question
stringlengths 37
38.8k
| group_id
stringlengths 2
6
| sentence_embeddings
listlengths 768
768
|
|---|---|---|
<ol>
<li><p><strong>Free field theory:</strong> Why is it said that different Fourier modes in case of a free field (say, real Klein-Gordon field) are independent of each other?</p></li>
<li><p><strong>Interacting field theory:</strong> How exactly does the addition of non-linear term in the Lagrangian make the Fourier modes couple to each other?</p></li>
</ol>
|
g2438
|
[
0.034823961555957794,
-0.018990637734532356,
0.00528687285259366,
-0.01093760784715414,
0.045779451727867126,
0.010424205102026463,
-0.023967335000634193,
0.013681458309292793,
-0.004355518613010645,
-0.057407572865486145,
-0.06375888735055923,
-0.03096391074359417,
0.012570954859256744,
0.04837123304605484,
0.011958829127252102,
-0.013112002052366734,
0.06951534003019333,
0.08386354148387909,
0.0329926460981369,
-0.003653238294646144,
-0.04970332235097885,
-0.0011387041304260492,
0.0366533063352108,
-0.030885402113199234,
-0.01766059547662735,
-0.05245450511574745,
0.03883238509297371,
-0.028845032677054405,
0.004547100514173508,
-0.04748748242855072,
-0.03257933631539345,
0.01853061281144619,
0.023030005395412445,
-0.03230024501681328,
-0.049913760274648666,
-0.03263623267412186,
0.03810674697160721,
0.022186003625392914,
0.004887379240244627,
0.047063734382390976,
-0.015213530510663986,
0.05431964993476868,
-0.03657462075352669,
-0.013199403882026672,
-0.040121279656887054,
-0.03620895370841026,
-0.03065331093966961,
0.028928767889738083,
0.01445602998137474,
0.00046276315697468817,
-0.01942724734544754,
0.02880818583071232,
0.06144195795059204,
-0.040560681372880936,
0.017098229378461838,
0.022888390347361565,
-0.006682145409286022,
0.02837079018354416,
0.005572243127971888,
-0.011670802719891071,
-0.034400131553411484,
-0.024790337309241295,
0.05909348279237747,
0.03265364095568657,
0.03816688433289528,
0.012606441974639893,
-0.04550187289714813,
-0.04797152057290077,
-0.008914987556636333,
-0.03367631509900093,
-0.02884789928793907,
-0.044675204902887344,
-0.021917011588811874,
-0.007567825261503458,
0.019538497552275658,
0.01286992710083723,
-0.009825946763157845,
0.025502702221274376,
-0.02394825965166092,
-0.0274189542979002,
-0.01151074655354023,
-0.04510029777884483,
-0.03228364139795303,
-0.027364226058125496,
0.023224996402859688,
-0.03746828809380531,
0.04539547115564346,
0.0006277969223447144,
-0.0017667635111138225,
0.04745522513985634,
0.06396278738975525,
0.03634677082300186,
0.026805773377418518,
0.037941884249448776,
-0.07296264171600342,
0.017231348901987076,
-0.051015835255384445,
0.020857524126768112,
0.005052244756370783,
-0.03837182745337486,
-0.018997671082615852,
0.0696285143494606,
0.01671602949500084,
-0.02291111648082733,
-0.007547484245151281,
0.009783844463527203,
0.015943355858325958,
0.04471263289451599,
-0.025053346529603004,
0.004168120678514242,
-0.043713804334402084,
0.032715216279029846,
-0.025862934067845345,
-0.04842890053987503,
-0.007919729687273502,
-0.044305458664894104,
0.05353395268321037,
-0.049994878470897675,
0.04860953614115715,
0.05251510813832283,
-0.010967064648866653,
0.004951374605298042,
0.026937536895275116,
0.007063291501253843,
-0.038548778742551804,
-0.03337542712688446,
0.07475446164608002,
-0.03377034515142441,
0.03433925658464432,
-0.008886514231562614,
0.03700842708349228,
-0.01833544485270977,
-0.018261875957250595,
0.04954003542661667,
0.057156406342983246,
0.0031235332135111094,
0.009238023310899734,
-0.008782677352428436,
-0.03655637800693512,
-0.02312360517680645,
-0.022470468655228615,
-0.07012087106704712,
0.021449916064739227,
-0.09491094946861267,
0.026874210685491562,
-0.01649504341185093,
0.0405886135995388,
-0.05996289104223251,
-0.024797774851322174,
0.0033025103621184826,
0.03805612027645111,
0.07365284860134125,
0.02802879549562931,
0.004949233494699001,
-0.03923102840781212,
0.0004056743055116385,
0.04671810194849968,
-0.006435723043978214,
0.03342811018228531,
-0.07449541985988617,
0.05933520197868347,
-0.05143134668469429,
0.03572160005569458,
0.02483631670475006,
-0.025211360305547714,
0.03530719131231308,
0.048797380179166794,
-0.10513222962617874,
0.01791774481534958,
0.006264266557991505,
-0.06008955091238022,
0.0014161509461700916,
0.007641167379915714,
0.06825634092092514,
0.04004818946123123,
0.06582804024219513,
-0.01924673654139042,
-0.05351640656590462,
0.01614244095981121,
0.04931797832250595,
-0.02432546392083168,
0.0006449128850363195,
-0.011109811253845692,
-0.027935562655329704,
-0.009242648258805275,
0.03434186801314354,
-0.010579121299088001,
0.03003879263997078,
-0.057902056723833084,
0.033415019512176514,
-0.016502754762768745,
0.03787645325064659,
-0.03198359161615372,
0.011352293193340302,
-0.01664368063211441,
0.016543153673410416,
0.009277350269258022,
-0.011603526771068573,
-0.027487069368362427,
-0.03692522644996643,
-0.03175574913620949,
0.027711935341358185,
0.009778083302080631,
0.01839986816048622,
0.00457812799140811,
-0.00269104540348053,
-0.035503312945365906,
0.012947442010045052,
0.03218534588813782,
-0.03106098249554634,
-0.0011664032936096191,
0.008937145583331585,
-0.050716862082481384,
0.014847327955067158,
0.057686664164066315,
-0.021024832502007484,
0.04339408501982689,
-0.05402950569987297,
-0.029989024624228477,
0.03811511769890785,
0.04056023806333542,
0.04016828164458275,
0.05685900151729584,
0.006291618570685387,
0.02799123339354992,
-0.030940085649490356,
-0.016090232878923416,
0.04016834869980812,
-0.061426207423210144,
0.017244067043066025,
-0.07263992726802826,
-0.12098931521177292,
0.003682006848976016,
0.01702382229268551,
0.023632867261767387,
0.026609061285853386,
0.014384801499545574,
0.022851653397083282,
-0.050943031907081604,
0.04450492933392525,
0.030406786128878593,
-0.019730551168322563,
-0.004108332097530365,
-0.0004865127266384661,
-0.028607584536075592,
0.0009535239660181105,
0.061938539147377014,
-0.010984010063111782,
-0.08213555812835693,
0.005539600737392902,
-0.01712014153599739,
0.027887308970093727,
-0.04108406975865364,
0.031196916475892067,
-0.01819024048745632,
0.007805479224771261,
0.03343907743692398,
0.0313769169151783,
-0.10684917867183685,
-0.013298514299094677,
0.058415621519088745,
-0.01370545756071806,
-0.022403864189982414,
-0.006482651922851801,
-0.06943786144256592,
-0.010640624910593033,
-0.004105991218239069,
0.03972332179546356,
-0.0497732050716877,
-0.04345951974391937,
-0.015501638874411583,
0.0778714045882225,
0.010149305686354637,
0.02446274645626545,
0.0028084053192287683,
0.008185901679098606,
0.015542568638920784,
0.006628149189054966,
-0.0009863043669611216,
-0.024954689666628838,
0.01613045483827591,
-0.014142744243144989,
-0.02013850398361683,
0.0014642365276813507,
0.04713787883520126,
-0.07650856673717499,
0.03628646582365036,
-0.007786646485328674,
-0.036502063274383545,
-0.006736604496836662,
0.028325064107775688,
0.01884414255619049,
-0.043662428855895996,
-0.03650575503706932,
-0.08424919843673706,
0.018350781872868538,
0.007379865739494562,
-0.06416481733322144,
-0.014009438455104828,
0.0026702014729380608,
0.008537357673048973,
0.0030113039538264275,
-0.016270164400339127,
0.013668837025761604,
-0.015931319445371628,
0.009659338742494583,
-0.02821572683751583,
-0.042815014719963074,
-0.03678128495812416,
-0.02768835611641407,
-0.0026585981249809265,
0.03735734522342682,
0.004620490595698357,
-0.034617941826581955,
-0.045838870108127594,
0.01947924681007862,
0.030752534046769142,
0.03647293895483017,
0.05890487879514694,
-0.01837080344557762,
-0.07354232668876648,
-0.04111494496464729,
-0.03103288821876049,
-0.03442898020148277,
-0.0042882622219622135,
-0.007753260433673859,
-0.019902188330888748,
-0.04984261840581894,
-0.046576254069805145,
-0.03166838735342026,
0.008032368496060371,
0.014089605771005154,
0.006679884158074856,
-0.025126105174422264,
-0.04987197741866112,
0.03420182690024376,
-0.008352725766599178,
0.014281949028372765,
0.04920874536037445,
0.024912802502512932,
0.027555745095014572,
-0.025800542905926704,
-0.09572842717170715,
0.0022229321766644716,
-0.02380167506635189,
0.029226846992969513,
0.0002480192924849689,
-0.016513822600245476,
0.010402032174170017,
-0.026840170845389366,
-0.01801086962223053,
0.04774872958660126,
0.010216153226792812,
-0.0068090613931417465,
-0.004426970612257719,
0.008459105156362057,
0.034244611859321594,
0.03289664909243584,
0.03545286878943443,
-0.0026606800965964794,
0.031318049877882004,
-0.026244357228279114,
-0.004938856232911348,
0.012944964691996574,
-0.040954623371362686,
0.026858104392886162,
0.01145164668560028,
0.019171513617038727,
0.01269262284040451,
-0.0064988271333277225,
0.0004624864086508751,
0.015413954854011536,
-0.020084965974092484,
0.019620483741164207,
0.02001524530351162,
0.02691681496798992,
0.05441154167056084,
0.024464556947350502,
-0.03778665512800217,
-0.018630854785442352,
0.005497395526617765,
0.04555002227425575,
0.014510794542729855,
0.03218581900000572,
0.05320363864302635,
0.003718245541676879,
0.027076486498117447,
0.04343002662062645,
-0.027335040271282196,
0.007905916310846806,
0.014674477279186249,
-0.01916869543492794,
0.017900388687849045,
0.0047730193473398685,
0.025090288370847702,
-0.005573834292590618,
0.01657113805413246,
0.007168397307395935,
0.02877715788781643,
0.006892141420394182,
0.023711079731583595,
-0.0055917296558618546,
-0.0465509332716465,
-0.049598995596170425,
-0.021759580820798874,
0.026777058839797974,
-0.025106891989707947,
-0.022059723734855652,
-0.026470066979527473,
-0.052577242255210876,
-0.0457143597304821,
-0.03043302521109581,
-0.0008665893110446632,
-0.04853903502225876,
0.01974906586110592,
-0.05226784572005272,
0.03713520988821983,
-0.048937901854515076,
0.013604330830276012,
-0.0035722837783396244,
0.03583093732595444,
-0.010193977504968643,
0.017254848033189774,
0.01098417118191719,
0.04003370553255081,
0.033205579966306686,
0.02749883010983467,
0.0667724758386612,
-0.000439141527749598,
-0.047077495604753494,
-0.010379998944699764,
-0.010405478067696095,
0.018703870475292206,
-0.009198566898703575,
-0.11547228693962097,
-0.012895372696220875,
-0.05653641000390053,
0.061890292912721634,
0.00042090879287570715,
0.027219146490097046,
0.03250865265727043,
-0.019573111087083817,
0.06613115966320038,
-0.04298609122633934,
0.049189694225788116,
0.000451719417469576,
-0.002152684610337019,
-0.029920926317572594,
0.006373823154717684,
0.01691295951604843,
0.014214009046554565,
0.03844110295176506,
-0.01648162491619587,
-0.021150000393390656,
0.006580288987606764,
-0.021361425518989563,
0.030709587037563324,
0.0523010678589344,
0.02813625894486904,
-0.005795666016638279,
-0.05075884610414505,
0.008806683123111725,
0.036964159458875656,
0.013511719182133675,
0.049593131989240646,
0.018576055765151978,
-0.014703511260449886,
-0.06468664109706879,
-0.10902290791273117,
-0.024854086339473724,
0.06809913367033005,
-0.0028609461151063442,
0.026011699810624123,
-0.01683107018470764,
-0.025485768914222717,
-0.01771765574812889,
-0.006779771763831377,
-0.03555452451109886,
-0.10799232125282288,
-0.06454674154520035,
0.021622981876134872,
-0.03972989693284035,
0.08413815498352051,
0.03578896075487137,
-0.02804458700120449,
-0.004034315701574087,
-0.022155484184622765,
-0.006481155287474394,
-0.07800908386707306,
-0.03803025931119919,
0.015224110335111618,
0.002947217086330056,
0.013954301364719868,
0.034365128725767136,
-0.014314369298517704,
0.02968025766313076,
0.013716785237193108,
-0.030831605195999146,
-0.01687069609761238,
-0.03132272884249687,
-0.02944498136639595,
0.013066223822534084,
-0.030772406607866287,
-0.007701535243541002,
-0.03991173207759857,
0.08122614026069641,
0.09000947326421738,
0.0018497951095923781,
0.007146178744733334,
0.037054549902677536,
0.0283631831407547,
-0.029459670186042786,
-0.025675222277641296,
0.007702853996306658,
0.022955967113375664,
-0.02042652666568756,
0.003033078508451581,
-0.039303313940763474,
-0.024459918960928917,
-0.045512400567531586,
0.015313536860048771,
0.018955780193209648,
0.031585320830345154,
-0.028398262336850166,
0.020083023235201836,
0.009671523235738277,
-0.040570564568042755,
0.03426634520292282,
0.07564126700162888,
0.036140166223049164,
0.010712157003581524,
0.03035649098455906,
0.017291689291596413,
0.051126230508089066,
0.06371530145406723,
-0.007471718825399876,
0.0037914852146059275,
-0.010367781855165958,
-0.03581531345844269,
0.04335677996277809,
0.04826973378658295,
-0.06434378027915955,
-0.020698880776762962,
0.01824955642223358,
0.010132435709238052,
0.013360020704567432,
0.07173275947570801,
-0.0019247981254011393,
0.027031714096665382,
0.03162992373108864,
-0.058780208230018616,
-0.004896931350231171,
-0.018478482961654663,
0.005064140539616346,
-0.013863891363143921,
0.015033245086669922,
-0.0027754995971918106,
0.006089520640671253,
-0.05255717411637306,
0.02918010763823986,
0.05637631565332413,
-0.008290041238069534,
0.03156961128115654,
0.004673954099416733,
0.012162439525127411,
-0.0040483660995960236,
0.03556704521179199,
-0.049028005450963974,
-0.017708921805024147,
-0.01766345277428627,
-0.06077873706817627,
0.03143010661005974,
-0.03277772665023804,
-0.014485751278698444,
0.024388981983065605,
0.021814225241541862,
0.014530607499182224,
0.01930978149175644,
-0.045606259256601334,
-0.02574123628437519,
-0.01392736379057169,
0.03084072284400463,
0.0033012430649250746,
-0.0538308285176754,
-0.054009582847356796,
0.02521989308297634,
0.007595888804644346,
-0.0347524993121624,
0.028410399332642555,
0.040425222367048264,
-0.0014560793060809374,
-0.02149304375052452,
-0.06546343863010406,
-0.01918802410364151,
0.004404867067933083,
0.017902612686157227,
-0.0362115204334259,
-0.016491303220391273,
-0.015652425587177277,
0.0023254358675330877,
0.0446753166615963,
-0.002449129708111286,
0.0760808140039444,
0.018244359642267227,
-0.007924837991595268,
0.043000128120183945,
0.024702971801161766,
0.01948716677725315,
-0.01970335841178894,
0.09512286633253098,
-0.02302895113825798,
-0.01785007119178772,
0.02269248478114605,
-0.01270837988704443,
0.021396948024630547,
-0.02532419003546238,
-0.016317885369062424,
-0.002726909937337041,
-0.06542681902647018,
0.051970917731523514,
0.055698223412036896,
-0.0622757188975811,
-0.05551895499229431,
-0.0032185441814363003,
0.005366748198866844,
0.027017172425985336,
-0.04781153053045273,
-0.018560070544481277,
0.028608113527297974,
-0.018266752362251282,
0.025774430483579636,
-0.00771825248375535,
-0.0003466931520961225,
0.002703361213207245,
-0.01420932449400425,
0.06647809594869614,
-0.13269007205963135,
0.008709471672773361,
0.012640690430998802,
-0.015356016345322132,
-0.021146565675735474,
0.08646344393491745,
0.1357986330986023,
-0.020798610523343086,
-0.0016565773403272033,
0.08166021853685379,
0.011091422289609909,
-0.10285891592502594,
-0.025348471477627754,
0.018473660573363304,
-0.014673806726932526,
0.032528866082429886,
-0.013915973715484142,
-0.011122048832476139,
0.01825229451060295,
0.009301900863647461,
0.015720240771770477,
0.05199287086725235,
-0.042401641607284546,
0.03335476294159889,
-0.039010703563690186,
-0.02582128345966339,
-0.02473614364862442,
-0.00023944581334944814,
0.06463947147130966,
0.013470563106238842,
0.014075119979679585,
-0.01748204231262207,
0.032056547701358795,
0.014444494619965553,
-0.016325823962688446,
-0.03681427612900734,
-0.0557682178914547,
-0.011700122617185116,
-0.02469116821885109,
0.0007324563921429217,
-0.03536812216043472,
0.029618555679917336,
-0.006390902679413557,
-0.003912378568202257,
0.036987416446208954,
0.05586487799882889,
0.009770208038389683,
0.05831686407327652,
-0.04399311542510986,
0.04990873485803604,
0.10453341901302338,
0.025645937770605087,
-0.011297293938696384,
0.004183134064078331,
0.004598931409418583,
0.03195476159453392,
-0.0060889325104653835,
-0.017297549173235893,
-0.013593435287475586,
0.032847512513399124,
0.0024674797896295786,
0.011486422270536423,
0.02931736223399639,
0.05963978171348572,
0.0016271580243483186,
-0.016078412532806396,
-0.044890254735946655,
-0.008627204224467278,
0.09462150931358337,
-0.0190664641559124,
0.030873941257596016,
-0.03491286560893059,
-0.01320590265095234,
0.03170441463589668,
-0.006034479010850191,
-0.017527000978589058,
0.015560200437903404,
0.030064469203352928,
0.015226397663354874,
-0.029483305290341377,
-0.006637090351432562,
0.0025591582525521517,
0.01658564619719982,
-0.03373013436794281,
-0.01197508443146944,
0.007344194687902927,
0.005853876005858183,
-0.012788878753781319,
-0.010772353038191795,
0.04341438412666321,
0.022678663954138756,
-0.03588297963142395,
0.019455183297395706,
0.02420746721327305,
-0.06900914013385773,
-0.06273683160543442,
-0.06884901970624924,
0.05119350180029869,
-0.031527142971754074,
0.017200572416186333,
-0.013403595425188541,
-0.014932351186871529,
0.03747796639800072,
0.008276081643998623,
0.007155246566981077,
-0.000772800063714385,
-0.006052065175026655,
-0.019113872200250626,
-0.022991519421339035,
0.017478272318840027,
-0.0137315783649683,
0.029270054772496223,
0.033539384603500366,
0.009257089346647263,
-0.007454014848917723,
0.03059723600745201,
-0.022686226293444633,
0.036768946796655655,
0.062364812940359116,
-0.06471314281225204,
-0.08392930775880814,
0.034081459045410156,
0.0967092290520668,
-0.00803298782557249,
0.03393031656742096,
-0.01075360644608736,
-0.001299267983995378,
-0.0010050185956060886,
0.0010494438465684652,
-0.045716989785432816,
-0.033537693321704865,
0.020898383110761642
] |
<p>Why is <a href="http://en.wikipedia.org/wiki/Earnshaw%27s_theorem" rel="nofollow">Earnshaw's Theorem</a> inapplicable for moving ferromagnets?</p>
<p>Can I get a mathematical classical proof for this?</p>
|
g2439
|
[
-0.010223716497421265,
0.02760043926537037,
-0.015102843753993511,
-0.02911505661904812,
0.08037612587213516,
0.016059648245573044,
0.03037399798631668,
0.019131533801555634,
-0.024098405614495277,
0.03249944746494293,
-0.06605082005262375,
0.04067331552505493,
0.024759924039244652,
-0.006452420726418495,
-0.06517571210861206,
0.040456898510456085,
0.030011169612407684,
-0.035187847912311554,
0.04785013198852539,
0.020317798480391502,
0.038885146379470825,
0.061285872012376785,
0.025056347250938416,
-0.019845476374030113,
0.04041283577680588,
0.03259195014834404,
0.03564092144370079,
-0.05807211995124817,
-0.023713354021310806,
0.003376880893483758,
0.0553508959710598,
0.013270304538309574,
0.035162460058927536,
-0.03605189546942711,
0.03977783024311066,
-0.07050050050020218,
-0.006031504832208157,
-0.00472909165546298,
0.007902865298092365,
-0.02805926278233528,
0.011327200569212437,
0.030895177274942398,
0.008353320881724358,
-0.00035512776230461895,
0.026492221280932426,
-0.022297319024801254,
0.01751246489584446,
0.006060104817152023,
-0.050209544599056244,
0.03708290681242943,
-0.030884483829140663,
0.005504505708813667,
0.07828140258789062,
0.04157952219247818,
-0.01466900110244751,
-0.029278842732310295,
0.011699846014380455,
-0.04545857757329941,
0.016950609162449837,
-0.014813783578574657,
-0.012979112565517426,
-0.028573278337717056,
0.022395793348550797,
-0.0012677796185016632,
-0.0281867403537035,
-0.016002705320715904,
-0.040070194751024246,
-0.0363340862095356,
0.004142910707741976,
-0.027183540165424347,
-0.038418643176555634,
-0.06194514036178589,
0.009694949723780155,
-0.00919310562312603,
-0.015464666299521923,
0.05691671371459961,
0.02220720611512661,
-0.020505310967564583,
0.033382877707481384,
-0.07078838348388672,
-0.05904174968600273,
-0.024180246517062187,
0.007332486100494862,
-0.0188352819532156,
0.03211851418018341,
0.029060201719403267,
0.01099714357405901,
-0.022729482501745224,
0.006164559628814459,
-0.03948978707194328,
-0.008333136327564716,
-0.00545145059004426,
0.03216111287474632,
0.007702574133872986,
0.016934942454099655,
-0.025522006675601006,
-0.01838492602109909,
0.040271587669849396,
-0.04695567116141319,
0.003484905930235982,
-0.06133763864636421,
0.0006708907894790173,
0.01042960211634636,
0.01868373528122902,
0.07404676079750061,
-0.035707321017980576,
0.042597945779561996,
0.02094985544681549,
-0.01758221909403801,
-0.006278541404753923,
0.0345429927110672,
-0.03964933007955551,
-0.011037874966859818,
0.018712781369686127,
-0.011848513968288898,
0.06902478635311127,
0.031960055232048035,
-0.02188478596508503,
-0.013413879089057446,
0.08120191842317581,
0.03772815316915512,
0.015076967887580395,
-0.01832166500389576,
0.09553653746843338,
-0.07443867623806,
-0.022417405620217323,
-0.005937113426625729,
-0.0026955604553222656,
0.009746070019900799,
0.019276991486549377,
0.04305918142199516,
0.028812838718295097,
0.06162787601351738,
0.006557495798915625,
-0.02614603191614151,
0.034138958901166916,
0.036809127777814865,
0.029867952689528465,
-0.04095221683382988,
0.009824107401072979,
0.042759593576192856,
-0.05424235388636589,
0.04111132398247719,
-0.012578032910823822,
0.006422074977308512,
-0.010435120202600956,
0.016504593193531036,
-0.009338855743408203,
0.0021601812914013863,
0.050930123776197433,
-0.02911129966378212,
0.06353990733623505,
0.010830901563167572,
0.002452063374221325,
0.05313970148563385,
-0.029587388038635254,
0.026171285659074783,
0.019559837877750397,
-0.01707213558256626,
-0.021143192425370216,
0.07047650218009949,
-0.02148744836449623,
-0.011620397679507732,
0.01874345727264881,
-0.007909759879112244,
0.038951002061367035,
-0.01334020309150219,
0.008962789550423622,
-0.03404098004102707,
-0.015142874792218208,
-0.016014346852898598,
0.022471116855740547,
0.05131849646568298,
0.011101579293608665,
-0.04951464384794235,
0.043512556701898575,
-0.03062845766544342,
-0.012773251160979271,
0.013919027522206306,
-0.015103145502507687,
-0.036952994763851166,
-0.013495264574885368,
0.004684862680733204,
-0.00972032267600298,
-0.022455673664808273,
0.03756605088710785,
-0.04747675731778145,
0.02006736397743225,
-0.04795699566602707,
-0.014392530545592308,
0.011802318505942822,
0.028178462758660316,
-0.03804466873407364,
0.049417026340961456,
-0.014511902816593647,
-0.07573415338993073,
-0.026074498891830444,
0.015088440850377083,
-0.01493722666054964,
-0.020368918776512146,
0.05985167250037193,
0.06304538249969482,
0.08104673027992249,
-0.054610125720500946,
-0.040874116122722626,
-0.026370488107204437,
-0.015022012405097485,
-0.02391098067164421,
0.05534111335873604,
0.008600506000220776,
0.03788136690855026,
-0.008519190363585949,
-0.010094685479998589,
0.013470431789755821,
0.01876324974000454,
-0.04157915711402893,
-0.002006425056606531,
-0.052072856575250626,
-0.04242449253797531,
0.06676272302865982,
-0.07115375250577927,
-0.04520260542631149,
-0.0026509170420467854,
0.0167746152728796,
-0.014259403571486473,
0.015807371586561203,
-0.04272661358118057,
-0.03996005281805992,
0.014566957950592041,
-0.0010482285870239139,
-0.05561830848455429,
-0.051302820444107056,
0.033500365912914276,
-0.004117688164114952,
0.07458720356225967,
0.05658441409468651,
-0.011319121345877647,
-0.0009748857701197267,
0.024129677563905716,
0.06701076030731201,
0.0175618939101696,
-0.001307933358475566,
-0.03294747322797775,
-0.05253065750002861,
0.009302381426095963,
0.0007629759493283927,
0.04449658468365669,
0.00016903827781789005,
0.0467899851500988,
0.06794452667236328,
0.015549630858004093,
-0.06362495571374893,
0.009521173313260078,
-0.005186611320823431,
0.007320758420974016,
0.014710444957017899,
-0.009262008592486382,
0.015347043052315712,
-0.0508374385535717,
0.01837286911904812,
-0.03945932537317276,
-0.010000032372772694,
0.009020785801112652,
-0.006284983828663826,
-0.06409547477960587,
-0.007513465825468302,
-0.036851074546575546,
-0.007978299632668495,
-0.0065008108504116535,
-0.006704221945255995,
-0.08363001048564911,
0.03325945883989334,
-0.0014895240310579538,
0.03818269819021225,
-0.05082743614912033,
-0.030865350738167763,
0.04206794500350952,
0.026251057162880898,
0.02142028883099556,
-0.005164273548871279,
-0.043256502598524094,
-0.046301040798425674,
-0.0644112303853035,
-0.017805417999625206,
-0.028674712404608727,
-0.00531678507104516,
-0.012902146205306053,
0.022515488788485527,
-0.03286757692694664,
-0.009914310649037361,
-0.06628654897212982,
0.0040361606515944,
0.06644392013549805,
0.00511678634211421,
-0.0182578694075346,
0.00045286380918696523,
-0.011178451590240002,
-0.043089915066957474,
0.0037642475217580795,
-0.00019047803652938455,
0.051202062517404556,
0.05061836540699005,
-0.027918733656406403,
-0.001441647415049374,
0.01937725953757763,
0.009681562893092632,
0.005088245961815119,
-0.03848561272025108,
0.03773011639714241,
-0.033937711268663406,
0.05617309361696243,
0.06433501094579697,
0.006590025965124369,
0.018729431554675102,
-0.010852067731320858,
0.002271845703944564,
0.06356178969144821,
0.01218444388359785,
0.11075962334871292,
0.03506189584732056,
-0.01671311818063259,
-0.0699290782213211,
0.0009915637783706188,
-0.028738580644130707,
0.07679251581430435,
-0.0356600396335125,
-0.01569458656013012,
0.035918157547712326,
-0.0014988431939855218,
0.012664558365941048,
0.02559923194348812,
0.020590899512171745,
-0.018760299310088158,
-0.07087390124797821,
-0.09027201682329178,
-0.04295550286769867,
0.0183509960770607,
0.03324363753199577,
-0.013628402724862099,
0.023116301745176315,
-0.020039133727550507,
-0.018976831808686256,
-0.08411602675914764,
0.022529229521751404,
0.022526215761899948,
0.05763757601380348,
-0.01294054463505745,
0.047019828110933304,
0.06725563108921051,
0.03953146934509277,
0.0006783272256143391,
-0.03612411394715309,
0.0648784339427948,
0.00035660594585351646,
-0.05545240640640259,
-0.010461932048201561,
0.03088844008743763,
-0.020381974056363106,
0.03713676705956459,
0.009357628412544727,
0.054357513785362244,
0.06494852155447006,
0.009527170099318027,
-0.027384279295802116,
0.02832401916384697,
0.06478332728147507,
-0.08660151064395905,
0.08621076494455338,
0.022525258362293243,
-0.016935329884290695,
0.013049612753093243,
-0.09662605822086334,
-0.00999242253601551,
-0.030201377347111702,
0.02063334919512272,
-0.06783805042505264,
0.010489453561604023,
0.040331821888685226,
-0.054957326501607895,
0.042406316846609116,
0.024802226573228836,
0.05880758538842201,
0.01131768710911274,
0.010193504393100739,
-0.010994928888976574,
0.035370733588933945,
-0.0509357750415802,
0.007447451818734407,
-0.0007623214041814208,
0.01840868778526783,
0.035437095910310745,
-0.006169941741973162,
0.03995634987950325,
0.00941561907529831,
0.014592651277780533,
0.035410571843385696,
-0.030763670802116394,
-0.049532242119312286,
-0.006519070826470852,
0.019841039553284645,
0.0051423246040940285,
0.01820886693894863,
-0.09718551486730576,
0.03352881222963333,
0.020871082320809364,
-0.02903762459754944,
0.0004962888779118657,
0.04645567759871483,
0.04251382127404213,
-0.022172758355736732,
-0.05919566750526428,
-0.033259402960538864,
-0.011818883940577507,
-0.007412762846797705,
0.10044528543949127,
0.05037456750869751,
-0.007221653126180172,
-0.0812334418296814,
-0.06494966894388199,
-0.03522220626473427,
-0.006866819690912962,
0.08035609871149063,
-0.001610469538718462,
-0.01168831530958414,
-0.009178213775157928,
0.10961697995662689,
-0.0045633865520358086,
0.01965966634452343,
0.003395706880837679,
-0.043739691376686096,
0.004689762834459543,
-0.005991202313452959,
0.002429935149848461,
0.02139515057206154,
-0.03278672695159912,
0.021453460678458214,
-0.06046020984649658,
0.06724480539560318,
-0.004244564566761255,
0.01447304803878069,
0.024404818192124367,
0.004909928422421217,
-0.0031637896317988634,
-0.0020367917604744434,
-0.05950907990336418,
0.01900964416563511,
-0.013888168148696423,
-0.07556317746639252,
0.011875378899276257,
-0.004875881131738424,
0.017679376527667046,
-0.021893521770834923,
-0.043612632900476456,
0.027386445552110672,
-0.03728025034070015,
-0.007694626227021217,
-0.01685372367501259,
-0.06571773439645767,
0.04340257868170738,
0.02835681661963463,
0.007214400451630354,
0.003110239515081048,
0.01043277233839035,
0.05030783638358116,
0.01885475404560566,
0.045125097036361694,
-0.028237102553248405,
-0.01179815735667944,
-0.0021926388144493103,
0.01689433678984642,
-0.012260259129106998,
0.010517582297325134,
0.009590325877070427,
-0.019241251051425934,
-0.02020244672894478,
0.010127967223525047,
0.029964374378323555,
-0.048195935785770416,
-0.02048235572874546,
-0.06277358531951904,
-0.018532276153564453,
0.030297081917524338,
0.04496392980217934,
-0.009028689935803413,
0.041609518229961395,
-0.0010595802450552583,
-0.0207821112126112,
0.0377795547246933,
0.058243077248334885,
-0.04175058752298355,
0.04032447934150696,
-0.02225000225007534,
0.012258368544280529,
-0.03116382285952568,
-0.019755516201257706,
-0.045803043991327286,
-0.009307822212576866,
-0.02779749408364296,
-0.05185268446803093,
0.005127215292304754,
-0.027714749798178673,
0.03799841180443764,
-0.01915845088660717,
0.06042669713497162,
0.031007392331957817,
0.05145835503935814,
0.04349210113286972,
0.008482628501951694,
-0.004986305721104145,
0.019070830196142197,
0.02525157667696476,
0.0036003116983920336,
-0.009394313208758831,
0.02164454013109207,
0.03105650469660759,
-0.01445186510682106,
-0.018366016447544098,
-0.05512106791138649,
-0.013325771316885948,
-0.007774542551487684,
-0.005220035556703806,
-0.015536771155893803,
0.043058864772319794,
-0.04840119555592537,
-0.04478249326348305,
0.0019984603859484196,
-0.060805756598711014,
-0.02646663971245289,
-0.005305835977196693,
0.05337870121002197,
0.049565255641937256,
-0.06579437106847763,
-0.0025037359446287155,
-0.010777510702610016,
0.0057539730332791805,
0.013333196751773357,
0.029802342876791954,
-0.00425624568015337,
-0.030374396592378616,
-0.012504883110523224,
-0.020557045936584473,
-0.0741259828209877,
0.0052053420804440975,
-0.00482984771952033,
-0.0017667432548478246,
-0.027009248733520508,
-0.013081847690045834,
-0.04177838936448097,
0.07621344178915024,
-0.037106458097696304,
-0.029871298000216484,
0.04695744812488556,
-0.06022182106971741,
-0.02155783213675022,
0.00625586835667491,
0.037322524935007095,
-0.053969211876392365,
-0.036359790712594986,
0.03500240296125412,
0.02627175860106945,
0.04427267611026764,
0.009574152529239655,
0.03176695853471756,
0.027649931609630585,
0.01436909381300211,
-0.05870300158858299,
-0.0328807532787323,
0.042886048555374146,
0.045261867344379425,
0.025065084919333458,
-0.028669878840446472,
0.03264915198087692,
-0.035682547837495804,
0.059620603919029236,
0.0015967653598636389,
0.006829696241766214,
-0.036695074290037155,
0.006129317916929722,
-0.01652136631309986,
-0.04222136735916138,
-0.006858920678496361,
0.017730263993144035,
-0.04006321355700493,
-0.02754919044673443,
-0.019228089600801468,
0.030423441901803017,
-0.07197616994380951,
-0.017213312909007072,
0.03580285608768463,
0.03867528960108757,
-0.045207489281892776,
0.0026487591676414013,
0.010146182030439377,
0.04378878325223923,
-0.06630091369152069,
-0.037180423736572266,
-0.030454425141215324,
0.04336913675069809,
0.0850803405046463,
0.051522526890039444,
0.02578582428395748,
-0.02749898098409176,
0.05055323243141174,
0.009154313243925571,
-0.02344336546957493,
0.04236498102545738,
0.015887459740042686,
-0.015750346705317497,
0.021463003009557724,
0.010421723127365112,
-0.0259706974029541,
0.02946627140045166,
-0.0436675027012825,
-0.0202264916151762,
-0.03708721697330475,
-0.07535048574209213,
-0.092880018055439,
-0.003062268951907754,
-0.00767378369346261,
-0.013091599568724632,
-0.02964349463582039,
-0.035400256514549255,
-0.01697026565670967,
-0.026815181598067284,
-0.0026638887356966734,
0.03322961926460266,
-0.07429641485214233,
0.017332440242171288,
0.0223794337362051,
0.014748386107385159,
0.012296886183321476,
0.03357858210802078,
-0.04578795284032822,
0.032430198043584824,
0.021774210035800934,
-0.013073960319161415,
0.00865949783474207,
0.010737665928900242,
0.04207439720630646,
0.014694729819893837,
-0.03249690681695938,
0.02094886638224125,
0.010944671928882599,
-0.0004060939827468246,
-0.06696099787950516,
0.02101888507604599,
-0.02172892726957798,
-0.004890647251158953,
-0.07168247550725937,
0.045446332544088364,
0.02332732081413269,
0.03951496630907059,
-0.008047346025705338,
0.017090322449803352,
-0.04753805324435234,
-0.05178679898381233,
0.004660694859921932,
-0.018714364618062973,
0.01997085101902485,
-0.003478066762909293,
-0.057029832154512405,
-0.011913404799997807,
0.013594433665275574,
-0.03515567630529404,
0.050312064588069916,
0.019258448854088783,
0.005671810824424028,
-0.00225365930236876,
-0.006261627189815044,
-0.019014781340956688,
-0.03263463079929352,
0.010102817788720131,
-0.04090071842074394,
0.007822847925126553,
0.0067153931595385075,
-0.04218447953462601,
0.028748678043484688,
-0.010633678175508976,
-0.000826270435936749,
-0.016320189461112022,
-0.025787953287363052,
-0.040682047605514526,
0.028640173375606537,
0.007730554323643446,
-0.014433490112423897,
0.0020442104432731867,
-0.056138500571250916,
0.05748315900564194,
0.08672334253787994,
0.03848233073949814,
0.03902191296219826,
0.02642889693379402,
0.0321735255420208,
0.015702662989497185,
0.046166203916072845,
-0.007936801761388779,
-0.032707419246435165,
0.004044216591864824,
0.061692964285612106,
-0.02686297707259655,
0.013199773617088795,
-0.03104725107550621,
-0.017080919817090034,
0.02975691482424736,
0.010166417807340622,
-0.008709189482033253,
-0.01819719560444355,
0.015942296013236046,
-0.0706026628613472,
-0.002865529153496027,
0.06697636842727661,
0.005954321939498186,
-0.025671126320958138,
0.03368517383933067,
0.08408182859420776,
0.028331033885478973,
0.006565472576767206,
0.01017015427350998,
0.04595166817307472,
-0.010036190040409565,
0.017575256526470184,
0.005704526323825121,
-0.029129758477211,
-0.06399813294410706,
-0.07428784668445587,
-0.014071835204958916,
0.012180248275399208,
0.022525640204548836,
-0.024027308449149132,
-0.020957591012120247,
0.0216677226126194,
-0.057920265942811966,
-0.053290627896785736,
-0.0020111240446567535,
-0.04532779008150101,
-0.03896324336528778,
-0.061878178268671036,
-0.03886265307664871,
0.035936616361141205,
0.018641529604792595,
-0.050564732402563095,
0.0016204428393393755,
0.0006365370354615152,
-0.07036976516246796,
-0.039827924221754074,
0.01107861939817667,
-0.001512425602413714,
0.04800540581345558,
-0.008032532408833504,
0.025531699880957603,
0.003806443652138114,
0.04019591212272644,
-0.04250450059771538,
0.011197838932275772,
0.06306997686624527,
-0.005972261540591717,
0.02821412682533264,
-0.01537033636122942,
0.03185974806547165,
0.04557744041085243,
-0.008157801814377308,
-0.037162914872169495,
-0.028391223400831223,
0.017201047390699387,
-0.03021393157541752,
-0.0073489234782755375,
-0.03621498495340347,
-0.021757617592811584
] |
<p>I am wondering if I mix up the notion of <em>proper distance</em> and <em>proper length</em>.</p>
<p>I have two cuves in Schwarzschild space-time describing the flight of two photons (think of it as photons guided in by optical fiber, not geodesics).</p>
<p>$\gamma_1(\lambda) = \big(t_1(\lambda),r_1(\lambda),\frac \pi 2, 0\big )$ and $\gamma_2(\lambda) = \big(t_2(\lambda),R,\frac \pi 2, \varphi_2(\lambda)\big )$ where $r_1(0)=R$ and $\varphi_2(0)=0$. </p>
<p>I now want both photons to fly the same length. With "same length" I mean, that I trimmed the two optical fibers in my lab so that they have the same lenght, measured by a tape.</p>
<p>For this purpose I arbitrarily define the end of the first curve at $\lambda=\Lambda$ and define the corresponding radial coordinate by $r_1(\Lambda)=R+\Delta R$.
Now comes the crucial point: Is it correct to say, that the length of the first optical fiber is</p>
<p>$\displaystyle l = \int_0^\Lambda \frac{1}{\sqrt{1-\frac{r_s}{r_1(\lambda)}}} r_1'(\lambda) \; d\lambda = \int_R^{R+\Delta R} \frac{1}{\sqrt{1-\frac{r_s}{r}}} \; dr$ ?</p>
<p>If this is true this would also define a $\Delta \varphi$ for the second optical fiber by</p>
<p>$\displaystyle l \overset{!}{=}\int_0^{\Delta \varphi} R \, d \varphi = R\Delta\varphi$</p>
<p>Is that correct?
My problem is, that <a href="http://en.wikipedia.org/wiki/Proper_length" rel="nofollow">wikipedia states</a> that I am dealing with <em>proper distance</em> instead of <em>proper length</em>. This confuses me since I want to be sure to have the same length for both optical fibers (measured by a tape).</p>
|
g2440
|
[
0.03847135603427887,
-0.0050742607563734055,
0.018802255392074585,
0.016499411314725876,
0.021663233637809753,
0.0011818911880254745,
-0.004725615028291941,
0.006721381563693285,
-0.049628544598817825,
0.029028842225670815,
0.039439212530851364,
0.042487237602472305,
-0.03079736791551113,
-0.01683811843395233,
0.05160882696509361,
-0.031550332903862,
0.12069723010063171,
-0.024734875187277794,
0.02412041649222374,
0.006884935311973095,
-0.019222257658839226,
-0.008008545264601707,
-0.002390556037425995,
-0.018234271556138992,
-0.007669590879231691,
-0.03767203539609909,
0.018725454807281494,
0.03981487825512886,
-0.09894956648349762,
-0.03509644418954849,
0.035956528037786484,
0.057521555572748184,
0.05144486203789711,
-0.00517027173191309,
0.009342862293124199,
-0.008061644621193409,
-0.01859036274254322,
0.016293151304125786,
0.031879112124443054,
0.00038503744872286916,
0.03307466581463814,
0.014660841785371304,
-0.002408561296761036,
-0.04146470129489899,
0.05629567801952362,
0.0006904731271788478,
-0.03452533110976219,
0.0048994217067956924,
0.04657246917486191,
-0.014133334159851074,
0.02554982900619507,
0.08555011451244354,
-0.057783979922533035,
-0.038496214896440506,
0.01629042997956276,
0.005215986631810665,
0.0014205757761374116,
0.006739410106092691,
0.04107411950826645,
0.027553757652640343,
0.005953832995146513,
-0.016109460964798927,
-0.04242166131734848,
0.03798700124025345,
0.033030152320861816,
0.06017489731311798,
0.012002847157418728,
-0.06630773842334747,
-0.044118694961071014,
-0.015143614262342453,
-0.04724670201539993,
-0.05414032191038132,
0.03295889496803284,
0.008409715257585049,
-0.055917415767908096,
-0.04911835864186287,
-0.02418164722621441,
0.04321333393454552,
-0.01871352456510067,
0.028579315170645714,
-0.055422645062208176,
-0.014635138213634491,
-0.008996007964015007,
0.024140097200870514,
0.03436104953289032,
0.0392242856323719,
-0.003879937808960676,
-0.029585519805550575,
-0.020837588235735893,
0.023135967552661896,
0.0062431651167571545,
-0.061656590551137924,
0.02909817546606064,
0.034092582762241364,
0.05108706280589104,
-0.030573645606637,
-0.011815841309726238,
0.04851313307881355,
-0.026989135891199112,
0.041036441922187805,
-0.006335378158837557,
0.07690174877643585,
0.005379957612603903,
0.03989997133612633,
-0.06947751343250275,
-0.004084291867911816,
0.002726555336266756,
-0.03921495005488396,
-0.028338389471173286,
-0.041650477796792984,
-0.022809138521552086,
-0.034915149211883545,
-0.038464684039354324,
-0.001492753392085433,
-0.02973247691988945,
-0.003345564706251025,
0.07835011929273605,
-0.01616433635354042,
-0.023734470829367638,
0.0873049795627594,
0.002713078400120139,
-0.05312036722898483,
0.12299986928701401,
0.04102558270096779,
0.05388130620121956,
0.009633989073336124,
0.010072700679302216,
0.024392295628786087,
0.023795591667294502,
0.029276488348841667,
-0.015308472327888012,
-0.010033559054136276,
-0.030375778675079346,
0.002247496275231242,
-0.04201652854681015,
0.008293124847114086,
0.04488202556967735,
0.0490136481821537,
-0.016745850443840027,
0.02269337698817253,
-0.030900739133358,
-0.11281779408454895,
0.008976233191788197,
-0.08022966235876083,
-0.041226282715797424,
0.033371925354003906,
-0.02453683689236641,
0.008629119955003262,
0.03571665287017822,
-0.024246731773018837,
0.02864498272538185,
0.08237046003341675,
-0.08550948649644852,
0.007167797069996595,
-0.06493005901575089,
-0.0018646955722942948,
-0.002049073576927185,
-0.006011392921209335,
-0.0021252259612083435,
-0.01005647610872984,
-0.00849068257957697,
-0.03612557426095009,
0.0016343723982572556,
-0.007748020812869072,
-0.04525286704301834,
0.04603669419884682,
-0.0018298930954188108,
-0.060122132301330566,
-0.031420014798641205,
-0.09217703342437744,
-0.0387004017829895,
0.02893403172492981,
0.04945513233542442,
-0.009004959836602211,
-0.02669043280184269,
0.057102806866168976,
0.03008509799838066,
0.02963555045425892,
-0.043725352734327316,
-0.041450340300798416,
-0.08264299482107162,
0.0036603445187211037,
0.008384903892874718,
-0.043236516416072845,
-0.0431082621216774,
0.023692796006798744,
0.017356330528855324,
-0.06004127115011215,
-0.0903901532292366,
0.031177548691630363,
-0.06213966757059097,
0.02973482571542263,
-0.038696687668561935,
0.05991089344024658,
-0.07299471646547318,
0.017866063863039017,
-0.009626355953514576,
-0.020234698429703712,
-0.02694060280919075,
0.029802951961755753,
-0.04356006160378456,
-0.00949013140052557,
0.015392312780022621,
0.009741546586155891,
0.011515618301928043,
0.0001398966705892235,
-0.011903947219252586,
-0.009206154383718967,
0.027934333309531212,
-0.0042980569414794445,
0.0336257740855217,
-0.02296152152121067,
0.013813305646181107,
0.002342846943065524,
-0.0011267458321526647,
-0.07334831357002258,
-0.004022756591439247,
0.025029318407177925,
-0.030086548998951912,
-0.0065780156292021275,
-0.010259388945996761,
0.01066245511174202,
0.10209693014621735,
-0.09527347981929779,
0.030300915241241455,
-0.023126039654016495,
-0.03718748688697815,
-0.029695086181163788,
-0.026200953871011734,
0.01772894337773323,
-0.04781581088900566,
-0.022063644602894783,
-0.009431418031454086,
0.003478600876405835,
0.06542155146598816,
-0.017208190634846687,
0.017722081393003464,
0.01277612429112196,
0.05606257542967796,
-0.03467080742120743,
0.07120552659034729,
-0.020141666755080223,
-0.030740585178136826,
0.07173401862382889,
-0.00016419211169704795,
0.00003549629764165729,
0.011747180484235287,
0.008375145494937897,
-0.04491835832595825,
-0.0327126681804657,
-0.00864891242235899,
0.007718879263848066,
-0.00693010538816452,
0.02502172254025936,
0.0064436690881848335,
-0.07170668244361877,
-0.010912861675024033,
0.054189447313547134,
-0.05387450382113457,
0.05164569243788719,
-0.03847513347864151,
-0.00997986365109682,
0.0121203837916255,
-0.013013302348554134,
-0.019474180415272713,
0.01559215784072876,
-0.0772860199213028,
0.07408333569765091,
0.02727738581597805,
0.016673849895596504,
0.06748320162296295,
-0.0009383747237734497,
0.030273359268903732,
-0.03705570474267006,
0.012560519389808178,
0.015164182521402836,
-0.015073484741151333,
-0.00932564027607441,
0.01937974989414215,
0.02523966133594513,
0.02793675661087036,
0.007456086575984955,
-0.04681550711393356,
0.013480102643370628,
0.018783679232001305,
-0.05438319593667984,
-0.03330591693520546,
0.05101393163204193,
-0.004864800255745649,
-0.009480657987296581,
-0.012773631140589714,
0.06817294657230377,
0.06739216297864914,
-0.023202285170555115,
0.011708168312907219,
-0.014340288005769253,
0.0004969987203367054,
-0.002153345150873065,
-0.010600471869111061,
-0.0013442605268210173,
-0.019816871732473373,
-0.03312474116683006,
-0.051829177886247635,
-0.00794263556599617,
0.047291144728660583,
-0.002747474005445838,
-0.05666566267609596,
-0.056471649557352066,
-0.02935066819190979,
0.023493461310863495,
0.04319994896650314,
0.07416126877069473,
0.018705904483795166,
-0.0009342653793282807,
0.014115089550614357,
-0.04916573315858841,
-0.013462775386869907,
-0.009115505032241344,
-0.000056785363995004445,
0.038634128868579865,
0.006805568467825651,
0.01291043870151043,
-0.03908633068203926,
0.027756698429584503,
0.03630976378917694,
0.0371573269367218,
0.00040157767944037914,
0.024744877591729164,
-0.04927287623286247,
-0.00589413195848465,
-0.0029539719689637423,
-0.012564267963171005,
-0.043516889214515686,
-0.04142666608095169,
0.006719517987221479,
0.015902599319815636,
0.02639397233724594,
0.03808891028165817,
0.016896497458219528,
0.01778816618025303,
-0.05389619246125221,
-0.012701091356575489,
-0.023483064025640488,
0.025025269016623497,
0.025120841339230537,
-0.015470472164452076,
0.009205484762787819,
0.0647454559803009,
-0.01642755977809429,
-0.009094431065022945,
0.009779321029782295,
-0.01288627739995718,
0.0003521588514558971,
-0.02800939232110977,
-0.021390341222286224,
0.06748446077108383,
-0.009442899376153946,
0.03667255491018295,
0.002806880511343479,
-0.03096509352326393,
0.019989801570773125,
0.04523663595318794,
-0.05337934195995331,
-0.02686445042490959,
0.010436893440783024,
0.0027601534966379404,
0.014749746769666672,
0.05722736939787865,
0.015834646299481392,
-0.014731229282915592,
0.028410810977220535,
0.04153988137841225,
-0.06567765772342682,
-0.01928866095840931,
-0.010333060286939144,
-0.015683528035879135,
0.02488635666668415,
0.011301289312541485,
-0.016671650111675262,
0.032290659844875336,
-0.03887040540575981,
0.03613154962658882,
0.0186659824103117,
-0.011624093167483807,
0.019168896600604057,
-0.0381878986954689,
-0.007916842587292194,
-0.03648987412452698,
0.04686441272497177,
0.025077853351831436,
0.00459797540679574,
-0.12721110880374908,
-0.028493640944361687,
-0.006889770273119211,
0.009861228056252003,
-0.012969940900802612,
-0.01323935016989708,
-0.0023745782673358917,
-0.045878536999225616,
0.0067455582320690155,
-0.04243792966008186,
0.05436908081173897,
0.048165325075387955,
-0.00516583863645792,
-0.04258274286985397,
-0.03317004814743996,
-0.010555015876889229,
-0.007614875677973032,
0.03898608684539795,
-0.02446470968425274,
-0.001801709528081119,
0.031661394983530045,
0.03698503598570824,
-0.06042766943573952,
0.04605654627084732,
0.0008465676219202578,
-0.042451586574316025,
-0.032218046486377716,
0.03727027401328087,
0.011161703616380692,
0.051630377769470215,
0.01993861235678196,
0.049825288355350494,
-0.05309469252824783,
-0.038805969059467316,
0.08113664388656616,
0.00699567049741745,
0.006637063808739185,
0.03694682940840721,
-0.02488267421722412,
-0.00041140930261462927,
0.019648293033242226,
-0.0017036596545949578,
0.06579072773456573,
-0.048996083438396454,
0.02515786699950695,
0.003456379286944866,
0.030051644891500473,
0.02186097949743271,
0.04824630916118622,
-0.019184760749340057,
-0.02152288518846035,
0.011356499046087265,
-0.03417815640568733,
0.014097614213824272,
-0.004621855914592743,
0.006135175004601479,
-0.032222289592027664,
0.008037367835640907,
-0.006782993208616972,
-0.005009130109101534,
0.0587482713162899,
0.03695946931838989,
0.033395104110240936,
-0.008500196970999241,
0.0005122574511915445,
-0.012973381206393242,
-0.002811640268191695,
0.025349650532007217,
-0.06504836678504944,
-0.02413514256477356,
0.0426190085709095,
0.03538262099027634,
-0.049621809273958206,
0.018395040184259415,
-0.020341383293271065,
-0.09800664335489273,
-0.03412149101495743,
-0.028747349977493286,
0.016895247623324394,
0.007134429179131985,
-0.008901912719011307,
-0.018862644210457802,
0.008231968618929386,
0.009976952336728573,
-0.04097481071949005,
-0.05794604495167732,
-0.010317047126591206,
-0.07984072715044022,
-0.028665652498602867,
-0.03248508274555206,
-0.00639989972114563,
0.028681417927145958,
-0.014869878999888897,
0.029244303703308105,
0.0037190637085586786,
0.028232937678694725,
0.00016529796994291246,
0.06872721761465073,
-0.012046119198203087,
0.028008487075567245,
-0.0777115449309349,
0.017768409103155136,
0.0048433453775942326,
-0.04895475506782532,
0.04805973544716835,
-0.010983089916408062,
-0.0014639974106103182,
0.00785432942211628,
-0.07378373295068741,
0.023124728351831436,
0.028671106323599815,
0.02281743474304676,
0.004381210543215275,
-0.040281303226947784,
0.007628600113093853,
0.056761451065540314,
0.02152932807803154,
-0.1235283836722374,
0.032650671899318695,
0.03279078006744385,
-0.005260583944618702,
0.03971121087670326,
0.0052040196023881435,
0.026719791814684868,
-0.02045604959130287,
0.012414025142788887,
0.07026712596416473,
-0.0054222107864916325,
-0.009385354816913605,
0.029052795842289925,
0.009328456595540047,
0.013773598708212376,
-0.006675087381154299,
0.03834560886025429,
0.020029745995998383,
-0.038138497620821,
0.01813831552863121,
0.011506151407957077,
0.03839467838406563,
-0.028893889859318733,
0.015372789464890957,
0.026597969233989716,
0.023151442408561707,
-0.022744107991456985,
0.01526343822479248,
-0.002186516998335719,
-0.03188791871070862,
0.004722824785858393,
-0.04785268008708954,
-0.050382062792778015,
0.015830019488930702,
-0.00841415487229824,
0.06706765294075012,
-0.03236931562423706,
0.005634634755551815,
0.06989730894565582,
-0.030581539496779442,
0.020020902156829834,
-0.05094075947999954,
-0.01370150689035654,
-0.05172127112746239,
-0.019980302080512047,
0.0020295411814004183,
0.03922015056014061,
0.05138762295246124,
0.051792677491903305,
-0.0028135988395661116,
-0.020260484889149666,
-0.008284242823719978,
0.01832975260913372,
-0.06209060549736023,
-0.028573093935847282,
-0.010747678577899933,
-0.02391163259744644,
-0.025674082338809967,
-0.007710382342338562,
-0.043381307274103165,
0.011733942665159702,
0.029369022697210312,
-0.0374334454536438,
-0.01795647293329239,
-0.009978916496038437,
0.00004168934901827015,
0.04074929282069206,
0.01651964895427227,
0.020614439621567726,
-0.06290923058986664,
-0.020031463354825974,
-0.014107611030340195,
-0.03261714428663254,
0.012795666232705116,
0.009027437306940556,
-0.06613809615373611,
-0.0066190543584525585,
0.034052446484565735,
-0.01410005334764719,
0.029505018144845963,
0.05403917655348778,
-0.04662537947297096,
-0.03602806106209755,
-0.004001463297754526,
-0.030047792941331863,
-0.010600785724818707,
-0.04030285403132439,
0.04191422462463379,
0.017446408048272133,
0.01891382969915867,
-0.03430440276861191,
0.03634218871593475,
-0.009443266317248344,
0.04953613504767418,
0.029119405895471573,
-0.035029336810112,
0.016410816460847855,
0.030536023899912834,
-0.026554664596915245,
0.03703920543193817,
0.07060430198907852,
0.005453956313431263,
0.024067159742116928,
0.021951274946331978,
-0.0355001725256443,
0.02814357355237007,
-0.03262597322463989,
-0.009428431279957294,
-0.0009460970177315176,
-0.013792057521641254,
0.0028159269131720066,
0.05208466574549675,
0.024188466370105743,
-0.023865265771746635,
0.0024098679423332214,
0.017285671085119247,
0.06229403614997864,
0.07353468239307404,
-0.0003768562455661595,
0.014931662939488888,
0.005006916355341673,
0.008622068911790848,
-0.007604076061397791,
-0.025267094373703003,
-0.01937798596918583,
0.018422890454530716,
0.059979163110256195,
0.03904339298605919,
-0.09411300718784332,
0.02585778199136257,
0.05407389998435974,
0.06698988378047943,
0.05447151139378548,
0.02045702002942562,
0.06592722237110138,
0.0023720250464975834,
-0.06478796899318695,
-0.04198114946484566,
0.011297518387436867,
-0.04019918292760849,
-0.013890436850488186,
0.009528245776891708,
0.022531427443027496,
0.024042239412665367,
-0.05169462785124779,
0.0400359146296978,
0.018815206363797188,
-0.0522296167910099,
-0.004331307485699654,
-0.01252016145735979,
-0.07279644906520844,
-0.00810582097619772,
0.021483851596713066,
-0.02980118617415428,
-0.03945113345980644,
-0.029567912220954895,
-0.029830213636159897,
0.013453654013574123,
-0.031680621206760406,
-0.013339405879378319,
-0.04975670576095581,
-0.008932479657232761,
-0.0015617761528119445,
-0.011063762940466404,
0.006650454364717007,
0.027054939419031143,
-0.006136673502624035,
0.036081597208976746,
0.03343053162097931,
0.05657894164323807,
-0.008118081837892532,
-0.02586926892399788,
0.007944450713694096,
-0.0012822439894080162,
-0.030226528644561768,
-0.0252227820456028,
-0.061687976121902466,
0.0069215805269777775,
-0.001888340339064598,
-0.009756950661540031,
-0.004254689905792475,
-0.020771825686097145,
-0.014980724081397057,
0.007565837353467941,
0.013198748230934143,
-0.0011683572083711624,
-0.008357703685760498,
-0.010481443256139755,
0.10686642676591873,
0.07692965865135193,
-0.010428876616060734,
-0.001926435506902635,
0.041747283190488815,
0.04129045456647873,
-0.01670232228934765,
-0.0021962139289826155,
-0.01800369843840599,
0.025440940633416176,
-0.013002105057239532,
0.0200799610465765,
-0.0015421397984027863,
0.012448321096599102,
-0.018785489723086357,
0.007465729955583811,
0.03258248418569565,
0.09060227125883102,
-0.01745474338531494,
-0.04713538661599159,
-0.024779610335826874,
0.0071863955818116665,
0.02816612459719181,
-0.04712976887822151,
-0.003042813390493393,
0.021206766366958618,
-0.0006691915332339704,
-0.04532109573483467,
-0.02117704413831234,
0.022201120853424072,
-0.015523673966526985,
-0.030924029648303986,
0.019475525245070457,
-0.027341056615114212,
0.00133016228210181,
-0.06406145542860031,
-0.012167074717581272,
-0.004478969145566225,
-0.04918348044157028,
-0.003748299553990364,
-0.031273189932107925,
0.00838062446564436,
-0.011088871397078037,
-0.023523075506091118,
0.02249392494559288,
-0.03773951902985573,
-0.047019824385643005,
0.015792232006788254,
-0.019843826070427895,
-0.017870957031846046,
0.037183236330747604,
0.04938194155693054,
0.03997549042105675,
-0.021479468792676926,
-0.031117869541049004,
0.05994052439928055,
0.00966664683073759,
0.06676404923200607,
0.09720952063798904,
-0.014433158561587334,
0.02312653884291649,
-0.02476482279598713,
0.0296932402998209,
0.00014286598889157176,
-0.016150984913110733,
-0.07864734530448914,
-0.008818353526294231,
0.05736236274242401,
-0.04870441183447838,
0.003663637675344944,
0.023815538734197617,
0.05368749424815178
] |
<p>I am trying to follow the steps to solve the integro-differential equation that arises from a plasma sheath problem given in <a href="http://scitation.aip.org/content/aip/journal/pop/13/11/10.1063/1.2388265" rel="nofollow">this paper</a>. This is the step I can't follow:</p>
<blockquote>
<p>$$\epsilon_o\frac{d}{d\varphi}\biggl(\frac{E^2}{2}\biggr) = \sqrt{\frac{m_e}{2e}}\frac{j_{eo}}{\sqrt{\varphi}} - \sqrt{\frac{m_i}{2e}}\frac{j_{eo}}{\lambda_I}\int_\varphi^{\varphi_w}\frac{\varphi'/\varphi_I - 1}{\sqrt{\varphi' - \varphi}}\frac{d\varphi'}{E'},\tag{4}$$</p>
<p>where $\lambda_I =1/\sigma_o n_a$ is the ionization mean free path for the electron energy $E_I$. The integration of Eq. (4) over $\varphi$ leads to an integral equation for the electric field $E(\varphi)$,</p>
<p>$$\begin{multline}\frac{\epsilon_o}{4j_{eo}}\sqrt{\frac{e}{2m_e}}(E_w^2 - E^2) = \bigl(\sqrt{\varphi_w} - \sqrt{\varphi}\bigr)\\- \frac{1}{\lambda_I}\sqrt{\frac{m_i}{m_e}}\int_\varphi^{\varphi_w}\biggl(\frac{\varphi'}{\varphi_I} - 1\biggr)\sqrt{\varphi(z') - \varphi(z)}\frac{d\varphi'}{E(\varphi')},\tag{5}\end{multline}$$</p>
</blockquote>
<p>The paper claims that instead of solving the integro-differential equation numerically from the form above, both sides of the equation can be integrated with respect to $\varphi$. I am not sure if it is valid to integrate both sides of this equation with respect to this variable since it appears in the lower limit of the integral. </p>
<p>Can someone explain how you would handle integrating both sides when $\varphi$ is in the the limit of the integral? Thanks!</p>
<p>Or if anyone has an argument for why a mistake might have been made in this step that would be helpful too. </p>
|
g2441
|
[
0.049954187124967575,
0.0589691624045372,
0.01506645604968071,
-0.006891450844705105,
0.01978447660803795,
0.012616493739187717,
0.011000804603099823,
0.019643569365143776,
-0.06361646950244904,
0.021185345947742462,
-0.018493905663490295,
0.06387995928525925,
0.004706248641014099,
0.03525913879275322,
0.03206435963511467,
-0.04133293032646179,
0.07937373220920563,
-0.009902228601276875,
-0.018436845391988754,
-0.00012843942386098206,
-0.068953737616539,
0.029771851375699043,
0.015289844945073128,
0.0027586091309785843,
0.01597743295133114,
-0.004268911201506853,
0.03773889318108559,
-0.005025533959269524,
-0.006602677050977945,
-0.013457742519676685,
-0.01956169307231903,
0.023112596943974495,
0.016658373177051544,
-0.034736402332782745,
-0.04153785854578018,
0.010588208213448524,
0.0425228588283062,
0.05469299107789993,
-0.01174671109765768,
-0.05974377691745758,
0.054364126175642014,
-0.050026580691337585,
0.0762680172920227,
-0.0030601155012845993,
-0.0032993797212839127,
-0.0014350168639793992,
-0.02548942156136036,
-0.05426502600312233,
0.0037639376241713762,
0.017014531418681145,
0.008443283848464489,
0.06730406731367111,
0.020513972267508507,
-0.06189332157373428,
-0.018692806363105774,
0.0411691851913929,
0.03817443177103996,
-0.025843437761068344,
0.029709240421652794,
0.060285989195108414,
0.09775212407112122,
-0.017644144594669342,
-0.01481568068265915,
-0.04367933049798012,
0.03984532505273819,
-0.04497138410806656,
-0.03328552842140198,
-0.005585829261690378,
0.01755894161760807,
-0.005363283213227987,
0.04205484688282013,
-0.04419387876987457,
0.00867016613483429,
-0.08511075377464294,
0.016820935532450676,
-0.0182411540299654,
0.05717654153704643,
0.02297205477952957,
0.05487288534641266,
-0.031976111233234406,
-0.05348711088299751,
0.017076553776860237,
-0.016498448327183723,
0.040447913110256195,
-0.06690855324268341,
-0.01766962930560112,
-0.015900075435638428,
0.025865932926535606,
-0.019462376832962036,
-0.04936579614877701,
-0.06812337040901184,
0.02031962014734745,
0.0016759684076532722,
0.014068246819078922,
0.04208946228027344,
-0.008250096812844276,
-0.026453223079442978,
0.06170699745416641,
-0.040085382759571075,
-0.01821422390639782,
-0.03523656725883484,
-0.010159030556678772,
0.01079691294580698,
-0.020617811009287834,
-0.046698931604623795,
-0.004654230549931526,
0.0395941287279129,
0.008245677687227726,
0.022749168798327446,
-0.056353963911533356,
0.012625275179743767,
-0.049635596573352814,
-0.011351623572409153,
-0.036827679723501205,
-0.047685910016298294,
0.07304225116968155,
-0.0075340429320931435,
-0.0013557663187384605,
-0.062640480697155,
0.03548288717865944,
0.009207337163388729,
-0.01831611432135105,
0.06253080815076828,
0.019328972324728966,
0.0039171804673969746,
-0.015498165041208267,
-0.0106305330991745,
-0.008234292268753052,
0.011772077530622482,
-0.02152162790298462,
0.02155838906764984,
-0.020998112857341766,
0.020621702075004578,
-0.02570524998009205,
0.02296704240143299,
0.015251116827130318,
-0.023539122194051743,
0.02701491490006447,
-0.015485832467675209,
-0.004974952898919582,
-0.004651644267141819,
-0.03418237343430519,
-0.026607586070895195,
0.0324137918651104,
-0.0027109074871987104,
0.003708175616338849,
-0.0048267836682498455,
-0.0409160777926445,
0.00980764627456665,
-0.03679562360048294,
-0.035014424473047256,
0.0657716765999794,
-0.014429905451834202,
0.0006144869257695973,
-0.020471086725592613,
-0.01615559682250023,
0.03027050383388996,
-0.014141816645860672,
0.01185392402112484,
-0.058574020862579346,
0.015881916508078575,
0.020722312852740288,
0.03990110009908676,
0.015563581138849258,
0.030943788588047028,
0.04512074962258339,
0.05078764259815216,
-0.05024348944425583,
0.009808049537241459,
-0.023462766781449318,
0.005157123319804668,
0.0026074687484651804,
0.04334816709160805,
0.02220047637820244,
0.0844295397400856,
0.08168403804302216,
0.04283164069056511,
-0.023837381973862648,
0.010669170878827572,
0.012332581914961338,
0.002024258952587843,
0.031575772911310196,
0.02625918760895729,
-0.04683024436235428,
0.049554694443941116,
-0.025007998570799828,
0.0034510802943259478,
0.02005787566304207,
0.007915697060525417,
-0.01699964329600334,
-0.022494958713650703,
0.02695417031645775,
0.04561983421444893,
0.04956624284386635,
-0.03241901472210884,
0.07198689132928848,
0.05185719206929207,
-0.09424275159835815,
-0.040630947798490524,
-0.06854753941297531,
0.0028927556704729795,
0.027198754251003265,
0.0428767055273056,
0.03568631783127785,
0.0697421208024025,
-0.0007073526503518224,
-0.02728692814707756,
-0.07402504235506058,
0.021790780127048492,
-0.006767091806977987,
-0.004163909703493118,
-0.024773336946964264,
-0.02502775564789772,
0.06973796337842941,
0.01374779548496008,
-0.10066360980272293,
0.024097859859466553,
0.026717517524957657,
-0.0427640862762928,
0.0007169071468524635,
-0.042456645518541336,
-0.019896412268280983,
-0.0013802911853417754,
0.003965482581406832,
0.010022369213402271,
0.030380817130208015,
0.0048674652352929115,
0.023963743820786476,
-0.062310945242643356,
-0.04674607515335083,
-0.041662268340587616,
-0.001252744230441749,
-0.04042533040046692,
-0.07969184219837189,
0.050017841160297394,
-0.006174765061587095,
0.014747709967195988,
0.005425340496003628,
0.018078535795211792,
-0.005026584025472403,
0.02639634534716606,
-0.0298288706690073,
0.05792368948459625,
0.009734624065458775,
-0.0031762609723955393,
0.016850514337420464,
0.01254210714250803,
0.027693133801221848,
-0.06632985919713974,
0.0393865704536438,
-0.015168445184826851,
-0.004135583061724901,
-0.045467644929885864,
0.0038874477613717318,
0.010978667065501213,
-0.03558587655425072,
-0.02440137416124344,
-0.029422994703054428,
0.047871559858322144,
0.03438486531376839,
-0.009961127303540707,
0.05376403033733368,
-0.005393432453274727,
0.017958493903279305,
-0.07623070478439331,
0.011347188614308834,
0.017675302922725677,
-0.014653279446065426,
0.09993278235197067,
-0.03547364100813866,
0.05126987770199776,
0.06988369673490524,
-0.05269140377640724,
0.027479263022542,
0.0810019001364708,
-0.014413178898394108,
-0.00585905509069562,
-0.03743160888552666,
0.08712797611951828,
-0.03214452043175697,
-0.02452145516872406,
-0.052941132336854935,
0.004229946527630091,
0.04519597440958023,
0.011295112781226635,
-0.020976709201931953,
0.02783750742673874,
0.004314186982810497,
-0.024654772132635117,
0.016792751848697662,
-0.05139072611927986,
-0.04603457823395729,
-0.032864272594451904,
-0.03171618655323982,
-0.0035162523854523897,
-0.0136567996814847,
0.0031548594124615192,
-0.06106431409716606,
-0.006901864893734455,
-0.06429772824048996,
-0.030006173998117447,
-0.021208232268691063,
-0.02705569565296173,
-0.017770513892173767,
0.04947312921285629,
-0.04056273400783539,
-0.03476865217089653,
-0.018770039081573486,
0.01730971783399582,
-0.029318250715732574,
0.015870649367570877,
0.0047577256336808205,
0.011031094938516617,
-0.06454714387655258,
-0.010863409377634525,
0.007510636933147907,
-0.033909741789102554,
0.0058226739056408405,
0.01996198296546936,
0.00373544218018651,
-0.08005702495574951,
-0.03925243020057678,
0.017765792086720467,
0.010606415569782257,
-0.01476660929620266,
0.006902472116053104,
-0.01123794075101614,
-0.0007968395948410034,
0.01734577864408493,
0.033557139337062836,
-0.025850215926766396,
0.024444477632641792,
0.055166084319353104,
0.007663463708013296,
-0.002219845773652196,
-0.025653475895524025,
0.02403360605239868,
0.060393206775188446,
0.05133726820349693,
0.01961684785783291,
-0.06538356095552444,
-0.08507537841796875,
0.00823707040399313,
0.00621098792180419,
-0.028091175481677055,
-0.07738203555345535,
0.030291056260466576,
0.07889388501644135,
0.025552324950695038,
0.026481868699193,
0.002840752014890313,
0.06401436030864716,
-0.020295623689889908,
-0.0025853991974145174,
-0.04336810111999512,
-0.004952511750161648,
0.034586332738399506,
0.06286162883043289,
-0.03564463555812836,
0.017296575009822845,
0.03247358277440071,
-0.035578131675720215,
0.001886204001493752,
0.004187826998531818,
0.007852951064705849,
-0.01970454677939415,
0.017708513885736465,
0.0053384811617434025,
-0.05831121653318405,
-0.05250357836484909,
-0.017181197181344032,
-0.007712231948971748,
0.021853290498256683,
0.0316334068775177,
-0.02282130904495716,
-0.03411674126982689,
-0.02683096006512642,
0.022126344963908195,
-0.03437716141343117,
0.028222281485795975,
-0.01700611785054207,
-0.010254533030092716,
0.0018622024217620492,
-0.010290582664310932,
0.04514264687895775,
-0.024846721440553665,
0.03875422477722168,
0.04033461958169937,
-0.014375573955476284,
-0.009205341339111328,
0.0404406413435936,
0.003976678475737572,
-0.04805765300989151,
0.05131594464182854,
0.0029204988386482,
0.0060593243688344955,
0.025379840284585953,
-0.008102978579699993,
-0.05716725438833237,
0.0004406936641316861,
0.04728204384446144,
-0.020335130393505096,
0.05816260725259781,
-0.019796330481767654,
0.01478807907551527,
0.02159935235977173,
0.00546133890748024,
0.01452300138771534,
0.014002598822116852,
-0.048950646072626114,
0.015030809678137302,
-0.01870664395391941,
-0.00540665490552783,
-0.00818759948015213,
0.005008412059396505,
-0.05196556821465492,
-0.03722872585058212,
-0.0012565861688926816,
-0.005380324553698301,
-0.0038005325477570295,
0.005025102291256189,
-0.010440745390951633,
-0.03006010130047798,
-0.01799163408577442,
-0.026192646473646164,
0.061658501625061035,
0.06006742641329765,
0.015370147302746773,
0.018427561968564987,
-0.0062567018903791904,
-0.02301696129143238,
0.04944029077887535,
-0.02538341097533703,
-0.029793255031108856,
-0.07298953086137772,
0.028717294335365295,
-0.023645762354135513,
-0.014333021827042103,
-0.027559351176023483,
0.09192042797803879,
0.04346004128456116,
-0.02653331123292446,
-0.009719467721879482,
0.037025999277830124,
0.010668770410120487,
0.012966189533472061,
-0.0022398189175873995,
-0.07189903408288956,
0.015371113084256649,
0.011848202906548977,
0.021522870287299156,
-0.02864903211593628,
0.007724679075181484,
-0.02320641465485096,
0.015147147700190544,
-0.007879947312176228,
-0.014823866076767445,
0.057341404259204865,
0.015299019403755665,
-0.05439584329724312,
0.020372817292809486,
0.05641273409128189,
-0.02998695708811283,
-0.00959605909883976,
0.04240553453564644,
-0.07497397065162659,
-0.01458101999014616,
0.0442434698343277,
-0.02688712440431118,
-0.052370425313711166,
0.030380966141819954,
0.013845602981746197,
0.004890188109129667,
-0.05455612763762474,
0.04129030182957649,
0.01025268156081438,
-0.03447110950946808,
0.022607410326600075,
-0.022029386833310127,
-0.019046548753976822,
-0.039743151515722275,
-0.026157138869166374,
0.014653800055384636,
0.0737813338637352,
-0.011783156543970108,
-0.01606270670890808,
-0.0640861764550209,
0.023996053263545036,
0.015886178240180016,
-0.04167482629418373,
0.048241302371025085,
0.07020081579685211,
0.046444863080978394,
0.04578367993235588,
-0.0027539110742509365,
0.056090448051691055,
0.018520642071962357,
-0.043644700199365616,
0.02157561108469963,
-0.014119998551905155,
-0.045446448028087616,
-0.021126020699739456,
-0.05853906273841858,
-0.030150718986988068,
0.029386233538389206,
-0.013188833370804787,
0.045725349336862564,
0.019064418971538544,
0.05640513077378273,
-0.016767460852861404,
-0.020644517615437508,
-0.07708071917295456,
0.06686364114284515,
-0.04389778897166252,
-0.003154756035655737,
-0.015103948302567005,
-0.027790529653429985,
0.004207002464681864,
-0.01882832683622837,
-0.02917158044874668,
0.07742041349411011,
-0.029947005212306976,
0.006803447846323252,
-0.012843078933656216,
0.027438214048743248,
-0.015855697914958,
0.009537427686154842,
-0.10980955511331558,
-0.012296583503484726,
-0.0000198894485947676,
-0.013039412908256054,
0.012945316731929779,
-0.008035817183554173,
0.04479481652379036,
-0.04739297926425934,
-0.03776758909225464,
-0.07142875343561172,
-0.0031548314727842808,
-0.003368034726008773,
0.02161754108965397,
0.0932593047618866,
0.0165230855345726,
-0.004224166739732027,
0.03998882696032524,
-0.07913986593484879,
0.024081207811832428,
0.02319098263978958,
0.027072723954916,
0.021836547181010246,
-0.020940471440553665,
0.012458865530788898,
-0.04801497235894203,
-0.0031167156994342804,
-0.0051163299940526485,
0.018509862944483757,
-0.033951446413993835,
0.04973037913441658,
0.01923391968011856,
0.020584480836987495,
0.0040127276442945,
0.024836933240294456,
-0.11845579743385315,
-0.01250022929161787,
0.004066769964993,
0.022227831184864044,
-0.056639816612005234,
-0.016041208058595657,
-0.03457622602581978,
0.031336721032857895,
-0.010709248483181,
-0.014359290711581707,
-0.013285537250339985,
-0.034244000911712646,
0.0007595494971610606,
0.04187363386154175,
-0.007012175861746073,
0.016757983714342117,
-0.013187206350266933,
0.02565251849591732,
-0.025602659210562706,
-0.045177310705184937,
0.003779085585847497,
-0.025340581312775612,
0.005607822444289923,
-0.017950870096683502,
0.023949798196554184,
-0.05536486580967903,
-0.03254729509353638,
0.030829748138785362,
0.0057902089320123196,
-0.04225734621286392,
-0.01113661378622055,
0.030503403395414352,
0.03206336125731468,
-0.020551592111587524,
0.006198822520673275,
0.04676163196563721,
0.02351798489689827,
-0.025484375655651093,
0.045676566660404205,
0.01833551563322544,
-0.022227132692933083,
-0.019817624241113663,
-0.02411297708749771,
0.028371332213282585,
-0.009568851441144943,
-0.022702550515532494,
0.005192517768591642,
-0.01740611530840397,
0.034240227192640305,
0.0068215359933674335,
-0.00022173966863192618,
0.037626393139362335,
-0.010862557217478752,
0.03481053560972214,
0.011001276783645153,
-0.044907890260219574,
0.05439809709787369,
0.006364727858453989,
0.027398264035582542,
0.03561908379197121,
0.005023612640798092,
-0.013406052254140377,
0.002237518783658743,
-0.051001645624637604,
-0.00963796116411686,
-0.03990469127893448,
-0.010270658880472183,
0.037788063287734985,
-0.052917007356882095,
-0.01045272033661604,
-0.02664410136640072,
-0.03286747261881828,
0.020047282800078392,
0.015292005613446236,
0.009067825973033905,
0.021929407492280006,
-0.004869356285780668,
0.04184304177761078,
0.07442865520715714,
-0.014965994283556938,
0.06265109777450562,
0.020624296739697456,
0.006767740473151207,
-0.0712207704782486,
0.031102662906050682,
-0.02657943032681942,
-0.03147187456488609,
-0.09394066780805588,
0.005127388518303633,
0.08464614301919937,
0.02802608534693718,
-0.0317055843770504,
-0.01302393339574337,
-0.004842543974518776,
-0.011365761049091816,
-0.0011142779840156436,
0.02399035170674324,
0.05141746997833252,
0.02884731814265251,
-0.00046115563600324094,
-0.024126077070832253,
-0.07002459466457367,
0.02162140980362892,
0.03940809145569801,
0.013167155906558037,
-0.015473728999495506,
-0.027214551344513893,
0.002278780099004507,
-0.05179772898554802,
-0.019448280334472656,
0.009761795401573181,
-0.018140217289328575,
0.05586748197674751,
0.01531197689473629,
-0.03028615564107895,
0.06593015789985657,
0.009174522012472153,
-0.03684070706367493,
-0.005707934498786926,
0.012393898330628872,
0.024925893172621727,
-0.009038287214934826,
-0.0044431984424591064,
-0.04740878567099571,
-0.10408186912536621,
0.005751246586441994,
0.011957623064517975,
-0.029057946056127548,
0.06763461232185364,
-0.006369035691022873,
0.030726727098226547,
0.024267813190817833,
-0.014495418407022953,
-0.01685011014342308,
0.014364059083163738,
0.002227981574833393,
0.03923574090003967,
0.014079110696911812,
0.029872141778469086,
0.06041202321648598,
-0.008443068712949753,
-0.005621692165732384,
-0.006622370332479477,
0.004026780836284161,
0.031099986284971237,
-0.010571093298494816,
0.01953529193997383,
-0.018605146557092667,
-0.027820728719234467,
-0.0037301923148334026,
0.04307880997657776,
-0.022715261206030846,
0.05734610557556152,
0.06437372416257858,
-0.02704247646033764,
-0.00970381312072277,
0.009071729145944118,
0.018127987161278725,
0.006803269498050213,
-0.009361056610941887,
0.019290002062916756,
0.013048919849097729,
-0.06519035249948502,
0.05609404295682907,
-0.002707752166315913,
-0.01700611412525177,
-0.05007604509592056,
0.016243357211351395,
-0.015142983756959438,
-0.0391734279692173,
-0.02986416406929493,
0.004171477165073156,
-0.02354063279926777,
-0.05410324037075043,
-0.03942510485649109,
-0.0044905515387654305,
-0.0560079887509346,
0.08720193803310394,
0.006592091638594866,
0.06676182895898819,
-0.05120541527867317,
-0.06009390950202942,
-0.017179453745484352,
-0.007829362526535988,
0.03394409269094467,
0.01671980880200863,
0.019839953631162643,
0.07271549105644226,
-0.000029729873858741485,
0.05605408549308777,
-0.018087895587086678,
-0.06627076119184494,
0.03020237199962139,
0.08290639519691467,
-0.02158249355852604,
-0.009755704551935196,
-0.02531273290514946,
0.025394244119524956,
0.08667394518852234,
-0.0050659277476370335,
-0.07962125539779663,
0.008682730607688427,
-0.0015724796103313565,
0.021905681118369102,
-0.06456142663955688,
-0.0012755447532981634,
-0.03339396417140961
] |
<p>I have $N$ distinguishable particles in a 1D harmonic oscillator potential with 'proper' frequency $\omega$. The particles also have internal spin-$\frac12$ degrees of freedom in a magnetic field $B$ with magnetic dipole $\mu$. The spin induced energy level splitting is
$$\varepsilon=2\mu B=0.1\hbar\omega$$</p>
<blockquote>
<p>Question: Show that the partition function is a product of the oscillator ($Z_1$) and spin ($Z_2$) partition functions.</p>
</blockquote>
<p>I have a response but I'm pretty dissatisfied with it. </p>
<p>I argued that
$$Z=\sum_n\exp(\beta\varepsilon_n)$$
so for $\varepsilon_i$ (oscillation energy) and $\varepsilon_j$ (spin energy) we have:</p>
<p>$$Z=\sum_n\exp(\beta\varepsilon_n)=\sum_{i,j}\exp\bigl(\beta(\varepsilon_{i}+\varepsilon_{j})\bigr)=\sum_i\sum_j\exp(\beta\varepsilon_i)\exp(\beta\varepsilon_j)=Z_1Z_2$$</p>
<p>(Edit: I actually don't think $\sum_{i,j}\leftrightarrow \sum_i \sum_j$ is valid)</p>
<p>This is where I left things for the time being but I wonder if I should elaborate.</p>
<p>For example, I considered... $$\varepsilon=2\mu B$$ ...for the 3 level spin and argued that...
$$\begin{align}
Z_2
&=\sum \exp(\beta\varepsilon_2)=\exp(-0.5\beta\varepsilon_2)+1+\exp(0.5\beta\varepsilon_2) \\
&=\exp(-0.05\beta\hbar\omega)+1+\exp(0.05\beta\hbar\omega)
\end{align}$$ ...for 3 energy levels $-0.5\varepsilon$, $0$ and $0.5\varepsilon$</p>
<p>For the harmonic oscillator I argued that... $$\varepsilon_1=\biggl(i+\frac{1}{2}\biggr)\hbar\omega$$ ...such that...
$$\begin{align}
Z_1
&=\sum_i \exp(\beta\varepsilon_1)=\sum_i \exp\biggl[\beta \biggl(i+\frac{1}{2}\biggr)\hbar\omega\biggr] \\
&=\frac{1}{2}\hbar\omega \sum_i \exp(\beta i\hbar\omega)=\frac{1}{\exp(-0.5\beta\varepsilon)-\exp(0.5\beta\varepsilon)}
\end{align}$$</p>
<p>If the above is correct then I should be able to arrive at $Z=Z_1Z_2$ easily. However, the outcome of the multiplication is unrecognisable to me. This is one of my challenges with this topic - trying to reconcile the maths with the physics</p>
<p>Clarification: </p>
<p>The above is the homework part. I'm also experiencing difficulty grasping some of the ideas in statistical physics, in particular, the relationship between the partition function, entropy and specific heat capacity</p>
<p>My understanding is that the partition function shows the number of microstates that are accessible within thermal energy range. Hence, the number of microstates that are accessible within thermal energy range is the product of microstates in the 1d oscillator and the 3 level system. Would this be 4 degrees of freedom in total (1 from the oscillator and 3 from the splitting)?</p>
<p>I have to say I'm very uncomfortable with my lack of physical understanding for the material. The relationship between the partition function, entropy and specific heat capacity is still very fuzzy in my mind.</p>
|
g2442
|
[
-0.0006128312088549137,
0.006363201420754194,
-0.004163953475654125,
-0.0417795293033123,
0.01596676930785179,
-0.0321628637611866,
0.08566548675298691,
0.07162410020828247,
0.003818113123998046,
0.019284633919596672,
-0.03657509386539459,
0.027469834312796593,
-0.013608316890895367,
-0.02718953602015972,
0.010405047796666622,
-0.009308656677603722,
0.05143677070736885,
0.02083684504032135,
-0.011993709951639175,
-0.012089617550373077,
-0.038777418434619904,
0.013534165918827057,
-0.0083901546895504,
-0.03300805762410164,
0.06152614206075668,
-0.024999605491757393,
0.0039006536826491356,
-0.02079862356185913,
-0.015556675381958485,
0.0030589404050260782,
0.0029200343415141106,
0.04734363779425621,
0.029656322672963142,
-0.04194780811667442,
-0.042673174291849136,
0.002459491603076458,
0.07727616280317307,
0.04196784645318985,
0.0023697244469076395,
0.012838390655815601,
-0.029364248737692833,
-0.042877037078142166,
0.019075745716691017,
-0.05406730994582176,
0.011720389127731323,
0.08325181156396866,
0.009137348271906376,
0.013033458963036537,
-0.00016438432794529945,
0.032952286303043365,
0.002882140688598156,
0.024323081597685814,
0.09909222275018692,
0.010045508854091167,
0.01869940012693405,
0.024668315425515175,
-0.0029362894129008055,
-0.021411512047052383,
0.04764295741915703,
0.05962081626057625,
0.025543024763464928,
0.03111588954925537,
-0.033792611211538315,
0.002140878001227975,
0.023470155894756317,
-0.013301336206495762,
-0.024905214086174965,
-0.010140985250473022,
-0.04675202816724777,
-0.06184212490916252,
0.002589278854429722,
-0.04466565325856209,
0.031965963542461395,
-0.0750587210059166,
-0.006055938079953194,
-0.0015466624172404408,
0.03298630937933922,
-0.03435107693076134,
0.02367418073117733,
0.030003298074007034,
-0.029279839247465134,
-0.012956824153661728,
0.002494288142770529,
0.05450810119509697,
0.028016313910484314,
0.0017522717826068401,
-0.02821349911391735,
-0.0008009650628082454,
0.027627870440483093,
0.07281117141246796,
0.011219941079616547,
0.0066756256856024265,
-0.006547269877046347,
0.003956872038543224,
-0.04021073877811432,
0.029768038541078568,
-0.049943286925554276,
0.006304921582341194,
-0.034578870981931686,
0.02742774970829487,
0.018441742286086082,
0.002036540536209941,
0.07412637770175934,
0.011235091835260391,
-0.008691656403243542,
-0.03656955808401108,
0.03347679600119591,
-0.004744479898363352,
0.01609628088772297,
0.061084993183612823,
-0.016699569299817085,
0.056151703000068665,
-0.002914181910455227,
-0.0025547626428306103,
-0.07208412885665894,
-0.026761511340737343,
0.08271218836307526,
-0.045287828892469406,
-0.06305821985006332,
0.028234103694558144,
0.0007390867685899138,
0.0013491944409906864,
0.013287991285324097,
0.060868192464113235,
-0.004584976471960545,
0.029261553660035133,
0.011005506850779057,
-0.021751273423433304,
0.043962884694337845,
-0.03950175270438194,
0.004804394673556089,
-0.02516133338212967,
0.00034844561014324427,
0.02823481895029545,
-0.03594107925891876,
0.04483380168676376,
0.05878666043281555,
0.005505450069904327,
-0.030335552990436554,
-0.014668293297290802,
0.033750664442777634,
-0.036331094801425934,
0.011839112266898155,
-0.052832555025815964,
-0.05157114937901497,
0.03612922504544258,
0.0031389847863465548,
-0.10009671002626419,
-0.03369767591357231,
0.05287495255470276,
0.023662300780415535,
0.048027798533439636,
-0.07602360099554062,
-0.007125666830688715,
-0.004938154481351376,
-0.028948824852705002,
0.027300788089632988,
-0.06706800311803818,
0.018404260277748108,
0.03920688480138779,
0.02813856117427349,
-0.03103179670870304,
0.018935123458504677,
-0.036674804985523224,
-0.05980319529771805,
0.03780047968029976,
0.020694268867373466,
-0.040107354521751404,
-0.0034922787453979254,
-0.0028463718481361866,
-0.02971484325826168,
0.025341534987092018,
0.017828818410634995,
0.022580726072192192,
0.011878359131515026,
0.026296580210328102,
-0.05762948840856552,
-0.021446889266371727,
0.02469119243323803,
0.03808364272117615,
0.017304155975580215,
-0.004985128063708544,
0.05442401394248009,
-0.0544431135058403,
-0.019709007814526558,
-0.023868253454566002,
0.04394872486591339,
0.03677944839000702,
-0.04552804306149483,
0.01827646978199482,
-0.03948872536420822,
0.03866581618785858,
0.009207379072904587,
-0.056389231234788895,
-0.0049439226277172565,
-0.0369703471660614,
0.029769210144877434,
-0.044478751718997955,
-0.03517833352088928,
-0.03623718023300171,
0.008006497286260128,
0.05065594241023064,
0.05648054927587509,
-0.05604607239365578,
0.04761732742190361,
-0.02928355522453785,
-0.007569843903183937,
0.013826115056872368,
-0.007079452276229858,
0.021583445370197296,
-0.009579019621014595,
-0.07347603887319565,
-0.03504500538110733,
-0.01407847460359335,
0.026756269857287407,
-0.06483056396245956,
0.024413494393229485,
0.0204783845692873,
0.0010621014516800642,
0.026464566588401794,
-0.03315155953168869,
0.009381682612001896,
0.0844421461224556,
-0.014590302482247353,
-0.02923617511987686,
0.014944442547857761,
-0.05522334575653076,
-0.035639967769384384,
-0.07278693467378616,
0.060043349862098694,
-0.042267050594091415,
-0.01436970941722393,
0.045048538595438004,
-0.0482662096619606,
-0.004459995776414871,
-0.023773446679115295,
-0.04200277104973793,
-0.012670117430388927,
0.009718358516693115,
0.003246569773182273,
-0.002306180540472269,
0.006475051864981651,
-0.028410492464900017,
-0.017886335030198097,
0.037458356469869614,
0.029635114595294,
-0.002973971189931035,
-0.0026351080741733313,
-0.00511661171913147,
-0.03972533717751503,
0.004166221711784601,
-0.02028452232480049,
0.010246016085147858,
0.03704969584941864,
-0.026589926332235336,
-0.02485002763569355,
0.0313025638461113,
0.033204615116119385,
-0.02605610154569149,
-0.027355385944247246,
-0.010244983248412609,
-0.028068533167243004,
-0.0034049032256007195,
0.06474043428897858,
-0.002153984038159251,
-0.02729518711566925,
-0.059574276208877563,
-0.031226785853505135,
-0.010980719700455666,
-0.01937764883041382,
-0.027457240968942642,
0.010134520009160042,
-0.012298276647925377,
0.04213625565171242,
0.02488812245428562,
-0.004299975000321865,
0.012778219766914845,
-0.005316011141985655,
0.05071774497628212,
-0.044253651052713394,
-0.01375552173703909,
0.01889752969145775,
-0.03038712777197361,
-0.02783665806055069,
0.03109722025692463,
-0.05220266059041023,
-0.023281414061784744,
-0.016555210575461388,
0.029915573075413704,
0.008486277423799038,
0.0008089725743047893,
0.02976243942975998,
0.015219787135720253,
-0.01607072912156582,
-0.021085290238261223,
0.007578314747661352,
0.016219954937696457,
-0.07800577580928802,
-0.011398893781006336,
0.051646433770656586,
0.08113759756088257,
0.02336549386382103,
-0.017896994948387146,
-0.030835021287202835,
-0.007390669081360102,
0.020390765741467476,
-0.048281408846378326,
0.005457942374050617,
0.017271187156438828,
-0.005312647670507431,
0.004725826904177666,
0.04299379885196686,
0.032885726541280746,
-0.027807652950286865,
-0.026787208393216133,
0.019557733088731766,
-0.02905328758060932,
-0.05031561478972435,
0.04017355665564537,
-0.05292655900120735,
-0.04755391180515289,
0.0022667741868644953,
-0.035860300064086914,
-0.06419819593429565,
0.026691485196352005,
-0.05682877451181412,
-0.023591510951519012,
-0.055858246982097626,
-0.09055796265602112,
0.008110138587653637,
-0.025570042431354523,
-0.0022304384037852287,
0.012270829640328884,
-0.005066961050033569,
-0.05701511353254318,
-0.04299231246113777,
-0.06632904708385468,
0.0138242207467556,
0.02168921008706093,
0.01044310349971056,
-0.018044060096144676,
-0.012157074175775051,
-0.008716292679309845,
-0.05246089771389961,
-0.04140171781182289,
0.010112854652106762,
-0.048429664224386215,
-0.010212906636297703,
0.020674733445048332,
0.04348992183804512,
-0.03313743323087692,
-0.005319981370121241,
0.03309332951903343,
0.06191999465227127,
0.057211972773075104,
0.014412272721529007,
0.07452409714460373,
0.014600180089473724,
-0.023639751598238945,
0.0008396885823458433,
0.0661601647734642,
-0.04974791780114174,
0.09284786134958267,
-0.020528893917798996,
0.007610597647726536,
0.04103074595332146,
0.016153184697031975,
0.038492556661367416,
-0.018412230536341667,
-0.03307763487100601,
-0.0008544411975890398,
-0.015384724363684654,
0.0141714196652174,
0.017040176317095757,
0.04842984676361084,
-0.07327994704246521,
-0.002516987035050988,
0.0018176697194576263,
-0.0120086669921875,
-0.040129296481609344,
0.009772398509085178,
-0.029207104817032814,
0.03870341181755066,
-0.011720001697540283,
0.05375828966498375,
-0.014865896664559841,
0.004668485373258591,
0.011124859564006329,
-0.03480497747659683,
0.018397394567728043,
0.008757244795560837,
-0.008944067172706127,
-0.03505842015147209,
0.021423105150461197,
0.0164431631565094,
-0.02158954367041588,
-0.021955877542495728,
-0.04697205126285553,
-0.04574732482433319,
0.057620324194431305,
-0.04774893820285797,
-0.06616172939538956,
0.0022183882538229227,
-0.0667678490281105,
0.0090557262301445,
-0.018480991944670677,
0.021992415189743042,
-0.028277050703763962,
-0.0003240915830247104,
-0.054816752672195435,
-0.030769214034080505,
0.01940661109983921,
0.014658941887319088,
-0.023755986243486404,
-0.015813522040843964,
-0.03624327480792999,
0.03085903264582157,
-0.049786485731601715,
0.021792341023683548,
-0.018959106877446175,
-0.041131921112537384,
-0.0029572444036602974,
-0.042355697602033615,
-0.015028261579573154,
0.008332273922860622,
0.01953227072954178,
0.019238581880927086,
0.011260095052421093,
-0.0450972281396389,
-0.035391587764024734,
0.00018202883074991405,
0.02269616909325123,
-0.005515660159289837,
-0.016973715275526047,
-0.07061605900526047,
0.016463827341794968,
-0.07405086606740952,
0.012081912718713284,
-0.04059753566980362,
0.03340154513716698,
0.028919709846377373,
0.00366754038259387,
-0.010907478630542755,
0.002898336388170719,
0.05363823100924492,
0.01463509351015091,
-0.04654155299067497,
-0.061027951538562775,
-0.017802180722355843,
-0.020598154515028,
0.06781210005283356,
0.05222080647945404,
0.008168200962245464,
-0.0033759104553610086,
0.01044941134750843,
-0.01566886343061924,
-0.022847244516015053,
-0.005661650560796261,
0.015178236179053783,
-0.004277336876839399,
-0.044715289026498795,
0.0036879258695989847,
-0.022154437378048897,
-0.07696948200464249,
-0.016384070739150047,
0.025080926716327667,
-0.04447579383850098,
0.015516341663897038,
0.034575335681438446,
0.024032561108469963,
0.05904542654752731,
-0.026669129729270935,
0.031845495104789734,
-0.049973245710134506,
0.002814589999616146,
0.01564931496977806,
0.007607568055391312,
-0.03039027377963066,
-0.024328337982296944,
-0.009633785113692284,
-0.008078369311988354,
0.007463687099516392,
0.03510101139545441,
0.05961226671934128,
0.008344434201717377,
-0.00044116939534433186,
0.010048194788396358,
-0.06709729135036469,
-0.03613870218396187,
0.003822267521172762,
0.041681576520204544,
0.027290543541312218,
0.05053894966840744,
0.022900313138961792,
0.010765797458589077,
0.007961893454194069,
0.0062385015189647675,
-0.027456726878881454,
-0.005667387042194605,
0.018002599477767944,
-0.018377317115664482,
0.02207435481250286,
0.005302551202476025,
0.00363957230001688,
-0.035925328731536865,
0.02156730182468891,
0.01043645478785038,
0.0037099667824804783,
0.002137622330337763,
0.010388926602900028,
0.031135153025388718,
0.0010995971970260143,
0.037418387830257416,
0.014361372217535973,
0.009035075083374977,
-0.047268688678741455,
0.02941221557557583,
0.0425921194255352,
0.057743482291698456,
-0.05164845287799835,
0.012698300182819366,
-0.009531312622129917,
0.03571374714374542,
-0.021968411281704903,
0.048717837780714035,
0.030961815267801285,
-0.026480762287974358,
-0.02134585939347744,
-0.01957693323493004,
0.08333117514848709,
0.03773311525583267,
0.040963903069496155,
-0.02233356609940529,
0.06329801678657532,
0.04683587700128555,
-0.010130555368959904,
-0.03466621786355972,
-0.03561510890722275,
-0.023599134758114815,
0.06442806124687195,
0.019196663051843643,
-0.052174702286720276,
0.004913496784865856,
-0.000008034996426431462,
-0.030975738540291786,
0.014460554346442223,
-0.024055076763033867,
-0.012085018679499626,
0.017455892637372017,
-0.045441724359989166,
-0.0051513612270355225,
0.0006331474869512022,
-0.009027279913425446,
-0.009126015938818455,
0.07287393510341644,
0.028581509366631508,
0.02013065293431282,
-0.024823885411024094,
0.045096974819898605,
0.04007332772016525,
0.00903509184718132,
-0.0203163530677557,
0.016471197828650475,
-0.005499806720763445,
0.013126225210726261,
-0.008808151818811893,
0.04216128587722778,
-0.05953122302889824,
-0.03271006792783737,
0.01325830165296793,
-0.02737487480044365,
0.01821781136095524,
0.00754426559433341,
0.03693600744009018,
0.0344221256673336,
0.017140358686447144,
-0.014905004762113094,
-0.008848169818520546,
-0.02942010574042797,
0.017752576619386673,
-0.027401532977819443,
0.024903127923607826,
0.03901109844446182,
0.027769897133111954,
0.0064332690089941025,
0.09477052092552185,
-0.0758155807852745,
-0.019907241687178612,
-0.007481584791094065,
-0.027767719700932503,
4.641657014303746e-8,
-0.006339582614600658,
-0.013279530219733715,
-0.026582755148410797,
0.02278207615017891,
-0.044660329818725586,
0.015472497791051865,
-0.03166850283741951,
0.00842847116291523,
0.005333802197128534,
0.034879572689533234,
-0.044466033577919006,
-0.018459362909197807,
-0.06413301825523376,
-0.04085158184170723,
0.042671237140893936,
-0.04871826991438866,
0.006132588721811771,
-0.06807992607355118,
0.05510982125997543,
-0.042012959718704224,
0.034608397632837296,
0.041133686900138855,
0.05673835054039955,
0.03808791562914848,
-0.0178829412907362,
0.04165714606642723,
0.0221425611525774,
0.025505930185317993,
0.04431212693452835,
0.009713340550661087,
0.033957622945308685,
0.028057126328349113,
-0.04220294579863548,
0.06781185418367386,
0.03206858038902283,
0.011688604950904846,
0.016940394416451454,
0.019246520474553108,
0.013656231574714184,
0.016155514866113663,
0.06402899324893951,
-0.01524217426776886,
0.04498555138707161,
-0.044360652565956116,
-0.025288231670856476,
-0.015309302136301994,
-0.03466370329260826,
0.01905170828104019,
0.05937599390745163,
-0.04718470200896263,
0.012762132100760937,
0.04577871039509773,
0.00012396022793836892,
-0.06297166645526886,
0.01277141273021698,
0.0729813501238823,
0.0639503225684166,
-0.11005493253469467,
0.01830292120575905,
0.043071430176496506,
-0.009828832000494003,
-0.00858377292752266,
-0.010553683154284954,
-0.022140758112072945,
-0.020383700728416443,
-0.022722819820046425,
0.004742470104247332,
0.06380165368318558,
0.0026644845493137836,
-0.046322040259838104,
-0.030549995601177216,
-0.016749335452914238,
-0.025017131119966507,
-0.04116419702768326,
0.07297666370868683,
0.01688096672296524,
0.07503907382488251,
0.017305372282862663,
-0.0857919454574585,
-0.03869654983282089,
-0.022918077185750008,
-0.05908416211605072,
0.03250619024038315,
-0.011907964944839478,
-0.005375178065150976,
-0.041934724897146225,
-0.001823481172323227,
0.03207892179489136,
-0.04791965335607529,
-0.03078387677669525,
-0.05668165534734726,
-0.003479012753814459,
0.015319138765335083,
0.002864685608074069,
0.016309401020407677,
-0.10681144893169403,
0.0038708276115357876,
0.08309558033943176,
0.09282331168651581,
-0.04012960195541382,
0.07414928078651428,
0.07631685584783554,
-0.0018343230476602912,
-0.04385678470134735,
0.025934383273124695,
0.030127450823783875,
0.06400295346975327,
0.07360918074846268,
0.07244760543107986,
0.04037223756313324,
0.00863740872591734,
-0.005974886938929558,
-0.01792922429740429,
-0.021826785057783127,
0.029215386137366295,
0.018261170014739037,
-0.031580109149217606,
0.008265339769423008,
-0.021549969911575317,
0.036943867802619934,
0.0020438788924366236,
0.014918635599315166,
0.005175106227397919,
0.04633047804236412,
0.034895800054073334,
-0.06665012240409851,
-0.004761068150401115,
0.016056541353464127,
-0.03196492791175842,
0.025777487084269524,
0.047537170350551605,
-0.024035722017288208,
0.002389003289863467,
0.010690636932849884,
-0.05735207721590996,
0.004834664519876242,
-0.005581479519605637,
0.06204250827431679,
-0.03247962146997452,
0.021854102611541748,
0.006932489573955536,
-0.030078131705522537,
-0.02085401862859726,
-0.03443280607461929,
0.001120923669077456,
-0.012601448222994804,
0.002253845101222396,
0.013784019276499748,
0.003970818594098091,
-0.00934459175914526,
-0.026521295309066772,
0.07040286809206009,
-0.041407424956560135,
-0.0377252921462059,
0.010144796222448349,
-0.10480549186468124,
0.042469531297683716,
0.06267546862363815,
-0.013412303291261196,
-0.08205733448266983,
-0.031257253140211105,
-0.02707396261394024,
0.00438226293772459,
0.06755784898996353,
-0.0995420515537262,
0.047906648367643356,
0.06274068355560303,
0.006625940091907978,
0.004303778056055307,
-0.013618512079119682,
-0.047855302691459656,
0.001381009817123413,
0.03550269082188606,
0.02642696164548397,
0.022717151790857315,
0.012964613735675812,
0.03826109692454338
] |
<p>For example say the gravitation constant instead of equaling G, was actually a range bounded between 0 and infinity. </p>
<p>Our Universe would be at a point on this range (equal to our G value) where things could physically exist and produce stars, galaxies and life. Yet in the gravitation constant's dimension it is able to be lower and higher then our G value. </p>
<p>All other physical constants being equal, this would allow the sort of full universe we recognise to exist on only a very tiny part of the full range of the gravitation constant's dimension. The rest of the dimension would be full of non-universes that would not be able to support anything.</p>
<p>The other non-dependent physical constants perhaps also represent dimensions. And there might even be a set of useful life supporting universe's on a continuous 'line' inside this n-dimensional structure.</p>
|
g2443
|
[
0.003136237384751439,
0.025836871936917305,
0.02050543949007988,
-0.041487012058496475,
-0.02822183072566986,
0.04657454416155815,
-0.039556074887514114,
-0.028686614707112312,
-0.0611259788274765,
-0.07670213282108307,
0.04853929579257965,
-0.025969943031668663,
0.015187352895736694,
0.015832116827368736,
0.027493424713611603,
-0.010615387000143528,
-0.03655928745865822,
-0.04761809483170509,
0.029234176501631737,
-0.026212545111775398,
-0.002265557646751404,
-0.00012321470421738923,
0.013366414234042168,
-0.0280399639159441,
-0.11324873566627502,
0.002890604780986905,
0.048565998673439026,
-0.010203912854194641,
-0.011353971436619759,
-0.0468614287674427,
0.027029456570744514,
-0.06398013234138489,
0.027533385902643204,
-0.002300532069057226,
-0.01510599348694086,
0.003911677282303572,
-0.008936742320656776,
0.07810958474874496,
0.05131305381655693,
-0.03961918503046036,
-0.018366342410445213,
0.01552653405815363,
-0.03590104356408119,
0.029679369181394577,
-0.013159246183931828,
0.0011496348306536674,
0.000591475865803659,
0.03038455732166767,
0.06585553288459778,
-0.07044387608766556,
-0.04033796489238739,
0.03926928713917732,
0.003371570259332657,
0.015984265133738518,
0.06513676792383194,
-0.02926703542470932,
0.0268514733761549,
0.021551627665758133,
-0.011034675873816013,
-0.022379811853170395,
0.01630105823278427,
-0.003181470325216651,
0.0201153215020895,
0.05659327656030655,
0.044662244617938995,
0.004367439076304436,
-0.048750270158052444,
-0.03507308289408684,
-0.042943499982357025,
-0.0013358447467908263,
0.002230527810752392,
0.01380354817956686,
-0.014428241178393364,
-0.031038183718919754,
0.00046646554255858064,
0.06809746474027634,
0.014072953723371029,
0.08127383142709732,
-0.03723091259598732,
0.022924106568098068,
-0.020706938579678535,
0.00641948077827692,
0.009501316584646702,
-0.002842176938429475,
0.079184889793396,
-0.04656056687235832,
-0.02651403099298477,
-0.027308909222483635,
-0.02554096281528473,
0.06048634648323059,
-0.004482518415898085,
0.040294669568538666,
0.04579108580946922,
0.0215425007045269,
0.013149227015674114,
-0.028293471783399582,
0.037363916635513306,
0.040640778839588165,
0.001109359785914421,
-0.01335114799439907,
0.01739676296710968,
0.04364822059869766,
0.06767652928829193,
-0.03165276721119881,
0.01943753845989704,
-0.0347585566341877,
0.07741627842187881,
-0.013335347175598145,
0.03491872176527977,
-0.03122340515255928,
0.025454625487327576,
0.008495144546031952,
-0.06426984816789627,
-0.04411543160676956,
-0.04187237098813057,
-0.04066071659326553,
0.08822564780712128,
-0.01143429335206747,
0.015623949468135834,
0.02333790622651577,
0.008924607187509537,
0.009854069910943508,
0.0016935169696807861,
0.05457799881696701,
-0.040096454322338104,
-0.01730579510331154,
-0.03354119136929512,
0.032659951597452164,
0.04093557223677635,
-0.0445423424243927,
0.04258309677243233,
-0.022635309025645256,
-0.06709928810596466,
0.027478931471705437,
-0.0006849705241620541,
0.009504187852144241,
-0.0006154080620035529,
-0.04987764358520508,
-0.056287266314029694,
0.03541068732738495,
-0.041519895195961,
-0.014221490360796452,
-0.05252772942185402,
-0.020866628736257553,
-0.011034965515136719,
0.02244274877011776,
-0.021634511649608612,
-0.008044666610658169,
-0.0408782958984375,
0.029049431905150414,
0.014944723807275295,
0.08758259564638138,
0.013071207329630852,
-0.010618384927511215,
-0.01743103377521038,
0.0016046117525547743,
0.03855808824300766,
0.008275349624454975,
0.007085764780640602,
-0.034223008900880814,
0.017182253301143646,
0.02663794532418251,
-0.023277120664715767,
-0.015357721596956253,
-0.026362182572484016,
0.06838103383779526,
-0.008420798927545547,
-0.04779404401779175,
0.0043265861459076405,
0.014385421760380268,
-0.05733361467719078,
-0.015329034067690372,
-0.00786960031837225,
0.020007533952593803,
0.054032668471336365,
0.03059501387178898,
0.036856938153505325,
-0.03018280304968357,
-0.029881879687309265,
-0.011614281684160233,
0.01786099001765251,
-0.04767091944813728,
0.009327149018645287,
-0.03021099977195263,
-0.018346283584833145,
0.014933044090867043,
-0.0012914808467030525,
-0.020239630714058876,
0.035635728389024734,
-0.0033114920370280743,
-0.022593962028622627,
-0.03944195434451103,
0.005986638367176056,
0.007939538918435574,
-0.026065777987241745,
-0.03114345856010914,
0.02935907058417797,
-0.02957581914961338,
-0.022100094705820084,
0.027375470846891403,
-0.01939385198056698,
0.07493207603693008,
0.034890107810497284,
-0.012400873936712742,
0.017873583361506462,
0.023370027542114258,
0.01590043306350708,
0.02033017948269844,
0.027290819212794304,
-0.05614938959479332,
0.03805002197623253,
-0.08130112290382385,
-0.014250379055738449,
0.03348778933286667,
0.0017842829693108797,
-0.020642386749386787,
-0.04373452439904213,
0.007665376644581556,
-0.0069780801422894,
0.0708441510796547,
0.022006604820489883,
-0.012676774524152279,
0.05522256717085838,
0.010743649676442146,
0.022569578140974045,
-0.030425790697336197,
-0.04415649175643921,
0.00205948855727911,
0.048514336347579956,
-0.04178834334015846,
-0.016176952049136162,
0.0016107626724988222,
0.01971736177802086,
-0.037916041910648346,
-0.018675319850444794,
0.01594185084104538,
-0.04485525190830231,
-0.03373763710260391,
-0.025485100224614143,
0.03621827811002731,
0.0028388185892254114,
-0.009241921827197075,
-0.02351546660065651,
0.03228694200515747,
0.004802455194294453,
-0.05695956200361252,
-0.005111289210617542,
-0.020494485273957253,
-0.04542209208011627,
0.05255778878927231,
0.01390847098082304,
-0.012379330582916737,
0.047107014805078506,
0.014023950323462486,
-0.009181872941553593,
-0.019349368289113045,
0.024676552042365074,
0.05186367779970169,
-0.03973977640271187,
-0.027225598692893982,
0.013646707870066166,
-0.040700312703847885,
0.06039112061262131,
0.05304774269461632,
0.0020544128492474556,
0.007659063208848238,
-0.03301651403307915,
0.018163220956921577,
-0.05082017555832863,
0.059649985283613205,
0.034318987280130386,
-0.020217718556523323,
-0.008822164498269558,
0.01566959358751774,
-0.009530636481940746,
0.028099697083234787,
0.028840623795986176,
-0.03328033164143562,
0.05093039199709892,
-0.017265401780605316,
0.024956421926617622,
0.043038830161094666,
-0.03791503980755806,
-0.006527787074446678,
0.01618843898177147,
-0.04383757337927818,
-0.007216476369649172,
0.008091924712061882,
-0.04340841993689537,
0.011553404852747917,
0.06785514950752258,
-0.01251375861465931,
-0.049853723496198654,
0.009758899919688702,
-0.02397194691002369,
0.055463872849941254,
-0.008922263979911804,
-0.0229956042021513,
-0.03835441917181015,
0.0347839817404747,
-0.024252282455563545,
-0.01746431179344654,
0.030678192153573036,
-0.017680268734693527,
-0.0806565061211586,
0.012344569899141788,
-0.0004778799775522202,
0.0023705593775957823,
-0.0332023948431015,
-0.05957650765776634,
0.030919373035430908,
0.04498092457652092,
0.027468165382742882,
0.015706447884440422,
-0.0010388202499598265,
0.006911204196512699,
0.02241126075387001,
-0.016744263470172882,
0.0035049482248723507,
-0.04658008739352226,
0.0790691003203392,
-0.05273785814642906,
-0.006801218260079622,
-0.008339847438037395,
0.021169766783714294,
0.040359921753406525,
-0.03974102437496185,
0.009549173526465893,
-0.05907175689935684,
0.07497693598270416,
0.05324935540556908,
-0.030192561447620392,
0.04976622015237808,
0.0440068393945694,
-0.02367193065583706,
-0.03561282530426979,
-0.02538544498383999,
-0.031235970556735992,
0.05566950514912605,
0.006574398372322321,
-0.07656021416187286,
-0.0023858824279159307,
0.0004249681660439819,
0.025331489741802216,
0.00028939571348018944,
0.06947886943817139,
-0.03239426389336586,
0.021158991381525993,
-0.017767811194062233,
-0.0006079056183807552,
0.0382203571498394,
-0.017789388075470924,
-0.01899396814405918,
0.012826550751924515,
0.0013896870659664273,
0.05314689874649048,
-0.0023498982191085815,
0.01652558520436287,
0.010589963756501675,
-0.026269054040312767,
0.037843137979507446,
-0.04317833110690117,
0.012673666700720787,
-0.0074824802577495575,
0.03704749420285225,
0.05308137461543083,
0.06903322041034698,
0.023536544293165207,
0.020863747224211693,
0.05902647227048874,
0.05707460269331932,
-0.013140418566763401,
-0.006901295389980078,
-0.024562053382396698,
0.07541663199663162,
-0.02497287653386593,
0.06169956922531128,
-0.042933542281389236,
0.006023325491696596,
0.033437736332416534,
0.05681772157549858,
-0.00853776652365923,
0.0054916394874453545,
-0.019416097551584244,
0.0011729708639904857,
0.030705951154232025,
-0.015811795368790627,
-0.028103798627853394,
-0.015313735231757164,
-0.008608906529843807,
0.028233136981725693,
-0.0705312192440033,
-0.0002541118592489511,
-0.006665412802249193,
0.004097092896699905,
-0.026215557008981705,
-0.036125943064689636,
-0.0715647041797638,
0.04882171005010605,
0.004795853514224291,
0.033453166484832764,
-0.026125149801373482,
0.009958242997527122,
0.01266260165721178,
-0.0059207347221672535,
-0.026922622695565224,
0.05351308360695839,
0.018868446350097656,
0.005622701719403267,
-0.007143540773540735,
0.005058058071881533,
-0.0042744893580675125,
0.017079995945096016,
-0.040821559727191925,
0.06559339910745621,
-0.012348074465990067,
-0.003420748747885227,
-0.04718252271413803,
0.05140291154384613,
0.04994833469390869,
0.061395313590765,
0.06276289373636246,
0.01987696997821331,
0.0372796505689621,
0.048809781670570374,
0.024063877761363983,
-0.013520395383238792,
0.0042793890461325645,
-0.016776736825704575,
0.03655365854501724,
-0.021550653502345085,
0.007367837708443403,
0.0056664347648620605,
0.013327853754162788,
-0.018955891951918602,
0.024675026535987854,
-0.09750773012638092,
-0.01135566271841526,
-0.037229739129543304,
-0.05977683514356613,
0.02572036162018776,
0.0028062930796295404,
0.021527443081140518,
0.016533583402633667,
0.014411727897822857,
0.06521594524383545,
-0.060162607580423355,
0.008879947476089,
-0.022581879049539566,
0.018961891531944275,
-0.03160453215241432,
-0.01794286258518696,
-0.05534883961081505,
-0.020275138318538666,
-0.012181436643004417,
-0.06181217357516289,
0.0023336673621088266,
0.022312752902507782,
0.07055684179067612,
0.03749464079737663,
-0.059501681476831436,
-0.020072929561138153,
-0.02806522510945797,
0.02795485220849514,
0.05154101178050041,
-0.015340681187808514,
-0.02874496392905712,
0.00827603880316019,
-0.0560329295694828,
0.041273824870586395,
-0.03496137261390686,
0.07362557202577591,
0.022525882348418236,
0.03521135449409485,
-0.011075841262936592,
-0.020056171342730522,
-0.029911205172538757,
-0.00020673105609603226,
-0.04037768393754959,
-0.04665610194206238,
-0.02477172575891018,
-0.030222531408071518,
0.06059229001402855,
0.004448264837265015,
-0.0009546840447001159,
0.025399520993232727,
-0.07010729610919952,
-0.010519016534090042,
-0.04178951308131218,
-0.002954452997073531,
0.026400605216622353,
-0.06242002919316292,
0.033367399126291275,
0.05014375224709511,
-0.018666686490178108,
-0.03337525203824043,
-0.06036650016903877,
-0.02561657689511776,
0.011627031490206718,
-0.03415416553616524,
0.007852254435420036,
-0.004665309563279152,
0.02355075813829899,
-0.047111157327890396,
-0.047274619340896606,
0.05267690494656563,
0.025968722999095917,
0.0021634730510413647,
-0.0017143497243523598,
0.04675380885601044,
-0.006086116656661034,
0.018189294263720512,
-0.034906599670648575,
-0.006122247315943241,
-0.005920792929828167,
-0.030210811644792557,
-0.015363733284175396,
-0.02434401772916317,
0.024935293942689896,
-0.014370737597346306,
0.00681816041469574,
-0.001435167621821165,
0.03179213032126427,
-0.039307691156864166,
0.04273473471403122,
0.07094010710716248,
0.01974666677415371,
-0.007278669625520706,
0.034205399453639984,
0.00951230525970459,
0.113179050385952,
-0.026224078610539436,
-0.013314212672412395,
-0.05064484104514122,
-0.024502640590071678,
0.013746744021773338,
-0.009184298105537891,
0.03714939206838608,
0.05182623863220215,
-0.056031957268714905,
-0.03448226675391197,
0.010074472054839134,
-0.03142433986067772,
0.031076189130544662,
-0.028521288186311722,
-0.027511194348335266,
-0.08292466402053833,
0.05819960683584213,
0.0509909987449646,
-0.05758872628211975,
-0.05016481131315231,
0.03206496313214302,
-0.00853637047111988,
0.05439716950058937,
-0.03464968502521515,
0.039935268461704254,
0.011655759997665882,
0.05901205912232399,
-0.06054838001728058,
-0.034517329186201096,
-0.03533243015408516,
0.051275163888931274,
0.01606857404112816,
0.022761177271604538,
-0.0709986761212349,
-0.027145184576511383,
0.03540440648794174,
-0.056579262018203735,
0.0910186693072319,
0.004996023140847683,
0.0017904082778841257,
0.020878728479146957,
0.018126564100384712,
0.010330203920602798,
-0.045097336173057556,
-0.046362731605768204,
-0.010617095045745373,
0.0007159765809774399,
0.009310629218816757,
0.01103297807276249,
-0.026047414168715477,
0.05733584240078926,
0.03042665682733059,
-0.000580121180973947,
-0.02263346128165722,
0.01849476620554924,
-0.007567535620182753,
0.015255244448781013,
-0.010105726309120655,
0.0020724639762192965,
-0.015953803434967995,
-0.02313169278204441,
-0.020184703171253204,
-0.01696969009935856,
-0.003192741423845291,
-0.059167057275772095,
0.03409409150481224,
-0.062120988965034485,
-0.08014516532421112,
-0.009335123933851719,
0.007774731144309044,
0.01745600998401642,
0.0558677613735199,
0.013027003966271877,
0.009987272322177887,
0.03745485842227936,
-0.09351205825805664,
-0.01806676760315895,
0.03748863562941551,
0.03703082725405693,
0.07475721091032028,
0.029819127172231674,
0.010122176259756088,
0.024649668484926224,
0.016292568296194077,
-0.03115951269865036,
0.014138862490653992,
-0.05613517016172409,
-0.024224326014518738,
0.043277557939291,
-0.03957921266555786,
0.014604251831769943,
0.006655864417552948,
0.00679943710565567,
0.0035480072256177664,
0.0308341383934021,
-0.04838946461677551,
0.038488924503326416,
0.023138506338000298,
-0.016527365893125534,
-0.05544503033161163,
0.010792814195156097,
0.05435944348573685,
0.02853192389011383,
-0.033351775258779526,
0.047485291957855225,
-0.04368896409869194,
-0.005546700209379196,
0.010813446715474129,
-0.03379072993993759,
-0.005624853074550629,
-0.06271566450595856,
0.05398626625537872,
0.0028080407064408064,
0.006474088877439499,
0.02290485054254532,
0.00819461327046156,
-0.008079256862401962,
-0.010446829721331596,
0.04338650032877922,
0.04496026411652565,
-0.019070452079176903,
-0.04389498382806778,
-0.014910202473402023,
-0.10878799855709076,
0.000939271820243448,
-0.03980178385972977,
-0.02347330003976822,
-0.044923778623342514,
-0.08219129592180252,
-0.011296712793409824,
0.0028303589206188917,
0.00599134573712945,
0.026214873418211937,
-0.026112673804163933,
0.04761085286736488,
0.05495327338576317,
-0.07364978641271591,
-0.019920779392123222,
0.008700207807123661,
-0.043373096734285355,
-0.053345534950494766,
0.03181964531540871,
0.01926238276064396,
0.022418517619371414,
-0.0036422403063625097,
-0.05449709668755531,
-0.013587715104222298,
0.03357016295194626,
0.013673009350895882,
-0.004429122433066368,
0.03604159504175186,
0.014104960486292839,
-0.02793934755027294,
-0.036886051297187805,
0.0071510071866214275,
0.045347392559051514,
-0.01757618971168995,
0.04640991613268852,
-0.021643463522195816,
-0.0242916326969862,
-0.0066641513258218765,
0.04975167661905289,
-0.04605792090296745,
0.022770866751670837,
-0.023742185905575752,
-0.012769799679517746,
0.04359685629606247,
0.032202184200286865,
-0.07002514600753784,
0.0018420371925458312,
-0.027379561215639114,
-0.03216053545475006,
-0.027484405785799026,
0.05312751978635788,
0.0019788797944784164,
-0.017622634768486023,
0.00793358962982893,
-0.034989386796951294,
-0.02658540941774845,
-0.015301275998353958,
