017322063,
-0.016160236671566963,
0.044510167092084885,
-0.01766398176550865,
-0.006066343281418085,
-0.009313254617154598,
-0.08011330664157867,
-0.00620827404782176,
-0.0277041494846344,
-0.02862498164176941,
-0.020501939579844475,
0.033665645867586136,
0.051402896642684937,
0.025086702778935432,
0.01925811544060707,
-0.022332409396767616,
-0.02890012040734291,
-0.020027419552206993,
-0.009264128282666206,
0.007115587592124939,
0.04442726448178291,
-0.02228480763733387,
-0.0190113615244627,
-0.037783779203891754,
-0.03432229533791542,
0.03403806313872337,
0.04991655424237251,
-0.0524306483566761,
0.006949822884052992,
-0.04131066054105759,
0.0031466821674257517,
0.012636452913284302,
-0.013151895254850388,
0.021754194051027298,
-0.07146397978067398,
-0.03983786329627037,
-0.020616408437490463,
-0.06367240846157074,
-0.040045853704214096,
-0.00312102772295475,
0.028215086087584496,
0.02987394481897354,
0.030010970309376717,
-0.0640810877084732,
0.06126561760902405,
-0.0169043131172657,
0.025390252470970154,
0.09333571046590805,
0.06279658526182175,
0.008106600493192673,
0.009919635951519012,
-0.005526260007172823,
0.01967950351536274,
0.03596019744873047,
-0.0023608901537954807,
0.043836560100317,
0.020643720403313637,
-0.01858697086572647,
-0.049676425755023956,
0.05937349051237106,
0.05838273465633392,
-0.04683617874979973,
0.0470760203897953,
0.001235891249962151,
0.009453427977859974,
0.009439432993531227,
-0.059909332543611526,
0.021415185183286667,
-0.04527201130986214,
-0.045233990997076035,
0.04846100136637688,
-0.022693509235978127,
-0.013142883777618408,
-0.03460000082850456,
0.002245407085865736,
-0.04964812472462654,
0.09482389688491821,
0.06457608193159103,
-0.03352395445108414,
0.023279566317796707,
-0.018357068300247192,
0.06834236532449722,
-0.013505006209015846,
0.0030433309730142355,
0.05761183053255081,
0.07647399604320526,
0.04359358921647072,
-0.055133234709501266,
-0.011148790828883648,
-0.08118601143360138,
0.03182913735508919,
-0.07926547527313232,
-0.019675901159644127,
-0.0036139015574008226,
-0.08475852012634277,
-0.02165028639137745,
0.07390212267637253,
0.05856397747993469,
0.003927464131265879,
-0.00662269676104188,
0.039985381066799164,
0.001839402480982244,
-0.02440720610320568,
-0.011065015569329262,
0.004234285093843937,
-0.047799382358789444,
-0.050663501024246216,
0.03940211236476898,
0.0027494782116264105,
0.034070853143930435,
-0.060128867626190186,
-0.020230986177921295,
0.05296739190816879,
-0.0455450713634491,
0.04025233909487724,
0.01852678880095482,
0.017945025116205215,
-0.05384546145796776,
0.010704349726438522,
-0.04964980483055115,
0.00732079753652215,
0.008754787966609001,
-0.09087183326482773,
-0.00762317655608058,
-0.009635111317038536,
-0.0625227615237236,
0.06967677921056747,
0.04775108024477959,
0.06847816705703735,
0.017903080210089684,
-0.04217206686735153,
0.02053002640604973,
-0.036156050860881805,
0.05278559401631355,
-0.030951250344514847,
0.0013557292986661196,
-0.0648062527179718,
-0.04193552955985069,
-0.01247988548129797,
-0.039842285215854645,
-0.0549652986228466,
0.039272285997867584,
0.03082672320306301,
-0.08447135984897614,
0.029667655006051064,
-0.010854680091142654,
-0.04064951464533806,
0.012031649239361286,
0.053337447345256805,
-0.02594752237200737,
0.022733742371201515,
-0.043716151267290115,
-0.009771745651960373,
0.0006750648026354611,
0.01264486275613308,
-0.05730902776122093,
-0.05093779414892197,
0.03256675973534584,
0.017415473237633705,
0.014500653371214867,
-0.0003214371099602431,
-0.029965531080961227,
-0.009064552374184132,
0.011383004486560822,
0.03638262674212456,
0.0028543216176331043,
-0.04326349124312401,
-0.015155631117522717,
0.04101845994591713,
-0.019209932535886765,
-0.0000972527705016546,
0.03593806177377701,
0.0065145548433065414,
-0.009079714305698872,
-0.014934307895600796,
-0.01664983108639717,
0.0250739436596632,
-0.03441896662116051,
0.04366937652230263,
-0.07424120604991913,
-0.03298531472682953,
0.00975546333938837,
0.051819074898958206,
-0.009981841780245304,
-0.007895277813076973,
-0.0035065594129264355,
0.02738156169652939,
0.05348700284957886,
0.01771596446633339,
-0.08456358313560486,
0.005284739192575216,
-0.09921026974916458,
0.03817082941532135,
0.0008549533667974174,
-0.03443249315023422,
0.014937025494873524,
0.037686314433813095,
-0.0030734091997146606,
0.022148214280605316,
-0.011333279311656952,
-0.0535409115254879,
0.03977159410715103,
-0.013658628799021244,
0.01440346147865057,
-0.014468656852841377,
-0.03423913195729256,
-0.011047073639929295,
0.019918151199817657,
0.03185294196009636,
-0.010363415814936161,
-0.03485853597521782,
0.018377630040049553,
-0.0070618935860693455,
0.020370393991470337,
0.0013428677339106798,
0.012336420826613903,
-0.021669084206223488,
0.005194794852286577,
-0.035999905318021774,
-0.008337078616023064,
0.009309010580182076,
0.03686842694878578,
-0.10576318204402924,
-0.05020463839173317,
0.02993238903582096,
0.02752685360610485,
0.013700105249881744,
0.0020969132892787457,
-0.00641183415427804,
0.03191680088639259,
-0.027148857712745667,
-0.007933605462312698,
-0.03259112313389778,
-0.024639347568154335,
-0.034147754311561584,
-0.00411323131993413,
0.03267506882548332,
0.02984987199306488,
-0.016068898141384125,
-0.03151711821556091,
0.022085625678300858,
0.03503164276480675,
-0.004786141682416201,
0.0411500483751297,
0.003170359181240201,
-0.022285668179392815,
0.00617156270891428,
-0.034803666174411774,
-0.019648199900984764,
0.04158083349466324,
0.011753955855965614,
-0.013685308396816254,
-0.03934141993522644,
-0.04188594967126846,
-0.009227333590388298,
0.015623075887560844,
0.0468730591237545,
-0.022217750549316406,
-0.013235365971922874,
-0.03945460170507431,
-0.009622953832149506,
-0.03650733456015587,
0.05642756447196007,
0.04655400291085243,
-0.0391380712389946,
-0.04152398183941841,
-0.10248176753520966,
-0.002238229848444462,
-0.0006142890779301524,
0.009261158294975758,
0.025858482345938683,
0.007518023252487183,
0.08014971017837524,
0.00482485955581069,
-0.019003527238965034,
-0.05585724860429764,
-0.03473127260804176,
0.0023200586438179016,
-0.024649344384670258,
0.03383541479706764,
0.04444363713264465,
0.04841716215014458,
0.03644857555627823,
0.009941665455698967,
-0.004798078443855047,
0.004371249116957188,
-0.025425365194678307,
-0.00468102702870965,
-0.011854137293994427,
0.032739151269197464,
0.03154058754444122,
-0.019149120897054672,
0.08956290036439896,
-0.02362840063869953,
-0.01933952607214451,
0.009336689487099648,
-0.0011853284668177366,
-0.029822440817952156,
0.03973037376999855,
-0.00128312932793051,
-0.00969657115638256,
-0.02811189368367195,
0.020421842113137245,
0.002373211085796356,
-0.012043852359056473,
0.04924393817782402,
0.023425959050655365,
0.02126198634505272,
0.009941408410668373,
0.06215325742959976,
-0.024712542071938515,
-0.06034489721059799,
-0.004660163540393114,
0.03272804990410805,
0.0033610437531024218,
0.05644279718399048,
0.026217235252261162,
0.02391253598034382,
0.051736533641815186,
-0.0014650137163698673,
-0.008583371527493,
0.027120066806674004,
-0.015317526645958424,
-0.040028370916843414,
0.02399635687470436,
-0.002261130604892969,
-0.051298532634973526,
-0.03205137699842453,
-0.014328153803944588,
-0.03992466628551483,
0.012612706981599331,
0.007116005290299654,
-0.05381316319108009,
0.017125654965639114,
-0.07715363055467606,
0.008518104441463947,
-0.012616878375411034,
0.03144141659140587,
-0.02814393863081932,
-0.009828596375882626,
-0.037208203226327896,
0.015093308873474598,
-0.03224148973822594,
0.03860063478350639,
0.02857935056090355,
-0.001184825785458088,
-0.032878223806619644,
-0.03528178855776787,
0.038661982864141464,
-0.02558107115328312,
0.05247754231095314,
0.03950439766049385,
0.043626412749290466,
0.01617574691772461,
-0.001617698697373271,
-0.00013778860738966614,
0.03262542933225632,
-0.04177526757121086,
0.0507037490606308,
-0.03786761686205864,
0.028299545869231224,
-0.0662965178489685,
-0.07261057198047638,
-0.018418705090880394,
0.09837242215871811,
0.02730555646121502,
-0.04374951496720314,
-0.030490970239043236,
0.033203426748514175,
0.0016030649421736598,
0.059855952858924866,
-0.016830410808324814,
-0.033795829862356186,
0.04692070558667183,
-0.012929096817970276,
-0.0532105416059494,
0.024172214791178703,
0.00498281791806221,
0.010877391323447227,
-0.02772088348865509,
0.022484881803393364,
-0.016066158190369606,
-0.021313732489943504,
0.02147047221660614,
-0.011037899181246758,
-0.012753529474139214,
-0.01108265109360218,
-0.11430247128009796,
-0.01121778879314661,
0.07317238301038742,
0.011950993910431862,
-0.059550993144512177,
0.06486274302005768,
-0.020739583298563957,
0.035732705146074295,
-0.019992977380752563,
0.010330671444535255,
0.05899549648165703,
-0.013199116103351116,
-0.0023684478364884853,
-0.02650129236280918,
0.004538137465715408,
-0.042107827961444855,
-0.09398412704467773,
-0.015139074996113777,
-0.03651254624128342,
-0.0030482804868370295,
0.07483229041099548,
0.011033760383725166,
-0.021580686792731285,
0.012299053370952606,
-0.034937407821416855,
-0.033754825592041016,
-0.04063716530799866,
-0.03248899430036545,
0.03699113801121712,
0.050853975117206573,
0.043893489986658096,
-0.03630002215504646,
0.04176821559667587,
0.06876671314239502,
0.04306083545088768,
0.02200288698077202,
0.008262376300990582,
-0.053747400641441345,
-0.03262916952371597,
0.004407503642141819,
-0.05882551893591881,
0.0191165991127491,
-0.017362389713525772,
-0.004991644062101841,
0.11146672815084457,
-0.03744281455874443,
-0.008633717894554138,
-0.03016834892332554,
-0.019959794357419014,
-0.06305570900440216,
0.028606528416275978,
0.002249122131615877,
0.04330170527100563,
-0.016884803771972656,
-0.06819942593574524,
-0.035535722970962524,
-0.026960350573062897,
-0.03663287311792374,
0.023377738893032074,
0.016283569857478142,
-0.003983397036790848,
-0.03065846860408783,
0.04939118027687073,
-0.04873026907444,
-0.045526161789894104,
-0.02196919545531273,
-0.020666904747486115,
0.07075636088848114,
0.017675727605819702,
-0.004464142490178347,
-0.012483792379498482,
0.03051348775625229,
0.06984899193048477,
0.009885277599096298,
0.02107168734073639,
0.000013321286132850219,
-0.05619185045361519,
-0.015063274651765823,
-0.026539787650108337,
-0.000659427372738719,
0.026216456666588783,
0.05785279721021652,
-0.024531710892915726,
-0.0023099423851817846,
0.05669926851987839,
0.018307365477085114,
0.07246062904596329,
-0.052641257643699646,
-0.02889973670244217,
-0.014173923060297966,
-0.041821278631687164,
-0.002585155423730612,
0.059330444782972336,
-0.005705420859158039,
-0.001022398704662919,
0.018314944580197334,
-0.007358042057603598,
0.01894807443022728,
-0.00441153347492218,
-0.07624300569295883,
-0.022292334586381912,
-0.025677205994725227,
0.0072028436698019505,
-0.0042273784056305885,
0.04211688041687012,
0.058193206787109375,
0.022732317447662354,
0.04366036504507065,
-0.05532358959317207,
-0.02304685488343239,
0.00858471542596817,
-0.04185327887535095,
0.01691662147641182,
0.005234254524111748,
-0.012672603130340576,
-0.002232395578175783,
-0.010197603143751621,
-0.05103480815887451,
0.019135821610689163,
0.02705683931708336,
0.02711203135550022,
-0.04845307767391205,
-0.03357480838894844,
0.03831363096833229,
-0.029589595273137093,
-0.08493031561374664,
0.01923276111483574,
0.026008442044258118,
-0.01493161916732788,
0.04745371639728546,
0.013981458730995655,
-0.00021963210019748658,
0.03630863130092621,
-0.014489378780126572,
-0.011326917447149754,
0.00884854607284069,
-0.007318185642361641,
0.046546969562768936,
0.06124131754040718,
0.001203256892040372,
0.010055344551801682,
-0.048153944313526154,
0.032278794795274734,
-0.002086823806166649,
0.01976768858730793,
0.0472794808447361,
-0.04607328400015831,
0.0328487865626812,
-0.00531707564368844,
-0.0407794788479805,
0.006451049353927374,
-0.0341627299785614,
0.0063737258315086365,
0.04290157929062843,
-0.029859058558940887,
-0.0005025382852181792,
-0.00940424669533968,
0.03736430034041405,
0.0552227757871151,
-0.0203796848654747,
0.014189322479069233,
-0.049947332590818405,
0.05278259143233299,
0.022685112431645393,
-0.009428720921278,
0.03749356046319008,
0.05158984288573265,
-0.00455364678055048,
-0.0027565481141209602,
0.02886631339788437,
-0.0283199530094862,
0.014401793479919434,
0.02659785747528076,
0.07585792243480682,
-0.04885285347700119,
0.0249017346650362,
0.016521459445357323,
-0.013256028294563293,
-0.04302292317152023,
0.025994576513767242,
0.031809575855731964,
-0.011704906821250916,
-0.02445761300623417,
-0.007608563639223576,
0.043910469859838486,
-0.021153056994080544,
-0.07599107176065445,
0.01788124069571495,
0.05144040659070015,
0.005874365568161011,
-0.03134489431977272,
-0.011138363741338253,
-0.010024475865066051,
0.02908877283334732,
0.049783993512392044,
0.027921633794903755,
0.014526143670082092,
-0.014645998366177082,
-0.018055561929941177,
0.0014549792977049947,
-0.025482449680566788,
-0.027454132214188576,
0.043470852077007294,
0.018776098266243935,
-0.012870188802480698,
-0.08386684954166412,
0.035741399973630905,
-0.07428682595491409,
0.02956501580774784,
-0.030717985704541206,
-0.03180437907576561,
0.02402082458138466,
0.09046130627393723,
0.0005597155541181564,
-0.0011637391289696097,
0.027304280549287796,
-0.08774193376302719,
-0.006386858411133289,
-0.04433266818523407,
0.051394280046224594,
0.04058310016989708,
0.005060091614723206,
-0.043228909373283386,
0.018119167536497116,
-0.0606619231402874,
-0.03806890547275543,
-0.007920471951365471,
0.03336010128259659,
0.00799693912267685,
0.01036104653030634,
0.02625773474574089,
-0.04646134749054909,
-0.015678059309720993,
0.020292872563004494,
0.0671500414609909,
-0.0009054612019099295,
0.001628451282158494,
0.03564600273966789,
0.040725793689489365,
-0.008309309370815754,
0.020231196656823158,
-0.04639151692390442,
0.00005596600749413483,
-0.0020761974155902863,
-0.036911845207214355,
-0.02835208550095558,
-0.027523109689354897,
-0.0016706788446754217,
0.04360543191432953,
0.03318687528371811,
0.00987857673317194,
-0.009817966260015965,
0.007697677705436945,
-0.013043039478361607,
0.019798146560788155,
0.015584773384034634,
0.00381936295889318,
-0.010233665816485882,
0.0085072573274374,
-0.008224050514400005,
-0.00381084019318223,
-0.004906763322651386,
-0.0024024888407438993,
0.005775907542556524,
-0.008692458271980286,
0.012808065861463547,
0.028070751577615738,
-0.027880793437361717,
0.021288473159074783,
-0.007133669685572386,
-0.018067996948957443,
-0.022835982963442802,
-0.04744453355669975,
-0.04343949258327484,
-0.004570200107991695,
-0.00012785625585820526,
-0.01780719868838787,
-0.0009762341505847871,
-0.0045114196836948395,
-0.03248753026127815,
-0.0032041757367551327,
-0.020332420244812965,
0.03293543681502342,
0.023622700944542885,
-0.056122466921806335,
-0.01374360267072916,
0.088722363114357,
0.016317687928676605,
-0.008838879875838757,
0.025559429079294205,
-0.00839775800704956,
0.08721324056386948,
0.03346525505185127,
-0.04897051677107811,
-0.00007474515587091446,
0.04661685228347778,
0.06626729667186737,
-0.004757916089147329,
0.007062471006065607,
-0.04748370125889778,
-0.034381166100502014,
0.05850835144519806,
0.01928623951971531,
-0.038654278963804245,
0.004999286495149136,
0.036864861845970154
] |
<p>I am studying a perturbed Toric Code model that is not analytically solvable.
On a torus the ground state degeneracy of the unperturbed model is 4.
Once we turn on the perturbation there is a change in the ground state degeneracy.
I would like to detect this change in ground state degeneracy numerically using exact diagonalization techniques. </p>
<p>On my computer I have stored the action of the Hamiltonian on a set of basis states. So if you give me some state $\left|\psi\right\rangle$ I can give you
$\hat{H}\left|\psi\right\rangle$ in terms of the basis states. Now I used this information to compute the spectrum using the Lanczos algorithm and the Jacobi-Davidson algorithm. While the spectrum itself is correctly reproduced neither of these algorithms reproduces the degeneracy of the ground state correctly - not even in the unperturbed case. </p>
<p>Hence the following question: What are common exact diagonalization algorithms for this type of many-body system that correctly resolve the degeneracy of the ground state? </p>
<p>I am looking forward to your responses!</p> | g5507 | [
0.018618043512105942,
-0.03831372410058975,
0.0024943866301327944,
-0.05128820240497589,
0.05247879400849342,
-0.03283889591693878,
0.03425203263759613,
0.05874272808432579,
-0.003446771763265133,
0.004110513720661402,
-0.010485092177987099,
-0.035861361771821976,
0.0023608810734003782,
0.07407017052173615,
0.022272728383541107,
0.03830896317958832,
0.052439168095588684,
0.043471984565258026,
-0.04148710146546364,
-0.04243384674191475,
0.03000696934759617,
0.00924330297857523,
0.032413214445114136,
-0.0344085656106472,
0.004900277126580477,
-0.08206676691770554,
0.013942345976829529,
0.0001697211409918964,
-0.026334933936595917,
0.013777290470898151,
-0.034566495567560196,
0.007460162043571472,
0.02872971072793007,
-0.010347497649490833,
-0.050230298191308975,
0.05481056123971939,
0.08925873786211014,
-0.013301754370331764,
-0.00700768968090415,
-0.06762083619832993,
-0.0004297585692256689,
-0.03611302003264427,
0.018342379480600357,
-0.017889605835080147,
-0.04270068183541298,
-0.05681796744465828,
0.022729113698005676,
-0.032968927174806595,
-0.04662315919995308,
0.06142599880695343,
-0.0026488436851650476,
-0.02684561349451542,
0.1284337043762207,
-0.05781278386712074,
-0.010014386847615242,
0.02591695263981819,
-0.06920843571424484,
-0.08721091598272324,
0.036387402564287186,
0.07380811125040054,
0.0051003722473979,
-0.02594134397804737,
-0.006911395583301783,
-0.0866321250796318,
-0.05465059354901314,
0.009655699133872986,
-0.06272754818201065,
0.012489804066717625,
0.015745317563414574,
-0.01806376688182354,
-0.01595824398100376,
-0.04885666072368622,
-0.011680792085826397,
0.003243023529648781,
-0.021404065191745758,
0.00904157292097807,
-0.0006672377930954099,
0.0031157026533037424,
0.04828178510069847,
0.030168088153004646,
-0.03543907031416893,
-0.044561441987752914,
-0.015074724331498146,
-0.05049543082714081,
-0.025340082123875618,
0.007494826801121235,
-0.006026885937899351,
0.050816334784030914,
0.024626227095723152,
0.013002772815525532,
0.0012607175158336759,
0.035026419907808304,
0.028211362659931183,
-0.001992398640140891,
-0.004583586007356644,
0.011961007490754128,
-0.05850618705153465,
0.0662955790758133,
-0.013776161707937717,
-0.020260561257600784,
-0.034152738749980927,
-0.0012289963196963072,
-0.045839712023735046,
-0.030350659042596817,
-0.015691058710217476,
0.002582530491054058,
0.07285260409116745,
-0.058773718774318695,
-0.02802935242652893,
-0.016786612570285797,
-0.032255955040454865,
0.030894001945853233,
-0.004144839942455292,
-0.017640599980950356,
-0.033065736293792725,
0.0018164205830544233,
0.021700937300920486,
0.008614669553935528,
-0.054174356162548065,
0.029882976785302162,
0.05221657454967499,
-0.025424698367714882,
-0.01365552470088005,
-0.03412387892603874,
0.045161325484514236,
0.02342814952135086,
-0.06270374357700348,
0.029701966792345047,
0.024421721696853638,
-0.00538629200309515,
0.016020720824599266,
-0.02194293402135372,
0.017512036487460136,
0.06583788990974426,
0.008434748277068138,
0.0022594232577830553,
0.02239580824971199,
-0.000023301354303839616,
0.03315200284123421,
0.009658507071435452,
-0.02271115779876709,
-0.03175206109881401,
-0.01895345374941826,
-0.01486206240952015,
0.040595486760139465,
-0.0023074978962540627,
-0.036809924989938736,
-0.04190162941813469,
0.06118552386760712,
-0.0027438439428806305,
0.015844371169805527,
0.02400505356490612,
0.06036859378218651,
-0.025944404304027557,
0.012044531293213367,
0.03876947984099388,
0.02099456824362278,
-0.03252137452363968,
-0.0007927096448838711,
0.04477941617369652,
-0.018114974722266197,
0.025893280282616615,
0.03410563990473747,
0.018369698897004128,
0.004113334696739912,
0.00954435858875513,
0.005945146083831787,
-0.0681735947728157,
-0.03539808467030525,
-0.029235804453492165,
-0.0015851501375436783,
-0.008629823103547096,
0.016959672793745995,
0.04199361801147461,
-0.01202191598713398,
0.09537435322999954,
-0.05389009788632393,
-0.05248811095952988,
0.03720690682530403,
0.016164327040314674,
0.05091116204857826,
0.01234076265245676,
0.02264840342104435,
0.030051257461309433,
-0.04186227172613144,
0.035925403237342834,
0.020907705649733543,
-0.0025957408361136913,
0.039347223937511444,
-0.0015499021392315626,
-0.04339073598384857,
0.034452151507139206,
0.005191591568291187,
-0.0016232429770752788,
-0.03100328892469406,
-0.03020532801747322,
0.031849782913923264,
-0.05867411196231842,
-0.017892634496092796,
-0.03977946937084198,
0.03518734127283096,
0.003970951307564974,
-0.0021523202303797007,
0.026734020560979843,
0.006265285424888134,
-0.01991429552435875,
0.03422868996858597,
-0.006155695300549269,
0.010242801159620285,
-0.027700038626790047,
0.01911231130361557,
-0.016608353704214096,
-0.011347134597599506,
0.021754413843154907,
-0.016744935885071754,
0.0019676063675433397,
0.021684180945158005,
-0.020471131429076195,
-0.008113443851470947,
0.0014490813482552767,
-0.002857858082279563,
0.01585233397781849,
-0.006422559265047312,
0.05120357125997543,
0.0026883361861109734,
0.017798494547605515,
-0.020148521289229393,
0.052943985909223557,
-0.023247642442584038,
-0.009332969784736633,
-0.0019093581940978765,
0.014736644923686981,
-0.016156518831849098,
-0.05583224818110466,
0.01696922816336155,
0.0664072185754776,
-0.009115652181208134,
-0.01859288662672043,
0.04188856482505798,
-0.017440883442759514,
0.001581614720635116,
-0.0004718864511232823,
0.0025252001360058784,
0.009304391220211983,
0.09094832837581635,
-0.0008612358942627907,
0.006571188569068909,
0.036411285400390625,
-0.04919534921646118,
0.009257948026061058,
0.0025719087570905685,
0.037100087851285934,
-0.05890629068017006,
-0.008937020786106586,
-0.01075446791946888,
-0.026886513456702232,
0.019528497010469437,
0.02065136283636093,
0.016796745359897614,
-0.043929293751716614,
-0.018672864884138107,
-0.02823432721197605,
0.009091426618397236,
0.020024944096803665,
-0.04820486158132553,
-0.013872219249606133,
0.04689885303378105,
-0.05906229093670845,
-0.0732221007347107,
-0.04287169873714447,
-0.038978271186351776,
0.07102259248495102,
0.01930859498679638,
0.03146270290017128,
-0.0007265869062393904,
-0.003330386243760586,
-0.02256081812083721,
-0.027263756841421127,
-0.044915586709976196,
-0.023023275658488274,
-0.026811916381120682,
0.001461361418478191,
0.0288185216486454,
0.02945103496313095,
0.037208281457424164,
-0.03875935822725296,
-0.03426153585314751,
0.029092464596033096,
-0.017956456169486046,
0.01642744056880474,
-0.012964550405740738,
0.029833678156137466,
0.034816090017557144,
-0.029310688376426697,
-0.02634904906153679,
-0.0059927161782979965,
-0.023314915597438812,
-0.029516959562897682,
0.02577422931790352,
0.1177474781870842,
0.05065695196390152,
-0.006523716729134321,
0.03424525633454323,
-0.045887384563684464,
0.031502872705459595,
-0.08190209418535233,
-0.04238096624612808,
0.033565834164619446,
0.037742383778095245,
0.049426253885030746,
-0.003185662440955639,
0.001764033455401659,
0.016672590747475624,
-0.018929973244667053,
0.03505007550120354,
0.012841373682022095,
0.016093585640192032,
-0.05427658557891846,
-0.01969955302774906,
0.03153381496667862,
0.000955709780100733,
-0.01562778651714325,
0.02968561463057995,
0.018121818080544472,
-0.01992952823638916,
0.054631758481264114,
-0.0772942379117012,
0.0243306215852499,
-0.05083409324288368,
-0.012359955348074436,
0.03041026182472706,
-0.026018982753157616,
0.03539121523499489,
0.005421506240963936,
-0.0579114630818367,
-0.07872849702835083,
-0.07998961210250854,
0.011528663337230682,
0.01983673684298992,
-0.017216471955180168,
-0.04172633960843086,
-0.02891196310520172,
-0.005917150527238846,
-0.025988103821873665,
0.0050679841078817844,
0.030409742146730423,
-0.026850340887904167,
-0.027000650763511658,
-0.10558523237705231,
-0.017482489347457886,
-0.013023726642131805,
-0.01601114310324192,
0.029013536870479584,
-0.043568551540374756,
-0.011693889275193214,
0.014985380694270134,
-0.02624896727502346,
0.03584606572985649,
-0.006256599444895983,
0.036745741963386536,
-0.028880901634693146,
-0.02288690023124218,
-0.00042036891682073474,
0.03279751166701317,
0.06009864807128906,
0.024903561919927597,
0.02914576232433319,
-0.019881388172507286,
0.029059194028377533,
0.009485259652137756,
0.0020840761717408895,
0.022763483226299286,
0.00786823220551014,
-0.04720162972807884,
0.03667778521776199,
-0.003522193292155862,
-0.0487477108836174,
-0.016105029731988907,
0.015931036323308945,
0.04596644267439842,
-0.03013777546584606,
0.004429533611983061,
0.026189133524894714,
-0.000049915568524738774,
-0.017992839217185974,
0.052743587642908096,
0.03311750292778015,
0.06865816563367844,
-0.017626967281103134,
0.02944820560514927,
0.00478738360106945,
-0.09186888486146927,
0.009033222682774067,
0.00848410464823246,
-0.021575413644313812,
0.0036489409394562244,
0.006598057225346565,
0.029049916192889214,
-0.008254699409008026,
0.04914594814181328,
-0.019035357981920242,
-0.06281013041734695,
0.009017492644488811,
-0.0456303246319294,
-0.009541871026158333,
0.030853746458888054,
-0.029804468154907227,
0.00608879653736949,
0.0023359484039247036,
0.018699755892157555,
0.011521152220666409,
0.00171866815071553,
0.021407976746559143,
-0.04374562203884125,
0.04145311564207077,
0.015454438515007496,
0.059811390936374664,
0.0177481546998024,
0.0487210638821125,
0.033416472375392914,
0.030303260311484337,
0.0656975731253624,
0.01273384876549244,
0.037413135170936584,
-0.00722398841753602,
0.020742174237966537,
-0.01772664487361908,
-0.00813806802034378,
-0.004360946360975504,
0.022291723638772964,
0.03086051531136036,
-0.05468006432056427,
-0.004559101536870003,
0.04055254906415939,
-0.06254471838474274,
-0.019160952419042587,
-0.03244640305638313,
0.045541465282440186,
0.012474077753722668,
0.0653112456202507,
0.07338933646678925,
0.026095157489180565,
0.022186806425452232,
-0.02953748218715191,
-0.05894612520933151,
0.034716032445430756,
-0.02929377369582653,
0.012833324261009693,
0.03923764079809189,
-0.009630152955651283,
0.00513409124687314,
0.029818447306752205,
-0.0019292521756142378,
0.01550870481878519,
-0.005477237980812788,
-0.07375925779342651,
-0.03890109062194824,
0.06528290361166,
-0.009970844723284245,
0.04551881179213524,
-0.005941067822277546,
0.00860046036541462,
-0.08573545515537262,
0.015426361002027988,
-0.02906103990972042,
-0.005570409819483757,
-0.025413507595658302,
0.07933788746595383,
0.0029072717297822237,
0.014257271774113178,
0.05291500687599182,
-0.01425929181277752,
0.02412450686097145,
-0.009182536974549294,
-0.024219593033194542,
0.050279442220926285,
0.0022978598717600107,
-0.04483778402209282,
0.0638437420129776,
0.007604791317135096,
-0.043374478816986084,
-0.028754297643899918,
0.06703634560108185,
0.017497196793556213,
-0.009422751143574715,
0.06777472794055939,
0.029450559988617897,
-0.04629211500287056,
-0.0678936019539833,
-0.033039391040802,
0.003429856849834323,
0.03476085513830185,
0.007808545604348183,
-0.039545346051454544,
0.052216533571481705,
-0.031888242810964584,
-0.01347652543336153,
-0.01311890035867691,
-0.026714293286204338,
-0.009736998938024044,
-0.04635968804359436,
0.013652730733156204,
0.031077228486537933,
0.039593927562236786,
-0.04752127826213837,
0.043043989688158035,
0.08003797382116318,
-0.028145868331193924,
0.00690331868827343,
0.0038484190590679646,
-0.06839542835950851,
0.04914933070540428,
0.06956518441438675,
0.026362942531704903,
-0.06222611293196678,
-0.05103723332285881,
0.0001735497935442254,
0.029120445251464844,
-0.02240096963942051,
-0.11670621484518051,
0.0012095558922737837,
-0.0403393916785717,
0.013043857179582119,
-0.019064495339989662,
0.02261260896921158,
0.022351235151290894,
0.04443799704313278,
-0.04557676613330841,
-0.09462644159793854,
0.04206481948494911,
0.03199106082320213,
0.01552093867212534,
-0.06602222472429276,
-0.008466999046504498,
0.01474581379443407,
0.010149946436285973,
-0.0073324148543179035,
-0.022232627496123314,
0.030480245128273964,
0.004308354575186968,
0.056683849543333054,
-0.026729250326752663,
0.0669092983007431,
0.00023842821246944368,
-0.07794155925512314,
-0.06983490288257599,
-0.024953486397862434,
0.03189290314912796,
-0.06041279807686806,
-0.043997783213853836,
-0.06393008679151535,
-0.00009772466728463769,
-0.013450803235173225,
-0.06108526140451431,
0.01983935758471489,
0.009334725327789783,
-0.04788239672780037,
-0.038979340344667435,
0.02453242428600788,
0.04228326678276062,
0.022610770538449287,
0.005168014205992222,
0.04918881505727768,
-0.03745793178677559,
0.02972196787595749,
-0.0011776229366660118,
-0.047210678458213806,
-0.030510399490594864,
0.04130159318447113,
-0.032250162214040756,
0.010889497585594654,
-0.012163589708507061,
0.014499258249998093,
0.029321923851966858,
-0.005635210778564215,
0.021348046138882637,
-0.04033982753753662,
-0.015455407090485096,
-0.01234742347151041,
0.06402613967657089,
-0.022276991978287697,
-0.003916643559932709,
0.061019133776426315,
0.02500169351696968,
-0.03263803571462631,
-0.011710258200764656,
-0.0022532681468874216,
0.014201437123119831,
0.023373857140541077,
0.017278093844652176,
-0.057784948498010635,
0.031723540276288986,
-0.012266010977327824,
-0.03853757306933403,
0.01334168016910553,
0.007432672660797834,
-0.009296366944909096,
0.019879404455423355,
-0.03159608691930771,
0.026714758947491646,
0.01523785199970007,
-0.05002571642398834,
0.04170903563499451,
-0.05551914498209953,
-0.006763650570064783,
0.04389242082834244,
-0.05025111883878708,
-0.014564153738319874,
-0.0433812253177166,
0.03152993693947792,
0.018383203074336052,
-0.0635111853480339,
-0.025091100484132767,
-0.024253541603684425,
0.006137799005955458,
-0.05352984368801117,
0.012923911213874817,
0.02108798362314701,
0.023624761030077934,
0.005185589659959078,
0.020826470106840134,
0.007958145812153816,
0.0522560216486454,
-0.022040100768208504,
0.015979688614606857,
0.04953800141811371,
-0.022273415699601173,
-0.0704704001545906,
0.01787819154560566,
-0.004470583982765675,
0.03975842148065567,
-0.05162820219993591,
-0.0024981354363262653,
0.008530233055353165,
0.04000871628522873,
0.04274151474237442,
-0.043172597885131836,
0.05397285521030426,
0.008254575543105602,
0.026648065075278282,
-0.007972859777510166,
0.015813464298844337,
0.028599316254258156,
-0.05033743754029274,
-0.030019957572221756,
-0.00033242450444959104,
0.019603058695793152,
0.004796181805431843,
-0.05529734119772911,
0.006311536766588688,
0.03576726093888283,
0.02524215169250965,
0.010663104243576527,
0.02057437039911747,
-0.02856036089360714,
-0.0006559953326359391,
0.06652864068746567,
-0.03272389993071556,
0.06609921157360077,
-0.015349994413554668,
0.006867247633635998,
-0.011279760859906673,
-0.0034539198968559504,
-0.005110279191285372,
0.06712102144956589,
0.03333447873592377,
-0.004754376132041216,
-0.029758650809526443,
0.022219689562916756,
-0.009355791844427586,
0.012656736187636852,
-0.014323118142783642,
-0.08664645999670029,
0.03044239804148674,
-0.012402388267219067,
0.03274230286478996,
0.006434516049921513,
0.0006098478334024549,
-0.010001320391893387,
-0.04213949665427208,
-0.012303289026021957,
0.011042632162570953,
-0.005658927373588085,
-0.044069938361644745,
-0.06807691603899002,
0.0359610989689827,
-0.006457214709371328,
0.030681028962135315,
-0.04091769829392433,
0.0004710528301075101,
0.020429827272892,
0.09576887637376785,
-0.02751803584396839,
0.005910975858569145,
-0.062054626643657684,
0.017675429582595825,
-0.05932139605283737,
-0.004797537345439196,
0.0722520500421524,
-0.021244307979941368,
-0.002935097785666585,
-0.05693870782852173,
0.018024057149887085,
0.004472727421671152,
0.018589595332741737,
-0.031215902417898178,
-0.01825777441263199,
0.004984772764146328,
-0.012069524265825748,
0.044307202100753784,
0.0381038673222065,
-0.03664449602365494,
-0.0203848909586668,
-0.0019946813117712736,
-0.01807452365756035,
-0.0006209167186170816,
-0.050443366169929504,
0.004338474944233894,
0.018493527546525,
-0.029420144855976105,
-0.01015207264572382,
-0.03196033090353012,
-0.020158512517809868,
0.07808640599250793,
0.006164561491459608,
-0.059898559004068375,
-0.038437485694885254,
0.03675833344459534,
0.039930831640958786,
0.021663594990968704,
-0.005501281935721636,
0.03542286530137062,
0.016790002584457397,
0.04282137751579285,
-0.033977363258600235,
0.05110190063714981,
-0.08838990330696106,
-0.06209900230169296,
-0.019147347658872604,
0.02100648172199726,
-0.04244481399655342,
-0.02512272633612156,
0.01219189539551735,
0.0004139624070376158,
0.07085208594799042,
0.054260216653347015,
0.01561286486685276,
0.03880247473716736,
0.046407319605350494,
-0.03272256627678871,
-0.03181042522192001,
0.005354628432542086,
0.009291223250329494,
0.0206918902695179,
-0.07996483892202377,
0.039248283952474594,
0.017345231026411057,
0.030215689912438393,
0.034286126494407654,
-0.0033038815017789602,
-0.0401063971221447,
-0.01075096894055605,
0.0027241010684520006,
-0.003469810588285327,
0.013231399469077587,
-0.0512210987508297,
-0.011865788139402866,
0.08044100552797318
] |
<p>I'm looking for the contactless methods to collect the information of the body construction especially skeletal structure to calculate in the computer model .
Are there physical methods to inspect internal side of the body other than X-ray and no any exposure of radiation ? For example, echo , MRI and so on . </p> | g5508 | [
0.03502444177865982,
-0.010331070981919765,
0.025734642520546913,
-0.017204703763127327,
-0.05185122787952423,
0.005444489419460297,
0.027732888236641884,
0.025767723098397255,
-0.03208043798804283,
-0.004411053843796253,
0.03400101140141487,
0.016353897750377655,
0.07477561384439468,
-0.028607653453946114,
-0.012648440897464752,
-0.03515203297138214,
-0.022135484963655472,
-0.019175194203853607,
0.007827489636838436,
0.060639530420303345,
-0.01843911036849022,
0.06023779138922691,
0.024883046746253967,
0.04341863840818405,
-0.08979984372854233,
-0.0186619833111763,
-0.017677893862128258,
0.039995938539505005,
0.0018379429820924997,
-0.02626190148293972,
-0.030355127528309822,
-0.04309006780385971,
0.02665850706398487,
-0.02794019505381584,
-0.011689851060509682,
-0.04684877023100853,
0.042350877076387405,
0.045424044132232666,
-0.037304334342479706,
0.026630915701389313,
0.013272853568196297,
-0.07610428333282471,
0.0025373862590640783,
-0.028701379895210266,
0.0007365652709268034,
0.05117765814065933,
-0.00610488373786211,
-0.045796655118465424,
0.016052966937422752,
0.018361639231443405,
0.009509203024208546,
-0.025971485301852226,
0.005300123710185289,
0.013344521634280682,
0.01799858547747135,
-0.06492557376623154,
0.019104687497019768,
-0.03808362036943436,
0.09814323484897614,
-0.08549272269010544,
0.015244785696268082,
0.02895660512149334,
-0.01482375431805849,
-0.0036687045358121395,
0.031651221215724945,
-0.010728609748184681,
-0.0659307911992073,
0.018847305327653885,
0.01681317575275898,
0.020379668101668358,
-0.0042624687775969505,
0.016093919053673744,
0.009874165058135986,
-0.02971513383090496,
-0.05881346017122269,
0.0012630191631615162,
-0.01901240274310112,
-0.027293717488646507,
-0.012239568866789341,
0.03341794013977051,
-0.041779614984989166,
-0.0173359178006649,
0.026372985914349556,
-0.03488510847091675,
0.020612496882677078,
0.03193146362900734,
-0.030874954536557198,
0.04582025483250618,
0.029394330456852913,
0.020061034709215164,
-0.013676058501005173,
0.03390183299779892,
0.06677839905023575,
0.023947250097990036,
0.006818538997322321,
0.03965604677796364,
-0.027692236006259918,
0.07155515998601913,
0.018856586888432503,
-0.03393426164984703,
-0.009282044135034084,
0.007710259407758713,
0.01631929539144039,
0.01295146718621254,
-0.042383525520563126,
-0.02597157098352909,
-0.019675789400935173,
-0.009853419847786427,
0.009416386485099792,
0.015853960067033768,
-0.020703397691249847,
-0.03288174420595169,
-0.02642258256673813,
0.05883748456835747,
0.05880965292453766,
-0.0492386557161808,
0.05692781135439873,
-0.030610911548137665,
-0.0037422196473926306,
0.036477867513895035,
-0.009007995948195457,
-0.05139784887433052,
-0.00041577365482226014,
-0.011645212769508362,
-0.05200481414794922,
-0.021832268685102463,
-0.018293026834726334,
0.02013811469078064,
-0.019724953919649124,
-0.022977769374847412,
0.029456298798322678,
0.027956005185842514,
0.0020951235201209784,
0.014882789924740791,
0.061518166214227676,
0.049444738775491714,
-0.02773907780647278,
-0.06395566463470459,
0.040991637855768204,
-0.06653354316949844,
-0.029963938519358635,
0.03781743347644806,
-0.04083484411239624,
-0.005549644120037556,
0.04190845414996147,
0.03645744174718857,
0.029658155515789986,
0.015203715302050114,
0.04030296206474304,
0.04269210994243622,
-0.036042142659425735,
0.07255752384662628,
-0.0031821972224861383,
-0.0685209110379219,
0.024959443137049675,
-0.011810806579887867,
0.03207429498434067,
-0.04674861207604408,
0.008062747307121754,
0.04886259511113167,
0.010348078794777393,
0.013211027719080448,
0.05463167279958725,
-0.0009177267784252763,
0.0003098819579463452,
-0.04543901979923248,
-0.05234162509441376,
-0.04214530810713768,
0.08276192098855972,
-0.027926284819841385,
-0.0021616839803755283,
-0.0035416868049651384,
0.003895658301189542,
0.08620379120111465,
-0.0007798397564329207,
-0.0008188980864360929,
-0.001808285596780479,
-0.06219492480158806,
0.08587121218442917,
0.03297465294599533,
-0.03683733567595482,
0.04631536826491356,
0.027785152196884155,
0.013022121042013168,
-0.042512547224760056,
-0.019875893369317055,
0.01876845210790634,
0.003100696252658963,
0.014293322339653969,
-0.022724349051713943,
-0.037413761019706726,
-0.015120766125619411,
0.005099376197904348,
0.024017898365855217,
0.0038892230950295925,
0.007863301783800125,
0.040346790105104446,
0.04821833595633507,
0.06686313450336456,
0.0056052375584840775,
0.00046579245827160776,
0.09602289646863937,
-0.03364529460668564,
0.040005091577768326,
-0.04951760917901993,
-0.0404624380171299,
-0.004748922772705555,
-0.032564181834459305,
-0.04028768464922905,
0.04361036792397499,
-0.01253163069486618,
0.03855004906654358,
0.0005500726983882487,
0.011664088815450668,
-0.003415871411561966,
-0.03978433832526207,
-0.048323336988687515,
-0.03499924764037132,
-0.0180948618799448,
-0.028177494183182716,
0.06977211683988571,
-0.032588891685009,
-0.002786947414278984,
-0.008596556261181831,
0.01923518255352974,
0.015549097210168839,
-0.01968899741768837,
0.036917079240083694,
0.0651622787117958,
-0.03718038275837898,
-0.06611042469739914,
-0.03434833884239197,
0.05341215804219246,
-0.005842389538884163,
0.019762970507144928,
0.050086792558431625,
-0.03925122693181038,
-0.004562702961266041,
0.026439644396305084,
0.014277511276304722,
0.05480396747589111,
-0.060217615216970444,
-0.07380424439907074,
-0.07413029670715332,
0.0296135563403368,
-0.03158655762672424,
-0.011097738519310951,
0.051053136587142944,
0.03234436362981796,
0.007676297798752785,
0.027484113350510597,
0.06938013434410095,
-0.0359044075012207,
-0.019175654277205467,
-0.03209381178021431,
0.016474053263664246,
-0.012252171523869038,
-0.01497916504740715,
-0.0456913486123085,
-0.0678696483373642,
-0.03252897411584854,
-0.02864445373415947,
-0.019725777208805084,
0.03282061964273453,
-0.0761970579624176,
0.004534451756626368,
-0.0843556597828865,
-0.03113713674247265,
-0.00601482018828392,
0.021395891904830933,
-0.038312505930662155,
0.021914934739470482,
0.051962703466415405,
0.03856143727898598,
0.025905542075634003,
-0.020109495148062706,
0.061577752232551575,
-0.005284311715513468,
-0.004941917490214109,
-0.06826844066381454,
0.039703041315078735,
-0.000891492236405611,
0.02111745811998844,
0.015020267106592655,
0.024100633338093758,
0.01478332094848156,
-0.017469920217990875,
-0.06008673459291458,
-0.009281286038458347,
-0.014741946943104267,
0.036809857934713364,
-0.07203178107738495,
-0.04593880474567413,
0.031815461814403534,
-0.06495248526334763,
0.04751216247677803,
0.0405551977455616,
-0.0034272901248186827,
0.027247771620750427,
0.06950888782739639,
-0.03952807933092117,
0.004919820930808783,
0.030184723436832428,
-0.06948830932378769,
-0.03685765713453293,
-0.03311996906995773,
-0.03971768170595169,
-0.026353688910603523,
0.029497642070055008,
0.010403374210000038,
-0.022419864311814308,
-0.012034053914248943,
0.05933407321572304,
-0.01677970588207245,
0.03753615543246269,
-0.04467089846730232,
-0.03991074487566948,
-0.002019446110352874,
0.010363532230257988,
0.02403438650071621,
-0.024281345307826996,
0.04006485641002655,
0.027748584747314453,
-0.04259967803955078,
0.007746725343167782,
-0.02146134153008461,
0.016484754160046577,
0.030300891026854515,
-0.05050280690193176,
-0.025610677897930145,
0.015549448318779469,
0.05453115329146385,
-0.015915565192699432,
-0.0071918242610991,
-0.050768982619047165,
-0.01101632323116064,
-0.02397930808365345,
0.013411098159849644,
0.033670954406261444,
0.030973950400948524,
0.022221706807613373,
-0.06651571393013,
0.003596583614125848,
-0.023520197719335556,
0.011509325355291367,
-0.029491320252418518,
-0.049529965966939926,
0.016457078978419304,
0.009459362365305424,
-0.07267430424690247,
0.05418946221470833,
0.08181969821453094,
-0.05766693502664566,
-0.06518346816301346,
-0.012443668209016323,
0.06431568413972855,
0.009172094985842705,
0.026045605540275574,
-0.004870058503001928,
-0.010655094869434834,
-0.022234836593270302,
-0.020683206617832184,
0.02415049448609352,
0.0005634603439830244,
-0.007989254780113697,
-0.04231196641921997,
0.062278177589178085,
0.03069937787950039,
0.05849871411919594,
-0.02121264487504959,
-0.04123130440711975,
-0.01043468527495861,
0.03925195708870888,
-0.06166599318385124,
-0.031042534857988358,
0.013853158801794052,
0.0023267539218068123,
-0.03134515881538391,
-0.0008621075539849699,
0.014254830777645111,
-0.021673766896128654,
-0.004698042757809162,
0.06547442078590393,
0.03714575245976448,
-0.002654521493241191,
0.00973124522715807,
-0.02295987866818905,
-0.005784349050372839,
-0.022738654166460037,
0.022174498066306114,
0.031036240980029106,
-0.08768211305141449,
-0.04067104682326317,
0.01280326396226883,
-0.009367376565933228,
-0.031978778541088104,
-0.02017086185514927,
-0.030021561309695244,
0.008441689424216747,
-0.015823446214199066,
0.024082966148853302,
0.005548837594687939,
0.040913619101047516,
0.03993174061179161,
-0.037369851022958755,
0.06999152898788452,
0.0035276112612336874,
-0.049810606986284256,
-0.020462332293391228,
-0.0006929738447070122,
-0.014105090871453285,
0.006011749617755413,
0.07843976467847824,
-0.02334120310842991,
0.05131508782505989,
0.03310437500476837,
0.020308101549744606,
-0.03867003321647644,
0.029173430055379868,
0.0752343162894249,
-0.010189538821578026,
0.015268281102180481,
-0.012728196568787098,
0.0012199317570775747,
-0.03371533006429672,
0.0404692143201828,
0.01796592026948929,
-0.020580828189849854,
-0.00975164957344532,
0.00736989127472043,
0.010218390263617039,
-0.024890825152397156,
0.006916244979947805,
0.09456606954336166,
-0.05883613973855972,
0.06042509526014328,
-0.030832698568701744,
0.02592437155544758,
0.0063072694465518,
-0.026729220524430275,
0.005185363814234734,
0.03702237457036972,
0.011948945000767708,
-0.022539425641298294,
-0.04241038113832474,
0.053282998502254486,
-0.05039124935865402,
-0.04118676111102104,
-0.044085755944252014,
-0.004056313540786505,
0.003006705781444907,
0.002486035693436861,
-0.027426229789853096,
-0.03631244972348213,
-0.026032648980617523,
0.0037161833606660366,
0.0009863226441666484,
-0.01491852942854166,
0.011701544746756554,
0.03448916971683502,
0.0014940730761736631,
-0.015531064942479134,
-0.026290833950042725,
-0.003990926314145327,
-0.04102609306573868,
-0.004907177295535803,
-0.0738452896475792,
0.012189614586532116,
-0.020704304799437523,
0.07131101191043854,
-0.0051282173953950405,
0.018499067053198814,
0.08010107278823853,
-0.08627800643444061,
-0.022069400176405907,
0.07145491242408752,
-0.04992937296628952,
0.013782146386802197,
-0.020586051046848297,
-0.009590813890099525,
0.0041219028644263744,
0.05190479755401611,
-0.05911210551857948,
-0.009070169180631638,
-0.01340316142886877,
-0.019207822158932686,
-0.02331332303583622,
0.050399504601955414,
-0.033009499311447144,
0.00131879688706249,
0.005116138141602278,
0.012418816797435284,
0.05098181962966919,
-0.02778770960867405,
-0.02082858420908451,
-0.03009648621082306,
0.017932135611772537,
0.01596999168395996,
0.023129859939217567,
0.03254275023937225,
-0.02441898174583912,
0.005515390541404486,
-0.036085329949855804,
-0.03601251542568207,
0.029591303318738937,
-0.010901612229645252,
0.055962640792131424,
-0.011270485818386078,
-0.040609098970890045,
0.05197164788842201,
0.034472767263650894,
-0.009446274489164352,
0.0006407511536963284,
0.002867873525246978,
-0.030951377004384995,
-0.009929060935974121,
0.017547104507684708,
0.02759033627808094,
-0.01944096013903618,
-0.038280509412288666,
0.027694303542375565,
-0.006601373199373484,
0.05740908160805702,
0.1052885428071022,
-0.0166882686316967,
-0.011605505831539631,
0.029962001368403435,
-0.031456246972084045,
0.02439742721617222,
-0.04477297514677048,
0.012094087898731232,
-0.011182493530213833,
-0.02544308267533779,
0.03562343865633011,
-0.0883568823337555,
-0.05357099324464798,
0.024920493364334106,
0.05955798178911209,
0.03802235424518585,
-0.05471043661236763,
0.07598576694726944,
0.03026106022298336,
0.023863330483436584,
0.02410355769097805,
-0.007879752665758133,
-0.042987119406461716,
0.013574382290244102,
-0.0008272864506579936,
-0.02010968141257763,
0.007597323972731829,
0.008397212252020836,
0.037245750427246094,
-0.014682352542877197,
0.019440261647105217,
-0.009116982109844685,
-0.035058919340372086,
-0.011005154810845852,
-0.015711408108472824,
0.01039975881576538,
-0.02842937968671322,
0.026313116773962975,
-0.013045127503573895,
-0.013077571988105774,
0.009274271316826344,
-0.0025912064593285322,
-0.0006875439430586994,
-0.006045141257345676,
0.004531719256192446,
0.016739415004849434,
-0.024929150938987732,
-0.002225394593551755,
-0.0395813062787056,
-0.023587768897414207,
0.000032160267437575385,
-0.023233164101839066,
0.051775142550468445,
0.02448863536119461,
-0.001298680785112083,
0.05064920708537102,
0.029639996588230133,
-0.018512848764657974,
0.030945343896746635,
-0.0018838753458112478,
0.026778455823659897,
0.061116062104701996,
0.05036796256899834,
-0.01412039902061224,
-0.0308871790766716,
-0.03159566596150398,
-0.008032375946640968,
-0.022048989310860634,
-0.0005971940117888153,
-0.021481486037373543,
-0.027145378291606903,
-0.023515773937106133,
-0.006290890276432037,
-0.018452346324920654,
0.021869385614991188,
0.023849403485655785,
0.0440637581050396,
-0.048730287700891495,
0.0028375100810080767,
-0.021011656150221825,
-0.05712512135505676,
0.01771172322332859,
-0.04645547643303871,
0.024516701698303223,
-0.008546886034309864,
-0.002899722196161747,
-0.06848073750734329,
-0.014766666106879711,
0.01972837746143341,
-0.03620481491088867,
0.002304486697539687,
-0.026461156085133553,
-0.016019189730286598,
-0.0015835558297112584,
-0.04253500699996948,
0.003561413148418069,
-0.036637336015701294,
-0.011548671871423721,
-0.010387270711362362,
0.007097163237631321,
0.0060241855680942535,
0.039851270616054535,
0.03277061879634857,
-0.015241535380482674,
0.019702935591340065,
0.025534722954034805,
-0.034563809633255005,
-0.0007737582200206816,
0.10353792458772659,
-0.0043496317230165005,
0.030687706544995308,
-0.02146773599088192,
0.071415014564991,
0.024549541994929314,
0.03862173110246658,
0.11578532308340073,
0.00009605924424249679,
0.03892655298113823,
-0.010401938110589981,
0.017938563600182533,
-0.009970059618353844,
-0.0142635777592659,
0.005640109069645405,
-0.012878552079200745,
0.0197700597345829,
-0.0391957089304924,
0.017582761123776436,
-0.014361578039824963,
-0.012497984804213047,
0.03130033239722252,
-0.0425015389919281,
-0.027165625244379044,
0.01951071247458458,
0.006695579271763563,
0.03536617383360863,
-0.00829931441694498,
-0.06229593977332115,
-0.020928235724568367,
-0.034277867525815964,
0.014841216616332531,
-0.039058323949575424,
-0.0033584553748369217,
-0.014721693471074104,
-0.005615933332592249,
-0.008692769333720207,
0.025509782135486603,
0.03701590374112129,
0.010778472758829594,
0.0006222390802577138,
-0.04977930337190628,
0.011134536936879158,
0.01050750631839037,
0.0413249172270298,
0.016252551227808,
-0.06067728251218796,
-0.04551643878221512,
0.013969006016850471,
0.01005899254232645,
0.08838096261024475,
0.03370789811015129,
0.04623263329267502,
-0.005800353363156319,
0.002271604258567095,
0.008355575613677502,
-0.008441116660833359,
0.0315600223839283,
0.014947585761547089,
0.0032275752164423466,
0.0031877681612968445,
-0.016722165048122406,
-0.05969372019171715,
-0.026645736768841743,
-0.04464779049158096,
-0.03381878882646561,
0.030988743528723717,
0.0029611606150865555,
0.01631821133196354,
0.057510532438755035,
-0.03555809333920479,
0.0630144476890564,
-0.00017459790979046375,
-0.03464077040553093,
-0.04409303888678551,
-0.049785394221544266,
-0.012847747653722763,
0.0010947714326903224,
0.07316665351390839,
0.03788004815578461,
0.041790179908275604,
0.026764698326587677,
-0.022632203996181488,
-0.09073638170957565,
0.052691299468278885,
-0.0062846774235367775,
0.07672486454248428,
0.03713657706975937,
-0.028489993885159492,
-0.04397427290678024,
-0.04274830222129822,
-0.0573253259062767,
-0.03570061922073364,
-0.024192873388528824,
0.04149157553911209,
-0.021939154714345932,
0.06034810096025467,
-0.03130762279033661,
0.018056746572256088,
0.02545665204524994,
0.02280118130147457,
-0.031723279505968094,
0.019973965361714363,
0.005608574487268925,
-0.012108729220926762,
-0.04211699962615967,
-0.06693175435066223,
-0.039631620049476624,
-0.014467828907072544,
0.003824074985459447,
-0.016289854422211647,
-0.0317799337208271,
-0.02837229147553444,
-0.027741283178329468,
-0.015298447571694851,
-0.022874897345900536,
0.03485026955604553,
0.06765572726726532,
0.019651783630251884,
-0.023227764293551445,
0.062085434794425964,
0.09156866371631622,
0.02345891483128071,
-0.10050766915082932,
-0.036170728504657745,
0.006606139708310366,
-0.06343192607164383,
0.03198820352554321,
0.023338474333286285,
0.017311088740825653,
-0.008862416259944439,
0.033202096819877625,
0.03189772367477417,
-0.03374630585312843,
-0.03780922293663025,
0.06143597885966301,
0.000247329066041857
] |
<p>A photons energy is given by $E=h *f$ and momentum $p=E/c$ (spin?) but the photon has no (rest) mass! Therefore it is the ultimate probing tool for looking at any mass position and velocity because mass transfer is not involved only momentum.But to calculate/ measure the particles exact position by scattering a photon from the mass into a detector
dictates some of the photons momentum has been transferred to the mass i.e. the mass has to move (is disturbed from it initial position by some delta). This is intuitively obvious ;I would like to see how Heisenberg quantified(proved) this uncertainty hopefully without referring to an ansatz wave function. </p> | g5509 | [
0.016927188262343407,
-0.016675744205713272,
-0.02518453449010849,
0.01975519396364689,
0.04371758922934532,
0.019299928098917007,
0.07315710932016373,
0.09097914397716522,
-0.039831019937992096,
-0.02574647031724453,
0.004213455133140087,
-0.02943151816725731,
-0.019225100055336952,
-0.0020790398120880127,
-0.027063751593232155,
-0.0027620026376098394,
0.08003270626068115,
0.015695776790380478,
0.04900858551263809,
0.021118024364113808,
0.012408179230988026,
0.039716724306344986,
-0.024409372359514236,
-0.028085658326745033,
-0.03334859013557434,
-0.010675349272787571,
0.003500259481370449,
-0.036389414221048355,
0.019953735172748566,
0.005985751282423735,
-0.016972152516245842,
-0.03874904662370682,
0.009641935117542744,
0.032206710427999496,
0.02606535702943802,
-0.01471041887998581,
0.04562954977154732,
0.052983034402132034,
-0.034664496779441833,
0.019037984311580658,
-0.003672512946650386,
-0.04821588099002838,
0.004500753246247768,
-0.027070458978414536,
0.0209673885256052,
0.07943003624677658,
0.002564414171501994,
0.0127181401476264,
-0.020786022767424583,
-0.007054781541228294,
-0.037574414163827896,
0.050409525632858276,
0.052284613251686096,
0.07203682512044907,
0.057106416672468185,
0.07174676656723022,
-0.00008214966510422528,
0.041233453899621964,
0.02477913908660412,
-0.0035060609225183725,
0.03390480950474739,
-0.0020964504219591618,
-0.027463087812066078,
-0.007385938428342342,
0.00423030648380518,
-0.037370167672634125,
-0.08240298181772232,
0.005540037993341684,
-0.05003894492983818,
-0.04289095103740692,
0.047876905649900436,
-0.013633552007377148,
0.006609742995351553,
0.04913151636719704,
-0.01459453720599413,
-0.017181938514113426,
-0.028235791251063347,
-0.021834250539541245,
-0.034433718770742416,
-0.03865888714790344,
-0.020639605820178986,
-0.020288430154323578,
0.03011653944849968,
-0.053072620183229446,
0.08296673744916916,
-0.0028823509346693754,
-0.026538219302892685,
0.0031010855454951525,
0.03920726105570793,
0.011030202731490135,
0.02112155593931675,
-0.01971987634897232,
0.09567877650260925,
-0.013271900825202465,
-0.0015302161918953061,
-0.007326193153858185,
-0.005871716421097517,
0.0605011060833931,
-0.016745712608098984,
-0.014709989540278912,
-0.045828986912965775,
0.05108971893787384,
-0.05278028920292854,
0.026828959584236145,
0.03793972730636597,
-0.04653900861740112,
0.014214301481842995,
-0.010926898568868637,
0.07888533174991608,
0.0051451176404953,
0.017381932586431503,
-0.03362969681620598,
-0.06390572339296341,
-0.044354747980833054,
-0.06494100391864777,
-0.04766911268234253,
0.05322670936584473,
0.014897787943482399,
-0.04975828155875206,
0.05163601413369179,
0.03794302046298981,
0.05894656479358673,
-0.02338576130568981,
0.12339802086353302,
0.021293338388204575,
0.028344452381134033,
-0.0011452294420450926,
0.023440154269337654,
-0.025811411440372467,
0.03074789047241211,
-0.002991995308548212,
0.00887379888445139,
-0.018465546891093254,
0.03362506628036499,
-0.004912940785288811,
0.0069895777851343155,
0.027784420177340508,
0.037559330463409424,
-0.016138432547450066,
0.006734209600836039,
0.02336627058684826,
0.026509853079915047,
0.004205123987048864,
0.005523698404431343,
-0.024376163259148598,
0.02396807074546814,
-0.0018585369689390063,
-0.023051219061017036,
-0.004889927804470062,
0.003705248236656189,
0.0023612426593899727,
0.0670531690120697,
-0.0399869866669178,
0.014220771379768848,
0.056127648800611496,
-0.06937453895807266,
0.05047432333230972,
0.004046413116157055,
0.005199330858886242,
0.047162268310785294,
0.013753434643149376,
-0.004482799209654331,
0.03176628425717354,
-0.037405628710985184,
0.011202092282474041,
-0.061306919902563095,
-0.004207574762403965,
0.0014769874978810549,
-0.04515731707215309,
-0.054268404841423035,
-0.04026840627193451,
-0.00856742449104786,
0.026445729658007622,
0.006274668034166098,
-0.020329449325799942,
0.04418080300092697,
-0.05377969145774841,
-0.005524749401956797,
0.01736730895936489,
0.06203506514430046,
0.0021841994021087885,
0.018361004069447517,
0.08202440291643143,
-0.05138832703232765,
-0.031105507165193558,
0.037650931626558304,
0.03431440889835358,
-0.0563814714550972,
0.008592331781983376,
0.005316904745995998,
-0.006731689441949129,
-0.01222899928689003,
-0.01164532732218504,
-0.010731884278357029,
-0.008443569764494896,
0.050586361438035965,
0.0010179600212723017,
-0.003394730156287551,
0.03121810406446457,
0.05129570513963699,
-0.014668882824480534,
0.04163483530282974,
-0.027238547801971436,
0.0008898004307411611,
0.05253734812140465,
-0.03902187570929527,
0.02328760363161564,
-0.0037287103477865458,
-0.037648387253284454,
-0.021764419972896576,
0.01798166148364544,
-0.024667108431458473,
0.03716469556093216,
0.021210927516222,
0.00934789702296257,
0.011031829752027988,
-0.0015687852865085006,
-0.007870451547205448,
0.07242537289857864,
0.0057863518595695496,
-0.08141592144966125,
-0.03243952617049217,
0.03462560102343559,
0.028672540560364723,
-0.04291003197431564,
0.03602684289216995,
-0.0516541451215744,
-0.019816918298602104,
-0.07938697934150696,
0.05355243757367134,
-0.044295087456703186,
0.015014559961855412,
-0.004262725356966257,
0.051633864641189575,
0.09726672619581223,
0.029354529455304146,
-0.06864040344953537,
-0.03068622387945652,
0.047619763761758804,
0.016508664935827255,
0.02954697050154209,
-0.002732486929744482,
-0.04820653423666954,
-0.03659545257687569,
0.03289704769849777,
-0.0026486446149647236,
0.03853883966803551,
0.008146299980580807,
0.011770261451601982,
-0.026117227971553802,
-0.006745575461536646,
0.02569892629981041,
0.057169750332832336,
-0.041155856102705,
-0.012661130167543888,
-0.017246391624212265,
-0.045148421078920364,
0.002594189252704382,
-0.10931673645973206,
-0.033918168395757675,
-0.010208692401647568,
-0.0454452708363533,
-0.009622826240956783,
-0.013757445849478245,
-0.014966423623263836,
-0.003435811959207058,
-0.059747014194726944,
0.057957228273153305,
-0.013610742054879665,
-0.07319388538599014,
-0.0024900902062654495,
0.04466024041175842,
0.09363151341676712,
0.004637077916413546,
-0.028383422642946243,
-0.046771712601184845,
0.03484940156340599,
-0.02474067360162735,
0.04409979656338692,
-0.03371904417872429,
-0.054977476596832275,
0.06803779304027557,
-0.07999028265476227,
-0.04814745858311653,
-0.045642245560884476,
0.00658497866243124,
0.0022322782315313816,
0.022139055654406548,
0.004849100485444069,
-0.04513201862573624,
-0.01683957874774933,
0.007454113103449345,
0.042288072407245636,
0.03333929926156998,
-0.013440640643239021,
0.08827713876962662,
0.06102903559803963,
-0.004571677651256323,
-0.004365498200058937,
0.0150271225720644,
-0.008770015090703964,
0.05064740031957626,
-0.03607088327407837,
-0.026508398354053497,
0.05951220169663429,
-0.04223691299557686,
0.005929214879870415,
-0.04090498760342598,
-0.017418427392840385,
0.03316713869571686,
-0.007688690442591906,
0.061993714421987534,
0.01540638692677021,
0.022541480138897896,
-0.004674497991800308,
-0.002116505755111575,
-0.03601207211613655,
0.02391231618821621,
-0.015630898997187614,
0.009865491650998592,
-0.010639687068760395,
-0.03665011376142502,
0.0464053750038147,
-0.03185352310538292,
0.046261005103588104,
0.013430562801659107,
-0.029735319316387177,
0.0102295633405447,
-0.07447399944067001,
-0.023403188213706017,
0.0014831505250185728,
0.016918249428272247,
-0.026352524757385254,
-0.000009495649464952294,
0.010797761380672455,
-0.04764449596405029,
0.014821474440395832,
0.041467368602752686,
0.05753505602478981,
0.0018524371553212404,
-0.015896502882242203,
-0.04704015702009201,
-0.04586869850754738,
0.05852320417761803,
-0.0038338422309607267,
0.0018555527785792947,
0.02522539347410202,
-0.06621675938367844,
0.02952124923467636,
-0.05103371664881706,
-0.0022124352399259806,
0.017937099561095238,
-0.014979076571762562,
0.020364895462989807,
0.009567813016474247,
0.027819417417049408,
0.022441914305090904,
-0.005783532280474901,
0.05349930003285408,
-0.01273477915674448,
-0.03089447319507599,
-0.01858089677989483,
0.07450040429830551,
-0.006603469606488943,
-0.0022318256087601185,
-0.016408149152994156,
-0.049121879041194916,
0.04360450431704521,
0.0018642458599060774,
-0.02504715695977211,
-0.021640807390213013,
-0.006909598130732775,
0.0070211500860750675,
-0.0018621168565005064,
0.02310858853161335,
-0.07673738151788712,
0.02455190382897854,
-0.00041526820859871805,
-0.030317533761262894,
0.01971118338406086,
-0.0145003916695714,
0.02714776247739792,
0.06596051901578903,
0.01736547239124775,
-0.009060801938176155,
0.029908888041973114,
-0.06938634812831879,
0.02943095751106739,
0.011391607113182545,
0.011578153818845749,
0.024267202243208885,
-0.036509811878204346,
-0.0020017572678625584,
0.03030732087790966,
0.038901232182979584,
-0.042109228670597076,
0.022097356617450714,
-0.06009134650230408,
-0.0073548732325434685,
0.012573293410241604,
-0.011217600665986538,
0.008608930744230747,
0.007017383351922035,
-0.01800571195781231,
0.014801783487200737,
0.052155885845422745,
0.057928308844566345,
-0.05307713523507118,
-0.005930847488343716,
0.0005988830816932023,
-0.0185280442237854,
0.011316544376313686,
0.04866925999522209,
-0.02864234149456024,
0.015070625580847263,
-0.0010672237258404493,
-0.03836783766746521,
-0.06816916167736053,
-0.011620239354670048,
0.007293571252375841,
0.0021288886200636625,
0.027309508994221687,
0.08799277245998383,
0.004141248296946287,
-0.07847811281681061,
0.03713979944586754,
0.04860880598425865,
0.06179683655500412,
-0.013593102805316448,
-0.026503998786211014,
0.020621027797460556,
0.003422015579417348,
0.027720700949430466,
0.041990168392658234,
-0.02982877381145954,
0.05012933537364006,
-0.0032685359474271536,
0.04214854538440704,
0.01757068745791912,
0.059709444642066956,
0.05594783276319504,
0.04126715660095215,
-0.012855705805122852,
-0.02910773456096649,
-0.04880661889910698,
0.0592234767973423,
-0.03372201696038246,
-0.012173479422926903,
0.021100586280226707,
-0.001480781938880682,
-0.005094790365546942,
0.016428640112280846,
-0.09834186732769012,
0.013789869844913483,
-0.019202329218387604,
-0.01835586316883564,
-0.01794707588851452,
-0.008974817581474781,
0.057121969759464264,
0.01184304803609848,
-0.04134233668446541,
0.027087466791272163,
0.024794554337859154,
-0.002872033277526498,
-0.0019485856173560023,
-0.03319545462727547,
-0.03995972499251366,
0.015036441385746002,
-0.044232871383428574,
0.002170915249735117,
-0.007745329290628433,
0.017942437902092934,
0.04565287381410599,
-0.0011717411689460278,
0.01712752878665924,
-0.01093329954892397,
-0.003462740918621421,
-0.014417055062949657,
-0.013213280588388443,
-0.05897853150963783,
-0.01664324291050434,
0.0030207722447812557,
0.004158867988735437,
-0.039746664464473724,
-0.018341774120926857,
0.041998621076345444,
-0.0756014734506607,
0.019131891429424286,
-0.02166609652340412,
-0.03743229806423187,
0.026221897453069687,
0.0008358574705198407,
-0.02191011793911457,
-0.08078907430171967,
0.03744542598724365,
-0.007965976372361183,
-0.00327455741353333,
-0.011237443424761295,
0.02671561762690544,
0.0135301873087883,
-0.03723141923546791,
0.04138235002756119,
-0.029593391343951225,
0.010165402665734291,
-0.032829396426677704,
0.020428432151675224,
0.045084331184625626,
-0.0162946954369545,
-0.07512389123439789,
0.0031154730822890997,
-0.012606427073478699,
0.04911370947957039,
-0.030192948877811432,
-0.0010534009197726846,
-0.002305140718817711,
0.007110306993126869,
-0.015634767711162567,
-0.006197701673954725,
-0.03677532821893692,
-0.02324598655104637,
0.0035464847460389137,
0.017642904072999954,
0.06063459441065788,
-0.00836886465549469,
0.021943505853414536,
-0.023668784648180008,
-0.04957529529929161,
-0.001843054429627955,
-0.014134441502392292,
0.005326937884092331,
0.053681157529354095,
-0.03009975701570511,
0.04143984243273735,
-0.028539249673485756,
-0.0093063460662961,
-0.045544058084487915,
0.04035506397485733,
-0.053198933601379395,
0.035377632826566696,
-0.013893794268369675,
-0.03248261660337448,
0.00640054140239954,
0.03981981426477432,
0.06993843615055084,
-0.0015507116913795471,
0.010690647177398205,
-0.010051848366856575,
-0.046351391822099686,
0.01768987812101841,
-0.12158529460430145,
-0.009719867259263992,
-0.013282159343361855,
-0.036347366869449615,
-0.03276499733328819,
-0.0377998948097229,
-0.0043105632066726685,
-0.005907857324928045,
-0.03708693012595177,
-0.06216375157237053,
-0.019182832911610603,
0.02392340637743473,
-0.0023977195378392935,
0.013830553740262985,
-0.0030806318391114473,
0.005900316406041384,
-0.01882217265665531,
-0.02565763331949711,
-0.0039031710475683212,
-0.021204011514782906,
0.0074992249719798565,
-0.05419772490859032,
0.03668783977627754,
-0.0292388666421175,
0.02709205076098442,
0.031168676912784576,
0.031619586050510406,
0.006932288873940706,
-0.0029560967814177275,
-0.03635415434837341,
-0.039370011538267136,
0.05319841206073761,
0.06306754797697067,
0.07734019309282303,
0.02014349400997162,
0.019885729998350143,
0.03102077730000019,
-0.03032461181282997,
0.018068421632051468,
0.04217186197638512,
0.046853840351104736,
-0.022625906392931938,
-0.02077498659491539,
-0.033629659563302994,
-0.047730233520269394,
-0.07599596679210663,
-0.017010683193802834,
0.06147985905408859,
-0.054904479533433914,
-0.028092870488762856,
0.023657716810703278,
-0.0064934976398944855,
0.01385978702455759,
0.006200473755598068,
0.004900190979242325,
0.017733056098222733,
-0.0037156823091208935,
0.03551791235804558,
-0.016526227816939354,
-0.0032188177574425936,
-0.0074693975038826466,
-0.002399671357125044,
-0.019072718918323517,
0.01133877132087946,
-0.008721849881112576,
-0.00021845793526154011,
-0.029052073135972023,
0.013302674517035484,
0.0343729704618454,
-0.04529646784067154,
0.0028021722100675106,
0.03671182692050934,
0.020819852128624916,
0.01838846318423748,
-0.04648212715983391,
0.08629290759563446,
0.03735041990876198,
-0.021835220977663994,
0.017880326136946678,
0.025835208594799042,
-0.021562300622463226,
0.016229216009378433,
0.053815655410289764,
0.024090014398097992,
0.027468757703900337,
-0.04051719978451729,
0.03508361428976059,
-0.02319166623055935,
0.043866124004125595,
0.04690805822610855,
0.018796732649207115,
0.0365670882165432,
0.03098813258111477,
0.04347705841064453,
-0.0069239274598658085,
-0.1141604632139206,
0.039951033890247345,
0.019950686022639275,
-0.016835978254675865,
-0.043591830879449844,
0.04630015417933464,
-0.039895884692668915,
-0.016036774963140488,
0.015311994589865208,
-0.04607996717095375,
-0.00016060596681199968,
0.019500799477100372,
0.009070727042853832,
-0.023897239938378334,
0.026847736909985542,
-0.08356425911188126,
-0.05766572803258896,
-0.06346023827791214,
-0.017064789310097694,
-0.05375418812036514,
0.012669868767261505,
0.026425471529364586,
0.002487359568476677,
-0.060230471193790436,
0.009194660000503063,
-0.005327698774635792,
0.018111806362867355,
-0.06309233605861664,
-0.04140461981296539,
-0.020539946854114532,
-0.023054074496030807,
-0.009905577637255192,
0.002673046663403511,
0.01971990428864956,
-0.10054437816143036,
-0.01297714188694954,
-0.02373887598514557,
0.06590554118156433,
-0.001770400907844305,
0.05281900241971016,
-0.034573744982481,
0.004606124013662338,
-0.056078020483255386,
0.03957636281847954,
-0.022931044921278954,
-0.0006331892218440771,
-0.03121640346944332,
0.013444015756249428,
0.0581110380589962,
-0.04264416918158531,
-0.030096834525465965,
-0.01019992958754301,
0.03689993917942047,
0.008161202073097229,
0.048632483929395676,
-0.004927249159663916,
0.002523347968235612,
-0.034651465713977814,
0.0722200945019722,
0.0003918220172636211,
-0.009744720533490181,
0.007173966150730848,
0.004332385025918484,
-0.05277280509471893,
-0.008342459797859192,
-0.013679513707756996,
0.07282023876905441,
0.01788134127855301,
-0.01725059561431408,
-0.002215675078332424,
-0.017526773735880852,
0.00947280041873455,
-0.04168253019452095,
0.023140769451856613,
0.03878801688551903,
-0.03489047661423683,
0.028592120856046677,
-0.03413517028093338,
-0.04693925753235817,
0.0020042844116687775,
-0.019820356741547585,
-0.0359891839325428,
-0.021529367193579674,
0.00013886870874557644,
0.030475974082946777,
-0.025218596681952477,
0.004388201981782913,
0.03239431604743004,
-0.0556354820728302,
-0.042067497968673706,
-0.07992134988307953,
0.025443432852625847,
-0.010023187845945358,
-0.023456960916519165,
0.0042345477268099785,
-0.014750968664884567,
-0.012797415256500244,
-0.07506230473518372,
-0.014718306250870228,
-0.014480029232800007,
0.004870344884693623,
-0.0008672376279719174,
-0.021964583545923233,
0.008728858083486557,
0.023503566160798073,
-0.05326402932405472,
-0.002283787354826927,
0.06080494821071625,
0.03354867175221443,
0.07212965190410614,
-0.0034770620986819267,
-0.06254845857620239,
0.05041688680648804,
-0.008333122357726097,
-0.006776771973818541,
-0.015480192378163338,
0.008335800841450691,
0.0024769834708422422,
-0.035388268530368805,
0.030879775062203407,
-0.04312241077423096,
-0.0322912260890007,
0.04661966487765312,
0.03750031068921089
] |
<p>I'm quite stuck with this problem. </p>
<p>I know that I have an object in orbit. I know the eccentricity of that orbit, as well as the semi-major axis of the orbit. </p>
<p>Giving a <a href="http://en.wikipedia.org/wiki/True_anomaly" rel="nofollow">true anomaly</a>, how do I find the speed and altitude of that object? The true anomaly is the angle between the line made with the focus of the ellipse and the position of the object.</p>
<p>Thank you!</p>
<p>P.S. I'm more looking for a general help, more than a specific answer. That's why I didn't give any numbers.</p> | g5510 | [
0.003669393714517355,
0.035065412521362305,
-0.004659636411815882,
-0.002478376030921936,
0.053313326090574265,
-0.028687814250588417,
0.03854723274707794,
0.013592809438705444,
0.005670805927366018,
0.01267401035875082,
0.016025325283408165,
0.01136600598692894,
0.06416444480419159,
-0.04333481565117836,
0.01651768758893013,
-0.019473522901535034,
0.03278809413313866,
-0.015833428129553795,
0.0412946417927742,
0.008194854483008385,
0.07736986130475998,
0.03551784157752991,
0.023126283660531044,
-0.006168972700834274,
0.054135750979185104,
-0.0029805379454046488,
-0.04511227086186409,
-0.021057160571217537,
-0.07124245911836624,
0.05237221717834473,
-0.022792289033532143,
-0.005711001809686422,
0.07199656963348389,
0.021407969295978546,
0.037675727158784866,
0.00485963374376297,
0.021663378924131393,
0.03615768998861313,
0.017471326515078545,
0.00599281582981348,
-0.015208261087536812,
-0.04001438990235329,
-0.004268335178494453,
0.006945013999938965,
0.03791297972202301,
-0.043778836727142334,
-0.022011280059814453,
0.009418614208698273,
0.005809147376567125,
-0.006379567552357912,
-0.01657944917678833,
0.07814358919858932,
0.04409041628241539,
-0.04474179819226265,
-0.03226058557629585,
0.06475462764501572,
0.05693864822387695,
0.009618643671274185,
0.02849263697862625,
-0.004279229789972305,
-0.034600790590047836,
-0.02334544248878956,
0.026897286996245384,
-0.03493198752403259,
0.041681475937366486,
0.0362236388027668,
-0.00043169994023628533,
0.015505658462643623,
-0.03812255337834358,
0.004540878813713789,
-0.006654337514191866,
-0.021082771942019463,
-0.02487117052078247,
-0.009327797219157219,
-0.12147919833660126,
0.008467662148177624,
0.037774935364723206,
-0.02359653078019619,
0.025754673406481743,
0.009884921833872795,
0.019778253510594368,
0.03210945427417755,
0.004267943557351828,
0.0002483015414327383,
0.05820069462060928,
0.013728211633861065,
0.01652909442782402,
0.002157054375857115,
0.024665996432304382,
-0.016995616257190704,
0.0042299930937588215,
-0.004790739621967077,
0.01111027505248785,
0.046644676476716995,
0.07219146192073822,
-0.030889732763171196,
-0.0282890722155571,
0.06862679123878479,
-0.03528716042637825,
0.03667905181646347,
0.0009486638009548187,
0.027436908334493637,
-0.006434194277971983,
-0.04225612059235573,
0.006349798757582903,
0.01649227738380432,
0.02691805176436901,
0.026670506224036217,
0.00822431780397892,
-0.03138973191380501,
0.040386904031038284,
-0.08175579458475113,
-0.02379760518670082,
-0.0670042634010315,
-0.003097419161349535,
-0.042553503066301346,
-0.01691918820142746,
0.010147488676011562,
-0.02034153789281845,
0.06973738968372345,
0.005308559630066156,
-0.008295753039419651,
0.01749599352478981,
0.12169573456048965,
-0.015817496925592422,
-0.016955360770225525,
0.01503730472177267,
-0.02404087781906128,
0.02410047873854637,
-0.01839553378522396,
0.001578070572577417,
-0.015791527926921844,
0.01315720658749342,
0.05263297259807587,
-0.03684132173657417,
0.046728771179914474,
-0.017623165622353554,
-0.02761700190603733,
-0.007584970910102129,
0.0006120472680777311,
-0.011285577900707722,
-0.015807246789336205,
0.03693192079663277,
-0.04555097594857216,
-0.04867231100797653,
0.004944455344229937,
-0.013311230577528477,
0.028126483783125877,
0.05453619360923767,
-0.0019321920117363334,
0.004158097319304943,
0.09817377477884293,
-0.05691695958375931,
0.016398252919316292,
-0.04041732847690582,
-0.04827473312616348,
-0.018979322165250778,
0.0438726581633091,
0.0074397060088813305,
0.006584338378161192,
0.07834450155496597,
0.01354202814400196,
0.009623872116208076,
0.02922525443136692,
-0.05277072265744209,
0.05628436431288719,
-0.011599554680287838,
0.009530840441584587,
0.03603928163647652,
-0.02930750697851181,
-0.046551745384931564,
-0.019180789589881897,
0.06091358885169029,
0.02751523070037365,
-0.05047675594687462,
0.0765710398554802,
0.038626667112112045,
-0.028071261942386627,
0.014807558618485928,
0.03384310007095337,
-0.017406854778528214,
-0.01710931397974491,
0.028113268315792084,
0.010222663171589375,
-0.045365121215581894,
-0.026515813544392586,
0.04145373776555061,
0.010867670178413391,
-0.05469762161374092,
0.04962075501680374,
0.026170983910560608,
-0.018463080748915672,
0.00916790310293436,
-0.06232240051031113,
0.051777731627225876,
-0.020787622779607773,
0.0748358964920044,
-0.03601513430476189,
-0.09623190015554428,
0.027404457330703735,
0.04469212144613266,
0.016570763662457466,
-0.01118733175098896,
0.03914458304643631,
-0.03452396020293236,
-0.050799041986465454,
0.015812592580914497,
0.00511140376329422,
-0.00783600565046072,
0.027463991194963455,
0.03094065561890602,
0.005706622265279293,
-0.005804123356938362,
0.053356822580099106,
-0.0010793375549837947,
0.08376602828502655,
0.0038270079530775547,
-0.07004636526107788,
-0.019177507609128952,
-0.008906429633498192,
0.006332760211080313,
0.023346517235040665,
0.04208427667617798,
-0.04841287434101105,
0.021170509979128838,
-0.0366925448179245,
0.008194332011044025,
-0.031382475048303604,
-0.027380162850022316,
-0.03216653689742088,
-0.03398454189300537,
-0.008812851272523403,
0.015230965800583363,
-0.008156620897352695,
0.04916200786828995,
0.015068164095282555,
0.019506879150867462,
0.005806357599794865,
0.03239545598626137,
0.024096600711345673,
0.023853670805692673,
0.012025769799947739,
-0.07301800698041916,
0.004919486120343208,
0.07009856402873993,
-0.031397927552461624,
0.04055572301149368,
0.030114809051156044,
0.001843001926317811,
0.049458980560302734,
-0.009176074527204037,
0.00043701761751435697,
-0.03932720050215721,
0.002894620643928647,
0.009376736357808113,
0.03476360812783241,
-0.0709410160779953,
0.034485988318920135,
-0.08032328635454178,
0.009612930938601494,
-0.07746940106153488,
0.031724631786346436,
0.022902972996234894,
-0.022704534232616425,
-0.006847953423857689,
0.03604119271039963,
-0.07338057458400726,
-0.05696696788072586,
-0.029902683570981026,
0.016515102237462997,
-0.08137529343366623,
0.032864369451999664,
0.012688533402979374,
-0.0017009128350764513,
-0.04127504676580429,
-0.001787814311683178,
-0.034067779779434204,
-0.03164593130350113,
-0.02703404240310192,
0.03687812387943268,
0.0007056707981973886,
-0.006144266109913588,
-0.01730874925851822,
0.05429782718420029,
-0.03845852613449097,
0.002885885536670685,
0.04546890780329704,
0.12496638298034668,
-0.029698658734560013,
-0.033328380435705185,
-0.010529558174312115,
0.012222236022353172,
0.020143559202551842,
0.023705702275037766,
-0.014347572810947895,
0.023331137374043465,
0.007147074211388826,
0.06141877546906471,
0.002247184282168746,
0.009215160273015499,
0.037087395787239075,
-0.029783720150589943,
0.00670217489823699,
0.001465450506657362,
0.02437615767121315,
-0.021969882771372795,
-0.004351817071437836,
-0.08245430886745453,
0.0007868274697102606,
-0.034464675933122635,
-0.032002512365579605,
-0.012810859829187393,
-0.01630612462759018,
-0.02208373323082924,
0.024708351120352745,
0.07723849266767502,
-0.06740491092205048,
0.03817854821681976,
0.0012871542712673545,
0.012377053499221802,
-0.040299683809280396,
-0.10832744836807251,
-0.015589555725455284,
0.05145280435681343,
0.0059457686729729176,
-0.022454967722296715,
0.024959245696663857,
0.03033554181456566,
0.021810127422213554,
-0.019642820581793785,
0.008687518537044525,
-0.008251781575381756,
-0.04938304051756859,
0.0020864377729594707,
0.01082523912191391,
0.014740262180566788,
0.030789993703365326,
0.01716572977602482,
0.016420291736721992,
0.04641464725136757,
-0.035469990223646164,
0.024885468184947968,
-0.00121730484534055,
-0.0436953641474247,
-0.004947182256728411,
-0.027489272877573967,
-0.020392168313264847,
0.007682121358811855,
-0.04154243320226669,
0.027592074126005173,
0.0339050367474556,
-0.05823438614606857,
-0.01262776181101799,
-0.0178532712161541,
0.03396659716963768,
0.01922454871237278,
0.034941788762807846,
-0.02215415984392166,
-0.03544355928897858,
-0.005231217946857214,
0.01328116562217474,
-0.035321854054927826,
-0.009632209315896034,
0.026960667222738266,
0.031206516548991203,
-0.0730670914053917,
-0.039142362773418427,
0.08945624530315399,
-0.019251134246587753,
0.0007362887263298035,
0.0026612591464072466,
0.01650354452431202,
0.01824585534632206,
-0.032930679619312286,
0.00848685298115015,
-0.020050734281539917,
0.023941779509186745,
-0.0025844306219369173,
-0.03745807707309723,
0.012485348619520664,
0.018791260197758675,
0.019109932705760002,
-0.011694625951349735,
0.01645812578499317,
0.03795956075191498,
0.002013266086578369,
-0.01416502520442009,
-0.024575674906373024,
0.08857332915067673,
-0.05177005007863045,
-0.022640733048319817,
-0.04917512834072113,
-0.033112477511167526,
-0.02413511648774147,
-0.011059285141527653,
-0.06333514302968979,
0.0029229987412691116,
-0.0237723458558321,
-0.041410814970731735,
0.030295653268694878,
-0.012807589024305344,
0.030179478228092194,
0.020582472905516624,
-0.0014757784083485603,
-0.06915390491485596,
-0.012792659923434258,
-0.014531121589243412,
0.006541970651596785,
0.02802237682044506,
0.015913452953100204,
0.017680352553725243,
-0.0029248471837490797,
0.01734001189470291,
-0.03023732826113701,
0.02589561603963375,
0.05608566850423813,
0.021467914804816246,
0.0031580578070133924,
0.011139859445393085,
-0.017970405519008636,
-0.027695307508111,
0.10197987407445908,
-0.008572623133659363,
-0.062017377465963364,
-0.018653783947229385,
0.05442502722144127,
0.005270086228847504,
0.008288082666695118,
0.009106225334107876,
0.03210859373211861,
-0.022823655977845192,
0.010522495023906231,
-0.0357077457010746,
0.029710182920098305,
-0.07080957293510437,
0.020096473395824432,
0.028412727639079094,
0.062389593571424484,
-0.0078135896474123,
0.02748158760368824,
-0.04056030884385109,
0.02494187094271183,
-0.000597652979195118,
-0.006413022987544537,
-0.026749642565846443,
0.050877541303634644,
-0.02083744667470455,
-0.015301746316254139,
-0.025328604504466057,
0.014766262844204903,
-0.018802670761942863,
-0.04266751930117607,
0.012592199258506298,
-0.0028666227590292692,
-0.03706953302025795,
-0.024463916197419167,
-0.031320180743932724,
-0.01428188942372799,
0.010340218432247639,
-0.009351632557809353,
0.015473989769816399,
-0.04127027466893196,
0.02577943168580532,
0.02818821556866169,
0.029648300260305405,
-0.012991061434149742,
-0.0396554097533226,
-0.014300376176834106,
-0.03785179555416107,
-0.05228045955300331,
-0.017883511260151863,
0.015011422336101532,
0.02652600035071373,
0.04418419674038887,
0.016137059777975082,
0.04172247275710106,
-0.005311671644449234,
-0.03365308791399002,
-0.019301950931549072,
0.010157888755202293,
-0.087642602622509,
-0.030254408717155457,
0.01140171941369772,
0.026633357629179955,
-0.028458576649427414,
0.010990098118782043,
0.01074623316526413,
-0.012058276683092117,
0.04659933224320412,
0.011770455166697502,
0.008114099502563477,
0.01903240755200386,
-0.04794401675462723,
-0.07296660542488098,
0.0087337177246809,
-0.014950746670365334,
0.02740265242755413,
-0.013267223723232746,
0.02936767041683197,
-0.018611948937177658,
-0.06366179138422012,
-0.02352253720164299,
0.0004370402602944523,
0.012143244035542011,
-0.018418405205011368,
0.039133697748184204,
0.10332709550857544,
0.01888694241642952,
-0.006040344014763832,
-0.027128886431455612,
-0.009609946049749851,
-0.022433407604694366,
0.017218811437487602,
-0.02476438693702221,
0.003859179560095072,
-0.0003753739292733371,
0.025205250829458237,
0.041639093309640884,
-0.005043964833021164,
-0.008596892468631268,
0.06355232000350952,
-0.019010785967111588,
-0.02119557000696659,
0.012407717294991016,
0.04826715588569641,
-0.025713354349136353,
-0.018058309331536293,
0.013683714903891087,
0.05632583051919937,
0.01434071734547615,
-0.032604657113552094,
-0.031026566401124,
-0.043226391077041626,
-0.05861147120594978,
-0.011305480264127254,
-0.02728034183382988,
0.021028103306889534,
-0.056530460715293884,
0.028422942385077477,
-0.05905824154615402,
-0.00808778963983059,
0.0002741057251114398,
0.03547480329871178,
0.04981234669685364,
0.0052542793564498425,
-0.04053084924817085,
-0.0439031608402729,
0.01989685744047165,
0.04671350121498108,
0.02343071438372135,
-0.005502888932824135,
0.05187273770570755,
-0.004742162302136421,
0.00393246952444315,
-0.04398651421070099,
-0.0014994965167716146,
-0.05505887791514397,
0.014222836121916771,
-0.09605912864208221,
-0.054768193513154984,
0.05185437202453613,
-0.03045714646577835,
0.04881385713815689,
0.07227884232997894,
-0.010046361945569515,
0.0010002930648624897,
0.001148394076153636,
0.014188028872013092,
0.039957571774721146,
-0.04230177775025368,
-0.0665673092007637,
0.01684110425412655,
-0.06849463284015656,
0.02744028903543949,
0.12350918352603912,
0.027622539550065994,
0.010581327602267265,
0.011675622314214706,
-0.008303752169013023,
0.02508147805929184,
-0.029294027015566826,
0.08513756841421127,
0.03602937236428261,
0.0020087342709302902,
0.007433372549712658,
-0.012364781461656094,
-0.051130350679159164,
0.001451032585464418,
-0.03465713933110237,
-0.047553081065416336,
0.003384792013093829,
0.016361761838197708,
-0.07271074503660202,
-0.007781556341797113,
-0.0842888355255127,
-0.038093771785497665,
-0.03374413773417473,
-0.04100530222058296,
-0.017073096707463264,
0.029669027775526047,
-0.039023347198963165,
-0.044121552258729935,
0.08242642134428024,
0.053990814834833145,
0.021198853850364685,
-0.04787907376885414,
0.006306878756731749,
0.013619211502373219,
-0.012025110423564911,
-0.06362824887037277,
0.026400646194815636,
0.0007322453893721104,
-0.02550019510090351,
0.029120804741978645,
-0.09437974542379379,
0.025098830461502075,
-0.01843329891562462,
-0.021315094083547592,
-0.06921342015266418,
-0.023801134899258614,
0.011601762846112251,
-0.006752632092684507,
-0.07831477373838425,
-0.020127499476075172,
-0.005479383748024702,
0.010887809097766876,
-0.023734785616397858,
-0.03705697879195213,
0.0090049859136343,
-0.0022789398208260536,
0.02322712354362011,
-0.009027762338519096,
-0.031036287546157837,
-0.016238337382674217,
0.06291162222623825,
0.029575608670711517,
-0.04053787514567375,
0.117307148873806,
0.004885760135948658,
0.065183125436306,
0.07992283999919891,
0.04193347692489624,
-0.032990116626024246,
-0.004812314175069332,
0.001451402436941862,
-0.06111767888069153,
0.01490473560988903,
0.020970772951841354,
-0.04096014425158501,
-0.005327179096639156,
0.035943664610385895,
-0.03651667758822441,
-0.013278021477162838,
0.01978442259132862,
0.0006897919229231775,
0.015855712816119194,
0.02300008200109005,
-0.03435860946774483,
-0.010834685526788235,
-0.06966476142406464,
-0.0075964233838021755,
0.016325581818819046,
0.007492466829717159,
0.0026227617636322975,
-0.003787493333220482,
-0.03761101886630058,
-0.045226920396089554,
-0.044829025864601135,
-0.06116398796439171,
-0.04086149111390114,
-0.035582348704338074,
-0.026236480101943016,
-0.06829723715782166,
0.0013907058164477348,
0.01318263728171587,
0.010811575688421726,
0.026963185518980026,
-0.011382143013179302,
-0.06210651248693466,
0.017337817698717117,
0.010588259436190128,
0.04848659783601761,
-0.01278675440698862,
0.0006870240322314203,
-0.017736800014972687,
0.018991123884916306,
-0.0719592422246933,
-0.03662325441837311,
0.013412571512162685,
-0.03422066941857338,
-0.053996212780475616,
0.07609265297651291,
0.006055735982954502,
-0.04906098172068596,
-0.047470781952142715,
0.013372647576034069,
-0.01889023557305336,
0.043577831238508224,
-0.01044136006385088,
-0.030840039253234863,
0.005808587651699781,
0.0349140539765358,
0.03385293856263161,
0.020185809582471848,
-0.006390868686139584,
0.02067098394036293,
0.01737123727798462,
0.002867449540644884,
-0.00883462093770504,
0.05129067227244377,
-0.0004091252922080457,
0.023977920413017273,
0.042862262576818466,
-0.06565900146961212,
0.02718377113342285,
-0.023276489228010178,
0.007486060261726379,
0.018774161115288734,
-0.04551507160067558,
-0.010013427585363388,
-0.03766950964927673,
-0.00561666302382946,
0.015505382791161537,
-0.05301380529999733,
0.007518604397773743,
-0.02770414762198925,
-0.031570915132761,
-0.0032207458280026913,
0.08085297048091888,
-0.05575503036379814,
0.050541117787361145,
0.04087503254413605,
0.007670477032661438,
-0.014789939858019352,
-0.00628743227571249,
0.0029474038165062666,
0.0051175616681575775,
-0.04410386085510254,
-0.0006061035091988742,
0.026603423058986664,
-0.021518737077713013,
0.02191285230219364,
0.006199555471539497,
-0.016014691442251205,
0.04395415633916855,
-0.0002051886694971472,
0.002123421523720026,
0.03673385828733444,
0.015569046139717102,
0.026706140488386154,
0.007497580721974373,
0.06839778274297714,
-0.03461722657084465,
0.02937324345111847,
-0.0261493269354105,
0.011243545450270176,
0.025614069774746895,
-0.0016885428922250867,
-0.03073899634182453,
-0.020021000877022743,
-0.02648335136473179,
0.012323101982474327,
0.02918265201151371,
0.05532708391547203,
-0.005528512876480818,
-0.028549250215291977,
-0.03235016018152237,
0.0065996646881103516
] |
<p>My question is regarding T-Duality between the 2 Type H string theories.</p>
<p>I know that the Type II String theories are T-dual to each other because T-Duality changes the sign of the Gamma Matrix so
$$\operatorname{T}:{{\cal P}}_{{\mathop{\rm GSO}\nolimits} }^ - \leftrightarrow {{\cal P}}_{{\mathop{\rm GSO}\nolimits} }^ + $$</p>
<p>Since the Type IIB String theory employs the same GSO Projections on the left and right movers while Since the Type IIA String theory employs the different GSO Projections on the left and right movers, the 2 theories are T-Dual to each other.</p>
<p>However, when one considers T-Dualities on the Type HE string theory and the Type HO String theories, why are they T-Dual to each other?</p>
<p>I presume that maybe T-Duality switches $\operatorname{Spin}(32)/\mathbb Z^2$ and $E(8)\times E(8)$, so therefore, the theories to T-Dual to each other. But if so, then why? Why does T-Duality switch $\operatorname{Spin}(32)/\mathbb Z^2$ and $E(8)\times E(8)$?</p>
<p>Thanks in advance.</p> | g5511 | [
0.020634958520531654,
-0.024594949558377266,
0.02009469084441662,
-0.001879387185908854,
0.07500525563955307,
-0.007598469499498606,
0.07084708660840988,
0.02685849741101265,
-0.03527616336941719,
0.058258552104234695,
-0.020249102264642715,
0.027711402624845505,
0.010584746487438679,
-0.02793136052787304,
0.03822186589241028,
-0.024614723399281502,
0.04484015330672264,
0.05509261414408684,
-0.021619856357574463,
0.007182424422353506,
-0.025168173015117645,
-0.009422088041901588,
-0.014813488349318504,
-0.018611164763569832,
-0.02814585156738758,
-0.04684070870280266,
-0.01385564636439085,
0.003773969830945134,
0.03528579697012901,
0.008809521794319153,
0.014889951795339584,
0.034888096153736115,
0.05254984274506569,
-0.06664007157087326,
-0.012749265879392624,
0.019405657425522804,
0.06014445051550865,
-0.0026822390500456095,
0.02776205539703369,
0.038419533520936966,
0.005442258436232805,
-0.004976698197424412,
0.013123974204063416,
-0.05522549897432327,
0.010948942974209785,
-0.025916308164596558,
-0.052523162215948105,
0.07359329611063004,
0.01459619402885437,
0.016673017293214798,
0.013562810607254505,
0.0205449927598238,
0.020193276926875114,
0.029516272246837616,
0.058140888810157776,
-0.048875514417886734,
-0.004403809085488319,
0.01018915418535471,
0.02250056341290474,
0.01672837696969509,
-0.0568193718791008,
0.052126768976449966,
0.007196762133389711,
0.05696737393736839,
-0.0018162719206884503,
-0.02751188725233078,
0.03932663053274155,
0.009883622638881207,
-0.013197779655456543,
0.004919694270938635,
-0.03866629675030708,
-0.010466949082911015,
0.016789300367236137,
-0.020956462249159813,
-0.03325647488236427,
-0.0030697344336658716,
0.04163407161831856,
-0.08248675614595413,
-0.0112744877114892,
-0.025356490164995193,
-0.01278749480843544,
-0.07442213594913483,
-0.011202908121049404,
0.014402562752366066,
-0.019634520635008812,
0.03406919538974762,
-0.02974260225892067,
0.012635071761906147,
-0.04686346650123596,
0.027403591200709343,
0.04515799880027771,
-0.034312937408685684,
0.028867004439234734,
0.07904760539531708,
-0.028116947039961815,
0.015307028777897358,
-0.011345748789608479,
0.020070554688572884,
0.023654602468013763,
-0.01851801760494709,
0.0037078449968248606,
-0.02099316008388996,
0.06085188686847687,
0.002946812892332673,
-0.017812579870224,
0.014819406904280186,
0.007688195910304785,
0.039886731654405594,
-0.056274306029081345,
-0.009560570120811462,
-0.03304228186607361,
0.015286748297512531,
-0.04204238951206207,
-0.002742566168308258,
0.007491879630833864,
-0.024812230840325356,
-0.04148199409246445,
-0.039789892733097076,
0.007799025159329176,
-0.020704710856080055,
0.0237725917249918,
-0.018400896340608597,
-0.022284235805273056,
0.010987924411892891,
-0.04474246874451637,
-0.03538504242897034,
-0.018796680495142937,
0.011750862002372742,
0.032436855137348175,
-0.019634922966361046,
-0.007070217747241259,
-0.011601284146308899,
0.05932823196053505,
0.07606182992458344,
-0.012188357301056385,
0.03588682413101196,
-0.00732879713177681,
0.01799241080880165,
0.03569178283214569,
-0.037658292800188065,
0.027324959635734558,
-0.05716046318411827,
0.021941840648651123,
-0.03507620468735695,
0.04157984256744385,
0.01269261073321104,
0.04437604919075966,
-0.06919924914836884,
0.03806925192475319,
0.02364891953766346,
0.023340383544564247,
0.021032789722085,
0.05067495256662369,
0.047420747578144073,
0.0007351452368311584,
-0.002173381857573986,
0.05762094259262085,
-0.019508840516209602,
-0.033164698630571365,
0.0332130491733551,
0.009650906547904015,
-0.031690359115600586,
0.009805210866034031,
-0.018262848258018494,
-0.03793937340378761,
-0.03336288407444954,
-0.022347500547766685,
0.023421311751008034,
0.0012807189486920834,
-0.0005444348207674921,
0.012813067995011806,
0.0708557590842247,
0.05679643526673317,
0.03461885079741478,
0.0379062294960022,
0.01746530458331108,
-0.07669888436794281,
-0.02216053567826748,
-0.03467449173331261,
0.07781970500946045,
-0.09027602523565292,
-0.030509648844599724,
0.007801246829330921,
0.014075813814997673,
0.03395777940750122,
0.014940912835299969,
0.00475212512537837,
-0.01336323469877243,
-0.03150099888443947,
-0.024954404681921005,
-0.029030250385403633,
-0.005575261078774929,
0.00026268063811585307,
0.039954621344804764,
-0.025373445823788643,
-0.035119809210300446,
-0.007246972527354956,
-0.007707280572503805,
-0.004741007462143898,
0.012986822053790092,
0.008854072540998459,
0.016673970967531204,
0.0660850778222084,
0.0009243012755177915,
-0.04378188028931618,
-0.02018655650317669,
-0.030038459226489067,
-0.02230381779372692,
0.049042709171772,
-0.03277027606964111,
-0.025147635489702225,
-0.0057128011249005795,
0.026621215045452118,
-0.026093153282999992,
-0.04609990864992142,
-0.03065180405974388,
0.016346001997590065,
0.021311238408088684,
-0.038225702941417694,
0.0177741888910532,
0.004226767458021641,
-0.02766462042927742,
0.025662872940301895,
0.06220172345638275,
-0.04126453399658203,
0.0036299536004662514,
0.015246614813804626,
-0.06140042096376419,
-0.04748135060071945,
-0.03845687955617905,
0.014041478745639324,
-0.031249653548002243,
-0.008922075852751732,
-0.031235525384545326,
0.0018084178445860744,
0.0022470378316938877,
0.0007572731701657176,
-0.0432455949485302,
0.05860183387994766,
-0.0031975472811609507,
-0.015569514594972134,
-0.03563136234879494,
0.03536243736743927,
-0.023730743676424026,
0.00898338295519352,
-0.009536500088870525,
0.061965424567461014,
-0.009508331306278706,
-0.024706901982426643,
0.06750288605690002,
-0.016410479322075844,
-0.008526976220309734,
-0.07018484175205231,
-0.0017628385685384274,
0.02903297357261181,
-0.09175023436546326,
0.02287239022552967,
0.03467819467186928,
-0.043904125690460205,
-0.0374586321413517,
0.038325972855091095,
-0.016542112454771996,
0.019577033817768097,
0.020472470670938492,
-0.09788912534713745,
0.007286707870662212,
-0.011885112151503563,
0.02008257806301117,
-0.019713429734110832,
-0.05030028894543648,
-0.03242303431034088,
0.06017234921455383,
0.012045754119753838,
-0.017555298283696175,
-0.04925716668367386,
-0.01900658756494522,
-0.04320412129163742,
-0.007184621877968311,
0.02423950657248497,
-0.03802744299173355,
-0.03535282984375954,
-0.0531003400683403,
-0.0004582364053931087,
-0.0018500403966754675,
0.020449219271540642,
-0.01165070105344057,
0.011509359814226627,
0.026755986735224724,
-0.0836528018116951,
0.05053098499774933,
-0.006109239067882299,
0.03477688506245613,
0.08069437742233276,
-0.03657146170735359,
0.026839716359972954,
0.009089152328670025,
-0.027410337701439857,
-0.017967702820897102,
-0.053782686591148376,
0.04399435222148895,
0.0028079748153686523,
0.007972942665219307,
-0.007368389051407576,
0.030131898820400238,
0.07595712691545486,
0.02139490470290184,
-0.0936165601015091,
-0.07018551230430603,
-0.0485590361058712,
0.06325749307870865,
-0.001773898140527308,
0.047265321016311646,
0.0060922615230083466,
0.04359537363052368,
0.046366140246391296,
-0.012492130510509014,
-0.0853320062160492,
0.012314188294112682,
0.029714005067944527,
-0.05604308471083641,
-0.08059598505496979,
-0.006565812975168228,
0.037369463592767715,
0.048373714089393616,
-0.05767221003770828,
-0.007297657895833254,
-0.018077945336699486,
-0.002741076285019517,
-0.06774711608886719,
0.004014854785054922,
-0.02445647306740284,
0.017997020855545998,
-0.029007837176322937,
-0.00032282184110954404,
-0.06224353238940239,
0.08549594134092331,
0.052763357758522034,
0.023719334974884987,
0.006759653799235821,
0.01445589866489172,
-0.014627591706812382,
0.0016789654036983848,
0.0038045281544327736,
-0.010335559956729412,
-0.00019884634821210057,
0.03516415134072304,
0.05376162379980087,
-0.00733634689822793,
-0.00008123791485559195,
0.026066284626722336,
-0.006523963995277882,
-0.0032844790257513523,
0.0390959195792675,
0.02820603735744953,
0.03471335768699646,
-0.01235206238925457,
-0.00875979196280241,
0.06736826151609421,
0.019700294360518456,
-0.01695084013044834,
-0.04124748334288597,
0.03768407553434372,
-0.0007191539043560624,
0.01167523954063654,
0.01784243993461132,
0.006644207052886486,
-0.002803865587338805,
-0.007148203440010548,
0.012663621455430984,
0.010898586362600327,
0.06949090957641602,
0.042217958718538284,
-0.012974136509001255,
-0.012277086265385151,
0.0056930710561573505,
-0.05276312679052353,
-0.009932519868016243,
-0.037104394286870956,
-0.015743985772132874,
0.047783054411411285,
-0.01686372607946396,
-0.01108749769628048,
-0.016567615792155266,
0.10536377876996994,
0.04894528165459633,
-0.03939041122794151,
-0.003821862628683448,
0.01792365126311779,
-0.0244893841445446,
-0.04401063546538353,
0.0018813596107065678,
0.027803106233477592,
0.0045609078370034695,
-0.06493847817182541,
0.07966644316911697,
0.040726784616708755,
0.004955718759447336,
0.025108352303504944,
0.0060294936411082745,
-0.04384588450193405,
-0.04105174541473389,
-0.003917251247912645,
0.05876879394054413,
-0.06614873558282852,
-0.01632305048406124,
0.03697264939546585,
-0.011971145868301392,
0.01945425011217594,
0.0006015401449985802,
-0.07817746698856354,
0.0357578843832016,
-0.004119659774005413,
0.00275848968885839,
0.02040378749370575,
0.03446164354681969,
-0.027638545259833336,
-0.005097601097077131,
0.005329221487045288,
-0.0023046997375786304,
-0.015724459663033485,
-0.03008529543876648,
0.011854132637381554,
0.04803489148616791,
-0.028620591387152672,
-0.019447315484285355,
0.01925034448504448,
0.011706456542015076,
0.06108245998620987,
0.020700620487332344,
-0.020297203212976456,
-0.02601296827197075,
-0.0005693642306141555,
-0.024965135380625725,
0.028825975954532623,
-0.018767138943076134,
-0.009791648015379906,
-0.010096880607306957,
0.03937054052948952,
0.002305512549355626,
-0.035047441720962524,
0.0884353518486023,
-0.01988060772418976,
-0.019937392324209213,
0.03162291273474693,
-0.02779114618897438,
-0.022309156134724617,
0.022126413881778717,
-0.012544088065624237,
0.0317668616771698,
0.006314774509519339,
-0.01650579646229744,
0.004012794699519873,
0.028865935280919075,
0.0028715089429169893,
0.007864698767662048,
-0.011674701236188412,
-0.022711612284183502,
0.046579234302043915,
0.035199135541915894,
-0.028173936530947685,
-0.03824535384774208,
0.021907618269324303,
-0.0031053258571773767,
0.017224153503775597,
0.025042667984962463,
-0.02219938114285469,
-0.09355629980564117,
0.010416709817945957,
-0.006321569439023733,
-0.033786650747060776,
-0.013599662110209465,
-0.04300385341048241,
0.030378295108675957,
0.026808546856045723,
-0.009422525763511658,
0.03347138315439224,
-0.005113336723297834,
-0.029552843421697617,
-0.062386129051446915,
-0.046706896275281906,
-0.007279312238097191,
-0.04192870482802391,
0.0020387908443808556,
0.05475391820073128,
-0.014325394295156002,
-0.008407690562307835,
-0.02860572561621666,
-0.03135741502046585,
0.05832734331488609,
0.0864686518907547,
0.008930858224630356,
-0.013487071730196476,
0.01337150763720274,
0.012807830236852169,
-0.04727713763713837,
-0.014419429935514927,
0.004242306109517813,
0.026946716010570526,
-0.0364692322909832,
-0.058519359678030014,
-0.0159095861017704,
-0.004556707572191954,
-0.033074211329221725,
-0.029937949031591415,
-0.015216668136417866,
0.014646499417722225,
0.11130917072296143,
-0.0015041043516248465,
0.04584868997335434,
-0.015140223316848278,
0.0071755810640752316,
0.03243979439139366,
-0.013835416175425053,
0.029048895463347435,
0.03270804509520531,
-0.007402359042316675,
-0.03132525458931923,
-0.03777303546667099,
0.03496944531798363,
-0.04549666494131088,
0.006075106095522642,
0.021644093096256256,
0.06180986016988754,
-0.057877492159605026,
0.038402654230594635,
0.047055888921022415,
-0.05298653244972229,
0.0018842126009985805,
0.07106903195381165,
0.041008781641721725,
-0.013642499223351479,
0.016451090574264526,
0.06105504557490349,
0.023303383961319923,
-0.03474283218383789,
-0.03608182072639465,
0.04590659588575363,
-0.004875794053077698,
-0.003438448067754507,
0.05195756256580353,
-0.023308107629418373,
0.01523170992732048,
-0.034339502453804016,
0.058034054934978485,
-0.03704366087913513,
0.0037976044695824385,
-0.04117425158619881,
-0.06007254123687744,
0.053595103323459625,
-0.0037894563283771276,
-0.0830962061882019,
-0.01288661826401949,
-0.015384204685688019,
0.0022237712983042,
0.0012140377657487988,
0.04547615349292755,
-0.020445864647626877,
-0.010297125205397606,
0.01931043341755867,
0.035474829375743866,
0.032860659062862396,
-0.010670824907720089,
-0.06427514553070068,
0.011167607270181179,
0.058580927550792694,
-0.013513779267668724,
-0.02449215017259121,
-0.011265048757195473,
0.015144838951528072,
0.07804417610168457,
-0.032144367694854736,
0.011309509165585041,
0.006119124591350555,
0.025688670575618744,
0.036470841616392136,
0.0465143546462059,
-0.014020336791872978,
-0.06459930539131165,
-0.06245926767587662,
-0.05163535848259926,
-0.005437181796878576,
-0.003495317418128252,
-0.013096693903207779,
-0.03365325555205345,
-0.023802071809768677,
0.03724472224712372,
-0.03807304799556732,
-0.06420271843671799,
0.05575994774699211,
0.027488401159644127,
-0.04633519425988197,
-0.007783340755850077,
-0.013685514219105244,
-0.006037586368620396,
-0.007874751463532448,
0.04323732107877731,
-0.03372465819120407,
0.1088622584939003,
-0.011905401013791561,
-0.017207978293299675,
0.04482496529817581,
-0.03481220826506615,
0.08316069841384888,
0.03361259773373604,
-0.05014669522643089,
0.07168744504451752,
-0.021095963194966316,
0.04222883656620979,
0.012230642139911652,
-0.00933121982961893,
-0.006996437441557646,
-0.024021923542022705,
-0.029317684471607208,
0.010808016173541546,
-0.02941528707742691,
-0.030604343861341476,
-0.032007429748773575,
-0.015782365575432777,
-0.05652153491973877,
0.004113448318094015,
0.07908162474632263,
-0.017071377485990524,
-0.011313383467495441,
0.021335337311029434,
0.023721838369965553,
0.05877648666501045,
-0.0095129469409585,
0.01010900642722845,
0.0043378653936088085,
-0.030860861763358116,
-0.006552109029144049,
-0.019662631675601006,
-0.0036495381500571966,
0.05676468834280968,
0.00044395096483640373,
-0.06501815468072891,
-0.11701282858848572,
-0.027923820540308952,
-0.06358364224433899,
0.02144503779709339,
-0.013787752017378807,
0.053834881633520126,
0.012409633956849575,
-0.04764118045568466,
-0.0003655587788671255,
0.08488216251134872,
-0.0017245752969756722,
-0.02510245330631733,
-0.09046816825866699,
0.033418457955121994,
-0.034683868288993835,
0.005624467507004738,
-0.05760462209582329,
0.007267206907272339,
-0.0434843972325325,
0.003967630211263895,
0.052821606397628784,
-0.011173811741173267,
0.008822972886264324,
-0.02575228549540043,
-0.05922143533825874,
-0.011014129035174847,
-0.03132382407784462,
-0.03604731336236,
0.013882611878216267,
0.02219308353960514,
0.032662197947502136,
-0.05396009609103203,
-0.013006758876144886,
0.033620260655879974,
-0.05529085919260979,
0.0753435343503952,
-0.06825874745845795,
-0.008402700535953045,
-0.022945726290345192,
-0.054663900285959244,
0.030647747218608856,
0.013107969425618649,
-0.07126127183437347,
0.00545128108933568,
-0.010136517696082592,
-0.01575126126408577,
0.007908115163445473,
0.028104407712817192,
-0.010127105750143528,
0.0009549736860208213,
0.011480123735964298,
0.005763896740972996,
-0.037962429225444794,
-0.00823219958692789,
0.055959928780794144,
-0.03169680014252663,
0.03221774473786354,
0.04913630709052086,
0.02672441676259041,
0.05064443126320839,
-0.025052346289157867,
0.049459412693977356,
0.010419868864119053,
0.04245034605264664,
0.014478756114840508,
-0.014588159509003162,
-0.019524119794368744,
-0.028627818450331688,
0.05084694176912308,
0.017979290336370468,
0.04723105952143669,
-0.02617778815329075,
-0.003933888394385576,
-0.0406627282500267,
-0.046004489064216614,
0.016650700941681862,
0.03153828904032707,
0.028992390260100365,
-0.007451602723449469,
-0.02327141910791397,
-0.003608012106269598,
-0.010358292609453201,
0.058540865778923035,
-0.014654776081442833,
0.011155813932418823,
-0.034586917608976364,
-0.004288917873054743,
-0.01326045487076044,
-0.039150163531303406,
0.006627220660448074,
0.05702247843146324,
-0.007935217581689358,
-0.006795479916036129,
0.055828649550676346,
-0.03481096774339676,
0.013851763680577278,
-0.029800262302160263,
0.013609496876597404,
-0.03655322641134262,
0.06524565815925598,
-0.01522236317396164,
-0.03213893249630928,
0.05418112501502037,
-0.07291901111602783,
0.04272737726569176,
-0.016523264348506927,
0.04954466223716736,
0.012173213995993137,
-0.05869127810001373,
0.018408047035336494,
-0.019007811322808266,
0.006490637082606554,
-0.030872326344251633,
-0.04080934822559357,
-0.011418923735618591,
0.03685585781931877,
0.02168116718530655,
0.07673878222703934,
-0.015595337375998497,
0.010110822506248951,
-0.051732875406742096,
0.0378323495388031,
0.012339984066784382,
0.06315480172634125,
0.02315475605428219,
-0.024636074900627136,
-0.006058890372514725,
-0.029158465564250946,
-0.006432968657463789,
-0.04227851703763008,
-0.0006409221095964313,
0.0428740568459034
] |
<p>Is it correct to define Quantum Physics as the study of Physics in sub-atomic scale? Does Quantum Physics studies something else other than sub-atomic phenomena?</p>
<p>This may be a very stupid question but realize that I am <strong>!!!VERY NOOB!!!</strong> at Physics.</p> | g5512 | [
-0.0067291888408362865,
0.06178108602762222,
0.039924416691064835,
-0.018681725487113,
0.024701707065105438,
0.04131754860281944,
-0.03853215277194977,
-0.01846981793642044,
0.04148392751812935,
-0.061478033661842346,
0.019475355744361877,
0.024134470149874687,
-0.03691132366657257,
-0.053925544023513794,
-0.028549304232001305,
-0.0381290502846241,
0.0566616952419281,
0.0004544784897007048,
0.04075093939900398,
0.02753344550728798,
-0.03444213047623634,
0.05311098322272301,
0.010111626237630844,
-0.01800425536930561,
-0.03287496790289879,
-0.02706495299935341,
-0.07799907773733139,
-0.03890126943588257,
-0.015071216970682144,
0.032147690653800964,
-0.023725435137748718,
-0.029725931584835052,
0.07995255291461945,
-0.004816894885152578,
0.005265320185571909,
-0.062482800334692,
0.03807670995593071,
0.04184294492006302,
0.02440715953707695,
0.004631923511624336,
0.008739333599805832,
-0.00959880743175745,
0.028701774775981903,
-0.09262324124574661,
0.007763137109577656,
-0.009032496251165867,
0.023053720593452454,
-0.00099844578653574,
0.027313921600580215,
0.029935067519545555,
0.020036786794662476,
0.0012215099995955825,
0.012972617521882057,
0.08128326386213303,
0.0505654513835907,
-0.018731242045760155,
0.007418736349791288,
0.00873725675046444,
0.08520306646823883,
-0.001224850188009441,
0.08622942864894867,
0.026822205632925034,
0.031240005046129227,
0.036588311195373535,
0.022185353562235832,
0.015645375475287437,
-0.050444554537534714,
-0.03268023952841759,
0.016152555122971535,
-0.025370916351675987,
0.011701011098921299,
-0.03627929836511612,
-0.0032833623699843884,
0.014788140542805195,
-0.01176544837653637,
-0.0163771640509367,
0.0555441752076149,
-0.03390331566333771,
0.019083183258771896,
0.054012466222047806,
-0.002942653838545084,
-0.051132045686244965,
0.012535251677036285,
0.024187033995985985,
0.06415608525276184,
-0.008827594108879566,
-0.09673577547073364,
-0.013181861490011215,
0.0024178519379347563,
0.012696696445345879,
0.0024463494773954153,
-0.015252294018864632,
0.052740972489118576,
-0.017202047631144524,
-0.03049681894481182,
-0.016547247767448425,
0.03375127911567688,
0.04034673050045967,
-0.017557475715875626,
0.03377806767821312,
-0.056340623646974564,
0.0032772037666291,
0.01815294288098812,
-0.0068006813526153564,
0.002604252193123102,
0.03223221376538277,
-0.011398565955460072,
0.0033111923839896917,
0.041462287306785583,
0.023097611963748932,
-0.027908403426408768,
0.010111899115145206,
0.012755599804222584,
-0.0007615442737005651,
-0.05942832678556442,
0.022639930248260498,
0.033077605068683624,
0.01818622648715973,
-0.009072653949260712,
0.03103259764611721,
0.05556095391511917,
0.03969039022922516,
0.06781462579965591,
0.004488849081099033,
-0.04493308439850807,
-0.029018353670835495,
-0.0007536489865742624,
-0.01886816881597042,
-0.0002640096645336598,
-0.061074480414390564,
0.03433803468942642,
0.01023559644818306,
-0.011221026070415974,
0.015927869826555252,
-0.0028781003784388304,
0.017401497811079025,
0.022692279890179634,
-0.030367428436875343,
-0.028165850788354874,
-0.004257796797901392,
0.027869628742337227,
0.04835035651922226,
-0.01248694397509098,
-0.0017081481637433171,
-0.024202780798077583,
-0.04650609567761421,
-0.01750204712152481,
0.03575330972671509,
0.01830088160932064,
0.008500276133418083,
0.03174259886145592,
0.022600779309868813,
-0.029764872044324875,
-0.08944585174322128,
0.006406220607459545,
0.006342707667499781,
0.0443824864923954,
0.016065672039985657,
0.04016605764627457,
0.016633326187729836,
0.04343275725841522,
0.0589837022125721,
-0.009588039480149746,
0.007692419458180666,
0.036551255732774734,
-0.0017010086448863149,
0.0010336525738239288,
-0.036263298243284225,
0.011605261825025082,
-0.008803862147033215,
-0.027738092467188835,
0.002902414882555604,
-0.007278295699506998,
0.0026203326415270567,
0.03932834416627884,
0.008996753953397274,
-0.010848421603441238,
-0.0006135067087598145,
0.015188045799732208,
-0.003664048621430993,
0.01608971320092678,
0.01621014066040516,
-0.016357803717255592,
-0.029974166303873062,
-0.028658375144004822,
0.041862692683935165,
-0.027374085038900375,
0.016331348568201065,
0.006028536707162857,
0.020124847069382668,
-0.009408725425601006,
-0.002779182977974415,
0.005328008905053139,
-0.03908854350447655,
-0.0026206818874925375,
-0.01135158259421587,
-0.017979707568883896,
0.0055601573549211025,
-0.028724920004606247,
-0.057922057807445526,
0.04015343636274338,
0.03111877664923668,
0.025192338973283768,
-0.026463670656085014,
0.016382472589612007,
0.02155863679945469,
-0.04757595807313919,
-0.02402486838400364,
0.007467568852007389,
0.044817060232162476,
0.037227973341941833,
-0.0401652567088604,
0.03349478170275688,
0.017193913459777832,
-0.020351272076368332,
-0.01690153405070305,
0.009150559082627296,
-0.004841460380703211,
-0.013730697333812714,
0.08781831711530685,
-0.0427822582423687,
0.020604582503437996,
-0.003629725193604827,
-0.013854030519723892,
0.008178195916116238,
0.0005057627568021417,
-0.058725230395793915,
-0.01666128821671009,
0.03520296886563301,
-0.014126786030828953,
-0.03495984151959419,
0.015559731051325798,
-0.017205873504281044,
-0.039394475519657135,
0.03202889859676361,
0.024589795619249344,
0.02005835622549057,
-0.057306066155433655,
0.015359662473201752,
-0.008827976882457733,
-0.007899574935436249,
-0.043631572276353836,
0.03011992760002613,
-0.00007361965981544927,
0.030715815722942352,
-0.015042039565742016,
0.0001809242385206744,
-0.021588413044810295,
-0.06457575410604477,
-0.0828980803489685,
0.07784762233495712,
-0.037030622363090515,
-0.022444497793912888,
-0.0019543603993952274,
-0.00210782908834517,
-0.0026988948229700327,
0.004447790328413248,
0.010435214266180992,
-0.032881129533052444,
-0.0184860210865736,
0.03028116188943386,
-0.021962720900774002,
-0.022898759692907333,
-0.02042483538389206,
0.011394336819648743,
-0.01981857419013977,
-0.008693799376487732,
0.050957947969436646,
0.02070062793791294,
-0.02202998474240303,
0.026945235207676888,
0.06359358131885529,
-0.04918399453163147,
-0.03249875456094742,
0.002423320198431611,
-0.02784065529704094,
-0.0232132226228714,
0.025129828602075577,
0.053049568086862564,
-0.004805783741176128,
-0.03346186876296997,
0.029602447524666786,
-0.04492463171482086,
-0.01681073196232319,
0.050460100173950195,
-0.07986772060394287,
-0.015442024916410446,
-0.04999798908829689,
-0.04205368459224701,
0.007017900701612234,
-0.013810215517878532,
-0.05732674151659012,
0.01790570095181465,
0.03960537537932396,
-0.03813546523451805,
0.048914726823568344,
0.04886350408196449,
-0.07046904414892197,
-0.030138475820422173,
0.08111554384231567,
0.013957087881863117,
0.0010846653021872044,
-0.04862795025110245,
0.04687214642763138,
0.017510278150439262,
0.010412583127617836,
0.007469825446605682,
-0.0287751704454422,
-0.06020161509513855,
0.0026483216788619757,
-0.05799245834350586,
0.08333002030849457,
0.0332314558327198,
0.02381187491118908,
-0.01844082400202751,
-0.010945424437522888,
0.009965011849999428,
0.029406379908323288,
0.038978397846221924,
-0.041902173310518265,
-0.03591484576463699,
0.011354451067745686,
-0.014061770401895046,
0.014397233724594116,
0.04798080772161484,
0.037602465599775314,
0.022572936490178108,
-0.06634316593408585,
-0.010467927902936935,
-0.02813398651778698,
0.0023641858715564013,
-0.010750818066298962,
-0.03468191996216774,
0.014179014600813389,
-0.05080089718103409,
-0.05692235380411148,
0.02070080116391182,
-0.03942384943366051,
0.006434050388634205,
-0.01953880488872528,
0.00833765510469675,
-0.03682944178581238,
0.03171467408537865,
-0.01627196930348873,
0.028764406219124794,
0.03429730236530304,
-0.07763509452342987,
0.05214457958936691,
-0.011707907542586327,
0.015957074239850044,
0.034060750156641006,
0.014684977009892464,
-0.01627243496477604,
-0.02590819075703621,
-0.020221535116434097,
0.03485731780529022,
0.08066624402999878,
0.018970094621181488,
-0.039603978395462036,
-0.013138010166585445,
-0.02349732257425785,
-0.005335675086826086,
0.053569063544273376,
0.0073425802402198315,
-0.08585469424724579,
-0.004503094125539064,
0.013056023977696896,
-0.027891885489225388,
0.047377754002809525,
0.007024961058050394,
-0.042312148958444595,
-0.012101175263524055,
-0.019432270899415016,
-0.012597269378602505,
0.007057953160256147,
-0.0439566969871521,
0.0394790880382061,
-0.06447320431470871,
-0.02767842635512352,
-0.07436875253915787,
-0.013876212760806084,
0.010044178925454617,
0.019972145557403564,
0.003166251815855503,
0.01723889261484146,
0.046974506229162216,
0.0031354303937405348,
-0.03397740051150322,
-0.014915983192622662,
0.027386130765080452,
0.003213634015992284,
-0.038513220846652985,
-0.05864502862095833,
-0.0032606530003249645,
-0.0008343684021383524,
-0.02049821987748146,
0.027227630838751793,
-0.002616194309666753,
-0.04232027754187584,
0.021022053435444832,
-0.0515834242105484,
-0.01714175008237362,
-0.033752210438251495,
0.014176431111991405,
-0.0022149584256112576,
0.03792910650372505,
-0.001956205815076828,
-0.018467020243406296,
-0.07006809115409851,
0.03416193276643753,
0.05287018418312073,
-0.026370834559202194,
-0.028386641293764114,
-0.0115877790376544,
-0.0661674216389656,
-0.0011115290690213442,
0.005962529219686985,
-0.024262262508273125,
0.007648032624274492,
0.030616391450166702,
0.02490178309381008,
0.07072310149669647,
0.07674533873796463,
0.018044710159301758,
-0.060097914189100266,
0.03904062137007713,
0.01665906049311161,
0.08072955161333084,
-0.007594545837491751,
-0.006020239554345608,
-0.015811746940016747,
0.0016816036077216268,
0.030981777235865593,
-0.004849212244153023,
-0.026787664741277695,
0.016440123319625854,
-0.021534854546189308,
-0.014557507820427418,
0.05869966745376587,
-0.019079620018601418,
0.07459567487239838,
0.047181349247694016,
-0.04568817466497421,
0.04397739842534065,
-0.04197094589471817,
-0.01814674772322178,
-0.0662783831357956,
-0.011565996333956718,
-0.07629398256540298,
-0.036584749817848206,
-0.061700738966464996,
0.04848434776067734,
-0.057151854038238525,
-0.10058198869228363,
-0.019083350896835327,
-0.04243363440036774,
0.009988551028072834,
0.012530663050711155,
-0.014025547541677952,
0.039384182542562485,
-0.08305814117193222,
0.038123589009046555,
0.021567413583397865,
0.02429039403796196,
-0.005350509658455849,
-0.02829916961491108,
-0.05060572922229767,
0.0056600323878228664,
-0.08707446604967117,
-0.05856569856405258,
0.021352387964725494,
-0.062208425253629684,
0.039788831025362015,
-0.02086522802710533,
0.0522313117980957,
-0.004434007219970226,
-0.030806617811322212,
0.04275599122047424,
-0.024948397651314735,
-0.03093635104596615,
0.031068606302142143,
-0.009485437534749508,
0.009617963805794716,
-0.005639765877276659,
-0.05390069633722305,
0.017464932054281235,
-0.050458818674087524,
0.03493332117795944,
-0.04062792286276817,
-0.04499320685863495,
-0.02265121601521969,
0.015349963679909706,
0.026423683390021324,
0.028233662247657776,
-0.019563546404242516,
-0.043668754398822784,
0.02697533369064331,
-0.016242723912000656,
0.03667674586176872,
-0.028751594945788383,
-0.02378130704164505,
0.0021073606330901384,
-0.038790974766016006,
0.011256149038672447,
0.0002398559736320749,
0.011819057166576385,
0.041124917566776276,
-0.019028736278414726,
-0.019281959161162376,
0.003743104636669159,
-0.05535265803337097,
0.04640386253595352,
-0.02598867006599903,
-0.02064540423452854,
-0.0003429346834309399,
-0.01522437110543251,
0.04095818102359772,
0.059268735349178314,
-0.0651942566037178,
-0.02771400846540928,
-0.011166772805154324,
-0.012156255543231964,
0.026790345087647438,
-0.01681060716509819,
0.008771275170147419,
0.0033676570747047663,
-0.029450898990035057,
0.039443377405405045,
0.049468815326690674,
0.07980972528457642,
0.052688322961330414,
0.023024803027510643,
0.08516667783260345,
0.041709017008543015,
-0.05049988999962807,
-0.009488345123827457,
-0.03405643254518509,
0.03320341184735298,
-0.020714659243822098,
0.05384515970945358,
-0.016187656670808792,
-0.005248228088021278,
0.025622529909014702,
0.005562616046518087,
0.00793098472058773,
-0.01451293844729662,
0.022404206916689873,
0.023295311257243156,
0.07854053378105164,
-0.039653532207012177,
-0.01536349393427372,
-0.027620144188404083,
-0.03252293914556503,
-0.001296666800044477,
-0.013147606514394283,
0.020382845774292946,
-0.0028885731007903814,
-0.019033288583159447,
0.02208443358540535,
-0.014499817974865437,
0.03061390481889248,
0.010675190016627312,
-0.013568736612796783,
-0.0565953329205513,
-0.0016316163819283247,
-0.007844500243663788,
-0.02979937009513378,
-0.06522363424301147,
0.041098590940237045,
0.043166693300008774,
-0.048479922115802765,
0.05462220683693886,
-0.019604144617915154,
-0.005999332293868065,
-0.0020149629563093185,
0.025527264922857285,
0.03615589439868927,
-0.0031913022976368666,
-0.026075830683112144,
0.013610406778752804,
0.015552139841020107,
0.05770077928900719,
-0.00611125398427248,
-0.04913337156176567,
-0.04237798973917961,
0.07511118054389954,
0.0052744923159480095,
0.03610706701874733,
-0.01680358499288559,
0.014527911320328712,
-0.012654026970267296,
0.026102649047970772,
-0.035081151872873306,
-0.020837068557739258,
-0.02693438157439232,
-0.0233513992279768,
0.03482108563184738,
-0.04333053529262543,
-0.05186915770173073,
0.015786176547408104,
-0.00578888226300478,
-0.05462624505162239,
-0.04694261774420738,
-0.024888381361961365,
0.039516959339380264,
0.09840385615825653,
0.012050341814756393,
0.012795232236385345,
-0.033661581575870514,
0.012632225640118122,
-0.023057563230395317,
0.05087900534272194,
0.0017871124437078834,
-0.001567615196108818,
0.0047528608702123165,
-0.08295153081417084,
-0.029650192707777023,
-0.05200079828500748,
0.027271877974271774,
-0.034354034811258316,
0.027343817055225372,
-0.0015418195398524404,
0.053869396448135376,
0.03618013858795166,
0.05568739026784897,
0.08883010596036911,
-0.008167935535311699,
0.11492232978343964,
0.07863829284906387,
-0.031786441802978516,
-0.016862666234374046,
-0.02083607017993927,
0.035187751054763794,
0.032308489084243774,
-0.03922611102461815,
0.07171810418367386,
0.00830041617155075,
-0.02237602509558201,
0.0577104426920414,
0.018520936369895935,
-0.004392064642161131,
0.04134444147348404,
0.04851897060871124,
-0.0351206474006176,
-0.020634988322854042,
0.019579429179430008,
-0.02119951695203781,
-0.00012411361967679113,
-0.043984752148389816,
0.012904967181384563,
-0.01153234951198101,
0.02933989278972149,
-0.04370194301009178,
0.015584821812808514,
0.03088480234146118,
0.029108192771673203,
-0.007303376216441393,
-0.022257471457123756,
0.008908080868422985,
-0.05244658514857292,
-0.04645201563835144,
0.016213329508900642,
-0.04659370332956314,
-0.0182662196457386,
0.005087588913738728,
0.09279375523328781,
-0.015468347817659378,
-0.04166024923324585,
-0.07685673236846924,
-0.046054691076278687,
-0.028632907196879387,
-0.0697963610291481,
-0.06344246864318848,
-0.00572138000279665,
0.023061199113726616,
-0.021617211401462555,
-0.035941824316978455,
-0.007476007100194693,
0.010340927168726921,
-0.06415213644504547,
-0.014672789722681046,
0.053451236337423325,
0.023923980072140694,
0.0056031630374491215,
-0.006190994288772345,
0.013493068516254425,
0.01588595099747181,
-0.06965626776218414,
0.02774016745388508,
-0.05993165448307991,
0.009344053454697132,
-0.0070938607677817345,
0.035800810903310776,
-0.042698170989751816,
0.042535483837127686,
-0.020280085504055023,
0.05939783528447151,
0.0005422251997515559,
0.01722574606537819,
0.0093153091147542,
0.036230385303497314,
0.04674097150564194,
0.0176580548286438,
0.038719385862350464,
0.015542877838015556,
0.0056901597417891026,
0.038916733115911484,
-0.019926657900214195,
-0.04346081614494324,
-0.017120065167546272,
-0.04469916224479675,
0.022041665390133858,
0.11384950578212738,
0.02292243018746376,
0.05876799300312996,
0.009717624634504318,
0.014374949969351292,
-0.07100723683834076,
0.011180023662745953,
-0.05178485065698624,
0.007883436977863312,
-0.011018365621566772,
0.014842525124549866,
0.02241305634379387,
-0.06824492663145065,
0.020965786650776863,
-0.006120102480053902,
-0.040727999061346054,
-0.0010525437537580729,
0.00942664872854948,
-0.015185081399977207,
0.003530965419486165,
-0.023260369896888733,
0.03601834177970886,
0.0005497484817169607,
0.04933328181505203,
0.050542980432510376,
-0.01599513739347458,
0.0449429415166378,
0.017234090715646744,
0.04504520073533058,
0.01877831295132637,
-0.006562586408108473,
0.05330463498830795,
-0.016026241704821587,
-0.07339782267808914,
-0.01619810424745083,
-0.009910793974995613,
0.0527496263384819,
-0.030498387292027473,
-0.03902070224285126,
0.07546494901180267,
0.02887289971113205,
0.07728199660778046,
-0.0023448520805686712,
-0.05576903373003006,
0.04385467246174812,
0.023865267634391785,
0.01143617369234562,
0.02911410853266716,
-0.020300956442952156,
-0.014428532682359219,
0.023370757699012756,
-0.03347809240221977,
-0.04362351447343826,
-0.027493666857481003,
-0.02978975512087345,
-0.020482705906033516
] |
<p>In more detail:
If i have two soda cans, both are cooled to exactly 4 degrees celsius,
And i put one in a 25 degrees room, and the other next to an AC vent set to 16 degrees.