0.07468757033348083,
-0.044970765709877014,
0.04267260432243347,
0.02640613168478012,
0.024813242256641388,
0.014061243273317814,
-0.008101828396320343,
0.06148938834667206,
-0.0024229332339018583,
-0.06444206833839417,
-0.05461851879954338,
-0.009065289981663227,
-0.05176016688346863,
-0.015259253792464733,
0.04642314836382866,
-0.034043751657009125,
-0.0760764330625534,
-0.03305993229150772,
-0.0000015528622725469177,
-0.017130790278315544,
0.021488938480615616,
-0.008779976516962051,
0.03202579542994499,
-0.01626718044281006,
0.03341639041900635,
-0.02787676453590393,
0.03578350320458412,
-0.08021355420351028,
-0.011156621389091015,
-0.06886380910873413,
-0.0006978639867156744,
0.045693568885326385,
0.020336760208010674,
0.043730344623327255,
-0.019938595592975616,
-0.052237268537282944,
0.04586344584822655,
0.09945018589496613,
-0.02820296585559845,
-0.033777642995119095,
-0.05157151818275452,
-0.021157249808311462,
-0.017706938087940216,
0.05034865811467171,
-0.004496759735047817,
0.00553044443950057,
0.018324732780456543,
-0.04876058176159859,
-0.0007134238840080798,
-0.014385223388671875,
0.013997364789247513,
0.021370025351643562,
0.030722541734576225,
0.01337847113609314,
-0.007481991779059172,
-0.027633560821413994,
0.04567054286599159
] |
<p><img src="http://i.stack.imgur.com/gQ3jg.gif" alt=""></p>
<p>I recently stumbled upon the above image describing partial transmittance, and was wondering what sort of equation would model such a wave propagating through varying mediums. Is there also an equation for continuous mediums, as opposed to the discontinuous transition in the picture?</p>
|
g2444
|
[
-0.0038322010077536106,
-0.02981095016002655,
-0.0293095912784338,
-0.001819865545257926,
0.002690426539629698,
-0.028466714546084404,
0.032491642981767654,
-0.006124619394540787,
0.013586346060037613,
-0.010185318998992443,
-0.039875734597444534,
0.0042615314014256,
0.017539240419864655,
0.021395936608314514,
0.007166725117713213,
-0.06966087222099304,
0.03583873435854912,
-0.0470273494720459,
0.008788025937974453,
0.016893694177269936,
0.011484518647193909,
-0.010350799188017845,
0.012583311647176743,
-0.015261407941579819,
0.005848460830748081,
0.010178023017942905,
0.023622507229447365,
-0.0231429822742939,
0.0037383276503533125,
-0.03929781913757324,
-0.007534526754170656,
-0.05480656400322914,
0.04109012708067894,
-0.015206562355160713,
-0.0216798298060894,
0.007684743497520685,
-0.016827942803502083,
0.025993919000029564,
0.03457220643758774,
0.0748981162905693,
0.036859385669231415,
-0.04765896126627922,
-0.059572767466306686,
-0.0011856872588396072,
-0.0010800277814269066,
-0.05041070282459259,
-0.07408441603183746,
0.014780638739466667,
-0.05651453509926796,
-0.02731146663427353,
-0.005280217621475458,
0.022635875269770622,
0.012829790823161602,
0.05206182226538658,
-0.0428459495306015,
0.02949737198650837,
0.00535960728302598,
0.015797307714819908,
0.05866508558392525,
-0.002176621463149786,
0.011415380984544754,
0.014519325457513332,
0.0076354979537427425,
-0.024656493216753006,
0.05545485019683838,
-0.04100579768419266,
-0.04686059430241585,
-0.03998386114835739,
0.003775664372369647,
-0.02015554904937744,
0.04817939177155495,
-0.0017775639425963163,
-0.01613960787653923,
-0.03273485600948334,
-0.011370309628546238,
-0.001141898101195693,
0.0009505453053861856,
-0.037938959896564484,
-0.06285975873470306,
-0.011830693110823631,
-0.031992107629776,
-0.008218983188271523,
0.008352144621312618,
0.016146402806043625,
0.04354552924633026,
-0.00405897805467248,
0.046176210045814514,
-0.006250289734452963,
-0.06293340772390366,
-0.0544130839407444,
-0.04139862582087517,
0.018533891066908836,
0.010364529676735401,
-0.037797633558511734,
0.05273771658539772,
-0.06209516152739525,
-0.07774373143911362,
0.050749827176332474,
0.014819318428635597,
-0.020086759701371193,
-0.03696642816066742,
-0.011693714186549187,
0.043344128876924515,
-0.01371585950255394,
-0.03656284883618355,
0.009169534780085087,
-0.020264137536287308,
0.014692178927361965,
-0.003402650123462081,
0.04268141835927963,
0.01843038573861122,
-0.07902296632528305,
-0.057066671550273895,
0.04722687974572182,
0.0032141031697392464,
-0.06861921399831772,
0.0065433671697974205,
0.009771188721060753,
-0.013023022562265396,
0.031634315848350525,
0.0023818404879420996,
0.005705986171960831,
0.004422467201948166,
0.06940361857414246,
-0.008173736743628979,
0.0351448580622673,
0.004367745481431484,
-0.006608155556023121,
0.051584526896476746,
0.041147757321596146,
0.04979483410716057,
-0.0027215550653636456,
-0.010490515269339085,
0.04222453385591507,
0.031275901943445206,
0.009153432212769985,
0.022413520142436028,
0.011026285588741302,
-0.02824016846716404,
0.032667286694049835,
0.014318648725748062,
-0.08934643864631653,
0.01319937501102686,
0.007036491297185421,
-0.01117208693176508,
0.01839640364050865,
0.027393819764256477,
0.006956298835575581,
0.04453379660844803,
-0.0801767036318779,
0.022924227640032768,
0.08118007332086563,
-0.0010719291167333722,
0.015726862475275993,
0.0014848036225885153,
0.02303965575993061,
0.08247008919715881,
-0.0466279573738575,
-0.00938492827117443,
-0.023957163095474243,
0.036303117871284485,
-0.038905587047338486,
0.020371180027723312,
0.014605320058763027,
-0.03990788757801056,
0.0041945930570364,
0.01601569540798664,
0.0177443940192461,
0.029097523540258408,
-0.016358425840735435,
-0.03659803792834282,
0.05043837055563927,
0.0025646656285971403,
0.029133865609765053,
0.017242388799786568,
0.057641878724098206,
0.09527771919965744,
-0.0066297054290771484,
-0.022667020559310913,
0.009868312627077103,
-0.07505130767822266,
-0.0033065855968743563,
-0.004391367081552744,
-0.10756786167621613,
0.040329162031412125,
-0.011922487057745457,
-0.07205614447593689,
-0.016458699479699135,
-0.05601106584072113,
-0.01079562772065401,
-0.02042422816157341,
-0.014705335721373558,
-0.015958290547132492,
0.016268836334347725,
-0.05463029816746712,
0.00014201519661583006,
0.043164800852537155,
-0.03593936562538147,
0.025268306955695152,
-0.004059276077896357,
0.03305268660187721,
0.053331512957811356,
0.09058201313018799,
0.027307994663715363,
0.04585768282413483,
-0.006377184297889471,
-0.017663881182670593,
-0.01926964521408081,
0.05003116652369499,
0.004383070394396782,
-0.02706131897866726,
-0.05171647295355797,
-0.031612150371074677,
0.060466963797807693,
-0.01820150390267372,
0.004132326692342758,
0.005582382436841726,
0.0260157510638237,
-0.00869932770729065,
0.018734190613031387,
0.02660207450389862,
0.016003204509615898,
-0.0007219106191769242,
0.0006281454116106033,
-0.04513879865407944,
-0.005500846542418003,
-0.0045197200961411,
0.0030933646485209465,
-0.020133227109909058,
0.07484836131334305,
0.012343637645244598,
0.0364350862801075,
0.02259340137243271,
-0.007400576490908861,
0.0638132318854332,
0.039134882390499115,
-0.043060850352048874,
-0.002692159730941057,
-0.05308439955115318,
-0.02737228386104107,
0.033788058906793594,
-0.019705284386873245,
-0.052661944180727005,
0.009395967237651348,
-0.01494048535823822,
-0.03884831815958023,
0.05451730266213417,
-0.025216933339834213,
0.047586578875780106,
-0.013352341018617153,
0.027982722967863083,
-0.08878317475318909,
0.038947440683841705,
0.006673050113022327,
-0.04578953981399536,
-0.062472376972436905,
-0.0022841691970825195,
0.06444013863801956,
-0.04779298976063728,
0.014049951918423176,
-0.04653310030698776,
-0.0027077430859208107,
0.04674452915787697,
0.023389410227537155,
-0.025714153423905373,
-0.03056502714753151,
0.0604003444314003,
0.05043734237551689,
-0.050527095794677734,
0.019566982984542847,
-0.0036402237601578236,
0.046654365956783295,
-0.011216356419026852,
0.007700984366238117,
-0.007278876379132271,
-0.01670796051621437,
0.0663994550704956,
-0.04587891325354576,
-0.031220190227031708,
0.018246974796056747,
-0.004846646450459957,
0.007171523291617632,
0.004294736310839653,
0.007591994013637304,
0.03956930339336395,
-0.0815499946475029,
0.07656123489141464,
0.04794292896986008,
0.009931930340826511,
0.08892854303121567,
-0.07026062905788422,
0.024633923545479774,
-0.017001226544380188,
0.05455343425273895,
-0.05622881278395653,
-0.010550841689109802,
0.03706210479140282,
-0.08725615590810776,
0.0199800506234169,
-0.00733529357239604,
-0.07920966297388077,
-0.011022385209798813,
-0.01965900883078575,
0.009684266522526741,
-0.011656704358756542,
-0.007326504215598106,
-0.0006776875234209001,
-0.0334654338657856,
0.030476512387394905,
0.03919801115989685,
-0.0033576188143342733,
0.01279162336140871,
0.025992371141910553,
0.032418567687273026,
0.01439870335161686,
-0.05971284210681915,
0.0038856815081089735,
0.03768115118145943,
0.004592446610331535,
0.010269667021930218,
0.009786443784832954,
-0.05902485549449921,
-0.0006319321691989899,
0.007308688946068287,
0.02557210624217987,
0.007841646671295166,
-0.015565936453640461,
0.029108276590704918,
-0.07326995581388474,
0.017693471163511276,
-0.004888426046818495,
0.005579395219683647,
-0.006102346815168858,
-0.03539567068219185,
0.025334276258945465,
-0.047598324716091156,
-0.03134346380829811,
0.054369743913412094,
0.040970172733068466,
0.027381839230656624,
-0.006324229296296835,
-0.0230527613312006,
-0.0958886444568634,
0.02569129690527916,
0.0010074847377836704,
-0.07303261011838913,
0.023466236889362335,
-0.018590915948152542,
0.022180648520588875,
-0.06962563097476959,
-0.0053121247328817844,
0.035008493810892105,
0.017841480672359467,
-0.02332262322306633,
-0.048218902200460434,
0.01876317895948887,
0.028920691460371017,
-0.038385409861803055,
0.07511664181947708,
0.000916957447770983,
0.04047849029302597,
-0.06013227626681328,
0.008729289285838604,
0.003957265522330999,
0.018704237416386604,
0.0038605984300374985,
0.07082311064004898,
0.07174745947122574,
0.0045627872459590435,
-0.006403179373592138,
0.05561957508325577,
0.005147289484739304,
-0.019443010911345482,
-0.05448788031935692,
-0.01154889166355133,
-0.014238758012652397,
-0.044687747955322266,
0.016008300706744194,
-0.06282874196767807,
0.040812041610479355,
-0.018851494416594505,
0.01644500158727169,
0.029994888231158257,
0.014979095198214054,
-0.008073028177022934,
0.04581630975008011,
-0.0037688654847443104,
-0.027202600613236427,
0.006314368918538094,
-0.036392711102962494,
0.03954800218343735,
-0.012314687483012676,
0.011724112555384636,
0.004215334542095661,
0.007048159837722778,
-0.031705498695373535,
-0.05364793539047241,
0.006621347740292549,
0.008596905507147312,
0.02435593493282795,
-0.0009134322172030807,
0.00866665318608284,
-0.037824228405952454,
0.013583007268607616,
0.006919702049344778,
0.006994916591793299,
0.014431554824113846,
-0.003028504317626357,
-0.007531038019806147,
-0.015978259965777397,
-0.031100045889616013,
0.006179929710924625,
-0.04250524938106537,
-0.062081482261419296,
-0.009952087886631489,
0.005315233021974564,
0.032269831746816635,
-0.03792531415820122,
-0.021681390702724457,
0.058291371911764145,
0.003881884505972266,
0.025016453117132187,
-0.07607241719961166,
0.018291430547833443,
0.03676510602235794,
0.01151471957564354,
0.06051751598715782,
-0.00377729837782681,
-0.04837077111005783,
-0.06121855601668358,
-0.05260820314288139,
0.05196538195014,
-0.010850916616618633,
0.06188360974192619,
-0.008540625683963299,
0.052840474992990494,
-0.1069537103176117,
-0.009844547137618065,
0.045973263680934906,
-0.033970851451158524,
0.03741108998656273,
-0.029311593621969223,
0.045889437198638916,
-0.024611545726656914,
0.01258085761219263,
0.06704210489988327,
-0.016600260511040688,
-0.031008101999759674,
0.015375121496617794,
-0.11016308516263962,
-0.07267113775014877,
0.008453124202787876,
-0.037998467683792114,
-0.04238494485616684,
-0.025729645043611526,
-0.07285743951797485,
-0.007033508270978928,
0.015311668626964092,
0.08932454138994217,
-0.028184102848172188,
-0.06225469708442688,
0.06218549981713295,
-0.0007669904152862728,
-0.03804193064570427,
0.023796970024704933,
-0.028845731168985367,
0.01734091155230999,
0.012166622094810009,
-0.05967001989483833,
-0.01751435548067093,
0.0008347094408236444,
0.0043654548935592175,
0.017658483237028122,
0.031817611306905746,
0.03641108423471451,
-0.012618198059499264,
-0.06196073815226555,
0.03778577223420143,
-0.005414650775492191,
0.002308832248672843,
0.014677274972200394,
-0.003283470869064331,
0.05064942315220833,
0.00933691393584013,
-0.02380298636853695,
0.04626990482211113,
0.00196631345897913,
0.062318604439496994,
0.013165449723601341,
-0.052086737006902695,
0.04928234964609146,
-0.04673750326037407,
-0.015001396648585796,
0.013122369535267353,
0.05013034865260124,
-0.012494522146880627,
0.053664542734622955,
-0.0016245979350060225,
-0.028184624388813972,
0.035609275102615356,
-0.007764016278088093,
-0.009668874554336071,
-0.02297934703528881,
-0.013015380129218102,
-0.02548137493431568,
0.06975820660591125,
0.022626783698797226,
-0.018807528540492058,
-0.014004879631102085,
0.07232087850570679,
0.015118781477212906,
-0.015838468447327614,
-0.061170972883701324,
0.004532762803137302,
0.025823689997196198,
-0.04520608112215996,
-0.13013768196105957,
-0.018278589472174644,
-0.048147715628147125,
-0.015592251904308796,
0.015164232812821865,
0.006830460391938686,
0.022811394184827805,
0.007180204149335623,
0.049460090696811676,
0.00968837272375822,
-0.06229236721992493,
0.02403259463608265,
0.0012750276364386082,
-0.03687984496355057,
0.044720325618982315,
0.02783316560089588,
-0.009200810454785824,
-0.0035858629271388054,
0.03171926736831665,
-0.017313456162810326,
0.018172841519117355,
0.0607495941221714,
-0.014258697628974915,
0.013364138081669807,
-0.0738249272108078,
-0.03726929426193237,
0.03496742248535156,
0.02638411708176136,
0.0361214205622673,
-0.00043314535287208855,
0.037341561168432236,
0.031364645808935165,
-0.006000455003231764,
0.05028654262423515,
0.029268639162182808,
0.020411277189850807,
0.016960645094513893,
0.06182419881224632,
0.026484625414013863,
-0.017806146293878555,
0.006010021083056927,
-0.007303119171410799,
-0.03686641529202461,
-0.015393396839499474,
0.05193847045302391,
0.03756913170218468,
0.05994188040494919,
-0.0455460287630558,
0.002641163533553481,
-0.08367102593183517,
0.010421710088849068,
0.017305178567767143,
0.07059872895479202,
0.049856096506118774,
-0.016956087201833725,
-0.01445300318300724,
-0.024932585656642914,
-0.003986125346273184,
-0.06767619401216507,
0.0045811948366463184,
-0.010313454084098339,
-0.050441958010196686,
-0.029491495341062546,
0.051460232585668564,
-0.0395558662712574,
-0.010687369853258133,
-0.005521863233298063,
0.05281781405210495,
-0.05910255387425423,
-0.0071520013734698296,
-0.024977313354611397,
-0.037700966000556946,
0.06433650851249695,
0.05968787521123886,
-0.019844643771648407,
0.010015823878347874,
0.009064743295311928,
0.01257883757352829,
0.037654515355825424,
-0.025103414431214333,
0.03633132204413414,
0.05444056913256645,
-0.013102819211781025,
0.01469704881310463,
0.02814280427992344,
0.03050292655825615,
-0.000884984852746129,
-0.008128538727760315,
0.03374951332807541,
-0.009302979335188866,
0.01751045137643814,
-0.020834796130657196,
0.06071558967232704,
0.04597053676843643,
0.03605305403470993,
0.02319559082388878,
0.02176298014819622,
-0.017596382647752762,
0.011102373711764812,
-0.0248581450432539,
-0.06913553178310394,
0.03678512200713158,
0.01605859212577343,
0.0007983726100064814,
-0.06277518719434738,
-0.02053353190422058,
0.03250446170568466,
0.008460297249257565,
0.0121068824082613,
-0.022774318233132362,
-0.03306938707828522,
-0.016974443569779396,
-0.022513480857014656,
-0.004386869724839926,
0.010487133637070656,
-0.006806254852563143,
0.00993188377469778,
0.005742162466049194,
-0.009501174092292786,
0.03422745317220688,
-0.029065631330013275,
-0.02417718805372715,
0.04524649679660797,
0.00925307534635067,
0.056861236691474915,
0.025136247277259827,
0.05322450026869774,
0.0000342382954841014,
-0.000008661634637974203,
0.02362205646932125,
0.03428840637207031,
-0.0563361681997776,
-0.03289690613746643,
0.009067748673260212,
0.0089566670358181,
-0.023923441767692566,
-0.0510932132601738,
0.036028116941452026,
-0.04826658219099045,
0.04148506373167038,
0.006643146276473999,
-0.012178712524473667,
0.025818362832069397,
-0.010272887535393238,
-0.0401332788169384,
-0.051798898726701736,
0.0039024855941534042,
-0.0036017620004713535,
0.000536682375241071,
0.017033735290169716,
0.0247520562261343,
-0.03963523730635643,
0.04407336935400963,
-0.010165838524699211,
-0.00007211830234155059,
0.004226164426654577,
0.025788597762584686,
0.039110299199819565,
0.005094833672046661,
-0.0011183671886101365,
-0.040238574147224426,
-0.007808955851942301,
0.05027091130614281,
0.0029315066058188677,
0.027787545695900917,
0.03535616770386696,
0.023086173459887505,
-0.05054321885108948,
-0.006739253643900156,
0.00868817139416933,
0.0012431925861164927,
0.009313869290053844,
-0.006541217211633921,
0.019003793597221375,
0.0023891120217740536,
-0.021344540640711784,
0.015476221218705177,
0.048124559223651886,
0.016121836379170418,
0.029978979378938675,
0.006731837522238493,
0.029243379831314087,
0.03268039599061012,
0.011819766834378242,
-0.03419177234172821,
0.056626468896865845,
-0.046077147126197815,
-0.007194893900305033,
0.013811967335641384,
-0.06029357761144638,
-0.04652559757232666,
-0.0755193829536438,
0.027785250917077065,
-0.05240042135119438,
-0.030343635007739067,
0.029741782695055008,
0.03285012021660805,
-0.005549580790102482,
-0.04757941886782646,
0.025293448939919472,
-0.046856172382831573,
-0.015284920111298561,
-0.02570921741425991,
-0.014482537284493446,
0.01723599247634411,
0.018883435055613518,
-0.022176945582032204,
-0.06898250430822372,
0.06447432190179825,
-0.024713465943932533,
-0.034289851784706116,
-0.0933118686079979,
0.017014646902680397,
0.002244999399408698,
-0.009656377136707306,
0.023381268605589867,
-0.023298224434256554,
-0.023821594193577766,
0.00985978078097105,
0.000277355604339391,
0.03877085819840431,
0.017484743148088455,
0.04747810587286949,
-0.0017296163132414222,
0.01396868098527193,
-0.04430835321545601,
-0.002407859079539776,
0.004385868087410927,
0.040635351091623306,
0.08659511804580688,
-0.031289707869291306,
-0.054150257259607315,
0.031478025019168854,
-0.007732140365988016,
0.014004097320139408,
-0.023644788190722466,
0.021541155874729156,
0.02671464905142784,
0.0022001301404088736,
-0.05192549154162407,
-0.019115231931209564,
0.004012821242213249,
0.01278249267488718,
-0.08172190189361572,
-0.02850411646068096,
-0.026036754250526428,
-0.009912523441016674,
0.02022428996860981,
-0.03947016969323158,
-0.03421055153012276,
-0.05150235444307327,
0.0030721891671419144
] |
<p>In the book <a href="http://books.google.ca/books?id=UaY1MLmC780C&printsec=frontcover&source=gbs_atb#v=onepage&q&f=false" rel="nofollow">Nonlinear Optics</a>, it is stated that the nonlinear effects start to become a problem in WDM systems (around 1550 nm) after about 1 mW of optical power. However, I measured the optical power at transmission of a transmitting laser of a 10GBASE-ZR on a short, 2 km link, and found that it was 2.5 mW. </p>
<p>What is the operating optical power of telecommunications lasers? Does it differ for inter-continental links compared to short links, i.e. between buildings on a campus? If they are above 1 mW, are nonlinear effects a concern?</p>
|
g2445
|
[
-0.013595392927527428,
0.007756158243864775,
-0.0038215324748307467,
0.0002657211443874985,
-0.07242901623249054,
-0.040894459933042526,
-0.023853637278079987,
0.031539592891931534,
-0.046897657215595245,
0.029676491394639015,
0.05211745202541351,
0.030098816379904747,
-0.013495760038495064,
-0.007681047078222036,
0.00762908486649394,
-0.014535234309732914,
0.02785598859190941,
0.006475837901234627,
0.04640308395028114,
0.04585906118154526,
-0.09820529073476791,
0.00016624180716462433,
-0.053311824798583984,
-0.0561557374894619,
-0.03731586039066315,
0.07676934450864792,
0.025661472231149673,
0.006527399178594351,
-0.11451941728591919,
0.01332202646881342,
0.027089377865195274,
-0.030842261388897896,
0.057550374418497086,
-0.00792577862739563,
-0.07584236562252045,
0.05367976427078247,
0.012740653939545155,
-0.041470326483249664,
0.0339617058634758,
0.06872201710939407,
0.00521769467741251,
-0.030382568016648293,
-0.02164430171251297,
0.04661820828914642,
0.012705794535577297,
-0.05709027126431465,
0.009819106198847294,
0.008859841153025627,
0.053477514535188675,
0.01597025990486145,
-0.0648161768913269,
-0.01690635271370411,
0.023119812831282616,
0.04441725090146065,
0.015268372371792793,
-0.009488177485764027,
-0.062323395162820816,
0.02628648467361927,
0.07031205296516418,
0.016307814046740532,
-0.013101193122565746,
-0.02391299046576023,
-0.006870820187032223,
0.01115382183343172,
0.003114698687568307,
-0.034717027097940445,
-0.019016258418560028,
-0.07879367470741272,
0.021744538098573685,
-0.006863885559141636,
-0.004564294591546059,
-0.014778577722609043,
-0.08142633736133575,
-0.025913311168551445,
0.02299194596707821,
-0.04669361189007759,
-0.011659372597932816,
0.010363100096583366,
-0.019304338842630386,
0.03742935135960579,
0.02922295220196247,
-0.023288268595933914,
0.036815792322158813,
0.02925715781748295,
0.014888294041156769,
0.02723945677280426,
0.03703765571117401,
-0.04405653104186058,
-0.01570921577513218,
0.05537327378988266,
0.07944740355014801,
0.05159076303243637,
0.04076916724443436,
0.02528260461986065,
0.010063694790005684,
-0.023142073303461075,
0.009789763949811459,
-0.027202880010008812,
0.04745575413107872,
-0.013616196811199188,
0.024836884811520576,
0.018272273242473602,
-0.025768693536520004,
0.02913394384086132,
-0.020693765953183174,
0.04602346196770668,
-0.012164497748017311,
-0.01857723668217659,
-0.07426390796899796,
0.0006119085592217743,
-0.027253931388258934,
-0.02164655365049839,
-0.023982489481568336,
0.0011105993762612343,
-0.0493338517844677,
-0.06119556725025177,
0.031158769503235817,
0.0005331722786650062,
0.03413521498441696,
0.007106103003025055,
0.007631811313331127,
0.027367547154426575,
-0.012760729528963566,
0.008605008013546467,
0.01966475509107113,
0.0151909701526165,
0.021455448120832443,
0.003962256014347076,
0.05541492998600006,
-0.009291860274970531,
-0.03369184955954552,
-0.001883029704913497,
-0.0841829776763916,
0.03744704648852348,
0.018647870048880577,
0.04562285915017128,
-0.03387121483683586,
-0.053721968084573746,
0.010602041147649288,
-0.002220615278929472,
0.029259881004691124,
-0.033028505742549896,
0.023555681109428406,
-0.007140185683965683,
-0.030933955684304237,
0.026654288172721863,
-0.03035735711455345,
-0.003248845227062702,
0.0714685469865799,
0.04519021138548851,
0.012322403490543365,
0.00501996697857976,
0.03636055067181587,
-0.06649594753980637,
0.007432002108544111,
0.04936717078089714,
-0.005460020154714584,
-0.003162389388307929,
-0.0013943321537226439,
0.006389684975147247,
0.004526323638856411,
-0.04742370918393135,
0.016570793464779854,
0.017529016360640526,
-0.07221704721450806,
-0.035664793103933334,
0.012271042913198471,
-0.024731038138270378,
-0.02557540498673916,
0.045626040548086166,
-0.03310861065983772,
-0.01782141998410225,
0.04969006031751633,
0.02919115498661995,
0.035187654197216034,
0.06274392455816269,
0.09013055264949799,
-0.0016133817844092846,
0.002564795780926943,
-0.0026389420963823795,
-0.08722493797540665,
-0.0530262254178524,
-0.02599012851715088,
-0.053104300051927567,
0.004247545730322599,
0.000873061828315258,
0.007915549911558628,
-0.029733922332525253,
0.00030124973272904754,
-0.028737757354974747,
-0.05009636655449867,
-0.023156723007559776,
-0.016744285821914673,
-0.02622055821120739,
-0.03370498865842819,
-0.006892974954098463,
0.008580969646573067,
0.008640564978122711,
-0.014137436635792255,
-0.0593627467751503,
-0.0060907406732439995,
0.040255315601825714,
0.005740299355238676,
0.0027946841437369585,
0.056614525616168976,
0.023990876972675323,
-0.021694257855415344,
0.042832471430301666,
0.009266047738492489,
-0.04686499387025833,
-0.034048061817884445,
-0.0711468830704689,
0.00943974032998085,
-0.0026355597656220198,
0.02336932346224785,
0.008158660493791103,
-0.009440429508686066,
0.028696563094854355,
-0.03793549910187721,
0.04860448092222214,
0.0018729601288214326,
0.027173778042197227,
0.03231658786535263,
0.015696879476308823,
-0.05988422408699989,
-0.03158573433756828,
-0.039577797055244446,
0.005465274676680565,
-0.01231655478477478,
0.02692435123026371,
-0.004608711693435907,
0.008121291175484657,
-0.008078656159341335,
-0.059213437139987946,
-0.004245678894221783,
0.013592117466032505,
0.028377318754792213,
-0.027880311012268066,
-0.004935794044286013,
-0.004718695767223835,
0.0602150484919548,
0.020030848681926727,
-0.008625426329672337,
0.025525769218802452,
-0.025658944621682167,
-0.11035410314798355,
0.03506721928715706,
-0.00858414638787508,
-0.03874056413769722,
-0.05493113771080971,
0.037129227072000504,
0.018237287178635597,
0.0676504597067833,
0.01877409778535366,
-0.049669887870550156,
-0.008902701549232006,
-0.022567465901374817,
0.03280564770102501,
-0.04687188193202019,
-0.006192128639668226,
0.016239795833826065,
0.0056055826134979725,
0.0006617269245907664,
-0.07453985512256622,
0.059000272303819656,
-0.0036105699837207794,
-0.03451746702194214,
-0.011010310612618923,
0.01454960834234953,
0.040158383548259735,
0.048260048031806946,
0.04002528637647629,
-0.08927402645349503,
-0.018215006217360497,
0.041855596005916595,
-0.061975643038749695,
0.023716125637292862,
-0.019928181543946266,
0.016869276762008667,
-0.025963788852095604,
-0.00032747327350080013,
-0.020200375467538834,
-0.06688269972801208,
-0.022122425958514214,
0.014069576747715473,
-0.08031938970088959,
0.055312950164079666,
0.03355459123849869,
0.0012416922254487872,
0.02639949694275856,
-0.04668469727039337,
0.007689873222261667,
0.03465016931295395,
0.008768805302679539,
-0.018648970872163773,
0.001301379525102675,
0.04126900061964989,
-0.014708347618579865,
-0.049636948853731155,
-0.024476829916238785,
0.04111136868596077,
-0.06789345294237137,
-0.0037971953861415386,
-0.0029885675758123398,
-0.021528717130422592,
0.05299650877714157,
-0.04241577163338661,
-0.05141220986843109,
0.053137920796871185,
0.04942565783858299,
0.014167911373078823,
0.037257540971040726,
0.06284506618976593,
0.0006594260921701789,
0.00030609036912210286,
-0.03577567636966705,
-0.01808503456413746,
-0.032668862491846085,
0.024403326213359833,
0.04170805215835571,
-0.02708093635737896,
-0.02309287339448929,
-0.010371946729719639,
-0.060535628348588943,
-0.032481126487255096,
0.008920141495764256,
0.036311157047748566,
-0.011309714987874031,
-0.04414260387420654,
0.015387182123959064,
-0.033703576773405075,
-0.01271748822182417,
-0.010346882976591587,
0.033165331929922104,
0.012146243825554848,
0.016326438635587692,
-0.01975954696536064,
-0.002182479714974761,
-0.007151767145842314,
0.07299955934286118,
0.012723231688141823,
0.013878792524337769,
-0.0843132734298706,
-0.017716560512781143,
0.0492098294198513,
0.0069690304808318615,
-0.043860867619514465,
-0.02450311742722988,
-0.04898029565811157,
0.012952154502272606,
0.0305294431746006,
-0.04470911622047424,
0.005031791981309652,
-0.026677029207348824,
-0.03752032294869423,
0.01497806329280138,
-0.014734480530023575,
0.023216556757688522,
0.02418789453804493,
-0.010177508927881718,
-0.010499954223632812,
0.01238538883626461,
0.06677298992872238,
-0.0157381109893322,
-0.06325674802064896,
0.021855080500245094,
-0.017798183485865593,
-0.01397756114602089,
0.010564127005636692,
0.006813150364905596,
0.007781191263347864,
-0.021531281992793083,
-0.06396762281656265,
-0.02836865559220314,
-0.023107580840587616,
0.03158228099346161,
0.04639340192079544,
-0.013944978825747967,
-0.008263301104307175,
0.04768705368041992,
-0.01675146445631981,
0.0378725491464138,
0.03426135703921318,
0.033962227404117584,
-0.010763549245893955,
-0.028277607634663582,
-0.009548031724989414,
-0.04219259321689606,
0.06162244826555252,
-0.03378382325172424,
-0.004557230044156313,
-0.06928056478500366,
0.012511448934674263,
-0.007403843104839325,
-0.035257644951343536,
0.027315206825733185,
-0.003787073539569974,
0.008971969597041607,
0.04527757689356804,
0.028762543573975563,
-0.013056370429694653,
-0.006340582389384508,
0.037880852818489075,
0.0455024391412735,
-0.002935784636065364,
-0.02782607637345791,
-0.033561114221811295,
0.02262704074382782,
-0.055135007947683334,
0.043488163501024246,
0.018414048478007317,
0.06569799780845642,
-0.02043784223496914,
-0.10002885013818741,
0.022831521928310394,
0.0455937534570694,
0.052489038556814194,
-0.043851204216480255,
0.053341664373874664,
0.02688322588801384,
-0.014194145798683167,
0.018204346299171448,
-0.0007232037023641169,
-0.03574466332793236,
-0.033156704157590866,
0.025416983291506767,
-0.04728793352842331,
-0.0593641996383667,
0.03030579537153244,
0.07616765797138214,
0.05148470774292946,
0.048326700925827026,
-0.04737197980284691,
-0.004487005993723869,
0.03600626066327095,
0.012844467535614967,
0.07018466293811798,
0.020676584914326668,
0.061935774981975555,
-0.04727393761277199,
0.06882242858409882,
-0.011948359198868275,
0.05221198499202728,
0.03947196155786514,
-0.0017392444424331188,
0.0714925229549408,
-0.04230077937245369,
0.006960339844226837,
-0.037429459393024445,
-0.0337875671684742,
-0.006508924998342991,
0.023900942876935005,
0.02326999418437481,
-0.12371286004781723,
0.03649963065981865,
0.0356457494199276,
0.0025061580818146467,
0.014768070541322231,
0.07466654479503632,
-0.015924151986837387,
-0.010328986681997776,
0.010648276656866074,
-0.059759803116321564,
-0.01805022731423378,
0.023289861157536507,
0.012241334654390812,
-0.07269854098558426,
-0.0017990220803767443,
-0.018154747784137726,
-0.05872229114174843,
0.02279462292790413,
0.005308353342115879,
0.00363017525523901,
0.053488392382860184,
-0.010789292864501476,
-0.04806414619088173,
-0.04249405115842819,
-0.046767428517341614,
-0.012793331407010555,
0.017965298146009445,
-0.01894916407763958,
-0.021426161751151085,
0.003860984230414033,
-0.015654489398002625,
0.008288386277854443,
0.02660122513771057,
0.008020077832043171,
0.054539624601602554,
0.04787129908800125,
-0.011226044036448002,
0.005965675227344036,
0.015387999825179577,
-0.10323040932416916,
-0.03196844831109047,
-0.07288581132888794,
-0.019144514575600624,
0.015383562073111534,
0.019058432430028915,
0.023497339338064194,
0.02024785615503788,
-0.002002504887059331,
0.03613261878490448,
-0.03397032991051674,
-0.00691149290651083,
-0.039554428309202194,
0.06569884717464447,
-0.025371573865413666,
-0.03412400558590889,
0.01673506386578083,
0.008608137257397175,
-0.04286711663007736,
0.005289835389703512,
-0.003920847550034523,
0.014644363895058632,
0.06697522103786469,
-0.10630861669778824,
-0.06081308424472809,
0.03556055575609207,
-0.0030666617676615715,
0.01945371925830841,
0.013883829116821289,
-0.03048909455537796,
0.012569637969136238,
-0.00301999575458467,
0.006700661964714527,
0.01901986636221409,
-0.03264981880784035,
0.03392038121819496,
-0.041576966643333435,
0.004902148153632879,
0.0030332724563777447,
0.09229870140552521,
0.028835806995630264,
-0.01391189731657505,
0.03398524597287178,
0.021390069276094437,
0.02200920693576336,
-0.0047775316052138805,
-0.04654046520590782,
0.022437958046793938,
-0.02680138684809208,
-0.005081957671791315,
0.01586436666548252,
0.059710439294576645,
-0.0034272284246981144,
-0.04881470277905464,
0.04566435143351555,
-0.03774723410606384,
0.011141370981931686,
0.015352195128798485,
0.03281053528189659,
-0.05676060914993286,
-0.019878534600138664,
0.03832916170358658,
0.036906734108924866,
0.0075950585305690765,
0.005062115378677845,
0.0162216704338789,
-0.022285746410489082,
-0.007067911792546511,
0.06450914591550827,
0.09565296024084091,
-0.039760421961545944,
-0.03993777558207512,
0.021921208128333092,
-0.051095589995384216,
0.003791164606809616,
-0.01142299734055996,
0.04047868028283119,
0.022212853655219078,
-0.005092526786029339,
0.04317459464073181,
-0.03409712016582489,
-0.01235752273350954,
0.03516591340303421,
0.08135592192411423,
-0.012845093384385109,
-0.02028541825711727,
-0.0251657422631979,
-0.018778029829263687,
-0.060350410640239716,
-0.04041730985045433,
0.04756302386522293,
0.016374506056308746,
-0.0006092388648539782,
-0.0045615024864673615,
0.008052188903093338,
0.023462023586034775,
0.04518040642142296,
-0.031526267528533936,
-0.010934649035334587,
0.0062395608983933926,
0.02457616664469242,
-0.009379389695823193,
0.05347205325961113,
-0.05817249417304993,
-0.002861230168491602,
0.0586356520652771,
0.008566380478441715,
0.020680587738752365,
0.016430048272013664,
0.06357571482658386,
0.043749891221523285,
-0.0459967777132988,
-0.015076372772455215,
0.010195106267929077,
0.007937794551253319,
-0.013279523700475693,
-0.004408813081681728,
0.026085013523697853,
0.03497392684221268,
0.013953162357211113,
0.013567106798291206,
0.009863092564046383,
-0.03288676217198372,
-0.06338201463222504,
0.0010211634216830134,
0.0046913824044167995,
-0.026324691250920296,
-0.02805749885737896,
0.01457215752452612,
-0.04812241718173027,
-0.025351742282509804,
-0.022803153842687607,
0.00507616950199008,
0.051994841545820236,
0.01755160465836525,
-0.006403720006346703,
0.023113667964935303,
-0.013616775162518024,
0.00916256569325924,
-0.012761358171701431,
0.010327151045203209,
-0.03484353795647621,
-0.038219381123781204,
0.0017305131768807769,
-0.04050884395837784,
0.012705079279839993,
0.027071349322795868,
-0.028656823560595512,
0.03821757435798645,
-0.009387613274157047,
-0.03373722732067108,
-0.012954932637512684,
0.0521051362156868,
0.018621312454342842,
-0.02490588091313839,
0.042583808302879333,
-0.028450511395931244,
0.017628666013479233,
0.01756168343126774,
-0.04924561828374863,
0.002072706585749984,
-0.004670051392167807,
-0.022295240312814713,
0.0374588668346405,
-0.014598395675420761,
0.05280236154794693,
0.0038643358275294304,
-0.013267945498228073,
0.021918009966611862,
0.030271515250205994,
0.0021990491077303886,
0.02418706938624382,
0.06414644420146942,
0.038954541087150574,
0.07312072813510895,
-0.06851553916931152,
-0.0071815429255366325,
0.02221982553601265,
-0.031859975308179855,
-0.07620009034872055,
0.02586064115166664,
0.054906267672777176,
0.012890384532511234,
-0.0016994092147797346,
-0.054627593606710434,
0.03405643254518509,
-0.03881673142313957,
0.028515728190541267,
0.01702306605875492,
-0.05161489546298981,
-0.007702653296291828,
-0.013578055426478386,
0.015318825840950012,
0.038803406059741974,
-0.027323042973876,
-0.01819535344839096,
0.04702784866094589,
-0.047286711633205414,
-0.010073724202811718,
-0.04091793671250343,
0.06621147692203522,
-0.04563143104314804,
0.014822347089648247,
0.013665106147527695,
0.042076945304870605,
0.03879513964056969,
-0.0034894743002951145,
0.0041387672536075115,
0.030882369726896286,
0.05498595908284187,
-0.06399261951446533,
-0.04130088910460472,
-0.019671335816383362,
0.006782726850360632,
-0.016717901453375816,
-0.038790054619312286,
0.03795601800084114,
-0.01474426593631506,
-0.02708601951599121,
-0.027104204520583153,
0.027070682495832443,
0.02784169837832451,
0.03652250021696091,
-0.02099473588168621,
0.03207677975296974,
-0.07967020571231842,
-0.017714858055114746,
0.03965625539422035,
-0.0051615252159535885,
0.030125871300697327,
-0.0017791579011827707,
-0.032683491706848145,
-0.0049199596978724,
-0.013663535937666893,
0.011581690981984138,
-0.0497572124004364,
-0.026998072862625122,
0.018001219257712364,
-0.04488952457904816,
-0.07661701738834381,
-0.030588423833251,
-0.025359613820910454,
-0.017636504024267197,
0.004796933848410845,
0.028657956048846245,
0.056502990424633026,
0.032156944274902344,
0.03977898880839348,
0.059877291321754456,
-0.05167066678404808,
-0.03562319278717041,
-0.0032920753583312035,
0.023243997246026993,
0.03815217316150665,
0.006546719931066036,
0.012980560772120953,
0.03648631274700165,
-0.013384092599153519,
-0.024491284042596817,
0.028324972838163376,
-0.018807942047715187,
0.04544268175959587,
0.029499657452106476,
-0.015577797777950764,
-0.03604669123888016,
-0.04089801385998726,
0.0174403116106987,
0.006921910215169191,
0.039703696966171265,
-0.02519773319363594,
0.0004066920664627105,
-0.03226323425769806,
0.03382530435919762,
0.01698490045964718,
-0.014061670750379562,
-0.05124054476618767
] |
<p>Assume a balloon filled with Hydrogen, fitted with a perfect valve, and capable of enduring vacuum (that is to say, it would retain it's shape and so well insulated that the extremes of temperature at high altitudes and in space would have little effect) were to be launched. </p>
<p>As long as the balloon were in atmosphere it would ascend upwards (and also affected by various winds/currents, and gravity). As the balloon passed through increasingly rare atmosphere, would it rise faster? </p>
|
g2446
|
[
0.00836152583360672,
0.006996421609073877,
0.025749653577804565,
0.07925146073102951,
-0.0036794403567910194,
0.06754160672426224,
-0.04341770336031914,
0.034121181815862656,
-0.015188236720860004,
-0.01100520882755518,
-0.03972466289997101,
0.07589428126811981,
0.021047841757535934,
-0.018604625016450882,
0.015346148982644081,
-0.010237596929073334,
0.07761672139167786,
-0.07055852562189102,
0.017520364373922348,
-0.018570024520158768,
0.053904637694358826,
-0.01754448004066944,
0.023039182648062706,
0.04206046089529991,
-0.033074840903282166,
0.0029674354009330273,
0.017329799011349678,
-0.04510611295700073,
-0.07178700715303421,
-0.010941233485937119,
-0.013767009600996971,
0.002021829364821315,
0.016631677746772766,
-0.008509251289069653,
-0.011573344469070435,
0.0011377505725249648,
-0.0065399594604969025,
0.04264160990715027,
-0.014910884201526642,
-0.05764370411634445,
-0.029749194160103798,
-0.04341968148946762,
-0.0015374177601188421,
0.032234348356723785,
-0.003449374809861183,
0.01991424337029457,
-0.021805154159665108,
0.016658293083310127,
0.008271358907222748,
-0.061217885464429855,
-0.021399538964033127,
0.026737049221992493,
-0.078703872859478,
0.0075527639128267765,
-0.014064418151974678,
0.02809157222509384,
0.03847266361117363,
-0.013744941912591457,
0.009389853104948997,
0.03001219592988491,
-0.026594551280140877,
-0.00041087059071287513,
0.07503359764814377,
-0.0019127875566482544,
0.046331729739904404,
0.015840750187635422,
-0.025685807690024376,
0.031820476055145264,
0.03899363800883293,
0.03768402710556984,
0.03046473115682602,
-0.06128368526697159,
-0.038640569895505905,
-0.058834295719861984,
-0.04821739345788956,
0.052131980657577515,
-0.002342483727261424,
-0.0930682122707367,
0.06617822498083115,
0.000343557505402714,
-0.046168193221092224,
0.03604130446910858,
0.058295149356126785,
-0.00843195803463459,
0.02839851565659046,
-0.04671187326312065,
0.006147214211523533,
-0.04572412371635437,
-0.01349062379449606,
0.030227242037653923,
0.006655742414295673,
-0.023560287430882454,
0.07213909178972244,
-0.004009384196251631,
0.01127937063574791,
-0.023283593356609344,
-0.009904202073812485,
0.04566790908575058,
-0.023452209308743477,
0.017643310129642487,
-0.03571508079767227,
-0.09015055745840073,
0.05201965942978859,
-0.0008179447613656521,
-0.07460769265890121,
-0.006612845230847597,
0.024568041786551476,
-0.03841741383075714,
-0.007111742626875639,
-0.03202660009264946,
0.014448858797550201,
-0.06935078650712967,
-0.05824282020330429,
-0.0016734503442421556,
-0.027352331206202507,
0.034504372626543045,
-0.012963683344423771,
-0.019080612808465958,
0.010032443329691887,
0.042149074375629425,
0.05285241827368736,
0.05889761447906494,
-0.010027097538113594,
0.005794278346002102,
-0.015667079016566277,
-0.04026181623339653,
-0.00475009810179472,
-0.04261566698551178,
-0.007068944163620472,
-0.0353076346218586,
-0.0034395442344248295,
-0.020631978288292885,
-0.017503170296549797,
0.007250551134347916,
-0.03650716692209244,
-0.027766799554228783,
-0.043939001858234406,
0.04253791272640228,
0.03501662239432335,
0.002249153796583414,
0.03527486324310303,
-0.0006464840844273567,
0.008408097550272942,
0.011043034493923187,
-0.0338997021317482,
-0.012626318261027336,
0.06328868865966797,
0.05292718857526779,
-0.0065270718187093735,
-0.01212905254215002,
-0.02535640075802803,
0.028346240520477295,
0.00725361704826355,
0.00873487163335085,
0.0017624808242544532,
0.05365801975131035,
0.024026239290833473,
0.05023224651813507,
0.023675959557294846,
-0.031630195677280426,
0.04943133145570755,
0.019274137914180756,
-0.019505463540554047,
-0.01354650966823101,
-0.06930224597454071,
0.026730302721261978,
0.00018805965373758227,
-0.054424870759248734,
-0.04178036376833916,
0.027108831331133842,
-0.00267230486497283,
-0.005278211552649736,
0.0030069644562900066,
0.05687811225652695,
0.06778772175312042,
-0.027298716828227043,
0.08203158527612686,
0.006969014182686806,
-0.06384938955307007,
-0.02506464160978794,
0.021361004561185837,
-0.0701775848865509,
-0.002065682550892234,
-0.01342281699180603,
-0.04258113354444504,
-0.022513097152113914,
0.020496249198913574,
0.006199629046022892,
-0.08986420184373856,
-0.03302566707134247,
0.006360066123306751,
-0.005009142216295004,
0.007417966146022081,
0.023968897759914398,
-0.0010322962189093232,
-0.07224118709564209,
0.005729783792048693,
-0.01949530839920044,
-0.08249244838953018,
0.057559531182050705,
0.01918715424835682,
-0.007854069583117962,
0.09423310309648514,
-0.06692290306091309,
0.005434001330286264,
0.025772511959075928,
0.016551245003938675,
-0.03914530575275421,
0.06996507197618484,
-0.023580344393849373,
0.0026751714758574963,
0.04748155549168587,
0.027463659644126892,
0.02850061096251011,
0.04385540261864662,
0.028097953647375107,
-0.02462851256132126,
0.02394336462020874,
0.05351432040333748,
-0.026926269754767418,
-0.023768804967403412,
0.0609864704310894,
-0.02908797189593315,
-0.04187968373298645,
-0.03129331022500992,
-0.0501742847263813,
0.008419202640652657,
-0.0437205471098423,
0.03039945475757122,
0.025337552651762962,
0.02611260861158371,
0.019075945019721985,
-0.0055029140785336494,
-0.05409698560833931,
-0.0046675135381519794,
0.01990375481545925,
0.00042368294089101255,
0.03517306596040726,
0.01844574511051178,
-0.0310561154037714,
-0.044819578528404236,
-0.024192756041884422,
-0.006977011915296316,
0.02718384377658367,
0.05466284602880478,
-0.0571674220263958,
-0.01979796588420868,
0.02366204373538494,
-0.02218441106379032,
0.07890228182077408,
0.02021360956132412,
-0.002109667519107461,
-0.01726420223712921,
0.012193780392408371,
-0.06306914240121841,
-0.016021450981497765,
-0.019157903268933296,
-0.009032603353261948,
-0.03151765838265419,
0.027850991114974022,
0.021496471017599106,
-0.024114668369293213,
-0.01361352764070034,
-0.013563085347414017,
-0.06423589587211609,
0.010529736988246441,
-0.01712966337800026,
0.010332003235816956,
-0.01760760508477688,
0.01909671165049076,
0.029934443533420563,
0.027729857712984085,
-0.03471219912171364,
0.052777308970689774,
-0.023858150467276573,
0.011167176067829132,
0.025410665199160576,
-0.012272116728127003,
0.029648296535015106,
0.008975290693342686,
0.004349507857114077,
-0.05254051089286804,
-0.06992526352405548,
-0.0003638679045252502,
0.023710714653134346,
-0.06165936589241028,
0.031597837805747986,
0.04439697414636612,
0.034606918692588806,
-0.0024299961514770985,
0.0020807478576898575,
0.05083117261528969,
0.008166983723640442,
0.08471302688121796,
-0.005383427254855633,
0.08737912029027939,
0.030305001884698868,
-0.04060911759734154,
-0.004307983443140984,
-0.05772851034998894,
0.03354833647608757,
-0.0352749265730381,
-0.0028702591080218554,
0.018036097288131714,
-0.016531988978385925,
0.009635258466005325,
-0.03222503885626793,
0.043349508196115494,
-0.04945310205221176,
0.003505929373204708,
0.030846957117319107,
0.030131105333566666,
-0.043052781373262405,
0.0725601315498352,
-0.037982162088155746,
0.0036415429785847664,
-0.04864894971251488,
0.006716862786561251,
-0.043850187212228775,
-0.0022094189189374447,
0.0009724608971737325,
-0.022328080609440804,
-0.009496220387518406,
-0.02967824973165989,
0.017400508746504784,
0.030671177431941032,
-0.012370679527521133,
0.03712755814194679,
-0.0015697149792686105,
0.0006093407864682376,
0.023665228858590126,
0.046871162950992584,
-0.023290786892175674,
-0.01261614914983511,
-0.049204036593437195,
0.029208308085799217,
-0.0061560445465147495,
0.015186160802841187,
-0.007060077507048845,
0.027158942073583603,
-0.005219579208642244,
-0.0251623447984457,
-0.06071120873093605,
-0.03159191459417343,
0.01899898424744606,
0.02288793958723545,
0.0322190560400486,
-0.007456939667463303,
0.013261064887046814,
-0.014925260096788406,
0.06179986894130707,
-0.06726528704166412,
0.011227567680180073,
0.017410410568118095,
0.03240394964814186,
0.017752744257450104,
0.08014696836471558,
0.02371283620595932,
-0.05034630745649338,
-0.05339723825454712,
0.01253073662519455,
0.01357855275273323,
0.020019810646772385,
0.034319739788770676,
-0.028886090964078903,
-0.020395951345562935,
-0.04422612488269806,
0.05482823774218559,
-0.01967637799680233,
0.01602264679968357,
0.027166282758116722,
0.030673177912831306,
-0.024730203673243523,
0.027625564485788345,
0.0220708716660738,
-0.03113819845020771,
0.02817039005458355,
-0.032731734216213226,
-0.06143328174948692,
0.020812802016735077,
0.07726110517978668,
-0.019146008417010307,
-0.014335657469928265,
-0.031723205000162125,
-0.025590138509869576,
-0.0075615523383021355,
-0.06834597885608673,
-0.005002335179597139,
0.048230987042188644,
-0.05151546373963356,
-0.058453403413295746,
0.02247496508061886,
-0.005415337160229683,
0.050160426646471024,
0.006609858479350805,
-0.012753148563206196,
0.029319168999791145,
0.019004402682185173,
-0.043376632034778595,
0.02374001033604145,
0.03629215434193611,
0.004701889120042324,
0.023449242115020752,
0.040013570338487625,
-0.0047290269285440445,
-0.026479603722691536,
0.04802927374839783,
0.010914240963757038,
-0.006238770205527544,
-0.04185568913817406,
0.03787943720817566,
0.01058061234652996,
-0.020503172650933266,
-0.08535879850387573,
0.011091581545770168,
-0.05207401514053345,
0.02617453597486019,
-0.010996591299772263,
0.03071092627942562,
0.014903425239026546,
0.010337104089558125,
-0.02361467480659485,
0.048714786767959595,
-0.0005250793765299022,
0.04579096660017967,
-0.019946984946727753,
0.05917135253548622,
-0.0004550069570541382,
-0.025329403579235077,
-0.01627623662352562,
0.029920322820544243,
0.03431209549307823,
-0.007893566973507404,
0.03276475518941879,
0.04618670418858528,
0.020442740991711617,
0.03132614493370056,
-0.015332330949604511,
0.03134198114275932,
0.023943070322275162,
0.06104185804724693,
0.004599757492542267,
-0.01621444709599018,
0.041437458246946335,
-0.027805937454104424,
0.02850765362381935,
-0.014325608499348164,
-0.02885487489402294,
0.01669473387300968,
0.000586027221288532,
-0.06530527025461197,
-0.01919262297451496,
0.09663667529821396,
0.0053551760502159595,
-0.04692954197525978,
-0.08371306210756302,
-0.02789168618619442,
-0.007063668686896563,
0.02348489873111248,
0.02670402266085148,
-0.056597013026475906,
-0.01908625289797783,
0.052449680864810944,
0.018540039658546448,
0.012583456933498383,
-0.03761711344122887,
0.0016546263359487057,
-0.006087669637054205,
-0.016430489718914032,
0.016271056607365608,
-0.029201433062553406,
0.039847347885370255,
0.009850292466580868,
0.10351375490427017,
-0.022458475083112717,
-0.023872582241892815,
-0.021919000893831253,
-0.053407974541187286,
0.05143946781754494,
-0.05656956881284714,
0.014825671911239624,
-0.01065228134393692,
-0.020794985815882683,
0.02009715512394905,
0.011614474467933178,
-0.0003628493577707559,
-0.07565028965473175,
-0.013582337647676468,
-0.0015333762858062983,
0.014721357263624668,
0.015385196544229984,
0.07269434630870819,
0.02210972085595131,
0.025482425466179848,
-0.04155653715133667,
-0.0482793003320694,
-0.0073775602504611015,
-0.020482555031776428,
0.039445821195840836,
0.004164096899330616,
-0.05135978385806084,
-0.023002957925200462,
0.018231958150863647,
-0.01599367894232273,
-0.04164368659257889,
0.013005961664021015,
0.005335641093552113,
0.03623375669121742,
0.03879178687930107,
0.027729569002985954,
-0.0551043301820755,
0.04289573058485985,
-0.013282643631100655,
0.029775943607091904,
0.03729386255145073,
-0.047341905534267426,
-0.013545417226850986,
-0.01679016649723053,
0.021733203902840614,
-0.090693399310112,
0.07647936046123505,
0.002141728065907955,
0.05313809588551521,
0.023591291159391403,
0.02160417102277279,
0.02173229120671749,
-0.03747112303972244,
0.016657739877700806,
-0.03271578624844551,
0.0064651151187717915,
0.04398440942168236,
-0.03433695062994957,
0.006100906059145927,
-0.044081855565309525,
-0.010239042341709137,
0.006835919804871082,
0.0019484333461150527,
0.068117156624794,
0.05729236453771591,
0.03253021463751793,
-0.06198136880993843,
-0.02621409296989441,
-0.0179271399974823,
0.06236324831843376,
0.04091958701610565,
-0.04057645797729492,
-0.033040907233953476,
0.028552429750561714,
0.08444241434335709,
-0.015735911205410957,
-0.05619095265865326,
-0.01605970226228237,
-0.031007977202534676,
0.04615001380443573,
-0.023206382989883423,
0.05729101225733757,
0.021044328808784485,
0.034214287996292114,
0.02267991006374359,
-0.024760687723755836,
0.02335115522146225,
0.004927142057567835,
0.04945380240678787,
0.03858920931816101,
-0.0498146153986454,
-0.035248156636953354,
0.0006926085916347802,
-0.028965981677174568,
0.08888164162635803,
0.013274882920086384,
-0.037896011024713516,
0.011384757235646248,
0.011924299411475658,
-0.034060824662446976,
0.014774095267057419,
-0.04086845740675926,
0.015487514436244965,
-0.009426803328096867,
0.016672218218445778,
-0.0006867795018479228,
-0.020006714388728142,
-0.025626230984926224,
0.05121617391705513,
-0.018632132560014725,
-0.011204935610294342,
0.0007782410248182714,
-0.03697582334280014,
0.0021173935383558273,
0.02306673489511013,
0.011533444747328758,
0.006128752138465643,
-0.009492127224802971,
0.008353360928595066,
-0.0617886483669281,
-0.052848562598228455,
-0.03045668639242649,
-0.06872757524251938,
-0.02969498001039028,
-0.0406811498105526,
0.03971773758530617,
0.05496912822127342,
0.01572365127503872,
0.02329651452600956,
-0.00840323232114315,
0.004979501944035292,
0.03365382179617882,
0.022083759307861328,
0.0646587535738945,
0.06248457729816437,
-0.002875879406929016,
-0.019562244415283203,
0.019512608647346497,
0.042608436197042465,
0.017091121524572372,
-0.02490033023059368,
-0.06792096048593521,
0.043247856199741364,
-0.011431305669248104,
0.010946612805128098,
0.00006851864600321278,
0.006659510545432568,
-0.012269462458789349,
-0.008840663358569145,
-0.06179868429899216,
0.007238034624606371,
-0.062355078756809235,
0.0072477106004953384,
0.054156795144081116,
0.041726574301719666,
-0.0006881309091113508,
0.022731781005859375,
0.025478214025497437,
-0.018696250393986702,
0.0320257842540741,
0.02351870946586132,
-0.03191212937235832,
-0.006629597395658493,
-0.026056203991174698,
-0.0748884528875351,
-0.026579244062304497,
-0.0009903513127937913,
0.020247140899300575,
-0.014033018611371517,
0.03236165642738342,
0.031290896236896515,
-0.018551766872406006,
0.05391664057970047,
0.013720199465751648,
-0.0009799174731597304,
-0.02961575984954834,
-0.020391037687659264,
-0.06279046833515167,
-0.05286461487412453,
-0.04766170307993889,
-0.009878050535917282,
0.00015210907440632582,
-0.038882266730070114,
0.009407611563801765,
-0.014967383816838264,
-0.01242094300687313,
0.045153096318244934,
0.0015271970769390464,
-0.03406458720564842,
-0.000031333260267274454,
0.05000199377536774,
0.007542786654084921,
-0.018086424097418785,
-0.013712797313928604,
0.015181103721261024,
0.003259024117141962,
0.021153219044208527,
0.0239507295191288,
-0.03761885315179825,
-0.0388389490544796,
0.011155916377902031,
-0.01846413128077984,
-0.060530830174684525,
0.0036103588063269854,
0.029576625674962997,
0.026763541623950005,
-0.023937175050377846,
-0.028324181213974953,
-0.0015835387166589499,
-0.03381289541721344,
0.020039720460772514,
0.03390762582421303,
-0.05984890088438988,
0.015050387941300869,
0.03592411056160927,
-0.06974150240421295,
0.01009763777256012,
0.01404788251966238,
0.018762852996587753,
-0.000814083672594279,
-0.016918975859880447,
0.016817111521959305,
0.015122259967029095,
-0.09180300682783127,
-0.01371616218239069,
-0.07501109689474106,
-0.042938221246004105,
0.07682107388973236,
0.014272079803049564,
-0.04802905023097992,
0.05187801644206047,
0.04925971478223801,
0.04389910772442818,
0.04333389177918434,
-0.04363151639699936,
0.02366330474615097,
0.023161135613918304,
0.035567235201597214,
-0.009252061136066914,
-0.0063822707161307335,
0.05058961361646652,
-0.08622604608535767,
-0.02587936632335186,
-0.07917936891317368,
-0.02051723375916481,
0.015386097133159637,
-0.021681293845176697,
0.03296465799212456,
-0.004261038266122341,
-0.06789102405309677,
-0.029430175200104713,
0.043244462460279465,
-0.05929511785507202,
0.0005124282324686646,
-0.022739972919225693,
-0.02680663950741291,
0.05124100670218468,
-0.05705089494585991,
-0.0056550269946455956,
0.019337672740221024,
-0.0010033071739599109,
-0.006890065502375364,
0.05339563637971878,
-0.005378413945436478,
-0.031765133142471313,
-0.020065195858478546,
-0.11463069170713425,
0.020103950053453445,
0.011246932670474052,
0.013860827311873436,
0.013152146711945534,
-0.03406626358628273,
-0.008112621493637562,
-0.003553215879946947,
0.06197389215230942,
0.017566336318850517,
0.06105850264430046,
-0.03498789668083191,
-0.016703803092241287,
-0.006768548395484686,
0.007242870982736349,
0.02347911335527897,
-0.023754535242915154,
0.0417054183781147,
-0.03763635456562042,
-0.03003022074699402,
0.020471632480621338,
0.0237565990537405,
-0.02790394425392151,
-0.04032084718346596,
-0.030743233859539032,
0.00697605824097991,
0.019350238144397736,
0.008956710807979107
] |
<p>I'm reading about how the soon-to-be-launched <a href="http://en.wikipedia.org/wiki/Nuclear_Spectroscopic_Telescope_Array" rel="nofollow">NuSTAR</a> is on the cutting edge of focusing x-rays, which captures 5 to 80 keV radiation by focusing them with optics that have a 10.15 meter focal length onto 2 sets of 4 32×32 pixel detector arrays. These are particular "hard" (high energy) x-rays, which is a part of what makes the task difficult and the NuSTAR telescope novel.</p>
<p>If I understand correctly, imaging gets particularly difficult with electromagnetic radiation beyond a certain energy, as true gamma rays (above 100 keV) are detected with a family of radiation detectors that sense the Compton scatter or photoelectric absorption with an electrical pulse that is (in a naive sense) insensitive to the originating direction or location within the detector. It should be obvious that imaging can still be done with the use of an array of detectors, each constituting a single pixel, and these capabilities may improve with time as semiconductor detector technology evolves.</p>
<p>So the critical distinction I'm trying to establish is between x-rays and gamma rays. It would seem that we focus x-rays and do not focus gamma rays. For a very good example of researchers <em>not</em> focusing gamma rays, consider Dr. Zhong He's <a href="http://czt-lab.engin.umich.edu/" rel="nofollow">Radiation Measurement Group</a> at UM, who do actual imaging of a gamma ray environment (the UM Polaris detector). They use a grid of room temperature semiconductors laid out bare in a room and use back-processing of the signals to triangulate a sequence of scatter-scatter-absorption reactions in 3D space. This is a lot of work that would be completely unnecessary if you could focus the gamma rays like we do for a large portion of the EM spectrum.</p>
<p>Both of the technologies I reference, the NuSTAR telescope and the UM Polaris detector, use CdZnTe detectors. Functionally they are very very different in that the telescope uses optics to capture light from just a few arc-seconds of the sky.</p>
<p>My question is what is the specific limitation that prevents us from focusing photons above a certain energy? It seems this cutoff point is also suspiciously close to the cutoff between the definition of x-rays and gamma rays. Was this intended? Could future technology start using optics to resolve low-energy gamma rays?</p>
|
g2447
|
[
-0.04027241840958595,
0.06654680520296097,
0.0024313940666615963,
0.013995341025292873,
0.0044993008486926556,
0.03418515995144844,
0.004184538498520851,
0.0029067792929708958,
0.015300527215003967,
-0.04647392779588699,
0.07135342061519623,
0.08601762354373932,
0.05024366453289986,
-0.04822195693850517,
0.033478740602731705,
-0.006539424415677786,
0.0762462392449379,
0.004928424954414368,
0.03277267888188362,
0.0668034702539444,
-0.023278160020709038,
0.019600631669163704,
-0.020108439028263092,
-0.05879909545183182,
-0.06685014069080353,
-0.017582006752490997,
0.009217428974807262,
0.021780768409371376,
-0.07023198157548904,
-0.03294658288359642,
0.02681487798690796,
-0.0609116405248642,
0.03229504078626633,
0.02312665805220604,
0.005634324625134468,
-0.0002758943010121584,
0.03240169957280159,
0.003994557540863752,
-0.013482768088579178,
0.0023181408178061247,
-0.03684030845761299,
-0.006167241372168064,
-0.020073097199201584,
-0.012928040698170662,
-0.002143645426258445,
0.03974393010139465,
0.019738011062145233,
-0.006848153192549944,
0.03451582416892052,
-0.037396736443042755,
0.027190934866666794,
-0.018668431788682938,
0.012889605015516281,
0.002183479955419898,
-0.0027739042416214943,
-0.034298788756132126,
-0.035614755004644394,
0.012939457781612873,
0.07019585371017456,
-0.045536551624536514,
-0.013673637993633747,
0.00037848029751330614,
-0.03417559340596199,
-0.002390532521530986,
0.027268296107649803,
-0.05739634111523628,
-0.0613294318318367,
-0.02831924892961979,
-0.0009043369209393859,
0.03628361225128174,
0.01864517293870449,
0.04647421836853027,
-0.06862626224756241,
-0.0023355267476290464,
0.030771858990192413,
-0.02761756256222725,
0.006410983391106129,
-0.025405652821063995,
-0.03662648797035217,
0.042422354221343994,
0.06202811002731323,
0.0026476618368178606,
-0.004647617693990469,
0.0015144831268116832,
0.05110831558704376,
0.01856277883052826,
-0.028520548716187477,
0.012095019221305847,
0.05046601966023445,
0.09881055355072021,
0.06244022399187088,
0.06525569409132004,
0.025917258113622665,
0.0038922943640500307,
0.041500262916088104,
0.03599466383457184,
0.027394471690058708,
0.03500642627477646,
0.026094581931829453,
0.013549325987696648,
-0.01752536930143833,
0.034070663154125214,
0.03335072100162506,
0.010441037826240063,
0.0028147243428975344,
0.018426313996315002,
-0.03471757099032402,
0.05688181892037392,
0.011201378889381886,
0.07241269946098328,
-0.07597832381725311,
-0.011511493474245071,
-0.01076409313827753,
-0.022519640624523163,
-0.020913120359182358,
0.03424843028187752,
0.05344273895025253,
-0.005032648798078299,
0.049755681306123734,
0.0024445895105600357,
0.0049803792499005795,
0.023170532658696175,
0.029216725379228592,
0.042564332485198975,
-0.05175190046429634,
-0.031670261174440384,
0.02743239514529705,
0.06355427205562592,
0.02168978750705719,
-0.016012873500585556,
-0.01665068231523037,
-0.044104114174842834,
-0.03156820684671402,
0.04782109335064888,
0.038140758872032166,
-0.014131243340671062,
-0.039614591747522354,
-0.016819993034005165,
0.03908326476812363,
0.021648703143000603,
-0.02443862520158291,
0.024744397029280663,
-0.030208982527256012,
0.0014522270066663623,
0.005633132066577673,
0.048893049359321594,
-0.06068626046180725,
0.0524265319108963,
0.02877567708492279,
0.0272043626755476,
0.007448280695825815,
0.05314406380057335,
0.026242738589644432,
-0.00013215404760558158,
0.024648727849125862,
0.00242615700699389,
0.005201912019401789,
-0.04521815851330757,
-0.04413978382945061,
-0.00396987097337842,
0.028224537149071693,
0.034349072724580765,
-0.010275927372276783,
0.0012404191074892879,
-0.03318682312965393,
-0.061836082488298416,
0.008443156257271767,
-0.07968027144670486,
-0.012531761080026627,
-0.03282087296247482,
-0.039892520755529404,
-0.0026622882578521967,
0.010236423462629318,
0.001665061921812594,
-0.006780701689422131,
0.0910038873553276,
0.054571084678173065,
-0.012455279007554054,
-0.03475390374660492,
-0.009337352588772774,
-0.12004644423723221,
0.004997973330318928,
-0.047017715871334076,
0.005688587669283152,
0.062152035534381866,
-0.03430929034948349,
-0.001735749072395265,
-0.020190222188830376,
0.05852946639060974,
0.022055096924304962,
-0.009875649586319923,
-0.034753136336803436,
0.018565261736512184,
0.008639371953904629,
0.0035427415277808905,
0.03719153627753258,
0.0213007815182209,
-0.04196785390377045,
-0.016489477828145027,
0.03591451048851013,
-0.03337094560265541,
0.04777303338050842,
-0.022463304921984673,
0.04146239534020424,
0.08002442121505737,
-0.007801218423992395,
-0.03082938864827156,
-0.021775124594569206,
0.002862731460481882,
-0.06376411020755768,
-0.039222586899995804,
-0.06917345523834229,
-0.009080121293663979,
-0.009192620404064655,
0.015663793310523033,
-0.018611695617437363,
-0.00601973757147789,
-0.015336181037127972,
0.021285492926836014,
0.0125759681686759,
-0.051373060792684555,
-0.004381999839097261,
0.061022624373435974,
-0.03073737397789955,
-0.0633753165602684,
0.04201648384332657,
-0.03721233084797859,
0.005289929453283548,
0.012090572156012058,
-0.001441807602532208,
-0.05964585766196251,
0.060610830783843994,
-0.004105854779481888,
-0.012458041310310364,
0.0007943226955831051,
-0.028491156175732613,
-0.021142546087503433,
-0.014098655432462692,
0.0042235516011714935,
0.005367850419133902,
-0.040264736860990524,
-0.03372133523225784,
-0.01758825220167637,
0.00966207031160593,
-0.009750026278197765,
-0.026984263211488724,
-0.006224130745977163,
0.004796657711267471,
-0.04607439413666725,
0.013454975560307503,
0.008231126703321934,
-0.02286677435040474,
0.007109755650162697,
-0.028858361765742302,
-0.02870936319231987,
-0.030965926125645638,
0.003033743239939213,
0.04707109183073044,
-0.10299120843410492,
-0.005577093455940485,
-0.05050796642899513,
-0.007642142940312624,
0.003831220092251897,
-0.0596417635679245,
0.08033616840839386,
0.01956750825047493,
-0.02668304182589054,
0.061068758368492126,
0.017732614651322365,
0.01828679069876671,
0.0163244791328907,
0.01610472984611988,
0.06368859112262726,
-0.0373840406537056,
-0.0016750289360061288,
-0.020038126036524773,
0.029028229415416718,
0.06746798753738403,
0.05969340726733208,
-0.003120794426649809,
-0.04557419568300247,
-0.00509334821254015,
-0.013753744773566723,
-0.04259957745671272,
-0.035306140780448914,
0.00010502559598535299,
-0.009393197484314442,
-0.013555248267948627,
0.03637230396270752,
-0.016970552504062653,
-0.028521660715341568,
-0.026090875267982483,
0.05162430182099342,
-0.06278855353593826,
-0.026250142604112625,
-0.04300367832183838,
0.058347295969724655,
0.029514892026782036,
-0.015886161476373672,
0.06787335872650146,
0.00520655931904912,
-0.008192823268473148,
0.05637954920530319,
-0.00008210318628698587,
0.03537240996956825,
-0.059672486037015915,
-0.03743372857570648,
-0.05523259565234184,
-0.034946419298648834,
-0.01576065458357334,
-0.014361904934048653,
0.011442277580499649,
0.03144495561718941,
0.0823163241147995,
-0.01223170105367899,
-0.015332350507378578,
-0.04555639624595642,
0.00481758639216423,
-0.04856157302856445,
0.04448786750435829,
-0.008832663297653198,
0.026813670992851257,
-0.045209020376205444,
-0.03578873723745346,
0.008391082286834717,
0.06423483043909073,
-0.017041577026247978,
-0.023674314841628075,
-0.012446779757738113,
0.02126792073249817,
0.05935056135058403,
-0.0116922901943326,
-0.040490664541721344,
-0.014603566378355026,
-0.024664269760251045,
-0.002016938291490078,
0.042802393436431885,
0.002354641677811742,
0.07682840526103973,
-0.03108893521130085,
0.01834050752222538,
0.006742408033460379,
-0.06523498147726059,
-0.034970782697200775,
0.020351415500044823,
0.015587512403726578,
-0.04833089932799339,
-0.02318497933447361,
-0.034839190542697906,
-0.0015128155937418342,
-0.002316317055374384,
-0.015344604849815369,
-0.04163900390267372,
-0.00048536196118220687,
-0.038329217582941055,
0.009741715155541897,
-0.04438408091664314,
0.038901396095752716,
-0.017509661614894867,
-0.0332515724003315,
0.02442980743944645,
0.03620121628046036,
0.01362417172640562,
-0.07058954238891602,
0.009859650395810604,
0.013465184718370438,
0.021760644391179085,
-0.0008808036218397319,
-0.01140551082789898,
0.012797432951629162,
-0.0023273970000445843,
-0.05474216863512993,
-0.0029038824141025543,
-0.010787582956254482,
-0.04241594299674034,
0.011784025467932224,
0.015649721026420593,
0.018595660105347633,
0.008131337352097034,
0.01763533242046833,
-0.009225883521139622,
-0.014477785676717758,
0.03647938370704651,
0.0077386703342199326,
0.003192720701918006,
-0.007650432176887989,
-0.012431214563548565,
-0.030315978452563286,
-0.038151759654283524,
-0.05071160942316055,
-0.005374433938413858,
-0.057982929050922394,
-0.08313784748315811,
-0.012948643416166306,
-0.017071129754185677,
-0.051308128982782364,
-0.00881967693567276,
-0.06113637238740921,
0.003562980331480503,
0.06845754384994507,
0.04656381160020828,
0.05773051083087921,
0.047181833535432816,
-0.07195417582988739,
-0.004513104911893606,
0.003914645407348871,
0.011553557589650154,
0.003997952677309513,
-0.05296565592288971,
-0.00733544398099184,
0.010905949398875237,
-0.010971618816256523,
0.028392234817147255,
-0.01105204876512289,
0.07484479993581772,
0.013383278623223305,
-0.0011124573647975922,
-0.024458453059196472,
-0.018908703699707985,
0.00948433205485344,
0.004489020444452763,
0.035487305372953415,
-0.03097396157681942,
0.029355550184845924,
-0.017089925706386566,
0.08343806862831116,
0.015301470644772053,
-0.0172940194606781,
0.0170093085616827,
0.053192388266325,
0.07998088002204895,
0.0034453650005161762,
-0.009109772741794586,
0.015257947146892548,
-0.006123893894255161,
-0.01809116080403328,
-0.03256935626268387,
0.00046202586963772774,
0.020398302003741264,
0.047945376485586166,
0.09700686484575272,
-0.05466640740633011,
-0.00580736855044961,
0.02646920457482338,
0.000688191270455718,
0.04658682271838188,
-0.006453480571508408,
0.009806076064705849,
-0.034277044236660004,
0.06822595745325089,
-0.020791538059711456,
-0.03439942002296448,
-0.022026527673006058,
-0.04116261005401611,
-0.002817501313984394,
-0.044402044266462326,
-0.07353132963180542,
-0.004844975657761097,
0.027800409123301506,
0.07830969244241714,
-0.0194227397441864,
-0.004595852456986904,
0.043460581451654434,
-0.0029312625993043184,
0.09559135884046555,
0.007170961704105139,
-0.06556985527276993,
-0.06861332803964615,
-0.06761118769645691,
0.022910859435796738,
-0.058564797043800354,
0.04371155425906181,
0.032749298959970474,
0.027966737747192383,
-0.06675849854946136,
-0.009286605753004551,
0.0033920835703611374,
-0.015575472265481949,
0.008464615792036057,
0.00968211330473423,
0.0013414056738838553,
-0.056716352701187134,
0.012590301223099232,
0.03861996904015541,
0.02756008692085743,
0.0731070339679718,
-0.03257602080702782,
-0.0015622403007000685,
0.03649672120809555,
-0.006208340637385845,
0.013695414178073406,
-0.001726061454974115,
0.03128235787153244,
-0.04548890143632889,
-0.007638315204530954,
-0.05515507608652115,
0.038537830114364624,
-0.007310686632990837,
0.011735541746020317,
-0.006552583072334528,
0.03667474538087845,
0.003107709577307105,
-0.07492590695619583,
-0.026569249108433723,
-0.002108510583639145,
0.055563852190971375,
0.054083261638879776,
-0.08319141715765,
0.011706104502081871,
0.06521668285131454,
0.010770734399557114,
-0.0017024310072883964,
0.04065922647714615,
-0.03701530396938324,
0.001621390227228403,
-0.05213082954287529,
-0.037009142339229584,
-0.0013876915909349918,
-0.018873393535614014,
-0.05945684760808945,
0.0103652598336339,
0.023432688787579536,
-0.011823323555290699,
0.010441028513014317,
0.06581039726734161,
-0.018747603520751,
0.012990258634090424,
0.022025274112820625,
0.004442363511770964,
0.02107294090092182,
0.020067399367690086,
0.01047923881560564,
0.008523900993168354,
0.049051687121391296,
0.020703420042991638,
-0.022815506905317307,
0.003801497630774975,
-0.005092260893434286,
0.013288654386997223,
-0.04268607124686241,
0.019368557259440422,
0.050653718411922455,
0.02603079564869404,
0.0796736627817154,
0.04382229596376419,
-0.030807698145508766,
0.027496539056301117,
-0.002216376131400466,
0.008012998849153519,
-0.06564493477344513,
0.00403950922191143,
-0.03503530099987984,
-0.010378996841609478,
-0.004323671571910381,
-0.02620241418480873,
0.019650373607873917,
-0.008663146756589413,
-0.0125682782381773,
-0.034187912940979004,
-0.07826188951730728,
0.04964042827486992,
-0.030972683802247047,
-0.038440171629190445,
0.02932441607117653,
0.06312640756368637,
-0.05502490699291229,
0.008862818591296673,
-0.07254085689783096,
0.022791337221860886,
0.01801925338804722,
-0.0425986722111702,
0.008151966147124767,
0.03830620273947716,
0.013400181196630001,
0.012696824036538601,
0.021899310871958733,
0.016334200277924538,
0.04978668689727783,
-0.04471828415989876,
0.022235115990042686,
0.003232113551348448,
0.024066464975476265,
0.016309717670083046,
-0.03789810463786125,
0.035987257957458496,
0.0190166886895895,
-0.01522852387279272,
-0.005302575882524252,
0.006783062592148781,
-0.053249143064022064,
-0.02951877750456333,
-0.07406331598758698,
0.07340148091316223,
0.016215551644563675,
-0.08822145313024521,
-0.0501108355820179,
0.006788225844502449,
0.004328951705247164,
-0.006147030740976334,
0.01928401179611683,
0.030822215601801872,
-0.002265749266371131,
0.02340344525873661,
0.007547196000814438,
-0.009004395455121994,
0.01748020015656948,
-0.0023806034587323666,
-0.010393583215773106,
0.06002361699938774,
-0.047656942158937454,
0.01172929722815752,
0.00713964831084013,
0.017865445464849472,
-0.004091734066605568,
-0.012186202220618725,
-0.021941017359495163,
-0.045132219791412354,
-0.05464394390583038,
-0.01025818008929491,
0.033913467079401016,
-0.012989426031708717,
-0.0003863624297082424,
-0.022476011887192726,
0.027752656489610672,
-0.039418257772922516,
0.048185575753450394,
-0.00986409466713667,
0.047805774956941605,
0.0644935816526413,
0.025961244478821754,
0.02795080840587616,
0.038561079651117325,
0.007416184991598129,
0.04773644730448723,
-0.022933615371584892,
-0.019803592935204506,
-0.0474638007581234,
0.007672714069485664,
-0.015151592902839184,
0.00539379520341754,
-0.0295516736805439,
0.003977868240326643,
0.00014161020226310939,
-0.007671377621591091,
0.015195662155747414,
0.04652881994843483,
-0.032301899045705795,
0.03225189074873924,
-0.04088865593075752,
0.018230460584163666,
0.03954891115427017,
-0.061956897377967834,
0.01494502928107977,
-0.08260885626077652,
-0.04057002812623978,
0.01959708146750927,
0.014880862087011337,
-0.060422901064157486,
0.01587522402405739,
-0.06874906271696091,
0.030942736193537712,
0.010647127404808998,
-0.026784848421812057,
0.016472313553094864,
-0.016934966668486595,
-0.003407734679058194,
0.054677531123161316,
0.007095863111317158,
-0.07196716964244843,
-0.04947780817747116,
-0.00584765337407589,
-0.005863012280315161,
-0.028698500245809555,
-0.02670580893754959,
-0.018393198028206825,
-0.003645641263574362,
-0.03983783349394798,
0.02859846130013466,
-0.008860360831022263,
0.002099068136885762,
0.006074112374335527,
0.019973216578364372,
0.023112798109650612,
-0.00095888483338058,
-0.01816498301923275,
0.019589051604270935,
-0.07099203765392303,
0.002013485413044691,
0.0730438306927681,
-0.0350685678422451,
-0.02808002382516861,
0.013165437616407871,
0.07372082024812698,
0.023526793345808983,
-0.002031960990279913,
-0.063273124396801,
0.006616511382162571,
0.06988698989152908,
0.003850463777780533,
-0.032574888318777084,
-0.008294550701975822,
-0.0057280538603663445,
0.05673164129257202,
-0.0002023431152338162,
-0.014845425263047218,
0.014956492930650711,
0.028300566598773003,
-0.04901086166501045,
0.04625421389937401,
0.007676339242607355,
-0.039359550923109055,
0.03655308485031128,
-0.03343832492828369,
0.03590952232480049,
0.01163765974342823,
0.011893237009644508,
-0.06872651726007462,
-0.01916985958814621,
0.04556088149547577,
-0.014421392232179642,
-0.018903687596321106,
0.026173744350671768,
0.022583726793527603,
-0.031145256012678146,
0.030414598062634468,
0.013644167222082615,
0.05463583767414093,
-0.024713750928640366,
0.07126276940107346,
-0.07833343744277954,
-0.045177195221185684,
-0.011010263115167618,
-0.03204270824790001,
0.0080705052241683,
0.030391989275813103,
0.01500535849481821,
-0.03131280094385147,
-0.03417554125189781,
-0.04260338097810745,
0.000023972452254383825,
0.026583125814795494,
0.03663346543908119,
-0.018166447058320045,
-0.04180337116122246,
-0.06323929131031036,
-0.03832979500293732,
0.001552751986309886,
0.019354311749339104,
0.02723412960767746,
0.016346195712685585,
-0.057747144252061844,
0.000709325831849128,
0.0372399240732193,
0.06126338243484497,
0.05412045121192932,
-0.04752354323863983,
0.028502976521849632,
0.02813580259680748,
0.0743923932313919,
-0.020311489701271057,
-0.00692055793479085,
0.007500345353037119,
-0.0100876335054636,
-0.01611017808318138,
0.006750893779098988,
-0.04015696421265602,
-0.0128864087164402,
0.008245022036135197
] |
<p>The text I am reading (Stars and Relativity by Ya. B. Zel'dovich) discusses the possible existence of a repulsive force proportional to total baryon number. At the time of the book's publication it was stated that if such a force existed, it woukd need to be on the order of $10^{46}$ times weaker than the Coulomb force between two protons. </p>
<p>It's also stated as a footnote that such a force would be incompatible with a homogeneous, isotropic universe. Why is this so? Has any of the above changed in the ~40 years since this text was published?</p>
|
g2448
|
[
0.028050320222973824,
0.0195196270942688,
0.009463035501539707,
-0.04246309772133827,
0.05981737747788429,
0.027785342186689377,
-0.005223396699875593,
0.06616578251123428,
-0.042327575385570526,
-0.06194823607802391,
0.046878792345523834,
-0.05303056538105011,
-0.011750509962439537,
-0.0023704664781689644,
0.049217261373996735,
0.04111301526427269,
0.07044962793588638,
-0.056707028299570084,
0.00841693114489317,
0.011217347346246243,
-0.060295090079307556,
0.0374586246907711,
-0.003612344618886709,
-0.07083170861005783,
0.016246547922492027,
0.008337737061083317,
0.039748989045619965,
-0.06893612444400787,
-0.06311985850334167,
-0.029969768598675728,
0.013927835039794445,
0.009290767833590508,
0.03836129978299141,
-0.050333909690380096,
-0.042835481464862823,
0.013869501650333405,
0.035584691911935806,
0.01328803226351738,
0.0468948669731617,
-0.009777413681149483,
-0.001207450870424509,
0.008289583958685398,
0.026887597516179085,
-0.08687524497509003,
-0.0110192084684968,
0.02074684016406536,
-0.014381454326212406,
-0.01741797663271427,
-0.015960033982992172,
0.016385860741138458,
-0.05131777003407478,
0.018625101074576378,
0.018394647166132927,
-0.004072563257068396,
0.0014546954771503806,
0.022234443575143814,
0.016156792640686035,
-0.058417659252882004,
-0.016951173543930054,
0.08329042047262192,
-0.011659232899546623,
0.05409369245171547,
0.028193410485982895,
-0.03200447931885719,
0.04154520109295845,
-0.03182801231741905,
-0.0344250425696373,
0.013733208179473877,
-0.03346759453415871,
-0.06532470136880875,
-0.03737639635801315,
-0.08162926137447357,
-0.023161372169852257,
0.0012317768996581435,
-0.058864228427410126,
0.010848199017345905,
-0.018616115674376488,
0.023884359747171402,
-0.018984822556376457,
-0.018218975514173508,
-0.0135426577180624,
-0.00198416062630713,
0.020022079348564148,
0.018763793632388115,
0.1105472594499588,
-0.06703561544418335,
0.02529969997704029,
-0.006571388803422451,
0.035584595054388046,
0.059102218598127365,
0.02290310338139534,
-0.003100404981523752,
0.054657064378261566,
-0.009424922987818718,
-0.006483676843345165,
-0.0544738844037056,
0.0042608315125107765,
0.0437118224799633,
-0.0018807981396093965,
-0.021981941536068916,
-0.04046653211116791,
0.013457738794386387,
0.026495402678847313,
0.025942333042621613,
-0.0038498176727443933,
-0.07408328354358673,
0.03555085137486458,
0.004745642188936472,
0.00768727483227849,
-0.0454978346824646,
-0.01511361077427864,
0.03151547163724899,
0.007322267629206181,
-0.0036843689158558846,
-0.003313206834718585,
-0.013877205550670624,
0.09095676243305206,
-0.031452734023332596,
-0.003018127055838704,
0.01967000402510166,
-0.0030199161265045404,
0.004311262629926205,
-0.00336531107313931,
0.059431202709674835,
-0.10906130075454712,
-0.04213487729430199,
0.013753019273281097,
0.007368681486696005,
0.025490475818514824,
-0.055457644164562225,
0.006297342013567686,
-0.006319841835647821,
-0.0030605271458625793,
-0.024323605000972748,
-0.011625334620475769,
-0.0018450386123731732,
-0.006613537203520536,
-0.011137109249830246,
-0.004455825313925743,
0.037853460758924484,
0.03367271646857262,
-0.03147509694099426,
0.007755291648209095,
0.01466406136751175,
0.004696712829172611,
0.01055797841399908,
-0.056384697556495667,
0.024709274992346764,
0.0092798862606287,
-0.02166513353586197,
0.01998228393495083,
0.041482388973236084,
0.04777779430150986,
-0.0270445067435503,
-0.039042551070451736,
-0.033668555319309235,
0.06830043345689774,
0.01798863336443901,
-0.03146687150001526,
-0.0022249699104577303,
0.07999016344547272,
0.03474341332912445,
-0.0018350363243371248,
-0.06936267763376236,
0.005181325599551201,
0.07338432222604752,
-0.03698459267616272,
-0.03498420491814613,
0.018804991617798805,
-0.02070854790508747,
-0.06795249134302139,
0.021027516573667526,
0.04753141850233078,
0.05814136937260628,
0.011421184986829758,
-0.03881334513425827,
-0.008731655776500702,
-0.013507094234228134,
-0.019697148352861404,
0.020921412855386734,
-0.0237794928252697,
-0.07154490053653717,
0.010659080930054188,
0.00075249356450513,
-0.008826459757983685,
-0.03587604686617851,
-0.010445762425661087,
0.05500839650630951,
-0.013900036923587322,
0.05957771837711334,
-0.05759315565228462,
0.05015668272972107,
-0.000027100537408841774,
0.06274136900901794,
0.02405422367155552,
0.004315921105444431,
0.013514830730855465,
-0.09149687737226486,
-0.028220413252711296,
0.06368333101272583,
-0.05902789905667305,
0.0824311226606369,
0.01460911612957716,
0.028794553130865097,
0.00464913435280323,
0.02391199767589569,
-0.027732860296964645,
0.05356603115797043,
0.057638365775346756,
-0.016133463010191917,
0.030012894421815872,
-0.0212519820779562,
0.026489252224564552,
0.03272432088851929,
-0.018857531249523163,
-0.07428248971700668,
0.025278419256210327,
0.03198655694723129,
-0.04165239259600639,
0.042384251952171326,
-0.0948956161737442,
-0.003869307693094015,
0.08047126978635788,
0.03772842139005661,
-0.03062097728252411,
-0.023157814517617226,
0.0033296288456767797,
0.016342967748641968,
0.04512501880526543,
0.005808398127555847,
-0.04625315964221954,
-0.007279078010469675,
0.012392156757414341,
0.02554931305348873,
0.02860988676548004,
0.05490521714091301,
0.03570518642663956,
-0.04221523553133011,
-0.007567161228507757,
-0.014757678844034672,
0.0163189098238945,
-0.060559969395399094,
-0.01277799904346466,
0.047500185668468475,
0.01302175410091877,
-0.03470481559634209,
0.03744906559586525,
-0.06396912038326263,
0.013224152848124504,
0.004290036857128143,
0.01010711956769228,
-0.04616963490843773,
-0.017006773501634598,
0.05101177841424942,
-0.03695158660411835,
0.048069506883621216,
-0.027486145496368408,
0.03495445474982262,
-0.07754285633563995,
-0.02734561823308468,
0.011836287565529346,
-0.025694239884614944,
0.00013356705312617123,
0.011055759154260159,
-0.06596551835536957,
0.03230974078178406,
-0.037954919040203094,
0.040364280343055725,
-0.008059087209403515,
-0.042519282549619675,
0.010731607675552368,
0.025340981781482697,
-0.0008316182065755129,
0.023884417489171028,
-0.013656246475875378,
0.05060223489999771,
-0.021802527830004692,
-0.06127409264445305,
-0.013763326220214367,
0.01831265352666378,
0.001376121654175222,
0.010937429033219814,
-0.023115454241633415,
-0.037483323365449905,
0.017449118196964264,
0.009649764746427536,
0.017352603375911713,
0.0034162201918661594,
0.0331161692738533,
0.0039925952441990376,
-0.027450626716017723,
0.06618594378232956,
-0.007596503011882305,
0.03029302880167961,
0.054225143045186996,
0.0266614630818367,
-0.034796856343746185,
-0.017733391374349594,
-0.07754717767238617,
0.04516655206680298,
0.04496963694691658,
-0.018856411799788475,
0.03435887396335602,
-0.004192797467112541,
-0.0004983449471183121,
-0.02270641177892685,
-0.05658866837620735,
0.0000972354828263633,
-0.012014467269182205,
0.029903536662459373,
0.011476081795990467,
0.06294463574886322,
0.012739211320877075,
0.022060774266719818,
-0.06144560128450394,
0.060173891484737396,
0.041225969791412354,
-0.014887496829032898,
0.002142797689884901,
0.005428214557468891,
-0.0034628964494913816,
-0.03479688987135887,
0.02976883575320244,
-0.03328873962163925,
0.06963681429624557,
0.004106837324798107,
-0.06634048372507095,
0.03079744055867195,
-0.032234352082014084,
-0.008046387694776058,
0.02914755418896675,
-0.0078800143674016,
0.06755957752466202,
0.009155317209661007,
-0.0652075856924057,
0.0025670405011624098,
0.0010952521115541458,
-0.002725607715547085,
0.04995174705982208,
0.020324066281318665,
0.021945131942629814,
-0.010291746817529202,
-0.054899413138628006,
0.008596939034759998,
-0.021378198638558388,
0.06387647986412048,
-0.0007556802011094987,
-0.003296847688034177,
0.007827148772776127,
-0.0019092477159574628,
0.002286431612446904,
-0.009637804701924324,
0.00001609302307770122,
-0.03376822546124458,
0.037375956773757935,
0.010060681030154228,
0.005810530856251717,
0.04065036028623581,
0.02677285112440586,
-0.007033685687929392,
0.0411653071641922,
-0.027198150753974915,
-0.00026301658363081515,
0.001432625693269074,
-0.010626656003296375,
-0.014328722842037678,
0.009234421886503696,
0.007357886526733637,
-0.04345397278666496,
0.008181750774383545,
0.001977058593183756,
-0.09051747620105743,
-0.001471384079195559,
-0.03455276042222977,
0.07586868107318878,
-0.0724480077624321,
0.09498679637908936,
-0.023572543635964394,
0.0049227382987737656,
0.043152663856744766,
0.09977635741233826,
0.001305802958086133,
-0.03958909586071968,
0.03457758575677872,
0.061910971999168396,
-0.01632167585194111,
-0.06879806518554688,
-0.06198984012007713,
0.01022864319384098,
-0.03268178179860115,
-0.0004814167332369834,
-0.04579674452543259,
0.010204105637967587,
0.023201296105980873,
0.032874736934900284,
-0.01788407936692238,
0.0030940938740968704,
0.025030486285686493,
0.036583807319402695,
0.014581114985048771,
-0.020587431266903877,
-0.035955749452114105,
-0.02927234396338463,
-0.014824187383055687,
-0.025750495493412018,
0.04405141621828079,
0.02910914644598961,
0.022169722244143486,
0.003769242437556386,
-0.034520432353019714,
0.03218083083629608,
0.005726031959056854,
-0.016883617267012596,
-0.106449656188488,
0.04545854032039642,
0.01723359525203705,
0.013006331399083138,
0.007360975723713636,
0.009852334856987,
-0.008097766898572445,
-0.016894550994038582,
0.0689798966050148,
-0.021921537816524506,
-0.031739939004182816,
0.04238852858543396,
0.08905439078807831,
0.043621525168418884,
0.027244968339800835,
0.04230796545743942,
0.022033682093024254,
0.027169108390808105,
0.03501318022608757,
0.006710846908390522,
0.0361185260117054,
-0.04046602547168732,
0.035584136843681335,
-0.01592865027487278,
0.03608402609825134,
-0.010209716856479645,
0.07540229707956314,
0.06580792367458344,
-0.004448879510164261,
0.03190718591213226,
0.024628886952996254,
0.047233495861291885,
0.05286455154418945,
-0.03691588714718819,
-0.043093763291835785,
-0.08804097771644592,
-0.06819576025009155,
-0.019170010462403297,
-0.03385869786143303,
-0.021587366238236427,
0.045643627643585205,
-0.008425366133451462,
0.0012318914523348212,
-0.005126818548887968,
0.003950490150600672,
-0.009322366677224636,
0.04552537202835083,
-0.01832800917327404,
-0.018494725227355957,
0.02393414080142975,
-0.0172735583037138,
0.01914369873702526,
0.02068064920604229,
-0.007802230305969715,
0.027352260425686836,
-0.045790188014507294,
0.01715853624045849,
-0.02687438204884529,
-0.0056848106905817986,
0.040347471833229065,
-0.0242620836943388,
-0.02385021187365055,
0.012702057138085365,
-0.002509883139282465,
-0.038348425179719925,
-0.004830915480852127,
-0.0142466826364398,
-0.059690073132514954,
-0.016490761190652847,
0.008241790346801281,
-0.00044528458965942264,
0.00042592198587954044,
-0.01532928366214037,
-0.03553568944334984,
0.005956055596470833,
-0.020352749153971672,
-0.02561103366315365,
0.0112850870937109,
0.01889646053314209,
-0.00028346653562039137,
-0.018917633220553398,
-0.012412773445248604,
0.015179285779595375,
0.04745437949895859,
-0.01086723804473877,
-0.004634743090718985,
0.08298123627901077,
-0.0061065866611897945,
0.02941802702844143,
-0.0015895902179181576,
-0.006133141927421093,
-0.03018980659544468,
-0.028719352558255196,
0.03132028505206108,
-0.008992300368845463,
-0.014970498159527779,
-0.005866271443665028,
-0.026118213310837746,
0.028226453810930252,
0.051561228930950165,
0.04850415885448456,
-0.027418402954936028,
0.05068661645054817,
0.013954798690974712,
-0.00920175388455391,
-0.00977781880646944,
-0.08833610266447067,
0.02157573215663433,
-0.021942369639873505,
0.002248893491923809,
0.0039914981462061405,
-0.051600150763988495,
0.03396206721663475,
0.005392309278249741,
-0.02699979580938816,
-0.07057986408472061,
-0.02010399103164673,
-0.02161789871752262,
-0.01054431963711977,
0.00681710010394454,
-0.0594891719520092,
0.0032221104484051466,
-0.04250183328986168,
0.045618414878845215,
0.010095766745507717,
-0.02507620118558407,
-0.01914793625473976,
0.0017111024353653193,
0.01160978153347969,
-0.029693959280848503,
0.03489243984222412,
-0.002435187576338649,
0.043760962784290314,
-0.03495825454592705,
-0.0029459218494594097,
0.05646386742591858,
-0.0541437566280365,
-0.04686471074819565,
0.04310337454080582,
-0.015501195564866066,
0.043043725192546844,
-0.005371032282710075,
0.012587001547217369,
0.00657707080245018,
-0.023733582347631454,
0.0008610430522821844,
-0.02027447335422039,
0.021442698314785957,
-0.0073291161097586155,
-0.024335134774446487,
0.04100338742136955,
0.043610334396362305,
-0.05074579268693924,
-0.0063143158331513405,
-0.02703745849430561,
0.03168140724301338,
0.01688542030751705,
0.016045479103922844,
0.039860937744379044,
-0.03700428083539009,
-0.01910303346812725,
0.04166201129555702,
-0.04519040137529373,
-0.06664890795946121,
-0.029216289520263672,
-0.014316507615149021,
0.04455354064702988,
0.001946037169545889,
-0.04318626597523689,
0.02259511686861515,
-0.026920070871710777,
-0.029514120891690254,
-0.029716458171606064,
-0.029923489317297935,
0.007724953815340996,
0.05552886053919792,
-0.052583564072847366,
0.07347221672534943,
-0.030281417071819305,
-0.038834527134895325,
-0.028442582115530968,
-0.04224800691008568,
0.012896553613245487,
0.022935861721634865,
-0.01634545996785164,
-0.03296145424246788,
-0.010262507013976574,
0.015047884546220303,
0.015362614765763283,
0.08225833624601364,
0.01464356854557991,
0.10820852220058441,
-0.022858915850520134,
-0.03215446323156357,
-0.00020184169989079237,
0.054095812141895294,
0.03459247574210167,
-0.03658559173345566,
-0.031481459736824036,
-0.05156709626317024,
-0.014676140621304512,
0.046700991690158844,
-0.05508073791861534,
0.01231129840016365,
0.03142038360238075,
-0.07128727436065674,
-0.014289322309195995,
0.011032989248633385,
0.0192022193223238,
0.025361936539411545,
0.0067223371006548405,
0.008732129819691181,
0.04139527305960655,
-0.045769721269607544,
0.051602188497781754,
0.031947165727615356,
-0.0025385254994034767,
0.0171737652271986,
-0.006713985465466976,
0.016418419778347015,
-0.020590147003531456,
-0.02107037417590618,
0.020573683083057404,
-0.00694211246445775,
-0.005353371147066355,
0.014861389994621277,
-0.0329621322453022,
-0.03106413222849369,
-0.023667337372899055,
0.04686581343412399,
-0.005318545736372471,
-0.04831302911043167,
-0.01772155798971653,
0.08132914453744888,
0.009619987569749355,
-0.037505391985177994,
0.04927506297826767,
-0.027958089485764503,
-0.0018005287274718285,
0.010430601425468922,
-0.0007626612787134945,
-0.0569617822766304,
0.0006337551749311388,
-0.008761577308177948,
-0.019774265587329865,
-0.0048928032629191875,
-0.03368090093135834,
-0.016043968498706818,
0.04288347437977791,
-0.03844628855586052,
0.05286072939634323,
-0.02499489113688469,
0.07067760080099106,
0.0391145721077919,
-0.04179660230875015,
0.044717900454998016,
-0.009583327919244766,
0.03574014827609062,
-0.008582104928791523,
-0.03627965971827507,
-0.04567647725343704,
-0.006905845366418362,
0.0289135929197073,
0.01524109672755003,
-0.009628684259951115,
0.09069609642028809,
-0.008618594147264957,
0.007689283229410648,
0.0637926459312439,
-0.006345649715512991,
0.04663850739598274,
-0.057873498648405075,
0.008205092512071133,
-0.01370044331997633,
-0.0391300730407238,
0.01400611363351345,
0.0018773017218336463,
-0.02652573399245739,
-0.022196374833583832,
0.0070222970098257065,
0.023696621879935265,
-0.026458216831088066,
-0.011692781932651997,
-0.014302919618785381,
0.04451250657439232,
0.04302297532558441,
-0.007292191963642836,
-0.016838304698467255,
-0.035704441368579865,
-0.012166904285550117,
-0.030625972896814346,
0.04476797953248024,
0.052119992673397064,
-0.04307708144187927,
-0.012451241724193096,
-0.04299192503094673,
-0.06169722229242325,
0.04745343700051308,
0.03189447894692421,
0.021173954010009766,
-0.0540403313934803,
0.06627418100833893,
-0.022421294823288918,
-0.02047441154718399,
-0.02982126921415329,
0.014154977165162563,
-0.028509870171546936,
0.029753252863883972,
-0.028695283457636833,
0.020618753507733345,
-0.080293670296669,
-0.0382726676762104,
-0.038729507476091385,
0.03681528940796852,
-0.013767365366220474,
0.0062997848726809025,
-0.011083167046308517,
0.013571175746619701,
-0.05509674921631813,
-0.018026554957032204,
0.0005782073130831122,
-0.012827250175178051,
0.02438751794397831,
-0.002202266827225685,
-0.010098591446876526,
-0.035953719168901443,
-0.02238859236240387,
-0.018257685005664825,
-0.011946909129619598,
-0.02092072367668152,
-0.0018913841340690851,
0.01058576162904501,
-0.028086049482226372,
-0.07185468077659607,
0.006467333063483238,
0.08698131144046783,
-0.018981697037816048,
0.016069360077381134,
0.013898588716983795,
-0.0008935805526562035,
0.0005726388189941645,
0.05984058603644371,
-0.0727580115199089,
-0.00784347578883171,
0.027435477823019028,
-0.048533160239458084,
-0.04171476140618324,
0.0412607416510582,
-0.0002846470451913774,
0.0222877636551857,
-0.0035036541521549225,
0.00857141800224781,
-0.02559192106127739,
-0.04121381789445877,
-0.0002501757408026606
] |
<blockquote>
<p>What are some common applications, uses, exploitations of the properties of surface tension? </p>
</blockquote>
<p>Here is what I mean. A water strider can walk on water, that is a consequence of surface tension. This is a consequence, but it is not human made.</p>
<p>On the other hand, I heard that in the construction of some tents, the upper cover of the tent is the rain protector. It is not really impermeable, but if water is placed on it then the water surface tension does not let the water pass through the fine, small pores of the tent cover. However, if you touch the cover while water is on it, you break the surface tension and water passes through. </p>
<p>I would say that the above fact is a clever use of the effect of surface tension. Are there any other known applications, or interesting experiments regarding the surface or interfacial tension?</p>
|
g2449
|
[
0.042243361473083496,
-0.0013089157873764634,
-0.00444085244089365,
0.013190295547246933,
-0.01160360500216484,
0.022315187379717827,
0.05581076070666313,
0.005012903828173876,
-0.002636593533679843,
-0.05261039361357689,
-0.008288429118692875,
-0.04921935871243477,
-0.011262967251241207,
0.016952404752373695,
-0.015956949442625046,
0.06288794428110123,
0.022831683978438377,
-0.017486708238720894,
0.011201738379895687,
-0.0006441791192628443,
0.002036157762631774,
0.007386502344161272,
0.005224370863288641,
0.022157326340675354,
-0.0708342120051384,
-0.025313029065728188,
0.028389345854520798,
-0.04058915376663208,
-0.004673738498240709,
-0.007622947916388512,
0.000729651190340519,
0.01918468065559864,
0.002740437863394618,
-0.07191072404384613,
-0.02754680998623371,
-0.0014092052588239312,
-0.048388585448265076,
-0.032685618847608566,
0.0022071520797908306,
-0.042669881135225296,
-0.020165560767054558,
0.02727111242711544,
-0.05679623782634735,
0.0475977286696434,
-0.0013053910806775093,
-0.03465946391224861,
-0.022575682029128075,
-0.00596878957003355,
0.007290520239621401,
-0.04018179327249527,
0.029277391731739044,
0.023779412731528282,
-0.011500315740704536,
-0.015009576454758644,
-0.0031811282970011234,
0.03146366775035858,
0.04014871269464493,
-0.0471620038151741,
0.0395977646112442,
0.017595257610082626,
-0.04219484701752663,
0.05574173480272293,
-0.022455105558037758,
0.007680207956582308,
0.05221131816506386,
-0.04551374539732933,
0.019698545336723328,
-0.0077348691411316395,
0.0279943086206913,
0.11585168540477753,
0.05367807671427727,
-0.014851906336843967,
0.007303291000425816,
-0.029049495235085487,
-0.05108509212732315,
-0.010058552026748657,
-0.007077670656144619,
-0.005273139104247093,
-0.01413085125386715,
0.03142928332090378,
0.04358331486582756,
-0.004106197040528059,
-0.038801755756139755,
0.011642376892268658,
0.037785448133945465,
-0.022633569315075874,
-0.010340463370084763,
-0.03990583494305611,
0.00023554894141852856,
-0.002468366175889969,
-0.009775158949196339,
0.0016395096899941564,
0.0066870530135929585,
0.03345145285129547,
-0.08159244805574417,
-0.022819172590970993,
0.04889889061450958,
-0.05200016498565674,
0.007879474200308323,
0.01593315228819847,
-0.023287422955036163,
-0.036175113171339035,
0.07767920196056366,
0.032683223485946655,
0.012330295518040657,
0.03692081943154335,
0.0063134548254311085,
0.039268266409635544,
0.016832580789923668,
0.0036237614694982767,
0.03052595630288124,
0.02747183106839657,
0.0038383835926651955,
-0.01047830656170845,
0.016658397391438484,
-0.04484407603740692,
0.028917042538523674,
-0.003359419759362936,
0.012058556079864502,
-0.01046845130622387,
-0.024526085704565048,
-0.0008462065597996116,
-0.013276863843202591,
0.007753101177513599,
0.026531293988227844,
0.006921272724866867,
0.04800606146454811,
0.022432299330830574,
-0.0015498643042519689,
-0.032619621604681015,
0.02316894568502903,
0.05089131370186806,
-0.047900669276714325,
-0.05763913691043854,
0.0404045544564724,
0.0114138750359416,
-0.048288315534591675,
-0.002601824002340436,
-0.030812814831733704,
-0.029573919251561165,
0.08031488955020905,
0.024008963257074356,
-0.06444375216960907,
0.0030002521816641092,
0.011265219189226627,
-0.033469654619693756,
0.00908984150737524,
-0.015167596749961376,
-0.026901889592409134,
0.0013448200188577175,
-0.030157409608364105,
0.006397087126970291,
-0.018820490688085556,
0.02395426295697689,
0.010426482185721397,
0.018039248883724213,
-0.01184762641787529,
-0.01204267144203186,
0.052812349051237106,
0.07032051682472229,
0.01844615489244461,
0.026470184326171875,
0.03198463097214699,
0.05961174517869949,
-0.0015577354934066534,
0.017212195321917534,
0.034039366990327835,
-0.0013798755826428533,
0.01851792261004448,
-0.013316215947270393,
0.016999593004584312,
-0.03603753447532654,
-0.08162546902894974,
0.02262147329747677,
0.002064834348857403,
-0.014869765378534794,
0.05387433245778084,
-0.06134193018078804,
0.017109934240579605,
-0.024118151515722275,
-0.03631225600838661,
-0.01933927647769451,
-0.009538087993860245,
-0.0005122825969010592,
-0.019683850929141045,
0.014551429077982903,
0.022427575662732124,
-0.07007131725549698,
-0.10159898549318314,
0.046716853976249695,
-0.08769726753234863,
0.0037039814051240683,
0.0053652068600058556,
0.016733363270759583,
-0.027083972468972206,
-0.018234169110655785,
0.030612440779805183,
0.02430865354835987,
0.008819552138447762,
-0.02820434421300888,
0.004563008435070515,
0.058657750487327576,
-0.011202992871403694,
-0.0035872652661055326,
-0.03062640316784382,
0.06285206973552704,
0.011215304024517536,
-0.003105930285528302,
0.04518973454833031,
0.0038435496389865875,
0.018868425861001015,
-0.05355466157197952,
0.020443011075258255,
0.0069195874966681,
0.02498757094144821,
0.011426279321312904,
-0.03637531027197838,
-0.04812991991639137,
-0.022106511518359184,
-0.014952140860259533,
0.032914355397224426,
-0.03304477408528328,
-0.008858493529260159,
0.09245356917381287,
-0.0006142762140370905,
0.021344633772969246,
-0.06480520963668823,
0.016047053039073944,
0.00294934562407434,
0.031865283846855164,
0.013704106211662292,
-0.0497903935611248,
0.018771523609757423,
0.029651537537574768,
-0.009677844122052193,
0.07760294526815414,
0.029667526483535767,
0.032561447471380234,
0.017741946503520012,
-0.028666691854596138,
0.0458257682621479,
-0.061431337147951126,
-0.06305285543203354,
-0.06500472128391266,
0.054884105920791626,
0.030921850353479385,
-0.03679851442575455,
-0.0233023539185524,
0.10638265311717987,
0.046606067568063736,
0.06089935824275017,
-0.0247690100222826,
0.03164168819785118,
0.027731457725167274,
0.011225517839193344,
-0.07340013980865479,
0.0009267195127904415,
-0.03440002351999283,
-0.03977462649345398,
-0.06831040233373642,
0.029297329485416412,
-0.03315065801143646,
0.026540514081716537,
0.012387800961732864,
0.020489389076828957,
0.00068752805236727,
-0.07208885252475739,
0.025850441306829453,
0.02973857894539833,
0.08400752395391464,
0.04274360463023186,
-0.01394347008317709,
-0.005812781862914562,
-0.0014382529770955443,
-0.06869860738515854,
-0.028613731265068054,
0.014468447305262089,
-0.04152308776974678,
0.021722616627812386,
0.0027304822579026222,
0.05192353576421738,
0.017740756273269653,
-0.039083242416381836,
0.08080187439918518,
0.03285424783825874,
-0.05841483548283577,
-0.015751928091049194,
0.0022970521822571754,
0.002162169199436903,
0.0051352824084460735,
0.054096248000860214,
-0.0407426692545414,
0.03156797215342522,
0.03512265533208847,
0.005969350226223469,
-0.0035934308543801308,
-0.05818020552396774,
0.01060269121080637,
-0.028047097846865654,
0.020238667726516724,
0.021776119247078896,
0.005906892009079456,
0.02954406477510929,
0.041461262851953506,
-0.005435118451714516,
0.018418526276946068,
-0.002039714017882943,
-0.01712799072265625,
0.043215565383434296,
-0.028369341045618057,
-0.008079071529209614,
0.06892433762550354,
0.006568956654518843,
-0.0012291718740016222,
-0.061711668968200684,
-0.0029255058616399765,
0.055631473660469055,
0.0083567900583148,
0.024383869022130966,
-0.057911716401576996,
-0.008623311296105385,
0.030326183885335922,
0.007106427568942308,
0.03435537964105606,
-0.010478154756128788,
0.019748905673623085,
-0.007057555019855499,
0.055768582969903946,
-0.04078333452343941,
-0.020739272236824036,
0.024984365329146385,
0.04785092920064926,
-0.00037310473271645606,
-0.0773288905620575,
-0.009816641919314861,
-0.05506047233939171,
0.02253551594913006,
0.04451552778482437,
-0.032937757670879364,
0.023713041096925735,
0.02103143185377121,
-0.03962072357535362,
-0.02552606724202633,
-0.0028092688880860806,
-0.006455202121287584,
-0.0035605947487056255,
0.04604455083608627,
0.011190417222678661,
-0.02208506315946579,
0.011519805528223515,
0.02858126536011696,
0.04012781009078026,
-0.024715838953852654,
0.015196360647678375,
0.010480094701051712,
0.049370598047971725,
0.02361440099775791,
0.005822017788887024,
0.004510380793362856,
0.02464558184146881,
0.023441256955266,
0.043882448226213455,
0.02757054567337036,
0.0028486631345003843,
-0.009314768016338348,
-0.020463842898607254,
0.039087601006031036,
0.11330725252628326,
-0.047582659870386124,
-0.02539670653641224,
0.061901479959487915,
-0.01799916662275791,
-0.007864166982471943,
0.04553668573498726,
-0.002396350959315896,
0.02812417596578598,
0.02357977256178856,
0.03560429438948631,
0.010889858938753605,
-0.006698636803776026,
0.06636330485343933,
0.050351228564977646,
0.04101363196969032,
0.05234868824481964,
-0.017275799065828323,
-0.03642210364341736,
-0.02101893536746502,
0.0000027069856969319517,
0.07359752804040909,
-0.04730338975787163,
0.01838778890669346,
0.014981013722717762,
-0.03970958665013313,
-0.035650964826345444,
0.0116569260135293,
-0.003918888978660107,
0.0029958547092974186,
-0.03221613168716431,
-0.025516144931316376,
-0.01701459102332592,
0.029641201719641685,
-0.041059788316488266,
-0.06277398020029068,
0.01773064024746418,
-0.05849357321858406,
-0.03784406930208206,
0.028555069118738174,
-0.0167759507894516,
-0.040982913225889206,
-0.019059771671891212,
0.059004731476306915,
-0.0232091061770916,
-0.03097100555896759,
-0.0405966155230999,
-0.046913180500268936,
0.02979383058845997,
-0.035175200551748276,
0.013462623581290245,
-0.02564365044236183,
-0.04678572714328766,
-0.03723420947790146,
0.07229007035493851,
-0.015504848212003708,
0.02973824366927147,
0.007920910604298115,
0.029986891895532608,
0.01855282299220562,
0.019212214276194572,
-0.008406723849475384,
-0.05313267931342125,
-0.02750534564256668,
0.028393270447850227,
-0.04496501758694649,
0.01738390326499939,
0.0032027673441916704,
0.019370490685105324,
0.04254945367574692,
-0.009635590948164463,
-0.04676724597811699,
-0.0009844424203038216,
-0.0460764579474926,
0.05502987653017044,
-0.02869383804500103,
0.060507260262966156,
-0.008814598433673382,
0.026147134602069855,
-0.0351744219660759,
-0.027566449716687202,
-0.019649533554911613,
-0.006004537455737591,
-0.06727178394794464,
-0.04832141846418381,
0.028808599337935448,
-0.0011249572271481156,
-0.006287186872214079,
-0.004467019811272621,
-0.01901034638285637,
0.02265978790819645,
-0.005860756151378155,
0.00365347764454782,
-0.008322666399180889,
-0.040565814822912216,
-0.027497882023453712,
0.04341956973075867,
-0.01718970760703087,
0.011891660280525684,
-0.069252610206604,
-0.01832149550318718,
-0.014037306420505047,
0.021290060132741928,
-0.0005014464259147644,
0.06670966744422913,
0.019366828724741936,
0.018302882090210915,
-0.07017798721790314,
0.027217013761401176,
0.028004728257656097,
0.02048606052994728,
-0.016552139073610306,
-0.03781244531273842,
0.034151218831539154,
0.03080141544342041,
-0.03510557487607002,
0.049670446664094925,
0.018906591460108757,
-0.07634378969669342,
0.0027437510434538126,
-0.007637049071490765,
-0.03820288926362991,
0.03209081292152405,
0.01967206411063671,
-0.021402083337306976,
-0.03224813565611839,
0.0431724451482296,
-0.058677490800619125,
-0.06908352673053741,
0.0461258590221405,
0.03720522299408913,
0.03890017792582512,
-0.016095537692308426,
0.06346812844276428,
-0.055668894201517105,
0.01480789203196764,
0.04603472724556923,
0.020471692085266113,
0.03963134437799454,
0.003482289845123887,
-0.034382980316877365,
0.029552938416600227,
0.07170112431049347,
-0.033980805426836014,
0.04376984387636185,
-0.07472164928913116,
-0.012158104218542576,
0.020656272768974304,
0.016726944595575333,
0.07578092813491821,
-0.014175551943480968,
-0.008550859056413174,
0.05606286600232124,
-0.007291328627616167,
-0.023386184126138687,
0.047612469643354416,
0.03281518071889877,
-0.00516919931396842,
-0.026135696098208427,
-0.031222227960824966,
0.013542711734771729,
0.02208334021270275,
-0.003040114650502801,
-0.010210603475570679,
0.008455393835902214,
-0.012715484015643597,
-0.05831053853034973,
-0.03097965382039547,
-0.0197631623595953,
-0.036436326801776886,
0.06139909848570824,
0.02564401738345623,
-0.04417193681001663,
-0.013826243579387665,
-0.023042848333716393,
0.007935886271297932,
0.010587997734546661,
-0.018804950639605522,
0.015925465151667595,
-0.05989324301481247,
-0.008585728704929352,
0.03863292187452316,
-0.017894316464662552,
0.06234977766871452,
0.003790389746427536,
-0.07944493740797043,
0.022711902856826782,
0.002484027063474059,
-0.033978819847106934,
-0.05997239053249359,
-0.05281369388103485,
-0.012470145709812641,
0.016285544261336327,
0.08402425795793533,
0.05743594467639923,
0.03865225240588188,
-0.039427921175956726,
-0.008494690991938114,
-0.04769669100642204,
-0.04988958686590195,
-0.00840580090880394,
-0.016042936593294144,
0.027605360373854637,
-0.007453739643096924,
-0.012558147311210632,
0.09345763921737671,
0.013831431046128273,
-0.042936526238918304,
-0.005961875431239605,
-0.0041169035248458385,
0.08228793740272522,
-0.07292772084474564,
0.022161860018968582,
0.011739162728190422,
-0.006896917708218098,
0.004987590946257114,
-0.029299531131982803,
0.006125268992036581,
-0.04189648851752281,
-0.05522087961435318,
-0.018701665103435516,
0.04749197140336037,
-0.006947303656488657,
0.007943692617118359,
0.006096318364143372,
-0.0012205635430291295,
0.04664890095591545,
0.049906350672245026,
-0.05277520790696144,
0.0018853277433663607,
0.07279226183891296,
0.006984736304730177,
0.04614156484603882,
0.009460540488362312,
-0.01475864090025425,
0.050790853798389435,
-0.025452956557273865,
0.04012979194521904,
0.051712434738874435,
0.017520515248179436,
0.008262746036052704,
0.01169128343462944,
-0.05351458117365837,
-0.0323217548429966,
0.026398615911602974,
0.00960471760481596,
-0.01363392174243927,
-0.06518563628196716,
-0.04156465828418732,
0.015536592341959476,
-0.024549217894673347,
-0.06448526680469513,
-0.045407235622406006,
-0.037788864225149155,
-0.028844619169831276,
0.005414654966443777,
-0.0009509502560831606,
-0.03908297419548035,
-0.03550923243165016,
0.0014940638793632388,
0.012686082161962986,
0.029974767938256264,
0.019850242882966995,
-0.023013431578874588,
0.0029304656200110912,
0.03818049281835556,
-0.00020108532044105232,
-0.026242045685648918,
0.061519261449575424,
-0.05259590968489647,
-0.029383767396211624,
0.01761176623404026,
0.06544888019561768,
-0.016973793506622314,
-0.015605580061674118,
-0.03422287106513977,
0.0032244061585515738,
0.008536363020539284,
0.022158367559313774,
-0.020672963932156563,
0.00668232562020421,
-0.014045263640582561,
-0.030490508303046227,
0.0636834055185318,
-0.04704181104898453,
-0.05352112278342247,
-0.0031402744352817535,
0.05206836014986038,
0.06638211011886597,
-0.002864447422325611,
-0.020526781678199768,
-0.009112383238971233,
0.046642642468214035,
-0.03157763183116913,
0.013575257733464241,
0.06882775574922562,
0.0013625584542751312,
-0.036569032818078995,
0.035335686057806015,
0.03708251938223839,
0.04253570735454559,
-0.0338798463344574,
0.052426036447286606,
0.030729390680789948,
-0.04456274211406708,
-0.05241166055202484,
-0.02603716403245926,
0.0177411288022995,
-0.010639523155987263,
0.05457949638366699,
0.02791978232562542,
-0.04574677348136902,
-0.05470515787601471,
-0.027978351339697838,
0.031160738319158554,
0.005926294252276421,
-0.04804425686597824,
-0.03239686042070389,
0.01101591158658266,
0.007228868082165718,
0.0162067748606205,
-0.0348285548388958,
-0.025778133422136307,
0.03422866761684418,
0.08464819192886353,
-0.023023230955004692,
-0.015935184434056282,
-0.005688496865332127,
-0.026852408424019814,
0.0488172322511673,
0.004033778794109821,
-0.007650141138583422,
0.03733932226896286,
-0.07743335515260696,
-0.03013051114976406,
-0.025767380371689796,
-0.04736737534403801,
0.05146489664912224,
-0.019392505288124084,
-0.030429640784859657,
0.02128532901406288,
-0.024527033790946007,
-0.07997455447912216,
-0.005072718020528555,
0.009519173763692379,
-0.045864883810281754,
-0.007652205880731344,
0.0029887910932302475,
0.0051162345334887505,
-0.01717671938240528,
0.01077769510447979,
-0.013832513242959976,
-0.01306094415485859,
0.020550495013594627,
-0.03849847987294197,
-0.015275410376489162,
-0.03338436409831047,
-0.060440585017204285,
0.04326580837368965,
0.02611812949180603,
0.0029099644161760807,
0.007388994563370943,
0.03252828121185303,
0.014464111067354679,
-0.0145258205011487,
0.0025463425554335117,
-0.04547637328505516,
-0.08357835561037064,
0.04000331461429596,
0.08851563185453415,
-0.015097173862159252,
-0.06981740146875381,
-0.03685364872217178,
-0.004458812531083822,
0.04627557098865509,
-0.014223909936845303,
-0.01905381679534912,
0.006561844144016504,
-0.03179103136062622,
0.013808058574795723,
0.024391232058405876,
-0.007435136940330267,
0.003934127278625965,
0.008021828718483448,
0.06734418123960495,
0.014378117397427559,
-0.069181427359581,
-0.056779809296131134,
-0.07791323959827423,
-0.04770771414041519,
-0.014307652600109577,
0.08268436044454575,
-0.0022677562665194273,
0.00996321439743042,
0.002821460599079728,
-0.011510193347930908,
-0.04253682866692543,
-0.08427327126264572,
-0.01879582740366459,
-0.014243079349398613,
0.004400019068270922
] |
<p>English Wikipedia in the <a href="http://en.wikipedia.org/wiki/Poisson%27s_ratio#Width_change" rel="nofollow">Poisson's ratio article</a> gives an equation for large deformation:
$$
\frac{\Delta d}{d}=-1+\frac{1}{\left(1+\dfrac{\Delta L}{L}\right)^\nu}
$$</p>
<p>I couldn't find any reference for this equation. Could someone help? I need it in my thesis, and I'd like to reference some other source than Wikipedia. Every other publication I've seen so far gives the approximate (linear) equation.</p>
|
g2450
|
[
0.004374445416033268,
0.019142212346196175,
-0.027689294889569283,
-0.07914846390485764,
-0.021643325686454773,
-0.01794464886188507,
0.04419052600860596,
0.007347581908106804,
-0.016589585691690445,
-0.011285432614386082,
0.014871851541101933,
-0.006427095737308264,
0.030265964567661285,
0.00094535545213148,
0.007923099212348461,
0.028185833245515823,
0.013358967378735542,
0.03686213865876198,
0.0026774320285767317,
0.0029744035564363003,
-0.0018526414642110467,
-0.024260662496089935,
-0.007953906431794167,
-0.0177516620606184,
0.013928837142884731,
0.026532085612416267,
-0.008104801177978516,
0.006424312479794025,
-0.045553162693977356,
0.01532831508666277,
0.007250241935253143,
0.06512217223644257,
0.026545001193881035,
0.007275160867720842,
-0.004895462188869715,
-0.0013225848088040948,
0.010584373027086258,
-0.044349197298288345,
0.07732703536748886,
-0.0371214784681797,
-0.018755890429019928,
-0.041647154837846756,
0.024150077253580093,
0.043235089629888535,
0.006438535172492266,
-0.013753137551248074,
-0.03486480191349983,
-0.014704208821058273,
0.004533931612968445,
-0.010862641967833042,
0.004963736981153488,
0.1053987592458725,
0.00519605353474617,
-0.02387196756899357,
-0.04161535203456879,
0.000950317014940083,
-0.027382632717490196,
-0.08743681013584137,
0.06174387037754059,
0.053453654050827026,
-0.034729428589344025,
-0.03708093613386154,
-0.043864160776138306,
-0.0606502965092659,
0.0211334191262722,
-0.04089181125164032,
0.005068491213023663,
-0.06977979838848114,
0.06512513011693954,
-0.03665132820606232,
0.04356645792722702,
0.01721171662211418,
0.011620582081377506,
-0.03070644848048687,
0.007085022050887346,
-0.018108466640114784,
0.015626076608896255,
-0.014084167778491974,
-0.017136048525571823,
-0.0530596487224102,
0.002400763798505068,
0.06148918718099594,
0.059039466083049774,
-0.03221077471971512,
0.06635145843029022,
-0.004161997698247433,
0.04151035472750664,
0.023529499769210815,
0.047380488365888596,
0.009145180694758892,
-0.007422921247780323,
-0.014676430262625217,
-0.05835794284939766,
-0.026022523641586304,
0.03773999214172363,
-0.025540422648191452,
-0.038021717220544815,
0.08284199982881546,
-0.05072600394487381,
0.02032257802784443,
-0.009956956841051579,
-0.012659788131713867,
-0.022077247500419617,
0.028199709951877594,
0.00641986820846796,
0.05793481320142746,
-0.0026709181256592274,
-0.03311736881732941,
0.006701143458485603,
-0.04301970452070236,
0.006495979614555836,
-0.00022228079615160823,
-0.039166275411844254,
-0.040950626134872437,
0.029379814863204956,
-0.0600457638502121,
0.04394548758864403,
-0.006385984364897013,
-0.02498488314449787,
0.08703761547803879,
0.036161862313747406,
-0.038763612508773804,
0.032115593552589417,
0.04374179616570473,
0.012579776346683502,
-0.05167504772543907,
-0.01492812018841505,
0.03346075862646103,
0.09771494567394257,
0.05576905980706215,
0.05387011542916298,
0.018190357834100723,
0.08434242010116577,
-0.01762271486222744,
0.01105280127376318,
0.14157867431640625,
-0.03793616220355034,
0.05044043809175491,
-0.004045757465064526,
0.023720797151327133,
0.006335912272334099,
-0.011958654038608074,
-0.03375554457306862,
-0.003151605138555169,
0.004461962729692459,
-0.0007845114450901747,
-0.01791420578956604,
-0.029430825263261795,
0.009924232959747314,
-0.01456455234438181,
0.06017757207155228,
0.014233366586267948,
-0.0004145470738876611,
-0.040387578308582306,
-0.011217395775020123,
0.06397771835327148,
0.049810390919446945,
-0.015552269294857979,
-0.025326654314994812,
0.061571311205625534,
-0.042850691825151443,
-0.02499445527791977,
-0.014390773139894009,
0.02514304593205452,
0.02941698208451271,
0.005972346290946007,
-0.011283626779913902,
-0.01950669102370739,
-0.08297398686408997,
-0.04011970013380051,
-0.042348627001047134,
-0.021761050447821617,
0.054984889924526215,
-0.0030488281045109034,
-0.018324315547943115,
0.05878647416830063,
0.0009717298089526594,
0.02264624461531639,
0.042443640530109406,
0.019759785383939743,
0.006417263764888048,
-0.018118862062692642,
0.038476474583148956,
-0.06803251802921295,
0.004382815677672625,
-0.019791381433606148,
0.02566504292190075,
0.02846492826938629,
0.016478484496474266,
0.024600746110081673,
-0.00021339012891985476,
0.02660769782960415,
-0.0010920099448412657,
0.020800402387976646,
-0.032959576696157455,
0.012077671475708485,
0.04385658726096153,
-0.10306278616189957,
-0.005143041256815195,
0.0014874814078211784,
-0.01819426752626896,
0.011025574989616871,
0.05679694190621376,
-0.024017004296183586,
0.019382206723093987,
-0.025880863890051842,
-0.03344575688242912,
0.05021911486983299,
0.005382787436246872,
-0.0031992169097065926,
-0.02229342982172966,
-0.010283999145030975,
0.028355496004223824,
0.020687773823738098,
0.0057668304070830345,
-0.026121212169528008,
0.015292519703507423,
0.025569433346390724,
-0.01011534035205841,
0.06338687986135483,
-0.011385442689061165,
-0.058859895914793015,
0.014481715857982635,
-0.0008503724820911884,
0.04664202407002449,
-0.03818297013640404,
0.024213949218392372,
-0.05538555234670639,
0.04148492217063904,
-0.020410001277923584,
-0.057147786021232605,
0.047275882214307785,
0.0012628583936020732,
0.03165172040462494,
-0.021996397525072098,
0.03902911767363548,
-0.04220854118466377,
0.02451282925903797,
-0.0059590814635157585,
-0.04158347100019455,
-0.014836467802524567,
0.018475672230124474,
-0.06151212006807327,
0.04042700678110123,
0.01054183766245842,
0.011792263947427273,
0.08307470381259918,
-0.0026736781001091003,
0.08548267185688019,
0.03068730980157852,
0.016452239826321602,
-0.028961241245269775,
0.016212042421102524,
0.018562214449048042,
0.046678029000759125,
-0.034545667469501495,
-0.05437980219721794,
-0.014295350760221481,
0.019099785014986992,
-0.03914964199066162,
-0.009433710016310215,
0.04338735714554787,
0.039605505764484406,
-0.03812004625797272,
-0.05955604836344719,
-0.01388546358793974,
-0.019758639857172966,
-0.005147456657141447,
0.016584601253271103,
0.04536416754126549,
0.029927758499979973,
0.02105986326932907,
0.00033092033118009567,
0.030558668076992035,
-0.003991616889834404,
-0.09708888083696365,
-0.032318659126758575,
-0.012439672835171223,
-0.010392600670456886,
-0.012379111722111702,
0.043282367289066315,
0.034312471747398376,
0.014323404058814049,
0.018567973747849464,
0.059548866003751755,
-0.04644886776804924,
-0.02349829487502575,
0.005659809801727533,
-0.010670837014913559,
0.03539802134037018,
-0.021551057696342468,
0.01170890312641859,
0.00010121547529706731,
-0.03183749318122864,
0.022842738777399063,
0.04577300697565079,
0.04269113019108772,
0.010157210752367973,
-0.004253764171153307,
0.025416459888219833,
0.027173327282071114,
-0.0021597896702587605,
-0.023291124030947685,
0.11976221203804016,
0.07012521475553513,
0.062020838260650635,
0.015253632329404354,
-0.007439837791025639,
-0.0221926998347044,
0.021290959790349007,
-0.008564342744648457,
-0.010908103547990322,
0.019190127030014992,
-0.012547404505312443,
-0.07338473945856094,
-0.0012398301623761654,
0.05214190483093262,
0.009712415747344494,
0.004871267359703779,
0.00924014113843441,
0.01951153390109539,
-0.06231292337179184,
0.023753009736537933,
-0.008706066757440567,
-0.05072085186839104,
-0.033214595168828964,
-0.02864551544189453,
0.031641885638237,
-0.01721055805683136,
-0.02098783478140831,
0.04669724777340889,
-0.011012948118150234,
0.06092069670557976,
-0.06783676892518997,
-0.019372647628188133,
-0.015551811084151268,
0.0027883932925760746,
0.007344935555011034,
0.07855138927698135,
-0.04161081090569496,
-0.06946635991334915,
-0.038608700037002563,
-0.0796380266547203,
0.02775917574763298,
0.013467123731970787,
-0.05618950352072716,
-0.002281678607687354,
0.009167724289000034,
0.038414835929870605,
-0.019132103770971298,
-0.013416985981166363,
-0.04679356887936592,
-0.04137149825692177,
-0.05003459379076958,
0.03854738548398018,
-0.0034012917894870043,
0.05029858276247978,
0.014998607337474823,
0.01979181542992592,
-0.014378480613231659,
0.05572902038693428,
-0.06802856177091599,
0.03788761794567108,
0.023918891325592995,
-0.04079475626349449,
-0.017375566065311432,
-0.011533905752003193,
0.006813294254243374,
-0.05204160884022713,
-0.016962414607405663,
-0.019689060747623444,
-0.048467300832271576,
0.0086550647392869,
-0.02700422704219818,
-0.003506990149617195,
-0.016232872381806374,
-0.07956469804048538,
0.07419507950544357,
-0.024290915578603745,
0.00042380092781968415,
0.026503687724471092,
0.035689011216163635,
0.014645514078438282,
-0.009652635082602501,
-0.05227239429950714,
-0.038014255464076996,
-0.009295186027884483,
-0.05662113055586815,
0.05178355798125267,
-0.0006517652655020356,
0.054138123989105225,
-0.03787769004702568,
-0.024145670235157013,
-0.020741138607263565,
0.03408515453338623,
-0.009305408224463463,
-0.033905453979969025,
0.012573142535984516,
-0.06637459993362427,
-0.02292713336646557,
0.01712140627205372,
0.02441316656768322,
0.01471326407045126,
0.0322907492518425,
-0.05409529432654381,
-0.03689632564783096,
0.04557808116078377,
0.015549898147583008,
-0.03694744408130646,
-0.03974992409348488,
-0.034603096544742584,
-0.025624653324484825,
-0.010408389382064342,
-0.019322702661156654,
0.011672302149236202,
-0.04177171364426613,
-0.008600561879575253,
-0.026581896468997,
0.04361770674586296,
0.03427949175238609,
-0.013708379119634628,
0.02551681362092495,
-0.020379753783345222,
0.01735103316605091,
0.007947541773319244,
-0.0022045201621949673,
0.04238082841038704,
-0.0010870412224903703,
0.03526901453733444,
0.0013559486251324415,
-0.005419418215751648,
0.08645978569984436,
-0.03374853357672691,
0.08609118312597275,
-0.010039158165454865,
0.04059106856584549,
0.010367722250521183,
0.026712628081440926,
-0.011897721327841282,
-0.051605891436338425,
-0.012131961062550545,
0.0005607737693935633,
0.034591708332300186,
-0.022963229566812515,
0.02866179682314396,
0.05759468302130699,
-0.031782086938619614,
0.003531155874952674,
0.01564856246113777,
-0.003990570083260536,
0.041229844093322754,
-0.026811465620994568,
0.03775632753968239,
0.020776143297553062,
0.02873896062374115,
-0.03838092088699341,
0.04065637290477753,
-0.04576388746500015,
-0.02700783871114254,
0.044516392052173615,
0.006883408408612013,
-0.007467782124876976,
0.029131688177585602,
-0.0029159688856452703,
0.018682751804590225,
-0.03802736476063728,
-0.026440974324941635,
-0.03520115464925766,
-0.04231049865484238,
-0.025914214551448822,
-0.02005629613995552,
-0.03265028074383736,
-0.06856612861156464,
-0.015105113387107849,
0.01663646474480629,
-0.0018216235330328345,
-0.011640235781669617,
-0.03403549641370773,
0.004524356219917536,
-0.09796300530433655,
-0.02156655304133892,
0.0029211496002972126,
0.012198218144476414,
-0.053554341197013855,
0.02052849344909191,
-0.0015958776930347085,
-0.029011281207203865,
0.015276629477739334,
0.03646913543343544,
0.0016908816760405898,
0.020421355962753296,
-0.03111589141190052,
0.0046090432442724705,
0.03538182005286217,
-0.013787396252155304,
0.06496906280517578,
0.018077224493026733,
-0.015800919383764267,
0.02836410515010357,
0.014371579512953758,
-0.007917429320514202,
-0.009348321706056595,
-0.023714106529951096,
-0.043057188391685486,
-0.03548926115036011,
0.06449879705905914,
0.05485618859529495,
0.03199247643351555,
-0.012745318934321404,
0.026966867968440056,
-0.014252900145947933,
0.039067450910806656,
0.06084679067134857,
-0.0032268266659229994,
0.01557966135442257,
0.00320160249248147,
-0.05671920254826546,
0.02039850503206253,
-0.008814498782157898,
-0.03107159398496151,
0.03422052785754204,
-0.011112667620182037,
-0.000841244007460773,
0.044445253908634186,
0.022521046921610832,
-0.014418698847293854,
-0.05738172307610512,
-0.042237937450408936,
-0.06600107997655869,
-0.04427090659737587,
-0.029314972460269928,
-0.03593744337558746,
-0.030238870531320572,
-0.02806585468351841,
0.00516567612066865,
0.02308201789855957,
-0.02609650418162346,
-0.012455318123102188,
0.01102512888610363,
-0.03896602988243103,
0.03164980933070183,
0.01165319886058569,
0.04866281896829605,
0.016775617375969887,
0.002828391268849373,
-0.01107250526547432,
0.0003455854021012783,
-0.02675040066242218,
-0.028520116582512856,
-0.023148417472839355,
-0.02149348519742489,
0.041477348655462265,
-0.0274515300989151,
-0.016957871615886688,
-0.005565171130001545,
-0.017396194860339165,
0.01868569850921631,
-0.06773784756660461,
-0.03894218057394028,
-0.024565573781728745,
0.018872706219553947,
-0.05744996666908264,
-0.017546063289046288,
0.015888886526226997,
-0.05488058552145958,
-0.1109914556145668,
-0.00950500275939703,
0.014286555349826813,
0.005189898889511824,
0.027030223980545998,
-0.04620719328522682,
0.000617825542576611,
0.025321325287222862,
0.01830926164984703,
0.020827267318964005,
0.002598560880869627,
-0.04169259965419769,
-0.12936459481716156,
-0.001785232569091022,
-0.01790158636868,
-0.021680962294340134,
0.010308516211807728,
0.019294850528240204,
0.01937403902411461,
-0.056599393486976624,
0.017696106806397438,
-0.009534592740237713,
0.019776050001382828,
-0.028134625405073166,
0.01255730539560318,
0.01948024146258831,
0.03799278661608696,
-0.05024316534399986,
0.008862328715622425,
0.0384121909737587,
0.008079317398369312,
-0.017743082717061043,
0.04100014641880989,
-0.026179764419794083,
0.0060818986967206,
0.008187268860638142,
0.05147344619035721,
0.04360164701938629,
0.005311756394803524,
0.02861124649643898,
-0.07205739617347717,
0.03083302639424801,
0.023446831852197647,
-0.025706961750984192,
0.06082507595419884,
-0.028163602575659752,
0.061877984553575516,
0.0076526133343577385,
0.00926677230745554,
0.0028985694516450167,
-0.02767794393002987,
-0.025739295408129692,
0.05381648615002632,
-0.007573328912258148,
-0.05227511003613472,
0.00005571289511863142,
-0.0577106848359108,
0.011574387550354004,
0.0021319384686648846,
0.02802135795354843,
0.0624786913394928,
-0.029575666412711143,
-0.022685807198286057,
-0.0019821631722152233,
0.02655874565243721,
0.003376658307388425,
-0.017304476350545883,
-0.016774307936429977,
0.050761763006448746,
-0.006119432859122753,
0.06296496093273163,
-0.06455140560865402,
0.01990291103720665,
0.03461660444736481,
0.07855536788702011,
-0.04186543449759483,
-0.04407723620533943,
0.0448811836540699,
-0.04536672681570053,
-0.08565624803304672,
-0.017602449283003807,
-0.04415939748287201,
0.013996127061545849,
-0.06545752286911011,
-0.018119871616363525,
0.025575950741767883,
0.015693943947553635,
0.033106885850429535,
0.08193571865558624,
-0.02533150091767311,
0.037294693291187286,
0.03909594938158989,
-0.06302512437105179,
0.05029087886214256,
-0.0020279984455555677,
-0.011002463288605213,
-0.02664364129304886,
0.05936157703399658,
0.011654713191092014,
-0.010705591179430485,
0.013557597994804382,
0.02576194331049919,
-0.03307836130261421,
0.05001847445964813,
0.014121241867542267,
-0.020130151882767677,
0.018239205703139305,
-0.008960231207311153,
0.04889742285013199,
-0.002302845474332571,
0.025914296507835388,
-0.01741066575050354,
0.002467723796144128,
0.00893987063318491,
0.00516347773373127,
0.049157120287418365,
0.01548610907047987,
0.00668677594512701,
-0.05261143296957016,
-0.018341416493058205,
-0.00019931516726501286,
-0.016903702169656754,
0.00851578637957573,
0.01092284731566906,
0.09806752949953079,
-0.06182613596320152,
-0.03628537431359291,
-0.03087834268808365,
-0.010014811530709267,
-0.03246087208390236,
0.01155406329780817,
0.008217528462409973,
0.017749326303601265,
0.044765405356884,
0.01627556048333645,
0.005666449200361967,
-0.023224804550409317,
-0.07330358028411865,
-0.04672643542289734,
0.018453238531947136,
0.018443850800395012,
-0.02118445374071598,
-0.027752097696065903,
0.02541675977408886,
0.02944774180650711,
0.0576920323073864,
-0.025655552744865417,
0.034551896154880524,
-0.0071973539888858795,
0.10584215819835663,
-0.0029748170636594296,
0.01306771207600832,
0.0020109000615775585,
-0.0282666627317667,
-0.007566720712929964,
0.0007299897260963917,
0.019122861325740814,
-0.03319801762700081,
-0.0639302134513855,
-0.00038630381459370255,
-0.02827364020049572,
-0.02943401411175728,
0.00563677866011858,
-0.02969755418598652,
0.031006060540676117,
-0.0344669409096241,
-0.027449924498796463,
0.025030359625816345,
-0.05846371129155159,
-0.07594279944896698,
-0.008409400470554829,
0.007306698244065046,
0.025822525843977928,
0.02363206446170807,
0.020037062466144562,
0.0021661913488060236,
-0.03943084925413132,
0.02835189923644066,
-0.0329129733145237,
0.0434538908302784,
-0.013243979774415493,
0.01370918843895197,
0.04635276272892952,
0.038284581154584885,
-0.06845702230930328,
0.015820644795894623,
-0.019253704696893692,
0.006149278953671455,
-0.012770118191838264,
0.05878216400742531,
-0.0012252498418092728,
-0.000586807494983077,
-0.004457702394574881,
-0.01358123030513525,
-0.010618582367897034,
0.01552629191428423,
-0.029660455882549286,
0.06670031696557999,
0.0191928930580616,
-0.006418289616703987,
-0.06300632655620575,
-0.02910356968641281,
0.0547039695084095
] |
<p><em>It's really shocking that the following question was voted down twice although the question is yet to be answered by anyone.</em></p>
<p>So please read the following and give an answer why physics community has taken a double standard in the following case.</p>
<p>We know about Michelson's experiment. We also know that despite of the null result how many times the experiment was revisited with the hope to get a positive result. </p>
<p>Unfortunately, this is not the case for Ehrenhaft's experiments (<a href="http://www.rexresearch.com/ehrenhaf/ehrenhaf.htm" rel="nofollow">http://www.rexresearch.com/ehrenhaf/ehrenhaf.htm</a>).</p>
<p>We have already performed a lot of experiments to find a real or artificial magnetic monopole but no monopole is found yet through any experiment.</p>
<p>Furthermore, while studying literature on magnetic monopole, I have found that very few researchers even recognized the work of <a href="http://en.wikipedia.org/wiki/Felix_Ehrenhaft" rel="nofollow">Ehrenhaft</a> who published more than 60 papers on this topic.</p>
<p>I don't understand why his work is so much ignored in the mainstream physics.</p>
<p><strong>Is there a large number of references</strong> (I don't expect this number to be comparable to the number of experimental attempts made in case of Michelson's experiment. I only expect a significant number of repetitions which can firmly conclude about the experimental outcome.) <strong>which show that his experiments were revisited thoroughly, carefully and honestly but his claimed outcome could not be reproduced?</strong></p>
<p>Please give your opinion about the following possible answers:</p>
<ol>
<li>Michelson's NULL result was favorable to Einstein's Relativity, while Ehrenhaft's result was not.</li>
<li>Ehrenhaft's magnetic monopole was not in agreement with Dirac's theory of magnetic monopole.</li>
</ol>
|
g2451
|
[
0.040140144526958466,
0.04343634471297264,
0.027163254097104073,
-0.07553797960281372,
0.07517312467098236,
0.017538923770189285,
0.03417615219950676,
0.030613472685217857,
0.03203492611646652,
-0.008808739483356476,
-0.01251604501157999,
-0.012630648910999298,
0.007517592050135136,
-0.034115321934223175,
-0.02694781869649887,
-0.03436560928821564,
0.017463969066739082,
0.016405116766691208,
0.07036412507295609,
-0.0473150759935379,
-0.01508188247680664,
0.03512855991721153,
0.03588060289621353,
-0.06513215601444244,
-0.0802682563662529,
0.021825337782502174,
-0.029087264090776443,
-0.016312390565872192,
-0.015551372431218624,
-0.04882461950182915,
0.031943827867507935,
-0.011270408518612385,
0.07434185594320297,
-0.010873791761696339,
-0.023326080292463303,
-0.05551762878894806,
-0.01177992857992649,
0.036739230155944824,
0.03958984464406967,
-0.033755287528038025,
-0.07397345453500748,
0.021303147077560425,
0.010105662979185581,
-0.025757931172847748,
0.03637154400348663,
0.012688672170042992,
-0.01553067471832037,
0.02546834759414196,
-0.03602057695388794,
-0.0017791163409128785,
-0.014387604780495167,
0.049444425851106644,
0.07137058675289154,
0.08052222430706024,
-0.0029199603013694286,
-0.04066191613674164,
-0.03861795738339424,
-0.02418043650686741,
0.0430922731757164,
0.009705445729196072,
-0.020282143726944923,
0.013584950007498264,
-0.021252408623695374,
0.01608879491686821,
0.005081518087536097,
0.0025798166170716286,
-0.07281163334846497,
-0.038718003779649734,
0.05681336298584938,
-0.004425729159265757,
0.0187771525233984,
-0.04711233451962471,
0.019648704677820206,
0.028493987396359444,
-0.019950391724705696,
0.05652475357055664,
0.05566897988319397,
-0.014978471212089062,
-0.00948893278837204,
0.034695904701948166,
-0.05838393419981003,
-0.04455069079995155,
-0.042703818529844284,
0.03827083483338356,
0.08425707370042801,
0.023272491991519928,
0.025491269305348396,
-0.023346759378910065,
0.005215418990701437,
-0.0004098449426237494,
0.046539414674043655,
0.021626200526952744,
0.0044469372369349,
-0.018165642395615578,
-0.033810220658779144,
0.013004576787352562,
0.03582565486431122,
-0.014944750815629959,
-0.03081325814127922,
0.033166129142045975,
0.013520628213882446,
-0.01881249248981476,
-0.044264134019613266,
0.05601729825139046,
0.009791147895157337,
-0.022037917748093605,
0.05251055955886841,
0.0023752637207508087,
-0.038125406950712204,
-0.05450928211212158,
-0.05587000772356987,
0.009895926341414452,
0.0137507738545537,
-0.07917343825101852,
-0.02805962599813938,
-0.020549695938825607,
0.07872898131608963,
-0.013977192342281342,
0.006108816713094711,
0.03732077777385712,
0.025171533226966858,
0.02796177566051483,
0.042303916066884995,
0.03791744261980057,
-0.07142990082502365,
-0.055941104888916016,
-0.014391348697245121,
0.01197582483291626,
0.016588395461440086,
-0.03587021306157112,
-0.004112864378839731,
0.011965839192271233,
-0.03082978166639805,
0.01806439459323883,
-0.062338687479496,
-0.01762518845498562,
0.020064249634742737,
0.017552392557263374,
0.02025727927684784,
0.025794798508286476,
0.015503468923270702,
-0.03478190302848816,
0.045788973569869995,
-0.003691913792863488,
0.025685599073767662,
-0.04757610708475113,
0.013756153173744678,
0.042075783014297485,
-0.005522061605006456,
0.06957221776247025,
0.0065023633651435375,
0.022706910967826843,
0.010407092981040478,
0.034647274762392044,
-0.05131899192929268,
-0.006124106235802174,
-0.008612756617367268,
0.004796196706593037,
0.02224614843726158,
0.041205115616321564,
0.028813697397708893,
-0.019721997901797295,
-0.019761480391025543,
0.03518400341272354,
0.031215675175189972,
0.012099836952984333,
0.06911920011043549,
-0.022478751838207245,
0.058358605951070786,
-0.04093746840953827,
0.00991817843168974,
-0.004226859658956528,
0.07197418063879013,
0.040321458131074905,
0.08009549975395203,
0.025966893881559372,
0.0002697143063414842,
-0.051421549171209335,
-0.04158198833465576,
0.023372458294034004,
-0.025440726429224014,
0.008145569823682308,
-0.013175355270504951,
-0.007752968464046717,
-0.013555440120398998,
-0.03454722464084625,
-0.009284147061407566,
0.0072713312692940235,
-0.025570042431354523,
0.0008286430966109037,
-0.0667504146695137,
0.005775735713541508,
-0.029334360733628273,
0.014843963086605072,
-0.018659653142094612,
-0.054771535098552704,
0.019361339509487152,
-0.030930742621421814,
-0.00512581504881382,
0.060847703367471695,
0.024643370881676674,
0.03471453860402107,
0.03344577178359032,
0.022982895374298096,
-0.035806503146886826,
-0.07510045170783997,
0.0003185656969435513,
-0.05856587737798691,
0.08243998885154724,
-0.06093525141477585,
-0.004761174786835909,
0.08529248088598251,
-0.0304579995572567,
0.038804639130830765,
0.0009003208251670003,
0.0005311587010510266,
0.015904312953352928,
0.041191890835762024,
-0.059867095202207565,
0.05275358259677887,
-0.03045659139752388,
-0.000664500636048615,
0.0014169519999995828,
-0.03437243029475212,
0.035308342427015305,
-0.06158993020653725,
-0.04087209701538086,
-0.11239980161190033,
-0.05473629757761955,
-0.03141741454601288,
0.00020998087711632252,
0.00034052637056447566,
-0.0022159956861287355,
0.0040824878960847855,
0.06282567977905273,
-0.01554345153272152,
0.004715277813374996,
-0.0399891622364521,
0.08598265796899796,
0.03633764386177063,
-0.04829591140151024,
0.02925354614853859,
-0.03119594044983387,
-0.011708767153322697,
0.0037951641716063023,
-0.024853302165865898,
0.020174695178866386,
-0.023752732202410698,
0.024096565321087837,
0.015710482373833656,
0.03554077073931694,
0.06506368517875671,
-0.00793690886348486,
0.012132303789258003,
0.017039829865098,
0.059873245656490326,
0.05689595639705658,
-0.002995104528963566,
-0.03576270490884781,
0.04892025887966156,
0.041201964020729065,
-0.010095278732478619,
0.017470894381403923,
0.005884338170289993,
-0.05940961092710495,
-0.05295918509364128,
-0.07453220337629318,
0.039727482944726944,
0.0131918303668499,
-0.05059843137860298,
-0.03722922503948212,
0.029823079705238342,
0.03586670756340027,
0.03397615626454353,
0.011271649971604347,
0.00919909868389368,
-0.03818615898489952,
-0.0387122705578804,
0.036193378269672394,
-0.03306405991315842,
-0.004716521594673395,
-0.0041787768714129925,
-0.0023520381655544043,
-0.04075295478105545,
0.020307935774326324,
-0.019853007048368454,
-0.08711040019989014,
-0.03648780286312103,
-0.06574159860610962,
0.003918687347322702,
-0.02287859469652176,
0.005352495238184929,
0.051138464361429214,
0.02041809633374214,
-0.028296373784542084,
0.04780299961566925,
0.021409250795841217,
-0.10302317887544632,
-0.05384307727217674,
0.02846776507794857,
0.027889177203178406,
0.014486363157629967,
0.0034430683590471745,
0.05504295602440834,
0.03519970551133156,
0.006746713072061539,
-0.0011266320943832397,
-0.02344694919884205,
-0.03197387233376503,
0.01725437492132187,
0.011764631606638432,
0.07190806418657303,
0.040821801871061325,
-0.031193381175398827,
0.0034004212357103825,
0.03752507269382477,
-0.020517606288194656,
0.04916507005691528,
0.03905161842703819,
0.013259482569992542,
0.017707379534840584,
0.04060422256588936,
-0.023808928206562996,
-0.01076506357640028,
0.053041111677885056,
0.010185007005929947,
0.013717773370444775,
0.04241329804062843,
0.0072106714360415936,
0.025096744298934937,
-0.005107511300593615,
0.01951414719223976,
0.03163902461528778,
-0.0008476249640807509,
-0.06963711231946945,
-0.015595469623804092,
-0.027608003467321396,
0.030857417732477188,
-0.0038340718019753695,
0.012345629744231701,
-0.002467644400894642,
-0.044275280088186264,
-0.05053078383207321,
-0.01001877523958683,
0.04123438149690628,
0.04834780469536781,
-0.008614986203610897,
-0.04139941558241844,
0.01565099135041237,
-0.004039181396365166,
0.03586723282933235,
-0.0029515165369957685,
-0.009466610848903656,
0.03232687711715698,
0.02099766582250595,
0.046238113194704056,
-0.007092628162354231,
0.051593221724033356,
0.027389977127313614,
0.016108183190226555,
-0.011902613565325737,
-0.029729582369327545,
0.014842187985777855,
-0.022140109911561012,
-0.019918661564588547,
0.02095857821404934,
-0.002803186420351267,
0.03205656260251999,
-0.01737802103161812,
-0.027592139318585396,
-0.022579267621040344,
0.08102884888648987,
0.006531643681228161,
0.03440148010849953,
0.0390256866812706,
-0.022020282223820686,
0.010454552248120308,
0.05027391016483307,
-0.0369986854493618,
-0.005452475510537624,
-0.0003490441886242479,
0.029950782656669617,
-0.029619919136166573,
0.014717641286551952,
0.010047289542853832,
-0.029584959149360657,
-0.046582818031311035,
-0.008570174686610699,
0.02570408023893833,
-0.011060775257647038,
-0.01253561396151781,
0.015020319260656834,
-0.025228198617696762,
0.029605364426970482,
-0.0218468327075243,
-0.010340279899537563,
0.015254803001880646,
-0.06381117552518845,
0.06282515078783035,
-0.035389017313718796,
0.022982632741332054,
-0.007555150892585516,
-0.0050076949410140514,
-0.004830009303987026,
-0.010551734827458858,
-0.0021539009176194668,
0.01123898383229971,
-0.014752625487744808,
0.03545265272259712,
-0.008785691112279892,
0.011880256235599518,
0.044511400163173676,
-0.004379103891551495,
-0.05133216828107834,
0.03450661152601242,
-0.025523405522108078,
-0.018576757982373238,
-0.04329918697476387,
-0.0017376479227095842,
-0.04090490937232971,
0.04895051568746567,
-0.0066420226357877254,
-0.04766024649143219,
-0.05760769546031952,
-0.0015663799131289124,
0.06127508729696274,
0.005402358714491129,
-0.006780498661100864,
-0.003524510655552149,
-0.02321457862854004,
0.02178657427430153,
0.042058974504470825,
-0.06793750822544098,
0.025665082037448883,
-0.027132248505949974,
0.05550123378634453,
0.05488147586584091,
0.020552922040224075,
-0.020015478134155273,
0.0432385616004467,
0.03699992969632149,
-0.021243780851364136,
0.05590725690126419,
0.0473347045481205,
-0.02448376640677452,
0.019475948065519333,
-0.07035860419273376,
-0.011762912385165691,
-0.004068831913173199,
-0.000006147394742583856,
0.020441308617591858,
0.01420692726969719,
0.008922223001718521,
0.029398063197731972,
-0.02570720575749874,
-0.02273392863571644,
-0.026272933930158615,
0.019086409360170364,
-0.003142967587336898,
0.040107231587171555,
-0.08606582134962082,
-0.0023903576657176018,
-0.038017865270376205,
0.022219490259885788,
0.03730297461152077,
0.03028665855526924,
-0.03401778265833855,
-0.0695267915725708,
-0.04806990176439285,
-0.03706373646855354,
-0.012281966395676136,
-0.0028187884017825127,
0.007142525166273117,
0.003209295216947794,
0.0006129638059064746,
-0.015082011930644512,
-0.01576918736100197,
0.02188832126557827,
-0.057636067271232605,
0.004414511378854513,
-0.05825978145003319,
-0.045475881546735764,
-0.009000146761536598,
0.0005485346773639321,
-0.011227971874177456,
0.007992235012352467,
-0.059446267783641815,
0.020589418709278107,
-0.04672553017735481,
-0.052013546228408813,
0.03680851683020592,
0.05638526380062103,
0.018963446840643883,
-0.060871388763189316,
0.045954637229442596,
-0.03401191532611847,
-0.09755847603082657,
0.0522046834230423,
-0.016035014763474464,
-0.0017462588148191571,
-0.111753910779953,
0.02262060157954693,
-0.003594633424654603,
-0.007433989085257053,
0.00887227151542902,
0.009547609835863113,
0.04843653365969658,
-0.0009187217801809311,
0.005234826356172562,
0.004398229066282511,
-0.018847260624170303,
-0.0463852658867836,
-0.03210447356104851,
-0.005910914391279221,
0.03759374842047691,
0.012470582500100136,
-0.0008056589285843074,
0.008876856416463852,
0.06606382131576538,
-0.042425692081451416,
-0.0024135992862284184,
0.022630373015999794,
0.017636245116591454,
-0.052649710327386856,
-0.010135458782315254,
-0.0015202914364635944,
-0.009661676362156868,
-0.04016178846359253,
-0.01230359822511673,
0.022853869944810867,
0.025573143735527992,
-0.018625838682055473,
0.08653154969215393,
-0.0013093323213979602,
0.0083833709359169,
-0.04370606318116188,
0.03629092499613762,
-0.044772449880838394,
-0.040151070803403854,
0.029272742569446564,
-0.008193016052246094,
-0.00150750030297786,
0.0629851445555687,
0.03959931433200836,
-0.04967747628688812,
0.04597030580043793,
-0.005452372133731842,
-0.018090231344103813,
0.04498795419931412,
-0.08039726316928864,
-0.017556386068463326,
-0.009270626120269299,
-0.03146329149603844,
0.013116448186337948,
0.008985173888504505,
0.005647249054163694,
-0.01780184730887413,
-0.029068639501929283,
-0.011132001876831055,
0.04058760777115822,
-0.020693855360150337,
-0.06797781586647034,
-0.0037876165006309748,
0.07012642920017242,
-0.03283827006816864,
0.02058781497180462,
0.06884220987558365,
-0.023838866502046585,
0.018311630934476852,
0.009870203211903572,
0.01478549838066101,
0.05938660353422165,
-0.02345258928835392,
0.03171813488006592,
0.0510726273059845,
0.02093532681465149,
0.008693190291523933,
-0.013879174366593361,
0.01697659306228161,
-0.04760650172829628,
0.02344556897878647,
0.023780569434165955,
0.06460969895124435,
-0.04487338662147522,
-0.016534611582756042,
0.0627843514084816,
-0.0824887603521347,
0.0020118223037570715,
0.005862835794687271,
-0.06341957300901413,
0.010925449430942535,
-0.014396083541214466,
-0.013125011697411537,
-0.012365837581455708,
-0.018457766622304916,
-0.05427657067775726,
0.009138802997767925,
-0.03407745435833931,
-0.049666356295347214,
0.019372262060642242,
-0.008996204473078251,
-0.0036185516510158777,
0.03419841453433037,
0.01168991532176733,
0.03077237494289875,
-0.015214300714433193,
-0.03929714486002922,
0.010230029001832008,
-0.021389147266745567,
-0.013469996862113476,
-0.06098748743534088,
0.013178612105548382,
-0.07304970920085907,
-0.02668287605047226,
-0.029443679377436638,
-0.07730267941951752,
0.02040998823940754,
0.02468241937458515,
-0.004259129520505667,
0.02739204838871956,
0.012755664996802807,
-0.05228206887841225,
-0.0007655061199329793,
-0.00020647156634368002,
-0.03667405992746353,
0.024046018719673157,
0.005490575451403856,
0.045146696269512177,
0.004417790099978447,
0.008014025166630745,
-0.02793622948229313,
-0.007491048891097307,
-0.04602455347776413,
0.04192483797669411,
-0.029849214479327202,
0.01800965704023838,
0.00023169346968643367,
0.02272135019302368,
-0.005424445029348135,
-0.018999099731445312,
-0.06923363357782364,
0.022072378545999527,
0.006336248945444822,
-0.006358958315104246,
-0.03544856235384941,
-0.023104548454284668,
0.038453102111816406,
0.03987104818224907,
-0.046498410403728485,
0.008753133937716484,
0.002295061247423291,
-0.011898448690772057,
0.04997981712222099,
-0.002275369130074978,
-0.029161028563976288,
0.01103733666241169,
0.00857347808778286,
0.04449201002717018,
0.03195570781826973,
-0.007676546461880207,
-0.02214624173939228,
0.009562845341861248,
-0.023448050022125244,
-0.018926827237010002,
-0.03985794633626938,
0.0010000368347391486,
-0.061780884861946106,
-0.02270440198481083,
0.06268084049224854,
-0.002175422152504325,
0.01707790605723858,
0.019652141258120537,
-0.053079333156347275,
0.020411038771271706,
-0.0071753161028027534,
-0.020827073603868484,
-0.0015942917671054602,
-0.08017326891422272,
0.01110257301479578,
0.033088695257902145,
-0.05231392756104469,
0.0321776419878006,
-0.015874003991484642,
-0.016323843970894814,
-0.045340802520513535,
-0.03200449049472809,
-0.09523870795965195,
-0.013548700138926506,
0.01758582890033722,
0.03695381432771683,
-0.01104477234184742,
0.021377909928560257,
0.07580171525478363,
-0.05320122465491295,
-0.05147216096520424,
0.04906238615512848,
-0.006677063647657633,
-0.014250565320253372,
0.03350238502025604,
-0.009025312960147858,
0.018681731075048447,
-0.01398211158812046,
-0.03441908210515976,
-0.024566879495978355,
0.05702590569853783,
0.03064231388270855,
0.030523641034960747,
0.03112730383872986,
-0.04472418129444122,
0.059006575495004654,
0.02155662141740322,
0.037628691643476486,
0.04313041269779205,
0.023665232583880424,
0.0740061029791832,
-0.012391124852001667,
-0.04295086860656738,
-0.02290506660938263,
0.050300758332014084,
-0.029040472581982613,
0.024953795596957207,
0.0406591072678566,
-0.026278212666511536,
-0.03193111717700958,
-0.04579561948776245,
-0.013533061370253563,
-0.03936952352523804,
0.011160355061292648,
0.030759388580918312,
-0.005341263022273779,
-0.036163780838251114,
-0.05315499007701874,
-0.0019224610878154635,
-0.004895471967756748,
-0.058152806013822556,
0.0025909014511853456,
0.014735274016857147,
0.020638352259993553,
-0.02501833625137806,
-0.011636963114142418,
0.0482584573328495,
-0.021015532314777374,
0.05113225057721138,
0.040511101484298706,
0.024826964363455772,
-0.019433634355664253,
-0.04551392421126366,
0.057650525122880936,
0.00986125972121954,
-0.03632105886936188,
-0.05549177899956703,
0.045174479484558105,
-0.08441910147666931,
0.04754019156098366,
0.04759940132498741,
-0.025114797055721283,
0.00893752183765173,
0.06590574234724045,
0.04471462592482567,
0.011300666257739067,
-0.004074552562087774,
-0.010783718898892403,
-0.00705249048769474,
0.014822263270616531,
-0.07010067254304886,
-0.009775256738066673,
0.02441822737455368,
0.06504561007022858
] |
<p>I've been lightly studying GR lately. Something that has been bothering me has been the lack of (Ricci) curvature produced from the Schwarzschild metric in the few lectures I've watched, as well as the few snippets of text book I've been able to read. Why is there no (Ricci) curvature outside this spherically symmetric, non-rotating, uncharged body that still has mass? Shouldn't there always be curvature in the presence of mass or am I missing something? I've read a bit about certain information that is unobtainable when dealing with Schwarzschild coordinates, is the curvature outside the body one of the specific quantities that cannot be defined with these coordinates?</p>
|
g2452
|
[
0.027814213186502457,
0.05174719914793968,
0.01343026664108038,
0.0368882492184639,
-0.007923371158540249,
0.060298509895801544,
0.046569082885980606,
0.02564849518239498,
-0.10047455132007599,
-0.03367873653769493,
0.0019393223337829113,
-0.009852871298789978,
0.05588572472333908,
0.010086167603731155,
-0.002990826964378357,
-0.014057488180696964,
-0.017016112804412842,
-0.051564931869506836,
0.06185819208621979,
0.026189075782895088,
0.01463705487549305,
-0.03522703796625137,
0.05311703681945801,
0.03724732995033264,
-0.006455747410655022,
0.03389083221554756,
0.08767643570899963,
-0.023607440292835236,
0.020218875259160995,
-0.05173095315694809,
-0.013794713653624058,
0.06044808402657509,
0.013585411012172699,
-0.019615842029452324,
0.03875958174467087,
-0.009508149698376656,
0.018513230606913567,
0.025785572826862335,
-0.011192887090146542,
0.024488262832164764,
0.04716432839632034,
-0.029453095048666,
-0.0287247896194458,
0.00585806043818593,
0.018659282475709915,
0.09403222054243088,
-0.02150385081768036,
0.01567293144762516,
0.009248688817024231,
0.003918223548680544,
-0.01592066138982773,
0.02424742840230465,
0.0046370853669941425,
-0.042355895042419434,
-0.025690432637929916,
-0.051505863666534424,
0.000652738322969526,
-0.001433340716175735,
0.030580895021557808,
-0.004246355965733528,
-0.011064302176237106,
0.014733470045030117,
-0.005919932387769222,
-0.002617361955344677,
0.011421025730669498,
0.026115182787179947,
-0.07492958009243011,
-0.050916824489831924,
0.00031991724972613156,
0.014429377391934395,
0.025963565334677696,
0.006494492292404175,
-0.008694645017385483,
-0.01629732735455036,
-0.031540095806121826,
0.00034411263186484575,
0.010430033318698406,
0.004090783651918173,
-0.0023398210760205984,
-0.030865201726555824,
0.023565303534269333,
0.02813231758773327,
0.02297631837427616,
0.009124303236603737,
0.12558768689632416,
0.05524757504463196,
-0.013890810310840607,
-0.004626782611012459,
-0.012660779058933258,
0.038696274161338806,
0.015903057530522346,
0.0008740532211959362,
0.005928919184952974,
-0.011671178974211216,
-0.02674883045256138,
-0.07011372596025467,
-0.032886579632759094,
0.07425261288881302,
-0.05733329802751541,
-0.003173687495291233,
0.004253614693880081,
0.004417296964675188,
0.041465818881988525,
0.05070352926850319,
0.03166359290480614,
-0.0018123339395970106,
-0.043961115181446075,
0.01605672761797905,
0.054419491440057755,
-0.06512337923049927,
0.006280001252889633,
0.0025463879574090242,
-0.006445270497351885,
0.05027059093117714,
-0.05529586598277092,
-0.0484735444188118,
0.10037778317928314,
-0.04766871780157089,
-0.006602116860449314,
0.07612667977809906,
-0.06958234310150146,
0.004701984114944935,
0.012060092762112617,
0.001862579258158803,
-0.031931597739458084,
0.011330132372677326,
0.07019796222448349,
0.003211909206584096,
0.06265682727098465,
0.007804790511727333,
-0.008656561374664307,
0.03731736168265343,
0.000532762089278549,
-0.024677617475390434,
-0.015034881420433521,
0.03830688074231148,
-0.0275800172239542,
0.04601476714015007,
-0.03817354515194893,
-0.0021425308659672737,
0.01820741407573223,
-0.008727745153009892,
0.004284347407519817,
0.015784019604325294,
-0.0023406364489346743,
-0.00006227379344636574,
-0.01119219046086073,
-0.009596496820449829,
0.03511355072259903,
0.057302575558423996,
-0.010712385177612305,
0.02646983042359352,
-0.021934572607278824,
-0.007366204168647528,
-0.01711438223719597,
-0.00010277301771566272,
-0.032312262803316116,
-0.018159208819270134,
0.019203757867217064,
0.024662893265485764,
0.04956042394042015,
-0.02723473496735096,
0.004200118128210306,
-0.025455761700868607,
0.01247032918035984,
0.028432391583919525,
-0.06134684011340141,
-0.0635448768734932,
-0.0043458351865410805,
-0.09945330768823624,
-0.05327325686812401,
-0.03562488034367561,
-0.034685105085372925,
0.020453505218029022,
-0.035300321877002716,
-0.022625025361776352,
-0.07781748473644257,
-0.011012657545506954,
0.07067455351352692,
0.027372904121875763,
-0.0632982850074768,
-0.0034807249903678894,
0.029163265600800514,
-0.04019469767808914,
0.011131367646157742,
0.004932337440550327,
-0.016199667006731033,
-0.05583026260137558,
0.03541198745369911,
0.009161336347460747,
-0.042783137410879135,
-0.031763650476932526,
0.005775017198175192,
0.08798860758543015,
-0.015672869980335236,
0.015369733795523643,
0.03649509698152542,
0.04909007251262665,
-0.010974422097206116,
0.07856778055429459,
-0.019985701888799667,
0.006844138260930777,
0.05668644607067108,
-0.01940414123237133,
0.005469601601362228,
-0.03640948235988617,
-0.0710751861333847,
0.0019662673585116863,
0.04609864577651024,
-0.030245566740632057,
0.03459198400378227,
-0.06369931250810623,
0.05091097205877304,
-0.08173716068267822,
-0.01657848246395588,
0.0031141529325395823,
-0.005069363862276077,
-0.018513023853302002,
0.011145971715450287,
-0.026243695989251137,
-0.031413812190294266,
-0.04798555001616478,
0.026509569957852364,
0.015297205187380314,
0.011113499291241169,
0.018570831045508385,
-0.0288830678910017,
0.02370651811361313,
0.027601629495620728,
0.009068289771676064,
-0.03847092390060425,
-0.024253450334072113,
0.027812262997031212,
-0.050412774085998535,
0.034025516360998154,
0.014184889383614063,
-0.02097751758992672,
-0.003393949242308736,
0.05473402887582779,
0.011178364977240562,
-0.025841202586889267,
-0.020611906424164772,
-0.056371066719293594,
-0.0304388627409935,
0.04661564528942108,
-0.009997280314564705,
0.028348011896014214,
0.010600927285850048,
-0.026190107688307762,
-0.028373071923851967,
-0.0026585881132632494,
0.00648925406858325,
-0.0017529581673443317,
0.006961574777960777,
0.03732862323522568,
0.03172352537512779,
0.00465393578633666,
-0.007531317416578531,
-0.06910822540521622,
-0.06979503482580185,
-0.045024432241916656,
-0.032521579414606094,
0.01737102121114731,
0.01359623670578003,
-0.13573136925697327,
0.018693238496780396,
0.0007049413397908211,
-0.027741597965359688,
-0.004463944584131241,
0.015043539926409721,
-0.031048722565174103,
0.08490391820669174,
-0.001429061172530055,
0.04542114958167076,
-0.03320123627781868,
0.005059502553194761,
-0.06251467764377594,
0.03045358881354332,
0.03481297567486763,
0.02784990519285202,
0.048678070306777954,
0.002210285048931837,
-0.02662385255098343,
0.0035671009682118893,
0.02848339080810547,
-0.01658719778060913,
-0.01981542818248272,
0.0071078017354011536,
0.04017389938235283,
-0.007082503754645586,
-0.009696593508124352,
0.011583245359361172,
0.00835055485367775,
-0.02614164724946022,
-0.02757354825735092,
0.02821694314479828,
-0.07958949357271194,
0.026861146092414856,
-0.021571049466729164,
-0.0037182432133704424,
0.029626792296767235,
-0.051118139177560806,
0.018005268648266792,
-0.004567455966025591,
-0.051037028431892395,
0.01506795920431614,
-0.014164373278617859,
-0.08745554834604263,
-0.04467510059475899,
-0.03866424784064293,
0.03250308707356453,
0.013358099386096,
0.016010932624340057,
0.03611849993467331,
-0.009815524332225323,
-0.08396979421377182,
-0.0755428597331047,
-0.020418955013155937,
-0.05460113659501076,
0.0050252946093678474,
-0.03874775394797325,
0.0001919701899169013,
0.017218424007296562,
-0.015705805271863937,
0.030030837282538414,
0.05644630640745163,
-0.028796467930078506,
-0.016654588282108307,
-0.024024417623877525,
-0.02310841716825962,
0.010406266897916794,
-0.0025496112648397684,
0.043091196566820145,
-0.015468614175915718,
-0.023148922249674797,
-0.05656527355313301,
-0.014740859158337116,
0.0019141166703775525,
0.09793749451637268,
-0.024726686999201775,
0.03335447236895561,
-0.003431083634495735,
-0.01182414498180151,
0.00007101398659870028,
-0.055940959602594376,
0.01165732927620411,
-0.004151529166847467,
-0.023085257038474083,
0.0036861433181911707,
0.012179921381175518,
0.03875526413321495,
0.043175939470529556,
0.005036111455410719,
-0.003549993271008134,
0.003778628306463361,
0.023782363161444664,
0.004098547622561455,
0.04386304318904877,
0.008098701015114784,
-0.017950257286429405,
0.03240274637937546,
-0.04008840397000313,
-0.0506364144384861,
-0.034521881490945816,
0.023690637201070786,
-0.04228562116622925,
0.04960286617279053,
-0.04136434569954872,
0.009601254016160965,
-0.016825051978230476,
0.006186554674059153,
0.020965753123164177,
0.014427432790398598,
-0.012566766701638699,
0.03523540869355202,
-0.044488828629255295,
0.03949366882443428,
0.07986205816268921,
0.000031218489311868325,
-0.024865806102752686,
-0.02328214794397354,
0.002191440435126424,
0.02680264785885811,
-0.018297873437404633,
-0.014863671734929085,
-0.0034731237683445215,
-0.03397032618522644,
0.025574946776032448,
-0.011858864687383175,
-0.06167756766080856,
0.0032974868081510067,
-0.06487442553043365,
0.003595988266170025,
0.02183987759053707,
0.022435970604419708,
-0.018919004127383232,
0.024174921214580536,
-0.010153206996619701,
0.033243339508771896,
0.03980669379234314,
0.008968861773610115,
0.018044134601950645,
0.04145171865820885,
-0.005012408830225468,
-0.007967419922351837,
0.005302525591105223,
0.05876275151968002,
-0.025285258889198303,
0.0009489130461588502,
-0.02532218210399151,
0.006935925222933292,
0.004519023932516575,
0.029604949057102203,
-0.06672892719507217,
0.04792531579732895,
0.007833101786673069,
-0.03970020264387131,
-0.03396220505237579,
-0.004326907452195883,
0.027587510645389557,
0.0037594428285956383,
-0.04229562357068062,
-0.000012734561096294783,
0.02860007993876934,
0.039447661489248276,
0.10870623588562012,
-0.034969113767147064,
-0.056195612996816635,
-0.046424832195043564,
-0.005154086276888847,
-0.004111680202186108,
-0.007208873052150011,
0.025568073615431786,
0.004053427372127771,
-0.03834482282400131,
0.045352790504693985,
-0.008538244292140007,
0.0663796216249466,
-0.026426153257489204,
0.022327717393636703,
0.03140220791101456,
0.013218753039836884,
-0.003739361185580492,
-0.04613913968205452,
0.0306157898157835,
-0.017829643562436104,
-0.023568736389279366,
0.025182748213410378,
-0.03800148144364357,
-0.02566254325211048,
0.028843896463513374,
-0.014358310028910637,
-0.03272954747080803,
0.03171519935131073,
-0.018871065229177475,
-0.02551466040313244,
-0.004003065172582865,
-0.03016955405473709,
-0.020655807107686996,
0.016748566180467606,
-0.054568056017160416,
-0.0021695669274777174,
-0.00678993808105588,
0.03120444528758526,
0.024689139798283577,
-0.03675008937716484,
0.0077507514506578445,
0.0019813182298094034,
0.017005139961838722,
-0.009470285847783089,
-0.030290750786662102,
0.08688314259052277,
0.00813691783696413,
-0.019168080762028694,
0.027767101302742958,
0.08083414286375046,
-0.00954094622284174,
-0.01803198643028736,
-0.04243570938706398,
-0.031454090029001236,
-0.00031695765210315585,
0.03487047553062439,
-0.004991760011762381,
0.023512883111834526,
-0.003220431739464402,
-0.038623832166194916,
-0.047173477709293365,
0.009459364227950573,
-0.022613374516367912,
-0.02513485960662365,
0.04801934212446213,
-0.011425117030739784,
-0.021881531924009323,
-0.02449207380414009,
0.03477960079908371,
0.0383676216006279,
0.01874391734600067,
-0.039911653846502304,
-0.026519406586885452,
-0.023624500259757042,
-0.020671794191002846,
0.016169216483831406,
0.015804816037416458,
-0.0010558638023212552,
0.01903889887034893,
0.07345220446586609,
0.037507038563489914,
-0.03904390335083008,
0.007158116903156042,
0.05105382576584816,
0.0353667326271534,
0.03627391159534454,
-0.005357684101909399,
-0.02026226744055748,
-0.011495592072606087,
-0.023417487740516663,
-0.033223457634449005,
0.021324560046195984,
0.020280804485082626,
-0.031828656792640686,
-0.035353872925043106,
-0.006719436030834913,
0.010195090435445309,
-0.037194885313510895,
0.029244888573884964,
0.008786379359662533,
0.003930277191102505,
-0.0325746014714241,
0.01672513596713543,
0.07337307929992676,
0.004683440551161766,
-0.057198021560907364,
0.03267760947346687,
0.014330606907606125,
0.010794841684401035,
-0.003126497147604823,
0.01986527442932129,
0.019371265545487404,
0.04326104000210762,
-0.026412244886159897,
-0.026526177302002907,
0.0011203548638150096,
-0.004100436810404062,
0.08232924342155457,
-0.04069868102669716,
0.028103847056627274,
0.010280792601406574,
0.02027634158730507,
0.00677316403016448,
-0.07018846273422241,
-0.04137042537331581,
0.03230864554643631,
-0.003704638220369816,
0.016116859391331673,
-0.0026068282313644886,
0.06685198098421097,
0.008431551977992058,
-0.030702197924256325,
-0.039256565272808075,
-0.005838181357830763,
0.07095330208539963,
-0.03554828464984894,
-0.025330543518066406,
0.035161860287189484,
-0.00927691999822855,
-0.038146935403347015,
0.023338977247476578,
-0.010149579495191574,
0.10850644111633301,
0.011196108534932137,
-0.05091164633631706,
-0.019274955615401268,
0.026468198746442795,
0.017996303737163544,
0.035445015877485275,
-0.038056761026382446,
-0.0744437724351883,
-0.011096738278865814,
0.023234399035573006,
0.03548109903931618,
0.06950540840625763,
-0.004791459999978542,
0.06102384999394417,
-0.06481359153985977,
-0.014155770651996136,
-0.02433430589735508,
-0.021788105368614197,
0.043835826218128204,
0.03914003446698189,
0.010793058201670647,
-0.0020647684577852488,
-0.02468322589993477,
-0.01683647558093071,
-0.04898453503847122,
-0.04024670273065567,
-0.012971658259630203,
0.014967209659516811,
0.0008052660268731415,
-0.036539480090141296,
-0.05800780653953552,
-0.014724740758538246,
0.006977288983762264,
0.020167376846075058,
0.020119333639740944,
0.04802178964018822,
-0.0477902926504612,
-0.02379647083580494,
0.010091053321957588,
-0.01155579648911953,
-0.02086648717522621,
-0.03915100544691086,
0.05497443303465843,
-0.047449301928281784,
0.006669703405350447,
0.0437079481780529,
-0.05920484662055969,
-0.03858867287635803,
0.0211503766477108,
-0.08668302744626999,
-0.10276052355766296,
0.01914045959711075,
0.019572841003537178,
0.05480261892080307,
-0.01469113864004612,
0.08343233168125153,
-0.015397939831018448,
0.004171163309365511,
0.04626573622226715,
-0.0032274879049509764,
0.01750735379755497,
0.01886206679046154,
0.040517427027225494,
-0.014778470620512962,
0.031763963401317596,
0.035814180970191956,
0.04028130695223808,
-0.021916572004556656,
0.054418835788965225,
0.1008090078830719,
0.028951391577720642,
0.002951529808342457,
-0.06504187732934952,
0.020890649408102036,
-0.022599896416068077,
-0.12207349389791489,
-0.026652876287698746,
0.02560669556260109,
0.017189666628837585,
-0.04033466428518295,
-0.0156692024320364,
-0.0033092766534537077,
0.014376314356923103,
0.005109949037432671,
-0.03938626870512962,
-0.0331357978284359,
-0.05163354054093361,
-0.05903308466076851,
0.010417232289910316,
0.03491690382361412,
-0.0786728784441948,
-0.054381098598241806,
0.0054052141495049,
0.05825502425432205,
0.05046569183468819,
0.003526784013956785,
0.04735785350203514,
0.04736601188778877,
-0.031374137848615646,
0.003341826843097806,
0.08701425045728683,
0.013420664705336094,
-0.013740235939621925,
-0.05150314047932625,
-0.03719503432512283,
0.014085853472352028,
0.0009001594153232872,
0.012412208132445812,
0.016884703189134598,
0.012840243987739086,
0.006602253299206495,
-0.028072675690054893,
0.0268259160220623,
-0.014781678095459938,
0.050935450941324234,
-0.07929860800504684,
-0.007088301703333855,
-0.03028087131679058,
0.03051905706524849,
0.0069761150516569614,
0.02753753960132599,
0.028206590563058853,
0.07410547137260437,
-0.007020135410130024,
0.0014891444006934762,
-0.009988395497202873,
-0.01690381020307541,
-0.019230544567108154,
0.09850680083036423,
0.013105088844895363,
-0.019275182858109474,
0.017981937155127525,
-0.003109731711447239,
-0.01782074198126793,
0.0277143195271492,
0.01928349956870079,
0.03673950210213661,
-0.06431087106466293,
-0.027219625189900398,
0.012424381449818611,
0.07660230249166489,
0.03181416541337967,
-0.005818258039653301,
-0.04033317789435387,
-0.01569994166493416,
-0.015024752356112003,
0.026156986132264137,
-0.014410668984055519,
0.024999506771564484,
-0.006040466018021107,
-0.10307621210813522,
-0.01578398235142231,
0.019954407587647438,
-0.02507294900715351,
-0.06449656933546066,
-0.035468269139528275,
-0.006522551644593477,
0.005083801224827766,
-0.0304626002907753,
-0.015111495740711689,
-0.02445933036506176,
-0.004750542342662811,
0.042630769312381744,
-0.031330861151218414,
0.011646692641079426,
-0.030692774802446365,
0.010208833031356335,
0.020676802843809128,
-0.004643436521291733,
0.009519759565591812,
-0.06968281418085098,
0.04313072934746742,
-0.01516694389283657,
0.007460219319909811,
-0.002570697572082281,
-0.006384146865457296,
0.011890730820596218,
0.03592851758003235,
0.05627784878015518,
0.016674602404236794,
-0.01708953268826008,
-0.04747550189495087,
0.06107518821954727,
0.011583056300878525,
0.005624426528811455,
0.030908476561307907,
-0.0611485131084919,
0.043304167687892914,
-0.009972102008759975,
-0.013072269968688488,
0.018405405804514885,
0.01517874002456665,
0.018369877710938454,
-0.002969928551465273,
0.025777939707040787,
-0.02370753325521946,
-0.0017393464222550392,
0.014275426976382732,
-0.05279025435447693
] |
<p>Now consider I went into a rocket which goes an infinite distance far from earth. By infinite I mean very far. The gravitational attraction between me and the earth will significantly decrease and after a certain distance it will cease to act as the inertia of my rocket would be bigger than the gravitational force between my rocket and the earth. So where will the gravitational potential energy be lost? It is no more stored in the rocket since it does not get affected by that force. I know to recover it I can go back closer to the earth and my rocket will automatically start getting affected by the gravitational force again. So my question is, where is the gravitational potential energy stored for an object or a massive body that goes very very far from earth or any massive object?</p>
<p>When the rocket is at earth the total energy is </p>
<p>$E = E_m = mc^2$</p>
<p>When it takes off, the mass of the rocket decreases due to the fuel consumption but this is compensated by the increase in kinetic energy and potential energy so the total energy becomes</p>
<p>$E = E_m + E_k + E_g$</p>
<p>But when it reaches a point where gravity no longer affects it then $E_g$ = 0 because there is no more potential energy.</p>
<p>So the energy of the system becomes</p>
<p>$E = E_m + E_k$</p>
<p>So where did $E_g$ vanish?</p>
|
g2453
|
[
0.05341505631804466,
0.02370271645486355,
0.017302146181464195,
0.000755506509449333,
-0.02314659021794796,
0.0683402419090271,
-0.009032083675265312,
0.08417143672704697,
-0.0997827872633934,
-0.02144317887723446,
-0.012257958762347698,
0.008301099762320518,
0.014285535551607609,
0.004339349921792746,
0.042969800531864166,
-0.01325039379298687,
0.11630513519048691,
-0.018082480877637863,
-0.027124958112835884,
0.01805761829018593,
0.017495160922408104,
0.005428141448646784,
-0.01777360960841179,
0.0012680953368544579,
-0.050319135189056396,
0.0011850533774122596,
0.06810153275728226,
0.017810067161917686,
-0.042364176362752914,
-0.03819048032164574,
0.016105182468891144,
-0.038605861365795135,
0.03425212204456329,
-0.03886956349015236,
-0.027579687535762787,
0.006078587844967842,
0.03699788078665733,
0.039859235286712646,
0.050577763468027115,
-0.01469592098146677,
0.04298880323767662,
-0.038667354732751846,
0.009353548288345337,
0.01749223843216896,
0.007273609284311533,
-0.013849500566720963,
0.008474390022456646,
-0.013031519018113613,
0.01452625822275877,
-0.04573392495512962,
-0.000911389768589288,
0.03679852932691574,
0.0010321589652448893,
0.008693400770425797,
0.01668442226946354,
-0.013972306624054909,
0.0146033875644207,
-0.03250554949045181,
0.005522964522242546,
-0.00875953957438469,
0.04653559997677803,
-0.048246849328279495,
-0.0062715127132833,
-0.002097170567139983,
0.02221931889653206,
-0.07406099885702133,
-0.10780814290046692,
0.017967894673347473,
0.0033487812615931034,
-0.029876869171857834,
0.0671243965625763,
0.025810014456510544,
-0.06559813767671585,
-0.07475998997688293,
-0.03083128295838833,
0.013262280263006687,
0.028656797483563423,
0.031594451516866684,
-0.015986153855919838,
0.04197679087519646,
-0.03245067968964577,
0.007905170321464539,
0.08091536164283752,
0.02774372510612011,
0.039208460599184036,
-0.003638369031250477,
0.03481239825487137,
0.045729249715805054,
-0.05342758446931839,
0.025202946737408638,
0.0030426590237766504,
-0.007923767901957035,
0.046412061899900436,
0.004633130040019751,
0.013712932355701923,
-0.0066589792259037495,
-0.019686415791511536,
0.06335274130105972,
-0.036513425409793854,
-0.02594582922756672,
0.023525265976786613,
-0.05563095957040787,
-0.015945112332701683,
0.020582901313900948,
0.06526090949773788,
0.0046059745363891125,
0.007446361239999533,
0.010238880291581154,
0.03767912834882736,
0.012194094248116016,
0.0015888791531324387,
-0.08222578465938568,
-0.009949726983904839,
-0.07976356148719788,
-0.034571290016174316,
0.020482812076807022,
0.028863422572612762,
-0.05811242014169693,
0.003354546381160617,
0.036879897117614746,
-0.01027909480035305,
0.08944353461265564,
-0.05396489426493645,
0.03260482847690582,
-0.005449157673865557,
-0.023636003956198692,
-0.042852334678173065,
-0.016194140538573265,
-0.0032585624139755964,
0.010522576048970222,
-0.01108089555054903,
-0.01383957453072071,
0.0037092366255819798,
0.00009768145537236705,
-0.03158226236701012,
-0.013213281519711018,
-0.014137139543890953,
-0.0024483397137373686,
0.01356083620339632,
0.035087067633867264,
-0.037735383957624435,
-0.014878857880830765,
0.033424753695726395,
-0.006186528131365776,
-0.052330926060676575,
0.051153846085071564,
0.04100850969552994,
0.029805012047290802,
0.041043587028980255,
-0.07273778319358826,
0.024717114865779877,
0.06500540673732758,
0.0313546359539032,
-0.07592518627643585,
0.03289422765374184,
-0.05975189059972763,
-0.019672947004437447,
0.023833822458982468,
-0.002887907437980175,
0.006278160493820906,
0.027107665315270424,
0.0395166240632534,
0.06524096429347992,
-0.006873956881463528,
-0.015158514492213726,
0.033813927322626114,
-0.0022549929562956095,
-0.0815073698759079,
-0.01647614687681198,
0.005557504948228598,
-0.07506606727838516,
-0.002365740481764078,
0.06222551316022873,
0.061616454273462296,
-0.037092454731464386,
0.022448178380727768,
0.05907929688692093,
-0.014983180910348892,
-0.007242352701723576,
0.013910825364291668,
0.033781424164772034,
-0.009123020805418491,
0.06234992295503616,
-0.004021885804831982,
-0.01956016942858696,
0.00260905921459198,
0.024010436609387398,
0.0742173045873642,
-0.01600845344364643,
-0.014090838842093945,
-0.0019778364803642035,
0.01840847358107567,
-0.0006652896990999579,
-0.0013486515963450074,
0.004533756989985704,
0.023817678913474083,
0.07609209418296814,
-0.01960386149585247,
-0.0946640744805336,
-0.017148839309811592,
-0.040188245475292206,
-0.01526554673910141,
0.05260517820715904,
0.021929562091827393,
0.017949238419532776,
-0.03905428946018219,
0.014999423176050186,
0.015326370485126972,
-0.0033739160280674696,
-0.03629785403609276,
0.03472522273659706,
-0.014365400187671185,
-0.009307284839451313,
0.009639316238462925,
0.012583485804498196,
0.01831103302538395,
-0.06482075154781342,
0.017413899302482605,
0.005057469476014376,
0.022451719269156456,
-0.016106493771076202,
-0.006253485102206469,
0.03630569577217102,
0.024293342605233192,
-0.003710846183821559,
0.03859001398086548,
-0.06006347015500069,
-0.045435864478349686,
0.053017351776361465,
0.004542808514088392,
-0.007030480541288853,
0.013731906190514565,
0.04137241467833519,
-0.03630418702960014,
0.01516768243163824,
0.00781647302210331,
-0.011592278257012367,
-0.001084733521565795,
-0.07699517160654068,
0.006479501258581877,
0.006225296761840582,
-0.017989812418818474,
-0.024242108687758446,
-0.03575059399008751,
0.041359271854162216,
-0.030235618352890015,
0.021694695577025414,
0.04746260121464729,
0.029088789597153664,
0.05023563653230667,
0.0032899619545787573,
0.04968950152397156,
-0.0380825400352478,
0.021082239225506783,
0.03790542483329773,
0.0390523299574852,
-0.05806566774845123,
0.026802172884345055,
-0.05535024777054787,
-0.06012105941772461,
-0.06234876066446304,
-0.012652978301048279,
0.03568549081683159,
0.017708245664834976,
-0.0284775011241436,
0.007834171876311302,
-0.030912533402442932,
-0.055577490478754044,
0.016999566927552223,
0.02213544212281704,
-0.017397278919816017,
0.0378606878221035,
0.006580082233995199,
0.09242931008338928,
0.03609853237867355,
0.007217643782496452,
-0.015256383456289768,
-0.01856321655213833,
0.056887999176979065,
-0.004333936143666506,
0.0018466933397576213,
-0.018363656476140022,
-0.04655711352825165,
-0.008930099196732044,
-0.0035371133126318455,
-0.029467495158314705,
-0.03907259181141853,
0.014558430761098862,
-0.015846438705921173,
-0.0804610401391983,
-0.024690622463822365,
0.01553634088486433,
0.06243189796805382,
0.0060944585129618645,
-0.049421194940805435,
0.04356054216623306,
-0.0001236119569512084,
0.004874671343713999,
-0.07947497069835663,
-0.04824744910001755,
0.04021458327770233,
-0.034933362156152725,
0.018505562096834183,
0.029161831364035606,
-0.03577322140336037,
0.030002854764461517,
-0.02495422773063183,
-0.0354289636015892,
-0.0027292780578136444,
-0.0142129585146904,
-0.007428045384585857,
0.05452418327331543,
0.014830737374722958,
0.006951546296477318,
-0.007808533497154713,
0.04978928714990616,
0.002843824913725257,
-0.004438447300344706,
0.02775057964026928,
-0.026539959013462067,
-0.006301638670265675,
-0.03517133742570877,
0.012924034148454666,
0.0020034904591739178,
-0.002662533661350608,
0.051994748413562775,
-0.09786063432693481,
-0.008431493304669857,
-0.007184708025306463,
0.03352448344230652,
-0.08296269923448563,
0.06032581254839897,
0.008429182693362236,
-0.03266653046011925,
-0.013018536381423473,
0.02115347422659397,
-0.015453272499144077,
0.0031572377774864435,
0.04482201859354973,
0.03219680115580559,
0.0264423955231905,
0.06113845482468605,
-0.006429798435419798,
-0.02067965269088745,
0.02018601819872856,
0.0816490650177002,
-0.023729797452688217,
0.018996622413396835,
-0.020881926640868187,
-0.01937934197485447,
-0.0005694276769645512,
-0.05167683959007263,
0.001043916679918766,
-0.06214512884616852,
-0.07592272013425827,
0.0008400395163334906,
-0.037114713340997696,
-0.000016200394384213723,
-0.029690591618418694,
-0.002254576189443469,
-0.0070924097672104836,
-0.01601908728480339,
0.05218380689620972,
0.039417166262865067,
-0.0005871848552487791,
-0.017527781426906586,
-0.021086199209094048,
-0.11257822066545486,
0.024640994146466255,
-0.043400153517723083,
0.01631099358201027,
0.0034627800341695547,
-0.05373688414692879,
0.009876126423478127,
0.03873634338378906,
-0.048054199665784836,
0.0439307764172554,
-0.016225455328822136,
-0.05083233490586281,
-0.03335854038596153,
0.05568447336554527,
-0.012662041932344437,
-0.03918834403157234,
-0.004205668810755014,
0.05063300207257271,
-0.02193947322666645,
-0.010051937773823738,
0.0033153241965919733,
0.058953460305929184,
0.016501720994710922,
0.019443068653345108,
-0.058712054044008255,
0.012175863608717918,
0.04132973030209541,
0.034313835203647614,
-0.022040266543626785,
-0.021105406805872917,
-0.013383646495640278,
0.03565554693341255,
0.03812365233898163,
-0.019279882311820984,
0.04102880880236626,
-0.021678058430552483,
-0.02929280325770378,
0.016281593590974808,
-0.018895864486694336,
0.03448774293065071,
-0.037337932735681534,
-0.04297822713851929,
-0.035943832248449326,
0.04655926302075386,
-0.0270573478192091,
-0.039729952812194824,
-0.04915330931544304,
-0.02683635987341404,
-0.03906421735882759,
0.03615214303135872,
0.004122855141758919,
0.04171331599354744,
-0.009788098745048046,
0.027887700125575066,
0.02309008687734604,
-0.029731277376413345,
-0.0013195956125855446,
-0.02178320661187172,
0.02915584109723568,
-0.030835574492812157,
0.019958186894655228,
0.007878265343606472,
0.022158924490213394,
0.00530773401260376,
0.023963414132595062,
0.02016342245042324,
0.06208974868059158,
-0.08943939954042435,
0.08477183431386948,
0.0269867405295372,
-0.03053014539182186,
-0.010443629696965218,
0.018611647188663483,
0.05096171423792839,
0.021833913400769234,
-0.00549109885469079,
0.0034872819669544697,
-0.04491202533245087,
0.06810472905635834,
0.008094635792076588,
-0.00944636482745409,
0.00007955197361297905,
-0.05521027371287346,
-0.06513882428407669,
-0.004194795619696379,
0.012532624416053295,
0.0030913613736629486,
-0.008811860345304012,
-0.006874815560877323,
-0.028467336669564247,
-0.020180491730570793,
0.03860592842102051,
0.003669212106615305,
-0.025746280327439308,
-0.014556920155882835,
-0.020385930314660072,
0.0877542793750763,
-0.0036697133909910917,
-0.04830991476774216,
-0.032031141221523285,
-0.01264125108718872,
-0.029478251934051514,
-0.02055499143898487,
0.007943016476929188,
0.024954965338110924,
0.04815758019685745,
0.06714387238025665,
0.002849205397069454,
0.005659321788698435,
-0.011304846964776516,
-0.036395661532878876,
0.08010710775852203,
-0.08437883108854294,
-0.07806172966957092,
0.00816280022263527,
-0.015037489123642445,
-0.0004528478893917054,
-0.0017601463478058577,
0.035134363919496536,
-0.00955590046942234,
0.002229023026302457,
0.012376089580357075,
0.029694557189941406,
0.05466529726982117,
0.03014260157942772,
-0.026770886033773422,
-0.03119168058037758,
0.033266372978687286,
-0.010132966563105583,
-0.033937882632017136,
-0.011995983310043812,
0.010683387517929077,
0.028318028897047043,
0.023471064865589142,
-0.013941922225058079,
-0.04997038096189499,
0.02704678475856781,
-0.04461367428302765,
0.056773338466882706,
0.041686903685331345,
-0.017778828740119934,
-0.03816569969058037,
0.06563058495521545,
-0.03639955073595047,
0.04211593419313431,
0.007047072984278202,
0.03695668652653694,
-0.01060839556157589,
-0.043381478637456894,
0.03366178646683693,
-0.007812368683516979,
-0.05040556937456131,
0.005098313558846712,
0.010899405926465988,
0.023120589554309845,
0.06932825595140457,
-0.013594921678304672,
0.04171431064605713,
0.01840115524828434,
0.002474844455718994,
0.012856226414442062,
-0.014243760146200657,
0.09330077469348907,
0.024708278477191925,
0.001585970283485949,
-0.032087426632642746,
-0.024911820888519287,
-0.055766455829143524,
0.03054358810186386,
-0.019950106739997864,
-0.028041809797286987,
0.03966779634356499,
-0.05396663770079613,
0.03838067501783371,
-0.032237458974123,
-0.015339754521846771,
0.06230282410979271,
-0.062455032020807266,
0.004992878995835781,
-0.07417130470275879,
-0.008083143271505833,
0.04228537902235985,
-0.0656760111451149,
-0.007681354880332947,
0.0264957956969738,
-0.011033045127987862,
-0.007281161844730377,
-0.009891215711832047,
0.01292545534670353,
0.04915831610560417,
-0.00045769906137138605,
-0.020423466339707375,
-0.04112718254327774,
-0.0352991446852684,
0.02389794960618019,
0.008247338235378265,
-0.017907394096255302,
0.02769133821129799,
-0.004600463900715113,
-0.004702761769294739,
-0.06971795111894608,
0.07941585034132004,
0.023291422054171562,
0.01690477877855301,
0.01221099030226469,
0.015872791409492493,
-0.013746310956776142,
0.0364452563226223,
0.012433896772563457,
-0.03812973573803902,
-0.030400345101952553,
-0.010059761814773083,
-0.03313104063272476,
0.013174930587410927,
-0.009403834119439125,
0.056859806180000305,
-0.04988487437367439,
-0.03319217637181282,
0.023228924721479416,
-0.003215329721570015,
-0.11316780745983124,
0.06164887920022011,
-0.01796770840883255,
-0.009443022310733795,
0.003977859392762184,
0.019037578254938126,
-0.03899640217423439,
-0.040541958063840866,
-0.015246354974806309,
-0.016028400510549545,
-0.0070542688481509686,
-0.0031620922964066267,
0.018054550513625145,
-0.009032020345330238,
0.0034073954448103905,
0.037038546055555344,
0.015802325680851936,
0.03302765637636185,
-0.001383850583806634,
-0.036361392587423325,
-0.01463725883513689,
-0.007597233168780804,
-0.030980214476585388,
0.04044922813773155,
0.004903881810605526,
-0.0060285176150500774,
-0.02177734300494194,
-0.008605005219578743,
0.005549543537199497,
0.04010713845491409,
0.041428983211517334,
-0.000680049997754395,
-0.0014698521699756384,
-0.01605655439198017,
-0.04875065013766289,
0.03412394970655441,
-0.034877412021160126,
0.03633451834321022,
0.04030667617917061,
-0.047412991523742676,
0.005860012955963612,
0.037616606801748276,
-0.05094796046614647,
-0.009388196282088757,
0.019691871479153633,
0.0061054048128426075,
0.04152408987283707,
0.026058882474899292,
0.020786836743354797,
-0.010310756973922253,
0.03397928923368454,
-0.0064734467305243015,
-0.00759376585483551,
-0.00700863404199481,
0.009343494661152363,
0.011374767869710922,
0.035632967948913574,
-0.038458481431007385,
0.009385031647980213,
0.01440242026001215,
-0.028610022738575935,
0.0037612691521644592,
-0.06872885674238205,
-0.05462148040533066,
0.0008607266936451197,
-0.008396356366574764,
0.02408509887754917,
-0.028991609811782837,
0.033895671367645264,
-0.05161065235733986,
-0.04550071060657501,
0.02320890501141548,
-0.08482306450605392,
0.016469310969114304,
0.006856766529381275,
-0.03113429620862007,
0.007210483308881521,
-0.01162381749600172,
0.03763433173298836,
0.027484435588121414,
-0.09464205056428909,
-0.03290378674864769,
0.02672521397471428,
0.016227856278419495,
-0.0238153338432312,
-0.057416513562202454,
0.014711422845721245,
0.005484347697347403,
0.02943512424826622,
0.03996329382061958,
-0.05793994292616844,
-0.0044628772884607315,
-0.00270593399181962,
-0.005344502627849579,
0.040894608944654465,
-0.03845225274562836,
0.044353824108839035,
-0.03276006132364273,
0.02424943633377552,
-0.028781890869140625,
0.014780344441533089,
-0.038498833775520325,
-0.017499824985861778,
-0.032836634665727615,
0.07965659350156784,
0.04082222282886505,
-0.06762026250362396,
0.021847499534487724,
-0.0558089017868042,
-0.007948900572955608,
0.020278450101614,
0.039013177156448364,
-0.0342942550778389,
0.016752859577536583,
-0.020764503628015518,
0.024145353585481644,
-0.01303934771567583,
-0.015028027817606926,
0.04675452411174774,
-0.004554066341370344,
-0.027536291629076004,
-0.022452808916568756,
0.06419254094362259,
0.05030292645096779,
0.013256452977657318,
0.06343615800142288,
0.008037546649575233,
-0.029700862243771553,
0.03381155803799629,
-0.010367103852331638,
0.0026352957356721163,
-0.007221527863293886,
-0.033674389123916626,
-0.002414642134681344,
-0.009902839548885822,
0.05433792620897293,
-0.08077047765254974,
-0.025511980056762695,
0.041232455521821976,
-0.04072929546236992,
-0.002111058449372649,
0.05779245123267174,
-0.01992657408118248,
-0.012757585383951664,
0.007113106548786163,
-0.009031749330461025,
-0.011980351060628891,
0.029853839427232742,
0.004572499077767134,
-0.0011681029573082924,
-0.022813932970166206,
-0.025041241198778152,
-0.01302021462470293,
-0.011664871126413345,
-0.07661996781826019,
0.0053252652287483215,
0.040715549141168594,
0.052968285977840424,
0.008539828471839428,
-0.04535220190882683,
-0.0004180065880063921,
0.0582720972597599,
0.006141982972621918,
0.05519978329539299,
-0.04023025184869766,
-0.005707407370209694,
0.07892156392335892,
-0.007530190050601959,
-0.02592005580663681,
0.028652988374233246,
-0.005230346228927374,
-0.07799418270587921,
-0.029332328587770462,
0.0001712017401587218,
0.04395740479230881,
-0.02882235310971737,
-0.04505808278918266,
0.027116546407341957,
-0.05467931926250458,
0.025729667395353317,
0.04011615365743637
] |
<p>I have a strong background in Fourier analysis, and I'm looking for QM resources that can build on that. Is there a book around or a little above the level of Griffiths that has that kind of emphasis? Any other resources are good too.</p>
|
g2454
|
[
0.041450321674346924,
-0.008600214496254921,
0.015986137092113495,
-0.08880370110273361,
0.0021313487086445093,
-0.06870124489068985,
-0.02278509922325611,
-0.014963897876441479,
-0.02574954926967621,
-0.02463814616203308,
0.025557106360793114,
-0.004876280203461647,
0.06488524377346039,
-0.02478095330297947,
-0.035875264555215836,
-0.010325491428375244,
-0.012942015193402767,
0.10134678333997726,
-0.06794121861457825,
0.026313254609704018,
0.015257783234119415,
0.0042241946794092655,
0.03295522555708885,
-0.047557562589645386,
-0.05156458541750908,
-0.0231028962880373,
-0.01273695845156908,
0.00021285230468492955,
0.030858123674988747,
-0.005574152804911137,
-0.08955492824316025,
-0.0124069694429636,
-0.01689840666949749,
-0.05662677064538002,
-0.06214166432619095,
0.021552477031946182,
0.04273919388651848,
-0.01933075301349163,
0.038910605013370514,
0.0008435642230324447,
0.026927663013339043,
-0.037388741970062256,
0.0026854563038796186,
0.06928477436304092,
-0.0074190404266119,
-0.01121512334793806,
0.012471800670027733,
0.034688372164964676,
-0.012972498312592506,
0.05540834739804268,
-0.01020327303558588,
0.017089277505874634,
0.07850747555494308,
-0.026416586712002754,
0.010791479609906673,
0.062903992831707,
-0.0038812290877103806,
0.04901403188705444,
-0.0006269107689149678,
-0.0024322231765836477,
-0.01296352967619896,
-0.013021466322243214,
-0.03732215613126755,
-0.03417335823178291,
-0.0225063543766737,
-0.012830142863094807,
-0.005085533019155264,
-0.056416191160678864,
-0.03757714480161667,
0.012708775699138641,
-0.03613423928618431,
-0.0014025348937138915,
-0.012098639272153378,
0.03823447600007057,
-0.02839057333767414,
0.05838274955749512,
0.0377529039978981,
0.03181656822562218,
0.0106806680560112,
-0.0015287547139450908,
-0.05924771726131439,
-0.0258529931306839,
0.03250313550233841,
0.01878148876130581,
0.02471751533448696,
-0.013333305716514587,
-0.014765451662242413,
0.032613933086395264,
0.05269676446914673,
-0.008521239273250103,
0.05783615633845329,
0.06363105028867722,
0.027867721393704414,
-0.01005695853382349,
-0.011179995723068714,
-0.013929176144301891,
-0.026420611888170242,
-0.017587168142199516,
0.023656580597162247,
-0.025081979110836983,
-0.0043584685772657394,
0.03942783921957016,
0.034317273646593094,
-0.021607225760817528,
-0.06527262181043625,
-0.019558094441890717,
0.008748683147132397,
-0.0013173555489629507,
0.013426671735942364,
0.049886856228113174,
-0.012572495266795158,
-0.0023274419363588095,
-0.059432096779346466,
-0.029673874378204346,
-0.050970952957868576,
0.027899280190467834,
0.06452891230583191,
0.01215722132474184,
0.035880789160728455,
0.08330196142196655,
0.03712700307369232,
0.04123007506132126,
0.07810965925455093,
-0.0016067158430814743,
0.01012648455798626,
-0.03280610591173172,
0.049317460507154465,
0.03337747976183891,
0.03415992483496666,
0.00966122467070818,
0.109731525182724,
0.0012271294835954905,
-0.045964207500219345,
0.011858876794576645,
0.016210466623306274,
0.05522233247756958,
-0.012172634713351727,
0.02513234317302704,
0.026059551164507866,
0.0033181479666382074,
-0.02020244300365448,
-0.03362184390425682,
0.012539137154817581,
-0.045064058154821396,
0.036364637315273285,
0.01839555986225605,
-0.006245412398129702,
-0.00570828327909112,
0.015271560288965702,
-0.027326742187142372,
-0.024299195036292076,
0.01574552245438099,
0.023639455437660217,
-0.01963839679956436,
0.010037224739789963,
0.028121868148446083,
0.036965709179639816,
-0.009440645575523376,
0.0021104190964251757,
-0.04253006726503372,
0.03287887945771217,
0.02767195738852024,
0.003829032415524125,
-0.0275818333029747,
0.022748397663235664,
-0.0006452917587012053,
-0.040450651198625565,
-0.13890555500984192,
-0.0016435456927865744,
0.011473127640783787,
0.0011707560624927282,
-0.0027105817571282387,
0.07566940039396286,
0.030000431463122368,
-0.044572874903678894,
0.024537554010748863,
0.009493540041148663,
-0.041642796248197556,
0.013052401132881641,
-0.01850155182182789,
0.02781936526298523,
-0.016718970611691475,
0.02783166989684105,
-0.05356885865330696,
0.0012563809286803007,
-0.01920625939965248,
0.02657553367316723,
0.03481803089380264,
-0.04794618859887123,
0.03494177758693695,
-0.006357938516885042,
-0.00292806513607502,
-0.004958976525813341,
0.0488455556333065,
0.016274163499474525,
-0.012602207250893116,
-0.011156209744513035,
-0.032178740948438644,
-0.028528735041618347,
0.04010792821645737,
0.062345389276742935,
0.014809978194534779,
0.08098512142896652,
0.05604234337806702,
0.03849014639854431,
0.04890425503253937,
-0.04295948147773743,
-0.04595817252993584,
-0.004806504584848881,
-0.034025855362415314,
-0.03554871678352356,
-0.0172868762165308,
0.014938587322831154,
0.0415213517844677,
0.012377786450088024,
0.039508819580078125,
-0.02490215003490448,
0.005508949980139732,
0.04237464815378189,
0.03139093518257141,
0.01567501202225685,
-0.014897879213094711,
-0.02716565877199173,
-0.029745914041996002,
-0.007017744239419699,
-0.001310293679125607,
0.008325455710291862,
-0.013651673682034016,
-0.038939084857702255,
0.04317319765686989,
-0.09174185991287231,
-0.02119012363255024,
0.008344445377588272,
-0.0628974437713623,
0.0364316962659359,
0.020673410966992378,
-0.020954586565494537,
-0.020707644522190094,
-0.006137227173894644,
0.047198548913002014,
0.04112827777862549,
-0.02918168343603611,
0.028510162606835365,
-0.01026647537946701,
-0.03458306938409805,
-0.01091315969824791,
-0.005106288939714432,
0.007529233582317829,
0.02110862545669079,
0.02307184599339962,
0.03149136155843735,
-0.028774360194802284,
0.0019986333791166544,
-0.013347172178328037,
-0.015938475728034973,
-0.013379325158894062,
0.012421508319675922,
0.030311599373817444,
-0.008661481551826,
-0.026555536314845085,
-0.008991329930722713,
-0.01071437168866396,
0.004160179756581783,
0.024318905547261238,
0.02675098553299904,
-0.011900072917342186,
0.01629115454852581,
0.05632491037249565,
-0.0632578656077385,
-0.017900265753269196,
0.008981331251561642,
0.04235130175948143,
0.028001707047224045,
-0.012044370174407959,
0.008997232653200626,
-0.025941936299204826,
-0.01301846094429493,
-0.020308511331677437,
0.043665602803230286,
-0.020365411415696144,
0.006436740979552269,
-0.06282636523246765,
0.056364756077528,
0.04342343285679817,
0.019773980602622032,
-0.013165761716663837,
0.02684563398361206,
0.002481677569448948,
-0.004890827927738428,
0.0044710757210850716,
0.0014598355628550053,
0.015105257742106915,
-0.020363282412290573,
-0.03232709318399429,
-0.11377763003110886,
0.02673286758363247,
0.04223070293664932,
-0.054973673075437546,
0.0033431495539844036,
-0.0015223035588860512,
-0.026880018413066864,
0.0036553391255438328,
0.013051017187535763,
0.04358699172735214,
0.01973479986190796,
0.03592642396688461,
-0.04036610201001167,
-0.04019637405872345,
-0.021479472517967224,
0.021468477323651314,
0.006948706693947315,
-0.05747443437576294,
-0.03527158498764038,
0.01640620268881321,
-0.04094701260328293,
-0.008976682089269161,
-0.009963857010006905,
0.030183888971805573,
0.008372178301215172,
-0.0024508226197212934,
-0.05676289647817612,
-0.06069280207157135,
0.035711973905563354,
-0.09534817934036255,
0.05851360782980919,
-0.005577178671956062,
0.018229562789201736,
-0.029835401102900505,
-0.03159715235233307,
-0.010665650479495525,
0.024249810725450516,
-0.0030003893189132214,
0.026498962193727493,
0.001395243569277227,
-0.02362503670156002,
-0.09331069886684418,
-0.027801504358649254,
-0.061185725033283234,
0.01027292013168335,
-0.03382820263504982,
0.03454776108264923,
0.0113048255443573,
0.02026526816189289,
-0.054548367857933044,
-0.04185805469751358,
0.015003912150859833,
-0.029638122767210007,
0.036164138466119766,
0.007553935516625643,
-0.05849273502826691,
-0.011264259926974773,
-0.006462180987000465,
0.039504699409008026,
-0.026744069531559944,
0.029150811955332756,
0.06208626180887222,
0.029015231877565384,
0.012712393887341022,
0.037244755774736404,
-0.023038314655423164,
0.0010938458144664764,
-0.0011929090833291411,
-0.01195005513727665,
-0.05404603108763695,
0.005201850552111864,
0.022016048431396484,
0.03174871206283569,
0.039313748478889465,
-0.01758550852537155,
0.027590777724981308,
0.013888641260564327,
0.05432386323809624,
0.01985025405883789,
0.025316715240478516,
-0.07364281266927719,
-0.04583849012851715,
-0.002107364358380437,
0.03459612652659416,
-0.002388365799561143,
-0.032027292996644974,
-0.037587374448776245,
-0.010026988573372364,
-0.007116169668734074,
-0.004562535788863897,
0.018245968967676163,
-0.03590298071503639,
0.02330734394490719,
0.004017768427729607,
-0.03219864144921303,
-0.0478958822786808,
0.05254216864705086,
-0.09487112611532211,
-0.03208708018064499,
-0.006599444895982742,
0.003153993980959058,
-0.06923696398735046,
0.019921166822314262,
-0.003447210881859064,
0.015872852876782417,
0.10300867259502411,
-0.020739970728754997,
0.012847056612372398,
-0.011722085066139698,
-0.002855074591934681,
-0.06126035004854202,
-0.017660411074757576,
0.011302875354886055,
-0.039824388921260834,
-0.07136591523885727,
-0.043937619775533676,
-0.04829096794128418,
-0.03659882768988609,
0.039862602949142456,
-0.041527193039655685,
0.03620024770498276,
-0.0072877355851233006,
-0.005076488479971886,
-0.049243904650211334,
0.03274741768836975,
-0.023344699293375015,
-0.07868203520774841,
-0.015356138348579407,
-0.01780756749212742,
-0.0036470468621701,
0.03146336227655411,
0.022017881274223328,
0.048065874725580215,
-0.002669376088306308,
0.03851741552352905,
0.00942682009190321,
-0.014316430315375328,
-0.026872731745243073,
0.029049018397927284,
0.00690441345795989,
-0.013096917420625687,
-0.015921495854854584,
-0.023020967841148376,
0.02465602569282055,
-0.017354536801576614,
-0.03900820016860962,
0.053993139415979385,
0.02340359054505825,
-0.008866121992468834,
0.04400822892785072,
-0.024854646995663643,
0.037362195551395416,
-0.01143124420195818,
0.018493665382266045,
-0.038257896900177,
-0.0015413067303597927,
0.03693307191133499,
-0.013454313389956951,
-0.03614769130945206,
-0.018460344523191452,
-0.02228831686079502,
-0.0428510420024395,
-0.04295673221349716,
-0.005756097845733166,
0.08881483227014542,
-0.006871333345770836,
0.025880906730890274,
-0.008954866789281368,
-0.08204419910907745,
0.03925270214676857,
-0.0027232265565544367,
0.005073735024780035,
-0.07194734364748001,
0.04648713767528534,
-0.00997027475386858,
-0.017894916236400604,
-0.03570098429918289,
0.00899947714060545,
0.05620897561311722,
0.008016745559871197,
0.04215940460562706,
-0.012689179740846157,
0.002767185214906931,
-0.04848793148994446,
-0.013454179279506207,
-0.00522568030282855,
0.008005181327462196,
-0.023562749847769737,
0.07832246273756027,
0.04132528975605965,
-0.002435959642753005,
-0.045721668750047684,
0.014098136685788631,
-0.027148962020874023,
-0.008846506476402283,
-0.034263238310813904,
0.0047464268282055855,
0.01950099878013134,
0.04270504415035248,
-0.010125763714313507,
-0.0672748014330864,
-0.0025830604135990143,
0.10136032849550247,
-0.020118195563554764,
0.005218814592808485,
0.015712343156337738,
0.004301619250327349,
0.05967271700501442,
-0.06317044794559479,
0.03202388063073158,
0.005092265550047159,
0.02854873798787594,
0.02341371774673462,
-0.03987845405936241,
-0.014671706594526768,
0.02169518545269966,
0.013303648680448532,
0.09011004120111465,
-0.007576052565127611,
0.010024188086390495,
0.06455467641353607,
0.005558678414672613,
0.030794166028499603,
0.01008409634232521,
-0.030804069712758064,
-0.03973344340920448,
-0.03943774104118347,
-0.044355083256959915,
-0.03291837498545647,
-0.015122332610189915,
0.03498189523816109,
-0.0030377281364053488,
-0.021855514496564865,
-0.010174200870096684,
-0.017900533974170685,
-0.005579096730798483,
0.07071146368980408,
-0.021368425339460373,
-0.036551471799612045,
0.011455150321125984,
0.0008047794108279049,
0.112704798579216,
-0.039597347378730774,
0.014439279213547707,
-0.04041874036192894,
0.046869292855262756,
-0.001986570656299591,
0.006278026383370161,
0.02225283719599247,
0.02893945761024952,
-0.006735613103955984,
-0.026950815692543983,
0.07684829831123352,
0.020582083612680435,
0.06689765304327011,
-0.039344653487205505,
0.014723733998835087,
-0.062419891357421875,
-0.03742627799510956,
-0.07089494168758392,
-0.01711040921509266,
0.07178383320569992,
-0.010934739373624325,
0.011205240152776241,
-0.03588644042611122,
0.05419769138097763,
0.0000967077721725218,
-0.04044919088482857,
0.012845386750996113,
0.009281236678361893,
0.021075274795293808,
0.000798492634203285,
-0.051009368151426315,
-0.006899399682879448,
0.1018616259098053,
0.02412218414247036,
-0.040104638785123825,
-0.020261194556951523,
-0.05121428146958351,
0.01956687495112419,
0.01117733120918274,
0.004286373034119606,
-0.013895329087972641,
-0.06696851551532745,
0.019461002200841904,
-0.08424733579158783,
0.0003287291619926691,
0.08759604394435883,
0.020605802536010742,
-0.025174584239721298,
-0.044558439403772354,
0.04600314423441887,
-0.01924758590757847,
0.08377980440855026,
0.03139674291014671,
0.03470296785235405,
-0.014203429222106934,
0.04296024888753891,
-0.04981626570224762,
-0.03645855933427811,
0.04500512406229973,
-0.034891385585069656,
0.035341598093509674,
0.0640883818268776,
0.012639598920941353,
-0.037731483578681946,
-0.0069346800446510315,
0.002539217472076416,
0.05362309515476227,
-0.008439880795776844,
-0.013721136376261711,
0.0443066842854023,
0.07986162602901459,
0.0033217112068086863,
-0.009615759365260601,
0.0736934095621109,
0.013350100256502628,
-0.012541044503450394,
0.042438410222530365,
0.033286675810813904,
-0.006000513210892677,
-0.09944512695074081,
-0.01518521923571825,
-0.009781710803508759,
-0.04571687802672386,
-0.027072660624980927,
0.052130550146102905,
0.015520171262323856,
-0.03709975630044937,
-0.07019457966089249,
-0.01620938628911972,
0.00982115138322115,
-0.0005158909480087459,
0.04344244301319122,
0.059816114604473114,
-0.06098102778196335,
-0.0035260780714452267,
-0.04841705039143562,
0.014772006310522556,
-0.03237910941243172,
-0.06625717878341675,
0.021694261580705643,
-0.06113167107105255,
0.03398063778877258,
-0.02060283161699772,
0.0017207268392667174,
-0.03316086530685425,
-0.0037054936401546,
-0.009260975755751133,
-0.057851605117321014,
0.04542975500226021,
-0.04307151585817337,
-0.0011828766437247396,
-0.012952655553817749,
-0.07693101465702057,
0.055835042148828506,
0.09629207849502563,
0.021189341321587563,
-0.0076230852864682674,
-0.015446251258254051,
-0.007808406371623278,
0.010690352879464626,
0.03452154994010925,
-0.027588842436671257,
0.09159713238477707,
0.010155719704926014,
0.028161579743027687,
-0.012373862788081169,
0.012614846229553223,
0.028925549238920212,
-0.007624849211424589,
0.060040030628442764,
-0.006602626293897629,
0.006380729842931032,
0.02566475234925747,
-0.025540446862578392,
-0.005189644172787666,
-0.008607652969658375,
-0.015278691425919533,
-0.03555593639612198,
0.011079925112426281,
0.0002474583452567458,
-0.04264107346534729,
0.020788513123989105,
-0.024890678003430367,
-0.022184103727340698,
-0.025473106652498245,
-0.021428709849715233,
0.016482792794704437,
-0.006351248361170292,
-0.022477004677057266,
0.03313581272959709,
0.0036824827548116446,
-0.004951184615492821,
0.011196288280189037,
-0.0020423070527613163,
-0.07824447005987167,
0.030695313587784767,
-0.0296703539788723,
-0.03459605947136879,
0.0023067332804203033,
-0.021400898694992065,
0.03842451050877571,
0.026378802955150604,
0.03440235182642937,
0.06572946161031723,
0.0008840963710099459,
-0.008526603691279888,
-0.006443274673074484,
-0.03724995627999306,
0.00413808599114418,
0.008456300012767315,
0.04577266424894333,
-0.03606769070029259,
0.039730727672576904,
-0.019199585542082787,
0.01627400703728199,
0.005972051061689854,
0.005476493388414383,
0.010601948015391827,
0.0201087798923254,
-0.016376139596104622,
-0.01423688605427742,
0.04980303347110748,
0.0065024662762880325,
-0.04049547761678696,
0.008451833389699459,
-0.046220310032367706,
-0.012481104582548141,
-0.01942199468612671,
0.004678754135966301,
-0.017008895054459572,
-0.006089590955525637,
0.0451536551117897,
-0.022688966244459152,
0.040334831923246384,
0.016468198969960213,
0.0015828607138246298,
-0.048436444252729416,
-0.009641848504543304,
0.00679435022175312,
-0.0037058908492326736,
0.03923654928803444,
-0.03712485358119011,
0.02577817253768444,
-0.0035271577071398497,
0.040714330971241,
0.02196330577135086,
-0.01683666929602623,
-0.031093213707208633,
-0.06755705922842026,
-0.06494889408349991,
0.004081600811332464,
0.02010236121714115,
-0.009675992652773857,
-0.008701471611857414,
-0.05200640484690666,
0.033603280782699585,
0.044977255165576935,
0.008245859295129776,
0.006334763020277023,
-0.05710215866565704,
-0.008544509299099445,
0.05598375201225281,
0.053451281040906906,
-0.046868495643138885,
0.04540851712226868,
-0.004318565595895052,
0.031983669847249985,
-0.005984176881611347,
-0.019950103014707565,
0.009281841106712818,
-0.03326888009905815,
-0.032735757529735565
] |
<p>The question basically amounts to whether I can construct the illusion of superposition with adjacent sine waves of varying frequency.</p>
<p><strong>Context</strong></p>
<p>I'm trying to play music on a Tesla Coil (like OneTesla and the works). If I want to play an A for instance, I'll modulate my input signal so that the Tesla coil sparks 110 times per second. Each time, it will turn air into plasma, a volume change whose pressure wave propagates through the air as sound.</p>
<p>However, as of now I can only play one note at a time. For example, I can play a C, followed by a F, followed by a G, but I can't play a CFG chord. In terms of sine waves (i.e. why I'm posting to the Physics StackExchange), I'm trying to model $\Sigma_{i=1}^{n} sin(\alpha_i x)$ from, say $0<x<\pi$ time units, with the approximation $sin(\alpha_i x)$ for $\frac{(i-1)\pi}{n}<x<\frac{i\pi}{n}$ for i from 1 to n, and x from 0 to $\pi$.</p>
<p>At least with light, I think that humans have a visual memory - e.g. if I show you red, and then blue, and then red, and alternate really, really, fast, you see purple (I think...). Is the same possible for sound? If so, how fast do I need to alternate notes?</p>
<p>I'm sure the same question has been asked somewhere else, but I couldn't find any answers that apply. Also, if this is in the wrong forum, feel free to move it.</p>
|
g2455
|
[
-0.021708756685256958,
0.03152935206890106,
-0.010101830586791039,
-0.08969767391681671,
0.006640707608312368,
-0.04688389599323273,
0.043257106095552444,
0.007174451369792223,
0.015409170649945736,
-0.022063791751861572,
-0.03558237478137016,
0.007200637366622686,
-0.03367859497666359,
0.0734054297208786,
-0.028445720672607422,
0.006029370240867138,
0.06956668943166733,
0.006886844057589769,
0.029931148514151573,
-0.01928199641406536,
0.033352211117744446,
-0.002491564955562353,
0.027768053114414215,
-0.02482849545776844,
0.020729759708046913,
-0.011772409081459045,
0.023357583209872246,
-0.08692014217376709,
0.019724320620298386,
-0.03613506630063057,
-0.0066871605813503265,
-0.06193896010518074,
0.010199747048318386,
-0.010984973981976509,
-0.05287489667534828,
-0.013973536901175976,
-0.048009488731622696,
-0.008080712519586086,
0.048073332756757736,
0.01742452383041382,
-0.02845822088420391,
-0.0035601076669991016,
0.05269310250878334,
-0.044254206120967865,
-0.0058851903304457664,
0.04647229611873627,
0.03328224644064903,
0.006510076578706503,
0.012804488651454449,
-0.043690990656614304,
-0.04485726356506348,
0.009591341018676758,
0.008455689996480942,
0.015474464744329453,
-0.027125032618641853,
0.03841281309723854,
0.028688132762908936,
-0.04034797102212906,
0.07201213389635086,
0.07851779460906982,
-0.008123381994664669,
0.026923000812530518,
0.021258287131786346,
-0.044983815401792526,
0.0497017465531826,
0.02900245040655136,
-0.0440031960606575,
0.0067402394488453865,
0.02440796047449112,
-0.003596616443246603,
-0.0018205122323706746,
0.0013388789957389235,
-0.0376921072602272,
-0.04382527992129326,
-0.028830701485276222,
0.010414687916636467,
-0.016752135008573532,
-0.01074542012065649,
-0.0036410188768059015,
0.04030663147568703,
-0.00459273299202323,
-0.0018783168634399772,
0.050775960087776184,
0.036151811480522156,
0.04692184925079346,
-0.06772058457136154,
0.029094399884343147,
0.022521665319800377,
-0.019800903275609016,
0.020525911822915077,
0.021051185205578804,
-0.013375919312238693,
-0.000991852837614715,
0.05077481269836426,
-0.014998764730989933,
-0.03942681476473808,
-0.08015473186969757,
0.09955759346485138,
0.005177406128495932,
-0.009010420180857182,
-0.01773831434547901,
0.02768249250948429,
0.05553862452507019,
-0.04153168573975563,
-0.08024271577596664,
0.05122504010796547,
0.034615520387887955,
-0.016450338065624237,
-0.004677434917539358,
-0.023126278072595596,
-0.04762890189886093,
-0.07788980007171631,
0.0035056029446423054,
-0.034274425357580185,
-0.08507280796766281,
-0.01567886956036091,
-0.044847432523965836,
0.028092052787542343,
-0.01790802925825119,
0.04261943697929382,
-0.008203652687370777,
-0.0049112169072031975,
0.04478471353650093,
0.013674554415047169,
-0.004609942901879549,
-0.004805112723261118,
-0.037933822721242905,
-0.006792482454329729,
0.04533823952078819,
-0.027659475803375244,
0.006169569678604603,
0.007145017851144075,
0.001734092365950346,
0.03565845265984535,
0.028875747695565224,
0.014570792205631733,
0.03905360400676727,
0.005090782884508371,
0.007486296351999044,
0.018279604613780975,
0.04102151095867157,
-0.0258689783513546,
0.03748418390750885,
-0.03004262037575245,
-0.03986672684550285,
-0.05922851711511612,
-0.014501153491437435,
-0.013746272772550583,
-0.027197830379009247,
-0.019466783851385117,
0.0030038796830922365,
0.012513394467532635,
0.027721699327230453,
0.01382790133357048,
0.002965955762192607,
0.007283315993845463,
0.022920457646250725,
0.018491260707378387,
-0.01213496457785368,
0.0001588479644851759,
0.02877596579492092,
-0.011764892376959324,
-0.007566685322672129,
0.007857625372707844,
-0.042675312608480453,
-0.055470190942287445,
0.027648169547319412,
0.03171692416071892,
-0.03280387818813324,
-0.07122571766376495,
-0.024632172659039497,
0.025848479941487312,
0.0030438010580837727,
-0.0029968840535730124,
0.028697574511170387,
-0.012541038915514946,
0.04734336584806442,
-0.07163923233747482,
0.007058489136397839,
0.04152737185359001,
-0.04748428240418434,
-0.0329759381711483,
-0.1091897189617157,
-0.013261021114885807,
-0.008433266542851925,
-0.008163627237081528,
-0.04958857595920563,
0.019844064489006996,
-0.029016025364398956,
0.04803311452269554,
0.01798306591808796,
-0.03144202381372452,
-0.03734753653407097,
-0.0055441176518797874,
-0.007556793745607138,
0.011589741334319115,
0.04173856973648071,
0.0028539893683046103,
0.008754322305321693,
0.06189560517668724,
0.04012143611907959,
0.08843901008367538,
0.09064876288175583,
-0.0421617366373539,
0.03809662535786629,
0.0037614256143569946,
-0.024057338014245033,
-0.04528236761689186,
-0.03853830695152283,
0.046165987849235535,
0.050141748040914536,
0.07031464576721191,
-0.018350007012486458,
0.040766242891550064,
-0.028326867148280144,
-0.04461878165602684,
0.009146254509687424,
-0.02712434157729149,
0.004443387500941753,
0.0442042239010334,
0.030721895396709442,
-0.02087852917611599,
0.03244602680206299,
-0.011580012738704681,
-0.03980109468102455,
-0.02487947605550289,
0.006672233808785677,
-0.010155142284929752,
0.0164068304002285,
0.029881676658988,
-0.05869242176413536,
-0.01048172079026699,
0.0009949752129614353,
-0.04280472919344902,
0.02370787225663662,
0.05409785360097885,
0.02907402440905571,
0.004926105495542288,
0.0010813305852934718,
0.02307903580367565,
0.03682028874754906,
-0.01111544482409954,
0.023307468742132187,
-0.007088241167366505,
-0.020978039130568504,
-0.032990116626024246,
-0.041853275150060654,
0.017492055892944336,
0.02309541217982769,
-0.0031099363695830107,
-0.07437007874250412,
-0.049580469727516174,
-0.06654451787471771,
-0.03904356062412262,
-0.01632717438042164,
-0.07411691546440125,
0.02833385206758976,
0.023512180894613266,
-0.025677591562271118,
0.04476897045969963,
-0.008669865317642689,
0.02327229082584381,
0.016817452386021614,
-0.0010286581236869097,
-0.05687069520354271,
-0.013699734583497047,
0.05964503437280655,
0.01834709383547306,
-0.02970224618911743,
-0.004463682882487774,
-0.03243088349699974,
0.00807119905948639,
-0.008881773799657822,
0.02818818762898445,
-0.033611152321100235,
0.03999323025345802,
-0.03772581368684769,
-0.00346318818628788,
0.029811251908540726,
0.04837506636977196,
-0.03933781385421753,
-0.0481889508664608,
-0.01828012429177761,
-0.019945664331316948,
-0.025684142485260963,
-0.05425732210278511,
0.06013495847582817,
0.009685547091066837,
0.008005673065781593,
0.11846322566270828,
-0.07662036269903183,
-0.0014015352353453636,
0.03170979022979736,
0.03535154089331627,
-0.051275987178087234,
0.04217848554253578,
0.020398039370775223,
-0.00244866032153368,
0.018738526850938797,
-0.008391117677092552,
0.04937903955578804,
0.004930504597723484,
0.03253045678138733,
0.05068650469183922,
-0.013874651864171028,
-0.019392313435673714,
-0.020472129806876183,
0.003735070815309882,
0.05145297199487686,
-0.01482312474399805,
0.05547795072197914,
0.03337793052196503,
0.03360855579376221,
0.013837921433150768,
-0.010682777501642704,
0.012617751955986023,
0.023607175797224045,
0.008357241749763489,
-0.020152661949396133,
0.046130675822496414,
-0.03774207457900047,
-0.04473181813955307,
-0.00598298991099,
-0.007818256504833698,
0.0377848818898201,
0.015422684140503407,
0.022291935980319977,
0.017721356824040413,
-0.06649108231067657,
-0.10627172887325287,
-0.004078063182532787,
-0.018017683178186417,
-0.014316914603114128,
-0.022181130945682526,
0.007741779554635286,
-0.041875209659338,
0.008684645406901836,
0.026399191468954086,
0.03854205086827278,
0.03825889155268669,
-0.0037472019903361797,
0.008088424801826477,
0.03056536614894867,
-0.04485505074262619,
0.02729686163365841,
0.06541657447814941,
-0.039291758090257645,
0.032815832644701004,
0.03417115658521652,
-0.0025058421306312084,
0.0011107682948932052,
0.0009839371778070927,
0.053908467292785645,
0.015020499937236309,
0.04485269635915756,
0.041723959147930145,
0.07059771567583084,
0.013230675831437111,
-0.051225002855062485,
0.0017354473238810897,
0.013404037803411484,
-0.04702300578355789,
-0.04503614455461502,
-0.031814008951187134,
0.023068847134709358,
-0.02557058073580265,
0.02070886269211769,
0.0418921522796154,
-0.022049764171242714,
0.011239733546972275,
0.023307759314775467,
-0.01855037733912468,
0.01195304561406374,
-0.037387914955616,
-0.03134744614362717,
-0.08569758385419846,
-0.02463136613368988,
0.04822935536503792,
-0.016397686675190926,
0.06871096789836884,
-0.017826255410909653,
0.013204884715378284,
0.0292937271296978,
-0.03066103346645832,
0.011893153190612793,
0.008011085912585258,
0.04280158877372742,
-0.007451568730175495,
0.009710581041872501,
-0.031492818146944046,
0.00538728479295969,
-0.07816478610038757,
-0.040790628641843796,
-0.0414811372756958,
0.0029531195759773254,
-0.0461636483669281,
0.00039621879113838077,
-0.0169304721057415,
-0.022578082978725433,
0.027142977342009544,
0.0661979615688324,
0.010823886841535568,
0.01900239661335945,
-0.006319873034954071,
-0.0341779962182045,
-0.015438358299434185,
0.045381736010313034,
-0.017844153568148613,
-0.049870770424604416,
-0.0683775469660759,
-0.053178030997514725,
0.005129858385771513,
-0.019394401460886,
-0.032101523131132126,
0.027208378538489342,
0.04865535721182823,
0.06445661187171936,
0.014385259710252285,
0.01615356281399727,
0.05736813321709633,
0.03251653537154198,
0.05983675643801689,
-0.009662680327892303,
-0.01478448137640953,
0.023293957114219666,
0.06011427193880081,
0.038854118436574936,
-0.018800321966409683,
0.0037241007667034864,
-0.023735305294394493,
0.02951032668352127,
-0.04867948219180107,
0.0075189173221588135,
0.007335773669183254,
-0.09146014600992203,
-0.017349334433674812,
-0.06630552560091019,
0.007278785575181246,
0.017081692814826965,
0.0549505315721035,
0.022649165242910385,
-0.04127204045653343,
0.030756309628486633,
-0.03029855154454708,
-0.004105698317289352,
0.0016891798004508018,
-0.0711582824587822,
-0.042233049869537354,
-0.0450773648917675,
-0.03930557146668434,
-0.06876445561647415,
0.03229404613375664,
-0.008444247767329216,
-0.029414193704724312,
-0.015265041962265968,
-0.038259897381067276,
-0.038054708391427994,
0.04984216392040253,
-0.002523870673030615,
-0.0081124696880579,
0.03202176094055176,
0.07453524321317673,
-0.057955365628004074,
-0.024854009971022606,
0.05319015309214592,
0.08103571832180023,
-0.038589123636484146,
-0.09471508860588074,
0.028497448191046715,
-0.0297714676707983,
0.057998716831207275,
-0.0056797899305820465,
-0.017988555133342743,
0.0188343096524477,
-0.0047640749253332615,
-0.0425899364054203,
-0.02287704311311245,
0.006330984644591808,
-0.03314046934247017,
0.009748514741659164,
-0.03577454760670662,
0.023742618039250374,
0.01800839975476265,
0.03528524935245514,
0.01959410309791565,
-0.02876729890704155,
-0.03220658376812935,
0.024027446284890175,
-0.008755357004702091,
-0.012740490958094597,
0.010881359688937664,
0.017427725717425346,
0.01818167045712471,
-0.021216196939349174,
0.015424171462655067,
-0.026063790544867516,
0.02835296094417572,
-0.024723218753933907,
-0.08259769529104233,
0.020174624398350716,
-0.037994515150785446,
0.028023790568113327,
0.047257911413908005,
-0.013319277204573154,
0.03477775305509567,
0.04444427043199539,
-0.013614294119179249,
-0.02237771265208721,
-0.060452479869127274,
0.09010148048400879,
-0.01155049167573452,
0.002457353984937072,
-0.034319598227739334,
0.027844388037919998,
-0.0007819351740181446,
0.0036393925547599792,
-0.05556020140647888,
-0.022005707025527954,
-0.06136731803417206,
-0.03801120072603226,
0.0626121237874031,
-0.014644824899733067,
0.007178892381489277,
0.0027529364451766014,
0.005430920049548149,
0.0055811433121562,
-0.04871586337685585,
-0.048196084797382355,
0.09304529428482056,
0.038671668618917465,
0.040074605494737625,
-0.0122274374589324,
-0.05675691366195679,
-0.027053413912653923,
-0.011253989301621914,
-0.017383266240358353,
-0.024430623278021812,
-0.008839498274028301,
-0.010907630436122417,
0.04910615459084511,
0.0037795037496834993,
0.000383495120331645,
0.013225406408309937,
0.073644258081913,
0.002120236400514841,
0.043050266802310944,
-0.022559212520718575,
0.028037438169121742,
-0.0035574426874518394,
-0.04087726026773453,
0.018386295065283775,
0.04944416880607605,
0.013814478181302547,
0.051876846700906754,
0.041724588721990585,
0.030401917174458504,
-0.06265251338481903,
-0.05948435887694359,
-0.00456389831379056,
-0.01343044638633728,
0.050679922103881836,
0.022165684029459953,
0.04589412361383438,
-0.03086758404970169,
0.052863460034132004,
-0.042741935700178146,
0.01205458678305149,
0.01575397700071335,
0.054761484265327454,
0.03998613357543945,
0.02687123790383339,
-0.048704594373703,
-0.07321713119745255,
0.0228411927819252,
-0.010759862139821053,
-0.040490228682756424,
0.04595864191651344,
-0.04989409074187279,
0.026275811716914177,
0.023537466302514076,
-0.024005327373743057,
-0.00679910508915782,
0.03130033612251282,
0.03992602601647377,
0.030238356441259384,
0.018299425020813942,
-0.02134156972169876,
0.019453689455986023,
0.016130469739437103,
-0.01456744596362114,
-0.06728040426969528,
-0.06749296933412552,
-0.0023635784164071083,
-0.018300890922546387,
0.014483870007097721,
0.009433521889150143,
-0.040053825825452805,
0.015828680247068405,
0.023259764537215233,
0.019267844036221504,
0.04014550894498825,
-0.008165951818227768,
0.04286041855812073,
-0.025209689512848854,
-0.02899360843002796,
0.05997413024306297,
-0.06197118014097214,
0.022210747003555298,
-0.04027295857667923,
-0.04452844709157944,
-0.009783240966498852,
0.009934227913618088,
-0.007901390083134174,
0.031481124460697174,
-0.022394198924303055,
0.02165931835770607,
-0.01749078556895256,
0.0036651177797466516,
0.005442822817713022,
0.04150970280170441,
0.06454791128635406,
0.011972957290709019,
-0.0014860890805721283,
0.042147234082221985,
-0.037936873733997345,
-0.030705194920301437,
-0.0008666522917337716,
-0.027721060439944267,
0.04506596922874451,
0.05521482229232788,
0.05025273188948631,
-0.046828221529722214,
-0.01652342826128006,
0.05674833804368973,
-0.0026937678921967745,
0.08461263030767441,
-0.012323501519858837,
0.030968474224209785,
0.01800195872783661,
0.00201997603289783,
-0.051912132650613785,
-0.004569572396576405,
0.004078459460288286,
0.04757687821984291,
0.00013033686263952404,
-0.012959258630871773,
0.06287889927625656,
-0.0013228697935119271,
-0.009105862118303776,
-0.018254078924655914,
0.047280408442020416,
-0.04950232058763504,
-0.05466192588210106,
0.008918154053390026,
-0.06748948991298676,
0.019439833238720894,
0.051675621420145035,
0.010819544084370136,
0.02793489396572113,
-0.031438156962394714,
-0.04641913250088692,
-0.022763917222619057,
-0.020532889291644096,
-0.045304153114557266,
0.024561401456594467,
0.0636959820985794,
0.032457996159791946,
-0.08774475008249283,
0.003354857675731182,
-0.005476746242493391,
0.029970921576023102,
0.0010211149929091334,
-0.006646298803389072,
-0.020205523818731308,
0.031868696212768555,
-0.051219694316387177,
-0.029285842552781105,
-0.010600056499242783,
-0.020653320476412773,
0.01743992045521736,
0.020039042457938194,
-0.00802414771169424,
0.0583311952650547,
0.04251062497496605,
0.007081660907715559,
0.015492359176278114,
-0.012159607373178005,
0.018948594108223915,
-0.05075722560286522,
-0.03762142360210419,
-0.007575370371341705,
0.005920948926359415,
-0.006560659967362881,
0.060006193816661835,
-0.005007632076740265,
0.013002892956137657,
0.06379430741071701,
0.0049607232213020325,
0.024374058470129967,
0.06066540628671646,
-0.021924100816249847,
-0.0192734245210886,
0.0069854347966611385,
-0.0499936006963253,
0.02727176807820797,
0.00537109375,
-0.029907500371336937,
-0.029699506238102913,
-0.028457704931497574,
-0.05228662118315697,
0.043165478855371475,
0.04466977342963219,
-0.033091820776462555,
0.015223314054310322,
0.08902225643396378,
0.006489182356745005,
-0.026172829791903496,
0.028322115540504456,
0.009596548043191433,
0.05242655426263809,
-0.06107987463474274,
0.025756897404789925,
0.022731447592377663,
-0.028520753607153893,
0.05305192619562149,
-0.019161270931363106,
-0.009512816555798054,
0.03423338383436203,
-0.008586326614022255,
-0.016057129949331284,
-0.018411988392472267,
-0.004835227504372597,
0.007412113714963198,
-0.04049346223473549,
-0.038382697850465775,
-0.042926255613565445,
0.013011704199016094,
-0.030590714886784554,
-0.002232267986983061,
0.0005159807624295354,
-0.02556876465678215,
-0.04786911606788635,
-0.006782310549169779,
-0.014639263041317463,
0.002771237399429083,
0.030870653688907623,
-0.02331761084496975,
-0.022541100159287453,
-0.02735537476837635,
-0.02520635351538658,
-0.005172098986804485,
0.058625463396310806,
-0.023187467828392982,
-0.013987262733280659,
0.06322051584720612,
0.013230018317699432,
-0.0058746361173689365,
0.03761124238371849,
0.06484097242355347,
-0.02956220880150795,
-0.05204251408576965,
0.0002604202018119395,
0.0020003628451377153,
-0.008861244656145573,
-0.01250452920794487,
-0.022395167499780655,
0.022156737744808197,
-0.04024132713675499
] |
<p>I'm programming a 1 dimensional physics simulator in python. How do I calculate the amount of time until two particle points that are traveling towards eachother collide? I am using the equation: </p>
<pre><code>time = (m2.pos - m1.pos) / (m1.velocity - m2.velocity).