After three minutes, which one should be colder than the other and why?</p>
<p>Edit: To clarify - if I have a cold soda can, should I place it near the AC vent or not (if I like my drink cold)? Which location will cause faster heating?</p> | g5513 | [
0.08002521097660065,
-0.024044213816523552,
-0.005839976482093334,
0.02890324406325817,
0.08433465659618378,
-0.05705371871590614,
0.01638629287481308,
0.03655824810266495,
-0.09937696158885956,
-0.012469260953366756,
0.009023748338222504,
0.014856559224426746,
-0.01658124104142189,
-0.018223920837044716,
0.013087602332234383,
-0.020214324817061424,
0.02113468199968338,
-0.0055945441126823425,
0.01758207567036152,
0.06673264503479004,
-0.004282699897885323,
-0.09279564023017883,
-0.022419966757297516,
-0.04026772081851959,
0.005523020401597023,
-0.02265547215938568,
-0.043342068791389465,
0.025969378650188446,
-0.02725166641175747,
0.018823878839612007,
-0.02319169044494629,
0.049437880516052246,
0.005914030130952597,
0.050449758768081665,
-0.01644147001206875,
-0.03917928412556648,
0.08285938203334808,
0.01683238334953785,
-0.01712864451110363,
-0.04955223575234413,
-0.020123587921261787,
0.0117448465898633,
0.01731974631547928,
-0.047636453062295914,
0.00810661818832159,
-0.010830434039235115,
-0.03246832266449928,
-0.009504757821559906,
-0.006903437897562981,
0.00026006074040196836,
-0.018519697710871696,
-0.06505977362394333,
-0.0031908482778817415,
0.03720185533165932,
-0.028818927705287933,
-0.008434009738266468,
0.00008320360939251259,
0.011456411331892014,
-0.028528967872262,
-0.0005667494842782617,
0.03815849497914314,
0.02247205562889576,
0.012090072967112064,
-0.03911420330405235,
-0.032593805342912674,
0.08223982900381088,
-0.004920042119920254,
0.040496576577425,
0.01547282561659813,
0.021507326513528824,
-0.0337681882083416,
-0.023726332932710648,
0.03834725543856621,
-0.049436651170253754,
-0.04272196814417839,
0.025883758440613747,
0.02485307864844799,
-0.024029038846492767,
0.01772402413189411,
0.004111323039978743,
-0.04196110740303993,
0.06304948031902313,
0.045046016573905945,
-0.05295655131340027,
-0.019255023449659348,
0.05469101667404175,
-0.018212560564279556,
0.01653059385716915,
0.029317831620573997,
-0.01464557833969593,
-0.033873509615659714,
0.0009079493465833366,
0.07962554693222046,
0.05055718868970871,
-0.00586611358448863,
0.0009158771717920899,
0.02295158989727497,
0.035874661058187485,
0.07135137170553207,
0.04966692999005318,
-0.028374452143907547,
-0.05351650342345238,
0.0020635295659303665,
0.028011659160256386,
-0.025656962767243385,
-0.009031139314174652,
0.005869550630450249,
0.0028510019183158875,
-0.041311390697956085,
0.013610693626105785,
-0.04923155531287193,
-0.05292747914791107,
-0.011891309171915054,
0.03449808433651924,
-0.03573639690876007,
-0.017517834901809692,
0.00620734179392457,
0.037942055612802505,
0.03948312625288963,
0.016843726858496666,
0.05429688096046448,
0.09114327281713486,
-0.018447764217853546,
0.01672331616282463,
0.014234446920454502,
-0.0540609247982502,
0.024971524253487587,
0.043149761855602264,
0.009699305519461632,
0.010135479271411896,
-0.024410974234342575,
-0.017469456419348717,
-0.029546251520514488,
-0.02768629975616932,
-0.051637135446071625,
0.0010261561255902052,
0.024221770465373993,
-0.023749733343720436,
-0.007891659624874592,
0.018630502745509148,
0.0061379908584058285,
0.028002247214317322,
0.04027792438864708,
-0.03550552576780319,
-0.04263928532600403,
0.006799668539315462,
-0.06382609903812408,
0.004191764630377293,
0.0002954556548502296,
-0.022469693794846535,
0.002778625814244151,
-0.040535151958465576,
0.00846166256815195,
0.042545150965452194,
-0.016699843108654022,
0.005071766208857298,
-0.029872527346014977,
-0.0464593805372715,
0.04597219079732895,
-0.017824897542595863,
-0.03392450511455536,
-0.04046444222331047,
0.03748571127653122,
0.018858538940548897,
-0.018778979778289795,
-0.020880142226815224,
0.026096174493432045,
-0.01901654712855816,
-0.005384551361203194,
-0.02139374613761902,
-0.05441668629646301,
0.0200661551207304,
-0.046282462775707245,
0.02304147556424141,
0.07341837882995605,
0.017437050119042397,
0.05480710044503212,
-0.0419662706553936,
0.019554805010557175,
-0.05087822675704956,
0.0025268548633903265,
0.04999050870537758,
-0.038779065012931824,
-0.02278660051524639,
-0.0009729789453558624,
-0.042830269783735275,
-0.00852013286203146,
0.0008827158017084002,
-0.03797564283013344,
0.009852155111730099,
0.00930275022983551,
-0.04254753887653351,
0.03410637006163597,
0.04737129434943199,
-0.018076011911034584,
-0.03140181675553322,
-0.03276430070400238,
-0.011287225410342216,
-0.08552971482276917,
0.040831033140420914,
0.004682998172938824,
-0.029703080654144287,
0.060866065323352814,
-0.006831740960478783,
-0.033488769084215164,
0.0698147565126419,
-0.03554082661867142,
-0.008231662213802338,
0.04794524610042572,
-0.018582670018076897,
0.017130766063928604,
0.028047360479831696,
0.0235267523676157,
-0.05307232588529587,
0.04219585284590721,
0.05381535738706589,
0.03610578924417496,
0.05760962516069412,
-0.016299253329634666,
0.01436894852668047,
-0.015422431752085686,
0.019344095140695572,
0.022331470623612404,
-0.07688164710998535,
-0.050077296793460846,
-0.04858310893177986,
-0.04362071305513382,
-0.0004678573168348521,
-0.02067970670759678,
0.012688595801591873,
-0.0722016766667366,
-0.015936806797981262,
0.05770206078886986,
-0.012935076840221882,
-0.03547365218400955,
-0.003320368705317378,
-0.00896399561315775,
0.028647294268012047,
0.10371927917003632,
-0.007688557729125023,
-0.01523854210972786,
0.04203193634748459,
-0.02295530028641224,
0.08003301173448563,
0.0030417507514357567,
-0.018134459853172302,
0.01577986218035221,
-0.06771646440029144,
0.024271998554468155,
0.01839529164135456,
0.009094761684536934,
0.07122150808572769,
-0.04001805931329727,
-0.0539165623486042,
-0.014172588475048542,
-0.002898374106734991,
-0.026842590421438217,
0.052032724022865295,
-0.04322909191250801,
-0.03191371262073517,
-0.011706079356372356,
-0.010212861932814121,
-0.0005654054693877697,
-0.04620932787656784,
0.039029836654663086,
0.04938662797212601,
-0.06460858881473541,
0.02050105854868889,
-0.01891515962779522,
0.016685867682099342,
0.05978960916399956,
0.06295256316661835,
-0.025857731699943542,
-0.02492654137313366,
-0.034644901752471924,
-0.004655944183468819,
0.055843453854322433,
-0.04713360220193863,
0.0031306357122957706,
-0.030986931174993515,
0.048217322677373886,
0.014092673547565937,
-0.01893734745681286,
0.010788270272314548,
0.046458352357149124,
-0.03274437412619591,
-0.05168544128537178,
0.024117641150951385,
-0.006074477918446064,
-0.07106461375951767,
-0.027300965040922165,
0.07440824061632156,
0.0071219950914382935,
0.036090560257434845,
0.044868115335702896,
-0.018556540831923485,
0.0342971608042717,
-0.0077128843404352665,
0.026323813945055008,
-0.018422456458210945,
0.017116446048021317,
-0.009478969499468803,
-0.02082028053700924,
-0.008946342393755913,
0.08146210014820099,
0.026974236592650414,
-0.04352749511599541,
-0.04370352625846863,
0.03895407170057297,
0.008833996020257473,
0.013703603297472,
-0.03324858844280243,
-0.027854174375534058,
0.04986880347132683,
-0.03209514170885086,
-0.012847917154431343,
-0.026827212423086166,
0.05852404981851578,
0.0020873998291790485,
-0.012595321983098984,
0.04459889605641365,
0.03583491966128349,
0.023582497611641884,
0.06646410375833511,
0.050737589597702026,
0.01407567597925663,
0.039959780871868134,
0.017942052334547043,
0.01744641736149788,
0.04434971511363983,
-0.014952970668673515,
0.01243169978260994,
-0.032731954008340836,
-0.03513530641794205,
0.013063476420938969,
-0.01591753587126732,
0.014098766259849072,
0.005953742191195488,
0.004024852067232132,
0.03398987650871277,
-0.011872430332005024,
-0.009097909554839134,
-0.0060972548089921474,
-0.016214126721024513,
-0.01705063134431839,
0.03388271480798721,
0.010928059928119183,
0.00030836445512250066,
0.03760688006877899,
0.042762354016304016,
0.029335396364331245,
-0.012165996246039867,
-0.06592925637960434,
0.0277650635689497,
-0.08441020548343658,
-0.00005771530413767323,
-0.05476243048906326,
0.025888459756970406,
-0.030704231932759285,
0.016292667016386986,
0.029622796922922134,
0.0018850859487429261,
-0.022959211841225624,
0.03466149792075157,
-0.005094901192933321,
0.06237449124455452,
-0.021330930292606354,
-0.0005313047440722585,
-0.009699080139398575,
0.007118468638509512,
0.0027083586901426315,
0.040059320628643036,
-0.01978256180882454,
0.022546863183379173,
0.10520371049642563,
-0.018072228878736496,
0.07052135467529297,
0.03507787361741066,
-0.06970902532339096,
0.03737141937017441,
-0.01501413807272911,
-0.0027757263742387295,
-0.014855104498565197,
-0.021332992240786552,
-0.010127333924174309,
0.016670485958456993,
-0.04703987017273903,
-0.001835782895796001,
-0.007632026914507151,
-0.09227855503559113,
-0.03266248106956482,
0.05343000218272209,
0.0020566312596201897,
0.06418868899345398,
-0.013742931187152863,
0.011911939829587936,
0.0198745746165514,
0.057610105723142624,
0.0239846371114254,
0.010175792500376701,
-0.05559150129556656,
0.04777699336409569,
-0.015476948581635952,
-0.028226183727383614,
-0.03378279134631157,
-0.002886512316763401,
0.028082065284252167,
-0.02712313085794449,
0.0013534314930438995,
-0.03468351438641548,
0.04093583673238754,
-0.0033595473505556583,
0.014104368165135384,
0.037435904145240784,
0.09400589019060135,
-0.016186954453587532,
-0.03185424581170082,
0.003232773393392563,
0.039930470287799835,
0.003645016113296151,
-0.012474017217755318,
-0.04535748064517975,
-0.03192424029111862,
-0.04339979216456413,
-0.002890682080760598,
0.014395656995475292,
0.04033946245908737,
-0.0052023837342858315,
-0.02780856564640999,
-0.029401596635580063,
0.004008591640740633,
0.00040961350896395743,
-0.028738707304000854,
-0.005338270682841539,
0.04899954795837402,
0.00895069632679224,
-0.02425456792116165,
-0.03380855172872543,
-0.005189013667404652,
0.07171490043401718,
-0.03266404569149017,
0.0068382807075977325,
-0.02172386460006237,
-0.016834300011396408,
-0.05825553461909294,
0.07178651541471481,
-0.012967674061655998,
-0.007747296243906021,
-0.00020997731189709157,
-0.05138537287712097,
-0.03790745511651039,
0.08409560471773148,
-0.007075679488480091,
-0.02605118229985237,
0.007260486483573914,
-0.005809190217405558,
0.02797980234026909,
0.002624175976961851,
0.007013848517090082,
0.0070863445289433,
-0.01322692446410656,
0.04113416373729706,
0.05849500745534897,
0.002515258267521858,
-0.013182004913687706,
-0.0443536676466465,
0.04278000444173813,
-0.09680549055337906,
-0.019390568137168884,
0.04896686598658562,
0.006279424764215946,
0.04904836416244507,
-0.029756145551800728,
0.07758157700300217,
0.014820734970271587,
0.03941613435745239,
0.02390427514910698,
0.03294858708977699,
0.025822713971138,
0.006976430304348469,
-0.045042939484119415,
-0.02474321983754635,
0.011027893982827663,
-0.010710982605814934,
0.005333523731678724,
-0.0369475893676281,
-0.07388119399547577,
0.023423118516802788,
0.0491073913872242,
-0.000017031848983606324,
0.020330354571342468,
0.015363246202468872,
0.004733726382255554,
-0.02026951313018799,
-0.04666261002421379,
-0.02727498486638069,
-0.03701437637209892,
-0.008538134396076202,
0.07988835871219635,
-0.029426850378513336,
0.015032321214675903,
-0.00416572205722332,
0.015792259946465492,
-0.024396203458309174,
-0.04100745543837547,
0.04828602448105812,
0.007566163316369057,
-0.07067552208900452,
-0.006626542191952467,
-0.003949797246605158,
0.007452185731381178,
-0.008024295791983604,
0.036925673484802246,
-0.00251403939910233,
0.051376957446336746,
-0.042337268590927124,
0.0055333152413368225,
-0.03354276716709137,
0.0307159461081028,
-0.011191691271960735,
0.04668480157852173,
0.009036676958203316,
-0.09133090078830719,
-0.02057177945971489,
-0.0455896258354187,
-0.019377483054995537,
-0.023442324250936508,
0.01773204281926155,
-0.019537176936864853,
-0.04045214131474495,
0.05496738851070404,
0.04513108357787132,
0.03802572190761566,
-0.0025279978290200233,
-0.04380430281162262,
-0.026779422536492348,
-0.053541578352451324,
-0.008629598654806614,
0.031001431867480278,
0.02298344112932682,
-0.010222812183201313,
-0.07269833981990814,
0.02573060803115368,
0.04358290880918503,
-0.04139629751443863,
-0.00573340430855751,
0.009478284977376461,
-0.003808091627433896,
0.033711399883031845,
0.01741977594792843,
0.009787701070308685,
0.02305692993104458,
-0.0008422961109317839,
0.03037598915398121,
0.056788910180330276,
0.024644000455737114,
0.020429085940122604,
0.02066168375313282,
0.032982442528009415,
-0.008360357023775578,
-0.041550178080797195,
0.011410881765186787,
0.06303495913743973,
-0.0067586409859359264,
-0.039853569120168686,
-0.05806238204240799,
-0.0659174844622612,
-0.002742352895438671,
0.06694558262825012,
0.06068601831793785,
0.05301656574010849,
-0.026998251676559448,
0.01631585694849491,
-0.04164796322584152,
0.008907088078558445,
0.022017858922481537,
0.0038500791415572166,
0.038359634578228,
0.0045396690256893635,
-0.025247758254408836,
-0.019119568169116974,
-0.03243129700422287,
-0.03396807238459587,
-0.006425834726542234,
0.04771164059638977,
0.08433552831411362,
-0.02715938352048397,
-0.015379653312265873,
0.03893589600920677,
-0.04289944842457771,
0.0040018921718001366,
-0.07800152897834778,
-0.005437362473458052,
0.0285948496311903,
-0.038498856127262115,
-0.028579240664839745,
0.01639942266047001,
0.00213048467412591,
-0.02922173961997032,
0.034551847726106644,
-0.03407300263643265,
0.040969885885715485,
0.021921155974268913,
0.0155105609446764,
-0.014964969828724861,
0.03473018482327461,
0.019141295924782753,
0.07711095362901688,
0.03942779451608658,
-0.01225297711789608,
-0.014744605869054794,
0.044812943786382675,
0.06382165104150772,
-0.0013531269505620003,
0.029600592330098152,
0.028060292825102806,
-0.016174964606761932,
-0.0013936773175373673,
0.0022500797640532255,
0.0058784447610378265,
0.03460559993982315,
-0.0032943973783403635,
-0.049896035343408585,
-0.014051346108317375,
-0.00037256599171087146,
-0.01707848533987999,
-0.030307596549391747,
0.030094215646386147,
0.01891389489173889,
-0.03050287254154682,
0.03317410498857498,
-0.03836122155189514,
-0.010811210609972477,
0.0010822213953360915,
-0.01866156794130802,
-0.02725416235625744,
-0.02860495075583458,
0.027943767607212067,
-0.05299471318721771,
0.005254851654171944,
0.00006612115248572081,
0.02764192782342434,
0.017575578764081,
0.0008722727652639151,
0.001024230383336544,
-0.04635496065020561,
0.04079817235469818,
0.000121344332001172,
-0.0739721804857254,
-0.010646332986652851,
-0.06091264635324478,
-0.019596433266997337,
-0.04237884283065796,
0.015565325506031513,
0.009204703383147717,
0.012189989909529686,
0.006042846944183111,
0.015520216897130013,
0.025206217542290688,
0.004607995040714741,
-0.0336134098470211,
-0.030548036098480225,
-0.061926160007715225,
0.058886636048555374,
-0.005962316878139973,
-0.011394206434488297,
-0.05572688579559326,
-0.030474932864308357,
0.032280974090099335,
-0.07162584364414215,
0.0003838653792627156,
-0.0418977253139019,
-0.038747638463974,
-0.06504978239536285,
0.05248429998755455,
0.032161325216293335,
0.02074882574379444,
-0.037995290011167526,
0.0496656596660614,
-0.011252772994339466,
-0.005390494596213102,
-0.009323087520897388,
-0.030618341639637947,
-0.06686920672655106,
0.009158327244222164,
0.027986127883195877,
-0.03909582272171974,
0.025258254259824753,
-0.012950905598700047,
-0.07704305648803711,
-0.02726413682103157,
-0.04384111613035202,
0.0020918764639645815,
-0.009805472567677498,
-0.004700288642197847,
0.028717907145619392,
0.006000335328280926,
-0.050832148641347885,
0.022990748286247253,
0.031892240047454834,
0.02551320753991604,
0.038910433650016785,
0.05205796658992767,
-0.008120052516460419,
0.031282901763916016,
0.009349541738629341,
-0.0009351384360343218,
0.06437359005212784,
-0.025633974000811577,
-0.02509440667927265,
-0.006014340557157993,
0.027951372787356377,
0.041496776044368744,
0.01819205842912197,
-0.031139297410845757,
-0.03328343480825424,
-0.0737404003739357,
-0.021406330168247223,
0.023468170315027237,
-0.010810126550495625,
-0.030163949355483055,
0.014991480857133865,
0.023461608216166496,
-0.027064180001616478,
-0.031868427991867065,
0.005876536015421152,
0.008884516544640064,
-0.004125822335481644,
0.003378328401595354,
0.015452798455953598,
-0.019746188074350357,
0.04338246211409569,
0.04190109297633171,
0.04054831340909004,
-0.04377062991261482,
0.0049804262816905975,
0.015174318104982376,
0.06253699213266373,
0.06493988633155823,
-0.001214727759361267,
-0.02944180928170681,
0.025894679129123688,
-0.04096047952771187,
-0.0042146798223257065,
0.020012954249978065,
-0.027662230655550957,
-0.012195064686238766,
0.06617818772792816,
0.07857754081487656,
-0.0709679126739502,
-0.05676309019327164,
-0.005935183260589838,
-0.11333956569433212,
-0.04455092176795006,
-0.012149538844823837,
0.01806686632335186,
-0.05863481014966965,
-0.034845441579818726,
-0.015383255667984486,
-0.0016225447179749608,
-0.027823757380247116,
-0.004153974819928408,
0.032516129314899445,
-0.02691272832453251,
-0.025850169360637665,
0.10007933527231216,
0.004770220257341862,
-0.06197277829051018
] |
<p>I was reading this page:</p>
<p><a href="http://www.guardian.co.uk/science/2011/oct/23/brian-cox-jeff-forshaw-answers" rel="nofollow">http://www.guardian.co.uk/science/2011/oct/23/brian-cox-jeff-forshaw-answers</a></p>
<p>and I found this sentence by Brian Cox:</p>
<blockquote>
<p>That seems to imply that everything is flying away from us and we're therefore somehow in a privileged position; that isn't true. The way it's often described is if you imagine some bread with raisins in it that you're baking in the oven and as you heat it, it expands. On any particular raisin, if you look, you can see all the other raisins receding from it. So it's space that stretching, it's not that everything's flying away.</p>
</blockquote>
<p>I already heard this raisins analogy, but it never persuaded me:</p>
<p>I understand that the "big bang" is more like a "big stretch", and I see how every 2 observers in the universe are being distanced farther and farther away (regardless of their position)</p>
<p>Yet one of the Big Bang ideas is that the universe isn't anymore considered infinite and completely homogeneous</p>
<p>But the fact that the universe is finite, while inflating to me implicates that it should have some kind of bounds (not that we can reach these "bounds", since our distance to them is getting bigger, but they should still exist)</p>
<p>(And the fact that it's spreading inhomogeneous mass and energy over big distances, is thus making it more homogeneous, but this doesn't probably matter)</p>
<p>So: the very idea of a big bang seems to me in contradiction to the assertion that there's no such thing as a "center of the universe":</p>
<p>If it has a finite mass and some kind of bounds, then it should also have a barycenter.</p>
<p>And if we consider the bread with raisins analogy: the bread has a center from which it's expanding</p>
<p>Surely, the universe isn't homogeneous (like the distribution of the raisins), and so, in its hypothetical center, there may not be actually anything... but I think (even if it's really unlikely) it should still be theoretically possible to have a raisin in the exact centre of the bread</p> | g5514 | [
0.05990702286362648,
0.06696554273366928,
0.015317386016249657,
-0.029615968465805054,
-0.0318792387843132,
0.008688167668879032,
-0.03290625289082527,
0.020109063014388084,
-0.0001859931362560019,
-0.09080827236175537,
0.04585965350270271,
0.016698753461241722,
0.015013071708381176,
0.059401921927928925,
0.06249552220106125,
-0.012280006892979145,
-0.0046426099725067616,
-0.05424953252077103,
0.02850642427802086,
-0.01665816642343998,
0.0017983873840421438,
-0.02960873953998089,
0.02674911357462406,
0.005722484551370144,
-0.10971995443105698,
-0.0979265347123146,
0.04105285182595253,
-0.0682535395026207,
-0.027759108692407608,
0.004008057527244091,
0.01593555323779583,
-0.007594493683427572,
-0.002456096699461341,
-0.04016875848174095,
-0.025910237804055214,
-0.003068120451644063,
-0.0008054968784563243,
0.018498582765460014,
0.005196218844503164,
0.00598895875737071,
-0.037329528480768204,
0.0335099883377552,
-0.01990446448326111,
-0.008233512751758099,
-0.006598375737667084,
0.08370961993932724,
-0.026022035628557205,
0.05619773641228676,
0.05249781161546707,
-0.07317611575126648,
-0.01346707995980978,
0.021709276363253593,
0.04291193559765816,
0.06242517754435539,
0.027591701596975327,
0.006980238016694784,
0.020144952461123466,
-0.015332013368606567,
0.0674123764038086,
0.035617176443338394,
-0.0177741851657629,
0.015456992201507092,
0.002157782204449177,
0.014474567025899887,
-0.0044492376036942005,
-0.010240820236504078,
-0.09255535155534744,
0.021471604704856873,
-0.05764124169945717,
-0.01658591441810131,
0.05869985371828079,
-0.10864365845918655,
-0.010440264828503132,
-0.01824992150068283,
-0.07000232487916946,
0.02933969721198082,
-0.0407828688621521,
-0.010229747742414474,
0.01352680567651987,
-0.014894476160407066,
-0.03965763375163078,
0.01850063167512417,
0.022121824324131012,
0.0621645450592041,
0.07494461536407471,
-0.023774655535817146,
0.047256387770175934,
0.0011032053735107183,
-0.023175016045570374,
0.035278648138046265,
0.011422696523368359,
-0.006379987113177776,
0.051663678139448166,
0.007430892903357744,
-0.003837219439446926,
-0.006177718751132488,
-0.027745883911848068,
0.02030770480632782,
-0.043687183409929276,
-0.03877466917037964,
-0.048507705330848694,
0.07691705226898193,
0.009721689857542515,
0.005218361504375935,
0.02290561981499195,
-0.03381344676017761,
0.03464573621749878,
0.01092082541435957,
0.038025058805942535,
-0.02625497803092003,
-0.004379075951874256,
-0.033074215054512024,
-0.008231386542320251,
-0.015234723687171936,
-0.0783911645412445,
0.004498641472309828,
0.11386702209711075,
-0.013641958124935627,
0.06846478581428528,
0.012149843387305737,
0.015871046110987663,
0.0499647781252861,
-0.005336773581802845,
0.06761249899864197,
-0.04995401203632355,
-0.019965188577771187,
-0.008291974663734436,
-0.028123900294303894,
-0.016552358865737915,
0.006028851494193077,
0.00636054202914238,
-0.027265075594186783,
0.01579766348004341,
0.03526773303747177,
0.03996438905596733,
-0.004550036508589983,
0.007495218887925148,
-0.06699655950069427,
0.029701456427574158,
0.016489282250404358,
-0.018288370221853256,
0.007421038579195738,
-0.001243126462213695,
-0.03123229742050171,
-0.019982539117336273,
0.02523614466190338,
0.0073396447114646435,
0.016399497166275978,
-0.0009492016979493201,
0.022603560239076614,
0.016040509566664696,
0.057885050773620605,
-0.03372540324926376,
0.034056346863508224,
-0.03074113465845585,
0.0021227316465228796,
0.021638186648488045,
0.030935002490878105,
0.006995899602770805,
0.04205403849482536,
-0.006211248692125082,
-0.01970275677740574,
0.017730293795466423,
-0.03663434088230133,
-0.08060815185308456,
0.056823570281267166,
-0.013273761607706547,
-0.0024807658046483994,
0.011172918602824211,
-0.01739276573061943,
-0.09358759969472885,
-0.05065872147679329,
-0.032988883554935455,
0.0336088165640831,
-0.026890533044934273,
0.01474017184227705,
0.052906036376953125,
-0.0036206282675266266,
0.007688031531870365,
-0.025988558307290077,
-0.07197245210409164,
-0.04772091656923294,
0.0005202537286095321,
0.03755999356508255,
-0.01593782939016819,
0.006517865229398012,
0.01698099449276924,
0.045384328812360764,
-0.009598028846085072,
-0.02421603538095951,
0.005719950422644615,
-0.0019500964554026723,
0.04352244362235069,
0.019014855846762657,
0.006096909753978252,
0.004876432474702597,
0.04446608945727348,
-0.0006508214864879847,
-0.011214297264814377,
-0.004330142866820097,
-0.005908450577408075,
0.004564293194562197,
0.0038054450415074825,
0.011354574002325535,
0.05130145698785782,
0.02544775791466236,
-0.009602411650121212,
0.04188445210456848,
-0.02450225129723549,
0.008701448328793049,
-0.0013128090649843216,
-0.05606270581483841,
-0.004812528379261494,
0.07252442836761475,
-0.0010006735101342201,
-0.014507105574011803,
-0.019332388415932655,
0.007243542466312647,
-0.012886691838502884,
0.06389822065830231,
-0.0358802005648613,
-0.050020650029182434,
0.05648777261376381,
-0.047127146273851395,
0.06968017667531967,
-0.048218607902526855,
-0.008255344815552235,
-0.049916502088308334,
0.013886027038097382,
0.05728074908256531,
-0.04590214043855667,
0.0047011105343699455,
0.05754319578409195,
-0.0023989134933799505,
0.03825744614005089,
0.0013216626830399036,
-0.006716551259160042,
0.0229076836258173,
-0.019255520775914192,
0.02791971154510975,
-0.021572265774011612,
-0.04140659421682358,
-0.06196470558643341,
0.012228639796376228,
0.04352064058184624,
0.0012673335149884224,
0.05169009044766426,
-0.0658494383096695,
-0.045002881437540054,
0.027356429025530815,
0.022079521790146828,
-0.02094755508005619,
0.02094966545701027,
-0.024290133267641068,
0.028904452919960022,
-0.04801040515303612,
0.017539191991090775,
0.03860895335674286,
-0.06378620862960815,
-0.047285452485084534,
0.008977988734841347,
-0.09291718155145645,
0.07804742455482483,
0.0356244258582592,
-0.01797962374985218,
0.06074880063533783,
-0.004509728867560625,
0.02715703658759594,
-0.013855704106390476,
-0.03130631148815155,
0.015437441878020763,
0.06654629111289978,
0.03218711540102959,
0.06040376052260399,
-0.04382409155368805,
-0.014641459099948406,
0.010355159640312195,
0.01037948951125145,
0.04498787224292755,
0.016308262944221497,
0.020729970186948776,
0.013973426073789597,
-0.0192220751196146,
-0.01993030123412609,
0.0058457134291529655,
-0.014820617623627186,
-0.05830999091267586,
-0.014428526163101196,
-0.003798640565946698,
-0.0375102199614048,
0.08490357547998428,
0.001321913325227797,
0.021063078194856644,
0.050226978957653046,
-0.010138512589037418,
0.06390299648046494,
-0.005856039002537727,
-0.03173390403389931,
-0.053591132164001465,
-0.006503127049654722,
-0.007563034072518349,
0.027416415512561798,
0.03810007870197296,
-0.004198563750833273,
0.005407171789556742,
0.06518904864788055,
-0.0130561962723732,
-0.061364706605672836,
0.021940790116786957,
-0.06189630180597305,
0.03873104602098465,
0.03648633882403374,
-0.011838560923933983,
0.0660620927810669,
0.04954058676958084,
0.055902715772390366,
0.00509359035640955,
0.0408940389752388,
0.049771975725889206,
-0.0021545670460909605,
0.008807912468910217,
0.010706675238907337,
0.000490650360006839,
-0.016317162662744522,
0.07943271100521088,
0.05572444200515747,
-0.08630882203578949,
0.0009606934618204832,
-0.03244611248373985,
-0.07575917989015579,
-0.015714487060904503,
-0.020139629021286964,
0.040601182729005814,
-0.041414737701416016,
-0.10564379394054413,
-0.030295010656118393,
0.007760551292449236,
0.02824794314801693,
0.07803544402122498,
0.017430664971470833,
0.006188857369124889,
-0.017538174986839294,
0.002815272193402052,
0.015344498679041862,
0.02064785733819008,
0.04980948567390442,
-0.04892798513174057,
-0.01948573626577854,
0.057837601751089096,
-0.0363587848842144,
0.03132447972893715,
0.019092824310064316,
-0.05008598789572716,
0.0033916172105818987,
-0.03459969535470009,
0.01850438117980957,
-0.017300011590123177,
-0.0034587711561471224,
0.02923804335296154,
0.0013009749818593264,
0.04895485192537308,
-0.04292158782482147,
0.034261465072631836,
-0.04171597212553024,
-0.004154340364038944,
-0.016169389709830284,
-0.023090850561857224,
0.021343160420656204,
-0.020241234451532364,
-0.01729530282318592,
0.018060976639389992,
-0.03306179493665695,
-0.042815424501895905,
0.01149277575314045,
0.0809841901063919,
-0.008093636482954025,
0.06969062238931656,
0.008427640423178673,
-0.04368079453706741,
0.02642311528325081,
0.022809188812971115,
0.0512881800532341,
0.012227301485836506,
0.03780946135520935,
0.06531132757663727,
0.01013212837278843,
-0.0067916265688836575,
-0.04223643243312836,
0.02744736149907112,
-0.031643155962228775,
0.04407426342368126,
-0.06317009776830673,
0.0220375694334507,
-0.04249957576394081,
0.0002468300226610154,
-0.05793492868542671,
-0.030920807272195816,
-0.018494360148906708,
0.012506704777479172,
0.0657152608036995,
0.033430684357881546,
-0.014261938631534576,
0.010672500357031822,
0.024357685819268227,
-0.0437467023730278,
-0.02766447141766548,
0.05461963638663292,
-0.01564803719520569,
-0.007509145420044661,
-0.06084643676877022,
0.0550042986869812,
0.0394451878964901,
-0.0032257612328976393,
-0.04797423630952835,
0.06459218263626099,
-0.05387302115559578,
0.05271255970001221,
-0.04977362975478172,
0.00942793395370245,
0.028703920543193817,
-0.0025447781663388014,
0.06375404447317123,
-0.022528696805238724,
-0.004296319559216499,
0.03199364244937897,
0.09727758169174194,
-0.024586910381913185,
-0.007762246765196323,
0.0033229722175747156,
0.0593094527721405,
-0.009499950334429741,
0.03668076545000076,
0.08131368458271027,
0.02576902136206627,
-0.016020245850086212,
0.01278352364897728,
-0.07449652999639511,
0.04165184497833252,
-0.009490772150456905,
-0.003528496716171503,
0.026614800095558167,
-0.041317906230688095,
-0.01758255623281002,
-0.006383954081684351,
0.035943321883678436,
0.02189800702035427,
0.010806489735841751,
0.006861038506031036,
-0.014779459685087204,
0.008756549097597599,
-0.00419129803776741,
0.03908516466617584,
-0.042252570390701294,
0.04216719791293144,
0.013191166333854198,
-0.056585900485515594,
-0.03661663457751274,
-0.047891464084386826,
0.058150291442871094,
-0.014778000302612782,
-0.06964630633592606,
0.0032322509214282036,
-0.06086020544171333,
0.02617621049284935,
0.03503050282597542,
0.015764227136969566,
-0.05726592615246773,
-0.04062243551015854,
-0.022255035117268562,
0.005696616601198912,
-0.012523484416306019,
0.04610851779580116,
-0.02240876294672489,
0.027889059856534004,
-0.0009845428867265582,
0.014188726432621479,
0.0060834432952106,
-0.01563630811870098,
-0.03707718849182129,
-0.019580449908971786,
-0.043362390249967575,
0.0012519926531240344,
0.019748391583561897,
-0.05002591013908386,
0.05763169005513191,
0.028752166777849197,
-0.02349279634654522,
-0.01607251539826393,
-0.008198585361242294,
-0.026307664811611176,
0.039103273302316666,
-0.05192136764526367,
-0.025596922263503075,
-0.014530766755342484,
0.015661004930734634,
-0.008617926388978958,
-0.010106025263667107,
-0.04147018864750862,
0.01578657329082489,
-0.027685072273015976,
-0.061611879616975784,
0.09101156145334244,
0.0483672060072422,
0.042995814234018326,
-0.04182061925530434,
0.019585445523262024,
0.029728563502430916,
-0.013685847632586956,
-0.03321540355682373,
0.04814056307077408,
0.003974987659603357,
0.009380106814205647,
-0.019155163317918777,
0.02123972959816456,
0.0309177003800869,
-0.02064194716513157,
0.0001805733481887728,
-0.01999783329665661,
0.03190600872039795,
-0.019984083250164986,
-0.008925736881792545,
0.03972066193819046,
0.0329584926366806,
-0.001424177666194737,
0.002621070249006152,
0.039949867874383926,
-0.05116983875632286,
-0.032337579876184464,
0.012802626937627792,
0.008075487799942493,
-0.025927282869815826,
0.0032202412839978933,
0.03550112992525101,
-0.015992557629942894,
0.013957669958472252,
0.06339790672063828,
-0.07125501334667206,
-0.0011397101916372776,
0.014871478080749512,
-0.03808196634054184,
0.006112309172749519,
0.004006516188383102,
-0.03724205866456032,
0.06310304254293442,
-0.039092715829610825,
0.0473756305873394,
-0.06604532152414322,
0.011360724456608295,
0.07240420579910278,
-0.04895571991801262,
-0.01294117234647274,
0.043425608426332474,
-0.02898099459707737,
-0.017596136778593063,
0.00306686875410378,
0.02230345457792282,
0.044023286551237106,
-0.012763315811753273,
-0.03003106825053692,
-0.03500965237617493,
-0.0282791368663311,
0.0007702577859163284,
0.01904868520796299,
0.029164979234337807,
-0.012280690483748913,
-0.0049444325268268585,
0.001635015825740993,
-0.02665228582918644,
0.01665247231721878,
0.01331007108092308,
-0.007168017793446779,
0.014686509035527706,
-0.038122277706861496,
0.023054027929902077,
-0.0304314773529768,
-0.02807897888123989,
-0.046058110892772675,
0.013304696418344975,
0.009676449932157993,
0.006613875739276409,
0.04194089397788048,
-0.027845898643136024,
0.08233524858951569,
-0.05239969119429588,
-0.0022202003747224808,
0.015193527564406395,
-0.029950162395834923,
0.00310552422888577,
0.05520682409405708,
-0.014440604485571384,
0.0008223821059800684,
-0.01858620159327984,
-0.020472023636102676,
0.027072329074144363,
-0.026737254112958908,
0.0060944021679461,
0.005571913439780474,
-0.08851591497659683,
-0.07400331646203995,
0.023631786927580833,
0.008052932098507881,
-0.0009825698798522353,
0.05086491256952286,
0.0002469183236826211,
0.03865246847271919,
0.021334385499358177,
0.008137665688991547,
0.047953296452760696,
-0.006393767893314362,
-0.0020482356194406748,
0.004350982140749693,
0.04989650472998619,
0.058170393109321594,
-0.008089619688689709,
-0.002725377446040511,
-0.03419072553515434,
-0.006839885376393795,
-0.024829333648085594,
0.0016872513806447387,
-0.03137703612446785,
0.03017868846654892,
0.005945037584751844,
-0.04365229606628418,
-0.01813928782939911,
-0.025851354002952576,
0.03766442462801933,
-0.041254494339227676,
0.01876453310251236,
0.011532429605722427,
-0.0000992192726698704,
0.0011081334669142962,
0.009865649975836277,
0.022807667031884193,
0.045826300978660583,
-0.02846146561205387,
0.02729034051299095,
-0.045842189341783524,
-0.0013365958584472537,
-0.054271914064884186,
-0.012987989000976086,
-0.059948667883872986,
-0.025073310360312462,
0.007598190568387508,
-0.011930682696402073,
-0.0026734862476587296,
-0.04214030131697655,
0.010750800371170044,
-0.009777163155376911,
-0.020060472190380096,
-0.02607402391731739,
-0.014187936671078205,
-0.01387727726250887,
-0.0024551451206207275,
-0.011352483183145523,
-0.039363425225019455,
-0.02784300036728382,
-0.02084365300834179,
-0.044606681913137436,
-0.05682613328099251,
-0.08789309859275818,
-0.0020368704572319984,
-0.038700733333826065,
-0.0031965598464012146,
0.009274291805922985,
-0.07225580513477325,
0.04534013569355011,
0.04289550706744194,
-0.010933088138699532,
-0.004310030490159988,
-0.035790786147117615,
-0.03606012463569641,
-0.02401450090110302,
-0.06254034489393234,
-0.014398176223039627,
0.01675788126885891,
-0.053047940135002136,
-0.02843019925057888,
0.027612127363681793,
-0.0037758266553282738,
0.0023664343170821667,
0.07526068389415741,
0.0647476315498352,
-0.00115092599298805,
0.06425940245389938,
-0.02707354724407196,
0.03563357889652252,
-0.026652377098798752,
-0.03288741782307625,
-0.007758617866784334,
-0.03380933031439781,
0.01187096443027258,
-0.004656484816223383,
0.0043030837550759315,
-0.006341726519167423,
0.012128994800150394,
-0.013057016767561436,
0.01243843138217926,
0.07988400012254715,
0.01585841178894043,
-0.08309763669967651,
-0.004472280386835337,
-0.02209019847214222,
-0.015765927731990814,
-0.009511791169643402,
0.03751753643155098,
0.04370930790901184,
-0.036871287971735,
0.0321333073079586,
-0.071139857172966,
0.016202135011553764,
0.061129380017519,
0.02901381254196167,
-0.005186248105019331,
0.030431821942329407,
-0.00793794821947813,
0.01667647995054722,
-0.003997397609055042,
0.0015530971577391028,
-0.02977198362350464,
-0.027584895491600037,
0.021602770313620567,
-0.0015282524982467294,
0.009178811684250832,
-0.037283945828676224,
-0.02536659874022007,
-0.019048836082220078,
-0.02092614583671093,
-0.054200343787670135,
-0.009784553200006485,
-0.027610160410404205,
0.014762762002646923,
0.028382573276758194,
-0.018733061850070953,
0.031800806522369385,
-0.04307105019688606,
0.06596729159355164,
-0.000016507960026501678,
-0.021929584443569183,
-0.0387868732213974,
-0.003972502425312996,
-0.04992201179265976,
-0.02113701030611992,
0.01726279966533184,
-0.01168135181069374,
0.005557230208069086,
-0.011865577660501003,
-0.006170968990772963,
-0.0021376728545874357,
-0.005795994773507118,
0.004195252899080515,
0.010714484378695488,
-0.011118213646113873,
-0.034348636865615845,
0.04050077497959137,
0.06534390896558762,
-0.05647188425064087,
0.0032842440996319056,
0.025624221190810204,
-0.002727875718846917,
0.007771819829940796,
0.010633241385221481,
0.0027655987069010735,
-0.00872033927589655,
-0.0326649509370327,
0.011669742874801159,
-0.05375863239169121,
-0.021473536267876625,
0.023680949583649635
] |
<p>In <a href="http://arxiv.org/abs/1004.0726" rel="nofollow">this paper</a> on co-orbital dynamics the authors discover, numerically, "Anti-Lagrangian" solutions to the restricted 3 body problem. These Anti-Lagrange $L_4$ and $L_5$ points are 120 degrees ahead and behind the planet (if I understand correctly).</p>
<p>It is possible, as Lagrange demonstrated, to prove that the usual $L_4$ and $L_5$ <a href="http://en.wikipedia.org/wiki/Lagrangian_point" rel="nofollow">points</a> are stable solutions to the restricted circular 3 body problem. But how can you prove that these new-fangled Anti-Lagrangian $L_4$ and $L_5$ points are stable solutions? The method used by Lagrange will not result in such a proof.</p> | g5515 | [
0.027527587488293648,
0.05419974774122238,
0.02504986897110939,
-0.046640295535326004,
0.05518685281276703,
0.06785779446363449,
0.04396660253405571,
-0.05152122303843498,
-0.039268240332603455,
0.006953895557671785,
0.009289560839533806,
0.06186698377132416,
0.03590579330921173,
0.030888808891177177,
0.02093752659857273,
0.011909302324056625,
-0.00944150984287262,
-0.017352623865008354,
0.031584545969963074,
0.03070632554590702,
0.033680509775877,
0.04384644702076912,
-0.017236050218343735,
0.0229527298361063,
-0.010522655211389065,
-0.002138979034498334,
0.01677228882908821,
-0.07361111044883728,
-0.005477761384099722,
-0.00477449968457222,
0.055306628346443176,
-0.041533272713422775,
0.047328364104032516,
-0.04984217509627342,
0.019433705136179924,
-0.05472760647535324,
0.035534314811229706,
-0.01786470040678978,
-0.04404166713356972,
0.03376978635787964,
0.004056903067976236,
-0.054957374930381775,
0.03767072409391403,
0.03864716738462448,
0.0008357928600162268,
-0.03279729187488556,
-0.011509551666676998,
-0.044068433344364166,
0.04047749191522598,
-0.03585309907793999,
0.02759811282157898,
0.0737256407737732,
-0.01553459744900465,
-0.12497914582490921,
-0.039643216878175735,
0.01425895281136036,
-0.014277494512498379,
-0.017946425825357437,
-0.02572590671479702,
-0.005358790513128042,
-0.009556439705193043,
-0.07388579845428467,
0.022937512025237083,
0.024688923731446266,
0.021999767050147057,
-0.04835101589560509,
-0.047062210738658905,
0.03935838118195534,
-0.013533692806959152,
0.007746049668639898,
0.0511566698551178,
-0.022609343752264977,
0.01577334851026535,
-0.07415089756250381,
-0.028755944222211838,
0.023314110934734344,
0.01582331769168377,
0.032394565641880035,
0.0052611990831792355,
-0.033439721912145615,
-0.09297386556863785,
0.01762082800269127,
-0.04469318315386772,
0.043674249202013016,
0.02857477031648159,
-0.031853917986154556,
0.02965216338634491,
0.01351574994623661,
0.0018028230406343937,
-0.03790624067187309,
0.008088852278888226,
-0.02495439536869526,
-0.023188820108771324,
-0.06668536365032196,
-0.001228495966643095,
0.05287252366542816,
0.025904187932610512,
0.04779837280511856,
-0.05825832486152649,
-0.030414877459406853,
0.007062163669615984,
0.042027492076158524,
-0.016415810212492943,
0.07365385442972183,
-0.01804145611822605,
-0.01910409703850746,
0.06278316676616669,
-0.0010009609395638108,
0.014430725015699863,
-0.03298361599445343,
-0.013820769265294075,
-0.018443148583173752,
-0.002279525389894843,
-0.002387087559327483,
-0.04161090776324272,
-0.018702920526266098,
0.017216553911566734,
-0.02644234150648117,
0.06392552703619003,
0.045854900032281876,
-0.020073432475328445,
0.01791377179324627,
-0.024882547557353973,
0.047089818865060806,
0.014489829540252686,
0.011641745455563068,
-0.00024863198632374406,
-0.07474072277545929,
0.0558423288166523,
-0.04907876253128052,
-0.022069176658988,
0.03864150494337082,
-0.014200158417224884,
-0.014052190817892551,
-0.02688322775065899,
0.014303124509751797,
-0.0235491581261158,
0.03647401183843613,
-0.011516871862113476,
-0.003327762708067894,
0.01180947944521904,
-0.0316251777112484,
0.07219512015581131,
0.0321972593665123,
-0.05974317342042923,
0.01707269437611103,
-0.025558652356266975,
0.03558744862675667,
-0.006262042559683323,
0.0653320923447609,
-0.022330595180392265,
0.0968332514166832,
-0.01814565621316433,
-0.014689193107187748,
0.011863553896546364,
-0.010950223542749882,
-0.00624890998005867,
0.02590959519147873,
-0.05233200266957283,
-0.009012375958263874,
0.01663648523390293,
0.03853977844119072,
-0.020262721925973892,
-0.0031343279406428337,
0.010087021626532078,
0.07051021605730057,
-0.07606607675552368,
-0.012599813751876354,
-0.06336561590433121,
0.03719348460435867,
-0.08376570045948029,
0.041730448603630066,
-0.02767101861536503,
0.018753310665488243,
0.002598368562757969,
0.034617140889167786,
0.009944883175194263,
-0.06728776544332504,
-0.016645245254039764,
-0.0067836749367415905,
0.017255306243896484,
-0.039959147572517395,
-0.008209784515202045,
0.043482840061187744,
0.02803562395274639,
0.007292617112398148,
-0.016563739627599716,
0.042425889521837234,
0.0010268586920574307,
-0.013134530745446682,
0.05755374953150749,
0.013112356886267662,
-0.07510967552661896,
-0.022838978096842766,
0.026053117588162422,
-0.02299634739756584,
0.045161861926317215,
-0.04244355484843254,
0.01296248845756054,
-0.022087693214416504,
-0.023494569584727287,
-0.011533532291650772,
0.032681871205568314,
-0.008383282460272312,
0.025710653513669968,
-0.023450378328561783,
-0.0030072680674493313,
-0.007757912389934063,
0.030507707968354225,
0.01747201196849346,
-0.01935812458395958,
-0.016917718574404716,
0.027857420966029167,
-0.010235659778118134,
0.0029363958165049553,
-0.005699462722986937,
0.00815160945057869,
0.05459488555788994,
-0.022739799693226814,
0.009956960566341877,
-0.02367965504527092,
0.006419851910322905,
-0.027676785364747047,
0.04113829880952835,
0.03961509093642235,
-0.0248213279992342,
-0.03789566084742546,
-0.061097197234630585,
0.052391938865184784,
0.023171698674559593,
-0.04948383942246437,
0.001819352968595922,
0.00040621383232064545,
0.01599237509071827,
0.01870707795023918,
-0.06500587612390518,
-0.004559066146612167,
-0.005673735402524471,
0.0071475510485470295,
0.10222820937633514,
0.04533657059073448,
0.0026618933770805597,
-0.020445480942726135,
0.016139153391122818,
0.07956208288669586,
-0.0346447192132473,
0.051701001822948456,
0.031260646879673004,
-0.07335413992404938,
0.0026978773530572653,
-0.014673764817416668,
-0.0022685464937239885,
-0.04564223065972328,
-0.004227905068546534,
0.005902648903429508,
0.046824537217617035,
0.0126588623970747,
0.02642534300684929,
0.0017074387287721038,
-0.007653652690351009,
0.008893762715160847,
0.008943282067775726,
0.02509104274213314,
-0.005418586079031229,
-0.023864837363362312,
-0.005989443976432085,
-0.005546294618397951,
-0.10195750743150711,
-0.010716123506426811,
-0.03583516553044319,
-0.029165159910917282,
0.04260780289769173,
-0.009431296028196812,
0.07868281751871109,
-0.018569281324744225,
0.035788923501968384,
-0.020248206332325935,
-0.05797698721289635,
0.009021095000207424,
0.02254972606897354,
0.02423924393951893,
-0.031296949833631516,
-0.004454867914319038,
0.04179700091481209,
0.012367944233119488,
0.04756961017847061,
-0.029391983523964882,
0.02772001549601555,
0.03272819146513939,
-0.05360342562198639,
-0.01652810350060463,
-0.0039697736501693726,
-0.00034627006971277297,
0.0011091761989519,
-0.009884456172585487,
-0.0014362072106450796,
-0.013456721790134907,
-0.03774620220065117,
-0.02085636369884014,
0.02882407419383526,
0.012839891947805882,
0.034777574241161346,
0.0007883413345552981,
-0.013706738129258156,
0.04881948605179787,
-0.023964012041687965,
-0.0031818326096981764,
0.017728323116898537,
-0.002152625471353531,
-0.020523548126220703,
0.019645433872938156,
0.0057189930230379105,
-0.06845688074827194,
-0.0072319963946938515,
0.019931700080633163,
0.04618702828884125,
-0.028682760894298553,
0.05225006490945816,
0.05207464471459389,
-0.042653437703847885,
-0.04944434016942978,
-0.003687076037749648,
-0.06297583132982254,
-0.011355851776897907,
0.03602597117424011,
-0.01726166345179081,
-0.04234644025564194,
-0.03187602385878563,
-0.0435103178024292,
-0.011309461668133736,
-0.010404041968286037,
-0.01886085420846939,
0.06852419674396515,
0.006076278164982796,
0.01648387871682644,
-0.007322314195334911,
0.036393798887729645,
-0.017453374341130257,
0.03163328021764755,
-0.007485458627343178,
0.004824289120733738,
-0.038370758295059204,
-0.06876634806394577,
-0.05013309046626091,
0.020614754408597946,
0.019524436444044113,
0.004676950164139271,
0.04789341986179352,
0.010664117522537708,
-0.07293590903282166,
-0.002116382122039795,
0.0011755599407479167,
0.03716535493731499,
-0.02325226366519928,
-0.018572548404335976,
0.023073427379131317,
-0.024273190647363663,
-0.013367881067097187,
0.018507104367017746,
-0.00394618883728981,
-0.020461775362491608,
0.03955154865980148,
0.008755022659897804,
-0.001653457642532885,
0.07622237503528595,
-0.01782255992293358,
-0.04192400351166725,
0.012604232877492905,
-0.01125508826225996,
-0.015054339542984962,
0.00787175539880991,
-0.07464399188756943,
0.0470406599342823,
-0.013036340475082397,
0.05325622856616974,
-0.054116107523441315,
-0.00726927537471056,
0.046163398772478104,
-0.017719309777021408,
0.0016091197030618787,
0.008130825124680996,
-0.04669066518545151,
0.017856312915682793,
0.0275978185236454,
-0.005392272025346756,
0.08826126158237457,
-0.03432871773838997,
-0.01242342684417963,
-0.043199557811021805,
-0.004790575709193945,
0.022106021642684937,
-0.03509276732802391,
0.017267653718590736,
-0.028359901160001755,
0.022663472220301628,
-0.0033142883330583572,
-0.02013140544295311,
-0.055791400372982025,
-0.016728488728404045,
0.015236346051096916,
-0.004735960625112057,
0.009920168668031693,
-0.0392037034034729,
-0.012182550504803658,
-0.013743212446570396,
0.025079132989048958,
0.00036373594775795937,
0.06159019097685814,
-0.01823725551366806,
-0.010268015787005424,
0.025774817913770676,
0.004898794461041689,
0.038574256002902985,
-0.04205280914902687,
0.06895922124385834,
-0.08427725732326508,
-0.019071459770202637,
-0.005009099375456572,
0.029018519446253777,
0.010815993882715702,
-0.058881115168333054,
0.05540309101343155,
-0.0004036967584397644,
-0.030818678438663483,
0.026840748265385628,
0.045178987085819244,
0.008356534875929356,
0.016031086444854736,
-0.04098391532897949,
0.026788802817463875,
0.02838294766843319,
-0.02361273765563965,
0.07202619314193726,
-0.030377142131328583,
-0.018318306654691696,
0.01439244206994772,
-0.02409355714917183,
0.037510648369789124,
0.0238692294806242,
-0.008497584611177444,
-0.015770597383379936,
0.08127522468566895,
0.10064324736595154,
-0.006752733141183853,
-0.0341445617377758,
0.031138615682721138,
-0.03309560939669609,
0.0058072395622730255,
0.08516395092010498,
0.008768673054873943,
-0.0008079239050857723,
-0.012374921701848507,
0.0169213954359293,
0.03735673427581787,
-0.022358661517500877,
-0.006083102431148291,
0.03948669880628586,
-0.008661284111440182,
-0.02930368483066559,
0.024643883109092712,
-0.04247824847698212,
-0.0650608241558075,
0.01070792693644762,
-0.030452966690063477,
0.06686093658208847,
0.009824895299971104,
-0.013614586554467678,
0.01823856681585312,
0.02418297342956066,
-0.033486880362033844,
0.02002597600221634,
0.018453409895300865,
0.0026616877876222134,
-0.010403365828096867,
-0.08105287700891495,
-0.06068233400583267,
0.05105564370751381,
-0.0077799404971301556,
0.010306419804692268,
-0.022576795890927315,
0.0553620383143425,
-0.00018904590979218483,
0.019073758274316788,
0.052580513060092926,
0.007334879599511623,
-0.006329879630357027,
0.00440133735537529,
-0.008988391607999802,
-0.039847515523433685,
-0.018616605550050735,
0.0007297436241060495,
-0.0022230958566069603,
-0.011800238862633705,
0.049496110528707504,
0.026912109926342964,
0.03975997865200043,
-0.021576792001724243,
-0.029220115393400192,
-0.018242675811052322,
0.0447431281208992,
-0.060414738953113556,
-0.0019409814849495888,
0.026841307058930397,
0.013383226469159126,
0.02445550076663494,
0.027257701382040977,
0.06769667565822601,
-0.0743212178349495,
0.014600683934986591,
-0.05033428966999054,
-0.03864660486578941,
0.0067301117815077305,
-0.012981321662664413,
0.004430831875652075,
-0.005824403837323189,
-0.07018377631902695,
-0.007094560656696558,
-0.02059563621878624,
-0.002947575179859996,
-0.03708357736468315,
0.021535860374569893,
0.0625002384185791,
0.005192190408706665,
-0.02054760791361332,
0.027146795764565468,
-0.013379446230828762,
0.0054642255418002605,
-0.013295329175889492,
-0.04170818254351616,
0.06017332896590233,
-0.05312033370137215,
0.007896320894360542,
-0.00336875906214118,
-0.007967798970639706,
-0.015096161514520645,
-0.032423581928014755,
0.01596684381365776,
-0.0009447136544622481,
0.05630520358681679,
-0.032789796590805054,
0.019978752359747887,
-0.05812280625104904,
0.005169992335140705,
0.04118165373802185,
-0.04871981218457222,
0.030949411913752556,
-0.05026526749134064,
0.07000499218702316,
-0.025928935036063194,
-0.042969200760126114,
-0.047784022986888885,
0.030974363908171654,
-0.004667218308895826,
-0.05421871691942215,
-0.03947309032082558,
0.009644978679716587,
0.000334509793901816,
0.013509734533727169,
-0.04597656428813934,
-0.013881131075322628,
-0.04501577839255333,
-0.03625020012259483,
0.07894846051931381,
0.0771266371011734,
-0.03528547286987305,
-0.026143334805965424,
-0.04014471918344498,
-0.013133205473423004,
-0.023824729025363922,
-0.013940099626779556,
-0.03638545423746109,
0.027017828077077866,
-0.0553429052233696,
0.0244032833725214,
0.07105415314435959,
-0.020819002762436867,
-0.018009090796113014,
-0.05741267278790474,
-0.05450472980737686,
0.016384031623601913,
-0.05754725635051727,
0.023397784680128098,
0.038019124418497086,
-0.01613481529057026,
-0.0565834641456604,
0.037739284336566925,
-0.04440544918179512,
-0.005606033839285374,
-0.03761929273605347,
-0.08345046639442444,
0.03544135391712189,
0.014831053093075752,
-0.052810583263635635,
0.015773767605423927,
0.01814868114888668,
0.040138933807611465,
-0.026270613074302673,
0.05158452317118645,
-0.06144852936267853,
0.031564824283123016,
0.06213134899735451,
0.005636928137391806,
0.04163559153676033,
-0.02108246646821499,
-0.004051624331623316,
0.017371322959661484,
0.010972072370350361,
0.04022179916501045,
0.030239056795835495,
-0.011315342038869858,
0.01400251965969801,
-0.024223018437623978,
0.08141763508319855,
0.022031841799616814,
0.03692174702882767,
0.007482272572815418,
0.029365085065364838,
0.006006935611367226,
-0.04407784342765808,
0.0076040723361074924,
0.024229345843195915,
-0.029527194797992706,
-0.04677238687872887,
0.01873205043375492,
0.02755456604063511,
0.008265121839940548,
0.008121464401483536,
-0.029959769919514656,
0.010624384507536888,
0.020057648420333862,
0.03966177999973297,
-0.05449430271983147,
0.006619731429964304,
0.02332155965268612,
0.019381968304514885,
0.03733870014548302,
-0.05886181443929672,
0.02919052354991436,
0.07439957559108734,
0.00966580305248499,
-0.03720923140645027,
0.02284819632768631,
0.07631104439496994,
0.005421615671366453,
-0.06132907420396805,
0.00659301970154047,
0.015903031453490257,
-0.03846593573689461,
-0.0023340170737355947,
-0.01508997566998005,
0.0012274155160412192,
-0.04228963702917099,
-0.09880442917346954,
0.029225658625364304,
-0.0069893645122647285,
-0.0006231112056411803,
0.0038780125323683023,
-0.014334435574710369,
-0.011525758542120457,
-0.013816900551319122,
-0.010591868311166763,
0.050663288682699203,
0.0276572797447443,
-0.01057636272162199,
0.02768819034099579,
0.03666870296001434,
0.005415876861661673,
-0.03075362555682659,
0.009232348762452602,
0.04824279993772507,
0.02491234801709652,
0.0025499253533780575,
-0.0629773661494255,
0.04897430166602135,
-0.007372009102255106,
0.013912972062826157,
0.013465508818626404,
-0.01768643781542778,
0.02439071424305439,
0.026444634422659874,
0.015787670388817787,
-0.006524899508804083,
-0.0012806726153939962,
0.023917417973279953,
-0.05502380058169365,
0.01278239767998457,
0.01544592622667551,
-0.016816366463899612,
-0.03843789920210838,
0.012400700710713863,
0.017965758219361305,
0.08717239648103714,
-0.000165811346960254,
-0.015469890087842941,
-0.0480048768222332,
-0.020656248554587364,
0.01958082988858223,
0.013023972511291504,
0.017563343048095703,
-0.016171742230653763,
-0.030144181102514267,
-0.03401091694831848,
-0.000009255734767066315,
0.021804990246891975,
0.0022148790303617716,
-0.023839781060814857,
-0.015608676709234715,
0.0009625697857700288,
-0.05717160552740097,
0.059020742774009705,
-0.01271347887814045,
0.0503428615629673,
-0.008799729868769646,
-0.021650809794664383,
0.07408294826745987,
-0.016524503007531166,
0.045707009732723236,
0.03043113648891449,
-0.009426816366612911,
-0.03577790781855583,
-0.027640340849757195,
-0.014347263611853123,
0.015260488726198673,
-0.09805801510810852,
0.06667615473270416,
-0.04219623655080795,
0.04394545406103134,
-0.051104962825775146,
0.04081990569829941,
-0.0473780483007431,
-0.033806927502155304,
0.05658140406012535,
-0.04878271371126175,
0.01655050553381443,
-0.033657584339380264,
-0.001036912202835083,
-0.06759213656187057,
-0.03887869045138359,
0.06242944300174713,
0.014545133337378502,
-0.06953435391187668,
-0.04594530537724495,
0.009635386988520622,
-0.01642315648496151,
-0.00044463181984610856,
0.0045654973946511745,
-0.014601201750338078,
0.011756635271012783,
0.032892145216464996,
0.013635283336043358,
0.06728463619947433,
0.04708801209926605,
-0.07194868475198746,
0.018001830205321312,
0.027715764939785004,
-0.009900772012770176,
-0.022960474714636803,
-0.09387598186731339,
0.035288989543914795,
0.039330221712589264,
-0.018968874588608742,
0.016030002385377884,
0.0644373670220375,
-0.04304694011807442,
-0.012542562559247017,
-0.05205538123846054,
-0.010657250881195068,
0.016646608710289
] |
<p>Let's say I have a cylindrical piston containing saturated liquid ammonia that is fitted with an electrical heater and a paddle wheel for stirring at an initial pressure and an initial temperature. When the gas expands, some of it evaporates to form a two phase, liquid-vapor solution inside the system. By the way, this process occurs at a constant pressure.</p>
<p>My real question is, what happens to the temperature as the pressure is constant and the volume increases, also causing the specific volume to increase. I would assume the temperature increases, but when I look at the steam table, there is only one temperature corresponding to the pressure. For example, if the initial temperature is 20C, the initial pressure is 8.57bar. If that pressure is constant so the final pressure is 8.57bar, the steam table still says the temperature is 20C.</p>
<p>Why is this? Because I was just looking at the ideal gas equation and it essentially says temperature increases as volume increases. But can I use this intuition with the ideal gas law when the system is 2 phase?</p> | g5516 | [
0.04248575121164322,
-0.009122412651777267,
0.01483068522065878,
0.019231364130973816,
0.023895220831036568,
-0.012612121179699898,
-0.04420369118452072,
0.05945303291082382,
-0.07827094942331314,
0.00993388146162033,
-0.022626502439379692,
0.026107260957360268,
0.05837477743625641,
0.02054734155535698,
0.02789945714175701,
-0.009103052318096161,
0.019120147451758385,
-0.06053734943270683,
-0.0056515769101679325,
-0.0028038080781698227,
-0.023222601041197777,
0.005459658335894346,
0.0033858169335871935,
-0.0551598034799099,
-0.01193742360919714,
-0.018244680017232895,
0.024404853582382202,
0.06276674568653107,
-0.02675170637667179,
0.01143413782119751,
-0.027519598603248596,
0.008891280740499496,
-0.015208289958536625,
-0.027237853035330772,
-0.06434735655784607,
-0.03619531914591789,
0.03852865472435951,
-0.01861773058772087,
-0.00578409293666482,
-0.07972346991300583,
0.056023210287094116,
-0.03747991845011711,
-0.017298130318522453,
0.05149148777127266,
-0.039023783057928085,
0.0330972783267498,
-0.034257613122463226,
-0.010484603233635426,
-0.021391037851572037,
0.043219637125730515,
0.02596254087984562,
-0.013282732106745243,
-0.027720313519239426,
-0.036020055413246155,
-0.013029240071773529,
0.06939195841550827,
-0.028420550748705864,
-0.020566020160913467,
-0.017399076372385025,
0.06189413741230965,
0.0000598622027609963,
-0.010157001204788685,
0.04014376178383827,
-0.02354520745575428,
-0.0060644992627203465,
-0.026995357125997543,
-0.039983659982681274,
-0.011449534446001053,
-0.0006347303278744221,
0.042886193841695786,
-0.023676767945289612,
-0.04832308739423752,
0.008173931390047073,
-0.025913037359714508,
-0.03246452659368515,
-0.02357247844338417,
-0.008168969303369522,
-0.044268716126680374,
0.0021078288555145264,
-0.0023239089641720057,
-0.017160870134830475,
0.05922447517514229,
0.018759405240416527,
0.00978982262313366,
-0.003140371758490801,
-0.032662034034729004,
0.05242092162370682,
-0.04706105589866638,
-0.03393648564815521,
-0.012402404099702835,
0.007676621433347464,
-0.007387617602944374,
0.09680663794279099,
0.04769087955355644,
0.010127702727913857,
0.0002030486211879179,
0.03881576284766197,
0.021356383338570595,
0.012954452075064182,
0.008546553552150726,
0.045500241219997406,
-0.04561011120676994,
0.0513865128159523,
-0.007237606681883335,
-0.017494579777121544,
0.03015606664121151,
0.008732086047530174,
0.025200339034199715,
-0.004531315062195063,
-0.005276578478515148,
-0.054896265268325806,
-0.05316914618015289,
-0.07068759948015213,
-0.0686585009098053,
-0.03413541242480278,
-0.02090861275792122,
-0.032046686857938766,
0.04730646312236786,
0.03552350401878357,
0.0008588347118347883,
0.08236676454544067,
0.007748743053525686,
0.0039001430850476027,
0.033537909388542175,
0.029877377673983574,
-0.008609006181359291,
0.0175116378813982,
-0.04326479882001877,
0.0014357527252286673,
-0.03238321840763092,
-0.010125515051186085,
0.031026192009449005,
-0.054173506796360016,
0.03524376079440117,
0.08832646906375885,
-0.0017073681810870767,
-0.008560240268707275,
0.028878968209028244,
-0.011646014638245106,
0.00455195177346468,
-0.013306181877851486,
0.004536429885774851,
-0.04147296026349068,
-0.004521526396274567,
-0.04775749519467354,
-0.01792198047041893,
0.006273174658417702,
0.020462386310100555,
0.024074314162135124,
-0.01648605428636074,
-0.05244544893503189,
0.06540392339229584,
0.03222918137907982,
-0.008118274621665478,
0.03450729697942734,
0.011977740563452244,
0.02285582758486271,
-0.025029882788658142,
0.048546358942985535,
0.00677454611286521,
0.035241205245256424,
-0.02070779725909233,
0.00203587394207716,
0.021269122138619423,
-0.09893164783716202,
0.061184875667095184,
-0.020238423720002174,
-0.029899144545197487,
0.005412223283201456,
-0.053498949855566025,
-0.04087395966053009,
0.02154376357793808,
-0.09020017087459564,
0.0540337897837162,
0.03405735269188881,
-0.002025956753641367,
0.12263400107622147,
0.0643637403845787,
0.024023331701755524,
-0.07015156000852585,
-0.04143071919679642,
-0.04699883982539177,
-0.014288116246461868,
-0.05840282514691353,
-0.009923508390784264,
0.04507080838084221,
-0.002100891899317503,
-0.019313832744956017,
-0.08187920600175858,
0.0037553731817752123,
0.009253873489797115,
0.030183441936969757,
-0.030885813757777214,
0.041848089545965195,
0.002352692885324359,
-0.021424992009997368,
-0.00028359785210341215,
-0.018176892772316933,
-0.08561862260103226,
-0.003134913742542267,
-0.04477692395448685,
0.0027484712190926075,
0.009590938687324524,
0.014505068771541119,
-0.001746018067933619,
0.01069559995085001,
-0.043241456151008606,
0.002516933251172304,
0.03116675093770027,
0.02174435183405876,
-0.03446166589856148,
-0.01130205113440752,
-0.049598176032304764,
0.0038949211593717337,
0.004074700642377138,
0.017724422737956047,
0.00939401425421238,
-0.00004962232560501434,
0.028174588456749916,
0.020876549184322357,
0.05816960707306862,
0.020173903554677963,
0.004636614117771387,
0.013979998417198658,
-0.038128260523080826,
-0.028398893773555756,
-0.003266994608566165,
-0.037250980734825134,
0.0001543998223496601,
0.05381840839982033,
-0.05837016925215721,
0.009694862179458141,
0.041197989135980606,
-0.004985697567462921,
-0.026435889303684235,
0.027019789442420006,
-0.03667666018009186,
0.05126558989286423,
0.03786809742450714,
0.05044025182723999,
0.004185365047305822,
0.0060600959695875645,
-0.01934744603931904,
0.03579772636294365,
0.03196548670530319,
0.02007400430738926,
0.029225919395685196,
0.02020534873008728,
0.021353743970394135,
0.01676313951611519,
-0.057624682784080505,
0.017929282039403915,
0.000003008919975400204,
0.012058914639055729,
-0.07099401205778122,
-0.017505725845694542,
-0.0032680502627044916,
0.03379109874367714,
-0.04391566663980484,
-0.037337612360715866,
0.04534727334976196,
-0.034266240894794464,
0.022150829434394836,
0.014440410770475864,
-0.05303691327571869,
0.05697871372103691,
-0.035543814301490784,
-0.02290641888976097,
0.023873047903180122,
0.009073822759091854,
0.007200160995125771,
0.005483841523528099,
-0.01207004114985466,
0.04196114465594292,
0.008260528557002544,
-0.011518539860844612,
-0.009352019056677818,
0.010089498944580555,
0.05571996420621872,
-0.018273500725626945,
-0.029880939051508904,
-0.049555014818906784,
-0.04996879771351814,
0.007836475037038326,
0.04920149967074394,
-0.02541944570839405,
0.03659085929393768,
0.031484656035900116,
-0.008758146315813065,
-0.023334698751568794,
0.02239971235394478,
0.03452230244874954,
-0.011130744591355324,
0.060699209570884705,
0.028210561722517014,
0.059056442230939865,
0.004600604064762592,
-0.012901995331048965,
0.025074411183595657,
-0.0073679652996361256,
-0.011310379020869732,
-0.07255415618419647,
-0.022007452324032784,
-0.01601969450712204,
-0.01862398162484169,
0.022082248702645302,
-0.08168359100818634,
-0.021992186084389687,
-0.010101262480020523,
0.0038931153248995543,
-0.0893450677394867,
-0.022548500448465347,
-0.0309334397315979,
-0.039185114204883575,
-0.06596094369888306,
0.07027091830968857,
0.028972623869776726,
0.011355345137417316,
0.010697627440094948,
0.010118380188941956,
-0.07021252065896988,
-0.03877260908484459,
0.0012692759046331048,
-0.029236087575554848,
0.00012425430759321898,
0.004893815610557795,
-0.01547317672520876,
-0.0031250568572431803,
-0.03582243621349335,
-0.00047493388410657644,
-0.016388725489377975,
-0.010409084148705006,
-0.0554974302649498,
-0.02193491719663143,
0.04543289914727211,
-0.024084771052002907,
-0.036377113312482834,
-0.032163504511117935,
-0.022828994318842888,
0.052578963339328766,
0.019196810200810432,
0.00598884979262948,
0.004354950971901417,
0.020787280052900314,
0.008570298552513123,
-0.028147945180535316,
-0.035314179956912994,
0.01809874176979065,
0.0133656095713377,
-0.016865869984030724,
0.10046569257974625,
-0.0243851225823164,
0.03198792785406113,
0.007394070737063885,
-0.03519542142748833,
0.02818101830780506,
0.05707501620054245,
-0.019603585824370384,
-0.06929544359445572,
-0.027907593175768852,
0.0045717572793364525,
-0.04770643636584282,
0.014222332276403904,
0.07864747941493988,
0.0024000934790819883,
-0.0001391126133967191,
0.05202788487076759,
0.07886487245559692,
0.019465019926428795,
-0.024285301566123962,
-0.008100803010165691,
-0.03582903370261192,
0.011548475362360477,
0.022668004035949707,
0.059969667345285416,
0.0011139977723360062,
-0.01800261065363884,
0.04773695394396782,
-0.03653274476528168,
0.068771131336689,
0.035350997000932693,
0.011151524260640144,
-0.02391243353486061,
0.00415478739887476,
0.0035632678773254156,
0.007663700729608536,
-0.03373673930764198,
0.05808665603399277,
0.07671314477920532,
-0.05283369868993759,
0.03608717769384384,
-0.014000112190842628,
-0.01509014330804348,
0.022324969992041588,
0.029428672045469284,
0.04869593679904938,
-0.004278980661183596,
-0.0286931823939085,
-0.020017210394144058,
-0.02391250804066658,
0.005582858808338642,
-0.04799392819404602,
0.012983094900846481,
0.0015971290413290262,
-0.0013940253993496299,
-0.032097961753606796,
0.08109807223081589,
-0.056427307426929474,
0.02792479656636715,
0.01765008457005024,
0.04391394183039665,
0.08717802911996841,
-0.0003215578617528081,
-0.013775797560811043,
0.05608109012246132,
-0.04281274601817131,
0.05097109079360962,
-0.02686903439462185,
0.03218677639961243,
-0.0019149366999045014,
-0.06783168017864227,
0.02588493563234806,
-0.05287215858697891,
-0.0014698506565764546,
-0.049236588180065155,
-0.011091496795415878,
0.026535984128713608,
-0.02687849849462509,
-0.00979587621986866,
-0.04221421107649803,
-0.030228981748223305,
-0.04254109784960747,
0.009792151860892773,
0.04949852079153061,
0.0030807028524577618,
0.03490526229143143,
-0.023804213851690292,
0.05805020034313202,
-0.027194729074835777,
0.057572029531002045,
0.04004373028874397,
0.052925556898117065,
-0.023571301251649857,
0.01209503598511219,
-0.01647825352847576,
-0.023928726091980934,
0.007685309741646051,
-0.01905582845211029,
0.0398077592253685,
-0.019959375262260437,
-0.04446139931678772,
0.05720312148332596,
0.04862409085035324,
-0.02862403355538845,
0.004328473936766386,
0.0067752148024737835,
-0.042746663093566895,
0.08626317977905273,
-0.00320099457167089,
-0.015555289573967457,
-0.03414986655116081,
0.00404342170804739,
-0.05835960805416107,
0.039050228893756866,
-0.010452304035425186,
-0.043192483484745026,
-0.017579127103090286,
-0.056787844747304916,
0.029432594776153564,
0.02315453439950943,
0.05082157999277115,
0.03300866484642029,
0.03579629585146904,
0.03887125104665756,
0.066607765853405,
-0.0061154975555837154,
0.017936592921614647,
-0.054464273154735565,
0.03702421486377716,
-0.07227280735969543,
-0.014655029401183128,
-0.0029578199610114098,
0.07207959145307541,
0.046145323663949966,
0.03361576423048973,
0.01333670038729906,
0.003657788038253784,
0.024175576865673065,
0.0443192757666111,
0.022067854180932045,
0.016972366720438004,
0.06338953226804733,
-0.0068229748867452145,
0.017585251480340958,
-0.01637931540608406,
-0.025674182921648026,
-0.011921733617782593,
-0.04496733844280243,
-0.017748087644577026,
0.029748033732175827,
-0.022083237767219543,
0.01775396801531315,
0.01104053482413292,
0.02463938482105732,
0.004705095198005438,
-0.008650044910609722,
-0.06356900185346603,
-0.007444377522915602,
-0.015005776658654213,
0.0152306342497468,
0.0728919506072998,
0.004477635491639376,
-0.0014403639361262321,
0.00020360098278615624,
0.02084350399672985,
-0.0462847463786602,
0.025312256067991257,
-0.06264496594667435,
-0.00895046629011631,
0.006772066932171583,
0.046943556517362595,
-0.026410328224301338,
0.054056886583566666,
0.032931867986917496,
-0.03674713522195816,
0.046726059168577194,
-0.009151145815849304,
-0.01220044307410717,
0.02250899374485016,
0.05037181079387665,
-0.019214734435081482,
0.01857406087219715,
0.04195759817957878,
0.01664416864514351,
-0.012307776138186455,
0.013346286490559578,
-0.007365687284618616,
0.006658276543021202,
0.09157488495111465,
-0.008543998934328556,
-0.03128556162118912,
-0.0028673140332102776,
-0.02238689549267292,
0.051143065094947815,
0.01073220744729042,
0.01657775603234768,
-0.03744162991642952,
0.032023511826992035,
0.029084796085953712,
-0.028881125152111053,
-0.02462542988359928,
0.025531573221087456,
-0.01395954005420208,
-0.0023507149890065193,
-0.017434578388929367,
0.013629567809402943,
0.026765938848257065,
0.02138371765613556,
0.0033206348307430744,
-0.02354414574801922,
0.0017469081794843078,
0.03417456895112991,
0.003382682567462325,
0.029452580958604813,
-0.0003101899055764079,
-0.017900655046105385,
-0.0091318404302001,
-0.006911809556186199,
0.02846408821642399,
0.0848187655210495,
0.0006657689809799194,
0.013437297195196152,
0.06178823858499527,
-0.06689097732305527,
0.0697779431939125,
0.009346368722617626,
-0.08503220975399017,
-0.026896821334958076,
-0.020635496824979782,
0.05992304906249046,
-0.05318104475736618,
0.013869425281882286,
-0.008181006647646427,
0.04361909627914429,
-0.03352290019392967,
-0.012799513526260853,
-0.04326071962714195,
-0.01462420355528593,
0.03832414001226425,
0.05829948931932449,
-0.023973004892468452,
-0.019001778215169907,
0.004222266376018524,
0.0026142101269215345,
0.05702577903866768,
0.015925079584121704,
-0.058152392506599426,
0.021410860121250153,
0.02324015460908413,
0.017784645780920982,
0.04401557520031929,
0.0173057671636343,
0.03637867048382759,
-0.03011765144765377,
-0.07057789713144302,
-0.002726094564422965,
-0.012042275629937649,
-0.02044695056974888,
0.03312314674258232,
0.0394253246486187,
-0.01866338402032852,
0.015043128281831741,
0.06259746104478836,
-0.025269128382205963,
0.0671297013759613,
-0.03500828519463539,
0.023589758202433586,
0.03678525984287262,
-0.011021102778613567,
-0.039548080414533615,
0.01128405798226595,
-0.05043964460492134,
0.046319231390953064,
-0.032904013991355896,
0.06650974601507187,
-0.017054835334420204,
-0.05617457628250122,
0.00046524094068445265,
0.07286328077316284,
-0.021637026220560074,
0.036844342947006226,
-0.021863466128706932,
-0.014492875896394253,
-0.02662421017885208,
-0.036350712180137634,
-0.001655493164435029,
-0.02804321050643921,
-0.012622845359146595,
0.031119506806135178,
0.037216708064079285,
-0.005391996819525957,
0.019440919160842896,
-0.017668213695287704,
0.04181959480047226,
0.0011280475882813334,
0.01195801142603159,
0.05287988483905792,
-0.03211427107453346,
-0.08017095923423767,
-0.0035308904480189085,
0.00920675415545702,
-0.11220896989107132,
-0.019301921129226685,
0.029081139713525772,
0.008739475160837173,
0.017537126317620277,
-0.0076867444440722466,
-0.07832144945859909,
0.032678667455911636,
0.01735396310687065,
-0.07948321849107742,
0.01530259009450674,
0.02155102603137493,
0.0221322663128376,
-0.005253282375633717,
0.039312735199928284,
0.023863207548856735,
-0.034615326672792435,
0.0365031473338604,
-0.069888636469841,
0.020191466435790062,
-0.02183092013001442,
-0.017325032502412796,
0.013440863229334354,
0.0373324416577816,
-0.029574353247880936,
-0.00006511899118777364,
-0.014575409702956676,
0.01777002215385437,
-0.036672621965408325,
-0.017976654693484306,
-0.0675356462597847,
0.005059359595179558,
-0.06806280463933945,
-0.05322717875242233,
0.027813410386443138,
-0.03930629789829254,
-0.032902270555496216,
0.017274079844355583,
-0.029188303276896477,
0.06113549321889877,
-0.030912689864635468,
0.002632987918332219,
0.00846745353192091,
-0.019718321040272713,
0.0295086819678545,
0.042405880987644196,
0.009572664275765419,
0.01197295542806387,
-0.0006947539513930678,
0.04130522161722183,
0.00021172039851080626,
-0.05546572431921959,
0.028389476239681244,
0.06271534413099289,
0.0062204147689044476,
0.03351633623242378,
-0.008851575665175915,
-0.04517574980854988,
-0.04898698255419731,
-0.01751209795475006,
0.021593553945422173,
0.046148501336574554,
-0.00814303569495678,
-0.010058284737169743,
-0.05674131214618683,
-0.06849358230829239,
-0.07268497347831726,
-0.006824967451393604,
-0.0013867554953321815,
-0.01579594425857067,
-0.04820071905851364,
0.01574382372200489,
-0.03197206184267998,
-0.02293272688984871,
-0.04119711369276047,
-0.029439203441143036,
-0.029648195952177048,
-0.00704963831230998,
0.03182704746723175,
-0.027030099183321,
-0.002990682376548648,
0.03827063366770744,
0.04442840442061424,
-0.025172647088766098,
0.018877336755394936,
0.024847660213708878,
-0.028104184195399284,
0.0038379081524908543,
0.013830975629389286,
-0.020120572298765182,
-0.05004269257187843,
0.0657929852604866,
-0.016696160659193993,
0.03577467426657677,
-0.023944612592458725,
-0.07669893652200699,
0.08388128131628036,
0.030410276725888252,
-0.02239631861448288,
0.010207511484622955,
-0.024825481697916985,
-0.040506571531295776,
-0.028880203142762184,
0.010057948529720306,
-0.05863913521170616,
-0.03705864027142525,
0.05793318524956703,
-0.05239810422062874,
-0.00176961999386549,
-0.04598906636238098,
0.01821867562830448,
-0.03898996114730835,
-0.04325265437364578,
-0.022310219705104828,
0.012317890301346779,
0.007207442540675402,
-0.004236034117639065
] |
<p>Srednicki writes the Lagrangian density of an interacting scalar field theory as
$$ \mathcal{L} = -\frac{1}{2} Z_\phi \partial^\mu \phi \partial_\mu \phi -\frac{1}{2} Z_m m^2 \phi^2 + \frac{1}{6} Z_g g \phi^3 + Y\phi $$</p>
<p>He claims that $Y=O(g)$ and $Z_i=1+O(g^2)$. What is the basis of this claim?
Why do we ignore the $Y_0$ in the expansion of $Y(g)$:
$$Y(g) = Y_0 + Y_1 g + Y_2 g^2 + \cdots \cdots $$
and again why do we take the $Z_0 = 1$ in the expansion of $Z_i(g)$:
$$Z(g) = Z_0 + Z_1 g + Z_2 g^2 + \cdots \cdots $$</p>
<p>Why $Z_1 = 0$ ?</p>
<p>Are there any references where $\phi^3$ diagrammatics is explained clearly?</p> | g5517 | [
0.0814187154173851,
0.00498233875259757,
-0.017428359016776085,
-0.015006083995103836,
-0.0034514020662754774,
0.04292707145214081,
0.08833204954862595,
-0.00427683349698782,
0.015010830014944077,
-0.0054069445468485355,
-0.0012226724065840244,
0.0015675650211051106,
0.043770212680101395,
0.06190378963947296,
0.02490898035466671,
0.04283410683274269,
0.004940299317240715,
0.028896164149045944,
0.0049265408888459206,
0.03166705742478371,
-0.11990082263946533,
-0.03515641763806343,
0.030211128294467926,
0.0014908455777913332,
0.026217246428132057,
-0.08746993541717529,
0.03016347624361515,
0.013466726057231426,
-0.04226457700133324,
-0.047669827938079834,
0.04742123559117317,
0.07909809798002243,
0.004563082009553909,
-0.044047534465789795,
-0.011810770258307457,
-0.006631060969084501,
0.033556122332811356,
0.005965471733361483,
0.05420241132378578,
-0.007891956716775894,
-0.025042211636900902,
-0.013704687356948853,
0.06365891546010971,
-0.0418664924800396,
-0.06149151176214218,
0.017009234055876732,
-0.057958055287599564,
0.0290397759526968,
-0.014350862242281437,
-0.006395012605935335,
0.025900259613990784,
0.053567297756671906,
0.03585398197174072,
-0.006798217073082924,
-0.027960214763879776,
0.07083924859762192,
0.03097274899482727,
-0.03046855889260769,
0.03178975731134415,
0.05915936455130577,
-0.01997707597911358,
0.018879562616348267,
0.024771615862846375,
-0.0239171851426363,
0.04688981547951698,
-0.015685025602579117,
-0.0644821971654892,
-0.056863997131586075,
0.016063528135418892,
-0.027403974905610085,
0.017837679013609886,
-0.06004664674401283,
-0.00285208853892982,
-0.050820473581552505,
-0.05637223646044731,
0.0633147582411766,
-0.0023239124566316605,
-0.005165934097021818,
0.05841180309653282,
-0.005858943331986666,
-0.04652644321322441,
-0.0573432482779026,
-0.030511459335684776,
-0.004566265270113945,
0.0807299092411995,
0.002451476640999317,
0.061742205172777176,
-0.03169010207056999,
-0.020143989473581314,
0.008706687018275261,
-0.026654114946722984,
-0.003703908994793892,
0.006183872930705547,
-0.007941110990941525,
0.0027360955718904734,
-0.011679675430059433,
-0.03638053312897682,
-0.00416572205722332,
-0.012929062359035015,
-0.0602799654006958,
-0.01860002614557743,
0.03354577720165253,
0.016114290803670883,
0.020244255661964417,
-0.03262946754693985,
-0.004809209145605564,
0.01524994894862175,
-0.03091524727642536,
0.04122738912701607,
0.033724840730428696,
-0.013083972036838531,
0.08063164353370667,
0.04976506903767586,
-0.03972834721207619,
-0.0023179282434284687,
-0.032348837703466415,
0.05017805099487305,
-0.01246630772948265,
-0.055159345269203186,
0.028493521735072136,
-0.038634851574897766,
0.0027734118048101664,
0.05673913657665253,
0.02684348076581955,
0.012624175287783146,
-0.0246519073843956,
-0.003202971303835511,
-0.01191750355064869,
-0.042283397167921066,
-0.008891455829143524,
0.013714334927499294,
-0.0029628302436321974,
0.0039643775671720505,
0.04181363433599472,
0.02894662320613861,
0.027124153450131416,
-0.03739127144217491,
0.014031593687832355,
-0.011386536993086338,
-0.0007675794768147171,
-0.005429437384009361,
-0.024919748306274414,
0.0036096868570894003,
-0.06705155223608017,
0.042665280401706696,
0.002642763778567314,
0.010245163924992085,
-0.04114777222275734,
-0.05088350921869278,
-0.03679190203547478,
0.01828877627849579,
0.07632550597190857,
0.008433200418949127,
0.030289392918348312,
-0.01653970591723919,
0.030552804470062256,
0.04088689014315605,
-0.004272563382983208,
0.0008591708028689027,
0.003198957070708275,
0.03635191544890404,
-0.04226984828710556,
0.012072664685547352,
0.026843924075365067,
-0.007055786903947592,
-0.006106888875365257,
0.016809755936264992,
-0.0844583585858345,
-0.03416905924677849,
-0.012545845471322536,
-0.02441352605819702,
0.031725332140922546,
-0.023478852584958076,
0.034634143114089966,
-0.00934872031211853,
0.011938130483031273,
-0.10641566663980484,
0.027830785140395164,
0.02849280834197998,
0.053317535668611526,
-0.02398182451725006,
-0.039438288658857346,
-0.007954519242048264,
0.012595465406775475,
-0.06349154561758041,
-0.01712733507156372,
-0.0003838727134279907,
0.058322709053754807,
-0.021670976653695107,
0.02268250100314617,
-0.017529960721731186,
0.037091970443725586,
-0.001238985569216311,
0.06014779210090637,
0.03163919225335121,
-0.002505440963432193,
0.0678074061870575,
-0.02106797881424427,
-0.02017383836209774,
-0.05173022300004959,
-0.033893883228302,
-0.0059993695467710495,
-0.003949142061173916,
-0.03955426812171936,
0.019853347912430763,
-0.02188015542924404,
-0.04436912387609482,
-0.008118555881083012,
0.0491320937871933,
-0.023827863857150078,
-0.05099247395992279,
-0.08025885373353958,
0.03188824653625488,
0.06286392360925674,
0.022204602137207985,
-0.07927409559488297,
0.05746980011463165,
0.00918453000485897,
-0.007841895334422588,
0.03127918019890785,
0.0441121943295002,
0.024692462757229805,
0.015758153051137924,
0.010860200971364975,
0.003039158182218671,
0.032166361808776855,
0.030439866706728935,
0.023822668939828873,
-0.06316006928682327,
0.009601643308997154,
-0.09942149370908737,
-0.03812219202518463,
-0.05643623694777489,
-0.0028168372809886932,
0.008376680314540863,
-0.013672810979187489,
-0.041108984500169754,
0.0194513238966465,
0.05950157344341278,
0.045872390270233154,
0.015693368390202522,
-0.008878848515450954,
0.02556859515607357,
-0.0109071871265769,
0.04800604656338692,
0.010539195500314236,
0.04129580780863762,
0.008604501374065876,
-0.04649602621793747,
0.009009471163153648,
-0.018848702311515808,
0.055983975529670715,
0.024529635906219482,
0.0035519993398338556,
0.011618725955486298,
-0.0244375579059124,
-0.015080645680427551,
0.0012620004126802087,
-0.004697049502283335,
-0.012572688981890678,
-0.002897878410294652,
0.010292885825037956,
-0.018738580867648125,
-0.0035779110621660948,
-0.0446278415620327,
-0.012711213901638985,
-0.02135172300040722,
-0.0450817309319973,
-0.06225204840302467,
-0.044199295341968536,
-0.056115586310625076,
0.021742098033428192,
0.025410959497094154,
0.01221583504229784,
0.005162668880075216,
-0.021992865949869156,
0.025290772318840027,
0.01250165980309248,
0.00996697973459959,
-0.028889907523989677,
0.030284730717539787,
-0.03345438838005066,
0.010540388524532318,
0.01812325231730938,
0.07552831619977951,
-0.07360055297613144,
0.0012492768000811338,
-0.02246495895087719,
-0.0035624410957098007,
0.020283134654164314,
0.02553245611488819,
0.04726426675915718,
-0.006964196916669607,
-0.015995757654309273,
-0.003366005839779973,
-0.00011751093552447855,
-0.02562660723924637,
-0.027102520689368248,
0.0014727616216987371,
0.03989223390817642,
-0.0022894463036209345,
0.017003722488880157,
0.033321812748909,
0.015848539769649506,
0.037190865725278854,
-0.009795552119612694,
-0.045581523329019547,
-0.033092718571424484,
-0.03815978392958641,
-0.011122146621346474,
-0.013675491325557232,
0.015597209334373474,
0.015373600646853447,
-0.04353569447994232,
-0.015018456615507603,
0.022257957607507706,
0.03722235560417175,
0.00777037488296628,
0.030512651428580284,
-0.010959072969853878,
-0.009263814426958561,
-0.022061126306653023,
0.03901401907205582,
0.02064163237810135,
-0.009510131552815437,
0.020141838118433952,
-0.09285162389278412,
0.009522911161184311,
-0.013880541548132896,
-0.00299903005361557,
-0.019231032580137253,
-0.042204782366752625,
0.03094717487692833,
-0.0465342253446579,
-0.09322848170995712,
-0.024283811450004578,
-0.08752362430095673,
-0.010916266590356827,
-0.001642813440412283,
0.008109817281365395,
-0.06238936632871628,
-0.013299589976668358,
-0.07128997147083282,
-0.006399195175617933,
0.0019739707931876183,
-0.0012078722938895226,
-0.027169184759259224,
0.025717783719301224,
0.0036937145050615072,
-0.03291337564587593,
-0.03553429991006851,
0.02541056089103222,
0.036974020302295685,
-0.012840056791901588,
0.0010455951560288668,
-0.0020998958498239517,
-0.01623283512890339,
0.02635519579052925,
0.03876452147960663,
0.01622029021382332,
0.05727572739124298,
0.007077429443597794,
0.0032424896489828825,
0.032758425921201706,
0.016254359856247902,
0.012207468040287495,
-0.033850256353616714,
-0.019950497895479202,
0.02045648917555809,
-0.006005018018186092,
0.04396641254425049,
0.022553514689207077,
0.03317519649863243,
0.05154944583773613,
0.06604306399822235,
-0.06130760535597801,
0.005970966070890427,
0.05081041529774666,
-0.0065957107581198215,
0.03281908109784126,
0.043733149766922,
0.03169208765029907,
-0.017288509756326675,
-0.01951979473233223,
0.03552313521504402,
-0.01601276732981205,
-0.003841142635792494,
0.002941201673820615,
-0.04353518784046173,
-0.02654222585260868,
-0.011494399048388004,
0.02187880501151085,
-0.004819065798074007,
0.006925442721694708,
0.024894816800951958,
-0.024993380531668663,
0.0009849286871030927,
0.047186288982629776,
0.003540369914844632,
0.041786644607782364,
-0.014305772259831429,
-0.01622292771935463,
0.023759419098496437,
-0.14098571240901947,
-0.011392204090952873,
-0.03465692698955536,
-0.011305115185678005,
-0.032227110117673874,
0.048726342618465424,
-0.07700056582689285,
-0.01116896141320467,
0.04860866442322731,
0.013849278911948204,
-0.052572622895240784,
0.015449895523488522,
-0.016926968470215797,
0.03636776655912399,
-0.08176910877227783,
-0.006338775157928467,
-0.029221294447779655,
0.03564170002937317,
0.03873620927333832,
-0.009661741554737091,
-0.019932279363274574,
0.006164794787764549,
0.052396826446056366,
0.03755617514252663,
0.007980971597135067,
-0.04603724926710129,
-0.04058092087507248,
0.00904366560280323,
0.01776372268795967,
-0.04917125403881073,
-0.01094822771847248,
-0.11738385260105133,
0.03575309365987778,
-0.031495384871959686,
0.08559423685073853,
0.026317719370126724,
0.05681227147579193,
0.037281397730112076,
-0.052513960748910904,
0.04436483606696129,
-0.015173501335084438,
0.07148851454257965,
-0.007473665289580822,
-0.056560274213552475,
-0.052913714200258255,
0.004323786124587059,
-0.03319484740495682,
-0.03454571217298508,
0.011066902428865433,
0.04416370391845703,
0.007033745292574167,
0.07030630111694336,
0.005095323547720909,
0.0010119028156623244,
0.021915515884757042,
0.000778203597292304,
0.010802583768963814,
-0.05279526114463806,
0.01580100692808628,
-0.03170640021562576,
-0.0024981298483908176,
0.0713254064321518,
-0.006273000501096249,
-0.03907819464802742,
0.042177341878414154,
-0.030815904960036278,
-0.010111437179148197,
0.035774532705545425,
0.02000371553003788,
0.04823320358991623,
-0.04455980658531189,
-0.016692498698830605,
-0.00017744766955729574,
-0.0010754800168797374,
0.03414535894989967,
-0.006366936024278402,
-0.028234682977199554,
0.00441137095913291,
-0.006696340162307024,
-0.027003979310393333,
0.009351161308586597,
0.016892438754439354,
0.01656889170408249,
0.025797145441174507,
0.005725433584302664,
-0.0515102855861187,
-0.04309292510151863,
0.016157157719135284,
-0.06162542849779129,
0.010256897658109665,
0.07854550331830978,
-0.03366010636091232,
0.018951255828142166,
0.05743110552430153,
-0.046914536505937576,
0.00006252859020605683,
-0.01669650711119175,
-0.04772669076919556,
-0.005512341391295195,
-0.02864597924053669,
-0.007739466615021229,
-0.020642243325710297,
0.04780875891447067,
0.08204927295446396,
-0.03957017883658409,
-0.04312939569354057,
0.04145077243447304,
0.034279290586709976,
-0.015899667516350746,
0.05012497678399086,
0.06080447882413864,
-0.024129897356033325,
-0.03194704279303551,
-0.04350000247359276,
-0.031084679067134857,
-0.009940631687641144,
-0.04946661740541458,
0.047122519463300705,
0.01366662047803402,
-0.03653481602668762,
-0.02216430753469467,
-0.015377051196992397,
0.04323137551546097,
-0.043377459049224854,
-0.04237782582640648,
0.052162181586027145,
0.017247846350073814,
-0.014838054776191711,
0.009707614779472351,
-0.025454217568039894,
-0.012628587894141674,
0.02197321690618992,
-0.002333896467462182,
-0.03023584373295307,
0.017164334654808044,
0.044883549213409424,
0.04961008206009865,
-0.022179612889885902,
-0.0269179567694664,
-0.018793385475873947,
0.02011428028345108,
-0.020483771339058876,
0.05089618265628815,
-0.0033986358903348446,
0.0478290319442749,
0.005344510544091463,
-0.03188035264611244,
-0.0056694671511650085,
0.005499813240021467,
-0.03862951695919037,
-0.0024296590127050877,
-0.009812504053115845,
-0.0028686760924756527,
0.035990141332149506,
0.01351997908204794,
-0.017024043947458267,
0.018272696062922478,
-0.0009571902337484062,
0.018108220770955086,
-0.0012201903155073524,
-0.01838407665491104,
0.025464586913585663,
-0.025907492265105247,
-0.016657955944538116,
-0.030090700834989548,
0.004878474865108728,
-0.024858810007572174,
0.02586008422076702,
0.054774392396211624,
0.04646671563386917,
0.06671234965324402,
0.082560233771801,
0.06430027633905411,
0.006248788442462683,
-0.0400550402700901,
0.003684588707983494,
-0.030128473415970802,
-0.0014472441980615258,
0.0654136911034584,
0.02276798151433468,
-0.07158002257347107,
0.020104719325900078,
0.0074792467057704926,
-0.02954401820898056,
-0.03861655667424202,
-0.019378939643502235,
0.034716542810201645,
0.03482036292552948,
0.02066565863788128,
-0.028652481734752655,
-0.0019562875386327505,
-0.006825290620326996,
0.021578408777713776,
-0.01688987761735916,
0.05137841776013374,
-0.005301345139741898,
0.005085165146738291,
0.019486814737319946,
0.02934899739921093,
0.01190378237515688,
-0.01977723278105259,
0.030119076371192932,
0.004413125105202198,
-0.054592669010162354,
0.02299901470541954,
0.007115683518350124,
-0.013024650514125824,
-0.0026504870038479567,
-0.009828451089560986,
-0.03183276206254959,
-0.003070080652832985,
0.07312202453613281,
-0.00501419510692358,
0.02738013304769993,
0.04893257096409798,
-0.03313632309436798,
-0.016734691336750984,
0.007301637902855873,
-0.01522824726998806,
-0.011772862635552883,
-0.04324962571263313,
0.003926160279661417,
-0.031706035137176514,
-0.005608938634395599,
-0.04184253141283989,
0.002352905459702015,
-0.03738030418753624,
0.03145444765686989,
0.017273735255002975,
0.010680293664336205,
0.010120552964508533,
0.032919880002737045,
-0.0013691338244825602,
-0.017691785469651222,
-0.00043745693983510137,
0.0673695057630539,
-0.0002689876710064709,
-0.02772487886250019,
0.056890442967414856,
0.067361980676651,
-0.028569642454385757,
-0.04588717967271805,
0.00712171895429492,
-0.005848592612892389,
-0.011610995046794415,
-0.10782159864902496,
-0.009527178481221199,
0.02318636327981949,
-0.015537457540631294,
-0.029094848781824112,
-0.03638669103384018,
-0.008735693991184235,
-0.06441669166088104,
0.004000971559435129,
0.057491425424814224,
0.030295101925730705,
-0.005979439243674278,
-0.03871150687336922,
0.02997860498726368,
0.05810479819774628,
0.02425955794751644,
-0.06982579827308655,
0.01757194846868515,
0.021646300330758095,
0.002673402661457658,
0.00465579004958272,
-0.015798255801200867,
-0.033907003700733185,
-0.04626450315117836,
-0.05023646354675293,
0.008191071450710297,
-0.015566173009574413,
-0.021077295765280724,
0.0007840165635570884,
-0.017177896574139595,
0.004434817470610142,
0.006903200875967741,
-0.019987206906080246,
0.04980788379907608,
0.007646830752491951,
-0.02392248995602131,
-0.06021326035261154,
-0.008431890048086643,
0.07733716815710068,
-0.07385844737291336,
-0.047001488506793976,
0.08138134330511093,
0.0028706947341561317,
-0.05268678441643715,
-0.033233728259801865,
0.03190461918711662,
0.022929197177290916,
0.012341015972197056,
-0.024354906752705574,
0.06830314546823502,
-0.0019770562648773193,
0.0736231878399849,
0.044932857155799866,
-0.0616057924926281,
-0.04659741371870041,
-0.0013033595168963075,
0.06484659761190414,
-0.039079729467630386,
0.05126133933663368,
0.032262589782476425,
0.00339326704852283,
-0.02372930385172367,
-0.025717085227370262,
-0.0574556328356266,
0.0050950003787875175,
0.012803399935364723,
0.0598091296851635,
0.023531474173069,
-0.03349107503890991,
-0.04044785350561142,
0.0290540624409914,
-0.04693407192826271,
0.0114289540797472,
0.008107844740152359,
-0.0030687949620187283,
-0.05544682592153549,
0.01664375141263008,
-0.03632201626896858,
-0.006030464544892311,
-0.023029308766126633,
0.04861064255237579,
0.1164468377828598,
-0.04653700441122055,
-0.013960637152194977,
-0.04491689056158066,
0.055193960666656494,
-0.0950598195195198,
-0.0018834341317415237,
0.01757957600057125,
-0.030044592916965485,
0.07947812974452972,
0.009258109144866467,
-0.01142469234764576,
-0.031145956367254257,
0.016724547371268272,
-0.010401864536106586,
-0.04224969819188118,
-0.02406063862144947,
-0.02680658921599388,
0.009479220025241375,
0.049641456454992294,
0.022074619308114052,
-0.006887421943247318,
0.019737999886274338,
-0.007447348441928625,
0.025900280103087425,
0.06530210375785828,
-0.005603843834251165,
-0.00825593527406454,
0.020276864990592003,
0.019430633634328842,
-0.0037914433050900698,
-0.010016527026891708,
-0.032943565398454666,
0.022026626393198967,
0.00633375346660614,
-0.05697838217020035,
0.00761623727157712,
-0.01100857276469469,
0.019427597522735596
] |
<p>In general relativity, time-like geodesics are the trajectories of free-falling test particles, parametrized by proper time. Thus, they are easy to interpret in physical terms and are easy to measure (at least in principle).</p>
<p>Is there a similar interpretation/measurement for space-like geodesics? For example, how do I measure the shortest path between two space-like separated points? What is the interpretation of such a path (apart from it being a geodesic)?</p>
<p>My first guess is that the answer will involve a static picture (with no change in time), e.g. how elastic springs stretch between two fixed points. The problem with this picture is that the curves the springs bend along depend on the stiffness of the spring. (I believe one gets a geodesic when the stiffness is infinite, but this is no effect one would be able to measure for everyday gravitational fields.) </p>
<p><strong>Addition:</strong></p>
<p>As VM9 pointed out below, I should fix something like a space (a space-like hypersurface) before talking about the geodesic distance.</p>
<p>So, let me define space-like geodesic for my purpose as follows, which will be a local notion: Take an observer, which simply shall be a time-like vector $u$ at an event $P$ of space-time $M$. Let $V$ be the orthogonal complement of $u$ (a three-dimensional space of space-like directions at $P$). Let $\Sigma$ be the image of a small neighborhood of $0$ in $V$ under the exponential mapping (that is the set of events that are connected to $P$ by small geodesics that are orthogonal to $u$ at $P$).</p>
<p>It is that space-like submanifold my observer is interested in. How can one physically measure lengthes in $\Sigma$? While every measurement process takes time as VM9 pointed out as well, let's assume that time flies rather slowly ($c \to \infty$) so that one could work, for example, in Gaussian coordinates (synchronous coordinates) with respect to $\Sigma$.</p> | g5518 | [
0.09664598107337952,
-0.0026926063001155853,
-0.0018115356797352433,
-0.026209894567728043,
-0.03655555471777916,
0.02565762773156166,
0.006839684676378965,
-0.015153269283473492,
0.004526406992226839,
-0.03306899219751358,
0.04313674941658974,
-0.061224326491355896,
0.06791766732931137,
0.009103412739932537,
0.008167139254510403,
-0.03748813271522522,
0.08408485352993011,
-0.03306617587804794,
0.008260409347712994,
-0.019317641854286194,
0.10115866363048553,
0.008256085216999054,
0.06956969946622849,
0.013794614002108574,
0.007396812085062265,
-0.042347099632024765,
0.04818067327141762,
-0.020314669236540794,
-0.047031648457050323,
-0.00007168349111452699,
0.04373287037014961,
-0.023389363661408424,
0.057288940995931625,
-0.01386241428554058,
0.011822693981230259,
-0.0248238667845726,
0.004986444488167763,
-0.005940403789281845,
0.03993520885705948,
-0.014567992649972439,
0.0033917739056050777,
-0.0389515645802021,
0.029168378561735153,
0.045092929154634476,
0.08931321650743484,
-0.02805868349969387,
0.00842096284031868,
0.018690036609768867,
0.09755707532167435,
-0.044770434498786926,
-0.051395393908023834,
0.0749153196811676,
-0.016402846202254295,
0.00835101492702961,
-0.005722450092434883,
0.002302755368873477,
0.0672946348786354,
-0.0021258273627609015,
0.06608995795249939,
0.040151454508304596,
-0.028154728934168816,
-0.014869333244860172,
0.007774448487907648,
-0.024189110845327377,
0.04452061653137207,
0.057409387081861496,
-0.034771569073200226,
-0.05900903418660164,
0.01782083883881569,
0.008684740401804447,
0.036177750676870346,
-0.017956921830773354,
-0.013245758600533009,
-0.010718346573412418,
-0.05483155697584152,
0.03736010566353798,
0.018772117793560028,
0.024183014407753944,
0.03145511448383331,
0.009981319308280945,
-0.041735146194696426,
0.041829440742731094,
-0.019973838701844215,
-0.016426097601652145,
0.07053758949041367,
0.0035893553867936134,
0.0047187162563204765,
0.007282208651304245,
-0.01615270785987377,
0.011706836521625519,
-0.00509639224037528,
-0.025072015821933746,
0.026486149057745934,
-0.010349092073738575,
-0.05642487481236458,
-0.020151393488049507,
-0.01935836486518383,
0.06581570953130722,
-0.0011007224675267935,
0.021423734724521637,
-0.013696962036192417,
-0.011115643195807934,
0.00048224773490801454,
-0.023515921086072922,
0.016106199473142624,
-0.023813579231500626,
-0.01571793481707573,
0.03923988714814186,
0.0593516007065773,
-0.07555490732192993,
-0.026615183800458908,
-0.01231483742594719,
-0.03129224479198456,
-0.05128149315714836,
0.0029476084746420383,
-0.03676297143101692,
0.0012419295962899923,
0.032133981585502625,
-0.002544382819905877,
0.05021665617823601,
0.03504468500614166,
0.02075585350394249,
0.014940088614821434,
0.02019192837178707,
-0.014424244873225689,
0.021044928580522537,
-0.007123899180442095,
-0.012555564753711224,
-0.0014233370311558247,
0.053055550903081894,
0.030279243364930153,
-0.0014723734930157661,
0.012462657876312733,
0.03152449429035187,
-0.06798989325761795,
0.03550020977854729,
-0.0059418887831270695,
-0.030816009268164635,
-0.05849946290254593,
0.033780526369810104,
-0.03441328555345535,
-0.08481982350349426,
0.01831657998263836,
-0.019540635868906975,
-0.0062797837890684605,
0.027368957176804543,
-0.05109303444623947,
-0.003747763577848673,
0.0330953486263752,
-0.00022603326942771673,
-0.021540218964219093,
0.05763505399227142,
0.008319944143295288,
-0.031090563163161278,
-0.0014782506041228771,
0.040803808718919754,
-0.026683447882533073,
0.007943615317344666,
0.019128790125250816,
-0.00542132742702961,
0.049866776913404465,
0.013792002573609352,
0.026527052745223045,
0.017153648659586906,
-0.018175488337874413,
0.004469434265047312,
0.026233982294797897,
-0.035617876797914505,
0.03311355412006378,
-0.05977788195014,
-0.09278654307126999,
-0.05117780715227127,
0.04743964597582817,
0.02107345685362816,
-0.08714266121387482,
-0.03359222412109375,
0.021565761417150497,
-0.015084988437592983,
-0.02771941013634205,
0.021158305928111076,
0.00753382034599781,
-0.03886020928621292,
0.015199791640043259,
-0.028195861726999283,
-0.013868567533791065,
-0.013920369558036327,
0.028748447075486183,
-0.037758857011795044,
0.013392036780714989,
-0.0322570838034153,
0.01989283785223961,
-0.023512352257966995,
-0.036266032606363297,
0.06589219719171524,
0.03042316809296608,
-0.010204857215285301,
0.030407847836613655,
-0.06854105740785599,
0.011175204068422318,
0.025329291820526123,
0.023325489833950996,
0.012279247865080833,
0.048844583332538605,
0.027089910581707954,
0.057286810129880905,
-0.010239592753350735,
-0.040804166346788406,
-0.04275176301598549,
-0.010964865796267986,
0.015155871398746967,
0.08246003091335297,
-0.03149858117103577,
-0.009314725175499916,
-0.014661699533462524,
-0.04166138544678688,
-0.005422581918537617,
0.013140864670276642,
-0.04360247403383255,
0.008798094466328621,
0.004698975011706352,
0.006736631505191326,
-0.028562860563397408,
0.03658753260970116,
-0.09571875631809235,
0.047222644090652466,
-0.007959873415529728,
-0.020987503230571747,
-0.01374850980937481,
0.01630997471511364,
-0.011500846594572067,
-0.023067109286785126,
0.03018462471663952,
-0.0027519522700458765,
0.009213818237185478,
0.051647916436195374,
0.017826903611421585,
0.007526210509240627,
0.022653385996818542,
-0.01109358575195074,
0.02535112202167511,
0.05888456478714943,
-0.0687268003821373,
-0.023084590211510658,
0.03094734624028206,
0.044484131038188934,
-0.04058190807700157,
0.04722428321838379,
-0.00429778965190053,
-0.029142919927835464,
-0.01285405084490776,
0.010441631078720093,
-0.014757610857486725,
-0.04916846752166748,
0.01203471515327692,
0.004808117635548115,
0.0008356465259566903,
-0.0217523742467165,
0.05253070592880249,
-0.07799094170331955,
-0.0697019100189209,
0.001231752336025238,
-0.030717460438609123,
0.008488364517688751,
0.06222699210047722,
0.03128223493695259,
-0.04183291643857956,
-0.027330631390213966,
0.05924895778298378,
-0.02291911654174328,
0.0036783500108867884,
-0.0034437484573572874,
0.06220756471157074,
-0.004123900085687637,
0.0503196194767952,
-0.049675870686769485,
-0.008218083530664444,
-0.002155713737010956,
0.0022626612335443497,
-0.0008484431309625506,
0.0011532322969287634,
0.011047162115573883,
0.026657240465283394,
-0.05111655220389366,
0.03944598510861397,
0.00036013833596371114,
-0.042980581521987915,
0.059022869914770126,
0.03824043273925781,
-0.02407226525247097,
0.0473322868347168,
-0.04343826696276665,
0.003839481621980667,
0.028983401134610176,
-0.002388251479715109,
-0.04109358415007591,
0.07574017345905304,
0.006716512609273195,
-0.009814972057938576,
-0.01341327652335167,
-0.011942697688937187,
-0.033021435141563416,
-0.035679034888744354,
0.07048553228378296,
0.03361663594841957,
0.008224645629525185,
-0.03120950236916542,
-0.04280068725347519,
-0.08675412088632584,
-0.027931679040193558,
-0.018218500539660454,
0.025387568399310112,
0.007694339379668236,
0.011368917301297188,
-0.04305969923734665,
-0.03273947536945343,
0.0017978622345253825,
-0.07659400999546051,
-0.02638685703277588,
-0.022751595824956894,
0.003579801879823208,
0.001708912430331111,
-0.0656491294503212,
-0.05756504088640213,
-0.001693551428616047,
-0.011631355620920658,
-0.03967297449707985,
0.011288302019238472,
-0.022771304473280907,
-0.10173256695270538,
-0.01082858070731163,
0.02290458045899868,
-0.048653263598680496,
-0.014093894511461258,
0.027825715020298958,
0.0019627229776233435,
-0.022067485377192497,
0.004973941016942263,
-0.010930760763585567,
0.05837690085172653,
-0.014514997601509094,
-0.005346894729882479,
0.06495460122823715,
-0.07360319793224335,
-0.020826470106840134,
0.002690390683710575,
-0.014811350964009762,
0.05793413892388344,
0.0692310705780983,
0.00832174252718687,
-0.06882200390100479,
0.048095300793647766,
-0.013249972835183144,
0.003651418024674058,
-0.08708494156599045,
0.02841152623295784,
0.04378091171383858,
0.02659454010426998,
0.03489629924297333,
0.003926328383386135,
-0.0616263709962368,
0.03289945423603058,
0.004827984143048525,
-0.04454784840345383,
0.05550271272659302,
0.006806975696235895,
-0.0762656033039093,
0.05273136869072914,
0.04886540770530701,
0.025232186540961266,
0.007283809129148722,
0.03786569833755493,
-0.020260529592633247,
0.028818216174840927,
-0.01048240065574646,
-0.00020772666903212667,
-0.0279015451669693,
-0.009922267869114876,
0.0031497261952608824,
0.0012322842376306653,
-0.0437924861907959,
0.04557894542813301,
0.03903941065073013,
0.054469700902700424,
-0.016179576516151428,
0.07625232636928558,
-0.007267299108207226,
-0.008571759797632694,
-0.027970662340521812,
0.014177145436406136,
-0.01953761838376522,
0.0573556087911129,
-0.06450480967760086,
-0.021868187934160233,
-0.0422951802611351,
0.03142450377345085,
-0.010665391571819782,
0.034092772752046585,
0.007153140846639872,
-0.08083681762218475,
0.05307053029537201,
-0.010619944892823696,
0.07859306782484055,
-0.005555313546210527,
0.03518717736005783,
-0.0024719068314880133,
-0.05931926891207695,
-0.004880404099822044,
-0.014991183765232563,
-0.01624266244471073,
-0.016585122793912888,
0.02727203257381916,
-0.03650288283824921,
0.011717270128428936,
-0.08662041276693344,
-0.01814468391239643,
0.056916043162345886,
0.003743586363270879,
0.006416504271328449,
0.040649719536304474,
0.03858374059200287,
-0.010246124118566513,
0.0463298000395298,
0.031227439641952515,
-0.05669517442584038,
-0.049696020781993866,
0.04352878779172897,
0.03884507715702057,
-0.0009603262296877801,
-0.028243055567145348,
-0.0298031996935606,
0.012331529520452023,
0.005614223424345255,
0.03390799090266228,
0.030635228380560875,
-0.031117383390665054,
0.0011810652213171124,
0.025481054559350014,
0.05987609550356865,
0.0011132146464660764,
0.008826262317597866,
0.006523609161376953,
0.022081755101680756,
0.04835084453225136,
0.000047124645789153874,
-0.03540154546499252,
0.010315386578440666,
-0.04825923591852188,
-0.02459838055074215,
-0.054019566625356674,
-0.013648094609379768,
-0.04289604723453522,
0.02746838703751564,
0.031010933220386505,
-0.025711895897984505,
-0.03812819719314575,
0.009972069412469864,
-0.05209736153483391,
-0.0012810128973796964,
0.008626213297247887,
0.005258806981146336,
-0.007704485207796097,
-0.020721089094877243,
0.03979215398430824,
-0.013109186664223671,
-0.017718756571412086,
-0.021444231271743774,
-0.13227254152297974,
-0.04883590340614319,
-0.0455918088555336,
0.014436639845371246,
-0.03281046450138092,
0.021635623648762703,
-0.028527023270726204,
-0.018463969230651855,
-0.011477569118142128,
0.010465848259627819,
-0.005061673000454903,
0.031227201223373413,
-0.019921232014894485,
-0.03619629144668579,
-0.005979593377560377,
-0.027288950979709625,
-0.005648438818752766,
-0.048190563917160034,
-0.007168250158429146,
0.03937464579939842,
-0.008608344942331314,
-0.01632763259112835,
0.019469350576400757,
-0.020363053306937218,
0.040470320731401443,
-0.032853685319423676,
-0.01736752688884735,
0.022469598799943924,
-0.021359141916036606,
0.005000791512429714,
-0.02831376902759075,
0.005134536884725094,
-0.03425474464893341,
-0.002177608199417591,
-0.060994043946266174,
0.06579502671957016,
-0.012917030602693558,
0.006899289786815643,
0.02085546962916851,
0.05085243284702301,
0.027639130130410194,
-0.009792144410312176,
-0.06237548217177391,
0.0192657969892025,
-0.03315713256597519,
0.0024180440232157707,
-0.023817215114831924,
0.044188208878040314,
0.026816369965672493,
0.025434963405132294,
0.010817197151482105,
0.01887407712638378,
-0.014443911612033844,
-0.030430858954787254,
-0.021067345514893532,
0.0030491286888718605,
0.03746827691793442,
-0.025924457237124443,
0.05789889022707939,
-0.021714674308896065,
-0.043815288692712784,
0.006936865858733654,
0.010637066327035427,
-0.00709856953471899,
0.013653472065925598,
-0.012747656553983688,
-0.01059091929346323,
-0.0056021204218268394,
-0.0092701381072402,
0.0007229977636598051,
-0.00044740905286744237,
0.014054633677005768,
0.06761208176612854,
-0.0414615124464035,
-0.07627812772989273,
-0.044341620057821274,
0.03543096035718918,
0.0524354912340641,
-0.04706840217113495,
-0.025014357641339302,
-0.01608683541417122,
-0.0014155664248391986,
0.05387863144278526,
0.004892040975391865,
-0.0594063326716423,
-0.01663398928940296,
0.01056168507784605,
0.006335956044495106,
-0.007436838466674089,
0.014633315615355968,
0.01624256931245327,
-0.03622487559914589,
-0.026863353326916695,
-0.03151208907365799,
0.02180042862892151,
0.00007733836537227035,
-0.02488517202436924,
-0.038524478673934937,
0.015253550373017788,
-0.034431785345077515,
0.004040099680423737,
-0.014859450049698353,
0.04871941730380058,
0.017640650272369385,
0.014259608462452888,
-0.04021957144141197,
0.053886838257312775,
0.04309269040822983,
-0.06537006050348282,
-0.012948093935847282,
-0.014420958235859871,
-0.054413944482803345,
-0.07468032091856003,
0.0029487409628927708,
-0.03951627016067505,
0.02131587639451027,
0.057200103998184204,
0.006490079220384359,
-0.048491522669792175,
0.04282188042998314,
0.0016116431215777993,
-0.013138355687260628,
0.011330792680382729,
-0.023742694407701492,
-0.040957868099212646,
-0.029707031324505806,
-0.06666070967912674,
-0.0034814360551536083,
-0.026909762993454933,
0.05879001319408417,
0.0013333730166777968,
-0.022979380562901497,
-0.04062968119978905,
0.07179359346628189,
-0.06918471306562424,
0.004544354975223541,
0.05121227353811264,
-0.03281477838754654,
-0.018017210066318512,
0.03363819047808647,
-0.009026595391333103,
-0.005815163720399141,
0.024023106321692467,
-0.09409426897764206,
0.032525334507226944,
0.07107357680797577,
-0.036131102591753006,
0.10484831035137177,
-0.03332778066396713,
-0.008258708752691746,
0.023637747392058372,
-0.040433574467897415,
0.01842547208070755,
-0.06293776631355286,
0.015501915477216244,
0.030191419646143913,
0.0021820298861712217,
-0.0004690268251579255,
0.00619804672896862,
-0.006100015249103308,
-0.009542928077280521,
0.018671579658985138,
-0.017471425235271454,
0.003275381401181221,
-0.009840788319706917,
0.027908578515052795,
-0.020369721576571465,
-0.0024309377186000347,
-0.010164875537157059,
0.03930767625570297,
-0.028725197538733482,
0.06695085018873215,
0.05213550850749016,
0.06532365083694458,
0.043845899403095245,
0.006160694174468517,
-0.017660316079854965,
-0.009679955430328846,
-0.08794393390417099,
-0.034466452896595,
-0.03659864515066147,
0.020749352872371674,
-0.002124008722603321,
0.004706315230578184,
0.01492694579064846,
-0.012338346801698208,
0.03490713983774185,
0.02040548250079155,
0.020944729447364807,
0.03563778102397919,
-0.028000205755233765,
0.007514967117458582,
0.02110806666314602,
-0.07796847820281982,
-0.04667135328054428,
0.034777089953422546,
0.003981355577707291,
0.00930921733379364,
-0.03995152562856674,
0.052392128854990005,
-0.028911028057336807,
-0.015521874651312828,
-0.014309823513031006,
0.011933214031159878,
0.025137024000287056,
-0.001040284289047122,
0.03641636297106743,
0.03066476248204708,
0.002249164506793022,
-0.039198990911245346,
-0.013238782994449139,
0.0474204383790493,
0.020741242915391922,
0.019829610362648964,
0.033797040581703186,
0.07451803237199783,
0.0458531491458416,
0.03578060120344162,
-0.013554868288338184,
0.04466624557971954,
-0.006871981080621481,
-0.021028505638241768,
-0.062448836863040924,
-0.028345836326479912,
0.004679778590798378,
0.03087601624429226,
-0.021748028695583344,
0.015331641770899296,
0.04592198133468628,
-0.0522274374961853,
0.1069483831524849,
0.026132695376873016,
-0.00805873703211546,
-0.055893950164318085,
0.007706223055720329,
0.04406450316309929,
0.028040088713169098,
0.03121206909418106,
0.03533502295613289,
-0.014187132939696312,
-0.021159565076231956,
-0.02563467249274254,
-0.024972502142190933,
0.0034643439576029778,
-0.024207700043916702,
0.04788534343242645,
0.023216618224978447,
0.019922273233532906,
0.0051373750902712345,
0.007110098376870155,
-0.046974968165159225,
-0.0005172247183509171,
0.013626071624457836,
-0.0499093197286129,
-0.04678548499941826,
-0.04774196445941925,
0.03528483957052231,
-0.07110972702503204,
0.04613958299160004,
0.029240544885396957,
0.0018968863878399134,
-0.03391549736261368,
0.03492530807852745,
-0.022633163258433342,
-0.004432936664670706,
0.009232009761035442,
0.02711997739970684,
0.07310029864311218,
-0.055097706615924835,
-0.0013900564517825842,
0.03314082324504852,
0.003396617481485009,
-0.022878846153616905,
0.01998925767838955,
0.012400913052260876,
-0.024029342457652092,
0.005126302596181631,
0.00768670067191124,
0.04880766198039055,
-0.024927936494350433,
0.03249255195260048,
0.032169513404369354,
0.015514767728745937,
-0.052696891129016876,
-0.0026166161987930536,
0.049701105803251266,
0.048909157514572144,
0.007867589592933655,
-0.02665053866803646,
-0.0012989344540983438,
0.03276323154568672,
-0.07256846129894257,
0.021533003076910973,
-0.02852145954966545,
-0.004099975805729628,
0.0021301950328052044,
-0.018091820180416107,
0.021138127893209457,
-0.06229809671640396,
-0.01828155294060707,
0.0025529663544148207,
0.058008335530757904
] |
<p>Here's a homework problem I'm working on. I am not asking for the answer, but any guidance or comments on the approach are appreciated.</p>
<blockquote>
<p>Given that a measurement of $L^2$ for a free particle has resulted in the value $6\hbar^2$, what are the possible results for a measurement of $L_x$?</p>
</blockquote>
<p>I've been following the approach given on pp. 378-380 in Liboff (4th ed.). I've made it as far as expressing the eigenfunctions of $L_x$ as sums of the eigenfunctions of $L^2$... Here's what I've got: </p>
<p>$$\begin{align*}
X_1 &= \frac{1}{2}\left(|2,2\rangle - |2,1\rangle + |2,-1\rangle - |2,-2\rangle\right)\\
X_2 = -X1 &= -\frac{1}{2}\left(|2,2\rangle - |2,1\rangle + |2,-1\rangle - |2,-2\rangle\right)\\
X_3 &= \frac{1}{2}\left(\sqrt{\frac{3}{2}}|2,2\rangle - |2,0\rangle + \sqrt{\frac{3}{2}}|2,-2\rangle\right)\\
X_4 = -X3 &= -\frac{1}{2}\left(\sqrt{\frac{3}{2}}|2,2\rangle - |2,0\rangle + \sqrt{\frac{3}{2}}|2,-2\rangle\right)\\
X_5 &= \frac{1}{2}(|2,2\rangle + |2,1\rangle - |2,-1\rangle - |2,-2\rangle)\\
X_6 = -X_5 &= -\frac{1}{2}\left(|2,2\rangle + |2,1\rangle - |2,-1\rangle - |2,-2\rangle\right)
\end{align*}$$</p>
<p>The next step appears to be to express $L^2$ as sums of the eigenfunctions of $L_x$, which does not seem possible.</p>
<p>It was a lot of algebra, matrices, determinants, etc. to get to this point so it is certainly possible that I've miscalculated something accidentally, but does anyone see anything fundamentally wrong here with this approach? And/or is there a simpler way?</p> | g5519 | [
-0.023228606209158897,
0.013516164384782314,
-0.01754196360707283,
-0.0810668021440506,
0.010651618242263794,
-0.050043657422065735,
0.05742727965116501,
-0.020182518288493156,
-0.018259834498167038,
0.024283505976200104,
-0.057889215648174286,
0.044797737151384354,
0.06036490201950073,
0.05243423953652382,
0.03170167654752731,
0.005085492506623268,
0.13137470185756683,
-0.011421460658311844,
-0.023135200142860413,
0.016010424122214317,
0.015537560917437077,
0.03830668702721596,
-0.035343848168849945,
-0.0075619518756866455,
0.03393586724996567,
-0.05165896937251091,
0.06054738536477089,
0.017796184867620468,
-0.06927966326475143,
0.019692467525601387,
0.0004439616168383509,
-0.003542762016877532,
-0.01056964136660099,
-0.04241602122783661,
-0.014078019186854362,
0.016286199912428856,
0.09706071764230728,
0.03302737697958946,
0.028638189658522606,
0.03335005044937134,
0.030616067349910736,
-0.030262194573879242,
0.010806716978549957,
0.03498818352818489,
0.02184872142970562,
0.011211968958377838,
0.010531608015298843,
0.002572654513642192,
0.005374186672270298,
0.005551988258957863,
-0.0026523899286985397,
0.0025087986141443253,
0.02404915541410446,
-0.018608421087265015,
-0.04272400215268135,
0.03601928800344467,
0.006112389732152224,
-0.0060813771560788155,
0.06900148093700409,
0.07087337970733643,
0.011034684255719185,
-0.01865198276937008,
-0.02901317924261093,
-0.02424592524766922,
0.0028773800004273653,
-0.0232177022844553,
-0.00470653036609292,
0.026820024475455284,
-0.048926401883363724,
-0.002644065534695983,
0.036200884729623795,
-0.019480010494589806,
0.0335550457239151,
0.011392761021852493,
-0.04340336099267006,
-0.0029002625960856676,
0.011718946509063244,
0.043576907366514206,
0.06268160045146942,
0.01342539768666029,
-0.00916878879070282,
-0.015784060582518578,
0.03375701978802681,
-0.022043654695153236,
0.021816886961460114,
0.017433123663067818,
-0.0077564409002661705,
0.01818588748574257,
-0.04911867529153824,
-0.007653807755559683,
0.0014808529522269964,
-0.061314906924963,
0.03139527887105942,
-0.017229245975613594,
-0.02407815121114254,
-0.026821376755833626,
0.005738919135183096,
-0.024362381547689438,
-0.04184349998831749,
-0.00898122787475586,
0.0054718079045414925,
0.051152028143405914,
-0.021474258974194527,
0.020423628389835358,
0.044670917093753815,
-0.035243064165115356,
0.01994684524834156,
0.017797032371163368,
0.014390386641025543,
-0.06273338198661804,
-0.06358490884304047,
0.0172139722853899,
-0.02666487544775009,
-0.0009700231021270156,
-0.06018448993563652,
-0.016736971214413643,
0.10837422311306,
-0.023695964366197586,
-0.055201902985572815,
0.07461539655923843,
0.03436215594410896,
-0.005491484422236681,
0.029525060206651688,
0.0360732227563858,
0.006787033285945654,
-0.006312043406069279,
-0.02006719261407852,
0.02350316382944584,
-0.004916834179311991,
0.04589436948299408,
-0.004397346172481775,
-0.010001685470342636,
0.010309501551091671,
-0.007253536023199558,
0.027247143909335136,
0.034168802201747894,
0.007429998833686113,
0.03781212866306305,
-0.017296267673373222,
-0.04199210926890373,
-0.0011562531581148505,
-0.03505347669124603,
0.03922201320528984,
0.0482976995408535,
0.00782644934952259,
-0.000667884829454124,
-0.007035696879029274,
-0.039048705250024796,
0.00788460299372673,
0.030680105090141296,
-0.0295263659209013,
0.07326430827379227,
-0.0050917924381792545,
0.014417962171137333,
0.007753301877528429,
0.04314215108752251,
0.0019112298032268882,
-0.04679280146956444,
-0.023700349032878876,
0.06704403460025787,
-0.011050858534872532,
-0.022903604432940483,
0.001836953335441649,
0.006460578180849552,
-0.07558606564998627,
0.020758457481861115,
-0.01414346881210804,
-0.03994696959853172,
0.012080512940883636,
-0.04048890992999077,
-0.027556929737329483,
0.036563191562891006,
-0.007721476722508669,
0.021420573815703392,
0.014962143264710903,
0.033483076840639114,
-0.007573955226689577,
-0.02200835756957531,
0.02720423974096775,
0.03759746626019478,
0.007964122109115124,
-0.008139822632074356,
0.04437507688999176,
0.0061958408914506435,
-0.008107343688607216,
-0.019458089023828506,
0.014335846528410912,
-0.01701502688229084,
-0.007428237237036228,
0.017684563994407654,
-0.029177706688642502,
0.0777629017829895,
-0.0008482770645059645,
0.01660703681409359,
-0.03531905263662338,
0.015709226951003075,
0.07434771209955215,
-0.07514318823814392,
0.038116853684186935,
0.024511793628335,
-0.004992224741727114,
0.02313775010406971,
0.032610584050416946,
0.026204627007246017,
0.017647482454776764,
-0.06804684549570084,
-0.0348597876727581,
-0.045348212122917175,
-0.02329964190721512,
-0.04240379109978676,
-0.009631840512156487,
-0.015549402683973312,
-0.024510376155376434,
0.009526151232421398,
0.018295621499419212,
0.024632619693875313,
-0.0031127515248954296,
0.004304986912757158,
0.009516015648841858,
0.004342502914369106,
-0.03760133311152458,
0.0031489236280322075,
-0.00929297599941492,
-0.01764037273824215,
0.06306231021881104,
0.026138557121157646,
0.019330760464072227,
0.015968993306159973,
-0.07051786035299301,
0.005083602853119373,
-0.05201161652803421,
-0.009501869790256023,
-0.008423656225204468,
-0.03975420445203781,
0.046950001269578934,
0.032567236572504044,
-0.018402518704533577,
0.002876825397834182,
0.048996955156326294,
0.011480038985610008,
0.022797316312789917,
0.016391675919294357,
-0.033458586782217026,
0.04450341314077377,
0.023929907009005547,
0.054350387305021286,
0.031798917800188065,
0.02161910943686962,
-0.03494799882173538,
0.03582195192575455,
-0.052605364471673965,
0.030262768268585205,
0.015199168585240841,
0.0005065292934887111,
0.0016762269660830498,
-0.001279704738408327,
-0.012595673091709614,
0.025728920474648476,
-0.02553999237716198,
-0.03154784068465233,
-0.030820995569229126,
0.01220992673188448,
-0.04908569157123566,
0.03615609556436539,
-0.050699736922979355,
-0.02669387310743332,
0.016619250178337097,
-0.008105207234621048,
-0.024551251903176308,
-0.04753206670284271,
0.017205551266670227,
0.004733397159725428,
0.007087219040840864,
0.07098241150379181,
-0.07997383922338486,
-0.014537905342876911,
-0.0011592237278819084,
-0.03518015891313553,
0.05955694615840912,
0.0052858502604067326,
-0.03633635863661766,
-0.0024204563815146685,
-0.03726879507303238,
0.05379198119044304,
0.01768939383327961,
0.0012061971938237548,
0.0032386831007897854,
-0.00967258308082819,
-0.02622261643409729,
0.005481863860040903,
-0.03960811719298363,
-0.04609377309679985,
-0.033634431660175323,
-0.006981944665312767,
-0.005577136762440205,
0.03402477502822876,
0.003930233884602785,
-0.027819475159049034,
0.016094733029603958,
0.05022406205534935,
-0.018079232424497604,
-0.016859326511621475,
-0.009266674518585205,
-0.03374534472823143,
-0.0022252872586250305,
-0.01012443471699953,
-0.03486690670251846,
-0.01132956612855196,
0.05271182954311371,
-0.01124253123998642,
0.0011135581880807877,
-0.013828108087182045,
-0.041952796280384064,
-0.04533869028091431,
-0.008510071784257889,
-0.01198554877191782,
0.023842323571443558,
0.06605871021747589,
-0.015784990042448044,
-0.04833982139825821,
-0.03881879895925522,
-0.042859140783548355,
0.006738501135259867,
0.026432503014802933,
0.018105950206518173,
-0.05843731388449669,
-0.06413086503744125,
0.025900594890117645,
-0.0076021780259907246,
-0.044746555387973785,
0.01921272650361061,
0.06931819766759872,
0.03180998936295509,
-0.0029724854975938797,
0.0034962152130901814,
0.008747045882046223,
-0.002061191713437438,
0.00340824481099844,
0.04555274173617363,
-0.03984152153134346,
-0.06745598465204239,
-0.065336674451828,