</code></pre>
<p>You can assume m1 is always on the left, and m2 is always on the right. This equation works fine in my program if both points are traveling in the same direction at slightly different speeds, but when m1 has a positive velocity and m2 has a negative velocity, that gives the denominator of my equation a negative number which produces a negative amount of time until the next collision.</p>
|
g2456
|
[
0.03337396681308746,
0.02203168161213398,
0.015045770443975925,
-0.024743666872382164,
0.04632077366113663,
0.004403749480843544,
-0.016238871961832047,
-0.0092328991740942,
-0.05959909409284592,
0.010367889888584614,
-0.011926730163395405,
0.031229402869939804,
0.007291493471711874,
-0.023521576076745987,
0.044378649443387985,
-0.013137714006006718,
0.07453407347202301,
0.012543434277176857,
-0.024561036378145218,
0.07515743374824524,
0.02483518049120903,
-0.004484935663640499,
-0.0005321605131030083,
-0.04633322358131409,
-0.013106522150337696,
-0.05983452498912811,
-0.02846342697739601,
0.017277279868721962,
-0.04972141981124878,
0.0052288672886788845,
0.034636445343494415,
0.022491443902254105,
-0.006980279926210642,
-0.039470478892326355,
-0.06458023190498352,
-0.0691109299659729,
-0.014244853518903255,
-0.042644042521715164,
-0.005057915113866329,
-0.00395425409078598,
0.04766299948096275,
-0.06476098299026489,
0.016211988404393196,
0.009111681021749973,
0.04569648951292038,
-0.04278389737010002,
-0.007413334213197231,
-0.009493726305663586,
-0.05014671012759209,
0.006797119975090027,
-0.013696946203708649,
0.06779731065034866,
-0.04245099425315857,
-0.02045336924493313,
0.011403492651879787,
0.0761142373085022,
0.01258403155952692,
-0.07495837658643723,
0.05488201603293419,
0.026376767084002495,
0.0177200585603714,
0.03023671731352806,
-0.014383378438651562,
-0.0030129237566143274,
0.07022065669298172,
-0.012682964093983173,
-0.04772594943642616,
-0.00658914539963007,
-0.0005705457297153771,
0.015422813594341278,
-0.02697332762181759,
-0.026641778647899628,
-0.014690026640892029,
-0.024854786694049835,
-0.017999999225139618,
-0.010676732286810875,
0.02934313379228115,
-0.015289664268493652,
-0.009677307680249214,
0.028033165261149406,
-0.09570448100566864,
0.0288003571331501,
0.002931408118456602,
-0.10505923628807068,
0.00041330259409733117,
-0.021184109151363373,
0.02918134443461895,
0.03899646922945976,
-0.10364856570959091,
-0.03780342638492584,
-0.04451810568571091,
0.003963766619563103,
0.021945934742689133,
-0.0011635477421805263,
-0.0021498226560652256,
0.020915444940328598,
-0.04574744030833244,
0.06780558824539185,
-0.008120277896523476,
0.020072972401976585,
0.021925559267401695,
0.003786263754591346,
0.017697198316454887,
-0.02867814153432846,
0.03229735419154167,
-0.031230662018060684,
0.01591118797659874,
-0.006430579349398613,
-0.00005777453407063149,
-0.08044325560331345,
-0.022240834310650826,
-0.073456309735775,
-0.02716219611465931,
-0.05109379068017006,
0.002416354836896062,
-0.03173832222819328,
0.03702952712774277,
-0.002182592870667577,
0.027125177904963493,
0.06984972953796387,
-0.02993413433432579,
-0.014014966785907745,
-0.029854651540517807,
0.05421869829297066,
-0.0058525800704956055,
-0.02889140136539936,
0.0002696716401260346,
0.03839779272675514,
0.04160027951002121,
0.04656734690070152,
0.014946560375392437,
-0.02161000296473503,
0.019602254033088684,
0.030140480026602745,
-0.09910330921411514,
0.0421503409743309,
0.05492699518799782,
0.03667997196316719,
-0.02209131233394146,
0.04470301792025566,
0.02221038192510605,
-0.02832813560962677,
-0.014273205772042274,
-0.0026306048966944218,
-0.07335306704044342,
-0.0013491470599547029,
-0.014405586756765842,
-0.08878881484270096,
-0.014600208960473537,
0.03586898371577263,
-0.008941025473177433,
0.03369729220867157,
-0.013552922755479813,
-0.00873040221631527,
0.020894812420010567,
0.012992101721465588,
0.01592891477048397,
0.01315765269100666,
0.02114938758313656,
-0.044077783823013306,
0.05777166783809662,
-0.000559101055841893,
0.014002085663378239,
0.011814182624220848,
-0.057448860257864,
0.06238250434398651,
0.009727091528475285,
-0.010317295789718628,
-0.030832519754767418,
-0.03388843312859535,
-0.021656563505530357,
-0.06567339599132538,
0.01902833580970764,
-0.020348113030195236,
0.005578568670898676,
0.016823457553982735,
-0.030662791803479195,
-0.007531949318945408,
-0.030771739780902863,
0.028576189652085304,
0.0469537153840065,
-0.04510101303458214,
0.07872284948825836,
0.03734815865755081,
-0.0005256729782558978,
-0.03949642926454544,
-0.043071527034044266,
0.09121385961771011,
-0.07523266971111298,
-0.014795804396271706,
-0.024361740797758102,
-0.049075666815042496,
-0.036478541791439056,
-0.023274961858987808,
-0.020047161728143692,
-0.010260695591568947,
0.03176066651940346,
-0.021175498142838478,
-0.029197240248322487,
-0.057953186333179474,
-0.027016887441277504,
0.07015907764434814,
0.07056376338005066,
0.05550578236579895,
0.011237427592277527,
-0.04926866292953491,
-0.0032680213917046785,
0.002225013915449381,
-0.0008709443500265479,
0.03332483395934105,
-0.0008348250412382185,
0.029080640524625778,
-0.019249025732278824,
0.04386115074157715,
-0.02510412596166134,
-0.03501015529036522,
-0.039111047983169556,
0.014371739700436592,
-0.02740933932363987,
0.006408146116882563,
0.010275771841406822,
-0.027875734493136406,
0.03482583537697792,
-0.030331872403621674,
-0.011915141716599464,
0.02179952710866928,
-0.009441389702260494,
-0.031913693994283676,
-0.054502878338098526,
0.007898954674601555,
-0.025238174945116043,
0.09988238662481308,
-0.05709115043282509,
-0.04216652736067772,
0.0410032644867897,
-0.004332986660301685,
-0.010733211413025856,
0.056199781596660614,
0.011558176018297672,
-0.013762453570961952,
0.024128690361976624,
-0.018645914271473885,
0.0036099578719586134,
0.05762609466910362,
0.02845296822488308,
-0.08923476189374924,
0.04726266860961914,
-0.02666897512972355,
-0.04457712173461914,
0.04526130110025406,
-0.03340502455830574,
-0.022568359971046448,
-0.044603072106838226,
0.017336973920464516,
0.008404157124459743,
-0.026629455387592316,
0.02857472561299801,
0.018392464146018028,
-0.05422885715961456,
-0.06899998337030411,
0.026466796174645424,
-0.010071713477373123,
0.0053967940621078014,
0.012655938044190407,
-0.022223109379410744,
0.005102150607854128,
-0.030660392716526985,
0.03580601140856743,
0.022500019520521164,
0.012197449803352356,
0.02062493935227394,
-0.01267311628907919,
0.059217989444732666,
0.007387901656329632,
0.017643436789512634,
-0.05186979100108147,
0.053705669939517975,
-0.019677460193634033,
0.03629182279109955,
0.013461709022521973,
0.003615668509155512,
-0.021414369344711304,
0.009535381570458412,
0.04826747626066208,
0.05334032326936722,
-0.07534802705049515,
0.011505491100251675,
0.03748587518930435,
-0.04095935821533203,
-0.005251490045338869,
0.03828101232647896,
0.030612032860517502,
-0.004924222361296415,
-0.017117835581302643,
0.04916089400649071,
0.051023516803979874,
0.029091959819197655,
-0.00764518603682518,
0.05412031710147858,
0.0003210540453437716,
-0.011401399970054626,
-0.0029980316758155823,
-0.01532203983515501,
0.022902794182300568,
0.06791370362043381,
0.006850408855825663,
-0.00469750864431262,
-0.00014778500190004706,
-0.01090788934379816,
-0.03524349629878998,
-0.012414838187396526,
0.07188987731933594,
-0.001777500961907208,
-0.004701710306107998,
-0.0036118682473897934,
0.03963492438197136,
0.004259931854903698,
0.04367189481854439,
-0.0020044913981109858,
0.015045679174363613,
0.004695421550422907,
-0.0769578069448471,
0.04190363734960556,
0.01052289828658104,
0.0025856199208647013,
-0.005953931249678135,
-0.001729093841277063,
-0.0024953093379735947,
-0.038277819752693176,
0.0031860850285738707,
0.01094740442931652,
0.0067602056078612804,
0.013150067068636417,
-0.025658974424004555,
-0.01390516385436058,
-0.05499874800443649,
0.04472796246409416,
-0.0008315081940963864,
-0.010130857117474079,
0.011388602666556835,
-0.04069185256958008,
-0.011741653084754944,
-0.07058923691511154,
0.028582409024238586,
0.030599845573306084,
-0.071585513651371,
0.061084236949682236,
0.08435061573982239,
0.06226605921983719,
-0.03447796404361725,
0.03895305469632149,
0.01887512393295765,
-0.012401523999869823,
-0.02592974528670311,
-0.0002325062669115141,
0.028413092717528343,
-0.020363856106996536,
0.011643235571682453,
-0.0642257109284401,
0.0805620402097702,
-0.014173286035656929,
-0.021602792665362358,
-0.07927960902452469,
0.03152095526456833,
0.04072418436408043,
-0.031761299818754196,
-0.04626353085041046,
0.011101947166025639,
0.05883592367172241,
0.008478068746626377,
0.015324883162975311,
0.002526954049244523,
0.028293302282691002,
-0.0229792483150959,
0.015457149595022202,
-0.07142510265111923,
0.03358045965433121,
0.013573016971349716,
0.053910400718450546,
0.025564156472682953,
-0.003006585640832782,
-0.0012626709649339318,
0.008672843687236309,
0.019874121993780136,
-0.0015391980996355414,
0.02633177861571312,
-0.0023693563416600227,
-0.030626224353909492,
0.03400838375091553,
-0.06692010164260864,
0.06467533111572266,
-0.016638772562146187,
-0.03290606290102005,
0.0033773803152143955,
0.08430145680904388,
0.019949469715356827,
-0.032955773174762726,
0.010320533998310566,
-0.014729231595993042,
-0.04367867857217789,
0.01283318642526865,
0.027926528826355934,
-0.0106204217299819,
-0.01815602369606495,
-0.006065846886485815,
-0.029318347573280334,
0.04690602421760559,
0.045584116131067276,
-0.0037358507979661226,
0.029757602140307426,
-0.013365773484110832,
-0.0029777996242046356,
0.0028359070420265198,
-0.003068485064432025,
-0.01779564470052719,
-0.03158896416425705,
0.005072045139968395,
0.01311426516622305,
0.033086586743593216,
0.025475116446614265,
0.028192877769470215,
0.05442478880286217,
-0.0005370272556319833,
-0.062297433614730835,
-0.051882922649383545,
0.013824693858623505,
0.005114727653563023,
0.03827418386936188,
-0.03489893674850464,
-0.012673771940171719,
0.04139714315533638,
0.046918854117393494,
-0.03397418558597565,
0.018560176715254784,
-0.048796605318784714,
0.078497976064682,
0.05471552163362503,
0.04073002189397812,
0.03281641751527786,
0.04276464879512787,
-0.019795408472418785,
-0.02521376684308052,
0.001979515654966235,
-0.0359453521668911,
0.02536972053349018,
0.07529909908771515,
-0.028531445190310478,
-0.07753157615661621,
-0.026621917262673378,
-0.03997126594185829,
0.012701127678155899,
0.03652593493461609,
-0.0354456752538681,
-0.036258798092603683,
-0.06378135085105896,
0.02126132696866989,
-0.023002436384558678,
0.04332902655005455,
-0.01659505069255829,
-0.004614654928445816,
-0.026111997663974762,
0.03667133301496506,
-0.025047168135643005,
-0.04450602829456329,
-0.06169533357024193,
0.003708121133968234,
0.029605289921164513,
-0.010330023244023323,
-0.04230803996324539,
-0.009053351357579231,
-0.04333715885877609,
-0.015056480653584003,
0.002272301819175482,
0.009756081737577915,
-0.006997423712164164,
-0.010108883492648602,
-0.030087346211075783,
0.031315773725509644,
0.04366622120141983,
0.002154539804905653,
0.02973305433988571,
-0.015002727508544922,
-0.00975724682211876,
-0.03491828590631485,
0.004967212211340666,
0.02421724610030651,
-0.010579662397503853,
-0.005408220924437046,
0.06142352521419525,
-0.06988859921693802,
-0.00856429897248745,
-0.00657683564350009,
0.033292777836322784,
-0.02532564476132393,
-0.02708015777170658,
-0.013567009009420872,
-0.053945280611515045,
0.04013305902481079,
0.008848453871905804,
-0.01968131959438324,
-0.024621624499559402,
-0.06929845362901688,
-0.02512493170797825,
-0.024027111008763313,
0.001784655381925404,
0.02919398993253708,
0.02451537549495697,
-0.003951239865273237,
-0.012996653094887733,
-0.001222327584400773,
0.05476832017302513,
0.06034766882658005,
0.06147396191954613,
0.03161596134305,
-0.027977922931313515,
0.015782484784722328,
0.009989503771066666,
-0.018383145332336426,
-0.064023457467556,
-0.023006560280919075,
0.08458338677883148,
0.027402713894844055,
0.02694079838693142,
0.006198267452418804,
0.006120456848293543,
-0.018849270418286324,
-0.00853718537837267,
-0.03404678776860237,
-0.006221855524927378,
-0.035413872450590134,
0.004331337288022041,
-0.05281219631433487,
-0.04684212803840637,
0.028500424697995186,
-0.056339893490076065,
-0.045056331902742386,
-0.025560690090060234,
-0.007344439160078764,
0.04145627096295357,
-0.03801373764872551,
-0.02923429198563099,
0.05033048242330551,
0.019778400659561157,
0.06146044656634331,
-0.051984451711177826,
0.02616031840443611,
-0.03687293082475662,
0.010346776805818081,
0.0013329499633982778,
-0.07176840305328369,
-0.0059648724272847176,
0.015382031910121441,
0.044508401304483414,
-0.054918333888053894,
0.03785426542162895,
0.026899753138422966,
0.006276934873312712,
0.031047293916344643,
0.009586949832737446,
0.0018262878293171525,
0.0029233295936137438,
-0.07528127729892731,
-0.0025295233353972435,
0.03359655663371086,
-0.005806398577988148,
0.023647818714380264,
-0.02895749919116497,
0.005740337073802948,
0.028505969792604446,
0.03313067927956581,
0.022813519462943077,
-0.03307311609387398,
0.00712999701499939,
0.008598308078944683,
0.0628565326333046,
0.06796269118785858,
0.006118645891547203,
-0.0871318131685257,
-0.04323020204901695,
0.006274544168263674,
0.009667891077697277,
0.02785622701048851,
-0.01198782492429018,
-0.023482058197259903,
0.0027386248111724854,
0.036397986114025116,
0.03163590282201767,
-0.05551770702004433,
-0.00466185575351119,
0.02004292421042919,
0.015845799818634987,
-0.025225531309843063,
0.04684501141309738,
-0.05426770821213722,
-0.0025052267592400312,
-0.05940425768494606,
-0.04366322234272957,
-0.02030877023935318,
-0.013360017910599709,
0.04504265636205673,
0.00035155078512616456,
0.003644809825345874,
0.0035604487638920546,
0.01666068099439144,
-0.04502258449792862,
0.03124265931546688,
-0.08663950115442276,
0.03539697453379631,
0.045005857944488525,
0.0035505942068994045,
-0.0020200423896312714,
0.004678035620599985,
-0.013583870604634285,
0.0518459677696228,
0.009058352559804916,
0.04643435403704643,
0.01253068633377552,
0.019518552348017693,
0.014414066448807716,
-0.054629240185022354,
0.02717120386660099,
0.0006909184739924967,
-0.033365797251462936,
0.0003618671034928411,
0.024542421102523804,
0.006861519999802113,
-0.030937697738409042,
0.018214205279946327,
0.04062674567103386,
0.0035101252142339945,
0.03612780198454857,
-0.05163736641407013,
-0.027714839205145836,
0.06728898733854294,
-0.008660921826958656,
0.03184190392494202,
-0.022571779787540436,
0.02879834920167923,
0.014051317237317562,
0.08433067053556442,
0.04104366526007652,
-0.010199112817645073,
-0.01339361909776926,
0.010988375172019005,
-0.050256550312042236,
-0.032016340643167496,
0.04329710081219673,
0.029179073870182037,
-0.05578986927866936,
-0.02627357468008995,
-0.009048973210155964,
-0.01658678986132145,
0.015152725391089916,
0.021838445216417313,
-0.026696359738707542,
-0.04687902331352234,
0.013942831195890903,
-0.017579147592186928,
-0.004404271021485329,
0.05296587944030762,
-0.013191486708819866,
-0.0785001814365387,
-0.07150769978761673,
0.017351189628243446,
0.0146412942558527,
0.036856427788734436,
-0.02605641819536686,
0.009490236639976501,
0.035451509058475494,
-0.07787873595952988,
-0.03814578056335449,
0.008876954205334187,
-0.07362917810678482,
0.009280181489884853,
-0.009302285499870777,
0.019825149327516556,
0.0046671913005411625,
0.005384896416217089,
-0.02680996246635914,
-0.018682917580008507,
0.05882380157709122,
-0.03790204972028732,
-0.03648586571216583,
-0.012974587269127369,
0.007657933514565229,
0.035513438284397125,
-0.01943078637123108,
-0.027377255260944366,
0.00614346656948328,
-0.017682848498225212,
0.021362558007240295,
0.012539627961814404,
0.05965738743543625,
-0.03126849606633186,
0.024873895570635796,
-0.05979045853018761,
0.054436057806015015,
0.05951506644487381,
0.011446007527410984,
0.05440041422843933,
0.05886923149228096,
-0.0020465850830078125,
0.05562961474061012,
0.04700449854135513,
-0.04547770693898201,
0.011656519956886768,
0.009910172782838345,
-0.01661967858672142,
0.004952490795403719,
-0.03476288169622421,
-0.00449777115136385,
0.04529701545834541,
-0.011983923614025116,
0.007134998217225075,
-0.016724800691008568,
0.00026866316329687834,
-0.01664692349731922,
0.009627812542021275,
0.024851929396390915,
0.02003747783601284,
0.019693523645401,
-0.060206785798072815,
-0.03995056450366974,
-0.04232516884803772,
0.017576586455106735,
-0.05317206308245659,
-0.021439358592033386,
0.011340688914060593,
-0.0011883898405358195,
0.006015947554260492,
-0.01681690290570259,
0.026194848120212555,
0.0011504348367452621,
0.08998216688632965,
-0.012093807570636272,
0.019578857347369194,
-0.030149709433317184,
-0.00171712099108845,
-0.08091192692518234,
0.031325556337833405,
0.004174209199845791,
-0.04625380039215088,
0.01153365708887577,
-0.012332789599895477,
-0.0018584751524031162,
-0.01122654601931572,
0.030817797407507896,
0.08782020956277847,
0.06918591260910034,
-0.02118048071861267,
0.06041611358523369,
0.017338622361421585,
0.005878594238311052,
0.062104206532239914,
0.06479918956756592,
-0.06613189727067947,
0.004290912300348282,
0.0070234728045761585,
-0.07211623340845108,
-0.015930846333503723,
0.019367223605513573,
0.006280022673308849,
0.03172089159488678,
-0.015394248068332672,
0.011939805001020432,
-0.011451827362179756,
-0.03524359315633774,
-0.010179737582802773
] |
<p>I'm working my way through Griffith's "Introduction to Electrodynamics". In Ch. 10, gauge transformations are introduced. The author shows that, given any magnetic potential $\textbf{A}_0$ and electric potentials $V_0$, we can create a new set of equivalent magnetic and electric potentials given by:</p>
<p>$$
\textbf{A} = \textbf{A}_0 + \nabla\lambda \\
V = V_0 - \frac{\partial \lambda}{\partial t}
$$</p>
<p>These transformations are <strong>defined</strong> as a "gauge transformation". The author then introduces two of these transformations, the coloumb and lorentz gauge, defined respectively as:</p>
<p>$$
\nabla \cdot \textbf{A} = 0 \\
\nabla \cdot \textbf{A}= -\mu_0\epsilon_0\frac{\partial V}{\partial t}
$$</p>
<p>This is where I am confused. I do not understand how picking the divergence of $\textbf{A}$ to be either of these two values actually constitutes a gauge transformation, as in it meets the conditions of the top two equations. How do we know that such a $\lambda$ even exists for setting the divergence of $\textbf{A}$ to either of these values. Can someone convince me that such a function exists for either transformation, or somehow show me that these transformations are indeed "gauge transformations" as they are defined above.</p>
|
g2457
|
[
0.026728222146630287,
-0.03783859685063362,
-0.01981258951127529,
-0.08482838422060013,
0.09152553975582123,
0.00908986572176218,
0.022397661581635475,
0.01737755350768566,
-0.021482957527041435,
-0.012029697187244892,
-0.06489609181880951,
-0.007513377349823713,
0.04763931408524513,
0.007176035549491644,
0.05233364179730415,
-0.007329075131565332,
0.06268486380577087,
-0.017655735835433006,
0.05187955126166344,
-0.06563913822174072,
0.045723773539066315,
0.06567162275314331,
0.035893213003873825,
-0.10435358434915543,
0.027742551639676094,
-0.07577609270811081,
0.020474882796406746,
0.01338503323495388,
0.005110932048410177,
0.009296673350036144,
0.0004468451370485127,
0.0911397635936737,
0.05399526655673981,
0.013905501924455166,
-0.0027962406165897846,
-0.004621612839400768,
0.08481751382350922,
0.062456730753183365,
0.020204097032546997,
0.01700465753674507,
-0.020669059827923775,
0.019789516925811768,
0.01675499603152275,
-0.016606932505965233,
0.02150784805417061,
-0.043765533715486526,
-0.016094012185931206,
-0.024069102481007576,
-0.011054476723074913,
0.00632068607956171,
0.03217681869864464,
-0.01044063363224268,
0.10460914671421051,
-0.04254651442170143,
-0.0015412862412631512,
0.01145454216748476,
0.04531456530094147,
-0.010131248272955418,
0.03253384307026863,
0.0007499459316022694,
0.011669128201901913,
-0.03994232788681984,
0.033145248889923096,
-0.020947536453604698,
0.0022677236702293158,
-0.0007278681732714176,
-0.004786081146448851,
-0.03506310284137726,
-0.01741076447069645,
-0.03421054407954216,
0.004973349627107382,
-0.04464162886142731,
0.017098842188715935,
0.02664492279291153,
-0.004891586489975452,
-0.0026884754188358784,
0.03468955680727959,
-0.05205019563436508,
0.046980056911706924,
-0.036774974316358566,
-0.0240566935390234,
-0.01644345000386238,
-0.03417690843343735,
0.00015186594100669026,
0.045147355645895004,
-0.03167233243584633,
0.006459295284003019,
0.022533103823661804,
-0.010849417187273502,
0.02630019746720791,
-0.028698913753032684,
-0.02623828500509262,
0.01568693481385708,
0.004848071839660406,
-0.029587583616375923,
0.013593439012765884,
0.02768229879438877,
0.008629663847386837,
-0.01967630349099636,
-0.008719771169126034,
-0.011104381643235683,
0.027217058464884758,
-0.034998565912246704,
0.03269026800990105,
-0.03834570199251175,
-0.011543034575879574,
0.05220514535903931,
-0.004467774648219347,
0.0014685511123389006,
-0.028906047344207764,
-0.05425895377993584,
0.004727998748421669,
-0.03203772008419037,
-0.045044105499982834,
-0.05326051265001297,
0.00719104427844286,
0.0356036052107811,
0.008765175938606262,
-0.046480730175971985,
0.06615688651800156,
0.0169405248016119,
0.016493339091539383,
0.034308772534132004,
0.02990388497710228,
-0.001633075880818069,
-0.031160788610577583,
-0.05667373538017273,
0.0537891611456871,
0.06760867685079575,
-0.033837832510471344,
0.031703148037195206,
0.003922068979591131,
0.03694557026028633,
-0.012816330417990685,
0.002814191160723567,
-0.0016857850132510066,
0.019691742956638336,
0.036774735897779465,
-0.0207830760627985,
0.05952458083629608,
0.006513751577585936,
-0.07125208526849747,
0.020236153155565262,
-0.006665204651653767,
-0.005239341873675585,
0.0525224544107914,
-0.05460265278816223,
-0.00029556776280514896,
0.037711236625909805,
-0.048190537840127945,
0.07176250219345093,
0.03613239899277687,
0.03879452124238014,
0.0008273506537079811,
-0.0225084125995636,
-0.011242983862757683,
0.06219682842493057,
0.0010668830946087837,
0.027667546644806862,
0.030380118638277054,
0.055718328803777695,
-0.09114361554384232,
0.011066420003771782,
0.027844300493597984,
-0.004225604701787233,
0.000557184626813978,
-0.00011035976058337837,
-0.013922257348895073,
0.00960899144411087,
-0.04684915021061897,
-0.05411405488848686,
0.03765545412898064,
0.05438924953341484,
0.028479887172579765,
0.003376152366399765,
0.0775797888636589,
0.0023138043470680714,
-0.02106771059334278,
-0.06868168711662292,
0.00764751061797142,
-0.014205974526703358,
0.008662999607622623,
0.039631202816963196,
-0.027511201798915863,
-0.010653181932866573,
-0.05933074653148651,
-0.055273447185754776,
0.008633441291749477,
-0.039981093257665634,
0.0031944101210683584,
-0.017721351236104965,
-0.030737200751900673,
-0.021670067682862282,
-0.0013724990421906114,
-0.0029404559172689915,
-0.0070635974407196045,
0.00029246232588775456,
-0.003302582772448659,
0.004919673781841993,
0.013296247459948063,
0.02467571757733822,
0.07726918160915375,
0.0287113469094038,
0.00883793830871582,
-0.007002125959843397,
0.04286542534828186,
0.008388074114918709,
-0.011456340551376343,
0.027719771489501,
0.010785192251205444,
0.013717038556933403,
-0.03838629275560379,
-0.007925462909042835,
-0.060498788952827454,
-0.0506395623087883,
-0.05070086196064949,
-0.014574683271348476,
0.08732468634843826,
-0.058033354580402374,
0.012633305042982101,
0.02375718764960766,
-0.0535348616540432,
0.013736105524003506,
0.023589584976434708,
-0.08083803206682205,
-0.0009982031770050526,
0.009516884572803974,
-0.010990984737873077,
-0.018473336473107338,
-0.035267435014247894,
0.012189212255179882,
0.032514650374650955,
0.01853295788168907,
-0.027720347046852112,
0.03645341098308563,
0.055692266672849655,
-0.019283808767795563,
-0.021207405254244804,
0.020632483065128326,
-0.05039120838046074,
0.02826080471277237,
-0.04975767806172371,
0.049024470150470734,
0.027099113911390305,
0.03358763828873634,
-0.023162594065070152,
0.04751777648925781,
0.02657593972980976,
-0.017355352640151978,
0.052148930728435516,
0.04225754737854004,
-0.03219114989042282,
-0.006504545453935862,
0.06418924778699875,
-0.04332851245999336,
-0.02194468304514885,
0.034820545464754105,
0.05178305134177208,
-0.08090505748987198,
-0.023916197940707207,
-0.034512847661972046,
-0.019927196204662323,
0.024830255657434464,
0.07508145272731781,
-0.06744346767663956,
0.008323232643306255,
-0.011973784305155277,
-0.005062556359916925,
-0.007753144018352032,
-0.05845297873020172,
-0.04286679998040199,
0.002828626660630107,
0.05831001326441765,
0.012510650791227818,
-0.0011786437826231122,
-0.050728656351566315,
0.003791865659877658,
-0.026602016761898994,
0.022756077349185944,
-0.05041811242699623,
-0.023442568257451057,
0.0190716702491045,
-0.01784284971654415,
0.03833913058042526,
-0.007310993038117886,
-0.03346105292439461,
0.007547762710601091,
-0.03606932610273361,
0.0157227274030447,
0.03307197615504265,
-0.019859010353684425,
-0.024339288473129272,
0.06640034168958664,
-0.044929388910532,
-0.00677320035174489,
0.006964013446122408,
0.01027309987694025,
-0.07391611486673355,
-0.047279905527830124,
-0.053085554391145706,
0.03219730779528618,
0.010078920982778072,
-0.06534817069768906,
0.06302909553050995,
0.05469923093914986,
-0.004729884210973978,
-0.020589200779795647,
-0.002698277123272419,
-0.03887147083878517,
0.02454567141830921,
-0.06378412991762161,
0.06282879412174225,
0.04674684256315231,
0.028853077441453934,
0.028346581384539604,
0.002774556865915656,
0.02990143559873104,
-0.03597641363739967,
0.04046458378434181,
0.006707808934152126,
-0.014406313188374043,
-0.04372971132397652,
0.02137666568160057,
-0.006141915451735258,
0.07739437371492386,
-0.06310493499040604,
0.006960767321288586,
-0.03242764249444008,
-0.005382172763347626,
-0.0036822098772972822,
0.013184336014091969,
0.010394513607025146,
0.009518418461084366,
0.0005573545931838453,
-0.04715660959482193,
-0.016092538833618164,
0.00379016250371933,
0.029947742819786072,
0.02236919291317463,
-0.05642101168632507,
-0.031849704682826996,
-0.07648635655641556,
-0.05613354966044426,
0.07603663206100464,
-0.0007106524426490068,
-0.013448130339384079,
0.01413224171847105,
-0.04076093062758446,
0.03222999721765518,
-0.035299934446811676,
-0.02616131491959095,
-0.0027432667557150126,
0.08460969477891922,
0.017807522788643837,
0.03966844081878662,
-0.05735863372683525,
0.01568426750600338,
-0.011226551607251167,
-0.003961731214076281,
0.039673108607530594,
0.05956219509243965,
-0.014229020103812218,
-0.013550576753914356,
-0.0377543605864048,
-0.024030636996030807,
0.0424770824611187,
0.01881508342921734,
0.02423364855349064,
0.00752351013943553,
-0.025479018688201904,
0.08174887299537659,
-0.022522760555148125,
-0.0428481362760067,
0.011422784999012947,
0.006292042322456837,
-0.0883636474609375,
0.035287655889987946,
0.06294100731611252,
-0.004715397022664547,
0.029675908386707306,
0.067599356174469,
0.00010129460133612156,
0.07369842380285263,
0.015700245276093483,
0.02467246726155281,
-0.0021274853497743607,
-0.0069329082034528255,
0.029458852484822273,
0.02068008854985237,
-0.04382381588220596,
0.03798328712582588,
0.04542063921689987,
-0.026802722364664078,
0.004478008486330509,
-0.04529839754104614,
-0.0017456408822908998,
0.019673962146043777,
-0.006454413291066885,
0.008197110146284103,
0.03339942917227745,
-0.03577706962823868,
0.037391986697912216,
-0.06913317739963531,
-0.01919872872531414,
-0.02322099171578884,
-0.032238226383924484,
0.040393177419900894,
-0.055122144520282745,
0.027195744216442108,
-0.01846150867640972,
0.04285789281129837,
-0.0795620009303093,
0.02970941923558712,
-0.05401894450187683,
0.01123566273599863,
0.011141253635287285,
-0.04521811380982399,
-0.02389923855662346,
0.040811073035001755,
-0.05815056711435318,
-0.019071362912654877,
0.024648919701576233,
0.021253783255815506,
0.010294348001480103,
0.005427929572761059,
0.0919857993721962,
0.03805651143193245,
0.055880866944789886,
0.028902243822813034,
-0.024283654987812042,
0.0026127661112695932,
0.025660322979092598,
-0.0435858815908432,
0.06823072582483292,
-0.037134695798158646,
0.011782044544816017,
-0.062077902257442474,
0.009675565175712109,
-0.02699674852192402,
0.027012895792722702,
0.05746488645672798,
-0.047519050538539886,
0.00911112129688263,
-0.018769143149256706,
0.00944850780069828,
-0.015157056972384453,
-0.07083211839199066,
-0.017225395888090134,
0.019619086757302284,
-0.021959148347377777,
-0.03812098503112793,
0.030806411057710648,
-0.019162891432642937,
0.015874071046710014,
-0.028776319697499275,
-0.0005986245232634246,
0.06632265448570251,
-0.008411445654928684,
0.06799519062042236,
-0.0036179786548018456,
-0.006117314100265503,
-0.024355025961995125,
0.025386868044734,
-0.00590317789465189,
0.02608480490744114,
0.025655975565314293,
-0.06410234421491623,
0.02344358153641224,
-0.0734538733959198,
-0.031076529994606972,
0.027138780802488327,
-0.019101768732070923,
-0.01795005239546299,
-0.0365026481449604,
0.0154702914878726,
0.03366949409246445,
0.04656960442662239,
-0.038568075746297836,
-0.0377800315618515,
-0.017390282824635506,
-0.0603579618036747,
0.0056264144368469715,
0.00926876999437809,
-0.00789174996316433,
-0.07644566893577576,
0.03018445149064064,
-0.029836922883987427,
-0.023392707109451294,
-0.04984988272190094,
-0.01842365600168705,
-0.01739973947405815,
0.03944668546319008,
0.07695621252059937,
-0.010291347280144691,
-0.003971402067691088,
0.025712545961141586,
-0.008164855651557446,
-0.007540068123489618,
0.010217664763331413,
-0.014661033637821674,
-0.04699072614312172,
0.03120555728673935,
0.00921105220913887,
-0.03404903784394264,
-0.00373608386144042,
0.00028262712294235826,
0.05238183215260506,
0.022699840366840363,
-0.012582169845700264,
0.011372324079275131,
-0.044848546385765076,
0.014891887083649635,
0.014392887242138386,
0.010228370316326618,
0.054213836789131165,
0.003750941250473261,
-0.05434281751513481,
-0.004346117377281189,
-0.02785579487681389,
-0.09029388427734375,
-0.0006382623105309904,
0.025471072643995285,
0.013469273224473,
-0.09698755294084549,
0.027626577764749527,
0.033587295562028885,
-0.0398491807281971,
-0.061503902077674866,
-0.010082555003464222,
0.04757245257496834,
0.00797263439744711,
0.022714883089065552,
-0.02037893608212471,
0.019162531942129135,
0.03812360018491745,
-0.023857474327087402,
-0.00278663937933743,
0.012867787852883339,
-0.028119763359427452,
-0.01880231872200966,
0.032354097813367844,
0.019671272486448288,
-0.01636122725903988,
0.025467121973633766,
-0.07120483368635178,
0.01557216141372919,
0.02406936138868332,
0.0010763671016320586,
-0.005269346293061972,
-0.0031891686376184225,
-0.05302664265036583,
0.02000384032726288,
-0.022078385576605797,
-0.009318993426859379,
-0.009580593556165695,
-0.015762344002723694,
0.047688212245702744,
-0.026539266109466553,
-0.03715812414884567,
-0.024853909388184547,
0.02901950292289257,
-0.005662479437887669,
-0.0035237593110650778,
-0.0010134842013940215,
-0.044211726635694504,
-0.04602089151740074,
0.012878776527941227,
0.00442815525457263,
0.07203513383865356,
0.037487372756004333,
-0.027914149686694145,
0.009324881248176098,
-0.03628741204738617,
-0.006887512747198343,
-0.007601919583976269,
-0.010183941572904587,
-0.01328600849956274,
-0.06317155808210373,
0.048643808811903,
-0.03798931464552879,
0.01794486679136753,
-0.005974306259304285,
0.0013379662996158004,
-0.04462483897805214,
-0.04840654507279396,
0.04553170129656792,
-0.06130705773830414,
-0.04648686200380325,
-0.012137886136770248,
0.018226496875286102,
-0.028437931090593338,
0.00034989675623364747,
-0.01108457613736391,
0.00027457188116386533,
0.055044710636138916,
0.005559381563216448,
-0.018713735044002533,
0.021481383591890335,
0.02454323321580887,
0.008131406269967556,
0.03268716484308243,
0.02675650641322136,
0.0032230704091489315,
0.006195444148033857,
0.04476892203092575,
0.02911607176065445,
-0.08149906247854233,
0.026181254535913467,
0.04496823996305466,
-0.020012004300951958,
0.04026120901107788,
0.008028998039662838,
-0.0637475997209549,
-0.04588751867413521,
0.048119716346263885,
0.024074604734778404,
-0.08190475404262543,
-0.019150538370013237,
0.004946564789861441,
0.07952041923999786,
0.05269847810268402,
-0.06141410395503044,
0.027830205857753754,
-0.02963307686150074,
0.004817404318600893,
0.030838163569569588,
-0.021312497556209564,
0.05913408473134041,
0.0022879301104694605,
-0.005913706496357918,
-0.0045965733006596565,
-0.012035544030368328,
-0.043253347277641296,
0.007440377026796341,
-0.03054751642048359,
0.014920171350240707,
0.022572342306375504,
-0.0008535351371392608,
0.025002771988511086,
0.01607280783355236,
-0.030150076374411583,
-0.02724039927124977,
0.06712564080953598,
-0.03131774440407753,
0.0025125842075794935,
-0.017253195866942406,
-0.0013662182027474046,
-0.05230210721492767,
-0.06728479266166687,
0.07987285405397415,
-0.014338620007038116,
0.03350324556231499,
-0.036109209060668945,
0.000016281503121717833,
0.014731579460203648,
0.03264963999390602,
-0.012838071212172508,
0.07745304703712463,
-0.037556134164333344,
-0.05296529084444046,
0.03181077167391777,
-0.03063349425792694,
-0.02529744990170002,
-0.004109796602278948,
0.01919463835656643,
0.04036673530936241,
-0.0032286669593304396,
-0.032653678208589554,
-0.0021801849361509085,
-0.026247700676321983,
-0.0020205967593938112,
-0.02214413322508335,
0.002893896773457527,
0.010463579557836056,
0.010540062561631203,
0.03636738285422325,
-0.021958276629447937,
0.08250268548727036,
-0.029848551377654076,
-0.03398873284459114,
-0.058159347623586655,
0.02510618045926094,
0.0049345605075359344,
-0.012110143899917603,
-0.010132154449820518,
-0.000627413101028651,
-0.04728579893708229,
0.02010146714746952,
0.03256653621792793,
-0.019777478650212288,
0.022215252742171288,
-0.02456015907227993,
0.020819298923015594,
0.023848220705986023,
-0.03995398059487343,
-0.013136650435626507,
-0.04352173954248428,
0.0377030074596405,
0.02630402147769928,
-0.009411226026713848,
0.03186939284205437,
-0.0125266807153821,
-0.03364535793662071,
-0.010223929770290852,
-0.019387314096093178,
0.056303296238183975,
-0.018611539155244827,
-0.03409423679113388,
-0.015393933281302452,
0.012637781910598278,
-0.012256894260644913,
0.03943447768688202,
0.06607913970947266,
-0.013888516463339329,
0.06449226289987564,
0.03770171478390694,
0.0019158560317009687,
0.028224395588040352,
0.025548791512846947,
0.014221795834600925,
0.0036155858542770147,
-0.03915393725037575,
0.007417164742946625,
-0.0494513213634491,
-0.013083689846098423,
-0.0008136926335282624,
0.02045837603509426,
-0.004138551186770201,
-0.0412287563085556,
-0.012431212700903416,
-0.04454216733574867,
-0.005109231919050217,
-0.04424924775958061,
-0.0034191072918474674,
-0.0024574908893555403,
-0.009519265033304691,
0.01732753776013851,
-0.03671400994062424,
-0.0014688209630548954,
0.0027526458725333214,
-0.0006913704564794898,
-0.07476568967103958,
-0.002420038916170597,
0.04435259476304054,
-0.04161585867404938,
0.03209811821579933,
-0.048708297312259674,
0.08656906336545944,
-0.03787969797849655,
-0.01728466898202896,
0.014033027924597263,
0.005948483478277922,
-0.008506662212312222,
0.05437808111310005,
-0.014935890212655067,
-0.019334789365530014,
0.001036550384014845,
0.07652633637189865,
0.07000980526208878,
0.021390050649642944,
-0.01733749732375145,
-0.012012230232357979,
0.039853647351264954,
0.01457127369940281,
-0.02983211912214756,
-0.021304765716195107,
-0.05612540245056152,
0.05960782244801521
] |
<p>There are known formulae relating a capacitor's voltage and current in its classic form (battery, wires, a capacitor circuit), but what if we had a charged plate (-ve), then we put on one of its surfaces a dielectric, then we put another plate (neutral, connected to the ground)? </p>
<p>Technically, this is a capacitor (2 differently charged plates separated by a dielectric). The other plate will be +ve charged (like charging by induction) and a current will flow in the wire connecting the second plate to the ground. If I wanted to calculate this current, should I use the same formulae or will they change because the voltage is changing only on one plate and the second plate will reach a equal and opposite voltage pretty quickly?</p>
|
g2458
|
[
0.05133967101573944,
0.016356300562620163,
-0.0043952008709311485,
-0.0014042466646060348,
0.04218249395489693,
0.025378722697496414,
0.02940261736512184,
-0.01082282979041338,
-0.07269775122404099,
-0.015552612952888012,
-0.06085425242781639,
0.09411505609750748,
0.005624399986118078,
0.03567419573664665,
0.02227158658206463,
0.00011601185542531312,
0.04984138533473015,
-0.034796733409166336,
0.00961293000727892,
0.06296935677528381,
0.01639026775956154,
-0.013886342756450176,
0.008648790419101715,
-0.0198831669986248,
-0.08139916509389877,
-0.03967253118753433,
-0.06455780565738678,
0.03174760565161705,
-0.03790368139743805,
-0.02456112951040268,
0.008951405994594097,
0.06033680960536003,
0.078236423432827,
0.0164994727820158,
-0.06364916265010834,
0.0019312312360852957,
0.02848091907799244,
0.05954110622406006,
-0.0004937057965435088,
-0.04367302358150482,
0.040736909955739975,
0.06731431186199188,
0.013190695084631443,
0.039944980293512344,
-0.00927211344242096,
-0.09399932622909546,
-0.04507647827267647,
-0.07475318014621735,
-0.037529997527599335,
-0.03876103088259697,
-0.0638681948184967,
0.005776971112936735,
0.0006556446896865964,
0.010350572876632214,
-0.02868948131799698,
-0.011523428373038769,
0.025321630761027336,
-0.025299184024333954,
0.017985166981816292,
0.05004258453845978,
0.006227596662938595,
-0.014600077643990517,
0.00832726527005434,
-0.007276980206370354,
0.03258184343576431,
-0.0021371871698647738,
-0.005308591295033693,
0.0011261150939390063,
0.04512142017483711,
0.055591560900211334,
-0.047398388385772705,
-0.041127126663923264,
0.021384522318840027,
-0.03124542348086834,
0.03676183894276619,
-0.0011558817932382226,
0.05319357290863991,
-0.005174942780286074,
0.028085503727197647,
-0.0454493910074234,
-0.03897619619965553,
0.0021999285090714693,
0.049010492861270905,
0.020302878692746162,
0.028423067182302475,
-0.014566438272595406,
0.010991467162966728,
0.016969753429293633,
-0.043471116572618484,
0.006874619051814079,
-0.02826547808945179,
-0.04012313485145569,
0.037803858518600464,
-0.022310640662908554,
-0.04844529554247856,
-0.05637052282691002,
-0.009777544066309929,
0.026208840310573578,
0.006173223722726107,
0.009469806216657162,
-0.04402242973446846,
0.024480022490024567,
0.0022632135078310966,
0.005822304170578718,
-0.04114282876253128,
0.01828497275710106,
0.10301580280065536,
0.002802665578201413,
-0.022882698103785515,
-0.062120333313941956,
-0.005776023957878351,
-0.09138723462820053,
-0.005203742068260908,
0.01812799647450447,
-0.03284086659550667,
-0.03514391556382179,
-0.006474403664469719,
-0.05872659757733345,
0.039269305765628815,
0.04672228917479515,
0.03200588747859001,
0.009953265078365803,
0.014499408192932606,
0.03139467164874077,
0.028626222163438797,
-0.01798180863261223,
0.008358687162399292,
0.04405190423130989,
0.04212510958313942,
-0.0064488002099096775,
0.021410752087831497,
-0.04279650002717972,
0.014991119503974915,
0.015323844738304615,
0.028772518038749695,
-0.020570307970046997,
0.02717486210167408,
0.010831763967871666,
-0.004690299741923809,
-0.02612566575407982,
0.05695227533578873,
-0.05650554969906807,
-0.038399726152420044,
0.024839425459504128,
-0.001924279611557722,
0.05159352347254753,
-0.05137079581618309,
-0.04820764437317848,
0.047965988516807556,
0.02105732448399067,
0.03067702054977417,
0.06955097615718842,
0.022300930693745613,
0.005930550862103701,
0.05066199600696564,
0.04524170607328415,
0.04507442191243172,
0.014162666164338589,
0.03600200638175011,
-0.038190629333257675,
0.012866129167377949,
-0.017030321061611176,
0.018211346119642258,
-0.0363333486020565,
-0.038609668612480164,
0.0068415869027376175,
0.0008295804727822542,
0.012123196385800838,
-0.024724995717406273,
-0.031802140176296234,
0.0580921471118927,
-0.024892538785934448,
-0.026490118354558945,
0.029300818219780922,
0.03789697214961052,
0.00011244566849200055,
0.03587685897946358,
0.048474568873643875,
0.03208094835281372,
0.03167390078306198,
-0.06099290773272514,
0.01611967571079731,
-0.030871039256453514,
-0.021306421607732773,
0.009960874915122986,
-0.01548816729336977,
-0.0002356029290240258,
-0.009313737042248249,
-0.05115903168916702,
-0.005343547556549311,
-0.0845712274312973,
0.018617356196045876,
0.035279326140880585,
0.07727925479412079,
-0.06554099917411804,
-0.012817896902561188,
0.0294819213449955,
0.001720576430670917,
0.010441433638334274,
-0.008777995593845844,
-0.027118828147649765,
0.06779178231954575,
0.07078640162944794,
0.01455273199826479,
0.0146229462698102,
0.03063945658504963,
0.014431102201342583,
-0.06005600839853287,
0.06381457298994064,
-0.005825493950396776,
0.017528587952256203,
0.046328045427799225,
-0.010667888447642326,
0.020614322274923325,
0.0032035999465733767,
-0.03876921534538269,
-0.036980461329221725,
-0.0026494557969272137,
-0.06943356990814209,
-0.02348227985203266,
-0.0017475602217018604,
-0.04946927726268768,
0.05490920692682266,
-0.03876650333404541,
-0.05244491994380951,
-0.009722135961055756,
0.0006716540083289146,
-0.028553221374750137,
-0.01877831481397152,
-0.020346829667687416,
-0.02568347193300724,
-0.01537715457379818,
-0.03905615583062172,
0.005457494407892227,
-0.02288220450282097,
0.08284406363964081,
-0.026132190600037575,
-0.021481133997440338,
0.036228008568286896,
-0.022820886224508286,
0.021422401070594788,
-0.06583848595619202,
0.024054456502199173,
0.03306501358747482,
-0.03565787896513939,
-0.018742267042398453,
-0.003978083375841379,
0.019785689190030098,
-0.04734285920858383,
0.04422643408179283,
-0.0008790189167484641,
-0.05376836284995079,
-0.07479093223810196,
0.06450492888689041,
-0.02833697386085987,
0.006905896123498678,
-0.029033303260803223,
0.021391848102211952,
-0.006304625421762466,
-0.02076909877359867,
0.007122201379388571,
-0.035422611981630325,
-0.04116469621658325,
0.05678403750061989,
-0.03224220499396324,
0.010366040281951427,
-0.0029363511130213737,
0.022350283339619637,
0.04145171493291855,
0.0043764361180365086,
0.023945126682519913,
0.03440447896718979,
0.03020518086850643,
-0.01356765441596508,
0.0003895857953466475,
-0.043424297124147415,
0.01547673624008894,
-0.024910323321819305,
-0.013306655921041965,
-0.016033712774515152,
0.008001129142940044,
0.005697239656001329,
-0.0649041160941124,
-0.010457964614033699,
0.0307597815990448,
-0.04826756566762924,
0.04397795721888542,
-0.040256988257169724,
-0.018469760194420815,
0.03238906338810921,
-0.030510662123560905,
0.021399836987257004,
0.07084594666957855,
-0.05593939870595932,
0.030284997075796127,
0.0184380691498518,
0.10951428860425949,
-0.005951229948550463,
-0.04249373823404312,
0.0378718264400959,
-0.013645939528942108,
0.006175051908940077,
-0.021359426900744438,
-0.01576855219900608,
0.04524734988808632,
0.08647539466619492,
0.01828310452401638,
-0.056580327451229095,
0.0919756293296814,
0.002685902174562216,
-0.03411560505628586,
0.030290167778730392,
0.003096196101978421,
-0.03955309838056564,
-0.02972692996263504,
-0.024018442258238792,
0.015239755623042583,
-0.029343625530600548,
-0.021283354610204697,
-0.0008477283990941942,
-0.03940235823392868,
-0.06486301869153976,
0.042973846197128296,
0.060487084090709686,
-0.006927539594471455,
0.04844256490468979,
-0.05581143498420715,
0.05162803456187248,
-0.028458278626203537,
-0.01941814459860325,
-0.004436000715941191,
0.05736337974667549,
-0.026637230068445206,
-0.005212611053138971,
0.02378358505666256,
-0.026117274537682533,
0.07130395621061325,
0.027568647637963295,
0.002163674682378769,
0.023131251335144043,
-0.006334835663437843,
-0.02188490517437458,
-0.030078064650297165,
-0.06246190890669823,
-0.012791751883924007,
-0.03767998144030571,
0.030827369540929794,
0.020582668483257294,
-0.049371786415576935,
-0.05586394667625427,
0.06765967607498169,
-0.026111489161849022,
-0.00008746392995817587,
0.03015999309718609,
-0.05220641568303108,
0.023944590240716934,
-0.026500122621655464,
0.07353191077709198,
-0.018576864153146744,
0.0458831824362278,
0.01600392535328865,
-0.0496879518032074,
0.037866830825805664,
0.02232467010617256,
0.020369717851281166,
-0.0338870994746685,
-0.02001127228140831,
0.05419057980179787,
-0.0697251632809639,
-0.07445047050714493,
-0.007980061694979668,
0.005213259253650904,
0.023310061544179916,
0.006376394536346197,
-0.01690284162759781,
-0.011468336917459965,
-0.012442341074347496,
0.03867201879620552,
-0.03765641152858734,
0.07305150479078293,
-0.01334848441183567,
-0.00878820288926363,
-0.0036386344581842422,
-0.007428988814353943,
0.01909375749528408,
-0.025763772428035736,
-0.01457966212183237,
0.06095509231090546,
0.010424175299704075,
-0.010847846046090126,
0.00725212087854743,
0.000568223069421947,
-0.03962407261133194,
-0.008497870527207851,
-0.006334535777568817,
-0.02544032409787178,
-0.028772834688425064,
-0.033028509467840195,
0.03573194891214371,
0.004672449082136154,
0.02548755519092083,
-0.030809039250016212,
0.0022234958596527576,
0.006221461575478315,
0.001892419415526092,
-0.02724156714975834,
0.0722748190164566,
-0.05588698014616966,
0.04914899915456772,
-0.023900864645838737,
-0.02393905259668827,
-0.03812963515520096,
0.016097258776426315,
-0.03798196092247963,
0.026980390772223473,
-0.0010984924156218767,
0.034755051136016846,
0.019196288660168648,
0.05490679666399956,
0.03777763247489929,
-0.006661533378064632,
-0.0050147464498877525,
-0.008290243335068226,
-0.03139925003051758,
0.014742569997906685,
-0.013684204779565334,
0.07807403057813644,
-0.06299972534179688,
0.033897336572408676,
0.0013900066260248423,
-0.004751462489366531,
0.038626886904239655,
-0.05797766149044037,
-0.035429053008556366,
-0.03460937738418579,
0.059887900948524475,
-0.033032990992069244,
0.06105571612715721,
-0.04027427360415459,
0.030250126495957375,
0.08214382827281952,
-0.020503055304288864,
0.00033388016163371503,
-0.03615625575184822,
0.0026208169292658567,
0.04944849759340286,
-0.08740352839231491,
-0.019495181739330292,
0.010578500106930733,
-0.054254233837127686,
-0.03984649106860161,
0.012273162603378296,
0.024923384189605713,
0.019182628020644188,
-0.005929012782871723,
0.012081789784133434,
0.036336399614810944,
-0.05491600185632706,
0.0010573584586381912,
0.01729384995996952,
-0.0035837064497172832,
0.03297853469848633,
0.048159029334783554,
-0.02738388068974018,
-0.027158424258232117,
-0.014172868803143501,
-0.04755429923534393,
-0.043897595256567,
-0.0676368847489357,
-0.028944872319698334,
-0.002483174204826355,
0.01838058978319168,
-0.03288308531045914,
-0.005230422597378492,
0.006387805566191673,
-0.03474244847893715,
0.005298993084579706,
0.006935196928679943,
-0.07005437463521957,
-0.07066641002893448,
-0.054385606199502945,
-0.00016768128261901438,
-0.0013686453457921743,
0.02856934815645218,
-0.027594996616244316,
-0.029842250049114227,
-0.016624152660369873,
0.0029627997428178787,
0.012393388897180557,
-0.01707329973578453,
0.0005090245394967496,
0.02398958057165146,
0.05214759707450867,
0.01881505735218525,
0.0016547112027183175,
0.0036143320612609386,
-0.021870343014597893,
-0.001304598874412477,
-0.04466146230697632,
0.03094812110066414,
-0.031177790835499763,
0.04408683255314827,
0.00859235879033804,
-0.003283828031271696,
0.022618941962718964,
0.06380895525217056,
0.020364711061120033,
-0.031149614602327347,
0.04391119256615639,
0.024203842505812645,
0.06021364778280258,
-0.01448905561119318,
0.04392978921532631,
0.04844304174184799,
0.035399485379457474,
0.027858277782797813,
-0.03749868646264076,
-0.05296032130718231,
-0.005188987590372562,
0.0004471615538932383,
0.09617064893245697,
-0.0070520020090043545,
0.004024312365800142,
0.012459424324333668,
-0.03045785427093506,
-0.0035666925832629204,
-0.03500989452004433,
-0.07709480822086334,
0.03860592469573021,
0.03793630748987198,
0.002617924939841032,
0.02764618769288063,
-0.09097499400377274,
-0.0009777271188795567,
-0.004509128164499998,
0.023722700774669647,
-0.05399784818291664,
-0.006314663682132959,
0.06716358661651611,
0.004268106073141098,
-0.05614188313484192,
0.02905496209859848,
0.021272752434015274,
0.05053463578224182,
0.01889408566057682,
-0.04789166897535324,
-0.03405945748090744,
-0.014129666611552238,
0.06141802296042442,
0.05522703379392624,
-0.05119237303733826,
-0.01243176031857729,
0.027930188924074173,
0.04699451103806496,
0.04765038192272186,
-0.02270054817199707,
0.002755185589194298,
-0.038606930524110794,
0.04316763952374458,
-0.026064351201057434,
0.03852592036128044,
0.01640746183693409,
-0.03003334067761898,
-0.004290659446269274,
0.027212176471948624,
-0.029447859153151512,
0.022467749193310738,
0.022913167253136635,
0.06091838330030441,
-0.0013310512294992805,
0.03146306052803993,
-0.08861517906188965,
0.022043557837605476,
-0.05711590126156807,
0.009478098712861538,
0.013358648866415024,
-0.04435189068317413,
0.020182166248559952,
0.023255355656147003,
0.01667219214141369,
-0.012570908293128014,
-0.06408237665891647,
-0.0480227917432785,
-0.014899199828505516,
0.03103853203356266,
0.008327227085828781,
0.027313746511936188,
-0.07784393429756165,
0.015741387382149696,
0.012594660744071007,
-0.011611977592110634,
0.0020310557447373867,
0.047892577946186066,
-0.03759108856320381,
0.028423873707652092,
0.029094740748405457,
0.04673537611961365,
0.03259492665529251,
0.06802015751600266,
0.06302403658628464,
-0.0012022781884297729,
0.01031432207673788,
0.004156294744461775,
-0.0645555704832077,
0.0026308964006602764,
0.01203037891536951,
0.0031208128202706575,
0.03959902003407478,
0.009208026342093945,
-0.04079881310462952,
-0.013541566208004951,
-0.0361286997795105,
-0.0015045589534565806,
-0.030098099261522293,
-0.023271765559911728,
0.021896176040172577,
0.013836348429322243,
0.00008442322723567486,
0.006565854884684086,
0.05476217716932297,
0.014657102525234222,
0.0023596889805048704,
-0.03750352934002876,
-0.007084796205163002,
0.013200460001826286,
0.013527079485356808,
-0.02936750464141369,
0.031666889786720276,
0.024169176816940308,
0.009776334278285503,
-0.04376881942152977,
0.03171906620264053,
0.025422433391213417,
0.024218512699007988,
0.05216579884290695,
0.020598899573087692,
0.005034796427935362,
-0.002544665476307273,
-0.03028014861047268,
0.028325067833065987,
-0.001523358398117125,
0.04868282377719879,
0.002616678364574909,
0.07483884692192078,
0.0007227862952277064,
0.014771255664527416,
0.06747083365917206,
0.0165935680270195,
-0.0589873269200325,
0.025296442210674286,
0.006765549071133137,
-0.008040166459977627,
-0.05094784125685692,
0.11422830075025558,
-0.013353212736546993,
-0.019170384854078293,
0.029100390151143074,
0.006617250386625528,
0.026972029358148575,
0.03883417323231697,
0.011269078589975834,
-0.03481898456811905,
0.009212403558194637,
-0.0111237782984972,
0.014617173001170158,
-0.02315400540828705,
0.018967613577842712,
-0.022069426253437996,
-0.02577667497098446,
-0.038095615804195404,
0.00680855568498373,
-0.05987069383263588,
-0.013108963146805763,
-0.0002333287993678823,
0.022617774084210396,
0.023224052041769028,
-0.018948741257190704,
-0.030169043689966202,
-0.0022684449795633554,
-0.021808043122291565,
0.020684462040662766,
0.036874186247587204,
-0.023922573775053024,
-0.006481630727648735,
-0.029347272589802742,
-0.01536604668945074,
-0.031931351870298386,
-0.04471597447991371,
-0.003486493369564414,
0.017847860231995583,
0.024168066680431366,
-0.07391457259654999,
0.0374344065785408,
-0.0035144430585205555,
-0.0325520895421505,
0.05024802312254906,
0.02149643935263157,
0.025972982868552208,
0.01869870536029339,
-0.015908081084489822,
0.06802428513765335,
0.0070079597644507885,
0.016544019803404808,
-0.027235716581344604,
-0.01919563300907612,
-0.007587810512632132,
-0.010784699581563473,
-0.041493140161037445,
-0.05361197516322136,
-0.025592083111405373,
0.02522357553243637,
0.058119770139455795,
0.004801500588655472,
0.026927832514047623,
-0.04877520725131035,
-0.009060027077794075,
-0.050070930272340775,
0.00862694252282381,
0.003416152438148856,
0.057638317346572876,
-0.05013497918844223,
-0.05466236174106598,
0.020045559853315353,
-0.07604321092367172,
0.00020767921523656696,
0.02714819833636284,
0.0077255237847566605,
0.016199475154280663,
0.012944241054356098,
0.027964016422629356,
-0.021457575261592865,
-0.041635747998952866,
0.01641654409468174,
-0.018120935186743736,
0.001961376518011093,
-0.038682445883750916,
0.03994045779109001,
0.016070464625954628,
-0.012855343520641327,
-0.013631585985422134,
-0.01910267397761345,
-0.03647443652153015,
0.004884961526840925,
-0.049431003630161285,
-0.033809468150138855,
0.01798279397189617,
-0.015511647798120975,
0.03537347912788391,
0.03949849307537079,
-0.028407348319888115,
0.010305187664926052,
-0.04716235771775246,
-0.02557515539228916,
-0.03081170655786991,
0.05521811917424202,
-0.02758067101240158,
-0.06973953545093536,
0.002417227253317833,
0.016193753108382225,
0.03920628875494003,
-0.058769721537828445,
0.014996379613876343,
-0.03864263370633125,
-0.03457349166274071,
0.013863476924598217,
-0.05273909866809845,
-0.022102659568190575,
-0.005504188593477011
] |
<p>I'm trying to calculate the induced $-V$ in a DC circuit when current starts to flow, and reaches it's maximum value.
The inductance of the conductor is 1000nH it carries large amounts of current (1000A), what formula is best to know the $-V$ due to self inductance?</p>
|
g2459
|
[
0.019662756472826004,
0.025447111576795578,
-0.006741563323885202,
-0.030079452320933342,
0.0030717826448380947,
-0.04218446835875511,
0.04023513197898865,
0.010080230422317982,
0.0023781773634254932,
0.04321853443980217,
-0.08788562566041946,
0.07136613130569458,
-0.016263388097286224,
0.060742802917957306,
0.035796307027339935,
0.005569595377892256,
-0.026893028989434242,
-0.020896321162581444,
0.04083015024662018,
0.011167927645146847,
-0.03550722822546959,
-0.03468969091773033,
0.045682117342948914,
-0.0026957497466355562,
0.013580060563981533,
-0.026365019381046295,
0.0218445286154747,
0.05570950731635094,
0.0019236191874369979,
0.019076958298683167,
-0.003607370425015688,
0.045778725296258926,
0.04396696388721466,
-0.007796441670507193,
-0.06732092052698135,
-0.0037478292360901833,
0.014011276885867119,
-0.001796129858121276,
0.08103911578655243,
-0.020567748695611954,
-0.0087104057893157,
-0.028388425707817078,
0.03447245806455612,
-0.00047861947678029537,
-0.046862177550792694,
-0.03702813759446144,
-0.029130376875400543,
0.001279538031667471,
-0.021602949127554893,
-0.03826342150568962,
-0.00941099040210247,
0.03139166533946991,
0.04146786779165268,
-0.018969934433698654,
-0.026348410174250603,
0.004151809960603714,
-0.012953775003552437,
-0.05087001621723175,
-0.06339996308088303,
0.058252137154340744,
-0.0033772909082472324,
-0.023517997935414314,
-0.027741579338908195,
-0.021359289065003395,
0.0343807190656662,
-0.004465166945010424,
-0.03494816645979881,
-0.022018330171704292,
-0.037877313792705536,
0.051668599247932434,
0.0028119550552219152,
-0.05899021402001381,
0.02924448251724243,
0.013357087038457394,
0.033493056893348694,
0.0015945712802931666,
0.06464105099439621,
0.027160638943314552,
0.06887307018041611,
-0.0518588088452816,
-0.011623981408774853,
-0.018398074433207512,
0.017897432669997215,
-0.018651561811566353,
0.04828030988574028,
-0.00840808730572462,
0.01892399787902832,
0.0005891236942261457,
-0.015614175237715244,
-0.014458656311035156,
-0.021077297627925873,
-0.01776151917874813,
-0.018549680709838867,
-0.033395443111658096,
0.024585843086242676,
-0.03313855826854706,
0.02904621884226799,
0.06273132562637329,
-0.034005291759967804,
-0.004481628071516752,
-0.018532564863562584,
-0.06553243845701218,
-0.04484808072447777,
-0.007391259074211121,
-0.06023238226771355,
0.00007077361078700051,
0.03428628668189049,
-0.027016062289476395,
0.016582418233156204,
-0.028096865862607956,
-0.051763247698545456,
-0.06380369514226913,
0.001988064032047987,
0.03562629222869873,
-0.008313150145113468,
-0.019030911847949028,
-0.03898770362138748,
-0.005601733457297087,
-0.006647439673542976,
0.05307541787624359,
-0.024468913674354553,
0.024252526462078094,
0.007932579144835472,
0.031189285218715668,
0.02236899361014366,
-0.017494868487119675,
-0.036000918596982956,
0.07445351779460907,
0.07424328476190567,
0.011615157127380371,
0.0625249519944191,
-0.06695425510406494,
0.009790453128516674,
-0.019373539835214615,
0.019527707248926163,
0.003944910131394863,
0.0020332850981503725,
-0.04695399850606918,
-0.022227229550480843,
0.0011897280346602201,
0.037568703293800354,
-0.023223912343382835,
0.005524072330445051,
0.03135661035776138,
-0.05728213116526604,
0.016333656385540962,
-0.010355975478887558,
-0.025489306077361107,
-0.03762234374880791,
-0.046447157859802246,
0.0762721449136734,
0.06911030411720276,
-0.02761632576584816,
-0.05636347457766533,
-0.0015036830445751548,
0.015259794890880585,
0.029473235830664635,
-0.004315391182899475,
0.004684708081185818,
-0.014754056930541992,
0.0016370131634175777,
0.041222088038921356,
-0.0056358990259468555,
0.0018581667682155967,
-0.04808459058403969,
-0.06382521986961365,
0.02015409991145134,
-0.048573873937129974,
-0.024166909977793694,
-0.0009884287137538195,
-0.045794565230607986,
0.016597069799900055,
0.005273755174130201,
0.02987503632903099,
0.02126356028020382,
-0.002472528489306569,
0.03687366470694542,
0.006609892472624779,
0.04488280415534973,
0.05119675025343895,
0.013071546331048012,
-0.04689311981201172,
0.043040089309215546,
-0.00651972834020853,
-0.01856965385377407,
-0.02680686116218567,
-0.045221827924251556,
0.035091158002614975,
-0.05543366074562073,
-0.007701474241912365,
-0.0556345209479332,
0.027352062985301018,
0.06132763996720314,
0.03635420650243759,
-0.07057264447212219,
0.012225189246237278,
-0.014965545386075974,
-0.06303168088197708,
-0.04053843021392822,
0.021902652457356453,
0.018187841400504112,
0.002089387970045209,
0.06656213104724884,
0.012013966217637062,
-0.04571771249175072,
0.04201758652925491,
-0.06269768625497818,
-0.017450887709856033,
0.048775311559438705,
0.010878914035856724,
-0.009335832670331001,
-0.009800434112548828,
-0.04924352467060089,
0.034763630479574203,
-0.004303344991058111,
-0.005333570763468742,
-0.024620966985821724,
0.025462988764047623,
-0.025726137682795525,
-0.01065603457391262,
0.07765086740255356,
-0.05879248306155205,
0.07702117413282394,
0.013261795043945312,
-0.05932316184043884,
0.028304189443588257,
-0.03672213852405548,
-0.06467080116271973,
0.03536762669682503,
-0.06458663195371628,
-0.01051037572324276,
-0.028662635013461113,
-0.039878908544778824,
-0.017554987221956253,
-0.022309914231300354,
0.1048639714717865,
0.010975300334393978,
-0.0008862692047841847,
-0.0013031443813815713,
-0.06854768842458725,
0.026878030970692635,
-0.010354484431445599,
0.024652725085616112,
0.004651294089853764,
-0.026082724332809448,
-0.02202926017343998,
0.025273721665143967,
0.029048118740320206,
-0.023133568465709686,
0.06211678311228752,
-0.018226275220513344,
-0.06433677673339844,
0.013328433968126774,
0.005634735804051161,
-0.04811764881014824,
0.014961745589971542,
-0.04730158671736717,
0.06808722019195557,
-0.005670367274433374,
-0.03508369252085686,
-0.035766106098890305,
-0.026027901098132133,
0.006451453547924757,
0.019268229603767395,
-0.05428505688905716,
0.008010096848011017,
-0.04294445365667343,
-0.07524435967206955,
0.03637589514255524,
0.025877319276332855,
-0.005108947865664959,
0.07034248113632202,
0.006410279311239719,
0.014417062513530254,
0.08267101645469666,
-0.027515515685081482,
0.014695007354021072,
0.026254944503307343,
-0.010395118966698647,
0.011111709289252758,
-0.0432974249124527,
-0.020835651084780693,
-0.0039100032299757,
0.016666164621710777,
-0.0007124011754058301,
-0.04402010142803192,
0.013904040679335594,
-0.010931731201708317,
0.00635744770988822,
0.007993470877408981,
-0.024474680423736572,
-0.01622900366783142,
-0.02943778783082962,
0.06379038840532303,
0.012502751313149929,
0.0069721294566988945,
0.08474348485469818,
-0.013001872226595879,
0.0038534486666321754,
-0.018978573381900787,
-0.019826767966151237,
-0.034255288541316986,
0.0011740541085600853,
-0.042092666029930115,
-0.006348164286464453,
0.053625307977199554,
0.040460746735334396,
-0.03794465586543083,
0.024679014459252357,
0.021609066054224968,
-0.038354720920324326,
-0.017960743978619576,
0.03967052698135376,
-0.08459042012691498,
-0.03565533086657524,
-0.004130697809159756,
0.006297783926129341,
0.018415210768580437,
-0.0051718479953706264,
-0.03619905561208725,
-0.022801602259278297,
-0.07833493500947952,
0.03538035973906517,
0.00021721463417634368,
-0.02158374898135662,
-0.014229847118258476,
0.004774909466505051,
0.03864944353699684,
0.01539503876119852,
-0.02851397544145584,
0.02041834406554699,
0.03249282389879227,
-0.002354403492063284,
0.05515775457024574,
0.02647864632308483,
-0.07175915688276291,
0.009123431518673897,
0.0510605089366436,
-0.009536799974739552,
0.08489488065242767,
-0.026615753769874573,
0.01465968880802393,
-0.045519981533288956,
-0.05545744299888611,
0.029748734086751938,
0.0017825575778260827,
0.040014151483774185,
0.0871208906173706,
0.021087925881147385,
-0.05833504721522331,
0.07165221124887466,
-0.016327014192938805,
-0.037029609084129333,
-0.0076516070403158665,
-0.07702603936195374,
0.006969050969928503,
-0.0068022944033145905,
0.057425107806921005,
-0.0006830660277046263,
-0.0010345433838665485,
0.010239819996058941,
-0.022203844040632248,
-0.02363746054470539,
0.06181091442704201,
0.01469190139323473,
-0.02414708212018013,
-0.022622505202889442,
0.006526052951812744,
-0.0475667379796505,
-0.03522663936018944,
-0.004509151913225651,
-0.02427852526307106,
0.028725558891892433,
0.016608474776148796,
-0.0045728525146842,
-0.014566793106496334,
-0.032695282250642776,
0.0575040839612484,
-0.023266369476914406,
0.053485482931137085,
0.03582633286714554,
-0.0008809527498669922,
-0.002236067783087492,
0.010186402127146721,
-0.013684352859854698,
0.0021387466695159674,
-0.009589404799044132,
0.028584936633706093,
0.029553106054663658,
-0.03967156261205673,
0.038316838443279266,
0.0001199784892378375,
0.030203519389033318,
0.015442370437085629,
0.0033483337610960007,
-0.03596053645014763,
0.001033653854392469,
0.057543110102415085,
0.0593237578868866,
-0.030651167035102844,
0.03671911731362343,
0.036004189401865005,
0.03999624028801918,
0.04538924619555473,
0.04695501551032066,
-0.030605362728238106,
0.04233655333518982,
-0.058242760598659515,
0.03146454691886902,
-0.007385180797427893,
-0.049215249717235565,
0.01508477982133627,
-0.05497688800096512,
-0.07578402012586594,
0.00536443293094635,
0.044616132974624634,
0.04099550470709801,
-0.04341055452823639,
0.03318743780255318,
0.005816023796796799,
0.01675763726234436,
-0.052320532500743866,
-0.04252490773797035,
-0.04686153680086136,
-0.02327524684369564,
-0.045435450971126556,
0.04892709478735924,
-0.029556507244706154,
0.0579633004963398,
0.016121041029691696,
-0.02089545875787735,
0.025924907997250557,
-0.09288079291582108,
0.005633666180074215,
-0.01640196330845356,
0.09693951904773712,
0.006812695413827896,
0.05098319426178932,
0.009794781915843487,
0.015429321676492691,
0.02665565349161625,
-0.009384466335177422,
0.03556092828512192,
0.020519021898508072,
0.010958665050566196,
0.014251838438212872,
-0.050914861261844635,
-0.03267984092235565,
-0.00955616869032383,
-0.02940298616886139,
-0.037504132837057114,
0.011559462174773216,
0.02142086997628212,
0.011771716177463531,
0.017758192494511604,
0.02091672644019127,
-0.016080720350146294,
0.003619650611653924,
0.008973495103418827,
-0.010531187988817692,
-0.05387191101908684,
-0.013099252246320248,
-0.0760328397154808,
0.03460187837481499,
0.025130590423941612,
-0.002268872456625104,
0.023003771901130676,
-0.04063624143600464,
-0.002291175303980708,
-0.0011869791196659207,
0.035035137087106705,
0.056426070630550385,
-0.030793529003858566,
0.02853143960237503,
0.029770392924547195,
-0.008771871216595173,
0.02109082043170929,
0.030375564470887184,
-0.04589983820915222,
-0.021566452458500862,
-0.010869906283915043,
-0.04031437262892723,
-0.03468520939350128,
0.038532186299562454,
0.02989790588617325,
-0.033362772315740585,
-0.05393959581851959,
-0.022681744769215584,
-0.02444799430668354,
-0.01826605014503002,
0.038425154983997345,
0.12354389578104019,
0.058671098202466965,
0.0004124248225707561,
-0.060342464596033096,
-0.027457220479846,
0.0039751483127474785,
-0.009294465184211731,
-0.015373585745692253,
0.033824846148490906,
-0.025671176612377167,
0.012155684642493725,
-0.025831284001469612,
-0.07015819847583771,
-0.02795652113854885,
0.056537166237831116,
-0.05115658417344093,
-0.008911467157304287,
0.004459444433450699,
-0.026178142055869102,
0.00932855810970068,
0.015512284822762012,
0.09139570593833923,
-0.017145415768027306,
0.03162297606468201,
0.07040046155452728,
-0.03579540550708771,
0.0050917561165988445,
0.002306227805092931,
0.035649146884679794,
0.08022007346153259,
-0.02404802478849888,
-0.007039045915007591,
0.05217922106385231,
0.021575482562184334,
0.019005820155143738,
-0.05765680968761444,
-0.030368851497769356,
0.11605587601661682,
-0.032315339893102646,
0.04695376381278038,
0.022064916789531708,
-0.06429609656333923,
0.009216356091201305,
0.02411251701414585,
0.0016205708961933851,
0.021314039826393127,
0.009347375482320786,
-0.021723121404647827,
0.01431900355964899,
0.03961034119129181,
0.01181795448064804,
0.0028541332576423883,
0.06729183346033096,
0.011697481386363506,
-0.03355681523680687,
-0.03422649949789047,
-0.02966451831161976,
0.049064233899116516,
0.03664640709757805,
-0.03509270399808884,
0.04545843228697777,
-0.006722835823893547,
0.021471580490469933,
0.03432377800345421,
0.001935732550919056,
0.018364908173680305,
0.05036703124642372,
-0.037381477653980255,
-0.006953168660402298,
0.04025927558541298,
0.01273181103169918,
-0.04259035736322403,
-0.012093838304281235,
-0.024794282391667366,
-0.02241581864655018,
-0.007083354517817497,
-0.0039171758107841015,
0.042527422308921814,
-0.015821078792214394,
0.03495030477643013,
-0.013762942515313625,
0.06938435882329941,
-0.079110287129879,
0.03508978337049484,
0.0472918376326561,
0.021838314831256866,
-0.04777805879712105,
0.029645128175616264,
0.013207337819039822,
-0.04252351075410843,
0.03585045412182808,
0.05007389932870865,
-0.023430652916431427,
-0.024312233552336693,
0.007756469771265984,
0.009863764978945255,
-0.012129097245633602,
-0.0034612524323165417,
0.07164238393306732,
0.004535285755991936,
-0.016722973436117172,
0.02554319240152836,
-0.012731376104056835,
0.05742606520652771,
-0.011810622178018093,
-0.006545481272041798,
-0.057004667818546295,
0.0474233478307724,
0.034429628401994705,
-0.009526655077934265,
0.05018661916255951,
0.00870478618890047,
0.0018892142688855529,
0.033000435680150986,
-0.04158082976937294,
-0.0070007662288844585,
-0.02168736234307289,
-0.04752744361758232,
0.01264486275613308,
0.07433883845806122,
-0.02420354075729847,
-0.022746453061699867,
-0.010840937495231628,
-0.0014712465927004814,
-0.0005790802533738315,
-0.000006509752893180121,
0.021768340840935707,
0.029997769743204117,
0.018483135849237442,
-0.006731268484145403,
0.007854861207306385,
-0.007547520566731691,
0.04463760554790497,
0.023433396592736244,
0.07348965108394623,
-0.03836018219590187,
-0.013945448212325573,
0.07334962487220764,
0.005439984146505594,
0.022839728742837906,
0.0016706170281395316,
-0.028035050258040428,
-0.02066524140536785,
0.05071058124303818,
-0.008008277975022793,
0.006244248244911432,
0.023141350597143173,
0.00937699619680643,
0.1111486405134201,
-0.02981504797935486,
0.003177386475726962,
-0.012758092023432255,
-0.04604616016149521,
0.0007769935764372349,
-0.044918060302734375,
-0.006468751933425665,
0.05108410865068436,
-0.016290275380015373,
-0.007996300235390663,
0.01531916856765747,
0.015064956620335579,
-0.02121051959693432,
0.048649828881025314,
-0.03640691190958023,
-0.03856537863612175,
-0.014045730233192444,
0.01575503870844841,
0.03466856852173805,
0.036793313920497894,
0.03226685896515846,
0.0027270850259810686,
-0.018955137580633163,
0.024190818890929222,
0.06534390151500702,
0.0122519014403224,
-0.022443708032369614,
-0.009678921662271023,
0.018831957131624222,
-0.05262302607297897,
-0.013635687530040741,
-0.041273776441812515,
-0.010245871730148792,
-0.012398372404277325,
-0.028557952493429184,
-0.04014873877167702,
-0.04370039328932762,
0.04968566820025444,
-0.04177863523364067,
0.0012463198509067297,
-0.023185037076473236,
-0.015503820031881332,
0.017085814848542213,
-0.06092118099331856,
-0.015814991667866707,
-0.06734007596969604,
-0.0223203394562006,
-0.02732228860259056,
-0.019373806193470955,
0.020044157281517982,
-0.015247240662574768,
0.0040947445668280125,
-0.012705150060355663,
0.004569041542708874,
-0.007926888763904572,
0.04875737056136131,
-0.017456207424402237,
0.0336739718914032,
0.02391360141336918,
0.02701001800596714,
0.07785913348197937,
0.002979160752147436,
0.006199956871569157,
0.043438587337732315,
-0.024445969611406326,
-0.016964279115200043,
-0.02442368119955063,
-0.018091313540935516,
-0.023323897272348404,
-0.0019098874181509018,
-0.027947835624217987,
0.012712186202406883,
0.029023045673966408,
-0.04783168062567711,
-0.04740893095731735,
0.024918338283896446,
-0.06828412413597107,
-0.02003178372979164,
0.002418211428448558,
0.05646396428346634,
-0.015770504251122475,
0.033403266221284866,
0.002892610616981983,
-0.049512773752212524,
-0.02303781732916832,
-0.014963330700993538,
-0.014039956033229828,
0.01579965464770794,
-0.05920470505952835,
-0.03652606159448624,
0.019736235961318016,
-0.06889158487319946,
0.014762683771550655,
-0.03379464149475098,
-0.03655063733458519,
-0.07247639447450638,
0.021512072533369064,
-0.02045588009059429,
0.0301574245095253,
0.03674139082431793,
-0.004678779281675816,
-0.061916742473840714,
-0.024976007640361786,
-0.01709146238863468,
0.02423000894486904,
-0.020411968231201172,
-0.04576477035880089,
-0.016269072890281677,
0.0719655230641365,
-0.03834248706698418,
0.06122329458594322,
-0.04506286606192589,
0.016316328197717667,
-0.030300358310341835,
0.0008789623971097171,
0.013570887967944145,
-0.04093358665704727,
0.01934296265244484,
-0.013665338046848774,
0.016592834144830704,
-0.040711410343647,
-0.009585755877196789,
-0.03104148432612419,
0.03654409572482109,
0.037849389016628265,
-0.03754798322916031,
-0.03487030416727066,
-0.05522194504737854
] |
<p>I want to understand the derivation of the partition function for two distinguishable non-interacting particles. </p>
<p>Let the energy of particles $1$ and $2$ be $E_1$ and $E_2$ respectively. Setting $\beta = 1/kT$, the partition function becomes:
$$
Z = \sum_{s} e^{-\beta[E_1(s)+E_2(s)]}
$$
Where $s$ represents the state of the whole system. But then the author says: the set of state of the system is equivalent to the set of all possible pairs of states, $(s_1,s_2)$, for the two particles individually. And he states:
$$
Z_{total} = \sum_{s_1} \sum_{s_2} e^{-\beta E(s_1)} e^{-\beta E(s_2)}
=\sum_{s_1}e^{-\beta E(s_1)}\sum_{s_2}e^{-\beta E(s_2)} = Z_1 Z_2
$$
My question is: how can you formally go from the summation over $s$ to the double sum over $s_1$ and $s_2$? And why is one allowed to do so? I believe this has to do with the fact the since $s_1$ and $s_2$ do not intersect, then $P(s) = P(s_1)P(s_2) \sim e^{-\beta E(s_1)} e^{-\beta E(s_2)}$. But that's still not enough to justify the double sum...</p>
<p>(If I have we written too much, could someone cut the unnecessary parts? I don't know how much information I should give to make myself understood.)</p>
|
g2460
|
[
-0.0032772794365882874,
0.0006722224643453956,
-0.0024546675849705935,
-0.017310645431280136,
0.05192427709698677,
-0.022525615990161896,
0.03884352371096611,
0.0493365079164505,
0.0005261767655611038,
0.0077856178395450115,
-0.07839492708444595,
0.04583809897303581,
0.05225842446088791,
0.007524307817220688,
-0.014316554181277752,
0.009706972166895866,
0.07590346038341522,
0.036219120025634766,
0.004018907435238361,
0.051179710775613785,
-0.025469575077295303,
0.036639850586652756,
0.002961170393973589,
-0.017926452681422234,
0.040557458996772766,
-0.051102615892887115,
0.007433667313307524,
0.027780117467045784,
-0.0369294211268425,
0.014638598076999187,
0.05781462788581848,
0.035779837518930435,
0.03880710527300835,
-0.020043233409523964,
0.011232869699597359,
-0.014453863725066185,
0.08466149121522903,
-0.040516674518585205,
-0.0117653151974082,
-0.03596482425928116,
-0.02141750603914261,
0.02575894258916378,
0.02555561438202858,
-0.031955886632204056,
0.028124066069722176,
0.02983913943171501,
0.012183330953121185,
0.01823144592344761,
-0.004538045264780521,
-0.045859627425670624,
0.035767193883657455,
0.0172777958214283,
0.02858594059944153,
0.022216247394680977,
-0.027395466342568398,
-0.036606740206480026,
0.04319768771529198,
-0.01789822243154049,
0.07367055863142014,
0.012870866805315018,
0.012430376373231411,
0.03959953039884567,
-0.02650202438235283,
0.04295950010418892,
-0.004092984367161989,
-0.05188571661710739,
-0.02595258131623268,
0.020661277696490288,
-0.023060498759150505,
-0.011729077436029911,
-0.007482750341296196,
-0.004437613300979137,
0.005185363348573446,
-0.06547384709119797,
-0.028482580557465553,
-0.07463651150465012,
0.03321191295981407,
-0.014137180522084236,
0.018125619739294052,
0.0067495242692530155,
0.00411169184371829,
-0.008443592116236687,
0.04324907809495926,
-0.0052609192207455635,
0.012527765706181526,
0.00271807168610394,
-0.04462249204516411,
-0.07168030738830566,
-0.03528100997209549,
-0.01723071001470089,
0.01337782759219408,
0.0038643067236989737,
0.0355963297188282,
0.019727768376469612,
-0.027125665917992592,
-0.04760202020406723,
-0.04939015954732895,
-0.0070874979719519615,
-0.0021779085509479046,
0.03589892014861107,
0.01373677421361208,
0.01778247579932213,
0.06665116548538208,
0.002989839529618621,
0.043798357248306274,
-0.03994588926434517,
-0.0021762920077890158,
0.025008074939250946,
0.0255532618612051,
-0.005512922536581755,
-0.02016298472881317,
0.006262346636503935,
-0.005237163510173559,
-0.022467976436018944,
-0.06020960956811905,
0.04596695676445961,
0.02337123267352581,
-0.05110076814889908,
-0.06491705775260925,
0.056059882044792175,
0.04988130182027817,
0.001852501416578889,
-0.00018357118824496865,
0.03652403876185417,
-0.06969914585351944,
-0.00446738488972187,
0.018868286162614822,
0.01072655338793993,
0.02345443144440651,
-0.04916056618094444,
0.006816421169787645,
-0.05662425607442856,
0.03515520319342613,
-0.0028908743988722563,
-0.021140653640031815,
0.01655382663011551,
-0.01237757969647646,
-0.02215728722512722,
-0.04076766595244408,
-0.00943996012210846,
0.004004030488431454,
0.027499033138155937,
-0.006123092491179705,
0.011042715981602669,
-0.025548910722136497,
-0.008802486583590508,
0.002004805253818631,
-0.08019876480102539,
-0.08066502213478088,
0.049687474966049194,
0.02206576056778431,
0.07891902327537537,
-0.04398132488131523,
-0.010527621023356915,
-0.0029840136412531137,
-0.012815343216061592,
0.06345431506633759,
-0.04572690650820732,
-0.00031755873351357877,
-0.019785501062870026,
0.01319744810461998,
-0.013910860754549503,
0.018089132383465767,
-0.04939207807183266,
-0.0399642251431942,
0.04216207191348076,
-0.003467982867732644,
-0.06693542748689651,
-0.006024119909852743,
-0.05420370399951935,
-0.015589477494359016,
0.04014906659722328,
-0.0017895884811878204,
0.053582239896059036,
-0.007820608094334602,
0.03322681039571762,
-0.038644179701805115,
0.012095269747078419,
-0.007410692051053047,
0.015416178852319717,
-0.04640132188796997,
-0.033468037843704224,
0.03556719049811363,
0.013093912973999977,
0.016610469669103622,
0.0053487783297896385,
-0.004059412516653538,
0.045842789113521576,
-0.013151424005627632,
0.04153250902891159,
-0.021149663254618645,
-0.0055879694409668446,
-0.007820060476660728,
-0.03932707756757736,
0.012828354723751545,
0.02756141498684883,
0.0411653071641922,
-0.021831288933753967,
0.005144186317920685,
-0.01865842379629612,
-0.028044627979397774,
0.03747116029262543,
-0.019298242405056953,
-0.029961101710796356,
0.05964048206806183,
0.012956595048308372,
-0.03406919911503792,
-0.020184451714158058,
-0.03856334835290909,
-0.01963324099779129,
-0.019459756091237068,
-0.08326145261526108,
-0.0035335489083081484,
-0.048140864819288254,
0.02935904450714588,
-0.009217111393809319,
0.015713665634393692,
0.015335479751229286,
-0.05076618492603302,
-0.03442404046654701,
-0.0827675610780716,
-0.051973044872283936,
0.012539351359009743,
0.007328257896006107,
-0.01040097139775753,
0.0708949863910675,
-0.03307792544364929,
0.028243452310562134,
-0.07432091236114502,
0.08255619555711746,
-0.07537764310836792,
-0.042599067091941833,
-0.029487384483218193,
-0.059139229357242584,
0.022398177534341812,
0.012677290476858616,
-0.007275979500263929,
0.03214890882372856,
0.07379794120788574,
0.029470382258296013,
0.022026026621460915,
-0.032949257642030716,
-0.05463762953877449,
0.052481841295957565,
0.041690729558467865,
0.03367447108030319,
0.02297975681722164,
0.011120419949293137,
-0.002671210328117013,
-0.04062714800238609,
-0.049799658358097076,
-0.020709434524178505,
-0.021969303488731384,
0.016509976238012314,
0.050397682934999466,
-0.07710347324609756,
0.04186442121863365,
0.02086614817380905,
-0.028557762503623962,
-0.005172944162040949,
0.017606114968657494,
-0.019593993201851845,
-0.00439820159226656,
0.03021050989627838,
0.011985213495790958,
-0.005306965205818415,
0.018387194722890854,
-0.048594456166028976,
0.005882481578737497,
-0.014243227429687977,
0.007866188883781433,
0.021939562633633614,
-0.029406433925032616,
0.053037941455841064,
-0.012556914240121841,
-0.009172581136226654,
0.012136404402554035,
0.006410541012883186,
0.04498826339840889,
-0.0219117384403944,
-0.024026423692703247,
-0.0027102071326225996,
0.02713920921087265,
0.04213516041636467,
0.060936782509088516,
-0.1008143201470375,
0.01486638281494379,
0.001145186135545373,
0.0190668236464262,
0.04060791805386543,
0.01675366796553135,
0.0454985648393631,
-0.03373412415385246,
-0.03640495240688324,
-0.027518894523382187,
0.026570124551653862,
-0.030892224982380867,
-0.09191137552261353,
-0.022030510008335114,
0.003944998141378164,
0.0020505934953689575,
-0.006362847052514553,
-0.013157304376363754,
-0.014080563560128212,
0.03979276865720749,
0.031633809208869934,
-0.09734717011451721,
-0.004210842773318291,
-0.03811303898692131,
-0.019702190533280373,
0.0007371470564976335,
0.02766580879688263,
0.024800939485430717,
-0.007394449319690466,
0.03631247952580452,
0.0449507012963295,
0.016826916486024857,
0.024991806596517563,
0.025904575362801552,
-0.052846379578113556,
-0.02930283173918724,
0.024637943133711815,
0.06093921884894371,
-0.0196185652166605,
0.0055661071091890335,
-0.01559093501418829,
0.01689760945737362,
-0.04734643176198006,
-0.013381135649979115,
0.030695104971528053,
0.021607091650366783,
-0.013387263752520084,
0.042459968477487564,
-0.06680690497159958,
-0.03567785024642944,
0.0013077884213998914,
-0.03773368522524834,
-0.008588206954300404,
-0.008287153206765652,
-0.0051347934640944,
-0.026441937312483788,
0.01936599239706993,
-0.014607724733650684,
-0.01486155018210411,
-0.03910953551530838,
0.01778354123234749,
0.012323208153247833,
0.011410935781896114,
0.0742390975356102,
-0.01599699817597866,
0.016764692962169647,
0.03946411982178688,
0.03666410967707634,
0.03732571378350258,
-0.022744324058294296,
0.004264702554792166,
0.07506812363862991,
-0.038036566227674484,
-0.01010651234537363,
0.04318465292453766,
0.059202469885349274,
-0.04119360074400902,
0.04903511330485344,
0.0236718337982893,
-0.010860628448426723,
-0.01984466426074505,
-0.014183200895786285,
0.009524460881948471,
0.019014479592442513,
-0.039563439786434174,
-0.03702091425657272,
0.012674406170845032,
0.023808861151337624,
0.0014718504389747977,
0.05505667254328728,
-0.05863916128873825,
0.045842017978429794,
0.03181964531540871,
-0.011747794225811958,
-0.013885500840842724,
0.02818121388554573,
-0.00646149180829525,
0.0178945641964674,
0.06069648265838623,
0.09617787599563599,
0.05256552994251251,
0.008748916909098625,
-0.008167123422026634,
0.006833929568529129,
-0.004024304449558258,
0.042416706681251526,
-0.0005132716032676399,
-0.02989318035542965,
0.010903558693826199,
0.04201504960656166,
-0.0013733634259551764,
-0.002922626445069909,
-0.018044844269752502,
-0.0071799797005951405,
0.04369977489113808,
-0.05178600922226906,
-0.0422888845205307,
-0.016049649566411972,
-0.10213854163885117,
0.01106034405529499,
-0.03915272653102875,
-0.034894973039627075,
-0.01546864490956068,
-0.0021281351801007986,
-0.05511122941970825,
0.0027226856909692287,
0.0766601637005806,
0.03812147304415703,
-0.04574856534600258,
-0.04447462782263756,
-0.0002818560169544071,
-0.03499278426170349,
-0.007274838164448738,
0.021573586389422417,
-0.011138762347400188,
-0.05444084852933884,
-0.018545344471931458,
-0.05354529619216919,
0.0007396221626549959,
0.01887332648038864,
0.11838474124670029,
-0.032212115824222565,
0.029682904481887817,
-0.06437147408723831,
-0.05772462114691734,
-0.0071403272449970245,
0.04395041987299919,
0.005270747002214193,
0.029616354033350945,
-0.10046659409999847,
0.003081317525357008,
-0.020730070769786835,
0.03026733361184597,
-0.024893248453736305,
0.01812395453453064,
0.049429506063461304,
-0.009119133464992046,
-0.029765194281935692,
0.0339614562690258,
0.08586010336875916,
0.01902519166469574,
-0.029285358265042305,
-0.08126505464315414,
-0.036094192415475845,
-0.020357459783554077,
-0.0005498071550391614,
0.04541904479265213,
0.007829270325601101,
-0.000685499922838062,
-0.04884716123342514,
-0.016599535942077637,
-0.004829953424632549,
-0.007482593879103661,
-0.013186915777623653,
0.005461856722831726,
-0.03461966663599014,
0.00811903178691864,
0.03139498457312584,
-0.01419359166175127,
0.026997817680239677,
0.05179255083203316,
-0.06488689035177231,
0.035497140139341354,
0.007834671065211296,
0.015762144699692726,
0.006272315047681332,
0.018538640812039375,
0.02732294239103794,
-0.04152960330247879,
0.010447067208588123,
-0.0529218427836895,
-0.0915122702717781,
-0.06148553639650345,
-0.008384030312299728,
-0.0009471587254665792,
-0.005972760729491711,
-0.003551314352080226,
0.003061678959056735,
0.04644843563437462,
0.028447041288018227,
0.0660184919834137,
0.02991737611591816,
-0.008390622213482857,
0.007684479001909494,
0.06292620301246643,
0.010263846255838871,
0.03210728242993355,
0.020406436175107956,
-0.013579280115664005,
0.05849502235651016,
0.006456699687987566,
0.018382765352725983,
-0.040183957666158676,
-0.02470128983259201,
0.04331498220562935,
-0.038414981216192245,
0.004794656299054623,
0.0026578668039292097,
0.03368515148758888,
0.008732425980269909,
0.049003954976797104,
0.05370086804032326,
0.01386216375976801,
-0.019036712124943733,
-0.02474311925470829,
0.042629461735486984,
-0.020834241062402725,
-0.008434463292360306,
0.012215631082654,
-0.04360578581690788,
-0.03349307179450989,
-0.021581444889307022,
0.02592015266418457,
-0.06384918838739395,
-0.03479783609509468,
0.03144098073244095,
0.003308656858280301,
0.001976222498342395,
-0.003388300072401762,
-0.0247392188757658,
-0.026432981714606285,
-0.0259034913033247,
-0.03999386727809906,
0.011872540228068829,
0.08225914090871811,
0.0419318787753582,
-0.004874147474765778,
-0.05904689431190491,
0.03268701583147049,
0.012278618291020393,
-0.041329242289066315,
-0.05041743814945221,
-0.007787163835018873,
0.005979788489639759,
-0.0012808706378564239,
-0.005499511957168579,
-0.039648137986660004,
-0.007539386861026287,
0.0053593553602695465,
-0.06092473864555359,
0.014395697973668575,
-0.037529680877923965,
0.0017576352693140507,
0.05024699494242668,
0.005751706659793854,
-0.01865227147936821,
-0.006443921010941267,
-0.012067652307450771,
-0.05450550466775894,
0.05219564214348793,
0.04533551260828972,
0.024998296052217484,
0.02514202706515789,
0.045927293598651886,
0.019577883183956146,
0.010373217985033989,
-0.030273327603936195,
0.04634691774845123,
0.02504117786884308,
-0.011687311343848705,
-0.05403139069676399,
-0.008802833035588264,
-0.036859672516584396,
-0.02067289501428604,
0.003604484722018242,
0.04014723747968674,
-0.0012351354816928506,
0.050896089524030685,
-0.002461413387209177,
-0.0030143449548631907,
0.02095787413418293,
-0.027627509087324142,
-0.019124075770378113,
0.004109653178602457,
-0.01697436347603798,
0.007954281754791737,
0.05383479967713356,
-0.0007717222906649113,
0.0024162600748240948,
-0.013176207430660725,
0.05700716748833656,
-0.015062057413160801,
-0.07020167261362076,
0.0058923568576574326,
-0.0012843009317293763,
0.02199280448257923,
-0.10263241827487946,
0.022997906431555748,
-0.009254513308405876,
0.0036980686709284782,
-0.01836787909269333,
0.010887278243899345,
0.019992999732494354,
0.031152214854955673,
-0.012607450596988201,
0.02068946324288845,
0.01481713354587555,
0.02439950220286846,
-0.05603622645139694,
-0.017910238355398178,
0.08597251027822495,
-0.06011095270514488,
0.006987839937210083,
0.0032532960176467896,
-0.009524970315396786,
-0.03730456903576851,
0.007826651446521282,
-0.009754661470651627,
0.019982174038887024,
-0.020536070689558983,
-0.07222258299589157,
-0.04533364996314049,
0.009202199056744576,
-0.05489705875515938,
0.015710629522800446,
0.02793252468109131,
0.003030418651178479,
0.05372412130236626,
-0.015266071073710918,
0.03362978622317314,
0.046748626977205276,
-0.00940830260515213,
0.033161845058202744,
0.06802105158567429,
0.005638891365379095,
0.016759958118200302,
-0.01696133241057396,
0.005410999525338411,
0.024002566933631897,
-0.012498302385210991,
0.004964083433151245,
-0.04144482687115669,
0.011788959614932537,
0.009450896643102169,
0.05150612071156502,
-0.061267171055078506,
0.04093410447239876,
0.10748410224914551,
-0.014274446293711662,
-0.050006747245788574,
0.037795115262269974,
0.046979762613773346,
0.014144695363938808,
-0.06847511231899261,
0.008860798552632332,
-0.0086021414026618,
-0.01868399605154991,
-0.05335956811904907,
-0.0209200419485569,
-0.0033267580438405275,
-0.04305969923734665,
0.01242965366691351,
-0.007845407351851463,
0.021805044263601303,
-0.0030879874248057604,
-0.03947262093424797,
-0.024514256045222282,
-0.04383297637104988,
0.010192491114139557,
0.0016369058284908533,
0.07165279984474182,
0.036408327519893646,
-0.01617753691971302,
-0.012835651636123657,
-0.07018951326608658,
-0.028528058901429176,
-0.06775037944316864,
-0.0629080981016159,
0.02628158964216709,
-0.004936059005558491,
-0.05312734842300415,
0.05052665248513222,
0.021218731999397278,
0.007377172354608774,
-0.03411167114973068,
0.025706779211759567,
-0.0025819907896220684,
-0.01800576038658619,
-0.007143684197217226,
-0.03956245630979538,
0.01685878448188305,
0.045303523540496826,
0.04541143774986267,
0.012049619108438492,
0.023841194808483124,
-0.0372723713517189,
0.034582577645778656,
-0.0029059406369924545,
0.0017137518152594566,
-0.05434121564030647,
0.04441557079553604,
0.05208809673786163,
0.01487637311220169,
0.033827587962150574,
0.037199024111032486,
0.014333300292491913,
0.004938618279993534,
-0.012716984376311302,
-0.004033839330077171,
0.01142771728336811,
-0.053828611969947815,
0.05979965254664421,
-0.003515164600685239,
0.014977287501096725,
-0.03515123948454857,
-0.0006711303140036762,
-0.0225216094404459,
-0.016567790880799294,
0.026209698989987373,
0.0011779401684179902,
-0.011534573510289192,
-0.05428102985024452,
0.0382721908390522,
0.042591266334056854,
0.005419660359621048,
0.06852050125598907,
0.034040290862321854,
0.000991553533822298,
-0.042064037173986435,
-0.02649039588868618,
-0.06338011473417282,
0.019576754420995712,
0.026225678622722626,
0.04339291900396347,
0.04970269650220871,
-0.03312911465764046,
0.05775744095444679,
-0.020611576735973358,
0.01575186476111412,
-0.075210340321064,
0.05615811049938202,
0.02366425283253193,
0.02278512716293335,
-0.015269833616912365,
-0.015948638319969177,
-0.050035033375024796,
-0.05883149802684784,
0.042413532733917236,
-0.0232124924659729,
-0.04752184450626373,
-0.004661352373659611,
-0.03967075049877167,
-0.03429614007472992,
0.07131565362215042,
0.05507877841591835,
-0.019013328477740288,
-0.00676981545984745,
-0.015618073754012585,
0.061330221593379974,
0.10835670679807663,
-0.05471204221248627,
0.06688060611486435,
0.013386713340878487,
-0.026725677773356438,
0.024163519963622093,
-0.06667288392782211,
-0.022865451872348785,
-0.03380589559674263,
0.032350800931453705,
-0.020815683528780937,
0.01315122377127409,
-0.015779048204421997,
0.05532325804233551
] |
<p>What does the following mean with respect to <a href="http://en.wikipedia.org/wiki/Special_relativity">special relativity</a>?</p>
<p>$$\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$</p>
|
g2461
|
[
0.02765829861164093,
0.013441444374620914,
-0.04221006855368614,
-0.008177612908184528,
0.024695325642824173,
0.05177813768386841,
0.05441651493310928,
0.015389364212751389,
-0.002779850037768483,
-0.024100299924612045,
-0.013698716647922993,
0.025135373696684837,
0.02879958786070347,
-0.012368893250823021,
-0.006498588249087334,
-0.01805298961699009,
0.054605063050985336,
-0.033151060342788696,
-0.015370545908808708,
-0.028825635090470314,
-0.02348288707435131,
-0.07374543696641922,
0.015948085114359856,
-0.04573296383023262,
0.06146620213985443,
0.03300170972943306,
0.01977892965078354,
0.024115394800901413,
-0.07213901728391647,
0.011710676364600658,
0.05771525949239731,
0.020369987934827805,
0.0679905116558075,
-0.008299651555716991,
0.02009955234825611,
0.02044335938990116,
0.03928745165467262,
0.010293401777744293,
0.039364319294691086,
-0.0334961824119091,
-0.01122888084501028,
-0.057520173490047455,
0.021145395934581757,
-0.06169644370675087,
0.011470724828541279,
0.0006455608527176082,
-0.0768178403377533,
-0.0066516585648059845,
-0.006732335779815912,
-0.007068237289786339,
0.06491603702306747,
0.04124726727604866,
0.018544716760516167,
0.026661543175578117,
0.04976527765393257,
-0.014460346661508083,
0.040966302156448364,
0.015759384259581566,
0.04432331770658493,
0.03751454874873161,
-0.026292933151125908,
-0.062283918261528015,
0.048583004623651505,
0.030590757727622986,
0.05167586728930473,
0.013292758725583553,
0.00037842747406102717,
-0.07386703789234161,
-0.009489553980529308,
-0.02864995226264,
0.010398645885288715,
-0.06323456019163132,
0.07803995162248611,
0.02555103413760662,
-0.06078501418232918,
-0.016501285135746002,
0.020123224705457687,
-0.016782337799668312,
-0.031504202634096146,
-0.011828979477286339,
0.009849033318459988,
-0.04281989857554436,
0.004188882652670145,
-0.01651664823293686,
0.09121783822774887,
-0.011184590868651867,
-0.021795498207211494,
0.000849199655931443,
-0.025041479617357254,
0.025616589933633804,
0.006034085061401129,
-0.03605475649237633,
0.017316846176981926,
0.02626398578286171,
-0.0158102884888649,
-0.056968413293361664,
0.008331580087542534,
-0.0297557320445776,
-0.0010466448729857802,
0.0004959928337484598,
-0.027148261666297913,
-0.0003986454103142023,
-0.008586238138377666,
-0.025757011026144028,
-0.016468917950987816,
-0.011043227277696133,
-0.08729273825883865,
0.05848341062664986,
0.03736594691872597,
-0.12371355295181274,
-0.055860091000795364,
-0.02117489092051983,
-0.017797287553548813,
-0.07179435342550278,
-0.05690186843276024,
-0.018033303320407867,
0.05282715708017349,
-0.05811585485935211,
-0.0030698557384312153,
0.03440206125378609,
-0.01804724708199501,
0.012293713167309761,
0.0427219457924366,
0.10872896015644073,
-0.03834919258952141,
0.029583806172013283,
-0.027735339477658272,
0.019404131919145584,
0.03284837305545807,
-0.010811354964971542,
-0.02057475410401821,
0.004894135985523462,
0.03314056247472763,
-0.04354105889797211,
-0.018466386944055557,
-0.02651153691112995,
0.01399089116603136,
0.009920402429997921,
0.02037074603140354,
0.0011733081191778183,
0.022295348346233368,
-0.000413538480643183,
0.02340560220181942,
-0.02836240641772747,
-0.0010703271254897118,
-0.043114058673381805,
-0.022247295826673508,
0.021366147324442863,
-0.03670249879360199,
-0.09467469155788422,
-0.045443374663591385,
0.06623385101556778,
-0.050843216478824615,
-0.07525282353162766,
0.0034576954785734415,
-0.003344470402225852,
0.009559920988976955,
0.051571186631917953,
-0.016486309468746185,
-0.03555680066347122,
0.07220976054668427,
0.026614919304847717,
0.02901426889002323,
0.036307498812675476,
-0.10353660583496094,
0.025964099913835526,
0.014227441512048244,
-0.08715742826461792,
-0.006969002541154623,
-0.03570041432976723,
0.0006717058713547885,
0.01237273495644331,
-0.011174904182553291,
0.06726235896348953,
0.033270929008722305,
-0.008639638312160969,
0.012809887528419495,
0.019902581349015236,
0.030715174973011017,
0.048505354672670364,
-0.03999784216284752,
-0.014954068697988987,
0.014079823158681393,
-0.04299797862768173,
-0.016167355701327324,
-0.03718890994787216,
-0.04161857068538666,
-0.019250288605690002,
-0.0839773565530777,
0.011932744644582272,
-0.026793222874403,
-0.03385620564222336,
0.004529076628386974,
0.06951732188463211,
-0.019060079008340836,
0.023841150104999542,
-0.022831395268440247,
-0.018181011080741882,
-0.04134456813335419,
0.04594559967517853,
-0.0024901379365473986,
0.010551908053457737,
0.020916972309350967,
-0.003847071435302496,
0.05080375820398331,
-0.0286000557243824,
-0.0031508104875683784,
-0.018900342285633087,
0.06052640825510025,
0.05050702765583992,
-0.008304485119879246,
-0.071307472884655,
0.019225334748625755,
-0.04179821535944939,
-0.02182614989578724,
-0.07662505656480789,
0.013512271456420422,
0.04294830560684204,
-0.03694360703229904,
0.0446077361702919,
0.03405223414301872,
0.035747166723012924,
0.02736751176416874,
-0.022357245907187462,
-0.024008892476558685,
-0.012953990139067173,
-0.03840872272849083,
-0.06060056760907173,
-0.0016542323864996433,
0.001955372979864478,
-0.0293433777987957,
-0.009041043929755688,
0.009355172514915466,
0.00788281112909317,
0.03588613495230675,
0.019143765792250633,
-0.02254316210746765,
-0.003814395982772112,
0.0031641533132642508,
-0.02472216822206974,
0.017479918897151947,
-0.04283337667584419,
0.0030847564339637756,
-0.015828149393200874,
0.047125931829214096,
0.08088969439268112,
0.04214652255177498,
-0.019621267914772034,
-0.01253795251250267,
-0.037544745951890945,
0.003992653917521238,
-0.041333336383104324,
-0.06112595647573471,
0.05340941250324249,
0.03350616618990898,
-0.028105637058615685,
-0.05240681394934654,
0.0184708833694458,
-0.05322995409369469,
-0.06298086792230606,
-0.043794821947813034,
-0.059648867696523666,
-0.004495598841458559,
0.010903229005634785,
0.01876971498131752,
0.0396522618830204,
-0.005635942332446575,
0.013333389535546303,
0.019633440300822258,
-0.024139244109392166,
0.006323913112282753,
0.01720597594976425,
-0.009696836583316326,
0.057091984897851944,
-0.034179069101810455,
-0.032097648829221725,
-0.005236231721937656,
0.00826306827366352,
0.016822759062051773,
-0.05587644502520561,
-0.04660441726446152,
0.0458187535405159,
-0.003176430705934763,
-0.005377620924264193,
0.015036682598292828,
0.012275347486138344,
0.022700102999806404,
0.04478827863931656,
-0.0313430093228817,
-0.015318281948566437,
0.004094232805073261,
0.0015789646422490478,
-0.015420650132000446,
0.0021583079360425472,
0.06856364011764526,
0.0065049221739172935,
0.008220764808356762,
0.003310892265290022,
-0.0012468114728108048,
0.0540880523622036,
0.030419832095503807,
-0.006002630107104778,
-0.030306708067655563,
-0.008441055193543434,
-0.12034700810909271,
-0.06365237385034561,
0.05731450021266937,
-0.06269434839487076,
0.014443798922002316,
0.0015244993846863508,
-0.001745471847243607,
0.026819966733455658,
0.056005362421274185,
-0.01691066473722458,
-0.03935466334223747,
0.01464835088700056,
-0.009524528868496418,
-0.01960490271449089,
-0.03414938971400261,
0.03641917556524277,
-0.015421392396092415,
0.0013006838271394372,
-0.03692152723670006,
-0.0065386174246668816,
0.009862079285085201,
-0.0343594066798687,
-0.040571507066488266,
0.022243795916438103,
-0.024703703820705414,
-0.03208259865641594,
-0.016932806000113487,
0.005450431257486343,
-0.022966256365180016,
-0.014562900178134441,
0.018758613616228104,
-0.004550720565021038,
-0.06964157521724701,
0.063798688352108,
0.03078487142920494,
-0.011388677172362804,
0.014378899708390236,
0.018498077988624573,
0.023510605096817017,
0.04574017599225044,
0.005820698104798794,
0.08076556771993637,
0.011248650960624218,
0.04379468411207199,
-0.006913937162607908,
-0.022211933508515358,
-0.012505043298006058,
-0.01729881577193737,
0.02229948528110981,
-0.023458855226635933,
-0.030148429796099663,
0.06297869980335236,
0.04873807728290558,
0.03006359562277794,
0.011060940101742744,
-0.01689262129366398,
0.026334328576922417,
-0.00976182147860527,
0.03516065701842308,
0.0967785194516182,
0.001258955104276538,
-0.015756534412503242,
-0.04864940792322159,
0.012969639152288437,
-0.016689706593751907,
0.05981084704399109,
-0.0075477310456335545,
-0.0005945502198301256,
0.020454734563827515,
0.06477683037519455,
0.0016694450750946999,
-0.0550578311085701,
-0.016000570729374886,
-0.01848539337515831,
-0.023056451231241226,
-0.007696412969380617,
0.0847395732998848,
0.02175571583211422,
-0.013249503448605537,
-0.04102743789553642,
0.0036318539641797543,
0.0011851750314235687,
-0.035491105169057846,
-0.04117511212825775,
0.002326799323782325,
-0.07283489406108856,
0.040263861417770386,
-0.016587847843766212,
-0.04033426567912102,
0.022205282002687454,
0.004256207961589098,
0.02934187278151512,
0.06770435720682144,
0.05405197665095329,
-0.045571696013212204,
0.08480053395032883,
-0.005618440452963114,
0.01354904007166624,
0.024154936894774437,
-0.03646937757730484,
-0.00008737967436900362,
0.011214387603104115,
0.046375639736652374,
-0.04960775375366211,
-0.010102854110300541,
0.007208345457911491,
0.00744070066139102,
0.023515405133366585,
-0.006018693093210459,
-0.0972791537642479,
0.04689037427306175,
0.03571874648332596,
0.0011661011958494782,
-0.03349306806921959,
0.014862926676869392,
0.002421453595161438,
0.0029793167486786842,
-0.014665965922176838,
0.06889522075653076,
-0.021120570600032806,
0.008605585433542728,
0.03090922348201275,
0.03350510075688362,
0.01430223137140274,
-0.003071865066885948,
0.010606329888105392,
0.05042172595858574,
0.04724608734250069,
0.014258072711527348,
0.01080178190022707,
-0.026747964322566986,
0.043807171285152435,
0.02827259711921215,
-0.03245443105697632,
-0.007346891798079014,
0.01788831688463688,
0.02969502843916416,
-0.011544903740286827,
0.006523854099214077,
-0.043770886957645416,
0.022921010851860046,
0.018055463209748268,
-0.015642812475562096,
-0.025909211486577988,
-0.018484191969037056,
-0.03287454694509506,
-0.0245071928948164,
0.020079441368579865,
-0.004400359466671944,
-0.05562205612659454,
0.05385071039199829,
-0.05052223429083824,
-0.006355460733175278,
0.028475875034928322,
0.01609596610069275,
0.005981281399726868,
-0.02003640867769718,
0.016082489863038063,
0.02690274827182293,
-0.011715663596987724,
0.05670207738876343,
0.02528526447713375,
-0.04504583403468132,
-0.032678376883268356,
-0.08805539458990097,
-0.03821806237101555,
-0.06894444674253464,
-0.025032181292772293,
-0.03353337571024895,
-0.03290681913495064,
0.07115743309259415,
0.00357607938349247,
0.013097311370074749,
0.010169395245611668,
0.0033072137739509344,
-0.04003570228815079,
-0.009107240475714207,
0.006597449071705341,
-0.025728868320584297,
-0.010253316722810268,
0.025998210534453392,
0.014683982357382774,
0.051094453781843185,
-0.0006597015308216214,
-0.026291631162166595,
-0.003377048997208476,
0.01640598103404045,
0.02040932886302471,
0.0048120226711034775,
0.000982836470939219,
-0.011922815814614296,
-0.012044248171150684,
0.06149335950613022,
-0.029726875945925713,
0.038921281695365906,
-0.004783784504979849,
-0.06407530605792999,
0.04806561395525932,
0.03347190469503403,
0.008590628392994404,
-0.005348398350179195,
0.0899006575345993,
0.050482988357543945,
0.015675988048315048,
-0.020449714735150337,
0.014439546503126621,
-0.0020976329687982798,
-0.03036116063594818,
0.10077586770057678,
-0.06696388125419617,
0.05886567756533623,
0.04906672239303589,
0.03207246959209442,
-0.0011006334098055959,
0.004039602354168892,
-0.017178798094391823,
-0.012461936101317406,
0.012653913348913193,
-0.00346957053989172,
0.016116376966238022,
0.024571964517235756,
-0.030016468837857246,
-0.04041968658566475,
-0.038267020136117935,
0.10232972353696823,
0.03471045568585396,
-0.029365364462137222,
0.006593406666070223,
0.03327770531177521,
-0.0007676919922232628,
0.02830791287124157,
-0.04226699844002724,
-0.027693841606378555,
-0.012129946611821651,
0.06338457763195038,
0.000048182530008489266,
-0.030966192483901978,
0.014979550614953041,
-0.03904366120696068,
0.04798394814133644,
-0.01075619738548994,
0.013602985069155693,
-0.034708231687545776,
-0.002344586420804262,
0.047829966992139816,
-0.021254392340779305,
-0.03620317950844765,
-0.0016365196788683534,
-0.019022734835743904,
-0.026461614295840263,
0.07798198610544205,
0.014796293340623379,
0.062205974012613297,
-0.012611374258995056,
0.041696738451719284,
-0.05591481178998947,
0.00044260197319090366,
-0.035190287977457047,
0.051246386021375656,
-0.014589717611670494,
-0.018845820799469948,
-0.06427040696144104,
0.009632145054638386,
-0.01576956920325756,
0.04290551692247391,
0.020991194993257523,
-0.05221967399120331,
0.05137175694108009,
0.031888749450445175,
-0.046547695994377136,
-0.045435551553964615,
0.00578667689114809,
-0.015305784530937672,
-0.06990267336368561,
-0.036702562123537064,
-0.01264240313321352,
0.006261913571506739,
-0.03499085456132889,
0.07986706495285034,
-0.04325733706355095,
-0.02759009785950184,
0.027622509747743607,
0.01534143928438425,
0.003503733081743121,
-0.022849641740322113,
0.019221505150198936,
-0.002933100564405322,
0.040159501135349274,
-0.008206933736801147,
-0.010957715101540089,
-0.009303214028477669,
-0.0048693278804421425,
-0.0002864696434698999,
0.007795548066496849,
-0.04281089827418327,
0.041441917419433594,
-0.02408713288605213,
0.043691471219062805,
0.03383297100663185,
0.017069580033421516,
0.030585890635848045,
0.023656630888581276,
-0.026198770850896835,
-0.033311814069747925,
-0.0034175640903413296,
0.046510789543390274,
-0.01455618441104889,
0.023305602371692657,
-0.005422414280474186,
0.051187556236982346,
0.002563081681728363,
-0.007234410848468542,
-0.0144813172519207,
0.0037979544140398502,
0.013018794357776642,
-0.07963654398918152,
0.07484778761863708,
0.023593991994857788,
-0.019180191680788994,
0.008186564780771732,
-0.015072769485414028,
-0.002443483332172036,
-0.00328685506246984,
0.006692611612379551,
0.04963289946317673,
-0.043335922062397,
-0.0691140666604042,
0.004081417340785265,
0.0014467110158875585,
-0.016451289877295494,
0.02249191887676716,
0.02008952759206295,
0.0056297993287444115,
0.007003182079643011,
0.06710638850927353,
0.0013145586708560586,
-0.039620447903871536,
-0.002467251382768154,
0.014797602780163288,
-0.011549626477062702,
-0.06251098960638046,
0.015444017015397549,
0.001079646172001958,
-0.03557239845395088,
-0.04622209072113037,
0.04029758274555206,
0.0432802215218544,
0.011165046133100986,
-0.0010817691218107939,
-0.0055605326779186726,
-0.02968725562095642,
-0.04466608166694641,
-0.037141796201467514,
-0.008714444935321808,
0.02528427168726921,
-0.05644165724515915,
-0.040772344917058945,
0.016322478652000427,
-0.024751462042331696,
0.04584571719169617,
-0.01680685393512249,
0.05747349187731743,
-0.013119544833898544,
-0.04465405270457268,
0.0023381353821605444,
-0.051725953817367554,
0.03611467778682709,
0.02844604104757309,
0.018364369869232178,
-0.024582557380199432,
0.0018800686812028289,
-0.013812507502734661,
-0.026113595813512802,
0.0489204041659832,
-0.007086951285600662,
-0.00323057291097939,
-0.006874324753880501,
0.047363169491291046,
0.019351212307810783,
-0.023454148322343826,
-0.05509855970740318,
-0.013797925785183907,
-0.005365194287151098,
-0.06687245517969131,
0.05358731001615524,
0.0535627044737339,
0.008079453371465206,
-0.030834943056106567,
-0.0067093404941260815,
0.03733242675662041,
0.01817346177995205,
-0.05350860580801964,
0.024658041074872017,
0.06547410041093826,
-0.05317556485533714,
0.02691381797194481,
-0.014036530628800392,
0.016111714765429497,
-0.021611923351883888,
0.01778220757842064,
0.02283201925456524,
0.023693697527050972,
-0.010086874477565289,
-0.009303814731538296,
-0.02518606372177601,
-0.012654384598135948,
-0.005690661258995533,
0.010696827434003353,
0.01591402478516102,
0.0004373767878860235,
0.011008494533598423,
0.024198805913329124,
-0.0050997962243855,
0.0683322623372078,
0.013176943175494671,
-0.06520909816026688,
-0.009730959311127663,
0.03539818897843361,
-0.036543164402246475,
-0.03829836845397949,
0.01626242697238922,
0.024727948009967804,
0.0015873406082391739,
-0.03274055942893028,
0.023159345611929893,
-0.034391965717077255,
-0.03843599930405617,
0.033092740923166275,
-0.02112393081188202,
0.06130005046725273,
-0.024433422833681107,
0.03487686812877655,
0.08421330899000168,
-0.02396376244723797,
0.011295785196125507,
0.10516868531703949,
-0.021543405950069427,
0.025887317955493927,
0.012797215953469276,
0.011478536762297153,
-0.02576666697859764,
-0.026172226294875145,
0.01497938297688961,
0.03789461404085159,
-0.021545713767409325,
-0.07985609769821167,
-0.001275835675187409,
0.011733544990420341,
0.015242151916027069,
-0.0014971974305808544,
0.08611061424016953,
-0.031146768480539322,
-0.027129201218485832,
-0.00018781005928758532,
-0.013698140159249306,
-0.006314688362181187,
-0.04782106727361679,
0.04232659563422203,
-0.04819432273507118,
0.008298724889755249,
-0.012251298874616623,
-0.07929766178131104,
-0.005618109833449125,
0.019470328465104103
] |
<p>If one is able to travel into the past but at a spatial distance that puts him outside of his own past light cone would this be considered a causality violating trip? Looking at a Minkoski diagram, it would seem that one ought to be able to travel to a spatially displaced past without producing causality violations. In fact, I'm not sure you could even say whether this was the past of not for sure. <img src="http://i.stack.imgur.com/U34I5.png" alt="Generic Minkowski diagram"></p>
<p>For instance: If you found a one way wormhole, that took you outside of your own lightcone but into the past, could you say for sure that you traveled through time? Would this be a form of timetravel that did not violate causality? Note; I'm not necessarily suggesting that it is an FTL trip, it may be considered to be instantaneous teleportation, but in the reverse direction of x'. </p>
|
g2462
|
[
0.03593050688505173,
-0.008416878059506416,
0.026977241039276123,
-0.049828290939331055,
-0.018346430733799934,
-0.02657478302717209,
0.02936338074505329,
0.04064996913075447,
-0.048258598893880844,
-0.04006709158420563,
0.02565585821866989,
-0.006630508229136467,
0.048731692135334015,
0.035237427800893784,
-0.05128844454884529,
-0.03397035598754883,
0.0593448169529438,
-0.00965629331767559,
0.07157832384109497,
0.03251909837126732,
0.0488421805202961,
0.024558747187256813,
-0.022525038570165634,
-0.025351407006382942,
0.003492339514195919,
-0.10708510875701904,
0.0850040540099144,
-0.03383951634168625,
-0.05459626019001007,
-0.012675230391323566,
0.08323424309492111,
-0.04526200890541077,
-0.011293538846075535,
-0.06615561246871948,
-0.027237195521593094,
-0.040520668029785156,
-0.017403237521648407,
-0.028824521228671074,
0.09922109544277191,
0.03514474630355835,
-0.05517217144370079,
0.05183599516749382,
-0.0040841600857675076,
-0.03745931014418602,
0.045289214700460434,
0.012740325182676315,
-0.00628215866163373,
0.0005707616219297051,
-0.007048988714814186,
-0.015176220797002316,
-0.06612572818994522,
0.008834026753902435,
-0.018323468044400215,
-0.014098589308559895,
-0.03972652554512024,
-0.013925870880484581,
0.013006975874304771,
-0.03359495848417282,
0.07195230573415756,
0.00810336135327816,
-0.033658117055892944,
0.04314263164997101,
0.0895330160856247,
0.03575892373919487,
0.05269141495227814,
-0.010294296778738499,
-0.05837193876504898,
0.00956864282488823,
-0.01672464795410633,
-0.04274528846144676,
0.0343884713947773,
-0.002159359399229288,
-0.03584473580121994,
-0.02696283347904682,
-0.004371988587081432,
0.02040119096636772,
0.014874101616442204,
-0.011675791814923286,
0.04756525158882141,
0.009938386268913746,
-0.06498229503631592,
-0.024175001308321953,
-0.0008467597654089332,
0.01567455194890499,
0.1306377798318863,
-0.009446307085454464,
0.02157372422516346,
-0.027216849848628044,
-0.02391650900244713,
-0.004840473178774118,
-0.0023303620982915163,
-0.033816348761320114,
0.09335613995790482,
0.003230090718716383,
-0.0021159425377845764,
-0.03605217859148979,
0.023924648761749268,
0.061607543379068375,
-0.0276653990149498,
0.03641688451170921,
-0.05132478103041649,
-0.007444747723639011,
0.012325335294008255,
-0.013104533776640892,
-0.03278719261288643,
-0.045811548829078674,
0.027465904131531715,
0.0026715269777923822,
0.05471634119749069,
-0.06206297501921654,
0.021251199766993523,
-0.05378546565771103,
0.007042851764708757,
0.0307341068983078,
0.02188114821910858,
-0.03957613557577133,
-0.028065720573067665,
-0.009347142651677132,
0.023366956040263176,
0.03600500524044037,
-0.033564601093530655,
0.022516226395964622,
-0.029399240389466286,
0.02747178263962269,
-0.02814965322613716,
0.05231223255395889,
-0.05562589690089226,
0.011441397480666637,
0.025908799842000008,
0.031799234449863434,
-0.05495217815041542,
0.024348318576812744,
0.020514562726020813,
0.11098075658082962,
-0.021846681833267212,
-0.035561151802539825,
0.04590976610779762,
0.036423392593860626,
-0.031479839235544205,
0.030241014435887337,
0.04569489508867264,
-0.0329262875020504,
0.009123213589191437,
0.02973497100174427,
0.03343150019645691,
-0.012869938276708126,
-0.007884918712079525,
-0.03552664816379547,
0.00894880574196577,
0.012773143127560616,
-0.003684202441945672,
0.038398854434490204,
-0.005082431249320507,
0.01540355198085308,
0.02942226268351078,
-0.014530498534440994,
0.024883609265089035,
-0.0022515796590596437,
-0.04418526217341423,
0.025308340787887573,
0.02644783817231655,
0.02206241711974144,
0.08689095824956894,
-0.003378757741302252,
-0.039653584361076355,
-0.02803782932460308,
0.006680868100374937,
0.017540771514177322,
0.011370169930160046,
-0.0917964056134224,
-0.05080642178654671,
0.04025375097990036,
0.04490774869918823,
0.012689804658293724,
0.0018580446485430002,
0.008876209147274494,
-0.020368875935673714,
-0.014313816092908382,
-0.007783879060298204,
0.005719894077628851,
-0.05509798973798752,
0.000973183719906956,
-0.019795013591647148,
-0.005818625912070274,
0.0008242164039984345,
-0.03978075459599495,
-0.019869832322001457,
-0.008937906473875046,
-0.026417510583996773,
-0.012208091095089912,
0.05157717317342758,
-0.06364504247903824,
0.004256234038621187,
0.005517229437828064,
-0.029624318704009056,
-0.0669872835278511,
0.013529326766729355,
-0.00688126077875495,
-0.009591822512447834,
0.006486843805760145,
0.016587667167186737,
0.028884967789053917,
0.015700533986091614,
-0.0056465379893779755,
-0.04307321086525917,
0.02428833395242691,
-0.08092018216848373,
-0.028141750022768974,
-0.013895124197006226,
-0.03034660406410694,
0.022953009232878685,
0.026645898818969727,
-0.013944781385362148,
-0.05779379606246948,
-0.06459955126047134,
-0.005228997673839331,
0.023462597280740738,
0.009787749499082565,
0.0009374942164868116,
0.005068933125585318,
-0.020464876666665077,
0.02534765563905239,
0.07775583863258362,
-0.037983570247888565,
-0.007492106407880783,
-0.03180324658751488,
-0.006030173506587744,
-0.07672785222530365,
0.006369126029312611,
0.014263657853007317,
-0.03240319341421127,
-0.0010788531508296728,
-0.06877768784761429,
0.006871823221445084,
0.0635717585682869,
0.028877900913357735,
0.017458176240324974,
0.0016915606101974845,
0.008023389615118504,
-0.03715270385146141,
0.035572681576013565,
-0.014677952043712139,
-0.05151452124118805,
-0.0001669734192546457,
0.011137261055409908,
-0.09723077714443207,
-0.014515869319438934,
-0.07226069271564484,
0.008401963859796524,
0.022163504734635353,
0.006594100035727024,
-0.010131778195500374,
0.006274326704442501,
0.03097551502287388,
-0.018126241862773895,
-0.029337484389543533,
0.058693867176771164,
0.06810097396373749,
-0.12681446969509125,
-0.03957090899348259,
-0.02803688310086727,
-0.016087651252746582,
-0.04034394025802612,
-0.03460795804858208,
0.0037090620025992393,
-0.05049604922533035,
0.03381768986582756,
0.011393021792173386,
-0.05961373448371887,
0.007997016422450542,
-0.024635199457406998,
0.01316085085272789,
-0.00631285272538662,
0.014104909263551235,
0.07013960182666779,
0.015058659017086029,
-0.011381225660443306,
0.032077349722385406,
0.005496695172041655,
0.029697921127080917,
-0.020297424867749214,
0.03106480836868286,
-0.05706973001360893,
-0.029782170429825783,
0.021841973066329956,
-0.07016699016094208,
0.004071216098964214,
0.025859849527478218,
-0.011417059227824211,
0.02524278312921524,
-0.02692447602748871,
-0.0044456529431045055,
0.009321997873485088,
-0.013961760327219963,
0.002369081135839224,
0.02314119040966034,
-0.0015479187713935971,
-0.015967214480042458,
0.026425328105688095,
-0.0363839752972126,
0.014570244587957859,
-0.02036094106733799,
0.03689293563365936,
0.005483814515173435,
0.012258273549377918,
-0.024169698357582092,
-0.0588509626686573,
-0.02539825439453125,
0.0405452698469162,
0.010799800045788288,
-0.004133574664592743,
0.05987883359193802,
-0.025648582726716995,
0.026633666828274727,
0.022209012880921364,
0.017849059775471687,
-0.037242770195007324,
0.03759623318910599,
-0.02299679070711136,
-0.029887979850172997,
0.014301263727247715,
0.04422217980027199,
-0.05095693841576576,
0.026435719802975655,
0.03614944592118263,
-0.0401986688375473,
0.0008350108982995152,
-0.02097395993769169,
-0.04408448189496994,
0.01706443727016449,
-0.0007841469487175345,
-0.07013557106256485,
0.011115197092294693,
-0.04997596517205238,
0.009224134497344494,
-0.013141141273081303,
0.01813010685145855,
0.04734322056174278,
0.007550519425421953,
-0.004479844123125076,
-0.03159397095441818,
-0.07781517505645752,
-0.014495007693767548,
-0.017852669581770897,
0.06210995092988014,
0.029571516439318657,
0.013338170945644379,
0.13097992539405823,
0.0057012708857655525,
0.001719693304039538,
0.03436403349041939,
-0.007407044991850853,
-0.03637118265032768,
-0.003603114280849695,
0.012036178261041641,
0.042783964425325394,
-0.02440688945353031,
0.06892799586057663,
0.024668652564287186,
0.004543640650808811,
0.04360423982143402,
0.03199728578329086,
-0.0461411215364933,
-0.02774166502058506,
0.025873661041259766,
0.03974387049674988,
0.028279662132263184,
0.0663214698433876,
0.0516563281416893,
0.02822405844926834,
0.036398470401763916,
0.046224676072597504,
0.0021190305706113577,
0.010788810439407825,
0.06506146490573883,
-0.008813299238681793,
0.045663122087717056,
0.025926867499947548,
-0.012403185479342937,
0.066669762134552,
0.02700045518577099,
0.0493379607796669,
0.05793990194797516,
0.03916686400771141,
0.04581470042467117,
0.03448689356446266,
-0.03761591389775276,
-0.010484283789992332,
-0.039396051317453384,
0.005209775175899267,
0.01675892248749733,
-0.004817241337150335,
0.015108841471374035,
-0.047171615064144135,
0.005499281920492649,
0.05451706051826477,
0.018644042313098907,
-0.06804150342941284,
0.024380998685956,
-0.014978829771280289,
0.06078369542956352,
0.02138017863035202,
0.042580511420965195,
-0.00019004088244400918,
-0.03763609379529953,
0.008351601660251617,
-0.008416343480348587,
-0.01514207012951374,
0.004556136205792427,
0.025696871802210808,
0.010409023612737656,
-0.03555205464363098,
-0.06299552321434021,
-0.05320645496249199,
-0.008177312090992928,
-0.04018629714846611,
0.07314255088567734,
0.022304778918623924,
0.002001526765525341,
-0.01807837188243866,
0.005260639823973179,
0.0020658241119235754,
0.0008865328854881227,
0.03746439516544342,
-0.005638439673930407,
0.057167306542396545,
0.022766921669244766,
-0.05045078322291374,
-0.016160326078534126,
-0.012754019349813461,
-0.052283912897109985,
0.03856683149933815,
-0.08358118683099747,
-0.024111308157444,
-0.020239459350705147,
-0.03683192655444145,
0.012098209001123905,
0.008958373218774796,
0.06937142461538315,
-0.013191758655011654,
0.030128562822937965,
-0.01478574424982071,
0.06927786767482758,
0.024121087044477463,
-0.03892894461750984,
0.0012998791644349694,
-0.027025574818253517,
-0.05169716104865074,
0.00858560111373663,
-0.00320397038012743,
-0.0405094213783741,
0.04749411344528198,
-0.008655508980154991,
-0.0024732507299631834,
-0.015665458515286446,
0.01688653789460659,
-0.043521247804164886,
-0.015443525277078152,
-0.0137027557939291,
-0.042217619717121124,
0.0015067834174260497,
-0.019706834107637405,
0.038971781730651855,
-0.012470089830458164,
-0.014219737611711025,
0.04742980748414993,
-0.018769295886158943,
-0.027776340022683144,
-0.04048483818769455,
0.028784440830349922,
-0.01161887589842081,
0.010437200777232647,
0.0008333413279615343,
0.021302612498402596,
-0.035498473793268204,
0.031759656965732574,
-0.02333120070397854,
0.006177453324198723,
-0.09105398505926132,
-0.029138507321476936,
-0.03472293168306351,
0.02937363088130951,
0.02728850021958351,
-0.007200636435300112,
-0.0037134590093046427,
0.03680930286645889,
0.0005556090618483722,
-0.01408850122243166,
0.05888310447335243,
-0.004719906486570835,
0.015560190193355083,
-0.02817692421376705,
0.0209505558013916,
-0.0036219165194779634,
0.015268110670149326,
0.03374648094177246,
0.014945819042623043,
0.03811845928430557,
-0.052555426955223083,
-0.03202017769217491,
-0.06244591996073723,
0.06742070615291595,
0.08775132149457932,
-0.051863908767700195,
0.008737852796912193,
-0.008957098238170147,
0.035339776426553726,
0.02589179016649723,
-0.058751996606588364,
0.011639446951448917,
-0.002887597307562828,
0.005071548745036125,
-0.0648743212223053,
-0.026175672188401222,
0.04721355438232422,
-0.06297758966684341,
-0.039604831486940384,
0.0065061673521995544,
0.006890903227031231,
-0.04245671629905701,
-0.03956993669271469,
0.029041683301329613,
0.029546648263931274,
-0.012391062453389168,
0.013650929555296898,
0.05565756931900978,
-0.028189320117235184,
-0.03556496277451515,
0.0032285002525895834,
-0.0031692106276750565,
0.01772388257086277,
0.01063723023980856,
0.04738735407590866,
-0.022263258695602417,
-0.05851977691054344,
-0.020502658560872078,
0.009320970624685287,
-0.023852352052927017,
0.028168577700853348,
-0.03294556215405464,
-0.021733958274126053,
-0.0777265727519989,
-0.015323436819016933,
0.0310351699590683,
-0.04272822290658951,
-0.002351697999984026,
0.010719720274209976,
0.033376265317201614,
-0.00017073894559871405,
-0.07095809280872345,
-0.04119894653558731,
0.02103310637176037,
-0.07167571038007736,
0.022961927577853203,
-0.007300737779587507,
0.05792655795812607,
-0.05050698667764664,
-0.015358260832726955,
-0.05164998024702072,
-0.03948323428630829,
0.05181187763810158,
-0.011068190447986126,
0.01682211272418499,
-0.01832083985209465,
-0.017081568017601967,
-0.04024053364992142,
0.014612621627748013,
0.006043640896677971,
0.0278979130089283,
0.03905187547206879,
-0.0004295340331736952,
-0.01526852697134018,
-0.024330561980605125,
0.024255802854895592,
0.0039503248408436775,
0.018546150997281075,
0.03038855269551277,
0.011346884071826935,
-0.013619702309370041,
0.01550205796957016,
-0.004109754227101803,
0.01293757651001215,
0.05877614766359329,
-0.06330303847789764,
-0.041799794882535934,
0.015499042347073555,
-0.043306052684783936,
0.028886310756206512,
0.02652750164270401,
-0.027988476678729057,
-0.030491776764392853,
-0.0019580803345888853,
-0.013120659627020359,
-0.030347222462296486,
-0.02724326215684414,
0.013968400657176971,
-0.012432518415153027,
-0.0009769403841346502,
-0.06962514668703079,
0.03557189553976059,
-0.007966574281454086,
-0.02584230899810791,
0.02440679632127285,
-0.019081827253103256,
-0.00796456728130579,
0.07743223756551743,
-0.03784969449043274,
0.07727734744548798,
0.027191290631890297,
-0.03695700317621231,
0.05998438596725464,
0.01811341941356659,
-0.023232491686940193,
0.0018547357758507133,
-0.032019130885601044,
0.05849306285381317,
-0.0827198177576065,
-0.0616585798561573,
-0.04386936500668526,
0.0322871170938015,
0.05337744206190109,
-0.017218738794326782,
-0.02160535752773285,
0.033929262310266495,
-0.013796425424516201,
0.07879168540239334,
-0.027117829769849777,
0.023128217086195946,
0.005371080711483955,
0.051278725266456604,
-0.0515873022377491,
0.005155012011528015,
-0.055106308311223984,
0.026669755578041077,
0.030036726966500282,
-0.008677461184561253,
-0.030813567340373993,
-0.0023919518571347,
-0.03267703577876091,
0.0007539278012700379,
0.03431018069386482,
-0.036532554775476456,
0.004311326425522566,
-0.007264977321028709,
0.00408451771363616,
-0.027860382571816444,
0.04530712217092514,
0.017634520307183266,
-0.038454167544841766,
-0.019277531653642654,
0.05105486512184143,
0.021418705582618713,
-0.007447761949151754,
0.010662557557225227,
-0.015621451660990715,
-0.060415443032979965,
-0.04975896701216698,
0.08500581979751587,
-0.02443491294980049,
-0.033020325005054474,
-0.02007552981376648,
0.008515785448253155,
-0.012050990015268326,
-0.013784403912723064,
-0.00016192762996070087,
0.05606254190206528,
-0.02757854200899601,
-0.05622543394565582,
-0.03898853063583374,
0.0018962239846587181,
0.02118927799165249,
0.0035796123556792736,
-0.024855170398950577,
0.030336789786815643,
-0.03222828730940819,
-0.009761983528733253,
0.01284123957157135,
0.058396510779857635,
0.0034839960280805826,
0.026419147849082947,
0.006043317262083292,
0.02115493081510067,
0.02422013320028782,
-0.005998757667839527,
-0.0470903106033802,
0.0095360754057765,
0.008970837108790874,
0.012091436423361301,
-0.02638872340321541,
-0.020279735326766968,
0.010644346475601196,
0.02239907532930374,
-0.02393554523587227,
-0.004881276283413172,
0.03707508742809296,
-0.041320011019706726,
0.02831481210887432,
0.058057013899087906,
-0.0397893525660038,
-0.022923870012164116,
-0.034792523831129074,
0.03288131207227707,
0.053901612758636475,
-0.03190207853913307,
-0.008140741847455502,
-0.015432476997375488,
0.015727851539850235,
0.025596749037504196,
-0.027530517429113388,
0.04214441031217575,
0.03136053681373596,
0.0889333039522171,
-0.023988837376236916,
-0.01538953185081482,
0.024295127019286156,
-0.035865385085344315,
0.008477375842630863,
0.02882128208875656,
0.055639006197452545,
-0.032985955476760864,
-0.006076302845031023,
0.05075957253575325,
-0.028272924944758415,
-0.05753740668296814,
-0.021060718223452568,
0.042379818856716156,
0.01283454429358244,
-0.02747187204658985,
-0.03226520121097565,
-0.025443773716688156,
0.04783860966563225,
0.021532922983169556,
-0.05134635791182518,
0.027114974334836006,
0.01022360846400261,
0.03716658055782318,
-0.03666456788778305,
0.02134408801794052,
0.024280067533254623,
0.018994541838765144,
0.026774652302265167,
-0.0031145852990448475,
-0.04967120662331581,
-0.011408246122300625,
-0.05204474553465843,
0.057541050016880035,
0.02526116743683815,
-0.01029707957059145,
0.009193388745188713,
0.004325367510318756,
0.03907907009124756,
0.031105171889066696,
0.012796762399375439,
0.03194897621870041,
0.001675529987551272,
-0.00685142120346427,
-0.048930469900369644,
-0.04667733982205391,
0.04931493476033211,
0.02042708359658718,
-0.015145886689424515,
0.0226689875125885,
0.03275715932250023,
0.002254129620268941,
-0.044148217886686325,
-0.030041120946407318,
0.00046131882118061185,
0.04998750239610672
] |
<p>I was reading up on the history of the solar neutrino problem, and as far as I can understand it, neutrinos supposedly oscillate from one form to another, thus explaining why there were only one-third the number of neutrinos detected than were expected, when they began neutrino observations in the 1960's.</p>
<p>The <a href="https://en.wikipedia.org/wiki/Solar_neutrino_problem">Wikipedia article on the topic</a> ends with this statement:</p>
<blockquote>
<p>The convincing evidence for solar neutrino oscillation came in 2001
from the Sudbury Neutrino Observatory (SNO) in Canada. It detected all
types of neutrinos coming from the Sun, and was able to distinguish
between electron-neutrinos and the other two flavors (but could not
distinguish the muon and tau flavours), by uniquely using heavy water
as the detection medium. After extensive statistical analysis, it was
found that about 35% of the arriving solar neutrinos are
electron-neutrinos, with the others being muon- or tau-neutrinos. The
total number of detected neutrinos agrees quite well with the earlier
predictions from nuclear physics, based on the fusion reactions inside
the Sun.</p>
</blockquote>
<p>But as far as I can see, none of this or anything else I've read seems to give any <em>proof</em> that solar neutrinos change type while <em>en route</em> to the Earth. It seems that the sun just emits about 1/3 of each of the three types. </p>
<p>Or is it that at the temperature of the solar core only electron neutrinos are emitted, and then they oscillate (randomly?) from that type to the others and back again? I'd welcome a little clarity about this.</p>
|
g2463
|
[
-0.00038799343747086823,
0.05393931269645691,
0.011642655357718468,
0.010144829750061035,
0.028340879827737808,
-0.025142500177025795,
0.007580663543194532,
0.0021312397439032793,
-0.0021553155966103077,
0.0037687676958739758,
0.028210172429680824,
0.07158618420362473,
0.05644442141056061,
0.02657596953213215,
0.02007414773106575,
-0.03275409713387489,
0.0028701743576675653,
-0.04729524627327919,
0.06322448700666428,
0.035732049494981766,
0.007059844676405191,
-0.001174612669274211,
0.04894942417740822,
-0.061922889202833176,
-0.08494126051664352,
0.021127089858055115,
-0.022625252604484558,
-0.051949407905340195,
-0.005845119245350361,
-0.023937422782182693,
0.0713261067867279,
-0.02215389534831047,
0.07896126806735992,
-0.0740024596452713,
-0.058463335037231445,
-0.0375082828104496,
0.04225803166627884,
-0.018859801813960075,
0.005086712073534727,
0.007917140610516071,
0.011315764859318733,
-0.015400390140712261,
0.0004949345602653921,
0.016030805185437202,
0.046546824276447296,
-0.006707575172185898,
-0.04426198452711105,
0.009493889287114143,
0.0067469035275280476,
-0.02203642576932907,
0.04953327029943466,
-0.05190698802471161,
0.036673419177532196,
0.0053600347600877285,
0.016369681805372238,
-0.025982040911912918,
0.010810893960297108,
-0.06956499069929123,
0.06974932551383972,
0.037128716707229614,
0.04136646166443825,
-0.012462073005735874,
0.008056060411036015,
-0.04372907429933548,
-0.0005100228590890765,
-0.028069881722331047,
0.0017059724777936935,
0.036453839391469955,
0.025751769542694092,
0.0015137563459575176,
-0.004589145537465811,
-0.04517181217670441,
0.007642327807843685,
0.0039840885438025,
0.07300357520580292,
0.00040148210246115923,
-0.03859013319015503,
-0.03088521771132946,
0.0010166562860831618,
0.017008526250720024,
0.09511101990938187,
-0.028237799182534218,
-0.04894213005900383,
0.04579649865627289,
0.05765186995267868,
-0.0423085018992424,
-0.012569132260978222,
0.036766257137060165,
0.0009982039919123054,
-0.06774982064962387,
-0.00696592777967453,
-0.03391672670841217,
0.01420795638114214,
-0.04477832093834877,
-0.006410971283912659,
0.0032697615679353476,
0.024463878944516182,
0.033742934465408325,
-0.03919057920575142,
0.004411187954246998,
-0.09729399532079697,
-0.02315809391438961,
0.00770954042673111,
0.006586998701095581,
0.006569092161953449,
0.02596769668161869,
-0.009688517078757286,
-0.002826347714290023,
-0.08176061511039734,
-0.04917740821838379,
0.014588747173547745,
-0.010264872573316097,
0.012698817066848278,
0.04282316938042641,
-0.07548973709344864,
-0.016557740047574043,
0.025407517328858376,
-0.016540944576263428,
0.045376911759376526,
0.012484281323850155,
-0.007494831457734108,
-0.008384939283132553,
-0.06412384659051895,
0.11945182830095291,
-0.05662490427494049,
-0.020902350544929504,
-0.00015992771659512073,
0.01224758941680193,
-0.0036100514698773623,
0.01963306963443756,
-0.019537372514605522,
-0.022497041150927544,
-0.02857651561498642,
-0.01726347953081131,
0.1066908910870552,
0.0038314496632665396,
0.03930260241031647,
0.021268777549266815,
0.019066696986556053,
-0.029044684022665024,
0.036569397896528244,
-0.043031178414821625,
0.03019041381776333,
-0.02857092209160328,
0.02236076444387436,
0.03751643747091293,
-0.013757623732089996,
-0.0007349881925620139,
-0.010289665311574936,
-0.009203704074025154,
-0.03453901410102844,
0.007477456703782082,
-0.01956554502248764,
-0.042209334671497345,
-0.015525756403803825,
-0.033938176929950714,
-0.07623422145843506,
-0.023382289335131645,
-0.015345354564487934,
-0.009642387740314007,
0.0303374994546175,
-0.036336351186037064,
0.014770114794373512,
-0.05342109128832817,
0.0005013504414819181,
0.026274224743247032,
-0.011739599518477917,
-0.0006580469198524952,
-0.02138437330722809,
0.005938592366874218,
-0.07006362080574036,
0.0053153131157159805,
-0.03603028133511543,
-0.02434108592569828,
-0.004654665477573872,
0.038542501628398895,
0.09107086807489395,
-0.04517681151628494,
-0.022039489820599556,
0.0578603520989418,
-0.08671877533197403,
-0.00587772810831666,
-0.0354231633245945,
-0.030936943367123604,
0.05026300624012947,
-0.019151847809553146,
-0.004841227550059557,
0.008563704788684845,
0.042418841272592545,
-0.010302223265171051,
-0.0222303569316864,
-0.03918803110718727,
-0.004569477867335081,
-0.013044917024672031,
0.021104060113430023,
0.011404348537325859,
-0.05976786091923714,
-0.05649367347359657,
-0.03018251247704029,
-0.005359027534723282,
0.03244004771113396,
0.0031890401151031256,
0.027971431612968445,
0.005836394149810076,
-0.038206927478313446,
-0.048498719930648804,
0.016053950414061546,
-0.013670978136360645,
0.004936296958476305,
0.002536388346925378,
0.045531101524829865,
-0.03946443274617195,
0.013636358082294464,
0.014234735630452633,
-0.07081843912601471,
0.0032613466028124094,
-0.0210857056081295,
0.028957979753613472,
0.03592638298869133,
-0.043410610407590866,
-0.03302481397986412,
0.027474744245409966,
-0.015450763516128063,
0.008662592619657516,
-0.04256492853164673,
0.10290814191102982,
-0.022080659866333008,
-0.0296329315751791,
0.007617924828082323,
0.011105874553322792,
-0.05237376689910889,
0.0432153157889843,
-0.02314121462404728,
-0.005135721061378717,
-0.04900174215435982,
-0.0336906798183918,
0.023884134367108345,
-0.0029900483787059784,
0.03158692270517349,
-0.049064576625823975,
-0.02466174028813839,
-0.018086718395352364,
-0.03115282766520977,
-0.03444606810808182,
0.06841255724430084,
-0.08439693599939346,
-0.02829090878367424,
0.008803775534033775,
0.004752020351588726,
0.06228794530034065,
0.028165854513645172,
-0.028792405501008034,
-0.027731696143746376,
0.08463448286056519,
0.02062670886516571,
0.006953303702175617,
-0.022739732638001442,
-0.015915270894765854,
-0.01526294369250536,
0.010854442603886127,
-0.009114464744925499,
-0.07345710694789886,
0.0400216206908226,
0.03121202066540718,
0.03404545038938522,
-0.026389092206954956,
-0.04226918891072273,
0.004836674779653549,
0.004176270216703415,
-0.012642467394471169,
-0.04820430278778076,
0.03247891739010811,
0.008777820505201817,
-0.02445422299206257,
0.008571626618504524,
-0.019211295992136,
-0.02313358522951603,
0.03254023194313049,
0.04208194091916084,
0.01641608029603958,
-0.025381779298186302,
-0.022249355912208557,
-0.0106351925060153,
-0.013464379124343395,
0.03650226071476936,
0.002163539407774806,
-0.043069638311862946,
-0.01769774593412876,
0.02128431759774685,
0.035119377076625824,
0.06268058717250824,
-0.01964532770216465,
0.0846409797668457,
-0.004984548315405846,
0.029143178835511208,
-0.0645383968949318,
0.007125226315110922,
0.02085232175886631,
-0.031588952988386154,
0.024025674909353256,
0.016549091786146164,
0.01220178697258234,
-0.014323406852781773,
0.006594265345484018,
0.062171779572963715,
0.011588072404265404,
-0.03613652288913727,
-0.031555987894535065,
0.046196747571229935,
-0.0014469032175838947,
0.026356294751167297,
0.014247355982661247,
-0.03375767543911934,
0.007492644712328911,
0.04482393339276314,
0.011432736180722713,
-0.04955684021115303,
0.017153127118945122,
0.054477762430906296,
-0.04388168826699257,
-0.026123929768800735,
-0.03225697576999664,
0.036375537514686584,
0.04384779557585716,
0.016420621424913406,
0.01727275922894478,
0.017396053299307823,
0.0008564903982914984,
-0.03440219536423683,
-0.024291228502988815,
0.016366317868232727,
0.02938920259475708,
-0.05064327269792557,
-0.024026183411478996,
-0.044055286794900894,
0.05363399162888527,
0.013193792663514614,
0.05805957317352295,
0.010255319997668266,
0.027395356446504593,
0.01703176088631153,
0.019680678844451904,
-0.02584117278456688,
0.013791925273835659,
0.031099393963813782,
-0.02035217359662056,
-0.03646865487098694,
-0.031424764543771744,
-0.0028293104842305183,
0.003813706338405609,
0.0781482383608818,
0.021292202174663544,
-0.013787226751446724,
0.01830955408513546,
-0.07039189338684082,
0.037422049790620804,
-0.025701528415083885,
-0.02275211177766323,
0.005685980897396803,
0.053629498928785324,
0.01201572734862566,
-0.0008415217162109911,
0.07210544496774673,
0.06995531171560287,
0.02075960673391819,
-0.019423598423600197,
0.010546118021011353,
0.023647964000701904,
0.014109412208199501,
-0.030307820066809654,
-0.00887433160096407,
-0.049138955771923065,
-0.036323193460702896,
-0.048673857003450394,
0.02644607238471508,
-0.04807095229625702,
-0.02057787962257862,
0.06505423039197922,
0.026354722678661346,
0.07999904453754425,
-0.001444075140170753,
-0.029159750789403915,
0.004299576859921217,
-0.10489558428525925,
0.06527925282716751,
0.03090784139931202,
-0.030017144978046417,
-0.03302900493144989,
-0.01988404244184494,
-0.09212049096822739,
-0.02596381865441799,
0.022168587893247604,
-0.015922097489237785,
0.020153049379587173,
0.002599651925265789,
-0.009601414203643799,
0.034787025302648544,
0.04190388694405556,
0.0635845810174942,
0.006790583021938801,
0.0005722389905713499,
-0.049760155379772186,
-0.012971716932952404,
-0.06381982564926147,
0.02479957602918148,
0.0669221580028534,
-0.017407502979040146,
-0.025138409808278084,
0.017618153244256973,
-0.047051623463630676,
0.0059709432534873486,
0.03505022078752518,
-0.003309098305180669,
-0.003109061624854803,
0.02669951692223549,
-0.0483904629945755,
0.027511151507496834,
-0.003466174006462097,
-0.005803486332297325,
0.027440743520855904,
-0.008419380523264408,
0.0030231766868382692,
-0.06593302637338638,
0.032632097601890564,
0.014161227270960808,
0.07184284180402756,
0.032785139977931976,
-0.0001832597190514207,
-0.04106704890727997,
-0.039614733308553696,
-0.028319235891103745,
0.02596292272210121,
-0.013078827410936356,
0.021589376032352448,
0.024529818445444107,
0.018118014559149742,
-0.0035513180773705244,
0.008629903197288513,
-0.028236713260412216,
0.06260176748037338,
0.04866799712181091,
-0.02470804564654827,
0.020246826112270355,
0.02184388041496277,
0.006252744235098362,
0.04301898926496506,
-0.006117032375186682,
0.0010639167157933116,
-0.004052376374602318,
-0.002446532715111971,
-0.026614544913172722,
-0.013655989430844784,
-0.052512869238853455,
0.06072229519486427,
-0.03764816001057625,
-0.02153695933520794,
-0.008908726274967194,
-0.005365405231714249,
-0.036004237830638885,
0.049008216708898544,
-0.04236564412713051,
-0.024894097819924355,
0.049258969724178314,
0.04048454016447067,
0.04105565696954727,
-0.024968108162283897,
-0.030386965721845627,
-0.00006282481626840308,
-0.021854640915989876,
-0.03715456277132034,
0.011533108539879322,
0.056414395570755005,
0.028260985389351845,
-0.0145098976790905,
0.007627067621797323,
-0.029305122792720795,
-0.022860795259475708,
-0.008325817994773388,
0.004250653553754091,
-0.00659308722242713,
-0.0024241877254098654,
-0.02202642522752285,
-0.016760434955358505,
-0.007399726193398237,
-0.05817858874797821,
0.016418714076280594,
-0.014552706852555275,
-0.004183952696621418,
0.026195848360657692,
-0.013216722756624222,
0.04395642131567001,
-0.07848985493183136,
0.06480399519205093,
-0.014899705536663532,
-0.014963211491703987,
0.0052686273120343685,
0.00014463164552580565,
-0.02179287001490593,
0.05804642289876938,
-0.04983881860971451,
-0.10521179437637329,
0.022879598662257195,
-0.04488685727119446,
-0.002586160320788622,
0.05144859477877617,
0.0010911613935604692,
-0.0020265348721295595,
0.012184405699372292,
0.027214160189032555,
-0.01861782930791378,
0.02786858379840851,
-0.019420351833105087,
-0.10031937062740326,
0.025407085195183754,
0.026640811935067177,
-0.024342592805624008,
-0.08753851801156998,
0.02275332808494568,
0.03768903762102127,
0.045993417501449585,
-0.007297673728317022,
-0.029263177886605263,
-0.018266070634126663,
0.03993889316916466,
0.04095172882080078,
-0.004605446010828018,
-0.031312551349401474,
-0.012279260903596878,
0.06591889262199402,
-0.03400736302137375,
0.045882441103458405,
0.031693171709775925,
0.04458635672926903,
0.0323856957256794,
0.03542039170861244,
-0.08073082566261292,
0.016088329255580902,
0.03565555438399315,
0.0718466117978096,
0.03125955909490585,
-0.027221431955695152,
-0.04591873288154602,
0.022307099774479866,
0.010979190468788147,
-0.001683137845247984,
0.0323508158326149,
-0.0017098530661314726,
0.018829064443707466,
-0.022072425112128258,
0.03861766308546066,
-0.008444663137197495,
0.06695395708084106,
0.019114656373858452,
-0.03680414333939552,
-0.025681303814053535,
0.013815403915941715,
0.0010540647199377418,
-0.011800775304436684,
0.03459586948156357,
0.012477638199925423,
0.041370537132024765,
0.007161226589232683,
0.01661890186369419,
0.045632533729076385,
-0.03582708165049553,
-0.01896504871547222,
-0.01366251241415739,
-0.025524063035845757,
0.007047061342746019,
0.047101281583309174,
0.09161227196455002,
0.015357576310634613,
0.005836465395987034,
-0.014793050475418568,
-0.018743788823485374,
-0.0692768543958664,
-0.00943252444267273,
0.02389327995479107,
-0.06536408513784409,
-0.024390874430537224,
0.020125064998865128,
-0.038856204599142075,
-0.01710621640086174,
-0.01901468262076378,
0.0052725146524608135,
0.0416003093123436,
-0.03417284041643143,
0.05075203999876976,
-0.04340873286128044,
-0.01492888294160366,
0.017262481153011322,
-0.041634730994701385,
-0.031026752665638924,
0.02405235916376114,
-0.037827812135219574,
-0.043726805597543716,
0.007832370698451996,
0.006834221072494984,
-0.018940456211566925,
0.041825562715530396,
0.03466688469052315,
0.022133566439151764,
0.039310522377491,
-0.011450571939349174,
0.022948993369936943,
-0.013576551340520382,
0.027731481939554214,
0.035052329301834106,
0.05343125760555267,
-0.00697074830532074,
0.004769131075590849,
0.04043218493461609,
-0.002383815823122859,
-0.039501089602708817,
0.004895348567515612,
-0.03780895099043846,
-0.07576561719179153,
-0.011997060850262642,
0.038617294281721115,
-0.0013699530391022563,
0.02258627861738205,
0.029869884252548218,
-0.003922089468687773,
0.032693054527044296,
0.02129712700843811,
0.05656598135828972,
0.01215280033648014,
-0.023480314761400223,
0.08269095420837402,
-0.04692807421088219,
0.026438884437084198,
0.013206981122493744,
-0.040689148008823395,
0.06597752124071121,
-0.0002208341029472649,
-0.05090023949742317,
0.05692801997065544,
-0.045437801629304886,
-0.04406748339533806,
0.017549801617860794,
-0.04065408185124397,
-0.02036122791469097,
0.04506693780422211,
-0.03662797808647156,
-0.008787923492491245,
0.003751621348783374,
0.03532379865646362,
0.0071035646833479404,
-0.06070413812994957,
-0.010132227092981339,
-0.0028556131292134523,
-0.042048726230859756,
-0.0026247722562402487,
0.012725471518933773,
0.0005062302225269377,
0.07074534893035889,
-0.004441935569047928,
0.03410019725561142,
0.013258738443255424,
-0.09078725427389145,
-0.016445402055978775,
-0.05643744766712189,
0.009048400446772575,
0.017962032929062843,
0.07565096020698547,
0.006954485550522804,
0.0016128417337313294,
-0.04910242557525635,
-0.004755063913762569,
-0.048225387930870056,
-0.028251197189092636,
0.059061888605356216,
-0.004943637177348137,
0.016917822882533073,
-0.04322660714387894,
-0.028819989413022995,
-0.026960138231515884,
-0.011799796484410763,
0.022771887481212616,
0.016529446467757225,
0.05650000274181366,
-0.04417773336172104,
0.011638311669230461,
0.025919202715158463,
0.039245497435331345,
9.559627187627484e-7,
-0.07692305743694305,
-0.024894995614886284,
-0.003613464068621397,
0.011322279460728168,
0.02722504362463951,
0.08932743966579437,
0.03260103240609169,
0.008167861960828304,
-0.03852153941988945,
0.006107615306973457,
-0.04452337697148323,
-0.05592409893870354,
0.02699378877878189,
-0.005688087083399296,
-0.08355193585157394,
0.006203223019838333,
0.014770167879760265,
0.00900511909276247,
0.0021821102127432823,
0.010390291921794415,
0.028656667098402977,
-0.04281216114759445,
-0.04069802165031433,
0.06581943482160568,
0.05032717064023018,
0.01887187920510769,
0.054327137768268585,
0.0538388229906559,
-0.0071309939958155155,
0.015903126448392868,
-0.07958914339542389,
-0.008791553787887096,
-0.01469409093260765,
-0.005057549104094505,
-0.025242267176508904,
0.0003756062942557037,
0.04437953233718872,
0.04392121732234955,
0.013749485835433006,
-0.005134172271937132,
0.0444643497467041,
0.017896907404065132,
0.03313997760415077,
-0.07135842740535736,
0.003919989336282015,
-0.007089323364198208,
0.01132386364042759,
-0.08485382795333862,
0.029157506301999092,
0.006214801222085953,
0.012656164355576038,
-0.02892008051276207,
-0.002050758572295308,
-0.02024620957672596,
0.003262368030846119,
0.011772877536714077,
0.03486853837966919,
-0.0037861596792936325,
-0.04553017020225525,
-0.04368772730231285,
-0.03074701502919197,
0.022567452862858772,
-0.057641226798295975,
-0.05119239166378975,
0.0024206119123846292,
-0.00982594583183527,
-0.007528611458837986,
0.026124486699700356,
0.039947509765625,
0.0008396340417675674,
-0.02705395594239235,
-0.01399542111903429,
-0.03026653081178665,
0.01158512569963932,
-0.010612529702484608,
-0.029429184272885323,
0.04501652345061302,
-0.03965530917048454,
0.0072492025792598724,
-0.009113505482673645,
0.021809445694088936,
0.02970835007727146
] |
<p>It is claimed that <a href="http://www.google.com/#q=de+Sitter+temperature" rel="nofollow">de Sitter temperature</a> is $$T=\frac{1}{2\pi}H,$$</p>
<p>where $H$ is the Hubble constant. I presume it is expressed in natural units with which I am not familiar. So what it will be in Kelvins? Is it higher than the temperature of CMB? If so, is there any heat exchange between the both?</p>
|
g2464
|
[
0.04711994156241417,
0.0004967962158843875,
-0.04436558485031128,
0.0037848753854632378,
0.00974783580750227,
0.007021086290478706,
-0.0037925411015748978,
0.05401333421468735,
-0.04755179211497307,
-0.015424441546201706,
-0.03254687413573265,
0.0021242969669401646,
-0.012335539795458317,
-0.015167243778705597,
0.015119812451303005,
-0.01789749786257744,
0.050117235630750656,
-0.01773267239332199,
0.020187940448522568,
0.05539759621024132,
-0.04150623083114624,
-0.013232867233455181,
-0.052996132522821426,
-0.03519183397293091,
-0.00421292707324028,
-0.02526238188147545,
-0.026465333998203278,
0.05145508795976639,
-0.023030158132314682,
-0.02807384729385376,
0.005013823974877596,
0.07061593234539032,
0.02112107165157795,
-0.06319431215524673,
-0.06085413694381714,
-0.03335634991526604,
0.05254330486059189,
0.020515577867627144,
0.017389321699738503,
0.0014213144313544035,
-0.04117985814809799,
-0.025193918496370316,
0.016846155747771263,
-0.014187297783792019,
-0.03148829936981201,
-0.009485353715717793,
-0.012547208927571774,
0.027834290638566017,
-0.03716001287102699,
0.006686221808195114,
-0.025484928861260414,
0.0480228029191494,
0.03417818620800972,
0.0066183931194245815,
0.016864193603396416,
-0.009026219137012959,
-0.007595674134790897,
-0.004320936743170023,
0.043260734528303146,
0.06004142016172409,
0.03076307475566864,
0.009732039645314217,
-0.010951602831482887,
0.022871218621730804,
0.04493686556816101,
0.02936551906168461,
-0.020885782316327095,
-0.011683396063745022,
-0.01620401255786419,
0.008463159203529358,
0.021301034837961197,
-0.020877381786704063,
-0.01774887926876545,
-0.04848800599575043,
-0.0640849620103836,
-0.005036288406699896,
-0.007481233682483435,
-0.047158341854810715,
0.05247502774000168,
0.018788112327456474,
-0.017687372863292694,
0.05539684370160103,
0.05122915655374527,
0.022679844871163368,
0.06055694445967674,
0.016420764848589897,
-0.012390442192554474,
0.043115608394145966,
-0.0040403325110673904,
0.021118393167853355,
-0.0075057800859212875,
0.018176384270191193,
0.046126704663038254,
0.03469458967447281,
0.04964824765920639,
-0.047037430107593536,
0.03888818249106407,
-0.0036285833921283484,
-0.01613854616880417,
-0.008819462731480598,
-0.009546720422804356,
0.06302092969417572,
0.01756877824664116,
0.02389357052743435,
-0.00925697386264801,
-0.02687007561326027,
-0.009820313192903996,
-0.017635172232985497,
-0.016675321385264397,
0.03274573013186455,
0.002377151744440198,
0.007903398014605045,
-0.01365039311349392,
-0.05492207035422325,
-0.06602662056684494,
-0.011531809344887733,
-0.006711190100759268,
-0.02798999659717083,
0.014531304128468037,
0.015231789089739323,
0.06876205652952194,
0.05541623383760452,
-0.01758076250553131,
0.11809641867876053,
-0.021127667278051376,
0.010786043480038643,
0.016554199159145355,
0.003346266457810998,
-0.03600332513451576,
-0.03524768352508545,
-0.020257651805877686,
-0.0020028227008879185,
-0.0725150853395462,
-0.016129225492477417,
-0.008619680069386959,
-0.006791713647544384,
0.03650369867682457,
0.006651382427662611,
-0.03217537701129913,
0.01380907092243433,
0.007217190694063902,
-0.012430384755134583,
0.04812591150403023,
-0.04105566442012787,
-0.08908200263977051,
0.057766273617744446,
-0.0074778893031179905,
-0.03564903885126114,
0.052687108516693115,
0.00896753091365099,
0.01758391037583351,
0.0845261812210083,
0.0594593808054924,
-0.045838478952646255,
-0.0018028899794444442,
-0.0047075324691832066,
0.05435692146420479,
0.03024924173951149,
0.054825104773044586,
0.014405823312699795,
0.0386909544467926,
-0.021907104179263115,
0.05375846475362778,
-0.010130179114639759,
-0.050928257405757904,
0.012435958720743656,
-0.025201058015227318,
-0.000041263647290179506,
0.04732344299554825,
-0.03643259406089783,
-0.033956050872802734,
-0.012586095370352268,
-0.027246274054050446,
0.02461404912173748,
-0.011604842729866505,
-0.04625384137034416,
-0.03606478497385979,
0.058876506984233856,
-0.01898529939353466,
-0.040090516209602356,
-0.019794056192040443,
-0.0204277615994215,
0.0699918270111084,
-0.03298342227935791,
-0.05902068689465523,
0.06562018394470215,
-0.019131075590848923,
-0.05512583255767822,
-0.013548143208026886,
0.04629918187856674,
-0.05014285817742348,
-0.02822243608534336,
0.03481045365333557,
0.07488622516393661,
0.056646838784217834,
0.013121996074914932,
-0.053480129688978195,
-0.0051217954605817795,
-0.00513273011893034,
0.05951790139079094,
0.009931479580700397,
-0.0023880316875874996,
0.05912450700998306,
-0.03797692432999611,
0.030069006606936455,
0.02564348094165325,
0.0025250406470149755,
-0.02906545251607895,
-0.008526940830051899,
-0.01970818266272545,
-0.03248064965009689,
-0.0020196563564240932,
0.01010430883616209,
0.0037332428619265556,
0.05525565892457962,
0.01208490040153265,
0.00856238603591919,
0.015368540771305561,
-0.021205179393291473,
-0.02854054979979992,
-0.05036230757832527,
0.046873196959495544,
0.02290152944624424,
0.004634401760995388,
0.014661536552011967,
-0.0632978230714798,
-0.028084399178624153,
-0.01033127959817648,
0.018643487244844437,
0.014786767773330212,
-0.047638751566410065,
0.03759128227829933,
0.02104259468615055,
0.07486770302057266,
0.05977100133895874,
0.017555447295308113,
0.04043427109718323,
-0.0410652793943882,
0.040610406547784805,
0.08381832391023636,
-0.012477041222155094,
0.004532156977802515,
-0.02409767359495163,
0.01778564602136612,
0.01464362908154726,
0.019924374297261238,
0.013235785998404026,
-0.03571348637342453,
-0.012153193354606628,
-0.023929215967655182,
0.00807588454335928,
-0.09307382255792618,
0.01832685060799122,
-0.02188485860824585,
-0.05121519789099693,
-0.003967591095715761,
-0.04508688673377037,
0.0006570778787136078,
-0.06160362437367439,
-0.06398509442806244,
0.016791902482509613,
-0.048375096172094345,
0.00637354189530015,
-0.012016515247523785,
-0.021343352273106575,
-0.08068469166755676,
-0.04383690655231476,
0.007133335806429386,
-0.01229354739189148,
-0.001884843921288848,
0.02354007586836815,
0.00787467323243618,
-0.02168547548353672,
0.0567106157541275,
0.004504196811467409,
0.005563446786254644,
0.0634278804063797,
-0.05092690512537956,
-0.009244750253856182,
-0.04942336305975914,
0.018351342529058456,
-0.000902744650375098,
-0.010811339132487774,
0.014227238483726978,
-0.0018938638968393207,
-0.024278372526168823,
-0.052316125482320786,
0.05099824070930481,
0.025152938440442085,
-0.04590275138616562,
0.044597018510103226,
0.0021847947500646114,
-0.027375880628824234,
0.038122355937957764,
0.036972761154174805,
0.03569604456424713,
0.05893484130501747,
-0.022779634222388268,
-0.0028310769703239202,
0.010847322642803192,
0.04507454112172127,
-0.0592154897749424,
0.017998287454247475,
-0.026616407558321953,
-0.012892873026430607,
0.027753185480833054,
-0.023586804047226906,
-0.0887453556060791,
-0.04218866676092148,
-0.03780880570411682,
-0.00634849164634943,
-0.0015255501493811607,
0.00976650882512331,
0.02976357750594616,
-0.03507246449589729,
-0.014287793077528477,
-0.02558302693068981,
-0.01614486239850521,
0.04623766988515854,
-0.020181719213724136,
0.01459578052163124,
-0.05676296725869179,
-0.04867195338010788,
-0.04071870818734169,
0.022283468395471573,
0.0637282282114029,
-0.02040022797882557,
-0.026253189891576767,
-0.08995254337787628,
-0.011590938083827496,
-0.019076207652688026,
-0.05151602625846863,
0.021717768162488937,
-0.0013023309875279665,
-0.03473343327641487,
-0.022069407626986504,
0.02472819946706295,
-0.021916691213846207,
0.03599219396710396,
0.024984491989016533,
0.004044088069349527,
0.0019726338796317577,
-0.018518835306167603,
0.04747907072305679,
0.0021084677428007126,
-0.0018793722847476602,
-0.012283410876989365,
0.0034585827961564064,
-0.00411220034584403,
-0.0023434357717633247,
0.020831750705838203,
-0.01936539076268673,
0.014189724810421467,
0.007723480463027954,
-0.027603834867477417,
0.00008908403106033802,
0.007792312186211348,
0.010563896037638187,
-0.04378888010978699,
0.02103242836892605,
0.066038116812706,
-0.038911785930395126,
0.052664417773485184,
0.030624492093920708,
0.029883000999689102,
-0.012880966998636723,
-0.03729761764407158,
0.05986786633729935,
0.010391442105174065,
-0.032106924802064896,
-0.03342725709080696,
-0.015533922240138054,
-0.012335674837231636,
0.07448101788759232,
0.13379351794719696,
-0.03864136338233948,
0.032772962003946304,
0.013400470837950706,
-0.005197235848754644,
0.019168389961123466,
-0.0294182188808918,
0.03296813741326332,
-0.001068313722498715,
0.0162104070186615,
0.06535027176141739,
-0.03982749208807945,
-0.0023168933112174273,
-0.006924092303961515,
0.022828372195363045,
-0.08101542294025421,
0.05425316095352173,
-0.02766864374279976,
0.027322541922330856,
0.03433100879192352,
-0.011683586053550243,
-0.017670826986432076,
-0.009248106740415096,
0.012761706486344337,
0.023044448345899582,
-0.033943045884370804,
0.031953487545251846,
-0.03569710627198219,
0.05671478807926178,
-0.027033409103751183,
-0.014771930873394012,
-0.010398180224001408,
0.013481642119586468,
-0.04895938187837601,
-0.013122417964041233,
0.007869329303503036,
-0.023075809702277184,
0.0223117396235466,
0.04678960517048836,
-0.06168895214796066,
0.00781251210719347,
0.0017245161579921842,
0.015104426071047783,
-0.02282034233212471,
0.09837069362401962,
0.008003134280443192,
-0.042608849704265594,
0.003425255650654435,
-0.010551978833973408,
-0.010379052720963955,
-0.006394988391548395,
0.021228792145848274,
-0.029257694259285927,
0.023664988577365875,
-0.00032164057483896613,
0.010908916592597961,
0.05038253217935562,
-0.052099939435720444,
0.03105912357568741,
0.05419658496975899,
-0.00949431024491787,
0.09714405238628387,
-0.03282030299305916,
0.014739524573087692,
-0.07157737761735916,
-0.01840364746749401,
0.011961049400269985,
0.0028018972370773554,
-0.0003549537213984877,
-0.0005123518640175462,
-0.0024166591465473175,
0.03982698544859886,
0.019631462171673775,
-0.07308025658130646,
-0.005856415256857872,
-0.07220374792814255,
0.030833281576633453,
0.018973015248775482,
-0.00854048877954483,
0.039992958307266235,
-0.010327174328267574,
0.015944384038448334,
-0.010685781016945839,
-0.007990540005266666,
-0.0438409261405468,
0.0497409887611866,
-0.08584161847829819,
0.020498182624578476,
0.033316124230623245,
0.005027574021369219,
0.06260894238948822,
-0.04963483661413193,
-0.023253552615642548,
-0.02174234203994274,
0.014940841123461723,
0.025639429688453674,
0.017508862540125847,
0.05142116919159889,
0.038498394191265106,
0.0015405990416184068,
0.04685511440038681,
0.004366280976682901,
0.02696085534989834,
-0.08295010030269623,
-0.03638232499361038,
-0.020406493917107582,
0.008019959554076195,
0.027263015508651733,
0.004704299848526716,
0.06740358471870422,
-0.0447031632065773,
-0.005404675379395485,
-0.03985625132918358,
0.0047851866111159325,
0.020067179575562477,
0.04605192318558693,
-0.012024610303342342,
0.007645621430128813,
0.04475177824497223,
0.025241756811738014,
-0.02150983177125454,
0.04076768085360527,
-0.01911763660609722,
-0.026742011308670044,
0.08837167918682098,
-0.001675192965194583,
0.001477553742006421,
0.0005356383044272661,
0.008432342670857906,
0.026873823255300522,
-0.019944138824939728,
0.09588414430618286,
0.07351658493280411,
-0.004903806839138269,
-0.0555129274725914,
0.05269532650709152,
-0.0042149075306952,
0.014736088924109936,
-0.00036754386383108795,
0.029797295108437538,
0.0068067931570112705,
0.01637277565896511,
0.02572866901755333,
0.013852385804057121,
-0.01574057899415493,
0.03308308497071266,
0.03592231497168541,
-0.008773156441748142,
0.08712122589349747,
-0.003266318468376994,
-0.0015251432778313756,
-0.01682269386947155,
0.009191918186843395,
0.024056635797023773,
0.014574996195733547,
0.001077881664969027,
0.02701619267463684,
0.012519091367721558,
0.05115193873643875,
-0.0241438839584589,
0.053391434252262115,
0.015871359035372734,
-0.02026430517435074,
-0.011637560091912746,
0.008574658073484898,
0.029698317870497704,
-0.056804511696100235,
-0.03165823221206665,
0.020716235041618347,
0.01836288906633854,
-0.014737801626324654,
0.024071432650089264,
-0.03825703635811806,
0.03251757472753525,
0.04824609309434891,
0.010465886443853378,
-0.05954769626259804,
-0.04977164790034294,
0.002078630030155182,
-0.0211754459887743,
0.04608030244708061,
0.034948669373989105,
0.050795137882232666,
0.02250136248767376,
-0.025353483855724335,
-0.012010232545435429,
-0.028030524030327797,
-0.003012468572705984,
0.0489131398499012,
0.03374939784407616,
-0.020358720794320107,
-0.05642704293131828,
-0.02814723737537861,
-0.01054358296096325,
0.0796789899468422,
-0.00522446958348155,
-0.019071366637945175,
-0.03026825375854969,
-0.014900276437401772,
-0.017509952187538147,
0.0946718081831932,
-0.0022209282033145428,
-0.06288367509841919,
-0.01757681742310524,
-0.03957722708582878,
0.01602225750684738,
-0.0034777473192662,
-0.020843643695116043,
-0.024862827733159065,
0.03083443082869053,
-0.02923845872282982,
0.05789625272154808,
-0.034937478601932526,
0.05051114782691002,
-0.0249720998108387,
0.05712036043405533,
0.017102347686886787,
-0.011767299845814705,
-0.01967490278184414,
0.015871897339820862,
0.03576688468456268,
0.002312860917299986,
0.000005336808953870786,
-0.027767736464738846,
-0.04333442077040672,
-0.044930875301361084,
0.0349898636341095,
-0.05842377617955208,
0.0008820293587632477,
-0.0007735621766187251,
0.06485892832279205,
-0.048788681626319885,
-0.040621574968099594,
-0.0007302988087758422,
-0.020222211256623268,
0.01930953748524189,
0.02085511013865471,
-0.01657765358686447,
0.024424675852060318,
-0.026095550507307053,
0.05089640989899635,
-0.05123487487435341,
0.061091482639312744,
0.018983639776706696,
-0.03780648484826088,
0.048229511827230453,
0.0018965298077091575,
-0.013948285952210426,
-0.03761538863182068,
-0.042473070323467255,
0.006813472602516413,
0.011749734170734882,
-0.014606068842113018,
0.041183821856975555,
0.02969273366034031,
0.009815994650125504,
0.013352845795452595,
0.024240577593445778,
-0.007670598104596138,
0.001707597984932363,
0.039048828184604645,
0.010323544032871723,
-0.10638885945081711,
-0.020290829241275787,
-0.0036347785498946905,
0.02585679478943348,
-0.021452518180012703,
-0.0008024699054658413,
0.08426393568515778,
-0.041913099586963654,
-0.04382217675447464,
-0.00691770575940609,
-0.004057145677506924,
-0.009083200246095657,
-0.04509375989437103,
0.025877440348267555,
-0.04340241104364395,
-0.06917503476142883,
-0.018352795392274857,
0.01217771414667368,
0.00120828568469733,
-0.018807072192430496,
0.0371343195438385,
0.007355451583862305,
0.001883352524600923,
-0.05486626178026199,
0.02203412540256977,
-0.04454721510410309,
-0.025187881663441658,
0.005433978512883186,
0.021703269332647324,
0.0019668578170239925,
0.011064949445426464,
-0.005286754108965397,
0.05325472354888916,
-0.06068052351474762,
-0.005838614422827959,
-0.07592631131410599,
-0.005902468226850033,
-0.04528868943452835,
-0.03339560702443123,
0.004175342619419098,
-0.05495442450046539,
0.008646780624985695,
0.019759392365813255,
0.028785465285182,
-0.036418214440345764,
-0.002648863010108471,
0.009629071690142155,
-0.03559053689241409,
-0.019756635650992393,
0.004756533540785313,
-0.040012579411268234,
-0.07227993756532669,
0.08564455062150955,
0.021167011931538582,
-0.0008655568235553801,
0.029212284833192825,
-0.01658898964524269,
-0.07545509189367294,
0.006713854614645243,
-0.0074667674489319324,
0.04490341991186142,
-0.010986944660544395,
-0.005466771312057972,
-0.04816064611077309,
0.0011042068945243955,
-0.04052489995956421,
0.011329304426908493,
-0.024706674739718437,
-0.008628162555396557,
0.06273037940263748,
0.013506216928362846,
-0.04479682072997093,
-0.09080515801906586,
-0.00880601815879345,
0.07706265896558762,
-0.009748083539307117,
0.049054067581892014,
-0.015173045918345451,
0.018556609749794006,
0.014513392932713032,
-0.06943727284669876,
-0.019045384600758553,
0.04697049781680107,
-0.05594105273485184,
-0.015222757123410702,
-0.029313605278730392,
-0.014536229893565178,
-0.04489262402057648,
0.005126869771629572,
-0.014747814275324345,
-0.002323920838534832,
-0.03723466023802757,
0.007013501133769751,
-0.03001137636601925,
0.019909238442778587,
0.044740378856658936,
0.020080015063285828,
0.00018796838412526995,
-0.044023577123880386,
0.016287846490740776,
0.02295585162937641,
-0.016303468495607376,
0.01887766271829605,
0.057200901210308075,
0.0191265307366848,
-0.0519174188375473,
0.0495237372815609,
-0.028144368901848793,
-0.047054968774318695,
-0.01261388510465622,
-0.1072317436337471,
0.017186030745506287,
0.036619555205106735,
-0.06871650367975235,
0.042279306799173355,
0.008969168178737164,
-0.0746845155954361,
-0.009048755280673504,
0.04896681383252144,
-0.051648836582899094,
-0.041528429836034775,
0.015957044437527657,
-0.03756270185112953,
-0.005173728335648775,
-0.027169784530997276,
-0.031922902911901474,
-0.03245264291763306,
0.013462431728839874,
0.056770406663417816,
0.021633829921483994,
-0.009675879031419754,
0.03326236829161644
] |
<p>We know that level-k Abelian 2+1D Chern-Simons theory on the $T^2$ spatial torus gives ground state degeneracy($GSD$):
$$GSD=k$$</p>
<p><strong>How about $GSD$ on $T^2$ spatial torus of</strong>: </p>
<p><strong>SU(N)$_k$ level-k Chern-Simons theory?</strong></p>
<p><strong>SO(N)$_k$ level-k Chern-Simons theory?</strong></p>
<p><strong>Sp(N)$_k$ level-k Chern-Simons theory?</strong></p>
<p>What are the available methods to compute them? such (i) algebraic geometry; (ii) Lie algebra; (iii) topological theory or (iv) quantum hall fluids parton construction?</p>
<p>an example of SU(2)$_k$ using <a href="http://physics.stackexchange.com/questions/80177/follow-up-question-on-wilson-loops-as-raising-operators">this approach</a> shows $GSD$ on $T^2$ is
$$GSD=(k+1)$$</p>
<p>SU(3)$_k$ using <a href="http://physics.stackexchange.com/questions/80177/follow-up-question-on-wilson-loops-as-raising-operators">this approach</a> shows $GSD$ on $T^2$ is
$$GSD=(k+1)(k+2)/2$$.</p>
<p>If there are examples of $G_2,F_4,E_6,E_7,E_8$ (level-k?) Chern-Simons theory and its $GSD$ on $T^2$, it will be even nicer. Reference are welcome.</p>
|
g2465
|
[
0.019838128238916397,
0.0011561872670426965,
-0.02132481522858143,
-0.014219935052096844,
0.018787603825330734,
0.010321998968720436,
0.04807548597455025,
0.05619998276233673,
-0.01958986558020115,
0.038557592779397964,
0.015153903514146805,
-0.026181574910879135,
0.02534518949687481,
0.04604148119688034,
-0.0020307658705860376,
-0.016974981874227524,
-0.016167694702744484,
0.05060075595974922,
0.00570628372952342,
-0.057368386536836624,
-0.07374873757362366,
-0.04532546177506447,
0.04287656769156456,
-0.04863724857568741,
0.048303645104169846,
-0.0354888029396534,
-0.0001825838116928935,
0.009137215092778206,
0.015301012434065342,
-0.02168835699558258,
-0.021625017747282982,
-0.04296165332198143,
0.03792799636721611,
-0.017871525138616562,
-0.05224849283695221,
0.03157272934913635,
0.07318533211946487,
0.007973711006343365,
-0.00711907260119915,
-0.04834736883640289,
0.023409806191921234,
-0.0588373988866806,
0.010919340886175632,
-0.02105104550719261,
-0.07187268137931824,
0.019330989569425583,
-0.05110463872551918,
0.058739885687828064,
-0.04102407768368721,
-0.027211416512727737,
0.008827133104205132,
0.09984759986400604,
0.05742363631725311,
-0.026673372834920883,
-0.0027256112080067396,
-0.0027397878002375364,
-0.03304072096943855,
-0.008233414962887764,
0.059299103915691376,
0.023062266409397125,
0.015449806116521358,
-0.0009378554532304406,
0.0297121312469244,
0.003075965913012624,
0.014894334599375725,
0.029463279992341995,
-0.016754407435655594,
0.03468489274382591,
-0.06553885340690613,
-0.014457432553172112,
-0.003833333496004343,
-0.01044989749789238,
0.03177929297089577,
0.009270095266401768,
0.018998347222805023,
0.030216477811336517,
0.022722365334630013,
-0.008582010865211487,
0.021233636885881424,
0.03232584893703461,
-0.01357238832861185,
-0.004003494046628475,
-0.07054797559976578,
-0.0676446184515953,
0.02337128110229969,
-0.025871306657791138,
-0.011788459494709969,
0.0423801988363266,
0.019821980968117714,
0.03544572740793228,
-0.026579316705465317,
0.05828594043850899,
0.024921312928199768,
0.05397411808371544,
0.01321960799396038,
0.010879313573241234,
0.039986733347177505,
0.01700940728187561,
-0.0221555233001709,
-0.022154944017529488,
-0.07006119191646576,
-0.020879969000816345,
0.05427871271967888,
0.017834439873695374,
-0.006789456587284803,
-0.010625134222209454,
0.013618149794638157,
0.010750330984592438,
0.007877398282289505,
0.027755307033658028,
-0.08115865290164948,
0.10982371121644974,
-0.004255878739058971,
0.04276154190301895,
-0.018963884562253952,
0.03338410705327988,
0.034676846116781235,
0.003796497592702508,
-0.008319882676005363,
0.006376977544277906,
0.06424126029014587,
-0.022712446749210358,
-0.010582102462649345,
0.0018552563851699233,
0.00823779683560133,
0.016982175409793854,
-0.05424871668219566,
-0.06586011499166489,
0.036315057426691055,
0.018259895965456963,
0.0581897608935833,
-0.04841885343194008,
-0.005291161127388477,
0.05658160522580147,
0.03996577858924866,
0.05527173727750778,
-0.054732948541641235,
-0.006172055844217539,
0.0170986857265234,
0.0006637586047872901,
-0.04614463448524475,
-0.01536317728459835,
-0.06477422267198563,
0.0005509908660314977,
0.0181223563849926,
0.0033663043286651373,
0.00262534711509943,
-0.045003145933151245,
0.01494904886931181,
-0.0005457937950268388,
0.07077062875032425,
-0.03178759291768074,
0.06326865404844284,
-0.048469290137290955,
0.007250661961734295,
-0.009260418824851513,
0.026570487767457962,
0.03312719240784645,
0.030034560710191727,
0.02200559340417385,
0.024193331599235535,
-0.019351957365870476,
0.04618259146809578,
-0.03448740020394325,
0.0003374882217030972,
-0.030587077140808105,
-0.015633508563041687,
-0.01120935007929802,
-0.04437629133462906,
-0.03394021466374397,
-0.04045392572879791,
0.0788458064198494,
0.03136231750249863,
0.008511771447956562,
-0.01527324691414833,
0.04079270735383034,
-0.11224444955587387,
-0.04602258279919624,
0.005857017822563648,
0.07355562597513199,
0.01744105853140354,
-0.009126979857683182,
-0.014650750905275345,
0.05974004045128822,
0.023856697604060173,
0.045677270740270615,
0.0035265719052404165,
-0.020845578983426094,
0.04121335223317146,
-0.04600285366177559,
-0.018427444621920586,
0.03459278121590614,
-0.0014095595106482506,
0.07806622982025146,
0.008261669427156448,
0.003621610812842846,
0.05725793540477753,
-0.06423497945070267,
0.013096657581627369,
0.02127804607152939,
-0.03173890337347984,
0.03575162589550018,
-0.02020484209060669,
-0.029912326484918594,
0.008902918547391891,
0.06746363639831543,
0.0036877247039228678,
0.01668749749660492,
0.0025087492540478706,
-0.04729659482836723,
-0.03569415584206581,
0.008254633285105228,
0.010913398116827011,
0.020417580381035805,
-0.03764673322439194,
-0.030741294845938683,
0.011023635976016521,
-0.037598319351673126,
0.017108749598264694,
-0.020475754514336586,
0.020510753616690636,
0.05370195955038071,
0.01676192879676819,
0.05049305409193039,
0.02393556572496891,
0.00822784285992384,
-0.015870632603764534,
0.0181875042617321,
-0.023656316101551056,
-0.0005452377954497933,
-0.05044180899858475,
-0.001957017695531249,
-0.02538459375500679,
-0.10143636912107468,
0.051555335521698,
0.06409966945648193,
-0.04204520210623741,
-0.011225194670259953,
0.039862897247076035,
0.059801455587148666,
-0.0015155125875025988,
-0.009643989615142345,
0.018889835104346275,
-0.023996401578187943,
0.013360464945435524,
-0.022685831412672997,
0.027345411479473114,
0.003717498853802681,
-0.019893670454621315,
0.03723147138953209,
-0.0018716489430516958,
-0.008855455555021763,
-0.0249549001455307,
0.025325432419776917,
0.0036180519964545965,
0.040127839893102646,
0.018058782443404198,
0.027325719594955444,
0.045229922980070114,
-0.042260561138391495,
0.022235723212361336,
-0.04321641847491264,
0.012324081733822823,
0.030369361862540245,
-0.05017095059156418,
-0.001827175379730761,
-0.019545257091522217,
0.013753211125731468,
0.02907358668744564,
0.014225850813090801,
-0.018608590587973595,
0.05783780291676521,
0.01454051211476326,
0.023441240191459656,
0.01132794190198183,
-0.03716395050287247,
0.014000910334289074,
0.04587147757411003,
-0.03860264644026756,
0.004354920703917742,
-0.02412024512887001,
-0.00697091082111001,
-0.006030202843248844,
0.062419548630714417,
0.03426095098257065,
-0.03455505892634392,
0.0160546712577343,
0.021080879494547844,
-0.01444069854915142,
0.01904640533030033,
0.018091661855578423,
0.03394966199994087,
0.01406047586351633,
0.008553841151297092,
-0.03383103758096695,
0.007031027227640152,
-0.08450372517108917,
-0.04467719793319702,
0.011745729483664036,
0.11484185606241226,
0.012524339370429516,
-0.043364766985177994,
0.01786421798169613,
-0.01962970569729805,
-0.032302431762218475,
-0.03892163932323456,
-0.034290164709091187,
0.01600542850792408,
0.03242829814553261,
-0.0208921916782856,
-0.0030311071313917637,
0.021311871707439423,
0.017222076654434204,
-0.024669133126735687,
0.03257470950484276,
0.04240519180893898,
-0.0026640738360583782,
-0.031619660556316376,
-0.012243551202118397,
0.031126713380217552,
0.020840628072619438,
-0.0576520711183548,
0.03390636667609215,
0.010674076154828072,
-0.006789760664105415,
0.030437827110290527,
-0.0013926938408985734,
-0.019304396584630013,
-0.01976402848958969,
-0.03772619366645813,
0.048485126346349716,
-0.018277106806635857,
0.015990396961569786,
-0.001968473894521594,
-0.04690355062484741,
-0.04964590445160866,
-0.08013913035392761,
-0.019247500225901604,
0.05811174958944321,
0.022639289498329163,
-0.07012078911066055,
-0.01552355196326971,
-0.037448346614837646,
-0.030383309349417686,
-0.004651679657399654,
0.04453190043568611,
-0.05473523586988449,
-0.010288520716130733,
-0.05014381557703018,
-0.026857487857341766,
-0.007648307830095291,
-0.0019419132731854916,
0.03881866857409477,
-0.00048064268776215613,
-0.016624780371785164,
0.023730747401714325,
0.007977595552802086,
0.03447737544775009,
0.034243516623973846,
-0.023767847567796707,
0.029098112136125565,
0.04313606023788452,
0.0014841487864032388,
-0.0002505540905985981,
0.020356232300400734,
-0.044144611805677414,
0.004582300316542387,
-0.020915716886520386,
0.013261758722364902,
0.03063194267451763,
0.03528178855776787,
0.04832642525434494,
-0.005159709136933088,
-0.008136417716741562,
0.07497473806142807,
-0.02717830054461956,
-0.006460473407059908,
-0.03604232519865036,
-0.05032152310013771,
-0.020283697172999382,
-0.003227237146347761,
0.004041651729494333,
0.024235209450125694,
0.028026573359966278,
-0.04050949960947037,
0.03562987223267555,
-0.012922005727887154,
0.04203663766384125,
-0.017395511269569397,
-0.03294732794165611,
-0.06704845279455185,
-0.05631215125322342,
0.012676705606281757,
-0.010419391095638275,
0.010330332443118095,
0.020527366548776627,
0.0706830620765686,
0.02576081082224846,
-0.045671530067920685,
0.04195954650640488,
-0.0030279471538960934,
-0.03133152052760124,
0.011011668480932713,
-0.0818103700876236,
-0.025007473304867744,
0.0003548560489434749,
0.028605656698346138,
0.0033950733486562967,
-0.026255177333950996,
-0.023615222424268723,
0.05218399688601494,
-0.04864535853266716,
0.09413393586874008,
-0.0884532779455185,
0.03232851251959801,
-0.05507175996899605,
-0.0369524247944355,
-0.02232152409851551,
-0.012730419635772705,
-0.03308739885687828,
0.052534569054841995,
0.014034394174814224,
0.03941952437162399,
0.006085340864956379,
-0.030326547101140022,
0.03747312352061272,
-0.04889611527323723,
0.008766314946115017,
0.0012280994560569525,
-0.03172306343913078,
-0.023477591574192047,
-0.0030602170154452324,
-0.022818217054009438,
-0.015606497414410114,
-0.06049934774637222,
0.03330432251095772,
-0.002969328546896577,
0.023299213498830795,
-0.05218391492962837,
0.03966528922319412,
0.06185797601938248,
-0.046906083822250366,
-0.022973371669650078,
-0.03378380462527275,
0.028895188122987747,
0.0036207749508321285,
-0.06086951494216919,
-0.013954360969364643,
0.029195299372076988,
0.002936913399025798,
-0.056455664336681366,
0.009960037656128407,
0.01812632940709591,
-0.011419466696679592,
-0.028595691546797752,
-0.02236059308052063,
0.010135131888091564,
0.05129393935203552,
0.007143871393054724,
-0.006175767630338669,
-0.07482729107141495,
0.023203760385513306,
-0.015026475302875042,
-0.05847945064306259,
0.02484641969203949,
-0.017913347110152245,
-0.054879434406757355,
0.056798312813043594,
0.0065024723298847675,
-0.02329789660871029,
0.01260723453015089,
-0.053420599550008774,
-0.012561391107738018,
-0.06501252204179764,
0.04910488426685333,
0.0094302948564291,
0.030446847900748253,
-0.00979514792561531,
0.013927215710282326,
-0.02047550491988659,
0.05392161011695862,
-0.0053865863010287285,
-0.0067576076835393906,
-0.00740020489320159,
-0.04172476381063461,
0.03514338657259941,
-0.02409215271472931,
-0.02179834619164467,
-0.048760782927274704,
0.026115410029888153,
-0.01973719708621502,
-0.05241312086582184,
-0.011426970362663269,
0.054415956139564514,
-0.008622138760983944,
-0.003085218369960785,
0.011203224770724773,
-0.00891469419002533,
-0.047520559281110764,
0.026667777448892593,
-0.0017424958059564233,
0.022038837894797325,
0.019014419987797737,
0.0668065994977951,
-0.019069485366344452,
0.0022226134315133095,
0.03900400549173355,
-0.07170680165290833,
0.011036183685064316,
-0.013992460444569588,
0.0003653662861324847,
0.0064150867983698845,
0.008859692141413689,
0.005380924791097641,
0.01663406938314438,
-0.017564108595252037,
-0.004095858428627253,
-0.0037395942490547895,
-0.014232426881790161,
-0.08115379512310028,
0.06617659330368042,
0.002911022398620844,
0.06080375984311104,
-0.03398317098617554,
-0.0010705211898311973,
0.06635443866252899,
-0.024389011785387993,
-0.02212725207209587,
-0.0035499120131134987,
0.023822596296668053,
-0.02620694972574711,
-0.08266367018222809,
-0.03211783990263939,
0.021400462836027145,
-0.021594759076833725,
-0.019219812005758286,
0.029305439442396164,
-0.01848873309791088,
-0.004475049674510956,
0.011743268929421902,
0.049615949392318726,
-0.031538352370262146,
-0.038016386330127716,
-0.020852085202932358,
0.011142561212182045,
-0.058782678097486496,
-0.049252334982156754,
-0.01423953752964735,
0.04324568435549736,
-0.011585138738155365,
-0.06176694855093956,
0.005085670854896307,
-0.010047106072306633,
-0.032952211797237396,
0.0038051526062190533,
0.001467307796701789,
-0.03258589655160904,
-0.01276386994868517,
-0.014764215797185898,
0.04704399034380913,
0.03182566910982132,
0.022349080070853233,
0.062099289149045944,
0.003466386115178466,
0.03866887837648392,
0.003916972316801548,
-0.014030412770807743,
0.01595296338200569,
0.08650986850261688,
0.045616935938596725,
-0.0374591089785099,
0.05189322680234909,
-0.03235011175274849,
0.022158091887831688,
-0.01815173216164112,
-0.03871127963066101,
-0.06897474080324173,
-0.07031459361314774,
0.003229287452995777,
0.0322410985827446,
-0.033787455409765244,
0.06935201585292816,
-0.00008869020530255511,
-0.03902813047170639,
-0.07468313723802567,
0.027793893590569496,
-0.030892513692378998,
-0.02105172909796238,
0.05283082649111748,
0.0508277527987957,
-0.038554247468709946,
0.04371365159749985,
-0.04824244603514671,
0.018728267401456833,
0.03225996717810631,
-0.004126063082367182,
0.07114972919225693,
-0.03182889148592949,
-0.021559961140155792,
0.026666242629289627,
0.07388904690742493,
-0.05703803151845932,
-0.006113902665674686,
-0.021998519077897072,
-0.04115412011742592,
0.08878405392169952,
-0.02106916531920433,
-0.00500482926145196,
0.017721187323331833,
0.0018401896813884377,
0.004747294820845127,
-0.003701053559780121,
-0.003419359913095832,
0.042259879410266876,
0.017077377066016197,
-0.09267283976078033,
-0.0037617525085806847,
-0.07469134032726288,
-0.023468663915991783,
-0.014425287954509258,
0.06051909551024437,
0.04231544956564903,
0.02245667390525341,
-0.004675828851759434,
0.06721742451190948,
0.05753445252776146,
0.011566909961402416,
0.0010247910395264626,
0.010134156793355942,
-0.010608197189867496,
0.00829994399100542,
0.02420669049024582,
0.013344982638955116,
0.002208107616752386,
-0.01647234708070755,
0.029627954587340355,
-0.0660206750035286,
0.00866116862744093,
-0.0495559461414814,
0.037791866809129715,
-0.08891107141971588,
0.01985333301126957,
0.04873492941260338,
0.007687206380069256,
0.042934782803058624,
-0.06628674268722534,
-0.02772083878517151,
-0.0024411831982433796,
-0.05497957766056061,
0.025683460757136345,
0.03763385862112045,
-0.04135635122656822,
-0.00018522830214351416,
-0.011201836168766022,
-0.024008458480238914,
-0.04102647304534912,
0.00204865587875247,
-0.033068809658288956,
0.03213278204202652,
-0.002431945875287056,
-0.040783338248729706,
-0.002760562114417553,
0.03236250951886177,
0.02447117306292057,
-0.03624443709850311,
0.08030050992965698,
-0.010161212645471096,
0.019258912652730942,
-0.011052976362407207,
-0.045008882880210876,
0.0038711775559931993,
-0.007054904941469431,
-0.06353379786014557,
-0.004405022598803043,
-0.08132888376712799,
0.019275056198239326,
-0.04375409707427025,
0.05745311826467514,
0.014440041035413742,
0.012779167853295803,
0.01418052613735199,
0.07792574167251587,
-0.014196828007698059,
-0.028747383505105972,
-0.016884081065654755,
-0.01549929566681385,
0.016769392415881157,
0.010935613885521889,
0.012458370067179203,
0.0011828216956928372,
0.04494732245802879,
-0.04617391899228096,
-0.012133042328059673,
0.0375889390707016,
-0.0062591019086539745,
-0.00916678924113512,
-0.0658019483089447,
-0.0276638213545084,
0.004372795578092337,
0.0338665246963501,
0.007323077414184809,
-0.03256513550877571,
-0.08588766306638718,
0.010422082617878914,
0.08550814539194107,
-0.04258642718195915,
0.004358217120170593,
0.031423140317201614,
-0.05767817422747612,
0.022172491997480392,
-0.037341438233852386,
-0.026105143129825592,
-0.043886829167604446,
0.05986126512289047,
-0.01808464154601097,
-0.00542877521365881,
0.013024309650063515,
-0.03499073162674904,
0.027008406817913055,
0.002804295625537634,
0.04027821496129036,
-0.04299183934926987,
0.02110534906387329,
0.020603155717253685,
-0.0040953089483082294,
-0.010860281065106392,
0.030124343931674957,
0.004436972085386515,
0.01782877743244171,
0.055023569613695145,
-0.023931531235575676,
0.021551258862018585,
0.006658606696873903,
0.036706794053316116,
-0.002381762722507119,
0.024825964123010635,
-0.01565878838300705,
-0.06716130673885345,
0.04142850637435913,
0.012385428883135319,
-0.009760785847902298,
-0.015885699540376663,
0.039136260747909546,
-0.06320842355489731,
-0.0025649764575064182,
0.04272738844156265,
-0.01143452525138855,
0.01888839714229107,
-0.0030000368133187294,
-0.04657605662941933,
0.07349905371665955,
-0.03354240581393242,
0.03580737113952637,
0.0009539570892229676,
-0.03387061133980751,
-0.007299347780644894,
0.050128448754549026,
-0.011091976426541805,
0.03448663279414177,
0.028366172686219215,
0.022688133642077446,
0.013172927312552929,
-0.006612149998545647,
-0.0002610000956337899,
0.009291606023907661,
-0.060803066939115524,
-0.05414297431707382,
0.007942206226289272
] |
<p>I know classical physics, quantum mechanics, special relativity, basic nuclear physics.
I would like to get into some particle physics. </p>
<p>I want to get into that higgs boson, lepton, quark things :D </p>
<p>Where to start? Any books, websites, video lectures? </p>
<p>Mathematical rigor required! </p>
<p>Thanks </p>
|
g154
|
[
0.03906332701444626,
0.07365019619464874,
0.006277906708419323,
0.01063842885196209,
0.04673103615641594,
0.01845354214310646,
-0.03550827503204346,
0.026970943436026573,
0.009760522283613682,
-0.06225130334496498,
0.008372975513339043,
0.04082119092345238,
0.04711072891950607,
0.008487285114824772,
-0.03309176489710808,
-0.016456255689263344,
0.04095893353223801,
0.006031538359820843,
0.028255198150873184,
0.040039703249931335,
0.053298428654670715,
0.05170854181051254,
0.0010716591496020555,
-0.050544291734695435,
-0.06349977105855942,
0.006930291652679443,
-0.0592476949095726,
-0.06682917475700378,
0.01404399611055851,
-0.007045823149383068,
-0.022957818582654,
-0.06338915228843689,
0.009356832131743431,
-0.03407413884997368,
0.036801159381866455,
-0.09223894029855728,
0.04139271005988121,
-0.01759769581258297,
0.03443216159939766,
-0.005772797856479883,
-0.00020345213124528527,
-0.040579475462436676,
-0.016429966315627098,
-0.031115509569644928,
0.04000319913029671,
0.018455658107995987,
0.007067821454256773,
-0.006864931900054216,
-0.02852780930697918,
0.05251319706439972,
-0.007659097667783499,
0.008817995898425579,
0.026851017028093338,
0.007948488928377628,
-0.004822098184376955,
0.044976167380809784,
-0.010538170114159584,
-0.014588464982807636,
0.10739002376794815,
-0.02973104827105999,
0.0015638890909031034,
0.042229242622852325,
-0.05456065014004707,
-0.03480628505349159,
0.004076463170349598,
0.05058857426047325,
-0.02080751769244671,
0.020701661705970764,
0.016669925302267075,
0.032087478786706924,
0.04376441612839699,
-0.06832186877727509,
-0.0011425383854657412,
0.033958062529563904,
-0.009720590896904469,
-0.024236423894762993,
-0.013242554850876331,
-0.014736359007656574,
0.006134616676717997,
-0.022126687690615654,
-0.09091346710920334,
-0.04337679594755173,
0.04290272668004036,
-0.02642620913684368,
0.037035342305898666,
-0.05186793580651283,
-0.06989796459674835,
0.005198835860937834,
-0.011630693450570107,
-0.061152681708335876,
-0.001572099165059626,
0.0013972618617117405,
0.0028836929704993963,
0.01970827952027321,
0.01713494025170803,
-0.04047408699989319,
-0.011839020997285843,
0.034427616745233536,
0.0582282654941082,
-0.007121081929653883,
-0.05392446741461754,
-0.018159106373786926,
0.03738206997513771,
-0.008152779191732407,
-0.0003891588421538472,
-0.021006330847740173,
0.008252453990280628,
0.002371600130572915,
0.04844838008284569,
0.015497013926506042,
-0.07763674855232239,
-0.005301578436046839,
0.004675679374486208,
-0.015756798908114433,
-0.04476818069815636,
0.03452159836888313,
0.02354555018246174,
0.008687079884111881,
0.030469026416540146,
0.10747331380844116,
-0.004476883914321661,
0.05328682065010071,
0.024005480110645294,
0.05791386589407921,
-0.04280252754688263,
-0.026825280860066414,
0.014626620337367058,
-0.016488859429955482,
-0.02733338437974453,
0.02556810900568962,
0.08325541764497757,
-0.016226787120103836,
-0.07692661136388779,
0.01395852118730545,
-0.020941220223903656,
0.05545423552393913,
0.08308269083499908,
-0.00669288681820035,
0.059329740703105927,
-0.009143928997218609,
0.0007152976468205452,
0.025149261578917503,
0.015524568036198616,
-0.011217290535569191,
-0.021002130582928658,
0.0018585814395919442,
-0.04317658394575119,
-0.0016318326815962791,
-0.03732200711965561,
0.007155403960496187,
0.04185036942362785,
0.044288117438554764,
0.004719935357570648,
0.020170750096440315,
0.0430864542722702,
-0.01293245516717434,
0.08334150910377502,
-0.013195590116083622,
0.05436624586582184,
-0.04461882635951042,
-0.007140497677028179,
0.0012917816638946533,
-0.08513568341732025,
0.00847714114934206,
0.03615051507949829,
0.034249648451805115,
-0.010843048803508282,
-0.05098022520542145,
0.021035555750131607,
0.007090203929692507,
-0.03787285462021828,
-0.01670386828482151,
-0.002258595312014222,
0.03272543475031853,
-0.028435884043574333,
0.02195102907717228,
-0.02980528213083744,
-0.04671340808272362,
0.001084882882423699,
-0.014443956315517426,
0.06384965032339096,
-0.03242883458733559,
0.025733977556228638,
0.016566790640354156,
-0.056358400732278824,
0.04132640361785889,
-0.042760927230119705,
0.03524621203541756,
0.010119374841451645,
0.03941521421074867,
-0.06391933560371399,
-0.003816792508587241,
-0.013097272254526615,
-0.018178390339016914,
0.030565882101655006,
0.011170970275998116,
0.0263492614030838,
-0.02182013913989067,
0.02201738767325878,
-0.021369541063904762,
0.052812930196523666,
-0.033559754490852356,
0.06179457902908325,
0.056939497590065,
0.07298025488853455,
0.01624995470046997,
-0.02694879099726677,
0.019643094390630722,
0.03643553704023361,
0.028440706431865692,
0.0011082924902439117,
-0.006713907700031996,
0.025192877277731895,
-0.03321820870041847,
0.024592939764261246,
-0.009888794273138046,
-0.05360613018274307,
0.002297273138538003,
-0.006860687863081694,
0.021701442077755928,
-0.04248829931020737,
-0.03409215807914734,
-0.007820043712854385,
-0.0003438554413150996,
0.0060197836719453335,
0.08163055032491684,
0.007046344690024853,
-0.035117827355861664,
0.06041797623038292,
0.006763049401342869,
-0.10165859013795853,
0.05507959425449371,
-0.015487989410758018,
-0.022428413853049278,
0.03535017371177673,
0.048359598964452744,
-0.02147098071873188,
-0.11991797387599945,
0.02683376334607601,
-0.003906924277544022,
-0.028563957661390305,
-0.006061410531401634,
0.005034762900322676,
-0.04117016866803169,
0.010299710556864738,
-0.06456069648265839,
0.034371498972177505,
-0.032362911850214005,
-0.04928291216492653,
-0.12709279358386993,
0.05387778580188751,
-0.02159421518445015,
-0.03719881922006607,
-0.01433336641639471,
0.01764269359409809,
0.019088728353381157,
0.009277411736547947,
0.022646894678473473,
-0.04445897415280342,
-0.03581302985548973,
0.04101230576634407,
-0.0261314008384943,
-0.04701536148786545,
0.04042181372642517,
-0.06192934885621071,
0.04970308393239975,
-0.07420434802770615,
-0.02920372597873211,
-0.037948884069919586,
-0.010452425107359886,
0.020208194851875305,
0.01805620640516281,
0.022436732426285744,
-0.05243508517742157,
-0.01618112623691559,
-0.02470484934747219,
0.018723996356129646,
0.02129479870200157,
0.035163622349500656,
-0.03864425793290138,
-0.00945521891117096,
-0.0033889315091073513,
0.008640173822641373,
0.013837217353284359,
0.029779769480228424,
-0.0431017130613327,
-0.005479636136442423,
-0.07088907808065414,
-0.03513136878609657,
0.0043206652626395226,
0.008111806586384773,
-0.027812274172902107,
-0.019619105383753777,
0.04638584703207016,
-0.03039228357374668,
0.03846598416566849,
0.003459542989730835,
0.030263610184192657,
-0.08941612392663956,
-0.011141221038997173,
-0.05282564088702202,
-0.033228471875190735,
0.0000019020693571292213,
-0.028651226311922073,
-0.013785679824650288,
-0.002200261689722538,
-0.0006717920186929405,
0.01565004512667656,
0.02558363974094391,
0.009642032906413078,
0.024180518463253975,
0.01591663807630539,
0.009384742006659508,
0.059884440153837204,
0.03372934088110924,
-0.044128019362688065,
0.03839234262704849,
0.07023482024669647,
-0.00456762732937932,
-0.08730648458003998,
-0.00823208037763834,
-0.025950251147150993,
0.016750246286392212,
-0.045698124915361404,
0.05303490161895752,
0.007951089181005955,
0.014475195668637753,
-0.04878317564725876,
-0.04616209864616394,
-0.0006621036445721984,
-0.011364109814167023,
0.012281163595616817,
-0.027693333104252815,
0.01026383601129055,
-0.03992220759391785,
-0.03754500672221184,
0.019834283739328384,
-0.04376782476902008,
0.02029803767800331,
-0.016537558287382126,
0.04996967315673828,
0.00920038390904665,
-0.04141487926244736,
0.011633244343101978,
-0.057241443544626236,
-0.020197533071041107,
0.020177088677883148,
-0.009631297551095486,
0.037715066224336624,
-0.06757568567991257,
0.021171078085899353,
0.029191065579652786,
0.011698967777192593,
0.02147790975868702,
-0.03769649192690849,
0.027003314346075058,
0.004843176808208227,
0.020919691771268845,
0.050688356161117554,
-0.02086769975721836,
-0.0492982491850853,
-0.01755828969180584,
-0.0011448126751929522,
0.05558399111032486,
-0.0837239921092987,
0.00739669194445014,
-0.044475626200437546,
-0.006765497382730246,
-0.005611890461295843,
0.007874070666730404,
-0.03685220703482628,
0.007710839156061411,
0.036045268177986145,
0.0039660451002418995,
-0.02706231363117695,
-0.015876151621341705,
0.01476153265684843,
0.01637592539191246,
0.030236901715397835,
-0.059778179973363876,
-0.03808850049972534,
0.005415049381554127,
0.03171198442578316,
-0.014459718950092793,
0.02653602883219719,
0.025639733299613,
0.0006767400773242116,
0.021491985768079758,
0.007105574011802673,
0.026683563366532326,
0.03706555813550949,
-0.04187370464205742,
-0.010046079754829407,
0.0152490995824337,
0.028271326795220375,
-0.043940674513578415,
0.03462870046496391,
0.014445849694311619,
-0.01695021241903305,
0.020674964413046837,
-0.0750289186835289,
-0.014022612944245338,
0.005821078550070524,
-0.03384317085146904,
0.011717465706169605,
0.03147771209478378,
-0.015197434462606907,
0.020068977028131485,
-0.004170597996562719,
-0.019734084606170654,
0.01573077030479908,
-0.014824273064732552,
0.02016519382596016,
-0.0001443254150217399,
-0.013253282755613327,
-0.048934899270534515,
-0.020683690905570984,
-0.06197759881615639,
0.020013706758618355,
0.01737363450229168,
-0.009675960056483746,
0.02452567033469677,
0.02288665436208248,
-0.027895143255591393,
-0.02681056223809719,
0.06900308281183243,
0.033848654478788376,
0.05233782157301903,
-0.05604851618409157,
0.02219310589134693,
0.04299820959568024,
-0.030113400891423225,
-0.005915672983974218,
-0.0022095320746302605,
-0.0440693162381649,
0.019121631979942322,
0.019622759893536568,
0.023582076653838158,
-0.002035653218626976,
0.00006877553096273914,
0.0628657415509224,
0.02987707406282425,
0.0008231836254708469,
-0.005155447870492935,
-0.010698107071220875,
0.10730952024459839,
-0.022495891898870468,
0.03937928006052971,
-0.01596573181450367,
-0.04316454753279686,
-0.02767813764512539,
0.017838770523667336,
-0.05705024302005768,
-0.044907014816999435,
0.007078351452946663,
0.004012760240584612,
0.012453002855181694,
0.03449251502752304,
0.02413005940616131,
-0.026966895908117294,
-0.041841741651296616,
0.04598230496048927,
0.00940809678286314,
-0.028478607535362244,
-0.02121356874704361,
-0.010697205550968647,
-0.05682942643761635,
-0.02678721956908703,
-0.020502952858805656,
-0.06471212953329086,
-0.028979316353797913,
-0.021706270053982735,
0.02828177437186241,
-0.05344456806778908,
0.03619418293237686,
0.01329683419317007,
-0.06258359551429749,
-0.010046099312603474,
-0.04265185073018074,
-0.024760382249951363,
0.030425775796175003,
0.00422084191814065,
-0.036357179284095764,
0.02171148546040058,
-0.022177232429385185,
0.02294560894370079,
-0.03353259712457657,
0.06421175599098206,
-0.016836613416671753,
-0.001510919420979917,
-0.03655816987156868,
-0.019762713462114334,
0.08542677015066147,
-0.037946462631225586,
-0.012467344291508198,
-0.012417745776474476,
-0.021106518805027008,
-0.010070493444800377,
0.026082077994942665,
0.0040419562719762325,
-0.05229596421122551,
-0.02481125108897686,
-0.028052061796188354,
0.0008928919560275972,
-0.019623510539531708,
0.03969626501202583,
0.002796900225803256,
-0.017059382051229477,
-0.056404389441013336,
-0.02680109441280365,
0.028274165466427803,
0.04373236000537872,
-0.03731919452548027,
0.01485306303948164,
0.008012790232896805,
0.0651729628443718,
-0.023593919351696968,
0.05425861477851868,
-0.0011806429829448462,
-0.033786654472351074,
-0.0427110381424427,
-0.01089409738779068,
-0.02514811046421528,
0.018080323934555054,
-0.0060234214179217815,
0.00497350562363863,
-0.10541767627000809,
0.026815148070454597,
0.014260493218898773,
-0.002682395977899432,
0.023276034742593765,
-0.004142716061323881,
-0.007070160936564207,
0.01406958419829607,
-0.05639336630702019,
0.012927830219268799,
-0.03293876349925995,
-0.015701934695243835,
0.00485713966190815,
0.03874508664011955,
-0.006873108446598053,
-0.004942328203469515,
0.03270376846194267,
0.008967810310423374,
-0.004937008023262024,
0.005155070219188929,
-0.007346184458583593,
0.04754750803112984,
0.07816097885370255,
-0.06817539036273956,
-0.04761020094156265,
-0.0011079051764681935,
0.020938722416758537,
-0.03824906423687935,
-0.01658618077635765,
0.012794328853487968,
0.005669204983860254,
0.03218086063861847,
-0.0022990242578089237,
0.04129774123430252,
0.007220936473459005,
-0.023708663880825043,
0.003649420803412795,
0.011283188126981258,
-0.009540138766169548,
-0.015750769525766373,
-0.025722291320562363,
-0.04388045519590378,
0.05247797071933746,
0.04000627249479294,
-0.033764343708753586,
-0.0014628339558839798,
-0.0552491769194603,
0.016159579157829285,
0.012934316881000996,
0.05097394436597824,
0.013199780136346817,
-0.06667664647102356,
-0.005622548051178455,
0.012517374940216541,
0.020100316032767296,
0.09772667288780212,
0.05205874517560005,
-0.038051966577768326,
-0.05289972200989723,
0.07304495573043823,
-0.0009515523561276495,
0.015805771574378014,
-0.0220321211963892,
0.040309883654117584,
-0.03197723627090454,
0.04271028935909271,
0.0022758517879992723,
-0.06828513741493225,
-0.023261921480298042,
0.015454279258847237,
0.0669548287987709,
-0.00935004185885191,
0.008241971023380756,
0.03535396233201027,
-0.06034635752439499,
-0.021574193611741066,
-0.029508285224437714,
0.01336984895169735,
0.017451537773013115,
0.08406427502632141,
0.035368889570236206,
-0.011800211854279041,
0.010486232116818428,
0.036083661019802094,
0.017272401601076126,
-0.021841229870915413,
0.010764741338789463,
-0.015212848782539368,
-0.009246229194104671,
-0.035009901970624924,
0.011071107350289822,
0.0025938935577869415,
0.03456359729170799,
-0.03475549444556236,
0.033911652863025665,
0.06878061592578888,
0.017660250887274742,
-0.025312691926956177,
0.028173834085464478,
0.03605874255299568,
0.006280404981225729,
0.05770876631140709,
0.050637390464544296,
-0.02181955613195896,
0.037730906158685684,
-0.023049665614962578,
0.06546849757432938,
0.023952187970280647,
-0.018023883923888206,
0.041347455233335495,
0.03613973781466484,
0.0032083503901958466,
-0.01757507026195526,
0.017035668715834618,
0.022449199110269547,
0.000298260769341141,
0.0055705951526761055,
-0.023642031475901604,
-0.008120127022266388,
-0.012977097183465958,
0.016493678092956543,
-0.036300767213106155,
-0.027671806514263153,
-0.022961005568504333,
0.02444932609796524,
-0.04365750402212143,
-0.03195763751864433,
-0.009145178832113743,
-0.014134797267615795,
0.010564824566245079,
0.017206650227308273,
0.00198114151135087,
0.08686671406030655,
-0.08427641540765762,
-0.003469676012173295,
-0.008843163959681988,
0.021430648863315582,
-0.03659001365303993,
0.046171966940164566,
0.053441207855939865,
-0.0294218510389328,
-0.018483242020010948,
-0.0037014400586485863,
0.0058713569305837154,
0.0030306540429592133,
-0.05077993497252464,
-0.1005319133400917,
0.03886976093053818,
-0.016859622672200203,
-0.02179689146578312,
-0.0036416868679225445,
0.039552588015794754,
-0.0027023395523428917,
-0.012041809968650341,
0.02807864546775818,
0.038998764008283615,
-0.020703181624412537,
0.010769223794341087,
-0.01310177706182003,
0.04938400909304619,
0.009546013548970222,
-0.01675906591117382,
0.0038343321066349745,
-0.005039921961724758,
-0.06402186304330826,
-0.03594866767525673,
-0.0033293943852186203,
-0.06060844287276268,
0.02725372649729252,
-0.018397795036435127,
0.05299115926027298,
-0.025759991258382797,
0.022611336782574654,
-0.007354478817433119,
-0.02077474631369114,
-0.01764049008488655,
-0.009391579777002335,
-0.043501123785972595,
0.010296046733856201,
0.04892970249056816,
-0.04934946820139885,
-0.007469290867447853,
-0.020489385351538658,
0.022799938917160034,
-0.0005120649584569037,
-0.008058784529566765,
0.07821861654520035,
0.046254582703113556,
0.01061800867319107,
-0.010878139175474644,
0.01906556263566017,
0.06549839675426483,
-0.01315642986446619,
-0.019915077835321426,
0.025643402710556984,
-0.012876952067017555,
-0.011998243629932404,
-0.023265263065695763,
-0.03913616016507149,
-0.012432749383151531,
-0.03535015508532524,
0.010382597334682941,
-0.02138254977762699,
0.007883581332862377,
0.0027926466427743435,
0.05229578912258148,
-0.04328157380223274,
0.0007179260719567537,
0.0045243483036756516,
0.041252803057432175,
0.03484366834163666,
-0.022096846252679825,
0.05793475732207298,
0.013193406164646149,
0.04585437849164009,
0.03560716658830643,
0.011666398495435715,
0.004649055656045675,
-0.010360215790569782,
-0.11118774116039276,
0.014788690954446793,
0.03801511973142624,
0.04432351514697075,
-0.03887740150094032,
-0.017325596883893013,
0.04397750273346901,
0.02743075229227543,
0.11430520564317703,
0.006965650711208582,
-0.061591215431690216,
-0.001725205685943365,
0.03652137890458107,
-0.013486490584909916,
-0.01876629702746868,
0.07674413174390793,
0.005719806533306837,
0.07718982547521591,
-0.006266111508011818,
-0.040155816823244095,
0.03518853709101677,
-0.016936618834733963,
-0.007307960651814938
] |
<p>Why is it that when we cut bread or anything else with a knife, the less effective way to cut it is just by pressing on it from above? And is it true that we can cut things with knife because of the thin edge that makes an interaction with the other material (like bread)?</p>
|
g2466
|
[
0.05892186984419823,
0.015357979573309422,
0.01938033290207386,
0.060347821563482285,
0.01940034329891205,
-0.007657572161406279,
-0.05070481821894646,
-0.004939808510243893,
-0.09757368266582489,
-0.036156460642814636,
0.01917234994471073,
-0.025392042472958565,
0.029884744435548782,
0.04066373035311699,
0.027419738471508026,
-0.01431503426283598,
0.0015387838939204812,
0.002143602352589369,
0.022979632019996643,
0.02304905094206333,
-0.10790858417749405,
0.0042755259200930595,
0.03899029269814491,
-0.07460147887468338,
-0.09785567969083786,
-0.021750997751951218,
0.03602568432688713,
0.0025653536431491375,
-0.029698936268687248,
0.030478255823254585,
0.0012612839927896857,
0.002964468440040946,
0.016858605667948723,
-0.04328694939613342,
-0.06040303409099579,
-0.0641021803021431,
0.05090126395225525,
-0.02219606190919876,
-0.04034465551376343,
-0.04199949651956558,
-0.06040211021900177,
0.055048100650310516,
-0.03272771090269089,
0.021313438192009926,
0.013998385518789291,
0.006254603620618582,
-0.03838430345058441,
0.035762984305620193,
0.03373003005981445,
-0.06958138942718506,
-0.015204823575913906,
-0.04822259768843651,
0.02063881978392601,
-0.00997232273221016,
0.0535721518099308,
-0.04867471009492874,
0.02687869779765606,
-0.00030104824691079557,
0.037516362965106964,
-0.0387277826666832,
-0.08664269000291824,
0.032071370631456375,
0.003148927353322506,
0.04526239261031151,
0.018270224332809448,
-0.039473649114370346,
-0.03514610603451729,
-0.031106814742088318,
0.02409745380282402,
0.007036865688860416,
0.03547682240605354,
-0.07942420244216919,
-0.02450859546661377,
-0.04569859430193901,
0.029111666604876518,
0.04937687888741493,
0.01507278997451067,
-0.018952608108520508,
-0.03494454547762871,
0.003523243358358741,
0.007453137077391148,
-0.0029827274847775698,
-0.04145820811390877,
-0.008032889105379581,
0.0011057249503210187,
-0.06339330971240997,
-0.012187574990093708,
-0.0454280860722065,
-0.01548595167696476,
0.003028301987797022,
0.018295299261808395,
0.028447004035115242,
0.05754595622420311,
-0.007444832939654589,
-0.08188695460557938,
0.02891540713608265,
0.027576100081205368,
-0.023342693224549294,
-0.03387565165758133,
-0.029908861964941025,
-0.0031991596333682537,
0.01263362169265747,
0.04232785105705261,
-0.008364678360521793,
0.03616467863321304,
0.016249334439635277,
0.035679299384355545,
0.002823752351105213,
-0.011017732322216034,
-0.008168783038854599,
0.025461135432124138,
-0.0023809242993593216,
-0.02105364389717579,
0.023215223103761673,
0.012421829625964165,
-0.03791441395878792,
0.06102494150400162,
0.030198266729712486,
0.01751449890434742,
0.03808898478746414,
-0.05199481546878815,
-0.008302338421344757,
0.008078187704086304,
0.027527514845132828,
-0.04327169060707092,
0.0017810695571824908,
0.04678863286972046,
0.006914387457072735,
0.013411205261945724,
-0.05290275439620018,
0.039544541388750076,
0.01346202939748764,
-0.03386598080396652,
0.01811971515417099,
0.05884743481874466,
0.023106561973690987,
-0.04159727320075035,
-0.0396406389772892,
0.03902208432555199,
0.017824264243245125,
-0.05487184226512909,
0.007257829420268536,
-0.06005881354212761,
-0.01746588759124279,
-0.009678392671048641,
0.03710908070206642,
-0.05943290516734123,
0.08908527344465256,
-0.046042896807193756,
-0.02986445277929306,
0.02970801666378975,
0.03326425328850746,
0.017886830493807793,
0.06077546626329422,
-0.01971488445997238,
-0.02482636086642742,
0.06615028530359268,
0.003128765383735299,
0.03049941174685955,
0.028626156970858574,
0.04176441207528114,
-0.015600094571709633,
-0.0012460127472877502,
0.02017919346690178,
-0.08111155778169632,
-0.017075130715966225,
0.004694374743849039,
-0.022474022582173347,
0.0312826931476593,
-0.02101140469312668,
-0.023602401837706566,
0.054729852825403214,
0.011266978457570076,
-0.008493268862366676,
0.05134882405400276,
0.026910915970802307,
0.08008021861314774,
-0.00777063425630331,
0.019833289086818695,
-0.06277115643024445,
-0.060972195118665695,
0.006967313587665558,
0.02692517265677452,
-0.08284434676170349,
-0.014580963179469109,
0.02657630480825901,
0.055742114782333374,
0.01660253293812275,
0.013926008716225624,
-0.04130164533853531,
-0.03473977372050285,
-0.04327595606446266,
-0.021759122610092163,
0.01928713545203209,
-0.021183747798204422,
-0.034042831510305405,
0.060044459998607635,
0.016714833676815033,
0.0007251910283230245,
-0.04808349162340164,
-0.016870485618710518,
0.008048548363149166,
0.024589350447058678,
-0.010920871049165726,
-0.029846441000699997,
0.019898083060979843,
-0.007066323421895504,
-0.007120200432837009,
0.04836953803896904,
-0.010933959856629372,
-0.019052142277359962,
-0.005198950879275799,
0.04676128178834915,
0.02745779976248741,
-0.024349985644221306,
-0.008286623284220695,
-0.023823140189051628,
-0.02510838396847248,
-0.023887652903795242,
0.01924215257167816,
-0.0487535186111927,
-0.04248344898223877,
0.04083217680454254,
0.008400828577578068,
-0.05628688260912895,
-0.03469786420464516,
-0.015770545229315758,
0.00036493391962721944,
-0.003875643014907837,
-0.012521506287157536,
-0.07927402853965759,
0.008976452052593231,
-0.013510402292013168,
-0.013711025938391685,
0.004089480731636286,
-0.0031120991334319115,
0.011218258179724216,
-0.02643226645886898,
0.0033571200910955667,
-0.0077660405077040195,
0.0045260777696967125,
-0.05593455582857132,
-0.047492410987615585,
0.019139794632792473,
-0.0031598687637597322,
0.006862288806587458,
-0.010892005637288094,
-0.04992413520812988,
0.05274566262960434,
-0.024560896679759026,
0.04245520755648613,
0.021210407838225365,
-0.07341545075178146,
-0.014523654244840145,
0.03746529296040535,
-0.04885967820882797,
-0.011599539779126644,
0.063526451587677,
-0.05279402434825897,
0.03271840140223503,
-0.03877011686563492,
0.030755164101719856,
0.03044092282652855,
0.0748249888420105,
-0.011012381874024868,
0.0022285832092165947,
-0.04324239119887352,
0.051623739302158356,
0.010885238647460938,
0.002310723066329956,
0.003785264678299427,
0.03897858038544655,
-0.0441986620426178,
-0.00242254720069468,
-0.018546879291534424,
-0.08494631201028824,
0.07033895701169968,
0.019901150837540627,
0.04133852571249008,
-0.015446285717189312,
0.029604895040392876,
0.04146047681570053,
-0.0662715956568718,
0.00277947005815804,
0.028270086273550987,
0.017941927537322044,
-0.052480489015579224,
-0.030104985460639,
-0.065463125705719,
-0.006033707410097122,
-0.013334465213119984,
-0.014954904094338417,
-0.01314107608050108,
-0.04809786006808281,
0.03782474994659424,
0.042755916714668274,
0.016914907842874527,
0.00653334753587842,
-0.06798671931028366,
-0.06320120394229889,
-0.013210369274020195,
-0.017716379836201668,
-0.04154795780777931,
-0.016417425125837326,
-0.05523969233036041,
-0.033668529242277145,
-0.0032150137703865767,
-0.03473895415663719,
-0.03319040313363075,
0.0397164560854435,
0.03727073222398758,
0.05167296901345253,
-0.03272756561636925,
0.05076465383172035,
-0.06365349888801575,
-0.0021448417101055384,
-0.007799082901328802,
0.028197716921567917,
-0.03146744892001152,
-0.02752395160496235,
0.03517509624361992,
0.058465249836444855,
-0.02192780189216137,
-0.03538304939866066,
0.020024925470352173,
0.02707696333527565,
-0.053288452327251434,
0.02315262146294117,
-0.011503452435135841,
-0.04840105399489403,
-0.015468738041818142,
0.07175785303115845,
-0.0034047190565615892,
-0.012409977614879608,
0.005763846915215254,
-0.015357435680925846,
0.03628021106123924,
0.00069822883233428,
0.03233010694384575,
0.009245404973626137,
0.0492527149617672,
0.018627341836690903,
-0.02710936777293682,
0.03395124897360802,
0.04906316101551056,
0.006779559422284365,
-0.011635447852313519,
-0.010271511040627956,
-0.04393884539604187,
0.0071752481162548065,
0.022782456129789352,
0.0137086296454072,
-0.03972078859806061,
-0.011702269315719604,
0.013180237263441086,
-0.011130024679005146,
-0.032916370779275894,
0.0503445565700531,
0.019313231110572815,
-0.007569411303848028,
0.05777222290635109,
-0.014901957474648952,
-0.017648398876190186,
-0.06588220596313477,
-0.023475414142012596,
0.02121330052614212,
0.042127761989831924,
0.053137775510549545,
-0.03153587505221367,
-0.020009828731417656,
0.03321630135178566,
-0.07107289880514145,
0.02652263082563877,
-0.01487469207495451,
0.013610980473458767,
0.03166584298014641,
0.014322182163596153,
0.0109306201338768,
0.05006592720746994,
0.0024433843791484833,
0.03739234432578087,
0.021729912608861923,
0.02820485085248947,
0.05210048705339432,
0.030291594564914703,
-0.005286401603370905,
-0.03731308504939079,
-0.04859272763133049,
0.0299167949706316,
-0.01625145971775055,
0.016613595187664032,
-0.005077897571027279,
-0.0012688323622569442,
0.02936219610273838,
-0.03154778853058815,
0.01913878694176674,
0.01160218846052885,
0.019299248233437538,
0.007748532108962536,
0.02924913540482521,
0.049845024943351746,
0.05149402841925621,
-0.01972193643450737,
-0.01744147017598152,
0.02049112692475319,
0.035089585930109024,
0.02233785390853882,
0.030137106776237488,
-0.02493227832019329,
-0.0011621679877862334,
0.043119706213474274,
-0.005073870532214642,
-0.023084551095962524,
-0.041488271206617355,
0.00013870968541596085,
-0.050863128155469894,
0.01713581755757332,
0.013721692375838757,
0.019111350178718567,
0.003019231604412198,
0.05511372536420822,
0.04852976277470589,
-0.016407975926995277,
0.02817925438284874,
-0.033373042941093445,
0.11398735642433167,
0.00760681601241231,
-0.0559418722987175,
0.04018256813287735,
0.019552290439605713,
0.017506588250398636,
0.05654677376151085,
-0.003661670256406069,
0.01034475490450859,
0.011161104775965214,
-0.011508334428071976,
-0.014813690446317196,
0.005010363180190325,
0.0010702393483370543,
0.04833058640360832,
-0.007786765694618225,
-0.042715635150671005,
-0.01486440934240818,
0.024323880672454834,
0.06767074018716812,
0.016777409240603447,
-0.032925620675086975,
0.02784978598356247,
-0.06054428219795227,
-0.014139682985842228,
-0.05508012697100639,
-0.007398960646241903,
-0.013956106267869473,
-0.0328347347676754,
-0.0008674112614244223,
-0.009043186902999878,
-0.04678759351372719,
0.019290557131171227,
0.0037891084793955088,
0.003602496348321438,
-0.03837436065077782,
-0.014875582419335842,
0.012605133466422558,
0.00712315458804369,
0.01665748842060566,
0.004464039579033852,
-0.035038966685533524,
-0.01723191887140274,
-0.027623755857348442,
0.06008237600326538,
0.01727539300918579,
0.042495619505643845,
0.01610971800982952,
0.08158125728368759,
0.0028090099804103374,
0.03812316060066223,
-0.048117849975824356,
0.04187259078025818,
-0.02433772198855877,
0.0007366021163761616,
-0.02394568733870983,
-0.043727099895477295,
-0.005470870062708855,
-0.026461884379386902,
-0.02598191611468792,
0.010798288509249687,
0.006922570988535881,
0.040315404534339905,
-0.007257269229739904,
-0.037930991500616074,
0.08244221657514572,
-0.03310729190707207,
0.042719632387161255,
0.007710708305239677,
-0.04463093355298042,
-0.010613184422254562,
0.05970878154039383,
0.014459974132478237,
-0.008991129696369171,
-0.007149679586291313,
-0.005948630627244711,
-0.002106104278936982,
-0.07316077500581741,
0.0036535453982651234,
0.030510801821947098,
0.002533982042223215,
0.03174329921603203,
-0.07417382299900055,
0.004970177076756954,
0.09918848425149918,
0.05247846990823746,
0.02052619308233261,
0.017232978716492653,
-0.002819773741066456,
0.017120923846960068,
0.011613630689680576,
0.014513595961034298,
-0.04663669317960739,
-0.020588526502251625,
0.00017892672622110695,
0.014453328214585781,
0.033264998346567154,
-0.08052700757980347,
-0.01994490623474121,
0.03080831468105316,
-0.005564333405345678,
-0.025289485231041908,
0.020442083477973938,
0.01307981088757515,
0.01313016191124916,
0.02291867882013321,
0.0036429320462048054,
0.030445590615272522,
0.041049979627132416,
0.010854242369532585,
0.05400630831718445,
0.04929959401488304,
0.0026858733035624027,
0.030866321176290512,
-0.019243329763412476,
0.038546375930309296,
-0.017027439549565315,
-0.015757570043206215,
0.08754857629537582,
0.044575657695531845,
0.011288261041045189,
0.001067073317244649,
0.02205386757850647,
-0.003993726801127195,
-0.03090786188840866,
-0.014212091453373432,
0.0611351802945137,
0.016727697104215622,
0.003647712292149663,
-0.08087204396724701,
0.003043908393010497,
0.02361948788166046,
-0.02676166407763958,
0.03259721025824547,
-0.02361595630645752,
0.061564017087221146,
-0.035433247685432434,
0.03013172559440136,
-0.016833512112498283,
0.040549300611019135,
-0.08098110556602478,
0.015552596189081669,
-0.02518681064248085,
-0.013467845506966114,
-0.018930558115243912,
-0.0017974383663386106,
-0.016280850395560265,
-0.007056171540170908,
0.06870278716087341,
-0.024274667724967003,
0.028378762304782867,
-0.07135699689388275,
0.01674775406718254,
-0.028301265090703964,
-0.014883220195770264,
0.020465029403567314,
-0.004291375633329153,
-0.05246777832508087,
-0.056896891444921494,
-0.028797471895813942,
0.06528429687023163,
-0.04376186057925224,
-0.030022360384464264,
0.0732467994093895,
-0.033000603318214417,
-0.007688706275075674,
0.04250220209360123,
-0.0033291352447122335,
-0.017524056136608124,
0.022592484951019287,
-0.007994262501597404,
0.047294098883867264,
0.00024864994338713586,
-0.02473585493862629,
0.019403835758566856,
0.08078085631132126,
0.03613615408539772,
0.07969420403242111,
0.026170015335083008,
-0.020560916513204575,
0.06503939628601074,
0.013588538393378258,
-0.018552828580141068,
0.07155929505825043,
-0.012892997823655605,
-0.023053696379065514,
0.08225654810667038,
0.01962140202522278,
-0.009099394083023071,
0.01616804488003254,
0.012823148630559444,
-0.08669793605804443,
-0.03364139050245285,
-0.01830156147480011,
-0.022427860647439957,
-0.01756562851369381,
-0.025378938764333725,
-0.057581331580877304,
-0.005718734115362167,
0.01760212890803814,
-0.03069770708680153,
-0.046250611543655396,
0.04331684112548828,
0.03122982569038868,
-0.05444340407848358,
-0.016332685947418213,
0.0029486354906111956,
-0.000616872392129153,
0.0660475492477417,
-0.03516632691025734,
0.005156365688890219,
-0.003149043768644333,
0.009504176676273346,
-0.03772874176502228,
0.020901409909129143,
-0.03175482898950577,
-0.006849830970168114,
0.05979160591959953,
0.06532387435436249,
0.037627480924129486,
-0.03003964200615883,
-0.0021559209562838078,
0.00976768508553505,
-0.03437497839331627,
0.01363395620137453,
-0.009781268425285816,
0.02416844107210636,
-0.03890858218073845,
-0.07466866075992584,
0.002918143989518285,
-0.05590652674436569,
-0.011373009532690048,
0.010155285708606243,
-0.016383202746510506,
-0.041165269911289215,
-0.00523593882098794,
-0.02047320269048214,
0.033433545380830765,
-0.008146489039063454,
-0.015206505544483662,
-0.010219158604741096,
0.00942758284509182,
0.024366341531276703,
-0.07490361481904984,
-0.0043090712279081345,
-0.06106027215719223,
-0.07788194715976715,
0.047948550432920456,
0.000021622336134896614,
-0.002313443459570408,
-0.014242866076529026,
-0.022944794967770576,
-0.02969307079911232,
-0.004081760998815298,
-0.036159925162792206,
0.01185539085417986,
0.01572471857070923,
0.0418560691177845,
-0.020981082692742348,
-0.019144903868436813,
0.01820078119635582,
0.01062022615224123,
0.022972367703914642,
-0.02904883399605751,
-0.0429191067814827,
0.017200063914060593,
-0.017816750332713127,
0.004826841410249472,
0.05132578685879707,
-0.021223679184913635,
-0.031369857490062714,
-0.010094662196934223,
0.019807979464530945,
0.01881108433008194,
0.052656322717666626,
-0.04223209619522095,
-0.0669640526175499,
0.03884216398000717,
-0.029352888464927673,
-0.025041520595550537,
0.022455479949712753,
-0.040901873260736465,
0.021472683176398277,
-0.04550131782889366,
-0.0414203442633152,
-0.04462591931223869,
0.08914230018854141,
-0.0034820777364075184,
0.05455179885029793,
-0.006176427472382784,
0.015152078121900558,
0.02815474383533001,
0.0048510790802538395,
-0.0576152577996254,
0.013416419737040997,
0.009852014482021332,
0.0016667256131768227,
0.013830507174134254,
-0.03477751463651657,
-0.051749855279922485,
0.05358058214187622,
0.04542103409767151,
-0.06058367341756821,
0.015287736430764198,
0.02938190847635269,
0.03504318743944168,
0.0005018841475248337,
0.01635761186480522,
0.03248482942581177,
0.008039080537855625,
0.08498045057058334,
0.03806107118725777,
0.021736398339271545,
-0.03902192413806915,
-0.0012725030537694693,
0.033952873200178146,
0.047455206513404846,
-0.0378311462700367,
0.02318255975842476,
0.006683419458568096,
-0.07081274688243866,
0.057768214493989944,
-0.022993113845586777,
-0.0019918065518140793,
0.11451182514429092,
-0.01033267006278038,
-0.01568671315908432,
-0.049527350813150406,
0.022352805361151695,
-0.027633074671030045,
-0.08732027560472488,
-0.011104577220976353,
-0.03904373198747635,
0.012824858538806438,
-0.018033184111118317,
0.0007426951196976006,
0.004783099517226219,
-0.011288408190011978,
0.02087990567088127,
-0.017519744113087654,
0.002082240767776966,
-0.011246421374380589,
-0.03403129428625107
] |
<p>Quantum Mechanics is very successful in determining the overall statistical distribution of many measurements of the same process.</p>
<p>On the other hand, it is completely clueless in determining the outcome of a single measurement. It can only describe it as having a "random" outcome within the predicted distribution.</p>
<p>Where does this randomness come from? Has physics "given up" on the existence of microscopic physical laws by saying that single measurements are not bound to a physical law?</p>
<p>As a side note: repeating the same measurement over and over with the same apparatus makes the successive measurements non-independent, statistically speaking. There could be a hidden "stateful" mechanism influencing the results. Has any study of fundamental QM features been performed taking this into account? What was the outcome?</p>
<hr>
<p>Edit: since 2 out of 3 questions seem to me not to answer my original question, maybe a clarification on the question itself will improve the quality of the page :-)</p>
<p>The question is about why single measurements have the values they have. Out of the, say, 1000 measure that make a successful QM experiment, why do the single measurements happen in that particular order?