-0.04134590923786163,
-0.017541060224175453,
-0.012549933977425098,
-0.0356370285153389,
-0.08180218189954758,
-0.019276654347777367,
-0.008402925916016102,
-0.01251196675002575,
-0.032702092081308365,
-0.024637311697006226,
-0.0008135003736242652,
-0.004359154962003231,
0.080353744328022,
0.032527584582567215,
0.07430461049079895,
0.025311537086963654,
0.025683468207716942,
-0.004044078756123781,
-0.0022820166777819395,
-0.015768369659781456,
0.024871308356523514,
-0.02666628174483776,
0.010754949413239956,
-0.04435379058122635,
0.027513084933161736,
0.047628093510866165,
0.01077990047633648,
-0.04167734831571579,
-0.010973992757499218,
-0.0389469675719738,
-0.008139841258525848,
0.04876936599612236,
-0.019546763971447945,
-0.020840421319007874,
0.021856896579265594,
-0.019974416121840477,
-0.01514213252812624,
0.061478473246097565,
-0.013793581165373325,
0.04068080335855484,
0.024275679141283035,
0.002548015210777521,
0.005285263527184725,
-0.008445522747933865,
0.010877793654799461,
0.04471804201602936,
0.027891578152775764,
0.015746664255857468,
-0.01826818846166134,
-0.030701544135808945,
-0.04625760018825531,
0.03668844699859619,
0.0025595941115170717,
-0.008769919164478779,
0.018918808549642563,
-0.00945774745196104,
-0.056898169219493866,
0.06187335401773453,
0.03794471547007561,
-0.026828594505786896,
0.020904764533042908,
-0.027391226962208748,
-0.035750605165958405,
0.002358401892706752,
0.08164333552122116,
-0.03875558078289032,
0.025305066257715225,
-0.029654551297426224,
-0.038091279566287994,
0.024519339203834534,
0.01690094545483589,
-0.05341757833957672,
-0.03439585119485855,
0.022179439663887024,
0.00401699123904109,
-0.008414172567427158,
0.02720745839178562,
-0.05139216408133507,
0.014180890284478664,
-0.011430040933191776,
-0.05332902446389198,
-0.031241992488503456,
-0.0070443181321024895,
0.033329591155052185,
0.020268326625227928,
0.02983931638300419,
-0.02242187038064003,
-0.021072406321763992,
-0.008643003180623055,
0.005698039196431637,
0.0030298358760774136,
0.04340646415948868,
-0.017895108088850975,
-0.06642670929431915,
-0.07003839313983917,
0.025995688512921333,
0.014454902149736881,
0.043503135442733765,
0.0030826253350824118,
0.02836780808866024,
-0.0007500817882828414,
-0.024801166728138924,
0.00699085695669055,
-0.03112412989139557,
0.013347030617296696,
-0.025212226435542107,
0.07498437166213989,
0.05437164381146431,
0.02198602631688118,
0.013126843608915806,
0.02712295576930046,
0.025946099311113358,
-0.0016661614645272493,
-0.04723094776272774,
0.03449466452002525,
0.06614271551370621,
0.007830964401364326,
-0.0017775505548343062,
0.024361232295632362,
-0.07043644040822983,
-0.04123522713780403,
-0.019130831584334373,
0.034951262176036835,
0.004981811624020338,
-0.09771811217069626,
0.021239997819066048,
-0.08002977818250656,
-0.059683699160814285,
0.001788684749044478,
0.00761830760166049,
0.04270761087536812,
-0.05646667629480362,
-0.016691233962774277,
-0.0016671833582222462,
-0.08465778082609177,
0.05099383369088173,
-0.007464430760592222,
-0.02285073697566986,
-0.02039714902639389,
-0.019641224294900894,
-0.00987415574491024,
-0.04696263372898102,
0.026928847655653954,
-0.027940984815359116,
-0.07059385627508163,
-0.05428208038210869,
-0.0070045702159404755,
-0.006848142948001623,
0.01968364417552948,
0.045279987156391144,
0.021154578775167465,
-0.007857786491513252,
-0.0060788653790950775,
0.04104098305106163,
-0.010692428797483444,
-0.04885596036911011,
0.01267774123698473,
0.04016275703907013,
-0.03668011724948883,
0.09251689910888672,
-0.036698292940855026,
0.005440582055598497,
0.013555432669818401,
0.002326711779460311,
0.09106684476137161,
-0.032329823821783066,
-0.0016650559846311808,
-0.028839798644185066,
0.010452778078615665,
-0.0011527842143550515,
0.04670950025320053,
-0.007095147389918566,
0.018741386011242867,
0.059019267559051514,
-0.00743224797770381,
0.08526846766471863,
-0.024448275566101074,
0.018230527639389038,
0.029476605355739594,
0.006483960896730423,
0.03348713368177414,
-0.008130669593811035,
0.03562433272600174,
-0.04172665625810623,
-0.05405524745583534,
-0.02587473951280117,
-0.048089299350976944,
0.06483275443315506,
-0.012431759387254715,
0.00686737010255456,
-0.004898752085864544,
0.025072826072573662,
0.033009953796863556,
-0.03631715103983879,
-0.01679316535592079,
-0.03315266966819763,
-0.02846192568540573,
0.04003477469086647,
0.028873782604932785,
-0.008425462990999222,
0.022765202447772026,
0.04508596286177635,
0.02227892354130745,
0.021326541900634766,
0.046609289944171906,
-0.046878550201654434,
0.08763604611158371,
0.0014981877757236362,
-0.07744434475898743,
-0.03921394422650337,
-0.024990493431687355,
-0.03999530151486397,
0.011270631104707718,
-0.00663970410823822,
0.01798431947827339,
-0.032298050820827484,
0.03684511408209801,
0.002616247860714793,
0.0739520713686943,
-0.05191585421562195,
0.039851680397987366,
0.0031324736773967743,
0.012240944430232048,
-0.012100282125175,
0.05306367576122284,
0.0390823669731617,
0.016697315499186516,
0.03128862753510475,
0.006318627391010523,
-0.002709365449845791,
0.05202383175492287,
-0.00910094752907753,
0.017488675191998482,
0.029137613251805305,
0.03283679112792015,
-0.03154372051358223,
0.06610093265771866,
0.01621752791106701,
-0.09993111342191696,
0.06298723816871643,
0.04240335151553154,
0.010972762480378151,
-0.0625813826918602,
0.03948897868394852,
0.030725587159395218,
-0.00922554824501276,
0.009763723239302635,
0.020634382963180542,
-0.020792903378605843,
-0.05333753675222397,
-0.06670041382312775,
0.00893239676952362,
-0.04329150542616844,
-0.02793470211327076,
-0.0031226701103150845,
-0.026363182812929153,
-0.014905190095305443,
-0.011730797588825226,
0.04828973859548569,
0.0019380433950573206,
0.05695365369319916,
-0.06585389375686646,
-0.018087994307279587,
0.008562623523175716,
-0.07128395885229111,
-0.054130617529153824,
-0.0385584831237793,
0.002912155818194151,
-0.06594866514205933,
-0.0024062558077275753,
0.01191288698464632,
0.03761911019682884,
0.015009908005595207,
-0.08521413058042526,
0.049607474356889725,
0.026492737233638763,
-0.0011096025118604302,
0.02202042192220688,
0.10637256503105164,
0.0450998954474926,
-0.030110888183116913,
-0.10209095478057861,
0.017745576798915863,
0.059451788663864136,
0.03600569814443588,
0.006500300019979477,
0.02772209793329239,
-0.009929165244102478,
0.007894421927630901,
-0.020147670060396194,
0.012556863017380238,
0.002459254115819931,
-0.05653177574276924,
0.01625658944249153,
-0.011090045794844627,
0.03545928746461868,
0.0403376966714859,
0.04790857806801796,
-0.0598878376185894,
0.04973917081952095,
0.02507629804313183,
-0.026922965422272682,
-0.05933932214975357,
-0.014839301817119122,
0.023258714005351067,
-0.004466069396585226,
-0.06235175579786301,
0.03228297457098961,
-0.013984189368784428,
0.01642121560871601,
0.0068579139187932014,
-0.009139412082731724,
0.006940961349755526,
-0.03487984463572502,
0.05347232520580292,
0.020171882584691048,
0.050835318863391876,
0.015026867389678955,
-0.07489986717700958,
-0.05685929208993912,
0.015946293249726295,
-0.021784722805023193,
-0.009672715328633785,
0.06656456738710403,
-0.022015543654561043,
-0.017763230949640274,
0.016858432441949844,
-0.08890755474567413,
0.014188749715685844,
-0.04659159854054451,
-0.03920424357056618,
0.018613586202263832,
-0.014756077900528908,
0.050007231533527374,
0.020859355106949806,
0.06585816293954849,
-0.040600452572107315,
0.028349772095680237,
0.044724687933921814,
0.01848169043660164,
-0.06811212748289108,
0.027075374498963356,
-0.06030673533678055,
0.04631428048014641,
-0.025934670120477676,
-0.01432497426867485,
-0.01703248731791973,
0.008174924179911613,
-0.01711554266512394,
0.0496734157204628,
0.017269955947995186,
-0.058454543352127075,
-0.0307504553347826,
-0.05711714178323746,
0.0354996882379055,
0.0058821109123528,
-0.02087516523897648,
0.021422114223241806,
-0.01752796210348606,
-0.04747380316257477,
-0.01054640393704176,
-0.024177512153983116,
0.04407728463411331,
-0.05094699189066887,
0.035505395382642746,
-0.007695741951465607,
-0.033774685114622116,
-0.029541121795773506,
-0.011764224618673325,
0.023517336696386337,
-0.08468978852033615,
-0.0084084402769804,
0.045889537781476974,
0.008682575076818466,
-0.004867834039032459,
0.06049693748354912,
0.06012395769357681,
-0.030456023290753365,
-0.006831187289208174,
0.010266564786434174,
-0.03944101184606552,
-0.024746663868427277,
-0.03942463546991348,
-0.03642004355788231,
0.008335381746292114,
-0.0005207864451222122,
-0.020155169069767,
0.02528870292007923,
0.0010790135711431503,
-0.02975848689675331,
-0.0051263910718262196,
0.021166915073990822,
-0.010070198215544224,
-0.028199033811688423,
0.005656095687299967,
0.018323851749300957,
0.0031168849673122168,
0.04666117578744888,
-0.04667728394269943,
-0.029242249205708504,
-0.027521077543497086,
-0.005249235313385725,
0.01375321764498949,
-0.04552111402153969,
-0.024853087961673737,
0.01772286742925644,
0.0240885429084301,
0.013289675116539001,
-0.04100221022963524,
0.04831746965646744,
-0.019609704613685608,
0.10961300134658813,
0.08507103472948074,
-0.05731900408864021,
-0.006979350466281176,
0.010681814514100552,
0.04557134583592415,
-0.006459547206759453,
-0.016263313591480255,
-0.027325492352247238,
-0.05101267620921135,
0.013112732209265232,
-0.01808016374707222,
-0.08615150302648544,
0.025467541068792343,
0.03728193789720535
] |
<p>now, I have read a lot of explanations on that but still can't really understand why it would happen so if you can give some examples for a such a thing happening. I mean lets say gravity attracts the air and due to air viscosity all of the air gets carried with the Earth but why will the speed be same ? </p> | g162 | [
0.09227275103330612,
0.02669190987944603,
0.011110254563391209,
0.07107430696487427,
0.017448069527745247,
0.06427734345197678,
0.04312050715088844,
0.007083500269800425,
-0.059214621782302856,
-0.049416135996580124,
0.016415592283010483,
0.002520510694012046,
-0.001318952301517129,
0.08815848082304001,
-0.019439127296209335,
0.021202659234404564,
0.005536436103284359,
-0.020252447575330734,
0.042859822511672974,
0.02862813137471676,
-0.014127640053629875,
0.002731539309024811,
-0.008396826684474945,
-0.04757941514253616,
-0.11027241498231888,
-0.023011237382888794,
0.008554753847420216,
-0.06259377300739288,
-0.01620432920753956,
-0.016081489622592926,
0.021153371781110764,
-0.006980929523706436,
0.0027220584452152252,
-0.04641149193048477,
-0.025915440171957016,
-0.027876118198037148,
-0.03438929095864296,
-0.03468934819102287,
0.007726110517978668,
-0.02275150455534458,
0.05772053822875023,
-0.020817922428250313,
-0.03443310409784317,
-0.00748473359271884,
0.010713255032896996,
-0.0011728700483217835,
-0.01337813213467598,
0.031309518963098526,
-0.006314232014119625,
0.004686480388045311,
-0.04430863633751869,
-0.017217526212334633,
-0.052982259541749954,
-0.05198249593377113,
0.0077323317527771,
-0.022025736048817635,
0.06845860928297043,
-0.015693988651037216,
-0.009422272443771362,
0.049089133739471436,
-0.013621778227388859,
-0.02759809046983719,
0.03682130202651024,
-0.015646832063794136,
0.025575952604413033,
0.02550043910741806,
-0.0060095880180597305,
-0.013495359569787979,
0.054102711379528046,
0.02713296003639698,
-0.01031093206256628,
0.0011594218667596579,
-0.017222650349140167,
-0.06667262315750122,
0.03592553362250328,
-0.01482982188463211,
0.009811535477638245,
0.0017098537646234035,
0.10130149126052856,
-0.0038239830173552036,
-0.013481027446687222,
0.004741249140352011,
-0.01895514689385891,
0.028015894815325737,
0.04490277171134949,
0.0036695885937660933,
0.00404407549649477,
-0.00879758968949318,
-0.04059538617730141,
-0.022588422521948814,
0.01128853764384985,
-0.06818996369838715,
0.04002362862229347,
0.023772036656737328,
-0.03342090919613838,
-0.0406312458217144,
-0.011587024666368961,
0.06205548346042633,
-0.058445729315280914,
-0.044951606541872025,
0.020875733345746994,
-0.006696674041450024,
0.02647058293223381,
0.01934133842587471,
-0.015118280425667763,
0.0070375362411141396,
0.0023828691337257624,
0.05454203858971596,
0.006024009082466364,
-0.058676328510046005,
0.017788337543606758,
-0.029333624988794327,
-0.03172946721315384,
-0.01028489414602518,
0.013466772623360157,
-0.06055545061826706,
0.002763073891401291,
0.02398701012134552,
0.013815742917358875,
0.01112620159983635,
-0.01941028982400894,
-0.010740960948169231,
-0.05608932673931122,
-0.025417812168598175,
-0.03729739785194397,
-0.025030042976140976,
0.08376027643680573,
-0.013406915590167046,
-0.00015562385669909418,
-0.038652606308460236,
0.018707821145653725,
0.019964028149843216,
-0.008570180274546146,
0.04181188717484474,
-0.03215697035193443,
-0.05047239735722542,
-0.005444247275590897,
-0.010507483966648579,
0.006563170347362757,
-0.03485224023461342,
-0.034709490835666656,
-0.02083195000886917,
0.02575031854212284,
0.028244568035006523,
-0.05117375776171684,
0.01764223724603653,
-0.013049832545220852,
0.031951338052749634,
0.044072333723306656,
-0.02062363550066948,
-0.06888462603092194,
0.059746671468019485,
0.03104443848133087,
-0.03744744136929512,
0.024489739909768105,
-0.0164334774017334,
0.0105726458132267,
0.0061981817707419395,
0.0036325454711914062,
-0.036402396857738495,
0.061306972056627274,
-0.008558818139135838,
0.015331849455833435,
-0.004452179651707411,
-0.058675747364759445,
0.07751728594303131,
0.036624807864427567,
-0.04555339366197586,
0.0007665560697205365,
0.031866371631622314,
-0.07400985062122345,
-0.02394883707165718,
-0.011206058785319328,
0.0979529470205307,
0.0528455525636673,
0.0029909624718129635,
0.06493270397186279,
-0.0031428311485797167,
0.0019731794018298388,
-0.04096044972538948,
-0.0008081230917014182,
-0.06032537668943405,
0.012148864567279816,
-0.07365211844444275,
0.00977388210594654,
-0.024334054440259933,
-0.022326679900288582,
-0.019391914829611778,
-0.07640834897756577,
-0.00011866632848978043,
-0.012109855189919472,
-0.0733041986823082,
-0.04818214103579521,
0.02333182469010353,
-0.01976858451962471,
-0.005714244209229946,
-0.008843090385198593,
-0.0456586517393589,
-0.09432444721460342,
0.025910284370183945,
-0.0038868174888193607,
-0.011599821038544178,
0.044403284788131714,
-0.04052804410457611,
0.01129318866878748,
-0.007236701902002096,
-0.0014072576304897666,
0.055570390075445175,
0.03510473668575287,
0.02827858179807663,
0.03864184021949768,
-0.014290469698607922,
0.040076255798339844,
0.0339176245033741,
0.016803408041596413,
0.037537459284067154,
-0.00592373963445425,
0.0382867231965065,
0.013448571786284447,
0.012314531952142715,
0.013031545095145702,
-0.025887837633490562,
-0.04093317687511444,
-0.03497292846441269,
-0.039290737360715866,
-0.03847150132060051,
-0.04780261591076851,
-0.014587508514523506,
0.04392372444272041,
0.021811965852975845,
0.06391404569149017,
0.03422890603542328,
-0.014057598076760769,
0.029056522995233536,
0.010917793028056622,
0.03309442847967148,
0.01267220638692379,
0.04116977006196976,
-0.029144424945116043,
-0.044718921184539795,
-0.012704303488135338,
-0.04877457395195961,
-0.0017569739138707519,
-0.03298840671777725,
0.04021170735359192,
-0.07399126142263412,
0.04263255000114441,
-0.024718735367059708,
0.04537753015756607,
0.05915152654051781,
0.043374523520469666,
-0.05132903531193733,
-0.04311723634600639,
0.02191230095922947,
0.017195694148540497,
-0.0003101241309195757,
-0.014551197178661823,
0.005972535349428654,
-0.046946585178375244,
-0.05399689823389053,
-0.02181057631969452,
-0.0048494706861674786,
0.01793137565255165,
-0.0012965439818799496,
-0.09826979786157608,
0.01618155464529991,
-0.008148794062435627,
0.025332540273666382,
-0.005691507365554571,
-0.007688775658607483,
-0.022508960217237473,
0.030741706490516663,
-0.0568494014441967,
0.044366370886564255,
-0.017571859061717987,
0.022032713517546654,
0.014381437562406063,
-0.0360860601067543,
0.014579192735254765,
0.006292670965194702,
-0.009678022935986519,
-0.011561671271920204,
-0.029110342264175415,
0.00459115207195282,
0.014729639515280724,
-0.047540049999952316,
-0.029514893889427185,
0.06590206921100616,
-0.02703222818672657,
0.07939020544290543,
0.02112009935081005,
0.03483109921216965,
0.05515312775969505,
0.04008101299405098,
0.06823737174272537,
0.05934048071503639,
0.028395559638738632,
-0.0055770776234567165,
-0.07733500748872757,
-0.03136167675256729,
0.024998784065246582,
-0.003902290714904666,
0.053207747638225555,
0.04171866551041603,
-0.016701841726899147,
0.00401239562779665,
-0.024872783571481705,
-0.032025739550590515,
-0.015710270032286644,
-0.011050038039684296,
0.0688929483294487,
0.004599694162607193,
-0.03890511393547058,
0.038505569100379944,
-0.015006599947810173,
-0.030763724818825722,
-0.022198086604475975,
0.044448938220739365,
0.039795976132154465,
-0.002684627892449498,
0.0006021757726557553,
-0.02022290602326393,
-0.036351170390844345,
-0.006597140803933144,
-0.010631177574396133,
0.050793468952178955,
-0.010849629528820515,
0.0003062819305341691,
0.004269457887858152,
0.029706884175539017,
-0.0014724505599588156,
0.0013307275949046016,
0.01791011355817318,
0.023498529568314552,
-0.09174621105194092,
0.011577452532947063,
-0.019632326439023018,
0.030214624479413033,
0.01858464814722538,
0.033608369529247284,
-0.01502104103565216,
-0.0005766120157204568,
-0.050106119364500046,
0.01626216247677803,
-0.06066635623574257,
0.06023278459906578,
0.07236741483211517,
-0.0025920465122908354,
-0.0009833023650571704,
0.031064847484230995,
0.07495537400245667,
-0.027702149003744125,
0.00027107802452519536,
-0.08480915427207947,
-0.05440075695514679,
0.0356983058154583,
-0.022656148299574852,
-0.006890946067869663,
0.0069511388428509235,
-0.03580022603273392,
0.004284378606826067,
0.02631535194814205,
-0.012679030187427998,
0.06855887919664383,
0.01190904714167118,
0.01981210522353649,
-0.04773842170834541,
0.019167419523000717,
-0.0096646873280406,
0.06410867720842361,
0.02463129721581936,
0.030738022178411484,
-0.03729378804564476,
0.08432849496603012,
0.04777829349040985,
-0.021573059260845184,
0.051401205360889435,
-0.019779972732067108,
0.020620575174689293,
-0.02285892330110073,
0.05937232822179794,
0.011984420008957386,
-0.03528566658496857,
0.01963469386100769,
-0.002600552048534155,
-0.011671571992337704,
-0.09534209966659546,
-0.0010057560866698623,
-0.02633606642484665,
-0.08094679564237595,
0.023319562897086143,
0.01726597733795643,
0.017290109768509865,
0.0053259264677762985,
0.006642706226557493,
-0.03881680592894554,
-0.004095187410712242,
-0.022584248334169388,
0.026197129860520363,
0.011929758824408054,
-0.056353360414505005,
0.014449741691350937,
-0.013583466410636902,
0.0252832043915987,
-0.022397812455892563,
0.0008999988785944879,
0.023862183094024658,
-0.010675736702978611,
-0.00972309522330761,
0.015144716016948223,
-0.005453724879771471,
0.026795517653226852,
0.005702804308384657,
-0.00596294179558754,
0.011383816599845886,
0.03261852636933327,
0.006523866672068834,
0.024100514128804207,
0.05556266009807587,
-0.018227173015475273,
-0.010289574041962624,
0.056698668748140335,
0.018380057066679,
-0.016985736787319183,
0.009736815467476845,
0.01914607360959053,
0.09080817550420761,
0.00005977512410026975,
-0.021357392892241478,
0.01311772596091032,
-0.04035467654466629,
0.004128261469304562,
0.012590138241648674,
0.03174407407641411,
-0.03138841316103935,
0.05468421429395676,
0.026471585035324097,
0.045592013746500015,
-0.0019373905379325151,
-0.004240629728883505,
0.04515622556209564,
0.016890978440642357,
0.01945739984512329,
-0.02588992565870285,
-0.01879875175654888,
0.053669486194849014,
0.0010146716376766562,
-0.04743560776114464,
-0.019879598170518875,
-0.024012824520468712,
-0.021722247824072838,
0.03499826043844223,
0.01675315387547016,
0.006401302758604288,
-0.031861938536167145,
-0.03063517063856125,
-0.026156922802329063,
0.017558520659804344,
0.00037790232454426587,
-0.012411899864673615,
-0.06221497431397438,
0.07606730610132217,
0.06640726327896118,
-0.0284285768866539,
-0.018966715782880783,
-0.06727507710456848,
0.048335034400224686,
0.019688576459884644,
-0.06308060139417648,
-0.07738957554101944,
0.03360781818628311,
0.013092766515910625,
-0.026615336537361145,
0.1312677562236786,
0.04106210172176361,
0.04912387579679489,
-0.007694813888520002,
-0.022699551656842232,
0.04100201278924942,
-0.041207343339920044,
-0.06949658691883087,
-0.015963397920131683,
0.05915386229753494,
0.013212103396654129,
-0.030184632167220116,
0.0073881917633116245,
-0.06910377740859985,
0.0480310320854187,
-0.02965446561574936,
-0.07635936141014099,
0.06583509594202042,
-0.005220286548137665,
-0.0439399853348732,
-0.0441565103828907,
-0.04582681879401207,
-0.022926336154341698,
-0.008711245842278004,
0.011599577032029629,
0.010399052873253822,
-0.017562175169587135,
0.007227130699902773,
-0.017479822039604187,
-0.005943699739873409,
-0.01536488626152277,
0.016117539256811142,
0.04085496813058853,
0.01106493640691042,
0.051009226590394974,
-0.03241855651140213,
0.05570419877767563,
-0.04727201908826828,
-0.020612098276615143,
-0.008444588631391525,
0.023167122155427933,
0.022773144766688347,
-0.021466102451086044,
-0.014546352438628674,
-0.035813651978969574,
0.05956340581178665,
-0.030417585745453835,
0.02582394890487194,
-0.0027739170473068953,
-0.014157692901790142,
0.009533312171697617,
0.02439194545149803,
0.029171545058488846,
-0.10217661410570145,
0.02865190990269184,
0.04095591604709625,
0.03021007403731346,
0.03406960144639015,
-0.010936982929706573,
0.07494154572486877,
-0.017119750380516052,
0.06474584341049194,
-0.047414399683475494,
0.028910646215081215,
0.025546256452798843,
0.059867486357688904,
0.007588490378111601,
-0.02213331311941147,
-0.020585613325238228,
0.01525222510099411,
0.06791868060827255,
0.0807354599237442,
-0.019432660192251205,
-0.0030506872572004795,
0.013123826123774052,
0.04327120631933212,
-0.030393356457352638,
-0.023552896454930305,
0.07055069506168365,
0.0008864691480994225,
0.01576601155102253,
-0.06216070428490639,
0.023759910836815834,
-0.01377372071146965,
-0.028607342392206192,
-0.013175088912248611,
-0.01718512736260891,
0.07006581872701645,
0.052278101444244385,
0.008465834893286228,
0.006116017699241638,
-0.003141974098980427,
-0.020878857001662254,
-0.018767131492495537,
0.00848766602575779,
0.045601747930049896,
0.006904438138008118,
-0.04281001165509224,
-0.020612917840480804,
0.01639728806912899,
-0.06544272601604462,
0.020834466442465782,
0.04823913425207138,
-0.006224015727639198,
-0.05044807121157646,
-0.008971307426691055,
-0.03910994529724121,
0.051990799605846405,
-0.04924899339675903,
0.03160092979669571,
-0.07549957185983658,
-0.038778699934482574,
-0.024141335859894753,
-0.014535018242895603,
-0.022582553327083588,
0.050090380012989044,
-0.043634627014398575,
-0.06175711005926132,
-0.03881888464093208,
-0.004010477568954229,
-0.02014732174575329,
-0.056013647466897964,
-0.0502597913146019,
0.004216786473989487,
-0.007832680828869343,
-0.004859588108956814,
0.03867199271917343,
0.03591696172952652,
-0.0010633075144141912,
0.09050218760967255,
-0.00441288948059082,
-0.010183863341808319,
-0.02508610673248768,
0.004646868444979191,
-0.07917987555265427,
-0.0010875853477045894,
0.07042045146226883,
-0.028572402894496918,
0.02924361266195774,
0.005687020253390074,
-0.028932446613907814,
-0.0021576795261353254,
-0.03831576555967331,
0.03235943987965584,
0.01996978558599949,
0.0386623740196228,
-0.03133714944124222,
-0.010105757974088192,
-0.007537984289228916,
0.03130302205681801,
-0.010352992452681065,
0.022221144288778305,
0.0002206462959293276,
-0.04459504783153534,
0.039106011390686035,
-0.010809863917529583,
0.014526603743433952,
0.022949961945414543,
-0.0015561539912596345,
-0.04941527917981148,
-0.007522193714976311,
-0.0076491557992994785,
0.01346377469599247,
0.009946199133992195,
-0.011874795891344547,
0.0448540598154068,
0.008213678374886513,
0.05419947952032089,
0.03342021256685257,
-0.00019981049990747124,
-0.02445434406399727,
-0.026581212878227234,
0.012807253748178482,
0.011662015691399574,
-0.06828638911247253,
-0.07077055424451828,
-0.08270513266324997,
-0.013101653195917606,
-0.004475395195186138,
-0.01943972520530224,
0.0641774982213974,
-0.021519148722290993,
-0.0006517742876894772,
-0.016796158626675606,
-0.0030502513982355595,
-0.001037459704093635,
-0.02110045962035656,
-0.09140409529209137,
0.015265937894582748,
-0.022714298218488693,
0.04270672798156738,
-0.012349366210401058,
0.05587929114699364,
0.04943206161260605,
-0.06373918056488037,
0.02230066806077957,
0.046645715832710266,
-0.016761276870965958,
0.008828089572489262,
0.020815009251236916,
0.0269568283110857,
0.0008409216534346342,
0.0009369694744236767,
0.013016591779887676,
-0.0023635653778910637,
0.04953734576702118,
-0.00040082159102894366,
0.014905323274433613,
0.031927451491355896,
0.013848801143467426,
0.05977229028940201,
-0.009003425016999245,
0.06166759505867958,
0.01564909890294075,
0.02128918655216694,
-0.021552518010139465,
-0.07023540884256363,
0.05762874707579613,
0.03401169180870056,
0.014502670615911484,
-0.013813819736242294,
-0.03840196132659912,
0.008054652251303196,
-0.007976891472935677,
-0.028859663754701614,
-0.01233756449073553,
-0.00855175033211708,
-0.010859235189855099,
0.06311577558517456,
0.009431214071810246,
0.023506971076130867,
-0.02838834933936596,
-0.0144519517198205,
0.017024017870426178,
-0.027722500264644623,
-0.03284180536866188,
-0.00029127937159501016,
-0.009391187690198421,
0.0184297077357769,
0.05655145272612572,
0.018000703305006027,
-0.042195871472358704,
-0.02004009671509266,
-0.026009324938058853,
-0.02420778013765812,
-0.0062079038470983505,
-0.02919641137123108,
-0.01028134673833847,
0.0021169341634958982,
-0.015112769789993763,
-0.06451211869716644,
-0.049664922058582306,
0.02562159299850464,
-0.0029744526837021112,
-0.05280301719903946,
-0.012543288990855217,
-0.005398041568696499,
-0.03401573374867439,
-0.006747587118297815,
0.01571713760495186,
-0.009136361069977283,
-0.023961640894412994,
-0.006493754219263792,
0.005084389355033636,
-0.04405655339360237,
-0.033647067844867706,
0.01016954891383648,
-0.035653769969940186,
-0.0012866067700088024,
0.004308217205107212,
0.02662097103893757,
0.007388270925730467,
-0.03714796155691147,
0.0002873141784220934,
0.042435746639966965,
0.020059671252965927,
-0.04453560337424278,
0.0073576695285737514,
0.030326928943395615,
-0.004717731848359108,
0.04563126713037491,
0.0064794584177434444,
0.015226654708385468,
0.0014399060746654868,
0.023665480315685272,
-0.022694703191518784,
-0.03275667130947113,
-0.019507167860865593,
-0.007581360638141632,
0.003807895351201296,
-0.024818342179059982,
-0.005008980631828308,
-0.04882524907588959,
-0.06152516230940819,
0.08898620307445526
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/2178/how-efficient-is-a-desktop-computer">How efficient is a desktop computer?</a> </p>
</blockquote>
<p>I believe the energy conversion efficiency of a modern CPU is extremely low, because it dissipates pretty much all of it as heat, which is not a desired product. But what's the order of magnitude of the fraction that gets spent on the actual computation?</p>
<p>Are there absolute maximums imposed on this efficiency by the known laws of physics, or can information processing occur without any waste heat generation as a by-product?</p>
<p>I'm a bit out of my depth here, having no idea quite how information processing relates to heat and energy (other than suspecting that there is a very deep connection), so apologies if this is nonsensical or vague.</p> | g198 | [
0.00937352329492569,
0.07270269840955734,
0.004922868218272924,
0.009782272391021252,
0.008399516344070435,
-0.0663786232471466,
0.02442370168864727,
0.05737757310271263,
-0.09912845492362976,
0.005737210623919964,
0.01634627766907215,
0.007380407303571701,
0.021679159253835678,
-0.019964167848229408,
-0.016586655750870705,
0.04094058647751808,
-0.009753519669175148,
-0.00026211264776065946,
0.06536678969860077,
0.10942652076482773,
0.017928488552570343,
-0.005938278045505285,
-0.0181590523570776,
-0.08707362413406372,
-0.045945677906274796,
0.010428661480545998,
-0.021907398477196693,
-0.026235530152916908,
-0.0815710574388504,
0.0010864330688491464,
0.017535071820020676,
-0.015977216884493828,
0.0077703772112727165,
-0.05945192277431488,
-0.14253289997577667,
0.03943776711821556,
0.05591738224029541,
-0.042625222355127335,
0.045026812702417374,
-0.01622971147298813,
0.000590097508393228,
-0.00919154193252325,
-0.031304772943258286,
-0.022040005773305893,
-0.049132250249385834,
0.031147683039307594,
0.004581427201628685,
-0.0318867452442646,
-0.03924473002552986,
-0.019427815452218056,
0.01895919069647789,
-0.031439684331417084,
0.09325258433818817,
0.01949254795908928,
0.03852761164307594,
0.027529573068022728,
-0.00395065126940608,
-0.0011013472685590386,
0.08063580095767975,
-0.01033275481313467,
0.06408603489398956,
0.03383015841245651,
0.01833108812570572,
-0.023203717544674873,
0.04069248214364052,
0.016961585730314255,
-0.032540276646614075,
0.029278142377734184,
-0.0395641103386879,
0.026346029713749886,
0.04341460391879082,
-0.035271186381578445,
-0.04287128895521164,
-0.050883542746305466,
-0.004217098467051983,
-0.04975329712033272,
0.02754126861691475,
-0.026783550158143044,
0.011390166357159615,
0.03733130916953087,
0.0030549918301403522,
-0.07475514709949493,
-0.00969198253005743,
-0.025282761082053185,
0.010972375981509686,
0.01353431586176157,
-0.07056710869073868,
0.004264856688678265,
-0.011757331900298595,
0.07001721858978271,
-0.029096664860844612,
0.01663592830300331,
0.10699035972356796,
-0.0026107653975486755,
-0.012324557639658451,
0.0182727612555027,
-0.01939736306667328,
-0.0038322547916322947,
-0.020739423111081123,
0.019878674298524857,
0.01748349517583847,
-0.03357578068971634,
0.02709328383207321,
-0.0011099142720922828,
-0.010540355928242207,
-0.01025217492133379,
0.04837481677532196,
-0.02999342419207096,
-0.05674959346652031,
-0.004087109584361315,
0.036943838000297546,
0.009041705168783665,
-0.03400601074099541,
0.013081996701657772,
-0.060907118022441864,
-0.014478947035968304,
0.04177280515432358,
-0.0209774412214756,
-0.0477210208773613,
-0.00009283843246521428,
0.03141269087791443,
0.019203070551156998,
-0.018481913954019547,
0.017147166654467583,
0.03142423927783966,
-0.052941616624593735,
0.031132668256759644,
0.005580993834882975,
-0.007099795155227184,
-0.006774131674319506,
-0.00874007772654295,
-0.04350452497601509,
-0.03389724716544151,
0.010510650463402271,
0.023058651015162468,
0.08016408234834671,
-0.022770531475543976,
0.023167809471488,
0.01761690340936184,
-0.042840130627155304,
0.019444718956947327,
-0.01443389244377613,
-0.031105222180485725,
-0.025406131520867348,
-0.01397672574967146,
0.03631598502397537,
-0.01669718697667122,
0.00315745547413826,
0.01723245345056057,
-0.004087492357939482,
-0.000545654387678951,
-0.008465291932225227,
0.0006346713635139167,
-0.08055952936410904,
0.04018576815724373,
0.006512414198368788,
-0.005562263540923595,
-0.024785438552498817,
-0.006077135913074017,
0.010458347387611866,
0.03427915647625923,
0.03130324184894562,
0.04397900030016899,
0.0011865951819345355,
-0.06562460958957672,
-0.04141378030180931,
0.014729487709701061,
-0.06672090291976929,
0.07342907786369324,
-0.028097936883568764,
-0.07302609086036682,
0.012283628806471825,
-0.03727908805012703,
-0.01652751863002777,
-0.044557247310876846,
0.009160557761788368,
0.04886498302221298,
-0.008114715106785297,
0.03380535915493965,
-0.05397062003612518,
-0.06285222619771957,
0.05791511759161949,
0.03411945700645447,
-0.007937926799058914,
-0.037468329071998596,
-0.011537068523466587,
0.014572461135685444,
-0.0015421250136569142,
0.013539103791117668,
0.0030987781938165426,
-0.06548579782247543,
-0.0008074092329479754,
0.05767682567238808,
0.010790274478495121,
-0.02372952736914158,
0.02664235420525074,
-0.022094354033470154,
-0.007250192109495401,
-0.032247330993413925,
0.008415975607931614,
0.024475770071148872,
0.01459410134702921,
0.009247261099517345,
-0.007302622776478529,
0.009556053206324577,
0.03665643185377121,
0.002780598821118474,
0.002517703687772155,
0.03585335612297058,
-0.007373147178441286,
0.03475656732916832,
0.02974661998450756,
0.04371015354990959,
0.03556719794869423,
0.044440802186727524,
-0.005620346404612064,
-0.06470117717981339,
-0.04773188754916191,
-0.02819064073264599,
-0.029869098216295242,
0.030880095437169075,
-0.00023954904463607818,
0.052014220505952835,
0.04053938761353493,
-0.004288945812731981,
0.011987177655100822,
-0.06836311519145966,
-0.004595824051648378,
-0.024991393089294434,
-0.013683280907571316,
-0.03090210072696209,
0.04680043086409569,
0.021508051082491875,
-0.03069121390581131,
0.025220077484846115,
0.029190536588430405,
-0.015474692918360233,
0.03456506505608559,
0.05641968548297882,
0.04782921448349953,
-0.010795802809298038,
0.0284794382750988,
-0.040519293397665024,
-0.014411485753953457,
0.03125115483999252,
-0.06219656020402908,
0.016478626057505608,
0.009540203027427197,
-0.02989199571311474,
0.004158245865255594,
0.009621978737413883,
-0.010915408842265606,
-0.01997780054807663,
0.03717922419309616,
-0.007448906544595957,
-0.0024640525225549936,
0.0007413110579364002,
0.022927602753043175,
-0.03712443262338638,
-0.03647095337510109,
0.0186497513204813,
-0.00831571500748396,
-0.03686368092894554,
0.012726325541734695,
0.025128623470664024,
-0.008024263195693493,
-0.009478647261857986,
-0.05045096203684807,
0.013389261439442635,
0.048423271626234055,
-0.014530862681567669,
0.06602545827627182,
-0.031076304614543915,
0.04710977524518967,
0.012194829992949963,
-0.043003957718610764,
0.016388509422540665,
0.01993606798350811,
0.03359620273113251,
-0.027914145961403847,
0.0031074662692844868,
-0.023690875619649887,
-0.04076792672276497,
0.041825950145721436,
0.06378453224897385,
-0.06117989122867584,
-0.043112579733133316,
0.034257885068655014,
0.0020006014965474606,
0.003342462470754981,
-0.025502195581793785,
0.015343192033469677,
-0.01507918443530798,
0.010063707828521729,
-0.015622809529304504,
-0.018211331218481064,
0.029398050159215927,
-0.019694838672876358,
-0.02630321867763996,
-0.02650294080376625,
-0.010524663142859936,
-0.020449453964829445,
0.004580589942634106,
0.04086398705840111,
-0.06821446120738983,
0.026144929230213165,
-0.08473154902458191,
-0.08196074515581131,
-0.026718411594629288,
-0.046533215790987015,
0.003396612359210849,
0.020514272153377533,
0.018796397373080254,
0.04800684005022049,
-0.034348633140325546,
-0.01739705540239811,
0.012238658964633942,
-0.04200678691267967,
-0.014703800901770592,
0.006584451999515295,
-0.004726530518382788,
-0.026398595422506332,
-0.026157096028327942,
-0.021505240350961685,
0.04910386726260185,
0.04487534984946251,
-0.0365169383585453,
-0.015614759176969528,
0.0113779092207551,
0.02689284458756447,
0.01906703971326351,
-0.022105492651462555,
-0.08771303296089172,
-0.0062886495143175125,
-0.05525008216500282,
-0.04358091950416565,
-0.011074346490204334,
0.008506551384925842,
0.014260792173445225,
0.023031344637274742,
0.023184586316347122,
0.04825344681739807,
-0.048607852309942245,
0.002638675272464752,
0.03661452978849411,
0.051091697067022324,
-0.02622692473232746,
-0.04861299693584442,
-0.007968593388795853,
-0.035284772515296936,
0.05259658768773079,
-0.006364860571920872,
-0.0006511298124678433,
0.023895593360066414,
-0.04228154942393303,
0.03829508647322655,
-0.015051260590553284,
0.04585225507616997,
-0.019109461456537247,
0.03445015475153923,
-0.032157860696315765,
-0.02763749286532402,
0.05660906061530113,
-0.056316811591386795,
-0.06975842267274857,
0.018310856074094772,
-0.024486714974045753,
0.0007545435219071805,
-0.003036372596397996,
0.0008831937448121607,
-0.025288596749305725,
-0.011178389191627502,
-0.00677284924313426,
-0.004445362836122513,
0.030164208263158798,
0.004118260461837053,
0.04467340558767319,
0.030507763847708702,
0.016744464635849,
0.040787480771541595,
-0.008609681390225887,
0.006767685525119305,
0.006850256118923426,
-0.059998251497745514,
0.005921588744968176,
-0.02820928394794464,
-0.05649895220994949,
-0.0025065357331186533,
-0.01971515826880932,
-0.018054665997624397,
0.008894621394574642,
-0.034632667899131775,
-0.0137562807649374,
0.05763748288154602,
-0.033170510083436966,
-0.015390668995678425,
0.0038989281747490168,
0.012265943922102451,
0.052020203322172165,
0.03420703485608101,
0.07282259315252304,
0.01355159841477871,
0.021125933155417442,
0.03182511404156685,
0.021639792248606682,
0.035008806735277176,
-0.023913800716400146,
-0.043971531093120575,
-0.030923090875148773,
-0.02808602713048458,
0.03599982708692551,
-0.010905293747782707,
0.01249297522008419,
0.0027633258141577244,
-0.001141420565545559,
0.023092621937394142,
-0.0374804325401783,
-0.04341989755630493,
0.04754488170146942,
0.01672508381307125,
0.02090204693377018,
-0.041489966213703156,
-0.0388110987842083,
0.026473581790924072,
-0.037529248744249344,
0.07098602503538132,
0.048419635742902756,
-0.042274169623851776,
-0.05741460621356964,
-0.02246340550482273,
0.07605325430631638,
-0.0028139553032815456,
-0.022185537964105606,
0.045659683644771576,
-0.02316294237971306,
0.0328463651239872,
0.008925880305469036,
0.03688473999500275,
0.018862837925553322,
0.016854627057909966,
0.03827540576457977,
-0.011935746297240257,
0.023442326113581657,
0.03849543258547783,
0.0011404225369915366,
-0.04254350811243057,
-0.014153804630041122,
-0.05325553938746452,
-0.036858681589365005,
-0.0625566765666008,
-0.0157589353621006,
0.0620524063706398,
-0.042682960629463196,
0.00010900320921791717,
-0.014088823460042477,
0.012252366170287132,
0.007737341802567244,
0.021525263786315918,
0.003752273041754961,
0.025811817497015,
-0.03933347016572952,
-0.04369793459773064,
-0.018679853528738022,
0.05386032536625862,
-0.048797618597745895,
0.009542534127831459,
-0.023846887052059174,
-0.015526422299444675,
-0.02522081509232521,
0.021144982427358627,
0.04200403392314911,
0.0393027663230896,
-0.012879696674644947,
-0.007169738877564669,
0.01636827550828457,
-0.006692548748105764,
-0.03298087790608406,
-0.004612247925251722,
0.02329169027507305,
0.07456210255622864,
-0.026547763496637344,
0.034773919731378555,
0.03274424001574516,
0.033585164695978165,
0.00902924221009016,
-0.014479801058769226,
-0.07137297838926315,
0.015628615394234657,
0.002385755069553852,
-0.013830414041876793,
-0.004498964175581932,
0.09268900007009506,
0.0032872390002012253,
-0.042777419090270996,
-0.025650862604379654,
0.011039486154913902,
0.04479784518480301,
-0.02186032198369503,
0.0023126231972128153,
0.028493981808423996,
-0.024356726557016373,
-0.008538701571524143,
-0.051287151873111725,
-0.048166435211896896,
0.003692077938467264,
0.0013286365428939462,
0.016196483746170998,
-0.0680566132068634,
0.009757994674146175,
0.02501579001545906,
-0.006210768595337868,
0.00980620551854372,
-0.0601707324385643,
0.009798601269721985,
-0.045307330787181854,
-0.034182917326688766,
0.005104357842355967,
0.02987443469464779,
0.006740149576216936,
0.0008073705248534679,
0.037551235407590866,
0.015068121254444122,
0.025847842916846275,
0.06375560909509659,
0.00039989547803997993,
0.0006937990547157824,
-0.09656095504760742,
-0.05139252543449402,
0.01473395898938179,
0.05774293094873428,
0.028497738763689995,
0.04830207675695419,
-0.014261563308537006,
0.009244969114661217,
-0.006189560983330011,
0.016030343249440193,
-0.04081353172659874,
-0.017744803801178932,
0.05509795993566513,
0.0395333431661129,
-0.0010149701265618205,
-0.01994236186146736,
-0.012080492451786995,
0.07937918603420258,
-0.03928523138165474,
-0.03392307087779045,
-0.008286328054964542,
-0.006404027808457613,
-0.0019349547801539302,
-0.0265315230935812,
0.051801495254039764,
0.025896774604916573,
0.13315972685813904,
-0.02741805464029312,
0.052540022879838943,
0.033541060984134674,
0.035712338984012604,
-0.02244885079562664,
0.05444446578621864,
-0.003490486415103078,
0.00723017193377018,
0.07095520198345184,
0.019504781812429428,
-0.016509220004081726,
0.02983119525015354,
-0.033852774649858475,
0.014265898615121841,
-0.07500862330198288,
0.01984408125281334,
0.048022303730249405,
0.04109160602092743,
0.011272881180047989,
0.0020881141535937786,
-0.001924717565998435,
0.042471207678318024,
-0.021828878670930862,
0.0022124687675386667,
-0.005652815103530884,
-0.034942615777254105,
-0.04713771492242813,
-0.008460807614028454,
-0.038049712777137756,
-0.023660778999328613,
0.020053576678037643,
0.05089787766337395,
0.04712444543838501,
-0.07352767884731293,
0.09525913745164871,
0.015271620824933052,
0.019060593098402023,
-0.03841609135270119,
0.003229598980396986,
-0.01210113987326622,
-0.011750318109989166,
0.03738480061292648,
-0.03453407436609268,
0.010273986496031284,
-0.08205755800008774,
-0.010372749529778957,
-0.013896183110773563,
-0.03684521093964577,
-0.01072676945477724,
0.02170555666089058,
-0.03417946398258209,
-0.005013668444007635,
0.05291721224784851,
0.0044034263119101524,
0.03681405633687973,
-0.06790722906589508,
-0.04079606756567955,
-0.07241473346948624,
-0.007501558866351843,
0.04310750961303711,
0.00625607231631875,
-0.01931474171578884,
-0.06769431382417679,
-0.010090557858347893,
-0.0767735093832016,
0.009308025240898132,
-0.055306315422058105,
0.019734136760234833,
-0.03838086128234863,
0.035574089735746384,
-0.05585620179772377,
0.006176868919283152,
0.07255494594573975,
0.011640178970992565,
0.09722542017698288,
0.12495240569114685,
0.02669565938413143,
0.03773973137140274,
0.04764215275645256,
0.025963205844163895,
0.1085064634680748,
0.004070251248776913,
0.013596439734101295,
-0.0404425747692585,
-0.008223626762628555,
-0.02728487178683281,
0.03028583526611328,
0.01166304387152195,
-0.05126778036355972,
-0.03169046342372894,
0.029951944947242737,
-0.03488332778215408,
0.005850944202393293,
0.05353885889053345,
0.005023880396038294,
-0.025873618200421333,
-0.02049761451780796,
-0.04642972722649574,
0.010456854477524757,
-0.01927287131547928,
-0.005024846643209457,
-0.0709647610783577,
0.024882754310965538,
-0.024032093584537506,
0.01096613984555006,
-0.0028210796881467104,
-0.06875057518482208,
0.023082835599780083,
0.0013565036933869123,
0.002862514229491353,
0.03522970527410507,
0.05524655431509018,
-0.004290291108191013,
0.010468202643096447,
-0.014135449193418026,
0.00040997087489813566,
-0.05867287889122963,
-0.005767893511801958,
-0.06247836351394653,
-0.04666951298713684,
0.006144587881863117,
0.07370082288980484,
-0.0175002571195364,
-0.02071548067033291,
-0.07358258962631226,
-0.02240654267370701,
0.0020445550326257944,
0.02268041856586933,
-0.0117556257173419,
0.012406010180711746,
0.006794656161218882,
-0.002489150268957019,
0.02269698679447174,
-0.02726864442229271,
0.0455189011991024,
0.026355668902397156,
-0.00014169752830639482,
-0.030724506825208664,
-0.01763562299311161,
0.07223032414913177,
-0.04250123351812363,
-0.041770089417696,
0.05930502712726593,
0.004955243784934282,
-0.029528165236115456,
0.053083401173353195,
0.05173711106181145,
0.0479656383395195,
0.0032844231463968754,
-0.022553451359272003,
0.012919586151838303,
-0.008522579446434975,
0.0508064329624176,
0.01232992298901081,
0.005342431832104921,
-0.010185634717345238,
0.02859712392091751,
0.019602442160248756,
-0.01726347766816616,
0.024259377270936966,
-0.03042738512158394,
0.06103629991412163,
0.009406858123838902,
-0.010756084695458412,
-0.03953959047794342,
-0.04162919893860817,
0.04838497191667557,
0.02375642955303192,
0.0068678706884384155,
-0.037606000900268555,
-0.03661113232374191,
0.0028202871326357126,
0.01037650741636753,
0.037196289747953415,
-0.025260906666517258,
0.007753198035061359,
0.008631984703242779,
0.04507748410105705,
-0.0492543950676918,
0.022606385871767998,
-0.02547096274793148,
-0.02499733678996563,
-0.002980029908940196,
-0.00611081114038825,
0.0643414780497551,
-0.004270771984010935,
-0.012959199957549572,
-0.013161111623048782,
-0.004583327565342188,
-0.04858145862817764,
-0.020657707005739212,
0.01914280652999878,
-0.04203365370631218,
-0.07378359884023666,
-0.008865960873663425,
0.04109829664230347,
-0.04231429845094681,
0.010028897784650326,
-0.02311846986413002,
0.000621801009401679,
-0.03093361109495163,
0.035016074776649475,
0.030203500762581825,
0.011135839857161045,
0.0011976435780525208,
0.00911108311265707,
0.04787469282746315,
-0.00820649042725563,
-0.010557040572166443,
-0.0012762723490595818,
-0.0032866650726646185,
-0.032694198191165924,
0.01692831702530384,
0.0437094084918499,
0.024645742028951645
] |
<p>This diagram from <a href="http://en.wikipedia.org/wiki/Lagrangian_point">wikipedia</a> shows the gravitational potential energy of the sun-earth two body system, and demonstrates clearly the semi-stability of the L1, L2, and L3 lagrangian points. The blue arrows indicate lower potential energy, red higher - so any movement in the plane perpendicular to the masses would require energy and without it, an object there would settle.</p>
<p><img src="http://i.stack.imgur.com/ehngn.png" alt="Lagrange Points"></p>
<p>However, the L4 and L5 are claimed to be stable, even though the direction arrows indicate it's at the top of a gravity well, and would fall into lower potential energy in any direction. What is it that makes these points stable if not gravity? What am I missing?</p> | g103 | [
-0.0013840891188010573,
0.045825615525245667,
-0.00390231772325933,
-0.027101857587695122,
0.04447468742728233,
0.06761334091424942,
0.04792292043566704,
-0.030016569420695305,
-0.08616191893815994,
-0.023586194962263107,
0.009512223303318024,
0.030034365132451057,
0.05518397316336632,
0.008033842779695988,
0.02645583637058735,
0.012419379316270351,
0.07729954272508621,
-0.03058997541666031,
0.061178453266620636,
0.020269252359867096,
-0.009770914912223816,
0.0013913747388869524,
0.021657727658748627,
-0.005278534255921841,
-0.01922306977212429,
0.0006575485458597541,
0.05861952155828476,
-0.015836860984563828,
-0.06471284478902817,
0.00012326314754318446,
0.03629729896783829,
0.004485752899199724,
0.0789790004491806,
-0.058000657707452774,
-0.03150347247719765,
-0.09697462618350983,
0.07865019142627716,
-0.04051939398050308,
-0.009322297759354115,
-0.020219773054122925,
-0.0013932209694758058,
-0.05075746402144432,
0.035525135695934296,
0.02397540956735611,
-0.003499476006254554,
-0.04435178264975548,
0.012289867736399174,
-0.014144773595035076,
0.028678376227617264,
-0.050518713891506195,
0.024554235860705376,
0.0325520820915699,
0.01397588849067688,
-0.04127703234553337,
-0.013530068099498749,
0.012495122849941254,
0.01210785936564207,
0.06464837491512299,
0.002575106453150511,
0.03291468694806099,
0.009326254948973656,
-0.037491440773010254,
0.01408386416733265,
0.04867026209831238,
0.006947679445147514,
-0.03535754233598709,
-0.07032259553670883,
-0.05801531299948692,
-0.004643494728952646,
0.006369718816131353,
0.023510411381721497,
-0.035886459052562714,
-0.03902812674641609,
-0.04376795515418053,
-0.01309177465736866,
0.02810245007276535,
-0.022935273125767708,
0.04073924571275711,
-0.027644691988825798,
-0.039534665644168854,
-0.0007547361892648041,
-0.008516932837665081,
-0.024556724354624748,
-0.0006297721993178129,
0.08776736259460449,
-0.02424747124314308,
0.011579885147511959,
0.01904960907995701,
-0.06584972888231277,
-0.008079812861979008,
0.025808904320001602,
0.002029387978836894,
0.04497801885008812,
-0.0066851479932665825,
-0.015670841559767723,
0.010345425456762314,
0.0414794385433197,
0.07219427824020386,
-0.04282049089670181,
-0.038822025060653687,
-0.03682622313499451,
0.02328270487487316,
0.009810764342546463,
0.06784040480852127,
0.03712344169616699,
0.01602909155189991,
0.005246530286967754,
0.008997317403554916,
-0.0033192643895745277,
-0.07170166820287704,
0.01551369670778513,
0.020603736862540245,
0.007294876966625452,
-0.017081299796700478,
-0.029907293617725372,
-0.0312032587826252,
0.05430222675204277,
-0.009523206390440464,
0.06825518608093262,
0.05814104154706001,
0.05640357732772827,
0.048996731638908386,
-0.008082128129899502,
0.05943740904331207,
0.010110398754477501,
-0.0009506079950369895,
-0.010657798498868942,
-0.03196128457784653,
0.002437904244288802,
-0.033110152930021286,
0.0063317641615867615,
-0.00034669286105781794,
-0.028454983606934547,
-0.01828637160360813,
0.004531710408627987,
0.028739864006638527,
0.017366522923111916,
0.02178841456770897,
-0.009542473591864109,
-0.03718622773885727,
-0.004287848714739084,
-0.0076940604485571384,
0.023872865363955498,
-0.03421306982636452,
0.015795763581991196,
0.048794351518154144,
-0.02197776548564434,
0.023170260712504387,
0.018962666392326355,
0.024594081565737724,
-0.016278814524412155,
0.08640243858098984,
-0.0023104532156139612,
-0.09293464571237564,
0.04355953261256218,
-0.0016389548545703292,
0.021706458181142807,
-0.044550906866788864,
-0.014531473629176617,
0.04338886961340904,
0.051250945776700974,
-0.011280097998678684,
0.04101084917783737,
-0.016649480909109116,
0.01500790473073721,
0.049156107008457184,
0.013304167427122593,
-0.027685528621077538,
-0.005453355144709349,
0.017630085349082947,
-0.07055888324975967,
-0.022280490025877953,
0.020436879247426987,
0.07195670157670975,
-0.003983646631240845,
0.03187713772058487,
0.048538919538259506,
-0.018018115311861038,
0.037834275513887405,
0.014512114226818085,
-0.00008444247941952199,
-0.017050178721547127,
-0.011418073438107967,
-0.029081471264362335,
-0.005396331660449505,
-0.007792493794113398,
0.041944414377212524,
0.07729626446962357,
0.01806030422449112,
-0.0055645909160375595,
-0.0074873510748147964,
-0.003946433309465647,
-0.104243703186512,
-0.040286142379045486,
0.015885617583990097,
-0.01926570199429989,
0.08270833641290665,
-0.07485532015562057,
-0.024638671427965164,
0.02985563315451145,
-0.035479988902807236,
-0.025141997262835503,
-0.00132319878321141,
0.023540597409009933,
-0.01699523814022541,
0.004125004634261131,
-0.04606916755437851,
0.0506717674434185,
0.012027476914227009,
-0.017916414886713028,
-0.00016928862896747887,
-0.009595201350748539,
0.10146616399288177,
0.018383128568530083,
0.023596927523612976,
-0.04577416181564331,
-0.030235877260565758,
0.04976453632116318,
-0.03521597385406494,
0.011865349486470222,
-0.01927405595779419,
0.021172598004341125,
0.02476203814148903,
0.056604985147714615,
0.000689510372467339,
0.0062443953938782215,
-0.03670012205839157,
-0.03127455338835716,
-0.004235635045915842,
-0.040427904576063156,
-0.04009588062763214,
0.014940756373107433,
0.025599393993616104,
0.04987328499555588,
0.03601403906941414,
-0.045672982931137085,
0.004376212600618601,
-0.04078623279929161,
0.05642218142747879,
0.020932374522089958,
0.024709034711122513,
-0.010438772849738598,
-0.0253462977707386,
0.054479826241731644,
0.08422964066267014,
0.0019895138684660196,
0.08861981332302094,
0.028757961466908455,
-0.052505362778902054,
0.07930705696344376,
0.002216123975813389,
-0.011811052449047565,
-0.06179824844002724,
0.0076112826354801655,
-0.02156967483460903,
0.0031773927621543407,
-0.03554889187216759,
-0.006293548736721277,
-0.0258102435618639,
-0.020482590422034264,
-0.038021281361579895,
-0.042157020419836044,
0.023999938741326332,
-0.004178847651928663,
-0.08785044401884079,
-0.0061837173998355865,
-0.0051560006104409695,
-0.100155770778656,
0.03167413920164108,
-0.042711853981018066,
-0.04957609996199608,
0.03987245634198189,
0.05531545728445053,
0.06458663195371628,
0.01605461724102497,
0.016648896038532257,
-0.0309311430901289,
-0.024332314729690552,
-0.0005798098864033818,
-0.0151745630428195,
0.026279469951987267,
-0.012609368190169334,
0.026199212297797203,
0.04327566549181938,
0.027489425614476204,
0.012787682004272938,
-0.020630493760108948,
0.028053317219018936,
-0.005834730342030525,
-0.0206461139023304,
-0.037347547709941864,
0.0021254185121506453,
0.021789763122797012,
-0.02307429537177086,
-0.022175738587975502,
-0.021921934559941292,
0.00009416365355718881,
-0.00047051653382368386,
-0.031270094215869904,
-0.02253294177353382,
-0.002693201182410121,
0.012914230115711689,
0.009343091398477554,
0.01992371864616871,
-0.0073021939024329185,
0.029714783653616905,
-0.015704691410064697,
-0.03882819786667824,
0.006602010689675808,
-0.016927706077694893,
0.007997318170964718,
0.027730792760849,
-0.014438229613006115,
-0.007623334880918264,
-0.03659447655081749,
0.03909900039434433,
-0.0164033193141222,
0.012348863296210766,
0.059143636375665665,
-0.04949253052473068,
-0.04800514504313469,
-0.026032591238617897,
-0.04051431268453598,
0.011905315332114697,
-0.002930627902969718,
0.006483764853328466,
-0.006469497457146645,
-0.07783389091491699,
-0.05464266240596771,
0.011912846937775612,
-0.000580949941650033,
0.028160512447357178,
0.02685084380209446,
0.04970443993806839,
0.002830327022820711,
-0.020907200872898102,
0.006177418399602175,
-0.07233559340238571,
0.0537293441593647,
0.003929903265088797,
-0.044851649552583694,
0.02884390391409397,
-0.04061886668205261,
-0.003595251590013504,
0.04682755097746849,
0.025430062785744667,
0.02118227258324623,
-0.023362046107649803,
-0.00898514874279499,
-0.04566563665866852,
0.02818514034152031,
-0.04103944078087807,
0.00011472621554275975,
-0.00691977608948946,
0.022039474919438362,
-0.022037044167518616,
-0.03067600354552269,
-0.031724173575639725,
-0.08338766545057297,
0.02888006903231144,
-0.03698774054646492,
0.029158418998122215,
0.01361754909157753,
0.040863119065761566,
0.024691950529813766,
-0.0036075476091355085,
-0.08118165284395218,
0.0011224007466807961,
-0.0010952369775623083,
-0.00882065948098898,
0.028625287115573883,
-0.06420842558145523,
-0.034510042518377304,
0.017216883599758148,
0.046011582016944885,
-0.039776116609573364,
0.061767831444740295,
-0.05990887060761452,
-0.023668857291340828,
0.027910955250263214,
0.04361754655838013,
-0.045772697776556015,
0.02775326743721962,
0.03985924273729324,
0.020862290635704994,
0.05327508598566055,
-0.06539630889892578,
-0.043239887803792953,
-0.003759605810046196,
-0.005654084496200085,
-0.007741918321698904,
-0.05278356373310089,
0.005138732027262449,
-0.021815655753016472,
0.04934728518128395,
0.017313184216618538,
-0.002717909635975957,
0.03385993093252182,
-0.026316864416003227,
0.04973364993929863,
-0.0009031582158058882,
0.023229386657476425,
-0.051861681044101715,
-0.04987327381968498,
0.0400814563035965,
0.06582169234752655,
0.014936760067939758,
-0.015936877578496933,
-0.01935727708041668,
-0.010106055065989494,
0.1142437681555748,
0.038794420659542084,
0.029448634013533592,
-0.036700181663036346,
0.03468339890241623,
-0.06815637648105621,
-0.038836438208818436,
-0.0458892285823822,
0.01571143977344036,
-0.011727613396942616,
-0.004736531060189009,
0.059526704251766205,
0.022779159247875214,
-0.03966514766216278,
-0.0057983784936368465,
0.0584716722369194,
0.0397554412484169,
-0.01543013472110033,
-0.03940989077091217,
0.022803887724876404,
0.039562687277793884,
0.0288127139210701,
0.07161139696836472,
-0.02328094281256199,
-0.013682759366929531,
0.07068485766649246,
-0.013272572308778763,
-0.013662527315318584,
0.008803654462099075,
0.021768076345324516,
0.06753776967525482,
-0.009582236409187317,
0.04397405683994293,
-0.04680459573864937,
-0.024640249088406563,
0.04165530204772949,
-0.03982853516936302,
0.0020132996141910553,
-0.006030359771102667,
-0.05675823241472244,
-0.03184383362531662,
-0.010249298997223377,
0.035063665360212326,
0.0009012015070766211,
-0.007461050059646368,
0.009105503559112549,
0.010695922188460827,
0.04177292436361313,
-0.006592650432139635,
0.006522809155285358,
-0.014253038913011551,
-0.0821446105837822,
0.015876825898885727,
0.005638107657432556,
0.032136738300323486,
-0.03943051025271416,
-0.04080437123775482,
-0.01880473643541336,
-0.014179698191583157,
-0.05199693888425827,
-0.004267361480742693,
-0.011585138738155365,
0.01739790104329586,
0.005045450292527676,
0.004677054937928915,
-0.02571156807243824,
-0.030237633734941483,
-0.022339502349495888,
0.027430053800344467,
-0.06100510433316231,
-0.03473618999123573,
0.020906822755932808,
0.019515683874487877,
0.017379233613610268,
-0.05130265653133392,
-0.0017094837967306376,
-0.00673036789521575,
-0.05524510145187378,
0.0020682443864643574,
0.04859427735209465,
-0.03858507424592972,
-0.04475319758057594,
0.012729455716907978,
0.002439624397084117,
0.013042386621236801,
-0.013080529868602753,
0.0235942080616951,
0.006438616197556257,
-0.006495829671621323,
0.033891696482896805,
-0.039682935923337936,
0.03543073683977127,
0.008088883012533188,
-0.0273759625852108,
-0.004043677821755409,
0.0021032097283750772,
0.05705535039305687,
-0.04763738438487053,
0.01667732372879982,
-0.006368572358042002,
-0.046804457902908325,
0.0035191860515624285,
0.044401273131370544,
0.041452016681432724,
0.013225922361016273,
-0.09731443971395493,
0.01813664846122265,
0.023444877937436104,
-0.040292058140039444,
0.0009769032476469874,
0.03784092515707016,
0.011753389611840248,
0.017133722081780434,
-0.000015781706679263152,
0.0825178325176239,
0.028449345380067825,
-0.04634789749979973,
-0.0398474782705307,
-0.021663544699549675,
0.038467030972242355,
-0.024768555536866188,
0.02886824868619442,
0.028825994580984116,
-0.012719707563519478,
0.01187086384743452,
-0.07888112217187881,
0.023428328335285187,
-0.03949188068509102,
0.09295835345983505,
-0.058571238070726395,
-0.0010693836957216263,
-0.04370706155896187,
-0.03714214265346527,
0.04761195182800293,
-0.009926728904247284,
0.038232654333114624,
-0.04376959055662155,
0.01767081581056118,
-0.025036005303263664,
-0.03874135762453079,
-0.03291679546236992,
0.083197683095932,
0.0021649664267897606,
0.052580978721380234,
-0.04957425594329834,
-0.049708276987075806,
-0.01589863933622837,
-0.011552498675882816,
-0.028932441025972366,
0.007230403367429972,
0.0425078459084034,
0.01692783460021019,
0.03211502358317375,
0.01823817752301693,
0.026849044486880302,
-0.05502796173095703,
-0.027679983526468277,
-0.040390171110630035,
0.016104450449347496,
0.022542256861925125,
-0.015405315905809402,
0.044118739664554596,
-0.012388890609145164,
0.01935488171875477,
0.020789900794625282,
-0.0019719726406037807,
-0.07297521084547043,
-0.03583195060491562,
-0.04604404419660568,
-0.07626982033252716,
0.014220756478607655,
0.03544004261493683,
0.03599737212061882,
-0.07707046717405319,
-0.03848257660865784,
0.009341306984424591,
-0.025010766461491585,
-0.02619411051273346,
0.0000060654801927739754,
-0.05971115455031395,
0.0023883685935288668,
0.04047442972660065,
-0.01785038784146309,
0.004897713661193848,
-0.012072861194610596,
0.028895307332277298,
-0.029051220044493675,
0.018259411677718163,
-0.05005650222301483,
-0.02045285329222679,
0.05605420842766762,
0.03815213218331337,
-0.0028355007525533438,
0.011606628075242043,
0.0251024067401886,
0.004404331557452679,
-0.006714198738336563,
0.029966069385409355,
-0.013509511947631836,
-0.026543503627181053,
-0.010839125141501427,
0.0028881244361400604,
-0.0038958864752203226,
0.014743632636964321,
0.03488856181502342,
0.0038987360894680023,
-0.015335123986005783,
0.01780926249921322,
-0.0723864734172821,
0.0011040560202673078,
-0.03617829829454422,
-0.027157247066497803,
-0.01504871528595686,
0.0003148841788060963,
0.0032063780818134546,
-0.011545159853994846,
-0.011277396231889725,
0.031074631959199905,
-0.009454715996980667,
0.009247483685612679,
-0.03877567499876022,
0.021499507129192352,
0.030428212136030197,
0.002198202535510063,
0.025736210867762566,
-0.006282565649598837,
-0.05373470485210419,
-0.0044408440589904785,
0.039532747119665146,
0.005589169915765524,
-0.03357450291514397,
0.013487922959029675,
0.0735810250043869,
0.0151068652048707,
0.005729793570935726,
-0.00003468997965683229,
-0.04261576011776924,
-0.03674047812819481,
-0.017491409555077553,
0.027226172387599945,
-0.05828874185681343,
-0.03674212470650673,
-0.07176516950130463,
-0.04363301023840904,
0.011518283747136593,
0.017891380935907364,
-0.026586849242448807,
0.027365392073988914,
0.022022932767868042,
-0.07255631685256958,
-0.0013597229262813926,
0.04423940181732178,
0.03787790983915329,
0.022102104499936104,
0.01716214045882225,
0.03666677698493004,
-0.043576400727033615,
-0.03749433532357216,
0.005187245551496744,
0.055575720965862274,
-0.00861622579395771,
0.00891922041773796,
-0.0018707744311541319,
0.04463125020265579,
-0.05872853845357895,
0.03550306335091591,
0.02620420977473259,
-0.0033736734185367823,
0.027568258345127106,
0.025824032723903656,
0.012558872811496258,
0.007855097763240337,
0.017570771276950836,
0.01815277896821499,
-0.054056912660598755,
0.05062015727162361,
0.027707315981388092,
-0.0027182879857718945,
-0.017999639734625816,
0.03942739591002464,
0.02129129320383072,
0.10438116639852524,
0.013169663958251476,
0.06998906284570694,
-0.020532019436359406,
0.0011435406049713492,
-0.030859239399433136,
-0.0019344583852216601,
0.05251070111989975,
-0.028825437650084496,
-0.00920845940709114,
-0.03615965694189072,
0.012868840247392654,
0.05244869738817215,
0.03210587427020073,
-0.016690390184521675,
0.004830738063901663,
-0.03020414710044861,
-0.06208508834242821,
-0.023456167429685593,
0.005296015180647373,
0.024729300290346146,
0.07420194149017334,
-0.03632674366235733,
0.03137463703751564,
0.024604033678770065,
-0.024218307808041573,
0.023564990609884262,
-0.01734003610908985,
0.02553032897412777,
0.021433405578136444,
-0.04134174808859825,
0.016954416409134865,
-0.03587917983531952,
-0.014851806685328484,
0.007082607131451368,
0.0381406731903553,
-0.04874950274825096,
-0.014094804413616657,
-0.02431471459567547,
-0.0547097884118557,
0.0248278696089983,
-0.017316104844212532,
-0.006626556161791086,
-0.03923124447464943,
-0.004342347849160433,
-0.0034406178165227175,
-0.036796506494283676,
0.04771563410758972,
0.025035535916686058,
-0.06977469474077225,
-0.10108058154582977,
-0.028319941833615303,
-0.060102008283138275,
0.012302919290959835,
-0.02587706409394741,
-0.013021750375628471,
0.05181194841861725,
0.07242892682552338,
-0.010396668687462807,
0.05059992894530296,
0.005772205535322428,
0.017064448446035385,
0.020970074459910393,
0.009169808588922024,
0.011947290040552616,
-0.02711094729602337,
-0.058401841670274734,
-0.009778912179172039,
-0.007386506535112858,
-0.013365322723984718,
-0.02043844200670719,
0.06288297474384308,
-0.049830950796604156,
-0.01812458597123623,
-0.020336652174592018,
-0.04241074249148369,
0.036710210144519806
] |
<p>I am taking a short introduction course on lasers. I never knew that the frequency of a laser is so high for a given wavelength (e.g. 780nm). I am wondering how people can measure the frequency of the laser. Do they downconvert the frequency of the light so that we could measure it with scope?</p> | g5520 | [
0.010617369785904884,
-0.03104979731142521,
0.02808549255132675,
-0.07871552556753159,
0.022892296314239502,
-0.012478823773562908,
-0.028446320444345474,
0.04337639734148979,
0.01414362620562315,
-0.01790536940097809,
0.005244669504463673,
-0.0032172605860978365,
0.04388512298464775,
0.006233551539480686,
0.012531937099993229,
-0.004369018599390984,
0.02206983044743538,
0.028541121631860733,
0.018083427101373672,
0.0133843207731843,
0.015840137377381325,
0.009094566106796265,
-0.059506502002477646,
-0.06636309623718262,
-0.05678562447428703,
-0.014996535144746304,
0.07072269916534424,
0.0009330422035418451,
0.01648593880236149,
0.007489548530429602,
-0.009411616250872612,
-0.026916569098830223,
0.04208485782146454,
0.003872520523145795,
0.03591085597872734,
-0.011949014849960804,
-0.004688534885644913,
0.01269674114882946,
0.014874614775180817,
0.06905444711446762,
-0.01315363496541977,
-0.02123650163412094,
-0.029006188735365868,
0.006838628556579351,
0.02029511332511902,
-0.04758436977863312,
0.0060548628680408,
-0.0667913407087326,
0.018330544233322144,
0.008025560528039932,
0.030605968087911606,
-0.015415465459227562,
-0.008338437415659428,
0.010713549330830574,
0.03717881441116333,
0.019588414579629898,
-0.03468741476535797,
0.05804385989904404,
0.09222065657377243,
0.010046682320535183,
0.02917458303272724,
-0.04674384370446205,
0.0404994934797287,
0.0548730306327343,
0.0026105735450983047,
-0.03427676483988762,
0.004833949264138937,
-0.019213099032640457,
-0.003142099129036069,
0.025857476517558098,
-0.013399472460150719,
-0.06857918947935104,
-0.0024643114302307367,
0.02971903420984745,
-0.055902499705553055,
0.016452832147479057,
0.09187614917755127,
-0.01784169115126133,
-0.02805544063448906,
0.010211252607405186,
-0.02445247210562229,
0.003879537107422948,
0.003482694970443845,
0.025807740166783333,
0.007004039362072945,
-0.0400485098361969,
-0.05355239659547806,
0.022625194862484932,
0.004239921923726797,
0.030143186450004578,
0.05675146356225014,
0.06291697174310684,
0.09522926807403564,
0.018411409109830856,
0.01813247799873352,
-0.025203000754117966,
-0.023583827540278435,
0.03223198279738426,
-0.022062864154577255,
-0.0036387729924172163,
-0.011575152166187763,
0.002323102205991745,
0.014952699653804302,
0.022186774760484695,
-0.04315802827477455,
0.015889212489128113,
0.050108492374420166,
-0.03455546498298645,
0.011395083740353584,
0.004625080153346062,
-0.005246136337518692,
-0.031348105520009995,
-0.09893199056386948,
-0.019616594538092613,
-0.02951877750456333,
0.023222435265779495,
0.05981935188174248,
0.07350613921880722,
0.0055912756361067295,
0.04152239114046097,
0.0444549135863781,
-0.004133280366659164,
0.016295159235596657,
0.014984222128987312,
-0.010814415290951729,
0.02190101332962513,
0.020227551460266113,
-0.01049581728875637,
-0.00917106494307518,
0.022766822949051857,
-0.04941551387310028,
0.038737449795007706,
-0.028331561014056206,
0.012650972232222557,
-0.009859100915491581,
0.057537030428647995,
0.007673950865864754,
-0.0103843342512846,
0.0023805557284504175,
0.05924328416585922,
-0.0007998768705874681,
-0.03006545454263687,
0.04217880219221115,
0.013398442417383194,
0.03606938570737839,
0.018544940277934074,
-0.032443881034851074,
0.007420697249472141,
0.01397167518734932,
0.030557161197066307,
0.029370253905653954,
0.04925483092665672,
0.07133124768733978,
-0.04339537397027016,
0.010833850130438805,
-0.02677847258746624,
-0.028046075254678726,
-0.007980680093169212,
-0.005337741691619158,
0.04505131021142006,
-0.010544199496507645,
-0.045066289603710175,
-0.043988898396492004,
0.02538433112204075,
-0.03253098577260971,
0.029772741720080376,
-0.021517757326364517,
-0.009527269750833511,
-0.009638551622629166,
-0.016988128423690796,
-0.03944158926606178,
0.011013041250407696,
-0.05172039568424225,
-0.03717014193534851,
0.05562540143728256,
0.07632317394018173,
0.01216604933142662,
0.012462124228477478,
0.02126084826886654,
0.011123286560177803,
-0.0025914355646818876,
0.03087584860622883,
0.02948930487036705,
-0.04414123296737671,
0.05775603652000427,
-0.014875443652272224,
0.026438916102051735,
-0.11285688728094101,
0.020916635170578957,
0.043124008923769,
-0.03206152841448784,
-0.006059738807380199,
0.015224942937493324,
-0.04728347808122635,
0.020401280373334885,
-0.04192788526415825,
-0.036712270230054855,
-0.0016363325994461775,
0.013813050463795662,
0.010416286997497082,
-0.03618089482188225,
-0.03480616956949234,
0.042358770966529846,
0.02445306070148945,
0.01269129291176796,
0.00878644734621048,
-0.017749899998307228,
0.019271494820713997,
-0.040156442672014236,
-0.0022805230692029,
-0.024957407265901566,
0.02573615312576294,
-0.003636770648881793,
0.0018397432286292315,
0.0147028099745512,
0.06438425183296204,
-0.06462196260690689,
0.006953130476176739,
-0.0029214562382549047,
-0.004039248451590538,
0.005084014497697353,
-0.029993858188390732,
0.08479859679937363,
0.027076277881860733,
-0.016152381896972656,
0.0703316330909729,
-0.061182547360658646,
0.029805172234773636,
0.005831755232065916,
0.0042007979936897755,
0.02537534572184086,
-0.00424431124702096,
-0.057488832622766495,
-0.04626430571079254,
-0.004260627087205648,
0.016387486830353737,
-0.005247199907898903,
0.037083521485328674,
0.001208157860673964,
0.0008408028515987098,
0.0050127687864005566,
-0.06296596676111221,
0.01200887095183134,
-0.03243989124894142,
-0.030434494838118553,
-0.06004990264773369,
-0.03586437553167343,
0.0433199480175972,
-0.037272416055202484,
-0.02294662781059742,
-0.016259459778666496,
-0.03297697380185127,
0.0034860773012042046,
-0.03730503469705582,
-0.02793499268591404,
-0.013581997714936733,
-0.010726172477006912,
0.05647648870944977,
-0.07647895812988281,
-0.059687163680791855,
0.020967794582247734,
0.014297163113951683,
0.011461909860372543,
-0.033087365329265594,
0.011009805835783482,
-0.055996332317590714,
-0.037429727613925934,
-0.0003376695094630122,
0.019308168441057205,
0.023095134645700455,
-0.0027441484853625298,
0.017326906323432922,
0.01815059408545494,
-0.061365481466054916,
-0.006922661792486906,
-0.06045152619481087,
-0.025641608983278275,
-0.05451037362217903,
0.04522009193897247,
-0.04413161054253578,
-0.013462681323289871,
0.039991918951272964,
-0.07023025304079056,
-0.04565449431538582,
0.03425918519496918,
-0.0490332655608654,
0.01585994102060795,
-0.0574740469455719,
0.027295013889670372,
-0.030206508934497833,
-0.01592857390642166,
-0.01535077579319477,
-0.03147619217634201,
-0.011319288052618504,
-0.032662294805049896,
0.01553383655846119,
0.11187554150819778,
-0.007369064260274172,
0.0339982844889164,
0.017964661121368408,
-0.0061976914294064045,
-0.01973152533173561,
0.007104819640517235,
-0.014169543981552124,
0.04675225540995598,
0.013141325674951077,
0.003941011149436235,
0.030105311423540115,
-0.029974164441227913,
0.02520756609737873,
-0.032257284969091415,
0.019429555162787437,
-0.009690879844129086,
-0.046376727521419525,
-0.018944034352898598,
0.019108667969703674,
0.011313612572848797,
-0.02495282143354416,
0.024473698809742928,
0.019648654386401176,
-0.05707922205328941,
-0.0457272082567215,
-0.00699517410248518,
-0.06099031865596771,
0.021253734827041626,
0.0030006440356373787,
0.06013015657663345,
-0.011347158811986446,
-0.02851082943379879,
-0.008277345448732376,
0.04575420543551445,
-0.026203665882349014,
-0.09177663177251816,
0.02670317329466343,
0.05390673130750656,
-0.010153518989682198,
-0.05176663398742676,
0.004618076141923666,
0.05221635848283768,
0.00185599725227803,
-0.02043028734624386,
0.001869133673608303,
-0.07334551215171814,
-0.042342398315668106,
0.018784454092383385,
0.029419517144560814,
-0.03298572823405266,
0.027509400621056557,
0.0026809093542397022,
-0.05010000616312027,
-0.019518056884407997,
-0.029195088893175125,
0.042732805013656616,
-0.06962292641401291,
0.001171580166555941,
0.040338482707738876,
0.03012298233807087,
0.04743684455752373,
-0.020065471529960632,
-0.0311281718313694,
0.0017017524223774672,
0.019243022426962852,
0.018679117783904076,
-0.05764269456267357,
-0.027583977207541466,
-0.047623615711927414,
0.016836650669574738,
0.0261217188090086,
0.004707532934844494,
0.04061508551239967,
-0.028506634756922722,
-0.05035632103681564,
0.02699812315404415,
0.028071247041225433,
-0.041329048573970795,
-0.03032330609858036,
0.054746583104133606,
0.014257867820560932,
-0.006417527794837952,
0.009430907666683197,
-0.009600388817489147,
0.03605895861983299,
0.0718502327799797,
-0.09018156677484512,
0.018366917967796326,
-0.01582910120487213,
-0.01104036159813404,
-0.024911794811487198,
0.028309950605034828,
-0.016250981017947197,
-0.007890433073043823,
-0.0768599882721901,
-0.02612345479428768,
-0.03378322347998619,
0.0038413184229284525,
-0.05948381870985031,
0.04763326048851013,
0.008618654683232307,
-0.005657735746353865,
0.0006461729062721133,
0.01750713773071766,
0.00648657837882638,
0.02979397214949131,
-0.0177824217826128,
-0.030944380909204483,
0.012226911261677742,
0.037290941923856735,
-0.02732362039387226,
-0.035563837736845016,
0.05816168338060379,
-0.000985348829999566,
-0.01153448224067688,
0.04770207405090332,
-0.027895808219909668,
-0.022179407998919487,
0.049453239887952805,
0.07609008252620697,
-0.00010538796050241217,
0.027521392330527306,
0.030286841094493866,
0.0003905160410795361,
0.014024623669683933,
-0.026581155136227608,
0.02571599744260311,
0.018918907269835472,
0.07316815853118896,
0.036709677428007126,
0.01729721389710903,
0.051267705857753754,
-0.00375157012604177,
0.051171328872442245,
-0.05796664580702782,
-0.009964014403522015,
0.014997996389865875,
0.05473237857222557,
-0.013370616361498833,
0.06156312674283981,
-0.0017027683788910508,
-0.00859773252159357,
0.07016720622777939,
0.0008358905324712396,
-0.008973635733127594,
-0.0634235069155693,
-0.00013748528726864606,
-0.05047205835580826,
0.0021275202743709087,
-0.054548509418964386,
0.0003294468915555626,
-0.05298918858170509,
-0.030099425464868546,
-0.031806159764528275,
0.02863086387515068,
-0.07221296429634094,
-0.045441094785928726,
-0.03222549706697464,
0.008067321963608265,
0.009607690386474133,
0.0006246161065064371,
0.022252269089221954,
0.027244040742516518,
-0.048735979944467545,
-0.005617685616016388,
-0.021156948059797287,
-0.03749735653400421,
0.03130403533577919,
-0.01001647301018238,
-0.023731011897325516,
-0.02692323364317417,
-0.01278152596205473,
-0.035859715193510056,
0.03950249403715134,
-0.06933905929327011,
0.05627109110355377,
-0.0033414573408663273,
-0.0012712801108136773,
0.005539464298635721,
0.02662982977926731,
-0.011751320213079453,
0.0029403374064713717,
-0.05890073627233505,
-0.015747645869851112,
0.03285359963774681,
0.048396844416856766,
-0.046044547110795975,
-0.04997630789875984,
0.0024346690624952316,
-0.03982604667544365,
0.008931523188948631,
-0.024696385487914085,
-0.02346678450703621,
-0.053597550839185715,
0.028430018573999405,
-0.002302025444805622,
0.03424292057752609,
-0.08420327305793762,
-0.009120447561144829,
0.02463306300342083,
-0.03775542601943016,
0.04634162038564682,
-0.04327329993247986,
-0.010137726552784443,
0.036445122212171555,
-0.048139337450265884,
-0.0032974376808851957,
-0.05719299986958504,
0.04277839884161949,
0.01962878927588463,
-0.034552548080682755,
-0.030778339132666588,
0.06120579317212105,
0.025461256504058838,
-0.0002656051074154675,
-0.011011524125933647,
0.0600384846329689,
0.06802303344011307,
-0.07581586390733719,
0.002501439768821001,
0.04907987639307976,
-0.008624552749097347,
0.01623515784740448,
-0.06158699095249176,
-0.010259335860610008,
0.05855786055326462,
-0.0019708285108208656,
-0.013188401237130165,
0.02601633034646511,
-0.052798740565776825,
0.020360389724373817,
-0.025763796642422676,
-0.06137602776288986,
-0.027301182970404625,
-0.0011117653921246529,
0.0023085512220859528,
-0.08454292267560959,
-0.019206665456295013,
0.05272082984447479,
0.004270667210221291,
-0.007362006232142448,
-0.039371658116579056,
-0.009559511207044125,
0.03723306581377983,
0.04276031255722046,
0.03107808530330658,
-0.001579458941705525,
-0.004389557056128979,
-0.011800834909081459,
-0.026539629325270653,
-0.0005681353504769504,
-0.011850654147565365,
0.0419701524078846,
0.012106978334486485,
-0.031792208552360535,
-0.017808496952056885,
-0.04753832146525383,
-0.007935702800750732,
-0.02149808406829834,
0.02768266759812832,
0.007439666893333197,
-0.013172783888876438,
-0.04874150827527046,
0.06272435933351517,
0.049448344856500626,
0.005245559383183718,
-0.010709966532886028,
-0.00689979363232851,
-0.04494782164692879,
0.010975317098200321,
-0.003779877442866564,
0.06976738572120667,
0.03182480111718178,
-0.08439767360687256,
-0.013427162542939186,
-0.011938990093767643,
-0.03183963894844055,
0.10023285448551178,
0.028525695204734802,
0.030372126027941704,
-0.03844095766544342,
0.030763808637857437,
-0.050391148775815964,
0.0013372726971283555,
-0.01606815494596958,
0.025845922529697418,
-0.00009671713632997125,
-0.012238304130733013,
-0.0015631949063390493,
0.04814206808805466,
0.01752980798482895,
-0.013035446405410767,
0.005489691160619259,
-0.029651841148734093,
0.034680385142564774,
-0.007562904618680477,
0.04754212871193886,
-0.02565154619514942,
-0.07871352881193161,
0.026201624423265457,
0.031407665461301804,
0.03995349258184433,
0.004493956454098225,
-0.007291748188436031,
0.01365038100630045,
0.02217767760157585,
0.022320697084069252,
0.02541167102754116,
0.05430353432893753,
0.025840474292635918,
-0.020960092544555664,
0.05164919048547745,
-0.03755120560526848,
-0.03214466571807861,
0.038562607020139694,
0.06001818925142288,
0.06078976392745972,
-0.005641758907586336,
-0.013481021858751774,
0.059364717453718185,
-0.0311626847833395,
0.010072548873722553,
0.04268316179513931,
0.03568395599722862,
-0.07548446208238602,
-0.0001941891387104988,
-0.010399052873253822,
-0.03394511714577675,
0.06516937166452408,
0.009471097029745579,
-0.02323748543858528,
0.033075347542762756,
-0.017075875774025917,
-0.002486314158886671,
0.007600240409374237,
0.0051677897572517395,
-0.0314730741083622,
-0.01149890385568142,
0.02778896689414978,
-0.0677172839641571,
0.050500623881816864,
0.03571127727627754,
0.04714714363217354,
0.04506705701351166,
0.003872908418998122,
-0.02411871962249279,
-0.004372608847916126,
0.006144050974398851,
0.003363099182024598,
0.018740924075245857,
-0.00794663280248642,
-0.004655640572309494,
-0.003254428505897522,
-0.00949503481388092,
-0.03669024631381035,
-0.0620969794690609,
0.0005730090197175741,
0.009937983937561512,
0.10833212733268738,
0.06543491035699844,
0.039527490735054016,
-0.021513639017939568,
-0.06330497562885284,
-0.01526838168501854,
-0.015608588233590126,
-0.0008961447747424245,
-0.04522627964615822,
-0.04588893800973892,
-0.009546026587486267,
0.022698942571878433,
0.0009011995862238109,
-0.07284316420555115,
-0.05376950278878212,
-0.026387909427285194,
-0.05657122656702995,
-0.014851128682494164,
-0.021195154637098312,
-0.037613674998283386,
-0.01692182756960392,
-0.0765916258096695,
0.10574236512184143,
-0.008243253454566002,
-0.036189742386341095,
-0.05040329694747925,
0.060011815279722214,
0.02249288558959961,
0.0020660622976720333,
-0.01947643607854843,
0.01629900000989437,
-0.0379774384200573,
0.007110876031219959,
0.08282343298196793,
-0.06248711794614792,
-0.034274548292160034,
0.005978559609502554,
0.02664605714380741,
-0.08965131640434265,
0.02740391530096531,
-0.04399338737130165,
0.0368027500808239,
0.015061753802001476,
-0.01922179013490677,
-0.0466543510556221,
0.027471870183944702,
-0.00736322021111846,
0.004506629426032305,
0.021499602124094963,
0.016700996086001396,
0.04289441555738449,
-0.020087340846657753,
-0.0336703322827816,
0.008148272521793842,
-0.022096795961260796,
-0.0373045951128006,
0.03874564543366432,
-0.007659699767827988,
0.027343427762389183,
0.060533151030540466,
0.012577444314956665,
-0.007570710964500904,
-0.02374362386763096,
-0.07562953978776932,
-0.03890833631157875,
0.013871676288545132,
-0.0015307291178032756,
0.08009805530309677,
-0.03941960632801056,
0.02961292304098606,
-0.01030390989035368,
0.027165276929736137,
0.04419790208339691,
0.026038462296128273,
0.013986188918352127,
0.02388044260442257,
0.040649816393852234,
-0.013484526425600052,
0.01293664425611496,
0.0027338878717273474,
0.012392653152346611,
0.008157954551279545,
0.047997668385505676,
-0.022207774221897125,
0.07024043798446655,
0.035782329738140106,
0.0464976541697979,
-0.019785119220614433,
0.016272224485874176,
0.008941429667174816,
-0.0032126742880791426,
-0.02519242838025093,
0.03811631724238396,
0.012021563947200775,
-0.04935452342033386,
0.009677020832896233,
0.04868200793862343,
-0.009654439054429531,
0.022633865475654602,
0.022484248504042625,
-0.03259449079632759,
0.009871243499219418,
0.03572743013501167,
0.026705525815486908,
-0.06351619213819504,
0.026296624913811684,
0.0509166494011879,
0.004660244565457106,
0.07651938498020172,
-0.019967054948210716,
-0.031877074390649796,
-0.05066138505935669,
-0.0023553858045488596
] |
<p>A good buddy of mine and I have had a friendly debate about the origins of the current state of our universe (namely; Earth and life on Earth) and have fundamentally disagreed in our stances with respect to probabability, infinity in time and space and possible/probable event outcomes. He maintains the position that given a set of possibilities and enough trials, each outcome <em>must</em> have occured; which is his reasoning for why life must exist. I do not necessarily take issue with this particular concept, as given an infinite amount of time and states of matter life is bound to come from one of those states. In our discussions, however, we have been using a specific example in which I disagree vehemently with his stance. The example:</p>
<blockquote>
<p>If you throw a handfull of sand in the air an infinite number of
times, and that sand lands on a flat surface, every
configuration <em>will</em> happen (according to his position). For instance,
the sand landing in a pattern which spells your name out is a
mathematically possible outcome, and will therefore happen given
enough trials.</p>
</blockquote>
<p>To counter his stance on this example, I took the position that there is a mathematical (but not physical) possibility that every grain of sand lands in the same one inch square of the surface; but I maintain that even though it is a mathematically possible outcome it will never happen because of the way the physical world works - that sand will be roughly evenly distributed for each throw, even if over an infinite number of trials, assuming consistent and fair trials (ie, no God or other being moving grains of sand). I submit that even though it is a mathematical possibility, you'll never see your name spelled out in block letter English anywhere in the universe without the influence of intelligence, even if you were able to attempt a verification for this - he disagrees. I held him liable for mathematical/physical proof of reasoning for his stance and he has taken to dismissing me as ignorant of probability and infinity. Can anyone provide some good reasoning for either side of this argument? I realize that either is an impossible stance to prove, since we can't verify our positions, but any well-reasoned insight will be appreciated. A similar question, with an answer I found to be relatively useful:</p>
<p><a href="http://physics.stackexchange.com/questions/22187/infinite-universe-jumping-to-pointless-conclusions">Infinite universe - Jumping to pointless conclusions</a></p>
<p><strong>EDIT:</strong></p>
<p>After reading some of the comments and answers here it has become apparent that I may have misrepresented my ultimate question. I realize that given a non-zero probability and an infinite number of trials, the mathematical probability of encountering the event described by said probability converges to 1. Some have taken the position that there is no disconnect between a mathematical probability and the likelihood (read: possibility) of a physical event happening.</p>
<p>To simplify the argument, the surface can be thought of as a grid - in which case every single configuration has some mathematical probability associated with it. My stance regards certain configurations as physically impossible, however, which is the reasoning behind my one-inch-square analogy. Can anyone show clear reasoning (and sources!) for their belief that it is possible to toss a handful of sand into a one inch square?</p> | g5521 | [
0.05532512068748474,
0.035232461988925934,
0.016966961324214935,
-0.04389918968081474,
0.01651744358241558,
0.05760571360588074,
0.03634105995297432,
-0.0035649517085403204,
-0.0034283797722309828,
-0.029879264533519745,
0.042736705392599106,
-0.05548395588994026,
0.011274448595941067,
0.05097486451268196,
-0.005989613477140665,
0.02120235562324524,
0.08227250725030899,
-0.006944706663489342,
0.005273140966892242,
-0.008296648971736431,
0.01442969124764204,
-0.007530245464295149,
0.006855661515146494,
-0.004239228088408709,
-0.10552618652582169,
-0.08028529584407806,
0.025882450863718987,
-0.024253061041235924,
0.017905671149492264,
-0.03722819685935974,
0.029731716960668564,
-0.024153701961040497,
0.00705573707818985,
-0.048789508640766144,
-0.06751765310764313,
-0.012727972120046616,
-0.02008957229554653,
-0.014675802551209927,
0.02752743661403656,
-0.01453535258769989,
-0.03421257808804512,
-0.004018246196210384,
0.02594749629497528,
0.01912613771855831,
-0.049661606550216675,
0.07524409890174866,
0.010254970751702785,
0.03880976140499115,
0.0534670352935791,
-0.04385139420628548,
-0.05747578665614128,
-0.005971717648208141,
0.07257498800754547,
0.03243306651711464,
0.0034160278737545013,
0.06193084269762039,
0.0408383309841156,
0.003458005143329501,
0.00653491448611021,
0.04989970475435257,
0.01191698294132948,
-0.018822798505425453,
-0.04389183595776558,
-0.015873514115810394,
0.04246065765619278,
-0.004638011567294598,
-0.08018221706151962,
0.03212383762001991,
0.014455260708928108,
-0.0016941900830715895,
0.041700579226017,
-0.08156858384609222,
-0.04511459171772003,
-0.04157790169119835,
-0.018605666235089302,
0.08256074041128159,
0.012233657762408257,
0.04194639250636101,
0.02353942021727562,
0.06057652086019516,
-0.01820012554526329,
0.01577123813331127,
0.03181483596563339,
-0.033752791583538055,
0.023725418373942375,
-0.04676162078976631,
0.008855219930410385,
-0.004240106791257858,
-0.0511166974902153,
0.003550759283825755,
-0.0004350742092356086,
0.026115048676729202,
-0.006568508688360453,
-0.005438259802758694,
-0.07125947624444962,
0.003733287565410137,
-0.033729881048202515,
0.0475890077650547,
0.0021762975957244635,
0.05996916443109512,
-0.03280572593212128,
-0.005831641610711813,
0.016324235126376152,
-0.0008096293895505369,
-0.013602817431092262,
-0.016539858654141426,
-0.02997305616736412,
0.05056300759315491,
-0.013344037346541882,
0.003621908836066723,
-0.04219202697277069,
0.0034182535018771887,
-0.06707437336444855,
-0.029406988993287086,
-0.011546118184924126,
-0.020549634471535683,
0.07024257630109787,
0.06816530972719193,
-0.003966345451772213,
0.047160156071186066,
-0.029606986790895462,
0.03931334614753723,
0.0245756134390831,
0.011277126148343086,
-0.0616462305188179,
0.00032256654230877757,
-0.016601640731096268,
-0.00258028507232666,
0.012427045032382011,
-0.02239832654595375,
-0.010862953029572964,
0.0265536867082119,
0.01660626009106636,
0.019832121208310127,
-0.09290152043104172,
-0.036798447370529175,
0.009874776937067509,
-0.06128538399934769,
0.0010237814858555794,
0.0013371191453188658,
-0.028805429115891457,
-0.019020840525627136,
0.003982160706073046,
0.0018166882218793035,
-0.002142028184607625,
0.03799336403608322,
0.00019087240798398852,
-0.008370363153517246,
-0.011368351057171822,
0.013225172646343708,
-0.029040906578302383,
0.06457099318504333,
0.004300084430724382,
-0.007784979417920113,
-0.007028956897556782,
-0.00375697435811162,
-0.017766715958714485,
0.04166385903954506,
0.0019419228192418814,
0.020320910960435867,
0.07275880873203278,
0.027548320591449738,
-0.04216425493359566,
-0.024058306589722633,
-0.05067451670765877,
0.0025069755502045155,
-0.023751460015773773,
-0.03159060329198837,
-0.022397739812731743,
-0.009885353967547417,
-0.03630738705396652,
-0.07302144169807434,
0.03802739828824997,
0.011833400465548038,
-0.016047604382038116,
0.029673580080270767,
0.021939201280474663,
-0.034144751727581024,
-0.008941005915403366,
-0.011600389145314693,
-0.013455742038786411,
-0.007044936530292034,
0.020863976329565048,
0.05195288732647896,
0.04300108179450035,
-0.01543900091201067,
0.06536063551902771,
0.0465172715485096,
0.014658442698419094,
-0.004250889644026756,
-0.06491144746541977,
-0.0756116658449173,
-0.020349673926830292,
0.009209631942212582,
0.051557593047618866,
-0.005358499009162188,
0.0677189826965332,
0.027445301413536072,
-0.0483277253806591,
-0.011180606670677662,
0.02790677547454834,
0.09628471732139587,
-0.01148449257016182,
0.036113642156124115,
-0.023305632174015045,
-0.005673040170222521,
0.03910163789987564,
0.005436246283352375,
-0.0539771132171154,
-0.00351788685657084,
0.05264612287282944,
-0.061327047646045685,
-0.02573232911527157,
0.04921768978238106,
0.02115773782134056,
0.015430785715579987,
-0.006655651610344648,
0.008361529558897018,
-0.024670744314789772,
-0.018631964921951294,
0.029077155515551567,
-0.06581291556358337,
0.04365319386124611,
0.00030117895221337676,
0.030469665303826332,
0.04114272817969322,
-0.034627802670001984,
-0.06603886932134628,
0.02129785344004631,
0.06973893195390701,
-0.030190737918019295,
-0.028530873358249664,
0.027955755591392517,
-0.05144420266151428,
0.014295907691121101,
0.0682111382484436,
-0.006761268712580204,
0.004991603549569845,
-0.02978779561817646,
-0.01967809535562992,
0.012568005360662937,
-0.01115230843424797,
-0.08362475782632828,
0.008134223520755768,
0.06052026525139809,
-0.06722113490104675,
-0.003402777947485447,
-0.03701050579547882,
0.02575875073671341,
0.08012627065181732,
0.005798362195491791,
-0.04049667716026306,
-0.021874144673347473,
0.008164437487721443,
0.027337927371263504,
-0.026528576388955116,
0.024306489154696465,
0.025354094803333282,
-0.03299972787499428,
0.03867070749402046,
-0.0018209858098998666,
-0.06184344366192818,
0.018411623314023018,
0.05212157964706421,
-0.07091384381055832,
-0.007335145957767963,
-0.06974644958972931,
0.019721955060958862,
-0.05990530923008919,
0.0073448484763503075,
0.015079963020980358,
-0.042003922164440155,
0.029839560389518738,
0.06970132887363434,
-0.010342545807361603,
0.03710990771651268,
-0.02964029647409916,
-0.01336605940014124,
0.06376373022794724,
0.0157209150493145,
-0.00021303488756529987,
0.020674634724855423,
-0.03365013003349304,
0.027100469917058945,
0.019100626930594444,
0.020227733999490738,
0.03992217779159546,
0.022640150040388107,
-0.04663626849651337,
0.04730984568595886,
-0.023279108107089996,
0.018965788185596466,
0.06547210365533829,
-0.003121396526694298,
-0.04870826378464699,
0.0794089064002037,
-0.04021831229329109,
-0.03712676092982292,
-0.0004384220519568771,
-0.009216268546879292,
-0.03335055708885193,
-0.005721570458263159,
-0.009115648455917835,
-0.023335155099630356,
0.01938759535551071,
0.058209728449583054,
-0.02152324467897415,
-0.016041768714785576,
0.047851189970970154,
-0.08599940687417984,
0.02275659143924713,
0.05450727418065071,
-0.033146582543849945,
-0.00793409626930952,
0.00026160472771152854,
0.03522112965583801,
-0.006461688783019781,
0.025123853236436844,
0.022516433149576187,
-0.006811138242483139,
-0.018956579267978668,
0.03878295421600342,
-0.015093419700860977,
-0.0015393212670460343,
0.028363877907395363,
0.024313870817422867,
-0.07494434714317322,
0.007551749236881733,
-0.031749218702316284,
0.018321774899959564,
-0.019553866237401962,
0.005807695910334587,
0.008617359213531017,
-0.013065200299024582,
-0.05875634029507637,
-0.0642751082777977,
-0.0055518001317977905,
0.0033416105434298515,
0.03425931930541992,
0.051999349147081375,
0.015982337296009064,
0.0298374742269516,
0.01856325753033161,
0.006295706611126661,
0.037411510944366455,
0.027512095868587494,
0.03488374501466751,
-0.013834025710821152,
-0.012828336097300053,
0.006268613506108522,
0.08192671090364456,
-0.02750992402434349,
0.0029245733749121428,
0.01608801819384098,
0.038719214498996735,
0.08561267703771591,
0.0012272035237401724,
0.049959201365709305,
0.02489514835178852,
-0.029248369857668877,
-0.022897934541106224,
-0.011065105907619,
0.03445364907383919,
-0.04427729547023773,
0.03843967989087105,
0.04350244998931885,
0.008774537593126297,
0.007074589841067791,
-0.014392671175301075,
0.00017483664851170033,
0.0352620892226696,
-0.058448586612939835,
-0.012565846554934978,
0.00725847901776433,
0.04957504943013191,
0.013089331798255444,
0.00973730068653822,
-0.0019426889484748244,
0.009458464570343494,
0.02956172451376915,
0.06151150166988373,
0.04443567991256714,
0.03425941616296768,
-0.005935331806540489,
-0.011987805366516113,
0.01787567511200905,
0.014065553434193134,
0.0023030440788716078,
-0.02229681983590126,
-0.027864543721079826,
0.02693988010287285,
-0.029583869501948357,
-0.03660818561911583,
-0.056079886853694916,
-0.02387799695134163,
0.000895075558219105,
-0.04536379873752594,
-0.04481876268982887,
-0.007005786523222923,
0.002380221616476774,
0.07746465504169464,
-0.002924732631072402,
-0.04129386693239212,
-0.017888780683279037,
-0.009992373175919056,
0.001362460432574153,
0.028564080595970154,
-0.041257601231336594,
-0.00724148890003562,
-0.05521122366189957,
0.07863415032625198,
0.06405603885650635,
-0.009845114313066006,
-0.03789038583636284,
0.03563506156206131,
0.017148315906524658,
-0.0247393436729908,
-0.004493475425988436,
0.032657116651535034,
0.001769464579410851,
0.007700461894273758,
0.0821138247847557,
-0.05945887789130211,
0.0033553987741470337,
0.03323326259851456,
0.008333355188369751,
0.017898693680763245,
-0.0023384029045701027,
0.0024301770608872175,
0.0494484007358551,
0.00032596109667792916,
0.045523568987846375,
-0.0029143032152205706,
0.06148868426680565,
-0.04391695559024811,
0.0013204367132857442,
-0.027581287547945976,
0.053728967905044556,
0.035066284239292145,
0.008632030338048935,
0.031887780874967575,
-0.017641598358750343,
0.0017367227701470256,
-0.02368735894560814,
0.02091773971915245,
0.049098312854766846,
-0.002612716518342495,
-0.04808804765343666,
0.017886854708194733,
0.03192511945962906,
-0.005031269509345293,
-0.024992357939481735,
0.004541787784546614,
-0.04282271862030029,
-0.03194715827703476,
-0.05440295860171318,
-0.0712677389383316,
0.03138117119669914,
-0.005411389749497175,
-0.008448547683656216,
0.02932131476700306,
0.0011206564959138632,
0.020570574328303337,
0.08565562218427658,
0.017654573544859886,
0.02123272977769375,
-0.03416281193494797,
-0.012621182017028332,
-0.007104194723069668,
-0.012863739393651485,
-0.037280451506376266,
0.03681723028421402,
0.04325117915868759,
0.035804327577352524,
-0.07100826501846313,
0.01588504947721958,
0.00918365828692913,
-0.0747387632727623,
-0.03447763994336128,
-0.012349043041467667,
-0.03432110697031021,
-0.0042619965970516205,
-0.027441661804914474,
0.03300120681524277,
-0.008958232589066029,
0.029409242793917656,
-0.0008759929914958775,
-0.04878411814570427,
0.024319279938936234,
-0.0012066866038367152,
0.04362219572067261,
-0.06492441892623901,
0.01215969305485487,
-0.010923067107796669,
-0.05790402740240097,
-0.0338483490049839,
-0.028212398290634155,
-0.025059012696146965,
-0.04091653600335121,
0.024533214047551155,
-0.019204845651984215,
-0.009160974062979221,
0.05368353798985481,
0.024447673931717873,
-0.0012767179869115353,
-0.011054795235395432,
0.004685687832534313,
0.0014075369108468294,
0.0005865973653271794,
0.026720978319644928,
0.005175518803298473,
0.010971231386065483,
-0.02548370510339737,
0.010677425190806389,
0.023121299222111702,
-0.02558492310345173,
-0.007077694404870272,
-0.059525348246097565,
0.03297460824251175,
0.00741556566208601,
0.00798291526734829,
0.007920426316559315,
-0.007975664921104908,
-0.062452856451272964,
-0.011559441685676575,
-0.030328383669257164,
-0.03994182497262955,
-0.0346689336001873,
-0.026264512911438942,
0.020923610776662827,
0.02764144353568554,
0.07103928178548813,
-0.012105247937142849,
-0.04491302743554115,
-0.07469671219587326,
-0.024882860481739044,
0.006796820089221001,
-0.006907965522259474,
0.051052700728178024,
-0.03717711567878723,
-0.00017634309187997133,
-0.011434877291321754,
0.0022464366629719734,
0.05220881476998329,
-0.030848581343889236,
0.028637582436203957,
-0.07258977741003036,
0.02634826861321926,
0.025468606501817703,
-0.018575197085738182,
-0.04679669812321663,
0.03623739629983902,
0.02363673970103264,
-0.01629926823079586,
-0.010837496258318424,
0.0393000990152359,
-0.02693459764122963,
0.04369930550456047,
-0.0238797590136528,
-0.015718460083007812,
0.0306542981415987,
0.03576607629656792,
-0.02508481964468956,
0.022643636912107468,
-0.01027783751487732,
0.028217775747179985,
0.010107054375112057,
-0.04501449316740036,
-0.03452761098742485,
0.037942368537187576,
0.0622468926012516,
0.01698552817106247,
0.04263908416032791,
-0.00799685437232256,
0.00043148541590198874,
-0.05268785357475281,
-0.022219279780983925,
-0.0352187417447567,
-0.007447670679539442,
0.0031094360165297985,
-0.031194128096103668,
-0.027087204158306122,
0.023002877831459045,
0.01980539597570896,
0.04643942788243294,
-0.0037978815380483866,
-0.046931445598602295,
-0.038311686366796494,
0.0005336274043656886,
-0.08222932368516922,
-0.026912977918982506,
-0.05415027216076851,
0.043333616107702255,
0.04344760626554489,
-0.08908724784851074,
0.004567089024931192,
0.0008225690689869225,
-0.05808151885867119,
-0.02210519276559353,
0.012300235219299793,
-0.021891407668590546,
-0.013802818022668362,
0.07153182476758957,
0.0042411149479448795,
-0.007640819065272808,
0.03061603009700775,
-0.05876534432172775,
0.0033786820713430643,
0.024048803374171257,
-0.03401706740260124,
0.052321307361125946,
0.027347439900040627,
-0.010330813005566597,
0.042984094470739365,
-0.058968860656023026,
-0.053693510591983795,
-0.01222049817442894,
-0.051818277686834335,
-0.018338900059461594,
-0.051800988614559174,
0.05302014574408531,
0.05690993741154671,
-0.01325139869004488,
-0.03585278242826462,
-0.04397730156779289,
-0.020294683054089546,
0.008414171636104584,
0.05449531227350235,
0.05307047441601753,
0.035528331995010376,
0.04131719470024109,
-0.041000548750162125,
0.04062105342745781,
0.025750616565346718,
-0.01836583763360977,
0.02915279194712639,
-0.0029962495900690556,
0.00016518711345270276,
-0.052051857113838196,
-0.004343306180089712,
-0.04105106368660927,
0.023336105048656464,
0.05339439958333969,
0.02480100840330124,
0.0009476480772718787,
-0.057625606656074524,
0.016482578590512276,
-0.04565422981977463,
-0.013311713002622128,
-0.006160354241728783,
0.039297059178352356,
-0.021473553031682968,
-0.049014873802661896,
0.027440322563052177,
-0.02156793884932995,
0.025653621181845665,
-0.07005088776350021,
-0.02549785189330578,
-0.04062348231673241,
-0.05806325003504753,
-0.05099190026521683,
-0.033568814396858215,
-0.00568174896761775,
-0.05094204843044281,
-0.08843183517456055,
0.027378691360354424,
-0.029993759468197823,
-0.03800284489989281,
-0.02633536234498024,
-0.002346631372347474,
0.006219279952347279,
-0.021949950605630875,
-0.06837861239910126,
0.01001616008579731,
-0.007992559112608433,
0.000020257239157217555,
0.0022174064069986343,
0.04763462767004967,
0.023759594187140465,
0.02877139113843441,
0.10332939773797989,
0.048369091004133224,
-0.025204185396432877,
0.012776393443346024,
-0.0038681828882545233,
-0.0011514895595610142,
0.034192994236946106,
0.048097800463438034,
-0.04212094843387604,
-0.060487546026706696,
0.023126842454075813,
0.027258215472102165,
-0.0038594063371419907,
0.014915786683559418,
0.03290906548500061,
-0.02315569296479225,
0.0442851185798645,
0.03709833323955536,
0.06756313145160675,
-0.005407015793025494,
-0.0075269779190421104,
-0.011167542077600956,
-0.046818725764751434,
0.004627280402928591,
0.0000718402661732398,
0.0029287440702319145,
0.0032642153091728687,
0.06369815021753311,
-0.02029859647154808,
-0.041550520807504654,
0.05647856742143631,
0.027524925768375397,
-0.04511473700404167,
0.009414270520210266,
-0.011881951242685318,
0.03331194818019867,
-0.023919109255075455,
0.003369200276210904,
0.05876738578081131,
0.06585151702165604,
-0.02222822979092598,
0.018874341621994972,
-0.00008955134399002418,
-0.012079630047082901,
-0.017735658213496208,
-0.0002816919004544616,
0.020962556824088097,
-0.04089425504207611,
-0.07425715029239655,
0.023997217416763306,
0.019500548020005226,
-0.04229804500937462,
-0.023805787786841393,
-0.007482355460524559,
-0.01926763355731964,
-0.004945127293467522,
-0.04631393775343895,
-0.007226584944874048,
-0.0834176242351532,
-0.027018174529075623,
-0.04971117153763771,
0.007781737018376589,
0.03830542787909508,
0.0010532471351325512,
-0.0006480363081209362,
0.003776164725422859,
-0.04830678179860115,
0.042769499123096466,
-0.029415227472782135,
-0.02337726578116417,
-0.02906235307455063,
0.022552665323019028,
-0.035299237817525864,
0.04473410174250603,
0.013685598038136959,
0.016908617690205574,
0.017323985695838928,
0.03401141241192818,
0.12796740233898163,
0.00884664710611105,
0.009540235623717308,
-0.0077725425362586975,
0.011488078162074089,
-0.01645727828145027,
-0.061882369220256805,
0.009363644756376743,
0.008558162488043308,
0.007650510873645544
] |
<p>So I came across a question while studying laws of motion. Roughly, this is how it goes:
There are two astronauts in a space shuttle, who together have mass 200 kg. If by doing exercise, they manage to lose 80 kg, what will be the percentage increase in speed of the shuttle. The question is pretty straight forward, if thought about directly. However, my instant reaction was that by conservation of mass, the mass that the astronauts lose will still be contained within the space ship in the form of water, CO2, etc. So technically there won't be any change in mass, thus no change in speed. </p>
<p>I would like to know if this assumption is correct and in what forms is the mass we lose released.</p> | g5522 | [
0.02290569618344307,
0.025520477443933487,
0.02019423246383667,
0.020901693031191826,
0.00038856815081089735,
0.0037979192566126585,
0.02725885808467865,
-0.007233865093439817,
-0.030542511492967606,
-0.03413055092096329,
0.03357629105448723,
-0.016134805977344513,
0.04641634598374367,
0.044177960604429245,
0.023313166573643684,
0.006640325766056776,
0.11992190033197403,
-0.11471104621887207,
0.000280129665043205,
0.04455818980932236,
-0.009087377227842808,
-0.01636158488690853,
-0.04172462224960327,
-0.006838424131274223,
-0.019283702597022057,
0.018006552010774612,
0.035508062690496445,
-0.031106924638152122,
-0.02927853725850582,
-0.006700572557747364,
0.01640305109322071,
-0.023675307631492615,
0.03456589952111244,
-0.06436173617839813,
-0.06836321204900742,
-0.01092278491705656,
0.03783373534679413,
-0.03293513506650925,
-0.021705307066440582,
0.002754079643636942,
0.05441213771700859,
-0.07578272372484207,
-0.03376248478889465,
0.025620130822062492,
0.017571724951267242,
7.639639534318121e-7,
-0.019734466448426247,
-0.0866551622748375,
-0.01683042384684086,
0.05194820836186409,
0.006652435287833214,
0.041819654405117035,
-0.03659987449645996,
-0.017589837312698364,
-0.0312484297901392,
-0.0002567950577940792,
0.027319738641381264,
-0.04248673841357231,
0.047029390931129456,
-0.015088430605828762,
0.0035877039190381765,
-0.049379605799913406,
0.03922063484787941,
-0.0028810238000005484,
0.059745464473962784,
-0.025736043229699135,
-0.03446435555815697,
0.04177604243159294,
0.08776485174894333,
0.004782964009791613,
0.015362401492893696,
0.02923772484064102,
0.00167535908985883,
-0.049779247492551804,
-0.02301589585840702,
-0.009608001448214054,
0.02796240523457527,
-0.0021879253908991814,
0.02364528737962246,
-0.006321917753666639,
-0.030865754932165146,
0.02328503131866455,
0.06169898062944412,
0.029758721590042114,
0.03552284464240074,
0.010193170048296452,
-0.048574309796094894,
0.02149835415184498,
-0.045460157096385956,
0.05337470769882202,
0.01588759571313858,
-0.05374223366379738,
0.09022296965122223,
0.026984907686710358,
-0.013200366869568825,
-0.04087619110941887,
0.009824356995522976,
0.032705459743738174,
0.021512266248464584,
-0.010433131828904152,
-0.010954138822853565,
-0.04163055121898651,
-0.012191183865070343,
0.008559660986065865,
-0.027660878375172615,
0.012668843381106853,
0.03348590433597565,
0.0586286224424839,
0.01458150614053011,
0.0018629425903782248,
0.03745407611131668,
-0.02345743589103222,
-0.03277098760008812,
-0.01348735298961401,
-0.06030438095331192,
-0.07422707974910736,
0.030626870691776276,
0.01231610868126154,
0.018032310530543327,
-0.0038723661564290524,
0.01477620005607605,
-0.012985647656023502,
-0.02413126453757286,
0.0002749611157923937,
0.0005500842817127705,
-0.011629927903413773,
-0.017210301011800766,
0.031728345900774,
0.039621926844120026,
-0.011332244612276554,
-0.08252697438001633,
0.01741991937160492,
0.027913998812437057,
0.013164378702640533,
-0.0433623231947422,
0.0015735445776954293,
-0.06041497737169266,
0.01798356883227825,
-0.025099407881498337,
-0.051616162061691284,
-0.014468084089457989,
0.035290203988552094,
0.021480722352862358,
0.03805007040500641,
-0.007484793197363615,
0.00936419703066349,
0.03858770430088043,
-0.0012975843856111169,
0.01505815889686346,
0.009334203787147999,
0.031870268285274506,
0.008899034932255745,
0.02726741135120392,
-0.06252855807542801,
0.003885991871356964,
-0.028826652094721794,
-0.0016480741323903203,
0.027904924005270004,
-0.01948140375316143,
-0.03515331447124481,
0.04343220964074135,
0.015560462139546871,
0.029144546017050743,
0.01539827324450016,
-0.06703044474124908,
0.030883243307471275,
0.06055502966046333,
-0.02420584112405777,
-0.013395640067756176,
-0.04055444896221161,
-0.045002344995737076,
-0.07758815586566925,
0.00442499527707696,
0.10936587303876877,
-0.05007380247116089,
0.004024970345199108,
0.049727682024240494,
-0.020332839339971542,
-0.016589408740401268,
0.000379260687623173,
-0.02997303567826748,
-0.0035370795521885157,
0.002547888085246086,
-0.01581067591905594,
0.039244070649147034,
0.02556278184056282,
0.027184106409549713,
0.03177017718553543,
-0.088516466319561,
0.024912510067224503,
-0.012328581884503365,
-0.04620074853301048,
0.008609759621322155,
-0.013248474337160587,
-0.027417754754424095,
0.009711166843771935,
0.03264050930738449,
0.026949124410748482,
-0.03272135555744171,
0.06899434328079224,
0.02549068070948124,
0.023193219676613808,
-0.025811320170760155,
-0.02764127030968666,
0.02086927928030491,
-0.04082729294896126,
0.018085738644003868,
0.015745768323540688,
0.012343625538051128,
-0.054500434547662735,
0.05837657302618027,
0.0024301318917423487,
-0.01738819107413292,
0.00349988229572773,
0.037002187222242355,
0.025517916306853294,
-0.03606035187840462,
0.04693901911377907,
0.042849358171224594,
-0.07376697659492493,
-0.0044874646700918674,
-0.03853772208094597,
-0.00035278144059702754,
-0.03417486324906349,
0.02287106215953827,
-0.012867044657468796,
-0.05580607429146767,
-0.06660027801990509,
-0.020582949742674828,
0.030312441289424896,
-0.004858889151364565,
0.050230853259563446,
-0.0185758825391531,
-0.01844441518187523,
0.024101292714476585,
-0.016445405781269073,
0.002674309303984046,
0.10145527869462967,
0.040280189365148544,
-0.00698747718706727,
0.022908758372068405,
0.024092555046081543,
-0.049894243478775024,
-0.023662369698286057,
0.007111040409654379,
-0.04815705120563507,
-0.017743239179253578,
-0.04615285247564316,
0.0021877801045775414,
0.015230855904519558,
0.011006792075932026,
-0.00002468556704116054,
-0.03864492475986481,
-0.01694989763200283,
0.041547298431396484,
0.05705053731799126,
-0.06960857659578323,
-0.012494576163589954,
-0.04905491694808006,
-0.05121878907084465,
0.0017286326037719846,
-0.03264710679650307,
0.02458319067955017,
0.030485033988952637,
-0.02651534602046013,
-0.021608255803585052,
0.026794224977493286,
-0.0381675623357296,
0.013525296933948994,
0.020909978076815605,
-0.033855732530355453,
0.0535590760409832,
-0.038910266011953354,
0.06748521327972412,
-0.03196180984377861,
-0.026022981852293015,
0.04971281439065933,
-0.0638904944062233,
-0.016273919492959976,
0.014367563650012016,
0.020728280767798424,
0.042525917291641235,
-0.048022639006376266,
0.05235079675912857,
-0.006006614305078983,
-0.041415322571992874,
0.02317049168050289,
-0.010180532932281494,
-0.009636735543608665,
0.03449515253305435,
-0.03548050299286842,
0.03959785774350166,
0.09098600596189499,
0.014921683818101883,
0.0333716943860054,
0.06324338912963867,
0.07370062172412872,
-0.013867569155991077,
-0.058209214359521866,
-0.07963220030069351,
0.032356083393096924,
-0.03825844079256058,
0.022325949743390083,
0.03166200593113899,
0.00551679078489542,
0.09338860958814621,
-0.06752444058656693,
-0.014378797262907028,
0.0361667238175869,
-0.027822092175483704,
0.009834766387939453,
0.04191155359148979,
0.0031359719578176737,
0.014972833916544914,
-0.08241410553455353,
0.020942986011505127,
0.03547317534685135,
-0.033161651343107224,
0.00900829117745161,
-0.004148103762418032,
0.013932550325989723,
-0.06180236116051674,
-0.0050915880128741264,
0.000148650593473576,
0.016270292922854424,
0.040438272058963776,
-0.008260658010840416,
0.009746795520186424,
-0.025145068764686584,
-0.020794464275240898,
0.007007272448390722,
0.011117757298052311,
-0.014685094356536865,
-0.030890105292201042,
-0.02505847066640854,
0.039832647889852524,
-0.0035377098247408867,
0.0014669956872239709,
0.04095715656876564,
0.04821623116731644,
0.018481845036149025,
-0.01060965470969677,
-0.037670403718948364,
0.029962072148919106,
0.019099701195955276,
-0.0105964420363307,
0.018837910145521164,
-0.04710029810667038,
-0.04910636320710182,
-0.03994123637676239,
0.08878489583730698,
-0.011581219732761383,
-0.009245509281754494,
-0.02750193141400814,
-0.07207459956407547,
-0.010251513682305813,
-0.036617763340473175,
-0.018566977232694626,
-0.045549530535936356,
0.0273005161434412,
-0.02921200729906559,
-0.04416227340698242,
0.0019405141938477755,
0.02433190494775772,
-0.004043148830533028,
-0.011093287728726864,
0.00006020121509209275,
0.04215369001030922,
-0.0554727166891098,
-0.037612270563840866,
-0.0043877665884792805,
-0.018348442390561104,
-0.05846096947789192,
0.05730333924293518,
0.023880690336227417,
-0.025663474574685097,
0.01604474149644375,
0.059231922030448914,
-0.02511836588382721,
-0.003858339972794056,
0.04426354914903641,
0.018759548664093018,
0.013207267969846725,
-0.05177466198801994,
0.027801670134067535,
-0.005906406324356794,
-0.01128681655973196,
0.016163747757673264,
-0.012001678347587585,
-0.01914883591234684,
-0.017817288637161255,
-0.041670046746730804,
0.004079624079167843,
-0.011960919946432114,
-0.0007609578897245228,
0.005512591451406479,
-0.018282892182469368,
-0.022560371086001396,
0.005215850193053484,
0.04482683911919594,
-0.005554679315537214,
0.07079418748617172,
-0.035643551498651505,
-0.032634537667036057,
0.024832643568515778,
0.042669907212257385,
0.04590526968240738,
-0.06826800853013992,
0.002103738719597459,
0.011074814945459366,
0.037759941071271896,
-0.005026534665375948,
0.0010219324612990022,
-0.03925800323486328,
0.011985060758888721,
0.045646898448467255,
-0.05780649557709694,
-0.013058306649327278,
0.02803765796124935,
0.028186941519379616,
-0.010703148320317268,
0.02779250405728817,
-0.030970638617873192,
0.012117899954319,
-0.008754325099289417,
0.0617099292576313,
0.052300237119197845,
-0.011584822088479996,
0.04560648277401924,
-0.020136762410402298,
-0.02021411620080471,
-0.010939731262624264,
-0.017329160124063492,
0.08426235616207123,
-0.06147843599319458,
0.019686900079250336,
0.041345030069351196,
0.009911620989441872,
-0.02453441731631756,
0.032623041421175,
-0.015104937367141247,
0.012555344961583614,
-0.018744168803095818,
0.00586664816364646,
0.01245531253516674,
0.0778348296880722,
0.008803783915936947,
-0.04390863701701164,
0.009474610909819603,
-0.05440753325819969,
-0.017143553122878075,
0.053761452436447144,
-0.00006412847869796678,
0.017594721168279648,
-0.006815453991293907,
0.06264599412679672,
-0.02344512939453125,
0.008269758895039558,
0.02082253061234951,
0.07838481664657593,
-0.05181083083152771,
0.02942054159939289,
0.06663054972887039,
0.04665237292647362,
-0.0077551971189677715,
-0.026946188881993294,
0.011432954110205173,
-0.026724107563495636,
0.0020492312032729387,
0.028739407658576965,
0.028912657871842384,
-0.024838963523507118,
0.007080764044076204,
0.0023028100840747356,
0.00708755012601614,
0.038200151175260544,
-0.013055789284408092,
-0.007889588363468647,
0.04645461589097977,
-0.03156222030520439,
-0.02818296104669571,
-0.013106411322951317,
0.012852040119469166,
0.01573777012526989,
0.0009578057797625661,
0.016116449609398842,
-0.049835264682769775,
0.006259002722799778,
0.0721956342458725,
-0.03774980455636978,
0.002206170931458473,
0.03338242322206497,
-0.008014997467398643,
-0.027093712240457535,
-0.022345514968037605,
0.04445986822247505,
-0.014941961504518986,
-0.032737601548433304,
-0.012380369938910007,
-0.0056151412427425385,
-0.01569852977991104,
0.02150895819067955,
0.038959287106990814,
0.031101876869797707,
-0.019029632210731506,
0.0232701413333416,
-0.04389788955450058,
-0.018759408965706825,
-0.09458596259355545,
0.04586559906601906,
-0.027946962043642998,
0.07752396166324615,
-0.023635655641555786,
-0.00017931278853211552,
0.00748917181044817,
-0.07120666652917862,
0.020276755094528198,
0.023103632032871246,
0.04562746733427048,
0.020128311589360237,
0.05635814368724823,
0.007848791778087616,
0.042573414742946625,
0.06321173906326294,
-0.017145441845059395,
0.02219012938439846,
-0.05496198683977127,
0.04341169446706772,
-0.028391312807798386,
0.04287668317556381,
0.014648051001131535,
-0.02854897454380989,
0.009817625395953655,
-0.051789287477731705,
-0.0825333371758461,
0.0182681642472744,
-0.006475844420492649,
0.04467339068651199,
0.06797397136688232,
-0.010458208620548248,
-0.03642895072698593,
0.04939202591776848,
-0.020721619948744774,
0.09743371605873108,
0.07099302113056183,
0.02622769959270954,
-0.039688415825366974,
-0.10293837636709213,
-0.026186814531683922,
-0.017514288425445557,
-0.04707156494259834,
0.011633609421551228,
0.01929847151041031,
-0.009791837073862553,
0.005353249609470367,
0.01586366444826126,
-0.06090398505330086,
-0.01891324669122696,
-0.005565677769482136,
-0.0029483577236533165,
0.014327539131045341,
0.058983009308576584,
0.040910542011260986,
-0.0044979979284107685,
0.05384667217731476,
-0.07738836854696274,
0.04024713113903999,
-0.005624317564070225,
0.0374843068420887,
0.008616270497441292,
-0.016919851303100586,
0.006364466622471809,
-0.009261113591492176,
-0.003016803879290819,
0.01419718749821186,
-0.008782641962170601,
-0.034872524440288544,
-0.05731325224041939,
-0.043427128344774246,
-0.001206842134706676,
0.0408567413687706,
-0.07514672726392746,
-0.04431521147489548,
-0.0570007748901844,
-0.01910221390426159,
0.01707410253584385,
-0.0028458323795348406,
0.01069595292210579,
-0.003125059185549617,
0.020378805696964264,
0.010622791945934296,
0.05754842609167099,
-0.029787486419081688,
-0.0188453271985054,
-0.06493203341960907,
-0.03424211964011192,
-0.03696175664663315,
-0.04331960156559944,
0.022497832775115967,
0.0464535653591156,
-0.0277512539178133,
0.02602030336856842,
0.048228129744529724,
-0.033726006746292114,
-0.005027963314205408,
0.0316939502954483,
-0.016522157937288284,
0.003074737498536706,
0.03146420046687126,
-0.044742368161678314,
-0.0691637396812439,
-0.01570885442197323,
-0.0012000127462670207,
-0.026843233034014702,
0.03626897931098938,
0.020479466766119003,
0.05585844814777374,
0.020178912207484245,
-0.031238144263625145,
-0.027203025296330452,
0.019510306417942047,
-0.007571002468466759,
0.030773047357797623,
0.0013094426831230521,
0.033175744116306305,
-0.00116034469101578,
0.016835154965519905,
0.049933116883039474,
0.042759574949741364,
-0.01794140413403511,
-0.004152672365307808,
0.0157979354262352,
-0.044398773461580276,
0.0036031275521963835,
-0.014589936472475529,
0.07030275464057922,
-0.04548773542046547,
0.05706339702010155,
0.033308349549770355,
0.024635374546051025,
0.014156795106828213,
-0.017428359016776085,
0.023826465010643005,
0.050257764756679535,
-0.12174499034881592,
0.03893574699759483,
0.01885494962334633,
-0.04919270798563957,
-0.013713840395212173,
-0.04966641589999199,
-0.038695093244314194,
-0.026804892346262932,
-0.04055437445640564,
-0.025431187823414803,
-0.024469198659062386,
0.01535350177437067,
-0.04358904808759689,
0.016731441020965576,
0.01170763187110424,
-0.0471951887011528,
-0.05412713438272476,
-0.05390068516135216,
0.07122428715229034,
0.00903647392988205,
-0.003203494241461158,
0.05516045168042183,
0.01488544698804617,
-0.006597638130187988,
-0.011029894463717937,
-0.0017029517330229282,
-0.00023884983966127038,
0.021053200587630272,
-0.039790887385606766,
0.047037918120622635,
-0.0010292197111994028,
0.018101781606674194,
0.0034311693161726,
-0.03756551444530487,
0.028196480125188828,
0.003013193141669035,
0.020916076377034187,
-0.004352672956883907,
0.00267010903917253,
0.07956571131944656,
-0.013297667726874352,
0.023350341245532036,
-0.029452096670866013,
-0.02346600405871868,
0.03231137618422508,
0.014621096663177013,
-0.028296681120991707,
0.06780003011226654,
0.006683564279228449,
-0.01899586245417595,
-0.033775296062231064,
-0.020294370129704475,
0.007037718780338764,
0.045113496482372284,
-0.01558639109134674,
-0.015158958733081818,
-0.001856334158219397,
-0.0035306005738675594,
0.01659063994884491,
0.05783353000879288,
-0.0032702446915209293,
0.014427823014557362,
-0.004180747549980879,
-0.058693528175354004,
-0.021480971947312355,
-0.010911306366324425,
0.008051185868680477,
-0.0424363911151886,
-0.0031806856859475374,
-0.025222552940249443,
0.03299172967672348,
-0.02038879506289959,
-0.02413143217563629,
0.0030474551022052765,
0.03708963096141815,
-0.01075125765055418,
0.012216241098940372,
0.02465939335525036,
-0.029628049582242966,
-0.07463889569044113,
-0.011664210818707943,
-0.011933112516999245,
0.02611120603978634,
0.007921124808490276,
-0.04927168786525726,
-0.003405775176361203,
-0.015206798911094666,
0.010149240493774414,
0.002729655709117651,
-0.02124836854636669,
0.03625847026705742,
-0.019125688821077347,
0.061817824840545654,
-0.008922459557652473,
-0.07267097383737564,
0.036020342260599136,
-0.010682596825063229,
-0.04404795169830322,
0.009009217843413353,
0.039540812373161316,
0.01801346056163311,
-0.029215095564723015,
-0.013584882952272892,
0.034092437475919724,
-0.014064772985875607,
-0.021554186940193176,
0.051794540137052536,
0.008510690182447433,
-0.037781983613967896,
0.05667079985141754,
-0.026691628620028496,
-0.04496696963906288,
-0.02325022965669632,
-0.07995279878377914,
-0.05516885221004486,
-0.016308486461639404,
-0.040277596563100815,
0.026200538501143456,
-0.005887322127819061,
-0.01773153245449066,
-0.049916259944438934,
-0.0461537204682827,
0.03824970871210098,
0.04012914374470711
] |
<p>Intuitively, if energy can be stored in rotational motion, it has to obey $E=mc^2$.