Why does the wave function collapse to a specific eigenvalue and not another? It's undeniable that this collapse (or projection) happens. Is this random? What is the source of this randomness?</p>
<p>In other words: what is the mechanism of choice?</p>
<hr>
<p>Edit 2: More in particular you can refer to chapter 29 of "The road to reality" by Penrose, and with special interest page 809 where the Everett interpretation is discussed - including why it is, if not wrong, quite incomplete.</p>
|
g2467
|
[
-0.006936243735253811,
0.034503236413002014,
0.0038407735992223024,
-0.00484969699755311,
0.06033884361386299,
0.026716990396380424,
0.04909384995698929,
0.01545263547450304,
0.014522385783493519,
-0.04984601214528084,
-0.0036605214700102806,
-0.037884850054979324,
0.030756622552871704,
0.03273399546742439,
-0.035685595124959946,
-0.018096959218382835,
0.07717971503734589,
-0.01825987733900547,
0.01406204141676426,
0.005488699767738581,
-0.05686454102396965,
0.009744877927005291,
-0.021485956385731697,
-0.03279595077037811,
-0.0728684589266777,
-0.04194705933332443,
-0.02237183228135109,
-0.020798906683921814,
0.016683429479599,
-0.007309638429433107,
-0.010430773720145226,
-0.0223536379635334,
0.05902571603655815,
-0.05403221398591995,
-0.030408566817641258,
-0.008183986879885197,
-0.0049463901668787,
-0.03935651481151581,
0.01709400862455368,
0.004387838300317526,
-0.011797530576586723,
-0.012810923159122467,
-0.015693077817559242,
-0.008024425245821476,
0.02501082606613636,
0.019649313762784004,
-0.002747252816334367,
0.020373698323965073,
0.0005037312512286007,
0.01783701963722706,
0.055231574922800064,
0.0008545574964955449,
0.088308185338974,
0.0678129568696022,
0.016818342730402946,
0.06698039174079895,
0.0036629645619541407,
0.06134308874607086,
0.04961402341723442,
0.013545116409659386,
0.025371387600898743,
0.021687651053071022,
0.024655576795339584,
0.04340444132685661,
0.07991420477628708,
-0.004428599029779434,
-0.023595957085490227,
-0.006381794344633818,
0.016738153994083405,
0.030154671519994736,
0.006117637734860182,
-0.05621922388672829,
-0.027532944455742836,
-0.009946361184120178,
-0.015441158786416054,
0.021917743608355522,
0.028367705643177032,
0.030422117561101913,
-0.02032286860048771,
0.01532889623194933,
-0.027051806449890137,
-0.015350311994552612,
0.03475145250558853,
0.02010403573513031,
0.07356978207826614,
0.02484496869146824,
-0.004974483512341976,
-0.014624591916799545,
-0.044515423476696014,
0.024089790880680084,
-0.00841768179088831,
0.04428441822528839,
0.06645441055297852,
0.0358598530292511,
-0.04899856448173523,
-0.08181770890951157,
0.008673574775457382,
0.024621376767754555,
-0.03523293510079384,
0.025429319590330124,
-0.005970855243504047,
0.028013287112116814,
-0.012024986557662487,
-0.033846016973257065,
-0.018561355769634247,
-0.008091839961707592,
-0.002983872778713703,
0.06885849684476852,
0.006296098697930574,
-0.01409999467432499,
-0.07539082318544388,
0.044084157794713974,
-0.008598140440881252,
0.013420742005109787,
-0.02328445576131344,
-0.021754689514636993,
0.08975059539079666,
0.014597324654459953,
-0.01275499165058136,
0.005487566348165274,
0.0067132911644876,
0.017362171784043312,
0.026943812146782875,
0.014295832253992558,
-0.042695801705121994,
0.033830273896455765,
0.00009725371637614444,
-0.001093156635761261,
-0.005773959681391716,
0.016247712075710297,
-0.00410899892449379,
0.031150272116065025,
-0.030246304348111153,
0.04095860943198204,
-0.014306068420410156,
0.004182376898825169,
0.03935312107205391,
0.02362799271941185,
0.05780726298689842,
0.03252270445227623,
-0.017401034012436867,
-0.038421183824539185,
-0.015377365052700043,
-0.030359143391251564,
-0.01592245139181614,
-0.0012798912357538939,
0.036425814032554626,
0.003385811811313033,
-0.029816843569278717,
-0.008123070001602173,
-0.00007393663690891117,
-0.021440528333187103,
0.00009587073145667091,
-0.01255369745194912,
0.008417964912950993,
-0.004442457575351,
0.028477150946855545,
0.004221012350171804,
-0.009975231252610683,
-0.003993853460997343,
0.06396108120679855,
-0.014453842304646969,
-0.039269398897886276,
0.035598982125520706,
-0.027042116969823837,
0.02372545562684536,
0.023037226870656013,
-0.06848873943090439,
0.010727643966674805,
-0.049977827817201614,
-0.019128059968352318,
-0.07072720676660538,
0.004229603335261345,
0.0698671042919159,
-0.0465240515768528,
0.04819251224398613,
0.02222917601466179,
-0.06691166758537292,
0.009355630725622177,
-0.02002907544374466,
0.02709633857011795,
0.05056878924369812,
0.024950994178652763,
-0.08355310559272766,
-0.020366506651043892,
-0.0007493548910133541,
0.01637394167482853,
0.03528965637087822,
-0.05313283950090408,
-0.0014156472170725465,
0.01811240240931511,
-0.08324778079986572,
-0.014716328121721745,
-0.011146007105708122,
0.03506501019001007,
-0.016929175704717636,
-0.0032952262554317713,
-0.018543364480137825,
-0.02839711867272854,
-0.01293619442731142,
-0.0136942183598876,
0.03787670657038689,
-0.023977505043148994,
0.027372941374778748,
0.01274681556969881,
0.0035182973369956017,
0.03432443365454674,
0.013093627989292145,
0.034212373197078705,
0.0001464484230382368,
0.024670680984854698,
0.03211965411901474,
-0.04060867056250572,
-0.00445776479318738,
0.019250590354204178,
-0.036992449313402176,
0.05762242525815964,
-0.023427963256835938,
0.045334771275520325,
0.006381174549460411,
0.018550435081124306,
0.011680133640766144,
0.0035442227963358164,
-0.019404398277401924,
0.05015837401151657,
0.03539756312966347,
-0.05444036424160004,
-0.06525932252407074,
-0.043808624148368835,
0.04471511393785477,
-0.08275458216667175,
-0.00689559755846858,
0.005686118267476559,
0.019952639937400818,
0.033008743077516556,
0.07319649308919907,
0.0014098425162956119,
-0.06182379275560379,
0.01645953394472599,
0.05376824736595154,
-0.01349753700196743,
-0.052081309258937836,
-0.041827112436294556,
-0.03475945442914963,
-0.019978631287813187,
0.013514222577214241,
0.007187202572822571,
-0.0008397306664846838,
0.02181164361536503,
0.02475128509104252,
0.011837764643132687,
-0.036466024816036224,
-0.03613016754388809,
-0.04124017059803009,
-0.019711077213287354,
-0.0427856482565403,
0.04214926064014435,
0.06173861771821976,
-0.07087953388690948,
-0.007380845956504345,
-0.0521780401468277,
-0.00896917749196291,
0.020195409655570984,
0.019447650760412216,
-0.02695751190185547,
-0.04066812992095947,
0.01435485202819109,
0.039766520261764526,
-0.03249530494213104,
-0.03536277636885643,
-0.008800282143056393,
0.04214467853307724,
0.013096364215016365,
0.05294622480869293,
0.0066761476919054985,
0.005266361869871616,
-0.043240293860435486,
-0.05968204140663147,
0.029890235513448715,
-0.03156404569745064,
-0.05248810350894928,
-0.012393268756568432,
-0.056024543941020966,
-0.007238461636006832,
0.019919950515031815,
-0.04864531010389328,
0.0345042385160923,
-0.08553539961576462,
0.007228722795844078,
0.023874426260590553,
-0.02134229615330696,
-0.007051923777908087,
0.043082185089588165,
0.031670164316892624,
-0.06105606630444527,
0.039629098027944565,
-0.05103486776351929,
-0.011511450633406639,
-0.00848489347845316,
0.020314570516347885,
-0.047332584857940674,
0.015773635357618332,
-0.03348154574632645,
0.028821304440498352,
0.03814439848065376,
0.050514109432697296,
-0.03272262588143349,
-0.03581658750772476,
-0.04652624577283859,
-0.012818776071071625,
0.01209583505988121,
0.024289080873131752,
-0.049953632056713104,
-0.0068221320398151875,
-0.07255738973617554,
-0.02800937555730343,
-0.06977659463882446,
0.06164441630244255,
0.0036580413579940796,
-0.029055308550596237,
-0.06989564001560211,
-0.008463949896395206,
0.022858722135424614,
-0.07531323283910751,
0.07885619252920151,
-0.003748546587303281,
-0.018194641917943954,
0.0035372748970985413,
-0.027599168941378593,
-0.027839217334985733,
0.007355427835136652,
-0.0087301479652524,
-0.013047538697719574,
-0.028501715511083603,
-0.032026536762714386,
-0.08229824155569077,
-0.061584871262311935,
-0.0047124349512159824,
0.02222568355500698,
-0.009679281152784824,
-0.010718723759055138,
-0.03901447728276253,
-0.05381515249609947,
0.006799238733947277,
0.03088105469942093,
0.013928926549851894,
-0.0032680544536560774,
-0.011861581355333328,
0.05868367478251457,
-0.020585695281624794,
0.03630047291517258,
-0.0005158149870112538,
-0.01576424576342106,
0.035862188786268234,
-0.022906595841050148,
0.03827885538339615,
0.009718609042465687,
0.0012826081365346909,
0.05861419066786766,
0.0064349668100476265,
0.0033691166900098324,
-0.05592195689678192,
-0.014836352318525314,
-0.08731492608785629,
-0.009327910840511322,
0.01358731184154749,
0.01708194985985756,
0.017848199233412743,
0.06324765831232071,
-0.001871950225904584,
-0.024316880851984024,
0.0220938753336668,
-0.04094798117876053,
0.031779944896698,
0.05203728750348091,
0.0016673036152496934,
0.04941978305578232,
0.04088442772626877,
-0.029870951548218727,
0.016229793429374695,
0.0008835820481181145,
0.05147121846675873,
-0.003088825847953558,
0.004292883910238743,
0.02451932244002819,
0.07086987793445587,
-0.10117466747760773,
-0.00465884106233716,
-0.03535681962966919,
-0.030510731041431427,
-0.0019595474004745483,
-0.05434628576040268,
-0.028915254399180412,
0.061508890241384506,
0.017081333324313164,
-0.019023088738322258,
0.00871779303997755,
-0.057182427495718,
0.04623916372656822,
0.049112167209386826,
-0.03570064902305603,
-0.05335478112101555,
-0.056368302553892136,
-0.00033407617593184114,
0.01276355516165495,
0.01996634155511856,
0.03165964037179947,
-0.007556905038654804,
-0.04015180841088295,
-0.01321762427687645,
-0.026249051094055176,
0.05080109089612961,
0.003975697793066502,
-0.07013386487960815,
0.04380597546696663,
0.05052351579070091,
-0.0018737099599093199,
-0.0421135351061821,
-0.016283007338643074,
-0.015799717977643013,
0.029649656265974045,
-0.0010657546808943152,
0.015202532522380352,
-0.035051580518484116,
0.004261687397956848,
0.007683885749429464,
-0.009431153535842896,
0.028656551614403725,
-0.002074306132271886,
-0.055452022701501846,
0.04518416151404381,
-0.03264666348695755,
0.06270572543144226,
0.02431752160191536,
-0.0231554564088583,
0.006774868816137314,
0.000558422994799912,
0.07000594586133957,
-0.00009409665653947741,
0.02751760557293892,
0.03788640722632408,
-0.0402694009244442,
-0.004399321973323822,
0.03895339369773865,
-0.0035936483182013035,
-0.01865137740969658,
-0.02496497519314289,
0.021918734535574913,
-0.052912890911102295,
0.004979063756763935,
-0.013027746230363846,
-0.01599169708788395,
-0.04199441149830818,
-0.032175611704587936,
-0.021818209439516068,
-0.06679262220859528,
-0.02285648137331009,
0.05622722581028938,
0.0678456723690033,
0.06649409234523773,
-0.09027157723903656,
-0.05385470762848854,
-0.030756082385778427,
0.06457450985908508,
-0.029803762212395668,
-0.01388544775545597,
-0.03450258821249008,
0.027067605406045914,
-0.052233777940273285,
-0.002963434439152479,
0.002356951590627432,
0.001960919937118888,
0.027889501303434372,
0.013128112070262432,
0.0328957661986351,
-0.023859135806560516,
-0.0013452989514917135,
-0.016202058643102646,
0.03965427353978157,
-0.07616104930639267,
0.025211375206708908,
-0.030524153262376785,
0.03162028640508652,
0.01895664446055889,
-0.01894444227218628,
0.0032435257453471422,
-0.024121403694152832,
-0.046592921018600464,
-0.006625818088650703,
-0.0076765818521380424,
0.048997167497873306,
0.09632333368062973,
0.07172334939241409,
-0.040412239730358124,
0.034082602709531784,
-0.0553736612200737,
0.053901635110378265,
-0.009956094436347485,
-0.022744303569197655,
-0.0002811003942042589,
-0.0619453489780426,
0.05418618023395538,
-0.018598422408103943,
-0.001471222611144185,
0.016664179041981697,
-0.01697632111608982,
0.01613580994307995,
-0.01280159130692482,
-0.0023190726060420275,
0.0015332713956013322,
0.015215333551168442,
0.012676647864282131,
-0.03248037025332451,
0.00242099491879344,
0.026237890124320984,
0.002958717755973339,
0.014864315278828144,
0.00035339081659913063,
0.004966038279235363,
-0.005305527243763208,
0.008262284100055695,
0.014326208271086216,
0.013219252228736877,
-0.011578360572457314,
0.012339599430561066,
-0.04027830809354782,
-0.12160683423280716,
-0.007403386291116476,
-0.018419357016682625,
0.03781348839402199,
0.04073977470397949,
0.015962714329361916,
0.05817749723792076,
-0.004616125021129847,
0.003739753272384405,
0.03723492845892906,
0.017911013215780258,
-0.010557413101196289,
0.004578511230647564,
0.04993049055337906,
-0.015128882601857185,
0.03867926448583603,
0.034236274659633636,
0.03659488260746002,
0.03478970378637314,
0.01995658501982689,
0.024396685883402824,
0.01810823194682598,
0.05864326283335686,
-0.03598881885409355,
-0.017672527581453323,
0.041670143604278564,
-0.046256035566329956,
-0.016466854140162468,
-0.02757720835506916,
0.0697154700756073,
-0.013995850458741188,
-0.009092453867197037,
-0.06530869752168655,
0.027624618262052536,
0.04049712046980858,
0.012194003909826279,
0.0737290233373642,
0.014792203903198242,
0.0396408885717392,
-0.007096192799508572,
-0.01668892428278923,
-0.03424672409892082,
0.001528491615317762,
0.09927098453044891,
-0.011453168466687202,
0.022914443165063858,
0.037902992218732834,
0.005888322833925486,
0.0010429968824610114,
0.04338077828288078,
-0.044763948768377304,
-0.04307502880692482,
-0.011009229347109795,
-0.0640302449464798,
0.015877746045589447,
0.02828535996377468,
0.052353568375110626,
-0.01397932879626751,
-0.011413978412747383,
0.09247232973575592,
-0.03888266533613205,
-0.019649852067232132,
0.05684306472539902,
0.02089023031294346,
-0.013453233055770397,
0.017781775444746017,
-0.00986266415566206,
-0.024418102577328682,
-0.04748921096324921,
-0.027279186993837357,
0.058804985135793686,
-0.041074659675359726,
-0.04158051684498787,
-0.01809065043926239,
0.03281640633940697,
-0.025099966675043106,
0.053581494837999344,
-0.028569860383868217,
-0.0066143786534667015,
0.04442013427615166,
-0.0036175937857478857,
-0.023158373311161995,
-0.0022005571518093348,
-0.0034086299128830433,
-0.05700202286243439,
0.04146861284971237,
-0.013101570308208466,
0.01621856726706028,
-0.00038667721673846245,
-0.05835137143731117,
-0.009724137373268604,
0.04425613954663277,
-0.03543298318982124,
0.04596840590238571,
0.044821809977293015,
-0.02485857903957367,
0.013882333412766457,
-0.008004182949662209,
-0.007877413183450699,
0.03600708767771721,
0.009221864864230156,
-0.010409737937152386,
0.0779450312256813,
-0.008695078082382679,
-0.033969685435295105,
-0.008900478482246399,
0.019711045548319817,
0.06592372804880142,
-0.06285898387432098,
0.044890161603689194,
-0.03541097417473793,
-0.029476609081029892,
0.0567394495010376,
0.028286412358283997,
0.030158545821905136,
0.019642915576696396,
0.05043353512883186,
-0.005897030234336853,
-0.038864344358444214,
0.03934596851468086,
0.028947262093424797,
0.008209369145333767,
-0.08733819425106049,
0.04750620573759079,
-0.00003232080416637473,
0.015975110232830048,
-0.05497949942946434,
0.02293234132230282,
0.03916463628411293,
0.07131653279066086,
0.04001680389046669,
-0.02387712523341179,
0.06417164951562881,
-0.03571254760026932,
-0.00428441446274519,
-0.022216536104679108,
-0.033552978187799454,
-0.011749868281185627,
0.028237666934728622,
-0.0070555866695940495,
-0.012906565330922604,
-0.0508481040596962,
0.033289145678281784,
-0.06883365660905838,
0.04648212343454361,
-0.0017332409042865038,
-0.019613005220890045,
-0.028020095080137253,
0.021943973377346992,
0.0021859887056052685,
0.021212240681052208,
0.04120180755853653,
-0.01668490096926689,
0.0027642131317406893,
-0.03428111597895622,
0.02597159519791603,
0.03752366825938225,
0.01170472614467144,
-0.060886841267347336,
0.04346996173262596,
-0.03242310509085655,
0.004846823401749134,
-0.049343742430210114,
-0.03007647767663002,
-0.00268653966486454,
-0.05600978434085846,
0.01488903071731329,
-0.0008529917686246336,
0.006333085708320141,
0.023004867136478424,
0.047387395054101944,
-0.01302686333656311,
0.007428702898323536,
0.023193826898932457,
0.003644791431725025,
-0.03736615180969238,
-0.016897916793823242,
0.039723873138427734,
0.028147703036665916,
-0.02250783145427704,
-0.0075317746959626675,
-0.03588106855750084,
0.020422395318746567,
0.012760033831000328,
-0.037681832909584045,
-0.049991171807050705,
0.022950664162635803,
-0.0037084079813212156,
0.003550102235749364,
-0.031139438971877098,
-0.0516517274081707,
0.05029262602329254,
0.054894011467695236,
-0.04134749993681908,
-0.032851506024599075,
-0.00947531033307314,
-0.013960759155452251,
-0.021623240783810616,
-0.022653458639979362,
-0.014996707439422607,
0.044156670570373535,
0.02871362306177616,
0.0032466407865285873,
-0.014993413351476192,
-0.011776515282690525,
-0.0518416203558445,
-0.033429183065891266,
-0.0023225070908665657,
-0.004687964916229248,
0.03190790116786957,
0.05963887646794319,
0.00456650136038661,
-0.04653827100992203,
-0.020897382870316505,
0.0063257971778512,
0.03340315818786621,
0.02185419201850891,
-0.034414514899253845,
-0.035344984382390976,
-0.09227047115564346,
-0.05033217743039131,
-0.02290203794836998,
0.012017210014164448,
-0.09094306081533432,
-0.03998084366321564,
-0.008329842239618301,
-0.002812738064676523,
0.09848013520240784,
0.028515562415122986,
-0.07358177751302719,
0.0219337847083807,
0.04534122347831726,
0.04148760810494423,
-0.031876686960458755,
0.045858778059482574,
-0.029211679473519325,
-0.04039852321147919,
0.00135639903601259,
-0.07513876259326935,
-0.011157981120049953,
-0.002439448144286871,
0.0006119076278991997
] |
<p>$g\phi^3$ , $d=4$ , 3 point One loop diagram (three external legs) Divergence</p>
<p>I am trying to find where the divergence factor/pole is on the following diagram in 4 dimensions so that I can use minimal subtraction...</p>
<p><img src="http://i.stack.imgur.com/lV1cy.png" alt="enter image description here"></p>
<p>I know it is proportional to...</p>
<p>$$
\int d^dy_1 \ d^dy_2 \ d^dy_3 \ D_f(x_1,y_1)D_f(x_2,y_2)D_f(x_3,y_3)D_f(y_1,y_2)D_f(y_2,y_3)
D_f(y_3,y_1)$$</p>
<p>where $D_f$ are Feynmann propagators. Which I can manipulate to get...
$$
\int d^dp_1 \cdots d^dp_3 \left(\frac{\textrm{Exp}[ip_1x_1]}{p_1^2+m^2}\right) \cdots \left(\frac{\textrm{Exp}[ip_3x_3]}{p_3^2+m^2}\right) \delta[p_1+p_2+p_3] \bullet \int d^dp_4 \left(\frac{1}{p_4^2+m^2}\right) \left(\frac{1}{(p_2+p_4)^2+m^2}\right) \left(\frac{1}{(p_2+p_3+p_4)^2+m^2}\right)
$$</p>
<p>Which looks like a renormalization to the coupling constant $g$. So I only mess around with the $p_4$ integral, however it seems to be finite (no divergences) when I use Feynmanns trick...
$$
\frac{1}{abc}=2 \int_0^1 dx \int^{1-x}_0 dy \ (ax+by+c(1-x-y))^{-3}
$$
and the following integral...
$$
\int \frac{d^dp}{(p^2+2p \cdot q +m^2)^n} \textrm{(Minkowski)} = i \pi^{d/2}(m^2-q^2)^{d/2-n} \frac{\Gamma[n-d/2] \Gamma[d/2]}{\Gamma[n]}
$$</p>
<p>Was just wondering if I am going in the right direction or if I did something wrong.</p>
|
g2468
|
[
0.04338090121746063,
-0.0074617257341742516,
0.00692112697288394,
-0.07869853079319,
0.025872960686683655,
0.011808370240032673,
0.0724799782037735,
-0.006736121606081724,
-0.04404535889625549,
-0.026983654126524925,
-0.06972920149564743,
0.00318917422555387,
-0.04398921877145767,
0.00885395985096693,
0.04255383461713791,
-0.02152075245976448,
0.02094249241054058,
-0.0246741883456707,
0.02754996158182621,
-0.004396296571940184,
-0.029813045635819435,
-0.04076230153441429,
0.02179967239499092,
0.012172487564384937,
0.02725592628121376,
-0.06680259853601456,
0.013080989941954613,
0.00004217986133880913,
-0.06662650406360626,
0.0022981869988143444,
-0.042544811964035034,
0.058274995535612106,
0.030720304697752,
-0.0432935394346714,
-0.015673862770199776,
0.0004509015998337418,
0.06521948426961899,
0.05473285913467407,
-0.0077239288948476315,
-0.0005262625054456294,
-0.03341561183333397,
-0.0499131865799427,
-0.006886271294206381,
0.06425076723098755,
-0.007230306509882212,
-0.00879694428294897,
-0.04845893383026123,
-0.009343810379505157,
-0.03507741540670395,
0.03553234413266182,
-0.02387256547808647,
0.096986785531044,
0.048120077699422836,
-0.03325647488236427,
-0.0141587620601058,
0.05603962019085884,
-0.009567374363541603,
-0.00722078513354063,
0.028471875935792923,
0.03149541839957237,
0.011823036707937717,
-0.046827033162117004,
0.0009792848723009229,
-0.0039704651571810246,
0.047116342931985855,
0.0070688435807824135,
-0.08755176514387131,
-0.05826951935887337,
-0.03922911733388901,
-0.0016665678704157472,
0.014256014488637447,
-0.06262770295143127,
0.03973360359668732,
-0.010568796657025814,
-0.05127187445759773,
0.05188048630952835,
0.011427152901887894,
-0.05116327479481697,
-0.029780350625514984,
-0.013709768652915955,
-0.03631279245018959,
0.01513676904141903,
-0.04544495418667793,
0.013195724226534367,
0.03968692198395729,
0.015814844518899918,
0.01617901399731636,
-0.01012280210852623,
-0.053541216999292374,
-0.02789757214486599,
-0.02235669642686844,
0.012066511437296867,
-0.007270985748618841,
-0.030334249138832092,
0.004255051724612713,
0.016578279435634613,
0.012016130611300468,
0.007092878222465515,
-0.018204914405941963,
-0.0213313065469265,
-0.005723645910620689,
0.06901361793279648,
0.0033469919580966234,
0.03358647972345352,
-0.04454231634736061,
-0.015135710127651691,
0.12893356382846832,
-0.02267550304532051,
0.031985681504011154,
-0.016069557517766953,
-0.0863795354962349,
-0.034379735589027405,
-0.059192389249801636,
-0.013605196960270405,
-0.004723496735095978,
-0.032474931329488754,
-0.038787826895713806,
-0.03419835492968559,
0.016312740743160248,
0.04377917945384979,
0.0008051389595493674,
-0.02864380180835724,
0.06290892511606216,
0.07387221604585648,
0.0289174672216177,
0.01843765750527382,
-0.049276307225227356,
0.03391188010573387,
0.02689266949892044,
0.0038427007384598255,
0.035824935883283615,
-0.01978602260351181,
0.021990284323692322,
0.010362914763391018,
-0.0031111391726881266,
0.026943005621433258,
-0.055552855134010315,
0.005650061648339033,
-0.018320320174098015,
0.05212675780057907,
-0.03613277152180672,
-0.049709025770425797,
-0.01350692193955183,
-0.028058253228664398,
-0.038000818341970444,
0.014204454608261585,
-0.01820339635014534,
-0.006200903560966253,
0.015961691737174988,
-0.014083929359912872,
0.07600658386945724,
0.06776624917984009,
0.031568318605422974,
0.053271252661943436,
-0.011795994825661182,
0.03547266125679016,
0.08081383258104324,
-0.008186877705156803,
0.02425250969827175,
-0.02695375680923462,
-0.010241968557238579,
-0.010777306742966175,
0.0364212840795517,
0.008930591866374016,
-0.03528427705168724,
0.01854019984602928,
0.07126852124929428,
-0.055996574461460114,
-0.018663745373487473,
-0.09292194247245789,
-0.024197716265916824,
0.03311998024582863,
0.07021202892065048,
-0.02433411218225956,
0.01886666566133499,
0.04210180416703224,
-0.03678873926401138,
-0.020203864201903343,
-0.06947186589241028,
0.01974303275346756,
0.04624003916978836,
0.020064296200871468,
0.018138686195015907,
-0.02237989380955696,
-0.04752056300640106,
-0.0020932157058268785,
-0.02397882379591465,
0.0208881925791502,
0.04838377237319946,
-0.03466131165623665,
0.011648967862129211,
0.006461529526859522,
0.0051365201361477375,
0.022644463926553726,
-0.024178946390748024,
0.0024897963739931583,
-0.022247543558478355,
-0.07410657405853271,
0.00708411168307066,
-0.02884112484753132,
-0.015470759943127632,
-0.002979544922709465,
0.04523194581270218,
-0.005097029265016317,
0.03602355718612671,
-0.04846493899822235,
-0.008262294344604015,
0.018483050167560577,
0.06106136739253998,
0.02469959482550621,
-0.008770044893026352,
-0.06374730914831161,
-0.04776812344789505,
0.002867775270715356,
-0.028819452971220016,
-0.06919004023075104,
0.0489010252058506,
0.03116566687822342,
-0.01700431853532791,
0.05638837441802025,
0.020124459639191628,
-0.0005925919394940138,
0.07518530637025833,
0.021090708673000336,
-0.0306563600897789,
0.018326858058571815,
-0.02354109100997448,
0.02644488774240017,
-0.006926656235009432,
-0.0036139125004410744,
-0.09692934900522232,
-0.030790148302912712,
0.001532668131403625,
-0.019840894266963005,
0.04411657899618149,
-0.019583571702241898,
-0.034583937376737595,
-0.03860708326101303,
0.0008782062795944512,
0.02876058779656887,
-0.017587020993232727,
0.016635233536362648,
-0.00921467412263155,
0.0024965135380625725,
0.012448743917047977,
-0.011383704841136932,
-0.004886586684733629,
0.07017462700605392,
-0.0539032518863678,
0.0025210166350007057,
0.06054838001728058,
0.08739645034074783,
0.029171673581004143,
0.06709975749254227,
-0.04025997966527939,
0.0071631078608334064,
-0.018098769709467888,
0.03899688273668289,
-0.006724738981574774,
-0.057505808770656586,
-0.03887065127491951,
-0.025357184931635857,
0.04640531539916992,
0.04520373418927193,
-0.06284498423337936,
0.00046261955867521465,
-0.0074319252744317055,
-0.0071867285296320915,
0.019856302067637444,
0.003443739842623472,
-0.06965968012809753,
-0.0002612772223073989,
0.038184016942977905,
0.014260774478316307,
-0.041757576167583466,
0.001458413666114211,
0.05068889260292053,
0.030920125544071198,
0.010727272368967533,
-0.036926139146089554,
0.0017407267587259412,
0.016303788870573044,
0.0026516523212194443,
0.02490612305700779,
0.032489113509655,
-0.044283878058195114,
0.025916770100593567,
0.020611513406038284,
-0.05815349146723747,
0.030700284987688065,
-0.030506912618875504,
-0.05704019218683243,
0.022343745455145836,
-0.03070247173309326,
0.052415166050195694,
0.0003523391205817461,
0.048548147082328796,
-0.04671278968453407,
0.05226796120405197,
0.02449907548725605,
0.004680296406149864,
0.021380694583058357,
-0.02524261735379696,
0.017037181183695793,
0.003804916748777032,
-0.033473215997219086,
-0.0007336297421716154,
-0.0074958703480660915,
-0.010800354182720184,
0.010369930416345596,
-0.010492964647710323,
0.0024485262110829353,
0.028507864102721214,
-0.06152687966823578,
0.012404563836753368,
0.014442063868045807,
-0.007937908172607422,
-0.01399321760982275,
0.03136769309639931,
0.010071828030049801,
-0.028094621375203133,
-0.06361545622348785,
-0.033857520669698715,
-0.013138844631612301,
0.051847826689481735,
0.02369191311299801,
0.008021971210837364,
-0.05021413788199425,
-0.009214148856699467,
0.03676013648509979,
-0.0029691702220588923,
0.00673255231231451,
0.008815880864858627,
-0.012707676738500595,
-0.06754285097122192,
-0.0170386154204607,
-0.05821114033460617,
0.03252119943499565,
0.013346812687814236,
-0.05053359642624855,
-0.05648279935121536,
-0.04836795851588249,
0.02630060724914074,
-0.033193182200193405,
0.01634279452264309,
-0.03219475969672203,
-0.02718210779130459,
0.09419112652540207,
0.01996440626680851,
-0.014606170356273651,
0.027431100606918335,
-0.02953624166548252,
0.005622972268611193,
0.015230240300297737,
0.04424339532852173,
0.010291803628206253,
-0.0029775563161820173,
0.06192867457866669,
-0.06534551829099655,
0.013291074894368649,
0.02186746895313263,
-0.03141499683260918,
-0.0027248661499470472,
-0.05580470338463783,
-0.006963544525206089,
0.02217985689640045,
-0.01094856671988964,
0.00732632540166378,
-0.0026558979880064726,
-0.0073193134739995,
0.025807347148656845,
0.022488463670015335,
-0.010608433745801449,
0.07267586886882782,
-0.02721518836915493,
-0.04380745068192482,
-0.006862157955765724,
0.03975521773099899,
-0.045598678290843964,
0.032751161605119705,
0.033438507467508316,
0.028031371533870697,
-0.036567311733961105,
0.053869105875492096,
0.011588800698518753,
0.05726942792534828,
-0.023654790595173836,
-0.023217730224132538,
-0.0238804891705513,
0.03298453614115715,
0.023828497156500816,
0.014021246694028378,
0.021058443933725357,
0.04789126291871071,
-0.0050193993374705315,
-0.0023187147453427315,
-0.00588478147983551,
0.05963275209069252,
-0.05318303778767586,
0.06623917818069458,
-0.02822837233543396,
-0.037055954337120056,
-0.0031636646017432213,
0.016364598646759987,
-0.04308328032493591,
-0.017257442697882652,
0.012716173194348812,
0.0070820157416164875,
0.08398053050041199,
-0.006820223294198513,
0.04136638715863228,
0.0490194633603096,
0.02264920063316822,
-0.036213938146829605,
0.014256437309086323,
-0.007561881560832262,
0.024279717355966568,
-0.02722334675490856,
0.025607477873563766,
-0.05347457155585289,
-0.0035602112766355276,
0.010159271769225597,
-0.03514857962727547,
-0.009136092849075794,
-0.00957652647048235,
0.01451039593666792,
0.01970631442964077,
0.04613327234983444,
-0.025733161717653275,
0.015646450221538544,
0.01519849430769682,
0.013360894285142422,
-0.07117972522974014,
0.020051080733537674,
-0.02106788381934166,
0.06061279773712158,
-0.01973988674581051,
0.004428742453455925,
-0.036060482263565063,
0.06845147907733917,
0.030528152361512184,
-0.039076972752809525,
0.023891031742095947,
0.021634988486766815,
0.0041529331356287,
0.029702426865696907,
-0.05186505243182182,
-0.01654963567852974,
0.04948555678129196,
0.0196362491697073,
-0.0009118237649090588,
0.026459097862243652,
-0.005679249297827482,
0.01753452606499195,
0.007820134051144123,
-0.003445665817707777,
-0.005196624901145697,
0.028905823826789856,
0.01231912337243557,
-0.021122615784406662,
-0.060382094234228134,
-0.0008677889127284288,
-0.06052910163998604,
-0.052027661353349686,
0.014540907926857471,
0.0017256193095818162,
-0.05940509960055351,
0.02897215075790882,
0.006455747876316309,
-0.018372610211372375,
0.03847166523337364,
0.01295629795640707,
0.04751753807067871,
0.04896937310695648,
-0.03440888226032257,
0.030773641541600227,
0.028857700526714325,
0.031286727637052536,
0.0024334655608981848,
-0.0437491349875927,
0.015498396940529346,
0.005817357916384935,
-0.0005999546265229583,
0.006184638477861881,
0.03886145353317261,
-0.01909545809030533,
-0.027110770344734192,
-0.07313616573810577,
-0.05202249065041542,
-0.028481245040893555,
-0.01783856190741062,
-0.0028740018606185913,
0.03024141862988472,
-0.009851657785475254,
-0.0057711186818778515,
-0.0018591337138786912,
0.03298720717430115,
-0.0005303576472215354,
0.02312280237674713,
-0.033102117478847504,
-0.01485111378133297,
0.006109796930104494,
-0.06190422922372818,
-0.021128108724951744,
-0.025275876745581627,
0.04203585535287857,
0.10734400153160095,
-0.03154236450791359,
0.04063969850540161,
0.07366836071014404,
-0.01693311147391796,
-0.06629900634288788,
0.02231813594698906,
-0.045666709542274475,
-0.02506103925406933,
-0.013855944387614727,
0.0028422935865819454,
0.004359361249953508,
0.029367800801992416,
-0.07659482210874557,
0.05468016117811203,
0.012308403849601746,
-0.03886210173368454,
-0.015421363525092602,
0.07564114034175873,
0.016206812113523483,
-0.05059640109539032,
-0.030472692102193832,
0.009496208280324936,
0.025226058438420296,
0.01263018324971199,
0.0061777750961482525,
0.013441617600619793,
0.04191279783844948,
0.022537706419825554,
-0.030453147366642952,
0.029344715178012848,
-0.01890462078154087,
0.016641726717352867,
-0.02136937342584133,
0.016679557040333748,
-0.018962137401103973,
-0.022037291899323463,
0.031599342823028564,
-0.03929923474788666,
0.008201882243156433,
0.023907212540507317,
-0.0034675244241952896,
0.03968209773302078,
-0.0314490981400013,
0.005542480852454901,
0.005912960972636938,
-0.026181135326623917,
-0.0062482161447405815,
-0.008209769614040852,
0.011433877050876617,
0.018016554415225983,
0.049390122294425964,
-0.06953565776348114,
0.005046834237873554,
-0.01805000938475132,
-0.049550361931324005,
0.029195979237556458,
-0.020820973441004753,
-0.018950847908854485,
-0.061170369386672974,
0.015506367199122906,
0.017011521384119987,
0.009375495836138725,
0.017250023782253265,
-0.016357317566871643,
-0.03816341981291771,
-0.005916093476116657,
0.08658214658498764,
0.01815756782889366,
0.023373780772089958,
0.04073132574558258,
-0.05806848406791687,
-0.0190869253128767,
-0.000028065778678865172,
-0.013327662833034992,
0.03991630673408508,
0.02076471596956253,
-0.06002989038825035,
-0.035206932574510574,
0.07299879193305969,
-0.07986839860677719,
-0.044139064848423004,
-0.04721055179834366,
0.007637502625584602,
-0.031329937279224396,
0.08860833942890167,
-0.01589534617960453,
-0.002474117325618863,
0.0549684502184391,
-0.06819187849760056,
0.03328116610646248,
0.014779245480895042,
0.01330841239541769,
-0.002352555049583316,
0.04680466651916504,
0.020395861938595772,
-0.04328491911292076,
-0.05001670867204666,
0.0055297850631177425,
0.019155612215399742,
0.0199718177318573,
-0.011728396639227867,
-0.04850107803940773,
-0.021424030885100365,
0.07607490569353104,
0.060072220861911774,
0.003611901542171836,
0.02286233939230442,
-0.009834078140556812,
0.01789587363600731,
-0.02608439326286316,
0.027462167665362358,
-0.01878272369503975,
0.04632839560508728,
0.04224409535527229,
0.031139038503170013,
-0.004876401741057634,
-0.028546685352921486,
0.021644243970513344,
0.044974759221076965,
0.0154825234785676,
-0.02839192934334278,
0.020057011395692825,
-0.005052166059613228,
0.018259765580296516,
0.008688564412295818,
-0.008969701826572418,
0.023914873600006104,
0.01963312178850174,
0.0401335135102272,
0.0027711880393326283,
0.0298114363104105,
0.008114419877529144,
0.08784598857164383,
-0.0012478937860578299,
-0.011080657131969929,
-0.003591551911085844,
-0.004693067632615566,
0.019483456388115883,
-0.02610884979367256,
-0.00461167935281992,
0.08243809640407562,
-0.02915637567639351,
-0.013928358443081379,
0.07429102063179016,
0.0019197037909179926,
0.004022879991680384,
0.012503013014793396,
0.0014636124251410365,
-0.013560263440012932,
-0.03660283982753754,
0.04798577353358269,
-0.005664194002747536,
-0.023196522146463394,
-0.014073779806494713,
-0.03519391268491745,
-0.0052084303461015224,
-0.03103724680840969,
0.032153621315956116,
0.008778518065810204,
-0.05734676122665405,
0.022050196304917336,
-0.009793263860046864,
-0.03012273833155632,
-0.021267615258693695,
-0.06074575334787369,
-0.032372236251831055,
0.06403432041406631,
0.006681438069790602,
0.011270520277321339,
0.018439076840877533,
0.00720221409574151,
-0.05272318422794342,
0.022710565477609634,
-0.01222119852900505,
0.012165265157818794,
-0.059821903705596924,
-0.06008671969175339,
-0.04880235344171524,
-0.004630871582776308,
-0.028331726789474487,
-0.09715152531862259,
-0.01365403737872839,
0.05832497030496597,
0.021235866472125053,
-0.004006265662610531,
0.002240842906758189,
-0.07356566935777664,
-0.004129314795136452,
0.06118045747280121,
0.056057628244161606,
0.012229529209434986,
-0.009346847422420979,
0.032527223229408264,
0.048968907445669174,
-0.07881614565849304,
0.015405181795358658,
-0.0495438389480114,
0.05013260245323181,
0.016891589388251305,
-0.004727014806121588,
-0.018414627760648727,
-0.025257878005504608,
0.04348447173833847,
0.01216784119606018,
-0.0028027885127812624,
-0.000991125009022653,
-0.01583053544163704,
0.045622751116752625,
0.013014615513384342,
-0.04496597498655319,
-0.00885846745222807,
0.048809051513671875,
-0.0204079020768404,
-0.022636378183960915,
0.010842236690223217,
-0.05306683108210564,
-0.043611377477645874,
-0.09152419120073318,
-0.03851217404007912,
-0.0740133747458458,
-0.006699333433061838,
0.04261622950434685,
-0.028163226321339607,
0.013496002182364464,
0.03149767965078354,
-0.06384941190481186,
0.033496394753456116,
-0.01277875155210495,
-0.04534683749079704,
0.014846035279333591,
-0.06754184514284134,
0.04423514008522034,
0.01512229535728693,
-0.0021541567984968424,
-0.057775236666202545,
0.016335681080818176,
-0.011287461966276169,
0.07947566360235214,
-0.037979837507009506,
-0.018598351627588272,
0.0518578477203846,
0.050561416894197464,
-0.03277910128235817,
-0.02323199436068535,
-0.005668579135090113,
0.008846784941852093,
0.005322679411619902,
0.029817786067724228,
0.009113633073866367,
0.017259320244193077,
-0.019414041191339493,
0.024947984144091606,
-0.013106671161949635,
-0.0390906035900116,
-0.06696023046970367,
0.0013223958667367697,
0.06766889244318008,
0.004692673683166504,
-0.00886605866253376,
-0.016449790447950363,
0.01501493714749813
] |
<p>Given reflectivity $R = 0.75$, an etalon is used as an interference filter, transmitting light of wavelength $4.3\mu m$ at normal incidence. The full width half maximum is about $\Delta \lambda = 0.2 \mu m$. Find the initial spacing of plate.</p>
<p>(a) Find the spacing of the plate.</p>
<p>(b) Find the change in mirror spacing to shift the centre wavelength to $4.5\mu m$.</p>
<p>(c) The spacing is now fixed at a value that gives maximum intensity at $4.3\mu m$ at normal incidence. The angle of incidence is changed to $17.5^o$, find the wavelength of light transmitted.</p>
<p>(d) Find a wavelength shorter and longer than $4.3\mu m$ that gives maximum intensity at normal incidence.</p>
<p>I'm quite confused by this question, as usually either the spacing or wavelength is fixed...now you can even change the wavelength of light merely by changing the spacing?!</p>
<p><strong>Attempt</strong></p>
<p>(a) Intensity is given by: $I = I_0 \frac{1}{1 + \frac{4R}{(1-R)^2}sin^2(\frac{\delta}{2})}$. At $I = \frac{I_0}{2}$,</p>
<p>$$ \delta = \frac{1-R}{\sqrt R} $$</p>
<p>Thus FWHM $\Delta \delta$ = $2 \times \delta = \frac{2(1-R)}{\sqrt R} $</p>
<p>Using $\delta = 2nd = \frac{4\pi d}{\lambda}$, $\Delta \lambda = \frac{4\pi d}{\lambda^2}\Delta \lambda$.</p>
<p>Using n = 1, $d = \frac{\Delta \delta}{\Delta \lambda} \frac{\lambda^2}{4\pi} = 4.25 \mu m$.</p>
<p>(b) Condition of maxima is $2d cos\theta = m\lambda$. Central maxima is given by $m_0 = \frac{2d}{\lambda} \approx 2$. (Quite a lousy etalon right? Only able to see 2 fringes)</p>
<p>Now for the same value of $m_0$, we want to increase $\lambda$, so naturally the LHS term $d$ must increase as well.
$$\Delta d = \frac{m_0}{2}\Delta \lambda = \frac{d}{\lambda}\Delta \lambda = +0.2 \mu m $$</p>
<p>(c) Again fixing $m_0$, and now the spacing is the original $4.25\mu m$.
$$2d cos (17.5^o) = m_0 \lambda$$</p>
<p>$$\lambda = 4.05 \mu m$$</p>
<p>The wavlength is now shorter! At this point I have no idea what I'm doing anymore, how can the wavelength be changed?!</p>
<p>(d) Since it's either m = 1 or m = 2,</p>
<p>$$m = \frac{2d}{\lambda} $$</p>
<p>For $m=1$, $\lambda = 2d = 8.5 \mu m$</p>
<p>For $m=2$, $\lambda = d = 4.25 \mu m$</p>
<p>I would really appreciate if anyone could explain what's going on, as I'm pretty much confused..</p>
|
g2469
|
[
0.01940230093896389,
-0.06536659598350525,
0.006530849263072014,
-0.055681515485048294,
0.026345020160079002,
-0.004646059591323137,
0.04449508711695671,
0.024140436202287674,
-0.04966188594698906,
-0.007708725985139608,
-0.020934974774718285,
0.06201472878456116,
-0.005138796288520098,
-0.002672136528417468,
0.014209115877747536,
0.03780973702669144,
0.03383111581206322,
-0.014663821086287498,
0.002408060012385249,
-0.023298710584640503,
-0.022287528961896896,
-0.00990185234695673,
-0.05465893819928169,
-0.09997784346342087,
-0.012898004613816738,
0.008963045664131641,
0.020985661074519157,
0.03408364579081535,
-0.022407978773117065,
0.03562671318650246,
0.0038857378531247377,
0.04439925029873848,
0.05596451461315155,
-0.007365023717284203,
-0.013875540345907211,
0.05323842912912369,
0.058436427265405655,
0.048225220292806625,
0.038304537534713745,
0.01961359567940235,
0.015701713040471077,
-0.00004158118099439889,
0.037188127636909485,
-0.008246224373579025,
0.04197995737195015,
-0.07758775353431702,
-0.03809677064418793,
-0.022347943857312202,
-0.0002340730861760676,
-0.033585093915462494,
-0.04513510316610336,
0.04522451013326645,
0.02540651708841324,
-0.05074164271354675,
-0.021966662257909775,
0.012992852367460728,
-0.045303553342819214,
-0.02394193224608898,
0.0578983835875988,
0.04183217138051987,
0.013078514486551285,
-0.07495685666799545,
-0.017944013699889183,
0.0520092248916626,
-0.02652796544134617,
-0.0014769237022846937,
0.035871367901563644,
-0.0684533342719078,
0.018043171614408493,
-0.04683513939380646,
-0.06763856112957001,
-0.038241490721702576,
-0.03332275152206421,
-0.06266401708126068,
-0.019686445593833923,
-0.04837699979543686,
0.022559016942977905,
0.05694935470819473,
-0.03561762347817421,
0.0061541893519461155,
-0.04506263881921768,
-0.048508744686841965,
-0.028608351945877075,
-0.001286820974200964,
-0.02305085025727749,
0.037551019340753555,
-0.007892230525612831,
-0.004223958123475313,
0.04145229607820511,
-0.020372094586491585,
0.04368110001087189,
-0.03316466510295868,
0.012680343352258205,
0.0050781117752194405,
0.02867487072944641,
-0.017556723207235336,
-0.0000882916065165773,
0.015538915060460567,
0.02976050227880478,
0.00864017941057682,
0.02982233092188835,
-0.02534651942551136,
0.022978298366069794,
0.0420929491519928,
-0.025191552937030792,
0.030137281864881516,
0.053197525441646576,
-0.002338739112019539,
0.02099134773015976,
0.0004654606163967401,
-0.053336262702941895,
-0.04944135993719101,
-0.029952844604849815,
-0.10023106634616852,
-0.022196870297193527,
-0.0013687213649973273,
0.04364192485809326,
0.039481643587350845,
0.05815759301185608,
0.06828628480434418,
0.057462144643068314,
-0.0000375271265511401,
0.03021104447543621,
0.025919025763869286,
0.019645504653453827,
-0.039359673857688904,
0.009893366135656834,
0.05176332965493202,
0.06599732488393784,
-0.009511089883744717,
-0.018176883459091187,
0.018690554425120354,
0.00921046081930399,
0.044556885957717896,
0.01907777041196823,
-0.01355610229074955,
0.03229691833257675,
-0.0063407844863832,
-0.01380002312362194,
0.022202664986252785,
-0.010589417070150375,
-0.014469186775386333,
0.026748251169919968,
-0.025255849584937096,
-0.02961275540292263,
0.016774047166109085,
-0.006153713446110487,
-0.049308836460113525,
0.03603645786643028,
-0.02380284108221531,
0.08957589417695999,
0.08895117044448853,
-0.013354461640119553,
0.018121974542737007,
-0.005955198314040899,
0.013301688246428967,
-0.01039003487676382,
-0.03768530488014221,
0.002123270183801651,
-0.005414355080574751,
0.04213860630989075,
-0.0018213640432804823,
-0.02521834708750248,
-0.010539914481341839,
-0.04682384803891182,
0.04812377691268921,
-0.017797013744711876,
-0.07201208919286728,
-0.05342966690659523,
-0.036568883806467056,
-0.04203179106116295,
-0.005229231435805559,
0.027612490579485893,
-0.008595201186835766,
-0.0022134315222501755,
0.13613563776016235,
0.03789263218641281,
0.006383465137332678,
0.010335431434214115,
0.04594022035598755,
-0.03828178346157074,
-0.06568188965320587,
-0.004089880734682083,
-0.060277312994003296,
-0.02575886994600296,
-0.03760955482721329,
0.033879976719617844,
-0.08428766578435898,
-0.01388298999518156,
0.02301301620900631,
-0.04304241016507149,
-0.01887921802699566,
0.03400608152151108,
0.0010113222524523735,
-0.01102351676672697,
0.02883867360651493,
0.02125435508787632,
-0.04804180935025215,
-0.02986047975718975,
0.010266832076013088,
-0.014549260959029198,
-0.01374348159879446,
0.018722055479884148,
0.054891154170036316,
0.019854586571455002,
-0.01698698289692402,
0.04035567119717598,
-0.01518339104950428,
-0.03868931904435158,
0.043322671204805374,
-0.019839340820908546,
-0.007301261182874441,
-0.060890354216098785,
0.0260442104190588,
-0.01008574478328228,
-0.005324818659573793,
-0.0173194520175457,
0.020504500716924667,
-0.010224738158285618,
-0.010127309709787369,
-0.033998921513557434,
0.016868529841303825,
0.04702235385775566,
-0.013820485211908817,
0.0067190490663051605,
0.036215443164110184,
-0.01429988257586956,
0.01554577425122261,
0.026647694408893585,
0.05083845555782318,
-0.030946779996156693,
0.017558028921484947,
-0.0025311617646366358,
-0.028696058318018913,
0.06551560759544373,
0.007876523770391941,
-0.04997462034225464,
0.007619035430252552,
-0.01052013412117958,
-0.015935901552438736,
-0.02244885079562664,
0.015156570822000504,
-0.07851804792881012,
-0.005642349366098642,
-0.006366586312651634,
-0.02929232083261013,
-0.01442656945437193,
0.029893284663558006,
-0.07855541259050369,
0.0526609905064106,
0.02338777296245098,
0.0034363449085503817,
0.033249735832214355,
-0.037634965032339096,
-0.050989218056201935,
-0.02238065004348755,
-0.03594755008816719,
0.0575525239109993,
-0.015584887936711311,
-0.017168281599879265,
-0.01169052254408598,
-0.015711309388279915,
0.07343294471502304,
0.015238046646118164,
-0.014842426404356956,
0.039219971746206284,
-0.058336321264505386,
-0.007626046426594257,
0.009124875999987125,
0.010639804415404797,
0.006115056108683348,
0.06572716683149338,
0.03506177291274071,
0.0056319707073271275,
0.024305395781993866,
0.019895561039447784,
-0.03326800838112831,
-0.0657011866569519,
0.026946231722831726,
0.01444033719599247,
-0.00598008232191205,
0.03085431456565857,
-0.07091604173183441,
-0.014483571983873844,
-0.001787335379049182,
-0.04535413160920143,
0.07640578597784042,
0.007971083745360374,
-0.051189884543418884,
0.028798513114452362,
-0.027620291337370872,
-0.012711374089121819,
-0.046359315514564514,
-0.0031230717431753874,
0.025881202891469002,
-0.0173516683280468,
0.0527639202773571,
0.0038579737301915884,
-0.014960633590817451,
0.010539891198277473,
-0.057039860635995865,
0.04389113932847977,
-0.054036226123571396,
-0.03997556120157242,
0.058962639421224594,
0.010387147776782513,
-0.029895508661866188,
-0.04148729518055916,
0.02084175869822502,
0.051052387803792953,
0.04276915267109871,
-0.028385329991579056,
-0.05362348631024361,
-0.017532071098685265,
-0.0049810586497187614,
0.014286189340054989,
-0.009763466194272041,
-0.034204497933387756,
-0.054518427699804306,
0.017338629812002182,
0.0036687550600618124,
-0.007680348586291075,
-0.025686997920274734,
-0.058499034494161606,
-0.006693361792713404,
-0.00034777220571413636,
0.017275497317314148,
-0.008471879176795483,
-0.05482841283082962,
0.005928678438067436,
0.03711726889014244,
0.03801612928509712,
-0.011442062444984913,
-0.04455229267477989,
-0.01180520560592413,
-0.020467547699809074,
-0.0046798656694591045,
0.019116738811135292,
0.02629798650741577,
0.030381320044398308,
0.0027904154267162085,
-0.0071181729435920715,
-0.0964304655790329,
-0.0063555496744811535,
0.04299107566475868,
0.014617704786360264,
-0.004702987149357796,
0.012011206708848476,
-0.06594817340373993,
0.057035237550735474,
0.01508763525635004,
0.041124697774648666,
0.004283330403268337,
-0.025222759693861008,
-0.024501895532011986,
0.01770208217203617,
0.0007369828526861966,
0.007360728457570076,
0.035544537007808685,
-0.04740923270583153,
0.02888110838830471,
-0.09527625888586044,
-0.008094925433397293,
-0.043600182980298996,
-0.033528637140989304,
0.00984838418662548,
0.03329784795641899,
0.02458840422332287,
0.004517946857959032,
0.0420009009540081,
0.0290335975587368,
-0.05799049884080887,
0.023087836802005768,
-0.01792619377374649,
-0.04843549057841301,
-0.009074215777218342,
0.009353606030344963,
0.020139379426836967,
-0.031964004039764404,
0.042361993342638016,
-0.016111847013235092,
-0.039897363632917404,
0.0031445305794477463,
-0.02159496583044529,
0.025910697877407074,
0.003506449982523918,
-0.040591709315776825,
-0.04684137552976608,
0.005014162510633469,
-0.025472525507211685,
0.003681976580992341,
-0.024592548608779907,
0.03845127299427986,
-0.010562164708971977,
-0.01451936922967434,
-0.02204436995089054,
0.00026939468807540834,
0.035103313624858856,
-0.08699284493923187,
0.02075446955859661,
-0.00621524453163147,
-0.008207735605537891,
-0.012571444734930992,
0.04780877009034157,
-0.08474787324666977,
-0.02534988336265087,
0.0457930825650692,
0.04453730210661888,
0.05471847951412201,
0.007883704267442226,
-0.030727995559573174,
-0.007079676724970341,
-0.004859279841184616,
-0.07973793148994446,
0.04180072247982025,
0.027904119342565536,
0.03676580265164375,
0.0033156252466142178,
0.007955458015203476,
-0.0016913898289203644,
-0.03980115428566933,
0.025017788633704185,
-0.036441318690776825,
0.018138471990823746,
0.08551163971424103,
0.0409075990319252,
0.007417104672640562,
-0.05219731107354164,
0.08295636624097824,
-0.00313414353877306,
-0.01117320079356432,
0.030052686110138893,
-0.0613950677216053,
0.04902141913771629,
-0.0637628585100174,
0.0355897918343544,
0.011654380708932877,
-0.02071043848991394,
-0.025190109387040138,
-0.014837485738098621,
-0.00667057977989316,
-0.03397870808839798,
-0.015384038910269737,
-0.01849720999598503,
0.07905981689691544,
-0.006141535006463528,
-0.027262995019555092,
-0.07875766605138779,
0.03583330661058426,
0.014846551232039928,
-0.018674958497285843,
0.009964114055037498,
0.07914726436138153,
-0.0015482051530852914,
-0.013538946397602558,
-0.08997265249490738,
-0.04026816412806511,
0.025524849072098732,
0.051445502787828445,
0.016994435340166092,
-0.05448625981807709,
0.005812418181449175,
-0.043868303298950195,
-0.04324699938297272,
0.08637107908725739,
0.04018598049879074,
-0.045369211584329605,
-0.038650646805763245,
-0.09098304063081741,
0.0004268270276952535,
0.04445585235953331,
0.02906825579702854,
0.020622223615646362,
0.011470953933894634,
-0.018708929419517517,
0.05771617963910103,
-0.07184629142284393,
0.002047971822321415,
-0.01741606369614601,
-0.052170298993587494,
-0.013143643736839294,
-0.08783317357301712,
0.04966510459780693,
0.08046814799308777,
0.016098350286483765,
-0.018946606665849686,
-0.041641127318143845,
-0.017080429941415787,
0.014619572088122368,
-0.02252236381173134,
-0.053376663476228714,
0.025841249153017998,
-0.00750656146556139,
-0.012008965015411377,
-0.012508871965110302,
0.017007051035761833,
0.024397917091846466,
-0.00018226868996862322,
0.026851534843444824,
0.03660082072019577,
0.01378114614635706,
0.03635447472333908,
0.02687082625925541,
0.02640160173177719,
-0.05600915476679802,
-0.005893012974411249,
0.035876259207725525,
0.042897582054138184,
0.0038631856441497803,
0.03150933235883713,
0.02412249706685543,
0.007067997008562088,
0.020793940871953964,
-0.012740464881062508,
0.01777081936597824,
-0.04149436578154564,
-0.007085885386914015,
0.0655602440237999,
-0.038532111793756485,
-0.026575716212391853,
-0.019256576895713806,
-0.038364309817552567,
-0.0017149184131994843,
0.03722217306494713,
0.002005685120820999,
0.039322856813669205,
-0.022365938872098923,
-0.031934574246406555,
0.01937379501760006,
-0.08412492275238037,
-0.03996764123439789,
0.07360468804836273,
-0.015048188157379627,
0.024296941235661507,
-0.0009274559561163187,
-0.01663636416196823,
-0.021687854081392288,
0.025016028434038162,
-0.02708279713988304,
-0.04636649787425995,
-0.0024461266584694386,
-0.03369647637009621,
0.035249900072813034,
0.018207116052508354,
-0.0014262229669839144,
-0.006156239192932844,
0.03855305165052414,
-0.031972672790288925,
0.03430889919400215,
0.0063767507672309875,
0.012551168911159039,
0.014841947704553604,
0.009523251093924046,
0.010502751916646957,
0.020656438544392586,
0.055705856531858444,
0.01380181685090065,
-0.04502716287970543,
0.005033976398408413,
-0.06390444189310074,
0.024804526939988136,
-0.013591723516583443,
-0.07635410875082016,
0.034576620906591415,
0.011259498074650764,
-0.018545223399996758,
0.005298451520502567,
0.01779184676706791,
0.04173450917005539,
-0.007762813940644264,
-0.041849225759506226,
0.01615126058459282,
-0.0332784503698349,
-0.0047937240451574326,
0.021501922979950905,
0.08100326359272003,
0.01997845247387886,
0.011140395887196064,
-0.04328508302569389,
-0.02860734425485134,
-0.08092859387397766,
-0.0039023244753479958,
0.0010860406327992678,
0.023012744262814522,
-0.05418035015463829,
0.01808752492070198,
-0.006701935548335314,
-0.027318522334098816,
0.07067355513572693,
-0.03981751948595047,
-0.028967605903744698,
-0.032357197254896164,
0.0036751204170286655,
0.006413114257156849,
0.03177913278341293,
-0.013889330439269543,
-0.01963046006858349,
0.04298625886440277,
-0.0044867792166769505,
0.06926937401294708,
0.058601412922143936,
-0.03923840820789337,
-0.000038899885112186894,
0.01655719056725502,
0.025197869166731834,
0.017361413687467575,
0.017064683139324188,
-0.0349021852016449,
0.027160130441188812,
0.014046418480575085,
0.019436800852417946,
0.03938288986682892,
0.06240195780992508,
0.023975394666194916,
-0.05783433839678764,
-0.019445663318037987,
-0.012458518147468567,
0.01909295842051506,
0.003714319784194231,
0.02346707321703434,
0.024490149691700935,
-0.01618192344903946,
0.006414760835468769,
-0.014139463193714619,
-0.0343271940946579,
0.015704507008194923,
0.009012358263134956,
-0.10042800009250641,
0.026731986552476883,
-0.005651141982525587,
0.01428566500544548,
-0.06667353212833405,
0.03061109036207199,
0.009440499357879162,
-0.03160075098276138,
0.01831120438873768,
-0.04877810180187225,
0.06739570945501328,
-0.003388859098777175,
0.09089347720146179,
0.027359625324606895,
0.04120161756873131,
-0.0013185618445277214,
-0.007237283047288656,
0.002483536722138524,
0.008166847750544548,
0.0016844540368765593,
0.021905869245529175,
-0.05511056259274483,
0.03556863218545914,
0.04408552497625351,
0.030376801267266273,
-0.02054622955620289,
0.050577908754348755,
0.017910422757267952,
-0.0009409963968209922,
-0.038369070738554,
0.030886001884937286,
-0.013813958503305912,
-0.00534334871917963,
0.0054093520157039165,
-0.007304356899112463,
-0.017777780070900917,
-0.0025991618167608976,
0.028574448078870773,
0.07100912183523178,
0.06861545145511627,
0.0011839126236736774,
-0.010949764400720596,
-0.03131166845560074,
-0.04674631729722023,
-0.028836850076913834,
-0.0030287886038422585,
-0.03804455325007439,
0.0448789969086647,
0.007482991088181734,
0.000756822235416621,
0.04009884223341942,
-0.007924703881144524,
0.008469188585877419,
0.010036582127213478,
0.014803733676671982,
0.022914685308933258,
-0.05867529287934303,
-0.003512050025165081,
0.039329979568719864,
-0.07527803629636765,
-0.03412641957402229,
0.06455212086439133,
-0.014800379984080791,
-0.014459584839642048,
0.01139693334698677,
-0.04836616665124893,
0.024628814309835434,
-0.033606503158807755,
0.029781624674797058,
0.002364886924624443,
0.02794339321553707,
0.009352798573672771,
-0.011766869574785233,
-0.004645548295229673,
-0.08538150787353516,
-0.03440336883068085,
-0.05593902990221977,
0.03941725566983223,
0.03924435377120972,
-0.03245885670185089,
0.013103610835969448,
0.019144296646118164,
-0.03258846700191498,
0.020903373137116432,
-0.006623965222388506,
-0.0009778301464393735,
0.06870725005865097,
0.03601500764489174,
-0.01648029498755932,
0.013384212739765644,
0.06016380712389946,
0.00690394127741456,
-0.0009528311202302575,
-0.014937997795641422,
-0.031053787097334862,
-0.0069421036168932915,
-0.057823166251182556,
-0.031592704355716705,
0.019094249233603477,
0.05408972501754761,
-0.0221700519323349,
0.04354444891214371,
0.014482773840427399,
0.03446664661169052,
0.00665621692314744,
-0.06819172948598862,
-0.07164926081895828,
0.006482379510998726,
0.016845667734742165,
-0.00423466507345438,
-0.015991879627108574,
0.021876787766814232,
0.0659046322107315,
0.021266663447022438,
0.008622925728559494,
0.002093044575303793,
-0.045287564396858215,
0.023387162014842033,
0.03064560890197754,
-0.02232344076037407,
-0.002232859143987298,
-0.015578239224851131,
-0.025019319728016853,
-0.04786984622478485,
0.06861412525177002,
-0.025054046884179115,
0.06804968416690826,
0.03897833451628685,
-0.03373526781797409,
0.012311242520809174,
0.0068686665035784245,
0.010924025438725948,
-0.03624941408634186,
0.003656374756246805,
-0.0005828072899021208,
-0.005711264908313751,
0.042227063328027725,
0.025091350078582764,
0.03663111850619316,
0.011138754896819592,
-0.003568759188055992
] |
<p>I've had it explained to me in a <a href="http://physics.stackexchange.com/questions/117013/is-there-a-difference-between-photons-that-act-as-virtual-particles-and-photon">separate post</a> that charged particles are constantly exchanging virtual particles with other charged particles and their energy is a steady state. How it is a surety that all of the virtual photons sent out by the charged particle will be exchanged with other charged particles? Are the particles sent in a directed manner toward other charged particles? How much do we know about this interaction/mechanism? Are some virtual particles just radiated away, leaving the charged particle with less energy?</p>
|
g2470
|
[
0.08075866103172302,
0.02313235029578209,
-0.028008325025439262,
0.006201376672834158,
0.05916846916079521,
-0.003576381364837289,
0.046086154878139496,
0.01329323835670948,
0.017158418893814087,
-0.019278325140476227,
-0.029058370739221573,
0.024721503257751465,
-0.0038597285747528076,
-0.026906833052635193,
-0.036229297518730164,
-0.023154666647315025,
0.091939277946949,
-0.017692910507321358,
-0.006150123663246632,
0.04405524209141731,
-0.01226980984210968,
0.0013707440812140703,
0.008981320075690746,
-0.03103984333574772,
-0.03599435091018677,
-0.03758763521909714,
-0.02743787318468094,
-0.012587597593665123,
-0.002785771619528532,
-0.08044181019067764,
0.022273829206824303,
-0.006608902011066675,
0.035569000989198685,
0.028175113722682,
-0.0032139720860868692,
-0.07273656874895096,
0.047880496829748154,
-0.02650480903685093,
-0.03926623612642288,
0.01029722299426794,
0.01089955773204565,
0.04345332086086273,
-0.002566216280683875,
-0.001797181903384626,
0.02044479362666607,
-0.010000106878578663,
-0.011266334913671017,
-0.0049672373570501804,
-0.029751824215054512,
-0.004539921879768372,
0.014805576764047146,
0.009716222994029522,
-0.028610512614250183,
0.08518894761800766,
0.06132292374968529,
-0.015894602984189987,
0.05769983306527138,
0.028559545055031776,
0.033345770090818405,
-0.008367490954697132,
0.022852344438433647,
-0.02136598527431488,
0.016428064554929733,
0.01200044434517622,
0.06752806156873703,
-0.05336574837565422,
-0.07673031091690063,
-0.0003165219386573881,
-0.019543549045920372,
-0.008283684961497784,
0.031955163925886154,
-0.05560125783085823,
-0.01940123178064823,
0.007658860180526972,
0.047060005366802216,
-0.00951716210693121,
0.015418648719787598,
-0.03206286206841469,
-0.0015433661174029112,
0.007770009338855743,
-0.018430473282933235,
-0.03760894387960434,
0.030098022893071175,
-0.08091051876544952,
0.06736137717962265,
-0.05485249310731888,
-0.037757232785224915,
-0.029207473620772362,
-0.009821140207350254,
-0.02207369916141033,
0.022430915385484695,
-0.01309585478156805,
0.08241527527570724,
0.044946204870939255,
-0.06412236392498016,
-0.014991414733231068,
-0.02744194120168686,
0.07112309336662292,
-0.028450844809412956,
-0.09487412869930267,
0.015380642376840115,
0.005881902761757374,
0.014600332826375961,
0.007316967472434044,
0.027983564883470535,
-0.014890352264046669,
0.000837267842143774,
-0.002967034000903368,
0.010836105793714523,
-0.008164872415363789,
-0.005110294558107853,
-0.06704972684383392,
-0.025467000901699066,
-0.026218626648187637,
-0.021934419870376587,
0.0003978521272074431,
0.054815832525491714,
0.006912598852068186,
0.01343925204128027,
0.029846640303730965,
0.023664945736527443,
0.009803840890526772,
-0.08171974122524261,
0.02008153311908245,
0.007526123430579901,
0.0034742048010230064,
0.07054154574871063,
-0.022977331653237343,
-0.03907327726483345,
0.04737472906708717,
0.03613845258951187,
0.009900272823870182,
-0.010995453223586082,
-0.0035270501393824816,
-0.04368872940540314,
-0.00585850328207016,
0.08383660018444061,
0.004172706510871649,
0.049418941140174866,
-0.04902833700180054,
0.03383447602391243,
-0.025165004655718803,
-0.01715392805635929,
-0.024570025503635406,
-0.029943974688649178,
0.02851681225001812,
-0.008869960904121399,
-0.011262076906859875,
0.02695225179195404,
0.027896661311388016,
0.07562856376171112,
0.07208812236785889,
0.042926572263240814,
-0.020626883953809738,
0.00007598920637974516,
-0.057894665747880936,
0.016322946175932884,
-0.005868446547538042,
-0.004696846008300781,
0.017253855243325233,
0.014498129487037659,
-0.012438060715794563,
-0.009578296914696693,
-0.03723481670022011,
-0.033831462264060974,
-0.04661279171705246,
0.044935669749975204,
-0.029722364619374275,
0.010607520118355751,
-0.04270639270544052,
-0.0274557676166296,
0.028617026284337044,
-0.01988898031413555,
0.01486844290047884,
0.0037204576656222343,
0.014023344032466412,
-0.017688756808638573,
-0.034628916531801224,
-0.012660243548452854,
-0.013455835171043873,
-0.0692070871591568,
-0.013289987109601498,
0.03943769633769989,
-0.036237429827451706,
0.006684187799692154,
0.007306061219424009,
-0.08855459094047546,
-0.028048112988471985,
-0.007372057065367699,
-0.02228938601911068,
-0.04909030720591545,
0.013314099051058292,
-0.02300630509853363,
-0.028437070548534393,
0.02528112195432186,
-0.004391408525407314,
-0.013763109222054482,
-0.04751977324485779,
0.013551636599004269,
-0.002230654703453183,
-0.06073348969221115,
0.06600284576416016,
0.009393925778567791,
0.02874927595257759,
0.05346361920237541,
-0.006181330885738134,
0.016929177567362785,
-0.02993255853652954,
0.027891099452972412,
-0.02539866231381893,
0.09245643019676208,
-0.04049742966890335,
0.056423258036375046,
0.0466335192322731,
-0.0012343608541414142,
-0.05089634284377098,
-0.01884559728205204,
-0.02111475169658661,
0.04371367394924164,
-0.04338361322879791,
-0.014921092428267002,
-0.0174087006598711,
0.02520308643579483,
-0.002803951734676957,
-0.014924433082342148,
0.0036461486015468836,
-0.0410732626914978,
-0.012325331568717957,
-0.00944798719137907,
0.06392043828964233,
-0.027475479990243912,
0.024136755615472794,
-0.030317772179841995,
0.009102389216423035,
0.049386635422706604,
0.03405594080686569,
-0.06254467368125916,
0.04374491050839424,
0.013536077924072742,
-0.02701742574572563,
0.047132741659879684,
-0.05552104860544205,
-0.00009639468044042587,
0.03068731352686882,
-0.004480598960071802,
-0.0428827665746212,
0.061162613332271576,
-0.019603747874498367,
-0.03384700417518616,
-0.03849000856280327,
0.04107147082686424,
0.0019802057649940252,
-0.00477941008284688,
0.01410632859915495,
-0.02492346800863743,
-0.028644487261772156,
0.009444775059819221,
0.03877482935786247,
-0.05112120881676674,
-0.03630988672375679,
-0.03315628692507744,
-0.01987902633845806,
-0.026546848937869072,
0.025091052055358887,
-0.010435220785439014,
-0.015168653801083565,
0.030814895406365395,
0.09391185641288757,
0.009502344764769077,
-0.03695157915353775,
-0.0016158074140548706,
0.06183391436934471,
0.045998215675354004,
-0.0018207046668976545,
-0.02162303403019905,
0.013535935431718826,
0.008449181914329529,
-0.015382223762571812,
0.022612856701016426,
-0.037598866969347,
0.018553325906395912,
0.019813047721982002,
-0.0398082360625267,
-0.039898160845041275,
0.03085777536034584,
-0.05415213480591774,
-0.01517115905880928,
-0.002009489806368947,
-0.031686797738075256,
-0.04251573607325554,
0.003937034402042627,
-0.019477667286992073,
0.07477555423974991,
-0.03747120127081871,
-0.019944218918681145,
0.027828745543956757,
0.07411538064479828,
-0.03550415858626366,
-0.058499619364738464,
0.025016289204359055,
-0.00546752754598856,
-0.02176007628440857,
-0.021472766995429993,
-0.0712808147072792,
0.039840493351221085,
0.038491636514663696,
-0.07665517181158066,
-0.00400172732770443,
0.00372709846124053,
0.006361499894410372,
-0.011347916908562183,
0.046352777630090714,
-0.025205891579389572,
0.017016563564538956,
0.004024511203169823,
-0.03285730257630348,
0.03030463121831417,
0.07478662580251694,
0.004315877333283424,
0.04109061136841774,
-0.052475884556770325,
0.02675412967801094,
0.04986869543790817,
-0.028942648321390152,
0.011890956200659275,
0.05460584908723831,
-0.024993132799863815,
-0.035176023840904236,
-0.048381078988313675,
0.018905747681856155,
0.02733105607330799,
-0.0014217160642147064,
-0.006675160024315119,
-0.01733473502099514,
-0.03735436871647835,
-0.033313922584056854,
-0.012267735786736012,
0.022196972742676735,
0.07705909013748169,
-0.028121519833803177,
0.06555105000734329,
0.022117435932159424,
-0.061476726084947586,
0.026749376207590103,
0.02109145186841488,
-0.019198229536414146,
-0.021512195467948914,
-0.027425892651081085,
0.015228431671857834,
-0.028216689825057983,
0.05967075750231743,
0.05527351796627045,
-0.006465286016464233,
0.008164707571268082,
-0.039780013263225555,
-0.009771965444087982,
-0.06373470276594162,
0.019288022071123123,
0.006140954326838255,
0.01846878044307232,
-0.009678966365754604,
-0.02171608805656433,
0.04378797486424446,
0.0160482469946146,
-0.042558807879686356,
-0.016437623649835587,
-0.009717979468405247,
-0.01612735167145729,
0.047195401042699814,
-0.02086021937429905,
-0.022983461618423462,
-0.003869337495416403,
-0.03884818032383919,
0.03107089176774025,
-0.031623873859643936,
-0.01940084435045719,
0.05488308519124985,
-0.0015376863302662969,
-0.02282935194671154,
0.00030557610443793237,
-0.011037898249924183,
0.04368727654218674,
0.05113139748573303,
-0.014641671441495419,
0.03400865197181702,
0.08153276890516281,
-0.04150031507015228,
0.024523844942450523,
-0.029298387467861176,
-0.03265620395541191,
0.04463592916727066,
-0.05534498766064644,
-0.034402381628751755,
0.02198571339249611,
0.036625929176807404,
-0.05401495099067688,
-0.004441948141902685,
0.007562183775007725,
0.07032151520252228,
0.024321842938661575,
-0.011189565993845463,
0.04399222508072853,
-0.004667732864618301,
-0.06836559623479843,
0.08464329689741135,
0.0040770042687654495,
0.009930338710546494,
-0.0308221485465765,
-0.05108112841844559,
-0.028194736689329147,
-0.008020914159715176,
0.004223597701638937,
-0.00943028461188078,
-0.033246420323848724,
-0.005603425204753876,
0.009451639838516712,
-0.028820551931858063,
-0.020672308281064034,
0.003483902895823121,
-0.02835709974169731,
-0.022962071001529694,
-0.0246695876121521,
0.033100519329309464,
0.005184887442737818,
0.03131385147571564,
0.11293850839138031,
0.05756423622369766,
0.011991090141236782,
-0.045517101883888245,
-0.03858758136630058,
0.08799736946821213,
0.027911175042390823,
0.02195199579000473,
-0.011350000277161598,
-0.012319847010076046,
0.05586972087621689,
-0.05072871968150139,
0.005907005164772272,
0.003466965164989233,
0.0701492428779602,
0.11819857358932495,
0.01929567940533161,
0.05127058923244476,
-0.02611090987920761,
0.010840607807040215,
0.027053575962781906,
-0.040795449167490005,
0.012577353976666927,
0.004653272684663534,
-0.04983861744403839,
0.017671775072813034,
0.026360196992754936,
-0.07776818424463272,
-0.027982071042060852,
-0.01943124830722809,
-0.0011848524445667863,
-0.005178040359169245,
-0.013722582720220089,
0.024130793288350105,
-0.022283218801021576,
-0.057485681027173996,
0.02340528555214405,
0.08992861211299896,
-0.005462633445858955,
0.004873417783528566,
-0.0034212612081319094,
-0.00889190100133419,
-0.004146897234022617,
-0.06717648357152939,
0.015195325948297977,
-0.008648599497973919,
0.060437969863414764,
0.024952009320259094,
-0.013810494914650917,
0.03843618929386139,
-0.09855721145868301,
-0.043832216411828995,
-0.029377328231930733,
0.00312759424559772,
-0.004740226548165083,
-0.010300029069185257,
-0.022239351645112038,
0.03792690485715866,
0.012137684971094131,
-0.08100645989179611,
0.010439346544444561,
-0.010780401527881622,
0.054248228669166565,
-0.022250879555940628,
-0.00258863577619195,
-0.0003226929693482816,
-0.0665324479341507,
0.014994745142757893,
-0.033188704401254654,
0.028479913249611855,
0.0025408314540982246,
-0.0071483189240098,
0.0029451169539242983,
-0.02497038058936596,
0.039032869040966034,
-0.0059517379850149155,
-0.027781318873167038,
-0.05813966318964958,
-0.03638385608792305,
-0.008369745686650276,
0.04607981815934181,
0.04554694518446922,
-0.07950406521558762,
-0.06120261922478676,
-0.026461035013198853,
-0.021143101155757904,
-0.007582713849842548,
-0.012755824252963066,
0.01487177237868309,
-0.017642205581068993,
0.05436186119914055,
-0.04885711148381233,
0.008227096870541573,
0.010099802166223526,
-0.03678432106971741,
0.0017693492118269205,
0.021896792575716972,
0.013933167792856693,
-0.010091667994856834,
0.008407697081565857,
-0.04334360361099243,
-0.047186098992824554,
0.009431777521967888,
0.0168231762945652,
0.013202346861362457,
0.004435649141669273,
0.017583129927515984,
-0.01241663284599781,
0.04450921714305878,
-0.021187273785471916,
-0.040632084012031555,
-0.007493640296161175,
-0.017000503838062286,
0.053252268582582474,
0.03268896043300629,
-0.000083004983025603,
-0.05282463878393173,
-0.016767431050539017,
0.10106168687343597,
0.03875674307346344,
0.00731099396944046,
-0.021025806665420532,
0.011206955648958683,
0.06071745604276657,
-0.0006844384479336441,
-0.025387577712535858,
0.0168002936989069,
-0.0037290353793650866,
0.011463177390396595,
0.002358522731810808,
-0.02294408343732357,
0.014391299337148666,
0.008853977546095848,
0.0203010905534029,
-0.027313340455293655,
0.02253805287182331,
0.020489512011408806,
0.005987278185784817,
-0.020841093733906746,
-0.0091494619846344,
-0.02794838882982731,
-0.026858702301979065,
-0.08110993355512619,
0.031805481761693954,
0.047333911061286926,
0.03200877085328102,
0.016931574791669846,
-0.03066905215382576,
-0.02182362601161003,
-0.02090241201221943,
-0.025834470987319946,
-0.04549720510840416,
-0.03492065891623497,
-0.07291803508996964,
-0.0008286784286610782,
0.08003339171409607,
0.019099878147244453,
0.04335618019104004,
-0.013909422792494297,
0.007758502848446369,
0.061734773218631744,
0.004465964622795582,
-0.02824210375547409,
0.032411109656095505,
0.03156315162777901,
0.017881430685520172,
-0.011132362298667431,
0.005456227343529463,
-0.009244745597243309,
-0.02226204238831997,
-0.017552034929394722,
0.03722917288541794,
-0.016477564349770546,
-0.033063385635614395,
0.014413381926715374,
0.0183678288012743,
0.029255179688334465,
-0.033563971519470215,
0.0013751792721450329,
-0.010175170376896858,
0.05978439003229141,
0.00007395204738713801,
0.0014550682390108705,
-0.03523654118180275,
0.012507010251283646,
-0.04578419774770737,
0.012680635787546635,
-0.018100162968039513,
-0.019785379990935326,
-0.00030539758154191077,
-0.048819348216056824,
-0.0396258682012558,
0.054353032261133194,
0.021464699879288673,
0.005664837080985308,
-0.015890201553702354,
-0.041768234223127365,
-0.01414319034665823,
0.04609252139925957,
0.04347250238060951,
0.05855497717857361,
0.0010009704856202006,
0.030889958143234253,
0.07941721379756927,
0.025205185636878014,
0.003138582454994321,
-0.027854783460497856,
0.02511531300842762,
0.030271245166659355,
0.05548630654811859,
0.025921571999788284,
-0.018926728516817093,
-0.008492507040500641,
0.0029564921278506517,
-0.03253478929400444,
0.007943063974380493,
0.027273768559098244,
0.06283920258283615,
0.029219133779406548,
-0.01557778101414442,
0.022123031318187714,
0.024571536108851433,
-0.0035177250392735004,
0.001347860204987228,
0.03603814169764519,
-0.03171652927994728,
-0.03217194974422455,
0.021444499492645264,
-0.0015841824933886528,
-0.008188679814338684,
0.03383202105760574,
-0.047441061586141586,
-0.016913169994950294,
-0.026788299903273582,
-0.05741611495614052,
-0.0009508499060757458,
-0.032644689083099365,
-0.011508454568684101,
0.008471667766571045,
-0.0024964630138128996,
0.007336704526096582,
-0.007842687889933586,
-0.032045334577560425,
0.026441499590873718,
-0.0433143749833107,
0.028737561777234077,
-0.0708753690123558,
-0.04706781730055809,
0.01508540753275156,
0.04338847100734711,
-0.04233619198203087,
-0.03136357292532921,
0.08098692446947098,
-0.016011405736207962,
0.0031960702035576105,
0.026544751599431038,
0.06978794932365417,
0.03178311511874199,
0.060640934854745865,
-0.009923343546688557,
0.06402327120304108,
-0.04122933745384216,
0.028292279690504074,
-0.059274714440107346,
0.04444321617484093,
0.0014746079687029123,
-0.07217276841402054,
-0.023289142176508904,
0.01434416975826025,
-0.00452926941215992,
-0.006817456800490618,
0.06275603920221329,
0.020237017422914505,
0.02165389619767666,
0.024022748693823814,
-0.060606446117162704,
-0.027831705287098885,
0.05373484268784523,
-0.000992641900666058,
0.035175591707229614,
0.03093312680721283,
-0.02962864376604557,
-0.04193580895662308,
-0.005965913645923138,
-0.017081046476960182,
0.024853883311152458,
-0.06652509421110153,
0.019909657537937164,
0.017953813076019287,
-0.05885493382811546,
-0.044186219573020935,
0.0024685284588485956,
0.07515985518693924,
0.0007998062646947801,
0.024460474029183388,
-0.009796557016670704,
0.026912746950984,
-0.026958730071783066,
0.001208469970151782,
0.04501011595129967,
-0.02136734314262867,
0.05734483525156975,
0.008665119297802448,
-0.02898755855858326,
0.016707802191376686,
-0.05564804747700691,
0.011424828320741653,
0.03293304145336151,
-0.007043660618364811,
-0.002254632068797946,
0.024769848212599754,
0.05969401076436043,
-0.01772187277674675,
0.02468024753034115,
-0.009162750095129013,
0.049313247203826904,
-0.07661616057157516,
-0.052698466926813126,
-0.017022088170051575,
-0.022031741216778755,
-0.029243430122733116,
-0.017794447019696236,
0.02946649119257927,
0.0475468784570694,
-0.04485543072223663,
0.0367610789835453,
0.042963650077581406,
-0.022964350879192352,
0.06634622067213058,
0.0950271263718605,
-0.07378025352954865,
0.0033976156264543533,
-0.007914891466498375,
-0.019933391362428665,
0.03149811923503876,
-0.03722952678799629,
0.01419806107878685,
-0.00007556556374765933,
-0.01756846345961094,
0.013764479197561741,
-0.06619195640087128,
-0.05960524082183838,
0.015333243645727634
] |
<p>I always thought that $force$ is $mass * acceleration$. Well, that's what I learnt at school a while back. Now, I have been enlightened that force is in fact the rate of change of momentum. </p>
<p>What makes this interesting to me, is that this takes into account a change in mass with respect to time as also playing a role in the force. A nice example of this is that of a rocket taking off. But clearly, this was not an example that Newton had in mind. </p>
<p>So my question: What did Newton have in mind of something where the mass changes with time?</p>
<p>I appreciate that my question is similar to say: <a href="http://physics.stackexchange.com/questions/2644/how-did-newton-discover-his-second-law">How did Newton discover his second law?</a> but I didn't read anywhere there about the concept of change of mass with time.</p>
|
g47
|
[
0.07033409178256989,
-0.002119100419804454,
0.015547636896371841,
0.004419655539095402,
0.07859352976083755,
-0.012304042465984821,
0.0036998277064412832,
-0.019172746688127518,
-0.048364393413066864,
-0.006028853822499514,
-0.012833280488848686,
-0.026044728234410286,
0.05615729093551636,
0.015894992277026176,
0.014629182405769825,
-0.0032947382424026728,
0.0901181548833847,
-0.03821611776947975,
0.043601881712675095,
0.008365356363356113,
0.020709024742245674,
0.005379373207688332,
-0.07150708884000778,
-0.021775439381599426,
-0.048332639038562775,
0.026511428877711296,
0.05298883095383644,
0.004563317168504,
-0.02976890467107296,
-0.01918252930045128,
0.04240942746400833,
-0.01245337724685669,
0.024341637268662453,
-0.030851533636450768,
0.024939032271504402,
-0.06210656091570854,
-0.01460584532469511,
0.02497659996151924,
0.03138192743062973,
0.015424077399075031,
-0.004835647065192461,
-0.06775257736444473,
-0.021388964727520943,
-0.0005953374202363193,
0.06034877896308899,
0.014390324242413044,
-0.06414228677749634,
-0.06746577471494675,
-0.03987331688404083,
-0.005403756629675627,
0.023510072380304337,
0.05640866979956627,
0.0225047804415226,
0.019359493628144264,
-0.023749535903334618,
0.029823383316397667,
0.029385250061750412,
-0.014382409863173962,
0.04685606062412262,
0.008100931532680988,
-0.028565093874931335,
-0.026144180446863174,
0.060406383126974106,
-0.014649944379925728,
0.05042291432619095,
-0.015801988542079926,
0.036645982414484024,
-0.001276166643947363,
0.016864188015460968,
0.021321270614862442,
-0.008060081861913204,
-0.0012307735159993172,
-0.040772635489702225,
-0.025952672585844994,
0.010838400572538376,
-0.023867718875408173,
0.010882689617574215,
-0.03027249127626419,
-0.025454863905906677,
-0.03784218057990074,
0.0342218279838562,
0.05858597531914711,
0.0526515357196331,
0.04533667117357254,
0.07240694761276245,
-0.04124743118882179,
-0.021488549187779427,
-0.01799314096570015,
-0.018405426293611526,
0.0056628636084496975,
-0.006405981257557869,
0.026917416602373123,
0.04857923835515976,
0.03211967647075653,
-0.06972955912351608,
-0.08523883670568466,
0.005099899601191282,
0.0564679279923439,
0.0393650159239769,
0.011928245425224304,
-0.004733249079436064,
-0.01946105994284153,
0.040862321853637695,
-0.003983746282756329,
0.002315894467756152,
0.044445332139730453,
0.01331542618572712,
0.008243350312113762,
-0.01420651562511921,
0.006491645239293575,
0.02976342849433422,
-0.029339632019400597,
-0.027614029124379158,
-0.033605244010686874,
-0.04617303982377052,
-0.07450336962938309,
0.016916636377573013,
-0.021943842992186546,
0.03715614974498749,
0.006773950066417456,
-0.019577430561184883,
-0.003104518400505185,
-0.03465122729539871,
0.03947015479207039,
-0.06603182107210159,
-0.03211938962340355,
0.026182658970355988,
-0.01455858163535595,
-0.015958664938807487,
-0.02788931503891945,
-0.004528877325356007,
0.032797921448946,
0.0423579178750515,
0.004678353667259216,
-0.033793915063142776,
0.03682495281100273,
-0.0632893368601799,
-0.02585837058722973,
0.0017370798159390688,
-0.005539075471460819,
0.04332761839032173,
-0.026487184688448906,
0.04578447341918945,
0.0026510986499488354,
-0.022000234574079514,
0.004720785655081272,
-0.0886370986700058,
-0.007609052117913961,
0.04531542956829071,
-0.016306748613715172,
-0.03251493722200394,
0.08543013781309128,
-0.024460354819893837,
-0.0620100311934948,
0.019774749875068665,
0.00784706324338913,
-0.00938862469047308,
0.01805192604660988,
-0.0013795422855764627,
0.02533552795648575,
0.05338147282600403,
-0.024525688961148262,
0.003317821305245161,
0.009986450895667076,
-0.0463755764067173,
0.022677788510918617,
-0.017758237197995186,
-0.04175219684839249,
-0.020772745832800865,
-0.047835011035203934,
-0.03791604936122894,
-0.022449884563684464,
0.030319076031446457,
0.03745583817362785,
-0.02306484989821911,
-0.023062584921717644,
0.029389746487140656,
-0.016728563234210014,
0.006607548799365759,
0.05780470743775368,
-0.030319318175315857,
-0.03972073271870613,
-0.01290969643741846,
-0.0022489973343908787,
-0.009064659476280212,
0.035064321011304855,
0.04790068045258522,
0.003796864300966263,
-0.0404476597905159,
0.014116069301962852,
-0.07028000801801682,
-0.09425836056470871,
-0.07941608130931854,
0.061039429157972336,
-0.007702562026679516,
0.0912928432226181,
0.01704474166035652,
-0.016410255804657936,
-0.055395908653736115,
0.042481038719415665,
-0.024476544931530952,
0.01154076587408781,
0.00041958311339840293,
0.033631570637226105,
-0.05238691344857216,
-0.003856576746329665,
0.031164735555648804,
0.01647511124610901,
0.037387870252132416,
0.015701448544859886,
0.08427587896585464,
0.017118431627750397,
0.010650910437107086,
-0.00757606653496623,
-0.07596427202224731,
0.059444610029459,
-0.01239476166665554,
0.03599715232849121,
0.023006603121757507,
0.02280784584581852,
-0.028829431161284447,
-0.021112386137247086,
-0.026620926335453987,
0.04625513777136803,
-0.020429058000445366,
-0.012805819511413574,
0.024271896108984947,
-0.04386662691831589,
-0.015156244859099388,
0.0294607263058424,
-0.00833768118172884,
0.05696934834122658,
-0.050747282803058624,
0.055990442633628845,
0.04985378682613373,
0.030112259089946747,
-0.02810853347182274,
0.005431655328720808,
0.042484454810619354,
0.0040602004155516624,
0.029753552749753,
-0.042081039398908615,
0.01271437481045723,
-0.08070816099643707,
0.00839693658053875,
-0.05507328361272812,
0.040773406624794006,
-0.01945582404732704,
-0.024006497114896774,
0.001593124819919467,
0.010537130758166313,
-0.013600902631878853,
-0.05669338256120682,
-0.02779325656592846,
0.03709753230214119,
0.00318066100589931,
-0.04584352299571037,
-0.0024207180831581354,
-0.10478117316961288,
-0.03438304364681244,
0.03969068452715874,
0.013693845830857754,
0.00302650174126029,
0.04904104024171829,
-0.03304881975054741,
-0.06469447165727615,
-0.039641495794057846,
0.04234727844595909,
-0.0025026805233210325,
-0.02455386146903038,
-0.02655598521232605,
0.04811442270874977,
-0.023395197466015816,
0.0021407343447208405,
-0.05650671198964119,
-0.024191999807953835,
0.01849992386996746,
-0.0779108852148056,
0.011641357094049454,
-0.00833623856306076,
-0.0141740208491683,
0.03214634582400322,
-0.05337049067020416,
0.06374330073595047,
0.06272910535335541,
-0.04430985823273659,
-0.0006588628748431802,
0.024121586233377457,
-0.00452251173555851,
-0.05674658715724945,
-0.014113660901784897,
0.03484335541725159,
0.010236354544758797,
-0.05339762941002846,
0.019766604527831078,
0.0662493035197258,
0.01519446074962616,
-0.028288904577493668,
-0.013157462701201439,
-0.030108990147709846,
0.044901292771101,
-0.04455522447824478,
0.013222635723650455,
0.009162834845483303,
0.05996106564998627,
0.03318531811237335,
-0.01976011134684086,
-0.015511710196733475,
-0.04665127396583557,
0.006667507812380791,
0.0053939251229166985,
0.06559591740369797,
0.021984588354825974,
-0.0054850890301167965,
-0.07855325192213058,
-0.05990993231534958,
0.004364924039691687,
0.0004551579477265477,
0.01643095538020134,
-0.03285924717783928,
-0.07816269993782043,
-0.04878947138786316,
0.06125224009156227,
-0.04681028053164482,
-0.003916461020708084,
0.07280540466308594,
-0.05354110896587372,
-0.0242888405919075,
-0.004800592083483934,
-0.012678498402237892,
-0.023767242208123207,
0.004795051645487547,
-0.0571923553943634,
-0.02122412994503975,
-0.06964989751577377,
0.001124512287788093,
0.015167946927249432,
0.004456052090972662,
0.02529393881559372,
0.015487214550375938,
0.03126515820622444,
0.028032392263412476,
-0.022293923422694206,
0.012688810005784035,
0.00605112686753273,
0.013957573100924492,
0.06395057588815689,
-0.03002258948981762,
0.04770020768046379,
0.0045998068526387215,
0.03949283808469772,
-0.05735170841217041,
0.0071771047078073025,
0.0591496080160141,
0.003936552908271551,
-0.003169400617480278,
0.0323757529258728,
-0.0038529166486114264,
-0.011080019176006317,
-0.015113879926502705,
-0.03869764506816864,
-0.015873797237873077,
-0.025220520794391632,
0.06006714701652527,
-0.01581316813826561,
-0.002396669937297702,
-0.028449635952711105,
-0.015543676912784576,
-0.009495935402810574,
0.0024807751178741455,
0.03776771202683449,
-0.05268854647874832,
-0.0037604139652103186,
0.02493448555469513,
-0.03234156221151352,
-0.05534055829048157,
0.03178749233484268,
0.02125832624733448,
0.054547615349292755,
0.03164203464984894,
0.027120867744088173,
0.015332956798374653,
-0.0012232251465320587,
0.0413878969848156,
-0.0035814300645142794,
-0.002452061278745532,
-0.03424607962369919,
-0.02356874756515026,
0.08371253311634064,
-0.026339249685406685,
-0.0014836227055639029,
-0.028883034363389015,
-0.01180388405919075,
-0.05095040053129196,
0.017136726528406143,
0.018023978918790817,
-0.008168883621692657,
-0.02064000815153122,
0.020699866116046906,
-0.04171668365597725,
-0.016165994107723236,
0.06793971359729767,
-0.03054835833609104,
-0.007656568195670843,
0.01545801479369402,
0.07760810106992722,
0.07339092344045639,
-0.04084966331720352,
0.033230531960725784,
0.0022660987451672554,
0.020718755200505257,
-0.007728343363851309,
-0.04185856506228447,
-0.05164368450641632,
-0.03517969697713852,
0.00891546905040741,
-0.04109414666891098,
0.0014179795980453491,
-0.006273176055401564,
0.011723354458808899,
-0.008904144167900085,
0.013007380068302155,
-0.035179901868104935,
-0.04255513474345207,
0.00683437567204237,
0.036746397614479065,
0.03477253019809723,
-0.017106741666793823,
0.06282800436019897,
-0.010140664875507355,
-0.03993019834160805,
-0.014687529765069485,
0.03662771359086037,
0.01102466695010662,
-0.038794733583927155,
-0.009122179821133614,
0.07076369225978851,
-0.020354943349957466,
-0.013792933896183968,
0.02168271318078041,
0.0801706463098526,
0.06644831597805023,
-0.012068511918187141,
0.001824574894271791,
-0.004587607458233833,
0.0031402683816850185,
0.053204599767923355,
-0.007822135463356972,
0.014208453707396984,
0.0007609525928273797,
-0.04080496355891228,
0.053644582629203796,
-0.0005258573219180107,
-0.020971978083252907,
-0.002733978210017085,
0.03321803733706474,
-0.06907419115304947,
0.003761445637792349,
0.00011630213703028858,
0.038765765726566315,
-0.07931893318891525,
-0.011584697291254997,
-0.046662475913763046,
0.02438126876950264,
0.022461406886577606,
0.014993655495345592,
-0.023351173847913742,
-0.013849656097590923,
-0.022718969732522964,
0.0121403057128191,
-0.034031227231025696,
-0.02516954205930233,
-0.04137807339429855,
-0.02781451866030693,
0.04628114402294159,
-0.012473287992179394,
0.019025621935725212,
-0.02462025173008442,
0.07885220646858215,
0.0052188183180987835,
0.0138770192861557,
0.008390194736421108,
0.056918080896139145,
-0.029536081477999687,
0.028564071282744408,
-0.0086052305996418,
-0.03581760823726654,
-0.012904983013868332,
0.03641897439956665,
-0.0404990091919899,
0.038848627358675,
0.048424672335386276,
-0.01721077226102352,
-0.05934536084532738,
0.014644556678831577,
0.03315645083785057,
0.012901552021503448,
-0.03513267636299133,
0.023042602464556694,
0.001222688821144402,
-0.06341910362243652,
0.05525302141904831,
0.0021217765752226114,
0.005079241003841162,
0.01537848636507988,
0.032220013439655304,
-0.005862839054316282,
-0.014578893780708313,
-0.029581015929579735,
0.06398256123065948,
0.01960970275104046,
0.09921888262033463,
-0.013533067889511585,
0.028559451922774315,
0.007889838889241219,
-0.009442134760320187,
-0.0033134985715150833,
0.025401778519153595,
-0.0026447696145623922,
-0.0279095359146595,
-0.01540552917867899,
-0.06286068260669708,
0.07553768157958984,
0.064278744161129,
-0.02416810765862465,
0.055669501423835754,
-0.024986015632748604,
-0.020033178851008415,
-0.03360048308968544,
0.036768581718206406,
-0.0502249151468277,
-0.04589191451668739,
0.04905005916953087,
-0.058943070471286774,
-0.04855168238282204,
-0.006226635072380304,
0.03750056028366089,
0.05539209768176079,
0.029651813209056854,
-0.0007899157935753465,
-0.07004790008068085,
-0.015787336975336075,
0.003731893841177225,
0.002353544579818845,
0.02446664869785309,
0.02925647236406803,
-0.008344783447682858,
-0.0065429965034127235,
0.07182413339614868,
-0.03798903524875641,
0.015488111414015293,
-0.013311021961271763,
0.012719199061393738,
0.0012591190170496702,
-0.005135242361575365,
0.038922470062971115,
0.006362907588481903,
-0.047515302896499634,
-0.03287114202976227,
-0.042211126536130905,
0.027398675680160522,
0.010663089342415333,
-0.01603122241795063,
0.002414011862128973,
0.004247749224305153,
-0.048588261008262634,
0.06890951842069626,
-0.006100447848439217,
0.0749838650226593,
0.008545455522835255,
0.009658423252403736,
0.02276785485446453,
-0.04282933101058006,
-0.019640525802969933,
0.045768480747938156,
0.00198184372857213,
-0.048027023673057556,
-0.015953758731484413,
-0.07069776207208633,
-0.02503683976829052,
0.058666814118623734,
-0.034854140132665634,
0.052838265895843506,
-0.04408210515975952,
-0.05240866541862488,
0.0023197263944894075,
-0.0061858538538217545,
-0.02219736948609352,
0.0652206689119339,
-0.022875076159834862,
-0.025864051654934883,
0.0035048844292759895,
0.0027443147264420986,
-0.030728289857506752,
-0.03318244218826294,
0.025442611426115036,
-0.0001877539762062952,
-0.005473742261528969,
0.03390722721815109,
0.02329781837761402,
0.00922133307904005,
0.01255714986473322,
-0.01579303853213787,
-0.0010427156230434775,
0.030777757987380028,
0.016659004613757133,
0.03255880996584892,
-0.004498577676713467,
0.07996727526187897,
-0.03490254282951355,
-0.05881558358669281,
-0.03591154143214226,
-0.024167269468307495,
0.01458658091723919,
0.029673542827367783,
0.017957760021090508,
0.01029975526034832,
0.027397435158491135,
-0.06052785366773605,
-0.019808730110526085,
0.04992331936955452,
-0.001053755171597004,
0.05008887127041817,
-0.011461203917860985,
-0.0128650376573205,
-0.00124066520947963,
-0.005688551347702742,
0.048274021595716476,
0.08053593337535858,
-0.04828998073935509,
-0.0018126210197806358,
-0.014388078823685646,
-0.01502876915037632,
0.035154830664396286,
0.013055123388767242,
0.01633782498538494,
0.035221654921770096,
0.05724409967660904,
-0.013428589329123497,
0.005788357462733984,
-0.02484763041138649,
-0.012109884060919285,
-0.018489625304937363,
0.008671690709888935,
-0.03595389053225517,
0.009989936836063862,
0.017078295350074768,
-0.023015987128019333,
-0.019265692681074142,
-0.006081693340092897,
-0.071214459836483,
-0.04787398874759674,
0.0011703938944265246,
0.023092610761523247,
-0.017171001061797142,
0.09474505484104156,
0.01530439592897892,
-0.006327503360807896,
0.0628328025341034,
-0.07709358632564545,
-0.05887710303068161,
-0.008361021056771278,
0.02625141851603985,
-0.030376261100172997,
0.007919290103018284,
0.03680690377950668,
0.015868771821260452,
-0.059768348932266235,
0.013395479880273342,
-0.007635776419192553,
0.005472026765346527,
0.04133443161845207,
0.010478748008608818,
-0.015003200620412827,
-0.028830166906118393,
-0.02398024871945381,
0.012213013134896755,
0.011596103198826313,
0.03708801046013832,
0.027973195537924767,
-0.027168607339262962,
0.0583924874663353,
0.004619146231561899,
-0.008742433041334152,
-0.035463642328977585,
0.0695548951625824,
-0.04953784868121147,
0.05285545438528061,
-0.025821220129728317,
-0.03888506814837456,
-0.020241597667336464,
-0.007449671626091003,
-0.009644852951169014,
-0.008639220148324966,
-0.02199169062077999,
-0.03077620081603527,
0.050704192370176315,
0.03594891354441643,
-0.01019858568906784,
-0.03403782844543457,
-0.04841737821698189,
-0.055225588381290436,
-0.016295261681079865,
-0.007091223262250423,
0.01249117311090231,
-0.009306468069553375,
-0.020565643906593323,
-0.0498105026781559,
-0.06787325441837311,
0.06271886080503464,
-0.01081753894686699,
-0.02571185678243637,
0.05608276650309563,
-0.030657127499580383,
0.030119940638542175,
0.04730862006545067,
0.01745895855128765,
0.03193105384707451,
-0.010829068720340729,
-0.039533089846372604,
-0.03378426283597946,
-0.014866949990391731,
-0.012639525346457958,
-0.08669757097959518,
-0.029012825340032578,
-0.014690281823277473,
0.006102410145103931,
0.026187153533101082,
-0.018790941685438156,
0.046451009809970856,
-0.007674278225749731,
-0.013637575320899487,
0.07192766666412354,
-0.040883176028728485,
0.005297224503010511,
0.024234874173998833,
0.07223884016275406,
0.00304252072237432,
-0.0324321947991848,
0.010144220665097237,
0.014550258405506611,
-0.06034908443689346,
-0.006341313943266869,
0.05713552609086037,
-0.0003507083165459335,
-0.059627603739500046,
0.006465246435254812,
0.03924282640218735,
0.016414904966950417,
0.0012605671072378755,
0.02234940230846405,
0.06266285479068756,
-0.043999578803777695,
0.004400946665555239,
-0.015642810612916946,
-0.03249169886112213,
-0.025737423449754715,
0.04370708391070366,
0.017059877514839172,
-0.023954052478075027,
0.00026167978649027646,
0.04634459689259529,
-0.03518485650420189,
-0.04619685560464859,
0.025910422205924988,
-0.02728920988738537,
0.03618151322007179,
0.009084763005375862
] |
<p>This question is related to the Big Bang Nucleosynthesis of light elements, more concretely I do not understand some features of the graph</p>
<p><img src="http://i.stack.imgur.com/GSfcM.png" alt="BBabundances"></p>
<ul>
<li><p>Why do the $^3$He and D abundances go down with increasing baryon to photon fraction while the Li abundance goes up?</p></li>
<li><p>And what is that strange dip in the Li abundance? </p></li>
</ul>
|
g2471
|
[
0.028376085683703423,
0.03661905974149704,
-0.019705068320035934,
-0.031736891716718674,
0.05633113905787468,
0.06270688027143478,
0.021886153146624565,
0.04922912269830704,
-0.030836543068289757,
-0.06695123761892319,
0.013791118748486042,
0.014367585070431232,
0.035739652812480927,
0.009987051598727703,
0.04622665420174599,
0.027994932606816292,
0.05122240260243416,
-0.0008700996986590326,
0.06844653934240341,
0.01899338699877262,
-0.059262629598379135,
0.058165550231933594,
-0.034313689917325974,
-0.01960204914212227,
0.024593431502580643,
-0.01766665279865265,
0.046440426260232925,
-0.0008205563062801957,
-0.032452695071697235,
-0.01581554114818573,
-0.004427144769579172,
-0.013341221958398819,
0.01324364636093378,
0.029745325446128845,
0.026747893542051315,
-0.03395812585949898,
0.08011146634817123,
0.044276729226112366,
0.0030782786197960377,
-0.007832917384803295,
0.009791874326765537,
0.025133201852440834,
0.07284973561763763,
-0.02281956747174263,
-0.057369135320186615,
-0.029776470735669136,
-0.03568169102072716,
-0.008424008265137672,
-0.015386408194899559,
-0.062091074883937836,
-0.025710072368383408,
-0.01001807488501072,
-0.004753496963530779,
0.028556548058986664,
0.07778749614953995,
0.042093608528375626,
-0.042092155665159225,
-0.10250037908554077,
0.056724630296230316,
0.02668512612581253,
0.0201860461384058,
0.005533919204026461,
0.05170154571533203,
-0.005048672668635845,
0.03708795830607414,
-0.008365005254745483,
-0.023821061477065086,
0.009149663150310516,
-0.005780593026429415,
-0.056720562279224396,
-0.006368905305862427,
-0.019925152882933617,
-0.03820252791047096,
-0.021285073831677437,
-0.01041327603161335,
-0.03508351743221283,
-0.018668798729777336,
0.007720266934484243,
-0.013282828964293003,
0.006538301706314087,
-0.0812380388379097,
0.05169053375720978,
-0.010041862726211548,
-0.01221674308180809,
0.005110925063490868,
0.04960696026682854,
0.019307738170027733,
0.014738899655640125,
-0.011587860062718391,
-0.012600797228515148,
0.06325563043355942,
0.0054914820939302444,
0.058557938784360886,
-0.02691306360065937,
-0.04707895591855049,
-0.01805485226213932,
0.008650929667055607,
0.06295275688171387,
-0.038130007684230804,
0.02550295740365982,
-0.03398098424077034,
0.010542011819779873,
0.00004157690273132175,
0.01605840027332306,
0.002141208155080676,
0.04749145731329918,
0.014910337515175343,
-0.015960466116666794,
-0.015654662624001503,
0.03209226578474045,
-0.05227607116103172,
-0.04032612964510918,
-0.027375025674700737,
-0.09335553646087646,
0.03940849006175995,
0.02978631481528282,
0.03961757570505142,
-0.01529043447226286,
0.04738368093967438,
0.011387389153242111,
0.07863421738147736,
0.022795699536800385,
-0.07074515521526337,
-0.010921033099293709,
-0.0423680879175663,
-0.02456842176616192,
0.06662821769714355,
0.008375691249966621,
-0.042649045586586,
0.0045028687454760075,
0.04398035258054733,
-0.013211965560913086,
-0.04747539386153221,
-0.0016109185526147485,
0.07996664196252823,
-0.009146175347268581,
0.004356286954134703,
0.07681287080049515,
0.011104554869234562,
0.0071618761867284775,
0.0392165407538414,
-0.0015540343010798097,
-0.024120520800352097,
-0.06146717071533203,
-0.008466830477118492,
0.022322343662381172,
-0.04674036055803299,
0.026251904666423798,
-0.03563489764928818,
0.0017387747066095471,
0.039898212999105453,
-0.008466687984764576,
0.03651818260550499,
-0.05451374500989914,
-0.003575060050934553,
-0.00909131858497858,
0.0420646071434021,
0.0008240266470238566,
-0.07787612825632095,
0.017119355499744415,
0.00015045542386360466,
-0.0034123146906495094,
0.0020393445156514645,
-0.02324657142162323,
-0.008810706436634064,
0.021124117076396942,
0.03440915793180466,
-0.045707475394010544,
-0.03145715221762657,
-0.023483682423830032,
-0.01861080713570118,
-0.02653227560222149,
0.007740852888673544,
0.006416718941181898,
-0.0038188344333320856,
0.07462971657514572,
0.061529990285634995,
-0.00043982305214740336,
0.01701771654188633,
0.04097096621990204,
-0.008941940031945705,
-0.01751118339598179,
-0.002903059823438525,
-0.04233058542013168,
-0.010140628553926945,
-0.00931287370622158,
-0.0005543484003283083,
-0.018184958025813103,
-0.0011903280392289162,
0.003685904201120138,
0.010480747558176517,
-0.014696035534143448,
0.03273078799247742,
-0.027434391900897026,
0.0037078862078487873,
-0.03990188241004944,
-0.019851787015795708,
-0.07058750838041306,
-0.03357956185936928,
0.042670249938964844,
-0.05993296205997467,
-0.04485415294766426,
0.0026976147200912237,
-0.019548214972019196,
0.04249199107289314,
0.036337338387966156,
-0.02744423784315586,
0.046687766909599304,
0.0387679859995842,
-0.0625288188457489,
-0.013133511878550053,
0.006927955895662308,
0.04189128056168556,
-0.014332921244204044,
0.003424873109906912,
0.042611394077539444,
0.010797637514770031,
0.0004962221719324589,
0.05019786208868027,
0.00821798387914896,
-0.04368250444531441,
-0.04398302361369133,
-0.023514362052083015,
0.029680263251066208,
0.0006986316293478012,
0.000498375331517309,
0.013040818274021149,
-0.0355486199259758,
0.0062162731774151325,
0.005524270702153444,
-0.04112784191966057,
0.058663468807935715,
-0.019880859181284904,
-0.01651560515165329,
0.025583939626812935,
-0.01259207259863615,
-0.010792150162160397,
-0.018102562054991722,
0.010010868310928345,
-0.014981720596551895,
-0.03495209291577339,
-0.03245715796947479,
-0.06449782103300095,
-0.0014412559103220701,
0.06708525121212006,
-0.08728227019309998,
0.032883621752262115,
-0.031812213361263275,
-0.0810861736536026,
-0.0045594642870128155,
0.022463815286755562,
-0.043811436742544174,
0.010545938275754452,
0.007572498172521591,
-0.0050308420322835445,
-0.03826567903161049,
-0.018198730424046516,
0.0341300405561924,
-0.04665272682905197,
-0.009181433357298374,
0.016924859955906868,
-0.018214059993624687,
0.0018510709051042795,
0.0036964956670999527,
-0.013287817128002644,
-0.0030456518288701773,
0.01318773441016674,
-0.03510819375514984,
0.022241219878196716,
-0.031994711607694626,
-0.01038757711648941,
-0.01552185695618391,
0.04534348472952843,
0.006912568584084511,
-0.009988964535295963,
0.031134862452745438,
0.01800195500254631,
-0.0050742593593895435,
0.03496391326189041,
-0.05244661495089531,
0.013516477309167385,
0.02239607274532318,
-0.03783275559544563,
0.016780372709035873,
0.029585551470518112,
0.03219476714730263,
-0.02987644635140896,
-0.07482309639453888,
0.0007952427840791643,
0.03063974902033806,
-0.0046622008085250854,
-0.04326580464839935,
0.010926437564194202,
0.034472450613975525,
0.04431043565273285,
-0.05442000925540924,
0.028682412579655647,
0.000028015985662932508,
-0.05788842961192131,
0.022321602329611778,
0.033893413841724396,
0.0006548184901475906,
0.020487051457166672,
-0.015483750030398369,
-0.009046964347362518,
0.06353139132261276,
0.0038693323731422424,
-0.057786840945482254,
-0.046918995678424835,
0.05995557829737663,
0.0009161083144135773,
-0.02276233397424221,
-0.003523854771628976,
0.04131117835640907,
-0.017617307603359222,
0.04641326516866684,
-0.018974095582962036,
0.021257752552628517,
0.014132806099951267,
-0.045037154108285904,
-0.04075900837779045,
-0.027953777462244034,
-0.0319913849234581,
-0.04209329932928085,
0.027742920443415642,