Does rotation of typical stellar-sized objects - BHs, pulsars, binaries - have measurable effect on their overall gravity? </p>
<p>(I'm not talking about nearby effects, like frame dragging described by Kerr metric, the effect on measurements from the Earth is of interest)</p> | g5523 | [
-0.007745723705738783,
0.06885135173797607,
0.002222609706223011,
-0.04456273466348648,
-0.017973562702536583,
-0.030791910365223885,
0.04546986147761345,
0.019417505711317062,
-0.06335557997226715,
-0.016305657103657722,
0.016651945188641548,
-0.010980391874909401,
0.028189826756715775,
-0.012948721647262573,
-0.0020503846462816,
-0.0265641026198864,
0.03989068418741226,
-0.022597556933760643,
0.026046575978398323,
0.0667923092842102,
-0.0026768313255161047,
-0.00668104225769639,
-0.043719470500946045,
-0.010387636721134186,
0.022276153787970543,
0.04108058661222458,
0.0886361300945282,
-0.022973179817199707,
-0.07058621197938919,
0.02726641856133938,
0.017662815749645233,
-0.011191225610673428,
0.030028903856873512,
-0.0626545399427414,
-0.09458834677934647,
-0.007149146869778633,
0.03863340616226196,
-0.003847897984087467,
0.07287444174289703,
-0.04027044400572777,
0.042594388127326965,
-0.016732916235923767,
-0.004407193046063185,
0.020077474415302277,
-0.006071270909160376,
0.01014816015958786,
0.09375790506601334,
0.008560619316995144,
0.022756263613700867,
-0.0016873993445187807,
-0.02066899463534355,
-0.004477678798139095,
0.07562743872404099,
0.05907614901661873,
0.023070799186825752,
0.013363474979996681,
0.024913758039474487,
-0.004251720383763313,
0.04978618770837784,
-0.011603380553424358,
0.007423348259180784,
-0.0700426697731018,
-0.07286391407251358,
0.012401869520545006,
-0.012313604354858398,
-0.06359914690256119,
-0.07689274102449417,
-0.041170116513967514,
-0.002565346658229828,
-0.020149778574705124,
0.0632958933711052,
0.033363938331604004,
0.013330298475921154,
-0.016273995861411095,
-0.04864860698580742,
0.01547824777662754,
-0.0352872796356678,
0.001298947143368423,
-0.05312163382768631,
0.0007375853601843119,
-0.0423155277967453,
-0.024205520749092102,
0.028818266466259956,
0.03892676159739494,
0.10803500562906265,
0.002617139369249344,
0.005127161741256714,
0.05265607312321663,
0.0024745010305196047,
0.07412079721689224,
0.04716520011425018,
-0.03397446498274803,
0.0554007925093174,
0.006320604123175144,
0.019876034930348396,
-0.012912234291434288,
0.014181938022375107,
0.01511352974921465,
-0.03686855360865593,
0.021035365760326385,
-0.03208551183342934,
0.01622614450752735,
-0.03672970086336136,
0.014137336052954197,
0.07685430347919464,
0.017539385706186295,
0.00022347239428199828,
0.022484784945845604,
0.04244079068303108,
-0.005820204969495535,
0.0021944798063486814,
-0.04153358191251755,
0.0614461787045002,
-0.010702848434448242,
-0.08273063600063324,
-0.015775997191667557,
0.06828545033931732,
-0.003701441688463092,
-0.022423919290304184,
0.10876413434743881,
0.010863506235182285,
0.05488480627536774,
-0.02032284624874592,
0.11524931341409683,
-0.04596487060189247,
-0.012473099865019321,
-0.047988299280405045,
-0.01778317615389824,
0.035794537514448166,
0.021892601624131203,
-0.019946830347180367,
-0.031690433621406555,
-0.026948753744363785,
-0.0077073099091649055,
0.0054237074218690395,
0.0017986573511734605,
-0.019500302150845528,
0.02446851320564747,
-0.04868994280695915,
0.019986964762210846,
0.010811984539031982,
-0.02679179422557354,
-0.008522894233465195,
0.024573028087615967,
-0.039414387196302414,
0.019505467265844345,
0.03653610870242119,
0.03588950261473656,
0.03300417959690094,
0.03761923313140869,
0.02151394635438919,
0.035705432295799255,
-0.022367343306541443,
-0.05217020958662033,
0.05745251849293709,
0.03041011281311512,
-0.053454846143722534,
-0.00455591082572937,
-0.03329743444919586,
0.075664222240448,
0.06346143037080765,
0.0026119400281459093,
0.08634430170059204,
-0.016399096697568893,
-0.017936455085873604,
0.020164676010608673,
-0.025644995272159576,
-0.031951822340488434,
0.0003229148860555142,
-0.023438813164830208,
-0.059128858149051666,
-0.013031802140176296,
0.010725156404078007,
0.025016475468873978,
0.003330979961901903,
0.022156622260808945,
0.02136591635644436,
-0.010122795589268208,
-0.008602967485785484,
0.0062581617385149,
-0.002830185228958726,
0.028751876205205917,
-0.019306741654872894,
-0.01799400895833969,
0.016416791826486588,
-0.04088880494236946,
0.03898392245173454,
-0.01420653611421585,
0.013937666080892086,
0.043024107813835144,
-0.015190196223556995,
0.03558545187115669,
0.04119495302438736,
0.02486514486372471,
-0.020491966977715492,
0.006143590435385704,
-0.012570344842970371,
0.027549758553504944,
-0.07889750599861145,
0.09052319079637527,
-0.024710772559046745,
0.005166443530470133,
0.058880601078271866,
-0.026239819824695587,
0.047698959708213806,
0.005440513603389263,
-0.02786940149962902,
-0.009121931158006191,
0.0027534528635442257,
-0.024703195318579674,
0.04075857251882553,
0.010601788759231567,
-0.024899134412407875,
0.044021591544151306,
0.01661396026611328,
-0.018814969807863235,
-0.035538095980882645,
-0.01397485937923193,
-0.0262540765106678,
0.015270362608134747,
-0.05579058825969696,
-0.023166263476014137,
0.03165214881300926,
-0.022661736235022545,
-0.000053216808737488464,
0.002744313795119524,
-0.023537887260317802,
-0.009866255335509777,
0.014564555138349533,
0.014858080074191093,
-0.044559117406606674,
0.04376353695988655,
0.07214462757110596,
0.053641702979803085,
0.016616933047771454,
-0.013869933784008026,
0.008144007995724678,
0.0011938727693632245,
0.03831901028752327,
0.02892255410552025,
0.0558493472635746,
-0.011232237331569195,
0.012826330959796906,
-0.07507511973381042,
0.046256378293037415,
-0.02125472202897072,
0.061966344714164734,
0.01686917431652546,
0.008276158943772316,
0.0051019443199038506,
0.047277163714170456,
-0.00199023075401783,
-0.04834524542093277,
0.02960018254816532,
0.004748272709548473,
0.03433096781373024,
-0.029881130903959274,
0.013408944010734558,
-0.08780304342508316,
-0.0048293485306203365,
-0.006239767652004957,
0.01602211967110634,
-0.022397862747311592,
0.049543581902980804,
0.021779358386993408,
-0.027397364377975464,
-0.03445979580283165,
0.023105956614017487,
-0.006502162665128708,
0.03260383382439613,
-0.022432565689086914,
0.011795771308243275,
-0.01190868392586708,
0.08213239163160324,
-0.021989375352859497,
-0.002667690860107541,
-0.0023735349532216787,
-0.020523525774478912,
-0.025998016819357872,
-0.003150405129417777,
-0.03708287328481674,
-0.028799979016184807,
-0.07865574210882187,
0.015252468176186085,
0.020672613754868507,
-0.012028864584863186,
-0.05091750621795654,
-0.003331891493871808,
-0.04870074242353439,
0.016430269926786423,
-0.011055857874453068,
0.08526717126369476,
0.04614722728729248,
0.04425395652651787,
0.03503939136862755,
0.029855547472834587,
-0.006642031949013472,
0.02931230515241623,
-0.04369478300213814,
0.018077300861477852,
0.04835458844900131,
-0.0030171882826834917,
-0.024457644671201706,
0.0005361865041777492,
-0.05403776094317436,
0.025232862681150436,
-0.052953556180000305,
-0.05347949266433716,
-0.020708292722702026,
-0.03143290430307388,
-0.07512649148702621,
0.02623511664569378,
-0.029070602729916573,
0.040085144340991974,
-0.05909763649106026,
-0.052338145673274994,
0.012773336842656136,
-0.010504650883376598,
-0.012212970294058323,
-0.028791839256882668,
0.05179359018802643,
-0.013669715262949467,
-0.03623006492853165,
0.0018303063698112965,
0.01357447449117899,
0.015165721997618675,
-0.034457016736269,
0.008097435347735882,
-0.021053925156593323,
0.00947815552353859,
-0.02494628354907036,
0.03601037710905075,
-0.010563102550804615,
0.06291036307811737,
-0.03596964851021767,
0.03394308313727379,
0.006951767951250076,
-0.008735372684895992,
0.03386210277676582,
0.01745578646659851,
-0.019749613478779793,
-0.0007737958803772926,
-0.021455349400639534,
-0.00929257832467556,
-0.005925904028117657,
0.03729637339711189,
-0.009997273795306683,
-0.03379827365279198,
-0.005327763967216015,
-0.027806345373392105,
0.026945417746901512,
-0.047685373574495316,
0.02171359211206436,
-0.036541711539030075,
0.05315104499459267,
0.0030913513619452715,
0.026020072400569916,
0.009473836980760098,
-0.0018336946377530694,
-0.000028455184292397462,
-0.027604589238762856,
-0.016954045742750168,
-0.005590210203081369,
0.045770443975925446,
0.003883523168042302,
-0.02127978578209877,
-0.01829376444220543,
-0.0394890159368515,
-0.010313635692000389,
-0.03248488903045654,
0.01672772318124771,
0.049737442284822464,
-0.03250562399625778,
-0.0032794629223644733,
0.06996294111013412,
-0.06936242431402206,
0.057619404047727585,
-0.007384218741208315,
-0.016116756945848465,
-0.011785373091697693,
0.05219315364956856,
-0.011237225495278835,
-0.0037272325716912746,
0.019094940274953842,
-0.008705798536539078,
-0.04831920936703682,
-0.021455837413668633,
-0.01629694737493992,
0.035187479108572006,
0.022022638469934464,
-0.04637628048658371,
-0.06768132001161575,
0.06394703686237335,
-0.016239728778600693,
0.0357186384499073,
-0.049551643431186676,
0.04681649059057236,
-0.0005223714397288859,
0.06881462037563324,
0.020929856225848198,
-0.011035874485969543,
0.006822879891842604,
0.03185019642114639,
-0.012484013102948666,
0.026537397876381874,
-0.015417151153087616,
0.0178062841296196,
-0.024336818605661392,
-0.07157685607671738,
-0.017247740179300308,
0.040639422833919525,
-0.010209622792899609,
-0.006001629400998354,
-0.05191650614142418,
0.020903434604406357,
-0.0045976764522492886,
-0.044607013463974,
-0.0025481670163571835,
0.04136589542031288,
0.013630146160721779,
0.014173388481140137,
0.04517578333616257,
-0.0052865841425955296,
0.0027739498764276505,
-0.031569696962833405,
0.08209559321403503,
0.03791428729891777,
0.0034837916027754545,
-0.029754310846328735,
0.006225352641195059,
0.069658562541008,
-0.002530096797272563,
0.06408941745758057,
-0.013362666592001915,
-0.03046918846666813,
0.02861758880317211,
-0.04918355494737625,
0.03923485055565834,
0.02377610094845295,
0.00801924243569374,
0.04312262684106827,
0.029468685388565063,
0.011034679599106312,
-0.007715572137385607,
-0.050239063799381256,
0.05979118496179581,
-0.033595550805330276,
-0.02666545659303665,
-0.034270476549863815,
-0.044139835983514786,
0.002900576451793313,
-0.031689051538705826,
-0.03266185522079468,
-0.019065259024500847,
-0.03152616322040558,
0.02140934020280838,
-0.039478693157434464,
0.019816730171442032,
0.0625467300415039,
-0.016917938366532326,
-0.03700905665755272,
-0.022714773193001747,
0.05595947429537773,
0.039523687213659286,
-0.0026503282133489847,
-0.0347873717546463,
-0.04941290616989136,
-0.02639840729534626,
-0.01251803245395422,
0.032447800040245056,
-0.021824555471539497,
0.003751887008547783,
0.02805229090154171,
0.007019240874797106,
0.014655486680567265,
0.025669069960713387,
-0.034379467368125916,
-0.03086761385202408,
-0.015574333257973194,
-0.09438491612672806,
-0.059266332536935806,
-0.0036850939504802227,
0.02665587328374386,
0.030522339046001434,
-0.0029945853166282177,
0.009847084060311317,
-0.04167445749044418,
0.012142864987254143,
0.01179452147334814,
0.010291416198015213,
-0.02049987018108368,
0.037242237478494644,
-0.016835110262036324,
-0.025523720309138298,
0.003936272580176592,
0.03764272481203079,
-0.0187675803899765,
-0.05403945967555046,
-0.029278907924890518,
-0.04072095826268196,
0.022045962512493134,
0.03591480478644371,
0.009616910479962826,
-0.008173803798854351,
-0.0336248017847538,
0.00918549858033657,
0.030728114768862724,
-0.03259974345564842,
-0.04621969535946846,
0.047913990914821625,
-0.11199330538511276,
0.017820194363594055,
-0.02060520648956299,
0.039741482585668564,
0.014041713438928127,
-0.02122524380683899,
-0.003236448857933283,
0.028445465490221977,
0.019980615004897118,
-0.021433889865875244,
-0.03546978160738945,
-0.05232181400060654,
0.031036702916026115,
0.008064532652497292,
0.04315206781029701,
0.040671929717063904,
-0.009602759964764118,
0.012479346245527267,
-0.0034087137319147587,
0.015130451880395412,
0.03205781430006027,
-0.06094517931342125,
0.009388660080730915,
0.035225942730903625,
0.010199255309998989,
0.0021843360736966133,
-0.027924228459596634,
-0.00010641859989846125,
0.08376258611679077,
-0.012886355631053448,
-0.010411716997623444,
-0.02179541252553463,
0.010964920744299889,
-0.00809724535793066,
0.0024314343463629484,
-0.0033407018054276705,
-0.013164148665964603,
-0.011223557405173779,
0.06067988649010658,
-0.03621838986873627,
-0.03115778975188732,
0.05551225692033768,
-0.021504968404769897,
-0.021351350471377373,
-0.044693250209093094,
0.05269205570220947,
-0.011678439565002918,
-0.03408926725387573,
-0.030910151079297066,
-0.039657849818468094,
-0.006410765927284956,
0.017375515773892403,
0.06469599157571793,
-0.025147978216409683,
0.03340749070048332,
-0.01176130399107933,
0.034075431525707245,
-0.05470215156674385,
0.05556661635637283,
0.025542639195919037,
-0.04452315717935562,
0.0012345155701041222,
0.004805148113518953,
-0.013256986625492573,
0.01981477066874504,
-0.01874884031713009,
-0.049570679664611816,
0.022700145840644836,
-0.014842155389487743,
0.000024847222448443063,
0.04961831122636795,
-0.022938288748264313,
-0.00047710086801089346,
-0.02975177951157093,
0.034202512353658676,
-0.011226671747863293,
0.04157254099845886,
0.043622937053442,
0.048017408698797226,
-0.03533005341887474,
0.0030901948921382427,
-0.005425674840807915,
0.003468512324616313,
-0.006815583445131779,
-0.014745034277439117,
-0.01254037395119667,
-0.0033871575724333525,
-0.023266276344656944,
-0.02170400880277157,
-0.056913696229457855,
0.00708337128162384,
-0.0024679526686668396,
0.10790924727916718,
-0.024813128635287285,
0.02402487024664879,
-0.018040234223008156,
-0.10739010572433472,
-0.0013320576399564743,
0.035544902086257935,
0.04081359878182411,
-0.06046745926141739,
0.006740447599440813,
0.06903189420700073,
0.017840327695012093,
-0.02294277586042881,
-0.02932603284716606,
0.019107628613710403,
0.01605186052620411,
0.01680614985525608,
-0.010025657713413239,
-0.0399777851998806,
-0.042088765650987625,
0.04158757999539375,
-0.09453906863927841,
0.03077593818306923,
0.023632025346159935,
-0.05490630492568016,
0.025628766044974327,
0.009135500527918339,
0.0035384322982281446,
0.017574340105056763,
0.04193313419818878,
-0.00793200358748436,
0.03119429014623165,
0.052616119384765625,
-0.01325955893844366,
-0.0636788010597229,
0.0447872094810009,
-0.009016049094498158,
0.0006598103791475296,
0.00262916530482471,
0.023360276594758034,
-0.06329457461833954,
0.009934957139194012,
-0.08749055862426758,
-0.002824642928317189,
0.008723045699298382,
0.011657684110105038,
-0.03351665288209915,
-0.018925882875919342,
0.003934768494218588,
-0.03264095261693001,
0.007862986996769905,
-0.002542725531384349,
-0.06568463891744614,
0.0017716519068926573,
-0.0008901136461645365,
-0.029027478769421577,
0.015318196266889572,
-0.09552410244941711,
0.0022226718720048666,
-0.03115287981927395,
-0.04186525195837021,
0.03523420915007591,
0.004414902999997139,
0.0017315233126282692,
0.018321868032217026,
-0.014863432385027409,
0.039448823779821396,
0.015080038458108902,
0.020866956561803818,
-0.004090087953954935,
-0.06263088434934616,
0.03853243589401245,
-0.02179913967847824,
-0.05156437307596207,
-0.032933253794908524,
-0.071261465549469,
0.0007276922115124762,
0.019878916442394257,
0.0028740589041262865,
0.005945608019828796,
0.03166257590055466,
0.0617404580116272,
-0.0375342033803463,
0.03988887742161751,
-0.09905768185853958,
-0.004590272903442383,
0.01968410238623619,
-0.04219665750861168,
0.013667704537510872,
0.05072304233908653,
-0.004827685188502073,
0.0319027416408062,
-0.012268654070794582,
-0.03496186062693596,
0.006850420497357845,
0.07132045179605484,
0.001393897575326264,
-0.04370344430208206,
-0.03146601468324661,
0.0002618037979118526,
0.01009836234152317,
-0.015261689200997353,
0.048893172293901443,
0.046475380659103394,
-0.0037097532767802477,
0.0023459824733436108,
-0.09614185988903046,
-0.01095806434750557,
-0.000518833810929209,
-0.0008597298874519765,
0.02889450080692768,
-0.016457462683320045,
0.04461722448468208,
-0.029500411823391914,
-0.036966774612665176,
0.00765592884272337,
-0.014717341400682926,
0.01943914219737053,
-0.01800159178674221,
0.02911120280623436,
0.026491399854421616,
-0.03138546273112297,
0.001897800830192864,
-0.05827778950333595,
-0.07167825102806091,
-0.005094928666949272,
0.045309826731681824,
-0.05277841538190842,
-0.03139594569802284,
0.01386722456663847,
-0.00880984216928482,
0.024355310946702957,
-0.01912609674036503,
0.027847275137901306,
-0.0022993511520326138,
-0.036189738661050797,
-0.031027965247631073,
0.019412430003285408,
-0.02971816621720791,
-0.05435870215296745,
0.01013271976262331,
0.004374085925519466,
-0.00898332241922617,
0.025503478944301605,
0.02824205532670021,
0.012731336057186127,
0.020320730283856392,
-0.023783355951309204,
0.059056635946035385,
0.05689486116170883,
-0.03668060153722763,
0.00111488439142704,
0.021922994405031204,
0.004087976645678282,
-0.042296696454286575,
-0.04194680228829384,
-0.07492402195930481,
-0.00820388738065958,
-0.008004392497241497,
0.03272483870387077,
-0.022339900955557823,
-0.03444664925336838,
0.0446927547454834,
-0.11241689324378967,
0.03515573590993881,
0.07842786610126495
] |
<p>suppose that, there is a plano convex lens and its thickness is 5.00cm. If you watch it straight from the convex side, it seems that its of 4.4 cm. What is the refractive index of this lens?</p> | g5524 | [
0.02671404741704464,
-0.004651493392884731,
0.01272619515657425,
0.006445371545851231,
0.018535111099481583,
0.03226734325289726,
-0.020230641588568687,
-0.020032834261655807,
-0.020405076444149017,
0.005784116685390472,
-0.022718816995620728,
0.03447858989238739,
0.024754183366894722,
-0.04923851788043976,
0.06292115151882172,
-0.023456953465938568,
0.006706543732434511,
-0.028372429311275482,
-0.016597244888544083,
0.008113606832921505,
-0.007226414512842894,
0.005424953997135162,
-0.06419072300195694,
0.007772431243211031,
-0.0009675491601228714,
0.033017583191394806,
-0.0140029052272439,
0.013280779123306274,
-0.07934365421533585,
0.00013324629981070757,
-0.05031407251954079,
-0.0004042423388455063,
0.047738686203956604,
-0.027828644961118698,
0.0006005008472129703,
0.05567530542612076,
0.043423231691122055,
0.03219147399067879,
0.037916574627161026,
-0.007246744353324175,
-0.03726901486515999,
0.042338140308856964,
-0.022225387394428253,
0.03129870072007179,
0.04581137374043465,
0.008784865960478783,
-0.023254333063960075,
0.034325141459703445,
0.05263260379433632,
-0.08185534924268723,
-0.05056994408369064,
0.08964484184980392,
-0.008392172865569592,
-0.018554670736193657,
-0.006910655181854963,
0.04221613332629204,
-0.07037957012653351,
0.029581570997834206,
0.04220839589834213,
0.015618832781910896,
0.013785009272396564,
-0.015976399183273315,
0.015298478305339813,
0.04881903901696205,
0.016685502603650093,
-0.02720790170133114,
-0.015362336300313473,
0.05301204323768616,
0.015022587031126022,
0.023900151252746582,
-0.019504448398947716,
-0.03968023136258125,
-0.011678038164973259,
0.0046078977175056934,
-0.1209268569946289,
0.021096322685480118,
0.015444413758814335,
-0.015854904428124428,
-0.05174824595451355,
-0.014433146454393864,
0.018542692065238953,
-0.01207959558814764,
-0.033974044024944305,
-0.030843643471598625,
0.00986461341381073,
-0.007919698022305965,
0.03942521661520004,
-0.048301976174116135,
-0.037309784442186356,
-0.005812141578644514,
0.07111969590187073,
-0.01423812098801136,
0.023732267320156097,
0.07177087664604187,
0.07291974127292633,
-0.021660447120666504,
-0.034038279205560684,
-0.007191844284534454,
-0.0024466130416840315,
-0.009580608457326889,
0.029908213764429092,
0.004611590411514044,
-0.0008199751609936357,
-0.01992667093873024,
0.06530646979808807,
0.054881736636161804,
0.03783848509192467,
-0.026664068922400475,
0.029571156948804855,
-0.047292426228523254,
0.0064827450551092625,
-0.017868049442768097,
-0.021993273869156837,
-0.00019425639766268432,
-0.07151667773723602,
-0.04750961810350418,
0.01924067549407482,
-0.035792574286460876,
0.005889825988560915,
0.08251487463712692,
-0.031892988830804825,
0.06425705552101135,
0.052942607551813126,
0.06366918981075287,
0.022995755076408386,
0.005984649062156677,
0.04745321348309517,
0.010680397041141987,
0.06498590856790543,
0.0031718877144157887,
0.011286494322121143,
-0.022438211366534233,
0.004613962955772877,
-0.09578368812799454,
-0.009104013442993164,
0.06140097230672836,
-0.013820811174809933,
-0.03322439268231392,
-0.06511428207159042,
0.04984389990568161,
0.0027832717169076204,
0.06352170556783676,
0.025638865306973457,
0.028888700529932976,
-0.020048510283231735,
-0.05158955231308937,
-0.03534602373838425,
0.012500514276325703,
0.0597761869430542,
0.022362088784575462,
-0.03178933635354042,
0.027304666116833687,
0.023519428446888924,
-0.011403745971620083,
-0.0008706433000043035,
-0.015034199692308903,
-0.010778898373246193,
-0.0081636318936944,
0.02155459299683571,
-0.03523396700620651,
-0.0029861859511584044,
0.00038138890522532165,
-0.01873367838561535,
0.03829070180654526,
-0.08460251986980438,
-0.05107314512133598,
-0.09461253881454468,
-0.02154145948588848,
0.016885126009583473,
-0.08236849308013916,
-0.013594729825854301,
0.002594345947727561,
0.034001871943473816,
-0.03174437955021858,
-0.03888484463095665,
0.07264447212219238,
0.0000479295413242653,
0.024678846821188927,
-0.010895797051489353,
0.03562772274017334,
-0.02039017714560032,
-0.0015488420613110065,
-0.004163210280239582,
-0.03801427036523819,
-0.03199445828795433,
-0.014560123905539513,
0.033809538930654526,
-0.019615789875388145,
-0.05054811015725136,
-0.013641276396811008,
0.02153746597468853,
0.01400031428784132,
-0.024016719311475754,
0.04299664869904518,
0.06628964841365814,
0.014007434248924255,
0.018225448206067085,
-0.048342060297727585,
-0.0013929714914411306,
-0.002226488431915641,
-0.06375457346439362,
-0.03466489911079407,
0.03604849800467491,
0.07524316012859344,
0.029296139255166054,
-0.03457777947187424,
0.036317527294158936,
0.041803207248449326,
-0.013227853924036026,
0.0059511433355510235,
-0.00037681052344851196,
0.029928740113973618,
0.014338154345750809,
0.01699507236480713,
-0.00012699335638899356,
0.08561306446790695,
0.015690959990024567,
0.050835561007261276,
-0.019675690680742264,
0.04425456002354622,
-0.03027898631989956,
0.05566956847906113,
-0.014801748096942902,
0.03019688092172146,
-0.0158945694565773,
-0.03832855448126793,
-0.056801918894052505,
0.040788136422634125,
0.04288920387625694,
0.021932043135166168,
-0.027058914303779602,
-0.004982267040759325,
-0.014791780151426792,
0.041283149272203445,
-0.01985287293791771,
0.05824635922908783,
-0.008278200402855873,
-0.0014798182528465986,
-0.024531470611691475,
-0.045589759945869446,
0.04663943871855736,
0.016251690685749054,
-0.05987485870718956,
-0.010943736881017685,
-0.007798255421221256,
0.024286191910505295,
0.04390363767743111,
0.05155167356133461,
-0.005889429245144129,
0.04765046760439873,
0.014427314512431622,
0.0052421740256249905,
0.029510827735066414,
0.047558076679706573,
-0.014035440050065517,
-0.0030559857841581106,
-0.03216138854622841,
0.060268089175224304,
-0.028803136199712753,
-0.02889426238834858,
-0.05119217187166214,
-0.02588442526757717,
0.013994169421494007,
-0.012511896900832653,
-0.022199353203177452,
0.01880866102874279,
0.023188387975096703,
0.06533612310886383,
0.058588895946741104,
0.006048423703759909,
0.04866242781281471,
0.08498571068048477,
-0.010741844773292542,
-0.03408345952630043,
-0.014988481067121029,
-0.008790924213826656,
0.012136812321841717,
-0.016377488151192665,
0.01593751087784767,
-0.07308945804834366,
-0.010310868732631207,
0.06116290017962456,
-0.014687729999423027,
0.03882303461432457,
-0.002947899280115962,
-0.011649164371192455,
0.010577975772321224,
0.03476100042462349,
0.05534713342785835,
-0.0086022624745965,
-0.06153280287981033,
0.051360733807086945,
-0.010736890137195587,
-0.02857660874724388,
0.049968983978033066,
-0.009325383231043816,
0.06326216459274292,
0.009736564941704273,
0.03172813355922699,
0.04028894379734993,
-0.061228759586811066,
-0.006926009431481361,
-0.0559760145843029,
0.0039914315566420555,
0.04356732591986656,
-0.05342956632375717,
-0.016543719917535782,
-0.06742163747549057,
-0.01284389104694128,
0.012046264484524727,
-0.006828820798546076,
0.01121589820832014,
0.05398303270339966,
0.014166532084345818,
-0.04099205508828163,
0.060610055923461914,
0.0006054189871065319,
0.001509045367129147,
-0.03840802609920502,
0.04625139385461807,
0.01858457736670971,
-0.04036532714962959,
-0.04818316921591759,
0.019190484657883644,
-0.02421458624303341,
-0.014405171386897564,
-0.044373009353876114,
0.01990411803126335,
0.006106163840740919,
-0.034228503704071045,
0.0014902526745572686,
-0.005978376138955355,
-0.05453375354409218,
-0.011743191629648209,
0.02970348484814167,
0.006763084791600704,
-0.029991593211889267,
0.037843577563762665,
0.031870994716882706,
0.048715315759181976,
0.03396681696176529,
0.0009743027039803565,
-0.04028492793440819,
-0.03545628488063812,
-0.03133845329284668,
-0.00723058357834816,
0.0075608654879033566,
0.0025468964595347643,
0.042608775198459625,
-0.0260902289301157,
0.01909789815545082,
0.024460401386022568,
-0.007803923916071653,
-0.0625380277633667,
0.018586549907922745,
0.03828761726617813,
0.016250913962721825,
0.027327312156558037,
0.03394939750432968,
-0.017055569216609,
0.060768477618694305,
-0.032916393131017685,
-0.005331914871931076,
-0.015509081073105335,
-0.0004621308471541852,
-0.03967558220028877,
-0.005753323435783386,
0.042092856019735336,
-0.009583525359630585,
0.014415756799280643,
-0.034076936542987823,
-0.05631840601563454,
-0.05378628149628639,
0.06340983510017395,
-0.059901006519794464,
0.093691885471344,
-0.098499596118927,
-0.02740321308374405,
-0.07401096820831299,
-0.017285896465182304,
0.02555445395410061,
-0.005550299305468798,
0.053737837821245193,
0.01639314740896225,
-0.06534931808710098,
-0.00507806520909071,
-0.041846904903650284,
-0.053660210222005844,
0.04387090355157852,
-0.02958860620856285,
0.06989116966724396,
-0.03742675110697746,
-0.002784879645332694,
0.00690090749412775,
0.010630222968757153,
-0.01074809767305851,
0.030989287421107292,
0.007010207045823336,
-0.06895537674427032,
-0.006512881722301245,
0.02218972146511078,
0.0605446994304657,
0.09331806004047394,
-0.002236607950180769,
-0.020864423364400864,
0.03986024484038353,
-0.013552210293710232,
0.018147876486182213,
0.00044755826820619404,
0.028008852154016495,
-0.016415826976299286,
0.041630424559116364,
-0.029075434431433678,
-0.03785237669944763,
0.07197431474924088,
0.1112910807132721,
0.014155152253806591,
-0.0005607461207546294,
0.016551190987229347,
-0.021375225856900215,
-0.07012287527322769,
-0.00137845310382545,
-0.03013620898127556,
0.024189593270421028,
-0.015456701628863811,
0.03648454695940018,
0.025812635198235512,
-0.018254049122333527,
-0.04720205068588257,
-0.03758969530463219,
0.004570626188069582,
0.020054088905453682,
0.04391784593462944,
0.03817211464047432,
-0.011025472544133663,
0.03661462664604187,
0.002870554570108652,
0.03274175897240639,
-0.030584778636693954,
0.0007191633922047913,
-0.014127162285149097,
0.01389178354293108,
0.011829732917249203,
-0.05079015716910362,
-0.032997265458106995,
-0.006980699487030506,
-0.04354429990053177,
0.0063517894595861435,
-0.09145433455705643,
-0.012106102891266346,
-0.032823193818330765,
0.00006392894283635542,
-0.043836887925863266,
-0.007549666333943605,
-0.046124231070280075,
-0.02912181243300438,
-0.05286246910691261,
-0.00283132866024971,
0.02478725090622902,
-0.0073082586750388145,
-0.02249203994870186,
0.014612451195716858,
-0.005862043239176273,
0.030934711918234825,
0.02158690057694912,
-0.048842791467905045,
0.0023197054397314787,
0.026740428060293198,
-0.03983878344297409,
0.02327551878988743,
0.014065448194742203,
0.006475124508142471,
0.022707033902406693,
0.02145477570593357,
-0.013717863708734512,
0.006128606852144003,
-0.026500098407268524,
0.009829647839069366,
-0.016831165179610252,
-0.01933879591524601,
-0.016950376331806183,
0.0047948164865374565,
0.05655593052506447,
-0.029002904891967773,
0.030870838090777397,
0.04427369683980942,
-0.010610714554786682,
0.031502559781074524,
0.01700330339372158,
-0.024935664609074593,
-0.04183357208967209,
0.027157671749591827,
-0.03781750798225403,
-0.03409527987241745,
-0.0009415527456440032,
-0.042060837149620056,
0.03150344267487526,
-0.0011038907105103135,
0.04498154670000076,
0.03764183446764946,
0.019577793776988983,
0.00016705669986549765,
0.004378810524940491,
0.0497131384909153,
-0.03233705833554268,
0.020573364570736885,
0.050525516271591187,
-0.08508969843387604,
0.06306753307580948,
0.04260344058275223,
0.04859020560979843,
-0.01064201071858406,
0.023482507094740868,
-0.008226936683058739,
-0.011248219758272171,
-0.05683564767241478,
-0.034816570580005646,
-0.0012010225327685475,
-0.015207251533865929,
0.048726435750722885,
-0.016417091712355614,
0.00789091270416975,
-0.01388598419725895,
-0.007616959046572447,
-0.05916053429245949,
-0.05184508115053177,
-0.0019496616441756487,
-0.01779305189847946,
-0.008361498825252056,
-0.02383331209421158,
0.0048128883354365826,
0.05648956820368767,
0.0035306757781654596,
-0.026003584265708923,
0.0027519005816429853,
0.022974079474806786,
0.0056321099400520325,
0.015789739787578583,
0.02501884289085865,
-0.04120921343564987,
-0.07584713399410248,
0.025845790281891823,
0.003421645611524582,
0.10401162505149841,
-0.010182191617786884,
-0.02328353375196457,
-0.015063397586345673,
-0.004713099449872971,
0.06202300637960434,
0.02195442095398903,
0.006253771483898163,
0.017530133947730064,
0.014914015308022499,
0.019271180033683777,
0.014226023107767105,
0.04202614724636078,
-0.01510356180369854,
-0.010272094048559666,
0.013150027021765709,
-0.04246789216995239,
0.03774107247591019,
-0.03208427131175995,
-0.04049704968929291,
0.011021561920642853,
-0.04872254654765129,
-0.06305991858243942,
-0.016895748674869537,
0.07500340044498444,
0.07299982756376266,
-0.0232855174690485,
-0.0612233430147171,
-0.036149684339761734,
-0.031343039125204086,
-0.016007833182811737,
0.035058725625276566,
0.00587235065177083,
0.026876533403992653,
0.027647752314805984,
-0.021417487412691116,
-0.03958531841635704,
0.04451201856136322,
-0.000875633442774415,
0.010225366801023483,
0.008205188438296318,
-0.07060303539037704,
0.016297904774546623,
-0.008634129539132118,
-0.01713239774107933,
-0.00020266657520551234,
-0.01706743985414505,
-0.015960078686475754,
-0.009179631248116493,
-0.006525746081024408,
0.0000525808718521148,
-0.0021690321154892445,
0.0252151507884264,
-0.0020095461513847113,
0.07565072923898697,
-0.030727779492735863,
0.043856751173734665,
0.06153026223182678,
0.010551177896559238,
0.019013511016964912,
-0.008427254855632782,
0.009279084391891956,
-0.025600193068385124,
-0.03426166623830795,
0.021627111360430717,
0.029143955558538437,
0.031209617853164673,
0.040648020803928375,
0.002764976117759943,
0.00628825044259429,
-0.020830780267715454,
-0.026834769174456596,
-0.017446815967559814,
-0.02668519876897335,
-0.010346655733883381,
-0.023694662377238274,
-0.12188443541526794,
0.037804774940013885,
-0.06445004045963287,
0.03802015259861946,
-0.008617927320301533,
0.03169217333197594,
-0.020241642370820045,
-0.0074651772156357765,
-0.023205658420920372,
0.03276616334915161,
0.0035095077473670244,
0.024909278377890587,
-0.04469696432352066,
0.019958926364779472,
0.05979810655117035,
0.021705778315663338,
0.00029089057352393866,
-0.13576675951480865,
0.026626717299222946,
-0.004902861081063747,
0.06725150346755981,
0.04577525332570076,
-0.024866651743650436,
-0.003991272300481796,
0.0036097983829677105,
-0.012798387557268143,
-0.01539522036910057,
-0.04317380487918854,
-0.04593292996287346,
-0.02013741061091423,
-0.056978341192007065,
-0.027096126228570938,
0.047647442668676376,
-0.031162049621343613,
0.031413767486810684,
-0.057070646435022354,
0.05073930323123932,
-0.006262130104005337,
0.0005987584008835256,
-0.001908961683511734,
-0.054270192980766296,
0.0003811317146755755,
-0.08010934293270111,
-0.033091481775045395,
-0.009494476020336151,
-0.03168483078479767,
0.02492852695286274,
0.06974049657583237,
0.00099843624047935,
0.0050065238028764725,
-0.006023081485182047,
0.050976116210222244,
-0.006651260424405336,
-0.043787118047475815,
0.026310425251722336,
-0.05949370190501213,
-0.023233721032738686,
-0.05397343263030052,
0.016602715477347374,
-0.01068988349288702,
0.04479992762207985,
-0.029635148122906685,
0.03138544410467148,
0.009472479112446308,
-0.01811678148806095,
-0.036130283027887344,
0.0014963285066187382,
0.003257198492065072,
-0.026642458513379097,
0.022323640063405037,
-0.0150502510368824,
0.003815174801275134,
-0.045471929013729095,
0.019214576110243797,
-0.01974787749350071,
-0.0002163641038350761,
-0.01314097736030817,
0.05977976322174072,
0.006926563568413258,
0.026734430342912674,
-0.004715919494628906,
0.005997850093990564,
0.0007508328999392688,
0.04512364789843559,
-0.04201626777648926,
0.020745377987623215,
-0.02412095107138157,
-0.05823444575071335,
0.06081581860780716,
0.0027688087429851294,
0.020086243748664856,
0.012254778295755386,
-0.06221989169716835,
0.02291068807244301,
-0.004816845059394836,
0.0010356031125411391,
-0.004980814643204212,
-0.04344065487384796,
0.013417375274002552,
-0.007235972210764885,
-0.040164582431316376,
-0.0542931854724884,
-0.004485256504267454,
-0.026629764586687088,
-0.04275364801287651,
-0.04856826737523079,
0.038602739572525024,
0.03817762807011604,
-0.05001513659954071,
0.009006369858980179,
-0.01995665207505226,
0.03862446919083595,
0.02946929819881916,
-0.053933028131723404,
-0.021356670185923576,
0.03623628243803978,
0.0029033441096544266,
0.046902868896722794,
-0.03727920353412628,
0.016208119690418243,
0.028763839974999428,
-0.005433281417936087,
-0.03412105515599251,
-0.01823297329246998,
-0.03538921847939491,
0.00971899926662445,
0.004190548788756132,
-0.007765586953610182,
-0.0014740393962711096,
0.043728023767471313,
-0.039596907794475555,
-0.007715791929513216,
0.0052981446497142315,
0.03517972677946091,
0.062359798699617386,
-0.006588897202163935,
-0.06182549148797989,
0.027870580554008484,
-0.034296803176403046,
-0.004329868592321873,
-0.038308724761009216,
0.0073354123160243034,
0.026884207502007484,
0.05327979847788811,
0.03289324417710304,
-0.015298694372177124,
-0.014197982847690582,
-0.038097966462373734,
-0.006681371480226517
] |
<p>We have studied so far that electric field inside a conductor if no charge is placed inside is zero. But we know that every conductor has only a limited number of electrons. What happens when ALL the electrons have aligned to cancel the field inside conductor under application of external field and then we increase the field a little bit more certainly there are no more electrons to cancel the field and this additiknal field must be present inside the conductor now.</p>
<p>I know that practically under electric fields of magnitude that can drag out all electrons from the conductor's body to surface field emission and/or electrical breakdown would be taking place, But is this phenomenon theoretically possible ?</p> | g474 | [
-0.00223164283670485,
0.04608511924743652,
0.01469438150525093,
0.004451402463018894,
-0.004386051092296839,
0.061355169862508774,
-0.016919486224651337,
0.04604537785053253,
-0.022131072357296944,
0.0038062590174376965,
-0.054109759628772736,
0.02624267153441906,
-0.0021596415899693966,
-0.029344284906983376,
-0.017718710005283356,
0.047518957406282425,
0.02258746325969696,
-0.04337301105260849,
0.032158344984054565,
0.024734841659665108,
0.00798733625560999,
-0.018428362905979156,
0.027393806725740433,
0.029281970113515854,
-0.07878389954566956,
0.017266230657696724,
0.05062029883265495,
-0.011515920050442219,
0.013447041623294353,
-0.08688750863075256,
-0.04309535771608353,
0.02808607928454876,
0.004387716297060251,
-0.03691747784614563,
-0.028473803773522377,
-0.01858588680624962,
0.03956776484847069,
0.05607612803578377,
0.003412960097193718,
0.0426364429295063,
0.03690887242555618,
-0.0349336639046669,
0.04278106242418289,
-0.05915827304124832,
-0.016994189471006393,
-0.0040052104741334915,
-0.006037471350282431,
0.01393407117575407,
0.00757232028990984,
-0.040689487010240555,
-0.07318273931741714,
-0.041186001151800156,
-0.0052476609125733376,
-0.057338736951351166,
0.022409895434975624,
-0.02073659747838974,
0.011609784327447414,
-0.045018553733825684,
0.04284099489450455,
-0.032072003930807114,
0.0022622658871114254,
-0.01900291256606579,
-0.013374635018408298,
0.007392341271042824,
0.0017347167013213038,
-0.0036664505023509264,
-0.11071751266717911,
0.0011675970163196325,
0.030558530241250992,
0.01154258195310831,
-0.0032119168899953365,
-0.008847255259752274,
-0.0597555972635746,
-0.04681764170527458,
0.003543821396306157,
0.06666160374879837,
0.01622113399207592,
0.016177471727132797,
0.062150988727808,
0.027956141158938408,
-0.07101380079984665,
-0.01589774899184704,
0.018020864576101303,
0.060218699276447296,
0.10254032909870148,
-0.048654790967702866,
0.03339868038892746,
-0.014236943796277046,
-0.032382238656282425,
-0.017360469326376915,
-0.03626237437129021,
0.019348666071891785,
0.025907672941684723,
-0.010209842585027218,
-0.024797124788165092,
-0.016915680840611458,
0.0083798011764884,
0.03332870453596115,
-0.033004216849803925,
-0.05099254474043846,
-0.008610019460320473,
-0.024656882509589195,
0.028768226504325867,
0.026247458532452583,
-0.008662449195981026,
-0.0035481827799230814,
0.025843923911452293,
0.009870443493127823,
-0.006355644203722477,
0.013152316212654114,
-0.004835718777030706,
-0.047238729894161224,
-0.08795873075723648,
-0.016373397782444954,
0.022116171196103096,
0.02888614684343338,
0.054542940109968185,
-0.08159662038087845,
-0.04364898055791855,
0.02468893676996231,
0.015576467849314213,
0.0038748891092836857,
0.008053012192249298,
-0.0259154811501503,
-0.027999097481369972,
0.027576202526688576,
-0.0067754401825368404,
0.021207308396697044,
0.04126590117812157,
-0.029762528836727142,
-0.005297133233398199,
0.006177012342959642,
0.045166414231061935,
0.022558167576789856,
0.030605018138885498,
-0.004842159803956747,
0.009460467845201492,
-0.031308624893426895,
0.002964295446872711,
-0.02509954757988453,
0.00719889160245657,
-0.02505689673125744,
-0.01581166684627533,
0.05671145021915436,
0.03473518416285515,
0.0008609826909378171,
0.018519926816225052,
0.046894680708646774,
0.024387050420045853,
0.06967613846063614,
0.05678354203701019,
0.0218313280493021,
-0.01422998309135437,
-0.08319524675607681,
0.004995259921997786,
-0.01274957787245512,
0.041557006537914276,
-0.0021359261590987444,
-0.02008194290101528,
-0.07769864797592163,
0.06696415692567825,
0.04372826963663101,
0.007984690368175507,
0.048402026295661926,
-0.08535930514335632,
-0.01914050616323948,
-0.045630138367414474,
-0.018500512465834618,
0.04144630208611488,
-0.03693766891956329,
-0.010779816657304764,
-0.020548148080706596,
0.039330240339040756,
0.07554787397384644,
0.01953171193599701,
0.045529287308454514,
0.01916208118200302,
0.04208410903811455,
0.04758716747164726,
-0.029432471841573715,
-0.05357804894447327,
0.0451105535030365,
-0.001749797840602696,
0.004327896982431412,
0.020807800814509392,
-0.03202035650610924,
-0.027659252285957336,
0.051251716911792755,
0.014037881046533585,
-0.0030889054760336876,
-0.015828486531972885,
0.0061365654692053795,
0.02540782280266285,
0.04284307360649109,
-0.013624007813632488,
-0.010661903768777847,
-0.013463161885738373,
-0.04599488154053688,
-0.011622010730206966,
-0.13204853236675262,
0.025707656517624855,
0.007594761438667774,
0.0261950995773077,
-0.0476435124874115,
0.027523934841156006,
-0.07566619664430618,
-0.006759703159332275,
-0.059773191809654236,
0.05932529270648956,
-0.017676305025815964,
0.07256578654050827,
0.0065794470719993114,
0.04142208397388458,
0.016320377588272095,
-0.014792506583034992,
-0.05518635734915733,
0.0007612218032591045,
-0.0230096485465765,
-0.019028425216674805,
0.01167347189038992,
-0.021489134058356285,
-0.013514974154531956,
0.03611180931329727,
-0.011567579582333565,
-0.03570995479822159,
0.018407680094242096,
-0.02654644101858139,
-0.011722688563168049,
-0.044287439435720444,
-0.038363296538591385,
-0.08016566932201385,
0.027168037369847298,
0.0397283211350441,
-0.059726934880018234,
0.017481835559010506,
0.02411523275077343,
-0.046411946415901184,
-0.004070567432790995,
-0.017186446115374565,
-0.021788347512483597,
-0.03214048966765404,
-0.02112933248281479,
-0.05779314786195755,
-0.019803842529654503,
0.04699961468577385,
-0.11574655026197433,
0.05510111153125763,
0.04269183799624443,
-0.022968461737036705,
0.004945430904626846,
0.015655847266316414,
0.025188559666275978,
0.014855579473078251,
0.06394040584564209,
-0.038709934800863266,
0.014117355458438396,
-0.06328792124986649,
0.08191250264644623,
0.01495938841253519,
-0.08177091926336288,
-0.01845327764749527,
0.025203917175531387,
-0.018550509586930275,
0.04840036481618881,
-0.03405220806598663,
-0.02686569094657898,
-0.0466618537902832,
-0.05694642290472984,
0.04463620111346245,
0.033803295344114304,
-0.005735047161579132,
0.09300946444272995,
-0.07909562438726425,
0.009388278238475323,
0.0254106055945158,
0.02695850469172001,
-0.04342828318476677,
0.013326343148946762,
0.07528458535671234,
-0.02330802194774151,
0.06357336044311523,
0.012813897803425789,
-0.04934387654066086,
0.014820881187915802,
-0.006635156460106373,
-0.025532133877277374,
0.011791595257818699,
-0.04632086679339409,
-0.011747993528842926,
-0.010402553714811802,
-0.052379634231328964,
-0.023254483938217163,
0.05943501368165016,
-0.0007899229531176388,
0.0008040464017540216,
0.047177307307720184,
0.029840879142284393,
-0.03379857540130615,
-0.04283670336008072,
0.020583979785442352,
-0.0309295691549778,
-0.039781901985406876,
-0.033384259790182114,
-0.0070811384357512,
-0.022099604830145836,
0.0031704690773040056,
-0.01677841506898403,
-0.057886142283678055,
0.01858421042561531,
-0.06601311266422272,
0.00007390750397462398,
0.018835915252566338,
-0.021764758974313736,
-0.019223134964704514,
-0.024701988324522972,
0.020798970013856888,
-0.015668857842683792,
0.044296812266111374,
0.007130064070224762,
-0.005018113646656275,
-0.005453601013869047,
0.006515801884233952,
-0.02913534827530384,
0.0016652430640533566,
0.043830521404743195,
0.012501290999352932,
-0.005901060067117214,
0.0017041930695995688,
-0.05151785537600517,
0.04780497029423714,
-0.04140650853514671,
-0.02752448245882988,
-0.0033434019424021244,
-0.02326325885951519,
0.027221685275435448,
-0.011659837327897549,
-0.012795365415513515,
0.09400718659162521,
0.050846848636865616,
0.05888775363564491,
0.03253850340843201,
-0.03786814585328102,
-0.047311875969171524,
-0.058868423104286194,
0.02397368848323822,
0.050153810530900955,
0.012770447880029678,
-0.031654007732868195,
0.007490560412406921,
-0.0009694624459370971,
0.056171443313360214,
-0.029305236414074898,
0.0016787730855867267,
0.0045909336768090725,
-0.0369989313185215,
-0.004728976637125015,
0.04410919174551964,
0.09694866091012955,
-0.015528831630945206,
-0.02337794378399849,
-0.008486048318445683,
-0.018496403470635414,
0.04603208974003792,
-0.011256671510636806,
0.006214492954313755,
-0.02199542708694935,
0.002094847848638892,
0.00986485369503498,
-0.01837579719722271,
-0.057794131338596344,
-0.010266406461596489,
-0.006382721941918135,
-0.0279705673456192,
0.009963635355234146,
0.019850218668580055,
-0.060530610382556915,
0.06034521758556366,
0.066451795399189,
-0.02122931368649006,
-0.010854262858629227,
0.027675345540046692,
0.02021796442568302,
-0.029136493802070618,
-0.027200045064091682,
0.0038158667739480734,
0.0030361879616975784,
-0.029558928683400154,
0.03425579145550728,
-0.025645671412348747,
-0.019574059173464775,
-0.06131191924214363,
-0.0153128020465374,
0.02011745050549507,
-0.0038974874187260866,
-0.034573156386613846,
0.00047479261411353946,
0.0035971736069768667,
-0.07010206580162048,
0.06961578875780106,
-0.03844524919986725,
0.06739072501659393,
0.03286741301417351,
0.006265261210501194,
0.03122071921825409,
0.00814000517129898,
0.004571809899061918,
0.055162400007247925,
0.003770956303924322,
0.014983147382736206,
-0.06846960633993149,
-0.03131389990448952,
0.003996122628450394,
-0.04254864528775215,
-0.019590873271226883,
0.017347730696201324,
0.04671623557806015,
0.015797223895788193,
0.03524917736649513,
0.028085537254810333,
-0.0034013118129223585,
0.061101850122213364,
-0.007369746919721365,
0.008560271933674812,
-0.017759259790182114,
-0.01323640439659357,
0.011309323832392693,
-0.015175087377429008,
-0.021871212869882584,
-0.00549004040658474,
0.016068778932094574,
-0.04234641045331955,
0.02421499229967594,
-0.04937022551894188,
-0.004383851308375597,
-0.06407161802053452,
0.026530686765909195,
-0.039906904101371765,
0.09241009503602982,
0.03777769207954407,
0.04432706534862518,
0.04303152114152908,
-0.025034895166754723,
0.0466332882642746,
-0.005009699612855911,
-0.04029813036322594,
0.008252698928117752,
-0.01377262081950903,
-0.05976003780961037,
0.036428987979888916,
-0.026605274528265,
-0.06063868850469589,
-0.006545302923768759,
-0.03708077222108841,
-0.008336578495800495,
-0.018713463097810745,
-0.07308059185743332,
-0.058645788580179214,
-0.02720201201736927,
-0.03716065734624863,
0.0007204421563073993,
-0.0302925743162632,
-0.03298454359173775,
0.03579983860254288,
0.04503472149372101,
0.05351366847753525,
-0.07030823826789856,
0.026138385757803917,
0.0003104612696915865,
-0.03820396959781647,
-0.01624194346368313,
0.019733235239982605,
0.0680731013417244,
0.05032753571867943,
-0.002034614561125636,
0.015509679913520813,
0.00180667859967798,
-0.004163194913417101,
-0.0010104550747200847,
-0.025983376428484917,
-0.049875203520059586,
0.007299159653484821,
-0.0410219170153141,
0.016499798744916916,
0.00023831416910979897,
-0.011834508739411831,
-0.009820702485740185,
-0.051753703504800797,
0.0499773807823658,
0.0013810304226353765,
-0.04535499960184097,
0.03435482829809189,
0.044005848467350006,
0.0026184883899986744,
-0.0021253847517073154,
-0.06983743607997894,
0.017774665728211403,
0.000576011894736439,
0.019529778510332108,
-0.04960785433650017,
-0.027205530554056168,
-0.012730010785162449,
-0.024674860760569572,
-0.06216876581311226,
0.011776696890592575,
0.029797041788697243,
0.047384120523929596,
-0.04129636287689209,
-0.020520571619272232,
0.029550105333328247,
0.010729876346886158,
-0.06861163675785065,
0.061011478304862976,
0.02023485116660595,
0.007669396698474884,
0.036135561764240265,
-0.0032062919344753027,
-0.06021053344011307,
-0.0457371287047863,
-0.010818656533956528,
-0.009706257842481136,
0.048727963119745255,
-0.02547784522175789,
-0.04011198505759239,
-0.00017055663920473307,
0.013998452574014664,
0.03264617174863815,
-0.010378987528383732,
-0.0019177868962287903,
0.06208628788590431,
0.037623241543769836,
0.03797711059451103,
0.04289930686354637,
0.008645922876894474,
0.04036946967244148,
0.0010863948846235871,
-0.042563971132040024,
0.011877703480422497,
0.01651296578347683,
-0.01591189019382,
0.08595844358205795,
0.02565467357635498,
-0.041776590049266815,
0.03621917590498924,
0.05248891934752464,
-0.058291759341955185,
-0.015129291452467442,
-0.10606610774993896,
-0.0038144129794090986,
0.025914715602993965,
-0.041670892387628555,
0.025639906525611877,
0.06444907933473587,
-0.025361500680446625,
0.025338059291243553,
-0.02992147207260132,
0.04214628413319588,
0.005114903207868338,
0.03445839136838913,
-0.029416564851999283,
-0.05518943816423416,
0.03704318404197693,
0.004971133545041084,
0.01848856918513775,
-0.02257130853831768,
0.013334114104509354,
0.08101924508810043,
-0.00987920444458723,
0.02859673835337162,
0.03495211899280548,
-0.04231519252061844,
0.029277276247739792,
-0.0068034157156944275,
-0.001611228915862739,
-0.00416962057352066,
-0.033944420516490936,
0.03193831443786621,
0.005508408881723881,
0.01769150421023369,
0.004210307728499174,
0.024431275203824043,
0.05111008509993553,
0.028837641701102257,
0.010455720126628876,
-0.0855005607008934,
-0.03744381293654442,
0.05241994932293892,
-0.06150748208165169,
-0.024065377190709114,
0.09160422533750534,
0.0028818175196647644,
-0.021007254719734192,
0.007440727204084396,
0.05737064778804779,
0.027025561779737473,
-0.0050409152172505856,
-0.03458917513489723,
-0.04335521534085274,
-0.015931131318211555,
-0.010112631134688854,
0.07045673578977585,
-0.023832527920603752,
0.01970520243048668,
-0.010433102957904339,
0.006412140093743801,
0.03820732235908508,
0.04100435599684715,
0.04024864360690117,
-0.02010982856154442,
-0.04127906635403633,
-0.015372062101960182,
-0.0018685860559344292,
-0.020160095766186714,
0.014580869115889072,
-0.00818509329110384,
-0.001284088590182364,
0.007704403251409531,
0.020848123356699944,
0.01491477806121111,
0.007714579347521067,
-0.00936658214777708,
-0.021919341757893562,
-0.027951132506132126,
-0.02951890043914318,
-0.02852500043809414,
-0.04732362926006317,
0.04740501195192337,
0.0067025162279605865,
-0.02930145524442196,
0.06302076578140259,
-0.02103363163769245,
-0.03541741892695427,
0.04855440929532051,
-0.006179700139909983,
0.013775344006717205,
0.009350725449621677,
0.028816604986786842,
0.0943022146821022,
-0.04866091534495354,
0.012721970677375793,
-0.0001162446933449246,
-0.03180467337369919,
0.004863265436142683,
0.0548771396279335,
0.020228732377290726,
-0.05212060362100601,
0.05058278515934944,
0.021418731659650803,
0.03978528827428818,
-0.03243843466043472,
-0.018712326884269714,
0.02382683753967285,
-0.0007024998776614666,
0.019490506500005722,
-0.014170472510159016,
-0.02680867165327072,
-0.00576054397970438,
-0.017126262187957764,
0.0009100250317715108,
-0.027970774099230766,
0.011063572019338608,
0.0015883093001320958,
-0.0007049879641272128,
0.0214814655482769,
0.002871536649763584,
0.03519463539123535,
0.010699686594307423,
0.028765996918082237,
-0.028201425448060036,
-0.04426832124590874,
-0.021652255207300186,
-0.003026575781404972,
-0.04614725708961487,
-0.03168416768312454,
-0.029495924711227417,
0.0195817481726408,
-0.0016856164438650012,
-0.01420043595135212,
0.04536714404821396,
0.029359430074691772,
0.0193018801510334,
0.0019452476408332586,
0.0353991761803627,
0.0020734998397529125,
-0.009080487303435802,
0.0021756035275757313,
-0.02317039854824543,
0.006830422207713127,
0.02312609925866127,
0.036822523921728134,
-0.006179644260555506,
0.02338588796555996,
0.008802122436463833,
-0.00947361346334219,
-0.06072219833731651,
0.009171603247523308,
0.019544029608368874,
-0.024116693064570427,
0.017495566979050636,
0.026049304753541946,
0.027565091848373413,
0.02542353793978691,
0.0009262659586966038,
0.029620280489325523,
-0.024958785623311996,
-0.00040495945722796023,
0.014933748170733452,
0.0008989341440610588,
-0.012632808648049831,
-0.009696537628769875,
0.07334323972463608,
0.01874386891722679,
0.02262343280017376,
0.07361700385808945,
0.03221290558576584,
0.040516190230846405,
0.0010052633006125689,
-0.040243394672870636,
0.054400693625211716,
0.051007967442274094,
0.04533134028315544,
-0.028682807460427284,
0.04518906772136688,
0.004851376637816429,
0.03690708056092262,
-0.004782390780746937,
0.056423697620630264,
-0.014546889811754227,
0.011865327134728432,
0.039837103337049484,
-0.06473647803068161,
0.006993791554123163,
-0.037502653896808624,
-0.033691540360450745,
-0.03379778563976288,
-0.029967855662107468,
-0.0089926952496171,
-0.008007586933672428,
0.011950942687690258,
0.03367368504405022,
-0.0527440570294857,
0.024038182571530342,
-0.014761969447135925,
-0.00890416745096445,
-0.03387009724974632,
0.013623968698084354,
-0.011101970449090004,
-0.027688486501574516,
0.025853322818875313,
0.007951270788908005,
0.04023148864507675,
-0.029895959421992302,
-0.04385081306099892,
-0.026927920058369637,
0.019618134945631027,
0.037904880940914154,
-0.04147337004542351,
-0.03489754721522331,
-0.01988833211362362,
0.017988713458180428,
0.07450718432664871,
-0.06061336398124695,
-0.02176525816321373,
0.013554293662309647,
0.008647418580949306,
-0.018781377002596855,
-0.022813186049461365,
0.03710438683629036,
-0.06456976383924484
] |
<p>Including air resistance, what is the escape velocity from the surface of the earth for a free-flying trajectile?</p> | g5525 | [
-0.0025387669447809458,
0.0834880843758583,
-0.0008697696612216532,
0.05760295316576958,
-0.06591427326202393,
0.055708616971969604,
0.056161943823099136,
-0.035422295331954956,
-0.01169213093817234,
-0.02418549172580242,
-0.0456908717751503,
-0.012379718013107777,
0.020514672622084618,
0.03091244399547577,
0.05911658704280853,
0.050282929092645645,
0.043267566710710526,
-0.06958921253681183,
0.04380699619650841,
-0.018928272649645805,
0.025797659531235695,
-0.06979243457317352,
-0.01935659535229206,
-0.03718281537294388,
0.005450362339615822,
-0.026904050260782242,
-0.037144530564546585,
-0.06662721931934357,
-0.07808899134397507,
0.0359639972448349,
0.002072220668196678,
-0.020748449489474297,
0.06133483350276947,
-0.03405226767063141,
-0.08957136422395706,
0.03172115981578827,
-0.013375955633819103,
0.00843089073896408,
0.011583601124584675,
-0.04208269715309143,
0.015273109078407288,
-0.055521298199892044,
-0.04756247624754906,
0.04363388568162918,
0.06448584049940109,
-0.03340540826320648,
0.03654779493808746,
-0.008969586342573166,
-0.041831329464912415,
0.001868747640401125,
-0.027001002803444862,
0.08304738253355026,
-0.013036880642175674,
0.0001426844100933522,
-0.10199781507253647,
-0.006272266153246164,
0.026435770094394684,
-0.07865364849567413,
0.019203122705221176,
-0.019220707938075066,
-0.016166070476174355,
-0.045987293124198914,
-0.033757440745830536,
-0.03477984666824341,
0.08991037309169769,
0.05520852282643318,
-0.0705624371767044,
0.027882110327482224,
0.01579608954489231,
-0.007397843059152365,
0.09177698940038681,
-0.0389266274869442,
-0.06124802306294441,
-0.02244456112384796,
-0.05927927792072296,
0.0027362590190023184,
0.013633166439831257,
-0.04699867591261864,
0.0567113421857357,
0.010127977468073368,
-0.013144785538315773,
0.021250132471323013,
0.006023768335580826,
0.021799361333251,
0.041563697159290314,
-0.026007845997810364,
0.03040282055735588,
0.0056051225401461124,
-0.04830903932452202,
-0.05345602706074715,
0.005480028223246336,
-0.026960600167512894,
0.042070068418979645,
0.006459545344114304,
0.015620706602931023,
-0.02034483104944229,
0.0023089610040187836,
0.037420935928821564,
0.015841953456401825,
0.0010395976714789867,
-0.026712780818343163,
-0.013619831763207912,
-0.025277210399508476,
0.019703498110175133,
0.013732866384088993,
-0.026565205305814743,
0.04855514317750931,
-0.024190030992031097,
0.06250300258398056,
-0.016224322840571404,
0.07748875021934509,
0.011842887848615646,
-0.02625148743391037,
-0.03505629301071167,
0.03698442876338959,
-0.03221993148326874,
-0.003201026003807783,
-0.09304088354110718,
-0.0035199110861867666,
0.03404945135116577,
0.005293870810419321,
0.007205257657915354,
0.017250075936317444,
0.04105260223150253,
-0.01961369998753071,
0.01415975857526064,
0.0032873665913939476,
-0.06909660995006561,
0.0064017921686172485,
0.016203148290514946,
-0.03435276076197624,
-0.001619420014321804,
0.0021879649721086025,
0.0189010351896286,
-0.01714140549302101,
-0.01691793091595173,
-0.007366351783275604,
0.011545458808541298,
-0.04639064520597458,
0.016753612086176872,
0.03636334463953972,
-0.02641877718269825,
0.07073581218719482,
0.013095922768115997,
-0.014487290754914284,
-0.03914187103509903,
0.029214465990662575,
0.05818430706858635,
0.04543274641036987,
-0.011772158555686474,
0.0410672165453434,
0.052359677851200104,
0.002644183812662959,
0.03566240519285202,
-0.057188719511032104,
-0.03303315117955208,
0.01886068657040596,
0.021996889263391495,
0.02040439285337925,
-0.03837340697646141,
0.04035092517733574,
-0.0414169579744339,
0.08375425636768341,
0.025981541723012924,
-0.03896492347121239,
0.01977534219622612,
-0.041895728558301926,
-0.016069035977125168,
0.0018607614329084754,
0.00982542335987091,
-0.05704326927661896,
-0.05896753817796707,
0.031117921695113182,
0.03432374447584152,
-0.02818435989320278,
-0.000525655981618911,
0.07195910811424255,
-0.007220789790153503,
-0.009938727132976055,
-0.027563147246837616,
0.08641843497753143,
-0.025233587250113487,
0.019397594034671783,
0.009241614490747452,
0.004813360050320625,
-0.032557062804698944,
-0.021561147645115852,
0.010437915101647377,
-0.02717101387679577,
0.006689118221402168,
0.00893888808786869,
-0.049171384423971176,
-0.010349420830607414,
-0.03354932740330696,
-0.0476190559566021,
-0.009021703153848648,
0.014860393479466438,
-0.002054008189588785,
-0.025598354637622833,
0.0016186016146093607,
0.007669409736990929,
0.05679474398493767,
0.02376323938369751,
-0.0387461893260479,
-0.010627680458128452,
-0.022170761600136757,
0.0023082853294909,
0.024172978475689888,
0.00030019835685379803,
0.05405566096305847,
0.06717746704816818,
-0.0010556537890806794,
0.05633268877863884,
0.041042909026145935,
0.050903234630823135,
0.002630552975460887,
-0.023809021338820457,
-0.025951288640499115,
-0.0015167301753535867,
0.007834955118596554,
0.022699646651744843,
0.0025883964262902737,
0.03287769481539726,
-0.020192619413137436,
0.024499768391251564,
-0.01774442568421364,
-0.017315831035375595,
-0.008097353391349316,
0.0023417046759277582,
0.013461130671203136,
0.006299125030636787,
-0.05551690608263016,
0.019615987315773964,
-0.011114257387816906,
0.01371055468916893,
0.02039574831724167,
0.05552735924720764,
0.05343027412891388,
-0.0224441010504961,
-0.017389876767992973,
0.05077558010816574,
-0.02163512632250786,
-0.060781583189964294,
0.004257172346115112,
0.025027485564351082,
-0.019798999652266502,
0.0067446185275912285,
0.024188047274947166,
0.012922065332531929,
0.017313912510871887,
-0.008925994858145714,
0.02894943207502365,
-0.01386059820652008,
0.09592056274414062,
-0.03988980874419212,
0.03954533115029335,
-0.06055891886353493,
-0.03572468459606171,
-0.07902386784553528,
-0.0006476746057160199,
-0.03504180163145065,
-0.025674065575003624,
-0.011186170391738415,
-0.010046040639281273,
-0.08573257178068161,
0.03023226372897625,
0.012155325151979923,
0.056773632764816284,
0.03129858151078224,
-0.028925403952598572,
-0.013794287107884884,
0.030493956059217453,
0.010379391722381115,
0.08237431198358536,
-0.020950643345713615,
-0.020397786051034927,
0.030161753296852112,
-0.02289927564561367,
-0.05513693019747734,
0.003627565922215581,
0.007950996980071068,
0.004246474243700504,
-0.04771415889263153,
0.04957135394215584,
0.03736408054828644,
-0.0476699136197567,
0.04296603426337242,
0.12596440315246582,
-0.029459208250045776,
-0.006233861669898033,
-0.03326321020722389,
-0.006252676248550415,
0.003721458138898015,
0.048039715737104416,
0.02701716683804989,
0.0013126999838277698,
0.016835754737257957,
-0.050614532083272934,
-0.03709074482321739,
-0.02524759992957115,
0.037681397050619125,
-0.02505671977996826,
0.008764676749706268,
0.01434243656694889,
-0.09774399548768997,
0.03201810643076897,
-0.0067831529304385185,
-0.016331994906067848,
0.035636309534311295,
-0.05615485832095146,
-0.0052167195826768875,
0.06681229919195175,
0.017290743067860603,
0.0052767847664654255,
0.008719165809452534,
-0.03459000214934349,
0.009502450004220009,
0.02038556896150112,
0.03873598948121071,
0.02655806392431259,
-0.016434643417596817,
-0.10561330616474152,
-0.012950130738317966,
0.04079308360815048,
0.007571838330477476,
-0.01631896011531353,
-0.011306742206215858,
0.006477393675595522,
-0.01922648958861828,
-0.029492929577827454,
0.04202113300561905,
0.10939199477434158,
-0.014958161860704422,
-0.008731135167181492,
-0.027210146188735962,
0.01663346216082573,
0.0442068949341774,
-0.0025322490837424994,
0.06941431015729904,
-0.012818937189877033,
-0.02300959639251232,
-0.0129670649766922,
-0.06584349274635315,
-0.01488859485834837,
0.03425576910376549,
-0.036143362522125244,
0.03921505808830261,
-0.010289463214576244,
-0.026955388486385345,
-0.005971505306661129,
0.05763547122478485,
-0.06283988803625107,
-0.040285058319568634,
-0.05918314680457115,
-0.03352605551481247,
0.0585302971303463,
0.017194051295518875,
0.016004223376512527,
0.004253068007528782,
-0.006547863595187664,
-0.017361663281917572,
0.0061545055359601974,
-0.010282859206199646,
0.04032019153237343,
0.0044618332758545876,
-0.07373228669166565,
-0.033606428653001785,
0.032940324395895004,
-0.06485670804977417,
-0.031924519687891006,
0.016822747886180878,
0.0050957524217665195,
-0.02375699020922184,
0.04076465964317322,
-0.0017280196771025658,
0.0067831408232450485,
0.008502745069563389,
-0.035408295691013336,
-0.024008281528949738,
-0.002997553674504161,
0.02340352162718773,
0.008483602665364742,
-0.0044569275341928005,
0.009184039197862148,
0.05227687209844589,
0.028091197833418846,
-0.042706068605184555,
-0.0051227170042693615,
-0.009845257736742496,
-0.015044132247567177,
-0.015462517738342285,
-0.04135880991816521,
0.008468948304653168,
-0.021405953913927078,
0.003179730847477913,
-0.0018870005151256919,
-0.011516968719661236,
0.029435202479362488,
-0.002390473848208785,
0.07470934838056564,
0.10150422155857086,
0.006572128273546696,
-0.030096692964434624,
0.06578019261360168,
-0.008135524578392506,
0.0426836833357811,
-0.02276456728577614,
-0.00952194631099701,
0.006868650205433369,
0.03270683437585831,
0.004251958802342415,
0.007836533710360527,
-0.06751152127981186,
-0.05400386452674866,
-0.014882453717291355,
-0.004525330383330584,
-0.035252634435892105,
-0.0006342804408632219,
0.020078444853425026,
0.012055603787302971,
-0.0342254675924778,
0.02167213149368763,
0.05361646041274071,
-0.05302250012755394,
-0.001208132365718484,
0.01377852726727724,
0.040639933198690414,
0.016864433884620667,
-0.035616226494312286,
-0.02635037526488304,
0.01580999605357647,
0.03320474177598953,
-0.028954079374670982,
0.02830515243113041,
-0.06246146932244301,
0.06828245520591736,
0.03134922310709953,
0.058416806161403656,
0.028292052447795868,
-0.02388829179108143,
-0.01023278571665287,
0.028885742649435997,
0.03058505244553089,
-0.007781293708831072,
-0.005941265728324652,
0.044574689120054245,
0.029636727645993233,
-0.06040630489587784,
0.017438430339097977,
-0.02312670275568962,
0.009038573130965233,
-0.02112969011068344,
-0.020773427560925484,
0.0667286068201065,
-0.08588653057813644,
0.000769684324041009,
-0.031584467738866806,
-0.03049086220562458,
0.016584541648626328,
0.019399911165237427,
0.005947023164480925,
-0.04726756364107132,
-0.0259256549179554,
0.0030505082104355097,
-0.019914697855710983,
0.002414154354482889,
-0.05817142501473427,
0.009835421107709408,
-0.006412393879145384,
-0.02884914167225361,
0.006130919326096773,
-0.003597076516598463,
0.015220019035041332,
0.049575742334127426,
-0.09507586807012558,
0.07704586535692215,
0.006577763240784407,
0.007919804193079472,
0.01847079209983349,
0.015408538281917572,
0.005149743054062128,
0.03916635364294052,
-0.011580017395317554,
0.059161074459552765,
-0.009022488258779049,
-0.007936287671327591,
-0.020430179312825203,
-0.025637414306402206,
0.006496293470263481,
-0.008714228868484497,
-0.022493066266179085,
0.014504623599350452,
-0.03552620857954025,
0.02132968045771122,
-0.06206844374537468,
0.03684162348508835,
0.01139781903475523,
-0.0178204495459795,
0.006791659630835056,
-0.009937004186213017,
-0.07097173482179642,
-0.01064132247120142,
0.012292559258639812,
0.02997826598584652,
0.03761819377541542,
0.017298907041549683,
0.02779514156281948,
-0.013109575025737286,
-0.008595000952482224,
0.030804481357336044,
-0.022856056690216064,
-0.02540450356900692,
-0.039743147790431976,
-0.03448221832513809,
0.015155584551393986,
0.027505144476890564,
0.017274511978030205,
0.04482162743806839,
0.031121155247092247,
0.015482478775084019,
0.06357364356517792,
-0.006060277111828327,
0.03825653716921806,
0.05985419079661369,
0.004451586399227381,
0.018050799146294594,
-0.03545266389846802,
-0.02738979458808899,
-0.000150578809552826,
0.010931074619293213,
-0.01624920964241028,
-0.0328417532145977,
0.030075624585151672,
-0.0075163631699979305,
0.04108969867229462,
-0.014756270684301853,
0.013441134244203568,
0.0011789248092100024,
0.0021248997654765844,
-0.09327396750450134,
-0.09931350499391556,
-0.007914324291050434,
-0.004217945039272308,
0.03391696885228157,
0.023208649829030037,
0.03787199407815933,
0.013313534669578075,
0.025352787226438522,
-0.018026795238256454,
-0.012589774094522,
-0.03916646167635918,
-0.005099039524793625,
0.003138086060062051,
0.003521757898852229,
-0.04577722027897835,
0.061425864696502686,
-0.03067728504538536,
0.0013904573861509562,
-0.020304040983319283,
0.016311144456267357,
0.04351804405450821,
0.004046743735671043,
0.046729836612939835,
0.03346678242087364,
0.005041627213358879,
-0.05037353187799454,
0.03550787270069122,
-0.021140102297067642,
-0.006861713714897633,
-0.03489384055137634,
-0.029061196371912956,
-0.007485369220376015,
0.003317824099212885,
0.03128121420741081,
-0.018119843676686287,
0.00427239341661334,
-0.018375469371676445,
-0.028635961934924126,
-0.02417939342558384,
0.0034222437534481287,
-0.027819959446787834,
-0.014544839039444923,
0.04315996170043945,
-0.07047080993652344,
-0.08282651007175446,
0.0026076387148350477,
-0.08265204727649689,
-0.03564023971557617,
-0.01862715743482113,
-0.014664932154119015,
-0.007887792773544788,
0.0009267731220461428,
0.034251656383275986,
-0.01731301099061966,
-0.018003614619374275,
-0.023539137095212936,
-0.043712615966796875,
-0.006369858980178833,
-0.024731995537877083,
0.04729573056101799,
0.040935710072517395,
-0.008046195842325687,
0.03607909381389618,
-0.04539317637681961,
0.04651011526584625,
-0.0006869117496535182,
0.02880934067070484,
-0.005687138065695763,
0.05345899984240532,
-0.03182392567396164,
-0.04235835745930672,
0.04988456144928932,
0.059639014303684235,
-0.006810311693698168,
-0.0044884770177304745,
0.015658656135201454,
0.0465354286134243,
0.010111461393535137,
-0.010533853434026241,
-0.02687714248895645,
0.021623609587550163,
0.017268139868974686,
0.00847598910331726,
0.004616370424628258,
-0.026123279705643654,
-0.06325319409370422,
0.01526755653321743,
0.05093162879347801,
-0.04212389141321182,
-0.0184025838971138,
-0.004032468423247337,
0.04081875830888748,
0.0026776858139783144,
-0.023033451288938522,
-0.004438885021954775,
0.024459663778543472,
-0.04017329961061478,
-0.0450122095644474,
0.03600580617785454,
0.029101355001330376,
-0.01207241602241993,
0.002530044876039028,
-0.039455596357584,
-0.011332200840115547,
-0.08171503990888596,
0.0309662576764822,
-0.011816618032753468,
-0.0706121176481247,
0.05257360637187958,
-0.03811991587281227,
-0.00008355867612408474,
-0.031044043600559235,
0.019203847274184227,
0.05998779460787773,
-0.007341509684920311,
-0.0008472107001580298,
-0.04938264936208725,
0.024276401847600937,
-0.017959624528884888,
-0.024470172822475433,
-0.004371656104922295,
-0.03310873731970787,
0.0011829988798126578,
0.007836783304810524,
0.007873276248574257,
0.005553910043090582,
0.0025559603236615658,
-0.006119164638221264,
-0.027411991730332375,
-0.031228089705109596,
0.006032906007021666,
0.053549572825431824,
-0.05548044294118881,
0.06451887637376785,
-0.057722873985767365,
0.03740652650594711,
-0.03839752450585365,
0.021375738084316254,
0.012004942633211613,
0.001751699368469417,
0.01460086926817894,
0.023540763184428215,
-0.004652039147913456,
0.0511283278465271,
0.04513564705848694,
0.002390401205047965,
-0.006056918762624264,
0.04092179611325264,
0.007783294189721346,
-0.03504208102822304,
-0.016337700188159943,
0.10245360434055328,
0.028404468670487404,
-0.06233843415975571,
-0.0229079257696867,
0.03907916694879532,
-0.010876400396227837,
-0.012054641731083393,
0.06118194758892059,
0.012506806291639805,
0.0006929059163667262,
0.022235864773392677,
0.0011712746927514672,
0.0034118008334189653,
0.007564293686300516,
-0.006798917427659035,
0.04279806464910507,
-0.03867311030626297,
-0.049063894897699356,
-0.016683993861079216,
-0.004256765358150005,
0.011719807051122189,
0.03747357800602913,
0.01829156093299389,
0.015390004962682724,
0.008908836171030998,
0.027827363461256027,
0.04152492433786392,
0.011316012591123581,
0.01140835601836443,
0.049043573439121246,
-0.007520877290517092,
-0.013923564925789833,
-0.0455223023891449,
0.00009046474588103592,
0.026256324723362923,
-0.037377625703811646,
-0.026168659329414368,
0.015149819664657116,
-0.11568882316350937,
-0.00550120510160923,
0.0031745543237775564,
0.03693733736872673,
0.05130528658628464,
-0.07348310947418213,
-0.0028553446754813194,
0.0054000383242964745,
-0.0007865306688472629,
-0.02006995677947998,
0.004143994767218828,
-0.021157970651984215,
0.04882519692182541,
0.022263597697019577,
-0.0035430695861577988,
0.0010831686668097973,
-0.009869529865682125,
0.0747738927602768,
0.04173268377780914,
-0.01927182637155056,
0.014101112261414528,
0.09425967186689377,
0.01011962816119194,
-0.034798916429281235,
0.005698577966541052,
-0.003707221243530512,
-0.052770961076021194,
-0.012418548576533794,
-0.020668400451540947,
0.022387079894542694,
-0.03435302525758743,
-0.04229357838630676,
-0.04881937429308891,
0.01977059617638588,
0.00923091173171997,
-0.036449968814849854,
-0.07094576954841614,
-0.013157201930880547,
0.04394865781068802
] |
<p>I'm taking an optics lab in which I'm required to construct an interferometer, and measure the wavelength of a laser, and the coherence length of the light emitted from a candle fire.</p>
<p>Now, I've been hinted by my instructor that when working with mirrors (which are present in an interferometer), it is best to make sure that the laser is polarized to either "P" or "S" polarization - otherwise, the mirrors might give an elliptic component to the polarization, which in turn will spoil the measurment, due to interference effects.</p>
<p><strong>So now comes the question: should the light from the candle be polarized as well??</strong></p>
<p>I have a reason to suspect that polarizing it will improve the coherence length, and on the other hand, I'm pretty sure that elliptical polarization will take effect if the light remains untouched.</p>
<p>What is your opinion on this dilemma??
Thanks!!</p> | g5526 | [
-0.04859549179673195,
-0.06957577913999557,
0.030217260122299194,
-0.03284279629588127,
0.01847834885120392,
0.04831234738230705,
-0.03659277409315109,
0.029806291684508324,
0.029780711978673935,
0.0018658371409401298,
0.05099331587553024,
0.009907755069434643,
-0.0059411851689219475,
-0.005210474599152803,
0.003165624337270856,
0.01631987653672695,
0.07605941593647003,
0.0035942550748586655,
-0.019547440111637115,
0.047507625073194504,
-0.03366269916296005,
0.02844061888754368,
-0.005194658879190683,
-0.050147127360105515,
-0.011998670175671577,
-0.000029805280064465478,
0.008721933700144291,
-0.03580310568213463,
0.0008310703560709953,
-0.00922301970422268,
-0.024713603779673576,
-0.03212808445096016,
0.029701652005314827,
0.0009998574387282133,
-0.10286961495876312,
0.0038436453323811293,
-0.007897445932030678,
0.053442273288965225,
0.05746222659945488,
-0.02322431653738022,
0.007130652666091919,
0.031094921752810478,
-0.009527369402348995,
0.017995495349168777,
0.05518212914466858,
0.009280492551624775,
0.04237383231520653,
0.018857404589653015,
0.040366511791944504,
-0.02629214897751808,
-0.008342534303665161,
0.005661595147103071,
0.012575304135680199,
0.014728008769452572,
0.039882510900497437,
0.06471210718154907,
-0.04965561255812645,
-0.021955501288175583,
0.020454274490475655,
0.029712244868278503,
0.06380315124988556,
-0.08062069863080978,
-0.09527629613876343,
-0.026923632249236107,
-0.04757935181260109,
0.03683244436979294,
-0.0373111292719841,
-0.020983949303627014,
0.00003427898991503753,
0.032402582466602325,
-0.01690935343503952,
0.00033246446400880814,
0.02518305554986,
-0.028514178469777107,
-0.05164685472846031,
0.03802643343806267,
0.03266654163599014,
0.048265255987644196,
0.04788389056921005,
0.03449526056647301,
-0.013036271557211876,
-0.032743364572525024,
0.03129062429070473,
-0.00037357970722950995,
0.0457427017390728,
-0.0036216790322214365,
0.007930795662105083,
-0.04911002889275551,
-0.00570639967918396,
-0.007846299558877945,
0.031734757125377655,
-0.046417541801929474,
0.07280300557613373,
0.0215847697108984,
-0.01848692074418068,
-0.001633160631172359,
0.05037218704819679,
0.01092479471117258,
-0.005850198213011026,
0.10801216214895248,
-0.045829176902770996,
-0.03447442874312401,
-0.08880136907100677,
0.03948083892464638,
0.040898118168115616,
-0.02181258052587509,
-0.041013069450855255,
0.02220987156033516,
-0.07475122064352036,
-0.007896644063293934,
-0.09772347658872604,
-0.03570965677499771,
-0.0925145149230957,
-0.022664733231067657,
-0.018782196566462517,
0.005231989547610283,
0.03932059183716774,
0.003726447466760874,
0.03639637678861618,
0.03187907114624977,
0.030933978036046028,
0.008544517681002617,
0.05908853933215141,
0.03567139804363251,
0.0021569940727204084,
-0.0006627116817981005,
0.0246683731675148,
-0.0031516854651272297,
0.06652893871068954,
-0.02484598383307457,
-0.04462563619017601,
0.049472056329250336,
-0.05729442462325096,
0.02575059048831463,
-0.012715591117739677,
0.019131813198328018,
0.019706428050994873,
-0.013667969964444637,
0.0014106265734881163,
0.04415782541036606,
-0.04658079147338867,
0.017555663362145424,
0.035132620483636856,
-0.014962445944547653,
-0.07654906809329987,
-0.006485630292445421,
-0.0030445328447967768,
0.01473822072148323,
0.06500029563903809,
0.05212469771504402,
0.011105144396424294,
0.05665052309632301,
0.010324660688638687,
-0.023259775713086128,
-0.013754738494753838,
-0.009081762284040451,
-0.08614811301231384,
-0.034909557551145554,
0.03032173588871956,
0.017138486728072166,
0.03437512740492821,
0.039873313158750534,
-0.046350348740816116,
-0.016394125297665596,
-0.06092989444732666,
0.0506998710334301,
0.02460213005542755,
-0.07613896578550339,
-0.017123203724622726,
0.002652129391208291,
-0.0777483731508255,
0.032934896647930145,
0.05998917669057846,
0.0045004431158304214,
-0.011388559825718403,
0.0375562459230423,
0.037805140018463135,
-0.026455046609044075,
0.036411356180906296,
0.03480101749300957,
-0.024494849145412445,
0.023101303726434708,
-0.041035331785678864,
-0.039561640471220016,
0.001569291460327804,
-0.01665966957807541,
0.011913968250155449,
-0.059413228183984756,
-0.0693882405757904,
0.023513266816735268,
0.04222886636853218,
0.0008429174777120352,
-0.030941249802708626,
0.04211600124835968,
-0.048640210181474686,
-0.009860651567578316,
-0.010250845924019814,
-0.024128396064043045,
-0.03908897191286087,
0.012714524753391743,
-0.07209838926792145,
0.012021549977362156,
0.04136474430561066,
0.034704193472862244,
-0.048347100615501404,
-0.03706689551472664,
-0.017609110102057457,
-0.024190161377191544,
-0.05180047079920769,
0.005255313590168953,
0.07391595095396042,
0.050567492842674255,
-0.01764165423810482,
0.008861595764756203,
0.001968735596165061,
0.026652386412024498,
-0.03719723969697952,
0.040511906147003174,
-0.01088692806661129,
0.030575115233659744,
-0.03703029081225395,
0.02595321275293827,
0.0372203104197979,
-0.0417540967464447,
-0.03551386296749115,
-0.031754445284605026,
-0.045709677040576935,
0.007693259045481682,
-0.025597410276532173,
0.054375242441892624,
-0.03190245479345322,
-0.018943000584840775,
0.014261981472373009,
-0.0014148243935778737,
0.055249664932489395,
0.025569239631295204,
-0.03738369047641754,
0.005434886552393436,
0.000951720867305994,
-0.0077062384225428104,
0.037981580942869186,
-0.028060823678970337,
0.003374276449903846,
0.012788549065589905,
0.032834243029356,
-0.030094074085354805,
-0.014894291758537292,
0.07096300274133682,
-0.009718761779367924,
-0.02574780583381653,
-0.027789724990725517,
0.010030696168541908,
0.025721710175275803,
-0.06325260549783707,
-0.04448636993765831,
-0.01424278225749731,
0.012239919044077396,
0.022029520943760872,
-0.047117263078689575,
0.07688740640878677,
0.0457349568605423,
-0.08007261157035828,
0.009535606019198895,
-0.035748112946748734,
-0.026589136570692062,
0.035138923674821854,
0.0001906666875584051,
-0.01054106280207634,
0.008724602870643139,
-0.01896357350051403,
-0.005267470609396696,
0.09874344617128372,
-0.02857995592057705,
0.07649445533752441,
0.06417237967252731,
0.02551303617656231,
-0.05658010020852089,
-0.0398937352001667,
0.034456927329301834,
-0.009870978072285652,
-0.02594071254134178,
0.014480821788311005,
-0.06484746932983398,
0.027061181142926216,
0.0459728017449379,
-0.011458558961749077,
0.019598163664340973,
0.040733423084020615,
0.00014300714246928692,
0.007138837594538927,
0.012605869211256504,
0.030568396672606468,
-0.03344873711466789,
0.006744447164237499,
0.00013392091204877943,
-0.03868841379880905,
-0.01671431213617325,
-0.0512913353741169,
0.04121579974889755,
0.022568169981241226,
-0.008787520229816437,
0.03801002725958824,
-0.06270401924848557,
-0.05477719381451607,
0.00744877103716135,
0.021061928942799568,
-0.07072734087705612,
-0.07167882472276688,
0.025932831689715385,
0.03028928115963936,
0.006175547372549772,
-0.008047462441027164,
-0.04340846464037895,
0.0022525815293192863,
0.006885678041726351,
0.0028632718604058027,
-0.07747013121843338,
-0.010284081101417542,
-0.015236733481287956,
0.055797088891267776,
-0.04105258733034134,
-0.009604225866496563,
-0.020451398566365242,
-0.04568054527044296,
0.0070766881108284,
0.02465672418475151,
0.05725551396608353,
-0.05713497847318649,
0.0032912627793848515,
0.013486858457326889,
0.011749550700187683,
0.03017798438668251,
-0.04175807535648346,
0.007532887626439333,
-0.0008088586619123816,
-0.010711881332099438,
-0.09121149778366089,
0.024577850475907326,
-0.006993537303060293,
0.05620339885354042,
-0.0033787116408348083,
-0.011816442012786865,
-0.02613637037575245,
-0.04158396273851395,
0.017889413982629776,
-0.03186015039682388,
-0.037980273365974426,
0.012464689090847969,
-0.057984817773103714,
-0.005390524864196777,
0.019775481894612312,
-0.022379187867045403,
0.007804716005921364,
-0.029972899705171585,
0.0021445436868816614,
0.0180683396756649,
-0.026286570355296135,
0.05026085302233696,
-0.019327813759446144,
-0.024267442524433136,
-0.012265734374523163,
0.028748609125614166,
-0.052995067089796066,
-0.0361679382622242,
-0.04057089239358902,
-0.04198523983359337,
-0.0035295577254146338,
-0.001390010118484497,
-0.004917192738503218,
0.05656364560127258,
0.00959615595638752,
0.007105776574462652,
-0.06706822663545609,
-0.05528225004673004,
0.029591621831059456,
0.0004342733009252697,
0.029769185930490494,
0.06845928728580475,
-0.05212332308292389,
-0.023195452988147736,
-0.04344085603952408,
0.03511831909418106,
-0.019211607053875923,
0.015281923115253448,
0.011312134563922882,
-0.027204420417547226,
0.019063254818320274,
0.029694076627492905,
0.014708741568028927,
-0.0433480404317379,
0.009618204087018967,
-0.004147549159824848,
-0.00918135792016983,
-0.0034807217307388783,
-0.021968912333250046,
-0.01453724317252636,
0.009350091218948364,
-0.015577190555632114,
-0.0010585241252556443,
-0.0028777667321264744,
0.02309914119541645,
0.03845492750406265,
0.02062855288386345,
0.019127456471323967,
-0.04589984938502312,
-0.01726355217397213,
-0.002471460262313485,
-0.011331249959766865,
-0.020893827080726624,
0.027137625962495804,
0.006022836081683636,
-0.017532633617520332,
-0.04021678492426872,
-0.025582266971468925,
-0.00848434492945671,
0.011259516701102257,
-0.042083989828825,
-0.01691223680973053,
0.054349277168512344,
0.009027931839227676,
0.01567031629383564,
0.02575845643877983,
0.03186911717057228,
-0.026029540225863457,
0.021137794479727745,
0.025391923263669014,
0.047727301716804504,
-0.04176885262131691,
-0.0083705959841609,
-0.010161839425563812,
0.008945336565375328,
0.012277171947062016,
0.012277750298380852,
-0.07861046493053436,
-0.000505650183185935,
-0.0028126207180321217,
0.03384304419159889,
0.040190257132053375,
0.00742768170312047,
0.01683434471487999,
0.020975060760974884,
0.02393765188753605,
0.031933289021253586,
-0.024203525856137276,
-0.02256338857114315,
-0.04717414453625679,
-0.027736200019717216,
-0.05169260501861572,
0.03037698194384575,
-0.03488091379404068,
-0.0029021960217505693,
0.020013457164168358,
-0.01754840649664402,
-0.03452814742922783,
-0.02314167097210884,
0.059325966984033585,
-0.048537030816078186,
0.08118001371622086,
0.0560094490647316,
0.01609581895172596,
-0.015785912051796913,
0.023633111268281937,
-0.08661673218011856,
0.007385897915810347,
0.0708293691277504,
-0.01875169761478901,
-0.04956483095884323,
-0.01325312815606594,
-0.045738477259874344,
0.009185424074530602,
0.020302826538681984,
-0.023353297263383865,
0.011593465693295002,
0.06189513951539993,
-0.0019023838685825467,
-0.03735281154513359,
-0.006347909104079008,
0.008905633352696896,
-0.04005742818117142,
-0.05088069289922714,
-0.0353974774479866,
-0.05298156663775444,
0.08785255253314972,
-0.033309247344732285,
0.0226035974919796,
-0.007936283946037292,
-0.03943749889731407,
-0.01516044419258833,
0.008482247591018677,
-0.045306768268346786,
-0.0073662251234054565,
0.08359061181545258,
-0.0018477612175047398,
-0.04591137543320656,
-0.048481766134500504,
0.03362426161766052,
0.0644170343875885,
-0.03189009800553322,
0.02718900889158249,
-0.007338705472648144,
-0.010110210627317429,
0.03671656548976898,
-0.012078944593667984,
0.019253557547926903,
-0.04114760085940361,
-0.01932096667587757,
0.01826169714331627,
0.017669841647148132,
-0.013067507185041904,
0.04021790623664856,
-0.004685825202614069,
-0.029824692755937576,
0.027139468118548393,
0.04566909745335579,
-0.0018844909500330687,
-0.025133196264505386,
0.02475915662944317,
0.039136383682489395,
-0.010280082933604717,
-0.005309954285621643,
-0.0015750001184642315,
0.00463582668453455,
-0.022083705291152,
-0.04881961643695831,
0.04941801354289055,
-0.01656096987426281,
0.012793317437171936,
0.02783862315118313,
0.013398912735283375,
0.011652951128780842,
0.061490219086408615,
0.05698954686522484,
0.009102851152420044,
-0.03348183631896973,
0.026605214923620224,
-0.038071054965257645,
-0.0007630179752595723,
0.03977435827255249,
-0.03388410806655884,
0.014814336784183979,
-0.05664852634072304,
0.027012920007109642,
0.06274967640638351,
0.04451630637049675,
-0.031100021675229073,
-0.03569790720939636,
0.045229386538267136,
-0.03006116673350334,
0.034983325749635696,
-0.0024810172617435455,
0.020263979211449623,
-0.01762315258383751,
0.01761656627058983,
-0.013208674266934395,
0.041991859674453735,
0.03263987973332405,
0.054875437170267105,
-0.014003165066242218,
-0.004324023146182299,
-0.07416094839572906,
0.009291376918554306,
-0.048471368849277496,
-0.024375885725021362,
-0.010306333191692829,
0.0398784801363945,
0.004718562588095665,
0.023152975365519524,
0.016566136851906776,
0.013226483948528767,
0.039789143949747086,
-0.04400438070297241,
-0.04456327483057976,
-0.050630178302526474,
-0.006907639559358358,
0.05486128851771355,
0.0546959824860096,
-0.07140856236219406,
-0.011852615512907505,
0.03801148384809494,
0.04012061282992363,
-0.025108564645051956,
0.03760216385126114,
0.05203840509057045,
0.012915928848087788,
-0.009997112676501274,
-0.014720053412020206,
-0.005083337891846895,
0.007189474068582058,
0.03875206410884857,
-0.05161411687731743,
-0.019392456859350204,
-0.037867605686187744,
0.03662523627281189,
0.026758871972560883,
-0.011169911362230778,
0.003955078311264515,
-0.04518941417336464,
-0.014589939266443253,
-0.025242676958441734,
0.04692007973790169,
0.009745342656970024,
-0.008706697262823582,
0.0742911845445633,
-0.012282321229577065,
0.02547464147210121,
-0.014902989380061626,
0.01480768620967865,
-0.0016228014137595892,
0.040945544838905334,
-0.006225994322448969,
0.017793230712413788,
0.053202684968709946,
0.016101747751235962,
0.03911154344677925,
-0.05269341543316841,
0.0267665833234787,
-0.010121212340891361,
-0.06669212877750397,
0.04195181652903557,
0.003972096834331751,
0.04044707119464874,
-0.04343191534280777,
0.0014047122094780207,
-0.02022464945912361,
0.04427576810121536,
0.07554911077022552,
-0.02446621097624302,
-0.013902860693633556,
-0.022089337930083275,
0.07854001969099045,
-0.030323803424835205,
-0.009909181855618954,
0.012241100892424583,
0.010629522614181042,
-0.000020891178792226128,
-0.002273914171382785,
-0.02469938062131405,
0.055390939116477966,
-0.0198647640645504,
0.038596946746110916,
0.00008651711686979979,
0.020966721698641777,
0.046733397990465164,
0.07506011426448822,
-0.01128291990607977,
0.07787192612886429,
-0.02200668677687645,
-0.04436824098229408,
-0.050499118864536285,
-0.01649024710059166,
-0.09284065663814545,
-0.017826778814196587,
-0.018288595601916313,
0.015559976920485497,
0.01469728909432888,
0.01678592897951603,
0.03520384803414345,
-0.04568009823560715,
-0.002081256126984954,
0.03175080567598343,
-0.028852444142103195,
-0.05833512544631958,
-0.024314606562256813,
-0.08046826720237732,
-0.012023176066577435,
-0.0309644415974617,
-0.005221658851951361,
-0.0027701843064278364,
-0.06448418647050858,
0.00462923152372241,
0.010471445508301258,
-0.06724562495946884,
0.001909579150378704,
-0.058233607560396194,
0.05024400353431702,
-0.004507950972765684,
-0.04057249799370766,
-0.0007405805517919362,
-0.042135898023843765,
-0.002203767653554678,
-0.030787549912929535,
-0.03867445886135101,
0.011316219344735146,
0.00871783122420311,
-0.036824703216552734,
0.017886696383357048,
-0.053371839225292206,
-0.002957429038360715,
-0.013848833739757538,
-0.04705151915550232,
-0.035397883504629135,
0.024146120995283127,
-0.05250930413603783,
0.015155572444200516,
0.015004915185272694,
0.031177448108792305,
0.02779831737279892,
0.05878683552145958,
0.04587964713573456,
-0.004164773039519787,
0.011265110224485397,
-0.0023944394197314978,
0.06183040514588356,
-0.012843095697462559,
0.018434062600135803,
0.07205908000469208,
0.016450196504592896,
0.04076320305466652,
0.03088950365781784,
0.008681219071149826,
0.00807099137455225,
0.023448612540960312,
0.04047088325023651,
0.051311392337083817,
0.018462272360920906,
-0.009248046204447746,
-0.034607719630002975,
-0.05416322499513626,
0.0032396758906543255,
0.027469053864479065,
-0.040159501135349274,
0.04575315862894058,
-0.006116079166531563,
-0.002392483176663518,
-0.008337660692632198,
-0.0428832583129406,
-0.03976566717028618,
-0.004369926638901234,
0.005610920954495668,
0.04074619337916374,
0.07955329865217209,
0.012945862486958504,
-0.02720370516180992,
0.020792733877897263,
-0.028389574959874153,
0.010588926263153553,
0.04586896672844887,
0.04119976982474327,
-0.018212182447314262,
0.03358817845582962,
0.04836326837539673,
-0.07120402157306671,
0.0033799412194639444,
-0.027973856776952744,
-0.00025336266844533384,
-0.015932416543364525,
-0.0035762106999754906,
-0.008147884160280228,
-0.026452943682670593,
0.022584950551390648,
-0.08007460832595825,
0.050315313041210175,
0.011862361803650856,
0.06347214430570602,
0.018370240926742554,
0.006431123707443476,
0.008879956789314747,
-0.027727995067834854,
0.05224144831299782,
0.008510968647897243,
0.04796057194471359,
0.02512742578983307,
0.003127503674477339,
0.0096607506275177,
-0.06866565346717834,
0.0007407275843434036,
-0.016779344528913498,
-0.006597165949642658
] |
<p>How do I go about finding the pressure exerted on a rectangular surface in a free flowing air stream?</p>
<p>I wouldn't imagine that this is directly related to the airspeed / surface area, but have no idea where to start. Is there even an equation, or does one need to do some kind of FEA?</p>
<p>For instance a 1.2m x 2.4m metal sheet suspended some distance above ground level, if I have a gust of wind at 8m/s (directly perpendicular to the sheet), what is the average pressure across the face of sheet?</p> | g5527 | [
0.07921285927295685,
0.017460862174630165,
-0.008827644400298595,
0.009404318407177925,
-0.0004366402863524854,
0.015587706118822098,
0.007596986368298531,
-0.005189829505980015,
-0.09071136265993118,
-0.054624177515506744,
-0.025647170841693878,
0.023546263575553894,
0.024472838267683983,
0.03688086196780205,
0.035402897745370865,
0.05681217834353447,
-0.017134444788098335,
-0.03971249237656593,
0.023801080882549286,
-0.0012893039966002107,
0.024147160351276398,
-0.05794061720371246,
0.03405996039509773,
-0.030730806291103363,
-0.025425300002098083,
-0.05515994504094124,
-0.03766028583049774,
-0.02303668111562729,
-0.06323576718568802,
-0.019980531185865402,
-0.039167292416095734,
0.021394168958067894,
0.05423039197921753,
-0.02859421633183956,
-0.0478617399930954,
-0.010817674919962883,
0.008663566783070564,
0.0363212414085865,
0.0073423972353339195,
-0.03720036521553993,
0.01636597327888012,
-0.04560379683971405,
-0.04035845398902893,
0.05272774025797844,
-0.0016729739727452397,
-0.0314207449555397,
-0.03596115484833717,
-0.03174371272325516,
-0.022622443735599518,
-0.008104613050818443,
-0.019332027062773705,
0.05458502471446991,
0.046799637377262115,
-0.04424605891108513,
-0.07604488730430603,
0.08074503391981125,
0.026994936168193817,
-0.07309728115797043,
0.017439382150769234,
0.041555795818567276,
-0.05975969880819321,
0.04332656040787697,
-0.03924938663840294,
-0.00826236978173256,
-0.020110711455345154,
0.027964726090431213,
-0.00925869308412075,
-0.03410084918141365,
0.009777725674211979,
-0.01300040353089571,
0.03685443475842476,
-0.022420935332775116,
0.02515854686498642,
-0.06788656115531921,
-0.07267232239246368,
-0.033698949962854385,
-0.05019160360097885,
0.04112338274717331,
0.024208977818489075,
-0.008180554024875164,
0.04697070270776749,
-0.04396754503250122,
-0.01421206071972847,
0.013210047967731953,
0.04014959558844566,
-0.02053682692348957,
-0.007404267322272062,
0.008950954303145409,
-0.03689389303326607,
-0.08386728912591934,
-0.009000459685921669,
-0.003362679621204734,
0.06968843191862106,
-0.020572930574417114,
-0.0016691110795363784,
-0.01836298406124115,
0.00044264912139624357,
0.04411110654473305,
-0.03224949166178703,
-0.015238798223435879,
-0.07883107662200928,
-0.03164798766374588,
-0.0006381193525157869,
-0.014972339384257793,
0.010383430868387222,
-0.008397898636758327,
0.04437663033604622,
0.04014478623867035,
-0.00629815086722374,
-0.054056912660598755,
0.03793254494667053,
0.04841030016541481,
-0.0531877726316452,
-0.000719150179065764,
-0.006641565356403589,
-0.04042764753103256,
0.030800290405750275,
-0.018078044056892395,
0.025607123970985413,
0.0757400393486023,
0.01007496751844883,
0.009801340289413929,
-0.016436384990811348,
0.022493932396173477,
-0.011091654188930988,
-0.031107082962989807,
-0.006159958429634571,
0.0010877352906391025,
-0.004371503833681345,
0.0005784780369140208,
0.057013869285583496,
-0.0383099727332592,
-0.010334712453186512,
-0.0076574101112782955,
0.038276027888059616,
0.06477537751197815,
-0.10540582239627838,
0.02677743509411812,
-0.07015127688646317,
0.0259175393730402,
0.024308258667588234,
-0.024665741249918938,
-0.011586230248212814,
-0.008917943574488163,
0.02274436503648758,
0.002273811027407646,
-0.049105316400527954,
-0.009007113054394722,
-0.012528722174465656,
-0.043039899319410324,
0.04048774763941765,
0.08066916465759277,
0.0158050749450922,
-0.009279107674956322,
0.012034031562507153,
-0.015051743946969509,
-0.05516018718481064,
-0.06630349904298782,
0.04632311314344406,
0.02322351187467575,
0.12489014863967896,
0.0005714630242437124,
0.07016032934188843,
0.029437391087412834,
-0.06463725119829178,
-0.01843392476439476,
-0.031282320618629456,
0.02320418879389763,
0.029406515881419182,
-0.01755252480506897,
-0.006205804646015167,
-0.02619471214711666,
0.03169405460357666,
-0.013360490091145039,
-0.000561846187338233,
-0.010682235471904278,
0.07237406075000763,
-0.0024772679898887873,
0.025091616436839104,
-0.005964271724224091,
0.026984576135873795,
0.030132293701171875,
0.0381285697221756,
-0.005600444041192532,
0.007741516921669245,
-0.004533236846327782,
0.0195733904838562,
0.009096345864236355,
-0.01943032070994377,
-0.001158749801106751,
-0.015380233526229858,
-0.021319890394806862,
0.035502467304468155,
0.012234142981469631,
-0.010289949364960194,
0.04732745885848999,
0.06503934413194656,
-0.06527671217918396,
-0.041466787457466125,
-0.09997967630624771,
-0.02156095951795578,
0.04051792249083519,
0.07548838108778,
0.01842034049332142,
0.012593544088304043,
-0.004241090267896652,
0.03690537065267563,
-0.024167843163013458,
-0.025269117206335068,
0.03988923877477646,
-0.023121975362300873,
-0.011081872507929802,
0.036837294697761536,
0.06347682327032089,
0.051976148039102554,
0.006552215199917555,
-0.06388965249061584,
-0.048634566366672516,
-0.032279614359140396,
0.027960825711488724,
-0.012571369297802448,
-0.020127249881625175,
-0.006952643860131502,
0.0020363745279610157,
-0.08769062161445618,
-0.017843924462795258,
-0.023495344445109367,
0.021964071318507195,
0.005676240660250187,
-0.005835140123963356,
0.014605293981730938,
0.00593894487246871,
-0.02653169445693493,
-0.011031831614673138,
-0.011037850752472878,
-0.009328819811344147,
0.04293201491236687,
0.02818536013364792,
-0.009842700324952602,
-0.04124167934060097,
-0.005520441569387913,
-0.047381334006786346,
-0.022546380758285522,
-0.01893797516822815,
0.003621383337303996,
0.0633038580417633,
0.03318062052130699,
0.009968812577426434,
0.027665577828884125,
0.023155860602855682,
-0.019598551094532013,
0.038748715072870255,
0.027466150000691414,
0.06316792964935303,
-0.020468518137931824,
-0.008857094682753086,
-0.02070104330778122,
-0.01733540929853916,
-0.050012603402137756,
-0.03189421817660332,
0.0031498479656875134,
-0.050433073192834854,
0.012179180048406124,
0.012971466407179832,
-0.046582553535699844,
0.03689198195934296,
-0.058712445199489594,
0.0018069148063659668,
0.04929393157362938,
0.014151522889733315,
0.03390680253505707,
0.032568082213401794,
0.002059666672721505,
0.03959274664521217,
0.0084229726344347,
-0.03691612929105759,
0.014542864635586739,
-0.007542854640632868,
-0.01386178843677044,
0.05532846227288246,
0.0054593258537352085,
-0.0078349020332098,
-0.03483656421303749,
0.041388001292943954,
0.012283172458410263,
-0.022825350984930992,
0.0667291134595871,
0.06731797009706497,
-0.04425334185361862,
0.011156412772834301,
0.012112482450902462,
-0.059344422072172165,
-0.0544247105717659,
-0.023706970736384392,
0.007867746986448765,
0.056108251214027405,
0.019415423274040222,
0.02414114959537983,
-0.03181837871670723,
0.020146658644080162,
-0.011849844828248024,
-0.03505629301071167,
0.0023081956896930933,
0.025492895394563675,
-0.055053308606147766,
0.05642614886164665,
0.024146215990185738,
-0.05654483288526535,
0.050907816737890244,
-0.03519400954246521,
-0.004872733261436224,
0.025645973160862923,
0.05761244148015976,
0.013755694031715393,
-0.057096343487501144,
-0.02043684385716915,
0.017358975484967232,
0.004639629274606705,
-0.020730379968881607,
0.055463943630456924,
-0.03180723637342453,
-0.046525273472070694,
0.04499104991555214,
0.03409074991941452,
-0.0008799586212262511,
-0.01626192219555378,
0.011745404452085495,
0.03244875371456146,
-0.029994266107678413,
-0.042847126722335815,
-0.041245363652706146,
0.0037054612766951323,
-0.0007662737043574452,
-0.03453947603702545,
-0.015614446252584457,
-0.008644962683320045,
0.04421187937259674,
-0.03369047865271568,
0.0042085289023816586,
-0.013806819915771484,
-0.014342736452817917,
-0.03617248684167862,
-0.04105537384748459,
-0.045277222990989685,
0.008977878838777542,
0.007375670131295919,
0.007839774712920189,
0.014110920019447803,
-0.03153124824166298,
-0.016085073351860046,
0.015680238604545593,
-0.028742456808686256,
-0.032103441655635834,
-0.029696490615606308,
0.055647920817136765,
0.01095268502831459,
0.014510215260088444,
-0.02860100008547306,
-0.013745307922363281,
0.04500361531972885,
0.01021001860499382,
-0.017080992460250854,
0.010101099498569965,
0.013179687783122063,
-0.02169506996870041,
-0.06143315136432648,
0.021158907562494278,
0.04650673642754555,
-0.04850292205810547,
-0.04088972136378288,
0.027276085689663887,
-0.05567922070622444,
-0.0024953531101346016,
0.010291347280144691,
-0.025468790903687477,
0.013499894179403782,
0.042181313037872314,
0.023793848231434822,
0.08901629596948624,
0.05475826933979988,
0.07038525491952896,
0.06098812073469162,
0.004593727178871632,
0.012534978799521923,
-0.023487558588385582,
-0.014685208909213543,
-0.09050195664167404,
0.060178764164447784,
0.07316780090332031,
-0.011527861468493938,
-0.012191696092486382,
-0.06761270016431808,
-0.04531329497694969,
0.0300951786339283,
-0.023078281432390213,
-0.006989383138716221,
0.0009636679315008223,
0.021304354071617126,
-0.06525205820798874,
0.023979539051651955,
0.07270249724388123,
0.011166322976350784,
0.013824451714754105,
0.06560565531253815,
-0.042736947536468506,
0.0645890012383461,
0.039462942630052567,
-0.023385047912597656,
-0.0060685500502586365,
0.04467125982046127,
0.004160757176578045,
-0.032759640365839005,
0.029304999858140945,
-0.047178130596876144,
0.02060573548078537,
0.003717013169080019,
0.00035693912650458515,
0.013627427630126476,
0.042117584496736526,
-0.04028662294149399,
-0.010698347352445126,
0.017327865585684776,
0.07296477258205414,
-0.014856147579848766,
-0.018833134323358536,
0.0666847750544548,
0.06992190331220627,
0.029328545555472374,
0.009992394596338272,
-0.03411247581243515,
-0.028455059975385666,
0.009045612066984177,
-0.015969133004546165,
0.02636868879199028,
-0.022949449717998505,
0.05873829871416092,
0.04381096735596657,
0.02728920988738537,
0.004535716492682695,
0.007769199088215828,
0.032251644879579544,
0.00358154671266675,
0.020038025453686714,
0.027715524658560753,
0.01583159528672695,
0.017617257311940193,
0.003084188560023904,
-0.04404282569885254,
-0.021484997123479843,
-0.00651950016617775,
-0.049947287887334824,
-0.07043808698654175,
-0.03622642159461975,
-0.025908809155225754,
-0.05108610540628433,
0.025685928761959076,
-0.024322159588336945,
0.002371333772316575,
0.08710372447967529,
0.03562804311513901,
-0.02874824032187462,
-0.02649914287030697,
-0.006387469824403524,
0.01709533855319023,
-0.020189372822642326,
-0.014392741024494171,
-0.04060431942343712,
0.025640398263931274,
-0.024662025272846222,
-0.09069625288248062,
0.0403803214430809,
0.027881765738129616,
-0.03190604969859123,
0.05890228599309921,
0.0020280624739825726,
0.057336848229169846,
-0.01862126775085926,
-0.055492568761110306,
-0.04254346713423729,
0.0049972981214523315,
-0.009086694568395615,
0.022617515176534653,
0.029387256130576134,
0.015493269078433514,
0.052300311625003815,
-0.07252755761146545,
-0.005484845954924822,
0.016295282170176506,
-0.0242726169526577,
-0.021945036947727203,
-0.0035526410210877657,
0.014200974255800247,
-0.07072927802801132,
0.02360730618238449,
-0.08128244429826736,
-0.016287775710225105,
-0.0016501713544130325,
-0.020808281376957893,
0.007697181776165962,
-0.022635748609900475,
-0.034176796674728394,
0.0008829173748381436,
0.0024720621295273304,
0.038885798305273056,
0.04055782034993172,
0.018619852140545845,
0.0015547991497442126,
-0.05469704046845436,
0.03218888118863106,
0.05224037542939186,
0.008192505687475204,
0.0172249898314476,
0.024401696398854256,
-0.04422362893819809,
0.003144235350191593,
0.03928079456090927,
0.010991539806127548,
0.02547440677881241,
-0.05710756778717041,
0.05030526593327522,
0.070933997631073,
-0.04056970402598381,
-0.0099531514570117,
0.029606768861413002,
-0.07662271708250046,
0.020981840789318085,
-0.06435338407754898,
-0.03081386350095272,
-0.024952098727226257,
-0.04742820933461189,
-0.03441143408417702,
-0.0363469198346138,
0.018967177718877792,
-0.059742365032434464,
-0.008707401342689991,
-0.020854651927947998,
0.05422773212194443,
0.020057518035173416,
0.06731052696704865,
-0.07018213719129562,
-0.05915290489792824,
0.007763113360852003,
-0.008569605648517609,
-0.013925263658165932,
-0.05141213908791542,
0.00034963569487445056,
-0.01847982592880726,
0.04536691680550575,
0.08767244219779968,
-0.003984145354479551,
-0.00889537949115038,
0.02306017279624939,
0.0254856888204813,
0.016154564917087555,
-0.024983273819088936,
0.029400426894426346,
0.01649811491370201,
-0.0337163507938385,
-0.01070583239197731,
-0.009904103353619576,
0.07820714265108109,
0.0016333995154127479,
0.022737162187695503,
-0.00272272783331573,
0.021293651312589645,
0.021539734676480293,
-0.022803938016295433,
-0.002660105936229229,
0.02992577664554119,
0.0009899892611429095,
-0.019700855016708374,
-0.021304264664649963,
0.048076119273900986,
0.00757926469668746,
0.029690081253647804,
0.04105889052152634,
0.018363218754529953,
0.03683194890618324,
0.008820837363600731,
0.023117825388908386,
-0.02150076813995838,
0.04129627346992493,
0.01731465384364128,
-0.053783006966114044,
0.01782205142080784,
-0.029859092086553574,
-0.027666015550494194,
-0.024150259792804718,
0.032866787165403366,
0.058798130601644516,
0.018128495663404465,
-0.01333340723067522,
0.016530558466911316,
-0.0017948277527466416,
-0.04101163521409035,
-0.0426567867398262,
0.028180235996842384,
0.05892295762896538,
-0.017749441787600517,
0.0318545401096344,
0.012799887917935848,
0.014603504911065102,
0.012345824390649796,
-0.061627939343452454,
0.05106518045067787,
-0.06574232876300812,
0.04032445326447487,
-0.015896810218691826,
-0.0243292897939682,
-0.021313155069947243,
-0.005269438959658146,
-0.008202949538826942,
-0.007280429825186729,
-0.015567724592983723,
0.009306581690907478,
-0.014699496328830719,
0.013695032335817814,
-0.02020721323788166,
-0.037305235862731934,
-0.03594670817255974,
0.01193727646023035,
0.0680924654006958,
0.005492561496794224,
-0.05342034623026848,
-0.004317152313888073,
-0.013159669935703278,
-0.06159743294119835,
0.035440843552351,
0.022653723135590553,
0.02089236117899418,
0.016429739072918892,
0.032158516347408295,
-0.009208121336996555,
-0.021035034209489822,
-0.02294032648205757,
0.016933657228946686,
-0.023045329377055168,
0.043685976415872574,
0.09207125008106232,
0.11553478986024857,
-0.028774697333574295,
0.03903625160455704,
-0.04938136786222458,
0.007467606104910374,
-0.0728539526462555,
-0.056236136704683304,
-0.022838879376649857,
-0.006226592231541872,
-0.002858218038454652,
-0.04323085397481918,
-0.016001511365175247,
-0.03821709752082825,
-0.032648663967847824,
0.026541614904999733,
-0.030937435105443,
0.0412670262157917,
-0.0004804250493180007,
-0.003268355969339609,
0.023730440065264702,
-0.015468865633010864,
-0.03466380760073662,
-0.05824916437268257,
0.038222216069698334,
0.041204750537872314,
0.013541817665100098,
0.03908728435635567,
0.042138759046792984,
0.019146010279655457,
0.011428053490817547,
-0.025960929691791534,
-0.06014816090464592,
-0.04090774804353714,
-0.0291649978607893,
0.011402808129787445,
-0.00772574357688427,
0.05096634849905968,
-0.00023407465778291225,
-0.014528063125908375,
-0.018641872331500053,
-0.027901381254196167,
0.020623261108994484,
0.0305298063904047,
-0.03339272737503052,
0.026306062936782837,
-0.02822953648865223,
0.027754368260502815,
0.00020829202549066395,
0.08032482117414474,
0.03391284495592117,
0.004954937379807234,
-0.035433992743492126,
0.05972665920853615,
0.05056454613804817,
-0.017999932169914246,
-0.033408183604478836,
0.02475946955382824,
0.0386534184217453,
-0.027404919266700745,
0.05840779468417168,
-0.03673742339015007,
0.04787631332874298,
0.008159594610333443,
-0.025545820593833923,
0.02537081390619278,
-0.004254922736436129,
-0.028239771723747253,
-0.02259230799973011,
0.015267683193087578,
-0.016486769542098045,
-0.06667151302099228,
0.011656920425593853,
-0.03439329192042351,
0.025463948026299477,
0.0012015154352411628,
0.01991923712193966,
0.0003221321676392108,
-0.009414863772690296,
0.015174289233982563,
-0.015077716670930386,
0.022414010018110275,
-0.0007503728847950697,
-0.025500746443867683,
-0.0202009454369545,
-0.03327392786741257,
-0.016202369704842567,
0.012884910218417645,
-0.04035118594765663,
0.04057076573371887,
0.02905348502099514,
-0.002716613467782736,
-0.019408980384469032,
-0.006014733575284481,
0.007499334402382374,
0.04376566410064697,
-0.03001497872173786,
-0.0367426835000515,
0.07179441303014755,
-0.0020022415556013584,
-0.018521547317504883,
0.022438954561948776,
-0.009609568864107132,
-0.014309665188193321,
-0.0003411947109270841,
-0.03578327223658562,
0.015971556305885315,
-0.07645285129547119,
0.032075315713882446,
0.05145235359668732,
0.027588145807385445,
0.0262546818703413,
0.06113063171505928,
0.052500735968351364,
0.0042452155612409115,
0.0043336814269423485,
0.010547569952905178,
-0.07163269072771072,
-0.009907220490276814,
0.02260291390120983,
0.0152449244633317,
0.012145803309977055,
-0.027635691687464714,
0.0011653391411527991,
0.021705182269215584,
-0.007093238178640604,
-0.0010279020061716437,
-0.05372368544340134,
-0.05548799782991409,
0.007373133674263954
] |
<p>According to the first law of thermodynamics, sourced from wikipedia
"In any process in an isolated system, the total energy remains the same."</p>
<p>So when lasers are used for cooling in traps, similar to the description here: <a href="http://optics.colorado.edu/~kelvin/classes/opticslab/LaserCooling3.doc.pdf">http://optics.colorado.edu/~kelvin/classes/opticslab/LaserCooling3.doc.pdf</a> where is the heat transferred? </p>
<p>From what I gather of a cursory reading on traps, whether laser, magnetic, etc the general idea is to isolate the target, then transfer heat from it, thereby cooling it.</p>
<p>I don't understand how sending photons at a(n) atom(s) can cause that structure to shed energy, and this mechanism seems to be the key to these systems. </p> | g608 | [
0.0065487888641655445,
-0.00496867997571826,
-0.019826790317893028,
-0.0011798246996477246,
0.00177583540789783,
0.006148684769868851,
0.006369819864630699,
0.06030186265707016,
-0.014159598387777805,
0.02661457285284996,
-0.014155109412968159,
0.033718645572662354,
0.03820689022541046,
-0.019739720970392227,
-0.013829201459884644,
-0.008765465579926968,
0.06648820638656616,
0.01969609223306179,
0.053714655339717865,
0.07970702648162842,
-0.06265950202941895,
-0.014834295026957989,
-0.05285806953907013,
-0.08622448146343231,
-0.0028388563077896833,
-0.030516931787133217,
0.012412338517606258,
0.017141735181212425,
-0.03737185150384903,
0.020743977278470993,
0.013452461920678616,
-0.04385995864868164,
0.053929828107357025,
-0.06858443468809128,
-0.012102467007935047,
-0.008688771165907383,
0.05043706297874451,
-0.005860251374542713,
0.013220081105828285,
-0.030274759978055954,
-0.009913060814142227,
-0.0035285158082842827,
-0.026493510231375694,
0.006274249404668808,