-0.004256992135196924,
-0.00929327867925167,
-0.054299283772706985,
-0.027932094410061836,
0.0133206183090806,
-0.02212938852608204,
-0.08077119290828705,
0.024054288864135742,
0.022471657022833824,
-0.0334172323346138,
0.026062097400426865,
-0.043244704604148865,
0.02163332886993885,
0.03544848784804344,
0.026164695620536804,
-0.0314469076693058,
0.02687661349773407,
-0.06444147229194641,
-0.0030188316013664007,
-0.011369484476745129,
0.012002148665487766,
0.0010001459158957005,
-0.0458117313683033,
-0.013537537306547165,
-0.04220454767346382,
-0.0015212667640298605,
0.03798121586441994,
-0.006211716681718826,
-0.031220950186252594,
-0.0529993399977684,
-0.03928108140826225,
-0.019368017092347145,
0.009839982725679874,
0.027008119970560074,
0.014781003817915916,
-0.006402987986803055,
-0.04280881956219673,
0.0017193076200783253,
-0.004650310147553682,
-0.04864077270030975,
0.012928972952067852,
-0.026036715134978294,
0.045047927647829056,
0.035009827464818954,
0.02434943988919258,
-0.034039631485939026,
0.03910041227936745,
-0.013601346872746944,
0.0014158706180751324,
-0.017766516655683517,
-0.06051885336637497,
0.04174244403839111,
-0.0031992425210773945,
-0.024865224957466125,
0.02585688605904579,
0.001262524165213108,
0.014686455018818378,
0.06434272229671478,
-0.02148478291928768,
0.033277932554483414,
-0.04770870879292488,
-0.021017638966441154,
-0.03768186643719673,
-0.07011602073907852,
-0.02289183810353279,
0.04742446541786194,
-0.01691022515296936,
-0.056360092014074326,
0.04006016254425049,
0.03490797057747841,
-0.04783821851015091,
0.019394295290112495,
0.04768025875091553,
0.022960666567087173,
0.03183984011411667,
-0.02916506491601467,
0.033545687794685364,
0.027144664898514748,
-0.019844762980937958,
0.02184937708079815,
0.03569699078798294,
0.012343019247055054,
-0.029222089797258377,
0.059274740517139435,
-0.014706283807754517,
0.02948366478085518,
0.003566231345757842,
0.011718430556356907,
0.015306718647480011,
-0.014311092905700207,
-0.01787068508565426,
0.028583237901329994,
-0.01052003912627697,
0.019938776269555092,
0.008211844600737095,
-0.011512408964335918,
0.034725889563560486,
-0.008332348428666592,
0.0008167268242686987,
0.011294581927359104,
0.05134403705596924,
0.018718594685196877,
0.0036356616765260696,
0.04448796808719635,
0.01813029684126377,
0.04688763990998268,
0.04822802171111107,
0.0681106224656105,
0.03240165859460831,
-0.043252114206552505,
0.08780816197395325,
0.006558779161423445,
0.052804648876190186,
-0.05704181268811226,
0.018994634971022606,
0.10397757589817047,
0.004509046673774719,
-0.04637152701616287,
0.014416896738111973,
0.05268022418022156,
-0.0014535473892465234,
-0.08452831953763962,
-0.003971883561462164,
0.04668305441737175,
-0.03473762422800064,
-0.003252902301028371,
0.01326451264321804,
-0.03900446742773056,
-0.014328275807201862,
0.026775019243359566,
0.021250303834676743,
0.029560981318354607,
0.07568037509918213,
-0.018440283834934235,
0.05669647455215454,
-0.03849295526742935,
-0.015504270792007446,
0.0021924665197730064,
-0.04422645643353462,
0.02915525622665882,
-0.0738445594906807,
-0.014057580381631851,
-0.05644198879599571,
0.031142927706241608,
-0.012415392324328423,
-0.015439588576555252,
-0.020198717713356018,
0.06232953444123268,
0.019263217225670815,
0.0032932606991380453,
-0.03498638793826103,
-0.019935481250286102,
-0.03808645159006119,
-0.024972600862383842,
-0.05324634909629822,
-0.012574429623782635,
0.00944249052554369,
0.0026240337174385786,
0.06430274993181229,
-0.06441814452409744,
-0.005636877845972776,
-0.01569867879152298,
-0.08875539153814316,
-0.005134185776114464,
-0.0037558863405138254,
0.01761503331363201,
0.0009790812619030476,
0.041875209659338,
0.013429964892566204,
-0.018763937056064606,
-0.00022481051564682275,
0.03549812734127045,
-0.00457635335624218,
0.01798158325254917,
-0.03897038847208023,
-0.018418293446302414,
0.037191301584243774,
-0.034427545964717865,
-0.05938486009836197,
-0.028713807463645935,
0.030573556199669838,
0.003254829440265894,
-0.006124373525381088,
0.04951271042227745,
-0.04349872097373009,
-0.022535450756549835,
-0.01148915570229292,
0.07447703927755356,
0.021352825686335564,
-0.01469702273607254,
0.024492787197232246,
-0.004793113097548485,
0.026562225073575974,
0.031397733837366104,
-0.018254872411489487,
-0.0877235010266304,
0.057313475757837296,
0.004245106130838394,
0.001323356875218451,
0.06023649498820305,
-0.01731717772781849,
-0.05780663713812828,
0.04261132702231407,
-0.0020991668570786715,
-0.010575061663985252,
-0.011095147579908371,
0.020149346441030502,
0.04550449922680855,
-0.008517897687852383,
0.05713125690817833,
0.07096322625875473,
0.010705768130719662,
-0.0247912909835577,
0.044934455305337906,
0.05960370972752571,
0.014127854257822037,
-0.024896033108234406,
0.00046527120866812766,
0.05195053666830063,
0.012279458343982697,
-0.04145018383860588,
-0.014468894340097904,
-0.00540132587775588,
0.03611564263701439,
-0.05498736351728439,
0.019989384338259697,
-0.002766181482002139,
0.02132130041718483,
0.035348061472177505,
-0.08934220671653748,
-0.022851664572954178,
0.025331147015094757,
0.03261300548911095,
-0.044935647398233414,
-0.003105011535808444,
0.002857534447684884,
-0.008568407036364079,
-0.009564140811562538,
0.029252244159579277,
0.057848505675792694,
-0.08072709292173386,
0.0008850977174006402,
-0.0098324129357934,
0.028576424345374107,
0.03163962438702583,
-0.02142813615500927,
0.016132695600390434,
-0.019511552527546883,
0.05670957639813423,
0.01391519419848919,
0.023220021277666092,
-0.07361699640750885,
-0.061816275119781494,
-0.0226932093501091,
-0.022342193871736526,
0.05941425636410713,
0.008364097215235233,
-0.0033260295167565346,
-0.032511405646800995,
-0.043324247002601624,
0.039721302688121796,
-0.015908515080809593,
0.0312502346932888,
0.0503406897187233,
-0.03362712264060974,
0.015978995710611343,
0.05177629739046097,
0.04562099277973175,
-0.028268808498978615,
-0.007735143881291151,
-0.024726519361138344,
-0.042077209800481796,
-0.022767318412661552,
-0.016348835080862045,
-0.061554618179798126,
-0.01735975593328476,
0.028483524918556213,
0.050643984228372574,
0.01155777182430029,
0.044682543724775314,
-0.047401078045368195,
-0.034921348094940186,
-0.006653411313891411,
-0.0013201002730056643,
0.04468265548348427,
0.04763465002179146,
-0.0148880984634161,
0.014545312151312828,
0.042817872017621994,
0.047871652990579605,
-0.05634050443768501,
0.00485948333516717,
0.01957869529724121,
-0.08726590126752853,
0.05856633931398392,
0.0239606611430645,
-0.08290962129831314,
0.030680613592267036,
-0.02599881961941719,
0.004747704602777958,
0.06678632646799088,
-0.004670505877584219,
0.004201371222734451,
0.021894479170441628,
0.02963191829621792,
0.006529453210532665,
0.05650049448013306,
0.022919369861483574,
0.054112084209918976,
0.029688676819205284,
0.006470615975558758,
-0.03909733146429062,
-0.02236008457839489,
0.03902726247906685,
0.013413095846772194,
-0.0029094850178807974,
0.0025292427744716406,
0.06699346005916595,
-0.03991222009062767,
-0.01953778974711895,
0.06364575028419495,
-0.007797808386385441,
-0.0748654156923294,
-0.0410926416516304,
0.039083682000637054,
-0.001572903711348772,
0.020629262551665306,
0.012064469046890736,
-0.02834516391158104,
0.043984007090330124,
0.010525333695113659,
-0.017684796825051308,
0.03169388696551323,
0.012047568336129189,
-0.09232743084430695,
-0.03625541925430298,
0.02253885008394718,
-0.023865817114710808,
0.01309212576597929,
0.06283207982778549,
0.00765765318647027,
0.040357060730457306,
-0.06639918684959412,
0.04034412279725075,
-0.0017894903430715203,
-0.0712040439248085,
-0.0390959158539772,
-0.06533385068178177,
-0.014322361908853054,
0.011733099818229675,
0.008933456614613533,
-0.03301096335053444,
-0.009286284446716309,
0.00558941625058651,
-0.002147084567695856,
0.022684957832098007,
0.07621420174837112,
-0.05137123540043831,
-0.04579026997089386,
-0.04838969558477402,
0.05327567458152771,
-0.04186899587512016,
-0.027850965037941933,
-0.007880025543272495,
0.021675340831279755,
-0.0014940393157303333,
-0.00016300191055051982,
-0.051877766847610474,
0.01635543443262577,
-0.030582761391997337,
-0.006500024814158678,
0.00006448582280427217,
-0.0229894258081913,
0.021957436576485634,
0.021535072475671768,
-0.014590580016374588,
-0.03696522116661072,
-0.027232136577367783,
-0.03435415029525757,
-0.012384873814880848,
0.04416429251432419,
-0.01554862130433321,
-0.006102290470153093,
0.01580364629626274,
-0.040661826729774475,
0.026944104582071304,
0.02357233315706253,
0.06640248000621796,
0.006765473634004593,
0.08462866395711899,
-0.0021573705598711967,
0.04129414260387421,
-0.014561588875949383,
-0.032885052263736725,
-0.006110995542258024,
-0.03763644024729729,
-0.02056526020169258,
0.02055649273097515,
-0.0600103996694088,
-0.045056913048028946,
-0.048595134168863297,
0.0334397554397583,
0.008400417864322662,
-0.014726758934557438,
0.05514048784971237,
0.020105523988604546,
0.036956384778022766,
-0.035507895052433014,
-0.07173378020524979,
-0.014974808320403099,
0.06600604206323624,
0.015025729313492775,
-0.02809440903365612,
0.0276590995490551,
0.04289732873439789,
-0.003692170837894082,
-0.053686805069446564,
0.0017785931704565883,
-0.026561781764030457,
0.012071465142071247,
-0.0009135870495811105,
-0.043307218700647354,
-0.023027101531624794,
0.08486350625753403,
-0.05268799141049385,
-0.009146331809461117,
-0.008404443971812725,
0.010672011412680149,
0.033550698310136795,
0.07049576938152313,
-0.016724545508623123,
0.03989548236131668,
-0.022417157888412476,
-0.09713675081729889,
0.007889988832175732,
0.027344217523932457,
-0.026838604360818863,
-0.0047530969604849815,
-0.01812119036912918,
0.03204774484038353,
-0.023453203961253166,
-0.07563316076993942,
0.02402503602206707
] |
<p>How does sub-ambient cooling work?</p>
<p>There are water cooling systems for computers that can cool components to below room temperature. The problem I see here is that the water is cooled using room temperature air. How can the cooling system keep a 150 watt computer component at a temperature below room temperature? The only powered device on the water cooling loop is the pump and since that isn't being cooled by anything else than the water it cannot contribute to the lower temperature.</p>
<p>I'm guessing this has something in common with a Geothermal heat pump, but reversed.</p>
|
g2472
|
[
0.03826449066400528,
0.02949516847729683,
0.0035417857579886913,
0.02086956612765789,
-0.02492600306868553,
0.07239750027656555,
-0.0015659356722608209,
0.011517883278429508,
-0.06885609030723572,
-0.0016660847468301654,
-0.01933109574019909,
0.09685618430376053,
-0.035339828580617905,
-0.02279878966510296,
-0.023913737386465073,
0.009842043742537498,
-0.04449069872498512,
0.005623393692076206,
0.03597388416528702,
0.022444266825914383,
-0.045540716499090195,
-0.030456334352493286,
0.005110741592943668,
-0.025186099112033844,
-0.03608687222003937,
-0.025419818237423897,
0.00730469636619091,
-0.0033202283084392548,
-0.046042848378419876,
-0.06726114451885223,
-0.06310625374317169,
-0.003981724847108126,
0.02473212592303753,
-0.09606804698705673,
-0.034014925360679626,
0.014316249638795853,
0.04968315362930298,
0.008670301176607609,
-0.06982533633708954,
-0.005665271542966366,
-0.03636132553219795,
0.001333537744358182,
0.001089406432583928,
0.0008012481266632676,
0.016874296590685844,
0.03989775478839874,
-0.0008882406982593238,
-0.026607142761349678,
-0.04844050854444504,
0.0342431403696537,
-0.0011210574302822351,
-0.04319297522306442,
-0.018121009692549706,
0.001375326537527144,
0.026337960734963417,
-0.07848488539457321,
-0.015352584421634674,
0.010775777511298656,
0.05950981006026268,
-0.003916678484529257,
0.004857099615037441,
0.03735917806625366,
0.06880077719688416,
0.03915596380829811,
0.01444846298545599,
0.0008895964710973203,
-0.028206072747707367,
-0.04611392319202423,
0.04615888372063637,
0.060248591005802155,
-0.0018409242620691657,
-0.01659073494374752,
-0.04532981663942337,
-0.014243301935493946,
0.06106354668736458,
0.0015153457643464208,
0.01675073243677616,
-0.007421557325869799,
0.031541094183921814,
0.04497301205992699,
0.03740653395652771,
-0.003725601127371192,
0.03421110287308693,
0.023113036528229713,
-0.01773584820330143,
0.03801024332642555,
-0.07441750168800354,
-0.00791543535888195,
-0.024296605959534645,
-0.031857218593358994,
-0.05907883495092392,
0.02842399850487709,
0.07256920635700226,
0.006882065907120705,
0.01711960695683956,
0.0352591797709465,
0.0038203748408704996,
-0.0054302457720041275,
-0.026727482676506042,
-0.024109655991196632,
0.04709016904234886,
-0.037774618715047836,
-0.01439947634935379,
0.00710713118314743,
-0.0379570834338665,
0.044000472873449326,
-0.008644718676805496,
0.031007587909698486,
-0.03532281145453453,
0.040934592485427856,
0.04311724752187729,
-0.05011652410030365,
-0.06739245355129242,
-0.07224652916193008,
-0.041433196514844894,
0.017667027190327644,
0.03621286898851395,
0.023064417764544487,
-0.0008493055938743055,
0.04057873785495758,
-0.006960780825465918,
0.07526864856481552,
-0.05925716087222099,
-0.023334752768278122,
0.005284063518047333,
-0.032645463943481445,
-0.020995447412133217,
-0.0049425349570810795,
-0.002692630747333169,
0.035028405487537384,
0.023523380979895592,
0.04520609974861145,
-0.09964226186275482,
-0.012375736609101295,
-0.011053653433918953,
-0.003831893438473344,
-0.017155855894088745,
-0.013746271841228008,
0.00913872942328453,
-0.052560847252607346,
0.005939463619142771,
0.04100637510418892,
0.03405202925205231,
-0.018392272293567657,
-0.04717439040541649,
0.02328246459364891,
-0.043071627616882324,
0.034572623670101166,
0.0156521275639534,
-0.030719662085175514,
-0.026759548112750053,
0.027606157585978508,
0.04626031965017319,
-0.03423359990119934,
0.05032919719815254,
0.000057665562053443864,
0.033736832439899445,
-0.045174963772296906,
0.0444568507373333,
0.05476903170347214,
0.011085581965744495,
0.013890711590647697,
0.04284093528985977,
0.0117949852719903,
-0.0875856801867485,
0.026108253747224808,
0.02328893542289734,
0.03485431149601936,
0.000912453222554177,
0.003260677447542548,
-0.09133162349462509,
0.052336789667606354,
-0.0793711468577385,
-0.0197973120957613,
0.029692446812987328,
0.02787306345999241,
0.06330680102109909,
-0.00754942512139678,
0.009411994367837906,
-0.05967758595943451,
-0.023297252133488655,
0.07027542591094971,
-0.024040216580033302,
0.006170711480081081,
-0.019050976261496544,
0.05946881324052811,
-0.07953226566314697,
0.05789204686880112,
0.045054804533720016,
-0.02039216086268425,
0.001585366320796311,
0.01344500482082367,
-0.012446173466742039,
0.023481732234358788,
-0.0034349444322288036,
0.00031521025812253356,
-0.011204404756426811,
-0.04468236863613129,
-0.03302270919084549,
0.01804477348923683,
0.05034922808408737,
-0.03965501859784126,
0.0034178781788796186,
-0.03228899464011192,
0.11310701817274094,
0.039586346596479416,
-0.05980962887406349,
-0.020177552476525307,
0.02148653380572796,
-0.054021891206502914,
-0.012076037004590034,
-0.026075012981891632,
0.03861137479543686,
0.017856428399682045,
-0.03137889876961708,
0.02290520630776882,
0.005469127558171749,
0.01404204498976469,
-0.02615470625460148,
-0.006721054669469595,
0.06080488860607147,
0.05780218541622162,
-0.02262953296303749,
0.03667242079973221,
-0.020264381542801857,
0.0007655597873963416,
-0.0684191882610321,
0.00903821736574173,
-0.04996134713292122,
-0.011695380322635174,
-0.04001026228070259,
0.010908493772149086,
-0.016272643581032753,
-0.043728187680244446,
0.04008494317531586,
0.043610040098428726,
0.010270562022924423,
0.022844476625323296,
0.03726993128657341,
-0.031880784779787064,
-0.02785424515604973,
0.005511007271707058,
0.03386455029249191,
0.0373045839369297,
0.026037009432911873,
-0.009510560892522335,
0.023487163707613945,
-0.006265256553888321,
-0.018716640770435333,
-0.03131309524178505,
0.04178711771965027,
0.008907618001103401,
-0.030286863446235657,
-0.0020327831152826548,
-0.06347357481718063,
-0.03214597702026367,
-0.025191085413098335,
0.007267296314239502,
0.06348391622304916,
-0.05625937879085541,
-0.007046898361295462,
-0.012851765379309654,
-0.0041865091770887375,
0.02732829563319683,
0.05535264313220978,
-0.04791330173611641,
-0.0012315129861235619,
0.0008422643295489252,
0.06449120491743088,
0.07879622280597687,
0.010897021740674973,
0.039830900728702545,
-0.0716092586517334,
0.03841555863618851,
-0.03988230228424072,
-0.021206244826316833,
-0.007930504158139229,
0.0023905527777969837,
0.04681532457470894,
0.055279482156038284,
0.03347635641694069,
-0.0036170813255012035,
-0.011235835030674934,
-0.040093157440423965,
0.037684597074985504,
-0.0518641360104084,
-0.025362592190504074,
0.05350010097026825,
0.020603574812412262,
-0.049767106771469116,
-0.013658278621733189,
-0.03182477876543999,
0.01319486927241087,
-0.023956065997481346,
0.062317535281181335,
0.024141868576407433,
0.06855615973472595,
0.02036333456635475,
0.029494820162653923,
0.044229861348867416,
0.032368939369916916,
-0.0590866282582283,
0.02234007604420185,
-0.0016771996160969138,
-0.0416710264980793,
-0.019875112920999527,
-0.02833786979317665,
-0.05182059854269028,
0.011122776195406914,
0.05183253064751625,
-0.02628123015165329,
-0.0145086869597435,
0.04963124170899391,
-0.026940708979964256,
0.014461427927017212,
0.052966371178627014,
-0.06267102062702179,
-0.027814848348498344,
-0.014142385683953762,
-0.02957421913743019,
-0.06977241486310959,
0.018933655694127083,
-0.02531563490629196,
0.0166586022824049,
-0.011130530387163162,
0.04936361685395241,
-0.006012133788317442,
0.0005177617422305048,
-0.019528023898601532,
-0.024467134848237038,
-0.016888713464140892,
-0.010524791665375233,
-0.02289632335305214,
-0.033507611602544785,
-0.028318719938397408,
-0.01796097867190838,
-0.03957256302237511,
0.00615101819857955,
-0.009931121952831745,
-0.02456875704228878,
-0.011631575413048267,
0.03059723787009716,
0.06328711658716202,
-0.015699394047260284,
0.046996910125017166,
0.05904966592788696,
-0.03993954136967659,
-0.008078966289758682,
-0.019615739583969116,
0.02633219212293625,
0.03740420565009117,
-0.011180922389030457,
0.01515897549688816,
-0.008391432464122772,
-0.05867306515574455,
0.05033011734485626,
-0.020489122718572617,
0.06299306452274323,
-0.056337982416152954,
0.029815159738063812,
0.04332877695560455,
0.014272910542786121,
0.04110604524612427,
0.006867601070553064,
0.011442669667303562,
0.030645154416561127,
0.01058855652809143,
-0.016620909795165062,
-0.013141986913979053,
0.000621843442786485,
0.06361958384513855,
-0.021440556272864342,
-0.04388577118515968,
-0.0027638718020170927,
0.032964203506708145,
-0.054807040840387344,
0.0631551668047905,
0.015136517584323883,
-0.027927709743380547,
0.005868411622941494,
-0.007029048632830381,
-0.04140482470393181,
-0.008470593951642513,
-0.018778985366225243,
0.0010667460737749934,
0.0112459696829319,
-0.032282840460538864,
0.03702065721154213,
-0.012262571603059769,
-0.017250264063477516,
0.0158084724098444,
-0.028786426410079002,
-0.037459857761859894,
-0.01610153540968895,
0.015735220164060593,
0.047830551862716675,
-0.034787628799676895,
-0.026536449790000916,
0.029757985845208168,
-0.016193870455026627,
0.00519901467487216,
0.0635470375418663,
0.027020921930670738,
-0.0322195328772068,
-0.014440871775150299,
-0.00434423703700304,
-0.042123280465602875,
-0.0021738235373049974,
0.015053312294185162,
0.002784908516332507,
0.07089153677225113,
0.004341098479926586,
0.029876571148633957,
-0.014983628876507282,
0.02722819522023201,
-0.012473784387111664,
0.041717756539583206,
0.022988036274909973,
0.042636528611183167,
0.028774578124284744,
-0.04969673231244087,
-0.012808593921363354,
-0.06622081995010376,
0.023954909294843674,
-0.015814045444130898,
0.04568934440612793,
-0.012557407841086388,
-0.02334410324692726,
-0.0344155915081501,
-0.060307037085294724,
0.003843541257083416,
0.008257070556282997,
-0.04056069999933243,
-0.025774292647838593,
0.03222713991999626,
0.013720575720071793,
0.0370347797870636,
-0.02727416716516018,
0.006193812470883131,
0.009499830193817616,
0.05804424360394478,
-0.02860274910926819,
-0.021001920104026794,
0.03149741515517235,
-0.013467120938003063,
0.054300177842378616,
-0.02535054087638855,
-0.014178781770169735,
-0.051698267459869385,
-0.027497919276356697,
-0.02981439232826233,
0.024625593796372414,
-0.053655870258808136,
-0.0594671256840229,
-0.023277655243873596,
0.04326299577951431,
-0.0309543889015913,
0.012029601261019707,
-0.018834354355931282,
0.019915970042347908,
-0.07704413682222366,
-0.030118169263005257,
-0.03839194402098656,
0.007801897823810577,
-0.0077277724631130695,
-0.029148176312446594,
-0.0027463557198643684,
-0.03534099459648132,
-0.03907918184995651,
-0.0015070333611220121,
0.0904243066906929,
0.06506127864122391,
-0.02852216176688671,
0.05269942432641983,
0.042468126863241196,
0.023103971034288406,
0.022790366783738136,
-0.019417183473706245,
0.0203451719135046,
0.0311200562864542,
0.007176884450018406,
0.038924477994441986,
-0.0515335276722908,
0.05428861826658249,
-0.058842118829488754,
-0.04093988984823227,
-0.04880615696310997,
0.02806217223405838,
0.006500377785414457,
0.01249123364686966,
-0.04149462655186653,
0.03853375464677811,
-0.000263043591985479,
0.02982153929769993,
0.03910991549491882,
-0.007098815403878689,
0.0062483218498528,
0.0069209495559334755,
0.048380814492702484,
0.006587430369108915,
-0.0020245735067874193,
-0.04595651477575302,
0.019647618755698204,
0.012198825366795063,
0.0328996405005455,
0.024449586868286133,
0.018019013106822968,
-0.02947615645825863,
0.0336344949901104,
0.05919507145881653,
-0.02948991023004055,
0.026233339682221413,
-0.002225532429292798,
0.041933704167604446,
0.0716194212436676,
-0.08560948818922043,
-0.046239424496889114,
-0.017230326309800148,
-0.04331355169415474,
0.020398268476128578,
0.037831343710422516,
-0.004422943107783794,
0.02359124831855297,
0.022933227941393852,
-0.039152588695287704,
0.03477751463651657,
-0.1043594479560852,
-0.028594383969902992,
0.010277271270751953,
0.023892894387245178,
0.04383733868598938,
0.06896200776100159,
0.0213187113404274,
-0.01896231435239315,
0.013104362413287163,
-0.04748198762536049,
-0.03410695493221283,
0.02977500669658184,
0.06765276938676834,
0.02127676270902157,
0.012684667482972145,
-0.027840273454785347,
0.036901991814374924,
0.028815677389502525,
-0.007054165471345186,
-0.01928277686238289,
-0.010473551228642464,
-0.0074615622870624065,
0.013352825306355953,
-0.06420423835515976,
0.01942497491836548,
0.06388619542121887,
-0.015688827261328697,
0.035187214612960815,
0.052438803017139435,
-0.07722889631986618,
0.00820240005850792,
0.002040529390797019,
-0.03442759066820145,
-0.02692752331495285,
0.05225551500916481,
0.023027975112199783,
0.018151838332414627,
-0.04306526482105255,
0.011158698238432407,
-0.008013332262635231,
-0.049682486802339554,
-0.008998760022222996,
0.011522877030074596,
0.0044667585752904415,
0.06738249212503433,
-0.018383655697107315,
0.0032552999909967184,
-0.08330388367176056,
-0.023805346339941025,
-0.03862134367227554,
-0.0563686229288578,
-0.020581675693392754,
-0.011966068297624588,
-0.01813715510070324,
-0.019926102831959724,
0.0005097308312542737,
-0.01655256561934948,
-0.009319368749856949,
0.021876588463783264,
0.016125071793794632,
-0.07261107861995697,
0.052839331328868866,
0.026817642152309418,
0.04372047260403633,
-0.01705625280737877,
0.01136193796992302,
-0.060979533940553665,
-0.006381409242749214,
0.026945950463414192,
-0.021675575524568558,
-0.03698534145951271,
0.03726060688495636,
0.011665988713502884,
-0.1079123243689537,
0.014616945758461952,
0.023732483386993408,
0.027485638856887817,
-0.06758873164653778,
-0.0028533409349620342,
0.046799901872873306,
-0.0013208354357630014,
0.0165219958871603,
-0.03898835554718971,
-0.004762993659824133,
-0.028441868722438812,
0.022364823147654533,
0.041840534657239914,
0.003264790400862694,
0.031328245997428894,
-0.03739280626177788,
-0.03532792627811432,
-0.0164656899869442,
-0.056533169001340866,
-0.00764574995264411,
0.03844846785068512,
0.001202187966555357,
0.0007227208116091788,
-0.07768461853265762,
0.014341938309371471,
0.024642620235681534,
0.04714412987232208,
0.05408162996172905,
0.10153467208147049,
0.01870623044669628,
-0.02996067889034748,
0.011186908930540085,
-0.0287996307015419,
0.024281062185764313,
-0.009865046478807926,
0.022113123908638954,
0.017450924962759018,
0.029511045664548874,
0.02048133872449398,
0.04245257377624512,
0.05416833236813545,
-0.02028348669409752,
-0.0228325966745615,
0.02366311103105545,
-0.05399002134799957,
-0.03654702752828598,
0.03743201494216919,
-0.016682125627994537,
-0.04594442993402481,
-0.02144046500325203,
-0.025447456166148186,
-0.02335376664996147,
-0.08749926090240479,
0.029823295772075653,
0.006469168234616518,
0.04050112143158913,
-0.0650138333439827,
0.024635180830955505,
-0.008060358464717865,
-0.009719361551105976,
-0.04042939841747284,
0.0017633005045354366,
0.05687355622649193,
0.09300819784402847,
0.03734452277421951,
0.04323301836848259,
-0.0024075829423964024,
0.006188276689499617,
0.039879314601421356,
-0.0421876385807991,
-0.035231493413448334,
-0.035600222647190094,
0.007317160721868277,
-0.033984843641519547,
0.016207439824938774,
0.016479158774018288,
-0.009804246947169304,
0.029732808470726013,
-0.007095371372997761,
-0.01212166529148817,
-0.006189723964780569,
0.030033806338906288,
0.022198650985956192,
-0.006765717640519142,
-0.0014063108246773481,
0.04388951137661934,
-0.02617676928639412,
0.005845151375979185,
0.041879020631313324,
-0.03567410632967949,
-0.009855194017291069,
0.02876978926360607,
0.02711290679872036,
0.008841398172080517,
-0.006530032027512789,
0.042378924787044525,
-0.023044513538479805,
-0.038380805402994156,
-0.03396275267004967,
-0.02417571097612381,
0.04790409654378891,
-0.004406891763210297,
0.08327990025281906,
0.022887922823429108,
0.050283052027225494,
0.0022542341612279415,
-0.0017626070184633136,
0.011007735505700111,
-0.014619950205087662,
0.02088885009288788,
-0.013826411217451096,
0.013584498316049576,
0.01969170570373535,
-0.04463106021285057,
-0.0506417490541935,
0.021363696083426476,
-0.010319269262254238,
-0.06789278239011765,
-0.023252790793776512,
-0.02002556622028351,
0.01229932066053152,
0.00550435297191143,
0.020764140412211418,
-0.06426570564508438,
-0.031479015946388245,
0.007655029185116291,
0.058551542460918427,
-0.006485457997769117,
0.013342347927391529,
-0.063038669526577,
-0.06087353825569153,
0.034409791231155396,
0.002835913561284542,
-0.03372633829712868,
-0.014129004441201687,
0.01867101527750492,
-0.03261490911245346,
-0.0016781323356553912,
0.022344082593917847,
-0.008241919800639153,
0.06868477910757065,
-0.009849758818745613,
-0.0006797274108976126,
-0.0207219161093235,
0.01733339950442314,
-0.04303202033042908,
-0.033065859228372574,
0.03747119382023811,
0.03881905972957611,
-0.062034156173467636,
0.008463491685688496,
0.011218098923563957,
-0.005270791240036488,
-0.02745419554412365,
-0.006869294214993715,
-0.011722338385879993,
-0.017719892784953117,
0.03524375334382057,
-0.06591785699129105,
-0.022098267450928688,
-0.007823771797120571,
0.029385391622781754,
0.009789330884814262,
0.00428851367905736,
0.004633521661162376,
0.013749392703175545,
-0.06112444028258324,
-0.011965295299887657
] |
<p>I have a model that represents a bicycle (a wood block with wheels), and I'm balancing the center of gravity so it's the same as a real bike. However, when the center of mass is kept constant, does the weight of it affect the effect torque has on it when it hits a wall?</p>
<p>I'm planning to measure the angle the back wheel bounces up.</p>
|
g2473
|
[
0.06020868942141533,
0.04271971434354782,
0.02270573191344738,
0.011570947244763374,
0.049329500645399094,
-0.00609091529622674,
0.06003181263804436,
0.02862595021724701,
-0.0785406157374382,
0.00881306640803814,
-0.049702856689691544,
-0.03904949873685837,
0.0011203400790691376,
-0.012808830477297306,
0.01783088967204094,
0.006652412936091423,
0.05470828711986542,
-0.02795850671827793,
0.06194083020091057,
-0.003506661159917712,
0.012416601181030273,
-0.015511906705796719,
-0.024087172001600266,
0.015655359253287315,
0.01950322464108467,
0.01564284786581993,
-0.0023492001928389072,
0.019828107208013535,
0.007740231230854988,
0.014742049388587475,
-0.0211934894323349,
-0.005777052138000727,
0.02567368559539318,
-0.06179213896393776,
-0.0583784393966198,
-0.012670624069869518,
0.005858689546585083,
0.040849942713975906,
-0.01109872106462717,
-0.03371715173125267,
0.057343948632478714,
-0.0015747143188491464,
-0.027559686452150345,
0.0074278973042964935,
-0.01739010214805603,
-0.0016245546285063028,
0.000335299497237429,
0.024971850216388702,
-0.028798162937164307,
0.027448590844869614,
-0.040358297526836395,
-0.016489064320921898,
0.007680744398385286,
0.029803358018398285,
0.06735087186098099,
-0.01429419033229351,
0.03149022161960602,
0.008468023501336575,
-0.031202303245663643,
0.02963547594845295,
-0.04373710975050926,
0.005221187137067318,
-0.03523661568760872,
0.016183611005544662,
0.05972512066364288,
-0.035926077514886856,
0.003813963383436203,
0.014330744743347168,
-0.00945734791457653,
0.018161913380026817,
0.0026348326355218887,
-0.0021027710754424334,
0.005287757609039545,
-0.011526389047503471,
-0.0231170691549778,
-0.0043990276753902435,
0.00046881524031050503,
0.009407594799995422,
0.0029832248110324144,
-0.004118784796446562,
-0.02106521837413311,
0.05677848309278488,
0.007203969638794661,
0.015790624544024467,
0.05493610352277756,
0.006188975181430578,
-0.01148915383964777,
0.017873886972665787,
-0.030536258593201637,
0.0026168401818722486,
0.059227410703897476,
-0.0612928606569767,
0.062304262071847916,
0.041529830545186996,
-0.026745885610580444,
-0.07515022158622742,
-0.02545325644314289,
0.0380086712539196,
0.006186210084706545,
0.0313301756978035,
-0.01302332989871502,
0.010879484936594963,
-0.02221747674047947,
-0.046776652336120605,
-0.021996231749653816,
-0.01087710540741682,
0.02981882356107235,
-0.032915785908699036,
0.009746737778186798,
-0.05399079993367195,
-0.020211081951856613,
-0.09118204563856125,
0.030460841953754425,
-0.04321599379181862,
-0.11786947399377823,
-0.031332626938819885,
0.12146201729774475,
-0.021689513698220253,
-0.009156418032944202,
-0.030194871127605438,
-0.0007239500992000103,
0.037668123841285706,
-0.049905914813280106,
0.08925721794366837,
-0.028127407655119896,
-0.011612582951784134,
-0.02808440290391445,
0.028099389746785164,
-0.017013123258948326,
-0.023228824138641357,
0.02778276801109314,
0.021655455231666565,
-0.04691215604543686,
-0.02893867716193199,
0.036228958517313004,
0.04580797627568245,
-0.04816624894738197,
0.0070722089149057865,
0.008485755883157253,
0.04469732195138931,
0.02751900814473629,
0.002633068012073636,
0.019052594900131226,
-0.020199904218316078,
-0.027806522324681282,
0.011425621807575226,
0.018833864480257034,
0.026222778484225273,
0.07435984164476395,
0.015460447408258915,
-0.02406446821987629,
0.0040991962887346745,
-0.05629438906908035,
-0.09087815880775452,
0.049807846546173096,
0.020972343161702156,
0.015564186498522758,
-0.02313627116382122,
0.026529114693403244,
-0.00831062626093626,
0.028970682993531227,
-0.04622946307063103,
0.08659191429615021,
-0.03314535319805145,
-0.03753044828772545,
-0.010210835374891758,
0.007056068163365126,
0.00123702606651932,
0.026716290041804314,
-0.02407066524028778,
-0.04915438964962959,
0.006042531691491604,
0.009647436439990997,
0.016089484095573425,
-0.010902849957346916,
-0.004640310537070036,
-0.014396198093891144,
0.00026322470512241125,
0.06466785818338394,
0.03671267628669739,
-0.036523085087537766,
-0.0019082295475527644,
0.024324284866452217,
-0.03558586910367012,
-0.09723514318466187,
-0.008559691719710827,
0.08924487233161926,
-0.00865461491048336,
-0.04093709588050842,
-0.010810310021042824,
-0.004417367745190859,
-0.028105365112423897,
-0.03182879462838173,
0.029682079330086708,
-0.06595753878355026,
-0.036795616149902344,
0.05021728575229645,
-0.014232328161597252,
-0.08156412094831467,
0.0233274158090353,
-0.032211195677518845,
0.018923887982964516,
0.033303990960121155,
0.024720003828406334,
-0.07297665625810623,
0.0036811139434576035,
0.02568373642861843,
-0.027622980996966362,
-0.002179273869842291,
-0.054136160761117935,
-0.01828211359679699,
0.06670277565717697,
-0.016341153532266617,
0.06545690447092056,
-0.02740819752216339,
0.026706645265221596,
0.007914580404758453,
0.03436551243066788,
0.05136483535170555,
0.03537614271044731,
0.0075055393390357494,
0.01303564291447401,
-0.010483309626579285,
0.006750589236617088,
-0.05669480562210083,
-0.04789433255791664,
0.01444030087441206,
-0.012546004727482796,
-0.022856174036860466,
-0.025286052376031876,
0.0018332100007683039,
-0.0034029141534119844,
0.04320366680622101,
0.01423678733408451,
0.05814860761165619,
0.059421688318252563,
0.015525814145803452,
0.005015546455979347,
-0.002300335094332695,
-0.07361938059329987,
0.04575701057910919,
0.016385642811655998,
-0.020922474563121796,
-0.047692570835351944,
0.0005031176842749119,
-0.01606166735291481,
0.018105056136846542,
0.009697167202830315,
0.03899608924984932,
0.0012002269504591823,
0.007233075797557831,
-0.004585793241858482,
-0.0957803949713707,
0.0033327066339552402,
-0.008608531206846237,
0.03554339334368706,
-0.016598697751760483,
-0.04382187873125076,
-0.010583300143480301,
-0.009165599942207336,
-0.027439462020993233,
-0.009291877038776875,
-0.0176352821290493,
0.08998457342386246,
-0.030987638980150223,
-0.03388229012489319,
0.006935622077435255,
-0.027408266440033913,
0.035241641104221344,
0.03768380358815193,
-0.003588855965062976,
0.07806484401226044,
0.017913801595568657,
0.07180564850568771,
-0.026571860536932945,
-0.09719560295343399,
0.009661308489739895,
-0.02398601733148098,
-0.0073678819462656975,
-0.030698055401444435,
0.026141710579395294,
0.022193215787410736,
0.008584205992519855,
0.04266887903213501,
0.030706629157066345,
-0.0008784267120063305,
-0.05169739946722984,
-0.016028525307774544,
-0.028062010183930397,
0.01892230100929737,
-0.04691976681351662,
0.07670716941356659,
0.038236334919929504,
-0.026529371738433838,
0.04334760084748268,
0.10617119073867798,
-0.021083200350403786,
-0.0022515638265758753,
-0.03500989452004433,
-0.003841525176540017,
-0.058460868895053864,
0.01644628681242466,
-0.008761156350374222,
0.009137222543358803,
-0.03662169724702835,
0.0014221160672605038,
-0.0043968502432107925,
0.002555575454607606,
0.061893295496702194,
0.04056317359209061,
-0.07927235960960388,
-0.018659474328160286,
-0.024182016029953957,
-0.012377179227769375,
-0.08188582956790924,
-0.021278684958815575,
0.017379770055413246,
-0.01947610080242157,
-0.07739751040935516,
-0.04802427813410759,
0.009631501510739326,
-0.01897568814456463,
0.012685555033385754,
0.006413142662495375,
-0.0188309159129858,
0.07164741307497025,
-0.019225789234042168,
0.07556255161762238,
-0.06186710670590401,
-0.07350626587867737,
0.0340358130633831,
0.023691799491643906,
-0.022932033985853195,
0.025931524112820625,
-0.016580555588006973,
0.00955402385443449,
0.03466031327843666,
-0.027750931680202484,
0.01483723521232605,
0.05692141875624657,
-0.03387465327978134,
0.03625097870826721,
0.0064139110036194324,
-0.04388991743326187,
0.03058484010398388,
0.020103177055716515,
-0.029821358621120453,
-0.049747761338949203,
-0.007132700644433498,
-0.048401009291410446,
0.06589871644973755,
-0.007404213771224022,
-0.02713770419359207,
-0.017713814973831177,
-0.0036751285661011934,
-0.032131291925907135,
-0.010365229099988937,
0.04916873574256897,
-0.07123085856437683,
0.024224527180194855,
-0.0023032296448946,
-0.011375488713383675,
0.0008572096121497452,
-0.027048258110880852,
-0.004488603677600622,
-0.020975008606910706,
0.018737653270363808,
0.03223288059234619,
0.03385838866233826,
0.012195606715977192,
-0.000256458850344643,
0.01148328185081482,
0.0006402214057743549,
0.06025264784693718,
0.036299221217632294,
-0.023856094107031822,
0.03952902927994728,
0.006664861459285021,
-0.013553897850215435,
-0.0017724467907100916,
0.035382937639951706,
0.05230123922228813,
-0.0213217381387949,
-0.02225053682923317,
-0.007829387672245502,
0.01048718299716711,
-0.011300734244287014,
-0.0018918982241302729,
0.07924088090658188,
0.005877019837498665,
-0.004161324817687273,
-0.07725584506988525,
-0.026859143748879433,
0.016601350158452988,
0.053758252412080765,
0.03484411537647247,
0.0048195431008934975,
-0.07618916779756546,
-0.020015260204672813,
0.028771953657269478,
0.02270849607884884,
0.07335475832223892,
0.006138930097222328,
0.03255769982933998,
0.013022747822105885,
-0.004842636175453663,
0.06264854222536087,
-0.020772868767380714,
-0.03477373346686363,
0.04209766536951065,
0.013188222423195839,
-0.019370540976524353,
-0.017305422574281693,
-0.07443669438362122,
0.023673832416534424,
-0.01126125268638134,
0.013134929351508617,
0.018438441678881645,
0.012422764673829079,
0.02486342005431652,
-0.00172773702070117,
0.05433974415063858,
-0.019774943590164185,
-0.04849353805184364,
-0.014933786354959011,
-0.011439157649874687,
-0.0023383325897157192,
-0.040799789130687714,
-0.0002815543266478926,
-0.023676201701164246,
-0.006936170626431704,
-0.008459002710878849,
-0.008834628388285637,
0.024370862171053886,
-0.008337696082890034,
0.05749353766441345,
-0.023239627480506897,
0.026147404685616493,
0.026111414656043053,
-0.010065238922834396,
0.0007955937762744725,
0.04990924149751663,
-0.022512618452310562,
-0.04802704229950905,
-0.05383983254432678,
0.0416044220328331,
-0.028160061687231064,
0.015514429658651352,
0.05566242337226868,
-0.032796915620565414,
-0.06682392209768295,
-0.014082896523177624,
-0.0005077795358374715,
-0.04554760083556175,
0.01500037219375372,
0.01011532824486494,
0.018053459003567696,
0.028788551688194275,
-0.0027144532650709152,
-0.03336743265390396,
-0.03930218145251274,
-0.03093612566590309,
0.005072418600320816,
-0.008311542682349682,
-0.03294622153043747,
-0.0692378506064415,
-0.026358282193541527,
0.03216074779629707,
-0.06495009362697601,
-0.0007699904381297529,
0.040126681327819824,
0.018253572285175323,
0.02790350280702114,
0.0747087374329567,
0.019443636760115623,
0.007036089431494474,
-0.03156328573822975,
-0.014887817203998566,
0.05272301286458969,
-0.03187844902276993,
0.002207526471465826,
-0.0356099009513855,
-0.01881737820804119,
-0.026872064918279648,
0.01634296029806137,
-0.0014232430839911103,
-0.03649771213531494,
-0.010700217448174953,
0.046214159578084946,
0.035056453198194504,
0.03438554331660271,
0.013197115622460842,
-0.03278360515832901,
-0.05793866142630577,
0.02693469449877739,
0.05067375674843788,
-0.02903023734688759,
-0.03632601350545883,
-0.018733013421297073,
0.010835052467882633,
-0.021280569955706596,
0.0907086580991745,
0.02593247964978218,
-0.0016489126719534397,
-0.041514329612255096,
0.04881223663687706,
-0.022781986743211746,
-0.036599237471818924,
-0.025305582210421562,
0.08444744348526001,
-0.056826151907444,
0.022846898064017296,
-0.005475195590406656,
0.059725549072027206,
-0.028439868241548538,
-0.001135222613811493,
0.05717117339372635,
0.039236199110746384,
0.015132746659219265,
0.04674879088997841,
0.009269822388887405,
-0.006863462273031473,
0.03419150412082672,
-0.02200145460665226,
-0.003022379707545042,
0.028381939977407455,
0.009325438179075718,
-0.0229586660861969,
-0.018894527107477188,
0.07394719123840332,
0.021583572030067444,
-0.018474066630005836,
0.08063749969005585,
0.01717824675142765,
-0.007884570397436619,
-0.016446340829133987,
0.0321514829993248,
0.0275187399238348,
0.03790697082877159,
-0.037630241364240646,
-0.028735635802149773,
0.025721987709403038,
0.06345008313655853,
0.03160412237048149,
0.049397602677345276,
-0.0333222821354866,
-0.03061840869486332,
-0.038042325526475906,
0.06112457811832428,
0.0032193597871810198,
-0.028642859309911728,
0.03799443319439888,
-0.04265519604086876,
0.04753308743238449,
-0.00519986217841506,
0.011531018652021885,
-0.031178418546915054,
-0.040927961468696594,
0.010311555117368698,
-0.023284880444407463,
0.01018993929028511,
-0.00516740046441555,
0.05964995175600052,
0.014602480456233025,
0.003535289317369461,
-0.02342810295522213,
-0.02426290139555931,
0.006595156621187925,
0.06892730295658112,
-0.0060022687539458275,
0.04887452349066734,
-0.01802654378116131,
-0.022668085992336273,
-0.021223751828074455,
0.029157720506191254,
0.01104885432869196,
-0.0650247260928154,
-0.0524442233145237,
-0.05182761326432228,
0.012976612895727158,
-0.0027924110181629658,
-0.047833461314439774,
0.03737396001815796,
-0.038796521723270416,
0.03154115751385689,
-0.005967875011265278,
-0.03144438564777374,
-0.03607317805290222,
0.017119234427809715,
-0.02922014147043228,
-0.04741527512669563,
0.016557008028030396,
-0.027764281257987022,
0.03070671670138836,
-0.019443292170763016,
-0.010123739019036293,
-0.027801193296909332,
0.023115046322345734,
0.01537321973592043,
0.020890461280941963,
0.054863329976797104,
-0.00745640741661191,
0.04985880106687546,
-0.022272946313023567,
0.017928238958120346,
-0.013749370351433754,
-0.009402728639543056,
-0.01883193850517273,
-0.018914731219410896,
0.02667907439172268,
0.029653746634721756,
0.03494524210691452,
0.026712501421570778,
0.0180424302816391,
-0.019773093983530998,
0.010885847732424736,
-0.01818849891424179,
-0.03175199404358864,
-0.059310100972652435,
-0.0014584073796868324,
-0.03064034879207611,
-0.025313429534435272,
0.014778530225157738,
-0.0645410493016243,
0.01325435470789671,
-0.03812231495976448,
-0.027035512030124664,
0.014141465537250042,
0.018689481541514397,
0.004935478325933218,
-0.020482949912548065,
0.06300153583288193,
-0.00349796237424016,
0.013567028567194939,
0.002270106226205826,
0.08216177672147751,
-0.032440170645713806,
0.0420135036110878,
0.06749381124973297,
0.06540539860725403,
-0.026749540120363235,
0.08692631125450134,
-0.05835545063018799,
0.018845362588763237,
-0.06345950067043304,
0.0203663632273674,
0.03722700476646423,
0.007303680293262005,
0.010056150145828724,
0.02190268412232399,
0.02205476351082325,
0.021701153367757797,
0.0006558297318406403,
-0.008656837046146393,
-0.049141183495521545,
0.0061251637525856495,
0.017250487580895424,
0.008242589421570301,
0.022207843139767647,
-0.008527790196239948,
-0.06345580518245697,
-0.07006888836622238,
0.010920585133135319,
-0.03498339280486107,
-0.00985792651772499,
0.038837041705846786,
-0.010283982381224632,
0.04195548966526985,
-0.008271259255707264,
0.04455598071217537,
-0.010695082135498524,
-0.0739012286067009,
-0.01439633872359991,
0.019198399037122726,
0.05459325760602951,
0.004995383787900209,
-0.05403975769877434,
-0.033942852169275284,
0.010872069746255875,
0.001401018351316452,
0.054508958011865616,
0.0352497361600399,
-0.02361408993601799,
-0.007638571318238974,
-0.004192003048956394,
0.03175336495041847,
0.005342582240700722,
-0.0063835675828158855,
0.06252742558717728,
-0.04939710348844528,
0.019804377108812332,
0.06774032115936279,
-0.0011606940533965826,
0.010777554474771023,
-0.09159509092569351,
-0.021328087896108627,
-0.000350223301211372,
0.07617607712745667,
0.0005315557937137783,
0.025041792541742325,
-0.001250233966857195,
-0.04566151648759842,
-0.004103843122720718,
0.060324277728796005,
0.03904856741428375,
0.026479965075850487,
-0.06528247892856598,
-0.011860176920890808,
-0.04071420431137085,
0.04669152572751045,
0.007717131171375513,
-0.00895014125853777,
0.03607189282774925,
-0.021772170439362526,
-0.04958677664399147,
0.04305024445056915,
-0.013607797212898731,
0.01581505686044693,
0.0017716189613565803,
0.005427907221019268,
-0.0404321514070034,
-0.016650492325425148,
-0.028644738718867302,
-0.016181878745555878,
0.0020573690999299288,
-0.09986745566129684,
-0.051590073853731155,
0.03455989435315132,
-0.007609689142554998,
0.06530284881591797,
0.017703518271446228,
-0.0032729499507695436,
-0.0322798453271389,
0.012256060726940632,
-0.008423171006143093,
0.005823993589729071,
0.04480356350541115,
-0.05157727748155594,
-0.029458999633789062,
-0.004730714950710535,
0.020584583282470703,
-0.0361148975789547,
0.006927813868969679,
-0.01730569452047348,
-0.014127591624855995,
0.0708678588271141,
-0.015771999955177307,
0.008910203352570534,
0.00444897310808301,
-0.007360659074038267,
0.013731017708778381,
-0.04698649421334267,
0.0057694800198078156,
-0.03586054593324661,
-0.05605896934866905,
-0.02524791657924652,
-0.06603073328733444,
-0.06317707896232605,
-0.02073333039879799,
-0.03579520806670189,
0.021315651014447212,
-0.017971163615584373,
0.012416454032063484,
-0.0483810156583786,
-0.06408651918172836,
-0.026326511055231094,
0.022439373657107353,
0.015696609392762184
] |
<p>Order parameter is used to describe second order <a href="http://en.wikipedia.org/wiki/Phase_transition" rel="nofollow">phase transition</a>. It seems that in some papers it is used in the first order phase transitions. Can first order phase transition have an order parameter? If so, how can we define the order parameter in liquid-gas transition (first order)?</p>
|
g2474
|
[
-0.023566411808133125,
-0.006480924319475889,
0.021137015894055367,
-0.019554046913981438,
0.0819447785615921,
-0.023706646636128426,
-0.022514617070555687,
0.028243685141205788,
-0.08313065022230148,
0.01642414554953575,
-0.01857123151421547,
0.00997084192931652,
-0.03225153312087059,
0.01895110495388508,
-0.036098726093769073,
-0.00698593445122242,
0.010607872158288956,
0.027842167764902115,
-0.02576633356511593,
0.004999260883778334,
-0.00536943506449461,
0.0001374296989524737,
-0.052904825657606125,
-0.050841234624385834,
-0.018288280814886093,
0.02285154163837433,
0.02161034196615219,
-0.07372481375932693,
-0.02846364490687847,
-0.006154593545943499,
-0.0030104261822998524,
0.021561507135629654,
0.04639914631843567,
-0.016474172472953796,
-0.02073383331298828,
-0.004844588693231344,
0.03376229852437973,
0.020954377949237823,
0.07198279350996017,
0.024485543370246887,
-0.01459469087421894,
0.052441563457250595,
0.04858709126710892,
-0.03659903258085251,
0.00035056876367889345,
0.010789148509502411,
-0.04820413887500763,
0.008167549967765808,
-0.0043877908028662205,
0.004062856547534466,
0.07768511027097702,
0.07005973160266876,
-0.019473180174827576,
-0.023973817005753517,
-0.01988074742257595,
0.024350464344024658,
-0.022203637287020683,
0.04922807589173317,
0.09925433248281479,
0.035209570080041885,
-0.02064719796180725,
0.027179870754480362,
0.031763557344675064,
-0.02813645638525486,
0.06967391073703766,
-0.0520467534661293,
-0.021041249856352806,
0.007978950627148151,
-0.003039054572582245,
0.00918606948107481,
-0.05759963020682335,
-0.024781392887234688,
0.0008781226351857185,
-0.05733669921755791,
-0.013244805857539177,
-0.0026397705078125,
-0.06624676287174225,
-0.03848212584853172,
0.04048741236329079,
-0.05328415334224701,
-0.0023591674398630857,
-0.01294153556227684,
-0.004901818931102753,
0.039607249200344086,
0.0014284324133768678,
-0.007045517675578594,
0.005312069319188595,
-0.05728718265891075,
0.03611642122268677,
0.026279721409082413,
0.004275649785995483,
0.047928303480148315,
-0.05883783847093582,
-0.040835436433553696,
0.021565290167927742,
0.00614455109462142,
-0.02880885638296604,
-0.0004890768323093653,
0.08662284165620804,
-0.03137220814824104,
-0.05641990527510643,
-0.0035092998296022415,
-0.013182233087718487,
-0.054397452622652054,
-0.00929106306284666,
0.0032377808820456266,
0.011872137896716595,
0.045470643788576126,
0.001281769247725606,
-0.03327761963009834,
-0.015807047486305237,
0.029387271031737328,
-0.019867831841111183,
0.010556464083492756,
-0.029393251985311508,
0.003990018740296364,
0.10609117150306702,
-0.01165304146707058,
0.010090266354382038,
-0.01283882837742567,
0.040244050323963165,
0.024012554436922073,
0.0655272975564003,
0.11565779149532318,
-0.020434964448213577,
-0.015669813379645348,
0.04857563599944115,
0.013483967632055283,
0.03413106128573418,
-0.013084536418318748,
-0.027254896238446236,
-0.023853041231632233,
-0.0024102572351694107,
0.01741868071258068,
-0.001279899850487709,
-0.026891767978668213,
0.028739748522639275,
0.014357990585267544,
0.0464799627661705,
-0.048014141619205475,
-0.004400226287543774,
-0.01123606227338314,
-0.023720309138298035,
-0.059603363275527954,
-0.005252111237496138,
-0.010170203633606434,
0.035629164427518845,
0.025233354419469833,
-0.023700956255197525,
-0.000128683474031277,
-0.003785960143432021,
-0.017136480659246445,
0.04331929236650467,
0.008566593751311302,
-0.015253016725182533,
-0.00950940977782011,
0.029364727437496185,
0.009681548923254013,
0.019662370905280113,
-0.03602796047925949,
0.03068392723798752,
0.005641372874379158,
0.019300466403365135,
0.008657324127852917,
-0.0652221068739891,
-0.032135166227817535,
-0.01364847831428051,
0.004814733751118183,
-0.003320397110655904,
-0.07438090443611145,
-0.007370760198682547,
-0.037398792803287506,
-0.004372568801045418,
0.04238148033618927,
0.05076396092772484,
0.041894037276506424,
0.02356783114373684,
0.04939696565270424,
0.018850872293114662,
0.019362440332770348,
0.0031266866717487574,
0.0031493075657635927,
-0.03910818323493004,
-0.0022793917451053858,
-0.012470151297748089,
0.016231538727879524,
0.010130711831152439,
0.026285696774721146,
-0.007467582821846008,
-0.013413653708994389,
-0.01405821181833744,
0.013368736952543259,
-0.003103990573436022,
-0.02201094664633274,
0.008462971076369286,
0.017241302877664566,
-0.028420554473996162,
0.0021186871454119682,
-0.07633063197135925,
-0.023693211376667023,
0.0139323053881526,
-0.0003361523267813027,
-0.019754493609070778,
0.0020494400523602962,
-0.028495686128735542,
0.019292786717414856,
-0.011577795259654522,
0.0528709776699543,
0.0026882069651037455,
0.04683411121368408,
0.01516894344240427,
-0.016118062660098076,
0.05388827994465828,
-0.007195229642093182,
-0.041197773069143295,
0.047855399549007416,
0.010327855125069618,
0.016313491389155388,
0.007109550293534994,
0.05474235862493515,
-0.02495698817074299,
-0.0025153944734483957,
0.014362537302076817,
0.0013546653790399432,
0.0331166610121727,
-0.0001561005919938907,
0.07788966596126556,
-0.013249450363218784,
0.03765266761183739,
-0.024487456306815147,
-0.049770209938287735,
-0.021026959642767906,
-0.056235428899526596,
-0.025083962827920914,
0.05328453704714775,
-0.010338197462260723,
-0.049748148769140244,
-0.011600758880376816,
-0.00896431878209114,
0.060051124542951584,
-0.02840670943260193,
-0.05196136236190796,
-0.00023396544565912336,
0.04303301125764847,
-0.016073085367679596,
-0.04274969547986984,
0.03711972013115883,
0.020315663889050484,
-0.0014659703010693192,
0.0006467356579378247,
0.006441276520490646,
-0.029021378606557846,
-0.016112837940454483,
-0.029825763776898384,
-0.011017447337508202,
-0.04723965376615524,
0.03487005457282066,
0.03511539846658707,
-0.04853324964642525,
-0.026721687987446785,
0.0027571667451411486,
0.010111789219081402,
0.0046637277118861675,
-0.03683434799313545,
-0.049057453870773315,
0.0022047567181289196,
-0.03845469281077385,
0.03811561316251755,
0.005586888641119003,
-0.02770816721022129,
0.03872716799378395,
-0.040338270366191864,
-0.04820406436920166,
0.010674851946532726,
0.039358559995889664,
0.006712069269269705,
-0.016467856243252754,
-0.03555465117096901,
0.05629337206482887,
-0.01692165620625019,
-0.05336988344788551,
-0.060280509293079376,
-0.02794947288930416,
0.05302644893527031,
0.025926705449819565,
-0.00871370080858469,
0.060198504477739334,
0.029095984995365143,
-0.01733018085360527,
-0.0038725051563233137,
0.00885797943919897,
0.06374195963144302,
-0.017268139868974686,
0.04046189785003662,
-0.028857940807938576,
-0.027063701301813126,
0.013192704878747463,
0.01028084009885788,
0.07680460065603256,
-0.02331451140344143,
0.006664172746241093,
-0.02791549079120159,
-0.033519867807626724,
0.010380459018051624,
0.021651368588209152,
-0.009989907965064049,
0.01650114730000496,
-0.036379728466272354,
0.0076165408827364445,
0.01442160364240408,
-0.00012072934623574838,
0.06631021946668625,
-0.015421993099153042,
0.05887391045689583,
-0.02669105865061283,
0.04844532907009125,
-0.0018707879353314638,
0.04776635020971298,
0.05004381388425827,
-0.04117751866579056,
-0.0030414124485105276,
-0.01779426634311676,
-0.00803958997130394,
-0.03215399384498596,
-0.007892681285738945,
0.024366822093725204,
-0.004117235541343689,
0.006652463227510452,
-0.015256735496222973,
-0.012833772227168083,
0.02641621045768261,
-0.03501742333173752,
0.007479844614863396,
-0.047701604664325714,
-0.014497212134301662,
-0.03283323720097542,
-0.03456951677799225,
-0.008222430013120174,
-0.04794204235076904,
-0.005183702800422907,
0.04856080934405327,
-0.0302406195551157,
0.022375525906682014,
0.07813664525747299,
-0.027282949537038803,
-0.02111561968922615,
0.03137262910604477,
0.008839133195579052,
-0.06414798647165298,
0.002775945235043764,
0.048008158802986145,
-0.040798645466566086,
-0.013337279669940472,
-0.020657135173678398,
-0.011068345978856087,
0.017590969800949097,
0.014355195686221123,
0.003332797670736909,
0.03860016539692879,
0.017386389896273613,
0.056324105709791183,
-0.02683119848370552,
0.029233848676085472,
0.05941540747880936,
0.016346629709005356,
0.0133866211399436,
-0.0533355250954628,
0.055394936352968216,
-0.011823715642094612,
-0.04249100387096405,
-0.0039003905840218067,
-0.003026292659342289,
0.051280125975608826,
-0.02646460197865963,
0.04937180504202843,
-0.02245517075061798,
-0.0060781147330999374,
0.009033255279064178,
-0.042448051273822784,
0.04112022742629051,
-0.008357184007763863,
-0.033505748957395554,
-0.02242635376751423,
0.013428174890577793,
-0.009581431746482849,
-0.04429182410240173,
0.016602102667093277,
-0.07790176570415497,
0.007629381027072668,
-0.12020128220319748,
0.04225177690386772,
0.010721983388066292,
-0.0011751377023756504,
0.005148143973201513,
0.05693794786930084,
0.038815952837467194,
0.031365036964416504,
0.03250788152217865,
-0.00850403681397438,
-0.006991156376898289,
0.0013149046571925282,
-0.04888872057199478,
0.00449144234880805,
-0.030284782871603966,
0.03841499984264374,
-0.050328727811574936,
-0.007282597478479147,
-0.030590509995818138,
-0.08434699475765228,
-0.028181185945868492,
-0.01750357076525688,
0.01679728925228119,
-0.09922577440738678,
-0.0322997123003006,
0.023900073021650314,
-0.012232492677867413,
-0.0310054961591959,
-0.08275327831506729,
0.025299562141299248,
0.058261655271053314,
0.0011058978270739317,
0.012595558539032936,
0.025983324274420738,
-0.06878739595413208,
-0.07991066575050354,
0.03255204111337662,
0.0337461456656456,
0.007574191316962242,
-0.02606159821152687,
0.019950712099671364,
-0.03087155893445015,
0.03012101724743843,
0.05458341911435127,
0.03647669032216072,
-0.014303545467555523,
-0.008047552779316902,
-0.06272890418767929,
0.012620882131159306,
0.030201133340597153,
-0.009579509496688843,
-0.0004942707601003349,
0.017354952171444893,
0.02171766571700573,
0.04320146515965462,
0.03388736769556999,
-0.023857906460762024,
0.06339483708143234,
0.004076081328094006,
-0.025826651602983475,
-0.028360947966575623,
-0.04114767163991928,
0.020268553867936134,
-0.036559976637363434,
-0.014797807671129704,
-0.0016509268898516893,
-0.02473948709666729,
0.0076824333518743515,
0.010496532544493675,
-0.058675263077020645,
0.002488359808921814,
0.01853848807513714,
-0.024838153272867203,
0.03088986873626709,
0.00752859003841877,
0.037821315228939056,
-0.02405671589076519,
0.003450858872383833,
-0.01648094318807125,
-0.05003071948885918,
-0.005474000703543425,
-0.05125194415450096,
-0.010183118283748627,
0.0833219587802887,
0.06641903519630432,
0.054542142897844315,
-0.0009151632548309863,
0.008209655061364174,
0.01305466890335083,
0.0045493473298847675,
-0.03313509747385979,
-0.031643666326999664,
0.03041459619998932,
0.0797867402434349,
-0.006537572480738163,
0.0532357357442379,
-0.027047814801335335,
0.021916715428233147,
-0.01132217701524496,
0.04468970745801926,
0.028509143739938736,
-0.010002910159528255,
0.0698392242193222,
-0.013420428149402142,
-0.02338353917002678,
0.05404737591743469,
-0.05770275369286537,
0.05885696783661842,
0.04154547303915024,
-0.0008725390071049333,
-0.0010875370353460312,
-0.057139426469802856,
0.038006462156772614,
0.02432239055633545,
0.0032284657936543226,
-0.04559050872921944,
0.07468865811824799,
-0.03588004782795906,
-0.010134599171578884,
-0.002677167532965541,
-0.019057998433709145,
-0.013750767335295677,
-0.015752149745821953,
-0.05586770176887512,
0.02250894345343113,
-0.005372931715101004,
-0.037315476685762405,
0.022692065685987473,
-0.01369399018585682,
-0.05350196734070778,
-0.03633732721209526,
0.007962186820805073,
0.012289635837078094,
0.07729915529489517,
-0.06231166422367096,
-0.05027271807193756,
-0.00011443077528383583,
0.0013104296522215009,
0.003720517735928297,
0.05701374262571335,
-0.03846052289009094,
-0.0050849164836108685,
0.04086936265230179,
-0.011670641601085663,
0.018650399520993233,
-0.029236147180199623,
-0.060484521090984344,
-0.06047077849507332,
0.05845428258180618,
0.044577933847904205,
0.040407996624708176,
-0.07472818344831467,
0.0586516372859478,
-0.011144135147333145,
0.030828380957245827,
0.05886919051408768,
0.03438348323106766,
-0.019804228097200394,
0.01975168101489544,
-0.047573868185281754,
-0.038457855582237244,
0.023411212489008904,
-0.04432712122797966,
0.021504100412130356,
-0.0038280286826193333,
0.027607589960098267,
0.08483198285102844,
-0.026845009997487068,
0.020646153017878532,
-0.013315712101757526,
-0.01865023374557495,
0.025892382487654686,
0.043142806738615036,
0.019882498309016228,
0.020382022485136986,
0.011925522238016129,
-0.06785315275192261,
-0.00911216251552105,
0.018105749040842056,
-0.02995140850543976,
0.027246462181210518,
0.0012006222968921065,
-0.04035625979304314,
-0.013296062126755714,
-0.007805784232914448,
0.04317011684179306,
-0.001409821561537683,
-0.013694296590983868,
-0.04369289055466652,
-0.005290704779326916,
0.002287647919729352,
-0.023396775126457214,
0.07871612161397934,
-0.012048810720443726,
0.004435115959495306,
-0.046680085361003876,
-0.01566077023744583,
0.011250847950577736,
0.027038972824811935,
-0.011246171779930592,
0.021163582801818848,
0.005060320254415274,
-0.05069109424948692,
-0.07521054893732071,
-0.01903492771089077,
0.012567609548568726,
0.033667612820863724,
0.02685648389160633,
0.03645208105444908,
0.023947443813085556,
0.04875526204705238,
0.018357520923018456,
0.006981424987316132,
-0.0013344649923965335,
0.01734306663274765,
-0.017747126519680023,
0.022512121126055717,
0.04351469501852989,
0.11217115819454193,
0.021594522520899773,
0.021638091653585434,
-0.003269364358857274,
0.040154553949832916,
-0.025470353662967682,
-0.045974116772413254,
-0.0072913384065032005,
-0.016720160841941833,
-0.03429006040096283,
0.052271973341703415,
-0.002999875694513321,
0.028925910592079163,
-0.039878904819488525,
-0.05801516771316528,
-0.027637949213385582,
0.001988969976082444,
-0.0007404058706015348,
0.0620957687497139,
-0.04346165060997009,
0.01598971337080002,
-0.02594570629298687,
0.03477012366056442,
-0.003703678958117962,
-0.09230756759643555,
-0.038409650325775146,
-0.022278495132923126,
0.043996311724185944,
-0.0313166119158268,
-0.12664593756198883,
0.00753163592889905,
0.04034142196178436,
0.018066823482513428,
0.04205074533820152,
-0.023875320330262184,
0.02527804486453533,
-0.017358113080263138,
-0.07422316074371338,
0.0566081702709198,
-0.030222879722714424,
-0.007061019539833069,
-0.03139054402709007,
0.04469228535890579,
-0.004164565354585648,
-0.04144435003399849,
-0.07308322191238403,
0.03851982206106186,
-0.008852503262460232,
0.08526866137981415,
0.031216558068990707,
0.011531926691532135,
0.011324252933263779,
0.043057508766651154,
-0.022372430190443993,
0.04534889757633209,
-0.01884288527071476,
-0.02396235242486,
0.00008282427734229714,
0.051628321409225464,
0.01781943254172802,
-0.0660068467259407,
-0.006031341385096312,
-0.014146490022540092,
-0.0697234645485878,
-0.01862543448805809,
-0.03921101987361908,
-0.017025865614414215,
0.015429718419909477,
0.04428047314286232,
0.02576281875371933,
-0.02193887159228325,
0.04712999239563942,
0.01733149029314518,
0.026606982573866844,
0.015813296660780907,
0.012002143077552319,
-0.07926400750875473,
-0.04292907565832138,
0.07511112093925476,
-0.015927908942103386,
0.07619064301252365,
0.011387408711016178,
-0.05440644547343254,
-0.0019957751501351595,
0.02991614304482937,
-0.06854620575904846,
-0.07748934626579285,
0.02874445542693138,
-0.04651765897870064,
0.006325737107545137,
-0.020520955324172974,
-0.04180148243904114,
0.00895028654485941,
0.038849715143442154,
-0.03075958415865898,
-0.08009524643421173,
-0.010313975624740124,
-0.0068845488131046295,
0.014659813605248928,
0.03316290304064751,
-0.008694964461028576,
-0.008533637039363384,
0.010964910499751568,
-0.0293166134506464,
-0.01212033350020647,
0.06425607949495316,
0.03456087037920952,
0.025176135823130608,
-0.015387977473437786,
-0.015769829973578453,
0.040747832506895065,
-0.043391864746809006,
0.027775466442108154,
0.03209123760461807,
-0.04937898740172386,
0.020137356594204903,
0.030272360891103745,
-0.013641692698001862,
0.05581183731555939,
-0.03340749442577362,
0.03515304997563362,
-0.021540330722928047,
-0.013640249148011208,
-0.03168420493602753,
-0.018609676510095596,
-0.013384508900344372,
0.06173019856214523,
0.004193694330751896,
0.015381179749965668,
0.050826188176870346,
-0.0056037153117358685,
-0.003714528866112232,
-0.015514214523136616,
0.024769533425569534,
0.050939057022333145,
0.061171356588602066,
0.014304447919130325,
0.02319643460214138,
-0.06518539041280746,
0.00844360888004303,
0.031693119555711746,
0.03480619937181473,
-0.05166928842663765,
-0.010353264398872852,
-0.01896199770271778,
0.09074344485998154,
-0.02468564175069332,
-0.026472896337509155,
-0.02396954596042633,
-0.029179343953728676,
0.020344840362668037,
-0.039991989731788635,
-0.03827405720949173,
-0.08182308822870255,
0.024130476638674736,
-0.00043026538332924247,
0.00849846936762333,
-0.046358056366443634,
0.009145058691501617,
-0.029188642278313637,
-0.010979454964399338
] |
<p>Dirac equation for the massless fermions in curved spase time is $γ^ae^μ_aD_μΨ=0$, where $e^μ_a$ are the tetrads. I have to show that Dirac spinors obey the following equation:
$$(−D_μD^μ+\frac{1}{4}R)Ψ=0\qquad(1)$$</p>
<p>where $R$ is the Ricci scalar.</p>
<p>I already know that $[D_\mu,D_\nu]A^\rho={{R_{\mu\nu}}^\rho}_\sigma A^\sigma$, but a key point is to know what $[D_\mu,D_\nu]\Psi$ is.</p>
<p>($D_μΨ=∂_μΨ+A^{ab}_μΣ_{ab}$ is the covariant derivative of the spinor field and $Σ_{ab}$ the Lorentz generators involving gamma matrices).</p>
|
g2475
|
[
0.01664847694337368,
-0.042389195412397385,
-0.009810651652514935,
-0.05765623226761818,
0.07342604547739029,
0.012439985759556293,
0.04678328335285187,
0.02530656009912491,
-0.028351128101348877,
0.042840007692575455,
-0.07352415472269058,
0.014326866716146469,
-0.005612876731902361,
0.033632103353738785,
0.041333746165037155,
0.04548076167702675,
0.010433859191834927,
-0.004945536144077778,
0.018736375495791435,
-0.019516168162226677,
-0.020210938528180122,
-0.04049919918179512,
0.04601354897022247,
-0.0379781648516655,
0.05090183764696121,
-0.025308340787887573,
0.02226177044212818,
-0.002734782174229622,
-0.04681702330708504,
-0.03228867053985596,
0.031545743346214294,
0.09595165401697159,
0.025699511170387268,
-0.03642131760716438,
0.0009867976186797023,
-0.01984148845076561,
0.07635121792554855,
0.031620223075151443,
0.03709699213504791,
0.028744680806994438,
-0.02538089081645012,
-0.028649767860770226,
-0.0017657571006566286,
-0.004613309632986784,
0.04331068694591522,
0.07022304087877274,
-0.016443787142634392,
0.07459226250648499,
-0.0827384889125824,
0.04063555970788002,
0.011349291540682316,
0.0009948809165507555,
0.0034633565228432417,
-0.021366046741604805,
-0.12007873505353928,
0.02084910310804844,
0.01683877594769001,
-0.008531974628567696,
0.06529930233955383,
0.09060356765985489,
-0.007157415151596069,
-0.033983755856752396,
0.010958580300211906,
0.029185468330979347,
0.021620389074087143,
0.012081202119588852,
0.011269386857748032,
-0.019447367638349533,
0.07977916300296783,
0.005179604049772024,
0.008650043979287148,
-0.041422370821237564,
0.048142991960048676,
-0.011537215672433376,
0.0036854150239378214,
0.0039958655834198,
0.027306165546178818,
-0.013473314233124256,
-0.04102037847042084,
-0.08527711778879166,
-0.014512551948428154,
-0.03411344811320305,
-0.030931273475289345,
-0.0038152718916535378,
0.09104162454605103,
0.01638001948595047,
0.02166460081934929,
0.03804774209856987,
0.017458390444517136,
0.05264429748058319,
-0.017471609637141228,
-0.07586155086755753,
0.019863728433847427,
0.005485909059643745,
-0.02411927841603756,
-0.00623319623991847,
-0.009068861603736877,
0.011411769315600395,
-0.047862160950899124,
-0.03665880113840103,
-0.02677629142999649,
0.04995381087064743,
0.05184852331876755,
0.054389577358961105,
0.017025047913193703,
-0.007481580134481192,
-0.03778371214866638,
-0.05295513570308685,
0.06661560386419296,
-0.01718394085764885,
-0.02824520319700241,
0.04008914902806282,
-0.02460566908121109,
0.004546611104160547,
-0.0011748020770028234,
0.02094075456261635,
0.03601343184709549,
-0.07354370504617691,
-0.003591750515624881,
0.0428151972591877,
-0.023895956575870514,
0.03287814185023308,
0.015640685334801674,
0.0029068870935589075,
0.017946798354387283,
0.00924321822822094,
0.014792566187679768,
0.019644910469651222,
0.06932172924280167,
-0.0020575111266225576,
0.014386055059731007,
0.05625304952263832,
-0.001817840151488781,
0.028659189119935036,
-0.015071029774844646,
0.07956013083457947,
-0.015960542485117912,
0.028592964634299278,
0.01812518760561943,
-0.005711494479328394,
-0.00014213054964784533,
-0.006185231264680624,
0.05477926880121231,
0.02005487121641636,
-0.06131882593035698,
-0.0015731115126982331,
0.015804611146450043,
-0.055871397256851196,
0.02729266881942749,
0.04252370074391365,
0.013744205236434937,
0.0659140795469284,
-0.01888207159936428,
0.017865486443042755,
0.05477656051516533,
0.00888154748827219,
-0.019360769540071487,
-0.062296830117702484,
0.0004828880191780627,
0.007182725239545107,
0.03421079367399216,
0.004446909762918949,
-0.0467575266957283,
0.004563251510262489,
-0.01606820710003376,
-0.017956117168068886,
0.01955583319067955,
-0.022457022219896317,
-0.033702950924634933,
-0.0704675242304802,
-0.047857023775577545,
0.009659538976848125,
-0.010104941204190254,
-0.03405757248401642,
-0.03330229967832565,
0.03293521702289581,
-0.045259565114974976,
0.010495779104530811,
0.0007918630726635456,
-0.0029290737584233284,
0.009828012436628342,
-0.04907906800508499,
0.02845340594649315,
-0.03847808390855789,
0.034647151827812195,
-0.033968716859817505,
-0.013212108053267002,
0.034016963094472885,
-0.015286194160580635,
-0.017070837318897247,
-0.015707192942500114,
-0.038254790008068085,
-0.014362732879817486,
0.08104616403579712,
0.026375334709882736,
0.022846736013889313,
0.05857716500759125,
-0.07654102146625519,
-0.00867830216884613,
0.0797170102596283,
0.0004402170015964657,
-0.0024753722827881575,
0.022462964057922363,
-0.023820891976356506,
0.011375836096704006,
-0.016973553225398064,
0.024570448324084282,
-0.03689476475119591,
0.07719411700963974,
-0.004377716686576605,
0.08432520925998688,
-0.021512992680072784,
-0.027233460918068886,
-0.008580048568546772,
-0.03839769959449768,
-0.030502278357744217,
0.025579528883099556,
-0.0163087360560894,
-0.014817829243838787,
0.07058588415384293,
0.0014215181581676006,
-0.026524418964982033,
0.028148246929049492,
0.03962453082203865,
0.03982896730303764,
0.05245530232787132,
-0.048969242721796036,
-0.02570599503815174,
0.022823087871074677,
0.03467480465769768,
-0.011588187888264656,
0.03096248395740986,
-0.02892095409333706,
-0.016783853992819786,
0.0006309191230684519,
-0.0005936670931987464,
-0.043416909873485565,
0.03212905302643776,
0.02289682812988758,
0.012768153101205826,
0.040120724588632584,
-0.01467034500092268,
-0.07308752089738846,
-0.024081803858280182,
-0.00816263072192669,
0.042528796941041946,
0.02412698231637478,
0.047894641757011414,
-0.029756490141153336,
-0.02414669096469879,
0.07835204154253006,
-0.031337082386016846,
-0.007766522001475096,
0.03869077190756798,
0.0135481683537364,
-0.04585033282637596,
0.02092883735895157,
0.04833688586950302,
-0.0844128429889679,
-0.01780208759009838,
0.0037751535419374704,
-0.01858966052532196,
0.01624150574207306,
0.031193071976304054,
-0.02032501995563507,
0.048550400882959366,
0.01705310121178627,
0.0594521202147007,
0.031362567096948624,
-0.003789597423747182,
-0.031443335115909576,
0.07838764786720276,
-0.0210610032081604,
-0.018883438780903816,
-0.052060749381780624,
-0.05470986291766167,
-0.008667754009366035,
0.02286745049059391,
0.018763696774840355,
-0.07441502809524536,
-0.020661335438489914,
-0.023282237350940704,
-0.011164268478751183,
0.0046586450189352036,
-0.0019158214563503861,
-0.03878885880112648,
-0.028084777295589447,
-0.011904105544090271,
0.01967501826584339,
-0.009439724497497082,
-0.028150422498583794,
0.03482675924897194,
0.016059860587120056,
-0.042330365628004074,
-0.030195655301213264,
0.0011822469532489777,
-0.0535186342895031,
0.008710857480764389,
0.029613351449370384,
0.10697834193706512,
-0.018843797966837883,
-0.028865216299891472,
-0.035489533096551895,
-0.04272754117846489,
-0.005706149153411388,
0.0049148909747600555,
-0.04550275206565857,
-0.07353824377059937,
-0.04426848143339157,
-0.0437491200864315,
0.017253976315259933,
0.033051520586013794,
0.042709268629550934,
0.022213155403733253,
-0.030146313831210136,
-0.015224247239530087,
-0.038220230489969254,
-0.022266585379838943,
0.02733970619738102,
-0.01564798131585121,
-0.00758574903011322,
-0.06755666434764862,
0.034187737852334976,
0.015393469482660294,
-0.008613133803009987,
-0.013701066374778748,
-0.014993946067988873,
0.018088338896632195,
-0.0293353833258152,
-0.013807750307023525,
-0.025609450414776802,
-0.0015539044979959726,
0.06940822303295135,
0.009184466674923897,
-0.042221780866384506,
-0.03922126069664955,
-0.09909369051456451,
0.012305465526878834,
-0.01295875757932663,
-0.0321650356054306,
-0.07196010649204254,
-0.010108311660587788,
-0.03900914639234543,
0.061088867485523224,
0.007530536036938429,
0.039097387343645096,
0.004805445205420256,
0.012635230086743832,
0.015154926106333733,
0.0071728285402059555,
-0.020668599754571915,
-0.03186510130763054,
0.043243229389190674,
0.011651303619146347,
-0.05198098346590996,
-0.02884901873767376,
0.012323337607085705,
0.061172690242528915,
0.06814869493246078,
-0.023944566026329994,
0.0031824654433876276,
0.007555201184004545,
-0.00504703726619482,
-0.00492656696587801,
-0.010033287107944489,
-0.01846783235669136,
-0.00243582297116518,
-0.030549541115760803,
-0.019160524010658264,
-0.0031011980026960373,
0.03351207822561264,
-0.0014115843223407865,
0.06463800370693207,
-0.0032414509914815426,
-0.05332155153155327,
0.010323956608772278,
-0.01863599568605423,
-0.039320994168519974,
-0.017708629369735718,
0.003718853462487459,
-0.015404635109007359,
-0.017288127914071083,
0.02226911298930645,
0.042938232421875,
-0.017567051574587822,
0.046826522797346115,
0.010265225544571877,
0.02496136911213398,
-0.0708354264497757,
-0.04769950732588768,
0.016153637319803238,
-0.015820419415831566,
0.010467317886650562,
0.015153627842664719,
-0.0010371434036642313,
0.0191450547426939,
0.036729712039232254,
-0.015387823805212975,
-0.040734514594078064,
-0.005947658326476812,
-0.059297140687704086,
0.007136845029890537,
0.07719172537326813,
-0.020278364419937134,
-0.05360473692417145,
0.01713959500193596,
-0.011703857220709324,
-0.026477715000510216,
0.0321134552359581,
-0.0024684735108166933,
-0.03583540767431259,
0.0217732023447752,
0.053237754851579666,
-0.04754025489091873,
0.0899573415517807,
-0.00776842562481761,
-0.008426938205957413,
-0.05046048387885094,
-0.021227683871984482,
0.00633055716753006,
0.04580125957727432,
-0.04323909059166908,
0.03493814915418625,
0.003915976267307997,
0.022700514644384384,
0.015154222957789898,
0.025716248899698257,
0.021216800436377525,
-0.03421603515744209,
-0.010005919262766838,
0.005274608265608549,
0.006544257048517466,
-0.07792918384075165,
0.06697635352611542,
-0.05996370315551758,
0.07706154882907867,
-0.02707626111805439,
0.016254011541604996,
-0.0033592390827834606,
0.011785212904214859,
0.031141895800828934,
-0.0363551527261734,
0.07285881042480469,
-0.0029505423735827208,
-0.019721340388059616,
0.056963738054037094,
-0.008893891237676144,
-0.05094254016876221,
-0.014289481565356255,
-0.013212389312684536,
0.04692875221371651,
0.012863470241427422,
-0.04652181267738342,
0.06410890072584152,
0.023929305374622345,
-0.015910325571894646,
-0.05793152377009392,
-0.023220442235469818,
0.05429543927311897,
0.031663697212934494,
-0.06314659118652344,
-0.034888748079538345,
-0.01890587992966175,
0.03264780715107918,
-0.01264872681349516,
-0.03479093685746193,
0.005744727794080973,
0.004789605271071196,
-0.06276960670948029,
-0.010199027135968208,
-0.0006217366317287087,
-0.021073125302791595,
-0.04317542165517807,
-0.04915652424097061,
-0.014523187652230263,
0.04323021322488785,
-0.0022539012134075165,
-0.006085309665650129,
-0.072929248213768,
0.017240969464182854,
-0.0030793827027082443,
-0.06724636256694794,
-0.03196778520941734,
-0.008693191222846508,
-0.014861391857266426,
0.03705810755491257,
0.018940143287181854,
-0.032698579132556915,
0.025434626266360283,
-0.04880374297499657,
0.004132676403969526,
0.0735652968287468,
-0.037354640662670135,
0.009223135188221931,
0.03908778354525566,
0.03907660394906998,
-0.04002790525555611,
-0.024711834266781807,
0.048790354281663895,
0.05136610567569733,
0.0210990309715271,
-0.0033803607802838087,
0.0018341107061132789,
0.019993314519524574,
0.0047272369265556335,
0.03877760097384453,
0.01805090345442295,
0.011983118951320648,
-0.01035380456596613,
0.024746472015976906,
0.03413081169128418,
0.0030891692731529474,
0.05189475417137146,
0.05195095017552376,
-0.029226163402199745,
-0.002821924863383174,
-0.010680287145078182,
-0.00310509349219501,
-0.017718924209475517,
-0.03771397843956947,
-0.02615112066268921,
-0.010194744914770126,
-0.021073367446660995,
-0.03980611637234688,
0.03480008989572525,
0.000752455263864249,
-0.009570332244038582,
-0.03267104923725128,
0.03608106076717377,
-0.009331314824521542,
0.014091920107603073,
-0.06018286198377609,
0.030750639736652374,
-0.009707864373922348,
0.01781967468559742,
-0.036572061479091644,
0.023186340928077698,
0.013979877345263958,
0.0046912492252886295,
-0.01796776056289673,
-0.01587892882525921,
-0.0843619853258133,
0.05997873470187187,
0.04156395047903061,
-0.06410089880228043,
-0.012493985705077648,
-0.007895808666944504,
-0.048855170607566833,
-0.0005278135649859905,
-0.006473858840763569,
-0.06073576956987381,
-0.025265827775001526,
0.019798889756202698,
0.03275381028652191,
0.017875727266073227,
0.02695368230342865,
0.005239252932369709,
-0.033841099590063095,
-0.043291449546813965,
-0.00504569336771965,
-0.029284605756402016,
-0.03251727670431137,
0.022166574373841286,
0.062167976051568985,
-0.05481352284550667,
-0.01357484795153141,
0.01968146488070488,
-0.023748531937599182,
0.06467299908399582,
-0.05564653500914574,
-0.04641003906726837,
0.050868820399045944,
0.0016229827888309956,
0.033051881939172745,
-0.008074995130300522,
-0.020472027361392975,
-0.0003209981950931251,
-0.06224576756358147,
-0.026037342846393585,
0.02334352768957615,
0.06844710558652878,
0.027620233595371246,
-0.002327719936147332,
-0.05588918924331665,
0.030574556440114975,
0.02527690678834915,
-0.013249343261122704,
0.032997146248817444,
0.03076336160302162,
0.05391624569892883,
-0.01927279494702816,
0.006818684283643961,
-0.038745585829019547,
0.04800748825073242,
0.006722972262650728,
0.051126837730407715,
-0.04384147748351097,
-0.03920299932360649,
-0.02617170661687851,
0.010220581665635109,
0.02762105129659176,
0.054283007979393005,
0.012561502866446972,
0.06261193007230759,
-0.005959511734545231,
-0.025849148631095886,
-0.04769432544708252,
0.032193299382925034,
-0.01060368400067091,
0.05589934065937996,
0.01724754087626934,
-0.006384618580341339,
-0.05086098238825798,
0.01906285621225834,
-0.005920209921896458,
-0.018037743866443634,
0.0015837345272302628,
0.059084706008434296,
-0.000882041291333735,
-0.02212403528392315,
0.019703786820173264,
0.0399957001209259,
0.02631409652531147,
-0.03757995739579201,
0.02526593767106533,
0.011721592396497726,
0.013100942596793175,
-0.014234599657356739,
-0.03714536130428314,
-0.020383307710289955,
0.007986742071807384,
-0.011790993623435497,
-0.008023378439247608,
0.0008092998759821057,
0.020009402185678482,
0.007383919786661863,
-0.06783569604158401,
0.045764025300741196,
0.023663390427827835,
0.06247180700302124,
0.0006228750571608543,
-0.015865880995988846,
0.0092398002743721,
0.0062372516840696335,
-0.06286705285310745,
0.009456630796194077,
0.01969427429139614,
0.039569564163684845,
-0.10262394696474075,
-0.028700225055217743,
0.047756925225257874,
0.0009098422015085816,
0.043761663138866425,
0.03303753212094307,
-0.04403860867023468,
-0.015097346156835556,
0.005611237604171038,
0.054571203887462616,
0.027783982455730438,
-0.04182787984609604,
0.001577163813635707,
-0.060425832867622375,
-0.020582767203450203,
-0.027640732005238533,
0.0046836938709020615,
0.080775186419487,
0.003081314032897353,
0.0036390742752701044,
0.021487422287464142,
-0.011990014463663101,
-0.06731466203927994,
-0.015280753374099731,
0.008269512094557285,
-0.07694775611162186,
-0.004114370793104172,
-0.029645690694451332,
-0.013017146848142147,
0.04065675660967827,
-0.0026264458429068327,
0.014392117038369179,
-0.022514890879392624,
-0.03323983773589134,
0.012277481146156788,
-0.04975942149758339,
-0.00865702610462904,
0.05617554485797882,
0.03372317552566528,
-0.05774650722742081,
-0.009709404781460762,
0.02004161849617958,
0.00323312496766448,
0.041601210832595825,
0.019266583025455475,
-0.0009541098843328655,
-0.02632198855280876,
-0.045442331582307816,
0.0010499658528715372,
0.04769420251250267,
0.016173971816897392,
0.0014040454989299178,
-0.02712865360081196,
-0.006814480759203434,
0.01790941134095192,
0.022924134507775307,
0.06204758957028389,
-0.00778580317273736,
-0.04944929853081703,
0.0017076906515285373,
-0.0383993498980999,
0.034733761101961136,
-0.03258255124092102,
0.00809966679662466,
-0.055969927459955215,
0.07481102645397186,
-0.009904053993523121,
0.01592577062547207,
-0.07483897358179092,
0.011813610792160034,
0.010450458154082298,
-0.027109500020742416,
-0.021285774186253548,
-0.0338984951376915,
-0.0025437739677727222,
-0.06405870616436005,
-0.016038544476032257,
-0.042998749762773514,
-0.019267642870545387,
-0.03019081801176071,
0.09072244167327881,
-0.011315192095935345,
-0.013715064153075218,
-0.000489701924379915,
-0.061678797006607056,
0.04408944770693779,
-0.049323420971632004,
0.03982606530189514,
-0.0026422077789902687,
0.015348090790212154,
0.026939520612359047,
-0.02525550313293934,
0.053123533725738525,
-0.02792343869805336,
0.00017440778901800513,
0.0008980532875284553,
-0.025244129821658134,
-0.014840442687273026,
-0.028999168425798416,
-0.02150581404566765,
0.030930830165743828,
-0.0020794265437871218,
-0.00863700546324253,
0.02553550712764263,
-0.016809795051813126,
0.06526512652635574,
0.039226893335580826,
-0.05485868826508522,
0.021535877138376236,
0.033030398190021515,
0.019284075126051903,
0.04690862447023392,
0.016628026962280273,
-0.030121443793177605,
-0.033054616302251816,
0.0576547347009182,
0.0026838595513254404,
-0.04049956426024437,
-0.040907133370637894,
0.0008217202848754823
] |
<p>It is well-known that Hooke's Law is only approximately true and thus that linear relation
is merely an idealization not strictly corresponding to the reality. Wouldn't it be necessary/appropriate that all linear relations decribing physical phenomena be reformulated to contain non-linear terms for use in cases where higher accuracy is desired? In particular, what would oppose Maxwell's Equations eventually being modified to have non-linear terms? (Or put in other words, why these equations "must" be linear?)</p>
|
g2476
|
[
-0.016501741483807564,
-0.01695733517408371,
0.013801169581711292,
-0.006603732705116272,
-0.006297619082033634,
-0.02263478934764862,
0.01138339750468731,
0.03850265592336655,
-0.01634656824171543,
0.0037921061739325523,
0.03508135676383972,
-0.039317287504673004,
-0.01602214388549328,
0.013247968629002571,
-0.017585985362529755,
-0.01429848000407219,
0.03524143621325493,
0.0018041030270978808,
0.007358287926763296,
0.00788151379674673,
0.02190447226166725,
0.0263249222189188,
0.02272943966090679,
-0.035365182906389236,
-0.07880440354347229,
-0.04922869801521301,
-0.028148066252470016,
-0.01745498739182949,
-0.060529615730047226,
0.008976548910140991,
0.09775333106517792,
-0.015866631641983986,
-0.002018735045567155,
0.004155902191996574,
-0.06948008388280869,
-0.004088300280272961,
-0.022879144176840782,
0.013528799638152122,
0.07841658592224121,
-0.004662752617150545,
0.048940133303403854,
0.0021617994643747807,
0.005990677047520876,
-0.00562345189973712,
-0.021861255168914795,
-0.038203127682209015,
-0.018227247521281242,
-0.004744880832731724,
0.02523821033537388,
-0.029616203159093857,
0.014907442033290863,
-0.03747336566448212,
0.07896110415458679,
0.01924172416329384,
0.07108613848686218,
0.05287633463740349,
0.04191585257649422,
0.013921919278800488,
0.06413039565086365,
-0.03086470067501068,
0.009799237363040447,
0.005647932644933462,
-0.024319106712937355,
0.008308223448693752,
0.03457197919487953,
-0.019619084894657135,
-0.016857020556926727,
-0.03190623223781586,
-0.02768073044717312,
-0.024730198085308075,
-0.002049677772447467,
-0.059989381581544876,
-0.02370375022292137,
-0.041313525289297104,
0.018295733258128166,
0.02024841122329235,
0.008689484558999538,
0.01490514725446701,
-0.03177393600344658,
-0.0015610724221915007,
-0.03015461005270481,
0.010982468724250793,
0.063663050532341,
0.026983367279171944,
0.13187944889068604,
-0.011881137266755104,
0.08011525124311447,
0.0038554684724658728,
0.01459433976560831,
-0.020508358255028725,
0.03042554296553135,
-0.002440680516883731,
0.06973661482334137,
0.023657428100705147,
-0.06325849145650864,
-0.016270533204078674,
-0.026620477437973022,
-0.012676239013671875,
0.06783168017864227,
0.028680874034762383,
-0.021194718778133392,
-0.004345163702964783,
0.008873570710420609,
-0.015243913978338242,
-0.018556678667664528,
0.04029364138841629,
0.050485506653785706,
0.06560458242893219,
-0.006403203122317791,
-0.04639023169875145,
-0.04021258279681206,
0.028543787077069283,
0.0014071399345993996,
0.005546647123992443,
-0.04139338433742523,
-0.06548847258090973,
0.04265127703547478,
-0.020210739225149155,
0.03984552621841431,
0.0954970195889473,
0.04313528165221214,
-0.0005918214446865022,
0.09617724269628525,
0.04299138858914375,
-0.0175075214356184,
-0.05815048888325691,
0.03302234411239624,
0.059904009103775024,
0.08071158081293106,
-0.08155492693185806,
0.01132285874336958,
0.007869320921599865,
-0.04494635388255119,
0.008974502794444561,
-0.02928422950208187,
-0.039986204355955124,
0.004259825684130192,
-0.046002235263586044,
0.019496044144034386,
-0.035970598459243774,
0.022040966898202896,
-0.05217750743031502,
0.051572658121585846,
-0.0016842035111039877,
-0.03570786863565445,
0.017028475180268288,
-0.00729838851839304,
0.03075225278735161,
0.03275502473115921,
0.040008772164583206,
-0.03563058376312256,
0.04186577722430229,
0.04661612957715988,
-0.06625988334417343,
-0.035510607063770294,
0.03071776032447815,
0.022641604766249657,
-0.02008730173110962,
-0.009228488430380821,
-0.06489850580692291,
0.0636306181550026,
-0.033896878361701965,
-0.028150733560323715,
0.004567926283925772,
-0.054565027356147766,
0.023777522146701813,
-0.05242113023996353,
-0.04889273643493652,
-0.0185586828738451,
0.004194637294858694,
0.011817499995231628,
0.035460762679576874,
-0.015266180969774723,
0.06044236198067665,
0.02283347398042679,
0.06620484590530396,
0.03461587429046631,
0.008566963486373425,
-0.026284705847501755,
-0.032248642295598984,
-0.03344858065247536,
0.01167962234467268,
0.042196325957775116,
0.012165085412561893,
-0.02513848803937435,
0.027093078941106796,
0.023486122488975525,
-0.03339952230453491,
-0.01583019644021988,
-0.003832134883850813,
-0.014300049282610416,
-0.000060609992942772806,
-0.11094504594802856,
0.008798059076070786,
-0.01023982185870409,
0.03928522765636444,
-0.001342421630397439,
0.045816436409950256,
-0.058067549020051956,
-0.01617051102221012,
-0.010982456617057323,
0.0543745793402195,
0.020622288808226585,
0.003054619301110506,
-0.018490789458155632,
0.0074975378811359406,
-0.006728567648679018,
-0.00009839738777372986,
0.036395363509655,
0.004311808850616217,
0.06985192000865936,
-0.039987292140722275,
-0.0032971645705401897,
-0.0178544819355011,
-0.060657937079668045,
-0.07383397221565247,
0.013280931860208511,
0.020016951486468315,
-0.040137410163879395,
0.0429503358900547,
-0.06312748789787292,
0.013370038010179996,
0.0008485255530104041,
0.028610674664378166,
-0.01425972394645214,
-0.023094244301319122,
0.03886525705456734,
-0.013884903863072395,
0.005733073223382235,
-0.013589895330369473,
0.0258615855127573,
-0.03642028197646141,
-0.019307896494865417,
0.021115945652127266,
0.016172239556908607,
0.07160160690546036,
0.0065049584954977036,
-0.06742790341377258,
0.0662737488746643,
0.013987408019602299,
0.009942823089659214,
0.02702106349170208,
-0.022817503660917282,
0.024184895679354668,
0.0037639900110661983,
-0.013589009642601013,
0.05492541566491127,
0.0075047691352665424,
-0.014574366621673107,
-0.012907197698950768,
0.019683068618178368,
-0.014238307252526283,
-0.040823809802532196,
0.04259359836578369,
0.0014073823112994432,
-0.0038719093427062035,
0.02872263826429844,
0.035615019500255585,
-0.0030105356127023697,
0.014699487946927547,
0.0410347506403923,
-0.023886263370513916,
-0.020235544070601463,
-0.021316014230251312,
-0.08510489761829376,
-0.0032912567257881165,
-0.048033472150564194,
0.059073083102703094,
0.06383867561817169,
0.03147536516189575,
0.00031650959863327444,
0.011770271696150303,
-0.0012649245327338576,
0.010370406322181225,
0.030310314148664474,
-0.05868319422006607,
-0.03801923245191574,
-0.020402269437909126,
0.03325026482343674,
0.024497797712683678,
0.000579030136577785,
0.013481474481523037,
-0.023001758381724358,
-0.029470624402165413,
0.03030482307076454,
-0.10229755938053131,
0.004209914244711399,
-0.026780620217323303,
-0.0031350990757346153,
0.009168834425508976,
-0.06613792479038239,
-0.011678926646709442,
0.014893503859639168,
-0.035978931933641434,
-0.07230652868747711,
0.043746620416641235,
0.009534440003335476,
-0.029976392164826393,
-0.010064410045742989,
0.032484788447618484,
0.02069522999227047,
0.037225160747766495,
0.0019448992097750306,
0.06041964143514633,
-0.017032034695148468,
0.055808547884225845,
-0.060117557644844055,
-0.057937003672122955,
0.018605630844831467,
0.019824029877781868,
0.017874186858534813,
0.035503413528203964,
-0.016449471935629845,
-0.025260400027036667,
-0.03745236620306969,
0.024372216314077377,
0.0465613454580307,
0.05332712084054947,
0.023704908788204193,
0.014356809668242931,
-0.011874985881149769,
-0.07039521634578705,
-0.038636256009340286,
-0.06075908988714218,
0.06294912844896317,
0.004525742959231138,
-0.02982427552342415,
-0.03143244609236717,
-0.029927507042884827,
0.006213825196027756,
0.02346663549542427,
0.00044144451385363936,
0.04381207004189491,
-0.02711072377860546,
-0.05167878791689873,
-0.08307928591966629,
-0.0018290085718035698,
-0.007562169339507818,
0.032498110085725784,
0.008457421325147152,
0.006018213927745819,
0.013727609068155289,
-0.10296585410833359,
-0.006014076992869377,
0.033268559724092484,
0.0059990230947732925,
-0.016402844339609146,
0.012144436128437519,
0.015972305089235306,
-0.0811455249786377,
0.014556245878338814,
-0.023291505873203278,
0.03128153458237648,
0.05273124575614929,
-0.012572531588375568,
0.020890872925519943,
0.053876351565122604,
0.003489087335765362,
0.03469385579228401,
-0.02931932359933853,
0.00410107895731926,
-0.00986720435321331,
-0.021121948957443237,
0.030211908742785454,
0.00315812393091619,
0.05773627758026123,
0.024854442104697227,
0.09025317430496216,
-0.10268764942884445,
-0.047879189252853394,
-0.034704193472862244,
-0.014246734790503979,
-0.015472021885216236,
0.003652384504675865,
0.059887517243623734,
-0.03438573703169823,
0.02424543909728527,
0.020671427249908447,
-0.08169694244861603,
-0.012241530232131481,
0.025301234796643257,
0.05153833329677582,
-0.044163577258586884,
0.005946510471403599,
-0.004042683634907007,
-0.04334995150566101,
0.01990051381289959,
0.006642316002398729,
0.006295597180724144,
0.024975968524813652,
-0.02493930049240589,
-0.004204331897199154,
0.0235932357609272,
-0.06098415330052376,
0.004367412067949772,
-0.02142168954014778,
-0.01638817973434925,
-0.038349322974681854,
0.001547063235193491,
-0.03376461938023567,
0.001928401063196361,
0.008352608419954777,
0.035494111478328705,
0.05923366919159889,
0.032580748200416565,
-0.01908775232732296,
0.00023364862136077136,
-0.03013531304895878,
-0.002497634384781122,
-0.05290208011865616,
-0.026951242238283157,
-0.01051247213035822,
-0.012918828055262566,
-0.04470616206526756,
0.030929401516914368,
0.020170098170638084,
-0.0071446155197918415,
-0.08391734212636948,
0.049231164157390594,
0.02713759057223797,
0.040864404290914536,
0.011570741422474384,
-0.045716073364019394,
-0.016893180087208748,
0.03821805119514465,
0.00975110288709402,
0.055101051926612854,
-0.03310858830809593,
0.01194840855896473,
-0.02251138538122177,
-0.0010190987959504128,
-0.006892352364957333,
-0.0024672148283571005,
-0.03403978422284126,
-0.041906844824552536,
-0.05068480223417282,
-0.013137093745172024,
0.0706637054681778,
0.00866050086915493,
0.021407712250947952,
-0.014610068872570992,
0.022311704233288765,
0.07002966850996017,
-0.042267393320798874,
-0.021195854991674423,
0.055363550782203674,
0.01268472895026207,
-0.02858842723071575,
-0.04408782348036766,
0.020371362566947937,
-0.010867299512028694,
0.028847087174654007,
0.05570268630981445,
-0.04338132590055466,
0.036288853734731674,
-0.021372409537434578,
-0.057278115302324295,
0.01166767068207264,
-0.025996049866080284,
0.000325443601468578,
0.001344968331977725,
0.02734437771141529,
-0.01012662798166275,
0.043030496686697006,
0.005272421054542065,
0.04318485036492348,
-0.030862541869282722,
0.008546655997633934,
-0.03632420301437378,
-0.02446860261261463,
-0.002861856948584318,
0.037589918822050095,
0.017631426453590393,
0.038465049117803574,
-0.02301069349050522,
-0.010407652705907822,
-0.01702464558184147,
-0.01589999534189701,
-0.11930197477340698,
-0.034808821976184845,
-0.0454786978662014,
0.025817984715104103,
0.047900427132844925,
0.048025328665971756,
-0.044000718742609024,
0.004629577975720167,
0.009219324216246605,
0.01689065434038639,
0.0323285274207592,
0.015311148017644882,
0.048350684344768524,
0.05332685634493828,
-0.022799786180257797,
-0.028836388140916824,
-0.06915076076984406,
0.019152170047163963,
0.028163155540823936,
0.020635081455111504,
-0.04305510222911835,
0.02854212187230587,
-0.09315178543329239,
0.021611901000142097,
0.008206160739064217,
-0.007017355877906084,
-0.01618446409702301,
0.06491792947053909,
0.052718617022037506,
-0.012324188835918903,
0.029971469193696976,
-0.01357443816959858,
0.06639879196882248,
0.04123435541987419,
0.006098221987485886,
0.014649526216089725,
0.009635030291974545,
0.00675004068762064,
-0.002440717304125428,
-0.03506927192211151,
-0.01284720003604889,
-0.033340901136398315,
0.061367880553007126,
-0.047021377831697464,
0.045231252908706665,
0.0002275157894473523,
-0.03333977237343788,
0.0347258523106575,
0.04478088393807411,
-0.03765474632382393,
0.06720041483640671,
0.031149448826909065,
-0.017462804913520813,
0.06790637224912643,
0.01782883144915104,
-0.04184693098068237,
0.004829049110412598,
-0.036528024822473526,
0.001170497853308916,
0.039380993694067,
0.04472455009818077,
0.03184422850608826,
-0.030785562470555305,
-0.03480445221066475,
0.07974468171596527,
0.031591180711984634,
0.02983897365629673,
-0.01946021057665348,
0.07037145644426346,
0.08436411619186401,
0.010288733057677746,
-0.027248863130807877,
-0.03198658674955368,
-0.05970556288957596,
-0.018879489973187447,
0.0037333713844418526,
0.012914123013615608,
-0.010376146994531155,
-0.00737595371901989,
-0.03001873753964901,
-0.029101405292749405,
-0.006538390647619963,
0.005917091853916645,
0.03102250024676323,
-0.0019872437696903944,
-0.015975341200828552,
-0.007551697548478842,
-0.04641087353229523,
-0.007257787976413965,
-0.0030841308180242777,
0.04061466455459595,
0.015391657128930092,
-0.003876120550557971,
-0.037964582443237305,
0.0022912248969078064,
0.017767366021871567,
0.00969944428652525,
-0.03940972685813904,
-0.048305388540029526,
-0.02083267644047737,
-0.03405214473605156,
0.006608964409679174,
-0.07841180264949799,
-0.03927825018763542,
0.010161593556404114,
-0.04925867170095444,
-0.061842285096645355,
0.0007761447341181338,
-0.051718469709157944,
0.03012694977223873,
0.03965488448739052,
-0.005393646191805601,
0.011172900907695293,
-0.005957168526947498,
-0.017696978524327278,
-0.01245275977998972,
0.007562186568975449,
-0.018512172624468803,
0.01812221109867096,
-0.016716616228222847,
0.0393114797770977,
0.0022878407035022974,
-0.0012493239482864738,
-0.04217694699764252,
0.011185375042259693,
0.005330819170922041,
0.051322102546691895,
0.017614662647247314,
-0.00844122376292944,
0.06514868885278702,
0.02980145439505577,
-0.007213206496089697,
-0.02854962646961212,
0.024252999573946,
-0.022900933399796486,
-0.047235649079084396,
-0.0005501818377524614,
-0.003232961054891348,
-0.0006390938651748002,
0.014802176505327225,
-0.06328178942203522,
-0.008584616705775261,
-0.03708135336637497,
-0.039801474660634995,
0.0038962007965892553,
0.061095718294382095,
-0.023239651694893837,
0.010982037521898746,
-0.014509783126413822,
0.00840537529438734,
0.02928031235933304,
-0.006566881202161312,
0.012091579847037792,
-0.024376023560762405,
-0.005892669316381216,
-0.010734076611697674,
0.04171326011419296,
0.02309485338628292,
-0.04281672462821007,
-0.027912510558962822,
-0.017628910019993782,
0.008073585107922554,
-0.04761936515569687,
-0.01729416288435459,
0.03477385267615318,
-0.010136803612112999,
-0.02639474906027317,
-0.05421048402786255,
0.025755859911441803,
-0.014813310466706753,
-0.09085651487112045,
0.004687219858169556,
0.018802421167492867,
-0.035079557448625565,
0.013384189456701279,
0.00800466351211071,
-0.014617502689361572,
-0.017384320497512817,
0.01858052797615528,
0.03745492920279503,
0.040062688291072845,
-0.037158410996198654,
-0.06546274572610855,
-0.02092929370701313,
0.057197753340005875,
-0.011867305263876915,
0.041771914809942245,
-0.007334930822253227,
0.033330805599689484,
-0.04729282483458519,
0.016768211498856544,
0.013099269941449165,
0.037780046463012695,
-0.029244370758533478,
0.05870390310883522,
-0.024711035192012787,
-0.013241534121334553,
0.02016393095254898,
0.009344401769340038,
-0.03986194357275963,
-0.03347303718328476,
0.01614115573465824,
0.0028818617574870586,
0.014653047546744347,
0.05645010992884636,
-0.040878940373659134,
-0.04277350381016731,
0.027334999293088913,
0.008667202666401863,
0.02303800918161869,
0.00433427095413208,
-0.007779105566442013,
-0.01798543706536293,
-0.00025633169570937753,
0.03222664073109627,
-0.05989845469594002,
0.00435098260641098,
0.006367230787873268,
0.024633968248963356,
-0.006844758056104183,
0.01718875765800476,
-0.019499432295560837,
0.01961272396147251,
0.02169813960790634,
-0.0649804100394249,
-0.031841348856687546,
0.018378162756562233,
-0.016975587233901024,
-0.010456648655235767,
-0.04100973904132843,
-0.013462381437420845,
0.051592402160167694,
-0.06525605916976929,
0.051154036074876785,
0.05417368933558464,
0.03162619471549988,
0.08217356353998184,
-0.011772939935326576,
0.01881999336183071,
-0.020182820037007332,
-0.04490261897444725,
-0.0377025231719017,
-0.012453729286789894,
0.0634813979268074,
-0.01664768159389496,
0.004824798088520765,
0.03171859309077263,
0.009177603758871555,
0.023463189601898193,
-0.056746456772089005,
-0.055239830166101456,
-0.025227829813957214,
0.011922012083232403,
-0.007688712794333696,
0.04338539019227028,
0.052864328026771545,
-0.07505600154399872,
-0.01597166620194912,
-0.00975525937974453,
0.045805592089891434,
0.005506371147930622,
-0.02165328525006771,
-0.010272311046719551,
-0.07398498058319092,
0.04011740908026695,
-0.054963476955890656,
0.006881602108478546,
-0.007676991634070873,
-0.01630707085132599,
0.009734724648296833,
0.05309159308671951,
0.016018370166420937,
-0.039250921458005905,
0.05381757393479347,
-0.028338003903627396,
0.022832032293081284,
0.02311369590461254,
-0.01011180691421032,
-0.023142818361520767,
0.06161786988377571,
0.035265594720840454,
0.020503543317317963,
0.015794668346643448,
-0.026372887194156647,
-0.0018016272224485874,
-0.027288783341646194,
-0.027774441987276077,
-0.0043813143856823444,
-0.060089025646448135,
0.03228352218866348
] |
<p>I spent some time studying about temperatures and color of objects. It turns out that as we heat something it turns to red, then yellowish white and if we heat it more it turns to bluish-white.</p>
<p>Like we can say a blue star is hotter than a red star.
But why isn't it the same with flames?</p>
<p>Blue flame isn't always hotter than a red flame. It's just the chemistry of it all. </p>
<p>I mean I know the electrons jump from one orbit to another and gets into excited state when heated.</p>
<p>But the questions in my mind are:</p>
<ol>
<li><p>If one object appears blue and another red, that doesn't always mean that the blue object is hotter than red. Is that correct? If yes then how is it so? I am sorry but I'm bit confused over it.</p></li>
<li><p>With the "Color Temperature" concept on Wikipedia. They say 1,700 K to match a flame. But 15,000–27,000 K for a clear blue poleward sky.</p></li>
</ol>
<p>This confuses me. The sky appears blue, does that mean its hot? But it isn't right? It's colder. I am not sure if I'm able to frame it properly. It's a bit confusing to me.</p>
<p>Is this something like a glowing object vs reflecting object?