0.021896757185459137,
-0.005905745550990105,
-0.005646706558763981,
-0.03558000549674034,
-0.017608055844902992,
0.041456811130046844,
0.021043621003627777,
0.04245000705122948,
-0.0035962946712970734,
-0.019921502098441124,
0.004120741970837116,
-0.021914593875408173,
-0.04893337935209274,
0.021242503076791763,
0.07815326750278473,
0.0067518968135118484,
0.06870202720165253,
0.007995608262717724,
-0.025599006563425064,
0.04616475850343704,
0.024901174008846283,
-0.009487493894994259,
-0.053052663803100586,
0.012901444919407368,
0.011024899780750275,
0.006706519518047571,
0.028986191377043724,
0.021626340225338936,
-0.03651741147041321,
-0.03514886647462845,
0.015185820870101452,
-0.023280596360564232,
0.0194028839468956,
0.02470868080854416,
-0.03087763860821724,
0.03624146804213524,
-0.02467779628932476,
-0.056667886674404144,
0.04234442114830017,
-0.01451247837394476,
0.06307608634233475,
0.043043117970228195,
-0.06055733561515808,
-0.018066544085741043,
-0.05001159757375717,
0.044696226716041565,
0.015270601026713848,
0.07001889497041702,
0.1397830843925476,
0.021263616159558296,
-0.019844025373458862,
0.03053797222673893,
-0.013902795501053333,
-0.0016929571283981204,
-0.01677548512816429,
0.007962201721966267,
0.04865584895014763,
-0.012164263054728508,
0.014317331835627556,
-0.01610856130719185,
0.026356054469943047,
0.0030473789665848017,
-0.0006921340827830136,
0.010456825606524944,
-0.022973384708166122,
0.04231278970837593,
-0.038228750228881836,
-0.01764392852783203,
-0.1131172850728035,
-0.005097656045109034,
-0.016994241625070572,
0.012309516780078411,
0.07119499891996384,
-0.022867852821946144,
-0.013518520630896091,
0.03654482215642929,
0.041456084698438644,
0.05555548518896103,
-0.016363857313990593,
0.05110328644514084,
0.013867969624698162,
0.013384666293859482,
0.014516920782625675,
-0.03372179716825485,
-0.0013525686226785183,
0.0014758090255782008,
-0.0004126110579818487,
0.009654035791754723,
-0.04553082585334778,
0.025947127491235733,
0.009160391055047512,
0.014183718711137772,
-0.023503392934799194,
0.00953623466193676,
0.041246864944696426,
-0.02648162469267845,
0.013316781260073185,
-0.021589059382677078,
-0.004407783504575491,
-0.013253551907837391,
-0.022373942658305168,
0.04877813160419464,
-0.09468250721693039,
0.0025339992716908455,
0.05474242940545082,
-0.022973544895648956,
0.037837907671928406,
0.07137591391801834,
0.01910107210278511,
-0.07120015472173691,
0.05368700250983238,
-0.04968300461769104,
0.013743174262344837,
-0.02301822230219841,
0.00512631656602025,
0.008735354989767075,
0.056102048605680466,
-0.006126683205366135,
0.033464215695858,
-0.029775576665997505,
-0.09692665934562683,
0.018381282687187195,
0.0303794015198946,
-0.06880728155374527,
0.02068375237286091,
-0.038507379591464996,
-0.06205674633383751,
0.012213745154440403,
-0.081301249563694,
0.018537398427724838,
0.04102432727813721,
0.07623615860939026,
0.06970272958278656,
-0.016633542254567146,
0.007634258363395929,
-0.07310551404953003,
-0.047517962753772736,
0.024134894832968712,
0.06374389678239822,
-0.039235301315784454,
-0.019049324095249176,
0.054211314767599106,
-0.0093254828825593,
-0.0471283495426178,
0.030962180346250534,
-0.013767325319349766,
-0.03217852860689163,
-0.006744494196027517,
0.04520558565855026,
-0.010132614523172379,
0.005934069398790598,
-0.056395936757326126,
-0.05194467306137085,
-0.0480729378759861,
-0.017709583044052124,
0.017461271956562996,
-0.031712424010038376,
-0.03507756441831589,
-0.028499389067292213,
-0.01829368993639946,
0.032252971082925797,
0.05369805917143822,
0.012184562161564827,
0.042873334139585495,
0.003488948568701744,
-0.06054321303963661,
0.0031238666269928217,
0.013507654890418053,
0.07927992194890976,
-0.02696147933602333,
0.014444700442254543,
0.007278117351233959,
-0.005955493077635765,
0.010488913394510746,
-0.029453447088599205,
-0.002479536458849907,
-0.04111390560865402,
0.015495494939386845,
0.003047820646315813,
0.0002757866168394685,
-0.015389824286103249,
0.00830548070371151,
-0.0943378210067749,
0.0035624594893306494,
-0.03036966361105442,
0.051616281270980835,
-0.11705964058637619,
0.010113488882780075,
0.004834149498492479,
-0.027722183614969254,
0.04312103986740112,
-0.000965858984272927,
-0.027361316606402397,
0.03050556406378746,
0.014819495379924774,
0.013049124740064144,
0.02062036842107773,
-0.018947448581457138,
-0.060229647904634476,
-0.014758256264030933,
0.01812855526804924,
-0.057305410504341125,
0.01443211268633604,
-0.02636304497718811,
-0.043053075671195984,
-0.05859154462814331,
-0.0012346565490588546,
0.006537740584462881,
-0.031032100319862366,
-0.03998737037181854,
-0.00495055690407753,
-0.026172736659646034,
-0.01911959983408451,
-0.010033490136265755,
-0.04762165993452072,
-0.07594015449285507,
-0.011024297215044498,
0.013340296223759651,
-0.006461372599005699,
-0.03526315838098526,
-0.038732945919036865,
-0.034475550055503845,
0.0002429215528536588,
-0.03001617267727852,
-0.007451887242496014,
-0.006269897799938917,
-0.04753613471984863,
0.07642190158367157,
0.046932436525821686,
0.04522146284580231,
0.02838105894625187,
0.020181989297270775,
0.025388484820723534,
-0.012544856406748295,
0.04086851701140404,
-0.044798776507377625,
-0.03183990716934204,
0.007967636920511723,
-0.07789364457130432,
-0.026331443339586258,
0.032469891011714935,
-0.0735650509595871,
0.0013594686752185225,
0.005782898981124163,
0.02624678425490856,
-0.053392939269542694,
-0.007508916314691305,
0.004132978618144989,
0.03313004598021507,
0.013594813644886017,
-0.05165795981884003,
-0.00812133215367794,
0.051828399300575256,
0.021663550287485123,
-0.007571245077997446,
0.05377064272761345,
-0.012235821224749088,
-0.027677126228809357,
0.004108348395675421,
-0.03164244443178177,
0.03999638929963112,
0.10913880914449692,
-0.04829980805516243,
-0.058149151504039764,
-0.009934572502970695,
-0.000722352066077292,
0.011844996362924576,
0.0056870910339057446,
0.04333176463842392,
0.03150865063071251,
-0.010137522593140602,
-0.004884106572717428,
-0.02880755066871643,
-0.062109287828207016,
0.0809340849518776,
-0.0357513353228569,
-0.0934189185500145,
0.029632387682795525,
0.03657657280564308,
-0.07501877844333649,
0.010347167029976845,
0.008575864136219025,
-0.010766321793198586,
-0.08271612226963043,
0.022270772606134415,
0.012752014212310314,
0.01249619945883751,
-0.005748482421040535,
-0.0335545651614666,
-0.0013305679894983768,
-0.0653240755200386,
-0.04689774662256241,
-0.07096949964761734,
0.008087875321507454,
0.05638866871595383,
-0.009242285043001175,
0.0033176096621900797,
-0.03599303960800171,
-0.040486764162778854,
0.013277582824230194,
0.05195281282067299,
0.021425744518637657,
-0.011005865409970284,
0.013803929090499878,
0.013091634027659893,
-0.03302214294672012,
0.01654914952814579,
-0.017851054668426514,
-0.006005474366247654,
-0.005608221981674433,
-0.093716099858284,
0.000719259085599333,
-0.03696734830737114,
-0.000007516757705161581,
0.01719924435019493,
0.028096111491322517,
-0.0042873164638876915,
-0.012526645325124264,
0.0693042129278183,
-0.02314462885260582,
-0.026148509234189987,
0.06020701304078102,
-0.04918665811419487,
-0.07464238256216049,
0.0339326485991478,
0.00245820009149611,
-0.02774232253432274,
0.007122581824660301,
-0.021091096103191376,
0.018013035878539085,
0.016009235754609108,
0.005130448844283819,
0.0495181642472744,
0.03908299282193184,
-0.048673804849386215,
-0.011548411101102829,
-0.030997259542346,
-0.03155047446489334,
0.024962930008769035,
0.02828121930360794,
0.03771476447582245,
0.009288918226957321,
-0.017993967980146408,
0.0011313905706629157,
-0.03475533425807953,
-0.0077732219360768795,
-0.004640666767954826,
-0.02150338515639305,
0.02520296722650528,
0.033084820955991745,
0.023218799382448196,
-0.001982357818633318,
0.0058115697465837,
-0.02807627059519291,
0.05243227630853653,
-0.022272516041994095,
0.0586230605840683,
0.015071425586938858,
-0.0045379213988780975,
-0.04154140129685402,
0.04288085550069809,
0.02445104718208313,
0.06433842331171036,
-0.02093479223549366,
-0.015708526596426964,
0.041135791689157486,
-0.0057811918668448925,
-0.006367855239659548,
-0.009979777038097382,
-0.030796857550740242,
0.024807095527648926,
-0.06083983555436134,
0.029865296557545662,
0.016435343772172928,
-0.01947838068008423,
0.012212257832288742,
-0.019658278673887253,
0.004693266469985247,
-0.01325277704745531,
0.03146354481577873,
0.006697272416204214,
0.04849047586321831,
0.02764659747481346,
0.005166012793779373,
0.015042778104543686,
-0.04299883916974068,
0.03401780501008034,
0.02342832274734974,
0.00014348218974191695,
0.014137799851596355,
-0.02054162509739399,
0.009243594482541084,
-0.06419207155704498,
0.01530242245644331,
0.021552540361881256,
0.0655311569571495,
0.08397016674280167,
0.0303557850420475,
-0.015345541760325432,
-0.006735632661730051,
-0.000012831084859499242,
0.03391651436686516,
0.007889003492891788,
-0.01882069930434227,
-0.0578453354537487,
-0.09880710393190384,
0.0007198356906883419,
0.006328670307993889,
-0.059733182191848755,
-0.009208837524056435,
-0.0014356059255078435,
0.019856346771121025,
0.0018049248028546572,
-0.0013980858493596315,
0.06625086069107056,
0.04611407592892647,
-0.02377856709063053,
-0.003179844468832016,
0.004125263541936874,
-0.02796364016830921,
0.007619522511959076,
-0.02604081481695175,
0.02541262097656727,
0.05062887445092201,
-0.011607348918914795,
-0.02525499276816845,
0.04958479851484299,
0.060116417706012726,
0.03874411806464195,
0.011156582273542881,
0.06637967377901077,
-0.032266970723867416,
0.030239535495638847,
-0.023205051198601723,
0.02940523810684681,
-0.014752496033906937,
0.010315424762666225,
0.017508214339613914,
0.04874467849731445,
0.02057357132434845,
-0.02503890171647072,
0.006424028426408768,
-0.03040081448853016,
0.014126827009022236,
0.0018832808127626777,
-0.008523538708686829,
-0.014698662795126438,
0.015665963292121887,
-0.026798885315656662,
0.006308360490947962,
0.007752490695565939,
-0.002909616334363818,
0.010266926139593124,
0.02519257739186287,
0.007522060070186853,
0.0017699183663353324,
-0.037818290293216705,
0.02645031549036503,
-0.061599001288414,
-0.006403212435543537,
-0.016057191416621208,
0.013939118012785912,
0.05887536704540253,
-0.008560137823224068,
0.015560291707515717,
-0.007177700754255056,
-0.013098849914968014,
0.022274907678365707,
-0.02648959867656231,
0.029833942651748657,
0.036168936640024185,
-0.011612450703978539,
-0.019930347800254822,
0.022450141608715057,
0.005531425587832928,
-0.012060016393661499,
0.00393455708399415,
0.028054459020495415,
-0.013337725773453712,
-0.02637220174074173,
0.02649514004588127,
0.04255799576640129,
-0.05645476654171944,
-0.031690508127212524,
-0.024082481861114502,
-0.02255924977362156,
-0.03014817088842392,
0.05313241109251976,
0.00954479817301035,
0.01479573268443346,
0.016051631420850754,
-0.013790658675134182,
-0.026801763102412224,
0.0006605897215195,
-0.044689521193504333,
0.027553744614124298,
0.01799149438738823,
-0.045199327170848846,
-0.008350259624421597,
0.03006662055850029,
-0.009861359372735023,
-0.016888832673430443,
-0.0028537416364997625,
-0.04169749096035957,
0.0553438775241375,
-0.03850596770644188,
0.012324734590947628,
-0.021997828036546707,
0.045767053961753845,
-0.03438083454966545,
0.05408552289009094,
0.0035934816114604473,
0.019256748259067535,
-0.00445262435823679,
-0.045579638332128525,
-0.029832594096660614,
-0.020677709951996803,
0.11312062293291092,
-0.0009163130889646709,
0.016649538651108742,
0.04559469595551491,
-0.0026795989833772182,
-0.02356134168803692,
-0.05984991788864136,
0.020440584048628807,
0.05830373242497444,
0.04740831255912781,
-0.05421621352434158,
-0.028434982523322105,
-0.013273928314447403,
0.016611142084002495,
0.05101052671670914,
-0.049530066549777985,
-0.009255612269043922,
-0.02792707085609436,
0.004623176530003548,
-0.007123536430299282,
0.01849379576742649,
0.0002494051295798272,
-0.010127004235982895,
0.03370396047830582,
0.041663188487291336,
-0.08004447817802429,
0.007239196915179491,
0.033158283680677414,
0.01689017191529274,
-0.004741096403449774,
-0.04383590817451477,
-0.018743783235549927,
0.039402469992637634,
-0.013062270358204842,
-0.025054167956113815,
0.023327307775616646,
0.019624827429652214,
-0.0009824539301916957,
-0.02921253629028797,
-0.030576974153518677,
-0.028860554099082947,
0.013993161730468273,
-0.07231959700584412,
-0.024395229294896126,
0.05937521159648895,
0.06135354936122894,
-0.019727030768990517,
-0.01571981981396675,
0.04253775626420975,
-0.03505517542362213,
-0.002312140539288521,
0.03812432661652565,
-0.041570376604795456,
0.009969856590032578,
-0.02151261270046234,
0.007137394044548273,
0.02340770699083805,
-0.007932578213512897,
-0.010468360036611557,
-0.00810471922159195,
-0.06340925395488739,
0.0454743467271328,
-0.022270681336522102,
0.026368213817477226,
0.03751649707555771,
-0.057834167033433914,
0.03691300004720688,
0.04746802896261215,
0.07296667993068695,
0.0034631122834980488,
0.06416811794042587,
-0.025211691856384277,
0.02432558499276638,
-0.021125394850969315,
0.04674180969595909,
0.002617476275190711,
0.009670927189290524,
0.06376378983259201,
-0.004762186203151941,
-0.0285667534917593,
0.001971636200323701,
0.016766443848609924,
0.06928856670856476,
-0.035099662840366364,
0.07289072871208191,
-0.003970724064856768,
-0.026091303676366806,
-0.05529835447669029,
-0.010460703633725643,
-0.09649453312158585,
-0.0436469204723835,
-0.05432794988155365,
-0.026183754205703735,
0.022061685100197792,
0.03894511237740517,
-0.028898509219288826,
0.01831788755953312,
-0.023028451949357986,
-0.08754776418209076,
-0.014262466691434383,
-0.019208669662475586,
0.030510442331433296,
0.004353977274149656,
0.05132533609867096,
0.05267547816038132,
0.04500909149646759,
-0.03352566808462143,
0.013796397484838963,
-0.007624667603522539,
0.00320590753108263,
-0.08583901822566986,
0.030809815973043442,
-0.019357001408934593,
-0.029117895290255547,
0.03211157023906708,
0.03881724178791046,
0.05127163603901863,
-0.0027988418005406857,
-0.005009015090763569,
-0.05485541746020317,
0.014974091202020645,
0.02309819683432579,
-0.052998241037130356,
0.017484255135059357,
0.04510843753814697,
-0.0752200335264206,
0.04545819014310837,
-0.02979191578924656,
-0.019615843892097473,
-0.018838025629520416,
0.01487027108669281,
0.011037968099117279,
0.020401839166879654,
0.0211795587092638,
0.01358865201473236,
0.07752227038145065,
0.032137442380189896,
0.007575002033263445,
0.00808161310851574,
-0.007124580442905426,
-0.037063926458358765,
0.049860693514347076,
0.005641612224280834,
0.04153270646929741,
0.02720431424677372,
0.0018626456148922443,
-0.040383417159318924,
0.009178375825285912,
0.011816775426268578,
-0.006934161297976971,
0.0035166838206350803,
0.0467090904712677,
0.04166421666741371,
0.02551450952887535,
-0.03704192116856575,
-0.03377334401011467,
0.019559338688850403,
-0.028591414913535118,
-0.001853728899732232,
0.006807321682572365,
0.042251765727996826,
-0.01102724950760603,
0.003945077303797007,
0.043264925479888916,
-0.039005111902952194,
0.06177663803100586,
-0.009607789106667042,
-0.031591422855854034,
0.00225400784984231,
-0.014739680103957653,
0.03781389817595482,
-0.02252243645489216,
-0.08675646036863327,
-0.012695111334323883,
0.022805077955126762,
0.031606435775756836,
-0.040368031710386276,
0.04293815791606903,
0.028106175363063812,
0.030888374894857407,
-0.03108779713511467,
0.01688738912343979,
-0.061039991676807404,
0.008694847114384174,
-0.07104925066232681,
-0.07341174781322479,
0.0014137321850284934,
0.006300054956227541,
0.002952536568045616,
-0.025913948193192482,
0.044657401740550995,
-0.030475515872240067,
-0.022065769881010056,
0.06291037797927856,
-0.038324784487485886,
-0.05037009343504906,
0.022998269647359848,
0.019710468128323555,
0.009965247474610806,
-0.053175006061792374,
0.008115778677165508,
-0.028240177780389786,
0.006871714722365141,
0.01957961544394493,
-0.0037764443550258875,
-0.0008123292936943471,
-0.00574830174446106
] |
<p>I have a question with regard to probabilistic quantum cloning - see for example <a href="http://prl.aps.org/abstract/PRL/v80/i22/p4999_1">http://prl.aps.org/abstract/PRL/v80/i22/p4999_1</a>.</p>
<p>It does seems like I can use the proof for no-cloning theorem to disproof the existence of equation (7) in the paper quant-ph/9704020. Do you think this is true?</p>
<p>Suppose probabilistic quantum cloning is actually possible, now according to the current papers, if the cloning process fails, the state that we intend to clone would be destroyed. Looking at the equation in the original paper, however, it does seem that a repair or a reverse operation might be possible in the event of a failure. More specifically, in the paper quant-ph/9704020, if I replace the $\left|\phi\right>$ state in Equation (7) with say, $\left|\psi_T\right>\left|0\right>$ where $\left|\psi_T\right>$ is a state orthogonal to the input state $\left|\psi\right>$, the proof would work just as fine. Do you think this is true? If this is true, a repair would be possible in case of cloning failure. The process would still be probabilistic, but I can repeat till it is successful.</p>
<p>I do hope for some feedback from experts out there. Thanks!</p> | g5528 | [
0.011669228784739971,
-0.03892439603805542,
0.027996834367513657,
-0.05017094686627388,
-0.031222235411405563,
-0.03304450213909149,
0.0010646107839420438,
0.014546033926308155,
-0.014106076210737228,
0.013895543292164803,
-0.008090739138424397,
0.03876540809869766,
-0.03292325511574745,
0.00402776850387454,
-0.03944593295454979,
0.01642484962940216,
0.06489507108926773,
-0.027336962521076202,
0.04673974961042404,
0.04474189877510071,
0.020565835759043694,
0.026045119389891624,
-0.033733438700437546,
-0.018980998545885086,
0.0065855239517986774,
-0.05701326206326485,
-0.03974402695894241,
-0.021619660779833794,
-0.04072989523410797,
-0.06352665275335312,
0.0414683036506176,
-0.0010355745907872915,
0.09686124324798584,
-0.04054177924990654,
-0.011210537515580654,
-0.0275303702801466,
0.024406615644693375,
0.0033986244816333055,
0.0029345680959522724,
-0.03940645605325699,
0.034740325063467026,
0.008125015534460545,
0.03386320173740387,
-0.06403439491987228,
0.022705834358930588,
0.025089707225561142,
0.025639669969677925,
0.017418306320905685,
0.050021927803754807,
-0.028387058526277542,
-0.00019644554413389415,
0.0774480402469635,
0.023234525695443153,
-0.03624741733074188,
0.002860558917745948,
0.06896016746759415,
0.025012891739606857,
0.03126085177063942,
0.017540378496050835,
-0.0034473647829145193,
-0.02131756953895092,
-0.03237627074122429,
0.011792611330747604,
0.02736329846084118,
0.05224902555346489,
-0.007021782919764519,
-0.007406370714306831,
0.03226132690906525,
0.0035869365092366934,
0.03174702823162079,
-0.027970928698778152,
-0.01004986371845007,
-0.0012815771624445915,
-0.009867353364825249,
0.012449037283658981,
0.03688614070415497,
0.012979176826775074,
-0.015781637281179428,
-0.0005496469093486667,
0.00787458848208189,
-0.048813290894031525,
-0.04114028438925743,
0.04358585551381111,
0.04706110432744026,
0.012888280674815178,
-0.020574145019054413,
-0.03426138311624527,
-0.02932148054242134,
-0.012408586218953133,
0.04508710652589798,
0.01998872309923172,
-0.007050366140902042,
0.02391679398715496,
-0.021860094740986824,
-0.007047903258353472,
0.0033275731839239597,
-0.02286910079419613,
0.025877097621560097,
-0.061015043407678604,
0.018292566761374474,
-0.04154892638325691,
-0.054638564586639404,
0.021068014204502106,
-0.08600650727748871,
-0.01853262074291706,
-0.017610982060432434,
0.054665084928274155,
0.020967630669474602,
-0.025792261585593224,
0.0028404202312231064,
-0.00674011604860425,
0.0184236578643322,
-0.036792654544115067,
-0.028864223510026932,
-0.027381718158721924,
0.02509976178407669,
0.013782340101897717,
0.022055940702557564,
-0.011901207268238068,
0.06443671137094498,
0.02739051729440689,
0.03560873866081238,
-0.010274283587932587,
-0.01798107847571373,
-0.07977050542831421,
0.0010694509837776423,
-0.07027389109134674,
0.018483033403754234,
0.04777338355779648,
0.019770001992583275,
0.008897374384105206,
0.008586946874856949,
0.04655199870467186,
0.07137960940599442,
-0.007871191017329693,
0.04534320533275604,
0.0335065983235836,
0.012587323784828186,
0.03911086544394493,
-0.0314166434109211,
0.00719257490709424,
0.018071163445711136,
0.008680112659931183,
0.03579467907547951,
-0.02270582504570484,
0.007544398307800293,
0.04841158539056778,
0.004985497333109379,
-0.03317112475633621,
0.051266640424728394,
-0.04504803195595741,
-0.0423000231385231,
-0.028043081983923912,
-0.005313816014677286,
-0.027789542451500893,
0.019058557227253914,
0.019134486094117165,
-0.008962458930909634,
0.028025494888424873,
-0.011524164117872715,
0.05277788266539574,
0.050650667399168015,
-0.010643129236996174,
-0.05467889457941055,
-0.004166873637586832,
-0.03747762739658356,
0.050084274262189865,
-0.04889706149697304,
-0.027794914320111275,
-0.04084628447890282,
-0.007953600957989693,
-0.010942788794636726,
0.06097851321101189,
0.037211112678050995,
0.0105902049690485,
0.04121719300746918,
-0.016524044796824455,
-0.01287541538476944,
-0.0679503008723259,
-0.007656559348106384,
-0.006872103549540043,
-0.014169092290103436,
0.011575965210795403,
-0.028753014281392097,
0.03246980533003807,
0.05265672504901886,
-0.031794704496860504,
0.05758538842201233,
-0.018871940672397614,
-0.032021429389715195,
-0.020205624401569366,
0.008995898067951202,
0.04511546716094017,
0.005589324049651623,
0.0044326274655759335,
-0.002209529047831893,
0.014630082063376904,
-0.00725536560639739,
0.026824137195944786,
0.0011083184508606791,
-0.00980366300791502,
0.03152948245406151,
0.033642787486314774,
-0.03641020506620407,
0.002532276324927807,
-0.017356829717755318,
-0.05717550590634346,
-0.011274699121713638,
0.01071245688945055,
0.013887152075767517,
0.07251900434494019,
-0.010749508626759052,
0.036220286041498184,
-0.029739538207650185,
0.033435504883527756,
-0.01344251912087202,
0.03526866436004639,
-0.020723802968859673,
-0.003191010793671012,
-0.02188359946012497,
0.04774131998419762,
0.02798236906528473,
0.08041118085384369,
-0.031397152692079544,
0.008302240632474422,
0.07378658652305603,
-0.02276681363582611,
-0.08359520137310028,
-0.051147233694791794,
-0.016272807493805885,
0.0020988776814192533,
-0.004740391857922077,
-0.04097273200750351,
-0.039090290665626526,
0.011812620796263218,
0.10465885698795319,
0.007217354141175747,
0.03443430736660957,
-0.000567814742680639,
0.03133126720786095,
0.043577294796705246,
0.005801841150969267,
-0.06548987329006195,
0.013568508438766003,
-0.01998916268348694,
-0.0905747339129448,
-0.017176324501633644,
-0.05147840827703476,
0.04480881616473198,
0.004983164370059967,
0.039614636451005936,
-0.055052418261766434,
0.006557410582900047,
-0.0018069425132125616,
0.0161113478243351,
-0.029759632423520088,
0.07395787537097931,
0.011524315923452377,
0.010357539169490337,
-0.02159172296524048,
-0.047848355025053024,
-0.03788164630532265,
0.00956279132515192,
0.03368102014064789,
-0.07907647639513016,
0.013271541334688663,
-0.08317359536886215,
0.008981699123978615,
-0.020330484956502914,
-0.010109088383615017,
-0.05895379185676575,
0.0569746233522892,
-0.033160801976919174,
0.0636024996638298,
0.02019036002457142,
0.0020007414277642965,
-0.016882335767149925,
0.028491290286183357,
-0.02044147066771984,
-0.005989330820739269,
-0.03730911388993263,
-0.02412658929824829,
0.017837807536125183,
0.004708835855126381,
-0.030047498643398285,
-0.07317190617322922,
-0.05253643915057182,
0.003213626565411687,
-0.0016416938742622733,
0.07853157073259354,
-0.037276241928339005,
-0.03617505729198456,
0.04030431807041168,
-0.004317700397223234,
-0.03039870411157608,
0.03150024265050888,
-0.02408047765493393,
-0.02804182469844818,
0.019968615844845772,
0.04056235030293465,
-0.027220889925956726,
0.019491977989673615,
-0.03601912781596184,
0.008215917274355888,
0.03384215012192726,
0.033245623111724854,
-0.07092099636793137,
0.0231342650949955,
-0.012618409469723701,
-0.013333829119801521,
-0.00005842113387188874,
0.04008762910962105,
-0.011962604708969593,
-0.04296671599149704,
0.021587228402495384,
0.0009179242188110948,
0.009234067052602768,
-0.021823011338710785,
0.08386685699224472,
-0.01069218385964632,
-0.09851444512605667,
-0.020069612190127373,
-0.0020797322504222393,
-0.013837256468832493,
0.040266990661621094,
-0.005037665367126465,
-0.0421338826417923,
0.08321329206228256,
0.003995428327471018,
-0.02259492687880993,
0.05753707513213158,
0.009458365850150585,
0.01913081854581833,
-0.04305377975106239,
-0.028862053528428078,
-0.050087280571460724,
-0.031655509024858475,
0.019059497863054276,
0.0394895002245903,
0.038804881274700165,
0.017076103016734123,
0.044096387922763824,
0.009244710206985474,
0.03507225587964058,
0.05015735700726509,
0.018094098195433617,
0.02727692201733589,
0.050949789583683014,
0.05338964983820915,
0.007226902060210705,
0.025424616411328316,
-0.048773325979709625,
-0.022357221692800522,
-0.00849225465208292,
0.07380171865224838,
0.06346838921308517,
0.01612160913646221,
0.023389993235468864,
0.024050161242485046,
0.016172440722584724,
-0.02841251529753208,
-0.042138051241636276,
0.11795032024383545,
0.0011017763754352927,
0.02325780875980854,
-0.000465077260741964,
0.038491811603307724,
0.018729301169514656,
-0.03790279105305672,
0.03099261410534382,
-0.034448105841875076,
-0.03802136704325676,
0.01678021065890789,
-0.030254654586315155,
-0.012113971635699272,
0.049671124666929245,
0.007693731226027012,
-0.0034823224414139986,
-0.05675749108195305,
0.03371516987681389,
0.031872402876615524,
-0.020235629752278328,
0.018839456140995026,
0.011239440180361271,
0.018785372376441956,
-0.015296775847673416,
-0.03033830225467682,
-0.010605941526591778,
-0.03270009160041809,
0.003329891711473465,
0.001770527334883809,
0.0286592785269022,
-0.014628909528255463,
0.055388983339071274,
0.02913350611925125,
0.05892973020672798,
0.017670920118689537,
-0.07818473130464554,
0.0016769935609772801,
0.013502031564712524,
-0.042406115680933,
-0.035399071872234344,
-0.010404299013316631,
0.028398850932717323,
0.007694970816373825,
-0.04732484742999077,
0.04721209406852722,
0.04194235801696777,
-0.006754156202077866,
-0.07652592658996582,
-0.03673916310071945,
0.021331900730729103,
0.00336650013923645,
-0.04494492709636688,
0.014727262780070305,
0.02599007822573185,
0.0032989599276334047,
-0.010503741912543774,
-0.028606176376342773,
0.033317551016807556,
0.01719813421368599,
0.031409475952386856,
0.022512352094054222,
0.05812539532780647,
-0.021925855427980423,
0.006381580606102943,
0.006469637155532837,
-0.004215645603835583,
0.06365052610635757,
-0.032096099108457565,
0.06211204081773758,
0.014068922027945518,
0.042464908212423325,
-0.005326871294528246,
0.03265116736292839,
-0.02763080969452858,
-0.04484821483492851,
0.07003471255302429,
0.020507458597421646,
0.01527225598692894,
0.0657067522406578,
0.01052781566977501,
0.012564705684781075,
0.045376088470220566,
0.014401055872440338,
0.026871470734477043,
-0.0185476653277874,
-0.02567513845860958,
0.004354424308985472,
-0.02024194225668907,
0.022171219810843468,
0.004750195890665054,
0.0015352722257375717,
-0.048059895634651184,
-0.0056594545021653175,
-0.050245191901922226,
-0.01670881360769272,
0.009488668292760849,
-0.0603560209274292,
0.11470459401607513,
0.006733885500580072,
0.020543353632092476,
0.0739101767539978,
0.0381903313100338,
0.03515061363577843,
-0.02076069824397564,
-0.073447585105896,
0.0069208526983857155,
-0.05160157009959221,
-0.03913308307528496,
-0.05164109170436859,
-0.02926686219871044,
0.03146280348300934,
-0.006269097328186035,
-0.04540066793560982,
-0.04229464381933212,
-0.02899298071861267,
0.016618531197309494,
0.031923841685056686,
-0.055774327367544174,
0.03671334311366081,
-0.0213149581104517,
0.018751660361886024,
-0.010530715808272362,
-0.005544486455619335,
0.01221123430877924,
-0.026608143001794815,
-0.012430780567228794,
-0.0014662598259747028,
-0.067562036216259,
0.05079345032572746,
0.03403891623020172,
0.014281065203249454,
-0.02621612697839737,
-0.0014471742324531078,
-0.053785305470228195,
-0.024332279339432716,
0.05027657374739647,
0.010695395991206169,
0.00989226158708334,
-0.0410333089530468,
-0.009166873060166836,
0.00875615794211626,
-0.028362151235342026,
-0.02027796022593975,
-0.02417128160595894,
0.02738194353878498,
0.04392995685338974,
-0.010985670611262321,
-0.017988277599215508,
-0.04698963835835457,
0.016665862873196602,
-0.03236743062734604,
-0.00018546062347013503,
-0.006954498123377562,
-0.00477392366155982,
-0.055400751531124115,
-0.031418781727552414,
-0.06775383651256561,
-0.03671398013830185,
0.017850399017333984,
0.005546558648347855,
-0.002752514323219657,
-0.027555735781788826,
-0.004506366327404976,
-0.03526617959141731,
-0.038210179656744,
-0.014399583451449871,
-0.027413753792643547,
0.03522476553916931,
0.01459513045847416,
0.010363237001001835,
-0.003032229607924819,
0.02990836091339588,
-0.065291628241539,
-0.00514732813462615,
-0.0010765759507194161,
0.007022386882454157,
0.03670898452401161,
0.0013053363654762506,
0.05169360712170601,
0.028374845162034035,
-0.016869325190782547,
0.05171531066298485,
-0.04793331027030945,
-0.010874687694013119,
-0.0649559274315834,
-0.003990950062870979,
0.003938981797546148,
-0.04833259433507919,
-0.03126451000571251,
-0.02314428612589836,
-0.03706859052181244,
0.0016621494432911277,
0.014649403281509876,
0.017989924177527428,
-0.020362740382552147,
0.03694261237978935,
0.039116472005844116,
0.037918053567409515,
0.013257786631584167,
-0.045654892921447754,
0.02701854705810547,
0.013261388055980206,
0.03307843208312988,
-0.006930992938578129,
-0.04004070907831192,
-0.0003073407569900155,
-0.04608191177248955,
-0.01656387932598591,
0.011736138723790646,
-0.052970558404922485,
-0.04479389265179634,
0.04092041030526161,
0.0029231542721390724,
0.016361327841877937,
0.006178627721965313,
-0.09411228448152542,
-0.049502938985824585,
-0.028236962854862213,
-0.02779896929860115,
0.041468556970357895,
-0.01915685087442398,
-0.037690527737140656,
-0.03691061586141586,
0.0066524590365588665,
0.012587068602442741,
0.012768196873366833,
0.0230852197855711,
0.07017368823289871,
0.006218926049768925,
0.053886059671640396,
-0.03131193667650223,
-0.01861531287431717,
0.00905570201575756,
0.015583446249365807,
0.030316246673464775,
-0.00036010806798003614,
-0.06947938352823257,
-0.015753572806715965,
-0.008211223408579826,
-0.04589239880442619,
0.042289696633815765,
-0.03568163514137268,
-0.05510272830724716,
0.03918955847620964,
-0.053160250186920166,
0.04162263125181198,
0.04051807150244713,
-0.0003443931054789573,
-0.03571256622672081,
0.000567976210732013,
0.02918519265949726,
0.036716263741254807,
0.024098409339785576,
-0.08797518163919449,
-0.027395600453019142,
0.058221444487571716,
-0.06944436579942703,
0.01895790919661522,
0.049212925136089325,
0.006107155699282885,
0.00574690755456686,
0.03794422000646591,
-0.03556579723954201,
0.053746193647384644,
0.026908792555332184,
-0.008623849600553513,
0.057196393609046936,
-0.003724185051396489,
-0.008964267559349537,
-0.04077424481511116,
-0.0712486207485199,
-0.005005442537367344,
-0.019109390676021576,
0.04049919918179512,
-0.06152432784438133,
0.003983539994806051,
0.030560385435819626,
-0.0007135997875593603,
0.013714471831917763,
0.023133203387260437,
0.052111148834228516,
-0.03807207942008972,
-0.09255541861057281,
0.043055545538663864,
-0.016188809648156166,
0.029518643394112587,
-0.07349677383899689,
0.014058203436434269,
0.001646599150262773,
0.028277866542339325,
-0.06782316416501999,
0.014135113917291164,
0.0033580304589122534,
0.03291422128677368,
0.017543399706482887,
0.012656643986701965,
-0.0010235527297481894,
-0.016994958743453026,
-0.022210082039237022,
-0.09857220947742462,
-0.0003860316937789321,
-0.05463431403040886,
0.00015351448382716626,
0.02989620342850685,
0.0448339506983757,
0.0000126337163237622,
0.05815567821264267,
-0.010431555099785328,
-0.0026738711167126894,
-0.052307285368442535,
-0.0636906623840332,
-0.037516336888074875,
-0.024561310186982155,
0.009451068937778473,
0.07723893970251083,
0.080593541264534,
-0.001762119703926146,
-0.0200667604804039,
0.003498383332043886,
-0.004203885793685913,
-0.025281155481934547,
-0.035484328866004944,
-0.006153833121061325,
-0.05730588361620903,
-0.02078821323812008,
0.04216829687356949,
-0.02073562704026699,
-0.0372399166226387,
-0.021943233907222748,
-0.017774704843759537,
0.04431140795350075,
0.001362169859930873,
0.008353855460882187,
0.05225677788257599,
-0.0075023542158305645,
0.012052142061293125,
0.05939256027340889,
0.03910697624087334,
0.06878248602151871,
-0.01454847864806652,
-0.011641956865787506,
0.028971487656235695,
-0.007224788423627615,
-0.008614987134933472,
-0.031813718378543854,
0.021289817988872528,
-0.03390407934784889,
-0.02216140180826187,
0.05498390644788742,
-0.025547537952661514,
-0.051868487149477005,
0.004868105985224247,
0.038615286350250244,
-0.05102669820189476,
-0.041156165301799774,
-0.013854707591235638,
0.08454865962266922,
-0.01383924763649702,
-0.03149561211466789,
-0.02842775546014309,
-0.05563266575336456,
0.026013387367129326,
0.007697217632085085,
0.0190886277705431,
-0.025561900809407234,
0.0623634047806263,
-0.06571007519960403,
-0.03391515091061592,
0.03835437446832657,
-0.002982809441164136,
-0.041880395263433456,
-0.005659800488501787,
0.034278761595487595,
0.019008098170161247,
0.024390513077378273,
-0.014292788691818714,
-0.022395595908164978,
-0.01765410229563713,
-0.004255663603544235,
-0.008821395225822926,
-0.009833875112235546,
-0.05196458101272583,
0.04030843824148178,
-0.050460394471883774,
-0.04062889143824577,
-0.008427968248724937,
0.04839283227920532,
-0.024189436808228493,
0.0009304767590947449,
-0.05335226282477379,
-0.02391943894326687,
0.02142300084233284,
0.04130320996046066,
-0.048729825764894485,
0.06391330063343048,
0.07423938065767288,
0.0990319773554802,
0.015331968665122986,
0.031693536788225174,
-0.003943315241485834,
-0.002722120610997081,
-0.00899793952703476,
-0.03343812748789787,
-0.04898308590054512,
-0.01767623797059059,
0.015502185560762882
] |
<p>Within my master's thesis, I try to model a machine elements and have to model the exact slipping and exact sticking between the bodies. So I noticed that such problems can be formulated as a LCP. </p>
<p>However I have difficulties at finding any literature where the usage is described well with examples..</p>
<p>I would like to have something like a 1-DOF model such a box on a plane pulled with a spring and friction modeled with coulomb or so. </p>
<p>I would be very grateful of mentioning any literature/sites which can bring me further. </p>
<p>I am really desperate at implementing the coulomb friction..</p> | g5529 | [
0.016657575964927673,
0.014681321568787098,
-0.0010428247042000294,
-0.03224807605147362,
0.08048218488693237,
-0.009583358652889729,
0.030045902356505394,
0.03538784757256508,
-0.019611859694123268,
-0.039780668914318085,
-0.011798839084804058,
-0.051536936312913895,
0.03827400505542755,
0.0325716994702816,
0.005259028635919094,
0.049242112785577774,
-0.002859235042706132,
-0.019948601722717285,
0.007866283878684044,
-0.0326114185154438,
0.03576309606432915,
0.05020911246538162,
0.03864898905158043,
-0.04458584636449814,
-0.041430678218603134,
-0.027394387871026993,
-0.020778656005859375,
-0.06325001269578934,
-0.001654415624216199,
0.01772984303534031,
-0.07005700469017029,
-0.08205653727054596,
0.02336837537586689,
-0.10415670275688171,
-0.07499733567237854,
-0.02365168370306492,
0.08674223721027374,
0.03839040920138359,
0.01304667815566063,
0.04708648845553398,
0.029262984171509743,
-0.08481484651565552,
0.0068605318665504456,
0.0022413525730371475,
0.010317981243133545,
-0.02732168883085251,
0.01332472451031208,
-0.01906641572713852,
-0.025722060352563858,
0.05971523001790047,
0.02012462541460991,
0.05592258647084236,
0.026181351393461227,
-0.013378612697124481,
-0.03507216274738312,
-0.006180754397064447,
-0.0016676441300660372,
-0.024169333279132843,
0.047875359654426575,
-0.01816430315375328,
-0.004084459040313959,
0.01759232208132744,
-0.049737654626369476,
-0.0379781648516655,
0.027199557051062584,
0.015385591425001621,
-0.008877403102815151,
0.004459529183804989,
0.020678682252764702,
-0.012338172644376755,
-0.04900136590003967,
0.011227212846279144,
0.05455860123038292,
-0.041943635791540146,
-0.047085072845220566,
-0.013636033050715923,
-0.010364627465605736,
-0.05153395235538483,
-0.005900250282138586,
0.0077433292753994465,
-0.06970755755901337,
0.030790606513619423,
-0.014062130823731422,
0.027763793244957924,
0.08516359329223633,
-0.03471451252698898,
0.031800828874111176,
0.05577116832137108,
0.00579876871779561,
-0.07503727823495865,
-0.007343793287873268,
-0.003821062156930566,
-0.007654260843992233,
-0.026363322511315346,
0.04559621587395668,
0.025598449632525444,
-0.02526276931166649,
0.047824498265981674,
0.0174625925719738,
0.012671739794313908,
-0.022276194766163826,
0.032026585191488266,
-0.018220359459519386,
0.013008292764425278,
-0.052669815719127655,
-0.06157854571938515,
0.056062646210193634,
0.014611644670367241,
0.010556385852396488,
0.009517357684671879,
-0.010978496633470058,
0.004860556218773127,
-0.10457748174667358,
-0.01786293275654316,
0.04275505244731903,
-0.03028622642159462,
-0.019381001591682434,
-0.007356870453804731,
-0.015992892906069756,
0.024452973157167435,
0.013748738914728165,
-0.05346231535077095,
-0.002081380458548665,
0.07997936010360718,
0.10038109123706818,
-0.021961010992527008,
-0.02568354830145836,
-0.005012465640902519,
-0.025756940245628357,
0.013152139261364937,
0.008887258358299732,
0.002024635672569275,
0.0027342087123543024,
-0.006279223598539829,
0.008544066920876503,
0.07432042062282562,
-0.05357646197080612,
0.003168178489431739,
0.058470841497182846,
-0.04948677495121956,
0.048423826694488525,
-0.0653189942240715,
-0.012836976908147335,
0.020490964874625206,
-0.029102792963385582,
0.014528787694871426,
-0.025778668001294136,
0.06590497493743896,
0.030135678127408028,
0.007910273969173431,
0.019248072057962418,
0.0782904177904129,
-0.021392788738012314,
0.008210300467908382,
0.0046904562041163445,
0.035812728106975555,
0.04444228485226631,
-0.050509437918663025,
0.04361473023891449,
-0.023942846804857254,
0.027016645297408104,
-0.025306662544608116,
-0.011597653850913048,
0.004598844796419144,
-0.009938474744558334,
0.013192201033234596,
-0.057770371437072754,
-0.003249046392738819,
0.048211418092250824,
-0.03035205788910389,
-0.05883903428912163,
-0.03512900695204735,
0.02893947809934616,
0.05223013460636139,
-0.011434360407292843,
0.044333070516586304,
0.06425508856773376,
0.015344580635428429,
0.048027463257312775,
-0.022291332483291626,
0.049360502511262894,
-0.029364021494984627,
0.046776413917541504,
-0.00022515466844197363,
-0.047713182866573334,
0.009340252727270126,
-0.013399112038314342,
0.024878432974219322,
0.019417809322476387,
-0.028678886592388153,
-0.06202792003750801,
-0.010287909768521786,
0.008218768984079361,
-0.015836482867598534,
-0.02076210267841816,
0.01752353459596634,
0.06354650855064392,
-0.08128425478935242,
0.013694562949240208,
-0.029539115726947784,
0.037160277366638184,
0.013751689344644547,
0.04662705585360527,
0.027168065309524536,
-0.003506242297589779,
-0.01247411035001278,
-0.015718676149845123,
-0.02220257930457592,
0.021962231025099754,
0.019529376178979874,
0.0245289895683527,
0.0312273558229208,
0.005178954917937517,
0.06068932265043259,
-0.005768877454102039,
-0.07298243790864944,
-0.004457694478332996,
-0.008374830707907677,
-0.011208160780370235,
0.005545294843614101,
-0.0025616849306970835,
-0.04651805758476257,
0.03217905014753342,
0.02698242850601673,
-0.007047953549772501,
-0.00861715991050005,
0.028432389721274376,
0.061848919838666916,
-0.024555286392569542,
0.02276112511754036,
-0.08853203803300858,
0.03280660882592201,
0.003168901428580284,
-0.047811515629291534,
0.005707877222448587,
-0.01756180077791214,
-0.04781687259674072,
0.04730656370520592,
-0.01990325190126896,
0.058354657143354416,
0.005605294834822416,
-0.03531269356608391,
-0.03421565145254135,
-0.05195258557796478,
0.0030535373371094465,
-0.04335955157876015,
0.04522320628166199,
0.05614300072193146,
0.0520719550549984,
0.014656501822173595,
-0.024903398007154465,
-0.049695294350385666,
-0.03905535861849785,
0.018629051744937897,
-0.017123406752943993,
0.04273191839456558,
0.00913560576736927,
0.023266348987817764,
0.046305350959300995,
-0.0030964079778641462,
-0.01232621818780899,
0.03284411132335663,
-0.04606224223971367,
0.03457850217819214,
-0.02625550702214241,
-0.005933227948844433,
-0.033525269478559494,
-0.08111825585365295,
0.03907217085361481,
0.03528306633234024,
0.049363430589437485,
-0.04034306854009628,
-0.00286163785494864,
-0.013998596929013729,
0.013057663105428219,
-0.05580948293209076,
0.030081497505307198,
-0.05438101664185524,
-0.06705084443092346,
0.006431681104004383,
0.036562733352184296,
-0.0694560632109642,
-0.02853287197649479,
-0.03425006568431854,
-0.030407646670937538,
-0.028770901262760162,
-0.01651122234761715,
0.026133816689252853,
-0.015208941884338856,
0.06780502945184708,
-0.016569286584854126,
0.023969558998942375,
0.03162528946995735,
-0.05070136860013008,
0.014171170070767403,
0.04508389160037041,
0.05325262248516083,
-0.009493817575275898,
-0.06254798918962479,
0.055810246616601944,
-0.007646478712558746,
-0.01659431867301464,
0.032513298094272614,
0.006661009043455124,
-0.011397301219403744,
-0.00769063550978899,
0.05370338261127472,
-0.008684867061674595,
0.05173814669251442,
-0.0011263977503404021,
-0.008250605314970016,
0.010376018472015858,
0.044175636023283005,
0.043140050023794174,
-0.04815990850329399,
0.004173915833234787,
0.017535433173179626,
0.012753297574818134,
0.0014882817631587386,
-0.03571179136633873,
-0.005490187555551529,
-0.03882747143507004,
0.05912834033370018,
-0.015383405610918999,
0.024866873398423195,
0.04109954461455345,
-0.0311910230666399,
0.014088175259530544,
-0.008609629236161709,
0.013372555375099182,
0.03519356995820999,
0.03936433047056198,
0.018186459317803383,
-0.043953780084848404,
-0.04484935477375984,
-0.02776539884507656,
-0.015454600565135479,
-0.007423588074743748,
0.03515256568789482,
0.018145650625228882,
-0.012806502170860767,
-0.046411510556936264,
-0.0036668365355581045,
-0.004013577941805124,
0.012824581936001778,
0.012745628133416176,
0.01935703493654728,
0.00831929873675108,
-0.023531576618552208,
-0.024784158915281296,
0.0500357411801815,
-0.04364461079239845,
0.028314633294939995,
0.004096968565136194,
0.039374593645334244,
0.04429486766457558,
0.03429747372865677,
-0.017983453348279,
-0.03489761799573898,
0.011380069889128208,
0.03038707748055458,
0.0033399537205696106,
-0.02111794985830784,
0.05598056688904762,
0.05013392120599747,
-0.009398003108799458,
-0.004359433427453041,
0.10482273995876312,
-0.013446187600493431,
-0.04450477659702301,
-0.038618288934230804,
0.01183125376701355,
0.029346175491809845,
0.006835452746599913,
-0.002534648170694709,
-0.003543608821928501,
-0.002702206140384078,
0.08220960199832916,
0.02284867875277996,
0.011629787273705006,
-0.0047286213375627995,
0.025974012911319733,
-0.017126722261309624,
0.07887677848339081,
0.026858951896429062,
-0.011952654458582401,
0.0019394072005525231,
0.01737115904688835,
0.0007531621376983821,
0.0025366151239722967,
0.014832742512226105,
-0.042057380080223083,
0.009324213489890099,
0.04844221472740173,
0.00024673331063240767,
0.0034960340708494186,
-0.05113627761602402,
-0.009216058067977428,
0.026612110435962677,
-0.05356506258249283,
0.013277838937938213,
-0.04345279932022095,
-0.05711927264928818,
0.036418743431568146,
-0.00007721533620497212,
-0.020061330869793892,
0.005074996035546064,
0.006319643463939428,
0.0102278683334589,
0.000026740681278170086,
0.03910783305764198,
-0.05636774003505707,
-0.00918372068554163,
0.019732603803277016,
0.04188462346792221,
-0.05689218267798424,
-0.0076749552972614765,
0.06711389869451523,
0.04297381639480591,
-0.0028716963715851307,
-0.011352735571563244,
0.08411457389593124,
-0.05404088273644447,
-0.03557805344462395,
-0.0028705515433102846,
-0.014795198105275631,
-0.02021363005042076,
0.06902863085269928,
-0.013599909842014313,
-0.07592611014842987,
-0.05324371159076691,
0.021369513124227524,
-0.01971803791821003,
0.02248450554907322,
-0.04482161998748779,
0.05784180015325546,
-0.047719769179821014,
-0.03282516449689865,
-0.025417711585760117,
0.03014235943555832,
-0.05244977027177811,
0.04042418301105499,
0.038949817419052124,
-0.0006950669921934605,
-0.049535010010004044,
0.043548159301280975,
-0.024743858724832535,
0.006705693434923887,
-0.03141096606850624,
-0.04199369624257088,
-0.0447998046875,
-0.015183244831860065,
-0.045653145760297775,
0.010135586373507977,
-0.0635896846652031,
-0.013115857727825642,
0.020111341029405594,
0.019542695954442024,
-0.015276022255420685,
-0.009529468603432178,
0.017249897122383118,
-0.04616164416074753,
-0.04211210459470749,
-0.04009886458516121,
-0.04588108882308006,
-0.013209112919867039,
-0.046823855489492416,
-0.017075739800930023,
-0.05234739929437637,
-0.000048648493248037994,
0.01784725859761238,
-0.023921027779579163,
-0.01451670192182064,
0.07649517804384232,
0.053229279816150665,
0.02115005999803543,
-0.008122972212731838,
-0.003174345940351486,
0.01793736405670643,
0.0027732865419238806,
-0.039778102189302444,
0.004499312024563551,
0.02737005241215229,
-0.005391845945268869,
-0.017541788518428802,
-0.04076790064573288,
-0.00965079665184021,
0.05541006848216057,
0.008077392354607582,
-0.036057356745004654,
0.11168605089187622,
0.03172324225306511,
0.01933962292969227,
-0.0011234033154323697,
-0.015424639917910099,
0.03551475703716278,
-0.009439255110919476,
0.00919568631798029,
-0.04700643569231033,
0.049520786851644516,
-0.07048886269330978,
0.03426153212785721,
-0.0011325515806674957,
-0.01952553354203701,
0.04562820494174957,
0.0002471350017003715,
0.03893198445439339,
-0.0027744814287871122,
0.005488543771207333,
-0.03725956007838249,
-0.007542456034570932,
0.0008388811256736517,
0.029955964535474777,
0.037086840718984604,
-0.025953039526939392,
0.025676237419247627,
-0.029138853773474693,
0.008974514901638031,
-0.031893640756607056,
-0.028355984017252922,
0.05586031451821327,
0.026679642498493195,
0.023376500234007835,
0.003062137169763446,
-0.00900727603584528,
0.01673588715493679,
-0.028423238545656204,
-0.0036228233948349953,
-0.03228224813938141,
-0.03928506001830101,
0.06326379626989365,
-0.017379552125930786,
-0.04527147859334946,
0.051455482840538025,
0.013106799684464931,
-0.039351582527160645,
0.040088772773742676,
-0.00776694854721427,
0.004552689380943775,
-0.03704335540533066,
-0.03907132148742676,
-0.005848912056535482,
0.02545025199651718,
0.03339308500289917,
0.02055213414132595,
-0.011143696494400501,
0.03392336517572403,
0.012623817659914494,
0.050454575568437576,
-0.07895122468471527,
0.0011961180716753006,
0.016441602259874344,
0.01849895343184471,
0.04276042431592941,
-0.019330620765686035,
-0.02903570793569088,
-0.06345610320568085,
-0.10259313881397247,
0.02661057747900486,
0.07539601624011993,
-0.00012007123586954549,
-0.015385095030069351,
0.06884445250034332,
0.005738828331232071,
0.01187378354370594,
0.01977531425654888,
0.015591021627187729,
0.004101940430700779,
0.0699537992477417,
0.010689759626984596,
-0.0546565055847168,
-0.0431843101978302,
-0.03911275789141655,
-0.0017805399838835,
-0.0180741585791111,
0.019165966659784317,
-0.029921511188149452,
-0.05833238735795021,
-0.01832674629986286,
0.056577280163764954,
0.01552257128059864,
0.044238828122615814,
0.004329416900873184,
-0.035819608718156815,
-0.05083581432700157,
0.022295359522104263,
-0.05461085960268974,
-0.06746599078178406,
0.011976907029747963,
-0.01607302576303482,
-0.0006401519058272243,
0.02010401152074337,
0.02095845155417919,
0.047610849142074585,
0.007198669482022524,
0.015829656273126602,
0.015558469109237194,
0.03678572550415993,
0.013674289919435978,
0.02771390788257122,
0.004137858748435974,
0.01765875332057476,
0.002486409852281213,
-0.04763798043131828,
-0.01676061376929283,
0.021318506449460983,
0.026275642216205597,
-0.008194669149816036,
0.029284045100212097,
-0.0019033525604754686,
-0.025578949600458145,
0.004606208764016628,
-0.07884302735328674,
-0.052299804985523224,
0.0011753691360354424,
-0.008575172163546085,
-0.004469240549951792,
0.02228572405874729,
0.005754982586950064,
-0.04308402165770531,
0.018516890704631805,
-0.009671816602349281,
0.04110445827245712,
-0.01572069153189659,
-0.07508570700883865,
-0.012893005274236202,
-0.0670740157365799,
0.048647958785295486,
0.03955952450633049,
0.025823261588811874,
0.013878609985113144,
-0.013553699478507042,
-0.021054109558463097,
0.009767998941242695,
-0.03572700917720795,
0.11415483057498932,
-0.05879763141274452,
0.01128808781504631,
0.05819954723119736,
0.0605437345802784,
-0.01105884462594986,
0.026935532689094543,
0.06102892756462097,
0.0381162092089653,
0.020991338416934013,
-0.008779224939644337,
0.00014678917068522424,
0.021277399733662605,
-0.03509785607457161,
-0.01707347109913826,
-0.010887243784964085,
-0.0498686246573925,
-0.06083785369992256,
0.018470168113708496,
0.02462759241461754,
-0.02853914350271225,
0.03396317735314369,
0.012136559002101421,
-0.05350274220108986,
0.0005026119179092348,
-0.04346799850463867,
0.00917258020490408,
0.013742543756961823,
-0.050754472613334656,
0.01340574026107788,
0.04062112048268318,
-0.03856361284852028,
0.030135972425341606,
0.03438218683004379,
0.009951986372470856,
0.015824172645807266,
-0.060510169714689255,
-0.027424054220318794,
0.07442823797464371,
-0.0010266747558489442,
0.018579404801130295,
-0.0019929816480726004,
-0.007924557663500309,
-0.0026063339319080114,
-0.02355780452489853,
0.026950202882289886,
0.06370978057384491,
0.020806342363357544,
0.007173605263233185,
0.0017360076308250427,
-0.011607866734266281,
0.011787249706685543,
-0.004908108618110418,
-0.015291710384190083,
0.01467457041144371,
0.056990791112184525,
0.07590971887111664,
-0.034479446709156036,
-0.031395550817251205,
-0.004866584669798613,
0.008621977642178535,
0.006196634378284216,
0.001493122079409659,
0.02307479828596115,
0.05115951970219612,
0.04583296552300453,
-0.017229530960321426,
0.013798967003822327,
0.00743565708398819,
-0.06272007524967194,
-0.002851315075531602,
-0.07383286207914352,
-0.002746190642938018,
-0.00749618373811245,
0.0034126865211874247,
-0.00003948204903281294,
0.06231383606791496,
0.0399186946451664,
-0.05015498399734497,
-0.010330956429243088,
0.03504516929388046,
-0.06655967980623245,
0.021906370297074318,
-0.021980511024594307,
0.025197744369506836,
0.00795825943350792,
-0.016231518238782883,
0.01178898848593235,
-0.0081459516659379,
0.07908748090267181,
-0.04554362967610359,
-0.07191907614469528,
-0.013309119269251823,
0.015233099460601807,
-0.018108289688825607,
0.026601960882544518,
-0.0333888903260231,
0.0013303800951689482,
-0.013113725930452347,
-0.040370069444179535,
-0.03815949708223343,
-0.016979914158582687,
-0.030355358496308327,
-0.014740180224180222,
0.002448047511279583,
-0.0004951191949658096,
-0.10269346833229065,
0.0005582175217568874,
-0.021374518051743507,
0.015794267877936363,
0.017174409702420235,
-0.03466901183128357,
0.0021951922681182623,
-0.03605677932500839,
0.031163182109594345,
-0.02062058262526989,
0.00043222797103226185,
0.03510111942887306,
-0.006892286241054535,
-0.01798301935195923,
-0.0847797691822052,
-0.029073763638734818,
0.031841959804296494,
-0.0032946739811450243,
-0.01730424538254738,
-0.06082107871770859,
-0.034286778420209885,
0.002770930528640747,
0.006417793221771717,
0.0017480680253356695,
-0.05333767458796501,
0.020446741953492165,
0.036171332001686096
] |
<p>I have been reviewing the basics of mechanics in preparation of studying Spivak's text book on mechanics (I am from a more mathematical background and I am taking an advanced analytical mechanics course next quarter which is using this text). I recently came across a problem in a text different from the one that I am using (University Physics), and I was having difficulty understanding how to approach it, and indeed even understanding the details of the situation (the problem is stated with little detail). Unfortunately, my text does not seem to cover anything like it, in the exercises or otherwise.</p>
<blockquote>
<p><em>Imagine a flat surface inclined at 45 degrees. A 1500 kg block is placed on the incline, and it is (according to the figure) attached directly to a pulley of radius $r$. The pulley itself has a cable rolling over it which extends along the incline with one end connected to the surface and the other end connected to a larger pulley of radius $3r$, but at a point of contact which is only $r$ from the center. Another block of unknown mass $m$ is attached to the larger pulley at the edge ($3r$ from the center) and is allowed to hang. We are asked to compute the mass $m$ of the hanging block required to counteract the motion of the block of mass 1500 kg. (The physical situation [I will try to update this with a picture as soon as I can] is basically just like the traditional one pulley/two-block system on an incline first encountered with problems involving Newton's laws; except here there are two pulleys involved as described above).</em></p>
</blockquote>
<p>To be perfectly honest, I am really not at all sure what is going on in this problem. If we take the axis of rotation to be the center of the larger pulley, then it is clear the second block imparts a torque of $3rmg\sin\left(\frac{\pi}{4}\right)$ and a tension on the cable is just $mg$. It seems to be the block on the incline imparts no torque since its action is directed parallel to the radial coordinate of the axis (if we are taking the natural coordinate system with axes perpendicular and parallel to the axis of rotation). What is the significance of the smaller pulley to which the mass is attached?</p> | g5530 | [
-0.0006717007490806282,
0.01860695891082287,
0.0017810019198805094,
-0.006752976682037115,
-0.003639227943494916,
0.018064802512526512,
0.05674333497881889,
0.006959924008697271,
-0.04848526790738106,
0.03075730986893177,
-0.026489663869142532,
-0.010311874561011791,
0.029514526948332787,
-0.015997326001524925,
0.025980370119214058,
0.039912279695272446,
0.08222360163927078,
-0.026950743049383163,
0.03331904485821724,
-0.004949691239744425,
-0.026393866166472435,
0.007596616167575121,
-0.04191116616129875,
-0.024201519787311554,
-0.03837298974394798,
0.00469801714643836,
0.022374680265784264,
-0.012930192053318024,
-0.04939651861786842,
0.02950434759259224,
-0.060805484652519226,
-0.02938006818294525,
0.01005885936319828,
-0.07921072095632553,
-0.0621175542473793,
0.015439465641975403,
0.08892124891281128,
0.0535736009478569,
0.007839436642825603,
0.013056592084467411,
0.003288462059572339,
-0.041501957923173904,
-0.00003789464972214773,
-0.00935970526188612,
0.012817168608307838,
-0.023434145376086235,
-0.039170533418655396,
0.01769505813717842,
0.04564926028251648,
0.02285626344382763,
0.010920093394815922,
-0.03249730169773102,
0.06857948005199432,
-0.042121946811676025,
-0.06868734210729599,
-0.002546875737607479,
0.05034927651286125,
0.000278803869150579,
-0.011466292664408684,
0.04659832641482353,
-0.03158443793654442,
-0.005417006555944681,
0.011811395175755024,
-0.013162024319171906,
0.07916636019945145,
-0.02804396115243435,
-0.006879452615976334,
0.0004624555294867605,
0.010507534258067608,
0.04505617916584015,
-0.009416261687874794,
-0.06102385371923447,
0.03629385307431221,
-0.11884190887212753,
-0.06869376450777054,
-0.0174840297549963,
0.024070044979453087,
-0.012609215453267097,
0.024406982585787773,
-0.06307506561279297,
0.0018956094281747937,
0.03229912370443344,
0.01900259219110012,
0.030237218365073204,
0.024896027520298958,
0.003297832328826189,
-0.052411533892154694,
0.0027606438379734755,
-0.09703526645898819,
0.036766283214092255,
0.05632784217596054,
-0.0008511203923262656,
0.07369385659694672,
0.02400701865553856,
-0.028618933632969856,
-0.06973963975906372,
-0.015794267877936363,
0.06611241400241852,
-0.012981794774532318,
0.02507842518389225,
-0.005155624821782112,
-0.019573980942368507,
-0.00784260407090187,
-0.008588828146457672,
0.03308909013867378,
0.026624074205756187,
0.014577866531908512,
0.032430585473775864,
0.005318408366292715,
-0.013551074080169201,
-0.042581863701343536,
-0.008990569971501827,
-0.02351217530667782,
-0.09665317088365555,
-0.008304656483232975,
-0.06020630523562431,
0.08227410912513733,
0.03945140168070793,
0.001294679008424282,
0.013932057656347752,
-0.02662569470703602,
0.017090003937482834,
0.003583667566999793,
0.0850069522857666,
-0.000705102866049856,
-0.05161362886428833,
-0.04038141667842865,
0.023942548781633377,
0.022658737376332283,
-0.059863705188035965,
-0.0025196769274771214,
0.005244538653641939,
-0.029842862859368324,
-0.03619289770722389,
0.028809331357479095,
-0.02296295203268528,
-0.041447944939136505,
-0.00019561230146791786,
0.005281785503029823,
-0.08760897070169449,
-0.008220524527132511,
-0.02346957102417946,
-0.02011137828230858,
0.0047620562836527824,
0.015381524339318275,
0.045286741107702255,
-0.005464273039251566,
-0.008889510296285152,
0.0519772544503212,
-0.023847395554184914,
0.01507004164159298,
0.08143524080514908,
-0.049562372267246246,
-0.05570432171225548,
0.06557107716798782,
0.027028383687138557,
-0.009390018880367279,
-0.01185654941946268,
-0.0029227961786091328,
0.00986831821501255,
0.02718937210738659,
-0.07309404015541077,
-0.019581861793994904,
-0.013800712302327156,
-0.09410855919122696,
0.046659063547849655,
-0.005455286707729101,
-0.05118902772665024,
0.00306513998657465,
-0.04233255982398987,
-0.04616321250796318,
-0.03320818021893501,
0.018618687987327576,
0.05162343010306358,
-0.0329272523522377,
0.05572532117366791,
0.1254339963197708,
-0.04031950607895851,
0.06533153355121613,
-0.017983585596084595,
0.030582796782255173,
-0.03580573573708534,
0.04236689582467079,
-0.0038749966770410538,
-0.04991758614778519,
0.03658688813447952,
0.06553075462579727,
0.005249981302767992,
-0.02889111451804638,
-0.02395620010793209,
-0.012374000623822212,
-0.016420239582657814,
-0.004486546386033297,
0.08869704604148865,
-0.07432471960783005,
-0.008531996048986912,
0.012278463691473007,
-0.013758694753050804,
0.0020215504337102175,
0.030830195173621178,
0.03511103615164757,
-0.006369594018906355,
0.003913732711225748,
0.00723823718726635,
0.016013147309422493,
-0.048592790961265564,
0.05592842772603035,
-0.007392878644168377,
0.015382369048893452,
-0.03020336665213108,
0.012493129819631577,
0.03004131279885769,
0.018618756905198097,
-0.007861379534006119,
-0.008335456252098083,
-0.031107569113373756,
0.04888254776597023,
0.047923844307661057,
0.011848630383610725,
-0.016162263229489326,
0.012436253018677235,
-0.04600204899907112,
0.007159694563597441,
-0.004274631384760141,
-0.0038281185552477837,
-0.031649816781282425,
-0.030512196943163872,
-0.01786772347986698,
-0.01683686673641205,
0.0201505646109581,
-0.05571015179157257,
0.02643519453704357,
0.028759580105543137,
-0.02285650745034218,
0.008198879659175873,
0.01964535564184189,
0.009476643055677414,
0.010715325362980366,
0.04687877371907234,
-0.014574791304767132,
0.05159406736493111,
-0.010449073277413845,
-0.03365132585167885,
-0.07951869815587997,
0.004456365946680307,
-0.00714197289198637,
0.11783720552921295,
-0.001882671844214201,
0.04807274416089058,
0.026189031079411507,
0.02285328321158886,
-0.004361569415777922,
-0.03867586329579353,
-0.00035311555257067084,
0.026726385578513145,
0.048809826374053955,
-0.022644907236099243,
-0.03013439103960991,
-0.004124219063669443,
-0.0014842809177935123,
-0.047614630311727524,
-0.0651644766330719,
0.009207754395902157,
0.07305359095335007,
-0.10466847568750381,
0.015058089978992939,
-0.026780609041452408,
-0.04461928829550743,
0.01689872518181801,
0.026247940957546234,
-0.012751087546348572,
0.014192964881658554,
-0.010244198143482208,
0.045692503452301025,
-0.051523108035326004,
-0.038171619176864624,
-0.0341702364385128,
-0.036507993936538696,
-0.029489876702427864,
0.032049067318439484,
0.027745243161916733,
0.04200459644198418,
-0.026920031756162643,
0.024577273055911064,
0.02254657633602619,
0.011522863991558552,
0.0067697372287511826,
-0.015813548117876053,
-0.028145883232355118,
-0.03797237575054169,
-0.050447214394807816,
0.004417499527335167,
0.052561841905117035,
-0.005650403909385204,
0.001405265531502664,
0.006199121940881014,
-0.024454908445477486,
-0.019888244569301605,
-0.05823102593421936,
0.0104672247543931,
-0.02336125075817108,
-0.04301540553569794,
0.01146251242607832,
0.0073342761024832726,
0.00800294615328312,
0.001760306884534657,
-0.008493296802043915,
-0.0576767772436142,
0.005141093861311674,
0.050690583884716034,
-0.061991848051548004,
0.009951476007699966,
0.027017993852496147,
-0.03401043266057968,
-0.029504384845495224,
0.005137987434864044,
0.016171228140592575,
0.004747204482555389,
-0.04295064136385918,
-0.01873081550002098,
-0.03359847888350487,
-0.01905292272567749,
-0.01922721602022648,
0.05916314944624901,
0.028122177347540855,
0.015461688861250877,
-0.10073341429233551,
0.09041725099086761,
-0.035647667944431305,
-0.02817722037434578,
-0.017403511330485344,
0.015167894773185253,
0.000028852049581473693,
-0.05821229889988899,
-0.0026415111497044563,
-0.04155672714114189,
0.029125835746526718,
0.03528705611824989,
0.02326257713139057,
-0.036572251468896866,
-0.05986867472529411,
-0.0033780084922909737,
0.018020974472165108,
-0.01825178973376751,
0.008535804226994514,
0.011419198475778103,
-0.019358495250344276,
0.01097867637872696,
-0.009900670498609543,
-0.0034836851991713047,
0.031227044761180878,
-0.016282841563224792,
0.04157117381691933,
0.016296641901135445,
0.012721206992864609,
0.03617089241743088,
0.007776037789881229,
0.017650388181209564,
-0.05179738253355026,
-0.0017979975091293454,
-0.011461561545729637,
-0.0010442276252433658,
-0.000053968622523825616,
0.018364593386650085,
0.018427638337016106,
0.004884089343249798,
0.033934373408555984,
0.029946384951472282,
-0.025974174961447716,
-0.07652479410171509,
0.036954205483198166,
-0.035690788179636,
-0.030345827341079712,
-0.029112836346030235,
0.015580140985548496,
-0.051442231982946396,
0.06460711359977722,
-0.004290915094316006,
-0.021043863147497177,
0.03513621166348457,
-0.025483226403594017,
0.011778244748711586,
-0.053799305111169815,
0.033309873193502426,
-0.029890645295381546,
0.0673237144947052,
-0.030006641522049904,
0.0350617952644825,
0.07176108658313751,
-0.0035027056001126766,
0.06404814124107361,
-0.06174858659505844,
-0.04629421606659889,
0.029284901916980743,
0.01156509481370449,
0.04042869806289673,
0.03645327314734459,
-0.00588664086535573,
0.02002544514834881,
-0.0031982590444386005,
0.005037207622081041,
0.019592558965086937,
0.015304832719266415,
0.02381114847958088,
-0.04895717278122902,
0.05296434462070465,
0.04764082655310631,
0.0010360010201111436,
0.017951790243387222,
0.014308061450719833,
0.03428123891353607,
-0.010285838507115841,
-0.007317289710044861,
-0.055073436349630356,
0.04684842750430107,
-0.019355086609721184,
0.0642632469534874,
0.02285619266331196,
0.01686871238052845,
-0.006387053523212671,
-0.038816679269075394,
0.016351044178009033,
0.005441949237138033,
-0.08457853645086288,
0.024907074868679047,
0.021793421357870102,
-0.008504590950906277,
-0.04623948037624359,
0.01142970286309719,
-0.005263590719550848,
-0.0868704542517662,
0.04282797500491142,
0.012010886333882809,
-0.023729324340820312,
-0.016597937792539597,
0.020836805924773216,
0.03264167159795761,
0.06821775436401367,
0.03775003179907799,
0.03529950603842735,
0.013149654492735863,
0.03590958192944527,
-0.026525361463427544,
0.005901397671550512,
-0.012483990751206875,
0.034373871982097626,
-0.011577703058719635,
0.01594742015004158,
0.02619377337396145,
0.04478348791599274,
-0.028480036184191704,
-0.0037645045667886734,
-0.00592929357662797,
-0.03914204239845276,
-0.012927751056849957,
0.0035117545630782843,
0.018945341929793358,
0.020504556596279144,
-0.01545488741248846,
-0.044122740626335144,
0.0265305507928133,
-0.08961508423089981,
-0.009641976095736027,
-0.007976487278938293,
0.014534913003444672,
0.006684407126158476,
-0.023139620199799538,
0.006394789554178715,
-0.03794173151254654,
0.04547137767076492,
-0.010743563994765282,
0.008799384348094463,
0.02575782872736454,
0.01071302592754364,
0.039799608290195465,
0.06829242408275604,
-0.009696397930383682,
0.038344595581293106,
0.06627669185400009,
-0.04594574496150017,
-0.03672359138727188,
-0.03902365639805794,
-0.041811879724264145,
-0.014595664106309414,
0.008389527909457684,
-0.05419602245092392,
-0.03896760940551758,
0.015565183945000172,
0.009802179411053658,
-0.032861847430467606,
0.029290098696947098,
0.03386223316192627,
-0.049778249114751816,
-0.005644038785248995,
-0.059760939329862595,
-0.03152305632829666,
0.0037384701427072287,
0.00928325392305851,
0.019203029572963715,
-0.019345665350556374,
0.009997991845011711,
0.04475085064768791,
0.007625387981534004,
0.052996907383203506,
0.022421084344387054,
0.009991738945245743,
0.004719036165624857,
-0.02562970481812954,
0.02541719190776348,
0.06232413649559021,
-0.04502975940704346,
0.031467318534851074,
0.020235516130924225,
0.0013802223838865757,
0.006034542806446552,
0.00010371958342147991,
0.02094627171754837,
0.012114185839891434,
-0.002012572018429637,
0.04739776998758316,
0.07009635865688324,
-0.011135347187519073,
0.04047374054789543,
-0.04655812680721283,
-0.019371576607227325,
0.001357103232294321,
-0.05799856781959534,
-0.01355399563908577,
-0.03404242545366287,
0.021244866773486137,
0.0003206128894817084,
-0.02630673162639141,
0.018060045316815376,
-0.027033669874072075,
0.0250822976231575,
0.02665187604725361,
-0.012416832149028778,
-0.026904942467808723,
0.048749689012765884,
0.01612134650349617,
-0.00868823379278183,
-0.07268276065587997,
0.01824306696653366,
0.019243886694312096,
-0.01770375296473503,
-0.02687392383813858,
0.012786616571247578,
-0.07181715220212936,
0.09259480983018875,
0.009007731452584267,
-0.011428510770201683,
0.00768105685710907,
-0.017960838973522186,
0.003371930681169033,
-0.04864708334207535,
-0.006622729357331991,
0.05193501338362694,
0.0023281071335077286,
0.029503867030143738,
-0.03556622564792633,
0.04069015756249428,
0.01936633326113224,
0.02671658806502819,
0.05131928622722626,
-0.0036011033225804567,
0.0005226054927334189,
-0.04097968339920044,
-0.00732803251594305,
0.02064366452395916,
0.053719621151685715,
0.00455473130568862,
-0.008073428645730019,
0.013521185144782066,
0.0792127326130867,
0.07382693141698837,
0.06422478705644608,
-0.09811162948608398,
0.04497469961643219,
0.032861433923244476,
0.04919060692191124,
-0.011026419699192047,
-0.0003854829992633313,
0.03643808513879776,
-0.04285469278693199,
0.0027280549984425306,
-0.022510455921292305,
-0.07174943387508392,
-0.014148745685815811,
0.03258935734629631,
-0.029159745201468468,
-0.05950116366147995,
0.003115340368822217,
-0.04888750985264778,
0.01503478642553091,
-0.02609974518418312,
-0.04914552718400955,
-0.02046302706003189,
0.012221922166645527,
0.017634309828281403,
0.0005730963894166052,
0.028798237442970276,
-0.00239028618671,
0.024840062484145164,
-0.014957200735807419,
0.059863265603780746,
0.00657931063324213,
0.0066140261478722095,
-0.01200065016746521,
-0.0011853956384584308,
-0.04004354402422905,
0.002084752544760704,
0.07601918280124664,
-0.038398947566747665,
0.016378531232476234,
0.008293494582176208,
0.03596997261047363,
-0.07233792543411255,
0.03729283809661865,
-0.05570026859641075,
-0.0644284263253212,
0.024612298235297203,
0.03012898378074169,
0.0005293073481880128,
-0.043055612593889236,
-0.03025289997458458,
-0.02596045285463333,
-0.028563646599650383,
0.007414276245981455,
0.027842001989483833,
0.016186492517590523,
-0.0032137660309672356,
-0.006359046790748835,
-0.04719984531402588,
0.008915808983147144,
-0.012531232088804245,
0.059500738978385925,
-0.03459663316607475,
0.06028619781136513,
0.03517862409353256,
0.08974888920783997,
-0.005934208165854216,
-0.001663553062826395,
-0.06012319028377533,
0.026844492182135582,
-0.045253999531269073,
-0.06985316425561905,
0.04097635671496391,
0.04668710008263588,
-0.04683519899845123,
0.011012651957571507,
0.0004423421632964164,
0.005525833927094936,
0.015224619768559933,
-0.0017754192231222987,
-0.03679680451750755,
-0.06460409611463547,
0.03866492584347725,
-0.046783920377492905,
0.07359311729669571,
0.004195616114884615,
-0.04708876460790634,
-0.009428448975086212,
0.010053686797618866,
0.0066586644388735294,
-0.01781679503619671,
0.07159080356359482,
-0.022277584299445152,
0.06596923619508743,
-0.0579724982380867,
0.006484195590019226,
-0.049173448234796524,
-0.03476123884320259,
0.01511170994490385,
0.03235708922147751,
0.015565110370516777,
0.043811991810798645,
0.037620577961206436,
-0.04608140140771866,
-0.03437359258532524,
-0.04177765175700188,
-0.005456138867884874,
0.013877815566956997,
-0.026656804606318474,
0.0302304457873106,
0.010475954972207546,
0.019564174115657806,
-0.011513070203363895,
0.0016973844030871987,
-0.010777744464576244,
0.002370146568864584,
0.02573472075164318,
0.07678481936454773,
-0.020621497184038162,
0.021803129464387894,
-0.04857557266950607,
-0.0367528460919857,
0.00025783322053030133,
0.03147314861416817,
0.01176553126424551,
0.015333050861954689,
-0.000366249616490677,
-0.000838235195260495,
-0.04146452993154526,
0.047415684908628464,
-0.03552989289164543,
0.04329102486371994,
0.007849414832890034,
0.008470031432807446,
-0.024678315967321396,
0.015836387872695923,
0.024331985041499138,
0.0031530025880783796,
-0.0551566407084465,
0.02831420861184597,
0.00934499129652977,
0.03206013888120651,
0.0005009608576074243,
0.06402521580457687,
-0.019931918010115623,
-0.005588385742157698,
-0.004961442202329636,
0.04925285652279854,
-0.008443142287433147,
-0.05534180626273155,
-0.0586826391518116,
-0.008573577739298344,
0.029829703271389008,
0.02675502374768257,
-0.013990410603582859,
-0.00828644074499607,
0.03199669346213341,
-0.03161659091711044,
0.005913650617003441,
0.042462222278118134,
0.007872120477259159,
0.0032927521970123053,
-0.026552274823188782,
-0.009042894467711449,
0.01619405299425125,
-0.006308599375188351,
0.04201594740152359,
-0.051771197468042374,
-0.04408423602581024,
-0.028990546241402626,
-0.01627500168979168,
0.012862320058047771,
-0.0005720101180486381,
0.037558212876319885,
0.008128151297569275,
0.013225244358181953,
-0.0183815099298954,
0.011304757557809353,
-0.008895283564925194,
-0.033121585845947266,
0.0037381979636847973,
-0.02468312717974186,
-0.0650685578584671,
-0.03121100924909115,
0.029153283685445786,
-0.023201435804367065,
-0.014193858951330185,
-0.020490478724241257,
-0.00706377113237977,
-0.06239182502031326,
0.051851388067007065,
-0.019705455750226974,
-0.018384456634521484,
-0.018618471920490265
] |
<p>I have seen a few Dalitz plots so far and tried to understand how they are useful.
So one of the advantages of these plot is that the non-uniformity in the plots can tell something about the intermediate states that we cannot detect. My question is how do you extract the mass of these resonant particles from such plots? What additional information would you need?</p> | g5531 | [
-0.025189146399497986,
-0.00948298443108797,
-0.011344844475388527,
-0.05942176282405853,
-0.020636314526200294,
-0.028446154668927193,
0.014598822221159935,
-0.003291662549600005,
0.01335563138127327,
-0.004244700074195862,
-0.046408720314502716,
-0.005870407912880182,
0.029455598443746567,
-0.029027489945292473,
-0.010024839080870152,
-0.0603485181927681,
0.013875806704163551,
-0.020901458337903023,
0.0416952446103096,
0.06083599478006363,
0.06968681514263153,
-0.005420763976871967,
0.05749049782752991,
-0.013644753023982048,
0.0000553911886527203,
-0.015912793576717377,
0.03300124779343605,
-0.012903680093586445,
0.004982646554708481,
-0.012417123652994633,
0.014389410614967346,
-0.05100015923380852,
-0.022336097434163094,
-0.00839568953961134,
-0.03593352437019348,
-0.0630892813205719,
-0.015210101380944252,
0.005276392679661512,
-0.07534036040306091,
0.01986655220389366,
-0.03537304326891899,
-0.0359070710837841,
0.0028608094435185194,
-0.024481484666466713,
-0.00902597140520811,
0.01317893248051405,
-0.04226202517747879,
-0.026608267799019814,
-0.05291472747921944,
0.00781983695924282,
-0.021098623052239418,
0.052930086851119995,
0.04599739611148834,
0.04458749294281006,
0.014631623402237892,
0.0071774129755795,
-0.026406429708003998,
0.004914057441055775,
0.12118340283632278,
0.0122086051851511,
0.017198562622070312,
0.04633558914065361,
-0.008191069588065147,
-0.026324821636080742,
-0.008596386760473251,
-0.007208343595266342,
-0.07713823765516281,
0.0008509973995387554,
-0.07950479537248611,
-0.036586735397577286,
0.029486751183867455,
0.026567034423351288,
-0.04215710237622261,
0.005344124045222998,
-0.0696992501616478,
-0.01992560178041458,
-0.04176318272948265,
0.020845266059041023,
0.005079277325421572,
0.020140131935477257,
-0.02022552862763405,
-0.029537009075284004,
0.05695386603474617,
-0.04941374063491821,
0.08273448795080185,
-0.005411769263446331,
-0.026584027335047722,
-0.028084469959139824,
0.03212790936231613,
-0.020157812163233757,
0.06597580760717392,
0.030560441315174103,
0.008511651307344437,
0.016891561448574066,
-0.04317614436149597,
-0.003936730790883303,
-0.005547752603888512,
0.059491418302059174,
-0.07033748179674149,
-0.049294982105493546,
0.02288440614938736,
0.05063419044017792,
-0.017530830577015877,
-0.0358784981071949,
0.019724510610103607,
-0.04317472130060196,
-0.029276801273226738,
-0.04705002158880234,
0.06506682932376862,
0.0351509228348732,
-0.07246217876672745,
0.009307155385613441,
-0.035947348922491074,
0.002000311389565468,
-0.02332136780023575,
-0.08074161410331726,
0.04289814829826355,
0.010965450666844845,
-0.015017330646514893,
0.007748480886220932,
0.03893527388572693,
0.012992391362786293,
-0.04604121297597885,
-0.018482835963368416,
-0.007518050726503134,
0.037082117050886154,
0.0034545129165053368,
-0.015317851677536964,
0.01730378530919552,
-0.007873707450926304,
0.01223054900765419,
0.015510665252804756,
0.025388384237885475,
0.02979431301355362,
-0.034841299057006836,
0.005427365191280842,
0.042559392750263214,
-0.03189936652779579,
-0.021796047687530518,
0.023151671513915062,
0.000053857707825955003,
-0.002416431438177824,
-0.029406564310193062,
-0.03283677622675896,
0.0017849027644842863,
-0.014147470705211163,
-0.02137611247599125,
0.03676028177142143,
-0.0030955204274505377,
0.06931773573160172,
0.013910099864006042,
0.00004634646757040173,
0.07707241922616959,
0.03781518340110779,
0.012014656327664852,
0.004738180432468653,
0.06037401035428047,
-0.01200363039970398,
-0.0024973037652671337,
0.002483143238350749,
0.03133414685726166,
-0.06172480061650276,
0.0029885198455303907,
0.007343915291130543,
0.018235959112644196,
-0.020190879702568054,
0.05708818882703781,
0.012517065741121769,
0.03746335953474045,
-0.04325338825583458,
-0.023787453770637512,
0.0457843653857708,
-0.008009817451238632,
0.045268330723047256,
-0.014585532248020172,
0.03609617054462433,
-0.00535637466236949,
0.0009502918110229075,
0.028476495295763016,
0.0458475798368454,
0.05091451480984688,
-0.008172896690666676,
0.036059435456991196,
-0.02347157709300518,
-0.010998355224728584,
-0.001691388781182468,
-0.009438157081604004,
-0.017231091856956482,
0.012139861471951008,
0.03875510394573212,
-0.021388674154877663,
-0.022433126345276833,
-0.04211343824863434,
0.0074028572998940945,
0.02104157768189907,
-0.017614660784602165,
0.00025395414559170604,
0.035729825496673584,
-0.02765740640461445,
0.009625112637877464,
-0.05059077590703964,
0.0003815065720118582,
0.014180474914610386,
-0.0048513347283005714,
0.004383852239698172,
-0.07231172174215317,
-0.046857114881277084,
0.011319947429001331,
-0.011383756063878536,
0.014593576081097126,
0.026575572788715363,
-0.01835857331752777,
0.012655598111450672,
-0.00024415840744040906,
-0.0396118201315403,
0.05979449674487114,
-0.015515332110226154,
-0.04171454906463623,
0.09960708022117615,
0.008897258900105953,
-0.036261092871427536,
-0.00190008245408535,
0.015810081735253334,
0.04889744520187378,
0.032996393740177155,
-0.02094178833067417,
0.02319415472447872,
0.00328858126886189,
-0.03417773172259331,
0.015354997478425503,
-0.07085038721561432,
-0.008433829993009567,
-0.008750119246542454,
0.026913337409496307,
0.000022664138668915257,
0.009769787080585957,
-0.03998126462101936,
-0.018656067550182343,
-0.012151995673775673,
-0.0340181328356266,
0.003660387359559536,
-0.06031719967722893,
-0.040674660354852676,
0.020270289853215218,
-0.029736680909991264,
0.011510423384606838,
0.029152793809771538,
-0.04261868819594383,
-0.018990909680724144,
0.014214083552360535,
0.016002902761101723,
0.011512295342981815,
0.05245641618967056,
0.0386490635573864,
-0.015395548194646835,
-0.0866314098238945,
-0.0044202618300914764,
0.01570916920900345,
-0.0031733328942209482,
-0.017409898340702057,
-0.026031866669654846,
-0.05768463760614395,
0.05866886302828789,
-0.03765694797039032,
-0.05608411505818367,
-0.03335387259721756,
0.07576704025268555,
-0.005870025139302015,
-0.0270382147282362,
-0.018673840910196304,
-0.040425509214401245,
-0.007840853184461594,
0.061378173530101776,
0.03249019384384155,
0.003440774977207184,
-0.007083198055624962,
0.05817200243473053,
-0.02339044027030468,
-0.03566141426563263,
-0.024831561371684074,
-0.036093585193157196,
0.01803860254585743,
-0.029886605218052864,
0.04884408786892891,
0.03404666483402252,
-0.04961862787604332,
0.005722396075725555,
0.016005739569664,
0.006241508759558201,
0.003153154393658042,
0.02699674479663372,
-0.03560621291399002,
0.06492505222558975,
0.033556029200553894,
-0.048224661499261856,
-0.020962418988347054,
0.01776271127164364,
-0.0023264295887202024,
0.05469546094536781,
0.05478537455201149,
0.005138894077390432,
0.006461543031036854,
0.00038804428186267614,
-0.016536695882678032,
-0.026296086609363556,
0.029286490753293037,
-0.009901461191475391,
-0.022055506706237793,
0.0021595077123492956,
-0.014308582060039043,
0.0397285595536232,
0.0100101288408041,
0.04689764603972435,
0.017200572416186333,
0.030688179656863213,
0.015377728268504143,
0.002786937402561307,
-0.03579394519329071,
0.015841472893953323,
0.02345631644129753,
-0.01966864801943302,
-0.011578375473618507,
0.050907112658023834,
-0.033357519656419754,
0.019822051748633385,
-0.053882915526628494,
0.00726964371278882,
-0.04171121492981911,
-0.04397593066096306,
-0.03420885279774666,
0.04511726275086403,
0.001037969603203237,
-0.0891643837094307,
-0.03100503981113434,
-0.07743798196315765,
-0.053832024335861206,
-0.04137808084487915,
0.04311458766460419,
0.09662621468305588,
-0.0258504506200552,
-0.05771048367023468,
0.021573254838585854,
-0.03068164363503456,
-0.04715757817029953,
-0.028768744319677353,
-0.00715120043605566,
-0.010568312369287014,
-0.02715068683028221,
-0.02578820288181305,
-0.07854317128658295,
-0.001773133990354836,
0.04425226151943207,
-0.03110620565712452,
-0.03230179101228714,
-0.0020540247205644846,
-0.0008436152129434049,
0.02303241565823555,
0.004753498360514641,
0.05586250126361847,
0.002815668936818838,
0.05871972069144249,
-0.07259302586317062,
-0.027307569980621338,
-0.028185147792100906,
0.009543541818857193,
-0.03683370351791382,
-0.011138934642076492,
0.049132540822029114,
0.013647893443703651,
0.005025709979236126,
-0.05796448513865471,
-0.008652579970657825,
0.04645277187228203,
0.04172506555914879,
-0.05075646936893463,
0.019894344732165337,
0.00806819461286068,
-0.016531959176063538,
-0.019618408754467964,
0.007426898926496506,
-0.013981298543512821,
0.040270883589982986,
-0.005088115576654673,
-0.016620688140392303,
0.020769046619534492,
0.019909869879484177,
-0.0037746333982795477,
-0.017135610803961754,
0.0013670246116816998,
-0.017094895243644714,
0.020613741129636765,
-0.04810594394803047,
-0.045964278280735016,
0.0197442639619112,
-0.03274552524089813,
-0.08639172464609146,
0.03726860135793686,
0.025816939771175385,
0.022914530709385872,
0.07862050831317902,
-0.02964616008102894,
0.01690397784113884,
-0.06904125213623047,
-0.048090655356645584,
0.04362691566348076,
0.015607577748596668,
-0.028660157695412636,
-0.03366078436374664,
0.0027333416510373354,
-0.005552401766180992,
-0.02216528356075287,
-0.023456744849681854,
0.07508814334869385,
-0.07129613310098648,
0.02838943526148796,
-0.01602788455784321,
0.015780946239829063,
0.006530629005283117,
0.004656962119042873,
0.04000166803598404,
-0.050821706652641296,
0.020186947658658028,
-0.03353715315461159,
-0.02063090354204178,
-0.03339681401848793,
0.006047953851521015,
0.019769856706261635,
-0.00010656387894414365,
0.04643445834517479,
0.010955346748232841,
0.035974279046058655,
-0.011041335761547089,
-0.024290552362799644,
-0.004057451616972685,
-0.05805126205086708,
-0.01903160661458969,
-0.026866348460316658,
0.0010846671648323536,
0.02968326210975647,
-0.015393274836242199,
0.012952236458659172,
-0.023873282596468925,
-0.07180246710777283,
-0.024102885276079178,
-0.024842891842126846,
0.0701470822095871,
-0.034327030181884766,
0.019002409651875496,
-0.02848375029861927,
0.03154245391488075,
-0.037453748285770416,
-0.005196761805564165,
-0.08263741433620453,
-0.035460539162158966,
0.035718441009521484,
-0.006325902417302132,
-0.017946036532521248,
0.06505540013313293,
0.037464603781700134,
0.05524110049009323,
0.01800411380827427,
0.028693651780486107,
0.009122570976614952,
-0.014085188508033752,
-0.04617490619421005,
-0.01665700413286686,
-0.046272069215774536,
0.009284403175115585,
-0.028408629819750786,
0.03240364417433739,
-0.03384498134255409,
-0.0004292763478588313,
0.05460713058710098,
-0.04318372905254364,
-0.0027169708628207445,
-0.04579121246933937,
-0.020367732271552086,
-0.006029846146702766,
-0.010202447883784771,
0.00813723262399435,
-0.037686221301555634,
0.0678834468126297,
0.007647096179425716,
0.03526737540960312,
-0.005916408263146877,
0.04875849187374115,
-0.05453740805387497,
-0.020185943692922592,
0.011513566598296165,
0.021087611094117165,
-0.0475037656724453,
0.021496271714568138,
0.0030374829657375813,
-0.0363442525267601,
0.008156906813383102,
-0.06753145903348923,
0.04919211193919182,
-0.07156369090080261,
-0.021640446037054062,
0.06258130073547363,
0.04487360641360283,
-0.004228316713124514,
0.0024003188591450453,
0.059350259602069855,
-0.003341828705742955,
-0.009967200458049774,
0.03247670456767082,
-0.06496406346559525,
0.0015057548880577087,
-0.017439380288124084,
0.020657164976000786,
0.05710341036319733,
0.04064519703388214,
0.01624595746397972,
-0.010848264209926128,
0.008267730474472046,
-0.010624218732118607,
0.08194075524806976,
-0.04365471750497818,
-0.031055275350809097,
-0.018416905775666237,
0.046866606920957565,
0.056003138422966,
-0.00490198191255331,
0.03707210719585419,
-0.0733378604054451,
-0.016739917919039726,
-0.005835856776684523,
0.004705885425209999,
0.0008639092557132244,
-0.04284773766994476,
-0.008744601160287857,
-0.003578646807000041,
0.05123255029320717,
0.02899951860308647,
0.020149560645222664,
0.04321393743157387,
0.010563184507191181,
0.03484298661351204,
0.000029210988941485994,
-0.021098176017403603,
0.03850235790014267,
0.012998743914067745,
0.03551365062594414,
-0.02907300367951393,
-0.03315679356455803,
0.038578882813453674,
0.03140224516391754,
0.04605206474661827,
0.028740407899022102,
-0.05774594098329544,
-0.017399631440639496,
0.010525141842663288,
-0.04431932047009468,
-0.03824039548635483,
0.04521094262599945,
0.029379479587078094,
0.017554089426994324,
-0.02862069569528103,
0.055021751672029495,
0.010736197233200073,
0.03930804505944252,
0.049276042729616165,
0.07596630603075027,
-0.004731235560029745,
-0.004897858947515488,
-0.033846307545900345,
0.02740360237658024,
0.04610935598611832,
-0.03821273520588875,
0.009358151815831661,
-0.03704933077096939,
0.04217568784952164,
0.07780683785676956,
-0.003826250322163105,
0.012620203197002411,
-0.008571657352149487,
-0.03922401741147041,
0.03337859734892845,
0.04705917835235596,
-0.0004809743259102106,
0.026332814246416092,
0.05666361749172211,
0.03086906671524048,
0.048057571053504944,
0.015843305736780167,
-0.007366048637777567,
-0.0035259639844298363,
-0.03483745455741882,
-0.02077927626669407,
-0.040692199021577835,
-0.02037850394845009,
0.05045679956674576,
-0.060924287885427475,
-0.06067190691828728,
0.0219358392059803,
-0.02350282482802868,
0.015557106584310532,
0.025943709537386894,
0.02669665217399597,
0.04987866431474686,
-0.016058117151260376,
0.008383039385080338,
0.04065074399113655,
0.014615709893405437,
-0.07458663731813431,
0.025692854076623917,
-0.02275025099515915,
-0.06822110712528229,
-0.012055996805429459,
-0.04835983365774155,
0.008808523416519165,
-0.057790275663137436,
-0.007268521003425121,
0.038027770817279816,
-0.046706706285476685,
0.017986180260777473,
0.012861741706728935,
-0.042505718767642975,
-0.043219342827796936,
0.03759370744228363,
-0.022911788895726204,
0.02183733507990837,
0.02583710290491581,
0.03328604996204376,
0.02957049570977688,
0.0003291936591267586,
-0.02675262838602066,
0.020369047299027443,
0.006207573693245649,
0.005440979730337858,
0.017946967855095863,
0.06290543079376221,
0.01748419925570488,
0.003632698906585574,
0.06510404497385025,
0.026486322283744812,
0.038054678589105606,
0.025638824328780174,
0.018592653796076775,
-0.031887486577034,
0.06939609348773956,
0.06244908645749092,
0.019216671586036682,
-0.07297336310148239,
0.04171299561858177,
0.043637558817863464,
0.030464449897408485,
-0.0305160079151392,
-0.013856313191354275,
0.029115188866853714,
-0.04247444123029709,
-0.01658782549202442,
0.05680106580257416,
0.0511801540851593,
0.025906868278980255,
0.020574845373630524,
0.03888759762048721,
0.054065342992544174,
-0.05344930291175842,
-0.07506823539733887,
-0.055320266634225845,
0.07300282269716263,
-0.025971587747335434,
0.005996575113385916,
0.03501327335834503,
0.01963188871741295,
-0.005251326132565737,
-0.002046501263976097,
-0.020538078621029854,
0.03719671070575714,
-0.0300820991396904,
-0.001590986386872828,
0.012001032009720802,
0.01735834591090679,
-0.0389634408056736,
-0.032461974769830704,
-0.014572844840586185,
0.016155540943145752,
-0.025601806119084358,
-0.041501734405756,
0.06944980472326279,
0.0133407823741436,
0.011198130436241627,
-0.02017960324883461,
0.028421994298696518,
-0.07102332264184952,
-0.03934990614652634,
-0.005973151884973049,
0.016296379268169403,
-0.0021910862997174263,
0.046182721853256226,
0.052516739815473557,
-0.02299393340945244,
-0.029362503439188004,
0.017101701349020004,
-0.01733413152396679,
-0.004543668124824762,
0.0710325539112091,
0.0019927164539694786,
0.028048818930983543,
0.023925673216581345,
-0.01587134227156639,
-0.0011871381429955363,
0.019216472283005714,
-0.0383170060813427,
0.026073429733514786,
-0.02537185698747635,
0.03868991509079933,
0.011001205071806908,
-0.0009630009299144149,
0.02914583869278431,
-0.061034463346004486,
0.01736735738813877,
0.03088379092514515,
0.015872618183493614,
-0.06878737360239029,
-0.015028143301606178,
0.002583145396783948,
0.021613063290715218,
0.005366834811866283,
0.03815719112753868,
0.016875874251127243,
0.013916048221290112,
0.01859455741941929,
-0.06076987832784653,
0.025859510526061058,
0.09412132203578949,
-0.024983014911413193,
0.055475346744060516,
-0.03454386070370674,
0.0983082577586174,
-0.030286625027656555,
0.01563471555709839,
-0.07681650668382645,
-0.02057739533483982,
0.004252636805176735,
-0.002624319400638342,
-0.050617069005966187,
0.03592371195554733,
0.03714130446314812,
-0.07097774744033813,
0.014151450246572495,
-0.01672510802745819,
-0.004963579121977091,
0.05179132521152496,
-0.05782447010278702,
-0.024302521720528603,
0.07480482012033463,
-0.026718277484178543,
0.032986510545015335,
-0.02869463711977005,
-0.03701408579945564,
0.061375733464956284,
-0.018487200140953064,
-0.03572666645050049,
0.033861931413412094,
0.01976843550801277,
0.0010436411248520017,
-0.019989660009741783,
0.07434889674186707,
-0.024463152512907982,
-0.06453893333673477,
0.06335362792015076,
-0.07243988662958145,
-0.020541183650493622,
-0.03164679557085037,
0.02048500068485737
] |
<p>Since a week or so a constant high pitch sound (~4khz) emanates from my active monitor speakers. After eliminating any ground or power source issues I noticed, that the sound rises in volume whenever I open my window - which is exactly between my speakers and an array of cellular antennas on the opposite building. I recall there were new antennas added a few weeks ago. Our public database shows that there are over 20 transmitters on there, with 3 pointing exactly in my direction.</p>
<p><strong>Question</strong>: Can HF-EMWs produce such a sound in an audio amplifier or through it's connectors (it's not the cables or whatever comes through them)?</p> | g5532 | [
-0.010965924710035324,
-0.04662066698074341,
-0.004158756695687771,
-0.001927745994180441,
-0.02339840680360794,
-0.014214000664651394,
0.04408610612154007,
0.040152668952941895,
0.014037776738405228,
-0.019610336050391197,
-0.03321586549282074,
0.06822472810745239,
-0.015825964510440826,
0.011236608028411865,
-0.005894999951124191,
0.004640880506485701,
0.0029632921796292067,
0.025389671325683594,
-0.02516349032521248,
0.04275352880358696,
0.024743320420384407,
-0.005200292449444532,
0.05182601511478424,
-0.028096964582800865,
-0.006249334197491407,
-0.0000913788826437667,
0.03439142554998398,
-0.04540702700614929,
-0.053223516792058945,
-0.0315619558095932,
-0.023054348304867744,
0.020298747345805168,
0.07131016254425049,
-0.013803803361952305,
-0.0805838480591774,
-0.0003275925701018423,
0.01685408130288124,
0.037284038960933685,
-0.07214681804180145,
0.031191712245345116,
-0.019561054185032845,
-0.02658809907734394,
0.02529788762331009,
-0.05059938132762909,
-0.015055102296173573,
-0.004822312388569117,
-0.008204166777431965,
0.031852614134550095,
-0.0017465321579948068,
-0.021539565175771713,
-0.03678811341524124,
-0.029091784730553627,
-0.0008613422396592796,
0.06949639320373535,
-0.014884363859891891,
-0.0006250534206628799,
-0.0422644317150116,
0.007309761829674244,
0.05277090519666672,
0.043417952954769135,
0.00949704647064209,
0.06317424774169922,
-0.05216825380921364,
-0.004254031460732222,
0.016722818836569786,
-0.011592557653784752,
-0.012689605355262756,
-0.004071701783686876,
-0.04018168896436691,
-0.023809412494301796,
0.06598343700170517,
-0.03419787809252739,
0.030538585036993027,
-0.003769409377127886,
0.0012242570519447327,
0.04015514254570007,
-0.011037767864763737,
0.008811872452497482,
-0.009437191300094128,
0.07018540799617767,
0.04433551803231239,
-0.033842917531728745,
0.06889618933200836,
-0.043788015842437744,
0.010998633690178394,
0.004586699418723583,
0.025303127244114876,
0.008784384466707706,
0.02494180202484131,
-0.08635639399290085,
0.06762461364269257,
-0.032689742743968964,
-0.007485472597181797,
0.04039294645190239,
-0.039776675403118134,
-0.03053889609873295,
-0.03036380372941494,
0.026853026822209358,
0.023350439965724945,
-0.07254701107740402,
0.0031913123093545437,
0.03541922569274902,
0.04451463371515274,
0.041813693940639496,
-0.06061426177620888,
0.03723951801657677,
0.028010332956910133,
0.001726737362332642,
-0.035965852439403534,
0.05111116170883179,
-0.0014738835161551833,
0.016096193343400955,
0.04129689559340477,
0.012388134375214577,
-0.07073673605918884,
-0.014777539297938347,
-0.0013470613630488515,
0.04006396234035492,
-0.0296020470559597,
0.06885778158903122,
0.022537579759955406,
-0.026217633858323097,
-0.002953363349661231,
-0.0010001750197261572,
-0.04485779255628586,
-0.005970827769488096,
0.041909217834472656,
-0.0027192148845642805,
-0.0004449743137229234,
0.004093579947948456,
0.019673245027661324,
0.008556267246603966,
-0.001414128695614636,
0.0028658334631472826,
0.10295535624027252,
0.023684166371822357,
0.054205965250730515,
-0.03417119383811951,
0.021484030410647392,
0.05155024304986,
0.00020527378364931792,
-0.006332059856504202,
0.08481103181838989,
-0.10683044791221619,
0.008969224989414215,
0.009943461045622826,
0.049243196845054626,
-0.03712962567806244,
0.08652763813734055,
0.012738439254462719,
-0.04811426252126694,
0.018216406926512718,
-0.07562070339918137,
-0.030784696340560913,
-0.04003814980387688,
0.0882248803973198,
-0.05214893817901611,
0.010072720237076283,
-0.004081618972122669,
-0.011279185302555561,
0.047338541597127914,
-0.022829750552773476,
0.01251063123345375,
-0.027464058250188828,
0.023950926959514618,
-0.04333503916859627,
-0.04026591032743454,
0.01766856759786606,
-0.01842425763607025,
0.04132678732275963,
-0.037774939090013504,
0.007956038229167461,
0.03449472412467003,
0.0207029078155756,
-0.0380963534116745,
-0.02013762667775154,
0.042217910289764404,
-0.042158789932727814,
0.0358748733997345,
-0.029641838744282722,
-0.08087506145238876,
-0.015774548053741455,
-0.009706227108836174,
-0.030867958441376686,
-0.014888282865285873,
-0.024343857541680336,
-0.062390249222517014,
-0.00848604366183281,
-0.0015854351222515106,
0.06630311906337738,
-0.09359464049339294,
-0.02444850467145443,
-0.04964717477560043,
-0.02675287239253521,
0.00164926762226969,
-0.014321981929242611,
-0.003372726496309042,
-0.04015473276376724,
0.046879205852746964,
0.08059651404619217,
0.048427119851112366,
0.002694629365578294,
0.0530347116291523,
-0.01832183636724949,
0.06280495971441269,
-0.004945265594869852,
0.0026508744340389967,
-0.05788251757621765,
-0.001252251211553812,
-0.008050408214330673,
-0.021628327667713165,
-0.028286932036280632,
-0.020422395318746567,
0.025247806683182716,
0.01737106405198574,
0.01961771585047245,
-0.006341998465359211,
-0.0028805045876652002,
0.03351568058133125,
0.0055270129814744,
0.015485057607293129,
0.03519664704799652,
0.022463634610176086,
-0.06116311252117157,
-0.07564803212881088,
-0.013761622831225395,
-0.012316660955548286,
-0.019764522090554237,
-0.01363305188715458,
-0.032863959670066833,
0.02297321707010269,
0.022493664175271988,
0.062330398708581924,
-0.026592956855893135,
0.0006015548133291304,
-0.028348587453365326,
0.04334815591573715,
0.017068225890398026,
-0.06320739537477493,
-0.023105517029762268,
0.07028479874134064,
-0.0352533683180809,
-0.013538824394345284,
0.0019481765339151025,
0.0005828217254020274,
-0.022310292348265648,
0.030212784186005592,
0.01241787988692522,
-0.022214574739336967,
-0.04549218714237213,
0.054053302854299545,
-0.028192095458507538,
0.04161791875958443,
0.014445720240473747,
-0.02457178756594658,
-0.027609502896666527,
-0.004830428399145603,
0.04710976406931877,
-0.028048859909176826,
0.009271804243326187,
-0.021291125565767288,
-0.0384221151471138,
0.07285638153553009,
-0.049193717539310455,
-0.008207028731703758,
-0.000718141789548099,
0.01937367394566536,
-0.014826714061200619,
-0.06566260755062103,
-0.003907941281795502,
-0.03145737946033478,
0.05427117273211479,
0.012841729447245598,
0.05824238806962967,
-0.029778126627206802,
0.06045945733785629,
-0.007140020374208689,
-0.0005985481548123062,
0.03706466406583786,
0.04370371624827385,
-0.002396712312474847,
0.030086340382695198,
-0.03672560304403305,
-0.04171546921133995,
-0.021844467148184776,
0.05204186215996742,
0.053344376385211945,
-0.009456347674131393,
-0.00866294652223587,
-0.016268467530608177,
0.05590160936117172,
-0.00837439950555563,
0.020182956010103226,
0.004456252325326204,
-0.024756528437137604,
0.020529596135020256,
-0.02003670297563076,
-0.0021660111378878355,
0.00047593945055268705,
0.012477630749344826,
0.03157343715429306,
-0.04978444054722786,
0.006700411904603243,
-0.056331489235162735,
-0.015853160992264748,
-0.012861287221312523,
0.0011353306472301483,
0.02068239077925682,
0.01366429217159748,
0.0015745823038741946,
-0.04270150139927864,
0.027283722534775734,
0.027926668524742126,
-0.02584681659936905,
-0.018430666998028755,
0.02242390252649784,
0.05120202898979187,
0.010643941350281239,
-0.008144394494593143,
-0.016678975895047188,
-0.011321350932121277,
-0.032729558646678925,
0.011530989781022072,
-0.02679077908396721,
-0.018977606669068336,
-0.06748463958501816,
0.09318742156028748,
0.050280291587114334,
-0.05929651856422424,
-0.057713598012924194,
0.018331222236156464,
-0.08051872998476028,
0.008103772066533566,
0.006804966367781162,
0.06876104325056076,
0.012784688733518124,
-0.0009019189164973795,
0.043326471000909805,
0.03594224900007248,
0.014536332339048386,
0.04881898686289787,
0.009149454534053802,
-0.009060359559953213,
-0.049522239714860916,
-0.02760389633476734,
0.03372098505496979,
-0.0032555621583014727,
0.012306292541325092,
0.020507022738456726,
-0.05365368351340294,
-0.019816311076283455,
-0.004110530950129032,
-0.003950894810259342,
-0.01613873615860939,
0.004707432817667723,
-0.017658192664384842,
0.0008639834122732282,
0.009168547578155994,
0.00784807838499546,
-0.06171022728085518,
-0.013133976608514786,
-0.047227852046489716,
0.07427823543548584,
-0.023276278749108315,
-0.050295140594244,
-0.04348541796207428,
0.022977428510785103,
0.09338901191949844,
-0.005813986528664827,
-0.052595850080251694,
0.059196338057518005,
-0.036061953753232956,
-0.05454757809638977,
0.009006980806589127,
-0.02747631072998047,
-0.0038281793240457773,
0.02166193537414074,
-0.011065301485359669,
-0.024530408903956413,
0.048039510846138,
0.01237405277788639,
0.06311732530593872,
-0.01026824489235878,
0.00869175884872675,
-0.01405701506882906,
-0.04239710792899132,
-0.0433882474899292,
0.025975119322538376,
0.007503311615437269,
-0.01355075929313898,
-0.042249441146850586,
0.053577832877635956,
0.02093452773988247,
0.006240412127226591,
-0.05284348875284195,
-0.03689650818705559,
-0.02868351899087429,
-0.0009765011491253972,
0.03246389329433441,
0.048924028873443604,
0.062174241989851,
0.029969044029712677,
-0.015355420298874378,
0.02786111831665039,
-0.026888877153396606,
0.019322223961353302,
0.013178947381675243,
0.0401107557117939,
-0.059468552470207214,
-0.0527975931763649,
-0.017633970826864243,
0.07981827110052109,
0.04348074644804001,
-0.06940560042858124,
0.010756125673651695,
0.03301012143492699,
0.049741603434085846,
0.00608067587018013,
0.09363777190446854,
0.02225392311811447,
-0.0062778666615486145,
0.019752366468310356,
0.020361630246043205,
0.04911743849515915,
0.04567455127835274,
-0.0014630950754508376,
0.006436049938201904,
-0.032706789672374725,
-0.011795478872954845,
-0.029266223311424255,
0.013555394485592842,
-0.014504414983093739,
0.005724925547838211,
-0.013441037386655807,
-0.006108070723712444,
0.016583139076828957,
-0.0541127473115921,
0.03982511907815933,
0.05175256356596947,
-0.008087558671832085,
0.006592344958335161,
-0.03628925606608391,
-0.0513351671397686,
-0.042157527059316635,
-0.0022584518883377314,
0.01889200694859028,
-0.009026036597788334,
0.031390320509672165,
-0.004872677382081747,
0.014675415121018887,
-0.04066396504640579,
0.021904803812503815,
-0.013770543038845062,
0.0029238227289170027,
0.059984754770994186,
0.012695626355707645,
-0.02420642413198948,
-0.041039783507585526,
0.021179592236876488,
-0.016540102660655975,
0.01663024351000786,
-0.04093143343925476,
-0.009037706069648266,
0.02917400747537613,
0.05693595111370087,
-0.004573443438857794,
-0.02277805656194687,
-0.08778809756040573,
-0.017461491748690605,
-0.01801750622689724,
0.019193686544895172,
0.0206897035241127,
0.009173110127449036,
0.11948588490486145,
-0.056349977850914,
0.03726815804839134,
-0.04705747961997986,
0.001168500049971044,
-0.06658339500427246,
-0.017799261957406998,
0.045183368027210236,
-0.05405757203698158,
-0.056129470467567444,
0.01861349120736122,
0.07700147479772568,
0.021393945440649986,
-0.004948558285832405,
0.04677296429872513,
0.03708163648843765,
-0.02629508636891842,
0.007104767952114344,
-0.034917332231998444,
-0.05134560912847519,
-0.04170956090092659,
-0.020129548385739326,
-0.05237707123160362,
-0.014120216481387615,
-0.08090813457965851,
-0.0020239122677594423,
-0.010837583802640438,
0.03392934799194336,
-0.021610470488667488,
0.011113818734884262,
0.004614411387592554,
0.03961234167218208,
0.01596185751259327,
-0.031291767954826355,
0.004751995205879211,
0.01635793410241604,
0.03150196373462677,
0.00920478068292141,
0.0014217314310371876,
0.01929566264152527,
0.011359833180904388,
0.027048379182815552,
-0.023466303944587708,
-0.03252829238772392,
0.04239385202527046,
-0.034629758447408676,
0.026213839650154114,
0.021912558004260063,
-0.03694351762533188,
-0.011645878665149212,
0.027099033817648888,
-0.016288232058286667,
-0.003208636771887541,
-0.023344671353697777,
0.040283478796482086,
-0.01694629341363907,
0.04038398712873459,
-0.012046067975461483,
0.09979341924190521,
0.023082518950104713,
-0.022126417607069016,
0.0631265863776207,
-0.04355695843696594,
0.055549584329128265,
-0.013847071677446365,
-0.038809310644865036,
0.03823244199156761,
-0.00010459517943672836,
0.00046927909716032445,
0.028957579284906387,
0.06968812644481659,
-0.01792902871966362,
-0.009320419281721115,
0.03358469903469086,
-0.07118719816207886,
0.007886724546551704,
0.04643029719591141,
-0.013412526808679104,
-0.014755599200725555,
0.019326087087392807,
0.032528504729270935,
0.00520484009757638,
0.01885409839451313,
0.00788321252912283,
0.0054034702479839325,
0.01700824312865734,
-0.06263292580842972,
0.06679760664701462,
0.04167279973626137,
0.01053358893841505,
-0.001534516573883593,
-0.02545972727239132,
0.04137425497174263,
0.044973570853471756,
0.05866599082946777,
0.0007797531434334815,
0.08971670269966125,
-0.0036651294212788343,
0.05899001285433769,
0.026408439502120018,
0.012014777399599552,
-0.009202782064676285,
0.015982087701559067,
-0.03443408012390137,
0.04992556571960449,
0.004464901052415371,
0.01952735148370266,
-0.060186609625816345,
-0.038962412625551224,
0.021475275978446007,
0.0052598826587200165,
0.012090431526303291,
-0.04279400408267975,
-0.008406133390963078,
0.004045240581035614,
-0.008757548406720161,
-0.0422620065510273,
-0.056258510798215866,
-0.01657756417989731,
0.014969964511692524,
0.031230267137289047,
-0.042914919555187225,
-0.058632299304008484,
0.011145522817969322,
0.05430776998400688,
0.00579053582623601,
0.000538032443728298,
0.030818291008472443,
0.010200416669249535,
0.017886098474264145,
-0.005040870513767004,
-0.03660156950354576,
-0.029903581365942955,
-0.014101540669798851,
0.021862948313355446,
-0.06932717561721802,
-0.07260384410619736,
0.007175242528319359,
-0.039489489048719406,
0.06523829698562622,
0.0031758055556565523,
-0.023223333060741425,
-0.03149038925766945,
0.049645256251096725,
-0.018057197332382202,
0.029169056564569473,
-0.013756953179836273,
0.06012071296572685,
0.03166590631008148,
-0.03554963693022728,
-0.002878303173929453,
0.009120253846049309,
-0.028154464438557625,
0.011643519625067711,
-0.022392388433218002,
0.028128335252404213,
-0.004637518897652626,
0.04624627158045769,
0.010885094292461872,
-0.01759376749396324,
-0.06375753879547119,
-0.028358621522784233,
-0.005908882711082697,
0.04873085767030716,
-0.052230533212423325,
-0.07017066329717636,
-0.00957427266985178,
-0.0333721749484539,
0.07417775690555573,
-0.030286014080047607,
0.019754767417907715,
0.00028927947278134525,
-0.02094845287501812,
0.016389749944210052,
-0.03239979222416878,
-0.06399025768041611,
0.025119276717305183,
0.0028533495496958494,
-0.12268108129501343,
-0.04042503610253334,
0.006071454845368862,
0.022383838891983032,
0.001979988534003496,
0.01335476990789175,
0.024284666404128075,
-0.004353716038167477,
0.03766792640089989,
0.02674398384988308,
0.004056442528963089,
0.02560771442949772,
0.08025416731834412,
-0.003539829282090068,
-0.038411665707826614,
0.06559552997350693,
-0.017992457374930382,
0.03864745423197746,
0.000401007360778749,
0.033387668430805206,
-0.04438203200697899,
-0.018189208582043648,
-0.03447524085640907,
-0.023770291358232498,
-0.023958854377269745,
-0.04243043437600136,
0.027829276397824287,
0.003929773345589638,
0.005201814230531454,
-0.016461540013551712,
-0.0181597750633955,
-0.037256259471178055,
0.007596779149025679,
0.018494121730327606,
-0.05128265917301178,
-0.021122917532920837,
-0.0027662513311952353,
0.00680572260171175,
-0.014405284076929092,
-0.060478344559669495,
0.005602523218840361,
0.03348272293806076,
-0.003322058590129018,
-0.06025422364473343,
0.02211286872625351,
0.0032421457581222057,
0.0007302727899514139,
-0.05145932734012604,
-0.018492987379431725,
-0.01825319603085518,
0.04690904542803764,
-0.027416495606303215,
-0.02539457567036152,
0.07880016416311264,
0.04498196393251419,
0.09200818091630936,
-0.03637963905930519,
-0.021076729521155357,
-0.004679525271058083,
-0.013940966688096523,
0.01528959907591343,
0.006893278565257788,
-0.006780548952519894,
-0.005816061515361071,
-0.005462413188070059,
-0.009509182535111904,
-0.017600074410438538,
-0.028731094673275948,
-0.059185925871133804,
-0.048077020794153214,
-0.00010442889470141381,
-0.016166146844625473,
-0.003592344932258129,
-0.0031034485436975956,
0.0038998860400170088,
0.02366357482969761,
-0.010063809342682362,
-0.038834910839796066,
0.009453772567212582,
-0.01271126139909029,
-0.05740005522966385,
0.03898073360323906,
0.016612732782959938,
-0.017573097720742226,
-0.08880683779716492,
0.038000404834747314,
0.05209585651755333,
0.027071304619312286,
0.016186758875846863,
0.03451205790042877,
-0.051449310034513474,
-0.009474403224885464,
0.03766646236181259,
0.003806651569902897,
0.012327851727604866,
-0.0027278291527181864,
0.003800877369940281,
0.024265943095088005,
-0.03540896251797676,
-0.01645771972835064,
0.00005238112134975381,
-0.0704529657959938,
0.051328279078006744,
0.008183518424630165,
-0.027138445526361465,
0.007621195167303085,
-0.006786105688661337,
0.015368183143436909,
-0.0319133959710598,
-0.039934366941452026,
0.009316614829003811,
0.00877073872834444,
-0.010373984463512897,
-0.027443772181868553,
-0.0014871594030410051,
-0.024382127448916435,
-0.00762664619833231
] |
<p>There are a lot papers explaining why Laughlin's wavefunction are energetically favorable, but seldom explain why a lower energy state could explain the plateau at $\nu=1/3$. I met at several places claims like: a lower energy state at $\nu=1/3$ will pin the electron density at $\nu=1/3$. But why is that? And what actually it means? when we move $\nu$ from $1/3$ what happens? electrons adjust there distance or new particle been added? And is this a phase transition?
Hope someone familiar this field could give me some help, thanks! </p> | g5533 | [
0.020168626680970192,
0.040009722113609314,
-0.01240755058825016,
0.019329886883497238,
0.054806485772132874,
0.05217989161610603,
0.012651843950152397,
-0.007806663401424885,
0.026191595941781998,
-0.02913855016231537,
-0.03147625923156738,
-0.0024179627653211355,
0.023276034742593765,
-0.026074016466736794,
0.014196052215993404,
-0.02385798469185829,
0.005339357536286116,
-0.00025429658126085997,
0.02934882789850235,
0.011433272622525692,
-0.10264125466346741,
-0.005332117434591055,
-0.010700740851461887,
-0.05559694021940231,
0.024174220860004425,
0.016019830480217934,
0.004993418697267771,
-0.03909199312329292,
0.020144348964095116,
0.017462845891714096,
0.0005929462495259941,
0.0033725444227457047,
0.012858790345489979,
-0.007746856193989515,
-0.00897689163684845,
-0.04925267770886421,
0.07760769128799438,
0.024960173293948174,
0.04016270488500595,
0.024881860241293907,
0.028918907046318054,
-0.023014796897768974,
0.016723401844501495,
-0.04653571546077728,
-0.02221420779824257,
0.023239394649863243,
-0.03831084817647934,
0.002716179471462965,
-0.03376079350709915,
-0.008014559745788574,
-0.00492110988125205,
0.03713535889983177,
-0.014977220445871353,
0.03875941038131714,
-0.00735397869721055,
0.03398003429174423,
-0.03803520277142525,
-0.007621266413480043,
0.03812955319881439,
0.05870475247502327,
0.008557088673114777,
0.02266247570514679,
0.047986939549446106,
-0.011842209845781326,
0.08444982767105103,
0.006674669217318296,
-0.04621336609125137,
-0.01625058427453041,
0.017149798572063446,
-0.005336655303835869,
0.015992624685168266,
-0.04742889851331711,
-0.09975885599851608,
-0.08030512928962708,
-0.04962949454784393,
-0.02795235626399517,
-0.02982821874320507,
-0.056053947657346725,
-0.014871879480779171,
0.010132591240108013,
-0.04177716001868248,
-0.03200022503733635,
0.02756500616669655,
-0.008221959695219994,
-0.010475002229213715,
-0.013358485884964466,
0.07777964323759079,
0.0321790911257267,
-0.008341415785253048,
0.024072127416729927,
-0.036432284861803055,
0.017450399696826935,
0.05790284276008606,
-0.03757910802960396,
-0.04207078740000725,
-0.005683188326656818,
-0.014547863975167274,
0.04697491228580475,
0.01869071274995804,
-0.020775828510522842,
-0.0320931039750576,
-0.015068893320858479,
0.025632062926888466,
0.01884406991302967,
-0.054852377623319626,
0.03656385838985443,
0.005081986542791128,
-0.016186555847525597,
0.030762474983930588,
0.02477049082517624,
-0.052235621958971024,
-0.010581116192042828,
0.003241232829168439,
-0.0011575737735256553,
-0.016426706686615944,
0.00108489824924618,
0.01888268254697323,
-0.0358126163482666,
-0.009074115194380283,
0.05512833222746849,
0.03322126716375351,
-0.007637022063136101,
-0.0033917175605893135,
0.03213902935385704,
-0.04563800245523453,
-0.023692531511187553,
-0.014958428218960762,
-0.0018142348853871226,
-0.03975026682019234,
-0.005489696748554707,
0.019134849309921265,
0.01719529740512371,
-0.10424759984016418,
0.015505729243159294,
0.07923634350299835,
0.026794010773301125,
-0.011140982620418072,
0.0268117506057024,
-0.011485544964671135,
0.04205534607172012,
0.06042136624455452,
-0.017439572140574455,
-0.0322052463889122,
-0.04520779475569725,
-0.011011788621544838,
0.004469325300306082,
-0.08945120871067047,
0.0007000438054092228,
-0.01907283440232277,
0.03713380545377731,
-0.0272302757948637,
0.0573153980076313,
0.013035419397056103,
-0.08965481072664261,
0.023801496252417564,
-0.02673243172466755,
0.04247868061065674,
0.021911215037107468,
-0.05029434338212013,
0.015680108219385147,
0.06889843940734863,
0.007825925946235657,
0.0016162048559635878,
0.03335172310471535,
-0.0498296283185482,
0.027141407132148743,
0.06062982603907585,
-0.04513398930430412,
-0.06963256746530533,
-0.019704844802618027,
-0.001483919215388596,
0.010852709412574768,
0.006894147489219904,
-0.016332434490323067,
-0.010921022854745388,
0.037547267973423004,
0.012560526840388775,
0.005487405229359865,
-0.020880931988358498,
0.004270610865205526,
-0.011407365091145039,
0.03245249018073082,
0.006237090099602938,
-0.021987849846482277,
0.0175701305270195,
0.0016852488042786717,
-0.0051162284798920155,
0.044346049427986145,
-0.010049384087324142,
-0.0012480393052101135,
0.03489303961396217,
-0.0019005468348041177,
-0.01896316558122635,
0.008472349494695663,
0.0112526286393404,
-0.031140001490712166,
0.00349710276350379,
-0.0845293402671814,
-0.03301622346043587,
-0.0622037872672081,
-0.06982411444187164,
-0.035600654780864716,
-0.013882871717214584,
0.0014126000460237265,
0.024347888305783272,
0.04519639536738396,
0.0019272303907200694,
0.053425680845975876,
0.04567448049783707,
-0.04616686329245567,
-0.025400901213288307,
-0.004990073386579752,
0.014717860147356987,
0.01798143796622753,
0.0030860737897455692,
0.008369071409106255,
0.018354889005422592,
-0.03953324630856514,
0.036337271332740784,
0.009984922595322132,
-0.030529499053955078,
-0.06102064624428749,
0.008500746451318264,
0.07241041958332062,
0.04315095394849777,
0.005952297709882259,
0.019983062520623207,
0.0204421728849411,
-0.010574417188763618,
0.025182561948895454,
-0.06524861603975296,
0.0415470115840435,
-0.037905316799879074,
-0.016037210822105408,
0.047268252819776535,
0.015470604412257671,
0.012528878636658192,
-0.0501926988363266,
0.03809786215424538,
0.013754825107753277,
-0.015043212100863457,
-0.0026670864317566156,
-0.02860437147319317,
0.02793842926621437,
-0.02214323915541172,
-0.014475689269602299,
-0.0095589654520154,
-0.038123905658721924,
-0.031891606748104095,
-0.0537954643368721,
0.004266050178557634,
0.013124583289027214,
-0.00476372754201293,
0.023298563435673714,
-0.02229665033519268,
-0.020155642181634903,
-0.02454323321580887,
0.05782441422343254,
-0.039230186492204666,
-0.07456454634666443,
-0.0017829316202551126,
0.010004994459450245,
0.09127364307641983,
-0.05486197769641876,
-0.043526045978069305,
-0.04036450386047363,
0.003412741469219327,
0.037436965852975845,
-0.05388559401035309,
-0.01395817007869482,
0.03845224529504776,
0.06509874761104584,
-0.018828019499778748,
-0.007579046767205,
0.0036359471268951893,
-0.058195315301418304,
0.031136300414800644,
-0.011036960408091545,
0.05196448042988777,
-0.05512342229485512,
-0.06819196045398712,
-0.047682635486125946,
-0.010686120018362999,
-0.027682386338710785,
0.01820102147758007,
-0.04476157948374748,
0.04637041687965393,
-0.038753610104322433,
-0.03145472705364227,
-0.01486851554363966,
-0.0007181703113019466,
-0.01395771186798811,
0.034117791801691055,
0.03794153779745102,
0.03087543696165085,
-0.02909967489540577,
0.04356870800256729,
-0.011121065355837345,
-0.01577538624405861,
0.040957119315862656,
-0.026997148990631104,
-0.03243870288133621,
-0.029279576614499092,
-0.00455298088490963,
0.0049379444681108,
0.04628315567970276,
0.02365139126777649,
-0.008894810453057289,
-0.08448296785354614,
0.02454836666584015,
-0.06240851432085037,
0.026231497526168823,
-0.014233274385333061,
-0.04930134862661362,
-0.01420597080141306,
-0.04522547125816345,
-0.03598326817154884,
0.051046937704086304,
0.027517402544617653,
-0.05796124041080475,
-0.027646852657198906,
-0.031320616602897644,
-0.052023157477378845,
-0.03859740123152733,
0.01605670526623726,
0.06975513696670532,
-0.06464145332574844,
-0.010075435042381287,
0.008197695948183537,
-0.005536751821637154,
0.05453632026910782,
-0.02376434952020645,
-0.010547240264713764,
-0.024006785824894905,
-0.0129696698859334,
-0.07965812087059021,
-0.08283015340566635,
0.09185163676738739,
0.06192352622747421,
0.04458114504814148,
-0.05471743643283844,
0.062166888266801834,
-0.039314575493335724,
0.036223042756319046,
0.027766061946749687,
0.017094610258936882,
-0.03051069937646389,
-0.03133521229028702,
-0.01595006324350834,
-0.004409946966916323,
-0.04093637317419052,
-0.003753823693841696,
-0.0022583622485399246,
0.015843331813812256,
-0.009015294723212719,
-0.015595495700836182,
0.015844672918319702,
-0.04423016309738159,
0.023648465052247047,
0.012521629221737385,
0.010262168012559414,
-0.026690086349844933,
0.014391453936696053,
-0.02346259169280529,
-0.044505756348371506,
-0.01118837483227253,
-0.054621729999780655,
0.022453995421528816,
0.03329334408044815,
0.02936706691980362,
-0.034750089049339294,
-0.02459145337343216,
0.051721878349781036,
0.01154759805649519,
-0.004683763720095158,
0.006210515275597572,
0.02286752127110958,
0.02591509371995926,
-0.08018357306718826,
0.009396065026521683,
0.03387691080570221,
-0.01619587279856205,
0.04777377471327782,
-0.03897566348314285,
-0.0005963663570582867,
0.01350182481110096,
-0.04139307886362076,
-0.02715846709907055,
-0.0014105677837505937,
-0.01889684796333313,
-0.026287535205483437,
-0.07180144637823105,
-0.0009334729402326047,
0.07486071437597275,
0.024551168084144592,
0.007183440029621124,
0.027849717065691948,
0.014608301222324371,
-0.011649157851934433,
0.029231753200292587,
0.016983531415462494,
-0.0009694175678305328,
-0.06164852902293205,
-0.03615216165781021,
-0.0021162352059036493,
-0.009770921431481838,
0.03344040364027023,
-0.006506644189357758,
-0.019090812653303146,
-0.06279288232326508,
0.04580917954444885,
0.05820971354842186,
-0.027683168649673462,
-0.05568569153547287,
-0.026668457314372063,
-0.01631421409547329,
0.039082348346710205,
-0.03824932500720024,
0.0015111850807443261,
0.04781218245625496,
-0.02342171221971512,
0.05651586502790451,
-0.02116400934755802,
0.04089698567986488,
0.019091466441750526,
0.03300217539072037,
-0.001978465588763356,
0.00044695043470710516,
-0.01607506163418293,
-0.0134610366076231,
0.06826331466436386,
0.05263813957571983,
-0.00429832749068737,
-0.025419222190976143,
-0.039123982191085815,
0.05542656034231186,
-0.021742016077041626,
0.015651222318410873,
-0.05312073603272438,
-0.01714499667286873,
0.07756619155406952,
-0.013635384850203991,
-0.02415570244193077,
0.014367552474141121,
-0.0166782196611166,
-0.040243376046419144,
-0.06912172585725784,
-0.008482856675982475,
-0.028816472738981247,
-0.0727577731013298,
-0.02740340121090412,
0.02332172729074955,
-0.026991529390215874,
-0.053137797862291336,
0.03348105028271675,
-0.05081907659769058,
-0.0009734383784234524,
0.03088304214179516,
0.03317040950059891,
0.023963501676917076,
-0.024295590817928314,
0.032827600836753845,
0.05381030961871147,
-0.03719246760010719,
-0.0027885858435183764,
-0.049787141382694244,
0.017283238470554352,
-0.05857163295149803,
-0.016229141503572464,
-0.022087911143898964,
0.02968410775065422,
-0.007200570777058601,
0.040551088750362396,
0.00048723790678195655,
0.05033672973513603,
-0.006039159372448921,
0.03426608070731163,
-0.018043216317892075,
0.04145657271146774,
-0.06575246155261993,
0.06020153686404228,
0.0007613229099661112,
0.0247468464076519,
0.06565243005752563,
-0.03675452992320061,
-0.00994900893419981,
-0.03872644901275635,
-0.008867628872394562,
-0.002154581481590867,
-0.037307996302843094,
0.025737890973687172,
0.009978539310395718,
0.05571836978197098,
-0.03574686124920845,
-0.005848871544003487,
0.0012960813473910093,
0.0028772177174687386,
0.009197225794196129,
-0.04231638461351395,
0.007619528099894524,
-0.04611019417643547,
-0.0034322047140449286,
-0.031572408974170685,
0.048955876380205154,
-0.015928594395518303,
-0.007590182591229677,
0.03216693177819252,
-0.01778509095311165,
0.05432916805148125,
-0.03142367675900459,
0.002677930286154151,
0.007963735610246658,
0.05168448016047478,
-0.0048895059153437614,
0.032942287623882294,
-0.024173665791749954,
0.014114271849393845,
0.048112716525793076,
-0.0392269492149353,
0.02941701002418995,
0.04072469472885132,
-0.027227338403463364,
0.02619936317205429,
-0.0110594742000103,
0.08201710879802704,
0.05099671706557274,
-0.03263257071375847,
0.0018520914018154144,
0.014101953245699406,
0.0676548108458519,
-0.03522411361336708,
0.0011673156404867768,
0.09883874654769897,
-0.007552138064056635,
-0.01968933828175068,
0.04122230038046837,
0.04235547035932541,
0.012070689350366592,
0.04686201736330986,
0.0006012690137140453,
0.018707241863012314,
-0.02152492105960846,
0.0019932640716433525,
0.07468093186616898,
-0.017298664897680283,
-0.04850555583834648,
-0.08707531541585922,
0.02739465981721878,
0.012368928641080856,
-0.036804310977458954,
0.059678446501493454,
-0.001011985121294856,
-0.033817727118730545,
-0.03237595409154892,
-0.002070031128823757,
0.020921990275382996,
0.05545700341463089,
-0.02568621188402176,
-0.04083453118801117,
-0.038228344172239304,
0.011014378629624844,
0.016854815185070038,
0.0934389978647232,
0.0514642558991909,
0.0931643694639206,
-0.07215800136327744,
-0.021458791568875313,
-0.008626732043921947,
0.05012748762965202,
-0.01863096095621586,
0.018361084163188934,
0.01586196757853031,
0.049838244915008545,
0.04352947324514389,
-0.0447828434407711,
0.03844935819506645,
0.000715801608748734,
0.005605349782854319,
-0.07095343619585037,
-0.02037043683230877,
-0.005343589931726456,
0.008717585355043411,
0.003764157649129629,
-0.006911287549883127,
-0.023210100829601288,
0.027329860255122185,
-0.01580982655286789,
-0.011793414130806923,
0.042728789150714874,
0.005717072635889053,
-0.02097759023308754,
-0.011228526011109352,
0.02094440534710884,
0.01517265010625124,
-0.04379568621516228,
-0.0018083250615745783,
-0.05885090306401253,
-0.03921758010983467,
-0.03410790115594864,
0.044651154428720474,
0.044095106422901154,
0.062057625502347946,
0.0014423206448554993,
-0.046089526265859604,
0.014986402355134487,
0.06179602071642876,
0.04292234778404236,
0.05016552656888962,
-0.015524218790233135,
0.04272603243589401,
0.004975639283657074,
0.042157113552093506,
0.010176237672567368,
0.00296777649782598,
0.016864700242877007,
-0.019388992339372635,
-0.0038023870438337326,
0.03277898207306862,
-0.07248426228761673,
0.02227201871573925,
0.01794765144586563,
-0.010615790262818336,
0.05330472066998482,
0.03843528777360916,
0.034355808049440384,
-0.012342932634055614,
-0.012564189732074738,
0.014681631699204445,
0.051647935062646866,
0.006629312410950661,
-0.0017813158920034766,
0.01261892169713974,
-0.018931960687041283,
0.10909121483564377,
-0.021405993029475212,
0.017437096685171127,
0.0020546438172459602,
-0.029653312638401985,
0.02899474836885929,
0.019506381824612617,
-0.03253772482275963,
0.03322100266814232,
0.06116501986980438,
-0.02897445484995842,
-0.01228688471019268,
0.017181796953082085,
0.029386185109615326,
0.01842796616256237,
0.026937013491988182,
0.05822320654988289,
-0.00478261336684227,
-0.04099833220243454,
-0.054054420441389084,
0.010065807960927486,
-0.02110198698937893,
0.006646466441452503,
-0.019253810867667198,
-0.008213736116886139,
0.01836659200489521,
-0.04376939311623573,
-0.013195207342505455,
-0.047933563590049744,
0.053239136934280396,
0.03934687748551369,
-0.014696483500301838,
0.000676161958836019,
-0.000056160850363085046,
0.0024301183875650167,
0.054246921092271805,
-0.04358965903520584,
-0.006612224038690329,
-0.05297568067908287,
-0.030287332832813263,
0.029098335653543472,
0.019030632451176643,
0.03926064819097519,
-0.02123139798641205,
0.015849750488996506,
0.07960930466651917,
-0.017024172469973564,
-0.008056441321969032,
0.0236771572381258,
0.036561306565999985,
-0.0814899280667305,
-0.04441909119486809,
0.013600626960396767,
-0.038018789142370224,
-0.03467591106891632,
0.002219892805442214,
0.07176586240530014,
0.0479436069726944,
0.02657453343272209,
0.007351454347372055,
-0.00907136406749487,
-0.05140119045972824,
0.03476677089929581,
-0.026981454342603683,
0.009356069378554821,
0.015294533222913742,
0.03670507296919823,
0.006600058637559414,
-0.039308272302150726,
-0.014159613288939,
-0.010551131330430508,
0.008232327178120613,
-0.010561041533946991,
0.02850065939128399,
-0.017619309946894646,
-0.06783749908208847,
0.015090731903910637,
0.042611245065927505,
-0.03892266005277634,
0.02398298680782318,
0.035868994891643524,
0.016716230660676956,
0.026293832808732986,
0.025269344449043274,
-0.00848682876676321,
-0.024029895663261414,
-0.029947524890303612,
-0.001082185423001647,
-0.022135166451334953,
-0.03264586627483368,
-0.04132339358329773,
0.04251706227660179,
-0.04482386261224747,
0.015811940655112267,
-0.026205969974398613,
0.024554895237088203,
0.04924324154853821,
-0.012732536531984806,
0.02848096378147602,
0.007126158569008112,
-0.04161930829286575,
-0.03545292094349861,
0.0416901595890522,
0.01232838910073042,
0.03583517298102379,
0.049965109676122665,
0.047039903700351715,
-0.01761840283870697,
-0.003928469493985176,
0.004805222153663635,
-0.04291997477412224,
-0.01680801436305046,
-0.07055070996284485,
-0.009977270849049091,
0.05608799681067467,
0.012224442325532436,
0.014967333525419235,
-0.04372943192720413,
-0.06982588768005371,
-0.06645992398262024,
0.09456156194210052,
0.0711650475859642,
-0.0250691045075655,
0.013273165561258793,
-0.010594615712761879,
0.029432211071252823,
-0.03671622276306152,
0.03235333785414696,
-0.03355588763952255,
0.024601317942142487,
-0.011023285798728466,
-0.03667858988046646,
0.03468325361609459,
-0.007129110395908356,
-0.0455380342900753
] |
<p>At lower altitude an aeroplane usually has more lift. However an aeroplane flying at low altitudes (with gear/flaps up) at low velocity burns the same amount of fuel it would flying much faster at a higher altitude. Why?</p> | g5534 | [
0.03213852643966675,
0.013053957372903824,
0.0005949860787950456,
0.07571757584810257,
-0.004461705684661865,
0.030368436127901077,
-0.022550830617547035,
0.017203861847519875,
-0.05213248357176781,
-0.05508517101407051,
0.03657073527574539,
0.005300244316458702,
-0.02128799632191658,
0.0038772919215261936,
0.03748679533600807,
0.007301659323275089,
-0.01288127712905407,
-0.03432445228099823,
0.04195123538374901,
0.019254248589277267,
0.03209306299686432,
0.005017781630158424,
-0.007995693013072014,
-0.023847535252571106,
-0.06944398581981659,
-0.02860947884619236,
-0.0897369310259819,
-0.05553928017616272,
-0.0534370020031929,
-0.006332901306450367,
0.06265345960855484,
-0.029775425791740417,
0.04469354823231697,
-0.012468736618757248,
-0.013699381612241268,
-0.03998091071844101,
0.01688240095973015,
0.02152084931731224,
0.024391938000917435,
-0.03529587388038635,
0.021241771057248116,
-0.005463872104883194,
-0.014413119293749332,
0.03654833137989044,
-0.01675773411989212,
-0.00484492676332593,
-0.002284702379256487,
0.00575509387999773,
-0.05838898569345474,
-0.01899762637913227,
-0.025478465482592583,
0.019259121268987656,
-0.0655679851770401,
-0.015221936628222466,
0.039929114282131195,
-0.027999961748719215,
0.014343063347041607,
0.03372512012720108,
-0.04588297754526138,
0.03156912326812744,
-0.040725383907556534,
0.008689755573868752,
0.01070012804120779,
-0.0012568121310323477,
0.044978123158216476,
0.008955471217632294,
0.021329542621970177,
-0.05859919637441635,
0.05126215144991875,
0.014864807017147541,
0.0015742843970656395,
-0.04268870875239372,
-0.04236831143498421,
-0.04296901077032089,
-0.03599856421351433,
-0.07109523564577103,
0.013599523343145847,
-0.015005430206656456,
0.04946495220065117,
0.025373389944434166,
-0.03611072525382042,
0.013991408050060272,
0.010968961752951145,
0.010129677131772041,
0.037820879369974136,
-0.004924500826746225,
-0.006116336677223444,
0.021355846896767616,
0.018337681889533997,
0.004688736516982317,
0.014222490601241589,
-0.01873612403869629,
0.09438835084438324,
-0.01294634398072958,
-0.028725452721118927,
0.0036502692382782698,
0.0024639710318297148,
0.059748150408267975,
-0.03490981459617615,
0.006454284768551588,
0.005655357148498297,
-0.021955691277980804,
-0.008535044267773628,
0.019935619086027145,
-0.015615541487932205,
-0.054625485092401505,
0.03998027369379997,
-0.021632714197039604,
-0.049574773758649826,
-0.02438117004930973,
0.023306123912334442,
-0.01653219759464264,
-0.041574496775865555,
-0.020195111632347107,
0.003170786425471306,
-0.011551696807146072,
0.04217565432190895,
-0.019627317786216736,
-0.03446327522397041,
-0.027415892109274864,
0.04030066356062889,
0.0049469368532299995,
-0.004845099989324808,
0.04314778745174408,
0.010897799395024776,
-0.01634492538869381,
0.02979985624551773,
0.008904686197638512,
0.015827927738428116,
0.05574343353509903,
0.020971806719899178,
-0.01529637910425663,
-0.048290956765413284,
0.03925983980298042,
0.035952601581811905,
-0.0320621132850647,
-0.043465349823236465,
0.01270428765565157,
0.02363819256424904,
-0.005437626037746668,
0.02240722067654133,
-0.0002775597386062145,
0.027955103665590286,
-0.01597726158797741,
-0.030242186039686203,
0.023679886013269424,
-0.011757707223296165,
0.01710941642522812,
0.0010053626028820872,
0.007157966028898954,
0.03376998379826546,
-0.011698519811034203,
0.021766023710370064,
-0.00950753502547741,
0.036017078906297684,
0.015346836298704147,
0.019416572526097298,
0.026877617463469505,
-0.00004208143218420446,
0.0491098016500473,
0.003780734958127141,
-0.027170002460479736,
0.009947333484888077,
0.02196158468723297,
-0.09197402000427246,
0.07657632976770401,
0.031950581818819046,
-0.053503476083278656,
-0.02116330899298191,
0.031401824206113815,
0.009839055128395557,
-0.011136207729578018,
-0.01901332475244999,
-0.006325863767415285,
0.06727081537246704,
-0.002828831784427166,
0.06305717676877975,
0.014858768321573734,
-0.027858275920152664,
-0.009673104621469975,
-0.03213046118617058,
0.049503181129693985,
-0.01695161499083042,
-0.016162797808647156,
0.047448668628931046,
0.013652137480676174,
0.020985398441553116,
-0.03635220229625702,
-0.08044548332691193,
-0.010052544064819813,
-0.0004770764790009707,
-0.01397133432328701,
0.012199642136693,
-0.025846758857369423,
-0.0808161124587059,
0.010668556205928326,
-0.009529387578368187,
-0.01295164879411459,
-0.05707373097538948,
0.06634416431188583,
-0.02539576217532158,
-0.047704700380563736,
0.02460315264761448,
-0.018886934965848923,
0.049970708787441254,
0.001340615563094616,
-0.013335108757019043,
-0.018476057797670364,
0.060506388545036316,
-0.04562445357441902,
-0.030039312317967415,
0.007161727175116539,
0.03507615998387337,
0.014705734327435493,
0.07633673399686813,
0.022854432463645935,
-0.0042755319736897945,
-0.011163607239723206,
-0.004699824843555689,
-0.06947643309831619,
0.014981798827648163,
-0.015235774219036102,
0.0024286771658807993,
0.0014913866762071848,
-0.0031988464761525393,
-0.008834618143737316,
0.008205466903746128,
-0.058668505400419235,
0.023782409727573395,
-0.031127309426665306,
0.01648508943617344,
0.0010435006115585566,
0.056251317262649536,
-0.0732177123427391,
0.0017700043972581625,
-0.037741806358098984,
0.06036240607500076,
0.024240991100668907,
-0.004048127681016922,
0.06948725879192352,
-0.02110680192708969,
0.0030878521502017975,
0.00653822161257267,
-0.019977480173110962,
0.06352027505636215,
-0.0528399832546711,
0.00008523250289727002,
0.029206659644842148,
-0.044409412890672684,
0.09719685465097427,
0.01870504394173622,
0.04907072335481644,
-0.0292664747685194,
0.055025212466716766,
-0.044203020632267,
-0.011235502548515797,
-0.02571369893848896,
-0.0013537498889490962,
0.012914707884192467,
0.0357796847820282,
-0.012159238569438457,
0.007999740540981293,
-0.029551571235060692,
-0.04950222745537758,
-0.05742025375366211,
0.04167179390788078,
-0.07884929329156876,
-0.036111850291490555,
0.014038825407624245,
0.006386992521584034,
-0.04379947856068611,
0.02340138517320156,
-0.0041657076217234135,
-0.002292459597811103,
0.0007898028125055134,
-0.07535918056964874,
-0.002982668811455369,
0.006854308769106865,
-0.00009715702617540956,
-0.03382930904626846,
0.007743967697024345,
-0.017741085961461067,
-0.026778241619467735,
0.026091285049915314,
0.02309490367770195,
-0.02703329175710678,
-0.04447298124432564,
0.0007966459379531443,
-0.035315144807100296,
-0.02749837003648281,
-0.024217871949076653,
0.050239697098731995,
0.02780066803097725,
0.009910971857607365,
0.060487739741802216,
0.06714075058698654,
0.08023955672979355,
-0.033769793808460236,
-0.07769046723842621,
-0.04438187927007675,
-0.02791495993733406,
-0.045236945152282715,
0.020574897527694702,
0.07367914915084839,
-0.0032630346249789,
0.026049785315990448,
-0.021549809724092484,
-0.0345982126891613,
-0.06146137788891792,
0.02695738524198532,
-0.010470199398696423,
0.016265688464045525,
-0.03661983460187912,
0.04512646794319153,
-0.009148567914962769,
-0.009886915795505047,
-0.0714041143655777,
-0.02635752223432064,
0.023409003391861916,
-0.055347222834825516,
0.005794495344161987,
-0.06786547601222992,
-0.05342337489128113,
-0.025885796174407005,
-0.031517960131168365,
0.046301160007715225,
-0.03013690561056137,
0.0026720589958131313,
0.05354068800806999,
0.030177399516105652,
0.02911774255335331,
0.0019070657435804605,
-0.05223313346505165,
0.005717711988836527,
-0.0013388216029852629,
0.003807483473792672,
0.0022254674695432186,
0.06607483327388763,
-0.023928506299853325,
-0.001954504055902362,
0.002402653219178319,
0.06871110200881958,
0.014103846624493599,
0.0323500782251358,
0.028914831578731537,
0.022817356511950493,
0.018842188641428947,
0.02418963797390461,
-0.026236599311232567,
-0.022712308913469315,
-0.04238947480916977,
-0.006249320227652788,
-0.02222990244626999,
-0.0029363539069890976,
-0.03368271514773369,
-0.007898738607764244,
0.0009886887855827808,
-0.012510948814451694,
-0.02449725940823555,
0.025141043588519096,
0.04822450876235962,
0.05777696892619133,
-0.011541055515408516,
0.04395817220211029,
-0.06703615933656693,
-0.0114220529794693,
-0.0695420354604721,
0.010612329468131065,
-0.0011524789733812213,
0.05577905848622322,
0.051586151123046875,
0.03389020636677742,
-0.016360456123948097,
0.04985450208187103,
0.03596724942326546,
-0.029393095523118973,
0.10958265513181686,
-0.00009655332542024553,
0.005365478340536356,
-0.01593547686934471,
0.04774903878569603,
-0.011653494089841843,
0.03044646978378296,
0.01417763065546751,
0.008255905471742153,
0.010865665972232819,
-0.03721696138381958,
0.004023924004286528,
0.008281191810965538,
0.0017631147056818008,
-0.05218495428562164,
-0.003322187578305602,
-0.039614543318748474,
0.026693502441048622,
-0.0051796650514006615,
0.011696730740368366,
0.003935802262276411,
-0.02663532644510269,
0.05538749694824219,
0.05642053857445717,
0.009030825458467007,
-0.006431971676647663,
-0.04089474678039551,
0.025857659056782722,
-0.004873316735029221,
0.05616060271859169,
0.0039033526554703712,
0.046604372560977936,
-0.01780552789568901,
0.02383233793079853,
0.06560859829187393,
0.053670693188905716,
0.017209116369485855,
-0.01575574092566967,
-0.08928342908620834,
0.028612179681658745,
-0.04616910219192505,
0.027738109230995178,
0.030133869498968124,
0.06311831623315811,
0.01975022628903389,
0.03997068479657173,
0.043639954179525375,
-0.00178348773624748,
-0.0038075982592999935,
0.033796876668930054,
-0.03494288772344589,
0.021578218787908554,
-0.008066543377935886,
-0.012132732197642326,
0.05878144130110741,
0.006852732505649328,
-0.019285624846816063,
-0.008293269202113152,
-0.03998265042901039,
0.07422032952308655,
0.06953238695859909,
0.020768869668245316,
0.06817596405744553,
0.006644518580287695,
0.03913413733243942,
0.03727937862277031,
-0.03605088219046593,
0.007827370427548885,
-0.002834242070093751,
0.011881308630108833,
0.041490428149700165,
0.015692178159952164,
-0.03158337622880936,
-0.04096177592873573,
-0.049610771238803864,
-0.013215773738920689,
0.010546647012233734,
-0.0001462424115743488,
-0.042404696345329285,
-0.01865258254110813,
-0.004053309094160795,
-0.0222287829965353,
0.03581912815570831,
0.01811094954609871,
-0.035551778972148895,
0.02326386794447899,
0.0017364444211125374,
-0.021341806277632713,
0.024979496374726295,
0.04165356233716011,
-0.07372657209634781,
0.010998866520822048,
-0.007666310295462608,
0.002577875042334199,
0.039933811873197556,
-0.02632291428744793,
-0.049339380115270615,
0.04059814289212227,
-0.006187222898006439,
0.0471336804330349,
0.029291687533259392,
-0.02964235097169876,
-0.020386969670653343,
-0.019601982086896896,
0.01929336041212082,
-0.010372382588684559,
-0.033847466111183167,
0.0032925717532634735,
0.02639078162610531,
-0.024556875228881836,
-0.05980147421360016,
-0.005576748866587877,
0.015307068824768066,
-0.052193783223629,
0.037545815110206604,
0.06121542304754257,
-0.031005067750811577,
-0.019546182826161385,
-0.006971323862671852,
-0.004524150863289833,
0.0102546950802207,
-0.0015260640066117048,
0.009794373996555805,
-0.05225684866309166,
-0.003738683881238103,
0.004357683937996626,
0.01811922714114189,
-0.08112780749797821,
0.025314603000879288,
0.022328559309244156,
0.06474070250988007,
0.03090844489634037,
0.018639598041772842,
0.0559382438659668,
-0.04662059620022774,
0.019848834723234177,
-0.05429178476333618,
-0.007352160289883614,
0.02832816168665886,
-0.0585809163749218,
0.036973170936107635,
0.026408368721604347,
0.04074392840266228,
0.021407917141914368,
0.06673769652843475,
-0.001473782118409872,
0.03668798506259918,
0.05565410479903221,
0.056870605796575546,
0.003905254416167736,
-0.032849762588739395,
-0.012990204617381096,
0.013155410997569561,
-0.08033813536167145,
0.030726613476872444,
-0.004684155806899071,
0.06043132767081261,
0.004824248608201742,
-0.05266321077942848,
0.056350868195295334,
0.03602256625890732,
-0.02262282371520996,
-0.0389971062541008,
-0.044402919709682465,
-0.0027458921540528536,
-0.028659235686063766,
0.0008065723231993616,
0.07676321268081665,
0.03742209076881409,
-0.04334556311368942,
-0.03847137466073036,
-0.007686628494411707,
0.01273568719625473,
-0.008219198323786259,
-0.015970446169376373,
-0.015440230257809162,
0.001103842630982399,
0.02148715779185295,
0.011861651204526424,
-0.003252477617934346,
-0.015096963383257389,
-0.006031648721545935,
-0.017265956848859787,
-0.021482987329363823,
0.01552549097687006,
0.035689886659383774,
0.09387247264385223,
-0.03317871317267418,
0.0614294596016407,
-0.03501463308930397,
-0.0021531060338020325,
-0.011216697283089161,
0.025820109993219376,
-0.05176485702395439,
-0.05572082847356796,
-0.025572268292307854,
0.00217836513184011,
0.006883809342980385,
0.00848428625613451,
0.021323690190911293,
-0.0016271868953481317,
-0.013655715622007847,
-0.04877058416604996,
-0.04550335183739662,
0.02237129770219326,
-0.039657749235630035,
-0.06465615332126617,
-0.01061855349689722,
-0.049402039498090744,
0.04663520306348801,
-0.0382804237306118,
0.025375131517648697,
0.02817920222878456,
-0.014130116440355778,
-0.030192095786333084,
0.01021487545222044,
0.005812160205096006,
0.009255695156753063,
-0.019995324313640594,
-0.03949442505836487,
-0.006852727849036455,
0.028966952115297318,
-0.04515254870057106,
-0.030460765585303307,
0.11764653772115707,
0.05009433627128601,
0.11641766130924225,
-0.07150998711585999,
-0.001852664165198803,
0.09455196559429169,
0.06960099190473557,
0.02954590506851673,
-0.0027496754191815853,
0.0005806514527648687,
-0.04865619167685509,
0.01797679252922535,
0.03826744854450226,
-0.02178001031279564,
-0.06545218080282211,
0.02651984803378582,
0.0012143213534727693,
-0.06455536931753159,
-0.028252428397536278,
-0.009912575595080853,
-0.018682582303881645,
-0.025003604590892792,
-0.03407944366335869,
-0.08130590617656708,
0.04341714829206467,
-0.04514779895544052,
-0.03845278546214104,
0.03611044958233833,
0.012579109519720078,
-0.001960760448127985,
-0.04355031996965408,
0.04344383254647255,
-0.02760177105665207,
0.031606998294591904,
-0.013689820654690266,
-0.0157280545681715,
-0.010420018807053566,
-0.009175810031592846,
-0.0024251253344118595,
0.005359737668186426,
0.012973355129361153,
-0.004927439149469137,
0.020768320187926292,
-0.01903659477829933,
0.003946984652429819,
0.0077990018762648106,
-0.014355186372995377,
-0.06778070330619812,
0.06614789366722107,
-0.07175345718860626,
-0.004672566894441843,
-0.05232687667012215,
0.019461240619421005,
-0.026181567460298538,
-0.05665396898984909,
-0.02445880137383938,
0.0008909688331186771,
0.00882711261510849,
0.02478793077170849,
-0.04072786495089531,
-0.01150894071906805,
0.005677334498614073,
-0.02006496861577034,
0.06439276784658432,
-0.014149746857583523,
-0.014087392017245293,
0.0269535630941391,
-0.06596313416957855,
0.013736117631196976,
0.006929824128746986,
-0.006442514713853598,
-0.016244206577539444,
-0.03824314847588539,
-0.03519120067358017,
-0.0051392801105976105,
0.04167966917157173,
-0.036760713905096054,
0.042049650102853775,
0.018924474716186523,
0.0010359918233007193,
0.013110114261507988,
-0.0010194042697548866,
0.03917674720287323,
0.007189134135842323,
0.025890778750181198,
0.022230874747037888,
-0.009889613837003708,
-0.0009755316423252225,
0.0038957693614065647,
-0.032862745225429535,
-0.004855226259678602,
-0.021583648398518562,
0.027488896623253822,
0.02840307727456093,
-0.06657146662473679,
0.03293280676007271,
0.010064704343676567,
-0.06407249718904495,
-0.06553837656974792,
-0.006760294083505869,
0.02833034098148346,
0.004905976355075836,
0.038124680519104004,
0.014188431203365326,
-0.014805406332015991,
-0.022928915917873383,
0.08958344906568527,
0.07044894993305206,
-0.0580034963786602,
-0.031455978751182556,
-0.010952389799058437,
-0.037379756569862366,
0.03454074636101723,
0.041887763887643814,
0.028037628158926964,
-0.029225574806332588,
0.04511463642120361,
-0.09670110791921616,
-0.03962818533182144,
-0.010537257418036461,
0.0510387122631073,
-0.05281906947493553,
-0.01291878242045641,
-0.06509475409984589,
-0.008517387323081493,
-0.013609664514660835,
0.022351887077093124,
-0.009747843258082867,
0.04342176392674446,
-0.01848214492201805,
0.030947353690862656,
0.015013275668025017,
0.012297905050218105,
0.004747413098812103,
-0.004333800170570612,
-0.014142772182822227,
0.019312851130962372,
-0.018216796219348907,
0.0270237997174263,
0.026762455701828003,
-0.03856269270181656,
0.07715858519077301,
0.00030196330044418573,
0.038162194192409515,
0.04908187687397003,
-0.08013348281383514,
0.03813408315181732,
0.018434884026646614,
0.0405861921608448,
0.013277031481266022,
0.0068539516068995,
0.011079920455813408,
-0.009551126509904861,
-0.016398165374994278,
-0.019801339134573936,
0.07284076511859894,
-0.014517583884298801,
0.010382892563939095,
-0.07663661241531372,
-0.060505032539367676,
-0.022533874958753586,
0.050801753997802734,
-0.025896327570080757,
-0.06271075457334518,
-0.07650166749954224,
-0.02139340527355671,
-0.020429769530892372,
0.015624061226844788
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/18527/does-the-pauli-exclusion-principle-instantaneously-affect-distant-electrons">Does the Pauli exclusion principle instantaneously affect distant electrons?</a> </p>
</blockquote>
<p>If this rule works, could you not set up an experiment to test the theory (as described by Brian Cox in his <em>A Night with the Stars</em> lecture$^1$) and monitor another piece of diamond to see if the electrons change levels in time with the changes in energy of the electrons in the heated piece? If you used a pin point heating element that could change temperature at different frequencies, would you detect the frequency change in the monitored piece?</p>
<p>--</p>
<p>$^1$ The Youtube link keeps breaking, so here is a <a href="http://www.youtube.com/results?search_query=brian+cox+night+with+the+stars" rel="nofollow">search</a> on Youtube for Brian Cox' <em>A Night with the Stars</em> lecture.</p> | g199 | [
0.03475498408079147,
0.06037011370062828,
-0.0021842822898179293,
-0.02668938599526882,
-0.006327223498374224,
-0.0014127152971923351,
-0.021088341251015663,
0.01652364805340767,
-0.023728007450699806,
0.02578486129641533,
-0.020610295236110687,
0.09364435821771622,
-0.012552724219858646,
0.003551729954779148,
0.0008360038627870381,
-0.00048008072189986706,
0.0767429992556572,
0.00772828096523881,
-0.006483876146376133,
0.05107342451810837,
-0.016798751428723335,
0.02831066958606243,
-0.014810541644692421,
-0.029015878215432167,
-0.019196901470422745,
-0.00987955555319786,
-0.015791095793247223,
-0.0037637618370354176,
-0.024612586945295334,
0.002108732471242547,
-0.044425707310438156,
0.014329511672258377,
0.052792273461818695,
-0.024104278534650803,
-0.015878934413194656,
-0.05086999014019966,
0.017575837671756744,
0.043386586010456085,
-0.06109628826379776,
0.023559898138046265,
-0.028152957558631897,
-0.0024897686671465635,
0.040979109704494476,
-0.03489619493484497,
0.03292195126414299,
-0.0029469917062669992,
0.014030003920197487,
-0.005812357179820538,
-0.014117526821792126,
-0.023394212126731873,
0.005633958149701357,
0.016671815887093544,
0.06273017078638077,
0.0537223219871521,
0.01434058416634798,
-0.015284518711268902,
-0.012732479721307755,
0.02747739665210247,
0.11786507815122604,
-0.005038080271333456,
0.010428662411868572,
0.015915771946310997,
0.03623509407043457,
-0.017634404823184013,
0.017658496275544167,
0.03541334718465805,
-0.03791709989309311,
0.001310183317400515,
-0.058955539017915726,
0.0400993786752224,
0.009594344533979893,
-0.05145128071308136,
-0.07116318494081497,
-0.013186872005462646,
0.024584127590060234,
0.016737934201955795,
0.023522857576608658,
-0.02558121457695961,
0.019155101850628853,
0.014180414378643036,
-0.09240075945854187,
0.01628793217241764,
0.018640724942088127,
0.05442482605576515,
0.0533941425383091,
-0.04772559925913811,
0.021548815071582794,
0.062424298375844955,
-0.019788255915045738,
0.02302510291337967,
0.014111275784671307,
-0.00017672467220108956,
0.054815374314785004,
-0.04034750908613205,
0.014783147722482681,
0.013864034786820412,
0.006108080968260765,
0.01982405036687851,
-0.05269785225391388,
-0.012361626140773296,
-0.044575680047273636,
0.037312377244234085,
0.047488000243902206,
0.02203471213579178,
-0.07138682901859283,
0.03377503901720047,
-0.013970169238746166,
0.005400524940341711,
-0.010215070098638535,
-0.03885862976312637,
0.008465802296996117,
-0.05699677765369415,
-0.028357503935694695,
0.019995102658867836,
-0.023749595507979393,
0.028849491849541664,
0.03226073086261749,
-0.011587572284042835,
-0.0345674529671669,
-0.0027002862188965082,
0.0022052933927625418,
0.0420207753777504,
0.0040842765010893345,
0.08679209649562836,
-0.03348839655518532,
0.028904691338539124,
-0.016928665339946747,
-0.01683935523033142,
0.02838738076388836,
-0.0024573560804128647,
-0.044455137103796005,
0.08315384387969971,
-0.01912854239344597,
0.026021074503660202,
-0.04785310849547386,
-0.01136796921491623,
0.052603065967559814,
-0.023031072691082954,
0.002824306720867753,
-0.016383111476898193,
-0.03270288184285164,
-0.011276138946413994,
-0.03188853710889816,
-0.05990614369511604,
0.005690063815563917,
0.016340216621756554,
-0.03692139312624931,
-0.03451673686504364,
0.017557255923748016,
0.006054989993572235,
0.004095791839063168,
0.028210807591676712,
0.02277727797627449,
-0.024883631616830826,
0.018245777115225792,
0.01744883693754673,
0.01008859183639288,
0.026253966614603996,
0.04374966770410538,
0.008329863660037518,
0.014642826281487942,
-0.04933400824666023,
0.010653833858668804,
-0.023489762097597122,
0.014051365666091442,
0.015792241320014,
-0.035093940794467926,
-0.002780626993626356,
0.04026874527335167,
-0.0012980283936485648,
-0.07632972300052643,
-0.05468054115772247,
-0.01927240751683712,
-0.017641639336943626,
-0.04524139687418938,
0.0752694383263588,
-0.02407236397266388,
-0.061607006937265396,
0.06549406051635742,
-0.03373684361577034,
-0.030981574207544327,
-0.003136754035949707,
-0.005855804309248924,
-0.04519065096974373,
0.014084769412875175,
-0.020615292713046074,
-0.007179963402450085,
0.008165951818227768,
-0.003834647359326482,
-0.0017105318838730454,
0.01101719681173563,
-0.07846683263778687,
-0.048025887459516525,
0.040845710784196854,
-0.04370754957199097,
-0.05937656760215759,
0.009246998466551304,
-0.03216755390167236,
-0.031461842358112335,
0.018772607669234276,
-0.005890047177672386,
0.04981754720211029,
0.004691652487963438,
-0.011943811550736427,
0.04913274571299553,
0.017267342656850815,
-0.0194000992923975,
-0.015173080377280712,
-0.030317094177007675,
0.002049094531685114,
0.039881475269794464,
0.07546776533126831,
-0.016242489218711853,
0.07584550976753235,
-0.022741958498954773,
-0.009984542615711689,
-0.008682451210916042,
0.023784201592206955,
0.04231608659029007,
0.019504256546497345,
-0.004882954992353916,
-0.0065916008315980434,
-0.008574876002967358,
-0.023338407278060913,
-0.00302764680236578,
-0.01684262417256832,
-0.005729815922677517,
-0.07105029374361038,
-0.06558051705360413,
0.006870284676551819,
-0.03962956368923187,
-0.045357007533311844,
-0.0652349442243576,
0.004742161836475134,
0.060645103454589844,
0.02106466330587864,
-0.02931443601846695,
-0.04231087863445282,
0.05086816847324371,
-0.009205489419400692,
0.008788404986262321,
-0.04831796512007713,
-0.04799177125096321,
0.016739359125494957,
0.003122493391856551,
-0.05552026256918907,
-0.018886420875787735,
0.006982610560953617,
-0.0062447963282465935,
-0.030445491895079613,
-0.001097222906537354,
0.010148011147975922,
-0.07115302979946136,
0.07701265066862106,
0.0021503823809325695,
-0.014500796794891357,
-0.013666429556906223,
0.02500244788825512,
-0.040726155042648315,
-0.03710578754544258,
0.023473309352993965,
-0.03345152735710144,
0.03572390228509903,
0.023482831194996834,
0.0053485240787267685,
-0.043085843324661255,
0.01950375735759735,
-0.022671382874250412,
0.01604854129254818,
0.009772444143891335,
-0.0742790699005127,
0.09205038100481033,
0.05293085053563118,
0.05995100736618042,
-0.013197815045714378,
0.07304340600967407,
-0.030680492520332336,
-0.0077252560295164585,
0.02726033516228199,
-0.0007368533406406641,
-0.005323486402630806,
0.0005174559191800654,
-0.1048625111579895,
-0.015550422482192516,
-0.009551487863063812,
0.004488978534936905,
0.01279077585786581,
-0.010002716444432735,
0.009935198351740837,
-0.015183043666183949,
-0.0019080397905781865,
0.031771477311849594,
0.05164293199777603,
0.03316260874271393,
-0.031200017780065536,
-0.028262125328183174,
0.0643097460269928,
-0.04315200075507164,
-0.020511340349912643,
0.04063647985458374,
0.08629323542118073,
0.006040300242602825,
-0.02645966410636902,
0.007515372708439827,
0.04062534123659134,
0.010254236869513988,
-0.03785829618573189,
0.005179452709853649,
0.04847276955842972,
-0.058529436588287354,
0.03197228163480759,
-0.026700366288423538,
0.09651067107915878,
-0.0267581045627594,
0.024017006158828735,
0.03490393981337547,
-0.020792273804545403,
0.05094916373491287,
0.04716803878545761,
0.009919076226651669,
-0.004470225423574448,
0.06165243312716484,
-0.016360802575945854,
-0.023700203746557236,
0.018797487020492554,
0.05589606240391731,
0.017359577119350433,
-0.04539911821484566,
-0.03685949370265007,
0.03326469659805298,
0.014854923821985722,
0.0004474278830457479,
0.022934025153517723,
-0.06549765169620514,
-0.04076065123081207,
-0.025447117164731026,
0.015057921409606934,
0.08436611294746399,
0.013668723404407501,
0.08073674142360687,
-0.00000551731682207901,
0.008751800283789635,
-0.028078995645046234,
-0.0014728311216458678,
0.007152699865400791,
0.0030113968532532454,
-0.008384213782846928,
0.009875682182610035,
-0.0025583570823073387,
0.010325050912797451,
0.03300490602850914,
-0.009039985947310925,
0.017054403200745583,
-0.041801538318395615,
-0.006924728862941265,
-0.0186673104763031,
0.03220444545149803,
0.021164437755942345,
-0.017763027921319008,
-0.011622780933976173,
0.006086072884500027,
-0.035627853125333786,
0.05006242170929909,
-0.026455922052264214,
-0.022238800302147865,
0.03901653736829758,
0.034699779003858566,
0.05131669342517853,
0.05614423379302025,
0.005912306718528271,
-0.04425494000315666,
-0.02421911247074604,
-0.04115533083677292,
0.032430730760097504,
0.05872957035899162,
0.016374759376049042,
0.05508873611688614,
-0.007452371530234814,
-0.07288067042827606,
0.07952981442213058,
-0.07217129319906235,
0.007660915609449148,
0.019168520346283913,
0.010050727985799313,
0.06761950254440308,
0.006012996193021536,
-0.035552967339754105,
-0.012230933643877506,
-0.014455587603151798,
-0.0673336535692215,
0.017420757561922073,
0.00270049343816936,
-0.024595195427536964,
0.002533616265282035,
0.018973955884575844,
-0.016312940046191216,
-0.013228541240096092,
-0.028656529262661934,
0.015162058174610138,
0.011861980892717838,
0.06837394088506699,
0.0161303598433733,
0.021726828068494797,
-0.00588600430637598,
0.021838245913386345,
-0.013965150341391563,
0.035842861980199814,
0.011734952218830585,
-0.010971925221383572,
0.024829203262925148,
-0.0572153702378273,
-0.08663904666900635,
-0.016070466488599777,
-0.05688456818461418,
0.0316038504242897,
-0.01634913496673107,
0.07067165523767471,
-0.01307512167841196,
0.010118423961102962,
-0.015309588052332401,
-0.03168412670493126,
0.03776216134428978,
-0.015109160915017128,
-0.017289837822318077,
-0.03492521867156029,
0.050431881099939346,
0.005314066540449858,
-0.0010027639800682664,
-0.02394096925854683,
-0.054552894085645676,
0.01356582436710596,
-0.024670802056789398,
-0.05305411294102669,
-0.10260218381881714,
-0.06219712644815445,
0.0229974165558815,
-0.0036900851409882307,
0.07369651645421982,
-0.0445282980799675,
0.05554581061005592,
0.051659323275089264,
-0.014366292394697666,
0.041989877820014954,
0.006298391614109278,
-0.009686671197414398,
0.056117311120033264,
0.01802578568458557,
-0.02746490202844143,
0.024851053953170776,
-0.06925569474697113,
-0.034564949572086334,
-0.0016330719226971269,
-0.0398024246096611,
0.026438571512699127,
0.006796170026063919,
-0.03431836888194084,
-0.031112492084503174,
0.008837511762976646,
0.05278149992227554,
0.027223296463489532,
-0.07118446379899979,
0.015968183055520058,
-0.045263368636369705,
0.0777648538351059,
0.001621176372282207,
0.038375284522771835,
-0.05506465956568718,
-0.02445390820503235,
0.007534575182944536,
0.014141942374408245,
0.026937974616885185,
-0.0048925490118563175,
0.05588909983634949,
0.015336922369897366,
0.05141644924879074,
-0.039015114307403564,
0.004679264035075903,
0.009695574641227722,
0.05907386541366577,
-0.11424114555120468,
-0.022811872884631157,
0.02089637517929077,
0.07145442068576813,
0.009819813072681427,
-0.011457468383014202,
-0.025480056181550026,
-0.07925906032323837,
0.050368666648864746,
-0.030764924362301826,
-0.08577635884284973,
0.004291770979762077,
-0.012152791023254395,
-0.009959308430552483,
0.01147730927914381,
-0.021220533177256584,
-0.017921576276421547,
0.07262171804904938,
-0.0014635431580245495,
-0.028474407270550728,
0.015642372891306877,
-0.004212891682982445,
0.04038650169968605,
-0.010814173147082329,
-0.013688324950635433,
-0.052475713193416595,
-0.003339693183079362,
0.020920056849718094,
-0.03239920735359192,
-0.0013624595012515783,
0.0034096483141183853,
-0.033754345029592514,
0.04942696541547775,
0.027060868218541145,
-0.04422292485833168,
-0.010535347275435925,
-0.05353228747844696,
-0.01920292153954506,
-0.05999990552663803,
-0.03361520171165466,
-0.045281507074832916,
0.04423319175839424,
0.0069475057534873486,
0.021135766059160233,
-0.03986009955406189,
-0.04552806168794632,
0.001951247570104897,
0.0011424924014136195,
-0.009493366815149784,
0.016237715259194374,
0.020837869495153427,
-0.04893824830651283,
0.009759439155459404,
-0.025805780664086342,
0.046616893261671066,
-0.0185029786080122,
-0.016041532158851624,
-0.0022621736861765385,
0.041016437113285065,
-0.040589552372694016,
-0.029990730807185173,
0.024474889039993286,
0.022523216903209686,
0.0849417895078659,
0.027756011113524437,
-0.016054676845669746,
0.003287722822278738,
-0.04497787356376648,
0.04265005514025688,
0.040744978934526443,
-0.0248856358230114,
0.04129168018698692,
0.08072490990161896,
0.016152147203683853,
0.04329492896795273,
0.006564314942806959,
0.028891347348690033,
0.020356347784399986,
-0.0388806089758873,
-0.011691536754369736,
-0.02169644460082054,
0.04007815569639206,
-0.011637778952717781,
0.023949753493070602,
0.011766509152948856,
0.045163433998823166,
-0.0713505893945694,
0.004253344610333443,
-0.009178790263831615,
0.02621511183679104,
0.008864576928317547,
0.007602931931614876,
-0.00681570777669549,
0.003299848409369588,
-0.014867608435451984,
-0.04397546499967575,
0.004008127376437187,
-0.0671573355793953,
-0.014848263002932072,
-0.03182362765073776,
-0.016304295510053635,
0.011501149274408817,
0.08813954144716263,
0.007861942052841187,
0.022280190140008926,
0.006851634941995144,
0.006994387600570917,
0.008529211394488811,
0.009096110239624977,
0.07001238316297531,
-0.02723771706223488,
-0.027078064158558846,
-0.06471683830022812,
0.031190717592835426,
0.004198829177767038,
-0.009456248953938484,
-0.03611054643988609,
-0.04018454998731613,
-0.026631904765963554,
0.027533071115612984,
0.0816686600446701,
0.007914518937468529,
-0.07020996510982513,
0.013524535112082958,
0.00012463518942240626,
0.002206783974543214,
0.07391244173049927,
0.004417973104864359,
-0.04008374735713005,
0.0034830323420464993,
0.005545798689126968,
-0.0511687770485878,
0.02392767369747162,
0.08704573661088943,
0.018469873815774918,
-0.0014950912445783615,
-0.015417229384183884,
0.00032725048367865384,
-0.022638604044914246,
0.035150960087776184,
0.04514297842979431,
0.012429764494299889,
0.007988117635250092,
-0.025220071896910667,
-0.036898788064718246,
0.02147224359214306,
0.06739717721939087,
-0.033094339072704315,
-0.052113648504018784,
0.05497987940907478,
0.034792639315128326,
-0.012428819201886654,
-0.006616031751036644,
-0.02081882953643799,
0.03140339255332947,
-0.02917947620153427,
0.007459025364369154,
0.043671224266290665,
-0.01966177672147751,
0.013484731316566467,
0.04972866550087929,
-0.005311545915901661,
0.023440543562173843,
0.020540758967399597,
-0.01600170135498047,
0.00800467748194933,
-0.004644729197025299,
-0.0004757651186082512,
0.0018980744061991572,
-0.06598842144012451,
0.03295436501502991,
0.03563493862748146,
0.009901649318635464,
-0.03159263730049133,
0.00760123785585165,
0.02869732305407524,
-0.001950497622601688,
-0.018374349921941757,
0.0035035826731473207,
-0.015389171428978443,
-0.037045788019895554,
-0.08436974138021469,
-0.04165811091661453,
-0.015139064751565456,
-0.013648957945406437,
-0.007968954741954803,
0.038574881851673126,
-0.011149328202009201,
-0.04704207926988602,
-0.06704232841730118,
-0.016090411692857742,
0.05145009234547615,
-0.01676253415644169,
-0.04949324205517769,
-0.027079610154032707,
0.022832142189145088,
-0.032060202211141586,
-0.04433213546872139,
-0.006766690406948328,
-0.04409743472933769,
0.026780184358358383,
0.01807095669209957,
0.012060245499014854,
0.06251812726259232,
-0.020749801769852638,
-0.009505963884294033,
-0.005787752103060484,
-0.09674753993749619,
0.029887283220887184,
-0.012432577088475227,
0.02418053150177002,
0.0020655891858041286,
-0.009113019332289696,
0.04228946939110756,
-0.01822436787188053,
0.06446640193462372,
-0.014753417111933231,
-0.021126415580511093,
-0.0012881418224424124,
-0.022209348157048225,
0.014401747845113277,
-0.01895028166472912,
0.0019925443921238184,
0.029483705759048462,
-0.008579707704484463,
0.0160042904317379,
0.03646862879395485,
0.029124952852725983,
0.015372099354863167,
-0.06674165278673172,
-0.011367710307240486,
0.039578456431627274,
0.0546448677778244,
-0.008399555459618568,
0.019927825778722763,
0.034476593136787415,
-0.01630125381052494,
-0.010378933511674404,
-0.01634148880839348,
0.004463586024940014,
0.04923025518655777,
-0.013574355281889439,
-0.04504398629069328,
-0.011941708624362946,
-0.012252324260771275,
0.003254504408687353,
-0.013300509192049503,
-0.03355681523680687,
0.011177301406860352,
0.08067276328802109,
0.012543290853500366,
-0.019546084105968475,
0.04843101650476456,
0.015309611335396767,
-0.032696522772312164,
-0.030307738110423088,
0.04486327990889549,
0.02689851075410843,
0.03364947810769081,
0.011501943692564964,
0.006993904244154692,
-0.030982300639152527,
-0.011239278130233288,
-0.007962758652865887,
-0.0464770570397377,
-0.054629504680633545,
-0.0037946412339806557,
-0.036945100873708725,
0.024550560861825943,
0.04421521723270416,
-0.02066904492676258,
-0.04800239950418472,
-0.023173820227384567,
-0.09089911729097366,
0.014200305566191673,
0.011313183233141899,
-0.013771777041256428,
-0.07826437056064606,
-0.032720066606998444,
0.03154999390244484,
-0.055470552295446396,
0.016475899145007133,
0.01982412301003933,
-0.032298002392053604,
0.044209666550159454,
0.017892537638545036,
-0.054646242409944534,
0.036936357617378235,
-0.04574916139245033
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/18950/how-to-debunk-the-electric-universe">How to debunk ‘The Electric Universe’?</a> </p>
</blockquote>
<p>I am just wondering why there exists such a strong feeling within the physics community against theories such as Plasma Physics and <a href="http://www.holoscience.com/wp/" rel="nofollow">The Electric Universe</a>. </p>
<p>Every single atom is governed by electromagnetic forces, molecules are formed through chemical (electromagnetic) bonds, the universe is 99% plasma which is an great conductor of electricity, the sun is made of plasma and bombards the solar system with electromagnetic energy, centers of galaxies radiate enormous amount of electromagnetic energy, etc.</p>
<p>It is such a simple and elegant solution that truly explains everything in a rational way which, most importantly, can be <strong><em>experimentally verified</em></strong>. It can explain the true nature of mass and matter, gravity, how our sun works, how the universe works, weather systems, earthquakes, and many other phenomena that are mysteries to modern science.</p>
<p>So my question is: can someone explain to me why mainstream scientists are <strong>SO</strong> against these theories that they won't even consider them? I'm not saying they are 100% correct, but why not at least look at the theories and consider their implications?</p>
<p>Here are some articles I have found that explain many of the things I am talking about (no affiliation with me, I just think they well-written):</p>
<ul>
<li><a href="http://www.holoscience.com/wp/sciences-looming-tipping-point" rel="nofollow">http://www.holoscience.com/wp/sciences-looming-tipping-point</a></li>
<li><a href="http://www.holoscience.com/wp/a-real-theory-of-everything" rel="nofollow">http://www.holoscience.com/wp/a-real-theory-of-everything</a></li>
</ul>
<p>Can any real physicist explain to me why these theories could not be at least plausible? I am not trying to create controversy, but merely trying to understand why they seem so outrageous.</p> | g200 | [
0.042201802134513855,
0.0512528121471405,
0.0029051457531750202,
0.03808240219950676,
0.061176855117082596,
0.011825296096503735,
-0.03759945183992386,
0.051916468888521194,
0.006677042692899704,
-0.0426056943833828,
0.07947780936956406,
-0.052777599543333054,
0.03157666698098183,
0.06432759761810303,
-0.031614575535058975,
0.009375055320560932,
0.033833347260951996,
0.002544454298913479,
0.04444458708167076,
-0.005460180342197418,
-0.024111269041895866,
-0.026102513074874878,
0.03761281073093414,
-0.07143888622522354,
-0.12486254423856735,
-0.020580852404236794,
-0.010024216026067734,
-0.06619925796985626,
0.051924627274274826,
-0.033492881804704666,
-0.038578156381845474,
-0.01879836618900299,
0.04014179855585098,
-0.019847335293889046,
-0.005645371042191982,
-0.03287554904818535,
0.003625056240707636,
0.02750963345170021,
0.021723680198192596,
-0.005472750402987003,
-0.015604844316840172,
-0.0021466794423758984,
0.048797015100717545,
-0.036490004509687424,
-0.03816552087664604,
-0.015305877663195133,
-0.009636450558900833,
-0.006730647291988134,
0.023987768217921257,
-0.0661361962556839,
-0.006065231282263994,
-0.017742592841386795,
0.06427859514951706,
0.04744386300444603,
0.04193347692489624,
0.005195851903408766,
0.012432372197508812,
0.06769552081823349,
0.043216001242399216,
-0.06944949179887772,
-0.026682991534471512,
0.05156473442912102,
0.028412824496626854,
-0.007714458275586367,
0.012306295335292816,
-0.014486890286207199,
-0.061876799911260605,
-0.013948692008852959,
0.06472057104110718,
0.019187884405255318,
0.033915694802999496,
-0.04995298758149147,
-0.028850045055150986,
-0.03651262819766998,
-0.003609408624470234,
0.019038747996091843,
-0.003985793795436621,
0.033267442137002945,
0.06475028395652771,
0.0008475384674966335,
-0.015423759818077087,
0.018769804388284683,
-0.03952157124876976,
0.004333831835538149,
0.014741367660462856,
-0.08327362686395645,
-0.0017463768599554896,
0.0058110677637159824,
0.013593045063316822,
0.01533628348261118,
-0.02559843473136425,
0.015124772675335407,
0.08547201752662659,
-0.021416014060378075,
-0.018079940229654312,
-0.023599930107593536,
-0.024675093591213226,
0.03631136566400528,
0.007723875809460878,
0.031047796830534935,
-0.028947025537490845,
0.009533547796308994,
0.011664405465126038,
-0.0012724421685561538,
-0.024524929001927376,
-0.011771858669817448,
-0.00969772320240736,
0.05706419795751572,
0.007350515108555555,
-0.020379215478897095,
-0.04582435265183449,
0.039266712963581085,
-0.05160947144031525,
-0.0054440731182694435,
-0.044366154819726944,
-0.008852687664330006,
0.06472216546535492,
-0.04411369934678078,
-0.007969401776790619,
0.0289287231862545,
-0.02634076215326786,
0.021843520924448967,
0.001478533842600882,
0.0076199304312467575,
-0.04717852920293808,
-0.07438406348228455,
0.029964478686451912,
-0.0386374406516552,
-0.049969784915447235,
-0.039402857422828674,
-0.014841265976428986,
0.0019542952068150043,
-0.08695147186517715,
-0.0029249079525470734,
0.015216846019029617,
0.06211379915475845,
0.0530211441218853,
-0.008249298669397831,
0.021984420716762543,
-0.009416150860488415,
0.0404590480029583,
0.03217223659157753,
0.04965370520949364,
-0.04718782752752304,
-0.048164524137973785,
0.028930891305208206,
-0.00817243941128254,
0.002525283955037594,
0.05941624939441681,
-0.012604597955942154,
-0.011989359743893147,
0.06139045208692551,
0.012886153534054756,
-0.0414775088429451,
-0.05727522075176239,
0.01096648070961237,
0.03880566358566284,
-0.0176834873855114,
-0.0020919109228998423,
0.009737257845699787,
0.03144481033086777,
-0.003868725383654237,
-0.02947283536195755,
-0.03077019192278385,
0.007085494231432676,
0.04310015216469765,
0.004601901862770319,
-0.037600934505462646,
0.012941337190568447,
0.00899847224354744,
-0.09746991097927094,
0.020712995901703835,
0.03477659821510315,
0.07423935830593109,
0.04384410381317139,
0.004802389536052942,
0.04106324166059494,
-0.07330811768770218,
-0.014500985853374004,
0.0011931261979043484,
-0.016033604741096497,
-0.0009349333704449236,
0.047708746045827866,
0.0299774669110775,
-0.025198156014084816,
0.032985009253025055,
-0.035057563334703445,
0.024481600150465965,
0.001014513080008328,
0.0129762664437294,
0.006072848569601774,
-0.035249169915914536,
-0.017820511013269424,
-0.007711971178650856,
0.03793167322874069,
-0.010052306577563286,
-0.03291398659348488,
0.016223063692450523,
-0.05008084699511528,
-0.030515728518366814,
-0.008168812841176987,
0.02058105170726776,
-0.005988890305161476,
-0.010168314911425114,
-0.0005116032552905381,
-0.00980285182595253,
0.007829511538147926,
-0.011075908318161964,
0.01586328074336052,
0.05060611665248871,
0.025332488119602203,
0.01575009897351265,
0.020919356495141983,
0.05867229029536247,
-0.008149013854563236,
-0.04780694097280502,
-0.035155393183231354,
-0.04970209673047066,
-0.06287845224142075,
0.057622142136096954,
0.002536746906116605,
-0.01706639863550663,
-0.0022858937736600637,
0.02326856181025505,
-0.01900218240916729,
0.010187161155045033,
-0.043970976024866104,
-0.03309803083539009,
-0.01859953999519348,
-0.04574953019618988,
-0.023739181458950043,
0.006419017910957336,
0.0017584353918209672,
-0.030017876997590065,
0.0237472802400589,
-0.0019709004554897547,
0.002243299735710025,
-0.06306547671556473,
-0.009748184122145176,
0.0168805830180645,
-0.010747048072516918,
-0.012986447662115097,
-0.01435917429625988,
0.01440402027219534,
0.03775034099817276,
-0.08713948726654053,
0.06590438634157181,
-0.08871019631624222,
-0.014701133593916893,
0.034392401576042175,
0.05032389238476753,
0.007747221272438765,
-0.018471598625183105,
-0.008472570218145847,
0.019645554944872856,
-0.018291985616087914,
0.018243299797177315,
0.07859781384468079,
0.018551189452409744,
0.004021102096885443,
0.03251828998327255,
-0.011404641903936863,
0.01632484793663025,
0.016638508066534996,
-0.06687097251415253,
0.04256623610854149,
-0.08687540888786316,
-0.018820079043507576,
-0.0236195158213377,
-0.040827978402376175,
0.04654764384031296,
0.03313293680548668,
-0.03146317973732948,
0.015515642240643501,
0.0038606864400207996,
0.05343690887093544,
-0.008621779270470142,
-0.014203306287527084,
0.10533326864242554,
-0.00968641322106123,
0.004398065153509378,
0.018814247101545334,
-0.06657440215349197,
-0.016532905399799347,
0.016926389187574387,
-0.0446377657353878,
-0.05641498789191246,
-0.04744948819279671,
-0.011568688787519932,
-0.018127737566828728,
-0.006169842556118965,
0.028124544769525528,
-0.022457605227828026,
0.026218736544251442,
-0.06489204615354538,
0.03297692537307739,
-0.038835179060697556,
-0.03916933014988899,
-0.10345032066106796,
-0.04863275960087776,
0.0008791888249106705,
0.03925667703151703,
0.02392551116645336,
0.05128850042819977,
-0.008767112158238888,
0.07515029609203339,
-0.012976952828466892,
0.005149425473064184,
-0.012432741932570934,
-0.01032303273677826,
0.04839319735765457,
0.0685996264219284,
0.05337412655353546,
0.021415911614894867,
0.011175515130162239,
0.06055780127644539,
-0.012642561458051205,
0.02550850436091423,
0.05833052471280098,
-0.018423641100525856,
-0.03123200125992298,
-0.009322741068899632,
-0.014929299242794514,
0.007861844263970852,
0.05400547757744789,
0.0019933588337153196,
-0.028796140104532242,
-0.030698049813508987,
-0.06316987425088882,
-0.018692072480916977,
0.007564368192106485,
0.00027472752844914794,
0.00492853531613946,
0.0009854254312813282,
-0.08599197119474411,
-0.023161549121141434,
0.01608116552233696,
0.03366059064865112,
0.07029666006565094,
-0.06509345024824142,
-0.05763857811689377,
-0.012311945669353008,
-0.029178040102124214,
0.008959720842540264,
-0.011049853637814522,
0.050469424575567245,
0.016385285183787346,
-0.009199305437505245,
0.009427929297089577,
-0.03977586701512337,
0.054385434836149216,
0.03835557401180267,
-0.009412969462573528,
-0.000006774729172320804,
-0.026337845250964165,
-0.0288965106010437,
0.019623680040240288,
0.039489567279815674,
0.058349840342998505,
0.01099365297704935,
0.02139918878674507,
0.04560091346502304,
0.009815319441258907,
-0.04545260965824127,
-0.012662497349083424,
0.05898892134428024,
0.0186795461922884,
0.03647163137793541,
-0.039350517094135284,
-0.05119017884135246,
0.02048179693520069,
0.014758357778191566,
-0.04258372262120247,
0.011563832871615887,
0.02791784703731537,
-0.04178668186068535,
0.030445100739598274,
0.054477669298648834,
-0.013946201652288437,
0.02267911657691002,
0.06815040111541748,
0.09157262742519379,
0.00956687331199646,
0.05057801678776741,
0.029034757986664772,
-0.028942296281456947,
-0.061408914625644684,
-0.000339209072990343,
-0.03591292351484299,
-0.060778696089982986,
0.018100891262292862,
0.00997272040694952,
0.012920527718961239,
-0.004190061241388321,
0.009628736414015293,
-0.054277773946523666,
0.006089231930673122,
-0.02612362615764141,
0.02847994863986969,
0.006326714996248484,
0.06133480742573738,
0.007771354168653488,
0.002319286111742258,
-0.021167395636439323,
-0.006544900126755238,
0.014234020374715328,
-0.04496953636407852,
-0.041393015533685684,
-0.02305176667869091,
-0.051711998879909515,
0.03597792237997055,
-0.0033583531621843576,
0.010562741197645664,
-0.04327317699790001,
0.023037824779748917,
0.007182278670370579,
0.00046152836875990033,
0.007271341513842344,
0.0708237737417221,
-0.02771761082112789,
0.036488402634859085,
0.03130173683166504,
-0.009470319375395775,
-0.030968545004725456,
-0.02577967382967472,
0.0685615986585617,
0.0006292254547588527,
0.011500474996864796,
0.006559231784194708,
0.025175483897328377,
0.06682305783033371,
0.012407250702381134,
-0.006733342539519072,
-0.00042355855111964047,
-0.011839509941637516,
0.017113756388425827,
-0.06663962453603745,
0.12240619957447052,
0.003281516255810857,
0.022873276844620705,
0.09200675785541534,
-0.011297640390694141,
0.020596174523234367,
0.01931767351925373,
-0.04120828956365585,
0.03210576996207237,
-0.04606606438755989,
0.02161613292992115,
-0.046478647738695145,
-0.038041435182094574,
-0.029171930626034737,
0.012453652918338776,
-0.022401046007871628,
-0.011068816296756268,
-0.05595894530415535,
0.016835147514939308,
0.003972966689616442,
0.045950643718242645,
-0.006184902507811785,
0.048545002937316895,
-0.09142427891492844,
-0.011406859382987022,
0.06715787202119827,
0.04016198217868805,
0.07930009812116623,
0.030614087358117104,
-0.04255681112408638,
-0.05230085924267769,
-0.02730310894548893,
-0.05997604876756668,
-0.023318398743867874,
0.035249315202236176,
-0.0029689616058021784,
-0.0029251258820295334,
-0.007049342151731253,
-0.028419632464647293,
0.04440877214074135,
-0.03437258303165436,
-0.07869989424943924,
-0.012224134989082813,
0.023968541994690895,
0.04688674956560135,
0.02034711465239525,
0.022884715348482132,
-0.02192622795701027,
0.006600165739655495,
-0.037588514387607574,
0.02724945917725563,
-0.053836870938539505,
-0.03214849904179573,
0.012187802232801914,
0.008829734288156033,
0.046588797122240067,
-0.002153926296159625,
-0.0610007606446743,
-0.00917280837893486,
-0.011101456359028816,
-0.01652533747255802,
-0.049576450139284134,
-0.030562978237867355,
-0.013611235655844212,
0.03553127124905586,
-0.003189344657585025,
-0.00772767374292016,
0.029508093371987343,
-0.00043113750871270895,
0.03078458271920681,
0.0033558649010956287,
0.0588613823056221,
-0.05235372856259346,
0.03626487776637077,
-0.014069649390876293,
-0.011737534776329994,
0.0557769313454628,
0.0496017262339592,
0.011977137997746468,
-0.07748106867074966,
-0.04064046964049339,
-0.009557492099702358,
-0.04656779766082764,
0.009716881439089775,
-0.008798975497484207,
0.06562881171703339,
-0.03100074827671051,
0.030455851927399635,
-0.022882986813783646,
-0.05360863730311394,
0.00981428474187851,
0.02635258436203003,
0.015304293483495712,
-0.012610293924808502,
0.03566434234380722,
0.03576727211475372,
0.04793013632297516,
0.00911800004541874,
0.010556621477007866,
-0.002820784691721201,
-0.024579409509897232,
-0.009857278317213058,
0.008336048573255539,
0.032663196325302124,
0.07538817822933197,
0.03502161428332329,
0.006154525559395552,
-0.04413073509931564,
0.03864924982190132,
-0.008744299411773682,
0.03330080583691597,
0.07883662730455399,
0.00700041837990284,
-0.01795991137623787,
-0.012386252172291279,
-0.0005267088417895138,
-0.05092516168951988,
-0.0026172928046435118,
0.0010323233436793089,
0.04610472917556763,
-0.027216678485274315,
-0.03389602154493332,
-0.012249689549207687,
-0.040664076805114746,
-0.020205998793244362,
-0.0001487341069150716,
0.027956252917647362,
0.02056843228638172,
0.023451510816812515,
0.0033179561141878366,
-0.0493713840842247,
-0.01086738333106041,
0.0191354863345623,
0.014140045270323753,
0.025654995813965797,
0.016088129952549934,
-0.022674569860100746,
0.00307587836869061,
0.003889532992616296,
-0.018271781504154205,
0.02480291947722435,
-0.038332875818014145,
-0.03648229315876961,
-0.020723586902022362,
-0.018192101269960403,
0.05797630921006203,
-0.07246442139148712,
0.018293892964720726,
-0.007396498695015907,
-0.05461013689637184,
0.00019302441796753556,
0.02414149045944214,
-0.04461251199245453,
-0.04118829220533371,
0.0026967967860400677,
-0.00624056113883853,
-0.050753332674503326,
-0.04845399782061577,
-0.057158444076776505,
0.05259580537676811,
-0.02206665277481079,
-0.04300766810774803,
0.02655516378581524,
-0.005700891371816397,
-0.055558592081069946,
-0.004214021842926741,
0.054734185338020325,
0.057367295026779175,
-0.0207657553255558,
0.01697359047830105,
-0.014919464476406574,
0.013008331879973412,
0.0008764100493863225,
0.016055533662438393,
0.006927867885679007,
-0.008589648641645908,
-0.037876542657613754,
-0.05768311396241188,
-0.049168143421411514,
-0.03528882563114166,
-0.010843326337635517,
0.011983059346675873,
0.006105225067585707,
-0.03695746883749962,
-0.007209487725049257,
0.03923841565847397,
0.002354132477194071,
0.042732082307338715,
0.005475834012031555,
-0.016684547066688538,
0.025455165654420853,
0.059873297810554504,
0.009368359111249447,
-0.014691350981593132,
0.015722548589110374,
0.01870645210146904,
0.047798432409763336,
-0.03191184625029564,
0.037939444184303284,
-0.012558107264339924,
-0.022874394431710243,
-0.006703613325953484,
-0.045628275722265244,
-0.05495108664035797,
0.030122067779302597,
0.10274150222539902,
0.017786793410778046,
-0.0493885837495327,
-0.05250227823853493,
-0.011775534600019455,
0.0008010281599126756,
-0.05437710881233215,
0.009748131968080997,
-0.019384240731596947,
-0.07379904389381409,
-0.021749459207057953,
0.01502340566366911,
-0.018315760418772697,
0.07817316800355911,
0.007492654025554657,
0.009323975071310997,
0.007147709373384714,
-0.04533758759498596,
-0.02257516421377659,
-0.004659016150981188,
0.017002703621983528,
-0.03191608190536499,
0.024140913039445877,
0.009593134745955467,
0.014650058932602406,
-0.06631464511156082,
-0.03818465769290924,
-0.0023017222993075848,
-0.006278356071561575,
-0.034728121012449265,
-0.05060112476348877,
-0.025574278086423874,
0.04306691884994507,
-0.08080913126468658,
0.034465864300727844,
0.0018678568303585052,
0.039930157363414764,
-0.029875418171286583,
-0.023439321666955948,
0.0754803940653801,
0.022136777639389038,
0.003832321846857667,
-0.03672408685088158,
0.03569177910685539,
0.02893024869263172,
0.04357365891337395,
-0.021658146753907204,
-0.021679453551769257,
0.02633790485560894,
-0.0035417021717876196,
0.014868379570543766,
-0.008832339197397232,
0.004378060810267925,
0.06235764920711517,
-0.009613722562789917,
-0.026938965544104576,
0.05144853517413139,
-0.03206779807806015,
-0.015962546691298485,
-0.042545393109321594,
-0.017322441563010216,
0.01825743354856968,
0.017262961715459824,
0.05118037387728691,
-0.00007947912672534585,
0.017533475533127785,
-0.03920649364590645,
0.031577643007040024,
0.030540265142917633,
0.0206492617726326,
-0.007556444965302944,
-0.013765878975391388,
0.032933447510004044,
0.01218404434621334,
-0.002962687285616994,
-0.0010524269891902804,
0.04851212352514267,
-0.014979369938373566,
-0.023205388337373734,
-0.03410889953374863,
-0.0011246928479522467,
-0.005750081967562437,
0.027053726837038994,
0.029042227193713188,
0.034091971814632416,
-0.04536169767379761,
-0.044659294188022614,
0.0030218884348869324,
0.013421275652945042,
0.021940574049949646,
0.02940356358885765,
0.013919691555202007,
-0.0659751296043396,
0.0015335180796682835,
-0.023777617141604424,
-0.01039391104131937,
-0.020556561648845673,
-0.021754000335931778,
-0.006258116569370031,
-0.03410947695374489,
-0.03552935644984245,
0.047569435089826584,
-0.004468375816941261,
-0.037664756178855896,
-0.07067936658859253,
0.05002816393971443,
0.024424131959676743,
-0.0030398243106901646,
0.048602573573589325,
0.0021519921720027924,
-0.026092177256941795,
0.02406807616353035,
0.03999432921409607,
-0.04356031492352486,
-0.021037420257925987,
0.027105344459414482,
0.030516402795910835,
0.07534127682447433,
0.028483953326940536,
-0.019729584455490112,
0.03249499946832657,
-0.01915295608341694,
0.0073861354030668736,
-0.004548810422420502,
-0.05004560574889183,
0.0225683581084013
] |
<p>Although the electromagnetic wave is made op of both electric and magnetic fields the electric field contributes much in vision and is thus, called the light vector. But, why is it that the electric field has a major role? </p> | g5535 | [
0.0056739691644907,
0.03921370208263397,
0.014980673789978027,
0.02413938380777836,
0.06188863515853882,
0.037966083735227585,
0.06605768203735352,
0.032998956739902496,
0.021258510649204254,
-0.03594529256224632,
0.029778286814689636,
-0.02300800196826458,
0.04681454598903656,
0.06266086548566818,
-0.007166119292378426,
0.018840817734599113,
-0.01043786946684122,
-0.0188588984310627,
0.026175102218985558,
-0.018864963203668594,
-0.0034763633739203215,
0.023082185536623,
0.0498434342443943,
-0.017660638317465782,
-0.06086844205856323,
0.05108330026268959,
0.0973084419965744,
-0.05911673232913017,
-0.013862544670701027,
-0.002998778596520424,
0.08333871513605118,
0.018768958747386932,
0.03625961020588875,
-0.01825486682355404,
0.006088820286095142,
-0.013062522746622562,
0.03860966116189957,
0.11171139776706696,
-0.011137066408991814,
0.03650371730327606,
-0.020555594936013222,
0.019004251807928085,
0.0027303295210003853,
-0.015010307542979717,
-0.0019080655183643103,
-0.03175585716962814,
-0.03051883727312088,
-0.01125177089124918,
-0.07431276142597198,
-0.05423679202795029,
0.0017559240804985166,
-0.039356864988803864,
0.04775185137987137,
0.031334321945905685,
0.10482914745807648,
0.012686860747635365,
-0.014322197064757347,
0.017725495621562004,
0.02728976309299469,
0.02776613086462021,
0.03516780585050583,
-0.007796960882842541,
0.0016854340210556984,
0.051555655896663666,
-0.04317466542124748,
-0.06580248475074768,
-0.03168080002069473,
-0.030304480344057083,
0.012650732882320881,
0.04094276204705238,
-0.02240881510078907,
-0.04440104961395264,
-0.04325905442237854,
0.034922365099191666,
0.027347443625330925,
-0.030852630734443665,
0.028734533116221428,
0.0350337028503418,
0.005915203597396612,
0.005208655260503292,
0.034056685864925385,
-0.02126750722527504,
-0.08850684762001038,
0.05237652733922005,
0.05465032905340195,
-0.0067863441072404385,
-0.0029647559858858585,
-0.03139278292655945,
0.010528575628995895,
-0.007186136208474636,
0.02888227067887783,
0.07099168002605438,
0.07974870502948761,
0.050880204886198044,
-0.03499383106827736,
-0.022487888112664223,
0.025953421369194984,
0.009964823722839355,
0.0007930004503577948,
0.06744707375764847,
-0.026828691363334656,
-0.024517223238945007,
-0.00553814647719264,
0.01538965106010437,
0.05612272769212723,
0.024763869121670723,
0.004967828281223774,
0.0038274272810667753,
-0.04378974810242653,
0.026390068233013153,
-0.04532135650515556,
-0.057273492217063904,
-0.050212517380714417,
0.01790606416761875,
-0.03331905975937843,
-0.024499833583831787,
0.1038748100399971,
-0.04837675765156746,
-0.028529446572065353,
0.09398755431175232,
-0.01474999450147152,
-0.03229599446058273,
-0.014920242130756378,
0.051202960312366486,
0.032204993069171906,
0.049264490604400635,
0.029773341491818428,
-0.003475982928648591,
-0.006132962182164192,
-0.040923744440078735,
0.04323990270495415,
0.033529769629240036,
0.03863628953695297,
-0.03816843777894974,
0.018329212442040443,
0.013592466711997986,
0.03452727198600769,
-0.022598493844270706,
0.027169862762093544,
0.017925234511494637,
0.0017532117199152708,
0.017709607258439064,
0.02926630713045597,
-0.04796495661139488,
-0.011655849404633045,
0.04551394283771515,
0.014877128414809704,
-0.013904156163334846,
0.06826697289943695,
-0.040063031017780304,
-0.01327854860574007,
0.03843732923269272,
-0.05092284455895424,
-0.023781592026352882,
0.021843677386641502,
-0.0636308491230011,
0.035481370985507965,
-0.03615644574165344,
-0.04498428851366043,
0.004211691208183765,
0.07025080919265747,
0.03423919156193733,
-0.0029684093315154314,
-0.007592147681862116,
0.022199789062142372,
-0.05205046758055687,
0.060793325304985046,
-0.07627206295728683,
0.009743561036884785,
-0.05986938998103142,
-0.01161084696650505,
-0.008883248083293438,
0.04334762319922447,
0.053286146372556686,
0.045126814395189285,
0.05833956226706505,
-0.022750454023480415,
-0.037985485047101974,
0.02933790534734726,
0.03884020075201988,
-0.05512244999408722,
0.006393351126462221,
-0.020602505654096603,
-0.03481612354516983,
-0.029922770336270332,
-0.025956476107239723,
-0.029306184500455856,
0.006978198420256376,
-0.09114029258489609,
0.01946255937218666,
0.0023277238942682743,
0.012042292393743992,
0.016106490045785904,
0.06324973702430725,
0.005622256081551313,
0.023947076871991158,
-0.05651441961526871,
0.010709953494369984,
-0.07678727805614471,
0.013862676918506622,
-0.07502692192792892,
-0.04021315276622772,
-0.024111824110150337,
0.022981300950050354,
-0.03184878081083298,
0.010218673385679722,
-0.033779580146074295,
-0.019872523844242096,
0.011926272884011269,
0.021157683804631233,
0.03005150519311428,
-0.022050123661756516,
0.034021470695734024,
-0.005199473816901445,
-0.01756521873176098,
-0.007791904732584953,
-0.0077062807977199554,
-0.007841906510293484,
-0.04425642639398575,
0.03783687949180603,
-0.047887273132801056,
0.007908009923994541,
0.06692278385162354,
-0.01651601493358612,
-0.07029429078102112,
0.023585516959428787,
0.00909592118114233,
-0.028319595381617546,
-0.0179547518491745,
-0.018491998314857483,
-0.007695256732404232,
0.04537370800971985,
0.041394516825675964,
0.07725681364536285,
0.009754340164363384,
-0.01632051169872284,
0.00885540246963501,
0.03170553222298622,
0.01270848885178566,
0.006581662688404322,
0.019870169460773468,
0.007502601481974125,
0.08060801774263382,
-0.02182953804731369,
-0.024286728352308273,
-0.01432537380605936,
0.0724356397986412,
-0.022312667220830917,
-0.015873273834586143,
0.07112765312194824,
0.007710746023803949,
-0.04249360039830208,
0.0020564203150570393,
-0.004243690520524979,
0.059718500822782516,
-0.010746135376393795,
0.015927528962492943,
0.03026784397661686,
-0.02010125108063221,
0.02672424167394638,
-0.014667334035038948,
-0.014125361107289791,
-0.021712271496653557,
-0.024545885622501373,
-0.032270923256874084,
0.04690669849514961,
0.003198317950591445,
0.0761372298002243,
0.03482518345117569,
-0.030486730858683586,
-0.026400545611977577,
0.04762982949614525,
-0.007227087393403053,
-0.05528413876891136,
-0.002645832719281316,
-0.039075832813978195,
-0.04409557208418846,
-0.03886131942272186,
0.047805242240428925,
-0.026849649846553802,
-0.008549640886485577,
0.004284568130970001,
-0.03687109053134918,
-0.02653319574892521,
0.03241220489144325,
-0.037924688309431076,
0.015146529302001,
-0.0003001919249072671,
-0.03551696613430977,
-0.02141764760017395,
-0.09133881330490112,
0.04391888529062271,
-0.025508606806397438,
-0.06901479512453079,
-0.02333577536046505,
-0.03689054772257805,
0.06402570754289627,
0.0032993718050420284,
-0.007635575253516436,
-0.0005022979457862675,
0.021469181403517723,
0.030453264713287354,
0.00642671063542366,
-0.006355001125484705,
0.037701573222875595,
0.004435104783624411,
-0.028265349566936493,
-0.053910862654447556,
-0.015784330666065216,
0.01978301629424095,
0.049249254167079926,
0.005939887370914221,
-0.021992262452840805,
0.007838340476155281,
-0.07224210351705551,
-0.008665218949317932,
-0.02334410510957241,
0.007723377551883459,
0.0255514495074749,
0.005299912299960852,
-0.03911826014518738,
-0.014435950666666031,
-0.03693530336022377,
-0.020327597856521606,
0.051190800964832306,
0.0044046491384506226,
0.002690086839720607,
0.005103129893541336,
0.029560713097453117,
0.01938985101878643,
-0.047205761075019836,
-0.02113310620188713,
-0.03294672816991806,
0.0311567485332489,
-0.012983007356524467,
0.024779187515378,
-0.015407000668346882,
0.0055088563822209835,
-0.007848303765058517,
-0.058159518986940384,
0.026800425723195076,
0.001714586978778243,
-0.10046476125717163,
-0.044948212802410126,
-0.008734248578548431,
-0.04399421438574791,
-0.02162260003387928,
-0.035520099103450775,
0.013804668560624123,
-0.022414738312363625,
-0.01775117963552475,
0.023712657392024994,
-0.00026187370531260967,
0.02307320199906826,
-0.03784305974841118,
-0.017032165080308914,
0.017877496778964996,
0.00028224303969182074,
0.025077717378735542,
-0.035832226276397705,
0.027285343036055565,
0.020641474053263664,
-0.00854487344622612,
-0.028617188334465027,
-0.0451207272708416,
-0.0053383116610348225,
0.01652710884809494,
0.021535532549023628,
-0.04616044461727142,
-0.011787309311330318,
-0.014078566804528236,
-0.026507284492254257,
-0.0317157544195652,
0.045056480914354324,
-0.024943724274635315,
-0.02110927179455757,
0.008060403168201447,
-0.015414922498166561,
-0.05844317376613617,
-0.044465698301792145,
0.04748745262622833,
0.07735379040241241,
0.04597838222980499,
0.027597885578870773,
0.02953300252556801,
-0.06512570381164551,
0.013061617501080036,
0.012885501608252525,
0.016617102548480034,
0.01585422083735466,
0.007758196443319321,
0.029265785589814186,
-0.010393219068646431,
-0.025896655395627022,
0.014849378727376461,
0.017796125262975693,
0.024233315140008926,
-0.016294021159410477,
-0.004431945271790028,
0.012335466220974922,
0.05941135808825493,
0.00009010077337734401,
0.0510188527405262,
0.01942603290081024,
0.010037052445113659,
-0.014131600968539715,
0.04473969340324402,
-0.01339884102344513,
0.023449262604117393,
0.017852166667580605,
-0.009032678790390491,
0.010586533695459366,
-0.01062791422009468,
-0.06791024655103683,
0.035881828516721725,
0.05650836229324341,
0.008735920302569866,
0.011826313100755215,
0.0615023598074913,
-0.013570756651461124,
0.06576090306043625,
0.02852894738316536,
0.004607693292200565,
-0.031450994312763214,
0.00893948320299387,
0.06381940096616745,
0.03821574151515961,
-0.022339196875691414,
-0.009363708086311817,
-0.042242273688316345,
-0.01619851030409336,
0.08003713190555573,
-0.034500885754823685,
0.0076006329618394375,
-0.03148145601153374,
0.05525992810726166,
-0.06755350530147552,
0.027064651250839233,
0.025337914004921913,
0.01842406950891018,
0.04366840794682503,
-0.00221923366189003,
-0.029770469292998314,
-0.04351399466395378,
-0.0005527486209757626,
0.01003473810851574,
0.032563045620918274,
0.009894683957099915,
-0.05385139212012291,
0.0006844981689937413,
0.034194253385066986,
0.04650197550654411,
-0.005678398068994284,
0.030552616342902184,
-0.006674628704786301,
0.021380743011832237,
-0.028588607907295227,
-0.037507008761167526,
0.03626751899719238,
0.02503369189798832,
-0.04100610315799713,
0.018026020377874374,
-0.04158589988946915,
0.03291759267449379,
0.1049436405301094,
-0.0010511442087590694,
-0.06186889484524727,
-0.04509396106004715,
-0.03436482325196266,
-0.03159520775079727,
0.002529503544792533,
0.01730535179376602,
-0.03138121962547302,
-0.015544689260423183,
0.02186330407857895,
-0.0105370432138443,
-0.030878175050020218,
-0.0023665737826377153,
-0.009434612467885017,
-0.03917929157614708,
-0.04218845069408417,
-0.06161250174045563,
0.02358764410018921,
0.010429320856928825,
-0.019676918163895607,
0.008697194047272205,
-0.002668219618499279,
0.016253221780061722,
-0.05030098557472229,
-0.07511050254106522,
0.0018859688425436616,
0.02635025419294834,
0.006532554514706135,
-0.010250885970890522,
-0.00636808667331934,
-0.022827675566077232,
-0.006901546381413937,
0.002426035003736615,
-0.0010675641242414713,
-0.03527955338358879,
-0.017530212178826332,
-0.009856649674475193,
-0.06726936995983124,
-0.07762603461742401,
-0.028979411348700523,
0.016785601153969765,
0.004756915383040905,
-0.03955329209566116,
0.027075648307800293,
0.022581586614251137,
-0.002614089287817478,
-0.09681634604930878,
0.018791625276207924,
0.017727471888065338,
0.043871499598026276,
-0.049540068954229355,
-0.0040185414254665375,
0.011348973959684372,
0.011637543328106403,
0.00024005031445994973,
0.052562613040208817,
-0.015409893356263638,
0.019484544172883034,
-0.049033332616090775,
0.004595128353685141,
0.000919755722861737,
-0.01864868588745594,
-0.0029012763407081366,
0.09222724288702011,
-0.01341312751173973,
0.006604994647204876,
0.03671271726489067,
0.026483619585633278,
0.029936110600829124,
0.013669025152921677,
-0.051824960857629776,
0.01972089149057865,
-0.004626888781785965,
0.013886948116123676,
0.0005342537187971175,
-0.02185717597603798,
-0.027520522475242615,
0.018757585436105728,
0.057850901037454605,
0.09414125978946686,
0.04664808139204979,
0.041578151285648346,
-0.007133565377444029,
-0.03194227069616318,
-0.03654281422495842,
-0.027041561901569366,
0.04088415205478668,
0.017874253913760185,
-0.029396409168839455,
-0.06855901330709457,
-0.004685410764068365,
-0.021727481856942177,
-0.01686192862689495,
-0.030742859467864037,
-0.022969936951994896,
0.07657463848590851,
0.028619397431612015,
-0.05169830098748207,
-0.024443069472908974,
-0.03492899611592293,
-0.016211025416851044,
0.015225736424326897,
0.023759806528687477,
0.00973154790699482,
-0.035096775740385056,
-0.047356948256492615,
-0.02054276317358017,
0.00030326336855068803,
0.04349792003631592,
0.006224352866411209,
0.04766495153307915,
0.0243076141923666,
-0.024417605251073837,
-0.1159944012761116,
-0.04266883805394173,
0.028719071298837662,
0.013391706161201,
-0.028691275045275688,
-0.07485201209783554,
-0.027782626450061798,
-0.04861242324113846,
-0.02856588549911976,
0.011304383166134357,
0.05487561970949173,
-0.001841050456278026,
-0.03594205155968666,
0.013205272145569324,
-0.03128667548298836,
-0.015293415635824203,
-0.06001316010951996,
-0.04958639666438103,
-0.015342538245022297,
0.02523084543645382,
-0.010439296253025532,
0.012471090070903301,
0.020281018689274788,
-0.024108322337269783,
0.01107084285467863,
0.07241977751255035,
0.0655515193939209,
-0.007643574848771095,
-0.035043325275182724,
-0.05575323477387428,
0.021600021049380302,
0.027233699336647987,
-0.021283820271492004,
-0.008307165466248989,
-0.05960424989461899,
-0.01013762317597866,
-0.009829267859458923,
0.017169438302516937,
-0.04583954066038132,
-0.017283516004681587,
-0.052145540714263916,
0.01554525550454855,
-0.07792309671640396,
-0.04733800143003464,
-0.0032936271745711565,
0.05817536264657974,
-0.01120750978589058,
0.018880849704146385,
-0.07408900558948517,
-0.018222251906991005,
0.028483327478170395,
0.012691802345216274,
0.018732156604528427,
-0.007320537697523832,
0.022755922749638557,
0.08226761966943741,
0.01627349480986595,
-0.0580354742705822,
-0.0018958946457132697,
-0.054349206387996674,
0.03114326484501362,
0.004187765531241894,
-0.01932891085743904,
0.07425868511199951,
0.00540519505739212,
0.001353538827970624,
-0.024394961073994637,
0.023001959547400475,
-0.0003734349156729877,
-0.034262362867593765,
-0.03458830714225769,
-0.015071648173034191,
-0.012574371881783009,
0.03341333940625191,
0.015755310654640198,
-0.06534039974212646,
-0.012360898777842522,
0.0030315842013806105,
-0.02268887311220169,
0.028113320469856262,
-0.003881126642227173,
-0.049105431884527206,
-0.001056301174685359,
0.008697939105331898,
-0.038576625287532806,
0.03231404721736908,
0.014545847661793232,
-0.04705822095274925,
-0.0014974875375628471,
-0.05415164679288864,
0.0349397137761116,
0.028438761830329895,
-0.020659759640693665,
-0.009667514823377132,
0.005936731584370136,
-0.020941944792866707,
-0.027997596189379692,
-0.02573336847126484,
-0.013813809491693974,
0.001035414868965745,
-0.010060787200927734,
0.005649729631841183,
-0.049443356692790985,
0.06574393063783646,
0.007890923880040646,
-0.02918212115764618,
-0.006724037230014801,
-0.046929698437452316,
0.02074749581515789,
-0.024813372641801834,
0.029635123908519745,
-0.011964336037635803,
-0.022190572693943977,
0.004197785630822182,
-0.014934461563825607,
-0.009855926036834717,
0.00816977210342884,
0.00526898680254817,
0.009507833980023861,
0.04401927441358566,
0.05597490817308426,
0.032258085906505585,
-0.0479278564453125,
-0.04480181261897087,
0.01943596825003624,
0.017583653330802917,
0.035264626145362854,
0.05052221193909645,
0.027574697509407997,
0.022124897688627243,
-0.004560104105621576,
0.01941371150314808,
0.012089810334146023,
0.049033671617507935,
-0.003007738385349512,
0.039233628660440445,
-0.025550564751029015,
0.04588926210999489,
0.0032662861049175262,
0.07297159731388092,
-0.03020961582660675,
0.022341294214129448,
0.03957540914416313,
-0.027337944135069847,
-0.018906492739915848,
-0.016678232699632645,
-0.012288917787373066,
0.02192966267466545,
0.0361335389316082,
-0.07107733190059662,
0.07129571586847305,
-0.04075853154063225,
0.01917622610926628,
-0.038147296756505966,
-0.05312220752239227,
-0.028017384931445122,
-0.023360712453722954,
0.012825990095734596,
-0.019034354016184807,
0.009901096113026142,
0.06388559937477112,
0.017565105110406876,
0.027148593217134476,
-0.06867747753858566,
-0.030265849083662033,
-0.012839766219258308,
-0.011558260768651962,
-0.01507410779595375,
0.009037939831614494,
-0.021584631875157356,
0.03178044781088829,
0.005668391473591328,
-0.03889141604304314,
-0.011191198602318764,
-0.006138095632195473,
0.02163294330239296,
0.11695373058319092,
0.013182977214455605,
0.053037986159324646,
-0.05081052705645561,
0.03390960022807121,
0.027748972177505493,
0.010143758729100227,
-0.008378513157367706,
0.01622985489666462,
-0.003989286255091429,
0.00917865987867117,
-0.0388186015188694,
-0.023246396332979202,
0.048821207135915756
] |
<p>The bar with length l, density r, diametr d, Young's modulus E, Poisson's ratio mu, is spinning around the cross-section, what is the change in the width of this bar?</p> | g5536 | [
-0.012173641473054886,
0.04588402062654495,
-0.020315593108534813,
-0.046314485371112823,
0.03366333618760109,
-0.006255552172660828,
0.04438881203532219,
0.0046114507131278515,
0.0033980458974838257,
-0.015612410381436348,
-0.016497472301125526,
-0.021426551043987274,
0.0045999749563634396,
0.0006485302001237869,
0.09255467355251312,
-0.025769121944904327,
-0.005179686937481165,
0.03171646222472191,
0.0064678555354475975,
0.013314287178218365,
-0.0267779603600502,
-0.07289952039718628,
0.005250806454569101,
-0.04591833055019379,
0.04461919888854027,
-0.0029453688766807318,
0.0017273850971832871,
0.02031164988875389,
-0.050080105662345886,
0.03434741497039795,
0.02297211065888405,
0.0234511848539114,
0.02881021238863468,
-0.03434406965970993,
-0.03633259981870651,
-0.003558781463652849,
0.047076333314180374,
-0.009910231456160545,
0.048692598938941956,
0.010727914050221443,
-0.044686365872621536,
0.03492618724703789,
0.05911805480718613,
0.01657298393547535,
0.05561109632253647,
0.007882430218160152,
0.03323064371943474,
0.032531823962926865,
-0.04220496863126755,
-0.018032340332865715,
-0.05927151069045067,
0.0414285808801651,
0.05811086669564247,
-0.022705314680933952,
-0.0007459791377186775,
0.011439221911132336,
-0.04010135680437088,
-0.04026683792471886,
0.049094438552856445,
0.04963283613324165,
0.014567816630005836,
-0.07997886836528778,
-0.026785913854837418,
-0.053843289613723755,
0.028211327269673347,
-0.025205519050359726,
0.017864255234599113,
-0.023074593394994736,
-0.0039539942517876625,
-0.002640882972627878,
0.012438000179827213,
-0.061527129262685776,
0.02386125735938549,
-0.024541586637496948,
-0.03827763721346855,
-0.010493198409676552,
-0.018659435212612152,
0.0331406444311142,
-0.042300425469875336,
-0.05528808757662773,
-0.09285011887550354,
0.015915649011731148,
-0.018106624484062195,
0.00165134749840945,
0.013927219435572624,
0.027931593358516693,
0.013904028572142124,
0.017211299389600754,
-0.014722650870680809,
0.0665639340877533,
0.10010311007499695,
-0.03551371768116951,
0.007473966106772423,
-0.02970052883028984,
-0.0046797944232821465,
-0.04415544122457504,
0.007282652426511049,
0.04338567703962326,
0.01508259866386652,
0.04064369201660156,
-0.004115202464163303,
0.007184167392551899,
-0.019074691459536552,
-0.005865132436156273,
0.009938697330653667,
0.10946308821439743,
0.014673253521323204,
-0.05791374668478966,
-0.024005835875868797,
0.010514757595956326,
-0.0037193880416452885,
-0.07364960759878159,
-0.037796489894390106,
-0.018064826726913452,
0.02320694737136364,
-0.02041548304259777,
0.05142839998006821,
-0.007900161668658257,
0.01635195128619671,
0.04277539998292923,
0.04559604823589325,
-0.0073103890754282475,
0.041208960115909576,
0.05887043476104736,
0.027878453955054283,
-0.07184062153100967,
0.0073714288882911205,
0.04010426625609398,
0.060181111097335815,
0.017854124307632446,
0.011588728986680508,
0.017774876207113266,
0.003182635409757495,
-0.010781870223581791,
0.01018502376973629,
0.093290314078331,
0.022910891100764275,
0.034107185900211334,
0.008965780027210712,
0.008798206225037575,
-0.009783421643078327,
-0.03582119941711426,
0.035276465117931366,
-0.0419410802423954,
0.007730488665401936,
-0.022476444020867348,
0.03792591765522957,
-0.05457836762070656,
-0.001296231523156166,
0.020738651975989342,
0.01682332530617714,
0.0651199147105217,
0.020642291754484177,
-0.006201423238962889,
-0.004195335786789656,
0.014772039838135242,
0.0777890682220459,
0.0004560231463983655,
0.022027697414159775,
-0.019044050946831703,
-0.004873041994869709,
-0.012960624881088734,
-0.011769857257604599,
-0.015491552650928497,
-0.08804861456155777,
0.008429279550909996,
0.0028237737715244293,
-0.030627967789769173,
-0.019693193957209587,
-0.002772279316559434,
-0.01684008724987507,
-0.029024828225374222,
0.01581426151096821,
-0.01890929974615574,
-0.05206480249762535,
0.07430461794137955,
-0.020847227424383163,
0.006434229202568531,
0.0506012961268425,
0.057951878756284714,
0.006796703208237886,
0.022271618247032166,
0.03356356918811798,
-0.08132956176996231,
0.04183145985007286,
0.005942266434431076,
0.054536569863557816,
0.004230095073580742,
-0.038095664232969284,
-0.049029335379600525,
0.006357336882501841,
-0.0005204231129027903,
-0.04997095838189125,
0.018727021291851997,
0.0049552335403859615,
-0.015424076467752457,
0.049174945801496506,
-0.01156822219491005,
-0.031232861801981926,
0.027867862954735756,
-0.07327555865049362,
0.002142279176041484,
0.06604743003845215,
0.03545141965150833,
-0.03140514716506004,
-0.06798843294382095,
-0.035334378480911255,
0.005563214886933565,
0.04339604079723358,
0.05189777910709381,
0.043341442942619324,
-0.00504161836579442,
-0.04378794506192207,
-0.012334181927144527,
-0.037102699279785156,
0.014606721699237823,
-0.0029421846847981215,
0.033875226974487305,
0.05063552409410477,
0.06625042855739594,
-0.03432181850075722,
-0.027526123449206352,
0.01850605383515358,
-0.01675339601933956,
0.03213043883442879,
-0.04051908105611801,
0.0070282951928675175,
-0.053643956780433655,
0.0195531714707613,
0.0525931790471077,
-0.01675025187432766,
0.01756593957543373,
0.06405849754810333,
0.05752711743116379,
-0.022618627175688744,
-0.019618289545178413,
-0.026688484475016594,
0.04586648568511009,
-0.02084706909954548,
-0.008129428140819073,
0.06429615616798401,
0.02104683592915535,
-0.03565335273742676,
0.0044429730623960495,
0.010001691058278084,
-0.0053651416674256325,
0.07387541979551315,
-0.020898200571537018,
0.017170056700706482,
0.046607233583927155,
0.02230001799762249,
-0.0450059175491333,
0.006753408815711737,
0.00040829708450473845,
-0.013482831418514252,
-0.019212840124964714,
-0.08874696493148804,
-0.05049506202340126,
-0.029372407123446465,
-0.06346634775400162,
-0.010902202688157558,
0.0023915176279842854,
0.05800385773181915,
-0.010922030545771122,
-0.042537495493888855,
0.0008245613425970078,
-0.002697053598240018,
-0.0031725778244435787,
-0.03808434307575226,
0.0012796501396223903,
-0.028079429641366005,
0.02079002372920513,
0.010956601239740849,
0.025295298546552658,
0.026054881513118744,
-0.040446873754262924,
0.016506636515259743,
-0.04114282503724098,
-0.02928297594189644,
-0.026653526350855827,
0.02421414852142334,
-0.02250412292778492,
-0.0341150276362896,
0.04000389203429222,
0.031544726341962814,
-0.01258577685803175,
0.03932774439454079,
0.01882205903530121,
-0.052726663649082184,
0.04329894855618477,
0.011345741339027882,
0.043213650584220886,
0.01730545610189438,
0.004088710527867079,
0.06542591005563736,
0.004713276866823435,
0.06101205199956894,
0.015545571222901344,
-0.039184581488370895,
-0.043526340276002884,
0.013849185779690742,
0.020514877513051033,
-0.04391106963157654,
0.015986768528819084,
0.06342697143554688,
0.07339458912611008,
-0.028997477144002914,
-0.011240789666771889,
0.0056938487105071545,
0.0006794788059778512,
-0.0103713134303689,
-0.005439976695924997,
0.026074819266796112,
-0.05782577395439148,
-0.05566669628024101,
-0.06536233425140381,
-0.010545408353209496,
0.029083123430609703,
0.03745647519826889,
-0.0019697381649166346,
0.012397227808833122,
-0.03176717460155487,
-0.005949229467660189,
-0.05329327657818794,
-0.0067222099751234055,
0.02524971216917038,
-0.05616144463419914,
0.025640245527029037,
0.024523306638002396,
0.006380658596754074,
-0.01649555005133152,
0.05699460208415985,
0.03182794526219368,
-0.025894848629832268,
-0.029105091467499733,
0.017196301370859146,
0.0236204843968153,
-0.007742827758193016,
0.012185617350041866,
0.022473257035017014,
-0.009041338227689266,
-0.07593117654323578,
-0.018567703664302826,
-0.00187103939242661,
-0.009590535424649715,
0.03462335467338562,
-0.04805101454257965,
-0.024960864335298538,
0.016794675961136818,
0.002350418595597148,
-0.02418346144258976,
-0.0009261801606044173,
-0.01040361262857914,
0.0003439854772295803,
0.053661737591028214,
0.027219129726290703,
0.015850290656089783,
-0.019912483170628548,
-0.001969560980796814,
-0.01705555059015751,
-0.049755748361349106,
-0.06936219334602356,
0.0018236037576571107,
-0.009278505109250546,
-0.0344463549554348,
-0.005265883635729551,
0.016948170959949493,
-0.01954198069870472,
-0.02412857487797737,
0.013046505860984325,
-0.027342967689037323,
-0.05494312942028046,
-0.04152204468846321,
-0.033634260296821594,
-0.018072737380862236,
-0.04286617413163185,
-0.08393213152885437,
-0.002846704563125968,
-0.0201120488345623,
0.02772996574640274,
0.010878053493797779,
0.0503193661570549,
-0.04154328256845474,
-0.013024036772549152,
-0.0853281244635582,
0.046057116240262985,
-0.019478898495435715,
-0.06529093533754349,
0.04644725099205971,
-0.0497731938958168,
0.043889354914426804,
0.05758310854434967,
0.02442689798772335,
-0.027504146099090576,
0.05420122295618057,
-0.021775513887405396,
0.01196763850748539,
-0.04599457606673241,
-0.0966525599360466,
0.03512024134397507,
-0.002985196653753519,
0.009077388793230057,
0.016164487227797508,
-0.01734987646341324,
-0.03568694368004799,
-0.025830354541540146,
0.04648255556821823,
0.02190370485186577,
0.006798224989324808,
-0.042335569858551025,
0.01285733375698328,
-0.019638532772660255,
-0.013449069112539291,
-0.0897761881351471,
0.0002793002931866795,
0.006591801531612873,
0.032865189015865326,
0.009104005992412567,
0.003329867497086525,
0.03594427928328514,
0.01747981645166874,
0.06165391951799393,
0.006945643108338118,
0.006368544418364763,
0.0008305487572215497,
-0.011120500043034554,
0.04900076612830162,
-0.03882920369505882,
0.000372201728168875,
-0.009487307630479336,
-0.03405226022005081,
0.030077727511525154,
-0.007950150407850742,
0.05682522431015968,
-0.04084615409374237,
0.004163568839430809,
-0.027756353840231895,
-0.047483958303928375,
-0.03774908185005188,
0.035661280155181885,
-0.025613894686102867,
-0.07764136046171188,
-0.03274757042527199,
-0.003888651728630066,
0.017022330313920975,
0.029124988242983818,
-0.028729785233736038,
-0.04124501347541809,
-0.01644427515566349,
0.0036644968204200268,
-0.059683702886104584,
-0.008829302154481411,
0.01711706817150116,
0.014125886373221874,
0.043971989303827286,
-0.015188131481409073,
-0.0007839400786906481,
-0.019028084352612495,
0.01909819059073925,
0.03451509401202202,
0.00831082183867693,
-0.03559621796011925,
-0.0872633159160614,
-0.00655567878857255,
-0.044316697865724564,
-0.012621358036994934,
-0.005858118645846844,
0.008672941476106644,
0.03799772262573242,
0.03440626710653305,
0.0061908308416605,
0.042713362723588943,
-0.02850574068725109,
-0.0023670163936913013,
0.005397139582782984,
0.04248613864183426,
-0.0035313249099999666,
-0.0004364411870483309,
0.008053709752857685,
-0.03538491576910019,
-0.02805912308394909,
0.01987376995384693,
0.014208667911589146,
-0.018368570134043694,
0.04226945340633392,
0.0026748075615614653,
-0.04326305538415909,
-0.028033189475536346,
-0.025142228230834007,
0.03148999437689781,
0.013268012553453445,
-0.005174292717128992,
0.015993192791938782,
-0.0009041395969688892,
-0.019385095685720444,
-0.00352543406188488,
0.01883610337972641,
-0.07000825554132462,
-0.01912781223654747,
0.04136461392045021,
0.02196737378835678,
0.007454732898622751,
0.027335548773407936,
0.019203873351216316,
-0.08877884596586227,
0.04661187529563904,
0.021852949634194374,
-0.019913718104362488,
-0.044911615550518036,
0.010487084276974201,
-0.04782151058316231,
-0.015839295461773872,
0.13735611736774445,
0.004436701536178589,
-0.022435547783970833,
-0.04264473915100098,
-0.02721388265490532,
0.07670128345489502,
0.026355542242527008,
0.029312536120414734,
-0.011978290043771267,
0.028950534760951996,
0.028872165828943253,
-0.002164361998438835,
-0.02614784426987171,
0.024061288684606552,
-0.06319357454776764,
0.04036247730255127,
0.0036913612857460976,
0.005026618018746376,
0.0064361561089754105,
-0.016193972900509834,
0.005673375446349382,
-0.02498309500515461,
-0.015618614852428436,
0.0037756646052002907,
-0.012234864756464958,
0.0019847156945616007,
-0.001145080430433154,
-0.012713680975139141,
0.004719140473753214,
-0.061331767588853836,
0.024205118417739868,
-0.014888246543705463,
0.02839631587266922,
-0.03026958927512169,
-0.042008399963378906,
-0.05189729109406471,
0.023986315354704857,
-0.025866957381367683,
0.08425866067409515,
0.03372349590063095,
-0.02782495506107807,
0.004542012233287096,
-0.0033204425126314163,
0.09148421883583069,
0.051050230860710144,
-0.019693465903401375,
0.00846208818256855,
0.0010504703968763351,
0.043669261038303375,
-0.05943978205323219,
-0.03614892438054085,
-0.005869213957339525,
0.009711985476315022,
-0.06375619769096375,
0.0053848810493946075,
0.017644714564085007,
0.04782892391085625,
0.007261432707309723,
-0.060841549187898636,
-0.0010714912787079811,
-0.01242970209568739,
0.029605519026517868,
0.0005305784870870411,
0.08491916209459305,
-0.0034361791331321,
-0.03527258336544037,
-0.02098625712096691,
0.006199479568749666,
0.010111825540661812,
0.0070734391920268536,
-0.025545554235577583,
-0.009115511551499367,
0.021200045943260193,
0.05323685705661774,
0.010925423353910446,
-0.02045600675046444,
0.021142562851309776,
-0.05014706030488014,
-0.0625734031200409,
0.03736894950270653,
-0.04680292308330536,
0.0009973819833248854,
-0.01785389333963394,
0.054585784673690796,
-0.07680583745241165,
-0.006108920089900494,
-0.026414254680275917,
-0.047741007059812546,
-0.011391236446797848,
0.023624205961823463,
0.04169896990060806,
0.028957294300198555,
0.03401177376508713,
-0.09544096142053604,
-0.011422091163694859,
-0.03562908247113228,
-0.019926270470023155,
0.005963068921118975,
0.0056282468140125275,
0.006482249591499567,
0.058663755655288696,
0.05680573359131813,
-0.03951545059680939,
-0.020757706835865974,
0.02644113078713417,
0.0035915598273277283,
-0.0044022779911756516,
-0.012690764851868153,
-0.0062998500652611256,
-0.04723917320370674,
0.06243820860981941,
-0.0636303499341011,
0.03563139960169792,
0.06594648957252502,
-0.04097748547792435,
-0.011935880407691002,
-0.012063500471413136,
-0.012289498932659626,
0.04561678692698479,
0.018160877749323845,
-0.030278867110610008,
0.03073848970234394,
-0.01721961982548237,
0.055076245218515396,
-0.0736759826540947,
0.06490962952375412,
0.07051913440227509,
0.0598122663795948,
0.0011210826924070716,
-0.008987337350845337,
0.003610589075833559,
-0.04450325295329094,
-0.04913700744509697,
-0.04120255634188652,
0.026289694011211395,
-0.05594475567340851,
-0.0011211686069145799,
0.04190411791205406,
0.007815202698111534,
0.03516650199890137,
-0.001124804257415235,
0.06120776757597923,
-0.03757341578602791,
0.015969591215252876,
0.01843275874853134,
-0.024370141327381134,
0.06329502910375595,
-0.009825845248997211,
-0.062407393008470535,
0.0066548180766403675,
0.029833335429430008,
-0.017526626586914062,
0.01403743401169777,
0.0206009391695261,
0.054382648319005966,
-0.026949936524033546,
0.026424208655953407,
-0.031245112419128418,
-0.03414682298898697,
-0.055638331919908524,
-0.026525704190135002,
0.028069090098142624,
0.030542323365807533,
0.0563170351088047,
0.016763566061854362,
-0.013173412531614304,
0.03597671911120415,
-0.010720998048782349,
-0.0021774203050881624,
0.014843455515801907,
-0.05245571583509445,
-0.02235124073922634,
0.013898256234824657,
0.0396372526884079,
-0.033149298280477524,
-0.04044670984148979,
0.06424690037965775,
0.027658063918352127,
0.041606344282627106,
-0.047745026648044586,
-0.023777302354574203,
0.014144190587103367,
-0.0542348176240921,
-0.028348298743367195,
0.03537904843688011,
0.01841404289007187,
-0.006302689667791128,
-0.021663866937160492,
0.04123343527317047,
-0.014209052547812462,
-0.027454398572444916,
-0.03755202516913414,
-0.02029048278927803,
0.004484986420720816,
0.01927020587027073,
-0.0635557621717453,
-0.03471936285495758,
-0.027332618832588196,
0.007360285148024559,
0.015564029105007648,
0.04721500352025032,
-0.045304834842681885,
0.006684128660708666,
0.05995679646730423,
0.021661967039108276,
0.016629977151751518,
-0.004550927318632603,
-0.0053098504431545734,
-0.012032088823616505,
-0.0008555739768780768,
-0.0388963483273983,
-0.006904697045683861,
0.0010884202783927321,
-0.08822895586490631,
0.0415918305516243,
0.09490540623664856,
-0.026930587366223335,
0.06000892072916031,
-0.023292670026421547,
-0.036202382296323776,
-0.013515065424144268,
-0.06825564801692963,
-0.07228000462055206,
-0.0023784504737704992,
0.03209780901670456,
0.04702293872833252,
0.03428643196821213,
0.016900593414902687,
0.022286972030997276,
-0.04653383418917656,
0.05914316326379776,
-0.010007400065660477,
-0.004756992682814598,
-0.01627136766910553,
0.010891896672546864,
0.06021955981850624,
0.07229714095592499,
-0.029603153467178345,
-0.04087633267045021,
0.0046332781203091145,
-0.03676711767911911,
0.04572267085313797,
0.01969423145055771,
-0.04106796532869339,
0.021607553586363792,
-0.006973516661673784,
0.01624857820570469,
-0.0014414488105103374,
0.016242284327745438,
-0.027269313111901283,
0.019212765619158745,
0.016789518296718597,
0.020094411447644234,
0.007748613599687815,
0.0062745255418121815,
0.05654327943921089
] |
<p>I watched this <a href="http://www.youtube.com/watch?v=_hmXrHvmwOM" rel="nofollow">video</a> featuring Michio Kaku explaining parallel universes. In the last two minutes he said that experiments in the LHC could reveal that there might be parallel universes and then he stops. What experiment was he talking about? And how would that be possible? </p> | g5537 | [
0.011809325776994228,
0.081748828291893,
-0.0014789056731387973,
-0.04328899085521698,
0.018520545214414597,
0.001689913566224277,
-0.009224758483469486,
0.032773882150650024,
0.006985357962548733,
-0.02613416686654091,
-0.037908002734184265,
0.029887814074754715,
-0.0029707509092986584,
0.08751761168241501,
0.026326768100261688,
0.013629008084535599,
-0.022381654009222984,
-0.034533459693193436,
-0.0145576111972332,
0.003969033248722553,
-0.03336219862103462,
0.023424793034791946,
-0.045307233929634094,
-0.024343131110072136,
-0.025507980957627296,
-0.0011850640876218677,
-0.008167575113475323,
0.030122892931103706,
-0.01398182287812233,
-0.03277323767542839,
0.04339161515235901,
-0.12608695030212402,
0.021788788959383965,
-0.00912929605692625,
-0.030577676370739937,
-0.02291266620159149,
0.0341741181910038,
0.005147869698703289,
0.026904156431555748,
0.006714084651321173,
-0.020149802789092064,
0.025067368522286415,
0.023942438885569572,
-0.04819429665803909,
0.04834148287773132,
-0.009321712888777256,
-0.007741300854831934,
0.04181515425443649,
0.059140559285879135,
-0.06821684539318085,
-0.02968479134142399,
0.0012526176869869232,
0.029825201258063316,
0.008893690072000027,
-0.023337462916970253,
-0.036622148007154465,
0.029216395691037178,
-0.013955453410744667,
0.1619882732629776,
-0.035272277891635895,
-0.020930984988808632,
0.03176526725292206,
0.041950926184654236,
0.012463938444852829,
0.0677005872130394,
0.02252493053674698,
-0.014882015064358711,
0.016975916922092438,
0.006594677921384573,
0.03784932568669319,
0.054562047123909,
0.011990385130047798,
-0.015113919973373413,
0.025534095242619514,
-0.013632530346512794,
0.05021485686302185,
0.0583653561770916,
-0.013765267096459866,
-0.011071384884417057,
0.0034220993984490633,
-0.06969966739416122,
-0.02245081216096878,
-0.03937659040093422,
0.03853512182831764,
0.00038542653783224523,
-0.05038701370358467,
-0.002558815060183406,
0.02864431031048298,
-0.026866886764764786,
0.04657755047082901,
-0.011016907170414925,
-0.012505498714745045,
-0.007609579246491194,
-0.02029458060860634,
0.036192432045936584,
-0.029062606394290924,
-0.0009959971066564322,
0.02555231563746929,
-0.053890161216259,
-0.0005295666633173823,
-0.05545445531606674,
0.019960684701800346,
0.029435204342007637,
-0.003521817037835717,
-0.0031005912460386753,
0.030068721622228622,
0.038322463631629944,
-0.021120620891451836,
0.05838754400610924,
-0.020703744143247604,
-0.006135218311101198,
-0.007401394657790661,
-0.027401704341173172,
0.044135238975286484,
0.03856101632118225,
-0.03439776599407196,
0.0541532002389431,
-0.006070531904697418,
0.037222255021333694,
-0.0187445767223835,
-0.016305238008499146,
0.0376802496612072,
-0.041450385004282,
0.030562624335289,
-0.03947114199399948,
0.027361012995243073,
0.0065504442900419235,
-0.010244729928672314,
0.020991822704672813,
0.01983772963285446,
0.011792394332587719,
0.029922988265752792,
-0.0021120018791407347,
0.09575565904378891,
0.00004016203456558287,
-0.03861595317721367,
0.06587329506874084,
-0.036723628640174866,
0.002430200343951583,
-0.05775268375873566,
-0.031092846766114235,
-0.03615522012114525,
0.0099566038697958,
0.010489425621926785,
0.03995123505592346,
-0.002392283407971263,
-0.04764043539762497,
0.017968539148569107,
-0.03806068003177643,
0.01381157711148262,
0.06252644211053848,
0.029833801090717316,
0.04920261725783348,
-0.014114659279584885,
0.006318157073110342,
0.005794567987322807,
-0.010646204464137554,
-0.002723964164033532,
-0.010641340166330338,
0.002841146197170019,
0.03579038754105568,
0.04368310049176216,
-0.05821959674358368,
-0.008126997388899326,
-0.011179345659911633,
-0.0009938584407791495,
0.01056278683245182,
-0.015144987031817436,
0.043477267026901245,
0.013779578730463982,
-0.07419119775295258,
0.00626389542594552,
0.02863413281738758,
0.06199179217219353,
0.028540978208184242,
0.07668265700340271,
0.01942853070795536,
-0.012819627299904823,
-0.02896745689213276,
0.010619139298796654,
0.02576661854982376,
-0.01974748820066452,
0.0411987379193306,
-0.031427882611751556,
0.013063705526292324,
-0.05579325929284096,
-0.020138589665293694,
-0.014705028384923935,
0.03098052181303501,
-0.032174088060855865,
0.0011237197322770953,
-0.026271888986229897,
-0.01579960435628891,
-0.03992236778140068,
0.022625258192420006,
-0.04083338752388954,
0.0364360474050045,
-0.05000194162130356,
0.005220786202698946,
-0.0026018479838967323,
-0.018247047439217567,
-0.038140542805194855,
-0.001163697917945683,
0.03934900462627411,
0.008744532242417336,
-0.027516089379787445,
-0.050563544034957886,
-0.027880504727363586,
0.011658541858196259,
-0.03068927302956581,
0.030008094385266304,
0.03435672074556351,
-0.02309403195977211,
0.01961149275302887,
-0.004089476075023413,
0.07354243844747543,
0.040209148079156876,
0.020976921543478966,
-0.05696806684136391,
0.04822172597050667,
-0.040236104279756546,
0.001459845807403326,
0.04149514436721802,
-0.0164005346596241,
0.020809438079595566,
-0.009747123345732689,
-0.026624945923686028,
-0.054082803428173065,
-0.02887614630162716,
-0.07162079960107803,
-0.022941067814826965,
-0.0244749803096056,
-0.04036788269877434,
0.014339652843773365,
0.02937813103199005,
0.030714737251400948,
-0.016979258507490158,
0.008271082304418087,
-0.017529653385281563,
0.03498084843158722,
0.006498746108263731,
0.0035069258883595467,
-0.045838817954063416,
0.03822743520140648,
-0.004806883633136749,
-0.0932604968547821,
0.10130804777145386,
-0.05941266939043999,
0.021630359813570976,
-0.04774881899356842,
0.06907494366168976,
-0.003110427875071764,
0.053818218410015106,
0.035720646381378174,
0.02575017511844635,
-0.029376208782196045,
0.037663329392671585,
0.06156476214528084,
-0.039797767996788025,
-0.02092192880809307,
0.09680549800395966,
-0.0072635747492313385,
-0.001053201500326395,
0.014341882430016994,
-0.044129565358161926,
-0.005991055630147457,
-0.06127912178635597,
-0.019639011472463608,
-0.02801588363945484,
0.00873287208378315,
-0.04473981261253357,
0.009600980207324028,
-0.020803438499569893,
0.0350886806845665,
-0.004966831766068935,
0.05836053565144539,
-0.0024292634334415197,
-0.00560883479192853,
0.030628720298409462,
-0.011007596738636494,
-0.015911536291241646,
0.0320982001721859,
0.008575784042477608,
-0.03267335891723633,
0.016732724383473396,
-0.009637916460633278,
-0.03421344980597496,
-0.030262146145105362,
-0.011573228985071182,
0.047541216015815735,
-0.05830332636833191,
-0.038655202835798264,
0.04907453432679176,
0.04467574506998062,
-0.0024218338076025248,
0.06086279824376106,
0.05866004154086113,
0.01265423372387886,
0.01566832885146141,
0.004405768122524023,
0.024554649367928505,
-0.04650314524769783,
-0.004444221965968609,
-0.0194455087184906,
0.006939713377505541,
0.007630585227161646,
0.02076132409274578,
0.018982643261551857,
0.008604301139712334,
-0.05049767717719078,
-0.034279078245162964,
-0.04088300094008446,
0.08810274302959442,
0.024448690935969353,
0.013880664482712746,
0.04561349377036095,
0.017199698835611343,
0.08367519080638885,
0.05741143226623535,
-0.01085455622524023,
0.0581497997045517,
0.02223792113363743,
-0.002582042943686247,
-0.04037347063422203,
0.018313845619559288,
0.019003743305802345,
0.014160025864839554,
-0.04443683847784996,
-0.03316567465662956,
0.010365135036408901,
-0.013038292527198792,
-0.026221737265586853,
-0.005945526994764805,
-0.015856098383665085,
-0.01101389154791832,
0.012563914991915226,
-0.03580509126186371,
0.03052104264497757,
0.008927623741328716,
0.06442053616046906,
0.042082130908966064,
-0.009735564701259136,
-0.021178988739848137,
0.03952572122216225,
0.021468358114361763,
0.022589068859815598,
0.012110801413655281,
-0.03426742926239967,
0.06639836728572845,
-0.027942117303609848,
0.04765262454748154,
0.026133332401514053,
0.0020259423181414604,
-0.0700874775648117,
-0.0638972595334053,
0.030672093853354454,
0.06290462613105774,
-0.014094794169068336,
0.03448740392923355,
0.010458649136126041,
-0.007147104479372501,
-0.07116372138261795,
0.024493254721164703,
-0.028661001473665237,
-0.03457438200712204,
0.024245744571089745,
0.017915474250912666,
0.015504753217101097,
-0.01301793847233057,
-0.003061991650611162,
0.020793450996279716,
0.003207401605322957,
-0.042041078209877014,
0.057257555425167084,
-0.012982886284589767,
-0.059429917484521866,
0.02086213231086731,
0.028707414865493774,
0.05445966124534607,
0.057163260877132416,
-0.01301545649766922,
0.04034353792667389,
-0.040568359196186066,
0.03319728001952171,
0.02341272123157978,
-0.026426423341035843,
-0.017917774617671967,
-0.012907414697110653,
-0.0024248738773167133,
0.013087506406009197,
-0.006007504183799028,
-0.0061616417951881886,
-0.03368430212140083,
-0.03250100836157799,
-0.03477294743061066,
-0.013009491376578808,
-0.031755343079566956,
-0.026372030377388,
0.03897811844944954,
-0.038433849811553955,
-0.028925711289048195,
-0.0008999132551252842,
-0.029979851096868515,
-0.02835751324892044,
-0.04833567887544632,
-0.015108633786439896,
0.010407757014036179,
-0.015155245549976826,
0.07538411766290665,
0.06428129971027374,
0.005913295783102512,
0.015758365392684937,
-0.03623451665043831,
-0.03855424001812935,
0.01699443906545639,
-0.018323399126529694,
0.026693208143115044,
-0.028979716822504997,
-0.016632869839668274,
0.018493464216589928,
0.043480418622493744,
0.026364149525761604,
-0.03286139667034149,
-0.04490692541003227,
0.005312786437571049,
0.00013511214638128877,
-0.037363480776548386,
0.04373404011130333,
-0.06691249459981918,
-0.009844962507486343,
0.04195421561598778,
-0.02059553563594818,
-0.0016326367622241378,
0.009565895423293114,
-0.0022387311328202486,
0.005041011143475771,
-0.011985271237790585,
-0.008662129752337933,
0.00529515603557229,
0.0378936342895031,
0.026813548058271408,
0.0074250344187021255,
0.023732174187898636,
-0.016114089637994766,
-0.039793819189071655,
0.03755725547671318,
-0.03947125002741814,
-0.024457477033138275,
-0.05057566240429878,
0.0033908593468368053,
-0.053427185863256454,
0.00996396318078041,
-0.030830351635813713,
0.04709455370903015,
0.018015116453170776,
-0.07559147477149963,
0.03270384296774864,
0.042000897228717804,
0.013795802369713783,
0.04110407829284668,
-0.048558153212070465,
-0.07774224132299423,
0.06061079725623131,
0.0043281265534460545,
0.07448039948940277,
0.007786155678331852,
0.012939159758388996,
-0.06650583446025848,
-0.04972309619188309,
0.03166063502430916,
-0.013761600479483604,
0.006237343419343233,
0.0011743735522031784,
0.030383344739675522,
0.005278170108795166,
-0.03737107291817665,
-0.016422588378190994,
0.022047271952033043,
0.021578166633844376,
0.021123163402080536,
-0.005568160209804773,
-0.0420028455555439,
0.030358267948031425,
-0.0927356407046318,
-0.00003308549275971018,
0.04766884073615074,
-0.05263415351510048,
0.009643713012337685,
-0.011021934449672699,
0.001489986665546894,
-0.026691406965255737,
0.021607527509331703,
0.04019329696893692,
0.013261829502880573,
0.018879611045122147,
0.007098051253706217,
-0.0065983072854578495,
0.013961242511868477,
-0.024528542533516884,
-0.018092231824994087,
0.056350674480199814,
-0.0016890023835003376,
0.029872799292206764,
-0.04602045938372612,
-0.059687595814466476,
-0.015714148059487343,
0.019899558275938034,
-0.021535571664571762,
0.03698322921991348,
0.008143254555761814,
0.00494905561208725,
0.025562042370438576,
-0.04802216589450836,
0.027366770431399345,
0.05839032679796219,
0.020188286900520325,
-0.05121127888560295,
-0.0014194140676409006,
0.027559828013181686,
-0.007971743121743202,
-0.013425366953015327,
-0.0320034995675087,
-0.020868366584181786,
0.024935223162174225,
-0.031195467337965965,
0.005721155554056168,
-0.044136714190244675,
0.0389384962618351,
0.018914539366960526,
-0.0032214249949902296,
0.015659280121326447,
0.04706788808107376,
0.08381201326847076,
0.018504858016967773,
0.007388323545455933,
-0.02535957843065262,
0.03956996649503708,
0.02292393147945404,
0.0112695237621665,
0.004168075975030661,
-0.039391521364450455,
-0.06776682287454605,
0.04571256414055824,
0.0032031743321567774,
-0.019587183371186256,
-0.026634830981492996,
-0.008652877062559128,
0.001231875387020409,
0.07889100164175034,
-0.12377855181694031,
-0.07086431980133057,
0.026530073955655098,
0.0527816116809845,
0.06614010035991669,
-0.0223975982517004,
-0.047606077045202255,
0.027991000562906265,
-0.0018486957997083664,
-0.03965410590171814,
-0.04994581639766693,
-0.044774286448955536,
-0.0022671520709991455,
-0.01621234603226185,
-0.0010834363056346774,
-0.046879786998033524,
0.02336278185248375,
-0.0056534139439463615,
-0.060991983860731125,
0.04170822352170944,
-0.03898053616285324,
-0.004184001591056585,
0.0054472689516842365,
-0.0038678457494825125,
0.009069827385246754,
0.043586090207099915,
0.0311497300863266,
0.05979935824871063,
0.03360394015908241,
-0.007460488472133875,
-0.03264145180583,
0.01816973090171814,
-0.011939622461795807,
0.08882234245538712,
-0.08692820370197296,
-0.006988019682466984,
0.0454983115196228,
-0.0034329816699028015,
0.032527197152376175,
0.011105801910161972,
-0.04550200328230858,
-0.05993480607867241,
-0.024882128462195396,
0.007349712774157524,
-0.015764843672513962,
0.01616627909243107,
-0.01703476905822754,
-0.04471663385629654,
-0.01659763790667057,
-0.06634789705276489,
0.030400678515434265,
-0.03722509369254112,
-0.04390358552336693,
-0.004367088433355093,
0.021335911005735397,
-0.020970292389392853,
0.020200056955218315,
-0.04433264583349228,
-0.013675355352461338,
0.020766032859683037,
0.01238009799271822,
-0.030885152518749237,
0.02072742022573948,
0.005497979931533337,
-0.01830136589705944,
-0.00044373510172590613,
-0.00106458505615592,
0.0026529384776949883,
-0.06522710621356964,
0.021883869543671608,
0.029287271201610565,
0.021390946581959724,
-0.028806662186980247,
-0.02633647806942463,
-0.01144675724208355,
-0.057492177933454514,
0.06570623070001602,
0.024969974532723427,
-0.006498434115201235,
0.07423503696918488,
0.02846367284655571,
-0.012745413929224014,
-0.0031673924531787634,
0.06367705017328262,
0.07611113786697388,
-0.0028476042207330465,
0.013597768731415272,
-0.0044166650623083115,
-0.008385934866964817,
0.024787195026874542,
-0.06501386314630508,
0.05622168630361557,
-0.030119195580482483,
0.03941452503204346,
-0.012689639814198017,
0.019968964159488678,
0.016310689970850945,
-0.018866201862692833,
0.03876302391290665,
-0.06609098613262177,
-0.04007238149642944,
-0.015508835203945637,
-0.013447768054902554,
-0.03387681767344475,
0.0005491376505233347,
-0.06963133066892624,
0.013494177721440792,
0.011383901350200176,
0.0015653676819056273,
-0.012072427198290825,
-0.10380364209413528,
-0.03366386145353317,
0.03488585725426674,
0.04078793525695801,
-0.01848706603050232,
0.026518668979406357,
0.018791938200592995,
-0.030643992125988007,
-0.07209475338459015,
0.007280843332409859,
-0.002381746657192707,
-0.016196714714169502,
0.021486595273017883,
-0.07014705240726471,
-0.008591591380536556,
0.000049263195251114666,
-0.08523238450288773,
-0.007561794016510248,
0.025897162035107613,
0.003330450737848878,
0.022529209032654762,
-0.06756851822137833,
0.0067926743067801,
0.026817593723535538,
0.023033173754811287,
-0.05417804419994354,
0.03259845823049545,
0.0038857972249388695,
0.0016058087348937988,
-0.08527421206235886,
-0.02931525558233261,
-0.02066974528133869,
-0.024452196434140205,
0.05999041348695755,
-0.021865159273147583,
0.08155325055122375,
0.012808865867555141,
0.005128046497702599,
0.045004408806562424,
-0.0038938638754189014,
0.007666736841201782,
-0.018851393833756447,
0.005223254207521677,
-0.014596552588045597,
0.05120814964175224,
-0.03861142694950104,
-0.0007012485875748098,
-0.07821106165647507,
-0.04194300249218941,
-0.0032797157764434814,
0.0032830247655510902,
-0.03930996358394623,
0.0804189071059227,
0.02322770282626152,
0.04552316293120384,
0.0038741359021514654,
-0.025598900392651558,
-0.009741527959704399,
-0.04511226341128349,
0.05684373155236244,
0.009954022243618965,
-0.05642036721110344,
-0.03269799426198006,
0.01828332617878914,
-0.048287007957696915,
-0.018249420449137688,
0.017198175191879272,
-0.010062051005661488,
0.007990619167685509,
-0.07252129167318344,
0.03339995816349983,
0.02617555297911167,
0.022283073514699936,
0.013788550160825253,
-0.012248306535184383,
-0.023151420056819916,
0.044123221188783646,
-0.04083026573061943,
0.00600529694929719,
0.0061598545871675014,
-0.011262250132858753,
-0.02151310443878174,
-0.031085949391126633,
0.06891746073961258,
-0.015612875111401081,
0.01231254730373621,
-0.07219205796718597,
-0.058017365634441376,
0.009846460074186325,
0.03657601401209831,
-0.03132765740156174,
0.021869497373700142,
-0.005822551902383566,
-0.0011271241819486022,
0.04201934486627579,
0.012896341271698475,
-0.0512382909655571,
-0.06939611583948135,
0.0305594764649868,
-0.03019590675830841,
-0.03574709594249725,
-0.024047480896115303,
0.019913000985980034,
0.008313330821692944,
0.031759731471538544,
0.014939464628696442,
-0.041952405124902725,
-0.011820759624242783,
-0.009913946501910686
] |
<p>In one derivation of the corrected period of a pendulum, we started off like so: </p>
<p>The mass has a height $y$ given by $l(1-\cos \theta )$. $E = K + E \rightarrow \frac{1}{2}ml^2 \dot{\theta}^2 + mgl(1-\cos \theta)$</p>
<p>The next step introduces $\theta _0$, and I've got no idea where this came from. </p>
<p>$$\frac{1}{2}ml^2 \dot{\theta}^2 + mgl(1-\cos \theta)= mgl(1-\cos \theta _0)$$</p>
<p>Now we just solve for $\dot{\theta}$ and solve the DE.W I'm interested in the theta side of the equation. </p>
<p>$$\int \frac{d\theta}{\sqrt{\cos \theta - \cos \theta _0 }}$$</p>
<p>We go through a bunch of subs and changes of vairble to arrive at </p>
<p>$$\int ^{2\pi} _0 \frac{du}{\sqrt{1-K^2 \sin ^2 u }}$$</p>
<p>So my two questions are </p>
<ul>
<li>Why are we involving two $\theta$ values? The text didn't make it clear why we needed an extra $\theta _0$. It appears that $mgl(1-\cos \theta _0)$ is the total energy of the system. Our total energy cannot surpass the initial gravitational potential energy, this is clear. My only thought as to what $\theta$ means is the instantaneous position of the angle. </li>
<li>My text mentioned that this is an elliptical integral. Mathematically speaking, what <em>is</em> an elliptical integral? Can this integral be solved exactly, or does it always require approximations from the expansion? </li>
</ul> | g5538 | [
0.07104260474443436,
0.002077079378068447,
-0.01251512672752142,
-0.012368539348244667,
0.026369988918304443,
0.054157909005880356,
0.08339578658342361,
-0.0003265343839302659,
-0.06580469012260437,
0.08224646002054214,
-0.04377773404121399,
0.04350937902927399,
0.053402092307806015,
-0.003906016470864415,
0.07894787192344666,
-0.024417193606495857,
0.08508496731519699,
0.01711290143430233,
0.012711545452475548,
-0.0013794077094644308,
-0.024497749283909798,
-0.028978858143091202,
-0.03330747038125992,
-0.03871256113052368,
-0.003146274946630001,
0.00005336290269042365,
0.05084526166319847,
0.009116549976170063,
-0.024677617475390434,
0.0003296171489637345,
-0.011341286823153496,
0.01352408342063427,
0.09132584184408188,
-0.051015518605709076,
-0.055341608822345734,
0.024507872760295868,
0.03435627743601799,
-0.016091831028461456,
-0.004762305878102779,
-0.02901572920382023,
-0.005558766890317202,
-0.08335530012845993,
0.04995124787092209,
0.0065657696686685085,
0.021148834377527237,
0.01924564316868782,
-0.014158313162624836,
0.005754419602453709,
-0.006172488909214735,
-0.023248841986060143,
0.010455131530761719,
0.060822952538728714,
0.06527616828680038,
-0.016425294801592827,
-0.05631436035037041,
0.042207490652799606,
0.07520792633295059,
-0.040726978331804276,
0.04021754860877991,
0.07360778748989105,
0.042105533182621,
-0.05108795687556267,
0.02997121587395668,
0.020714879035949707,
0.009064054116606712,
-0.02062382735311985,
0.01222140621393919,
-0.02774144895374775,
-0.0014776962343603373,
0.0038165405858308077,
0.007924594916403294,
-0.0517568401992321,
-0.010147281922399998,
-0.03424818441271782,
-0.006871857680380344,
0.017637504264712334,
0.07584082335233688,
0.010857447050511837,
-0.006284093949943781,
-0.053400877863168716,
-0.06136693060398102,
0.04359715059399605,
0.02539043128490448,
-0.016606144607067108,
0.030968880280852318,
-0.030231675133109093,
0.011132162995636463,
0.058771248906850815,
-0.02731182985007763,
0.005905540660023689,
0.014301326125860214,
-0.023318186402320862,
0.06512489169836044,
-0.024981990456581116,
0.00987789686769247,
-0.009704346768558025,
-0.03343017026782036,
0.04100475832819939,
0.017705539241433144,
0.04748908430337906,
-0.019141750410199165,
0.017926344648003578,
-0.018276358023285866,
0.02848505601286888,
0.0144072026014328,
0.04784190282225609,
0.005552035756409168,
-0.01571548543870449,
0.009197486564517021,
-0.022241035476326942,
-0.05428874120116234,
0.013723603449761868,
0.0028696702793240547,
-0.05874953418970108,
-0.050598081201314926,
-0.004502600524574518,
0.0816275104880333,
0.01422158069908619,
0.03884773701429367,
0.028026828542351723,
-0.00011314341827528551,
0.0023275476414710283,
0.01940680667757988,
0.07351460307836533,
-0.02820851467549801,
-0.032120585441589355,
-0.007597828283905983,
-0.008983326144516468,
0.02046864479780197,
-0.06457042694091797,
-0.018744710832834244,
0.0521402433514595,
-0.013377146795392036,
0.036037374287843704,
0.04095958545804024,
-0.021817877888679504,
0.024213062599301338,
-0.000738645379897207,
-0.04567001760005951,
0.02478960156440735,
-0.049983538687229156,
-0.0866270586848259,
0.0098798843100667,
-0.014578351750969887,
-0.01857205107808113,
0.06330268085002899,
-0.00917004980146885,
-0.034176308661699295,
0.03239433839917183,
0.013584278523921967,
0.00966161023825407,
0.04471542686223984,
-0.0140816206112504,
-0.05216303467750549,
0.013653180561959743,
-0.03255363926291466,
0.010658788494765759,
0.007044873666018248,
0.0357426255941391,
0.04386701062321663,
0.05796026065945625,
-0.023801211267709732,
0.04926026239991188,
0.03897019103169441,
-0.020059552043676376,
0.0843573808670044,
0.03015999123454094,
-0.0358121283352375,
-0.013318134471774101,
-0.023949477821588516,
-0.0060461596585810184,
-0.010052572935819626,
-0.018326515331864357,
0.0029394845478236675,
-0.035943739116191864,
0.044049348682165146,
0.0194792952388525,
-0.07787138223648071,
0.006789127830415964,
-0.017045486718416214,
0.021690094843506813,
-0.0031962920911610126,
-0.019202355295419693,
0.00009875898103928193,
0.02163633704185486,
-0.0050659035332500935,
0.038528259843587875,
0.017318423837423325,
-0.01747843250632286,
0.003290541237220168,
0.01837501861155033,
-0.0040905107744038105,
-0.008173755370080471,
0.04756136238574982,
-0.010737399570643902,
0.04684838280081749,
0.03522136062383652,
-0.056702978909015656,
-0.08165378123521805,
0.05556125193834305,
-0.039796095341444016,
0.009484161622822285,
0.07059143483638763,
0.014046935364603996,
0.03561881184577942,
0.02986340969800949,
0.06353755295276642,
-0.052941594272851944,
-0.008227882906794548,
-0.003747418988496065,
0.025983955711126328,
-0.0483529157936573,
-0.0027429177425801754,
0.008364523760974407,
-0.001236487994901836,
-0.01796898990869522,
0.0017183175077661872,
0.034860242158174515,
0.03779983147978783,
-0.006232472136616707,
-0.04685000702738762,
0.00304407998919487,
0.03438659384846687,
-0.035294730216264725,
0.010273768566548824,
-0.0005681660841219127,
-0.029196253046393394,
-0.02655007317662239,
-0.058430273085832596,
0.04912340268492699,
-0.024969512596726418,
0.024226775392889977,
-0.00017878905055113137,
-0.016950419172644615,
0.046413663774728775,
0.005529284942895174,
-0.0026426673866808414,
-0.032156605273485184,
0.011179745197296143,
0.02543601021170616,
-0.007398132234811783,
-0.012500335462391376,
0.044989485293626785,
-0.0151896420866251,
-0.0032705473713576794,
0.01633640192449093,
0.04741569235920906,
0.06437988579273224,
-0.04072761908173561,
0.029804479330778122,
0.007390862330794334,
-0.040066011250019073,
-0.03673206642270088,
0.025075919926166534,
0.02805398590862751,
0.0011378470808267593,
-0.026852425187826157,
-0.02151128649711609,
-0.049984026700258255,
0.023481324315071106,
0.03180238977074623,
-0.06652458012104034,
-0.00563993863761425,
0.04417838156223297,
-0.09006975591182709,
-0.00501637440174818,
-0.04414259269833565,
-0.06361949443817139,
0.02917737513780594,
-0.059894315898418427,
-0.006645514164119959,
0.04450606927275658,
0.004497508052736521,
0.07955198734998703,
-0.005389752797782421,
-0.030331183224916458,
-0.000604066182859242,
-0.04524226486682892,
0.045370422303676605,
-0.026699313893914223,
0.0070355478674173355,
-0.05284697562456131,
-0.00556924007833004,
0.07215964794158936,
0.022617684677243233,
-0.05746529623866081,
0.0139576131477952,
0.04852475970983505,
-0.007192703895270824,
-0.0392780564725399,
-0.0369725227355957,
0.029307538643479347,
0.012814179994165897,
0.03626132383942604,
-0.013855013065040112,
0.04607294499874115,
0.03158280625939369,
-0.05582750588655472,
-0.0055565559305250645,
0.027467111125588417,
0.0035544023849070072,
0.02036328986287117,
-0.024631401523947716,
-0.02726208046078682,
-0.00018631973944138736,
0.00894199963659048,
0.01969657652080059,
-0.004775322042405605,
-0.002580321626737714,
-0.02211872860789299,
0.036737967282533646,
0.06272746622562408,
0.02557043731212616,
-0.023043695837259293,
-0.055967554450035095,
0.04304388910531998,
0.001017365138977766,
-0.11550329625606537,
-0.06777078658342361,
0.01807824894785881,
-0.07197831571102142,
-0.06176447868347168,
-0.0228562131524086,
-0.009403666481375694,
0.017535537481307983,
0.00477443216368556,
-0.027384484186768532,
-0.048544224351644516,
-0.04093160107731819,
-0.007853452116250992,
-0.0004891360877081752,
0.01471195463091135,
-0.0061796181835234165,
0.0043464838527143,
0.024894196540117264,
-0.04793453961610794,
-0.01322937197983265,
0.0009553648997098207,
0.047091081738471985,
0.033896010369062424,
-0.062182094901800156,
0.049690715968608856,
-0.017614416778087616,
0.011737458407878876,
0.025351135060191154,
-0.05955023318529129,
-0.010088426060974598,
0.007798731327056885,
-0.0167207233607769,
-0.008311069570481777,
-0.004408079199492931,
-0.011378624476492405,
-0.004106723237782717,
-0.019162055104970932,
0.0032167464960366488,
0.060739219188690186,
0.04400766268372536,
0.060247812420129776,
-0.004342842847108841,
-0.008467604406177998,
0.0012972239637747407,
-0.04947897046804428,
-0.005180915351957083,
0.0614934079349041,
0.048798687756061554,
-0.0137205570936203,
-0.015770886093378067,
0.021146608516573906,
-0.025908198207616806,
-0.002629183465614915,
0.026928894221782684,
-0.03455854952335358,
0.04514956846833229,
-0.05742265284061432,
0.049090735614299774,
-0.08090971410274506,
-0.024760376662015915,
0.0024760866072028875,
-0.057777561247348785,
-0.006344781722873449,
0.02026693895459175,
-0.06611645966768265,
0.01694757118821144,
0.014455439522862434,
0.032573506236076355,
0.03637778013944626,
-0.05697919428348541,
-0.01758418418467045,
0.017471717670559883,
-0.08373513072729111,
0.034500639885663986,
0.01715659350156784,
-0.01347386371344328,
0.025053787976503372,
0.03857039660215378,
-0.0006643393426202238,
0.06471046805381775,
-0.03315889462828636,
-0.059554558247327805,
-0.002416820265352726,
-0.026732072234153748,
-0.020800316706299782,
-0.008280402980744839,
0.031477395445108414,
-0.049436576664447784,
0.04401678591966629,
0.016439924016594887,
-0.04188196361064911,
0.036284781992435455,
0.02559535950422287,
0.02418385073542595,
-0.006867441814392805,
0.03208046033978462,
-0.02294345386326313,
0.039267197251319885,
0.035563305020332336,
0.051633864641189575,
-0.045095477253198624,
0.0075711472891271114,
-0.004670123569667339,
0.0018336927751079202,
0.0649157166481018,
-0.020579688251018524,
-0.016110477969050407,
-0.020596377551555634,
0.04481179639697075,
0.032155729830265045,
-0.008645575493574142,
-0.01664920523762703,
-0.10303889214992523,
0.041963085532188416,
0.010694400407373905,
-0.007398935034871101,
-0.0023772581480443478,
-0.03407391533255577,
0.01802871935069561,
0.01581031084060669,
0.017226655036211014,
-0.023307938128709793,
0.0651903748512268,
0.08224714547395706,
0.014708996750414371,
-0.023512262850999832,
0.0020197625271975994,
0.03464469686150551,
0.019455108791589737,
0.006493427790701389,
-0.04658609256148338,
0.04323748126626015,
0.00644930312409997,
-0.010578780435025692,
0.020125487819314003,
0.04670780897140503,
-0.0029529444873332977,
0.05984736979007721,
-0.06257520616054535,
-0.00029113833443261683,
0.04409142583608627,
-0.01969754695892334,
0.030965832993388176,
-0.007114863023161888,
0.007079427130520344,
-0.04196186363697052,
0.01764296554028988,
0.07305479049682617,
-0.039017535746097565,
-0.036623213440179825,
-0.030746813863515854,
-0.0140542546287179,
-0.038140490651130676,
0.012763654813170433,
-0.017240440472960472,
0.021272918209433556,
-0.06300769746303558,
0.02448282018303871,
-0.03256312012672424,
0.005338921677321196,
-0.03599293529987335,
0.03914918750524521,
-0.030354654416441917,
-0.018090462312102318,
-0.017785022035241127,
0.0024353961925953627,
0.05465341731905937,
-0.05840840935707092,
0.0013759913854300976,
-0.013624440878629684,
-0.04448285698890686,
0.04359583929181099,
0.01677631214261055,
0.002404401544481516,
0.02359841763973236,
0.03555450215935707,
-0.031203951686620712,
-0.0026748378295451403,
0.045012250542640686,
-0.004437013529241085,
0.012279254384338856,
0.0433737114071846,
-0.03685767948627472,
-0.0626748651266098,
0.0835711807012558,
-0.060958828777074814,
0.06738310307264328,
0.027933260425925255,
0.06368241459131241,
0.02769627422094345,
-0.00806956086307764,
-0.0035161315463483334,
0.05927412584424019,
-0.027242477983236313,
-0.0529261976480484,
0.007546740584075451,
0.006701698526740074,
0.017943883314728737,
-0.055689480155706406,
-0.008030997589230537,
-0.008216115646064281,
-0.013248687610030174,
-0.01311556901782751,
0.02590707130730152,
0.00941565539687872,
0.0011077271774411201,
-0.034547559916973114,
0.006410418078303337,
-0.011754794977605343,
-0.009484123438596725,
-0.09150711447000504,
-0.010595060884952545,
0.004886283073574305,
-0.01343939546495676,
-0.02287985570728779,
-0.01578388921916485,
0.0004851817211601883,
-0.030507385730743408,
-0.0031406304333359003,
-0.03331412374973297,
0.0020606420002877712,
-0.00036279187770560384,
-0.010015608742833138,
-0.050900813192129135,
-0.0697798877954483,
0.008157326839864254,
0.022451933473348618,
-0.043248798698186874,
0.022434385493397713,
-0.0031614117324352264,
-0.028143052011728287,
-0.02169257216155529,
-0.024802789092063904,
-0.05358046665787697,
-0.017313964664936066,
0.045468769967556,
-0.026611246168613434,
-0.044840000569820404,
0.02985355257987976,
0.04073222354054451,
0.0015969303203746676,
-0.073702372610569,
-0.017732203006744385,
0.003294566413387656,
-0.05766117945313454,
0.03399502858519554,
0.03848158195614815,
0.009895840659737587,
-0.05958116799592972,
-0.004679800011217594,
-0.0059572807513177395,
0.03813670948147774,
-0.023195669054985046,
-0.010155541822314262,
0.054534971714019775,
-0.06792613118886948,
-0.005805994849652052,
0.04690610617399216,
0.03531617298722267,
-0.0677538737654686,
-0.009973596781492233,
-0.01847527176141739,
-0.026903336867690086,
-0.049140170216560364,
0.013606984168291092,
-0.027766205370426178,
0.02605508454144001,
-0.008620532229542732,
0.018964415416121483,
-0.07821585237979889,
-0.02184324525296688,
0.04406074061989784,
-0.06504373997449875,
-0.018535112962126732,
-0.033794961869716644,
-0.034326326102018356,
-0.006789768114686012,
-0.027346869930624962,
-0.012966272421181202,
-0.02468162588775158,
0.008744061924517155,
-0.004911556839942932,
0.03667400777339935,
0.04439898952841759,
-0.018157310783863068,
0.029578929767012596,
-0.029024947434663773,
0.046719808131456375,
-0.006068728864192963,
0.005203383509069681,
0.014262199401855469,
-0.005294535309076309,
0.013712938874959946,
0.04498200863599777,
0.07730360329151154,
0.015150695107877254,
-0.02152416482567787,
-0.05622953176498413,
-0.05015056952834129,
-0.028178047388792038,
0.03098999708890915,
-0.01062028668820858,
-0.008134237490594387,
0.0561172217130661,
-0.0003261677920818329,
0.06026647612452507,
-0.004465776961296797,
-0.027094023302197456,
-0.015538724139332771,
-0.0028112849686294794,
0.015624195337295532,
0.012150848284363747,
-0.030852945521473885,
0.0028056325390934944,
0.02745111659169197,
-0.04432845860719681,
0.05049559846520424,
-0.053240615874528885,
0.055934175848960876,
-0.03416461870074272,
0.034669287502765656,
0.03896503150463104,
0.03560379147529602,
0.013196581043303013,
0.030396372079849243,
-0.014998852275311947,
0.010348580777645111,
-0.0521596223115921,
-0.018951434642076492,
0.03189191594719887,
0.016264956444501877,
-0.0686187669634819,
0.01450111623853445,
0.010955201461911201,
-0.06495043635368347,
-0.03352651372551918,
0.03908950835466385,
0.00312451901845634,
0.007419649977236986,
-0.006108008790761232,
0.027375882491469383,
0.037936121225357056,
0.012432010844349861,
0.0055571915581822395,
0.01961253397166729,
-0.0028836559504270554,
0.018441908061504364,
-0.03594960272312164,
0.08717609196901321,
0.03438268229365349,
-0.048475224524736404,
-0.014330443926155567,
-0.0359102338552475,
-0.016941620036959648,
-0.0189647413790226,
-0.03513538837432861,
0.019417166709899902,
-0.022859325632452965,
0.037810102105140686,
-0.03408282250165939,
-0.056234896183013916,
-0.03853198140859604,
0.023132232949137688,
-0.03665429353713989,
0.005680551286786795,
-0.019284293055534363,
-0.032489679753780365,
-0.004908723756670952,
-0.009661027230322361,
-0.014664877206087112,
0.005900350399315357,
0.006411211099475622,
0.05433231219649315,
-0.00006916710117366165,
0.0778588131070137,
0.01055273786187172,
0.05172163248062134,
-0.004296275321394205,
-0.040160197764635086,
0.009699944406747818,
0.03951587900519371,
0.024876074865460396,
0.0011924547143280506,
0.06411320716142654,
-0.048074185848236084,
-0.026021748781204224,
-0.001653274754062295,
0.03930045664310455,
0.04284258186817169,
-0.010031060315668583,
0.02074144035577774,
-0.04062192142009735,
0.021361930295825005,
0.0635448470711708,
-0.01124582253396511,
0.008334500715136528,
0.016356738284230232,
0.06861753761768341,
0.05411122739315033,
-0.019863205030560493,
0.022510968148708344,
-0.009739378467202187,
-0.02608269639313221,
-0.05896366387605667,
-0.037632670253515244,
-0.038004837930202484,
-0.10717600584030151,
0.006046402268111706,
-0.0006823309813626111,
-0.008718579076230526,
-0.02937301993370056,
-0.02056966908276081,
-0.014768270775675774,
0.010974952019751072,
0.004888331051915884,
-0.028021084144711494,
0.03493312746286392,
-0.01715662330389023,
-0.022455016151070595,
-0.02064581587910652,
-0.03800399228930473,
0.034117259085178375,
-0.027305196970701218,
-0.03370095044374466,
-0.12044620513916016,
0.05445791035890579,
-0.035671260207891464,
-0.015133258886635303,
-0.009813413955271244,
-0.03466228023171425,
0.005735649261623621,
0.029137706384062767,
-0.02935515157878399,
-0.016961336135864258,
0.049483541399240494,
-0.06209481507539749,
0.03400316461920738,
-0.0053380923345685005,
-0.05946335569024086,
0.02663164958357811,
-0.02168915793299675,
0.008215919137001038,
-0.010508733801543713,
0.003552424255758524,
-0.020069731399416924,
0.055448081344366074,
-0.0069541349075734615,
0.050203144550323486,
0.006149923894554377,
-0.010773909278213978,
0.010181629098951817
] |
<p>The game <a href="http://gamelab.mit.edu/games/a-slower-speed-of-light/">"A slower speed of light"</a> from MIT claims to simulate effects of special relativity:</p>
<blockquote>
<p>Visual effects of special relativity gradually become apparent to the
player, increasing the challenge of gameplay. These effects, rendered
in realtime to vertex accuracy, include the Doppler effect (red- and
blue-shifting of visible light, and the shifting of infrared and
ultraviolet light into the visible spectrum); the searchlight effect
(increased brightness in the direction of travel); time dilation
(differences in the perceived passage of time from the player and the
outside world); Lorentz transformation (warping of space at near-light
speeds); and the runtime effect (the ability to see objects as they
were in the past, due to the travel time of light).</p>
</blockquote>
<p>But does restricting the render engine to special relativity not miss out several effects that might happen close to the speed of light? Especially I'm thinking about effects related to inertia and acceleration/rotation of the observer. So are there any important effects missing which would make the game a even more realistic simulation of the movement close to the speed of light?</p> | g5539 | [
0.004202627576887608,
0.07368919998407364,
-0.0017252314137294888,
0.003051444888114929,
0.00521654449403286,
0.012078596279025078,
0.030013443902134895,
0.04317045211791992,
0.023675434291362762,
0.01045274455100298,
0.08448564261198044,
-0.008015132509171963,
0.0539066419005394,
0.03650758042931557,
0.0013755628606304526,
-0.016934355720877647,
0.07290932536125183,
-0.02745668962597847,
0.024744592607021332,
0.005146611947566271,
0.07382648438215256,
-0.04211404547095299,
0.01055939681828022,
-0.019717661663889885,
-0.025834759697318077,
0.054175037890672684,
0.033818863332271576,
-0.060680944472551346,
-0.03517107293009758,
0.013451005332171917,
0.039275944232940674,
-0.05496883764863014,
-0.007572081871330738,
-0.011934452690184116,
0.03695236146450043,
-0.016817424446344376,
0.03960030525922775,
0.03354152292013168,
-0.004874167963862419,
0.022569138556718826,
-0.02575564570724964,
0.01675741747021675,
-0.0496535524725914,
0.009426918812096119,
0.0541401170194149,
0.029506152495741844,
0.016907289624214172,
0.014019712805747986,
0.0160483717918396,
-0.028677189722657204,
-0.032359398901462555,
-0.008033456280827522,
-0.012461700476706028,
-0.00909801758825779,
0.0540095716714859,
-0.028376836329698563,
-0.04040031507611275,
0.032161153852939606,
0.046820852905511856,
0.042416006326675415,
0.004858474712818861,
-0.017817871645092964,
0.0570506788790226,
0.015732502564787865,
0.028101224452257156,
-0.003169021336361766,
-0.013487696647644043,
-0.04451591148972511,
-0.01533507090061903,
-0.0076119257137179375,
-0.00523053715005517,
0.012096269056200981,
-0.07550767809152603,
-0.011791693046689034,
-0.029742831364274025,
0.030534178018569946,
0.012487680651247501,
-0.028501015156507492,
-0.07135771214962006,
0.015325930900871754,
-0.07229482382535934,
-0.002801542868837714,
-0.015023850835859776,
-0.011208008043467999,
0.06388029456138611,
-0.008341477252542973,
-0.022255340591073036,
0.008878322318196297,
0.026078905910253525,
0.010481351055204868,
0.07341624796390533,
-0.04963656887412071,
0.031030403450131416,
0.021682659164071083,
-0.07072088867425919,
0.003412221558392048,
-0.03901863470673561,
0.05301535129547119,
0.039032239466905594,
0.04263006150722504,
-0.004939374513924122,
0.01268311869353056,
0.02202296070754528,
0.015166808851063251,
-0.006260985042899847,
-0.04428614675998688,
-0.021605975925922394,
0.05354224517941475,
0.03221997991204262,
-0.015232308767735958,
-0.005794375203549862,
-0.10377535969018936,
0.010510748252272606,
-0.06542576849460602,
-0.0822855681180954,
-0.04680861905217171,
0.06030121445655823,
-0.008636686950922012,
-0.004005884286016226,
0.00894257053732872,
-0.013977404683828354,
0.03306366503238678,
-0.025088690221309662,
-0.001400528009980917,
0.0011291367700323462,
-0.024926140904426575,
-0.03909915313124657,
0.00951966643333435,
-0.010090786963701248,
-0.01182091236114502,
-0.033280372619628906,
0.013550972566008568,
-0.012393149547278881,
0.039727795869112015,
-0.04395220801234245,
-0.0005802791565656662,
0.048376332968473434,
0.009659238159656525,
-0.01467814203351736,
0.011399051174521446,
0.051653165370225906,
-0.014252126216888428,
-0.006708746775984764,
-0.0034091193228960037,
-0.03335149213671684,
-0.0008990110363811255,
0.018301479518413544,
0.04623176530003548,
-0.023443343117833138,
-0.004049845039844513,
0.01777133345603943,
0.017692256718873978,
0.04127028211951256,
0.008270826190710068,
-0.012679466046392918,
-0.007730049081146717,
0.017236623913049698,
-0.004174005705863237,
-0.06010638549923897,
0.03795861825346947,
0.05955160781741142,
-0.034033600240945816,
0.019694242626428604,
0.02357763610780239,
-0.054354842752218246,
0.027971787378191948,
0.040116600692272186,
-0.055358875542879105,
-0.0013150302693247795,
-0.056563038378953934,
-0.010684216395020485,
-0.03957139328122139,
0.0016231343615800142,
0.08930694311857224,
-0.00004915557656204328,
-0.014446397311985493,
0.04319114610552788,
-0.0378631167113781,
-0.06760024279356003,
0.031158868223428726,
-0.02943020686507225,
-0.05996326729655266,
-0.04025742784142494,
-0.07037044316530228,
0.04013637453317642,
-0.04156316816806793,
0.0019180260132998228,
-0.041640013456344604,
-0.050981685519218445,
0.019639529287815094,
-0.005435312166810036,
-0.043961357325315475,
-0.01873861253261566,
0.00034637999488040805,
-0.011998819187283516,
-0.021029040217399597,
0.036494430154561996,
-0.001350560924038291,
-0.030983585864305496,
0.062316350638866425,
-0.027693457901477814,
0.0867985188961029,
-0.0011524519650265574,
-0.0522727333009243,
0.03730688989162445,
-0.005745577160269022,
-0.007422572933137417,
0.011144888587296009,
0.01697072759270668,
-0.05296045169234276,
0.06720688194036484,
-0.023554986342787743,
0.05446835234761238,
-0.027936097234487534,
0.01932709291577339,
0.01781296730041504,
-0.04489567130804062,
0.035031963139772415,
-0.0023057933431118727,
0.024828504770994186,
0.0039380392991006374,
-0.026745952665805817,
-0.024723796173930168,
-0.014936371706426144,
-0.043500177562236786,
-0.05682465806603432,
-0.06068548560142517,
0.009137550368905067,
0.02225344628095627,
0.053396400064229965,
-0.009708601981401443,
0.0252371933311224,
-0.018432285636663437,
-0.027055054903030396,
0.02324412204325199,
0.002296145772561431,
-0.012451060116291046,
-0.01775136962532997,
0.06049393489956856,
-0.02684376761317253,
0.01825670152902603,
0.023488888517022133,
-0.020731037482619286,
-0.012950966134667397,
0.013750049285590649,
-0.04361119493842125,
0.025940638035535812,
-0.07979673892259598,
0.01894953101873398,
-0.031090790405869484,
-0.0304524227976799,
0.04160246253013611,
-0.02864820882678032,
0.0054354979656636715,
0.00973314419388771,
0.030637411400675774,
-0.012656064704060555,
0.04928476735949516,
-0.05943097546696663,
0.021759942173957825,
-0.02118505910038948,
0.011808579787611961,
-0.004235942382365465,
0.021795444190502167,
0.04391980543732643,
0.08300402760505676,
0.007131122052669525,
0.012349884957075119,
0.0027094713877886534,
0.02825397066771984,
-0.07142788916826248,
-0.0071263499557971954,
-0.044764529913663864,
0.003208376932889223,
0.0005004869308322668,
-0.004242312163114548,
-0.005451476201415062,
0.031745556741952896,
-0.0179902333766222,
0.01845809631049633,
0.00265319156460464,
-0.049216851592063904,
-0.007767533417791128,
-0.002624174579977989,
-0.002861929591745138,
-0.035926517099142075,
-0.01133823860436678,
-0.026129402220249176,
-0.012284562923014164,
0.029016122221946716,
-0.0657854974269867,
0.06019963324069977,
-0.02142498455941677,
0.007476241793483496,
-0.022204387933015823,
0.02459688112139702,
-0.06383717060089111,
-0.023782750591635704,
-0.026259586215019226,
0.049038756638765335,
0.035547759383916855,
-0.0023471012245863676,
0.007330647204071283,
0.12714523077011108,
-0.04512351006269455,
-0.016924848780035973,
-0.05531230941414833,
-0.018863914534449577,
-0.0038455291651189327,
-0.0013304321328178048,
0.013086252845823765,
0.016189545392990112,
-0.012854435481131077,
0.02709280699491501,
-0.06148792803287506,
-0.015324159525334835,
-0.017698485404253006,
0.01818954199552536,
-0.028172146528959274,
0.003750978037714958,
0.08811984956264496,
-0.03464055061340332,
-0.05615982040762901,
-0.007925069890916348,
0.022993924096226692,
0.04674232006072998,
0.04560479894280434,
-0.011861669830977917,
-0.02449173480272293,
-0.0006870859651826322,
0.05166815221309662,
-0.028795981779694557,
-0.049110740423202515,
0.0447721965610981,
-0.06213819235563278,
0.023948639631271362,
-0.025754783302545547,
0.012942450121045113,
0.028343256562948227,
-0.05945555865764618,
0.0695449635386467,
0.0122350063174963,
-0.04147703945636749,
0.03775734826922417,
0.027507077902555466,
-0.03654615208506584,
0.012106548063457012,
0.0017868810100480914,
0.006597178056836128,
-0.01659298688173294,
0.06535830348730087,
-0.03373732417821884,
-0.010917693376541138,
-0.03477850556373596,
0.030587781220674515,
0.03532633185386658,
0.052011556923389435,
0.005365768913179636,
0.050003498792648315,
-0.025372270494699478,
-0.02530008926987648,
0.01452378835529089,
-0.043096333742141724,
0.025583872571587563,
0.0194571353495121,
0.06422973424196243,
-0.012464313767850399,
0.044779468327760696,
-0.036667805165052414,
0.01722736656665802,
0.02362488955259323,
-0.005786695051938295,
-0.03789520636200905,
0.029153110459446907,
0.04617202654480934,
-0.030400633811950684,
0.03759577125310898,
0.05691448599100113,
-0.01447294931858778,
-0.005729304160922766,
0.006223252043128014,
0.0688788965344429,
0.018525870516896248,
-0.0025695187505334616,
0.05091068148612976,
-0.0028625698760151863,
0.02152380160987377,
-0.06641973555088043,
0.02004415914416313,
-0.05403558164834976,
-0.01488908939063549,
-0.017027297988533974,
-0.033524077385663986,
0.007847150787711143,
-0.013943086378276348,
0.03103800304234028,
0.00907460693269968,
-0.05581197142601013,
-0.014070355333387852,
-0.021495234221220016,
-0.03293446823954582,
0.031119277700781822,
-0.01628851518034935,
0.016167044639587402,
-0.04854308068752289,
-0.04971123859286308,
0.0035385240335017443,
0.02986721135675907,
0.005297629162669182,
0.030446939170360565,
-0.05082125589251518,
0.04072848707437515,
-0.022737406194210052,
-0.0694625973701477,
-0.03643492981791496,
0.026828322559595108,
-0.014898039400577545,
-0.02901419810950756,
-0.03608161211013794,
0.037887103855609894,
0.0023815457243472338,
0.0369555838406086,
0.026324061676859856,
0.014827324077486992,
0.042025331407785416,
0.023245904594659805,
0.036966390907764435,
-0.009383957833051682,
-0.035923071205616,
-0.013444838114082813,
0.0394413061439991,
0.017789317294955254,
0.020253056660294533,
0.010598930530250072,
0.00039598788134753704,
0.036211274564266205,
0.004237083718180656,
0.009951385669410229,
0.05125673487782478,
0.04857303202152252,
-0.04249236360192299,
-0.00002774622043943964,
0.09262390434741974,
-0.04786951467394829,
-0.08812574297189713,
0.08932148665189743,
-0.0662277415394783,
0.017105432227253914,
-0.06032010167837143,
-0.022375550121068954,
-0.024284740909934044,
0.021208079531788826,
0.0045662205666303635,
-0.0035051212180405855,
0.02258736453950405,
-0.025886330753564835,
-0.075358085334301,
0.02477305941283703,
-0.007045450620353222,
-0.0014885185519233346,
0.05317089706659317,
0.06377311050891876,
-0.01156475767493248,
-0.023629704490303993,
-0.018552040681242943,
0.0011208303039893508,
-0.04380187764763832,
-0.022987637668848038,
-0.022875718772411346,
-0.026404205709695816,
-0.04222144931554794,
-0.04991469532251358,
0.015996837988495827,
0.03930934518575668,
0.011586584150791168,
-0.004997985437512398,
-0.06601215153932571,
-0.01090828888118267,
0.02369612269103527,
-0.019808420911431313,
-0.0329071506857872,
-0.0018937870627269149,
0.0037043013144284487,
-0.0022900840267539024,
-0.043387480080127716,
0.03619692474603653,
-0.04697596654295921,
0.036057282239198685,
-0.02788069099187851,
-0.04582504555583,
0.0054681128822267056,
-0.018927089869976044,
-0.04898247495293617,
-0.05154126510024071,
-0.014456231147050858,
0.05564301460981369,
0.05803671106696129,
0.03787994384765625,
-0.010946295224130154,
-0.016201432794332504,
-0.07084072381258011,
0.03576483950018883,
0.0837254747748375,
-0.051747240126132965,
-0.025344794616103172,
0.016019372269511223,
0.052337244153022766,
0.01969134621322155,
-0.049935031682252884,
0.02476203255355358,
0.00853473600000143,
0.03506128862500191,
0.03396144509315491,
-0.05118999257683754,
0.04334857314825058,
-0.007506879512220621,
0.019403140991926193,
-0.0068964529782533646,
0.01773574762046337,
-0.0700911432504654,
-0.014087586663663387,
-0.031496793031692505,
0.00849869940429926,
-0.021874433383345604,
0.048583246767520905,
0.026442065834999084,
0.03405865281820297,
0.0069072251208126545,
0.013733168132603168,
0.028018364682793617,
0.026891041547060013,
0.015502631664276123,
-0.035542022436857224,
-0.006937077734619379,
0.0024767396971583366,
-0.008718554861843586,
0.018309326842427254,
-0.04078235477209091,
-0.014176150783896446,
0.02672114036977291,
-0.0248713418841362,
-0.01107786875218153,
-0.010649424977600574,
0.09068600088357925,
0.01995016634464264,
-0.04871726408600807,
0.01096588559448719,
0.04314453899860382,
0.06497468799352646,
-0.04736517369747162,
-0.0183805450797081,
-0.020718300715088844,
0.02125568315386772,
0.0640430673956871,
0.028193006291985512,
0.008645981550216675,
0.008962028659880161,
-0.024584731087088585,
0.025630613788962364,
0.004736818838864565,
0.03701045364141464,
0.04708008095622063,
0.005983458831906319,
-0.019616473466157913,
-0.02680186554789543,
-0.005506342742592096,
0.02255422994494438,
-0.011860119178891182,
0.07797644287347794,
-0.014829904772341251,
0.005734680220484734,
-0.018577968701720238,
0.008864238858222961,
0.006750255357474089,
-0.003828423796221614,
-0.024287905544042587,
-0.011383520439267159,
-0.007097737863659859,
-0.07407378405332565,
0.016543759033083916,
-0.08840733766555786,
-0.014129272662103176,
-0.026412244886159897,
-0.02664085105061531,
-0.0009080301388166845,
0.000893686490599066,
-0.0405677929520607,
0.037740182131528854,
0.012625949457287788,
-0.04781477898359299,
0.04462740570306778,
-0.0020577397663146257,
-0.025721753016114235,
-0.06843104213476181,
0.0030310163274407387,
-0.05926674231886864,
-0.04229350760579109,
-0.013666410930454731,
-0.05005273595452309,
0.06149942800402641,
0.011421946808695793,
-0.017870549112558365,
0.05503837764263153,
-0.04416881129145622,
0.012158936820924282,
0.025909636169672012,
-0.1095476746559143,
0.024358157068490982,
0.050125475972890854,
-0.0018569889944046736,
0.016685545444488525,
0.016815388575196266,
-0.02577493153512478,
0.022585172206163406,
-0.027751337736845016,
0.025553056970238686,
0.006702912040054798,
-0.03725079819560051,
-0.023686187341809273,
-0.06101033464074135,
0.025193756446242332,
-0.044993337243795395,
0.02667250670492649,
0.012675484642386436,
0.00300329620949924,
0.009876825846731663,
-0.07193723320960999,
0.025698013603687286,
-0.0035257330164313316,
0.028851525858044624,
0.014187781140208244,
-0.010414425283670425,
-0.006342954467982054,
0.052176013588905334,
0.07204319536685944,
0.047906722873449326,
-0.0030744983814656734,
0.007113938685506582,
0.04496566578745842,
0.05128698796033859,
-0.023065682500600815,
-0.03338545188307762,
-0.035372164100408554,
-0.0051301042549312115,
-0.011115784756839275,
-0.0335545688867569,
0.05394361540675163,
0.05387968197464943,
0.019686749204993248,
-0.008620164357125759,
-0.015560531057417393,
-0.015481863170862198,
-0.009565107524394989,
-0.05633215978741646,
-0.03239656239748001,
-0.006723116617649794,
0.001953257480636239,
0.016427043825387955,
0.02189975045621395,
-0.12324690073728561,
-0.08008560538291931,
-0.07579704374074936,
-0.04328588396310806,
-0.0028805681504309177,
0.01577499322593212,
0.012687255628407001,
-0.013088646344840527,
-0.026924364268779755,
0.03259440138936043,
0.05500572547316551,
0.02115158922970295,
-0.028085796162486076,
-0.010142996907234192,
0.02883901074528694,
0.02709229104220867,
0.017733173444867134,
-0.031038878485560417,
0.05954517796635628,
0.0024739899672567844,
-0.038478538393974304,
-0.02785397879779339,
0.06555124372243881,
0.039962705224752426,
0.062495388090610504,
-0.021136386319994926,
0.034074533730745316,
-0.011267787776887417,
-0.011096596717834473,
-0.049866948276758194,
-0.0318022258579731,
-0.009839779697358608,
0.038287051022052765,
-0.04113845154643059,
0.03229794278740883,
-0.0013860056642442942,
-0.03711028769612312,
0.0021085557527840137,
0.04718896746635437,
-0.005145495757460594,
0.024373063817620277,
-0.06756875663995743,
-0.03890670835971832,
0.01968390680849552,
0.007006756495684385,
0.03058520331978798,
0.05875508859753609,
-0.03828459233045578,
0.033071257174015045,
-0.018829097971320152,
-0.012277229689061642,
0.045128487050533295,
0.009087775833904743,
-0.05036499723792076,
-0.05057329684495926,
-0.005163188558071852,
0.023752884939312935,
0.017236139625310898,
-0.036096952855587006,
-0.006469067186117172,
-0.019302910193800926,
-0.00840824469923973,
0.03386139124631882,
-0.04388737305998802,
-0.044354867190122604,
0.08797495812177658,
0.004124537575989962,
0.05830442160367966,
-0.043710920959711075,
0.011983747594058514,
-0.07076945900917053,
0.02449849247932434,
0.00033253341098316014,
0.0011515221558511257,
0.027578754350543022,
-0.06223773583769798,
0.037303242832422256,
0.008871720172464848,
0.009359347634017467,
-0.04634257033467293,
0.016819728538393974,
0.0030878493562340736,
0.0027746791020035744,
0.03171247988939285,
0.004911520984023809,
0.05556194856762886,
0.007883420214056969,
0.02889452688395977,
0.007321010809391737,
0.0036642516497522593,
0.046101342886686325,
-0.047849319875240326,
0.04139324277639389,
-0.051943495869636536,
-0.013849851675331593,
0.0667189434170723,
0.025301937013864517,
0.008204340934753418,
-0.04719211161136627,
0.013232904486358166,
0.011800609529018402,
-0.0009494043188169599,
-0.02276974357664585,
0.03751083090901375,
0.038018710911273956,
-0.052511874586343765,
-0.036355551332235336,
0.050070974975824356,
0.008421624079346657
] |
<p>I have read that plasma is a state of matter that resembles gas but it consists of ions and electrons coexisting. So my question is : If plasma is just ionized gas, will ideal gas law apply for it ?</p> | g5540 | [
0.02640652470290661,
-0.00034584247623570263,
0.011593123897910118,
0.018712418153882027,
0.02341676875948906,
0.021735476329922676,
-0.1223813071846962,
0.040291834622621536,
-0.0148081099614501,
0.011809560470283031,
0.042440611869096756,
-0.015237299725413322,
-0.010386106558144093,
0.008374239318072796,
-0.02061951905488968,
-0.014246984384953976,
0.07768528163433075,
0.030639586970210075,
-0.029594583436846733,
0.006852355320006609,
-0.026564981788396835,
-0.051761772483587265,
0.021772237494587898,
-0.07529573887586594,
-0.002627782989293337,
-0.035810425877571106,
-0.018977973610162735,
0.02716163732111454,
0.015835285186767578,
-0.005564527120441198,
0.010369988158345222,
0.009319012053310871,
-0.05545457452535629,
-0.05279384180903435,
-0.045366231352090836,
-0.05987691134214401,
0.008649936877191067,
0.03966900706291199,
0.008562902919948101,
-0.06577713042497635,
0.045007165521383286,
0.006984691601246595,
-0.0001371165126329288,
-0.006379581987857819,
0.015089614316821098,
0.02771102450788021,
0.039266426116228104,
-0.02320515364408493,
0.028048720210790634,
0.0007628052262589335,
-0.06086333096027374,
0.059948090463876724,
-0.026365630328655243,
-0.05969860404729843,
0.0059254588559269905,
0.03224441781640053,
0.015537003055214882,
-0.0118870185688138,
0.03798595443367958,
0.007183763664215803,
0.08013865351676941,
0.04600917175412178,
0.009407171979546547,
-0.044449422508478165,
0.00891154631972313,
-0.027631696313619614,
-0.03984980285167694,
0.039565712213516235,
0.041112445294857025,
0.029476840049028397,
0.05214119702577591,
-0.013365711085498333,
-0.052967023104429245,
-0.05234481021761894,
0.016065066680312157,
-0.0131705766543746,
-0.005938311573117971,
-0.030116790905594826,
0.0561661459505558,
-0.0042755636386573315,
-0.02185271680355072,
-0.012733307667076588,
0.015551603399217129,
-0.011384903453290462,
0.019882239401340485,
-0.022781874984502792,
0.01135350577533245,
-0.038924433290958405,
0.017934953793883324,
-0.03510653227567673,
-0.013699943199753761,
-0.027005285024642944,
0.060818757861852646,
-0.009243757463991642,
-0.02737499214708805,
-0.020365441218018532,
-0.03333311155438423,
0.06705436110496521,
-0.008298576809465885,
-0.002557483036071062,
-0.03756006434559822,
-0.0410538986325264,
-0.01467409823089838,
-0.06542745232582092,
-0.005744489375501871,
0.010683325119316578,
0.027667446061968803,
0.0014269562670961022,
0.03272222727537155,
-0.045831069350242615,
-0.01111430674791336,
-0.010706202127039433,
-0.015785973519086838,
-0.018077900633215904,
-0.07770038396120071,
0.018427429720759392,
0.018095089122653008,
0.007136743050068617,
0.004212218802422285,
0.07187819480895996,
0.0706532746553421,
0.059616513550281525,
0.018389679491519928,
0.050655901432037354,
0.011877170763909817,
-0.017783086746931076,
0.04692859202623367,
-0.02333994209766388,
-0.039458271116018295,
-0.03081698901951313,
0.024015314877033234,
-0.042869456112384796,
-0.03920236602425575,
-0.005683549214154482,
0.0022219414822757244,
-0.030666688457131386,
-0.006893061101436615,
0.03927227854728699,
-0.06982828676700592,
-0.05569031089544296,
0.04114028066396713,
0.0068670655600726604,
-0.016246860846877098,
0.020201750099658966,
-0.04228542372584343,
-0.01941831037402153,
-0.03681560233235359,
0.0019999227952212095,
0.013647434301674366,
0.035520680248737335,
-0.005212047602981329,
0.005342986900359392,
0.06192878261208534,
-0.07007769495248795,
0.001979200169444084,
-0.04918287694454193,
0.036237478256225586,
0.02804613672196865,
-0.004032785072922707,
-0.04352635517716408,
-0.004415369126945734,
0.0037090240512043238,
0.01356497872620821,
-0.002215046202763915,
0.011921883560717106,
-0.022311216220259666,
0.040591854602098465,
0.005622173193842173,
0.026728879660367966,
0.01660774275660515,
-0.034089699387550354,
0.04015565663576126,
-0.038024917244911194,
0.09523480385541916,
0.051970839500427246,
0.0016626244178041816,
-0.0028709948528558016,
0.04898448660969734,
-0.00704794330522418,
-0.06221623718738556,
0.019628474488854408,
-0.019021794199943542,
-0.03803178295493126,
-0.020553303882479668,
-0.014843235723674297,
0.08058056235313416,
-0.026188479736447334,
0.003574653062969446,
-0.00954354926943779,
0.00819108635187149,
-0.029641414061188698,
0.042724963277578354,
-0.02794800139963627,
-0.03187461569905281,
0.049503304064273834,
0.007290913723409176,
0.010392987169325352,
-0.017445050179958344,
-0.062048740684986115,
-0.027372103184461594,
-0.018659008666872978,
0.06788277626037598,
-0.05040139704942703,
0.013703140430152416,
-0.009089040569961071,
0.014453145675361156,
-0.009675620123744011,
-0.09355182945728302,
0.07745090872049332,
0.023380350321531296,
0.042836517095565796,
0.006144177168607712,
-0.03512836992740631,
0.10088988393545151,
-0.044189076870679855,
0.03355850651860237,
0.024922464042901993,
0.04420284554362297,
0.009716348722577095,
-0.03054848499596119,
-0.04363425448536873,
-0.028610914945602417,
0.015815382823348045,
0.019727233797311783,
0.025558799505233765,
-0.01750366762280464,
-0.0011262991465628147,
0.050885509699583054,
0.013428403064608574,
0.014115297235548496,
0.02154143527150154,
0.03273066505789757,
0.025115514174103737,
-0.06970925629138947,
-0.0017550294287502766,
0.0815127044916153,
-0.04410102218389511,
0.005453651305288076,
0.009760407730937004,
0.005060464143753052,
-0.023013802245259285,
-0.027077099308371544,
0.008387402631342411,
0.025913545861840248,
0.021782029420137405,
-0.012934290803968906,
-0.024346519261598587,
0.0031714157667011023,
0.016584273427724838,
0.0007479942869395018,
-0.006462710909545422,
-0.009461822919547558,
-0.022378256544470787,
0.033226195722818375,
0.0090348981320858,
-0.03428545594215393,
-0.0022294525988399982,
0.009550033137202263,
-0.03146745637059212,
-0.013677306473255157,
0.020696021616458893,
-0.042554449290037155,
-0.0258743017911911,
0.006592433899641037,
-0.12251580506563187,
0.02006080374121666,
0.03640115633606911,
-0.0009408467449247837,
0.0036236667074263096,
0.0034307576715946198,
0.056419726461172104,
0.03117585927248001,
-0.08129658550024033,
0.047808874398469925,
0.06282569468021393,
0.010965882800519466,
0.0048155286349356174,
-0.037417784333229065,
0.009916682727634907,
-0.0719064474105835,
-0.01595320925116539,
0.01744312420487404,
-0.04018133878707886,
0.034238025546073914,
-0.02612846903502941,
-0.03571145609021187,
0.03621508926153183,
0.014383233152329922,
-0.018594319000840187,
0.05063202977180481,
-0.06549627333879471,
-0.015998588874936104,
0.0104226591065526,
-0.0063078803941607475,
-0.053616464138031006,
0.048173535615205765,
0.020673971623182297,
0.004452580586075783,
-0.028946667909622192,
0.050713688135147095,
-0.03257076069712639,
-0.059630244970321655,
-0.0032779404427856207,
-0.017361784353852272,
0.012590087950229645,
0.03037007339298725,
-0.08752474188804626,
-0.03439048305153847,
-0.0012808419996872544,
-0.0009054120164364576,
-0.013465045019984245,
0.04739319533109665,
-0.046655941754579544,
0.003559512086212635,
0.015110057778656483,
-0.019415372982621193,
-0.02433396689593792,
-0.002182397758588195,
-0.0028664804995059967,
0.039198532700538635,
-0.056744568049907684,
-0.037177879363298416,
0.07330472767353058,
-0.05595913901925087,
0.029621072113513947,
0.008475756272673607,
-0.008868146687746048,
-0.03103995881974697,
-0.039133332669734955,
0.04366723448038101,
-0.004425434395670891,
0.0001410897239111364,
-0.01829567179083824,
0.02025933936238289,
0.0026881855446845293,
-0.01607639342546463,
0.01571505516767502,
0.03167515993118286,
0.035889655351638794,
-0.006146324332803488,
0.03289689123630524,
-0.05179429426789284,
-0.02831839583814144,
-0.06386811286211014,
-0.021727237850427628,
0.02672034129500389,
-0.018978219479322433,
-0.006623039022088051,
0.04221660643815994,
-0.019457919523119926,
0.05270528793334961,
0.05147111788392067,
0.030383538454771042,
0.006214332301169634,
-0.028084155172109604,
-0.0212103258818388,
0.07270500063896179,
-0.00849681906402111,
-0.007636868394911289,
0.01155799813568592,
0.002346573630347848,
-0.028704794123768806,
0.05271496623754501,
-0.006669813301414251,
-0.0020906352438032627,
-0.008414587005972862,
-0.024904757738113403,
-0.010202552191913128,
0.005637194029986858,
-0.024845024570822716,
-0.037034980952739716,
-0.08486323058605194,
0.061795756220817566,
0.02157904952764511,
0.024331122636795044,
-0.023612912744283676,
-0.03158119320869446,
0.037626512348651886,
-0.016598116606473923,
0.020078210160136223,
-0.0006681418162770569,
0.027188602834939957,
0.014502035453915596,
0.037372034043073654,
0.03733308985829353,
0.01770365983247757,
0.03173689916729927,
0.08520302921533585,
0.05059053748846054,
-0.05687795579433441,
-0.014145933091640472,
-0.030395841225981712,
-0.02249300479888916,
-0.02081332914531231,
0.05948233976960182,
0.008234968408942223,
0.017198678106069565,
0.019560586661100388,
-0.02385527826845646,
0.03246230632066727,
0.03313520923256874,
0.03864806145429611,
0.030831020325422287,
-0.034489527344703674,
0.07044753432273865,
-0.004216342233121395,
0.03482700511813164,
-0.08765082061290741,
0.0006681235390715301,
-0.036866430193185806,
-0.016318511217832565,
0.04896159470081329,
0.022082507610321045,
0.01242824550718069,
0.020156335085630417,
0.026523426175117493,
-0.0199848935008049,
-0.013882224448025227,
0.026481349021196365,
0.02423986978828907,
-0.012257162481546402,
0.05086404085159302,
-0.016468467190861702,
-0.009088187478482723,
-0.031866405159235,
0.02691940777003765,
0.04671892896294594,
-0.00016514038725290447,
-0.013774149119853973,
0.00486575486138463,
-0.023067161440849304,
-0.045224498957395554,
0.0036056633107364178,
0.012159674428403378,
-0.085772305727005,
-0.011041436344385147,
-0.057652805000543594,
-0.0064362515695393085,
0.0040114871226251125,
0.06887053698301315,
0.021179743111133575,
0.02555110678076744,
0.04107123613357544,
-0.003193071810528636,
-0.012630371376872063,
0.015011041425168514,
-0.03276798501610756,
0.0035432809963822365,
-0.021480219438672066,
-0.032172393053770065,
0.03384304791688919,
-0.06909501552581787,
-0.005519334226846695,
-0.031072648242115974,
-0.029682928696274757,
-0.006028342060744762,
-0.0533805713057518,
0.032351959496736526,
0.006748783867806196,
0.010760301724076271,
-0.01053269486874342,
0.03272152692079544,
0.06986633688211441,
0.02665008418262005,
0.04446634277701378,
-0.014846702106297016,
-0.033933982253074646,
-0.006404408719390631,
-0.010031884536147118,
-0.005126545205712318,
0.027919979766011238,
-0.02492588572204113,
0.0007586772553622723,
-0.01582065038383007,
0.060714058578014374,
-0.015533071011304855,
-0.01601996086537838,
-0.031012315303087234,
0.00661102682352066,
-0.05325595661997795,
0.005353234242647886,
-0.030472269281744957,
0.07331813871860504,
-0.0003940882452297956,
-0.037006109952926636,
0.014046411029994488,
-0.020339444279670715,
0.022371642291545868,
-0.025314029306173325,
-0.06613904982805252,
-0.007349646184593439,
0.036399371922016144,
0.0440790131688118,
0.02931160479784012,
0.004129286389797926,
0.01214824989438057,
-0.07242471724748611,
-0.04009174183011055,
-0.020909728482365608,
0.019402818754315376,
-0.03365682438015938,
-0.016309941187500954,
-0.02547922171652317,
0.06168519705533981,
-0.011502468958497047,
0.04623621702194214,
-0.05905309319496155,
-0.02878842130303383,
-0.02122511900961399,
0.009925714693963528,
-0.017983639612793922,
-0.0289187952876091,
0.007372783962637186,
0.025746097788214684,
-0.05695332586765289,
0.007162249647080898,
-0.04719142988324165,
0.017977919429540634,
0.034440867602825165,
-0.03489714488387108,
0.028773855417966843,
-0.09924960136413574,
0.043638329952955246,
0.025430889800190926,
0.00009952968684956431,
-0.02291904203593731,
0.03677424415946007,
0.034519776701927185,
0.055496420711278915,
0.06203828752040863,
0.0395149365067482,
0.027982397004961967,
0.014372307807207108,
-0.02184920758008957,
-0.017864495515823364,
-0.03209998086094856,
-0.046691812574863434,
0.10782048851251602,
0.11471107602119446,
0.04146748036146164,
-0.03181101009249687,
-0.05283777415752411,
0.019855597987771034,
0.01839502714574337,
0.07440400123596191,
0.03941478952765465,
-0.06616371870040894,
0.03920980915427208,
0.027744950726628304,
-0.07504718750715256,
-0.039825085550546646,
-0.019656749442219734,
-0.005601345095783472,
-0.05197960138320923,
0.059379544109106064,
-0.002960546175017953,
0.038650739938020706,
0.0017884292174130678,
0.01488608680665493,
-0.02386380173265934,
0.006241484545171261,
0.10239632427692413,
-0.041930511593818665,
-0.03381090238690376,
0.038202762603759766,
-0.041613880544900894,
0.011204363778233528,
-0.009922022931277752,
0.023788634687662125,
-0.015268647111952305,
-0.044061947613954544,
-0.007406361401081085,
0.026733528822660446,
-0.002250894671306014,
0.03543305769562721,
-0.034104783087968826,
-0.004020662046968937,
-0.00011769905540859327,
-0.021694479510188103,
0.0058486582711339,
0.07792946696281433,
-0.013743022456765175,
-0.022566450759768486,
0.09038938581943512,
-0.015020539052784443,
-0.020872078835964203,
0.02287629432976246,
0.016335858032107353,
0.03441311791539192,
0.02746797353029251,
-0.01927615888416767,
-0.02226809412240982,
-0.019797172397375107,
-0.023193081840872765,
-0.015249432995915413,
0.024139270186424255,
-0.002264995127916336,
-0.02968943864107132,
0.008375115692615509,
0.023584801703691483,
-0.005231321789324284,
0.02686319127678871,
-0.07917261123657227,
-0.005281344056129456,
0.036076441407203674,
0.03360763192176819,
0.0015498042339459062,
0.036682214587926865,
-0.02993733622133732,
0.04074128344655037,
-0.03733221814036369,
-0.03593340516090393,
0.0008509753388352692,
-0.015671322122216225,
0.04655129835009575,
-0.003984786570072174,
-0.02851538546383381,
0.020740902051329613,
-0.03373195603489876,
0.005593401845544577,
-0.019478274509310722,
-0.00044469625572673976,
0.032504454255104065,
-0.02906421758234501,
-0.0019027891103178263,
0.01239437609910965,
0.0036167590878903866,
0.07632551342248917,
0.061235103756189346,
0.003164224326610565,
-0.015349766239523888,
-0.013463085517287254,
0.03173670172691345,
-0.038499053567647934,
0.025518061593174934,
-0.038105692714452744,
0.03443913906812668,
-0.04877954348921776,
0.07158203423023224,
-0.021935272961854935,
-0.01719711907207966,
-0.03164420276880264,
0.0657910630106926,
0.006113333161920309,
-0.06473333388566971,
0.013462322764098644,
0.03172900527715683,
-0.055073332041502,
-0.041396789252758026,
-0.023948824033141136,
-0.028913866728544235,
-0.03827128931879997,
-0.008304840885102749,
0.00862729363143444,
-0.02070976421236992,
0.031368982046842575,
0.036846622824668884,
-0.009990664198994637,
0.059604398906230927,
-0.044509463012218475,
-0.04950985684990883,
0.011628768406808376,
-0.01426859013736248,
0.004346000030636787,
0.04451984167098999,
0.014059641398489475,
0.05408228933811188,
-0.05475287511944771,
-0.06944072246551514,
-0.07966822385787964,
0.005018261261284351,
-0.05379170551896095,
0.015270779840648174,
0.037904877215623856,
0.03232796862721443,
0.008581249043345451,
-0.03981354087591171,
0.015777720138430595,
0.053373049944639206,
-0.023798402398824692,
0.015527465380728245,
0.04801683872938156,
0.0419580340385437,
0.0014053885824978352,
-0.02013566717505455,
-0.0074495598673820496,
0.03362365812063217,
0.010341372340917587,
-0.06530708819627762,
-0.04189644381403923,
0.02532430924475193,
-0.02345164306461811,
0.05244027450680733,
-0.032500144094228745,
-0.056964728981256485,
-0.006994192488491535,
0.05544953793287277,
-0.00002169352228520438,
-0.042769547551870346,
-0.017716893926262856,
0.0025348220951855183,
-0.024159831926226616,
-0.019858000800013542,
-0.020625168457627296,
0.0012089221272617579,
0.0006195455207489431,
0.02052648365497589,
-0.010019311681389809,
-0.062381502240896225,
-0.0766601711511612,
0.02756180614233017,
0.007082856725901365,
0.05780688673257828,
0.005069179460406303,
0.028173919767141342,
-0.06036490947008133,
0.022636307403445244,
0.0017586168833076954,
0.037368498742580414,
-0.012400253675878048,
0.01791232079267502,
-0.003579666605219245,
0.05152790620923042,
-0.0324283204972744,
0.010372321121394634,
0.010712425224483013,
0.018316170200705528,
-0.02581280842423439,
-0.007216030731797218,
-0.02094084769487381,
-0.03521686792373657,
0.058301232755184174,
0.043314944952726364,
0.015682782977819443,
-0.0658678412437439,
-0.011741283349692822,
0.05144766718149185,
-0.04137459769845009,
0.04115716367959976,
0.029582204297184944,
-0.056177642196416855,
-0.02299386076629162,
0.00008274172432720661,
-0.022012503817677498,
0.08383232355117798,
0.004555356223136187,
-0.0107248704880476,
-0.04175053909420967,
-0.0011584694730117917,
0.0248424019664526,
0.030434872955083847,
-0.024151504039764404,
-0.02910095453262329,
0.02369845099747181,
0.032473161816596985,
-0.06313739717006683,
0.03372650220990181,
-0.007205929607152939,
0.009896276518702507,
0.06256283074617386,
-0.006798666901886463,
0.029514187946915627,
0.05757199227809906,
-0.017400987446308136,
-0.020107222720980644,
-0.020703138783574104,
0.0065254163928329945,
-0.016487503424286842
] |
<p><img src="http://i.stack.imgur.com/GkwGl.jpg" alt="enter image description here"></p>
<p>How eq(4.4) is a solution of eq(4.3) </p> | g5541 | [
0.021618708968162537,
0.02244812250137329,
0.011841426603496075,
-0.04973102733492851,
0.031724799424409866,
0.007721997331827879,
0.01779203675687313,
0.0330926850438118,
-0.03996327146887779,
0.002758549526333809,
-0.05889630690217018,
-0.021785641089081764,
0.04739316552877426,
0.021835584193468094,
-0.020306868478655815,
0.04125401750206947,
0.03335251286625862,
-0.032824281603097916,
0.038736604154109955,
0.02812935598194599,
0.020762458443641663,
0.041803620755672455,
-0.009480567649006844,
0.002823227783665061,
0.027451036497950554,
-0.05523472651839256,
0.059190258383750916,
0.06714332848787308,
-0.02498580515384674,
-0.028931915760040283,
-0.000703374040313065,
0.030814580619335175,
0.04015623778104782,
-0.006703111343085766,
0.006989196874201298,
0.052131619304418564,
0.04349657520651817,
0.05597689375281334,
-0.02928629331290722,
-0.03832782432436943,
0.018275663256645203,
-0.053458768874406815,
-0.0003766050795093179,
0.04099268466234207,
0.05177636817097664,
-0.02213919907808304,
-0.013858181424438953,
0.039990536868572235,
0.0031425468623638153,
-0.01612216606736183,
-0.04654984548687935,
0.03970670700073242,
-0.006864453665912151,
-0.08254094421863556,
0.027422409504652023,
0.03998146578669548,
0.02361225336790085,
0.02875826135277748,
-0.023355625569820404,
0.0854659453034401,
0.027584247291088104,
-0.06429611146450043,
0.021243048831820488,
-0.0062740338034927845,
0.04125384986400604,
-0.018797799944877625,
0.01045291032642126,
0.030123937875032425,
0.022175664082169533,
-0.00696587935090065,
-0.006922406610101461,
0.02256889082491398,
0.011434385553002357,
-0.05611170455813408,
-0.005335808731615543,
-0.016921620815992355,
0.07663433998823166,
0.05697688087821007,
-0.06878368556499481,
-0.020103268325328827,
-0.012410566210746765,
0.024740304797887802,
-0.02820192277431488,
0.03289042413234711,
0.034390855580568314,
0.01770421862602234,
-0.00016532950394321233,
0.03242043778300285,
-0.005243654828518629,
-0.07065727561712265,
-0.055480506271123886,
-0.007604510989040136,
0.004978759679943323,
-0.009802381508052349,
0.013013068586587906,
-0.05066483095288277,
0.008386993780732155,
-0.03508695587515831,
-0.007003006525337696,
-0.051649872213602066,
0.030685588717460632,
0.021952981129288673,
-0.013531718403100967,
0.028898779302835464,
-0.062104757875204086,
0.03834082558751106,
0.1074429601430893,
0.03572152927517891,
-0.07041110098361969,
0.027479656040668488,
-0.0417969636619091,
0.010043279267847538,
-0.0029105227440595627,
0.002911072224378586,
-0.04182397574186325,
0.07398109138011932,
0.02902100794017315,
-0.021046310663223267,
-0.044183149933815,
0.04125342145562172,
0.023787805810570717,
-0.010375618934631348,
-0.007266236003488302,
0.04771687090396881,
0.014471407979726791,
-0.012449052184820175,
0.016860036179423332,
0.051137667149305344,
0.03549477085471153,
0.027530984953045845,
0.010147607885301113,
-0.01207720022648573,
0.04730338230729103,
0.05807875469326973,
0.02176700346171856,
0.0637960210442543,
0.030790269374847412,
0.01008764747530222,
-0.0325506217777729,
0.0432550348341465,
-0.027167461812496185,
-0.0068231248296797276,
0.008704379200935364,
0.013873609714210033,
-0.03773529455065727,
-0.08173995465040207,
-0.0026769160758703947,
0.0168760959059,
-0.012881106697022915,
-0.023056307807564735,
-0.0415491946041584,
0.0673343762755394,
0.027093982324004173,
0.006256740540266037,
0.07484041154384613,
-0.011278605088591576,
0.007779501378536224,
-0.020259682089090347,
-0.056102391332387924,
0.01781713031232357,
-0.02037242241203785,
-0.029480552300810814,
-0.008059476502239704,
0.017543459311127663,
-0.01062350906431675,
0.021144818514585495,
0.03872771933674812,
-0.05060463771224022,
-0.054175667464733124,
0.03268060460686684,
-0.04667914658784866,
0.01645422726869583,
-0.013379266485571861,
-0.010262218303978443,
-0.021325934678316116,
0.04065384343266487,
0.05280030891299248,
-0.08825436234474182,
0.0026571103371679783,
-0.008447157219052315,
0.0505579374730587,
-0.005864995997399092,
-0.0024172526318579912,
0.01255938969552517,
-0.013844991102814674,
0.016094807535409927,
0.06258797645568848,
-0.052553996443748474,
0.02310962975025177,
0.001373404636979103,
-0.018716849386692047,
0.023007871583104134,
-0.029730593785643578,
-0.016446687281131744,
-0.020254401490092278,
-0.05385748669505119,
-0.01744968444108963,
-0.06699089705944061,
-0.014768348075449467,
0.007324575446546078,
-0.004143201746046543,
-0.016768736764788628,
0.002529827645048499,
0.030819173902273178,
0.01981697604060173,
0.01667209342122078,
-0.02269349992275238,
-0.03575259819626808,
0.05133315175771713,
-0.015494795516133308,
-0.019805360585451126,
0.03165040165185928,
-0.002358662895858288,
0.05412712320685387,
0.03321365267038345,
-0.018960628658533096,
0.06263046711683273,
-0.002312994794920087,
-0.05799040570855141,
0.04283113405108452,
-0.011810691095888615,
-0.009209941141307354,
-0.070828877389431,
-0.0002901545667555183,
-0.00882506463676691,
-0.002855803584679961,
-0.07689280807971954,
0.016628693789243698,
-0.031937066465616226,
-0.054989978671073914,
-0.042820751667022705,
-0.05888437107205391,
-0.035765163600444794,
-0.012830078601837158,
0.06964978575706482,
0.024759724736213684,
-0.029342610388994217,
0.013704058714210987,
0.015748487785458565,
0.06285321712493896,
0.04574721306562424,
0.054611686617136,
-0.027916856110095978,
-0.03525606170296669,
0.058562591671943665,
0.016168532893061638,
0.007786494679749012,
0.020637087523937225,
-0.06338323652744293,
0.02970738336443901,
-0.0010035184677690268,
-0.0085555799305439,
-0.0009602522477507591,
-0.003794575808569789,
-0.020924482494592667,
-0.02902313694357872,
-0.003123033791780472,
0.03156697005033493,
0.06334055215120316,
0.005805609747767448,
-0.05439741164445877,
-0.0071004764176905155,
0.05847654491662979,
-0.0320512093603611,
-0.032293710857629776,
-0.017147215083241463,
-0.03922317549586296,
-0.02101602777838707,
-0.016604667529463768,
0.03279966115951538,
-0.05439302325248718,
-0.05098232626914978,
-0.0377080999314785,
0.08645376563072205,
-0.07093755155801773,
-0.02294952981173992,
0.05211041122674942,
-0.005767730996012688,
0.03947669640183449,
-0.012724986299872398,
0.0298737995326519,
0.00956092868000269,
-0.046825408935546875,
0.025627028197050095,
0.025043055415153503,
0.0038669223431497812,
-0.027160881087183952,
0.02503011003136635,
0.001447924878448248,
0.016945406794548035,
0.00948281493037939,
-0.05261138081550598,
0.006440071854740381,
-0.02789321355521679,
-0.05009125918149948,
-0.012678040191531181,
0.005466753151267767,
-0.02358432486653328,
0.0024144998751580715,
-0.020983269438147545,
-0.07603367418050766,
0.03251674398779869,
0.005704463925212622,
-0.044377777725458145,
-0.00847621075809002,
-0.015023940242826939,
-0.023181460797786713,
-0.01717306487262249,
0.06851348280906677,
0.0068734935484826565,
0.0013885358348488808,
-0.0576772540807724,
-0.06326760351657867,
-0.006099835503846407,
0.02495068870484829,
-0.02364630438387394,
-0.024159789085388184,
0.0008852356695570052,
0.03326594829559326,
-0.04813767224550247,
-0.0338912159204483,
-0.05320136621594429,
0.03886120393872261,
-0.011932425200939178,
-0.047622017562389374,
0.003134842263534665,
-0.002546092262491584,
0.008296261541545391,
-0.003909343387931585,
0.04670475050806999,
0.019797436892986298,
-0.02220379188656807,
-0.0027149992529302835,
-0.00539482943713665,
0.054374050348997116,
-0.015780389308929443,
-0.024596665054559708,
0.012076462619006634,
-0.016854923218488693,
0.032004464417696,
-0.03332967683672905,
-0.06911848485469818,
-0.0444980226457119,
-0.024307144805788994,
-0.07139849662780762,
0.004043637774884701,
-0.006121638230979443,
0.021528413519263268,
0.020225131884217262,
-0.027180828154087067,
-0.014541834592819214,
0.06992917507886887,
0.053340520709753036,
0.03439585492014885,
0.026974311098456383,
-0.026483584195375443,
-0.03724415600299835,
0.0000941167090786621,
0.026063935831189156,
0.018701855093240738,
0.0727546215057373,
-0.057696033269166946,
0.040540825575590134,
-0.02371586300432682,
0.047389790415763855,
0.0020091044716537,
-0.01160922646522522,
0.045524224638938904,
-0.02402169071137905,
0.05730968341231346,
0.00811072252690792,
-0.050901759415864944,
0.018266333267092705,
-0.006651727948337793,
0.04885898903012276,
-0.04719904810190201,
-0.06406509131193161,
0.008159519173204899,
0.01399207767099142,
-0.00011200673907296732,
0.0531427264213562,
-0.05505680665373802,
0.014282875694334507,
-0.0750928670167923,
-0.01993175968527794,
0.08335420489311218,
0.010033498518168926,
-0.004611049313098192,
-0.030797157436609268,
-0.0072361500933766365,
0.0013566677225753665,
0.02245880477130413,
-0.006966586224734783,
0.014296422712504864,
-0.04344988986849785,
0.025043031200766563,
-0.05557314306497574,
-0.032949987798929214,
-0.13398952782154083,
-0.008621776476502419,
-0.020487526431679726,
-0.01355991791933775,
-0.010541603900492191,
0.06663338840007782,
-0.01873679831624031,
-0.031062904745340347,
-0.019712334498763084,
-0.07397625595331192,
0.03736945241689682,
-0.054631557315588,
-0.013801537454128265,
0.05920356884598732,
-0.0306276623159647,
-0.014580100774765015,
0.027568163350224495,
0.017222939059138298,
0.03264184296131134,
0.07772152125835419,
0.03754592314362526,
-0.037755414843559265,
0.012633406557142735,
0.017743472009897232,
0.00949646346271038,
-0.024911168962717056,
0.05232942849397659,
0.055093832314014435,
0.023727040737867355,
0.09163863211870193,
0.008284219540655613,
0.058182764798402786,
-0.026328548789024353,
0.01811208762228489,
0.0013524835230782628,
-0.025535831227898598,
-0.008220277726650238,
0.000539523724000901,
0.001328814891166985,
-0.008219895884394646,
-0.02111448161303997,
0.0047674356028437614,
-0.012640247121453285,
0.03597266972064972,
-0.03673446550965309,
-0.03979466110467911,
-0.016962852329015732,
0.009653664194047451,
-0.02089838497340679,
0.0035049710422754288,
-0.02632046677172184,
-0.017882509157061577,
0.058181554079055786,
-0.02116289548575878,
0.0056838709861040115,
0.020441951230168343,
-0.0454479455947876,
-0.03263181075453758,
0.0175549928098917,
-0.005760472733527422,
0.043870627880096436,
0.021804166957736015,
-0.015683267265558243,
0.03261471167206764,
-0.02602364309132099,
0.00934548582881689,
0.029390551149845123,
-0.02212921343743801,
-0.015724116936326027,
0.04403258115053177,
0.018554987385869026,
0.050585854798555374,
0.018016718327999115,
0.005207286216318607,
-0.03990672901272774,
0.013404040597379208,
0.002451818436384201,
-0.0069207362830638885,
0.008949662558734417,
0.03868035227060318,
0.033232029527425766,
-0.045196618884801865,
0.03205866366624832,
-0.082219697535038,
-0.013031375594437122,
0.03770889714360237,
0.005385607946664095,
0.04168139770627022,
-0.028079314157366753,
0.000913107767701149,
-0.02581111341714859,
0.020641641691327095,
0.025811808183789253,
-0.006724874023348093,
0.010648165829479694,
-0.010423601604998112,
-0.008049330674111843,
-0.03253227099776268,
0.006282092072069645,
-0.033717986196279526,
0.024014780297875404,
0.03330029919743538,
0.01190614327788353,
0.014858407899737358,
-0.05609126016497612,
0.036535270512104034,
0.02359086461365223,
0.04698861017823219,
0.11767745018005371,
-0.027601752430200577,
0.051566168665885925,
0.0014808735577389598,
0.02756567671895027,
-0.07465361803770065,
0.028512390330433846,
0.020559564232826233,
-0.00322191440500319,
-0.020650731399655342,
-0.011985411867499352,
-0.01825343631207943,
0.004219904541969299,
-0.0020486318971961737,
-0.030544115230441093,
0.04035530611872673,
-0.047038160264492035,
0.029515059664845467,
-0.023082340136170387,
-0.05492101237177849,
-0.0024556629359722137,
-0.04337269067764282,
-0.012591647915542126,
-0.0016401195898652077,
0.013159587047994137,
0.03696085512638092,
0.007615691516548395,
-0.006003702059388161,
0.0457085445523262,
0.02990865707397461,
-0.039589229971170425,
-0.06425067782402039,
0.0006022824090905488,
0.03692871704697609,
0.04666856676340103,
-0.04107266664505005,
0.019861575216054916,
0.06889723986387253,
0.0242150966078043,
-0.032170552760362625,
-0.0799039751291275,
0.03904803469777107,
0.051648110151290894,
-0.003014585468918085,
0.011296775192022324,
-0.026447925716638565,
-0.01909892074763775,
0.017267249524593353,
-0.04129583761096001,
0.0012374103534966707,
-0.006838338915258646,
0.0028963813092559576,
-0.017641177400946617,
-0.024499783292412758,
0.06914888322353363,
0.00743043003603816,
0.01476868987083435,
0.026662157848477364,
0.047873564064502716,
-0.029032638296484947,
0.019645551219582558,
0.06135798618197441,
-0.015389428474009037,
0.07031934708356857,
-0.05740051716566086,
-0.016877656802535057,
0.032963208854198456,
-0.010368462651968002,
0.008462460711598396,
0.004356599412858486,
0.02549254149198532,
-0.021066559478640556,
-0.04286724328994751,
-0.04432171210646629,
-0.028781376779079437,
0.022789910435676575,
-0.0023452555760741234,
-0.05414484441280365,
-0.03234978765249252,
0.03611580654978752,
-0.019308509305119514,
-0.011646393686532974,
-0.005121335387229919,
0.00489436648786068,
-0.028153356164693832,
0.007511693984270096,
-0.02230984903872013,
0.007546063978224993,
0.06501695513725281,
0.07495160400867462,
0.0682336762547493,
0.10739285498857498,
-0.01936095766723156,
-0.011785500682890415,
0.021062836050987244,
-0.012214470654726028,
0.039141133427619934,
-0.017854150384664536,
0.01154850609600544,
0.01883220113813877,
-0.004065236542373896,
0.01511580590158701,
-0.04638225957751274,
0.002423326252028346,
-0.008669598028063774,
0.04868881404399872,
0.026416674256324768,
0.00685757864266634,
0.04173913225531578,
0.010355964303016663,
0.017050370573997498,
-0.01300782896578312,
0.020312199369072914,
-0.027941204607486725,
-0.04614909365773201,
0.010270409286022186,
-0.004200408700853586,
-0.03971819952130318,
0.0542588047683239,
-0.04225315526127815,
0.028237441554665565,
-0.0619044303894043,
0.036955270916223526,
0.025067893788218498,
0.03844093531370163,
-0.08799265325069427,
-0.014703135937452316,
-0.0009535556891933084,
-0.019843431189656258,
-0.01595405675470829,
-0.10521999001502991,
0.023792119696736336,
-0.028280412778258324,
0.05633360147476196,
-0.018630973994731903,
-0.020271191373467445,
0.010565532371401787,
0.018583325669169426,
-0.028376100584864616,
0.02844312973320484,
0.03206929937005043,
-0.033964671194553375,
-0.07999252527952194,
-0.028940223157405853,
0.03815511241555214,
0.001219540135934949,
-0.05755256861448288,
0.05336877331137657,
0.02093305066227913,
-0.03798642009496689,
0.02319917269051075,
-0.010807455517351627,
0.05898614972829819,
0.035165935754776,
-0.024707667529582977,
0.004682030063122511,
0.0443846769630909,
0.021678796038031578,
0.052387386560440063,
-0.061959587037563324,
0.01563943177461624,
0.00283696036785841,
0.0332120843231678,
-0.04354250058531761,
-0.03661298006772995,
-0.002669533947482705,
-0.005731350276619196,
-0.0028884958010166883,
0.0460161492228508,
-0.024823889136314392,
-0.022238459438085556,
0.000839001964777708,
-0.029823822900652885,
0.0043031880632042885,
-0.0543186329305172,
0.04953523352742195,
0.025271618738770485,
0.0067957122810184956,
-0.028065096586942673,
0.02712552808225155,
-0.025525392964482307,
0.00422778120264411,
-0.011134404689073563,
0.01848224177956581,
0.03540246561169624,
0.06122884154319763,
0.007569365203380585,
-0.005844326224178076,
0.012009469792246819,
0.019703328609466553,
-0.044695451855659485,
-0.07929252088069916,
0.014284475706517696,
-0.014203139580786228,
-0.03931795060634613,
-0.03672349825501442,
0.0411403551697731,
-0.006060198415070772,
0.04064932465553284,
-0.05976218730211258,
-0.010199297219514847,
0.01718091405928135,
-0.05253249406814575,
-0.04187942296266556,
-0.04465829208493233,
-0.07758017629384995,
-0.03020152822136879,
-0.01337413676083088,
0.025634460151195526,
-0.0022554700262844563,
-0.02217215672135353,
0.05609868839383125,
-0.023984169587492943,
-0.007597466465085745,
0.0027395766228437424,
0.0347682349383831,
-0.0372982881963253,
0.0036030441988259554,
-0.03182104602456093,
-0.03069777600467205,
0.02500993385910988,
-0.014700845815241337,
0.01197944488376379,
-0.033415038138628006,
0.0006093070842325687,
-0.019470982253551483,
0.025089414790272713,
0.0054818508215248585,
0.030226023867726326,
-0.007726629730314016,
-0.027742911130189896,
-0.04292849451303482,
0.03585030883550644,
0.05286097526550293,
-0.0307314433157444,
-0.06655413657426834,
-0.03199756518006325,
-0.007567345164716244,
0.017235906794667244,
-0.048094309866428375,
-0.031136387959122658,
0.013349801301956177,
0.06389555335044861,
-0.07013341784477234,
-0.03766397759318352,
-0.029818492010235786,
-0.08671235293149948,
0.02233698032796383,
0.020934240892529488,
-0.00926067866384983,
0.038902558386325836,
-0.0012082832399755716,
-0.015098821371793747,
0.001322748139500618,
-0.0012986017391085625,
-0.0017414023168385029,
-0.06007817015051842,
0.08343221247196198,
0.024826938286423683,
-0.025792500004172325,
-0.0031943952199071646,
0.019736625254154205
] |
<p><a href="http://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment" rel="nofollow">The Stern Gerlach experiment</a> was meant to prove the orbital quantization of electrons where there should be +ml,0,-ml states. So for l=2, there should be 5 beams.</p>
<p>But they saw 2 beams, which was shown to be due to the 2 states of spin.</p>
<p>Now, because of the addition of the spin magnetic moment, shouldn't there be now 10 beams?(2 additional states for each the 5 orbital states).</p>
<p>What happened to the orbital magnetic contribution?</p> | g5542 | [
0.023213496431708336,
0.00994939636439085,
-0.006839300040155649,
0.0014421521918848157,
0.026999931782484055,
0.0164482444524765,
0.05021090805530548,
0.06307101994752884,
0.01658226177096367,
-0.035091642290353775,
-0.032819706946611404,
0.010406464338302612,
0.041470881551504135,
0.036927659064531326,
0.02576822228729725,
0.005175232887268066,
0.053781021386384964,
0.03325488045811653,
0.040266841650009155,
-0.009386152029037476,
0.027223803102970123,
0.04017462953925133,
-0.03464322164654732,
-0.05016060173511505,
0.042472127825021744,
0.003002309473231435,
-0.017732013016939163,
0.015051187016069889,
-0.005530926398932934,
0.010060954838991165,
0.01908925734460354,
-0.024106072261929512,
0.010282620787620544,
-0.04441221058368683,
0.017477698624134064,
-0.07098884880542755,
0.03892169147729874,
0.09459535777568817,
-0.021681273356080055,
-0.03330497816205025,
-0.033309124410152435,
-0.005156411323696375,
-0.06357193738222122,
0.0028667503502219915,
-0.059042129665613174,
0.020492106676101685,
0.008484777994453907,
-0.01088302955031395,
0.027347277849912643,
-0.027068058028817177,
-0.032371338456869125,
0.04851514846086502,
0.06646896153688431,
-0.02832799032330513,
0.0631246343255043,
0.01324678398668766,
-0.08794079720973969,
0.00823963526636362,
0.03237199783325195,
0.10023263841867447,
0.028535066172480583,
0.001787408022210002,
-0.019308412447571754,
0.007737400010228157,
-0.04863228276371956,
-0.02514556609094143,
0.020557962357997894,
0.03980199247598648,
-0.04691558703780174,
0.019211789593100548,
0.018321724608540535,
-0.051349908113479614,
-0.0298111904412508,
-0.009915733709931374,
-0.01964249648153782,
0.010213827714323997,
0.018157795071601868,
0.043862830847501755,
0.024552620947360992,
0.012247096747159958,
-0.05102579668164253,
-0.012199781835079193,
-0.022171271964907646,
0.012735344469547272,
0.006659206468611956,
0.005282739643007517,
-0.011645995080471039,
0.03496292978525162,
0.034014083445072174,
0.002826410112902522,
0.015144649893045425,
-0.04209837689995766,
0.027441414073109627,
0.07649156451225281,
-0.045950643718242645,
-0.03985077142715454,
0.034176055341959,
0.03728216141462326,
-0.01321636512875557,
-0.024807503446936607,
-0.01393468864262104,
-0.024949349462985992,
-0.0026766511145979166,
0.011551911011338234,
0.06813711673021317,
-0.01937314309179783,
0.021683475002646446,
-0.005282171070575714,
0.030181696638464928,
0.053307391703128815,
-0.035607192665338516,
-0.008813092485070229,
-0.045612312853336334,
0.005383462179452181,
-0.06279223412275314,
0.014487633481621742,
0.09867721050977707,
-0.10395228862762451,
-0.02300402522087097,
-0.014966035261750221,
0.00609658332541585,
-0.03218071907758713,
-0.032497137784957886,
0.06158599629998207,
-0.0038437265902757645,
0.03404057398438454,
0.009788504801690578,
-0.02873339131474495,
0.05063564330339432,
-0.012736610136926174,
-0.026482567191123962,
-0.0009280710364691913,
0.059110127389431,
0.056306142359972,
0.004746792837977409,
-0.005480893421918154,
-0.044528231024742126,
-0.0009207089897245169,
-0.00907003041356802,
0.03067971020936966,
-0.0037145151291042566,
-0.05425966531038284,
-0.002754590008407831,
-0.025469349697232246,
0.02901034615933895,
-0.009847469627857208,
0.025533009320497513,
0.029386315494775772,
-0.002058684593066573,
0.036539316177368164,
0.011722144670784473,
-0.043238162994384766,
0.03138250857591629,
-0.01979193463921547,
-0.026487307623028755,
-0.03538704290986061,
0.07699418067932129,
-0.05844767391681671,
0.020890576764941216,
0.04350202530622482,
-0.009827855043113232,
0.03152891993522644,
-0.024596063420176506,
-0.007739898283034563,
-0.07009755074977875,
0.07810156047344208,
0.0058221276849508286,
-0.011390470899641514,
0.013319849036633968,
-0.0010268978076055646,
0.029283564537763596,
-0.004086194559931755,
-0.03974124789237976,
0.030180225148797035,
0.018340861424803734,
0.09144029766321182,
0.02624218724668026,
-0.021455269306898117,
0.03264353424310684,
0.0886550322175026,
0.013120975345373154,
0.07756133377552032,
0.007907482795417309,
-0.03527446836233139,
0.030910754576325417,
0.00894266739487648,
-0.041027653962373734,
0.029285328462719917,
-0.024929849430918694,
-0.004817752167582512,
0.015443746000528336,
0.004084091167896986,
-0.029910268262028694,
0.015814950689673424,
-0.02964167669415474,
0.006714088376611471,
0.018824106082320213,
0.00917514692991972,
-0.025759203359484673,
0.051950305700302124,
-0.03278704732656479,
0.012823640368878841,
-0.07287970185279846,
-0.01657254248857498,
0.0003334555367473513,
-0.028491126373410225,
0.007113730534911156,
0.04386194050312042,
0.07394441962242126,
-0.05069687217473984,
-0.017101245000958443,
0.011583578772842884,
-0.01207236759364605,
-0.02456781454384327,
-0.01949889399111271,
0.056349750608205795,
0.03362841159105301,
0.0024857327807694674,
0.016307372599840164,
0.05335037782788277,
-0.021826768293976784,
0.02521377056837082,
0.058080825954675674,
0.022787349298596382,
0.03179516643285751,
0.024646040052175522,
0.008584116585552692,
-0.03703230619430542,
-0.07906728237867355,
0.02475970983505249,
-0.016186829656362534,
0.02616775780916214,
-0.06382828950881958,
-0.006842340808361769,
0.011243629269301891,
0.01539365854114294,
-0.0074125053361058235,
-0.008182376623153687,
-0.008654378354549408,
0.05708068609237671,
0.02622947096824646,
0.027859730646014214,
-0.057037968188524246,
-0.01735558919608593,
0.05584380775690079,
-0.04540063440799713,
0.003919006325304508,
-0.01842650957405567,
-0.030075084418058395,
0.02414574846625328,
0.02555919624865055,
-0.011085080914199352,
-0.04058904945850372,
0.02368517965078354,
0.04814605787396431,
0.004657173529267311,
-0.04699768126010895,
0.0052232989110052586,
-0.024671753868460655,
-0.0077292053028941154,
-0.02552511729300022,
-0.03680017217993736,
0.054258253425359726,
-0.03163648769259453,
-0.0023512488696724176,
-0.016542715951800346,
-0.008463284932076931,
-0.023572737351059914,
-0.004380067344754934,
-0.035963788628578186,
-0.02630654163658619,
0.0713164433836937,
-0.02382291480898857,
-0.016298750415444374,
-0.016653364524245262,
-0.023989979177713394,
-0.02558061294257641,
0.052406568080186844,
-0.017918501049280167,
-0.0018660641508176923,
-0.10213920474052429,
-0.03684861212968826,
-0.042177073657512665,
-0.005790810100734234,
-0.008092384785413742,
-0.01520739309489727,
-0.01901681162416935,
-0.020350078120827675,
0.017479734495282173,
-0.04627399519085884,
-0.06827495247125626,
-0.024387924000620842,
0.08857013285160065,
-0.01617254503071308,
-0.01815740391612053,
-0.023170078173279762,
0.05673925578594208,
0.010706370696425438,
-0.0645991787314415,
0.1048974096775055,
-0.017433233559131622,
0.0040187351405620575,
-0.03751639276742935,
-0.021289074793457985,
-0.002047981135547161,
0.012694031000137329,
-0.022965755313634872,
-0.05484316125512123,
-0.08850029855966568,
0.011170019395649433,
0.016122298315167427,
0.04422355815768242,
-0.029725665226578712,
0.028605012223124504,
-0.0335526280105114,
-0.01204609777778387,
-0.02804025448858738,
0.05584802106022835,
0.05922047793865204,
-0.06388317048549652,
-0.06569118052721024,
0.02694801427423954,
-0.005092944018542767,
-0.07619495689868927,
0.07009308785200119,
0.04284980520606041,
-0.01368590909987688,
-0.02648850344121456,
0.0028836922720074654,
0.02664620243012905,
0.03253697231411934,
0.02258378453552723,
-0.025761056691408157,
-0.003932928200811148,
-0.03914530947804451,
-0.012168730609118938,
-0.01762382499873638,
0.029567010700702667,
-0.0042687514796853065,
0.029615767300128937,
-0.033182162791490555,
0.02284984290599823,
-0.053599704056978226,
-0.010919427499175072,
0.050648897886276245,
0.004167395643889904,
-0.04216489568352699,
-0.011013762094080448,
0.001409035176038742,
0.04603764787316322,
-0.0039020755793899298,
0.045891232788562775,
0.014067874290049076,
0.06507007032632828,
0.004991674795746803,
-0.022117551416158676,
-0.010650042444467545,
0.0004011758719570935,
0.06487330049276352,
0.050725724548101425,
-0.005066072568297386,
-0.03562651202082634,
0.015659241005778313,
-0.041561104357242584,
-0.047381699085235596,
0.009735521860420704,
-0.012767697684466839,
-0.005860686767846346,
0.016773970797657967,
-0.02791655622422695,
-0.03244900703430176,
-0.05939451605081558,
-0.01311078667640686,
-0.0365399532020092,
0.05048048123717308,
-0.02126411534845829,
0.04992120712995529,
0.054800424724817276,
-0.06143592670559883,
0.013950657099485397,
0.05789133906364441,
0.06290479004383087,
0.023747986182570457,
-0.020049313083291054,
-0.054484665393829346,
-0.03567241504788399,
-0.037689246237277985,
0.0445932000875473,
-0.05113246664404869,
-0.020573945716023445,
-0.018894722685217857,
0.029380040243268013,
-0.007050678599625826,
-0.011272412724792957,
0.05271462723612785,
0.021658264100551605,
0.0056837173178792,
-0.0291295163333416,
-0.005398245062679052,
0.05954831838607788,
-0.023770146071910858,
0.03965479135513306,
-0.022415708750486374,
-0.048890285193920135,
-0.004625366069376469,
0.015873771160840988,
0.00672778720036149,
0.05475153774023056,
0.04037671163678169,
0.01837603747844696,
-0.034784525632858276,
-0.009123115800321102,
-0.013844390399754047,
-0.04381366819143295,
0.041162390261888504,
-0.012144051492214203,
-0.024505913257598877,
-0.004050965886563063,
-0.03173748031258583,
-0.003164144465699792,
-0.02164424955844879,
0.07948683947324753,
0.014905828982591629,
-0.014226201921701431,
-0.01621553674340248,
0.044377878308296204,
-0.05591970682144165,
0.005493078846484423,
0.034609418362379074,
-0.03261581435799599,
0.030102454125881195,
0.003241082187741995,
-0.02719901315867901,
-0.014663388021290302,
-0.057491037994623184,
0.02710491232573986,
-0.0228995680809021,
0.0240316279232502,
-0.05365291237831116,
0.06582655012607574,
0.010736938565969467,
-0.020852861925959587,
-0.004455713089555502,
0.03920773044228554,
0.04940098524093628,
-0.0007692452636547387,
-0.06839843094348907,
-0.02060970664024353,
-0.010739249177277088,
-0.01228894293308258,
-0.04934258759021759,
-0.04179071635007858,
0.05409768596291542,
0.08319073170423508,
0.016807714477181435,
-0.020501505583524704,
-0.02081359177827835,
0.01725756749510765,
0.001016539754346013,
0.06233495846390724,
-0.13720886409282684,
0.03248733654618263,
0.0038211457431316376,
0.022649232298135757,
0.009514056146144867,
-0.0019981025252491236,
-0.05058877915143967,
-0.020159658044576645,
-0.018862778320908546,
-0.017873257398605347,
-0.024549778550863266,
-0.027133572846651077,
0.042923133820295334,
0.03081376850605011,
0.01280196476727724,
-0.001067773555405438,
0.009751367382705212,
-0.037683844566345215,
0.02313125878572464,
-0.021846426650881767,
-0.03382563963532448,
-0.05508126690983772,
0.0463077537715435,
-0.014011277817189693,
0.017831239849328995,
0.0114331915974617,
-0.008227253332734108,
-0.018017567694187164,
0.06995090842247009,
0.012250551953911781,
0.036434415727853775,
0.001608450198546052,
-0.032020699232816696,
-0.06822066754102707,
0.024024400860071182,
0.02807697094976902,
-0.03832821175456047,
-0.0715019702911377,
-0.024178294464945793,
0.017770612612366676,
-0.023249538615345955,
0.033653173595666885,
-0.03862156718969345,
-0.008369476534426212,
-0.032802022993564606,
0.011984613724052906,
0.017969094216823578,
-0.060852617025375366,
0.0017348007531836629,
-0.0248723067343235,
-0.04579620063304901,
0.0044544292613863945,
-0.011710858903825283,
-0.0006905485060997307,
0.06286393105983734,
-0.025047386065125465,
-0.0027656618040055037,
0.02760785073041916,
0.03751256689429283,
-0.05715041980147362,
0.02358967252075672,
0.020915569737553596,
0.023257115855813026,
-0.0672576054930687,
-0.0041595445945858955,
-0.00006743216363247484,
0.0150777418166399,
0.011768113821744919,
-0.0026234411634504795,
0.0790105015039444,
0.032094527035951614,
-0.015291023999452591,
0.027950869873166084,
0.039228394627571106,
0.04110565409064293,
-0.061571963131427765,
0.029712077230215073,
-0.01679658517241478,
0.01451878808438778,
0.027809808030724525,
-0.02211068384349346,
0.044696226716041565,
0.012508055195212364,
0.10675551742315292,
0.017180008813738823,
-0.005492461379617453,
-0.03306739777326584,
-0.023397576063871384,
0.03930079936981201,
-0.07212064415216446,
-0.022196082398295403,
0.008586892858147621,
0.009883963502943516,
-0.012918900698423386,
0.00039100516005419195,
0.046518951654434204,
0.024220678955316544,
-0.020381761714816093,
0.004123415797948837,
0.007190056145191193,
0.0410180538892746,
-0.019350068643689156,
0.019994370639324188,
0.012637323699891567,
0.04620715603232384,
0.037983838468790054,
-0.060666684061288834,
-0.040604252368211746,
0.008622007444500923,
-0.01087688934057951,
0.039757467806339264,
0.02730640396475792,
-0.07866935431957245,
0.05081148445606232,
0.048175208270549774,
0.006345985922962427,
-0.026233622804284096,
-0.022029222920536995,
-0.042218487709760666,
-0.03675316646695137,
-0.03652271255850792,
0.026900658383965492,
0.0418599471449852,
-0.010056134313344955,
0.02547776885330677,
0.010885939933359623,
0.015227362513542175,
-0.008047115989029408,
0.06837920099496841,
0.0024680185597389936,
-0.022383613511919975,
0.04799599200487137,
-0.012694825418293476,
-0.010084287263453007,
-0.028276769444346428,
0.0267774797976017,
0.019027620553970337,
0.008930101990699768,
-0.011853140778839588,
0.0329836830496788,
0.006955512333661318,
0.021322686225175858,
0.07125270366668701,
0.1082099974155426,
0.0025955745950341225,
0.022226393222808838,
-0.0464385524392128,
-0.03096744418144226,
0.006521532312035561,
0.07335323840379715,
-0.02202976495027542,
-0.055098723620176315,
-0.07306747138500214,
-0.01487342081964016,
0.053993117064237595,
0.015569884330034256,
0.017637254670262337,
-0.014879882335662842,
-0.05540624260902405,
0.011619932949543,
-0.005290993023663759,
-0.016919566318392754,
-0.04140833020210266,
-0.0413145050406456,
0.021088939160108566,
0.060245681554079056,
0.015721939504146576,
-0.04151174798607826,
0.0026859953068196774,
-0.022638604044914246,
-0.016167055815458298,
0.013772254809737206,
0.018798839300870895,
0.009801119565963745,
-0.0347103625535965,
-0.00018565724894870073,
0.036990903317928314,
-0.010422153398394585,
0.03213942050933838,
0.01209220290184021,
-0.02025647461414337,
0.005053624976426363,
0.03160867467522621,
0.00615680543705821,
-0.015036772936582565,
-0.04308025911450386,
0.0033306076657027006,
-0.02035895176231861,
0.03141886368393898,
0.03950999677181244,
-0.01665220968425274,
-0.0025343981105834246,
0.00036790710873901844,
-0.013379075564444065,
-0.017946720123291016,
-0.006212135311216116,
0.010023277252912521,
0.05794788897037506,
0.03267030417919159,
-0.08413666486740112,
-0.015635883435606956,
0.006384372711181641,
0.022916993126273155,
-0.018795298412442207,
-0.02762013114988804,
-0.0419740229845047,
-0.037688352167606354,
-0.038559772074222565,
0.07597482204437256,
-0.04585174843668938,
-0.042553648352622986,
-0.01943790540099144,
-0.05714600533246994,
-0.009095609188079834,
-0.07018567621707916,
0.012361620552837849,
0.05753744766116142,
-0.03076649270951748,
-0.002813897794112563,
-0.0032287396024912596,
-0.042135223746299744,
0.08612529933452606,
-0.03819257766008377,
-0.0007486892864108086,
-0.05409974604845047,
-0.0412500724196434,
-0.05248861014842987,
-0.020637454465031624,
-0.011319492012262344,
0.0026661043521016836,
0.006793742533773184,
0.028583025559782982,
0.06025616452097893,
0.00465973187237978,
0.002146417973563075,
0.011330333538353443,
-0.027536461129784584,
0.024531951174139977,
-0.0005161943845450878,
-0.026702076196670532,
0.04986593872308731,
-0.027281364426016808,
-0.04663972929120064,
-0.0011427921708673239,
0.00700604310259223,
0.008515066467225552,
0.053446389734745026,
-0.0455394871532917,
0.002593154553323984,
-0.012120884843170643,
-0.01514853909611702,
0.05155288800597191,
0.029550883919000626,
-0.012626965530216694,
0.03925240412354469,
-0.011927066370844841,
0.023539526388049126,
0.009801797568798065,
0.038995519280433655,
0.014186487533152103,
-0.016229448840022087,
-0.024253128096461296,
-0.03604673594236374,
0.012206962332129478,
-0.008001000620424747,
0.014451565220952034,
0.04267924651503563,
-0.02598370984196663,
0.07175993919372559,
0.012569683603942394,
0.00002513325489417184,
0.001000975607894361,
-0.06543144583702087,
-0.07617834955453873,
0.010241787880659103,
-0.008870668709278107,
-0.019250860437750816,
-0.02174181491136551,
0.019680483266711235,
-0.018048062920570374,
-0.006541349925100803,
-0.004269839730113745,
0.0134434774518013,
-0.013334873132407665,
0.00853742565959692,
0.007915297523140907,
-0.06331687420606613,
-0.011369425803422928,
0.047653477638959885,
-0.003558119060471654,
-0.00947535503655672,
-0.007178222294896841,
-0.06152614578604698,
0.0038669060450047255,
0.06461074948310852,
-0.005423973314464092,
0.0014372264267876744,
-0.010038900189101696,
0.0597078762948513,
-0.02635364420711994,
-0.006103374995291233,
-0.008168885484337807,
-0.02577034756541252,
-0.02609846740961075,
-0.07958115637302399,
-0.07460013031959534,
-0.01388491503894329,
0.03225117176771164
] |
<p>For a static electric field $E$ the conservation of energy gives rise to $$\oint E\cdot ds =0$$ Is there an analogous mathematical expression the conservation of momentum gives rise to?</p> | g5543 | [
0.09189499169588089,
0.0029372824355959892,
-0.01013431791216135,
-0.033129431307315826,
0.06343604624271393,
0.03725840523838997,
-0.006753439549356699,
0.020350251346826553,
0.0002804976829793304,
-0.013689436949789524,
-0.03198423981666565,
-0.028861312195658684,
0.04867447912693024,
0.009864229708909988,
-0.0028593367896974087,
-0.011609100736677647,
0.04520417004823685,
-0.03274733945727348,
-0.0005568398628383875,
0.0025123630184680223,
-0.007628495804965496,
-0.059741076081991196,
0.037515927106142044,
0.007018817588686943,
-0.008045824244618416,
-0.000432749540777877,
-0.04629196226596832,
0.03651915490627289,
-0.014835884794592857,
-0.05322650447487831,
0.015028216876089573,
0.04997710883617401,
0.07590921968221664,
0.03665309026837349,
-0.04325929656624794,
-0.030876973643898964,
0.017850248143076897,
0.027165478095412254,
0.07381841540336609,
0.023507917299866676,
0.08242125809192657,
-0.04389859735965729,
0.03736254945397377,
0.05655333399772644,
-0.017315974459052086,
-0.036168359220027924,
-0.0470314659178257,
0.009893380105495453,
-0.0718599185347557,
-0.01758599281311035,
-0.00876788143068552,
0.007782513275742531,
0.03163069114089012,
-0.02416290156543255,
0.01263642217963934,
0.01158045418560505,
-0.0340503454208374,
-0.04796596243977547,
-0.011476160027086735,
0.05791369080543518,
0.013923837803304195,
-0.000831273733638227,
0.005934509914368391,
-0.027186432853341103,
0.05591170862317085,
-0.012405166402459145,
-0.0024139394517987967,
0.010678604245185852,
0.019818788394331932,
-0.0011902438709512353,
0.04027574136853218,
0.033961378037929535,
-0.022524064406752586,
0.007684072479605675,
0.008394375443458557,
0.005983034148812294,
-0.016961650922894478,
-0.024781586602330208,
-0.01745857298374176,
-0.024640150368213654,
-0.07023787498474121,
0.021759919822216034,
0.025972651317715645,
0.0022413735277950764,
0.018791701644659042,
-0.019636278972029686,
0.039759982377290726,
0.06754539161920547,
0.003415689803659916,
-0.039129335433244705,
-0.009654738008975983,
-0.0017405523685738444,
0.028757549822330475,
-0.026709819212555885,
-0.012317633256316185,
-0.01525878719985485,
-0.009693410247564316,
0.024988548830151558,
-0.03675496205687523,
-0.07248713821172714,
-0.024351390078663826,
-0.023445788770914078,
0.0023286042269319296,
-0.026582086458802223,
0.007853099144995213,
0.032992031425237656,
0.013853415846824646,
-0.022327618673443794,
0.042343758046627045,
0.011061953380703926,
0.010442337021231651,
-0.03610531985759735,
-0.07718129456043243,
-0.04258953034877777,
-0.0479854941368103,
-0.009076452814042568,
0.0693061575293541,
-0.10246671736240387,
-0.007576928474009037,
0.028988590463995934,
0.03582017123699188,
-0.018262553960084915,
0.0634036734700203,
0.06300438940525055,
0.02334783971309662,
0.018578113988041878,
-0.03191196545958519,
0.04371935874223709,
0.01672123372554779,
0.014522679150104523,
0.009872790426015854,
-0.011470369063317776,
0.013709922321140766,
-0.011171656660735607,
0.023687947541475296,
0.024662388488650322,
-0.07335522770881653,
0.023226091638207436,
0.025466911494731903,
0.03738139569759369,
-0.002950152615085244,
-0.03291398286819458,
0.0036127890925854445,
-0.01289374753832817,
0.005450242664664984,
-0.006528665777295828,
0.06924250721931458,
-0.01562557741999626,
0.03670831397175789,
0.013585951179265976,
-0.02456773817539215,
0.011430423706769943,
-0.019085684791207314,
-0.02617303654551506,
0.03422006592154503,
-0.000646925182081759,
0.017824240028858185,
-0.026434363797307014,
-0.003905692370608449,
-0.04359259828925133,
0.06974567472934723,
-0.003503468120470643,
0.04812740162014961,
-0.03358260914683342,
-0.03572148084640503,
-0.04355897754430771,
0.05664891377091408,
-0.0308366771787405,
-0.02001756988465786,
0.048578228801488876,
-0.009702456183731556,
-0.016055934131145477,
0.024474497884511948,
0.061763327568769455,
0.002813497791066766,
0.0274190753698349,
-0.04401734098792076,
-0.029389848932623863,
0.014239389449357986,
-0.023744210600852966,
0.010675910860300064,
-0.0064646778628230095,
0.05316358059644699,
0.03187824785709381,
0.04369690269231796,
0.006749684456735849,
-0.026632972061634064,
0.02770276367664337,
-0.038842931389808655,
0.0025910933036357164,
-0.010514872148633003,
0.029478101059794426,
-0.018157076090574265,
0.05827487260103226,
-0.0287881251424551,
0.027556849643588066,
-0.05786857381463051,
-0.018488846719264984,
-0.056502241641283035,
0.0035940678790211678,
0.006899820175021887,
0.053262270987033844,
-0.000282507564406842,
-0.019031474366784096,
0.023425234481692314,
0.026574164628982544,
0.03856884315609932,
-0.029703408479690552,
0.0803503543138504,
-0.0007030920241959393,
0.012237018905580044,
-0.018596630543470383,
-0.06781264394521713,
0.02691638097167015,
-0.0038152425549924374,
-0.035581592470407486,
-0.0019588693976402283,
-0.010690869763493538,
-0.054043110460042953,
-0.007353575434535742,
-0.0904809832572937,
-0.03239722177386284,
0.03037910908460617,
-0.007654216140508652,
-0.07732762396335602,
0.016927143558859825,
0.02812935784459114,
-0.0040694610215723515,
-0.021893830969929695,
0.045160505920648575,
-0.03289088234305382,
0.03505180776119232,
0.02413533627986908,
-0.06096826121211052,
0.011535570956766605,
0.0003006146289408207,
-0.008760708384215832,
-0.023898283019661903,
0.003540121018886566,
0.046787142753601074,
-0.009646543301641941,
-0.0045244102366268635,
-0.01219882071018219,
0.023032546043395996,
0.00388709781691432,
0.0027405081782490015,
0.03366271033883095,
0.0748777836561203,
-0.04569689929485321,
-0.008317369967699051,
0.024518031626939774,
0.00926855206489563,
-0.00628717290237546,
0.058770060539245605,
-0.023844124749302864,
-0.04942221939563751,
0.006525665055960417,
0.00889622699469328,
-0.035635896027088165,
0.015475446358323097,
0.004724713508039713,
0.009241479448974133,
0.0009702101233415306,
0.024271544069051743,
-0.012722229585051537,
0.018013078719377518,
0.01965269073843956,
-0.03291540592908859,
0.02755013108253479,
-0.008646155707538128,
0.00682162307202816,
0.05842192843556404,
-0.035576507449150085,
0.03411862254142761,
-0.02997627854347229,
-0.07185936719179153,
0.04745631664991379,
-0.014667393639683723,
0.028529588133096695,
-0.07685517519712448,
0.00015835721569601446,
0.018388811498880386,
-0.03274524211883545,
0.03963880613446236,
0.03598412498831749,
-0.0651896521449089,
-0.0010502769146114588,
-0.033112987875938416,
-0.07318467646837234,
-0.028856920078396797,
-0.00746129872277379,
0.017998773604631424,
0.05641806125640869,
-0.0018854817608371377,
0.011883310042321682,
0.05713219195604324,
0.037595801055431366,
-0.05750482156872749,
-0.025072894990444183,
0.03452356904745102,
-0.021615052595734596,
-0.0010012418497353792,
-0.027089031413197517,
-0.0078656654804945,
0.03999972715973854,
0.03814086318016052,
-0.013496072962880135,
0.008846525102853775,
0.013099952600896358,
-0.036365289241075516,
-0.040183331817388535,
0.03523697704076767,
0.00177492736838758,
-0.056430354714393616,
-0.06590835005044937,
-0.02705257013440132,
0.06197843700647354,
-0.03586727753281593,
0.014094200916588306,
-0.02780996263027191,
-0.0200332198292017,
-0.04982085898518562,
0.024499131366610527,
-0.0359933078289032,
0.026206020265817642,
0.03720727562904358,
-0.06013936176896095,
0.09951004385948181,
-0.004461685195565224,
-0.017893243581056595,
0.025095373392105103,
-0.006959849968552589,
-0.00019382826576475054,
-0.02520325593650341,
-0.039597827941179276,
0.011045892722904682,
-0.033561449497938156,
0.007741967216134071,
0.012591996230185032,
0.0396609902381897,
0.039477866142988205,
0.014630844816565514,
-0.09218775480985641,
0.004665692802518606,
-0.05172489583492279,
-0.010497123934328556,
0.02616524137556553,
-0.009574005380272865,
0.02276834473013878,
-0.016848551109433174,
0.030935533344745636,
-0.025218743830919266,
-0.013291432522237301,
0.0241792444139719,
-0.019506918266415596,
-0.024143224582076073,
0.04075603559613228,
0.04228643327951431,
-0.031092019751667976,
0.007729785982519388,
0.02106815204024315,
-0.008848810568451881,
0.06786572188138962,
0.0010719291167333722,
-0.025271447375416756,
-0.0064443848095834255,
-0.012709698639810085,
0.011294880881905556,
0.007589018903672695,
-0.04416949674487114,
-0.0016681657871231437,
-0.02698681689798832,
-0.043626729398965836,
0.009815732948482037,
-0.011209501884877682,
-0.03780794516205788,
0.007944037206470966,
0.012207119725644588,
-0.07926645874977112,
-0.016499226912856102,
0.020650876685976982,
0.01216317992657423,
-0.025780819356441498,
0.0361841581761837,
-0.006990240421146154,
0.016613926738500595,
-0.05332782864570618,
0.05897334963083267,
0.020527012646198273,
-0.013635176233947277,
0.002812559250742197,
-0.007396314758807421,
-0.012707267887890339,
0.011342670768499374,
0.020856231451034546,
-0.006520773284137249,
0.019422177225351334,
-0.044584304094314575,
-0.007062654942274094,
0.004124027211219072,
0.05899133160710335,
0.006222120486199856,
0.02843816578388214,
0.0011939869727939367,
-0.0015236649196594954,
0.011990942060947418,
0.07670195400714874,
-0.03195202723145485,
0.01960146613419056,
-0.007860986515879631,
0.005857258569449186,
-0.05633966624736786,
-0.006384516134858131,
-0.017226841300725937,
0.018825408071279526,
0.027512582018971443,
0.03667783364653587,
-0.012929629534482956,
0.07459652423858643,
0.011541392654180527,
0.023143351078033447,
0.01279548928141594,
0.0023366103414446115,
-0.01023106463253498,
0.002248539589345455,
0.084112249314785,
0.05202215909957886,
0.020041652023792267,
-0.037475936114788055,
0.012493305839598179,
-0.0015716289635747671,
0.036289360374212265,
-0.008736598305404186,
0.025827689096331596,
-0.10403724759817123,
0.06260474026203156,
-0.0333174504339695,
0.014242089353501797,
-0.039230991154909134,
0.02017444744706154,
0.1049581989645958,
0.02995282970368862,
0.006969616748392582,
-0.03994731232523918,
0.002264103153720498,
0.07631425559520721,
0.023721128702163696,
-0.04774464666843414,
-0.0014690450625494123,
-0.021992703899741173,
-0.023453906178474426,
0.0374746136367321,
0.042100947350263596,
-0.025569748133420944,
-0.0005993637023493648,
-0.02203184738755226,
-0.06650153547525406,
-0.006145973689854145,
0.0048537482507526875,
0.011908256448805332,
-0.07579272985458374,
-0.01067119836807251,
-0.02987489104270935,
0.0075707160867750645,
0.06366638094186783,
-0.016085918992757797,
-0.07208342105150223,
-0.020829100161790848,
-0.050018057227134705,
-0.03251688927412033,
0.043993812054395676,
0.07315992563962936,
-0.004402607679367065,
-0.05219321325421333,
0.01881042867898941,
-0.026905331760644913,
0.003295204136520624,
0.005721224006265402,
0.03422665596008301,
-0.08487941324710846,
0.03958290070295334,
-0.010340250097215176,
-0.03936091065406799,
0.020157434046268463,
0.020368866622447968,
0.024331694468855858,
-0.07675758004188538,
0.059147365391254425,
0.026112914085388184,
-0.06117907911539078,
0.003316607791930437,
0.09893058240413666,
-0.013903334736824036,
-0.017993390560150146,
0.0032883912790566683,
0.09312926232814789,
-0.023226313292980194,
-0.04023216292262077,
-0.010801849886775017,
0.006093702279031277,
-0.06951962411403656,
-0.009310726076364517,
-0.03183210641145706,
0.04746789112687111,
0.05269410088658333,
0.0388646200299263,
0.05092095583677292,
0.024959640577435493,
0.009189051575958729,
0.012581697665154934,
-0.03411038592457771,
0.038081906735897064,
0.04260888695716858,
0.00474558025598526,
0.0332891009747982,
0.01877240277826786,
-0.018668951466679573,
-0.05385182425379753,
-0.0014541480923071504,
-0.02104501985013485,
0.09569115191698074,
-0.07729785144329071,
0.00031758795375935733,
0.018941408023238182,
0.005737693049013615,
0.04454438388347626,
-0.07083568722009659,
-0.044093795120716095,
0.014591965824365616,
0.0725710317492485,
0.045420460402965546,
-0.022356905043125153,
0.013598915189504623,
-0.0541975311934948,
-0.026059754192829132,
-0.035253554582595825,
-0.047043610364198685,
0.03357753902673721,
-0.01421134453266859,
0.024459388107061386,
-0.040997546166181564,
0.008664816617965698,
0.08616656810045242,
0.006157760042697191,
0.0023240188602358103,
-0.0007160863024182618,
0.00032286293571814895,
-0.0557122528553009,
-0.0056471265852451324,
-0.08777492493391037,
-0.013620296493172646,
0.02439934015274048,
-0.04263599216938019,
-0.026210036128759384,
-0.019383832812309265,
-0.02811431884765625,
0.0033373800106346607,
0.0003601954667828977,
-0.022138118743896484,
-0.018805114552378654,
-0.023902248591184616,
0.04092198982834816,
0.01139598898589611,
0.01589496061205864,
0.04642704874277115,
-0.02687896229326725,
0.0240943543612957,
-0.020613400265574455,
0.048759378492832184,
0.024738574400544167,
-0.01221467461436987,
0.037445079535245895,
0.032660484313964844,
-0.0046181571669876575,
-0.03371208533644676,
-0.03150736168026924,
-0.00662629259750247,
-0.011174187064170837,
-0.07400296628475189,
-0.021566208451986313,
-0.02433413453400135,
0.005095616448670626,
0.04856160655617714,
-0.05310622602701187,
-0.03044724091887474,
0.029429834336042404,
-0.04866354539990425,
-0.018157025799155235,
0.03219282627105713,
0.1080663651227951,
-0.0304213035851717,
0.027308283373713493,
0.029288752004504204,
-0.00890387874096632,
0.006293116603046656,
0.016448024660348892,
-0.018881428986787796,
-0.03291626647114754,
0.023803306743502617,
0.06361973285675049,
-0.024263715371489525,
0.03703433647751808,
0.03818643093109131,
-0.013417292386293411,
0.007112143561244011,
0.056012775748968124,
-0.006418710574507713,
0.0023818763438612223,
-0.006301037967205048,
-0.0414019450545311,
-0.006279658526182175,
-0.007403125986456871,
0.018057672306895256,
-0.04945677891373634,
-0.058726850897073746,
0.0400262326002121,
0.031042497605085373,
0.0051800343208014965,
0.030918579548597336,
-0.012772445566952229,
-0.02037736587226391,
-0.03049348294734955,
0.009317231364548206,
-0.011222542263567448,
0.032558392733335495,
0.009533675387501717,
-0.01981283351778984,
0.008552944287657738,
0.02686898224055767,
0.0025435348507016897,
-0.02898719720542431,
0.03737909719347954,
-0.05205056071281433,
0.050056714564561844,
-0.012277859263122082,
0.0075795832090079784,
0.03251529484987259,
0.011044193990528584,
0.04824061319231987,
0.0222572423517704,
-0.0015406699385493994,
0.0441671758890152,
0.06501331180334091,
0.01603415422141552,
-0.06193474307656288,
-0.011326081119477749,
0.0043153283186256886,
0.009659163653850555,
-0.06749018281698227,
-0.014702226966619492,
0.04938090592622757,
-0.039305172860622406,
0.03074277564883232,
-0.027321653440594673,
-0.042995840311050415,
0.014924784190952778,
0.04481230676174164,
0.036213893443346024,
0.006986929569393396,
-0.017326384782791138,
0.051370758563280106,
-0.02744157426059246,
-0.0024597400333732367,
-0.029319316148757935,
0.02809644117951393,
0.01248736958950758,
0.01526611763983965,
-0.07118932902812958,
-0.01982681080698967,
-0.012828830629587173,
0.003630346152931452,
-0.010133779607713223,
-0.052471354603767395,
-0.0014353140722960234,
-0.03990313038229942,
-0.010617791675031185,
-0.021398339420557022,
0.02043204940855503,
0.0106498496606946,
-0.06200284883379936,
-0.052391696721315384,
0.04318714141845703,
-0.047600157558918,
-0.05642138421535492,
0.01375142764300108,
0.0020095547661185265,
-0.04928940162062645,
0.008713250048458576,
-0.0002805226540658623,
0.033256299793720245,
-0.005616080481559038,
0.010211830027401447,
0.028814056888222694,
-0.0578865148127079,
-0.011899499222636223,
-0.0376499779522419,
0.022532571107149124,
0.009995661675930023,
0.031214747577905655,
0.007256454322487116,
-0.0015011721989139915,
-0.024313723668456078,
-0.01649537868797779,
0.01646844483911991,
0.010448399931192398,
-0.035060685127973557,
-0.018262317404150963,
-0.07972689718008041,
-0.0172575730830431,
0.05143323913216591,
0.015641316771507263,
-0.03222574666142464,
-0.021631967276334763,
0.05477701500058174,
0.023674529045820236,
0.04019901528954506,
-0.05788618326187134,
0.057031434029340744,
0.011423026211559772,
0.04008900001645088,
0.006474007852375507,
-0.015666939318180084,
-0.05367952585220337,
-0.06255516409873962,
-0.0381806381046772,
0.0076785641722381115,
-0.062476251274347305,
-0.011719191446900368,
0.11425444483757019,
0.030133895576000214,
-0.021968411281704903,
-0.07360093295574188,
-0.006187676452100277,
0.042827606201171875,
0.042858682572841644,
-0.008826504461467266,
-0.021747983992099762,
-0.020945310592651367,
0.0018104399787262082,
0.02456786297261715,
-0.02071409486234188,
-0.0913834199309349,
0.0017550167394801974,
-0.00041473377496004105,
0.06638234853744507,
-0.01684519089758396,
0.025141797959804535,
0.015049518086016178,
0.08795487135648727,
-0.0070208036340773106,
0.06227065995335579,
-0.01346530206501484,
-0.051400575786828995,
0.047318313270807266,
0.048412106931209564,
-0.04977421462535858,
-0.008400745689868927,
-0.03642426058650017,
-0.0253167524933815,
-0.004725356586277485,
-0.04998668283224106,
-0.016593320295214653,
-0.005101701244711876,
-0.014769895002245903,
-0.03991501033306122,
-0.058948736637830734,
0.007171710021793842,
0.04757662117481232
] |
<p>....is an oblate spheroid because centrifugal force stretches the tropical regions to a point farther from the center than they would be if the planet did not rotate. So we all learned in childhood, and it seems perfectly obvious. However...</p>
<p>I am at $45^\circ$ north latitude. Does that mean</p>
<ul>
<li>An angle with vertex at the center of the earth and one ray pointing toward the equator at the same longitude as mine, and one ray pointing toward me, is $45^\circ$ (that would mean I'm closer to the north pole than to the equator, measured along the surface, as becomes obvious if you think about really extreme oblateness); or</li>
<li>The normal to the ground where I stand makes a $45^\circ$ angle with the normal to the ground at the equator at the same latitude (this puts me closer to the equator than to the north pole); or</li>
<li>something else?</li>
</ul>
<p>If for the sake of simplicity we assume the earth is a fluid of uniform density, it seems one's potential energy relative to the center of the earth would be the same at all points on the surface.</p>
<ul>
<li>Would the force of gravity at my location, assuming no rotation, be directly toward the center? Would it be just as strong as if the whole mass of the earth were at the center and my location is just as far from the center as it is now?</li>
<li>Would the sum of the force of gravity (toward the center or in whichever direction it is) and the centrifugal force (away from the axis) be normal to the surface at my location?</li>
<li>Given all this, how does one find the exact shape?</li>
<li>How well does that shape in this idealized problem match that of the actual earth?</li>
</ul> | g5544 | [
0.054224155843257904,
0.014530561864376068,
0.002765519777312875,
-0.023465685546398163,
0.019687596708536148,
0.03550780564546585,
0.03803488239645958,
0.0024177206214517355,
-0.02247007191181183,
-0.013179300352931023,
0.006664965767413378,
-0.020857270807027817,
0.03276905044913292,
-0.033338118344545364,
0.06833416223526001,
-0.026717104017734528,
0.025708550587296486,
-0.017294101417064667,
0.07092813402414322,
0.022160790860652924,
-0.0007633149507455528,
-0.030491279438138008,
0.04157508537173271,
0.015857286751270294,
-0.049656178802251816,
-0.026866205036640167,
-0.017295992001891136,
-0.015340903773903847,
-0.07208338379859924,
-0.0018238509073853493,
0.0009061687742359936,
0.0054765911772847176,
0.09665970504283905,
-0.09563761949539185,
-0.06765663623809814,
0.018730496987700462,
0.02195141464471817,
0.051632046699523926,
0.0372634157538414,
-0.02804509364068508,
0.0056362091563642025,
-0.02250211127102375,
0.01675235666334629,
0.0024073710665106773,
-0.0006205601966939867,
0.0034871299285441637,
0.010538686998188496,
-0.02859855815768242,
0.05866626277565956,
0.0028464028146117926,
-0.09630171954631805,
0.007904588244855404,
0.024817978963255882,
0.0021449830383062363,
-0.03408146649599075,
0.05563569813966751,
0.052332956343889236,
0.011569175869226456,
-0.03663096949458122,
0.06119954213500023,
0.033834051340818405,
0.01331263966858387,
-0.009866421110928059,
0.01364440843462944,
0.029228275641798973,
-0.01923123188316822,
-0.03794899210333824,
0.021169904619455338,
-0.0030273371376097202,
-0.021678194403648376,
-0.002749817445874214,
-0.04901794344186783,
-0.007940680719912052,
-0.05794687569141388,
-0.09086768329143524,
0.036895688623189926,
0.02916879579424858,
0.021544765681028366,
0.017156103625893593,
0.00045036926167085767,
0.013221935369074345,
-0.00905037485063076,
0.004120332188904285,
-0.015713879838585854,
0.08867739140987396,
0.004721613600850105,
0.02722601220011711,
0.00867290236055851,
-0.007674441207200289,
0.01793537102639675,
0.0392601415514946,
-0.03428230062127113,
0.0514589361846447,
-0.017850248143076897,
0.0018578777089715004,
-0.050375767052173615,
0.013815466314554214,
0.08340302109718323,
-0.005684244446456432,
0.040871575474739075,
-0.05013924837112427,
0.023859653621912003,
-0.010425198823213577,
0.030252384021878242,
0.004083293490111828,
-0.02088991180062294,
0.01539001613855362,
0.009763994254171848,
0.046654608100652695,
-0.012164423242211342,
-0.033703308552503586,
-0.02543065883219242,
-0.00407277699559927,
-0.01784355938434601,
-0.024927806109189987,
-0.02907310239970684,
0.07026375830173492,
-0.022680213674902916,
0.06811604648828506,
0.05813303962349892,
0.018247690051794052,
0.05037854239344597,
0.04841804876923561,
0.09718091040849686,
0.018327148631215096,
0.0009711921447888017,
0.043270692229270935,
0.014167885296046734,
-0.015495994128286839,
-0.009515231475234032,
0.025439992547035217,
0.0017405282706022263,
-0.05913899838924408,
-0.030475929379463196,
0.01878088153898716,
-0.015371923334896564,
-0.10184578597545624,
0.024484368041157722,
0.02163090370595455,
-0.0032433567102998495,
-0.016270028427243233,
0.008187535218894482,
0.04154662787914276,
0.0022102221846580505,
0.015084894374012947,
0.05074871703982353,
-0.045013245195150375,
-0.0025288579054176807,
0.09641549736261368,
0.02475874498486519,
-0.048479896038770676,
0.02642194926738739,
-0.009266494773328304,
-0.04138663411140442,
-0.00493743596598506,
-0.01612164080142975,
0.0007549022557213902,
-0.020439254119992256,
0.002774518681690097,
-0.008846516720950603,
0.007286150939762592,
-0.0348321795463562,
0.043923087418079376,
-0.011684485711157322,
-0.006343947257846594,
-0.01697317697107792,
0.004030904732644558,
0.012736272998154163,
-0.013378848321735859,
0.044089674949645996,
-0.06332270801067352,
-0.015387363731861115,
0.021694837138056755,
-0.017862645909190178,
-0.04417465627193451,
0.016012374311685562,
0.032902318984270096,
-0.030315792188048363,
0.04304805025458336,
0.0005906521109864116,
0.023240642622113228,
0.016259117051959038,
0.009595314972102642,
0.001471057184971869,
-0.028735043480992317,
-0.037092018872499466,
0.0407336950302124,
0.001039886730723083,
0.034542378038167953,
0.02703000232577324,
-0.011101959273219109,
-0.0017396077746525407,
-0.03945311903953552,
0.05877237021923065,
-0.00826810859143734,
0.015500576235353947,
0.007515282835811377,
-0.0472094900906086,
-0.07169069349765778,
0.0219121053814888,
-0.027723632752895355,
0.016121666878461838,
0.0324423611164093,
0.04053087532520294,
-0.03195308893918991,
-0.00853526871651411,
0.06228184700012207,
0.022913997992873192,
0.03721149265766144,
0.021244307979941368,
-0.024123696610331535,
-0.028077732771635056,
-0.005521334707736969,
0.03136109560728073,
-0.0014632252277806401,
0.05754075571894646,
0.017858481034636497,
-0.00008319071639562026,
-0.06960558146238327,
-0.01205396931618452,
0.00010260282579110935,
-0.004570852033793926,
0.05343509837985039,
0.04423941299319267,
0.0036197586450725794,
-0.016433270648121834,
-0.060913581401109695,
0.043637122958898544,
0.0066811745055019855,
0.0282076857984066,
-0.030938714742660522,
-0.021594654768705368,
0.10328634083271027,
-0.0017307472880929708,
-0.02008797787129879,
0.047953177243471146,
-0.00882766768336296,
-0.0242936871945858,
-0.011382395401597023,
-0.024222547188401222,
0.024521401152014732,
-0.022527551278471947,
-0.00856498908251524,
-0.007982717826962471,
0.05704958736896515,
0.026781940832734108,
0.07940282672643661,
-0.008053834550082684,
-0.007002189755439758,
0.018852803856134415,
0.04369562864303589,
-0.033061329275369644,
-0.043032947927713394,
0.025195002555847168,
-0.017348241060972214,
0.026429221034049988,
-0.04752195253968239,
0.01605130545794964,
-0.08139383047819138,
-0.06427507847547531,
-0.07022683322429657,
-0.06456830352544785,
0.012867332436144352,
0.018519120290875435,
-0.07434748113155365,
-0.00870460830628872,
-0.05956564471125603,
0.011445480398833752,
0.005803331732749939,
0.036094438284635544,
-0.010167612694203854,
0.07563845813274384,
0.004585340619087219,
0.07139169424772263,
-0.023184552788734436,
-0.010985895991325378,
-0.0690944492816925,
-0.050560370087623596,
-0.03745907172560692,
0.034030571579933167,
0.023941613733768463,
0.05941728875041008,
-0.003081724513322115,
0.0605081282556057,
0.05375692620873451,
-0.01841210387647152,
-0.027144895866513252,
0.0486101470887661,
-0.0006802609423175454,
0.003126101568341255,
-0.033218178898096085,
0.03031368926167488,
0.08622949570417404,
0.01633218675851822,
0.004960895515978336,
0.041057948023080826,
0.04398130252957344,
-0.00017766316886991262,
-0.012865978293120861,
0.047430746257305145,
0.006560035981237888,
-0.02222222462296486,
0.004364641848951578,
0.01777004636824131,
-0.034196335822343826,
0.032763246446847916,
-0.007744483649730682,
-0.06801214069128036,
-0.018209034577012062,
-0.0042510926723480225,
-0.07026901841163635,
0.03430609032511711,
-0.021224098280072212,
-0.04238108918070793,
-0.045783646404743195,
-0.06428392976522446,
-0.023621931672096252,
-0.00788902398198843,
-0.003691884456202388,
0.02027156390249729,
-0.03670017048716545,
-0.05948256328701973,
-0.02554587833583355,
0.013444125652313232,
-0.0037198495119810104,
0.0437442809343338,
-0.08638092875480652,
0.027413923293352127,
-0.04569092392921448,
-0.03432757034897804,
0.03804773464798927,
0.03677874431014061,
-0.04176187142729759,
0.0347110889852047,
-0.018674036487936974,
0.01214607059955597,
-0.0034790479112416506,
0.001266820472665131,
0.04267444834113121,
0.03299714997410774,
-0.03876122087240219,
-0.028961829841136932,
-0.038126833736896515,
-0.0977768823504448,
-0.012740839272737503,
0.015748612582683563,
-0.01691054180264473,
-0.045657120645046234,
-0.020879032090306282,
0.030763844028115273,
0.01204011868685484,
-0.025959333404898643,
0.034067824482917786,
0.014521878212690353,
0.08160912990570068,
0.022042419761419296,
-0.009453043341636658,
0.024203762412071228,
-0.04550669342279434,
0.04021907597780228,
-0.013936158269643784,
-0.015665367245674133,
-0.009980989620089531,
-0.0163872167468071,
-0.03648281469941139,
-0.03783843666315079,
0.027745844796299934,
-0.023710031062364578,
-0.006382242310792208,
0.0051872627809643745,
-0.02331485040485859,
-0.02881336212158203,
0.02714976854622364,
0.015321816317737103,
0.03680608049035072,
-0.037007398903369904,
-0.007299765478819609,
-0.022779326885938644,
0.00030692500877194107,
0.0046648187562823296,
0.019791118800640106,
-0.03101307339966297,
0.010009431280195713,
-0.049651503562927246,
0.016758041456341743,
0.010939320549368858,
-0.029675723984837532,
-0.013890520669519901,
0.05076039209961891,
-0.02176237851381302,
0.044045452028512955,
-0.0955781564116478,
-0.011395785957574844,
0.01604919321835041,
0.08069495856761932,
0.03292660042643547,
-0.0016531803412362933,
0.020490115508437157,
-0.01063473429530859,
0.003060857532545924,
0.03934207558631897,
0.007054461631923914,
0.01629229635000229,
-0.01325093675404787,
-0.022361448034644127,
-0.050646379590034485,
-0.0005104222800582647,
0.027352627366781235,
-0.02738003246486187,
-0.02065657079219818,
0.057191699743270874,
0.02018425427377224,
0.034700024873018265,
-0.04547891765832901,
0.07065171003341675,
0.000986460829153657,
0.04939131811261177,
0.010200477205216885,
-0.00234430655837059,
-0.049294643104076385,
-0.012747665867209435,
0.03919815272092819,
-0.011597996577620506,
-0.016727648675441742,
-0.02126590721309185,
0.06481718271970749,
0.048666320741176605,
-0.0017892156029120088,
-0.002237014239653945,
-0.03559834510087967,
-0.05461982637643814,
0.012148387730121613,
0.05138465389609337,
0.04987683892250061,
-0.05742892622947693,
-0.004542190115898848,
-0.0160630214959383,
-0.01738581620156765,
0.014037096872925758,
0.03326791524887085,
-0.050966326147317886,
0.059829991310834885,
0.04043571650981903,
-0.012013809755444527,
-0.020753638818860054,
0.053349968045949936,
-0.02383345365524292,
-0.017686577513813972,
0.003562833881005645,
-0.03095092438161373,
0.006491795182228088,
-0.0069220163859426975,
-0.0001461261126678437,
0.031244855374097824,
-0.03351351618766785,
-0.014773470349609852,
0.02720578759908676,
0.011934773996472359,
-0.015079198405146599,
-0.019720230251550674,
0.032751720398664474,
-0.07003243267536163,
0.019252529367804527,
-0.02031073160469532,
0.048498623073101044,
-0.024852462112903595,
-0.02729608863592148,
-0.024815525859594345,
-0.029095206409692764,
-0.03145334869623184,
0.005594696383923292,
0.023369790986180305,
0.08685758709907532,
-0.00499806459993124,
-0.03155224770307541,
0.03426065295934677,
0.0011660164454951882,
-0.05633885785937309,
-0.01790652796626091,
-0.026964211836457253,
-0.06773589551448822,
-0.02847982943058014,
-0.0018315775087103248,
0.03647484630346298,
-0.021531328558921814,
-0.04083641991019249,
-0.009670580737292767,
-0.04797085002064705,
0.0008453150512650609,
0.02957582287490368,
-0.013227310962975025,
-0.038842108100652695,
-0.0041047995910048485,
-0.04653437063097954,
0.006873471662402153,
0.05600736290216446,
-0.033998001366853714,
-0.02277340553700924,
-0.016951611265540123,
0.020401518791913986,
-0.03116866946220398,
0.10465998202562332,
-0.04343584179878235,
0.028836678713560104,
-0.009202728979289532,
0.02712230756878853,
0.07748066633939743,
0.026660703122615814,
0.016482604667544365,
0.07690615952014923,
-0.008829737082123756,
-0.018856531009078026,
-0.003928259946405888,
0.012500119395554066,
-0.0007827265653759241,
-0.028583047911524773,
-0.03330366685986519,
0.06580138951539993,
-0.012124549597501755,
0.036923687905073166,
0.0394698791205883,
0.0030154730193316936,
-0.04825934022665024,
-0.017526237294077873,
0.04936382547020912,
-0.025664960965514183,
-0.03284958004951477,
0.027212753891944885,
-0.015009323135018349,
0.046123795211315155,
0.0013717152178287506,
0.020221270620822906,
-0.018162691965699196,
-0.013694713823497295,
-0.01389812771230936,
-0.010617668740451336,
0.016237691044807434,
-0.03961274400353432,
0.12116661667823792,
-0.06406945735216141,
-0.04798872396349907,
-0.046332988888025284,
0.0320209302008152,
0.009248350746929646,
-0.0420076958835125,
0.03025023452937603,
-0.04100951552391052,
0.015889329835772514,
0.017192143946886063,
-0.007216485682874918,
-0.07229918986558914,
0.03360231593251228,
0.0033765339758247137,
0.04010795056819916,
-0.03249624744057655,
-0.006350437644869089,
0.012721587903797626,
-0.01707283966243267,
-0.01027755904942751,
-0.013002525083720684,
0.060117725282907486,
-0.021380558609962463,
0.009511604905128479,
0.026557743549346924,
0.006328816059976816,
-0.026652172207832336,
-0.03371565043926239,
-0.05386125668883324,
0.07373037189245224,
0.041960302740335464,
0.03325723484158516,
-0.04343573749065399,
0.0008240032475441694,
-0.012079904787242413,
0.048253655433654785,
-0.01480185892432928,
-0.03829557076096535,
0.050982676446437836,
-0.011460177600383759,
0.07213250547647476,
-0.0008535110973753035,
-0.054115019738674164,
0.0372341088950634,
-0.016159819439053535,
0.020580219104886055,
0.05392032861709595,
-0.04138463735580444,
0.012797863222658634,
0.033602263778448105,
-0.04931583255529404,
0.0251238401979208,
-0.022763600572943687,
0.0027600128669291735,
-0.021795760840177536,
-0.05010861158370972,
-0.020793985575437546,
0.010893166996538639,
-0.03303668648004532,
-0.019810743629932404,
-0.026690078899264336,
0.014344867318868637,
0.031989965587854385,
0.03378170356154442,
0.01114360149949789,
0.03221675008535385,
-0.03862139955163002,
0.013339109718799591,
0.009516161866486073,
0.003777087898924947,
-0.033647261559963226,
0.04545043408870697,
0.05881466716527939,
-0.03731617331504822,
0.020163442939519882,
0.006778581999242306,
-0.005993364378809929,
-0.030258730053901672,
0.0020523525308817625,
-0.002984261605888605,
-0.0052893212996423244,
0.002386801177635789,
0.017368264496326447,
-0.047354377806186676,
-0.06367320567369461,
-0.010654308833181858,
0.020793594419956207,
-0.03511187434196472,
0.01578826829791069,
0.046366505324840546,
0.00969709362834692,
0.04650871455669403,
0.04403809458017349,
0.01963113248348236,
0.04214908555150032,
0.059569258242845535,
0.002126428997144103,
-0.04980037361383438,
-0.006670468952506781,
0.021457476541399956,
0.0817410871386528,
-0.03257621079683304,
0.014471037313342094,
-0.015177563764154911,
-0.022915193811058998,
-0.06699438393115997,
0.03717011213302612,
0.01274381298571825,
-0.049949754029512405,
-0.0387243889272213,
0.007963476702570915,
0.02437620796263218,
-0.040237244218587875,
0.03305972367525101,
0.032858867198228836,
-0.01721104048192501,
0.05295459181070328,
0.008752383291721344,
0.037777338176965714,
-0.013390716165304184,
-0.0789044201374054,
-0.0186754260212183,
-0.01158453244715929,
-0.02296750247478485,
-0.04374781623482704,
-0.08132818341255188,
0.006830829661339521,
-0.00472439406439662,
-0.03470771387219429,
-0.032612189650535583,
-0.0047928583808243275,
0.03484087064862251,
-0.05161290615797043,
-0.055728405714035034,
0.0034693004563450813,
-0.025702130049467087,
0.05120092257857323,
-0.02485005557537079,
-0.07518167793750763,
0.009109468199312687,
-0.038649994879961014,
0.027162114158272743,
0.04325626417994499,
-0.0023068184964358807,
0.05030234530568123,
-0.05812942981719971,
-0.012380901724100113,
-0.002526155672967434,
-0.04350026324391365,
-0.02355360798537731,
-0.01743432879447937,
-0.0035617209505289793,
0.07875647395849228,
-0.04459590092301369,
-0.006712494418025017,
-0.01680430956184864,
0.0007362185860984027,
0.013906367123126984,
0.047141414135694504,
0.0019677861128002405,
-0.02631666325032711,
-0.0005258614546619356,
-0.03001825511455536,
-0.017283832654356956,
-0.04247165098786354,
0.051123037934303284,
-0.0012907716445624828,
0.00013409620441962034,
-0.022532302886247635,
-0.07422398775815964,
0.018536720424890518,
0.07125670462846756,
-0.0012773147318512201,
0.0720701515674591,
0.020111383870244026,
0.06446364521980286,
0.07273311167955399,
-0.01207752712070942,
-0.0026738811284303665,
-0.011325003579258919,
-0.0329122357070446,
-0.06310603022575378,
0.0304540004581213,
0.03181447833776474,
-0.05397063493728638,
-0.033996183425188065,
0.045437365770339966,
-0.03927158564329147,
-0.02510835975408554,
0.02429243177175522,
-0.017089325934648514,
-0.013453850522637367,
-0.00021719826327171177,
-0.003299265168607235,
-0.023071900010108948,
0.006740967743098736,
0.03804868459701538,
-0.030842453241348267,
-0.07227931916713715,
-0.009552002884447575,
-0.03797975182533264,
-0.03272709622979164,
-0.023764662444591522,
-0.038669660687446594,
-0.0007675376255065203,
-0.006552322767674923,
0.0236640814691782,
-0.03767923638224602,
0.053584400564432144,
0.011346486397087574,
0.025524241849780083,
-0.0023148744367063046,
0.018714845180511475,
0.011537608690559864,
-0.023556167259812355,
-0.021434687077999115,
-0.05761008709669113,
-0.008278587833046913,
-0.024880612269043922,
0.018603237345814705,
-0.035991132259368896,
-0.030943339690566063,
-0.03356296196579933,
0.06465154141187668,
-0.021949773654341698,
0.01644567772746086,
0.024077018722891808,
-0.038640353828668594,
0.043079495429992676
] |
<p>The argument for <a href="http://en.wikipedia.org/wiki/Eternal_inflation" rel="nofollow">eternal inflation</a> is we have some patch of metastable vacuum with positive cosmological constant, and so it expands exponentially a la de Sitter. Most of the patch decays to something which expands more slowly, but only a tiny fraction continues to expand at that fast exponential rate. The magic of exponentiality is despite only being a tiny fraction, it still dominates, and this process continues forever.</p>
<p>OK, but add in causal patch complementarity, and well, only the causal patch counts, right? The fraction counting is no longer admissible because we can only measure the fraction within the causal patch, and any observer will always exit the inflationary phase with probability 1. What gives? </p>
<p>The spatial multiverse presupposes there is such a thing as outside the patch. Is that a no no? The multiverse of different string compactifications, well, how many of them are there inside a causal patch simultaneously? As for many worlds multiverses, is many worlds even true?</p> | g5545 | [
0.04731253534555435,
0.044660575687885284,
-0.00018890986393671483,
-0.03165459632873535,
-0.017166834324598312,
0.021027034148573875,
-0.019799333065748215,
0.02988484874367714,
-0.023782342672348022,
-0.06745269149541855,
0.01888827420771122,
-0.022220147773623466,
0.025376224890351295,
0.02219412289559841,
0.02320256270468235,
-0.011146917007863522,
0.016264161095023155,
-0.054381370544433594,
0.07978608459234238,
0.006669268012046814,
0.042640913277864456,
0.016712460666894913,
0.02667945995926857,
-0.03311990946531296,
-0.004041552543640137,
-0.039087895303964615,
0.013770850375294685,
-0.00897682923823595,
-0.015692485496401787,
-0.0808418020606041,
0.13219082355499268,
-0.003457220271229744,
0.004793503321707249,
-0.036067359149456024,
-0.005949826445430517,
-0.038932181894779205,
0.003264293074607849,
0.03101767785847187,
0.010516636073589325,
0.007260139100253582,
-0.016196828335523605,
0.015509692952036858,
0.041136953979730606,
-0.016932841390371323,
-0.020606230944395065,
0.034750230610370636,
-0.046264197677373886,
0.03314729779958725,
0.07001112401485443,
-0.08182450383901596,
-0.007011315785348415,
0.012960262596607208,
-0.061705246567726135,
0.05956081673502922,
0.018057508394122124,
0.07395041733980179,
-0.03787253797054291,
-0.005581355188041925,
0.034794483333826065,
0.024391522631049156,
0.01335220504552126,
-0.05608123913407326,
0.04918311536312103,
0.0337940938770771,
0.009458793327212334,
0.0416865274310112,
-0.040341585874557495,
-0.03855679929256439,
0.004094543866813183,
-0.009097584523260593,
0.019909026101231575,
-0.03353274241089821,
-0.005859210155904293,
0.02767883613705635,
-0.008189837448298931,
0.10536207258701324,
-0.01845124550163746,
-0.02441495656967163,
-0.026892496272921562,
0.0009545376524329185,
-0.03660937026143074,
0.004204261116683483,
-0.014222404919564724,
-0.006457420997321606,
0.04043106362223625,
-0.01341073215007782,
-0.01410005148500204,
-0.061424002051353455,
-0.03392015025019646,
-0.02075166255235672,
0.018066853284835815,
0.02483879216015339,
0.05811242759227753,
0.005073730368167162,
-0.02861524373292923,
0.0032082446850836277,
-0.024363268166780472,
0.06573260575532913,
-0.06322368234395981,
-0.05017463117837906,
-0.03551308438181877,
0.04582899063825607,
0.04388229548931122,
-0.02818583883345127,
0.021836645901203156,
-0.002526164287701249,
-0.0051203155890107155,
-0.031505268067121506,
-0.008880573324859142,
-0.015050547197461128,
0.001251850975677371,
-0.03485441207885742,
-0.035426028072834015,
-0.01077981572598219,
-0.04665360972285271,
0.025134192779660225,
0.027342790737748146,
0.01348088774830103,
-0.008237131871283054,
0.016890928149223328,
0.025400906801223755,
-0.020541273057460785,
0.02131139300763607,
0.02686459571123123,
-0.06711409240961075,
-0.002831982681527734,
0.024430351331830025,
-0.0016157503705471754,
0.030966725200414658,
0.034899596124887466,
0.005829200614243746,
0.05260980874300003,
0.014883712865412235,
0.055922701954841614,
-0.01951131597161293,
-0.03606915473937988,
0.012479228898882866,
-0.009757300838828087,
-0.03621494770050049,
0.028988435864448547,
-0.06128956004977226,
-0.05285042151808739,
0.009949379600584507,
0.004236636217683554,
-0.032588161528110504,
-0.012928970158100128,
0.02318764477968216,
-0.008130576461553574,
-0.01967831887304783,
0.0008365628309547901,
0.006933517288416624,
0.05785265937447548,
0.014809343963861465,
0.002592650009319186,
-0.017419276759028435,
0.036451131105422974,
0.049277547746896744,
0.00004252186408848502,
-0.007691175676882267,
-0.014480111189186573,
0.00038080872036516666,
0.025988660752773285,
0.0019432761473581195,
-0.014763034880161285,
-0.03384946659207344,
0.06971260905265808,
0.013742618262767792,
-0.0009285194100812078,
-0.03659925237298012,
0.004985832143574953,
-0.03823314607143402,
-0.007804489228874445,
-0.0031238736119121313,
-0.021277330815792084,
0.060562875121831894,
0.018346769735217094,
-0.0025110242422670126,
0.0434461385011673,
-0.04151032492518425,
-0.05817801505327225,
-0.015649940818548203,
-0.002216118387877941,
0.015088504180312157,
0.0099380724132061,
0.10184504091739655,
-0.029522664844989777,
0.011780069209635258,
0.04188435897231102,
-0.03757942467927933,
-0.00185570796020329,
0.02848813496530056,
-0.029033390805125237,
-0.0012668428244069219,
0.06840837001800537,
0.000967162661254406,
-0.03556940332055092,
0.02502080611884594,
-0.03488321602344513,
-0.038546640425920486,
-0.04546409472823143,
0.030938351526856422,
0.04166972264647484,
-0.008703093975782394,
-0.05843508243560791,
-0.02234763465821743,
0.020467331632971764,
0.005428996402770281,
-0.010366457514464855,
-0.024201421067118645,
0.005419941619038582,
0.05828258395195007,
-0.12003902345895767,
0.021662602201104164,
0.031190630048513412,
-0.017680665478110313,
0.016172807663679123,
0.007576061878353357,
-0.028445608913898468,
0.018989942967891693,
0.026918280869722366,
0.018009960651397705,
0.0350070483982563,
0.06191837415099144,
-0.04866882041096687,
0.035731587558984756,
-0.00878978706896305,
-0.02423805184662342,
-0.015459885820746422,
0.006293522659689188,
0.030972350388765335,
-0.06170918792486191,
0.0058207097463309765,
-0.04554915055632591,
-0.018995581194758415,
0.01831815578043461,
-0.0061938147991895676,
-0.013424109667539597,
0.04571247100830078,
-0.029009031131863594,
0.0855185016989708,
0.038995712995529175,
-0.024510936811566353,
-0.030659684911370277,
0.04274677112698555,
0.03849634900689125,
-0.029325595125555992,
-0.022632615640759468,
-0.010859901085495949,
-0.007171106990426779,
0.043065395206213,
-0.019907791167497635,
-0.07265384495258331,
-0.011390662752091885,
-0.015399950556457043,
0.011970309540629387,
0.01106923446059227,
0.018841205164790154,
0.06673575192689896,
-0.04286663979291916,
-0.012562566436827183,
0.05956074595451355,
-0.021757446229457855,
0.03097289428114891,
-0.020345836877822876,
-0.02033299393951893,
-0.02280186489224434,
-0.039229586720466614,
0.02129819244146347,
-0.08280628174543381,
0.0024871299974620342,
-0.007110936101526022,
0.056607794016599655,
-0.04065408930182457,
0.010802924633026123,
0.006283956579864025,
0.06809569895267487,
0.02977956086397171,
-0.01360520999878645,
0.030194813385605812,
-0.01689930073916912,
0.007588648237287998,
0.024455759674310684,
-0.020035047084093094,
-0.02030637487769127,
0.027611510828137398,
-0.0597095862030983,
-0.028373489156365395,
0.028259268030524254,
0.0014925508294254541,
0.039651963859796524,
0.0016521909274160862,
-0.02315484546124935,
0.01272017415612936,
0.02920253574848175,
-0.014603329822421074,
0.0816817432641983,
-0.0131481122225523,
-0.04965658858418465,
-0.025525983422994614,
-0.000014464128071267623,
0.009415974840521812,
-0.03636553883552551,
0.03399927541613579,
-0.02180512808263302,
0.021027175709605217,
0.015329441986978054,
0.032024990767240524,
0.009545043110847473,
0.020528163760900497,
-0.09182227402925491,
0.03166285157203674,
0.05629881098866463,
0.01624375954270363,
-0.020127560943365097,
0.0395803228020668,
0.03946419805288315,
0.014223041012883186,
0.029628869146108627,
0.07214830815792084,
0.0028629822190850973,
0.000260245957178995,
0.024825450032949448,
0.012307189404964447,
0.03323911130428314,
-0.018513614311814308,
0.0005300687626004219,
-0.021285615861415863,
0.0029260904993861914,
-0.053811460733413696,
0.06636597216129303,
-0.02129940502345562,
-0.060452044010162354,
-0.046154387295246124,
-0.04753294587135315,
0.011241568252444267,
-0.029253849759697914,
-0.07143117487430573,
-0.01270900946110487,
0.046159904450178146,
0.05541840195655823,
-0.0559859462082386,
0.0078018903732299805,
0.021679792553186417,
0.05576290190219879,
0.0014627594500780106,
0.023807944729924202,
-0.04830395057797432,
0.044773947447538376,
0.030451230704784393,
0.0030273799784481525,
0.03789784759283066,
-0.026140552014112473,
0.019405236467719078,
-0.06643636524677277,
-0.006706545129418373,
0.05641785264015198,
0.024786964058876038,
-0.012691115960478783,
0.024191075935959816,
-0.053490687161684036,
0.03005845472216606,
-0.06504195183515549,
0.027393348515033722,
0.0017409503925591707,
-0.01441287063062191,
0.04379119351506233,
0.014922230504453182,
0.015637747943401337,
0.032035358250141144,
0.01709797792136669,
0.028885843232274055,
-0.0059883915819227695,
-0.04901304095983505,
0.0379435271024704,
0.05137048661708832,
-0.05565289780497551,
0.016760671511292458,
-0.005517945624887943,
0.00456356443464756,
0.04529877007007599,
0.058844856917858124,
0.02890203148126602,
0.04602549597620964,
-0.023991508409380913,
-0.017657505348324776,
0.011890648864209652,
-0.003513114294037223,
-0.05567139387130737,
-0.025810938328504562,
-0.08400329947471619,
0.026759479194879532,
0.005270253401249647,
-0.012698445469141006,
-0.005309150088578463,
-0.021443424746394157,
-0.029253998771309853,
0.024233678355813026,
-0.05409273877739906,
0.05564945563673973,
-0.006566114258021116,
0.06496382504701614,
-0.03216325119137764,
-0.0026373201981186867,
0.041561901569366455,
0.0157131627202034,
-0.030411554500460625,
-0.012616698630154133,
0.0454634428024292,
0.010786556638777256,
-0.05496302619576454,
0.02045375481247902,
0.022059164941310883,
0.016416124999523163,
-0.07465896755456924,
0.05599768087267876,
-0.025381341576576233,
0.08505077660083771,
-0.05866921320557594,
0.06237837299704552,
-0.010467911139130592,
0.0076837423257529736,
0.06734245270490646,
-0.00970383733510971,
-0.026845110580325127,
-0.000028687827580142766,
0.08418531715869904,
-0.010989456437528133,
-0.02891177497804165,
-0.054403193295001984,
0.038077667355537415,
0.03647904470562935,
-0.013092570938169956,
0.034901827573776245,
0.03396107628941536,
-0.043929241597652435,
0.02233453467488289,
-0.059311117976903915,
0.04364318028092384,
-0.052393920719623566,
-0.037528254091739655,
0.10347148776054382,
-0.03529340773820877,
-0.03617127984762192,
0.04163116216659546,
-0.04086069390177727,
0.06871884316205978,
0.022550862282514572,
-0.048001714050769806,
-0.05567597970366478,
-0.01209099031984806,
-0.048522453755140305,
0.034917112439870834,
-0.007693892810493708,
-0.005503309424966574,
0.016903938725590706,
-0.022520966827869415,
0.026827339082956314,
0.04746459424495697,
0.037284016609191895,
0.02539088949561119,
-0.06762183457612991,
0.018953068181872368,
0.0013862927444279194,
0.007907298393547535,
0.014761880971491337,
0.008998086676001549,
-0.03461775183677673,
-0.044734351336956024,
-0.0502745658159256,
-0.003988652490079403,
0.03367934376001358,
0.023836717009544373,
0.005994082894176245,
0.037318527698516846,
0.008014687336981297,
-0.04348350688815117,
0.00865375529974699,
-0.04217378422617912,
0.00399733567610383,
0.012020105496048927,
0.04776677116751671,
-0.034412793815135956,
0.02659749612212181,
-0.016099555417895317,
0.012768098153173923,
0.0016769709764048457,
-0.027828335762023926,
0.028758984059095383,
-0.0967819094657898,
-0.008647582493722439,
0.01692659966647625,
-0.011428640224039555,
0.08915900439023972,
0.0017899497179314494,
-0.06194491311907768,
-0.023222606629133224,
-0.03847891464829445,
-0.04911208897829056,
0.0017527587478980422,
-0.023532820865511894,
-0.026717621833086014,
0.05532607063651085,
0.013264905661344528,
-0.006633882876485586,
-0.05397312715649605,
0.009183610789477825,
0.03154401853680611,
-0.006502445321530104,
-0.009068245068192482,
0.03365311399102211,
-0.01794573664665222,
-0.0038345425855368376,
-0.05310235917568207,
0.001564839156344533,
0.07771573215723038,
-0.08695042133331299,
-0.0014778804033994675,
-0.09502866119146347,
-0.0062799882143735886,
-0.0363747701048851,
-0.010846156626939774,
0.012583390809595585,
-0.017271099612116814,
0.04496278241276741,
0.06949236243963242,
0.007084966637194157,
0.006957891397178173,
-0.07514557987451553,
-0.02402159571647644,
0.02680840902030468,
0.07936974614858627,
-0.0004175487847533077,
0.01450386829674244,
-0.0016230542678385973,
0.0058702947571873665,
0.024153990671038628,
0.039823707193136215,
-0.022198377177119255,
0.04924239590764046,
-0.004929640330374241,
0.011398634873330593,
-0.04500999674201012,
0.004698673728853464,
0.014039553701877594,
-0.02991928532719612,
-0.03213971108198166,
-0.06836196035146713,
0.05623244121670723,
0.041237473487854004,
-0.0654279962182045,
-0.05085842311382294,
0.032660022377967834,
0.06389723718166351,
0.07616478204727173,
0.0027303893584758043,
0.03066140040755272,
-0.009817421436309814,
0.029620099812746048,
-0.041628412902355194,
-0.05232171341776848,
-0.0047133490443229675,
0.006387230008840561,
0.02262319065630436,
-0.013184008188545704,
-0.03275145962834358,
-0.02677076868712902,
0.012743992730975151,
-0.0424342155456543,
0.05018417909741402,
0.043923839926719666,
0.041100095957517624,
0.052753690630197525,
0.027942705899477005,
0.019671104848384857,
0.0226153414696455,
0.02324349246919155,
-0.06141665205359459,
0.013109495863318443,
-0.0353848896920681,
-0.016319725662469864,
-0.03162027522921562,
-0.017397670075297356,
0.07984547317028046,
-0.028694497421383858,
0.03418126329779625,
-0.011360318399965763,
-0.03807443007826805,
-0.05773995444178581,
0.0023726613726466894,
-0.03676926717162132,
-0.040686458349227905,
0.0066213589161634445,
0.0012784581631422043,
-0.010288415476679802,
-0.02118537947535515,
0.01661878637969494,
-0.0002798529458232224,
-0.06858129799365997,
-0.04348786175251007,
-0.049730125814676285,
-0.00895154569298029,
0.008412536233663559,
0.07707513868808746,
-0.0408577099442482,
-0.0187882948666811,
0.04462725296616554,
-0.008403214626014233,
0.005370034370571375,
-0.026316553354263306,
0.014875421300530434,
-0.004600003827363253,
0.04554124176502228,
0.03015577606856823,
-0.009657579474151134,
0.015795813873410225,
-0.020730560645461082,
0.025348814204335213,
-0.030670955777168274,
-0.026420243084430695,
-0.023592351004481316,
0.011624797247350216,
0.031082239001989365,
-0.03050016611814499,
0.01344019453972578,
-0.011218908242881298,
0.02881379798054695,
0.027677403762936592,
0.0059494031593203545,
-0.005382551811635494,
-0.023960256949067116,
-0.01611614227294922,
0.06001624837517738,
0.018580233678221703,
-0.003468281589448452,
0.0017759037436917424,
0.04287688806653023,
-0.011230976320803165,
-0.01697731763124466,
-0.03167799115180969,
-0.021573584526777267,
-0.013618308119475842,
-0.00896964780986309,
0.04694786295294762,
0.012647762894630432,
0.019694311544299126,
0.001527375541627407,
-0.006317474413663149,
0.025566639378666878,
-0.054568130522966385,
0.02335522137582302,
-0.01695362851023674,
-0.003924886230379343,
-0.017713112756609917,
0.05536040663719177,
-0.021977994590997696,
0.022136062383651733,
0.013577088713645935,
-0.023797670379281044,
-0.017458852380514145,
-0.028826070949435234,
-0.01261010393500328,
-0.008588535711169243,
0.027366027235984802,
-0.018913356587290764,
-0.07560312747955322,
-0.02934454381465912,
0.030665986239910126,
-0.07439391314983368,
0.019715091213583946,
-0.033112067729234695,
0.03438904881477356,
0.002396579831838608,
-0.04950268194079399,
-0.017647037282586098,
0.0241619274020195,
-0.06202109903097153,
-0.022133134305477142,
-0.01196065079420805,
0.0861252024769783,
0.0321272537112236,
0.0127616161480546,
0.04588141292333603,
0.027623841539025307,
-0.009602108970284462,
-0.07060068100690842,
0.04052593559026718,
-0.01965293101966381,
-0.003357459092512727,
0.0022074859589338303,
-0.022751079872250557,
0.08663276582956314,
-0.01533622294664383,
0.02688584104180336,
-0.03367886319756508,
0.022932568565011024,
0.028929267078638077,
-0.010066580027341843,
-0.00806443952023983,
-0.035827215760946274,
-0.0153142549097538,
0.044373221695423126,
-0.04460539668798447,
0.009150183759629726,
-0.04485856741666794,
0.050511933863162994,
0.016543611884117126,
-0.004165872931480408,
-0.020896384492516518,
-0.030968764796853065,
0.02032456174492836,
0.0015610201517120004,
0.0038554163184016943,
-0.05580960959196091,
0.00883184839040041,
0.012685107067227364,
-0.06120774522423744,
-0.04160763695836067,
-0.0618538036942482,
0.03232146427035332,
-0.01258691307157278,
-0.04668482020497322,
-0.040918949991464615,
-0.05211520567536354,
-0.02210746891796589,
-0.037358615547418594,
0.026876598596572876,
-0.006139467470347881,
-0.046884480863809586,
-0.014035223983228207,
0.044673167169094086,
-0.015076245181262493,
-0.005546698812395334,
0.029306834563612938,
0.020087458193302155,
-0.01683734729886055,
0.026761533692479134,
0.027860941365361214,
0.024505415931344032,
-0.023423170670866966,
-0.02001376636326313,
0.03155360370874405,
-0.0772891715168953,
0.04894880950450897,
0.030531860888004303,
-0.029740173369646072,
-0.017771756276488304,
-0.06696940958499908,
0.035181187093257904,
0.012727471999824047,
-0.02782943658530712,
0.0010360872838646173,
-0.0524158775806427,
-0.01433288399130106,
-0.030898883938789368,
0.0036143423058092594,
-0.01865728572010994,
0.026209089905023575,
-0.03354513272643089,
0.030091747641563416,
-0.022368350997567177,
0.0196693055331707,
0.039171043783426285,
0.020932644605636597,
-0.006771013140678406,
-0.019768817350268364,
-0.05113178864121437,
0.06442037969827652,
0.02895737811923027
] |
<p>Schrodinger believed that the phisical interpretation of the wavefunction $\Psi$ was the vibration amplitude and $ |\Psi|^2 $ was the electric charge density. While no-one disagrees with his interpretation of $\Psi$, many physicists believed Schrodinger was wrong about about $|\Psi|^2$ and argued that $|\Psi|^2$ is a probability. Schrodinger never accepted this view, but registered his "concern an disappointment" that this "transcendental, almost psychical interpretation" had become "universally accepted dogma." Why did Schrodinger forever think that $|\Psi|^2$ was the electric charge density and not a probability?</p> | g5546 | [
0.05742364376783371,
0.008666048757731915,
-0.000781607290264219,
-0.0431026928126812,
0.007719461806118488,
0.046962495893239975,
-0.002952728420495987,
0.01969091035425663,
-0.013620528392493725,
-0.009737258777022362,
0.033573150634765625,
-0.04004737734794617,
0.013581992127001286,
0.03826672211289406,
0.01698945462703705,
0.015855243429541588,
0.04247407987713814,
0.0068627758882939816,
-0.007303742691874504,
0.0041122534312307835,
-0.03924814239144325,
-0.06282808631658554,
-0.021431099623441696,
-0.05363430827856064,
-0.023496555164456367,
-0.05374636873602867,
0.0053483652882277966,
-0.036862973123788834,
0.04189109802246094,
-0.02171000838279724,
0.0011401849333196878,
0.0667736679315567,
0.03213299810886383,
-0.018014289438724518,
-0.03422284498810768,
-0.006549398880451918,
0.030679866671562195,
0.003640697570517659,
0.0353667214512825,
0.001950728939846158,
0.012300288304686546,
-0.004068982321768999,
0.01470539253205061,
-0.03947680443525314,
-0.0037581545766443014,
-0.016217954456806183,
-0.00033100269502028823,
0.05982320010662079,
-0.04132012277841568,
-0.013503558933734894,
-0.007317480631172657,
-0.01352989487349987,
0.04018652066588402,
0.09532265365123749,
0.04624387249350548,
0.02106885425746441,
0.031434930860996246,
0.016860613599419594,
0.007734641898423433,
0.03257729858160019,
0.01467366423457861,
-0.043419111520051956,
0.05786817893385887,
0.025013014674186707,
0.009490575641393661,
-0.030065782368183136,
-0.05559676140546799,
-0.023562749847769737,
0.04228835180401802,
-0.011532621458172798,
0.005972391460090876,
-0.1042473092675209,
-0.06330657750368118,
0.03229764103889465,
0.00863698124885559,
-0.011430877260863781,
0.005780539941042662,
-0.024641938507556915,
0.021998099982738495,
0.003939141985028982,
-0.02794645167887211,
-0.03290892019867897,
0.024614326655864716,
-0.04094255343079567,
0.09083370119333267,
-0.04064321145415306,
0.015507427975535393,
-0.01702146977186203,
0.0345248319208622,
0.06277919560670853,
0.004054084420204163,
0.0013819911982864141,
0.07557670027017593,
-0.018939275294542313,
-0.03424064815044403,
-0.043642666190862656,
-0.05804229527711868,
0.03179014101624489,
0.023345142602920532,
0.010169919580221176,
-0.05912374332547188,
0.02596919983625412,
0.09227469563484192,
0.03460113704204559,
0.012573838233947754,
0.003066372824832797,
-0.07134033739566803,
0.025226667523384094,
0.01238445844501257,
-0.00374561152420938,
-0.001710290089249611,
0.038292478770017624,
0.013012146577239037,
-0.03535899147391319,
-0.03076275624334812,
-0.09264036267995834,
0.04998147860169411,
0.0022160543594509363,
-0.0565267913043499,
0.04438824579119682,
-0.022341622039675713,
-0.027549663558602333,
0.030185872688889503,
0.023550216108560562,
-0.0410207062959671,
0.0344209261238575,
-0.045365799218416214,
-0.024349408224225044,
-0.0187977384775877,
-0.04117542505264282,
0.05378490313887596,
0.05507701635360718,
-0.01633783057332039,
0.0668422132730484,
-0.002666984684765339,
0.045885149389505386,
0.00882712472230196,
-0.05192824825644493,
0.013336427509784698,
0.02481425553560257,
0.04691345617175102,
-0.031205955892801285,
0.008856928907334805,
0.0014087181771174073,
-0.03000921942293644,
-0.025887515395879745,
-0.021305501461029053,
-0.051132529973983765,
0.02143283374607563,
0.008655338548123837,
-0.029179735109210014,
-0.006421783939003944,
-0.009892327710986137,
-0.0009213539306074381,
-0.03448725491762161,
-0.03997416794300079,
0.05389060825109482,
0.0591864176094532,
-0.007050185929983854,
0.0008307402022182941,
0.024591388180851936,
0.056002359837293625,
0.01687658205628395,
-0.012089226394891739,
-0.01480552926659584,
0.02632567472755909,
0.03042592667043209,
-0.038306012749671936,
-0.002912352792918682,
-0.0812668576836586,
0.026054266840219498,
0.010988503694534302,
-0.011806915514171124,
0.009436177089810371,
0.012897669337689877,
0.01110449992120266,
-0.03652527183294296,
-0.04208112880587578,
0.032799676060676575,
0.06638471782207489,
-0.04939252510666847,
0.004610944073647261,
0.001125156763009727,
-0.02320975996553898,
-0.03315853700041771,
0.015166262164711952,
0.0352017842233181,
-0.013108288869261742,
-0.03656017780303955,
0.034665483981370926,
0.020309889689087868,
-0.019909225404262543,
-0.04307076707482338,
0.08464096486568451,
-0.008610603399574757,
-0.03452422842383385,
0.0028826030902564526,
0.07226280122995377,
-0.01045258529484272,
0.03581935539841652,
0.0259048193693161,
0.0008218337898142636,
0.01961003616452217,
-0.0011163046583533287,
0.007848403416574001,
0.02631296217441559,
0.015281770378351212,
-0.08647091686725616,
0.03612266108393669,
-0.031150462105870247,
0.036658935248851776,
-0.024980628862977028,
-0.05685897171497345,
0.04228108376264572,
-0.00676565058529377,
-0.062191441655159,
-0.023637430742383003,
-0.0440576933324337,
0.004157145973294973,
0.005513633135706186,
-0.03296961635351181,
-0.01943174935877323,
0.018485376611351967,
0.008215761743485928,
0.034913044422864914,
0.0667794793844223,
-0.022521570324897766,
-0.04113677889108658,
-0.0335218720138073,
0.02384914644062519,
-0.035812389105558395,
-0.013133966363966465,
-0.02430214360356331,
0.06477665901184082,
0.019321991130709648,
0.0761706754565239,
-0.039520349353551865,
-0.0004669735499192029,
0.10221558809280396,
-0.05203748866915703,
-0.006186032667756081,
-0.01015712134540081,
0.011326269246637821,
0.010959528386592865,
-0.0066180964931845665,
-0.00033418831299059093,
-0.047625429928302765,
-0.04453844577074051,
-0.013240639120340347,
-0.030439553782343864,
0.016067542135715485,
-0.018501345068216324,
-0.022851072251796722,
0.019900444895029068,
-0.013473681174218655,
-0.028952782973647118,
-0.014151987619698048,
-0.0005028326995670795,
-0.026861010119318962,
-0.04226486384868622,
-0.038487717509269714,
0.004649273119866848,
0.03354767709970474,
-0.005459154956042767,
-0.004803227260708809,
-0.03143274039030075,
-0.012251543812453747,
0.04395631328225136,
-0.006008616182953119,
-0.08214122802019119,
0.04588408023118973,
0.07905258238315582,
-0.03443935513496399,
0.014438971877098083,
0.008386033587157726,
-0.04134600982069969,
-0.01347314938902855,
0.009000551886856556,
0.05107417330145836,
-0.04904738441109657,
-0.018505003303289413,
0.005121976602822542,
-0.010046403855085373,
0.059773385524749756,
0.04226110503077507,
-0.07016580551862717,
0.037668872624635696,
0.003494977718219161,
0.004081628751009703,
-0.00844341330230236,
0.03914712369441986,
0.016946306452155113,
-0.04239813610911369,
0.000850629061460495,
-0.056947361677885056,
0.047668348997831345,
-0.02039037086069584,
-0.021447421982884407,
-0.035112980753183365,
0.051450215280056,
0.0073725637048482895,
0.040087249130010605,
-0.00865602120757103,
0.01282546017318964,
0.049842365086078644,
-0.02838858962059021,
-0.059259697794914246,
0.048622481524944305,
-0.013595648109912872,
-0.0003197992919012904,
-0.024419596418738365,
0.03310224041342735,
-0.00012612229329533875,
-0.007269797846674919,
-0.10058574378490448,
0.0410829596221447,
0.0178648941218853,
0.036095112562179565,
0.03459487855434418,
0.015953997150063515,
-0.03833966702222824,
0.007937290705740452,
-0.011612864211201668,
-0.04046604409813881,
0.06075520068407059,
0.003472977550700307,
-0.09782619774341583,
0.021084368228912354,
0.06919332593679428,
-0.050066471099853516,
-0.025226298719644547,
-0.011222729459404945,
-0.0017284025670960546,
0.014709008857607841,
-0.052766986191272736,
-0.02054782584309578,
-0.02504860609769821,
0.048476558178663254,
-0.05235939845442772,
0.031084848567843437,
0.03717590495944023,
-0.042216505855321884,
-0.013985522091388702,
-0.0025530538987368345,
-0.030164703726768494,
-0.0011693056439980865,
-0.04558078944683075,
0.007960347458720207,
0.0033452571369707584,
0.0036145905032753944,
-0.00537101412191987,
0.0015062956372275949,
0.016220102086663246,
0.06423509865999222,
0.008673605509102345,
0.00535817863419652,
0.017234500497579575,
-0.020625635981559753,
-0.004285417031496763,
-0.00514413695782423,
0.024106774479150772,
-0.029273290187120438,
-0.005287947133183479,
-0.04501752182841301,
-0.003122846595942974,
-0.0162850022315979,
-0.01912720501422882,
0.040349844843149185,
0.02196623757481575,
-0.029201600700616837,
-0.0032678768038749695,
-0.015347860753536224,
0.015112083405256271,
0.08806531131267548,
0.05091900750994682,
-0.051405169069767,
0.002795788925141096,
0.0008398170466534793,
-0.0018964310875162482,
0.03627115488052368,
-0.004300557542592287,
0.019197523593902588,
0.004346474073827267,
-0.017594294622540474,
0.03538919612765312,
-0.03593996912240982,
-0.011775282211601734,
0.03269820660352707,
-0.004981205333024263,
-0.000774528831243515,
0.02198183722794056,
0.00009549570677336305,
-0.060387831181287766,
0.031492091715335846,
-0.02163836732506752,
-0.030677255243062973,
0.03915094584226608,
-0.02225387655198574,
-0.002841036068275571,
0.053154464811086655,
0.009218130260705948,
-0.010990801267325878,
0.005958502646535635,
-0.0352657213807106,
0.009518454782664776,
0.035614367574453354,
0.08518262952566147,
-0.0787481740117073,
0.025405025109648705,
-0.07243962585926056,
-0.015888463705778122,
-0.023324016481637955,
0.03913480043411255,
-0.04199647903442383,
-0.057402096688747406,
0.03777168318629265,
0.014375722035765648,
-0.028684258460998535,
0.043743617832660675,
0.04650800675153732,
0.050074923783540726,
0.04328172281384468,
0.017596354708075523,
-0.005662145558744669,
0.03799057751893997,
-0.023100588470697403,
0.037188075482845306,
0.004611094482243061,
-0.05206455662846565,
-0.0469028539955616,
0.026724491268396378,
-0.008919427171349525,
-0.004387274384498596,
-0.017467765137553215,
-0.02147085592150688,
-0.012324962764978409,
0.005641523282974958,
0.009393834508955479,
-0.04806997627019882,
0.04236780107021332,
0.08297386765480042,
-0.02658376656472683,
-0.03741203993558884,
0.016173958778381348,
0.03634508326649666,
-0.04326664283871651,
-0.019962063059210777,
-0.006575106177479029,
0.005210233852267265,
0.03798483684659004,
-0.01629384234547615,
-0.006810028571635485,
0.00631798105314374,
0.0012132897973060608,
0.045304179191589355,
-0.00846724770963192,
-0.04597717523574829,
0.020600680261850357,
-0.0015320245875045657,
0.040180593729019165,
-0.046603716909885406,
-0.010105551220476627,
-0.022953489795327187,
0.009213053621351719,
0.03823278844356537,
0.01679377816617489,
-0.05275937542319298,
0.004639100283384323,
-0.0447993166744709,
-0.03227434679865837,
-0.018754979595541954,
0.004784001968801022,
0.048505768179893494,
-0.052231717854738235,
0.046998653560876846,
0.03594428673386574,
0.0029036779887974262,
-0.024057092145085335,
-0.03281591087579727,
-0.0342884324491024,
0.015288238413631916,
0.006966566201299429,
0.06595086306333542,
0.012268383987247944,
-0.030178118497133255,
-0.016355343163013458,
-0.014024537056684494,
0.00912231020629406,
-0.03407837450504303,
-0.054132215678691864,
0.06534398347139359,
0.05089638754725456,
0.02079767920076847,
0.017722466960549355,
0.01571962982416153,
-0.017578499391674995,
-0.004928633105009794,
-0.05734146758913994,
0.005542806815356016,
0.01716551184654236,
-0.07043076306581497,
0.047977566719055176,
0.0037060168106108904,
0.01008099690079689,
-0.052654899656772614,
-0.011011130176484585,
0.020925048738718033,
-0.006904844660311937,
-0.031149327754974365,
0.04128134250640869,
-0.0027213208377361298,
0.023099346086382866,
0.06521743535995483,
0.047677043825387955,
0.0966157466173172,
0.012072334997355938,
-0.04862212762236595,
0.0446370430290699,
-0.007377247326076031,
-0.00482117710635066,
0.06458664685487747,
0.03929687291383743,
0.059081897139549255,
-0.042401887476444244,
-0.0014571825740858912,
0.012703443877398968,
0.006882406305521727,
-0.08226972818374634,
0.03137172758579254,
0.03706592321395874,
0.003678899724036455,
-0.010852242819964886,
0.05583743751049042,
-0.031048646196722984,
0.006492864806205034,
0.017200972884893417,
0.006815312430262566,
0.014989783056080341,
-0.017603835090994835,
-0.001913389889523387,
0.0006618834449909627,
0.014673097059130669,
0.008305621333420277,
0.028604654595255852,
-0.0010067294351756573,
0.03946323320269585,
-0.02540023997426033,
0.03457237780094147,
0.016967369243502617,
-0.008525202982127666,
-0.013205479830503464,
0.03314099833369255,
-0.08220647275447845,
-0.035884689539670944,
0.034751761704683304,
0.04636237025260925,
-0.0307755209505558,
-0.00586790731176734,
-0.02578084170818329,
0.022747989743947983,
0.010626927018165588,
-0.01384719554334879,
0.0016577019123360515,
0.03196275606751442,
0.03138425573706627,
-0.012632043100893497,
-0.012536044232547283,
0.05101962760090828,
-0.0347994863986969,
0.03961652144789696,
-0.06491336971521378,
0.035245321691036224,
0.0022554746828973293,
0.030038783326745033,
0.03626611828804016,
-0.011488115414977074,
-0.026810502633452415,
-0.06759633868932724,
0.03671073168516159,
-0.07076875120401382,
0.020511368289589882,
-0.04912032186985016,
-0.000011905981409654487,
-0.025721922516822815,
-0.0321400947868824,
0.028682203963398933,
0.024110760539770126,
-0.03812840208411217,
0.04586934670805931,
-0.006552095524966717,
-0.003835582174360752,
0.01353105716407299,
-0.03743333742022514,
-0.02653154358267784,
-0.01346653327345848,
-0.07151344418525696,
0.03059627301990986,
-0.051795341074466705,
-0.000014855384506518021,
0.0098640788346529,
0.05453206226229668,
-0.029145192354917526,
0.010630297474563122,
0.019651520997285843,
0.005841094069182873,
-0.016408687457442284,
0.003921777941286564,
0.010991617105901241,
-0.048294566571712494,
0.05413766950368881,
-0.05731319636106491,
0.013502090238034725,
-0.07115309685468674,
-0.044672079384326935,
0.03506719321012497,
-0.01947503164410591,
0.0331876166164875,
0.06849653273820877,
-0.036355748772621155,
-0.01204244140535593,
0.0643041804432869,
0.05669306963682175,
0.030845480039715767,
0.01335152331739664,
0.03806503862142563,
-0.025871027261018753,
0.04978903755545616,
0.0009100626339204609,
0.09085401892662048,
-0.020107053220272064,
-0.009400198236107826,
0.027247807011008263,
0.04333095625042915,
0.05317337065935135,
-0.05694833770394325,
0.016266288235783577,
-0.022687867283821106,
-0.01108680572360754,
0.032544974237680435,
-0.0393565408885479,
0.012373605743050575,
-0.019989296793937683,
0.06952197849750519,
-0.04551112279295921,
-0.056944217532873154,
-0.0029106803704053164,
-0.013124971650540829,
-0.009625154547393322,
-0.07260747253894806,
0.03191381320357323,
0.0043634376488626,
-0.03076961450278759,
0.03292323648929596,
-0.0015085218474268913,
-0.02165677584707737,
0.03664357587695122,
0.0017699534073472023,
0.023265305906534195,
0.05375174805521965,
-0.1113937571644783,
-0.00020329894323367625,
-0.006969444919377565,
0.022896867245435715,
-0.01852664351463318,
-0.0323854498565197,
0.010516046546399593,
0.01933096908032894,
-0.09901861101388931,
-0.03071741573512554,
-0.04419606551527977,
0.05663308501243591,
0.053705524653196335,
-0.04616021364927292,
-0.026636840775609016,
-0.032828062772750854,
-0.05841383337974548,
0.012223733589053154,
-0.0016608149744570255,
0.011313908733427525,
0.027992086485028267,
-0.04376022517681122,
0.0035907814744859934,
0.02735099010169506,
0.02816830761730671,
-0.026644038036465645,
0.02661146968603134,
-0.03321569412946701,
-0.01168915256857872,
-0.0445823073387146,
0.07033564150333405,
-0.035240538418293,
-0.05093122646212578,
-0.03898921236395836,
-0.027239928022027016,
-0.018327420577406883,
0.0047736517153680325,
0.057613618671894073,
0.041052982211112976,
0.08469673991203308,
0.022947754710912704,
-0.005228456109762192,
-0.07803402096033096,
-0.018688775599002838,
0.04140445962548256,
-0.01963045820593834,
0.020048042759299278,
0.027535952627658844,
-0.027113009244203568,
-0.0039536310359835625,
0.012107796035706997,
0.032901301980018616,
-0.04875152185559273,
0.031074335798621178,
0.04911090433597565,
0.05385436490178108,
0.011401602067053318,
-0.03697188198566437,
0.05416741222143173,
0.0023268258664757013,
-0.042701561003923416,
0.023760376498103142,
-0.004405261483043432,
-0.01908688247203827,
-0.013658461160957813,
0.011595149524509907,
0.0021776848006993532,
-0.031118784099817276,
-0.020946811884641647,
-0.01493461336940527,
-0.014173243194818497,
0.008389820344746113,
0.0399574376642704,
-0.0018621047493070364,
0.01811343990266323,
-0.061848849058151245,
0.011961078271269798,
-0.027794647961854935,
0.05766705423593521,
-0.006293464917689562,
-0.019477954134345055,
-0.022632697597146034,
0.00711808679625392,
-0.025478873401880264,
-0.0066268108785152435,
-0.06247656047344208,
-0.010015809908509254,
-0.04080779850482941,
0.007858753204345703,
0.048080794513225555,
-0.001355805085040629,
-0.014417207799851894,
0.009210714139044285,
-0.037465497851371765,
0.05967530980706215,
0.016504228115081787,
-0.06284146010875702,
0.08061562478542328,
0.009253611788153648,
-0.005475539248436689,
-0.025837833061814308,
0.007921750657260418,
-0.0646318644285202,
0.027570992708206177,
-0.03931394964456558,
-0.03091748058795929,
-0.09450599551200867,
0.02794254943728447,
0.003889727871865034
] |
<p>I have tough problem I am not sure how to solve:</p>
<p>For this question, we are confined to a plane. Consider a gravitational field that is proportional to $\frac{1}{r^3}$ instead of $\frac{1}{r^2}$, and consider its potential which is then proportional to $\frac{1}{r^2}$. Suppose that I put $n$ identical point masses in this plane, all at different locations and let $U(x,y)$ be the potential function. </p>
<blockquote>
<p>What can we say about the critical points of $U(x,y)$? Specifically, can we show that the number of critical points is always $\leq n$?</p>
</blockquote>
<p>Thank you for your help!</p>
<p><strong>Remark:</strong> By critical point, I mean the usual definition in vector calculus, that is a place where both partial derivatives are zero.</p> | g5547 | [
0.05626154690980911,
0.041870687156915665,
0.012249285355210304,
0.010938957333564758,
0.05822746455669403,
0.06187744066119194,
0.008334260433912277,
-0.03723858669400215,
-0.10339862108230591,
0.026771180331707,
-0.0015652832807973027,
0.01035352237522602,
0.028011344373226166,
0.007161809131503105,
0.04406662657856941,
-0.03733124956488609,
0.09956967085599899,
-0.0770624577999115,
0.012213556095957756,
-0.04142104461789131,
-0.01369179505854845,
-0.016419783234596252,
0.0356098897755146,
-0.004282847046852112,
0.025865038856863976,
0.040100909769535065,
0.09094110131263733,
-0.040028203278779984,
-0.095710888504982,
0.035149041563272476,
0.04118059575557709,
-0.01772395521402359,
0.03410758078098297,
-0.03958708047866821,
-0.0039733094163239,
-0.020283900201320648,
0.030955489724874496,
0.061917684972286224,
-0.010424735024571419,
-0.004441452212631702,
0.012101803906261921,
-0.038969386368989944,
0.009835057891905308,
-0.02048969268798828,
-0.004511892795562744,
0.0003064314369112253,
-0.048315148800611496,
-0.01630273088812828,
0.07704739272594452,
-0.0190963763743639,
-0.0187702476978302,
0.06266306340694427,
0.017995566129684448,
-0.09248095750808716,
-0.01868690364062786,
0.08163221925497055,
-0.03272353857755661,
-0.02290233224630356,
-0.015721509233117104,
0.04842473566532135,
0.017507201060652733,
0.005697413347661495,
-0.005072970874607563,
-0.0624072402715683,
0.016684645786881447,
-0.007106497418135405,
-0.06809216737747192,
0.016164807602763176,
-0.028382491320371628,
0.0356033556163311,
-0.0076979221776127815,
-0.02907680720090866,
-0.013689973391592503,
-0.042743489146232605,
-0.053811606019735336,
-0.0031100476626306772,
0.008915962651371956,
0.016582533717155457,
-0.022954467684030533,
-0.024924438446760178,
-0.040933143347501755,
-0.04950379207730293,
0.04533341899514198,
0.06490370631217957,
0.027922889217734337,
-0.03646170720458031,
0.049820709973573685,
-0.026667308062314987,
-0.06451252847909927,
0.023051898926496506,
-0.013942410238087177,
-0.011083264835178852,
0.017536086961627007,
0.005102425813674927,
0.0025080370251089334,
0.027901211753487587,
0.013187790289521217,
0.047268450260162354,
-0.05518254637718201,
-0.04020753502845764,
0.044959574937820435,
0.010808528400957584,
-0.000751238432712853,
-0.02315705269575119,
0.028639325872063637,
-0.03633718565106392,
0.07610590010881424,
0.0383598655462265,
0.04972437769174576,
-0.05279483273625374,
-0.0047217002138495445,
-0.030516795814037323,
-0.06230020895600319,
0.0014140554703772068,
-0.047115523368120193,
0.0173953827470541,
0.044967472553253174,
-0.05562697350978851,
-0.01857065036892891,
0.0672445297241211,
-0.033013321459293365,
0.0174968671053648,
0.00448228744789958,
-0.013490734621882439,
-0.02767174318432808,
-0.008203859440982342,
-0.015471074730157852,
0.03069112077355385,
0.024161892011761665,
0.006735059432685375,
-0.0160988699644804,
-0.0286619383841753,
-0.013680432923138142,
-0.005320379510521889,
-0.03812215477228165,
0.03880294784903526,
0.04476969689130783,
-0.008705437183380127,
0.011379744857549667,
-0.010628912597894669,
-0.05482065677642822,
-0.015514258295297623,
0.0035534955095499754,
0.029266051948070526,
-0.024451300501823425,
-0.027405105531215668,
0.019618066027760506,
-0.015248103067278862,
0.022448087111115456,
0.01247342862188816,
0.026152784004807472,
0.10296939313411713,
-0.0304062832146883,
-0.06255251169204712,
0.016054915264248848,
0.00796501338481903,
0.004422065801918507,
0.005917283706367016,
0.0022842984180897474,
0.007520867045968771,
0.02378162555396557,
0.010869176127016544,
0.021685155108571053,
0.037376195192337036,
-0.03048756718635559,
0.024818219244480133,
-0.027903301641345024,
-0.029017427936196327,
0.0023055528290569782,
-0.037647612392902374,
-0.051000792533159256,
0.027068713679909706,
0.03926467522978783,
0.044628944247961044,
-0.009225322864949703,
0.013559195213019848,
-0.007485357578843832,
-0.010736551135778427,
0.02159305289387703,
0.05398032069206238,
0.008575361222028732,
-0.04620130732655525,
0.03585727512836456,
-0.013273701071739197,
-0.007397018373012543,
-0.019972234964370728,
0.024996448308229446,
0.008238786831498146,
0.009209268726408482,
-0.047263067215681076,
-0.05752814933657646,
0.04163902625441551,
-0.025364909321069717,
0.03399757668375969,
0.01954829692840576,
0.04977027699351311,
0.04875249043107033,
-0.06518177688121796,
0.004468108993023634,
0.025693483650684357,
-0.018411217257380486,
0.043950557708740234,
0.06792059540748596,
0.03595062345266342,
-0.008684786036610603,
-0.003870568936690688,
0.02259497344493866,
0.023838741704821587,
0.02199188992381096,
0.0412667952477932,
0.006214024964720011,
-0.08048682659864426,
0.06650415062904358,
0.019418440759181976,
-0.04023917391896248,
-0.010512142442166805,
0.009208206087350845,
-0.004056921694427729,
0.014809107407927513,
0.03673044219613075,
-0.0464056059718132,
0.02415495365858078,
0.06409592181444168,
0.024325942620635033,
0.0015286293346434832,
-0.0011465077986940742,
-0.04357552528381348,
0.0050594075582921505,
0.07615678012371063,
-0.018285278230905533,
-0.04334285110235214,
0.0029835470486432314,
0.05074466019868851,
-0.06357534229755402,
0.0013654548674821854,
-0.034218113869428635,
-0.06491048634052277,
-0.00034327825414948165,
-0.015312660485506058,
0.01250133290886879,
0.023927513509988785,
-0.03226860612630844,
0.030321110039949417,
0.042268816381692886,
0.047333117574453354,
-0.04615041986107826,
0.021540192887187004,
-0.011482242494821548,
0.01434245239943266,
0.06490744650363922,
-0.018465913832187653,
-0.02954748645424843,
-0.0399077869951725,
0.07236567884683609,
-0.009983090683817863,
0.06362941861152649,
-0.028678029775619507,
0.06237517669796944,
0.0029562637209892273,
-0.051088593900203705,
-0.03474230691790581,
-0.0474744588136673,
0.022487344220280647,
0.004678514786064625,
-0.048953596502542496,
0.0650925263762474,
-0.0193808451294899,
-0.0413450226187706,
0.04051665961742401,
0.012761423364281654,
0.007502646651118994,
0.044159989804029465,
0.008890589699149132,
0.09792814403772354,
-0.013309606350958347,
-0.0502394363284111,
-0.009157541207969189,
-0.004318310413509607,
-0.0010297553380951285,
0.0006863197195343673,
0.04204767569899559,
0.00828393455594778,
-0.0507703572511673,
0.035399869084358215,
0.04942477121949196,
-0.038244687020778656,
0.010463453829288483,
0.061240315437316895,
-0.08363266289234161,
0.026921922340989113,
0.008581732399761677,
0.03166702017188072,
0.05657338723540306,
-0.0017636148259043694,
-0.012157268822193146,
0.024566322565078735,
-0.04332059994339943,
-0.027056371793150902,
0.011623233556747437,
0.002255516592413187,
0.02202686294913292,
0.03090006299316883,
-0.0022633846383541822,
0.03265063092112541,
0.020411154255270958,
0.010780587792396545,
0.026424823328852654,
-0.046520281583070755,
0.010443169623613358,
-0.025403015315532684,
0.007813922129571438,
0.04577525705099106,
0.039229001849889755,
-0.04043545573949814,
-0.02595648728311062,
0.02678050473332405,
-0.004207009915262461,
0.01532419491559267,
-0.0350169911980629,
-0.044069766998291016,
-0.021134454756975174,
-0.053076814860105515,
0.003256766591221094,
-0.0246368907392025,
0.058868858963251114,
0.05357610061764717,
-0.060322847217321396,
0.04744645580649376,
-0.07909701019525528,
-0.019304363057017326,
-0.056876715272665024,
0.003337562782689929,
0.009382952004671097,
-0.004553407430648804,
-0.04979345202445984,
-0.014143841341137886,
-0.0015350907342508435,
0.008132054470479488,
0.0935075655579567,
0.006641217041760683,
-0.038118887692689896,
0.04400289058685303,
-0.023062098771333694,
-0.028754103928804398,
-0.007415258791297674,
-0.0028040120378136635,
0.020833950489759445,
0.02450644224882126,
0.03586973249912262,
-0.017633188515901566,
-0.006315523758530617,
-0.07280036062002182,
0.01992359571158886,
-0.016820766031742096,
0.02764139138162136,
-0.020700804889202118,
0.00893916841596365,
0.018433332443237305,
-0.041745375841856,
0.015487400814890862,
0.060072269290685654,
-0.022113831713795662,
0.03736042231321335,
0.034983303397893906,
0.04784287512302399,
-0.005249152425676584,
0.021617835387587547,
-0.024144159629940987,
-0.007669269572943449,
-0.025586936622858047,
0.04305439069867134,
-0.06040894240140915,
0.019304266199469566,
0.02633221261203289,
0.019073791801929474,
-0.10706891119480133,
-0.0566888153553009,
-0.05895101651549339,
0.008808192797005177,
0.02078816294670105,
0.01287893671542406,
-0.021263139322400093,
-0.0023155631497502327,
-0.04128053039312363,
0.028533291071653366,
0.012956988997757435,
-0.023442743346095085,
-0.040819473564624786,
0.06641311198472977,
-0.02761872671544552,
-0.005208752583712339,
-0.08812657743692398,
-0.05922635644674301,
0.0021037294063717127,
-0.002988668391481042,
0.009714208543300629,
0.010201439261436462,
0.007405763957649469,
-0.03162461891770363,
0.04696442186832428,
0.030179042369127274,
0.019998824223876,
-0.019176684319972992,
0.002602193970233202,
-0.02099415846168995,
-0.043129391968250275,
0.05551471933722496,
0.009672771207988262,
0.012487241998314857,
0.009939407929778099,
0.022117318585515022,
-0.06314411759376526,
0.0012466439511626959,
-0.047280531376600266,
0.008112943731248379,
-0.0030389379244297743,
-0.004646915942430496,
0.007559994701296091,
0.05352553352713585,
-0.02242736704647541,
0.0005308978143148124,
-0.0007875487790443003,
-0.03649241477251053,
-0.0634872168302536,
-0.003237819764763117,
0.023959264159202576,
0.07483510673046112,
-0.01591026410460472,
0.014370265416800976,
0.03528584912419319,
0.004332707729190588,
0.06269620358943939,
-0.021830743178725243,
0.02935684099793434,
-0.010535282082855701,
-0.006534105632454157,
-0.0453682616353035,
-0.01528399158269167,
-0.022690080106258392,
0.0224743764847517,
0.02164248749613762,
-0.024819275364279747,
0.0009984058560803533,
-0.020646288990974426,
-0.006565842777490616,
0.02265373058617115,
-0.00753135047852993,
-0.045294202864170074,
-0.0007448831456713378,
-0.023390857502818108,
-0.05440785363316536,
-0.042409706860780716,
0.038874659687280655,
-0.023753447458148003,
0.019577214494347572,
-0.0178837850689888,
-0.01895468682050705,
0.025729594752192497,
0.027843086048960686,
0.021043092012405396,
0.06011710315942764,
-0.014672940596938133,
0.0504121370613575,
-0.025482071563601494,
0.057556603103876114,
-0.00480977026745677,
-0.0588744580745697,
-0.031009484082460403,
-0.008998434990644455,
-0.11196839809417725,
0.0016474148724228144,
0.023171573877334595,
0.008464889600872993,
0.014548920094966888,
-0.0596795417368412,
-0.002163694705814123,
0.035193201154470444,
-0.0026373309083282948,
0.03564164787530899,
-0.06640105694532394,
0.019809236750006676,
-0.02467271499335766,
-0.005794347729533911,
-0.004400706384330988,
0.012814040295779705,
-0.008633649908006191,
-0.05248316749930382,
-0.03528252989053726,
0.0015842797001823783,
-0.06057297810912132,
0.02688015252351761,
-0.013646071776747704,
0.006274238228797913,
0.021064812317490578,
-0.020535629242658615,
-0.05006932094693184,
0.004259888548403978,
-0.08554136753082275,
-0.03108423575758934,
-0.0057792034931480885,
-0.027000898495316505,
0.01691756397485733,
0.029339157044887543,
0.04467485100030899,
-0.016909612342715263,
0.0755934938788414,
0.02403639443218708,
-0.022159826010465622,
0.02602762170135975,
0.0584130734205246,
0.005218188744038343,
-0.031539157032966614,
0.005882479250431061,
0.021013621240854263,
-0.004034597892314196,
-0.0036603680346161127,
-0.024701975286006927,
-0.03307955339550972,
-0.04471278563141823,
-0.07762780040502548,
0.08261808007955551,
0.007778684142976999,
0.01113382913172245,
0.012820543721318245,
0.06322992593050003,
-0.0282269474118948,
-0.052910301834344864,
-0.06529577821493149,
0.012320996262133121,
0.005802318453788757,
-0.014743652194738388,
-0.032241739332675934,
-0.05920768529176712,
-0.008133495226502419,
0.003834498580545187,
-0.004571202676743269,
0.0047523644752800465,
-0.014561965130269527,
0.07336175441741943,
-0.019274776801466942,
-0.06259112805128098,
0.008015302009880543,
0.005471615586429834,
-0.012750484980642796,
-0.05074754357337952,
0.07288672775030136,
-0.07418353855609894,
-0.019574018195271492,
0.021493803709745407,
-0.019801167771220207,
-0.014795451425015926,
0.020278040319681168,
0.014374317601323128,
-0.032178543508052826,
-0.02141345664858818,
0.029565483331680298,
0.0006475516129285097,
0.00550740584731102,
-0.027591083198785782,
0.0015659198397770524,
-0.012252160347998142,
0.0027944031171500683,
0.0004358801816124469,
-0.040430087596178055,
0.00014543691941071302,
-0.05954744666814804,
-0.02106550708413124,
-0.050907548516988754,
0.025912916287779808,
-0.03188024461269379,
-0.014166505075991154,
0.057144708931446075,
0.014777759090065956,
-0.02245386131107807,
0.07672411948442459,
0.04468713700771332,
-0.02180716022849083,
0.046085722744464874,
0.025201797485351562,
-0.013911597430706024,
-0.04690268635749817,
0.03659840673208237,
0.035789988934993744,
-0.11226958781480789,
-0.038296520709991455,
0.03745284304022789,
-0.00495246984064579,
-0.0418868288397789,
0.019202623516321182,
-0.002675224095582962,
-0.011911332607269287,
-0.05182167515158653,
-0.02217569388449192,
0.03860682249069214,
0.011118495836853981,
-0.06021193414926529,
0.021566661074757576,
0.02847844362258911,
-0.033236369490623474,
0.02065734565258026,
0.059311918914318085,
0.04037967324256897,
0.05543994903564453,
0.018958276137709618,
-0.038455478847026825,
0.0004096939810551703,
-0.015063836239278316,
-0.0728292316198349,
-0.007382484618574381,
-0.004241319838911295,
0.03522711247205734,
0.02824040874838829,
0.014103500172495842,
-0.004031026735901833,
-0.009412284009158611,
0.014774130657315254,
0.052795153111219406,
0.025230877101421356,
-0.053675565868616104,
-0.028527365997433662,
0.04512300714850426,
0.02287515625357628,
-0.010427936911582947,
-0.061460718512535095,
0.020021313801407814,
-0.03013925999403,
-0.021953783929347992,
-0.05214766785502434,
0.0395449697971344,
-0.010413922369480133,
0.03750359266996384,
-0.003988582640886307,
-0.02415851131081581,
0.053700968623161316,
-0.024711163714528084,
0.011928590014576912,
-0.051501765847206116,
-0.006952131167054176,
-0.010951465927064419,
-0.04128832742571831,
-0.010587266646325588,
0.06485141813755035,
0.03654557466506958,
0.03133057430386543,
0.006756804883480072,
-0.022182440385222435,
0.012483865022659302,
-0.011700612492859364,
-0.03275487199425697,
0.009605957195162773,
0.005237811245024204,
0.018869495019316673,
-0.02559211105108261,
-0.024353787302970886,
-0.0450948104262352,
0.009641066193580627,
0.03782620280981064,
0.010483021847903728,
-0.042511940002441406,
-0.0034926922526210546,
-0.03969693183898926,
0.04871581867337227,
0.012453255243599415,
0.048479266464710236,
-0.04885561019182205,
0.03338966146111488,
0.028241442516446114,
-0.015510364435613155,
-0.022656317800283432,
-0.028350019827485085,
0.03222174569964409,
-0.018759606406092644,
-0.04653393477201462,
0.06212437152862549,
0.0033838150557130575,
0.019456831738352776,
0.06350140273571014,
-0.0035804868675768375,
0.09143979102373123,
0.015415380708873272,
0.007510263007134199,
0.020499106496572495,
-0.060483891516923904,
-0.026136284694075584,
-0.009941413067281246,
0.010026746429502964,
0.003659095847979188,
-0.055482812225818634,
0.022496215999126434,
-0.02746042236685753,
0.016396019607782364,
0.0017007668502628803,
0.04450177028775215,
0.002116626361384988,
0.044713664799928665,
-0.06187716871500015,
-0.00781589187681675,
0.03917080909013748,
0.026903869584202766,
-0.004065739922225475,
-0.001277992851100862,
0.006880023516714573,
-0.023264212533831596,
0.018318036571145058,
-0.03685649111866951,
0.004117629490792751,
0.0006948555819690228,
0.03346972167491913,
-0.0405789352953434,
0.003030597697943449,
0.06470844894647598,
0.04344145953655243,
-0.008505363017320633,
-0.038583096116781235,
0.0040953210555016994,
-0.0012029297649860382,
-0.022332657128572464,
0.024641143158078194,
0.02808493748307228,
-0.07193578034639359,
-0.02009771205484867,
-0.007633612025529146,
0.003881034441292286,
-0.07680746912956238,
-0.010268502868711948,
0.005064476281404495,
-0.010308383032679558,
-0.03861572593450546,
0.05276314541697502,
0.007090381346642971,
-0.015224660746753216,
-0.016330864280462265,
-0.03608321771025658,
0.0648217499256134,
0.015857664868235588,
0.016074873507022858,
-0.03629360347986221,
-0.01827426627278328,
0.019476473331451416,
-0.021162593737244606,
-0.035271670669317245,
-0.045714445412158966,
0.0063726832158863544,
0.018552834168076515,
0.013994444161653519,
0.006474021356552839,
-0.05648050084710121,
0.07887387275695801,
0.04348873347043991,
0.062258146703243256,
-0.03977065533399582,
-0.01648346520960331,
0.017170600593090057,
0.0686533972620964,
0.0039390153251588345,
-0.04093727841973305,
0.029950059950351715,
-0.02955722063779831,
0.005095504689961672,
-0.030014822259545326,
0.015096058137714863,
0.003008718602359295,
-0.0001593568013049662,
0.024638159200549126,
0.009685159660875797,
-0.005568735767155886,
0.05350220203399658,
0.01970394141972065
] |
<p>I was wondering, why in Newtonian physics <a href="http://en.wikipedia.org/wiki/Torque" rel="nofollow">torque</a> is called "torque" while in static mechanics they call it "moment"? </p>
<p>I prefer by far the term "torque", for not only it sounds strong, but also instead of moment, the correct synonym of torque is moment of force.</p> | g5548 | [
0.06795775890350342,
-0.0018150797113776207,
0.0021204736549407244,
-0.035282108932733536,
0.05359197407960892,
-0.0429450087249279,
0.03726016357541084,
-0.022815195843577385,
-0.05083229020237923,
0.03727942332625389,
0.05115756765007973,
-0.06538493186235428,
0.031229542568325996,
-0.00675206258893013,
0.0047035906463861465,
0.0055625117383897305,
0.045130372047424316,
-0.0009211290744133294,
0.09026128053665161,
0.029431739822030067,
0.028819892555475235,
-0.045086607336997986,
-0.0312979631125927,
-0.014580730348825455,
-0.010386068373918533,
-0.004711553454399109,
-0.032352201640605927,
-0.009167113341391087,
0.005566688254475594,
-0.03433570638298988,
0.02738240733742714,
0.03385542333126068,
0.07308907061815262,
-0.0011757926549762487,
0.001393381622619927,
-0.006767324637621641,
0.016194840893149376,
0.03307776153087616,
0.05177969112992287,
-0.0068678283132612705,
0.030385702848434448,
-0.02939080260694027,
-0.022455336526036263,
-0.031099915504455566,
0.00980124156922102,
-0.06849107891321182,
-0.045632120221853256,
-0.019947068765759468,
-0.0009601482306607068,
-0.004550987854599953,
0.028050342574715614,
-0.0015918327262625098,
-0.0018885720055550337,
-0.03739773854613304,
0.0707603171467781,
-0.02146853879094124,
0.016296053305268288,
0.05690421536564827,
-0.02895328402519226,
0.013119269162416458,
-0.030592944473028183,
0.00205498980358243,
0.015226990915834904,
0.007763361092656851,
0.017862660810351372,
-0.011593900620937347,
-0.007844111882150173,
-0.0027855122461915016,
-0.0056195431388914585,
0.008160129189491272,
-0.023669438436627388,
-0.03168293461203575,
-0.02455955371260643,
-0.0021313969045877457,
-0.017458412796258926,
-0.04258451983332634,
-0.04518475383520126,
-0.0005343251395970583,
0.012678208760917187,
-0.043650753796100616,
-0.008290383033454418,
0.050337329506874084,
0.06479014456272125,
0.048414453864097595,
0.07893390953540802,
0.029328787699341774,
-0.03494301438331604,
0.049851417541503906,
0.06715966761112213,
0.019371401518583298,
0.014807447791099548,
-0.013586018234491348,
0.07482335716485977,
0.031101686879992485,
-0.05457191914319992,
-0.03419218212366104,
-0.0502462312579155,
0.05615125596523285,
0.04883979633450508,
0.036552611738443375,
0.0049060615710914135,
-0.05840916186571121,
0.023472653701901436,
-0.03056454472243786,
0.078275665640831,
-0.011857617646455765,
-0.030610116198658943,
0.0036511195357888937,
-0.046125881373882294,
-0.029597371816635132,
0.006467617116868496,
0.058293938636779785,
0.015979835763573647,
-0.035341955721378326,
-0.04265546426177025,
-0.014643166214227676,
0.0401860736310482,
-0.04489566385746002,
-0.009936168789863586,
0.02387549914419651,
-0.0312938392162323,
0.01982060819864273,
0.024635059759020805,
0.06397311389446259,
-0.029434625059366226,
0.0010235040681436658,
-0.0037488839589059353,
0.009595973417162895,
0.008407060988247395,
-0.08278804272413254,
-0.046959664672613144,
0.006294720806181431,
-0.005196106154471636,
-0.0026145947631448507,
-0.030312027782201767,
0.0338311642408371,
-0.01857214793562889,
-0.01455016527324915,
0.03178800642490387,
0.013522573746740818,
0.024374311789870262,
-0.05249563977122307,
0.038389381021261215,
0.004822333808988333,
-0.02302681840956211,
-0.0036027811001986265,
-0.05418342724442482,
0.010711935348808765,
0.08835544437170029,
0.008215481415390968,
0.052704695612192154,
-0.005202171392738819,
0.010764171369373798,
-0.06474985927343369,
-0.015050522051751614,
-0.0014527380699291825,
0.047870103269815445,
-0.004347069188952446,
-0.03814242035150528,
0.06689833849668503,
0.053256191313266754,
-0.011982779949903488,
0.008274980820715427,
-0.055518221110105515,
-0.05794024467468262,
0.014400476589798927,
-0.049796946346759796,
-0.049960993230342865,
0.03668750077486038,
-0.10628092288970947,
-0.0471712090075016,
-0.0012526490027084947,
0.004201705567538738,
0.005226081237196922,
0.02015971578657627,
-0.00750115979462862,
0.020735684782266617,
0.015427767299115658,
0.000013673048670170829,
0.03729777783155441,
-0.025316573679447174,
0.0025571214500814676,
0.009064216166734695,
-0.007190740201622248,
-0.012036065571010113,
0.02612495981156826,
0.031032823026180267,
-0.04449707269668579,
-0.012348965741693974,
0.03683994710445404,
-0.06035033240914345,
-0.09363637119531631,
-0.027553360909223557,
0.10396164655685425,
-0.07371500879526138,
0.006241599563509226,
-0.030018452554941177,
-0.01342689711600542,
-0.08061996847391129,
0.02762693725526333,
-0.00856486614793539,
-0.01294737495481968,
-0.019576089456677437,
0.027508694678544998,
-0.012691418640315533,
-0.019198572263121605,
0.029495637863874435,
0.008617241866886616,
0.05820535123348236,
0.02507888153195381,
0.05615613982081413,
0.005000756122171879,
-0.00928069930523634,
-0.0006670326110906899,
-0.011738184839487076,
-0.04959902912378311,
0.024560965597629547,
0.0029069394804537296,
-0.05913805216550827,
-0.006821819115430117,
0.01565324328839779,
-0.004260247573256493,
0.02028341218829155,
-0.03179845213890076,
-0.02545168250799179,
-0.01657911017537117,
0.03618314489722252,
-0.01343301497399807,
-0.013134353794157505,
0.0009472459787502885,
-0.005758645478636026,
-0.04542028158903122,
-0.005874530412256718,
0.043897468596696854,
0.05817784368991852,
0.08623068034648895,
0.01477167196571827,
0.00274019711650908,
-0.0371517613530159,
0.0037904384080320597,
0.018599990755319595,
-0.02565326727926731,
0.00271300645545125,
-0.022118423134088516,
-0.032297417521476746,
-0.02253430150449276,
0.007503969129174948,
-0.042432140558958054,
0.05152325704693794,
-0.01904248632490635,
0.0026939595118165016,
-0.09332555532455444,
-0.026793556287884712,
-0.0582316629588604,
0.030127370730042458,
0.04301518201828003,
0.04357490688562393,
0.00341748702339828,
-0.05126975104212761,
-0.02315058372914791,
-0.022107167169451714,
0.0321265384554863,
0.013213461264967918,
-0.01860174350440502,
-0.035606302320957184,
-0.000058428024203749374,
-0.03635353967547417,
0.04135257750749588,
-0.024530544877052307,
0.03562191501259804,
-0.0025456147268414497,
0.05657072737812996,
-0.04164763540029526,
-0.04608411341905594,
-0.026826387271285057,
-0.03567265719175339,
-0.0038287718780338764,
0.001665704883635044,
-0.012126651592552662,
-0.04005253314971924,
-0.014897182583808899,
0.03843068331480026,
0.03140481561422348,
0.06758669018745422,
0.015460662543773651,
-0.049687933176755905,
-0.06936150789260864,
-0.0407341867685318,
-0.056424785405397415,
-0.0484246090054512,
0.022495152428746223,
0.06870339065790176,
0.03207680955529213,
-0.029375774785876274,
0.009902886115014553,
0.042303673923015594,
0.02109830267727375,
-0.026281215250492096,
-0.034654829651117325,
0.03831996023654938,
-0.008643192239105701,
0.047129981219768524,
-0.029479844495654106,
0.030376672744750977,
0.05622167885303497,
0.03975990414619446,
-0.002920089988037944,
-0.04048340767621994,
-0.01683911867439747,
-0.006430996581912041,
-0.021411551162600517,
0.04147807136178017,
0.007286480627954006,
0.02589704841375351,
-0.08968215435743332,
-0.018007932230830193,
-0.009157850407063961,
0.015489333309233189,
0.000029682232707273215,
-0.018337609246373177,
-0.02170759066939354,
-0.01971639133989811,
-0.0032162771094590425,
0.014689349569380283,
0.007236827164888382,
0.08647501468658447,
-0.06374499946832657,
0.07205799221992493,
-0.03492157906293869,
-0.05064725875854492,
0.005246079061180353,
0.015534612350165844,
0.009478075429797173,
-0.02703900635242462,
-0.03953298181295395,
-0.010450044646859169,
-0.024658745154738426,
0.00642438093200326,
0.05639699473977089,
-0.014594228006899357,
0.06035168096423149,
0.050733909010887146,
-0.07357117533683777,
0.011721706949174404,
-0.020139077678322792,
0.06442706286907196,
-0.02417806163430214,
-0.02106095850467682,
0.00428625475615263,
0.015617947094142437,
0.003947230987250805,
-0.05161617323756218,
0.03575288504362106,
-0.0441136509180069,
0.018969539552927017,
-0.008306370116770267,
-0.007835320197045803,
0.0071806274354457855,
-0.03941486030817032,
0.008640173822641373,
0.0656011626124382,
-0.008217895403504372,
-0.02304324321448803,
0.022374523803591728,
-0.011737692169845104,
-0.027141880244016647,
0.03688613325357437,
0.03401092812418938,
0.008664244785904884,
-0.026430251076817513,
-0.028089212253689766,
-0.013724127784371376,
-0.007465403992682695,
0.033685557544231415,
0.05514373630285263,
-0.05610043928027153,
0.01416196208447218,
-0.011378484778106213,
0.004005437716841698,
-0.051418278366327286,
0.016329675912857056,
0.018246619030833244,
-0.06643428653478622,
0.0458996556699276,
-0.0027488393243402243,
-0.007575610186904669,
-0.009806361980736256,
-0.0027157296426594257,
0.04007896035909653,
-0.03968822583556175,
0.005025879479944706,
0.01565718464553356,
0.007781304884701967,
-0.005302175413817167,
0.03451908007264137,
0.022284548729658127,
0.022154146805405617,
-0.022941654548048973,
-0.017949655652046204,
0.04861859232187271,
-0.02746499702334404,
0.0017478119116276503,
0.0023377188481390476,
0.06896933913230896,
0.03325919806957245,
0.00598231190815568,
0.05340324714779854,
-0.011191624216735363,
-0.011489063501358032,
0.009506331756711006,
0.011259145103394985,
-0.0005899575189687312,
-0.011876887641847134,
-0.016661088913679123,
0.025641940534114838,
0.0013940109638497233,
0.018281420692801476,
-0.018144158646464348,
0.006846257951110601,
0.019122907891869545,
0.005495095159858465,
0.03671512007713318,
0.04546113312244415,
-0.006551681086421013,
-0.02893097698688507,
-0.0069260066375136375,
0.022457962855696678,
0.02243591472506523,
0.03791290521621704,
-0.026822496205568314,
-0.026981821283698082,
-0.021718082949519157,
0.02917734533548355,
0.002327055437490344,
-0.011470635421574116,
-0.007919460535049438,
-0.02267308346927166,
0.016610195860266685,
0.0655069425702095,
-0.01059711817651987,
0.03724962845444679,
0.03888476639986038,
0.0007383990450762212,
-0.015193695202469826,
-0.038162246346473694,
0.04229789972305298,
0.0440688356757164,
-0.013454698026180267,
-0.0648777186870575,
-0.01746189035475254,
-0.0566110722720623,
0.044997263699769974,
-0.00040829487261362374,
0.002246128162369132,
0.047113146632909775,
0.020516613498330116,
-0.03904689475893974,
-0.02793029509484768,
-0.014958645217120647,
-0.008875761181116104,
-0.08116509020328522,
0.0035702516324818134,
-0.00871816836297512,
0.029476569965481758,
0.07243393361568451,
0.047481782734394073,
-0.05054457485675812,
-0.0030026736203581095,
-0.04824209213256836,
-0.06936163455247879,
0.02614501677453518,
-0.054145634174346924,
-0.009628179483115673,
0.05838878080248833,
0.0513906329870224,
0.022646604105830193,
0.05712413787841797,
-0.02028776705265045,
-0.037343814969062805,
-0.05164285749197006,
-0.01456602942198515,
-0.02536669373512268,
0.055083710700273514,
-0.034757085144519806,
0.02493954263627529,
-0.01462192740291357,
0.011634644120931625,
-0.033077653497457504,
0.0015515430131927133,
0.0032183050643652678,
0.0648685097694397,
0.022460469976067543,
-0.039660170674324036,
-0.00547018414363265,
-0.07011924684047699,
0.08391201496124268,
0.019796812906861305,
-0.043942421674728394,
-0.021120021119713783,
-0.032342493534088135,
-0.09341796487569809,
0.041964054107666016,
-0.053153544664382935,
0.011687328107655048,
-0.0032729078084230423,
0.03812022879719734,
0.08544135838747025,
0.003391093108803034,
-0.002393377711996436,
0.011221409775316715,
0.04091818258166313,
0.007897607050836086,
-0.013852539472281933,
0.04023327678442001,
0.04399619624018669,
0.026350414380431175,
0.0635404884815216,
-0.009084856137633324,
-0.03844238817691803,
-0.01493991818279028,
0.04659442976117134,
0.019623974338173866,
0.03683941066265106,
0.004405971150845289,
0.005427890457212925,
-0.0034890847746282816,
0.0071487585082650185,
-0.015500192530453205,
-0.0633116140961647,
0.05278509482741356,
0.000757952278945595,
0.0241197869181633,
0.12489204853773117,
-0.016272705048322678,
-0.014029266312718391,
0.0037406610790640116,
-0.029613150283694267,
-0.008024062030017376,
-0.028906352818012238,
-0.03429902717471123,
-0.05022718384861946,
0.009511745534837246,
-0.03285153955221176,
-0.015987904742360115,
-0.030478335916996002,
0.038388803601264954,
0.014025283046066761,
-0.016726089641451836,
0.025406546890735626,
-0.005555156152695417,
0.004131257999688387,
0.01874430477619171,
-0.04157448187470436,
-0.06421778351068497,
-0.0499093197286129,
0.03800712898373604,
0.05520027130842209,
-0.04008499160408974,
-0.09005405008792877,
-0.03107084520161152,
-0.02981061302125454,
0.014262530952692032,
-0.027872417122125626,
0.02226247824728489,
-0.004311731550842524,
0.014673511497676373,
-0.027107328176498413,
-0.022019175812602043,
0.008660843595862389,
0.04047274589538574,
0.020325638353824615,
-0.006109138950705528,
-0.027003858238458633,
-0.011808727867901325,
-0.0010579786030575633,
0.02141045778989792,
-0.03476528078317642,
-0.011071788147091866,
-0.007211499381810427,
-0.040076445788145065,
-0.06322884559631348,
-0.05039368197321892,
0.02249016985297203,
-0.03184092789888382,
-0.02163727767765522,
-0.04908487945795059,
-0.01819615066051483,
0.014870704151690006,
0.04024240002036095,
0.03472794592380524,
0.02575482241809368,
0.008875267580151558,
-0.004147890955209732,
0.011720052920281887,
0.009126037359237671,
0.0032447045668959618,
-0.04400748759508133,
0.0373125895857811,
-0.02660144679248333,
0.056302789598703384,
0.03514707460999489,
0.0150713250041008,
0.0708615705370903,
0.023241117596626282,
0.03934621438384056,
0.0575869046151638,
0.04677700623869896,
-0.030869947746396065,
0.01597495935857296,
0.018856817856431007,
-0.03929667919874191,
0.04033619910478592,
-0.07249803096055984,
0.00006490668602054939,
-0.017901716753840446,
-0.0008953502983786166,
-0.03900566324591637,
-0.010095537640154362,
0.039721883833408356,
-0.029924942180514336,
-0.02166452258825302,
-0.05053787678480148,
0.019149968400597572,
-0.003202552907168865,
0.009532274678349495,
0.013718895614147186,
-0.06906239688396454,
0.04649210721254349,
0.038554102182388306,
-0.0019076791359111667,
0.006567859090864658,
-0.052965033799409866,
-0.06661253422498703,
0.09166030585765839,
-0.03499000146985054,
0.000842475623358041,
-0.06182417646050453,
-0.021455936133861542,
0.07039593160152435,
0.025516169145703316,
-0.029210804030299187,
-0.01207803189754486,
0.05450617894530296,
0.000750916893593967,
-0.0306545402854681,
-0.012411490082740784,
-0.004145401064306498,
-0.014110904186964035,
-0.02738363668322563,
0.05508863180875778,
-0.0301273874938488,
-0.016589269042015076,
-0.0184054933488369,
0.08189982920885086,
-0.02528536692261696,
0.05582359433174133,
0.028121868148446083,
0.00044036205508746207,
0.03523964062333107,
-0.024188950657844543,
-0.030997831374406815,
0.06545789539813995,
0.00564447371289134,
-0.018965542316436768,
0.011265519075095654,
0.0729236751794815,
0.010971130803227425,
-0.02520299330353737,
-0.0496862530708313,
-0.004919740837067366,
0.009422051720321178,
-0.038037966936826706,
0.02294483780860901,
-0.05476582422852516,
-0.02529788203537464,
0.027950234711170197,
0.009247113019227982,
-0.035432327538728714,
-0.05008864030241966,
-0.038821473717689514,
-0.028220055624842644,
0.002906093606725335,
0.003972160629928112,
-0.010455100797116756,
-0.05334986001253128,
0.04033713415265083,
-0.050554659217596054,
0.039990637451410294,
0.05106967315077782,
-0.03545033559203148,
0.07169821858406067,
0.01914137788116932,
-0.01280947308987379,
-0.0400291308760643,
0.017159640789031982,
-0.06893832981586456,
0.06254290789365768,
0.014136097393929958,
-0.019906694069504738,
-0.015463345684111118,
0.01383932400494814,
-0.03811243921518326,
-0.002140228869393468,
0.059434205293655396,
-0.035116471350193024,
0.014123528264462948,
0.055241093039512634,
-0.02622205950319767,
-0.0019623017869889736,
0.030194265767931938,
-0.0008527988102287054,
0.017979389056563377,
0.03515766188502312,
0.0754464864730835,
-0.03266236186027527,
0.0041955458000302315,
0.054978836327791214,
0.045441705733537674,
-0.020905738696455956,
-0.03456733748316765,
0.03527123108506203,
-0.021893301978707314,
0.0066434117034077644,
-0.018874406814575195,
-0.092926025390625,
0.0090184910222888,
0.004669292829930782,
-0.029891736805438995,
-0.01895085535943508,
-0.018992703408002853,
-0.026712564751505852,
-0.012379906140267849,
0.025224285200238228,
0.016837095841765404,
-0.028322990983724594,
-0.0027057465631514788,
0.005153954960405827,
0.021132037043571472,
0.022411927580833435,
0.030385438352823257,
0.03728313371539116,
0.0028157634660601616,
0.008251289837062359,
-0.018532976508140564,
0.00118139514233917,
-0.002222276758402586,
0.015302356332540512,
0.08612837642431259,
-0.0020719734020531178,
0.02765573374927044,
-0.04219268634915352,
0.03315633535385132,
-0.04745126888155937,
-0.03676867485046387,
0.043318621814250946,
0.031236199662089348,
-0.05180279538035393,
0.02816016413271427,
0.04323467239737511,
-0.02451208420097828,
-0.04510089010000229,
0.04828561097383499,
0.01799307018518448,
-0.06301025301218033,
0.0036199907772243023,
-0.02854323759675026,
-0.044313255697488785,
-0.006943586748093367
] |
<p>There is a recent paper on arxiv receiving lot of acclaim <a href="http://arxiv.org/abs/1105.4714">http://arxiv.org/abs/1105.4714</a></p>
<p>The authors experimentally show that moving a mirror of a cavity at high speeds produces light from high vacuum. The usual doubts about the experimental techniques seem to be very clearly addressed and reviewed (as per Fred Capasso's comments) <a href="http://www.nature.com/news/2011/110603/full/news.2011.346.html">http://www.nature.com/news/2011/110603/full/news.2011.346.html</a>)</p>
<p>My question is :
Can someone explain how correlated/squeezed photons are generated in this process ? I can get a feel for how a moving mirror can generate real photons by imparting energy to the vacuum (correct me if this is not consistent with the detailed theory). But, I don't see how photons are generated in pairs. Could someone describe the parametric process happening here ? </p> | g5549 | [
-0.02064742147922516,
0.027246613055467606,
-0.015768591314554214,
0.017378732562065125,
0.049433305859565735,
0.04139411449432373,
0.050078507512807846,
0.045715007930994034,
-0.00967384409159422,
-0.01688874140381813,
-0.010493340902030468,
0.018007121980190277,
0.045656509697437286,
-0.009941523894667625,
-0.0515083447098732,
-0.008090125396847725,
0.09344538301229477,
0.0019985304679721594,
-0.005751250311732292,
0.003906771540641785,
-0.05018508806824684,
0.00451549980789423,
-0.016806915402412415,
-0.06086223945021629,
0.014201140031218529,
0.027322307229042053,
0.04607337713241577,
-0.023167870938777924,
0.03185798600316048,
-0.02599707618355751,
0.05366016924381256,
-0.015440601855516434,
0.017833033576607704,
-0.03310806676745415,
0.0045585655607283115,
-0.021250616759061813,
0.054159585386514664,
-0.012490100227296352,
-0.020730800926685333,
0.01918177492916584,
-0.0055576832965016365,
-0.010900039225816727,
-0.010979803279042244,
-0.02121245115995407,
0.0207006074488163,
0.03293415158987045,
-0.009714588522911072,
-0.022566145285964012,
0.0030958866700530052,
0.024982480332255363,
0.0007798147853463888,
0.05806995555758476,
0.010673369280993938,
-0.007473014295101166,
0.061181046068668365,
0.010017400607466698,
0.0040354132652282715,
-0.002578119980171323,
0.09282758086919785,
0.01674485020339489,
-0.0549217164516449,
-0.03551185131072998,
0.02431502565741539,
0.012313143350183964,
0.03912830352783203,
0.0269035454839468,
-0.018564678728580475,
-0.04595235735177994,
0.012400487437844276,
-0.004803776741027832,
-0.030138250440359116,
-0.012677829712629318,
-0.019382935017347336,
-0.006160201504826546,
0.0037526581436395645,
-0.01835697330534458,
0.05330784618854523,
-0.02785997837781906,
0.002659072168171406,
0.008039845153689384,
-0.00014086092414800078,
-0.023122092708945274,
0.0005784282693639398,
-0.024048179388046265,
0.03649640083312988,
-0.03008427657186985,
-0.04315328225493431,
0.04552547633647919,
-0.00946620013564825,
-0.04439340904355049,
0.039774373173713684,
-0.003486426780000329,
0.05219647288322449,
0.0065586804412305355,
-0.029210586100816727,
0.03232206031680107,
-0.05916159600019455,
0.08180578798055649,
-0.04350759834051132,
-0.030755281448364258,
-0.02137577533721924,
0.013291810639202595,
0.0514255054295063,
0.027810964733362198,
0.004248188808560371,
-0.024673249572515488,
-0.04051090031862259,
0.008683320134878159,
-0.049570560455322266,
0.016076618805527687,
-0.07703709602355957,
0.001750426134094596,
-0.06471831351518631,
-0.028521493077278137,
-0.034842945635318756,
-0.015520191751420498,
0.034390199929475784,
0.04252200573682785,
0.03294069319963455,
0.0787213146686554,
0.06608550250530243,
0.05983059108257294,
-0.050650887191295624,
-0.018062174320220947,
-0.01720193587243557,
0.0074752578511834145,
0.0016196647193282843,
-0.017148472368717194,
0.011095996014773846,
0.02254772000014782,
0.01973857916891575,
-0.0014575739623978734,
-0.042546529322862625,
0.03065980225801468,
0.024741774424910545,
0.02263917587697506,
0.03349519893527031,
-0.03422052785754204,
0.04984613135457039,
-0.0064355130307376385,
0.006669467315077782,
-0.005902938544750214,
-0.03798934444785118,
-0.030837828293442726,
0.008169815875589848,
0.0017108231550082564,
-0.03125621750950813,
0.004408933687955141,
0.0077466401271522045,
0.046500563621520996,
0.038945555686950684,
0.07300058007240295,
0.007998188957571983,
-0.05239422246813774,
0.06163345277309418,
0.014764237217605114,
0.04260649159550667,
-0.030731214210391045,
-0.03405194729566574,
-0.015017291530966759,
0.09338153153657913,
-0.03180878236889839,
-0.01908501610159874,
-0.0028214510530233383,
-0.006597649306058884,
-0.011568804271519184,
0.03887907415628433,
-0.0811787024140358,
-0.020232615992426872,
-0.022708965465426445,
-0.06738399714231491,
-0.014759860932826996,
-0.020739469677209854,
0.041057370603084564,
-0.033490441739559174,
0.040097009390592575,
0.03390485793352127,
-0.005371700040996075,
0.013226574286818504,
-0.008714479394257069,
-0.0343371219933033,
-0.05603964626789093,
0.021644746884703636,
-0.039692118763923645,
0.026838887482881546,
0.0026968643069267273,
-0.052015822380781174,
-0.013727691024541855,
-0.05650331825017929,
-0.005369311198592186,
0.016483046114444733,
-0.03138819336891174,
-0.010773155838251114,
-0.009199251420795918,
-0.05906044691801071,
-0.0406256765127182,
0.033320069313049316,
-0.0768289864063263,
0.03807095065712929,
0.023444676771759987,
-0.061095867305994034,
0.03865848481655121,
0.01347996387630701,
0.013273688964545727,
0.05320853367447853,
0.0052824467420578,
0.013858129270374775,
-0.031243005767464638,
-0.05197185277938843,
-0.007833536714315414,
0.014408969320356846,
0.02946840226650238,
0.003294827649369836,
-0.01812003366649151,
-0.035543546080589294,
0.017155559733510017,
-0.06202729791402817,
-0.015964357182383537,
0.031138459220528603,
0.00048004533164203167,
-0.007963618263602257,
-0.012244874611496925,
-0.004774722270667553,
-0.009908503852784634,
-0.01828436739742756,
0.00017329501861240715,
-0.0576707161962986,
0.036473751068115234,
0.019948335364460945,
0.07032501697540283,
-0.015340485610067844,
0.02275361679494381,
-0.061895523220300674,
-0.03621561825275421,
-0.0003689081931952387,
0.02738266810774803,
-0.034841809421777725,
0.07120546698570251,
0.01752547360956669,
0.03956591337919235,
0.046856824308633804,
-0.02620573714375496,
-0.0641525611281395,
-0.030656062066555023,
-0.030483964830636978,
-0.06464958190917969,
0.07237953692674637,
0.013148738071322441,
0.000606943154707551,
-0.014063261449337006,
0.032665178179740906,
-0.036222610622644424,
0.0012941744644194841,
-0.09367210417985916,
0.0006413232767954469,
-0.009652686305344105,
0.04905923455953598,
0.08470971882343292,
-0.013023214414715767,
-0.012602217495441437,
0.006645153742283583,
-0.02390093170106411,
-0.019131913781166077,
-0.05463330075144768,
-0.014770007692277431,
0.004655533470213413,
0.023285796865820885,
-0.040774911642074585,
-0.03522838279604912,
-0.011480540968477726,
-0.04832100868225098,
0.09896277636289597,
0.032085295766592026,
-0.03346944972872734,
0.007888870313763618,
-0.01943923719227314,
0.03490573167800903,
-0.06416386365890503,
0.01705852523446083,
-0.06607388705015182,
-0.03964455798268318,
-0.02200886979699135,
-0.026925327256321907,
-0.05927576869726181,
-0.004161213990300894,
-0.06970918923616409,
0.019693000242114067,
-0.01250582654029131,
-0.0026705109048634768,
0.04446340724825859,
-0.0521823987364769,
0.0019869201350957155,
-0.010199353098869324,
0.013890125788748264,
-0.022723929956555367,
0.0611688494682312,
0.039173662662506104,
-0.009488659910857677,
-0.022943301126360893,
0.013866612687706947,
-0.02412981353700161,
-0.04336228594183922,
0.019482450559735298,
-0.030600059777498245,
0.028335366398096085,
0.031443968415260315,
-0.0507795549929142,
-0.054073236882686615,
-0.010328639298677444,
0.046098992228507996,
-0.027683289721608162,
0.03254343569278717,
-0.016204090788960457,
0.03858890011906624,
-0.0005515359225682914,
-0.02906688302755356,
0.024073287844657898,
-0.007316378876566887,
-0.0014701873296871781,
-0.0045793317258358,
-0.023021182045340538,
-0.005656579975038767,
0.04723760485649109,
-0.028107939288020134,
0.07567761093378067,
0.009627525694668293,
-0.033899545669555664,
-0.004424589220434427,
-0.03145121783018112,
-0.02489451877772808,
0.04360455647110939,
-0.026091156527400017,
-0.008380825631320477,
-0.012684205546975136,
-0.048960935324430466,
-0.021736962720751762,
-0.02287711575627327,
0.049227721989154816,
0.07100361585617065,
-0.014434640295803547,
0.0031538179609924555,
0.011888820677995682,
-0.03430834412574768,
0.007748125586658716,
0.028327258303761482,
0.0522889718413353,
0.01726234145462513,
0.027641018852591515,
0.022481566295027733,
-0.005314038135111332,
0.011414078995585442,
0.024375641718506813,
0.059153251349925995,
-0.020094169303774834,
-0.07561606168746948,
0.06043463572859764,
-0.030169550329446793,
-0.0013923904625698924,
0.04719717800617218,
-0.03054928034543991,
0.0008290187688544393,
0.00608009472489357,
0.025721350684762,
-0.04979921132326126,
-0.02636834792792797,
-0.007252845447510481,
-0.0157998688519001,
0.04465502128005028,
0.00646052323281765,
0.04827146604657173,
-0.028596876189112663,
-0.045133691281080246,
-0.03571568429470062,
-0.0014961145352572203,
0.016535405069589615,
-0.011880464851856232,
0.05574541538953781,
-0.05407734587788582,
0.0028882063925266266,
0.02564539946615696,
0.007764846086502075,
0.016655661165714264,
0.05353518947958946,
0.009887175634503365,
0.03527030348777771,
0.019804516807198524,
-0.08282151818275452,
0.041393548250198364,
0.011407298035919666,
-0.07442587614059448,
0.073763906955719,
-0.02533804625272751,
-0.01701023057103157,
0.004285151604562998,
0.03329300135374069,
0.003592693479731679,
0.040066856890916824,
-0.03539634868502617,
0.0041512977331876755,
-0.040452197194099426,
-0.027530115097761154,
0.08730579912662506,
0.0034683349076658487,
0.01132197491824627,
-0.08321651071310043,
-0.05698493868112564,
0.03090871311724186,
-0.008598321117460728,
-0.0006568842218257487,
-0.031455203890800476,
-0.03138883784413338,
0.035278741270303726,
0.00819497462362051,
-0.04917873069643974,
0.044337693601846695,
0.03082793392241001,
0.01635752245783806,
0.01897694543004036,
-0.005470404401421547,
0.020144883543252945,
-0.02510787732899189,
0.01765085943043232,
0.08221675455570221,
0.06358032673597336,
0.008289382793009281,
0.08075406402349472,
0.011522982269525528,
-0.04886527359485626,
0.026172878220677376,
-0.06527427583932877,
0.06705573946237564,
0.018606029450893402,
0.03851354122161865,
0.04104754701256752,
0.019521629437804222,
0.03812822699546814,
-0.01703072525560856,
0.00033254464506171644,
0.03945775702595711,
0.012505868449807167,
0.08255469799041748,
-0.009410491213202477,
0.08221662044525146,
0.017850002273917198,
0.011030797846615314,
0.026926476508378983,
-0.016201430931687355,
-0.06535597890615463,
-0.002979051787406206,
-0.0510764941573143,
-0.011139090172946453,
0.05712303891777992,
-0.02939438819885254,
-0.04329608008265495,
0.04193491488695145,
-0.0033814876805990934,
0.014924788847565651,
0.015981676056981087,
0.043389834463596344,
0.0029761900659650564,
-0.05334443971514702,
0.02791588567197323,
0.07283023744821548,
-0.05105770379304886,
0.04759916290640831,
-0.018835095688700676,
-0.05096159130334854,
-0.008841770701110363,
-0.04299930855631828,
-0.062461622059345245,
0.022062893956899643,
0.009226325899362564,
-0.04658142477273941,
0.012934187427163124,
-0.014394387602806091,
-0.0021156123839318752,
0.007930650375783443,
0.013746923767030239,
-0.004053650889545679,
0.020262034609913826,
0.05256970599293709,
0.04802051931619644,
0.03423004597425461,
-0.06599588692188263,
-0.020054001361131668,
-0.03163173422217369,
-0.06652121245861053,
-0.011022860184311867,
-0.017431247979402542,
-0.01325387042015791,
0.013563417829573154,
-0.005071387626230717,
-0.010870415717363358,
-0.022548390552401543,
-0.009225099347531796,
0.033676061779260635,
0.022398538887500763,
0.0010332873789593577,
-0.02393817901611328,
0.022465359419584274,
-0.02188318595290184,
-0.030537473037838936,
0.015357165597379208,
-0.003741093911230564,
-0.01674918457865715,
-0.04291534796357155,
0.05077993497252464,
0.010013332590460777,
0.06301344186067581,
0.024957962334156036,
-0.002295764861628413,
0.015296272933483124,
-0.008803555741906166,
0.007943241856992245,
0.02414843998849392,
-0.027469919994473457,
0.01190483383834362,
-0.005470324773341417,
-0.008656923659145832,
-0.04252472147345543,
0.03644071891903877,
0.024954790249466896,
0.010476806201040745,
-0.035331644117832184,
0.01203246135264635,
0.01869731768965721,
-0.08754205703735352,
0.04141705110669136,
0.02349007874727249,
0.005210984963923693,
0.0025611419696360826,
-0.025495046749711037,
0.08396676182746887,
-0.011285231448709965,
-0.021112607792019844,
-0.05252012982964516,
0.0593743659555912,
-0.005387404467910528,
0.005728160496801138,
0.018851542845368385,
-0.04484431818127632,
-0.06915941834449768,
-0.014038085006177425,
0.07335886359214783,
0.025217119604349136,
0.015151104889810085,
-0.007699759677052498,
0.020500872284173965,
0.039438940584659576,
0.031385719776153564,
-0.038841359317302704,
-0.02936369925737381,
0.01940968446433544,
0.02352764829993248,
0.01900581456720829,
-0.03157135844230652,
-0.026843560859560966,
-0.03323308005928993,
-0.03857465088367462,
-0.007758656982332468,
0.04074779897928238,
0.0400577113032341,
0.07592913508415222,
-0.050862908363342285,
-0.009060942567884922,
-0.029328905045986176,
0.02803589217364788,
0.013731889426708221,
-0.008121997117996216,
0.042812056839466095,
0.0060029709711670876,
0.045189596712589264,
-0.016455315053462982,
-0.027070967480540276,
-0.013655966147780418,
0.017991729080677032,
-0.028340129181742668,
-0.03420400992035866,
-0.10164264589548111,
0.03927943855524063,
0.04773544520139694,
-0.02924005687236786,
0.03216990455985069,
-0.0005727636162191629,
-0.036824848502874374,
0.033199913799762726,
0.03515774384140968,
-0.01690787635743618,
0.026628661900758743,
-0.033737391233444214,
-0.0700952559709549,
0.02629101276397705,
-0.012965339235961437,
-0.02887710928916931,
-0.01469908282160759,
-0.02296505868434906,
0.007234528195112944,
0.0020516510121524334,
-0.060692381113767624,
0.008808312006294727,
-0.02241186797618866,
0.003692448837682605,
-0.029764967039227486,
-0.02929878979921341,
-0.023015400394797325,
-0.024296989664435387,
-0.05043576657772064,
0.04212278872728348,
0.003582355100661516,
0.08322665095329285,
-0.07472075521945953,
-0.0011185123585164547,
-0.04608338698744774,
0.006153400521725416,
-0.004213700070977211,
-0.013003704138100147,
0.040794309228658676,
0.03177672252058983,
0.06572195142507553,
0.001530298963189125,
-0.01932276040315628,
-0.05577138811349869,
0.016572842374444008,
-0.013281167484819889,
0.019220970571041107,
0.06571431457996368,
-0.039163243025541306,
0.0017523346468806267,
0.028497368097305298,
0.02452298067510128,
-0.003830198897048831,
-0.039226751774549484,
-0.029109572991728783,
-0.0004898394108749926,
0.005926153156906366,
0.07530753314495087,
-0.033622413873672485,
0.07164040952920914,
0.013521984219551086,
-0.038995031267404556,
0.04600415378808975,
0.02837500534951687,
-0.01030723750591278,
0.043660879135131836,
-0.006835300475358963,
0.0359707809984684,
-0.05484491586685181,
-0.023471370339393616,
-0.059990156441926956,
-0.025544550269842148,
-0.07889141142368317,
-0.0665358155965805,
-0.06768788397312164,
0.07508321851491928,
-0.018764475360512733,
0.08375569432973862,
-0.026053333654999733,
0.0345306433737278,
-0.024014469236135483,
-0.03976522386074066,
-0.027624953538179398,
-0.028846807777881622,
-0.02061137557029724,
0.0031477876473218203,
0.034059468656778336,
0.017078960314393044,
-0.008696085773408413,
-0.01279985811561346,
0.018798572942614555,
-0.009613621979951859,
0.03584979102015495,
-0.02881971187889576,
-0.01050349697470665,
0.025083236396312714,
-0.004183484707027674,
-0.024875521659851074,
-0.0016957931220531464,
0.06359176337718964,
-0.02399333566427231,
-0.010836534202098846,
-0.037658024579286575,
-0.016896409913897514,
-0.002849342068657279,
0.008934912271797657,
-0.04036944732069969,
0.05598029866814613,
-0.07964060455560684,
0.007855668663978577,
-0.021662745624780655,
-0.03158178552985191,
-0.016733696684241295,
-0.04886212944984436,
0.004905122797936201,
0.049177657812833786,
0.01741850934922695,
0.02211541309952736,
0.0418422557413578,
-0.018375109881162643,
-0.011100958101451397,
0.027828391641378403,
-0.015553486533463001,
0.04470197856426239,
-0.060488905757665634,
-0.005293366964906454,
0.012415498495101929,
0.021349580958485603,
0.01951722800731659,
-0.03783034533262253,
0.05382199585437775,
0.00380163942463696,
0.001700198627077043,
-0.023117301985621452,
-0.0620407834649086,
-0.0048555657267570496,
0.028814880177378654,
-0.04194868355989456,
-0.019729694351553917,
0.07162417471408844,
0.03759147971868515,
0.033387571573257446,
0.013075685128569603,
0.035090506076812744,
0.008745488710701466,
-0.028027260676026344,
0.012179521843791008,
-0.03506716340780258,
0.03098973073065281,
-0.0063702985644340515,
-0.01602238416671753,
0.04680941626429558,
0.04919711500406265,
-0.029202228412032127,
-0.008427799679338932,
-0.03528984263539314,
-0.011533957906067371,
-0.030108323320746422,
0.011118491180241108,
0.02689964696764946,
0.07046210020780563,
0.02027154713869095,
-0.03586561605334282,
-0.0853063315153122,
0.020589258521795273,
-0.047436632215976715,
0.035519037395715714,
-0.023826394230127335,
-0.07593356817960739,
0.01124612893909216,
-0.031508106738328934,
0.019294900819659233,
0.018974585458636284,
0.0022693765349686146,
-0.03902517259120941,
0.06066440790891647,
0.07328251749277115,
-0.06662790477275848,
0.00925775058567524,
0.005033445078879595,
0.0015839086845517159,
-0.013390754349529743,
0.00009911298548104241,
0.024767665192484856,
0.0050736283883452415,
-0.01794821210205555,
-0.03696821630001068,
-0.007732917554676533,
-0.033409975469112396,
0.030457457527518272
] |
<p>Landau writes "It is found, however, that a frame of reference can always be chosen in
which space is homogeneous and isotropic and time is homogeneous."</p>
<p>Does he mean that we can prove the existence of an inertial frame or does he want to say that it is assumed by doing enough number of experiments?</p>
<p>Can we start with some axioms and definitions of properties of space and time and then deduce the existence of such a frame in which space is homogeneous and isotropic and time is homogeneous?</p> | g5550 | [
0.018910959362983704,
0.06901051104068756,
0.020534822717308998,
0.018832899630069733,
0.06111462786793709,
0.01909497380256653,
0.07102875411510468,
0.02066134661436081,
0.02450721338391304,
0.013886485248804092,
-0.02293919213116169,
0.004507663194090128,
-0.05402209237217903,
0.03764645755290985,
-0.013022257015109062,
-0.029888294637203217,
0.06745600700378418,
-0.012248621322214603,
0.011373687535524368,
-0.012584959156811237,
0.02260196954011917,
0.05257687345147133,
0.022233907133340836,
-0.03695441037416458,
0.007867151871323586,
0.036559294909238815,
0.02343936823308468,
-0.07729217410087585,
0.007088139187544584,
0.005947265308350325,
0.018696440383791924,
0.00015226755931507796,
-0.02069081924855709,
-0.00083893135888502,
0.07280881702899933,
-0.07094736397266388,
0.0172265712171793,
0.018579406663775444,
0.03791454806923866,
0.030350472778081894,
0.031102363020181656,
-0.04508655518293381,
-0.04957525432109833,
-0.00878484733402729,
0.014531930908560753,
0.1258050948381424,
-0.03455821052193642,
-0.006499038077890873,
-0.03606429323554039,
-0.022680431604385376,
-0.008838080801069736,
0.07510879635810852,
0.03589038550853729,
-0.02437419816851616,
-0.015638066455721855,
0.01668516732752323,
0.027942610904574394,
-0.05998176708817482,
0.09575244784355164,
0.05410601943731308,
-0.025437962263822556,
-0.02660006284713745,
0.0067462739534676075,
-0.007198059931397438,
0.01606018655002117,
0.011581763625144958,
-0.02064097300171852,
-0.025295615196228027,
-0.009047786705195904,
-0.02417188137769699,
0.04782453924417496,
-0.06478100270032883,
0.0172401275485754,
0.024521322920918465,
-0.0508759431540966,
0.07196437567472458,
0.02057010866701603,
-0.008831516839563847,
0.026839137077331543,
0.003919990733265877,
-0.06278189271688461,
0.009810932911932468,
0.040921106934547424,
-0.021954325959086418,
0.04060651734471321,
-0.02758694253861904,
0.0565105639398098,
0.017401915043592453,
0.008064686320722103,
0.016872651875019073,
-0.02618633210659027,
-0.013884847052395344,
0.06378426402807236,
0.05664089322090149,
-0.00974905677139759,
0.03062148578464985,
-0.06414805352687836,
0.024872785434126854,
-0.01708853617310524,
-0.010618462227284908,
-0.0745195746421814,
-0.0017856891499832273,
-0.0005184464971534908,
-0.05057978630065918,
0.0400485061109066,
-0.05607599392533302,
-0.01812342181801796,
-0.0011663619661703706,
-0.04959825053811073,
-0.07405631244182587,
-0.004970335401594639,
0.012850314378738403,
-0.03129906579852104,
-0.009324237704277039,
-0.051141414791345596,
0.023582326248288155,
0.11999715119600296,
-0.03809255734086037,
-0.003243915503844619,
0.033755265176296234,
-0.03325202688574791,
-0.01262601837515831,
0.005506306421011686,
0.07997576147317886,
-0.03854899853467941,
0.008171959780156612,
-0.0396740697324276,
-0.00022467397502623498,
-0.027128683403134346,
0.005828517489135265,
0.0077270385809242725,
0.034675631672143936,
0.018443521112203598,
0.014557740651071072,
-0.010664811357855797,
-0.029038645327091217,
0.017693649977445602,
0.026873668655753136,
-0.016881834715604782,
0.05168166384100914,
-0.0019435558933764696,
-0.01710337959229946,
-0.013262651860713959,
-0.00486137717962265,
0.0009865702595561743,
-0.011508490890264511,
-0.030782176181674004,
0.00455702468752861,
0.02310636267066002,
0.04516330733895302,
-0.04754802584648132,
0.10088084638118744,
-0.010369714349508286,
-0.01582609862089157,
0.03376052528619766,
-0.015664206817746162,
0.002104554558172822,
-0.014968914911150932,
0.01795121468603611,
-0.015340428799390793,
0.05325021222233772,
0.04359360411763191,
-0.02385828271508217,
-0.01319293025881052,
-0.0355447381734848,
-0.00047253858065232635,
0.006118720397353172,
-0.02241669036448002,
0.05938897281885147,
-0.052795156836509705,
-0.06989826261997223,
-0.00993615947663784,
-0.0045241317711770535,
0.05537549406290054,
-0.0043029156513512135,
-0.02078087627887726,
-0.029906921088695526,
-0.029071994125843048,
0.03788306191563606,
0.0017990448977798223,
-0.0009157137246802449,
0.0003982988419011235,
-0.01617181859910488,
-0.05875352397561073,
-0.04731905832886696,
0.060761645436286926,
0.018379660323262215,
-0.05524905398488045,
-0.05846308171749115,
-0.005161786451935768,
0.01609473116695881,
-0.005184739362448454,
-0.01919257827103138,
-0.0031438558362424374,
0.035761862993240356,
-0.0021449571941047907,
0.038403093814849854,
-0.018273428082466125,
-0.024265583604574203,
0.025393955409526825,
-0.02900788187980652,
-0.0023795131128281355,
0.04447050765156746,
0.05154877156019211,
0.013049844652414322,
-0.012777399271726608,
-0.00864882580935955,
-0.02032589167356491,
0.011278827674686909,
0.007713621482253075,
0.017620626837015152,
-0.013588210567831993,
-0.01134428009390831,
0.07608366757631302,
0.010357665829360485,
-0.04960360750555992,
0.036909230053424835,
-0.03554011508822441,
-0.0011209598742425442,
0.004175420850515366,
-0.022857317700982094,
0.0020412495359778404,
-0.028630230575799942,
0.02514692023396492,
-0.00955885834991932,
-0.07513146847486496,
-0.017405681312084198,
0.004271456506103277,
0.030647704377770424,
0.023488208651542664,
-0.029829977080225945,
-0.01114814542233944,
-0.007281484082341194,
-0.0024318161886185408,
0.036931734532117844,
-0.01642695441842079,
0.0014971161726862192,
-0.00941399298608303,
-0.006058667786419392,
0.07558085024356842,
-0.051374923437833786,
0.03972477838397026,
-0.005945324897766113,
-0.0031379677820950747,
-0.03036266192793846,
-0.07066747546195984,
0.035232048481702805,
-0.035448119044303894,
0.02876669354736805,
0.0007003335631452501,
-0.01122200582176447,
-0.007092372048646212,
-0.009562057442963123,
-0.02776201255619526,
0.016150332987308502,
0.021401727572083473,
-0.019432388246059418,
0.007956274785101414,
-0.08196156471967697,
0.0001798088342184201,
0.04142754152417183,
-0.05838852748274803,
-0.010384675115346909,
0.04071252420544624,
-0.0943673625588417,
0.021813886240124702,
-0.0022999171633273363,
0.034539345651865005,
-0.03730333596467972,
-0.009372822009027004,
0.011852104216814041,
0.0635361298918724,
0.039879657328128815,
0.08473938703536987,
-0.05953191593289375,
-0.016041459515690804,
-0.027260806411504745,
-0.04121366888284683,
0.017477335408329964,
-0.03497513383626938,
-0.02260143868625164,
0.01116627361625433,
-0.07005395740270615,
0.020225170999765396,
0.04661104455590248,
0.009329384192824364,
-0.006589185446500778,
0.033727534115314484,
-0.03470577299594879,
0.0006897622370161116,
-0.039083100855350494,
0.016701433807611465,
-0.003489188849925995,
0.01663130149245262,
-0.07028189301490784,
0.0495351180434227,
-0.029304465278983116,
-0.057418547570705414,
-0.0033892819192260504,
0.07077678292989731,
0.007596869952976704,
0.016088783740997314,
0.07731065154075623,
0.04511148855090141,
0.04280272498726845,
0.021231381222605705,
-0.04810678958892822,
-0.02635890804231167,
-0.03985266387462616,
-0.03203190490603447,
-0.03458087518811226,
0.06168777868151665,
-0.025140317156910896,
0.024136975407600403,
-0.06089644506573677,
0.014063983224332333,
0.02344667539000511,
-0.052352141588926315,
-0.025090890005230904,
-0.04642975702881813,
-0.0016626158030703664,
0.0005025652935728431,
-0.0049071479588747025,
-0.09725023061037064,
0.052257880568504333,
0.011620443314313889,
-0.04836348816752434,
-0.010601337999105453,
-0.037843309342861176,
-0.003995971288532019,
0.0027401456609368324,
-0.010209369473159313,
0.008015577681362629,
0.007605397142469883,
-0.06859245151281357,
-0.028279336169362068,
-0.035918522626161575,
-0.0010660111438483,
0.06406132876873016,
0.0050022355280816555,
0.04268626496195793,
0.011568397283554077,
-0.03260166198015213,
0.048777587711811066,
-0.002117542549967766,
-0.0010592180769890547,
-0.011841590516269207,
0.016005991026759148,
0.023889563977718353,
0.04335878789424896,
0.027812695130705833,
0.01575334556400776,
0.01660037413239479,
-0.0585951991379261,
-0.020614447072148323,
0.030119428411126137,
0.027662862092256546,
0.06387245655059814,
-0.044423703104257584,
-0.06824090331792831,
0.019489221274852753,
-0.04030280187726021,
0.015981825068593025,
-0.032194510102272034,
0.028835276141762733,
-0.004184901248663664,
-0.004172354005277157,
0.008496315218508244,
0.03242680802941322,
-0.01223866268992424,
0.0017984817968681455,
-0.05920308083295822,
0.0047792475670576096,
-0.021340442821383476,
0.05415216088294983,
-0.08557116240262985,
0.04254942759871483,
0.025101497769355774,
-0.011391397565603256,
-0.0058323098346591,
0.030050000175833702,
0.027719220146536827,
-0.04128461331129074,
-0.01250714622437954,
0.04103562980890274,
0.02040121890604496,
-0.01526725199073553,
0.004518349654972553,
-0.0046640969812870026,
-0.05783269926905632,
-0.03401069715619087,
0.022845475003123283,
-0.07632856070995331,
-0.0674668401479721,
0.020274382084608078,
0.018942981958389282,
0.024603676050901413,
0.012745424173772335,
0.001464290777221322,
-0.007667985744774342,
0.04673986881971359,
-0.01501403283327818,
-0.05716652423143387,
0.009792447090148926,
-0.009832057170569897,
0.014250981621444225,
0.013438265770673752,
-0.03271716460585594,
0.02879185974597931,
0.005394128151237965,
-0.024695076048374176,
-0.008831311017274857,
0.01703929342329502,
-0.09068594872951508,
0.03976660221815109,
0.011581596918404102,
0.014737416058778763,
-0.06598861515522003,
0.01921634003520012,
0.00082543765893206,
0.002264236332848668,
0.0892445370554924,
-0.03976033627986908,
-0.07536324113607407,
-0.004216647706925869,
0.054784804582595825,
0.06214875355362892,
0.011884807609021664,
-0.0153641477227211,
0.01609513908624649,
-0.00225027441047132,
0.011261596344411373,
0.00693594291806221,
0.019076872617006302,
-0.02531002089381218,
-0.025717053562402725,
-0.013989116065204144,
-0.015647856518626213,
0.029806822538375854,
0.06008679419755936,
0.010958893224596977,
-0.020974071696400642,
-0.01564435288310051,
-0.058428648859262466,
-0.03906849026679993,
0.05772602930665016,
0.06358495354652405,
-0.0526488795876503,
-0.0382365956902504,
-0.013060923665761948,
-0.02290733903646469,
0.00611139927059412,
-0.041529618203639984,
0.06408791989088058,
-0.001279781456105411,
-0.025745417922735214,
-0.07587239891290665,
0.004227536730468273,
-0.008913589641451836,
0.03394603729248047,
-0.0240038949996233,
-0.01001203153282404,
0.027461230754852295,
0.010907141491770744,
0.000052741124818567187,
0.0334056094288826,
-0.047343239188194275,
0.02817694842815399,
-0.07274288684129715,
-0.002797576831653714,
0.02148905210196972,
0.037220392376184464,
-0.03811576962471008,
-0.024625755846500397,
0.017239363864064217,
-0.018339384347200394,
0.00912360567599535,
-0.018725519999861717,
0.012637305073440075,
0.03249964118003845,
-0.010278045199811459,
-0.021423952654004097,
-0.008461921475827694,
0.0026018295902758837,
0.020250197499990463,
0.029175642877817154,
-0.12086740136146545,
0.03200002759695053,
0.009299852885305882,
-0.0796227753162384,
0.014355214312672615,
-0.00024693767772987485,
0.033761829137802124,
-0.007134426385164261,
-0.01912589557468891,
0.015079733915627003,
-0.050539255142211914,
-0.04073726013302803,
-0.045147184282541275,
0.0249723382294178,
-0.016935348510742188,
0.00002873081211873796,
0.042215172201395035,
0.005580368917435408,
-0.0184720940887928,
0.022229671478271484,
0.03850427642464638,
-0.00016616267384961247,
-0.05307778716087341,
0.00808244850486517,
0.03864024206995964,
0.03910418972373009,
-0.044199854135513306,
0.027458658441901207,
-0.0009358386159874499,
-0.0124531090259552,
0.008024570532143116,
-0.007923674769699574,
-0.010495397262275219,
-0.11518194526433945,
0.05588307976722717,
0.018722563982009888,
0.05816897377371788,
-0.05486031621694565,
-0.07638124376535416,
0.08594058454036713,
-0.04858583211898804,
-0.05089814215898514,
-0.024010835215449333,
0.07236222177743912,
0.0034235832281410694,
-0.02504311129450798,
-0.013268139213323593,
-0.05637930706143379,
0.03627891093492508,
-0.03115926682949066,
-0.021548684686422348,
0.013159951195120811,
-0.009038885124027729,
0.014677942730486393,
-0.07637984305620193,
-0.0324278362095356,
0.015822134912014008,
0.020115070044994354,
0.01807635836303234,
0.010129425674676895,
-0.005630915053188801,
0.01428629644215107,
0.02495317906141281,
-0.07704859972000122,
-0.07406063377857208,
0.01127312146127224,
-0.030202282592654228,
-0.029668623581528664,
-0.03543773666024208,
-0.01121525652706623,
0.03964320197701454,
0.0075644697062671185,
-0.036055151373147964,
0.05295189470052719,
0.0347122885286808,
0.02054731734097004,
0.010968591086566448,
-0.026066895574331284,
-0.020497526973485947,
-0.009277175180613995,
0.010838567279279232,
-0.03944149240851402,
0.03578300029039383,
0.00187536864541471,
0.02507266215980053,
-0.018288955092430115,
-0.06483671814203262,
-0.024970900267362595,
0.03315219283103943,
-0.016427064314484596,
-0.047511737793684006,
-0.029278790578246117,
-0.056438200175762177,
0.011865650303661823,
0.008631420321762562,
-0.03888338804244995,
0.05399859696626663,
-0.058248601853847504,
-0.07632540166378021,
0.04739200696349144,
0.012139111757278442,
-0.02103077620267868,
-0.06394878774881363,
0.02399197593331337,
-0.02104290947318077,
-0.056493185460567474,
-0.003185092704370618,
-0.029568353667855263,
-0.07286324352025986,
0.056272346526384354,
-0.03429948166012764,
-0.010959587059915066,
-0.008078372105956078,
0.05565382167696953,
-0.02332277037203312,
-0.00695217726752162,
0.045106105506420135,
-0.008374943397939205,
-0.0035033137537539005,
0.07234173268079758,
0.00410175696015358,
0.00973218958824873,
0.03156374767422676,
-0.005676407366991043,
-0.019710062071681023,
0.005225786939263344,
0.029806092381477356,
0.019214117899537086,
-0.035999447107315063,
-0.018162472173571587,
0.011321292258799076,
-0.01274881325662136,
0.04097505658864975,
-0.028715817257761955,
0.03833037242293358,
-0.03270503133535385,
-0.0064851632341742516,
0.019130324944853783,
0.027385476976633072,
0.04220650717616081,
-0.050409406423568726,
0.03506874665617943,
0.054917193949222565,
-0.01862407475709915,
0.04704319313168526,
-0.029750538989901543,
-0.015918510034680367,
0.04151364415884018,
-0.0034243694972246885,
0.004306767601519823,
0.026595331728458405,
0.02676687389612198,
0.044893499463796616,
-0.01516806147992611,
0.014190709218382835,
0.019747935235500336,
0.011634464375674725,
0.0074727400206029415,
-0.022334832698106766,
-0.017118366435170174,
0.036894556134939194,
-0.03694101423025131,
-0.018119340762495995,
0.004231746774166822,
0.008788184262812138,
0.007226741407066584,
-0.012744912877678871,
0.02451244927942753,
-0.01233403105288744,
0.012684566900134087,
0.012929682619869709,
0.00702453451231122,
0.015864666551351547,
-0.04041534289717674,
0.00691217789426446,
0.04183322563767433,
-0.0033944146707654,
-0.01186532061547041,
-0.07015780359506607,
0.028558604419231415,
-0.04663482680916786,
-0.025830285623669624,
0.03464328870177269,
-0.017587292939424515,
-0.013621193356812,
0.026349080726504326,
0.03729074448347092,
0.019641852006316185,
-0.025695128366351128,
0.01770872063934803,
0.002564962487667799,
0.04648711159825325,
0.019084574654698372,
-0.04546276479959488,
0.05259767174720764,
0.05803389102220535,
-0.0005660020397044718,
0.018072085455060005,
0.03001461923122406,
0.014793225564062595,
0.02287657931447029,
-0.11176697909832001,
0.030929643660783768,
-0.035371821373701096,
0.02477416768670082,
0.04407484456896782,
0.04103250801563263,
-0.04415660351514816,
-0.04308111220598221,
-0.0015033767558634281,
0.02993706986308098,
0.04215941205620766,
-0.028173500671982765,
-0.04060320183634758,
0.0012890049256384373,
0.024289404973387718,
-0.000667918473482132,
0.04363233223557472,
0.041258372366428375,
0.012726405635476112,
-0.01572517864406109,
-0.023049497976899147,
-0.0043540233746171,
0.05931925028562546,
0.019808871671557426,
0.08464442938566208,
0.005789283197373152,
-0.013896066695451736,
-0.006068910006433725,
-0.015378927811980247,
-0.0543135330080986,
-0.014896366745233536,
0.043631523847579956,
-0.009557120501995087,
0.03780614212155342,
0.0036625713109970093,
-0.011649686843156815,
-0.030873674899339676,
0.01577087864279747,
0.002392049413174391,
0.010102221742272377,
-0.04659662023186684,
0.02418932132422924,
0.010902747511863708,
0.012505931779742241,
-0.025077328085899353,
-0.044870223850011826,
0.0351475365459919,
0.02172252908349037,
0.028948258608579636,
0.039386942982673645,
-0.05797238275408745,
-0.019419889897108078,
0.03537268564105034,
-0.008798815310001373,
0.005828792694956064,
0.001437687431462109,
0.03468405455350876,
0.02856610342860222,
-0.04427409917116165,
-0.01822880282998085,
0.0006610591080971062,
0.020555375143885612,
-0.003260859753936529,
-0.06054042652249336,
0.05349519103765488,
0.054214976727962494,
0.035660065710544586,
0.05451761186122894,
-0.04369666054844856,
0.06773656606674194,
0.02374442107975483,
0.024169357493519783,
0.05956696346402168,
-0.0047348421066999435,
-0.010121865198016167,
0.029372001066803932,
0.030622677877545357,
-0.02947423607110977,
0.010960196144878864,
0.024967068806290627,
0.020346790552139282
] |
<p>Supposing there is an iron nail that is left to rust, if we compare the time it takes to rust with that of a magnetized iron nail, will there be any difference in the time of corrosion (assuming other environmental factors are constant)?</p> | g5551 | [
0.07839863002300262,
0.01805826462805271,
0.005920840427279472,
-0.004306394141167402,
0.05832470953464508,
0.05670689791440964,
0.03530944511294365,
0.024411965161561966,
-0.0386214479804039,
0.026648024097085,
-0.007899378426373005,
0.017049221321940422,
-0.0103678610175848,
-0.0625230222940445,
0.017393406480550766,
-0.015561919659376144,
0.0026951110921800137,
-0.0162716843187809,
-0.011231012642383575,
0.011625956743955612,
-0.005060750525444746,
0.024023041129112244,
-0.008115417324006557,
0.005592555273324251,
-0.02903297357261181,
0.01768152043223381,
-0.01645660027861595,
-0.006873621139675379,
0.007847096771001816,
0.021288881078362465,
-0.010186375118792057,
0.009207340888679028,
0.03593823313713074,
0.015702499076724052,
-0.03780897334218025,
-0.06740429252386093,
-0.037465158849954605,
0.029276249930262566,
0.06191772222518921,
0.015463967807590961,
0.010916967876255512,
-0.0010482440702617168,
0.044226206839084625,
-0.03241298720240593,
-0.028953038156032562,
-0.010592731647193432,
-0.002389922272413969,
-0.030466461554169655,
0.01601964794099331,
-0.003389999270439148,
-0.05907600373029709,
-0.007227547466754913,
0.03262265399098396,
0.026334380730986595,
0.02479792945086956,
-0.028593184426426888,
0.0277171079069376,
0.00773064186796546,
-0.03065929189324379,
0.03721006587147713,
0.04147108271718025,
-0.006574973929673433,
-0.05300161615014076,
-0.018657691776752472,
-0.04047057777643204,
-0.0006593965808860958,
-0.012078095227479935,
0.005896855145692825,
0.05613100901246071,
0.03291699290275574,
-0.0048690494149923325,
-0.015181942842900753,
-0.0715520977973938,
-0.009613528847694397,
-0.04182930290699005,
0.09286446869373322,
0.018904196098446846,
-0.021898329257965088,
0.05315970629453659,
0.05770881846547127,
-0.032573189586400986,
-0.02652435190975666,
-0.015465140342712402,
0.03259903937578201,
-0.02801406942307949,
0.03731830418109894,
0.008191666565835476,
0.035764239728450775,
0.017180820927023888,
0.052124984562397,
0.005465374328196049,
-0.03706111013889313,
0.014875240623950958,
0.028842005878686905,
0.03535373508930206,
0.03238644823431969,
-0.026910873129963875,
0.051947060972452164,
-0.036332182586193085,
0.03312157467007637,
-0.01072766724973917,
-0.08229529857635498,
-0.001417469815351069,
-0.057632870972156525,
0.006590337958186865,
0.0049940296448767185,
0.042211174964904785,
-0.0028809960931539536,
-0.052057135850191116,
0.0029822220094501972,
0.04922427982091904,
-0.0193598885089159,
-0.07101401686668396,
0.046136725693941116,
-0.01469102781265974,
-0.0020786563400179148,
0.01257589366286993,
-0.06219925731420517,
0.02562118135392666,
-0.01302756741642952,
0.03283854201436043,
-0.029367025941610336,
-0.01893259771168232,
0.05565834045410156,
0.03253931179642677,
0.019346678629517555,
0.016999389976263046,
0.016503985971212387,
0.012400282546877861,
0.03338522091507912,
-0.026176124811172485,
0.031202495098114014,
0.0440148301422596,
-0.02194182761013508,
-0.03756621852517128,
0.004331778734922409,
0.0012590463738888502,
0.03401480242609978,
-0.05169953405857086,
-0.0005762532236985862,
0.053318873047828674,
0.023911623284220695,
-0.023081865161657333,
0.006309425458312035,
-0.05391688644886017,
0.06077566742897034,
-0.005244523286819458,
0.04853181540966034,
0.027716292068362236,
0.05614273622632027,
-0.006634763907641172,
-0.005474199540913105,
-0.008084849454462528,
-0.011493204161524773,
-0.06411391496658325,
-0.026989726349711418,
-0.04946465790271759,
0.0014745705993846059,
0.020449602976441383,
0.028643455356359482,
0.008372305892407894,
-0.001771448296494782,
0.040377501398324966,
0.03433153033256531,
0.0185376163572073,
-0.029877502471208572,
0.036368053406476974,
0.005577163305133581,
-0.005906153470277786,
-0.0548473596572876,
-0.03652951866388321,
-0.007822921499609947,
-0.010805729776620865,
0.02511340193450451,
0.0550852008163929,
0.019510136917233467,
0.021230190992355347,
-0.08556590229272842,
0.0021213090512901545,
0.03423942252993584,
0.04154948517680168,
0.050099220126867294,
0.008991565555334091,
-0.019121170043945312,
-0.0038149203173816204,
-0.03157908469438553,
-0.04033797234296799,
-0.01314771268516779,
-0.060338590294122696,
0.02344171702861786,
-0.035662803798913956,
-0.011888682842254639,
-0.0028756556566804647,
0.05811554193496704,
-0.01814272813498974,
-0.03547229990363121,
-0.06514742225408554,
0.012474020011723042,
0.0024885693565011024,
-0.0043970877304673195,
-0.02283594384789467,
0.06484672427177429,
0.04364726319909096,
-0.026442641392350197,
-0.04948854073882103,
-0.016833538189530373,
0.01214805617928505,
-0.00740604056045413,
-0.005666274111717939,
0.011326936073601246,
-0.015609148889780045,
0.07195443660020828,
-0.02726193517446518,
0.009596551768481731,
-0.010714607313275337,
0.014956023544073105,
-0.021431148052215576,
0.10514739900827408,
-0.01639493741095066,
0.0536334402859211,
-0.029479095712304115,
-0.02717376872897148,
0.04390362277626991,
-0.004542016424238682,
0.025362925603985786,
-0.0441126711666584,
0.012954236008226871,
0.012321279384195805,
0.037971023470163345,
-0.01703115738928318,
0.03494677320122719,
0.01475528534501791,
0.022486640140414238,
-0.0625302642583847,
-0.06186477094888687,
0.018530558794736862,
0.06209162622690201,
0.0013989615254104137,
-0.0021053447853773832,
0.0022904176730662584,
0.00515518244355917,
-0.017179209738969803,
-0.031479813158512115,
0.06189294904470444,
0.024309424683451653,
-0.10656653344631195,
0.0012897043488919735,
0.05070772394537926,
0.023850731551647186,
0.004354719538241625,
0.01887660101056099,
0.031151412054896355,
-0.010245306417346,
0.014325957745313644,
-0.05792617425322533,
-0.04800363630056381,
-0.02169848047196865,
-0.015626132488250732,
-0.0593438595533371,
-0.01403939537703991,
-0.0012325524585321546,
-0.10039771348237991,
0.04043509438633919,
0.0014371610013768077,
-0.04116265848278999,
-0.034522902220487595,
-0.05631660297513008,
0.007511189207434654,
0.009085939265787601,
-0.03127170354127884,
-0.049064602702856064,
-0.011038883589208126,
0.001671543694101274,
0.03137994557619095,
-0.02697332575917244,
-0.032456282526254654,
0.0064688511192798615,
-0.00566465500742197,
-0.013394980691373348,
-0.026795176789164543,
-0.038710273802280426,
-0.04763807728886604,
-0.09394243359565735,
0.02591998316347599,
0.022174928337335587,
-0.0015444804448634386,
0.020677048712968826,
-0.02694738283753395,
-0.0007624498684890568,
0.014870340935885906,
-0.022350426763296127,
0.030882081016898155,
0.03511693701148033,
0.06056732311844826,
0.02583637833595276,
-0.00842279102653265,
0.015867074951529503,
-0.023606643080711365,
0.02357647754251957,
0.05787932500243187,
0.09755003452301025,
-0.035241514444351196,
0.006072778254747391,
0.0027511275839060545,
0.05928058177232742,
-0.03810451179742813,
-0.07775787264108658,
0.027065930888056755,
-0.0037620384246110916,
-0.04006076604127884,
-0.051291320472955704,
0.06409070640802383,
0.017328012734651566,
-0.0013077417388558388,
-0.03525269404053688,
-0.03375411406159401,
-0.02891339547932148,
-0.012243029661476612,
0.039983514696359634,
0.022742372006177902,
-0.028817351907491684,
-0.03201822564005852,
-0.00511840358376503,
-0.017860328778624535,
0.002805301221087575,
0.015283104032278061,
0.033149223774671555,
0.04055407643318176,
-0.04395262897014618,
0.14132565259933472,
0.025815527886152267,
0.0467522032558918,
-0.05197281762957573,
-0.02225894294679165,
-0.0693494901061058,
0.0057832938618958,
0.03694840148091316,
0.04791509360074997,
-0.017511537298560143,
0.02521253190934658,
0.05567745119333267,
0.007908296771347523,
-0.03705227002501488,
0.02388598956167698,
0.01840415969491005,
0.019506145268678665,
0.004585204180330038,
0.018662510439753532,
0.03141534700989723,
0.035592686384916306,
0.04144597426056862,
-0.04132441058754921,
0.020858855918049812,
0.01579323038458824,
0.0018591544358059764,
0.034253329038619995,
-0.018385043367743492,
0.05799382925033569,
0.00252549652941525,
-0.018615294247865677,
-0.0020558414980769157,
0.03356946259737015,
0.036423634737730026,
-0.0749480128288269,
0.000012631762729142793,
0.04736308753490448,
0.02223203144967556,
0.019422253593802452,
0.08209401369094849,
-0.007791172247380018,
-0.016733156517148018,
0.05620994791388512,
0.061717186123132706,
0.04046287387609482,
0.0008631274104118347,
0.02416771836578846,
0.014600603841245174,
0.029659058898687363,
-0.04383227229118347,
0.05227768421173096,
-0.02911144681274891,
0.03501623123884201,
-0.03727840632200241,
-0.0057751950807869434,
-0.017803801223635674,
-0.05188554525375366,
-0.009203528985381126,
0.03941621258854866,
-0.08195382356643677,
-0.024713007733225822,
-0.04363071918487549,
0.023564977571368217,
-0.0018931899685412645,
-0.01386768463999033,
0.02157493308186531,
0.040529925376176834,
0.024242859333753586,
0.008955083787441254,
0.03317924961447716,
-0.06038312613964081,
0.02318134531378746,
0.01702871359884739,
0.007033221423625946,
0.06749531626701355,
0.04681231454014778,
-0.034570738673210144,
0.05871352180838585,
0.018957095220685005,
-0.017789682373404503,
-0.05261895805597305,
-0.062330521643161774,
0.036811795085668564,
-0.016944490373134613,
0.06673132628202438,
-0.010474657639861107,
-0.009467081166803837,
0.0025890988763421774,
0.021323805674910545,
0.006203268654644489,
-0.033634744584560394,
-0.014187243767082691,
0.05391170457005501,
0.010202717036008835,
-0.06894432753324509,
0.03580483794212341,
-0.03981772065162659,
0.014317204244434834,
0.02199384942650795,
-0.0031615670304745436,
-0.058113399893045425,
0.04034413769841194,
0.0007314527174457908,
-0.0057351174764335155,
-0.04535789042711258,
0.00870401319116354,
0.06265651434659958,
-0.022301960736513138,
0.009572266601026058,
0.00878602173179388,
0.010371590033173561,
-0.020480073988437653,
0.08528876304626465,
0.0400504395365715,
0.0604025200009346,
-0.04795824736356735,
-0.004485446028411388,
-0.01208388339728117,
-0.08860157430171967,
-0.01092122495174408,
-0.03762596473097801,
-0.00038494812906719744,
0.04786277562379837,
-0.008589526638388634,
-0.028199762105941772,
-0.041877392679452896,
-0.023245759308338165,
-0.026882659643888474,
-0.025100499391555786,
0.030252570286393166,
0.05073080584406853,
-0.07289398461580276,
-0.020591918379068375,
-0.08314891904592514,
0.021423758938908577,
-0.044103384017944336,
-0.028161970898509026,
0.03483058139681816,
-0.005741936154663563,
-0.029062800109386444,
0.06807378679513931,
0.014715027995407581,
-0.033139247447252274,
0.07690126448869705,
0.03162577003240585,
0.07244956493377686,
-0.027758361771702766,
0.029511328786611557,
-0.031821027398109436,
0.03295604884624481,
-0.027869446203112602,
-0.05495321750640869,
-0.01884135603904724,
0.05189630761742592,
-0.008240185678005219,
0.027087850496172905,
-0.027020754292607307,
-0.07046578079462051,
0.001183045795187354,
-0.008363663218915462,
-0.01043614000082016,
0.03739127144217491,
0.041071683168411255,
0.01654469594359398,
-0.0036414540372788906,
-0.003007335588335991,
0.002654978772625327,
-0.04318363592028618,
0.0035288638900965452,
-0.0366174690425396,
-0.08158814162015915,
-0.0009532368858344853,
0.03847049921751022,
-0.0180510226637125,
0.004030967131257057,
-0.0038144555874168873,
0.06796985864639282,
0.060848817229270935,
-0.040624506771564484,
0.02814529649913311,
0.07896057516336441,
-0.04638880863785744,
-0.07186146080493927,
-0.03346046432852745,
0.009644178673624992,
0.023748211562633514,
-0.035262688994407654,
-0.017162486910820007,
0.05612330138683319,
0.005261722020804882,
-0.036803387105464935,
0.007486069109290838,
0.038027573376894,
0.05496135726571083,
-0.05179567635059357,
-0.041462287306785583,
0.016323192045092583,
0.002721296390518546,
-0.01627635769546032,
-0.05473772808909416,
-0.04325132817029953,
0.04675741866230965,
-0.008599565364420414,
0.018608052283525467,
-0.006309567950665951,
0.023238610476255417,
-0.0034572246950119734,
0.044422030448913574,
-0.0198347307741642,
-0.00568018713966012,
0.003160814754664898,
0.0025818722788244486,
-0.029124844819307327,
0.08037900179624557,
0.025639772415161133,
-0.043796878308057785,
0.0009696701308712363,
-0.020891228690743446,
0.018921755254268646,
-0.05757676810026169,
-0.06417814642190933,
-0.03657703101634979,
-0.00939854234457016,
-0.04151547700166702,
-0.011728945188224316,
-0.00560292974114418,
-0.00433985935524106,
0.05187620222568512,
-0.01049693301320076,
0.014892780221998692,
-0.029716892167925835,
0.03368212282657623,
0.04948833957314491,
-0.001059578382410109,
-0.025957582518458366,
0.02179962955415249,
-0.018828097730875015,
-0.044779885560274124,
0.012754854746162891,
0.06461212784051895,
0.03818860650062561,
0.01399291679263115,
-0.04942425712943077,
-0.023629456758499146,
-0.018587416037917137,
-0.024681376293301582,
-0.04705450311303139,
-0.05861198529601097,
0.01413983665406704,
0.022808196023106575,
-0.00029688075301237404,
0.042336609214544296,
0.006917881779372692,
-0.07160672545433044,
0.057148270308971405,
0.018470464274287224,
-0.03401647508144379,
-0.04692106693983078,
-0.037319596856832504,
0.03736623004078865,
0.04429916664958,
-0.03104289248585701,
0.019990967586636543,
0.013984746299684048,
0.011052372865378857,
-0.0037546034436672926,
0.02816939726471901,
-0.036309368908405304,
-0.0163019560277462,
0.055989254266023636,
0.028586912900209427,
-0.046592727303504944,
0.0021461204160004854,
0.014008443802595139,
0.005954876076430082,
0.020683081820607185,
-0.009748905897140503,
-0.010157951153814793,
0.05639202892780304,
0.020048383623361588,
-0.01512659527361393,
-0.009752631187438965,
0.004233780317008495,
-0.03882381319999695,
0.0378853864967823,
-0.03368066996335983,
-0.011391411535441875,
0.01903156377375126,
0.0018987524090334773,
-0.050819262862205505,
0.048672839999198914,
-0.026085035875439644,
-0.05939630791544914,
-0.015203991904854774,
-0.0628778263926506,
0.021591126918792725,
0.05353008210659027,
-0.0021965799387544394,
-0.011387216858565807,
-0.03778797388076782,
0.0039849248714745045,
-0.021454500034451485,
-0.07918623089790344,
-0.05161261186003685,
0.01000943873077631,
-0.0011290173279121518,
-0.019268792122602463,
0.010114685632288456,
-0.03006843663752079,
0.03145435079932213,
0.0312679186463356,
0.03862868621945381,
-0.05520712956786156,
-0.026292743161320686,
0.02545701526105404,
-0.03359954059123993,
0.028388146311044693,
0.0589267760515213,
0.006845980416983366,
-0.06122177466750145,
0.0462641604244709,
-0.0234164260327816,
0.026093680411577225,
-0.028087962418794632,
0.0026014666073024273,
0.012129554525017738,
0.008970900438725948,
-0.018251776695251465,
-0.007570771966129541,
0.02408280037343502,
-0.010174018330872059,
-0.04597971960902214,
-0.00567563297227025,
-0.04138389974832535,
-0.010356411337852478,
0.005604615900665522,
-0.005428294185549021,
0.01866488717496395,
-0.051399365067481995,
0.007002354133874178,
0.01374830026179552,
-0.005129792727530003,
0.0040173958986997604,
0.0649152398109436,
-0.018549246713519096,
0.04420142620801926,
0.04342484101653099,
-0.02667396515607834,
-0.07128144055604935,
0.017186453565955162,
-0.028081325814127922,
-0.006662887521088123,
-0.03162062540650368,
0.03791528567671776,
-0.03797587379813194,
0.01598985306918621,
0.01676119863986969,
-0.045175909996032715,
-0.0012010118225589395,
0.048354633152484894,
-0.029261363670229912,
0.024972213432192802,
-0.0008644970366731286,
0.02910701557993889,
0.0436343289911747,
-0.0199538916349411,
-0.019614698365330696,
0.030596263706684113,
0.03700895234942436,
0.05099496990442276,
0.008270706050097942,
-0.005202832166105509,
0.04450394585728645,
0.039076369255781174,
0.014285356737673283,
-0.04282230883836746,
-0.005125741474330425,
-0.1136435866355896,
-0.02550416998565197,
-0.05679802596569061,
-0.014603671617805958,
0.06203043460845947,
0.05492506921291351,
-0.025653205811977386,
-0.03320949524641037,
0.02420050837099552,
-0.05494021624326706,
-0.015422449447214603,
-0.04812541604042053,
-0.05019666999578476,
0.024392737075686455,
-0.07706397771835327,
-0.05331035330891609,
-0.008206235244870186,
-0.02509062923491001,
-0.014272703789174557,
0.054157406091690063,
-0.004283362999558449,
-0.025688057765364647,
-0.0032571444753557444,
0.0013607144355773926,
0.05548730865120888,
-0.024260086938738823,
-0.04849804565310478,
0.0028725808952003717,
0.0015351888723671436,
-0.05176211893558502,
0.01989421620965004,
0.030968304723501205,
-0.0462346225976944,
-0.010519437491893768,
-0.011051306501030922,
-0.02069992385804653,
-0.027261488139629364,
-0.003094664542004466,
0.04784826189279556,
0.06157331168651581,
-0.04153567925095558,
0.017808696255087852,
-0.016062647104263306,
0.023036399856209755,
-0.04229222983121872,
0.04715096578001976,
-0.020757142454385757,
0.01571180485188961,
0.022453105077147484,
-0.01388644054532051,
-0.02233288623392582,
0.03402670472860336,
0.022401778027415276,
-0.009814003482460976,
-0.03622347116470337,
0.030341779813170433,
-0.06644213944673538,
0.0033624509815126657,
0.012172131799161434,
-0.008200202137231827,
-0.028492053970694542,
-0.020113524049520493
] |
<p>Well I have a couple of questions regarding Black holes so here they are,</p>
<p>1.Shouldn't they be called black spheres?(holes are in 2D right?)</p>
<p>2.What will happen if black holes collide?(If they can)</p>
<p>3.Will they have the "information" of what they have eaten?</p>
<p>4.What's a white hole?
(i'm only 16, so sorry if these seem stupid)</p> | g5552 | [
-0.016713257879018784,
0.0018696420593187213,
0.022003818303346634,
-0.022162269800901413,
0.06642527133226395,
0.04191367328166962,
-0.028436750173568726,
-0.023437023162841797,
-0.02105918526649475,
0.026133716106414795,
0.008929131552577019,
0.02625441923737526,
0.030181940644979477,
-0.014967980794608593,
-0.07233501225709915,
-0.03404315188527107,
-0.020397508516907692,
-0.02545020543038845,
-0.009670176543295383,
-0.04086603596806526,
0.05326027423143387,
-0.023137914016842842,
-0.01628357730805874,
-0.03905574977397919,
-0.029244443401694298,
-0.02339581586420536,
-0.018550604581832886,
0.022540967911481857,
-0.09428149461746216,
-0.03862493485212326,
0.005126877222210169,
0.04088831692934036,
0.03975914791226387,
-0.00743574695661664,
0.0003788337344303727,
-0.006059757899492979,
0.045504555106163025,
-0.06963696330785751,
-0.027353979647159576,
-0.02130727842450142,
0.021343285217881203,
-0.010928956791758537,
-0.002877070102840662,
-0.0010198135860264301,
0.0083279674872756,
-0.0020957307424396276,
-0.016070622950792313,
0.017006179317831993,
0.06327280402183533,
0.015616984106600285,
0.045688431710004807,
0.03891311213374138,
0.0627039298415184,
0.002155208494514227,
-0.005405541975051165,
0.016577759757637978,
0.034708619117736816,
-0.019977644085884094,
0.09631025791168213,
0.05098908767104149,
-0.05325869470834732,
-0.014774631708860397,
-0.023976154625415802,
0.0031855502165853977,
0.058670345693826675,
-0.06604216992855072,
-0.07244308292865753,
0.04105764627456665,
-0.038308143615722656,
0.0274036955088377,
0.03281915932893753,
0.028444714844226837,
0.023858439177274704,
0.019857291132211685,
-0.011625661514699459,
0.05665848031640053,
0.01739819347858429,
0.012675144709646702,
0.016323272138834,
-0.011325054802000523,
-0.022406889125704765,
0.012363581918179989,
0.01556878350675106,
-0.03355642408132553,
0.0669391006231308,
0.013294853270053864,
-0.01815352961421013,
-0.05243181437253952,
-0.03356435149908066,
0.01564055122435093,
0.0418296717107296,
-0.0401139035820961,
0.017874915152788162,
0.04400581121444702,
0.029629206284880638,
0.04334436357021332,
-0.011196811683475971,
0.018452055752277374,
0.010841665789484978,
-0.008824052289128304,
-0.05229510739445686,
0.028003092855215073,
0.03517526760697365,
0.004917360842227936,
0.03647151589393616,
-0.022176401689648628,
0.01949567347764969,
0.054981499910354614,
0.06496110558509827,
0.04592480883002281,
-0.008656742982566357,
-0.06171751394867897,
-0.0010236578527837992,
-0.01517636887729168,
0.0016976912738755345,
0.01433549728244543,
0.030904162675142288,
0.010091404430568218,
0.017382176592946053,
0.08931221067905426,
0.031220827251672745,
0.026902733370661736,
0.058414846658706665,
-0.0036548739299178123,
0.039580345153808594,
-0.019338345155119896,
0.030450809746980667,
-0.032671406865119934,
0.032438501715660095,
-0.020468980073928833,
0.0007765761693008244,
-0.006094310898333788,
0.008670368231832981,
0.04743363335728645,
-0.021470515057444572,
0.02344624698162079,
-0.0007084280950948596,
0.017643781378865242,
-0.0048987045884132385,
-0.023558635264635086,
-0.020559847354888916,
-0.02065296284854412,
-0.01874038390815258,
0.032574187964200974,
-0.021723056212067604,
-0.03380688279867172,
0.014594068750739098,
-0.05690262094140053,
0.027547521516680717,
0.04062245041131973,
-0.014377995394170284,
0.0691329762339592,
-0.00971295591443777,
-0.03748645260930061,
0.006663402076810598,
0.06372380256652832,
0.018513094633817673,
0.024340525269508362,
0.023007910698652267,
0.004154111258685589,
0.04972752556204796,
0.010671149007976055,
0.05878305435180664,
0.11482621729373932,
-0.051906879991292953,
-0.021221669390797615,
0.007407042197883129,
-0.052184369415044785,
0.05044984817504883,
0.022224185988307,
0.014223339967429638,
0.04116970673203468,
-0.01339979562908411,
0.08439179509878159,
-0.033125028014183044,
-0.026129690930247307,
-0.02872633934020996,
-0.023137500509619713,
0.039743758738040924,
-0.028259946033358574,
-0.03335999324917793,
-0.03984849154949188,
0.0025937508326023817,
0.008122324012219906,
0.07080540060997009,
-0.03770483285188675,
0.0034519508481025696,
0.061346881091594696,
0.015189535915851593,
0.02512488141655922,
-0.09954123944044113,
-0.061911266297101974,
0.057428378611803055,
0.048192866146564484,
0.05153829604387283,
-0.010176445357501507,
0.0733841136097908,
-0.005174354650080204,
0.00726157333701849,
0.01522847916930914,
0.03214012831449509,
0.04484064504504204,
-0.007733841892331839,
0.03389320895075798,
0.03660554811358452,
0.04820571839809418,
-0.00593276834115386,
0.005993148311972618,
-0.019525909796357155,
0.029358034953475,
0.024186430498957634,
-0.05571109056472778,
0.035422272980213165,
0.01541015412658453,
-0.023603877052664757,
0.06370216608047485,
-0.03207419067621231,
0.032303012907505035,
-0.029193278402090073,
-0.02483385056257248,
-0.020327558740973473,
-0.020289752632379532,
0.009872579015791416,
-0.11239437758922577,
0.032573260366916656,
0.04163680598139763,
-0.0771632045507431,
-0.0461571104824543,
0.014549432322382927,
0.013715303502976894,
-0.04586639627814293,
-0.025274479761719704,
0.0894826352596283,
-0.00803611520677805,
0.03701282665133476,
0.06922748684883118,
-0.01664230413734913,
-0.023678382858633995,
-0.010206799954175949,
-0.012017032131552696,
0.05613593012094498,
-0.008145795203745365,
0.026800747960805893,
-0.04754054546356201,
0.06646943837404251,
-0.04631110280752182,
0.06231605261564255,
-0.02816762588918209,
-0.049738433212041855,
0.06345725804567337,
0.02957967109978199,
-0.019245384261012077,
-0.004512866493314505,
0.03478461503982544,
-0.02074316330254078,
-0.025385674089193344,
0.03601660579442978,
0.07081576436758041,
-0.027119919657707214,
-0.03410695120692253,
-0.0028725233860313892,
-0.005353948567062616,
-0.05512567237019539,
0.016187092289328575,
-0.05531599000096321,
-0.04900917038321495,
-0.04643416032195091,
0.010226809419691563,
-0.01377114187926054,
0.0066178347915410995,
-0.04188854619860649,
-0.05540517717599869,
0.028443478047847748,
0.014749886468052864,
0.01459730789065361,
-0.00816223956644535,
-0.03143969550728798,
0.00850167591124773,
0.04091246798634529,
-0.018550751730799675,
0.0034804667811840773,
0.0612684041261673,
-0.038980815559625626,
-0.011290204711258411,
0.06576695293188095,
-0.017300568521022797,
-0.05797530338168144,
0.03987111523747444,
-0.04311329871416092,
-0.014389695599675179,
-0.01730610430240631,
0.021065281704068184,
0.035203833132982254,
0.05995328724384308,
0.0230982955545187,
0.007997720502316952,
-0.016733698546886444,
0.007832727394998074,
-0.04980802163481712,
0.03015492670238018,
-0.02988887019455433,
0.010655445978045464,
0.007182389032095671,
0.04621760547161102,
0.013896254822611809,
0.02353161759674549,
-0.02112000435590744,
0.005512527655810118,
0.009866970591247082,
-0.05773972347378731,
0.011163134127855301,
-0.01585575006902218,
0.012245197780430317,
0.06078248471021652,
0.008024310693144798,
0.017868157476186752,
0.008321724832057953,
0.013694878667593002,
0.004083953332155943,
-0.022687621414661407,
-0.0007472569704987109,
0.018870817497372627,
0.01468005683273077,
-0.05529700219631195,
0.011088590137660503,
0.07481255382299423,
0.020520245656371117,
-0.09015461802482605,
-0.01964079961180687,
0.010265749879181385,
-0.01210909802466631,
0.007523560430854559,
-0.0372149832546711,
0.004923625383526087,
0.00551752420142293,
0.013493304140865803,
-0.034763943403959274,
-0.03242199867963791,
0.0355081707239151,
-0.015077521093189716,
0.04353829845786095,
-0.054924383759498596,
0.004617674276232719,
-0.013964631594717503,
-0.0028018669690936804,
-0.04354051873087883,
0.002789774676784873,
-0.06465815007686615,
-0.0021856678649783134,
-0.03745054081082344,
0.042745862156152725,
-0.05050520971417427,
0.05016934126615524,
-0.023840228095650673,
0.020721912384033203,
0.035156697034835815,
-0.025578178465366364,
-0.01002336386591196,
0.0019754928071051836,
0.015527714975178242,
0.0014982994180172682,
-0.013950101099908352,
0.011722588911652565,
0.014257267117500305,
-0.04237527400255203,
-0.07462016493082047,
-0.019177688285708427,
-0.03527085483074188,
0.016316035762429237,
-0.02669089287519455,
0.011506082490086555,
0.08156652748584747,
-0.010411109775304794,
0.0035510973539203405,
0.041228488087654114,
-0.03957587480545044,
0.002089503686875105,
0.013452033512294292,
0.02968321181833744,
-0.039225365966558456,
-0.01342514157295227,
-0.025578906759619713,
0.014312892220914364,
0.04415186867117882,
0.0032615349628031254,
0.01618434116244316,
-0.005851664114743471,
-0.05550982058048248,
-0.041088465601205826,
-0.09311427175998688,
0.019146302714943886,
-0.024975890293717384,
-0.018885672092437744,
-0.0820954442024231,
0.040325064212083817,
-0.011151507496833801,
-0.029794536530971527,
-0.023993806913495064,
-0.014128925278782845,
-0.013966912403702736,
0.02550087310373783,
0.04037518426775932,
0.034251000732183456,
-0.005483159329742193,
0.04819358140230179,
0.010543985292315483,
-0.010950648225843906,
-0.0057869539596140385,
0.033634353429079056,
-0.007902872748672962,
0.0496382936835289,
0.05729788541793823,
0.03226030617952347,
-0.005524730309844017,
0.027129363268613815,
-0.017561854794621468,
-0.02537730149924755,
-0.00918724574148655,
-0.057235103100538254,
-0.012882210314273834,
0.019412508234381676,
-0.04717351496219635,
0.0032791977282613516,
-0.01197749376296997,
0.0009347746963612735,
-0.024640705436468124,
0.0015997982118278742,
-0.03852922096848488,
-0.02582227624952793,
0.030768945813179016,
0.039465777575969696,
-0.006235873326659203,
-0.019984526559710503,
-0.007841509766876698,
-0.06288536638021469,
0.024907249957323074,
-0.043867792934179306,
-0.012345051392912865,
-0.02018928900361061,
0.003961979877203703,
0.03728882595896721,
0.023657890036702156,
0.0110971350222826,
-0.07017069309949875,
0.024143224582076073,
0.04975742846727371,
-0.04018014296889305,
0.04091419279575348,
0.028188364580273628,
0.021704860031604767,
0.0007937521440908313,
-0.015239834785461426,
0.0062767937779426575,
-0.0978834331035614,
0.005086285527795553,
-0.012919925153255463,
0.006451091263443232,
0.030819155275821686,
-0.07218410819768906,
0.014693020842969418,
-0.06728120893239975,
-0.04869328439235687,
0.029205577448010445,
-0.01979256421327591,
0.0006371001363731921,
-0.05512089654803276,
-0.020408162847161293,
-0.0407879576086998,
-0.029749352484941483,
-0.014835059642791748,
-0.09465783834457397,
-0.010941672138869762,
-0.016783028841018677,
0.029039230197668076,
-0.03733982518315315,
0.00569685734808445,
-0.05913401395082474,
-0.02989736944437027,
0.05783911794424057,
0.003279404016211629,
0.027352171018719673,
-0.020716313272714615,
0.004313609562814236,
0.0012020808644592762,
0.0031835236586630344,
0.02404754050076008,
-0.0034006997011601925,
0.03981444984674454,
0.02980276197195053,
0.040444131940603256,
-0.02118578925728798,
-0.02714131958782673,
-0.02388428896665573,
0.038291651755571365,
-0.09007854759693146,
-0.03233766183257103,
0.002023868728429079,
0.009994959458708763,
-0.00026116720982827246,
0.06304048001766205,
-0.052370455116033554,
-0.02929316647350788,
0.03027588501572609,
-0.015476301312446594,
0.004253784194588661,
0.06942782551050186,
0.025841083377599716,
-0.032113879919052124,
0.038716480135917664,
0.033692728728055954,
-0.009063467383384705,
0.02283341810107231,
-0.025476135313510895,
0.06958535313606262,
0.0033259436022490263,
-0.04601220414042473,
0.024678057059645653,
0.006333682686090469,
-0.012480085715651512,
0.052160006016492844,
-0.02643352374434471,
-0.005776643753051758,
0.014657877385616302,
0.04441524296998978,
0.013774980790913105,
-0.013302031904459,
-0.02146603725850582,
-0.03886997699737549,
0.05669276788830757,
-0.010978654026985168,
0.014347580261528492,
-0.03806924447417259,
0.01628957688808441,
-0.02964669093489647,
-0.03928769752383232,
-0.007539077196270227,
-0.01039784587919712,
-0.016348687931895256,
0.08801804482936859,
-0.019684690982103348,
-0.035756126046180725,
0.03339909389615059,
-0.030519532039761543,
0.06302600353956223,
0.029234372079372406,
-0.03497471287846565,
0.013938537798821926,
0.026450857520103455,
-0.002000398701056838,
0.024632617831230164,
-0.07582566142082214,
0.01882278360426426,
0.024181047454476357,
0.018289100378751755,
-0.03581419587135315,
0.015609080903232098,
-0.001303769531659782,
-0.04215242341160774,
0.009394618682563305,
-0.04331798851490021,
0.03533200919628143,
0.016651557758450508,
-0.07619933784008026,
-0.038734983652830124,
-0.022564085200428963,
-0.027558984234929085,
-0.001289845211431384,
0.010413218289613724,
0.05725117772817612,
-0.0019284049049019814,
-0.023380326107144356,
0.007587905041873455,
0.011984665878117085,
-0.007763911038637161,
-0.0032032106537371874,
-0.021013783290982246,
0.00714135030284524,
0.05883879214525223,
0.020243044942617416,
-0.04215598106384277,
0.017696989700198174,
0.005373058374971151,
0.05543716996908188,
-0.04062512889504433,
-0.004394973162561655,
0.04890550673007965,
0.04900116100907326,
0.024523040279746056,
0.010935554280877113,
-0.04734859615564346,
0.025171447545289993,
0.016817623749375343,
0.09195198118686676,
-0.01710934191942215,
-0.029488885775208473,
-0.012920125387609005,
0.016723226755857468,
0.009915787726640701,
-0.03575229272246361,
-0.06523392349481583,
-0.028575384989380836,
0.02641037292778492,
0.018646297976374626,
0.03236224874854088,
-0.02988879755139351,
-0.01925617642700672,
-0.08006463199853897,
-0.03153130039572716,
0.025765089318156242,
0.02704625204205513,
0.013644558377563953,
0.022331153973937035,
-0.025499233976006508,
0.02699238620698452,
-0.023685775697231293,
-0.042674534022808075,
-0.015823643654584885,
-0.09034641832113266,
0.04844197630882263,
-0.054504960775375366,
0.013407647609710693,
0.009569958783686161,
-0.06776025146245956,
-0.0669199600815773,
0.009768812917172909,
0.02583210915327072,
-0.01701163500547409,
0.04817042872309685,
0.045658789575099945,
0.040698546916246414,
0.009166756644845009,
-0.02101205848157406,
0.0313245952129364,
0.0278114452958107,
0.00027934176614508033,
0.04252728819847107,
-0.006777128670364618,
0.0303877592086792,
-0.03808438777923584,
0.017397286370396614,
0.06371665745973587,
-0.002562781563028693,
0.02252577431499958,
0.08590857684612274,
0.03581888601183891,
0.04146900773048401,
0.017297467216849327,
-0.02167327329516411,
-0.0625530406832695,
-0.006624210625886917,
-0.014548342674970627,
-0.030941125005483627,
-0.018101397901773453,
-0.01344734150916338,
-0.048073675483465195,
-0.04490078240633011,
-0.028526395559310913,
0.004629853181540966,
0.0099867545068264,
0.03229629248380661,
0.011292598210275173,
0.024220800027251244,
-0.12169044464826584,
-0.029855743050575256,
-0.0319075770676136,
-0.0012282098177820444,
0.04376060888171196,
-0.0018066078191623092,
-0.03165854513645172,
-0.035588208585977554,
-0.05956145375967026,
-0.03089102916419506,
-0.06350519508123398,
-0.0024604930076748133,
-0.030597541481256485,
-0.058091334998607635,
-0.004934325814247131,
0.044677019119262695,
0.07551351189613342,
0.03240020573139191,
0.10849006474018097,
-0.004697499331086874,
0.007102626841515303,
0.03309580311179161,
-0.058853596448898315,
0.025883758440613747,
-0.03516845405101776,
0.0025728850159794092,
0.0012513876426964998,
0.026012279093265533,
0.0015010138740763068,
-0.04326529800891876,
-0.020275570452213287,
-0.02553442493081093,
-0.030185410752892494,
-0.06209748983383179,
-0.0008038987871259451,
0.06298097223043442,
-0.06560227274894714,
-0.025344939902424812,
0.07029561698436737,
-0.03905070200562477,
-0.03879217430949211,
-0.012863785028457642,
-0.00949488952755928,
-0.0011729756370186806,
0.006483658216893673,
0.00690183462575078,
-0.033994026482105255,
0.020742522552609444,
0.022898508235812187,
0.0410144217312336,
0.013739538379013538,
-0.00998629629611969,
-0.06741698086261749,
-0.05122444033622742,
0.007213754579424858,
-0.003044926794245839,
0.010673502460122108,
-0.04557671770453453,
0.02679075486958027,
0.009741014800965786,
-0.015912435948848724,
0.006957137957215309,
-0.02628808654844761,
-0.012026873417198658,
0.00431834626942873,
0.029214153066277504,
-0.04013204947113991,
-0.0051827761344611645,
-0.0626746118068695,
-0.003147493116557598,
-0.02575041726231575,
0.007631800603121519,
0.007331837434321642,
0.037367548793554306,
-0.005380807910114527,
0.005331479944288731,
-0.04851965233683586,
0.010410775430500507,
0.025453990325331688,
-0.014267420396208763,
-0.01575140282511711,
-0.038675617426633835,
-0.021104557439684868,
-0.048048850148916245,
0.013747606426477432,
0.04917660355567932,
0.05935290455818176,
0.0246354378759861,
0.05054127797484398,
0.0023306680377572775,
0.03106192871928215,
0.027841052040457726,
0.011304263025522232,
-0.039200812578201294,
-0.03520122915506363,
0.004613182973116636,
-0.03503066673874855,
-0.022675497457385063,
-0.0025084444787353277,
0.011883994564414024,
-0.015177075751125813,
0.04831782728433609,
-0.040103621780872345,
-0.0019008927047252655,
-0.002843104302883148,
0.008032484911382198
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.