The sun is white but Earth is blue. But sun is hotter than the earth. It's the sun radiating light but earth is just scattering it.</p>
<p>But the surface temperature of sun is 5778K while the Wikipedia states our sky is about 15000K-27000... I know there's something I'm missing here. I'm hoping someone can tell me what is it.</p>
|
g2477
|
[
0.02879944071173668,
0.005139696411788464,
0.01647312566637993,
-0.020646987482905388,
0.08977710455656052,
0.005834479350596666,
-0.05575883388519287,
0.037282656878232956,
-0.019912730902433395,
-0.07848132401704788,
0.018347222357988358,
0.06000635027885437,
0.05877383053302765,
0.030523117631673813,
0.03859742358326912,
-0.02476593852043152,
0.006453292910009623,
-0.04268086701631546,
0.004056398756802082,
0.02433648519217968,
0.004454837180674076,
0.012284543365240097,
0.02330631949007511,
-0.028937295079231262,
-0.05630024895071983,
-0.03237859532237053,
-0.03617589548230171,
-0.011680095456540585,
0.02618909813463688,
-0.04460249841213226,
-0.0012862576404586434,
0.047809429466724396,
0.047519318759441376,
-0.01748291775584221,
0.02951183170080185,
-0.03873402997851372,
0.009545586071908474,
-0.01657123677432537,
-0.004770832136273384,
-0.014606678858399391,
0.019700653851032257,
0.029976993799209595,
0.04988089203834534,
0.0088566979393363,
0.025861049070954323,
-0.014360186643898487,
-0.05598156526684761,
0.012417363934218884,
0.05317019671201706,
0.04999902471899986,
-0.01414627954363823,
0.05956537649035454,
0.001629522768780589,
0.010587888769805431,
0.018719060346484184,
-0.027592899277806282,
0.007956501096487045,
-0.03264414519071579,
0.02680807374417782,
0.012348460964858532,
0.0016908958787098527,
0.027615373954176903,
-0.020730551332235336,
-0.015584466978907585,
0.022407611832022667,
0.004392286762595177,
-0.04784996435046196,
-0.0035499553196132183,
0.00623434828594327,
0.01713499054312706,
-0.008018631488084793,
0.030957205221056938,
-0.04623318463563919,
0.008434229530394077,
-0.0200781412422657,
-0.004044890869408846,
-0.013729616068303585,
-0.033737000077962875,
0.010819311253726482,
0.03494013100862503,
0.027885375544428825,
0.012244082055985928,
0.0030427586752921343,
0.030756520107388496,
0.05640561506152153,
-0.010534894652664661,
-0.017526250332593918,
0.02534857578575611,
-0.0026332843117415905,
-0.04522170126438141,
-0.010898875072598457,
0.007708435412496328,
0.10184194892644882,
0.026248184964060783,
0.012115038000047207,
-0.009153054095804691,
-0.0165172778069973,
0.012408738024532795,
-0.039399176836013794,
0.02543911524116993,
-0.034346289932727814,
-0.011489968746900558,
0.02700721099972725,
0.012870212085545063,
0.020245136693120003,
-0.05336613208055496,
-0.028110409155488014,
-0.0011769735720008612,
-0.07764153927564621,
0.003950550686568022,
-0.03209733963012695,
-0.027264796197414398,
-0.05164409056305885,
-0.04044870659708977,
-0.05554034933447838,
0.022640328854322433,
0.03907744213938713,
0.00787324644625187,
0.030207037925720215,
0.0852823480963707,
0.057066649198532104,
0.05698645859956741,
0.02527759037911892,
0.02318659983575344,
0.006907173432409763,
-0.047662511467933655,
0.032133039087057114,
-0.09454803168773651,
-0.018551146611571312,
-0.03766247630119324,
-0.02760493755340576,
0.002854206832125783,
-0.0399014875292778,
0.03035411238670349,
0.02518881857395172,
-0.008757328614592552,
0.022327499464154243,
-0.010440828278660774,
-0.02269737981259823,
0.02533077821135521,
0.07744494080543518,
-0.014027195982635021,
0.0012853287626057863,
-0.07706949859857559,
-0.04876657575368881,
0.018991557881236076,
-0.03238867595791817,
-0.027479659765958786,
0.0907699316740036,
0.00011585511674638838,
0.03315482288599014,
0.03095906227827072,
0.04713894799351692,
-0.027638737112283707,
-0.03127461299300194,
-0.04416489973664284,
0.03351426124572754,
-0.00757308304309845,
0.031023580580949783,
-0.004588249605149031,
0.03674289211630821,
-0.0418144091963768,
0.01634138636291027,
-0.0026382384821772575,
-0.019151680171489716,
-0.009150058031082153,
0.003441960085183382,
-0.03363911807537079,
-0.01707581989467144,
-0.03293986991047859,
-0.03941931203007698,
-0.007916577160358429,
-0.04293306916952133,
0.008296532556414604,
0.009258879348635674,
-0.03792836517095566,
0.05642963945865631,
0.04088599979877472,
-0.0321049839258194,
-0.04494535177946091,
-0.05998501181602478,
-0.049824491143226624,
0.023432297632098198,
-0.017967870458960533,
0.034391604363918304,
0.018849823623895645,
-0.03839309513568878,
-0.041196174919605255,
0.035678185522556305,
0.08899787813425064,
-0.06320458650588989,
-0.06394653767347336,
0.02733246609568596,
-0.002091269474476576,
0.04574261233210564,
-0.07059919089078903,
-0.026038849726319313,
0.017765751108527184,
-0.08459202945232391,
0.011100029572844505,
0.005049760453402996,
0.0007664241711609066,
-0.019659601151943207,
0.02733384445309639,
0.0280908215790987,
0.0440903976559639,
-0.0135823804885149,
0.028328968212008476,
0.007553465198725462,
-0.016848783940076828,
0.010542419739067554,
-0.038154516369104385,
0.05138499289751053,
0.06799102574586868,
0.017733199521899223,
0.05173217132687569,
-0.012663422152400017,
0.005322653334587812,
-0.03312766179442406,
-0.0558902807533741,
0.02532641775906086,
-0.03384282439947128,
0.07806651294231415,
-0.06794119626283646,
-0.0369231142103672,
0.04536222666501999,
-0.07595102488994598,
0.0035070774611085653,
0.07910756766796112,
0.02587019093334675,
-0.0747438445687294,
0.005823215469717979,
0.03040536679327488,
0.02656431309878826,
0.059287313371896744,
-0.005289506167173386,
0.06278960406780243,
-0.03898690268397331,
0.03722532466053963,
0.03893047571182251,
-0.04701795056462288,
-0.03291735053062439,
-0.04021324962377548,
0.045623622834682465,
0.07075870037078857,
0.015961704775691032,
-0.017769457772374153,
-0.017614290118217468,
-0.0553569421172142,
0.03770378977060318,
0.014054539613425732,
0.035071663558483124,
-0.06758884340524673,
0.0281948521733284,
-0.04616905376315117,
-0.015313243493437767,
-0.07972664386034012,
0.051430825144052505,
-0.017891643568873405,
-0.03643875569105148,
-0.013663087971508503,
-0.022034235298633575,
0.0023192879743874073,
-0.015044532716274261,
-0.048212043941020966,
0.023429421707987785,
-0.0748223215341568,
-0.017440924420952797,
-0.02332320250570774,
-0.026884201914072037,
-0.02962651662528515,
-0.019536495208740234,
-0.028410861268639565,
-0.029983285814523697,
-0.00047495891340076923,
-0.015381335280835629,
-0.05325056612491608,
-0.028116434812545776,
0.01467518974095583,
-0.0412929467856884,
0.07888886332511902,
0.010901601985096931,
-0.05610256269574165,
-0.004054227843880653,
0.01812146045267582,
-0.009705917909741402,
-0.02527611516416073,
0.10015052556991577,
0.0172348041087389,
-0.03728153929114342,
0.018156245350837708,
0.04355137422680855,
0.03739261254668236,
0.02683078683912754,
-0.0467771515250206,
-0.002741672331467271,
0.018742525950074196,
0.0019743512384593487,
-0.015031440183520317,
-0.008574049919843674,
0.06542308628559113,
-0.07366771996021271,
0.0003193089796695858,
0.01363298762589693,
0.10666651278734207,
0.015046368353068829,
-0.08067096769809723,
-0.003110919613391161,
-0.032736603170633316,
0.0003097450826317072,
0.02243640087544918,
-0.019271887838840485,
-0.040872953832149506,
0.04977002739906311,
0.015060693956911564,
0.015771813690662384,
-0.05150321498513222,
0.03204162046313286,
0.04462088271975517,
-0.03351953253149986,
-0.01401570625603199,
-0.029213037341833115,
-0.003985836170613766,
-0.04769448935985565,
0.007295885123312473,
-0.004640903323888779,
-0.035313040018081665,
-0.032242000102996826,
-0.021296169608831406,
-0.0380903035402298,
-0.030244097113609314,
0.039472293108701706,
-0.005150176119059324,
-0.009227047674357891,
0.005164869129657745,
0.001149914925917983,
-0.01949930191040039,
-0.03464025631546974,
0.048700813204050064,
0.017211243510246277,
0.030978381633758545,
-0.03105020895600319,
-0.007561608217656612,
-0.030448205769062042,
0.05137552320957184,
0.02118244208395481,
-0.03556900843977928,
-0.015052025206387043,
-0.04016003757715225,
-0.020197324454784393,
0.01940029114484787,
-0.0006621971260756254,
0.06165701150894165,
-0.03875012695789337,
-0.03325644135475159,
-0.003270162036642432,
0.0006935425335541368,
0.030324416235089302,
-0.025689760223031044,
0.04621059447526932,
0.04031011089682579,
0.016097314655780792,
0.015878140926361084,
0.006643397267907858,
-0.01384166069328785,
-0.03643455728888512,
0.05808500573039055,
0.010010059922933578,
-0.006717848125845194,
-0.01191553846001625,
0.0016739313723519444,
0.0313991978764534,
-0.04364953935146332,
0.008660298772156239,
0.1015782281756401,
-0.02941708452999592,
0.051900818943977356,
0.013996418565511703,
-0.01150920893996954,
-0.0008033576887100935,
0.020738352090120316,
0.017461668699979782,
0.0111054927110672,
0.03500031679868698,
0.08860087394714355,
0.03506968170404434,
0.04160301759839058,
-0.043271150439977646,
0.0057107326574623585,
-0.12060096114873886,
0.019129982218146324,
-0.045438993722200394,
-0.016432203352451324,
0.01609642431139946,
0.059208545833826065,
-0.05580964311957359,
0.018147660419344902,
0.016219256445765495,
0.014150748029351234,
-0.022996868938207626,
-0.015184410847723484,
0.00836728885769844,
0.02935146726667881,
-0.07108453661203384,
-0.04565275460481644,
-0.01391481515020132,
0.020386774092912674,
-0.02792728878557682,
-0.03303501754999161,
-0.014688557013869286,
-0.013024634681642056,
0.061396557837724686,
-0.005526136606931686,
-0.03341376781463623,
-0.01188826747238636,
-0.02473890781402588,
0.02775164507329464,
0.04705050587654114,
0.03753865882754326,
0.010079429484903812,
0.013244244270026684,
-0.0077989595010876656,
0.003329990664497018,
-0.01663961634039879,
0.041161373257637024,
0.042718566954135895,
0.009609868749976158,
0.00619998574256897,
0.009443284943699837,
0.01957247406244278,
0.044274602085351944,
0.013731228187680244,
-0.04989272356033325,
0.046746689826250076,
-0.06722185760736465,
0.06230049952864647,
-0.011007298715412617,
0.05452539399266243,
0.002497429493814707,
0.03155222535133362,
0.03306998312473297,
0.03430880606174469,
-0.004557809326797724,
-0.012511709704995155,
0.03908524662256241,
-0.007973735220730305,
-0.015056123025715351,
0.0061615039594471455,
-0.037551045417785645,
-0.050392359495162964,
-0.03013862483203411,
0.02811688557267189,
-0.018603505566716194,
0.030528180301189423,
-0.03965184465050697,
-0.02823927253484726,
-0.018802106380462646,
0.046473268419504166,
-0.016632424667477608,
0.03984183818101883,
-0.02728221006691456,
-0.031461503356695175,
0.031345006078481674,
0.030906153842806816,
0.06215859204530716,
-0.014031982980668545,
-0.03998180478811264,
-0.0038628161419183016,
0.006816352717578411,
0.031214604154229164,
-0.012673109769821167,
0.034626107662916183,
-0.006565340794622898,
0.018312547355890274,
0.04201550409197807,
-0.002247435273602605,
0.022153392434120178,
-0.04769665002822876,
0.042993053793907166,
0.0029439942445605993,
-0.06031500920653343,
0.011426408775150776,
0.02980615943670273,
0.037634868174791336,
-0.046269744634628296,
0.04226616397500038,
-0.02448797971010208,
0.06015285849571228,
-0.0013787847710773349,
0.0164784025400877,
0.019457489252090454,
-0.036767635494470596,
0.01815054751932621,
0.011431928724050522,
-0.04337982460856438,
-0.009458326734602451,
-0.026398828253149986,
-0.0043899076990783215,
0.013010933995246887,
0.016068555414676666,
-0.014159069396555424,
0.04038383066654205,
-0.016730720177292824,
0.02174520492553711,
0.00803403090685606,
0.019638584926724434,
0.05053281411528587,
-0.07111459225416183,
0.024530356749892235,
0.02939695306122303,
0.022086573764681816,
-0.00948621891438961,
0.0011571976356208324,
0.014008225873112679,
-0.033272162079811096,
-0.041786499321460724,
-0.05284503102302551,
-0.014323689974844456,
0.08029331266880035,
-0.004224317613989115,
-0.05696508288383484,
-0.016961373388767242,
-0.0001621507399249822,
0.004463271703571081,
0.0007982582901604474,
0.025831375271081924,
0.021820472553372383,
0.006149784661829472,
0.02815195918083191,
0.031097998842597008,
0.037553805857896805,
0.059194885194301605,
0.015237459912896156,
0.011635147966444492,
-0.043129824101924896,
-0.009761746041476727,
-0.0006880406872369349,
0.000041023176891030744,
0.01169232651591301,
0.08904784917831421,
-0.004390159156173468,
-0.0007705799653194845,
-0.02726832963526249,
0.042877569794654846,
0.0416177473962307,
0.022417720407247543,
-0.03315702825784683,
-0.012388606555759907,
0.010844198986887932,
0.05106647312641144,
-0.00025098476908169687,
0.022392068058252335,
0.02219492569565773,
0.027405234053730965,
0.07379333674907684,
0.0060063861310482025,
-0.003028140403330326,
-0.007549259811639786,
-0.010689799673855305,
-0.031260956078767776,
-0.003781065810471773,
-0.03734702244400978,
0.028422197327017784,
0.02302604727447033,
0.06024262309074402,
-0.039966557174921036,
-0.005012663546949625,
-0.022333336994051933,
0.028485137969255447,
0.04167775437235832,
0.03695358708500862,
-0.005737527273595333,
0.010038805194199085,
-0.02508450485765934,
0.015179178677499294,
-0.007639351766556501,
-0.053792715072631836,
-0.03637814521789551,
-0.03509242460131645,
-0.02818174473941326,
0.0708436667919159,
0.020199434831738472,
-0.05808259919285774,
-0.0012807169696316123,
0.0002104297309415415,
0.008773629553616047,
0.0028241504915058613,
-0.029010407626628876,
-0.008152694441378117,
-0.03515554964542389,
0.020428171381354332,
-0.0032452340237796307,
0.0010350898373872042,
-0.008179163560271263,
-0.01957176998257637,
-0.03169567510485649,
-0.05459391698241234,
0.011058246716856956,
-0.07227141410112381,
-0.024157388135790825,
0.04332960397005081,
-0.023542147129774094,
0.04649479314684868,
-0.03199407830834389,
0.007824170403182507,
0.028838517144322395,
-0.008236092515289783,
-0.01683715172111988,
0.07192579656839371,
0.009132947772741318,
-0.01407165452837944,
0.0005922098644077778,
0.00353538291528821,
0.028098225593566895,
0.006986682768911123,
-0.04061638191342354,
0.00340538052842021,
0.019016506150364876,
0.025693153962492943,
-0.0051711974665522575,
0.006934191100299358,
-0.033602505922317505,
-0.020674709230661392,
0.00133324705529958,
0.10506262630224228,
0.03506382182240486,
-0.05125875771045685,
0.06374198198318481,
0.07696398347616196,
-0.022846832871437073,
0.007391420658677816,
-0.045284148305654526,
0.008226295933127403,
0.04232409968972206,
0.05222976207733154,
-0.05630702152848244,
-0.024438342079520226,
-0.015080894343554974,
-0.056348808109760284,
0.02403450757265091,
-0.011994625441730022,
-0.05564674735069275,
0.04037220776081085,
0.055658597499132156,
0.005587663967162371,
-0.0010580922244116664,
-0.005925140343606472,
-0.06386653333902359,
-0.07527096569538116,
-0.04673556983470917,
-0.005377740599215031,
-0.029955679550766945,
-0.03786708414554596,
-0.043271686881780624,
0.005788386333733797,
0.003737959312275052,
0.026082023978233337,
0.02846602350473404,
-0.014485035091638565,
0.006642062682658434,
-0.014133957214653492,
-0.0025642598047852516,
-0.1177264079451561,
0.04445882514119148,
0.030405795201659203,
0.02398574911057949,
0.028757618740200996,
-0.02833155170083046,
-0.022734539583325386,
-0.009350228123366833,
-0.02602490782737732,
0.014768659137189388,
-0.009130521677434444,
-0.036027636379003525,
-0.0010213006753474474,
0.004391945898532867,
-0.06397504359483719,
0.05888284742832184,
0.03712121397256851,
0.005912993103265762,
0.018186233937740326,
0.05504384636878967,
0.035699374973773956,
-0.0025931301061064005,
0.0023831382859498262,
-0.028818810358643532,
-0.06768040359020233,
0.03403697535395622,
0.016153085976839066,
-0.05724181607365608,
-0.03288916498422623,
0.01459445245563984,
0.0017785558011382818,
-0.07502007484436035,
-0.005871505476534367,
-0.025470132008194923,
0.00910992082208395,
-0.017193417996168137,
0.04944801330566406,
-0.03579312935471535,
-0.0010878460016101599,
-0.026066197082400322,
0.050301045179367065,
-0.06667774170637131,
0.08508765697479248,
0.011321510188281536,
0.013534988276660442,
0.0413556732237339,
-0.0667717307806015,
-0.05129329115152359,
0.026981476694345474,
0.02051594667136669,
0.04733164235949516,
-0.025683172047138214,
-0.03215516731142998,
-0.0038653009105473757,
-0.002149313921108842,
-0.004272643476724625,
-0.06945647299289703,
-0.006690110079944134,
-0.040603868663311005,
-0.020584002137184143,
0.0028700698167085648,
-0.03263260796666145,
0.021887758746743202,
-0.01479075662791729,
0.024233996868133545,
-0.021012485027313232,
0.01298429910093546,
0.018249113112688065,
-0.04619728773832321,
0.043367497622966766,
0.03809119015932083,
0.01679075136780739,
-0.07432016730308533,
0.03280632942914963,
0.05289863049983978,
-0.031241923570632935,
0.04251233860850334,
-0.014151942916214466,
0.006519685033708811,
0.03813054412603378,
-0.023859631270170212,
0.005773366428911686,
-0.019759083166718483,
-0.05520375072956085,
-0.03401649370789528,
0.05235114321112633,
0.028852565214037895,
-0.03392137214541435,
-0.03268846124410629,
0.049538999795913696,
-0.03602796047925949,
-0.017425140365958214,
0.013415930792689323,
0.03983604535460472,
-0.05261705443263054,
0.04413827136158943,
-0.045886363834142685,
-0.018314193934202194,
-0.053706541657447815,
0.03299938514828682,
-0.03861289843916893,
0.016744792461395264,
0.011057974770665169,
-0.03545762971043587,
-0.045231159776449203,
-0.0069787162356078625
] |
<p>According to <a href="https://en.wikipedia.org/wiki/Mohs_scale_of_mineral_hardness" rel="nofollow">Wikipedia's article on the Mohs scale of mineral hardness</a>, materials / minerals with a higher rating cannot be "visibly" scratched by materials with a lower rating.</p>
<p>It goes on to admit that microscopic dislocations on the harder material do emerge though by trying to scratch it.</p>
<p>I always thought that physical damage mainly depends on the force being exerted to the material, however the explanation on Mohs hardness suggests that force and work are negligible because there is no mention on <em>how</em> exactly the scratching is to be performed, at which velocity, for how long, at which temperature etc.</p>
<p>This implies that sliding and rubbing two materials against one another will basically have the same outcome regardless of whether the sliding happens through manual movement or at cosmic scales like satellite movement.</p>
<p>Also, would a material be considered "harder" on the Mohs scale if we were to scratch it near its melting point so that it sort of "self-repairs" scratches when being scratched due to friction-induced melting ?</p>
<p>Sorry if these questions sound silly to physics experts and mineralogists.</p>
|
g2478
|
[
0.04748670384287834,
0.04655557870864868,
-0.009896669536828995,
-0.0061967517249286175,
0.03212863579392433,
0.007257559802383184,
-0.0470295213162899,
0.004054671619087458,
-0.014493645168840885,
-0.004047878086566925,
0.015117497183382511,
0.014239941723644733,
-0.009480355307459831,
-0.0629391074180603,
-0.008836960420012474,
0.03042410872876644,
0.020034004002809525,
0.01994221843779087,
0.054002050310373306,
0.06190110370516777,
-0.016352340579032898,
0.010024440474808216,
-0.0089165810495615,
-0.05838748812675476,
-0.03981514275074005,
0.0010413725394755602,
-0.0077202473767101765,
-0.06575127691030502,
0.057285431772470474,
-0.021230485290288925,
0.04607930779457092,
0.008832315914332867,
0.02126462385058403,
-0.01184384897351265,
-0.024481812492012978,
-0.036207061260938644,
0.03947966545820236,
-0.03857925906777382,
0.016308577731251717,
-0.00043443645699881017,
-0.000763599993661046,
-0.020174264907836914,
0.020838288590312004,
-0.019728073850274086,
-0.031129926443099976,
0.008653782308101654,
-0.04297048598527908,
-0.00041259557474404573,
0.022864334285259247,
0.08116202801465988,
0.01663309894502163,
0.006510669365525246,
0.10449150204658508,
0.005816943012177944,
-0.04934605211019516,
-0.02464769408106804,
0.002543752547353506,
-0.021484697237610817,
0.10237928479909897,
0.0008772002765908837,
-0.008220728486776352,
-0.025420820340514183,
0.0024775818455964327,
-0.001053247251547873,
-0.008481636643409729,
-0.022000521421432495,
0.009692654013633728,
0.024707552045583725,
0.03733833134174347,
-0.008501945994794369,
-0.0406021922826767,
0.028609078377485275,
-0.02678951807320118,
-0.05456489324569702,
-0.0611036941409111,
-0.01910112053155899,
0.03414367511868477,
-0.0043970379047095776,
-0.006908899173140526,
0.05718058720231056,
-0.03531903028488159,
0.0009465788025408983,
0.01563297025859356,
-0.03899943828582764,
0.054381176829338074,
-0.03930799663066864,
-0.029438631609082222,
-0.005448371171951294,
-0.02559858188033104,
0.07046675682067871,
-0.02088255248963833,
-0.020298749208450317,
-0.031228013336658478,
-0.012397917918860912,
0.003318121423944831,
0.009709890000522137,
-0.009052231907844543,
0.04800054803490639,
-0.04108612239360809,
-0.008130648173391819,
-0.020281801000237465,
-0.06582188606262207,
0.01552448607981205,
-0.0009333734051324427,
0.03371661901473999,
-0.01870807260274887,
0.022439399734139442,
-0.006250943522900343,
-0.034610167145729065,
0.03813137114048004,
0.03289182856678963,
0.004036614205688238,
-0.009570338763296604,
-0.012012902647256851,
0.022805016487836838,
-0.004598497413098812,
0.019183333963155746,
0.08154883235692978,
-0.004371816758066416,
0.054608266800642014,
0.051777131855487823,
-0.004406181629747152,
0.004176776856184006,
0.040103137493133545,
-0.03747886046767235,
-0.026271909475326538,
0.027658818289637566,
-0.018471602350473404,
0.041191134601831436,
-0.03673222288489342,
-0.013218127191066742,
0.06523226946592331,
0.018263908103108406,
-0.0510331466794014,
-0.07278729975223541,
0.02527971938252449,
0.049999553710222244,
0.003943644929677248,
-0.032807014882564545,
0.02246498502790928,
-0.013663746416568756,
0.0485050268471241,
-0.05199667066335678,
0.029291043058037758,
-0.035171836614608765,
-0.008032397367060184,
-0.07439470291137695,
0.04647930711507797,
0.037816137075424194,
0.004188339691609144,
0.032899968326091766,
0.02400141954421997,
0.03170303255319595,
-0.06770286709070206,
0.04970585182309151,
0.002935683587566018,
-0.0047233751974999905,
0.03224818781018257,
0.020951000973582268,
0.08319791406393051,
0.05356583744287491,
-0.013962802477180958,
-0.012372547760605812,
0.03921067714691162,
0.04825200140476227,
-0.005664106924086809,
-0.03630242869257927,
-0.025555122643709183,
0.06189891695976257,
0.03558788821101189,
-0.00045733345905318856,
0.009328254498541355,
0.03786516934633255,
0.06246652826666832,
-0.007198987063020468,
0.03568059206008911,
0.07167147845029831,
-0.028371749445796013,
-0.022866541519761086,
0.020148079842329025,
0.06342654675245285,
-0.07802649587392807,
-0.009125149808824062,
-0.009833356365561485,
0.0494825504720211,
-0.026971323415637016,
0.0028518037870526314,
0.006349931936711073,
0.04229572042822838,
0.01638917624950409,
-0.06061602756381035,
-0.040172137320041656,
-0.007465168368071318,
0.013807198032736778,
0.02248903177678585,
-0.06320133805274963,
0.003667372278869152,
0.043385785073041916,
0.0017526864539831877,
-0.070464588701725,
0.011999772861599922,
0.07611972093582153,
-0.007714593783020973,
-0.008555536158382893,
-0.018108798190951347,
0.0449739508330822,
-0.05701909586787224,
0.006089898757636547,
-0.04315071925520897,
-0.017560625448822975,
-0.03137786313891411,
0.04063048213720322,
-0.01666371151804924,
-0.01943877525627613,
-0.034472208470106125,
-0.017267147079110146,
-0.03158838301897049,
-0.01171093713492155,
-0.030327679589390755,
-0.005380577873438597,
0.008789055049419403,
0.032733313739299774,
0.010290234349668026,
-0.008985173888504505,
-0.003309657797217369,
-0.02643038146197796,
-0.044900089502334595,
-0.02030143141746521,
0.04439050704240799,
0.0029900972731411457,
0.018841933459043503,
-0.02744217775762081,
0.0129177151247859,
-0.028894538059830666,
-0.0065397885628044605,
0.032853901386260986,
0.015999477356672287,
-0.012222472578287125,
0.028636101633310318,
0.05292470380663872,
0.05282030254602432,
-0.0689023807644844,
-0.02307572215795517,
-0.04033495858311653,
-0.011620852164924145,
-0.07925809919834137,
0.020086638629436493,
0.009468411095440388,
0.014455092139542103,
0.05692366883158684,
0.058376699686050415,
0.007746984716504812,
-0.025582721456885338,
-0.03701852634549141,
-0.027326103299856186,
0.017829565331339836,
-0.01871379092335701,
0.015954583883285522,
-0.02485387772321701,
-0.009900806471705437,
-0.004529083147644997,
-0.03275177627801895,
-0.0037834658287465572,
0.007415053900331259,
-0.036539673805236816,
-0.02820534072816372,
-0.037609610706567764,
0.00182704150211066,
-0.06642352044582367,
0.013700634241104126,
0.023273823782801628,
0.01610919088125229,
0.020842213183641434,
0.011186864227056503,
0.00466137332841754,
-0.0331396721303463,
0.06094294786453247,
-0.06635749340057373,
-0.04321605712175369,
-0.000808922981377691,
-0.026943624019622803,
-0.0006933557451702654,
0.014252670109272003,
-0.04673212021589279,
0.006404906511306763,
-0.009781883098185062,
-0.057007335126399994,
-0.03911846503615379,
-0.11083754897117615,
0.013722296804189682,
-0.015683459118008614,
-0.017657462507486343,
0.013491746969521046,
0.02961050532758236,
-0.007124916650354862,
0.09093094617128372,
0.0029445511754602194,
-0.01739504747092724,
-0.0017874959157779813,
0.045168545097112656,
0.06776250153779984,
-0.008000344969332218,
-0.02992897853255272,
0.023946553468704224,
0.003727380884811282,
0.06443726271390915,
-0.0038090005982667208,
-0.0044751884415745735,
-0.05151680111885071,
-0.023884430527687073,
-0.013107162900269032,
0.05170229822397232,
0.05123806744813919,
0.03066837601363659,
-0.02764657698571682,
-0.036034468561410904,
-0.011129118502140045,
0.02373441867530346,
0.017176859080791473,
0.0006845314637757838,
-0.025094369426369667,
0.040797118097543716,
0.046797994524240494,
-0.023565568029880524,
-0.014521634206175804,
0.027580788359045982,
-0.038366276770830154,
0.0003297718067187816,
-0.04482616111636162,
0.01915426179766655,
0.06984920054674149,
0.05156945064663887,
-0.06759293377399445,
-0.039463769644498825,
-0.07260258495807648,
-0.05657200515270233,
-0.03439239412546158,
-0.027634546160697937,
0.04417852684855461,
0.01713445596396923,
-0.013352916575968266,
-0.004106760956346989,
-0.05070427432656288,
0.044207826256752014,
0.028683863580226898,
0.04177282005548477,
-0.0009677420603111386,
0.02562519535422325,
0.0001508779387222603,
0.0055071511305868626,
0.09875094145536423,
-0.019661294296383858,
0.009919146075844765,
0.014759685844182968,
0.05093267560005188,
0.04886244609951973,
0.011704728938639164,
0.057372529059648514,
-0.00027646851958706975,
-0.008149799890816212,
0.03528834506869316,
-0.00199786014854908,
-0.0073830909095704556,
-0.03638864681124687,
0.009708975441753864,
0.053014304488897324,
0.027738729491829872,
0.04072367027401924,
-0.02273026667535305,
0.014551659114658833,
-0.01992891915142536,
-0.02825675718486309,
0.009465856477618217,
0.018940554931759834,
0.046459224075078964,
0.03919559344649315,
0.044846344739198685,
-0.017449961975216866,
-0.00775188859552145,
-0.003942541312426329,
-0.02907247468829155,
0.02406342327594757,
0.02208651602268219,
0.06345532089471817,
0.0422188937664032,
0.0018047704361379147,
-0.06590116769075394,
-0.0161186121404171,
-0.02878759428858757,
-0.02498987503349781,
0.024414794519543648,
0.030680973082780838,
0.043054718524217606,
-0.002810391364619136,
0.02331177331507206,
-0.05764099583029747,
0.007322023157030344,
-0.0014971854398027062,
0.07375147938728333,
-0.00455490592867136,
0.01902749575674534,
0.027785668149590492,
-0.05667169392108917,
0.03819978982210159,
0.002310947747901082,
-0.006786974612623453,
-0.005149513948708773,
0.002165471436455846,
0.033232297748327255,
-0.024951010942459106,
-0.009220346808433533,
-0.029156465083360672,
-0.05534134432673454,
0.000806211493909359,
-0.016859089955687523,
-0.0035715331323444843,
-0.05211900174617767,
0.004773440305143595,
0.026580261066555977,
0.01299472525715828,
-0.051051508635282516,
0.03170924633741379,
0.01790364645421505,
0.026221228763461113,
-0.01417525950819254,
0.0485457107424736,
0.029898161068558693,
0.04001446068286896,
0.04782629385590553,
-0.030853774398565292,
-0.004339494276791811,
0.030680209398269653,
-0.0033783200196921825,
0.0010411293478682637,
0.010945586487650871,
0.056470319628715515,
-0.021206144243478775,
0.04097605496644974,
-0.001888916827738285,
-0.023056212812662125,
-0.022068265825510025,
0.038426000624895096,
0.011662768200039864,
0.06428121775388718,
0.07081837207078934,
0.05037912353873253,
-0.05346096307039261,
0.006995920091867447,
-0.09730848670005798,
-0.04317696392536163,
-0.09164940565824509,
-0.04391138628125191,
-0.001408192329108715,
-0.05444388464093208,
-0.03961203619837761,
-0.04091610014438629,
0.031969793140888214,
-0.04838986694812775,
-0.03841952979564667,
0.06086716800928116,
-0.0015923191094771028,
0.0064502558670938015,
0.02044816128909588,
0.018276605755090714,
-0.04110274836421013,
-0.0031123191583901644,
-0.0455758310854435,
0.018121322616934776,
-0.0361737497150898,
0.05589796602725983,
0.006444098427891731,
-0.05084934085607529,
0.037745874375104904,
0.03326902166008949,
0.03918624296784401,
-0.0376850962638855,
-0.019948912784457207,
-0.019549040123820305,
-0.021737949922680855,
-0.04522938281297684,
-0.017855597659945488,
0.03857159614562988,
0.11865805089473724,
-0.02873222716152668,
-0.046646252274513245,
0.01588115096092224,
-0.06913550943136215,
0.019482895731925964,
-0.016720153391361237,
0.018038617447018623,
0.12685933709144592,
-0.022009432315826416,
0.05398596450686455,
-0.009238938800990582,
-0.050280410796403885,
0.026109375059604645,
-0.029923051595687866,
0.06919422000646591,
0.019479556009173393,
0.0021379096433520317,
0.0004163366393186152,
0.017932353541254997,
-0.0037524085491895676,
0.03180953860282898,
0.018973270431160927,
0.00972282886505127,
0.069394052028656,
-0.06505013257265091,
0.05116462707519531,
0.019403239712119102,
-0.030218636617064476,
0.06836430728435516,
-0.006766284815967083,
-0.011067948304116726,
0.029300248250365257,
-0.011761973612010479,
0.012208138592541218,
0.015863832086324692,
-0.02646743319928646,
-0.07596782594919205,
-0.0037856954149901867,
0.040541939437389374,
-0.043092407286167145,
-0.027931975200772285,
-0.043357644230127335,
0.010402971878647804,
-0.0217137448489666,
-0.028965910896658897,
-0.04125680401921272,
0.0485338531434536,
0.1129641979932785,
-0.021325500681996346,
0.02141566388309002,
0.04301096126437187,
-0.0058645582757890224,
0.0009781443513929844,
0.041906315833330154,
-0.01883598044514656,
-0.031195705756545067,
0.011798734776675701,
-0.015102604404091835,
-0.0063490490429103374,
0.03575796261429787,
0.06143241375684738,
0.03940529748797417,
0.00007291542715393007,
0.010945894755423069,
-0.008320190943777561,
0.043985553085803986,
-0.019270598888397217,
-0.05809371545910835,
0.04767882823944092,
-0.03529281169176102,
0.017282726243138313,
-0.041577696800231934,
0.048718083649873734,
-0.007748725358396769,
-0.04568040370941162,
0.028266509994864464,
0.017304640263319016,
-0.0019106881227344275,
-0.009241284802556038,
-0.03137213736772537,
0.0009521482861600816,
0.04302068427205086,
-0.04038018733263016,
-0.009431512095034122,
-0.05472002550959587,
0.050672613084316254,
0.011493468657135963,
-0.023004891350865364,
0.011516986414790154,
-0.025580300018191338,
-0.004292262252420187,
-0.02392120286822319,
0.019960157573223114,
-0.11655126512050629,
-0.008967844769358635,
-0.013812498189508915,
0.011748123914003372,
0.005185661371797323,
0.013323454186320305,
-0.058219801634550095,
0.017872491851449013,
-0.008503585122525692,
-0.031471941620111465,
-0.024808399379253387,
-0.021525084972381592,
0.054796528071165085,
-0.02382061257958412,
0.0208051148802042,
0.029522668570280075,
-0.010188465006649494,
0.0020990949124097824,
-0.05990198254585266,
-0.01560748927295208,
0.014835921116173267,
0.03822735324501991,
-0.0364140123128891,
0.026279713958501816,
0.008889936842024326,
0.02467208541929722,
0.08604121953248978,
0.010603662580251694,
0.02987898513674736,
-0.010704985819756985,
-0.020856555551290512,
0.0491303950548172,
0.061520472168922424,
0.031887274235486984,
-0.07425075024366379,
0.09999989718198776,
-0.03427755460143089,
-0.0041406163945794106,
0.015966450795531273,
-0.004999373573809862,
-0.025591613724827766,
-0.03346790745854378,
-0.02871653065085411,
-0.06544763594865799,
-0.04040931910276413,
0.00034898536978289485,
-0.018500493839383125,
-0.010488937608897686,
-0.0316322036087513,
-0.029300594702363014,
-0.016445662826299667,
0.055932655930519104,
0.02413981594145298,
-0.05857159569859505,
-0.032797202467918396,
-0.037009015679359436,
-0.009605051949620247,
0.07650808244943619,
-0.014722847379744053,
-0.015417422167956829,
-0.062317900359630585,
-0.018911538645625114,
-0.01527988538146019,
-0.029635850340127945,
0.036507558077573776,
-0.029927385970950127,
-0.020403988659381866,
0.02684880793094635,
0.03162284940481186,
-0.04536503925919533,
-0.024341007694602013,
-0.0011825020192191005,
0.002656367840245366,
-0.022290736436843872,
0.01414650771766901,
0.013199843466281891,
-0.034400664269924164,
-0.00931324902921915,
0.01621079072356224,
0.0316753126680851,
-0.062385376542806625,
0.027461644262075424,
0.028587235137820244,
0.021390477195382118,
-0.0037671502213925123,
-0.023419033735990524,
-0.02110378071665764,
0.0005283858045004308,
-0.036986056715250015,
0.024197610095143318,
-0.020379535853862762,
-0.057550668716430664,
-0.0004100942169316113,
0.03167939558625221,
-0.005892856977880001,
-0.014386205933988094,
0.025753185153007507,
0.06908489018678665,
0.0021530857775360346,
-0.02156730182468891,
-0.05206260830163956,
0.004017355386167765,
0.015969974920153618,
0.047584276646375656,
0.029145419597625732,
-0.0093682324513793,
0.07592809200286865,
-0.025436053052544594,
0.03296508267521858,
-0.05541025474667549,
-0.06336545944213867,
0.008524852804839611,
0.0332273431122303,
-0.04228968918323517,
-0.012674571014940739,
-0.06924547255039215,
0.0036902304273098707,
0.024273764342069626,
0.02620335854589939,
-0.03806775063276291,
0.0551123283803463,
0.019426390528678894,
-0.004915070720016956,
0.02048318274319172,
0.00037539112963713706,
-0.027086183428764343,
0.034552570432424545,
0.008762050420045853,
0.0017384993843734264,
0.0055880178697407246,
0.009654584340751171,
0.03909163177013397,
-0.027109073475003242,
-0.016968369483947754,
0.004599990788847208,
-0.02372782677412033,
0.0032965298742055893,
-0.0449252650141716,
-0.018999338150024414,
-0.010484082624316216,
0.004935190547257662,
-0.054127130657434464,
-0.000048187495849560946,
-0.010202990844845772,
0.025998223572969437,
0.0032446959521621466,
0.00212870049290359,
-0.07694162428379059,
0.034200914204120636,
0.008284450508654118,
-0.012405084446072578,
-0.08422721177339554,
-0.025109274312853813,
-0.049357105046510696,
0.023836741223931313,
-0.041346512734889984,
0.035065434873104095,
0.01795390248298645,
0.018102318048477173,
0.0023953397758305073,
0.01703265681862831,
-0.0037762848660349846,
-0.07258408516645432,
0.002802604343742132,
-0.015816744416952133,
-0.0022134631872177124,
-0.04503047466278076,
0.008899493142962456,
-0.04039362445473671,
0.030421597883105278,
-0.06053853780031204,
0.07097944617271423,
-0.03676152229309082,
-0.008758951909840107,
-0.028654024004936218,
-0.03428208827972412,
0.007508384995162487,
-0.014171332120895386,
-0.023736460134387016,
-0.028924720361828804,
-0.06286046653985977,
0.010640350170433521,
0.0253954716026783,
-0.029057683423161507,
-0.01156987901777029,
-0.024621887132525444,
0.01628354750573635,
-0.030962780117988586,
0.002827878575772047,
-0.04999178275465965,
-0.032944999635219574,
0.03829798847436905
] |
<p>I can unterstand why because the integration over Grassman variables has to be translational invariant too, one has </p>
<p>$$
\int d\theta = 0
$$</p>
<p>and </p>
<p>$$
\int d\theta \theta = 1
$$</p>
<p>but I dont see where the rule for this double integration</p>
<p>$$
\int d^2 \theta \bar{\theta}\theta = -2i
$$</p>
<p>comes from.</p>
<p>So can somebody explain to me how this is motivated and/or derived?</p>
|
g2479
|
[
0.04350848123431206,
0.04613516479730606,
-0.03757696598768234,
-0.007986465469002724,
0.0328216515481472,
0.0008491383050568402,
0.06306373327970505,
0.038297586143016815,
-0.0911954864859581,
0.012314758263528347,
-0.10948347300291061,
0.04388067126274109,
0.0012390254996716976,
0.01835397444665432,
0.03398960083723068,
-0.01585841178894043,
-0.0028694921638816595,
0.061463505029678345,
0.047181420028209686,
-0.01318451575934887,
-0.0725746601819992,
-0.004145692568272352,
0.006610903888940811,
-0.07529556006193161,
0.058090053498744965,
-0.060209400951862335,
0.005443913862109184,
0.0018144804053008556,
-0.07402903586626053,
0.017599930986762047,
0.048195671290159225,
-0.013559706509113312,
0.05663082376122475,
-0.0277765691280365,
-0.0008928278693929315,
0.008572918362915516,
0.045961324125528336,
-0.008471203967928886,
-0.015753040090203285,
-0.01904320903122425,
-0.007322757970541716,
0.042602647095918655,
0.03681216016411781,
0.016105923801660538,
0.007616130635142326,
-0.003495539305731654,
0.0225698109716177,
0.016981398686766624,
-0.07347727566957474,
-0.030083203688263893,
0.0026559375692158937,
0.01698947325348854,
0.015412173233926296,
0.023034395650029182,
-0.06648663431406021,
-0.013993250206112862,
0.018765902146697044,
-0.0658254623413086,
0.03637079894542694,
0.04931730777025223,
0.0058109452947974205,
-0.10110576450824738,
0.009768799878656864,
0.06217231974005699,
0.06214775890111923,
0.02006452903151512,
-0.028724536299705505,
-0.042480118572711945,
0.008721228688955307,
-0.01161210983991623,
-0.03346293047070503,
-0.041412513703107834,
0.024318698793649673,
-0.04419615864753723,
-0.015177472494542599,
0.012303607538342476,
0.056582558900117874,
-0.002316187834367156,
-0.0055843559093773365,
-0.038388967514038086,
-0.015476501546800137,
0.016263533383607864,
0.0046202996745705605,
0.018696743994951248,
0.05930274724960327,
-0.018780417740345,
-0.012943699024617672,
-0.006295050494372845,
-0.10140753537416458,
0.04535180330276489,
0.03227447345852852,
-0.025614842772483826,
0.0476718544960022,
0.0033975113183259964,
0.024614905938506126,
-0.0479428768157959,
-0.0406506210565567,
0.06202726066112518,
-0.011659565381705761,
-0.014806360006332397,
-0.0006209646817296743,
0.019093671813607216,
0.07480116933584213,
0.0038184013683348894,
0.002114651957526803,
0.02166682481765747,
0.058514371514320374,
-0.008090161718428135,
-0.03346861153841019,
0.008444618433713913,
-0.03721464425325394,
0.0341816246509552,
-0.022975098341703415,
-0.01158518623560667,
0.023176388815045357,
0.01905188336968422,
0.038496166467666626,
-0.0037353832740336657,
0.01381041668355465,
0.0580119863152504,
0.04080023616552353,
-0.005395426880568266,
0.05751561000943184,
0.06175008788704872,
0.003115435829386115,
-0.02044290490448475,
-0.04160997271537781,
0.05457255616784096,
0.07256221771240234,
-0.014796738512814045,
0.017766477540135384,
0.009018679149448872,
-0.018117630854249,
-0.0038782169576734304,
-0.005427200812846422,
0.017874248325824738,
-0.0485544316470623,
-0.028557581827044487,
-0.006015394348651171,
-0.015169327147305012,
-0.07235941290855408,
-0.0018215832533314824,
0.012135355733335018,
-0.01587705686688423,
-0.043598368763923645,
-0.017832797020673752,
-0.009570718742907047,
-0.035763103514909744,
-0.0016048946417868137,
-0.03846172243356705,
0.05168568342924118,
0.06792695075273514,
0.03589462488889694,
-0.010476469993591309,
0.0008476138464175165,
-0.008902780711650848,
0.09270653128623962,
-0.014348471537232399,
0.05792372673749924,
-0.0201766025274992,
0.05680821090936661,
0.008521486073732376,
0.0045553105883300304,
-0.04332690313458443,
-0.02074052207171917,
0.049142926931381226,
-0.001503012957982719,
-0.03109605982899666,
-0.027461549267172813,
-0.052229609340429306,
0.02311338670551777,
0.03832993656396866,
-0.004020643420517445,
0.01036908384412527,
0.025958722457289696,
0.055041972547769547,
-0.09555485099554062,
0.030671747401356697,
-0.00012448400957509875,
0.017564577981829643,
-0.007896574214100838,
-0.0330415740609169,
-0.0066237980499863625,
-0.07361797988414764,
0.023755183443427086,
-0.0273456834256649,
0.04784000664949417,
0.016504060477018356,
-0.03350289165973663,
0.003309839405119419,
0.03862307593226433,
0.04740989953279495,
0.03972116857767105,
0.05728473514318466,
-0.0034697679802775383,
-0.007952006533741951,
0.053223561495542526,
-0.041039783507585526,
-0.002845269627869129,
0.06393968313932419,
0.03730224445462227,
0.008739872835576534,
0.016790099442005157,
-0.045656848698854446,
0.003120283829048276,
-0.007933946326375008,
-0.006347960326820612,
-0.02580690197646618,
0.009774367325007915,
-0.024076584726572037,
0.000740592076908797,
-0.01968761533498764,
-0.013524433597922325,
-0.005115822423249483,
0.015317055396735668,
-0.022566480562090874,
0.008653444238007069,
-0.028125861659646034,
-0.005435022991150618,
-0.014143799431622028,
-0.00000789280511526158,
-0.020126840099692345,
0.049763161689043045,
0.03889395296573639,
-0.04428195208311081,
0.04675763100385666,
-0.02171648107469082,
-0.013240060769021511,
-0.027691995725035667,
-0.011855893768370152,
-0.06729105114936829,
-0.08822492510080338,
-0.052826881408691406,
0.004092068877071142,
0.038401082158088684,
-0.002009062096476555,
-0.0035992737393826246,
0.042325276881456375,
0.028730962425470352,
0.04489296302199364,
0.0016477833269163966,
-0.0398138090968132,
0.01781211979687214,
0.007618696894496679,
0.005887884646654129,
-0.00578920217230916,
0.05475051328539848,
0.01781851425766945,
-0.01291208527982235,
0.01261052954941988,
-0.030969198793172836,
-0.020289303734898567,
-0.038666773587465286,
-0.04734041169285774,
-0.015500951558351517,
-0.01667715422809124,
-0.0054118032567203045,
-0.05068347603082657,
0.006705934647470713,
0.034994274377822876,
0.01637202501296997,
-0.03748193755745888,
0.02046463079750538,
0.002444271696731448,
-0.010462959297001362,
-0.05065534636378288,
0.03752685710787773,
0.023197228088974953,
0.04495145380496979,
-0.04079490900039673,
-0.026545871049165726,
0.060717515647411346,
-0.010110527276992798,
-0.015364573337137699,
-0.0024856554809957743,
-0.017115436494350433,
0.031681012362241745,
-0.032368794083595276,
0.040358856320381165,
0.03761079162359238,
-0.00298508838750422,
-0.04836759716272354,
-0.03691620007157326,
0.015195837244391441,
0.01655089110136032,
-0.042024437338113785,
-0.011422540061175823,
0.06953896582126617,
-0.03311451897025108,
0.021506384015083313,
0.014334258623421192,
-0.009944136254489422,
0.0060369702987372875,
-0.0598977729678154,
0.013387015089392662,
-0.034995101392269135,
0.006884824018925428,
-0.03796667605638504,
-0.0019896377343684435,
0.020356671884655952,
0.008387717418372631,
-0.0006898111896589398,
0.008614047430455685,
-0.04321537911891937,
0.045260991901159286,
-0.033705513924360275,
0.052809759974479675,
0.015051959082484245,
-0.05769087001681328,
-0.04417721554636955,
0.05467832088470459,
-0.0018565430073067546,
0.025052053853869438,
-0.03901335969567299,
-0.06018534302711487,
-0.003531004535034299,
-0.023862797766923904,
-0.03476342186331749,
0.038852475583553314,
-0.0009959388989955187,
-0.03798697888851166,
-0.04632578790187836,
0.011738737113773823,
0.058548253029584885,
0.02890077792108059,
-0.07458256930112839,
-0.029691355302929878,
-0.0007969962898641825,
0.0030011185444891453,
0.005941176787018776,
0.04207620769739151,
0.01898086816072464,
0.040824297815561295,
0.019011905416846275,
-0.06956350058317184,
-0.06154828518629074,
-0.026703184470534325,
0.04047277942299843,
0.008480937220156193,
0.007860938087105751,
-0.031451646238565445,
0.017652975395321846,
-0.0005356417968869209,
-0.018552852794528008,
0.004574985709041357,
0.010265969671308994,
0.04416760802268982,
0.022411566227674484,
0.0020046646241098642,
0.007722774054855108,
-0.01461618859320879,
0.03647008538246155,
0.03073759749531746,
-0.01823924109339714,
0.02304694429039955,
0.029659366235136986,
0.01779148541390896,
0.03230594843626022,
-0.032381631433963776,
-0.03133000433444977,
0.034168872982263565,
0.009248269721865654,
-0.06511151045560837,
0.042934760451316833,
0.048148974776268005,
0.009447135031223297,
-0.046433281153440475,
0.0569709949195385,
-0.039140623062849045,
-0.00999059621244669,
-0.0013772154925391078,
0.028174014762043953,
0.006128552369773388,
-0.004397944547235966,
-0.06386695802211761,
-0.07963794469833374,
-0.018947945907711983,
0.03428640216588974,
0.007787039037793875,
0.02770909108221531,
0.043217942118644714,
0.0160660520195961,
-0.043278928846120834,
0.07463626563549042,
0.04036257788538933,
-0.010030427016317844,
-0.03748299553990364,
0.03672391176223755,
0.0032945207785815,
0.003889675484970212,
0.04983263835310936,
0.052268415689468384,
0.022269535809755325,
0.030369699001312256,
0.043341752141714096,
-0.03160431236028671,
0.0037233626935631037,
0.04779518023133278,
-0.031208662316203117,
0.03589363768696785,
-0.06359844654798508,
0.002261074725538492,
0.014665381982922554,
-0.04613565281033516,
-0.06462422013282776,
0.05199558660387993,
0.04772000387310982,
-0.01714986190199852,
0.061328403651714325,
0.03703011944890022,
0.006775823887437582,
0.005031258799135685,
-0.0002866934228222817,
-0.04373552277684212,
0.037631407380104065,
0.03827657178044319,
0.033575210720300674,
-0.002611017320305109,
-0.022850491106510162,
-0.03768553212285042,
-0.03027304820716381,
0.022524666041135788,
0.0034201343078166246,
0.02614504285156727,
0.015165090560913086,
0.05328236147761345,
-0.018388088792562485,
-0.00043376628309488297,
-0.001803963677957654,
-0.051389046013355255,
0.0008799045463092625,
-0.008603363297879696,
-0.04595911130309105,
0.018755659461021423,
-0.05660293996334076,
0.01913902349770069,
-0.017778128385543823,
0.024338651448488235,
-0.06971671432256699,
-0.0020359635818749666,
0.053535740822553635,
-0.014885896816849709,
-0.04701285436749458,
-0.0021495630498975515,
0.040583062916994095,
0.03716278821229935,
0.050135571509599686,
-0.06612727791070938,
0.05448902025818825,
-0.0026245370972901583,
-0.01862984150648117,
0.05370553582906723,
0.02405880205333233,
-0.019887849688529968,
0.033729422837495804,
0.025363950058817863,
-0.07801000773906708,
0.015603001229465008,
0.0019147106213495135,
-0.010036065243184566,
-0.056511715054512024,
-0.05030595883727074,
-0.0620422326028347,
0.015307169407606125,
0.07817593216896057,
-0.025990402325987816,
-0.07022907584905624,
0.047869548201560974,
-0.005947277415543795,
0.054315198212862015,
-0.019059868529438972,
0.02295297384262085,
-0.04723234102129936,
0.020996591076254845,
0.07007789611816406,
0.008494459092617035,
-0.04249119013547897,
-0.0011859029764309525,
0.06355974823236465,
-0.08588079363107681,
-0.029505904763936996,
0.008263031020760536,
0.035738974809646606,
-0.03262745589017868,
-0.02083134837448597,
-0.020489268004894257,
0.039672575891017914,
-0.05839628353714943,
0.012393869459629059,
0.004057890269905329,
0.012461626902222633,
0.005460845306515694,
0.04766140878200531,
0.024825535714626312,
-0.02255278080701828,
0.0005221271421760321,
-0.01803066022694111,
-0.059428609907627106,
0.025247491896152496,
-0.04573722556233406,
-0.10376815497875214,
0.00886543933302164,
0.004766921512782574,
0.027384549379348755,
-0.0029812026768922806,
0.03979748114943504,
0.07713627815246582,
0.0033173300325870514,
-0.044550418853759766,
0.026980837807059288,
0.041418928653001785,
0.0007948079146444798,
0.03553164005279541,
-0.06893991678953171,
0.010957335121929646,
-0.029849976301193237,
0.039011068642139435,
0.00430133705958724,
0.005888083018362522,
-0.01777602918446064,
0.013434575870633125,
-0.0013262606225907803,
-0.0004609120369423181,
-0.07061024755239487,
-0.013733434490859509,
0.025309493765234947,
0.012247273698449135,
-0.055019110441207886,
-0.0026320863980799913,
0.009294945746660233,
0.03873135522007942,
-0.06596328318119049,
0.007515534292906523,
0.0483999103307724,
-0.0021021473221480846,
-0.03356320783495903,
0.012032892554998398,
-0.008077571168541908,
-0.028939226642251015,
-0.0009059262811206281,
-0.03397166356444359,
-0.07199355959892273,
0.0032917761709541082,
0.04764460772275925,
-0.04737953841686249,
0.037952523678541183,
0.0023089535534381866,
0.023924337700009346,
-0.010719437152147293,
-0.020828451961278915,
-0.030590467154979706,
-0.02363842912018299,
0.019632816314697266,
-0.03771667182445526,
-0.007427597884088755,
0.039594411849975586,
0.018034951761364937,
0.012938127852976322,
0.008470350876450539,
0.005289369262754917,
0.0293144341558218,
0.01956768147647381,
0.01143635343760252,
0.020684804767370224,
0.011631575413048267,
-0.03951491042971611,
0.017708515748381615,
0.044632237404584885,
0.047591209411621094,
0.0018857341492548585,
-0.0002624741173349321,
0.011218732222914696,
0.014990178868174553,
0.06213689595460892,
0.005125736352056265,
0.04027830809354782,
-0.017318444326519966,
-0.03129419684410095,
-0.004509915132075548,
-0.005057822447270155,
0.00973573885858059,
0.031618498265743256,
0.005536099895834923,
-0.05350133404135704,
-0.05317302420735359,
0.04976997151970863,
-0.05724623426795006,
-0.04720009118318558,
0.03357158601284027,
-0.008447941392660141,
-0.01834661141037941,
0.00822936836630106,
-0.006962178740650415,
-0.07630985230207443,
0.021502407267689705,
-0.03477432206273079,
0.017039086669683456,
0.034401051700115204,
-0.03509121015667915,
-0.0736720860004425,
0.019908707588911057,
-0.016040533781051636,
0.05833081156015396,
-0.02180793136358261,
0.04407120496034622,
-0.013170210644602776,
0.021447522565722466,
-0.08220105618238449,
-0.007794767152518034,
0.02793194353580475,
-0.012992434203624725,
-0.007712272461503744,
-0.007541365455836058,
-0.0036081187427043915,
-0.02038397453725338,
-0.0728597417473793,
-0.016888314858078957,
0.015736715868115425,
-0.07976330071687698,
0.06671606004238129,
0.04860811308026314,
0.013365711085498333,
0.013004039414227009,
0.025323109701275826,
0.017715400084853172,
0.05557391792535782,
-0.00016445790242869407,
0.025647979229688644,
0.048579733818769455,
-0.03377434238791466,
-0.011625019833445549,
0.004714543931186199,
-0.030040981248021126,
-0.006408253218978643,
-0.05144793167710304,
-0.019479192793369293,
-0.017696430906653404,
0.045954104512929916,
0.055409517139196396,
0.050740960985422134,
-0.014682712964713573,
0.11750868707895279,
0.004773510154336691,
-0.0455930158495903,
-0.008228078484535217,
0.1103944480419159,
-0.02624734491109848,
-0.008643641136586666,
-0.09635087847709656,
0.006474688183516264,
0.04948793351650238,
-0.0012859851121902466,
0.0062482524663209915,
-0.014019210822880268,
-0.01792198047041893,
-0.009780270978808403,
-0.00549261923879385,
0.026321521028876305,
-0.006851107347756624,
-0.011657634750008583,
-0.013881470076739788,
-0.008558583445847034,
-0.03818110376596451,
0.02462920919060707,
0.01219214964658022,
0.051123540848493576,
0.07021227478981018,
-0.026756759732961655,
0.008583628572523594,
-0.04050397127866745,
-0.02435641549527645,
-0.014440697617828846,
-0.013288979418575764,
0.03961838409304619,
0.004085257649421692,
0.006720692850649357,
-0.00161318713799119,
0.02257111668586731,
-0.016254618763923645,
0.008461123332381248,
-0.006011242978274822,
0.007528176996856928,
-0.020349975675344467,
-0.07758282124996185,
-0.014185633510351181,
-0.013274670578539371,
0.03241197392344475,
0.03518829494714737,
-0.00880042091012001,
0.05948203057050705,
-0.05316644161939621,
-0.012813188135623932,
0.0015697667840868235,
0.029635023325681686,
-0.007918237708508968,
0.034833747893571854,
0.027581261470913887,
0.04168841615319252,
-0.0096976850181818,
0.037477441132068634,
0.06810926645994186,
0.00614687567576766,
-0.07687433809041977,
0.020869748666882515,
-0.007585722021758556,
0.04012627527117729,
0.00004546649506664835,
-0.010488040745258331,
0.01896560937166214,
-0.022633356973528862,
-0.014397375285625458,
-0.02539709396660328,
-0.03813200816512108,
0.015063737519085407,
0.024895446375012398,
0.03610941767692566,
-0.05596489831805229,
0.020465651527047157,
0.027886707335710526,
-0.035828106105327606,
0.03350718691945076,
-0.037574123591184616,
0.010041209869086742,
-0.05997856333851814,
0.016564007848501205,
-0.051645126193761826,
-0.03251974284648895,
-0.014419990591704845,
-0.0065958499908447266,
0.014213009737432003,
-0.03094029426574707,
-0.05957514047622681,
-0.025273872539401054,
0.032265547662973404,
-0.06288404762744904,
-0.00048726703971624374,
-0.003488069400191307,
-0.011967225931584835,
0.013221713714301586,
0.006581805646419525,
-0.007097424939274788,
-0.03417891636490822,
-0.014519116841256618,
0.00042273791041225195,
-0.053117912262678146,
-0.05476980656385422,
0.021550394594669342,
0.018764115869998932,
0.02223893068730831,
-0.06482481211423874,
0.02657521702349186,
-0.008799813687801361,
-0.04910089075565338,
0.01239254605025053,
0.03914255276322365,
-0.10355320572853088,
-0.008963235653936863,
0.0061913421377539635,
0.021841051056981087,
0.018976248800754547,
-0.015341323800384998,
-0.015200253576040268,
-0.037213489413261414,
-0.008673019707202911,
0.02788354456424713,
0.0003458837454672903,
-0.06478186696767807,
-0.02985440194606781
] |
<p>I consider an electron (charge $-e$) in $x=0$ and a constant electric field $E(x) \equiv E $. If the electron has initial velocity $v_0$ with the same direction of $E$, then its potential energy is
$$ U(x) = -eV(x) = -e E x $$
The total energy for $x=0$ is
$$ K(0) + U(0) = \dfrac{1}{2} m v_0^2 $$
Now if I try to obtain the point where the electron will eventually stop and begin moving in the opposite direction I obtain from the energy conservation
$$ \dfrac{1}{2} m v_0^2 = K(0) + U(0) = K(z) + U(z) = -e E z $$
$$ z = -\dfrac{m v_0^2}{2eE} $$
But if $E > 0$ I obtain $z<0$, while $z$ should be $z>0$ since $v_0$ has the same direction as $E$!</p>
|
g2480
|
[
0.04864884540438652,
-0.008127115666866302,
0.0015027524204924703,
0.03027784265577793,
0.07816518843173981,
-0.008675891906023026,
0.046054840087890625,
0.0519835501909256,
-0.06288160383701324,
0.03607708960771561,
-0.016394609585404396,
0.06577032804489136,
-0.015349761582911015,
0.024891575798392296,
0.027164900675415993,
-0.011293651536107063,
0.06279932707548141,
-0.007088450249284506,
-0.00023925861751195043,
0.025344017893075943,
-0.0342131182551384,
-0.017198963090777397,
0.009201950393617153,
-0.010679780505597591,
0.0285397507250309,
-0.008312986232340336,
-0.008987126871943474,
0.01202568132430315,
-0.01530893798917532,
-0.02092120610177517,
0.03871067240834236,
0.0028131958097219467,
0.0584719218313694,
-0.059498660266399384,
-0.05814680829644203,
-0.00946334470063448,
0.06588325649499893,
0.004788171034306288,
0.060064319521188736,
-0.030279677361249924,
0.046300530433654785,
-0.05933234840631485,
0.0458114854991436,
0.02917785942554474,
0.05418011173605919,
-0.057990461587905884,
-0.014808866195380688,
-0.015731146559119225,
-0.016804387792944908,
0.02744881808757782,
0.02939499355852604,
0.08023687452077866,
0.03257186710834503,
-0.009032905101776123,
-0.009063251316547394,
0.00709631759673357,
-0.05616839602589607,
-0.01987176202237606,
0.025128135457634926,
0.004114067181944847,
0.053944941610097885,
-0.0012919532600790262,
-0.0215612780302763,
0.00889871921390295,
0.029608404263854027,
-0.029215874150395393,
-0.0613124817609787,
0.021553505212068558,
-0.023978397250175476,
-0.014618624933063984,
0.05272762477397919,
-0.04007597267627716,
-0.04060986265540123,
-0.004191375337541103,
-0.03415814787149429,
-0.0033583547919988632,
0.03197088837623596,
-0.028950432315468788,
0.02003735676407814,
-0.03904065489768982,
-0.07592234015464783,
-0.007383999414741993,
0.04431411251425743,
0.014139864593744278,
0.07024025917053223,
-0.01596926711499691,
0.01877203956246376,
0.056913431733846664,
-0.025096470490098,
-0.040922559797763824,
-0.01861923187971115,
0.007077861577272415,
0.014289120212197304,
-0.037630386650562286,
0.0132474759593606,
-0.053732942789793015,
-0.02606789767742157,
0.07666215300559998,
0.016344863921403885,
-0.03529736027121544,
0.009401440620422363,
-0.049662817269563675,
-0.00037855785922147334,
0.028716938570141792,
0.01738116890192032,
-0.05138988047838211,
-0.018613796681165695,
-0.02761176973581314,
0.02624593861401081,
-0.015492548234760761,
0.018492165952920914,
-0.06559327244758606,
-0.010631266981363297,
-0.038930583745241165,
-0.01673022098839283,
0.0013677884126082063,
0.05004237964749336,
-0.015223735012114048,
-0.018630489706993103,
0.022028589621186256,
-0.025214601308107376,
0.0002586955379229039,
0.008244246244430542,
0.03947139531373978,
-0.006141540594398975,
-0.013691104017198086,
-0.046165771782398224,
-0.02484867349267006,
0.01879079081118107,
0.02797355316579342,
-0.0019489600090309978,
0.004613079596310854,
0.06871820986270905,
0.006992620881646872,
0.00038392722490243614,
0.02459348738193512,
-0.021396145224571228,
0.03422349691390991,
0.036473728716373444,
0.004305859096348286,
-0.006507552694529295,
-0.024261727929115295,
0.021991724148392677,
-0.017613371834158897,
-0.050644904375076294,
-0.012257139198482037,
0.003077098401263356,
-0.022963153198361397,
0.05633166432380676,
0.019253909587860107,
-0.02188323251903057,
0.054110705852508545,
-0.06772307306528091,
0.038987305015325546,
0.0038868242409080267,
-0.0935513973236084,
0.04927497357130051,
0.026297282427549362,
0.01334966067224741,
-0.04656904563307762,
0.016527963802218437,
0.021924534812569618,
0.051086485385894775,
0.006750110536813736,
-0.02188890054821968,
-0.044908151030540466,
0.019291089847683907,
-0.03351207822561264,
0.00595205370336771,
-0.021923281252384186,
-0.04561041668057442,
0.03600700572133064,
0.02598918043076992,
0.035129301249980927,
0.005165931768715382,
0.03982403501868248,
-0.008382296189665794,
-0.02533310279250145,
0.015352628193795681,
-0.010696610435843468,
0.008287799544632435,
-0.025452665984630585,
0.07505407184362411,
0.019450576975941658,
0.07081854343414307,
-0.0041221859864890575,
-0.004313012585043907,
0.09589129686355591,
-0.034015391021966934,
-0.06111729517579079,
0.04730285331606865,
0.000633395800832659,
-0.032363880425691605,
-0.021831193938851357,
-0.07324345409870148,
0.03598406910896301,
-0.02919640578329563,
-0.05774131044745445,
-0.10226792097091675,
-0.035665467381477356,
-0.017883403226733208,
0.06840266287326813,
0.0022152431774884462,
0.035334665328264236,
-0.007907773368060589,
-0.014972364529967308,
0.007566012907773256,
-0.03448081389069557,
0.028430458158254623,
0.0438564233481884,
0.0018417553510516882,
-0.01741182431578636,
-0.05212957784533501,
0.037864282727241516,
-0.01516887079924345,
-0.0010644645662978292,
-0.0003056233108509332,
0.03607441484928131,
-0.04691603407263756,
0.014785673469305038,
-0.07872755080461502,
0.016366837546229362,
0.05309709161520004,
-0.008259713649749756,
-0.04286004602909088,
0.0013357680290937424,
-0.03124435618519783,
-0.0747995525598526,
-0.06717123836278915,
-0.007760452106595039,
-0.020812740549445152,
0.04012212157249451,
0.03617994859814644,
-0.052010428160429,
0.054765280336141586,
-0.03470361977815628,
-0.019730206578969955,
0.03355003148317337,
0.009032038040459156,
-0.07181588560342789,
0.006025596521794796,
0.01705574244260788,
0.0069765206426382065,
-0.02260786108672619,
0.0539030097424984,
-0.01588004268705845,
0.0545547753572464,
-0.008201519027352333,
0.011693662032485008,
-0.011955793015658855,
0.03923145309090614,
0.015631550922989845,
-0.03843635320663452,
0.0838310495018959,
-0.010324051603674889,
-0.03709614649415016,
-0.04366818442940712,
0.031845998018980026,
-0.013710974715650082,
-0.039001163095235825,
-0.006786322686821222,
0.03866903483867645,
0.02014699950814247,
-0.011098990216851234,
0.0030575282871723175,
-0.013044445775449276,
0.01627444289624691,
0.04402947798371315,
0.02989467978477478,
-0.03414659574627876,
-0.003188636852428317,
0.0688958689570427,
0.005315279588103294,
0.06957005709409714,
0.033242423087358475,
-0.03939295560121536,
0.02812565490603447,
-0.02237522043287754,
0.012530672363936901,
-0.025651851668953896,
-0.05285465344786644,
-0.016443628817796707,
0.0014922789996489882,
0.06735023111104965,
0.03219516575336456,
-0.05562470108270645,
0.03413592278957367,
0.0330214686691761,
-0.04949497431516647,
-0.04592957720160484,
-0.05653313547372818,
0.06690525263547897,
0.0765463337302208,
-0.022753344848752022,
0.007941218093037605,
0.03387855365872383,
0.03196016326546669,
-0.01873379573225975,
-0.0476926825940609,
0.01756187528371811,
0.0018048614729195833,
-0.029639149084687233,
-0.01276485901325941,
0.002994504990056157,
0.06551726162433624,
0.016674073413014412,
-0.04626886174082756,
-0.049811627715826035,
0.012644588947296143,
0.014424165710806847,
0.006504597142338753,
0.00031892157858237624,
-0.04433935508131981,
-0.004018825478851795,
-0.04514080286026001,
0.015026818960905075,
0.0023418711498379707,
-0.01871427334845066,
0.046332698315382004,
0.013188936747610569,
-0.01779933087527752,
-0.015596313402056694,
0.012281323783099651,
0.0292265135794878,
0.008993726223707199,
0.07896900922060013,
-0.027890730649232864,
0.067471444606781,
-0.03231516107916832,
0.049588825553655624,
-0.0033460487611591816,
0.05485779792070389,
-0.0006839572452008724,
-0.03460234776139259,
0.04614980146288872,
-0.019252393394708633,
0.01134900189936161,
0.025993581861257553,
0.05380738154053688,
0.017913416028022766,
-0.030094189569354057,
0.062222305685281754,
-0.04472639039158821,
0.034953296184539795,
0.01837668940424919,
-0.03775647282600403,
0.004666508175432682,
-0.00513672037050128,
-0.015757525339722633,
-0.02213732898235321,
0.030983103439211845,
-0.03914434090256691,
0.0014370413264259696,
0.0048720380291342735,
-0.07725656777620316,
-0.027243150398135185,
-0.006933832541108131,
0.013157028704881668,
-0.04166867956519127,
0.04852505028247833,
-0.022848885506391525,
-0.04843549430370331,
-0.017021529376506805,
0.03466186299920082,
0.003992111887782812,
-0.003628404811024666,
-0.07926938682794571,
0.008660582825541496,
-0.01274854876101017,
-0.027199504896998405,
0.023426594212651253,
-0.04663214087486267,
0.025558162480592728,
0.05059070512652397,
-0.058453842997550964,
-0.027678243815898895,
-0.003102074610069394,
0.01494946051388979,
-0.039831243455410004,
0.01823791116476059,
0.028516247868537903,
0.009013226255774498,
0.003638393245637417,
0.01646004058420658,
-0.00038388973916880786,
0.04492732509970665,
-0.01869373396039009,
0.002640010556206107,
0.008511727675795555,
-0.0031862996984273195,
0.053225673735141754,
-0.008548094891011715,
0.0467754490673542,
0.03837905451655388,
0.008040612563490868,
0.014869580045342445,
0.04433787614107132,
-0.025540681555867195,
0.019782336428761482,
0.026157334446907043,
0.045213330537080765,
-0.00820159912109375,
-0.009309002198278904,
-0.017709793522953987,
-0.0352606475353241,
0.017741618677973747,
0.051964595913887024,
-0.011539610102772713,
0.011629193089902401,
-0.06165694817900658,
-0.022513272240757942,
-0.0010839516762644053,
-0.007181895896792412,
-0.02557859942317009,
-0.04737713932991028,
0.01053796149790287,
-0.01084618829190731,
0.030246978625655174,
0.018943216651678085,
-0.038792919367551804,
0.07076891511678696,
0.023946726694703102,
0.004503902979195118,
-0.05861222371459007,
-0.0009819347178563476,
0.06169446185231209,
0.06485586613416672,
0.00823246780782938,
-0.03903656452894211,
-0.014318999834358692,
-0.026091082021594048,
0.07275424152612686,
0.024928346276283264,
0.028134014457464218,
-0.105343297123909,
0.05890694260597229,
0.00963333249092102,
0.0115920165553689,
-0.048187319189310074,
0.04780760407447815,
0.053357966244220734,
0.005600972566753626,
0.016237974166870117,
0.0008320382330566645,
-0.04293842241168022,
0.025510238483548164,
-0.007114862557500601,
-0.06884501874446869,
0.06586256623268127,
-0.07111091911792755,
-0.02023928239941597,
0.041317492723464966,
-0.03521791845560074,
0.022746292874217033,
-0.026985544711351395,
-0.05505605414509773,
-0.051169611513614655,
0.002755695953965187,
-0.020041871815919876,
0.04368104413151741,
-0.005515613593161106,
0.018807146698236465,
0.03245850279927254,
0.01073752623051405,
0.018246877938508987,
-0.030513253062963486,
-0.03511686250567436,
-0.0027445678133517504,
-0.0466742143034935,
0.005294807720929384,
0.03692317754030228,
0.06264384835958481,
0.008468704298138618,
0.0009871829533949494,
0.016956346109509468,
0.004787377547472715,
-0.05265107750892639,
0.0121802082285285,
-0.008364391513168812,
-0.04483231157064438,
-0.02230188436806202,
-0.09169092029333115,
0.034271884709596634,
0.01250139158219099,
-0.011204730719327927,
-0.020725717768073082,
-0.04337409883737564,
0.03117961809039116,
0.04975845292210579,
-0.012970474548637867,
0.021864423528313637,
0.0688791424036026,
-0.007508726324886084,
-0.0545506626367569,
0.03474101051688194,
0.04538767784833908,
0.011138384230434895,
0.014626791700720787,
0.014160986058413982,
-0.0003954762942157686,
-0.05500134825706482,
0.002550232456997037,
-0.08203056454658508,
0.010237154550850391,
0.024667594581842422,
0.07895444333553314,
0.046455465257167816,
-0.007994238287210464,
-0.02662762813270092,
-0.0017138023395091295,
-0.005516042932868004,
0.0007877197931520641,
0.05419046804308891,
-0.028544651344418526,
0.02113422565162182,
0.023070430383086205,
-0.029521862044930458,
0.012574483640491962,
-0.023946665227413177,
-0.03277201950550079,
0.10475370287895203,
0.02595781348645687,
0.01925591751933098,
-0.029682353138923645,
0.03690321370959282,
0.015903951600193977,
-0.021365059539675713,
-0.05509045720100403,
-0.01979135349392891,
0.03785110265016556,
0.03377142548561096,
-0.011156789027154446,
-0.009608952328562737,
-0.00472008204087615,
-0.017743904143571854,
-0.0028836082201451063,
-0.030199266970157623,
-0.045389674603939056,
0.02237153798341751,
-0.004125142470002174,
-0.04620465636253357,
-0.014260221272706985,
0.020885609090328217,
0.021282903850078583,
-0.0857190266251564,
0.028068840503692627,
-0.07528723776340485,
-0.02639908157289028,
-0.022242624312639236,
-0.08932333439588547,
0.01000305637717247,
0.0007789671653881669,
-0.038016077131032944,
-0.03033788688480854,
-0.038986966013908386,
0.011579429730772972,
0.04452431574463844,
0.005481507629156113,
-0.06992563605308533,
-0.02267787978053093,
0.022314107045531273,
-0.023235607892274857,
0.05530106648802757,
0.02140217274427414,
0.03451893478631973,
-0.009745619259774685,
0.00990016758441925,
-0.03132692724466324,
0.03641770780086517,
0.03851994499564171,
0.008424188941717148,
0.003096564905717969,
-0.015361507423222065,
0.009827105328440666,
0.033341169357299805,
-0.0002210638631368056,
-0.01932930015027523,
-0.006837824359536171,
-0.09924035519361496,
0.020633094012737274,
-0.0008353185839951038,
0.00875127874314785,
0.012135312892496586,
-0.040924072265625,
-0.041337352246046066,
0.05923609435558319,
-0.03429504483938217,
-0.052254319190979004,
0.08977597951889038,
0.016667364165186882,
0.003676340449601412,
-0.012714914046227932,
-0.006387548986822367,
-0.010057026520371437,
-0.016305329278111458,
-0.03510928899049759,
0.021572833880782127,
-0.09823621064424515,
-0.04496242478489876,
0.075722835958004,
-0.015810269862413406,
-0.03582879528403282,
-0.03452686220407486,
-0.02289769984781742,
0.02373695746064186,
0.02589987963438034,
0.028856204822659492,
0.048219941556453705,
0.011466113850474358,
-0.0407051220536232,
-0.023913433775305748,
0.029019413515925407,
0.013724477030336857,
-0.014509563334286213,
-0.0373816080391407,
0.02932087704539299,
-0.002728754188865423,
0.055104970932006836,
0.013629731722176075,
-0.0013888687826693058,
0.03531467169523239,
0.013100206851959229,
-0.060766350477933884,
0.005625350866466761,
0.05367281287908554,
0.020509283989667892,
-0.026437198743224144,
0.04313014820218086,
0.06517743319272995,
-0.0334840826690197,
0.01028392743319273,
0.039142217487096786,
-0.03570127859711647,
0.05979570746421814,
0.02177559956908226,
-0.022226091474294662,
-0.01573084481060505,
0.02734754979610443,
0.0041897958144545555,
0.014059660024940968,
-0.022808454930782318,
0.03753415867686272,
-0.009827754460275173,
0.025451377034187317,
-0.05880608409643173,
0.03882849961519241,
0.01665491610765457,
0.008450478315353394,
-0.04189659282565117,
-0.029428590089082718,
-0.0027408499736338854,
-0.0028783439192920923,
0.020650241523981094,
-0.0432109609246254,
-0.04505425691604614,
0.0354691743850708,
0.034841474145650864,
0.011435004882514477,
0.022619644179940224,
-0.027886319905519485,
0.032815467566251755,
-0.06403033435344696,
0.00593600794672966,
0.042234551161527634,
-0.020608805119991302,
-0.001473963842727244,
-0.08272936940193176,
-0.07773923873901367,
-0.02226385660469532,
-0.06591794639825821,
0.01756538823246956,
-0.04991030693054199,
-0.044314343482255936,
0.04082350805401802,
-0.022053459659218788,
0.03069176897406578,
-0.0025425583589822054,
0.03509226068854332,
-0.024949636310338974,
-0.04659407213330269,
-0.01800728589296341,
-0.00377734680660069,
-0.03739330545067787,
-0.05671678110957146,
0.00024266930995509028,
-0.018408076837658882,
-0.06751425564289093,
0.006434595212340355,
0.0004256849642843008,
0.016997508704662323,
-0.011883074417710304,
-0.00606950931251049,
0.0705532655119896,
-0.045676086097955704,
0.005596221890300512,
-0.004686553031206131,
-0.01074021216481924,
0.04122861102223396,
-0.012554104439914227,
0.037329357117414474,
0.048088379204273224,
-0.02078350819647312,
0.04554301127791405,
0.05456332117319107,
-0.022393278777599335,
-0.022308185696601868,
-0.024939576163887978,
-0.0707789808511734,
-0.03816239908337593,
0.029009705409407616,
0.012312017381191254,
-0.004029379226267338,
0.005939267110079527,
0.01061495766043663,
0.03054284118115902,
-0.028949201107025146,
-0.026265433058142662,
0.07832708954811096,
0.034547824412584305,
0.033318258821964264,
-0.007908345200121403,
0.00990226212888956,
0.024726083502173424,
-0.016570648178458214,
0.02023547887802124,
0.007923892699182034,
-0.04870849475264549,
-0.010850397869944572,
0.03888752683997154,
-0.035271938890218735,
-0.001351462211459875,
-0.005199367646127939,
-0.012525255791842937,
0.005160495173186064,
-0.02727429009974003,
-0.000992432120256126,
-0.02317511849105358,
-0.007979242131114006,
0.04139832407236099,
-0.02022687904536724,
-0.01413135975599289,
-0.030076857656240463,
0.00872405432164669,
-0.02660653553903103,
-0.03621280938386917,
-0.018380356952548027,
0.03348885104060173,
0.02260621264576912,
0.07201001048088074,
-0.019238537177443504,
0.04810686036944389,
-0.06310364603996277,
-0.04110874608159065,
0.04938378557562828,
0.055192481726408005,
-0.02487313561141491,
-0.02152847684919834,
-0.019162477925419807,
-0.038209542632102966,
0.01653694547712803,
-0.04168523848056793,
-0.03118148073554039,
0.007236194331198931,
-0.0027820453979074955,
0.0036391562316566706,
-0.02368985116481781,
-0.0253303162753582,
0.0401717908680439
] |
<p>I've recently seen that space is or could be a quantum vacuum full of particles like matter and anti matter appearing and possibly colliding causing in theory the same effects that dark energy has. My question is could Dark energy or dark matter be a left over waste product of matter/anti matter collisions? </p>
|
g2481
|
[
0.05963185802102089,
-0.013070066459476948,
0.006485599558800459,
-0.021420346572995186,
0.034385014325380325,
0.060111530125141144,
-0.0470438189804554,
0.004865247756242752,
0.0158601775765419,
-0.04497113823890686,
0.057588543742895126,
0.002349472837522626,
0.009588390588760376,
0.008107142522931099,
-0.031173288822174072,
0.00028073907014913857,
0.03521027788519859,
-0.03398638591170311,
-0.04139316454529762,
-0.03658250346779823,
-0.021351393312215805,
-0.060186102986335754,
-0.009689375758171082,
-0.0648663267493248,
-0.06100829318165779,
-0.021290892735123634,
0.009085003286600113,
-0.029146835207939148,
0.022916678339242935,
-0.008521586656570435,
0.030416762456297874,
0.027639247477054596,
-0.013945641927421093,
-0.02395646832883358,
-0.043038032948970795,
-0.013599739409983158,
0.061616335064172745,
0.007702026516199112,
0.038444314152002335,
-0.0213422030210495,
-0.045799240469932556,
-0.027400264516472816,
-0.01568739488720894,
0.008055624552071095,
0.008183898404240608,
0.06643938273191452,
-0.05495768412947655,
0.018353166058659554,
-0.01660473272204399,
-0.015552513301372528,
-0.054621610790491104,
0.009276231750845909,
-0.0032400598283857107,
0.05485329404473305,
0.023472461849451065,
-0.013364854268729687,
0.027222730219364166,
-0.0513700433075428,
0.12110472470521927,
0.013881118968129158,
-0.02308412455022335,
0.04318048059940338,
-0.01695813611149788,
0.03299323841929436,
0.04586375504732132,
-0.01902487501502037,
-0.033181238919496536,
-0.0023625041358172894,
0.024654237553477287,
0.013852395117282867,
0.10191594809293747,
0.014059420675039291,
-0.022764137014746666,
-0.00004993261973140761,
-0.01820858009159565,
0.04097839072346687,
0.03851380571722984,
0.013802237808704376,
0.03177518770098686,
-0.011051786132156849,
-0.09394332021474838,
-0.041252680122852325,
-0.000014134213415673003,
-0.023599740117788315,
0.09807861596345901,
-0.054741840809583664,
-0.019401248544454575,
0.014256477355957031,
0.03296925500035286,
0.04132086783647537,
0.0255894735455513,
0.003813230898231268,
0.01802993379533291,
-0.002549754222854972,
-0.018773794174194336,
0.040001146495342255,
-0.014071756042540073,
0.05681231617927551,
-0.021009234711527824,
-0.02000596560537815,
-0.051887042820453644,
-0.00478333467617631,
0.0471351332962513,
-0.025367071852087975,
0.09836825728416443,
-0.0275846179574728,
0.0022268067114055157,
-0.010289006866514683,
-0.018553320318460464,
0.025350235402584076,
-0.03693271800875664,
0.006483720149844885,
-0.05158371478319168,
-0.010811316780745983,
0.01466365996748209,
-0.039539825171232224,
0.050663791596889496,
0.0007010598201304674,
-0.0010068747214972973,
0.02623872645199299,
-0.0023913646582514048,
-0.003337637986987829,
-0.025601478293538094,
-0.04253997281193733,
-0.012404735200107098,
-0.00956201646476984,
0.04521669074892998,
-0.057461779564619064,
0.021974103525280952,
-0.02703622542321682,
0.004327208735048771,
-0.04729268699884415,
0.008885573595762253,
0.022282296791672707,
0.0247823353856802,
0.03189961239695549,
-0.00030519923893734813,
0.03204599395394325,
-0.0053527746349573135,
-0.006548346020281315,
0.05156179517507553,
-0.004442763049155474,
-0.04962344095110893,
0.03730209916830063,
-0.024646250531077385,
-0.004256352782249451,
0.013582038693130016,
-0.009222901426255703,
-0.07307441532611847,
0.0015791872283443809,
0.0371389240026474,
0.040797822177410126,
-0.032269805669784546,
-0.07831722497940063,
-0.00926316436380148,
0.022113870829343796,
-0.05278482288122177,
0.006690422538667917,
0.0043241060338914394,
-0.0694849044084549,
0.027013087645173073,
0.008455263450741768,
0.054179705679416656,
-0.047635920345783234,
-0.030585583299398422,
-0.036485761404037476,
-0.025154022499918938,
-0.07273858785629272,
0.04860561713576317,
0.013919738121330738,
-0.03940629959106445,
0.008698089979588985,
0.04175332933664322,
0.006086130626499653,
0.020475182682275772,
0.022760313004255295,
0.0049415878020226955,
-0.02453223243355751,
0.0012892873492091894,
-0.06319825351238251,
0.020891018211841583,
-0.007316416595131159,
0.029223177582025528,
-0.02339046820998192,
0.08518189936876297,
-0.003212295938283205,
-0.02497909404337406,
-0.0003642207884695381,
-0.007453376892954111,
0.030810700729489326,
-0.0025217437651008368,
-0.00850221049040556,
-0.011876960285007954,
0.03418101370334625,
0.062105558812618256,
-0.02720719575881958,
-0.027825064957141876,
0.0027223725337535143,
-0.055383577942848206,
0.018618596717715263,
0.0067071979865431786,
-0.013795911334455013,
0.01435296144336462,
0.005612550303339958,
0.023431023582816124,
0.004380630794912577,
-0.008168279193341732,
-0.03491108492016792,
-0.008306167088449001,
0.02386920526623726,
0.056598056107759476,
0.04230940714478493,
0.03989449143409729,
-0.003883583936840296,
-0.0853240042924881,
0.0557306669652462,
-0.040804628282785416,
0.054899826645851135,
-0.005804589483886957,
0.02122635580599308,
-0.09982437640428543,
-0.02347317524254322,
0.03189895302057266,
-0.03551498055458069,
0.02391028217971325,
-0.013305039145052433,
-0.03879591450095177,
-0.035635046660900116,
-0.04616372287273407,
0.022012388333678246,
-0.023559367284178734,
0.037321772426366806,
0.01843167096376419,
-0.016271159052848816,
0.07477680593729019,
0.010407816618680954,
-0.014878321439027786,
0.022301897406578064,
-0.003860343946143985,
0.04593390226364136,
-0.008510833606123924,
-0.01992572471499443,
-0.0429045595228672,
0.04184141382575035,
0.060471437871456146,
-0.07687971740961075,
-0.0013201667461544275,
0.008702595718204975,
0.049681756645441055,
-0.06861760467290878,
0.012516197748482227,
0.012494778260588646,
0.00641633290797472,
-0.02353033982217312,
0.017198845744132996,
-0.0002832262252923101,
-0.032957207411527634,
0.06626202911138535,
-0.046246662735939026,
-0.03808322921395302,
0.003189366776496172,
0.026207270100712776,
-0.027757899835705757,
0.03159288689494133,
0.011385583318769932,
0.016277944669127464,
0.004734927788376808,
0.027638543397188187,
-0.029925379902124405,
0.029157929122447968,
-0.01585647277534008,
-0.028426503762602806,
0.00002864663656509947,
-0.002828100463375449,
0.05802996829152107,
0.04086632654070854,
-0.0025984805542975664,
-0.020810438320040703,
0.06454000622034073,
-0.041166242212057114,
-0.035226523876190186,
0.06933647394180298,
-0.0446818545460701,
0.017313793301582336,
0.013445516116917133,
-0.015259511768817902,
-0.04318353906273842,
-0.0294059868901968,
-0.014477567747235298,
0.01776408962905407,
0.01494632288813591,
0.04708584025502205,
0.03274896740913391,
0.0259083341807127,
-0.016209399327635765,
0.06743068993091583,
-0.018008112907409668,
0.015608801506459713,
-0.03668007627129555,
-0.016336796805262566,
-0.011233227327466011,
-0.04744816571474075,
0.020377926528453827,
0.05173046514391899,
0.022655148059129715,
0.023276284337043762,
-0.05314838886260986,
0.04027983173727989,
-0.016475651413202286,
-0.04107630252838135,
0.03228064253926277,
0.03432812914252281,
-0.016945142298936844,
0.0375315397977829,
-0.027977166697382927,
-0.008411791175603867,
0.045170582830905914,
-0.018425552174448967,
-0.008891958743333817,
-0.010413486510515213,
0.01688787154853344,
-0.05585695430636406,
0.05126594007015228,
-0.04741030931472778,
0.04664570838212967,
0.01140639279037714,
-0.02684209682047367,
-0.0018273625755682588,
-0.003941928967833519,
0.021051257848739624,
0.026169532909989357,
-0.06680336594581604,
-0.02269880659878254,
-0.009100870229303837,
-0.041345901787281036,
0.02137625776231289,
-0.03311925753951073,
0.003572427434846759,
0.04091644659638405,
0.048849452286958694,
0.01611243188381195,
0.04225575178861618,
-0.0057192593812942505,
0.04834907501935959,
-0.025022797286510468,
0.061193712055683136,
0.03439376875758171,
-0.0498136505484581,
0.031038837507367134,
-0.007028572261333466,
0.017962681129574776,
-0.040428660809993744,
0.06181054934859276,
0.003844920080155134,
-0.027080588042736053,
0.07557304203510284,
0.03461368754506111,
0.03316153213381767,
0.03940599039196968,
-0.05602068454027176,
-0.03236464783549309,
-0.0510086864233017,
0.03300844877958298,
-0.050937116146087646,
0.02911071479320526,
-0.01236721407622099,
-0.01722303032875061,
-0.04366461932659149,
0.00145327381324023,
-0.02777017280459404,
0.04422450065612793,
-0.0016912365099415183,
-0.02908644825220108,
0.04263652488589287,
0.033055711537599564,
-0.022951539605855942,
0.01722063682973385,
0.012628765776753426,
-0.006537049077451229,
-0.05313321202993393,
0.06498951464891434,
0.04023800417780876,
0.0028844412881881,
0.018545355647802353,
-0.021622393280267715,
-0.004561521578580141,
-0.06049838662147522,
0.0023410129360854626,
-0.04189854487776756,
0.020218968391418457,
0.0031363884918391705,
-0.011083682999014854,
-0.03181930258870125,
0.00561732891947031,
-0.0340050645172596,
-0.013843260705471039,
0.057420361787080765,
-0.007942194119095802,
0.020542096346616745,
-0.005042648874223232,
0.04899993911385536,
0.07418946921825409,
0.006726703606545925,
-0.04239240661263466,
0.04297330603003502,
0.017473885789513588,
0.026474595069885254,
-0.015676571056246758,
-0.0633067786693573,
-0.04790925234556198,
0.00964503176510334,
-0.02143240161240101,
-0.030261114239692688,
0.007509618066251278,
-0.023672346025705338,
0.002866261638700962,
0.006865919567644596,
0.04071022570133209,
0.07065083831548691,
0.008070668205618858,
0.0010100107174366713,
0.013275831006467342,
0.038787636905908585,
0.04001263529062271,
-0.02880159206688404,
0.07177387923002243,
-0.0014334901934489608,
-0.013583652675151825,
-0.04488867521286011,
-0.0005797489429824054,
0.019576914608478546,
0.005301979836076498,
-0.04748062044382095,
0.027608899399638176,
-0.015467824414372444,
0.03358529508113861,
-0.07717043161392212,
-0.008752853609621525,
0.00031236623181030154,
0.01205880381166935,
0.10970169305801392,
-0.00032677865237928927,
0.06273358315229416,
-0.00968528725206852,
0.017010455951094627,
0.08929178863763809,
-0.02763557620346546,
-0.07604458183050156,
-0.019220387563109398,
-0.02498990297317505,
-0.006724483333528042,
0.008730270899832249,
0.031030215322971344,
-0.03155355527997017,
-0.005440212786197662,
0.01910807378590107,
-0.02245762012898922,
-0.017169294878840446,
-0.040317099541425705,
0.02607320249080658,
-0.03405825421214104,
-0.0073996842838823795,
0.03932901844382286,
-0.00810422096401453,
-0.005146284122020006,
-0.030596505850553513,
-0.04938354343175888,
0.00035176865640096366,
-0.06056688353419304,
0.032552074640989304,
-0.012696339748799801,
0.02979947067797184,
-0.03541989624500275,
0.010400310158729553,
-0.015972765162587166,
-0.06838571280241013,
-0.03966163843870163,
-0.028375942260026932,
-0.0021698286291211843,
0.025666210800409317,
0.026547890156507492,
-0.012910166755318642,
0.03965962305665016,
-0.04270746186375618,
-0.04570762813091278,
0.0216587632894516,
-0.05058236047625542,
0.036049626767635345,
-0.029807494953274727,
-0.01806819438934326,
-0.02103050984442234,
0.030187459662556648,
-0.0072320918552577496,
-0.011659558862447739,
-0.03344470635056496,
0.07183077186346054,
-0.02846512757241726,
-0.028807969763875008,
-0.05805521085858345,
0.017490845173597336,
0.044693391770124435,
-0.044756509363651276,
0.0031320257112383842,
-0.042005740106105804,
-0.04025844484567642,
0.002812538295984268,
-0.005656149238348007,
-0.021407153457403183,
0.009881600737571716,
-0.0219624862074852,
-0.053287338465452194,
0.007758965250104666,
-0.028586946427822113,
0.09250682592391968,
0.0062433346174657345,
-0.010721352882683277,
0.006757604889571667,
0.044282302260398865,
0.029153333976864815,
-0.03728489577770233,
-0.03514676168560982,
0.0178411565721035,
0.0292294230312109,
0.07039668411016464,
0.04847852140665054,
-0.013314906507730484,
-0.012751512229442596,
0.0823897272348404,
-0.03766931593418121,
0.05790485441684723,
0.05256016552448273,
0.008396347053349018,
0.04554779827594757,
0.027057526633143425,
-0.025014188140630722,
-0.028802091255784035,
-0.009306825697422028,
0.04739663004875183,
0.06302438676357269,
0.043825872242450714,
-0.02989625744521618,
-0.07346845418214798,
-0.0026041052769869566,
0.06709253042936325,
0.00048017228255048394,
0.002293731551617384,
-0.06906543672084808,
-0.008084564469754696,
-0.010576433502137661,
-0.09974940121173859,
-0.01902405172586441,
0.009177492931485176,
-0.0017047951696440578,
-0.021973013877868652,
-0.0384540893137455,
-0.03455653041601181,
0.005233342293649912,
0.006270154844969511,
-0.042669445276260376,
0.002214049454778433,
0.030273476615548134,
0.0018359411042183638,
-0.0172412246465683,
0.014654157683253288,
-0.024533381685614586,
-0.004173021763563156,
0.042500998824834824,
-0.008840999566018581,
0.009605038911104202,
-0.08466450870037079,
0.015698092058300972,
0.06346304714679718,
-0.03577525541186333,
-0.032462384551763535,
0.009849004447460175,
-0.05769122391939163,
0.01503811776638031,
-0.062297362834215164,
-0.08330349624156952,
0.002337476471439004,
0.11425695568323135,
0.005497204139828682,
0.04206797480583191,
-0.04575878381729126,
-0.03440289571881294,
0.03719080612063408,
-0.013273565098643303,
0.005971002858132124,
0.015275378711521626,
0.02646610699594021,
-0.059710659086704254,
0.0009073858382180333,
0.02451009675860405,
0.020800964906811714,
-0.029475286602973938,
-0.03188399225473404,
-0.02598540112376213,
-0.014498050324618816,
-0.035615768283605576,
-0.006232594605535269,
-0.036763161420822144,
0.02433273382484913,
-0.029042547568678856,
0.016290167346596718,
0.028672300279140472,
-0.0065221842378377914,
-0.06513354927301407,
0.02090456895530224,
0.002773918677121401,
0.014085694216191769,
0.00400218041613698,
-0.025102850049734116,
-0.06189022213220596,
0.08953174948692322,
-0.0451929047703743,
-0.018035298213362694,
-0.016797278076410294,
-0.030644819140434265,
0.008414988406002522,
0.0011882586404681206,
0.027415867894887924,
0.03489096835255623,
-0.02610360085964203,
-0.02519136480987072,
0.030489694327116013,
0.06249850615859032,
-0.053710319101810455,
0.06828583776950836,
0.0824260488152504,
0.07967410981655121,
0.0076707652769982815,
-0.0063830274157226086,
0.02343853749334812,
-0.03200908750295639,
-0.09421610832214355,
0.014935936778783798,
0.011865888722240925,
-0.003293177578598261,
-0.018231185153126717,
-0.028741104528307915,
0.04484696313738823,
-0.06144566461443901,
0.020118307322263718,
0.0031827613711357117,
-0.02498031221330166,
0.018436668440699577,
0.07158418744802475,
0.0016754824900999665,
-0.006908010225743055,
-0.0526638925075531,
-0.05115919187664986,
0.00482600275427103,
0.019401274621486664,
-0.058496855199337006,
-0.055408917367458344,
0.012072178535163403,
-0.018815692514181137,
-0.01274608913809061,
-0.005374306812882423,
-0.053867876529693604,
0.033062584698200226,
-0.04958958551287651,
-0.04519224539399147,
0.005312154069542885,
0.01925268955528736,
0.014745701104402542,
0.03296451270580292,
-0.015712032094597816,
0.012928935699164867,
-0.039583150297403336,
-0.024708323180675507,
-0.04564895108342171,
-0.059644829481840134,
0.0533364862203598,
-0.015932004898786545,
-0.04427243396639824,
0.003695311490446329,
0.027240434661507607,
0.03591949865221977,
0.027111634612083435,
0.016072088852524757,
-0.015110369771718979,
-0.02677851915359497,
0.007378957234323025,
0.013814604841172695,
0.05929732695221901,
0.049407947808504105,
-0.024455413222312927,
-0.020316006615757942,
-0.0025240322574973106,
0.025801032781600952,
-0.012725990265607834,
0.006078542210161686,
-0.07733248919248581,
-0.018047621473670006,
0.032224372029304504,
0.07318457961082458,
0.04453139379620552,
-0.0013653668574988842,
0.01719594933092594,
-0.013074399903416634,
0.053122133016586304,
-0.004354889504611492,
-0.021278344094753265,
-0.024103527888655663,
0.025162549689412117,
0.03492550924420357,
-0.025190606713294983,
-0.02497568167746067,
0.051482509821653366,
0.08177676051855087,
0.040376462042331696,
0.023832596838474274,
0.02148897759616375,
0.008789683692157269,
-0.032482415437698364,
0.03404304385185242,
-0.007080879062414169,
0.04178319498896599,
0.0008641979657113552,
-0.03126564621925354,
-0.023386670276522636,
-0.03555845096707344,
-0.006009409204125404,
0.020092930644750595,
-0.0028854082338511944,
-0.005417949054390192,
0.001761506893672049,
-0.023884890601038933,
0.025283655151724815,
-0.013226077891886234,
0.010193848051130772,
0.01062776893377304,
-0.02551371417939663,
0.01550474762916565,
-0.009302199818193913,
0.02855709008872509,
-0.024622982367873192,
-0.02660110406577587,
0.03663412481546402,
0.04241814464330673,
-0.04247279092669487,
-0.002663874300196767,
-0.0028014115523546934,
0.004977589473128319,
-0.04307401552796364,
-0.008551725186407566,
-0.027869481593370438,
-0.007279159501194954,
0.009285608306527138,
0.02064508944749832,
-0.023405423387885094,
0.02356869913637638,
0.03494357690215111,
0.08101893216371536,
-0.03810494765639305,
0.038112491369247437,
0.03663446381688118,
-0.08036205917596817,
0.00230006268247962,
0.0257208663970232,
-0.016028709709644318,
0.005021007731556892,
-0.009368480183184147,
0.002208363264799118,
-0.039753951132297516,
-0.006542279850691557,
0.027177732437849045
] |
<p>Basically, what are all the parameters that completely describe an electron in quantum theory.</p>
<p>In classical physics a complete and fundamental description of an electron is given by its mass, charge, and position. So $(m, q, \vec{x}(t))$ gives you complete information about the electron.</p>
<p>I would like the analogous description of the quantum electron. Typically I only see electrons described by a state vector over position or a state vector over spin. But <a href="http://www.eng.fsu.edu/~dommelen/quantum/style_a/complexs.html#SECTION07451000000000000000" rel="nofollow">this page</a> explains how to represent both . I am guessing the quantum picture of an electron is something like $(m, q, \phi(\vec{x},s;t))$ where $\left| \phi\right\rangle$ is the state vector and $(\vec{x},s)$ is its "index". $s\in\{-{1\over2}\hbar,{1\over2}\hbar\}$ is the spin measured along some axis in space. Am I missing anything? Like for instance, lepton number? Does this picture change when relativity is introduced? I don't care about how the state evolves for this question, just what mathematical objects are present in the computations.</p>
|
g2482
|
[
0.012629853561520576,
-0.00561168510466814,
-0.03808438405394554,
-0.022976642474532127,
0.013749966397881508,
-0.0302128829061985,
0.02987869642674923,
0.012189777567982674,
-0.021025093272328377,
0.034918006509542465,
0.037501513957977295,
0.022924508899450302,
0.05282950401306152,
0.012491371482610703,
0.0022257291711866856,
-0.042381078004837036,
0.05186130478978157,
-0.005375623237341642,
0.045746345072984695,
-0.019913405179977417,
0.041325222700834274,
0.0028412467800080776,
0.006831348408013582,
0.005966672208160162,
-0.03126133233308792,
0.0010370000964030623,
0.010768893174827099,
0.033661991357803345,
0.007462162058800459,
0.04658978804945946,
-0.03614374250173569,
0.02122787944972515,
0.08507426083087921,
-0.036099277436733246,
0.0264667347073555,
-0.03474260866641998,
0.014519141055643559,
0.05272504687309265,
0.006405224557965994,
-0.0018839978147298098,
-0.016430174931883812,
-0.06251209229230881,
-0.03568263724446297,
-0.016627131029963493,
0.023010574281215668,
0.0010136773344129324,
0.018589667975902557,
0.031933221966028214,
-0.05575679615139961,
0.013019584119319916,
-0.01206277497112751,
0.043459367007017136,
0.032302480190992355,
0.011619937606155872,
0.06918144226074219,
-0.0012181056663393974,
-0.044342346489429474,
0.03702204301953316,
0.11884506791830063,
0.030414951965212822,
-0.0314931757748127,
0.03581130504608154,
-0.045723807066679,
0.02140667289495468,
0.07470729947090149,
0.03088182397186756,
-0.031947411596775055,
0.03651297837495804,
-0.02874141000211239,
0.022122718393802643,
-0.007264384534209967,
-0.08625227212905884,
-0.030450966209173203,
-0.028920186683535576,
-0.00831935741007328,
0.03469539433717728,
-0.016066720709204674,
-0.06841017305850983,
0.049781206995248795,
0.001884928555227816,
0.0008886519353836775,
-0.015151920728385448,
0.036520298570394516,
-0.011095686815679073,
0.03268418833613396,
-0.003657163819298148,
-0.027016881853342056,
0.005464446730911732,
0.0023620969150215387,
-0.0049705407582223415,
0.016090286895632744,
-0.046423450112342834,
0.027625326067209244,
0.014674696139991283,
-0.016009880229830742,
-0.040844399482011795,
-0.05060828477144241,
0.01875549741089344,
-0.005986353848129511,
0.00931619107723236,
-0.01831398904323578,
0.00299438345246017,
0.03974705561995506,
-0.03175083175301552,
0.010439571924507618,
-0.0007591829635202885,
0.02001236006617546,
-0.002712516114115715,
0.0631544440984726,
0.028580399230122566,
-0.022787712514400482,
-0.0006394684896804392,
-0.01845235377550125,
0.0064441910944879055,
-0.08720239251852036,
-0.026760930195450783,
0.07877551764249802,
-0.028620120137929916,
-0.014345004223287106,
0.0396328829228878,
0.017726678401231766,
0.05553796887397766,
0.08970731496810913,
0.06630256772041321,
-0.004661069251596928,
0.016060201451182365,
0.013403575867414474,
-0.013569839298725128,
0.028419718146324158,
0.033087167888879776,
-0.016019323840737343,
-0.0364077165722847,
-0.03460151329636574,
0.032310158014297485,
0.020205644890666008,
0.07624298334121704,
-0.016744662076234818,
0.037069931626319885,
0.0033424103166908026,
-0.0070073576644063,
0.00509968027472496,
-0.023630604147911072,
-0.06528417766094208,
-0.04925226420164108,
-0.0037952172569930553,
-0.02271568402647972,
0.02264423668384552,
-0.05123147740960121,
0.05402655154466629,
-0.01499028131365776,
0.00833575613796711,
0.0686715617775917,
-0.017422040924429893,
-0.02048983983695507,
0.0005719100590795279,
-0.05869356915354729,
0.08478858321905136,
-0.00962219201028347,
-0.01245596632361412,
0.023705951869487762,
0.029063189402222633,
-0.03660619631409645,
0.04013753682374954,
-0.028854021802544594,
0.0004640008555725217,
-0.03359502926468849,
-0.016173191368579865,
-0.08351606875658035,
0.03483159467577934,
-0.04174214228987694,
0.06782840192317963,
-0.013209548778831959,
-0.0030750075820833445,
0.010906646959483624,
0.009883624501526356,
0.019859688356518745,
0.008333197794854641,
0.008177477866411209,
0.03706273064017296,
0.045562393963336945,
0.0010247939499095082,
0.005294036585837603,
0.07682020217180252,
0.01323729008436203,
-0.026651833206415176,
0.006994158960878849,
0.0029896479099988937,
0.027046838775277138,
-0.009814118966460228,
-0.016769198700785637,
0.018772510811686516,
-0.00031059712637215853,
0.029334913939237595,
0.025278721004724503,
-0.03738267719745636,
0.0014493971830233932,
0.01975569687783718,
-0.025386856868863106,
-0.05533702298998833,
-0.006995673291385174,
0.037957556545734406,
0.04855639114975929,
0.009963656775653362,
0.08811618387699127,
-0.0022289457265287638,
0.025134677067399025,
-0.016271695494651794,
0.0007396885775960982,
0.01543634943664074,
0.03147056698799133,
0.028296640142798424,
0.03276779130101204,
0.03881526738405228,
0.05574188381433487,
-0.0542854443192482,
-0.022300155833363533,
0.032631151378154755,
0.0034156416077166796,
-0.012150831520557404,
0.0012842727592214942,
-0.006538723595440388,
-0.1063934788107872,
0.05421406775712967,
0.01579734869301319,
-0.03185707703232765,
0.03700248524546623,
0.001682206173427403,
-0.055829908698797226,
0.02028917521238327,
0.08251965045928955,
-0.01791311614215374,
0.007697860710322857,
-0.001621513394638896,
-0.014315280131995678,
0.062235020101070404,
0.026371166110038757,
-0.04437597841024399,
0.001980103785172105,
0.00014736961747985333,
0.010656324215233326,
0.048842400312423706,
0.022863755002617836,
-0.005058123730123043,
0.00877681840211153,
0.016555095091462135,
0.016364222392439842,
-0.0017327842069789767,
-0.03996748849749565,
0.025499485433101654,
0.04272287338972092,
-0.07911108434200287,
-0.061515796929597855,
-0.06518611311912537,
0.056464847177267075,
0.030981339514255524,
-0.010977079160511494,
-0.04048594459891319,
-0.024278441444039345,
-0.05064677447080612,
-0.04225803539156914,
-0.044699303805828094,
-0.002478017471730709,
-0.016222789883613586,
0.03283977136015892,
-0.05931592732667923,
-0.04637421295046806,
0.03434772416949272,
-0.014175284653902054,
0.009293325245380402,
-0.06154247000813484,
-0.024353178218007088,
0.054962705820798874,
-0.05904656648635864,
-0.02496473304927349,
0.023190412670373917,
-0.09065958857536316,
-0.05135802552103996,
0.050947315990924835,
-0.015612155199050903,
-0.08775070309638977,
-0.005629885476082563,
-0.04277222603559494,
-0.018711376935243607,
0.026228906586766243,
-0.002356321085244417,
-0.025761762633919716,
0.0143754743039608,
0.00969544518738985,
-0.020658766850829124,
0.027902156114578247,
-0.058391422033309937,
0.041729625314474106,
0.044504836201667786,
-0.032102905213832855,
-0.054722193628549576,
0.03213508799672127,
0.03256544843316078,
0.015157146379351616,
-0.036438219249248505,
0.028646288439631462,
-0.008495647460222244,
-0.010342697612941265,
-0.01221016701310873,
0.014403720386326313,
0.07957781851291656,
0.008058398962020874,
-0.03923485055565834,
-0.018249666318297386,
-0.051811423152685165,
-0.021793773397803307,
-0.025674767792224884,
-0.027263177558779716,
-0.009323843754827976,
0.003522096201777458,
-0.02614900842308998,
0.011167681775987148,
-0.03138141706585884,
0.027792518958449364,
0.020221536979079247,
-0.008088130503892899,
-0.036614421755075455,
-0.0209942739456892,
0.04480471462011337,
0.019100811332464218,
0.027586573734879494,
0.031562689691782,
-0.022029297426342964,
0.03651142865419388,
-0.04711892828345299,
0.0030874558724462986,
0.035284772515296936,
0.006043193396180868,
0.002776386449113488,
-0.011764030903577805,
-0.008615091443061829,
0.010162996128201485,
-0.024408603087067604,
-0.036188799887895584,
0.037230923771858215,
-0.04298229143023491,
0.0339755043387413,
-0.028968842700123787,
-0.03965003415942192,
0.04544324800372124,
0.04657713696360588,
-0.022066010162234306,
-0.0364360511302948,
-0.07920525968074799,
0.038187820464372635,
-0.07624059915542603,
-0.0217986349016428,
0.03668450936675072,
-0.01969142071902752,
0.03396948054432869,
-0.044880449771881104,
0.026866521686315536,
0.006068589631468058,
0.01755026914179325,
0.0211928840726614,
0.018024103716015816,
0.050180092453956604,
-0.03197651728987694,
0.028686679899692535,
0.025384780019521713,
0.010072263889014721,
-0.024254407733678818,
-0.04395248740911484,
0.018764132633805275,
0.02565600909292698,
-0.02711738646030426,
-0.02164279669523239,
-0.003839735873043537,
0.015366633422672749,
-0.039007559418678284,
0.02333654835820198,
-0.038096629083156586,
-0.03375418484210968,
-0.02138383872807026,
-0.09942074865102768,
-0.003191683441400528,
0.010945305228233337,
0.031238507479429245,
0.052645690739154816,
0.030150754377245903,
0.028507210314273834,
-0.01882336102426052,
-0.00292004831135273,
0.019198594614863396,
-0.030714649707078934,
-0.020582038909196854,
0.017437003552913666,
-0.08582881838083267,
0.0015517050633206964,
0.014509422704577446,
-0.0028175851330161095,
0.0177669245749712,
0.08622751384973526,
-0.0485185869038105,
-0.02879161946475506,
-0.0011272248812019825,
-0.03770698606967926,
0.011276043951511383,
0.042270783334970474,
-0.013264474458992481,
0.014702342450618744,
0.016906915232539177,
0.003928658086806536,
-0.03797939419746399,
0.02145005203783512,
-0.03573017939925194,
0.0015188463730737567,
0.07623249292373657,
-0.00811934843659401,
-0.01803908310830593,
-0.027449004352092743,
0.10262502729892731,
-0.013218778185546398,
-0.07573336362838745,
-0.034634076058864594,
0.012059839442372322,
-0.025032855570316315,
0.0212752353399992,
0.05407304689288139,
-0.03582203388214111,
-0.04677160829305649,
0.048624832183122635,
0.019217995926737785,
0.011948184110224247,
-0.0015334589406847954,
0.01182851754128933,
0.00037618953501805663,
0.024147549644112587,
0.04693611338734627,
0.06011544540524483,
-0.03896182402968407,
-0.008442137390375137,
-0.08134062588214874,
-0.017389841377735138,
0.0021155420690774918,
-0.029939889907836914,
0.042173657566308975,
0.0024066364858299494,
0.04198170825839043,
0.009184183552861214,
-0.04601476714015007,
-0.010371739976108074,
-0.02650292217731476,
-0.0025197037030011415,
-0.07242269814014435,
-0.05672571808099747,
-0.04776029288768768,
0.037018049508333206,
-0.06046324595808983,
-0.001260866760276258,
0.0023231059312820435,
-0.004756717476993799,
-0.010347919538617134,
-0.024856723845005035,
0.02940032258629799,
-0.01706823892891407,
-0.042512666434049606,
-0.0043907384388148785,
-0.03197594732046127,
0.021408965811133385,
0.02413434349000454,
-0.018279293552041054,
-0.12678088247776031,
0.05907844379544258,
-0.07413899153470993,
-0.013898340053856373,
0.03740803524851799,
-0.030644627287983894,
0.07529816776514053,
-0.00015159013855736703,
0.08334657549858093,
-0.038005679845809937,
-0.028560081496834755,
-0.03628401830792427,
-0.03758084401488304,
-0.021858785301446915,
-0.007379733957350254,
-0.022534998133778572,
0.04097607359290123,
-0.018120761960744858,
0.016522560268640518,
-0.025487253442406654,
0.025879992172122,
0.03501691296696663,
-0.0005698207532986999,
0.006810896564275026,
0.02795565314590931,
0.025583835318684578,
-0.01905009336769581,
-0.020272793248295784,
0.015748267993330956,
-0.06122324615716934,
0.03198736533522606,
-0.04395421966910362,
0.05271371081471443,
0.03481673449277878,
-0.013716083019971848,
0.03177128732204437,
0.0025065443478524685,
0.026763755828142166,
0.03102436475455761,
0.018447425216436386,
0.05752796679735184,
-0.04719638451933861,
-0.062377288937568665,
0.04105072095990181,
-0.021527159959077835,
0.0052902610041201115,
-0.00843136291950941,
0.023618541657924652,
0.0037202138919383287,
0.0024009919725358486,
-0.0379876010119915,
0.023300789296627045,
-0.03094848059117794,
-0.0022259526886045933,
-0.011518041603267193,
-0.04950888082385063,
0.04081925377249718,
-0.03313891589641571,
0.033014703541994095,
-0.009367870166897774,
-0.017153823748230934,
0.00026849802816286683,
0.052735380828380585,
0.04403724521398544,
0.0051490021869540215,
-0.00392195675522089,
0.001644896692596376,
0.004293421749025583,
-0.007625629659742117,
-0.020165422931313515,
0.004618870094418526,
0.024184783920645714,
0.033645112067461014,
0.04086806997656822,
-0.04795752093195915,
-0.014991304837167263,
-0.01813550852239132,
0.07740053534507751,
-0.0028167327400296926,
-0.027193421497941017,
-0.024620296433568,
-0.02932780608534813,
-0.006338354665786028,
0.017871856689453125,
-0.037786729633808136,
0.02731787972152233,
0.02628760226070881,
-0.03181065618991852,
0.015441790223121643,
0.03207338601350784,
0.011973107233643532,
-0.02187572978436947,
-0.03637707233428955,
0.0035138861276209354,
0.04364858567714691,
0.011758221313357353,
0.007378606591373682,
0.05656643956899643,
0.007789777126163244,
0.009955902583897114,
-0.007982187904417515,
-0.0007561659440398216,
0.053752824664115906,
0.02445145510137081,
-0.015320547856390476,
-0.022817378863692284,
-0.005578205920755863,
-0.013641578145325184,
-0.006491607986390591,
-0.00112082005944103,
0.013274931348860264,
-0.028346538543701172,
-0.06493135541677475,
-0.007748459465801716,
0.048297218978405,
0.036976903676986694,
-0.05056056007742882,
-0.01852559670805931,
0.0026517221704125404,
0.046289633959531784,
-0.06369933485984802,
-0.0039179506711661816,
0.034353338181972504,
0.06808716058731079,
0.0012680472573265433,
0.023755168542265892,
-0.037252068519592285,
-0.056326232850551605,
0.029176481068134308,
0.05211729183793068,
0.03977862372994423,
-0.03030906431376934,
-0.03767823055386543,
0.012069814838469028,
0.04445619508624077,
0.0009168313699774444,
0.0245649591088295,
0.031025724485516548,
0.06723727285861969,
0.019946612417697906,
-0.040553707629442215,
-0.021551156416535378,
-0.012048793025314808,
-0.041264958679676056,
-0.025685420259833336,
0.007755497470498085,
-0.0063649616204202175,
0.01713119074702263,
-0.027756884694099426,
-0.025781678035855293,
-0.02602800913155079,
0.03411651402711868,
-0.06950508058071136,
0.022215742617845535,
-0.042493436485528946,
0.0015598213067278266,
-0.018895737826824188,
0.02134040929377079,
0.043863002210855484,
0.022173933684825897,
0.02417328581213951,
0.07819509506225586,
0.08310329914093018,
-0.007582926191389561,
0.013563270680606365,
-0.009730756282806396,
0.0044894469901919365,
0.055037349462509155,
0.03343150019645691,
0.0159000176936388,
-0.03348919749259949,
0.013493121601641178,
0.022742990404367447,
0.07282941788434982,
-0.025226639583706856,
-0.037431538105010986,
0.039357878267765045,
-0.002937429118901491,
-0.09244490414857864,
-0.06851217150688171,
-0.0071221934631466866,
-0.05349437892436981,
-0.048319585621356964,
-0.004397556651383638,
0.04532857611775398,
-0.006070928648114204,
-0.02745087258517742,
0.02803972363471985,
-0.02715717814862728,
-0.012578335590660572,
0.030334895476698875,
-0.02280215173959732,
0.06382427364587784,
-0.08132033795118332,
-0.0029657725244760513,
-0.03307801112532616,
0.0052585420198738575,
-0.037215180695056915,
0.010253243148326874,
0.06277583539485931,
-0.017345938831567764,
-0.06696179509162903,
0.033789996057748795,
-0.009945922531187534,
-0.03391280397772789,
-0.017265038564801216,
-0.010430768132209778,
0.07562053203582764,
-0.04621221497654915,
-0.01737482286989689,
-0.019712496548891068,
0.06832750886678696,
-0.031354162842035294,
-0.020390605553984642,
-0.02568691596388817,
0.08311591297388077,
0.03827311098575592,
-0.004120384342968464,
-0.03155554458498955,
-0.06528446823358536,
-0.014006012119352818,
0.028337186202406883,
-0.030279159545898438,
-0.0000758475944167003,
0.044513728469610214,
-0.08099907636642456,
0.001781501923687756,
-0.057536009699106216,
0.020468827337026596,
-0.019961906597018242,
-0.016415206715464592,
-0.006277758162468672,
0.028563521802425385,
-0.019434742629528046,
0.07580113410949707,
-0.026284603402018547,
-0.004590251948684454,
-0.03307566046714783,
0.04078061878681183,
-0.002971465466544032,
-0.013357261195778847,
-0.04055996984243393,
-0.02274283953011036,
0.01545166689902544,
0.04618816450238228,
0.021790219470858574,
0.06898330897092819,
-0.019262375310063362,
0.0038965868297964334,
0.01815098337829113,
-0.014550037682056427,
0.053710274398326874,
-0.024346888065338135,
-0.025525888428092003,
-0.03708350658416748,
0.009830737486481667,
0.025836165994405746,
-0.04313192144036293,
0.002659375313669443,
0.016778111457824707,
0.0119407307356596,
0.03088209219276905,
-0.01097091380506754,
-0.022306282073259354,
-0.002391088055446744,
0.02394060604274273,
-0.06772521138191223,
0.08338113129138947,
-0.012607576325535774,
0.044116515666246414,
0.004742848686873913,
-0.0433189831674099,
-0.0015725856646895409,
0.0010458029573783278,
-0.011368849314749241,
-0.028974948450922966,
-0.014749899506568909,
-0.006670581642538309,
-0.05789075791835785,
-0.006976221222430468,
0.02102949097752571,
-0.07038655877113342,
0.05205424502491951,
-0.019743291661143303,
-0.023843571543693542,
0.009948402643203735,
0.01960146054625511,
0.017479686066508293,
-0.011891651898622513,
-0.02309952676296234,
0.001070139347575605,
-0.005067626945674419,
0.0426001101732254,
0.017869798466563225,
0.008994744159281254,
-0.010406299494206905,
0.02583250030875206,
-0.00048695396981202066,
-0.091440349817276,
-0.05218995362520218,
-0.04681957885622978,
0.014889316633343697
] |
<p>The basic Randall-Sundrum model is given by the metric,</p>
<p>$$\mathrm{d}s^2 = e^{-2|\sigma|}\left[ \mathrm{d}t^2 -\mathrm{d}x^2-\mathrm{d}y^2 - \mathrm{d}z^2 \right]-\mathrm{d}\sigma^2$$</p>
<p>where $\sigma$ denotes the additional fifth dimension. Notice the brane is localized at $\sigma=0$; this 'slice' is precisely Minkowski spacetime. To compute the stress-energy tensor, I define a vielbien,</p>
<p>$$\omega^\mu = e^{-|\sigma|}\mathrm{d}x^\mu \qquad \omega^\sigma = \mathrm{d}\sigma$$</p>
<p>where $\mu=0,..,3.$ Taking exterior derivatives and expressing in the orthonormal basis yields,</p>
<p>$$\mathrm{d}\omega^\mu = \epsilon(\sigma) \, \omega^\mu \wedge \omega^\sigma$$</p>
<p>where we have defined,</p>
<p>$$\epsilon(\sigma)=\theta(\sigma)-\theta(-\sigma)$$</p>
<p>which arises because of the absolute value function in the exponent, and $\theta(\sigma)$ is the Heaviside step function. By Cartan's first equation, the non-vanishing spin connections $\gamma^a_b$ are,</p>
<p>$$\gamma^{\mu}_{\sigma}= \epsilon(\sigma)e^{-|\sigma|} \mathrm{d}\omega^\mu$$</p>
<p>Taking exterior derivatives once again, and expressing in terms of the basis yields,</p>
<p>$$\mathrm{d}\gamma^\mu_\sigma = \left[ \epsilon^2 (\sigma)-2\delta(\sigma)\right]\, \omega^\mu \wedge \omega^\sigma$$</p>
<p>which arises by applying the product rule, and noting that,</p>
<p>$$\frac{\mathrm{d}\epsilon(\sigma)}{\mathrm{d}\sigma} = 2 \delta(\sigma)$$</p>
<p>because the delta function is the first derivative of the step function. From Cartan's second equation,</p>
<p>$$R^a_b=\mathrm{d}\gamma^a_b + \gamma^a_c \wedge \gamma^c_b$$</p>
<p>the components of the Ricci tensor are,</p>
<p>$$R^\mu_\sigma = \left[ \epsilon^2 (\sigma)-2\delta(\sigma)\right]\, \omega^\mu \wedge \omega^\sigma$$
as the second term vanishes. By the relation,</p>
<p>$$R^a_b = \frac{1}{2}R^a_{bcd} \omega^c \wedge \omega^d$$</p>
<p>we may deduce the Riemann tensor components,</p>
<p>$$R^\mu_{\sigma \mu \sigma} = 2\epsilon^2 (\sigma)-4\delta(\sigma)$$</p>
<p>I believe, in this case, both tensors in the coordinate basis and orthonormal basis are identical. Therefore we obtain the rank $(0,2)$ Ricci tensor,</p>
<p>$$R_{\sigma \sigma}=8\epsilon^2 (\sigma)-16\delta(\sigma)$$</p>
<p>As the only diagonal component, the Ricci scalar is identical to the Ricci tensor at $(\sigma,\sigma)$. Using the Einstein field equations, the stress-energy tensor is given by,</p>
<p>$$T_{55} = \frac{1}{8\pi G_5}\left[ 4\epsilon^2 (\sigma)-8\delta(\sigma) + \Lambda\right]$$</p>
<p>where $\Lambda$ is the cosmological constant, and $G_5$ is the five-dimensional gravitational constant. The function $\epsilon^2(\sigma)$ is given by,</p>
<p>$$\epsilon^2(\sigma)=\theta^2(\sigma)+\theta^2(-\sigma)-2\theta(\sigma)\theta(-\sigma)$$</p>
<p>The last term appears to be the delta function, as it is zero everywhere, but singular at zero. The first terms are unity everywhere, but undefined at zero, therefore,</p>
<p>$$T_{55}= \frac{1}{8\pi G_5}\left[ 4\theta^2(\sigma)+4\theta^2(-\sigma) -16\delta(\sigma) + \Lambda\right]$$</p>
<p>However, this disagrees with Mannheim's <em>Brane-Localized Gravity</em> which states,</p>
<p>$$T_{ab}=-\lambda \delta^\mu_a \delta^\nu_b \eta_{\mu\nu}\delta(\sigma)$$</p>
<p>where $\lambda = 12/\kappa^2_5$. In his text, $T_{\mu\nu}\propto -\eta_{\mu\nu}$, but in my calculation the entire purely 4D stress-energy vanishes. I can only assume I've done something wrong.</p>
|
g2483
|
[
0.001376017346046865,
0.021072296425700188,
-0.00665131863206625,
-0.019943231716752052,
0.021833941340446472,
-0.006900722160935402,
0.06791967153549194,
0.005512573290616274,
-0.039702001959085464,
0.015993665903806686,
0.016843382269144058,
-0.003706516232341528,
0.038679517805576324,
-0.038773875683546066,
0.067146897315979,
-0.004562690854072571,
0.03348737210035324,
-0.02388502098619938,
0.03783680126070976,
-0.071996308863163,
-0.03941861167550087,
0.019760573282837868,
0.04403465613722801,
-0.04980155825614929,
-0.008039274252951145,
0.01736421324312687,
0.08620905131101608,
-0.016283808276057243,
-0.08161458373069763,
0.007086683064699173,
0.05117705836892128,
0.012569575570523739,
0.04336636886000633,
-0.04653152823448181,
-0.032472796738147736,
0.016892828047275543,
0.06148215010762215,
0.019569022580981255,
0.04074600338935852,
-0.0070005119778215885,
0.038804661482572556,
-0.056508686393499374,
0.016571294516324997,
0.019376546144485474,
0.030887659639120102,
0.018812714144587517,
-0.04784514009952545,
0.0017160605639219284,
0.02977639064192772,
0.013828014954924583,
0.011485305614769459,
0.0947241485118866,
0.06749101728200912,
-0.060604795813560486,
0.04158196225762367,
0.040968578308820724,
0.03691624850034714,
-0.009500032290816307,
0.058804094791412354,
0.07036937773227692,
0.03398127853870392,
-0.018674729391932487,
-0.018504174426198006,
0.005674879532307386,
0.026753421872854233,
-0.012595930136740208,
0.0026556311640888453,
-0.00991787202656269,
0.031071744859218597,
0.028840621933341026,
0.053891297429800034,
-0.03740273043513298,
0.013224591501057148,
-0.019206080585718155,
-0.03845499828457832,
0.01679244264960289,
0.02554030902683735,
0.004839715547859669,
0.01728956401348114,
0.015617815777659416,
-0.008230520412325859,
0.029225289821624756,
0.030406596139073372,
0.006586376111954451,
0.05080608278512955,
-0.07056999951601028,
0.002066778251901269,
0.06235649436712265,
-0.055959079414606094,
0.031158216297626495,
-0.03154202178120613,
0.007915407419204712,
-0.02872554026544094,
-0.011405345983803272,
0.09458744525909424,
-0.025135587900877,
-0.018993334844708443,
0.03086659125983715,
0.021692529320716858,
-0.05927997827529907,
-0.005184631794691086,
0.010798215866088867,
0.03735528886318207,
-0.017734957858920097,
0.01977737806737423,
-0.00033137830905616283,
0.01523509994149208,
0.017670823261141777,
0.00044383309432305396,
0.007306509651243687,
-0.09000491350889206,
0.04742709547281265,
-0.030746284872293472,
-0.024679740890860558,
-0.033614642918109894,
0.02052469365298748,
0.014068379066884518,
-0.048854995518922806,
-0.06045638769865036,
0.030449192970991135,
-0.020743899047374725,
-0.033524222671985626,
-0.010798548348248005,
0.11419498920440674,
-0.005276453215628862,
0.02234264835715294,
0.012404347769916058,
0.03371257707476616,
0.02377914823591709,
0.006441027391701937,
0.00739939184859395,
-0.009279307909309864,
0.03870614990592003,
-0.008881853893399239,
0.036726366728544235,
0.03267691284418106,
-0.04853954166173935,
0.06206933408975601,
-0.022260235622525215,
-0.004218746908009052,
-0.0568421371281147,
-0.005674432031810284,
-0.050578728318214417,
-0.016969146206974983,
-0.03096248209476471,
-0.03469974920153618,
-0.024008097127079964,
-0.0316978320479393,
-0.029698217287659645,
-0.010095161385834217,
0.0303457360714674,
0.040109965950250626,
-0.03666021302342415,
0.011397670023143291,
-0.038277484476566315,
0.009420745074748993,
-0.014740332029759884,
-0.04953105002641678,
-0.03342883661389351,
0.00019497136236168444,
-0.02396336942911148,
-0.031197886914014816,
0.09426236152648926,
0.04055234417319298,
-0.0030113784596323967,
0.0015936261042952538,
0.012504499405622482,
-0.043800994753837585,
0.03871715068817139,
-0.05228535458445549,
-0.03413458168506622,
-0.03129272535443306,
-0.010458478704094887,
0.004775560926645994,
0.005372434854507446,
0.016969092190265656,
-0.0018985698698088527,
0.009026498533785343,
0.04809892922639847,
-0.009511247277259827,
0.04819011688232422,
-0.02157517708837986,
0.024137983098626137,
-0.01889149472117424,
-0.034550271928310394,
-0.023567870259284973,
0.016346916556358337,
0.0005952881183475256,
0.038681864738464355,
-0.016242386773228645,
-0.03429548442363739,
-0.016671856865286827,
0.051173530519008636,
0.031000079587101936,
0.05935567989945412,
0.017721418291330338,
-0.0040947310626506805,
-0.0895150676369667,
-0.013921698555350304,
0.07725841552019119,
0.003969703335314989,
0.0011237149592489004,
-0.010167173109948635,
-0.011124863289296627,
-0.03259406238794327,
-0.0021982877515256405,
-0.038292597979307175,
0.008764664642512798,
0.05033428594470024,
-0.018340203911066055,
-0.009705249220132828,
-0.0625060424208641,
-0.04400058835744858,
-0.033019404858350754,
0.008368803188204765,
-0.023797832429409027,
0.012056412175297737,
0.02980365790426731,
-0.04096755012869835,
0.07462841272354126,
-0.025155460461974144,
-0.03317606821656227,
0.01717887818813324,
0.06024327874183655,
-0.021027736365795135,
-0.023008370772004128,
-0.04957184940576553,
0.007820146158337593,
0.014953387901186943,
0.01087652426213026,
-0.07011709362268448,
-0.007818972691893578,
0.0008837010245770216,
0.09057207405567169,
0.036982886493206024,
-0.009858929552137852,
-0.006405599880963564,
0.008265852928161621,
-0.0074445209465920925,
0.0001380617031827569,
0.012326981872320175,
0.0562899224460125,
-0.025973299518227577,
-0.015073930844664574,
0.05322433263063431,
-0.010606452822685242,
0.035733550786972046,
0.020024370402097702,
0.008113428018987179,
0.03416511043906212,
0.06579196453094482,
-0.03256087377667427,
-0.03335011377930641,
0.017884209752082825,
-0.005175953730940819,
-0.0301401037722826,
-0.030441926792263985,
0.013574023731052876,
-0.0699440985918045,
-0.04891727864742279,
-0.036240819841623306,
-0.012983156368136406,
0.05895591154694557,
0.04165605455636978,
-0.0650831013917923,
0.018025711178779602,
-0.03512926772236824,
0.057507313787937164,
0.008122898638248444,
-0.018479520455002785,
-0.013069404289126396,
0.06599771231412888,
0.05783683806657791,
0.03274857997894287,
-0.0065462891943752766,
-0.02491801232099533,
-0.01523090060800314,
0.01547201070934534,
-0.054262056946754456,
0.015215746127068996,
-0.05535371974110603,
-0.006973531562834978,
-0.03442220762372017,
-0.04494372755289078,
-0.037571631371974945,
-0.04739295691251755,
-0.006439248099923134,
0.031151827424764633,
-0.005137573927640915,
0.04901614412665367,
0.009112406522035599,
0.057841189205646515,
-0.005207700654864311,
0.007616087328642607,
-0.047483280301094055,
0.03922199085354805,
0.008869603276252747,
-0.04808094725012779,
-0.02865717001259327,
0.07431335747241974,
0.021300502121448517,
-0.03620516136288643,
0.018412144854664803,
0.05727441981434822,
-0.056831300258636475,
-0.020435359328985214,
-0.08858676254749298,
-0.05950109660625458,
-0.041437748819589615,
-0.04574859142303467,
0.044947583228349686,
0.01084755826741457,
-0.017778877168893814,
0.014642670750617981,
-0.014558365568518639,
0.014831695705652237,
-0.029064953327178955,
-0.03395874425768852,
-0.015280003659427166,
-0.02919514663517475,
0.009467768482863903,
-0.03453643247485161,
-0.03161277621984482,
0.015763940289616585,
0.02765621244907379,
0.0823737159371376,
-0.02635832130908966,
0.013003719970583916,
-0.07897167652845383,
0.028552908450365067,
0.03617820888757706,
0.0032545162830501795,
0.027718614786863327,
0.05307620391249657,
-0.08898763358592987,
-0.01787140592932701,
-0.06610049307346344,
0.06075722724199295,
0.03353392705321312,
0.07738030701875687,
-0.014386162161827087,
-0.015506809577345848,
0.010456603951752186,
-0.0027030787896364927,
-0.015315755270421505,
0.01800789125263691,
-0.030570272356271744,
-0.000117001254693605,
-0.030570056289434433,
0.06599091738462448,
-0.01563170552253723,
-0.0028375659603625536,
-0.012838593684136868,
-0.05022774636745453,
-0.026139069348573685,
0.019351014867424965,
0.032117463648319244,
0.025179481133818626,
0.01568312756717205,
-0.01287843193858862,
0.02205890603363514,
-0.055393677204847336,
0.010743696242570877,
0.008726611733436584,
-0.016349636018276215,
-0.039720721542835236,
0.024627437815070152,
-0.008513852953910828,
-0.020332371816039085,
-0.004398608114570379,
0.05493142083287239,
0.019246097654104233,
0.03452174365520477,
-0.0192988570779562,
-0.037154801189899445,
-0.032769933342933655,
0.012668099254369736,
-0.011319377459585667,
-0.004644251428544521,
0.05769484117627144,
0.07720648497343063,
-0.030073797330260277,
0.05626274645328522,
0.05423593893647194,
0.014816979877650738,
0.0036622665356844664,
-0.014549952931702137,
-0.05071000009775162,
0.006109197624027729,
0.03317902237176895,
0.004709997680038214,
-0.04799191653728485,
0.01415503490716219,
0.011328357271850109,
0.04095244035124779,
-0.005715091247111559,
0.035563401877880096,
0.03186715766787529,
-0.06811608374118805,
0.06046657636761665,
0.025331448763608932,
-0.005603621248155832,
-0.009065366350114346,
0.004624099936336279,
-0.00530041940510273,
0.041797902435064316,
-0.008349426090717316,
-0.028670912608504295,
0.008977610617876053,
0.031662967056035995,
0.05340825021266937,
0.02662782371044159,
0.021370677277445793,
-0.0469319112598896,
0.0820259228348732,
-0.037510231137275696,
0.002660368802025914,
0.00043032292160205543,
-0.02612162008881569,
0.04738986864686012,
-0.005116553511470556,
0.01727806031703949,
0.015097500756382942,
-0.018069546669721603,
0.02989298850297928,
0.05415608361363411,
0.011693290434777737,
-0.014209428802132607,
-0.07903852313756943,
-0.03094199299812317,
0.01889237016439438,
-0.019686967134475708,
-0.009184361435472965,
0.04332009702920914,
-0.05652537941932678,
0.02183900587260723,
0.012694706209003925,
0.00018320402887184173,
-0.02875291369855404,
-0.01936507411301136,
-0.00045874889474362135,
0.0447099506855011,
0.0641637071967125,
-0.0164185781031847,
-0.009714997373521328,
0.04463282227516174,
0.020653825253248215,
-0.03338732197880745,
0.01252018939703703,
-0.030198825523257256,
-0.01432884857058525,
-0.002048153430223465,
0.04496932402253151,
0.007433050312101841,
0.053549155592918396,
-0.02632630616426468,
-0.01651018299162388,
0.01856120117008686,
0.02616642788052559,
-0.007635578978806734,
-0.03156615421175957,
0.02906249649822712,
0.01944691315293312,
0.012544072233140469,
-0.0034700785763561726,
-0.021416455507278442,
-0.05172766000032425,
0.032106805592775345,
-0.009660735726356506,
-0.0445733368396759,
0.08312613517045975,
-0.016239356249570847,
-0.032158784568309784,
-0.06976718455553055,
-0.006796648725867271,
0.07609012722969055,
-0.05371649190783501,
-0.039480287581682205,
0.005448258016258478,
-0.004752989858388901,
0.017674269154667854,
-0.006908893119543791,
-0.020050395280122757,
-0.005184637848287821,
0.0008110173512250185,
0.021274307742714882,
-0.043392427265644073,
-0.03604324162006378,
-0.04040597751736641,
0.0228272657841444,
-0.042999234050512314,
-0.02199145220220089,
-0.004593764431774616,
-0.06254427880048752,
0.013207809068262577,
0.0301108006387949,
0.006821844726800919,
-0.015158540569245815,
-0.015049734152853489,
0.006635652389377356,
-0.00845429953187704,
-0.016459234058856964,
0.029107704758644104,
-0.038653839379549026,
-0.0034798134583979845,
0.0076017058454453945,
0.044579628854990005,
0.010349757969379425,
-0.006273703183978796,
0.04741509631276131,
0.020264478400349617,
-0.015494124963879585,
0.03479460999369621,
0.004901433829218149,
-0.0644150972366333,
-0.006330292206257582,
0.024665627628564835,
0.03307666629552841,
-0.002379070036113262,
-0.03454665094614029,
-0.012396532110869884,
-0.038602374494075775,
0.07366261631250381,
-0.0295098926872015,
0.01786985993385315,
0.030846500769257545,
0.030833236873149872,
-0.033973127603530884,
-0.021238068118691444,
0.029144935309886932,
-0.029064631089568138,
-0.027924224734306335,
-0.0032420551870018244,
0.014340091496706009,
0.0003297746297903359,
-0.06475649029016495,
-0.018495697528123856,
-0.0035328539088368416,
0.04369286820292473,
-0.03619903698563576,
-0.00026410355349071324,
-0.028099944815039635,
-0.012424786575138569,
0.02185913920402527,
-0.06187741458415985,
0.06089752912521362,
-0.02721479721367359,
0.033192310482263565,
-0.007089466787874699,
-0.07292526215314865,
-0.020685141906142235,
0.0002522218564990908,
0.025470148772001266,
0.04224977269768715,
0.018590155988931656,
0.02421179786324501,
0.025312842801213264,
-0.08068934082984924,
-0.03613344207406044,
-0.006334755569696426,
0.0056494963355362415,
0.0059869796968996525,
0.002554971259087324,
-0.0007381166215054691,
0.01490667276084423,
-0.04379284754395485,
-0.0038338920567184687,
-0.029052384197711945,
0.026761719956994057,
-0.07417057454586029,
0.008435034193098545,
0.020647350698709488,
0.009884356521070004,
0.00763000687584281,
-0.026827262714505196,
0.03955943137407303,
0.023669051006436348,
-0.025910943746566772,
-0.012589536607265472,
0.008281636983156204,
-0.0031058613676577806,
0.05942467227578163,
0.02648209035396576,
0.017086699604988098,
-0.036360468715429306,
-0.016898399218916893,
-0.07818873226642609,
-0.04804741591215134,
0.05978110805153847,
0.04797081649303436,
-0.012644817121326923,
0.02188984490931034,
-0.028579125180840492,
-0.020733976736664772,
-0.023961076512932777,
0.0157468281686306,
0.07242388278245926,
-0.03611722216010094,
-0.0427095890045166,
0.04384344071149826,
-0.020858626812696457,
-0.004739811643958092,
0.0538753941655159,
-0.027680935338139534,
-0.00021651860151905566,
0.0061879837885499,
-0.04940742999315262,
-0.05651888623833656,
-0.06202567741274834,
0.06242774426937103,
0.0045013390481472015,
0.010580641217529774,
0.005028417333960533,
0.025367707014083862,
0.048365190625190735,
-0.028485717251896858,
0.03829098492860794,
0.06839576363563538,
0.025262396782636642,
-0.026793748140335083,
0.04033547639846802,
0.094918392598629,
0.03537631034851074,
-0.008393527939915657,
0.005570353474467993,
-0.0032885924447327852,
-0.002322528976947069,
0.012624039314687252,
-0.02368229627609253,
-0.003990135155618191,
0.02483062632381916,
-0.07074899226427078,
-0.06729227304458618,
0.0598062165081501,
-0.023485766723752022,
0.02221025712788105,
-0.03728495165705681,
0.02694152481853962,
0.041876066476106644,
0.04452870413661003,
-0.053811512887477875,
-0.0001696885155979544,
0.022677632048726082,
-0.0637187510728836,
0.013762133195996284,
-0.0298614539206028,
-0.0032123213168233633,
-0.03182068467140198,
-0.08435970544815063,
0.016036197543144226,
0.021735219284892082,
-0.018715646117925644,
-0.013134336099028587,
-0.024077141657471657,
-0.03196818381547928,
0.010424832813441753,
-0.030118491500616074,
-0.024376822635531425,
0.0623212568461895,
-0.08248677849769592,
-0.03993993625044823,
0.0026364552322775126,
-0.032571494579315186,
0.023720629513263702,
-0.031151745468378067,
0.04453929886221886,
-0.00851353257894516,
-0.03953840956091881,
0.08140548318624496,
0.010386672802269459,
-0.0013072603615000844,
-0.01720023714005947,
-0.03573803976178169,
-0.000055610067647648975,
-0.03136999160051346,
-0.009440750814974308,
0.015447950921952724,
-0.018575411289930344,
-0.0061218831688165665,
0.006286255549639463,
0.013075791299343109,
0.0009499241132289171,
-0.06024966388940811,
0.02041693590581417,
0.014011385850608349,
0.008793807588517666,
0.06419870257377625,
-0.022127283737063408,
0.02641170658171177,
0.08390584588050842,
0.033110227435827255,
0.0769379734992981,
-0.0485326386988163,
0.022604411467909813,
0.015058708377182484,
0.005208980292081833,
-0.006239900831133127,
-0.008642489090561867,
-0.05008796602487564,
0.009059086441993713,
-0.01914111152291298,
-0.01578560657799244,
-0.03476880118250847,
-0.028067704290151596,
-0.020368490368127823,
-0.005733831319957972,
-0.006728335749357939,
-0.006707658991217613,
-0.046196166425943375,
-0.011728801764547825,
0.07764916121959686,
-0.0218652430921793,
-0.0035224384628236294,
-0.003154780948534608,
-0.01739020086824894,
0.04254543036222458,
-0.06763419508934021,
0.020165443420410156,
0.033941008150577545,
-0.06155640631914139,
-0.03341959789395332,
-0.01804340071976185,
0.015673721209168434,
0.028001682832837105,
-0.038356561213731766,
0.025137197226285934,
-0.03321976959705353,
-0.012457677163183689,
0.021479282528162003,
0.01507794950157404,
-0.04793236404657364,
-0.031040381640195847,
-0.07848715037107468,
-0.06881023198366165,
0.021698234602808952,
0.0030500199645757675,
0.01736375503242016,
0.010633153840899467,
0.06470812112092972,
-0.032115012407302856,
-0.04920714348554611,
-0.09930090606212616,
-0.023253506049513817,
-0.0012502901954576373,
-0.02830447256565094,
-0.04171990975737572,
-0.046430058777332306,
-0.012542163953185081,
0.053838539868593216,
0.032774101942777634,
0.006017128471285105,
0.037171442061662674,
0.06468527764081955,
0.009247963316738605,
-0.01233887393027544,
-0.006758277770131826,
0.03421304002404213,
0.0010384195484220982,
0.05975812301039696,
-0.0525103360414505,
-0.009646008722484112,
-0.06383100897073746,
-0.016402097418904305,
0.023031627759337425,
0.037381984293460846,
0.028265511617064476,
0.011519432067871094,
0.034582722932100296
] |
<p>They say <a href="http://en.wikipedia.org/wiki/Inflation_%28cosmology%29" rel="nofollow">inflation</a> must have occured because the universe is very homogeneous. Otherwise, how could one part of the universe reach the same temperature as another when the distance between the parts is more than light could have traveled in the given time?</p>
<p>Why can't this problem be solved without inflation? If each part started with the same temperature to begin with, then they can have the same temperature irrespective of the distance between them. Am I missing something here?</p>
|
g2484
|
[
0.03579283878207207,
0.03271908313035965,
-0.005629842635244131,
0.013038232922554016,
0.02413029596209526,
0.028193797916173935,
-0.014838757924735546,
0.02812310680747032,
-0.04208524897694588,
-0.001488013775087893,
0.007278850767761469,
-0.02659628354012966,
0.019092518836259842,
0.039141785353422165,
0.004172618966549635,
0.0681685209274292,
0.005803602281957865,
-0.043790001422166824,
0.022426648065447807,
0.03188750147819519,
0.015350270085036755,
0.0038829678669571877,
0.04672491177916527,
-0.018708180636167526,
-0.04797734320163727,
-0.0744878500699997,
0.006817248649895191,
-0.029180273413658142,
-0.0510939322412014,
-0.038074638694524765,
0.043682876974344254,
0.010573132894933224,
0.04766515642404556,
-0.04613107815384865,
0.015132482163608074,
-0.04716750234365463,
0.026181692257523537,
-0.0002361247461521998,
0.025896521285176277,
0.03772406652569771,
-0.0053740194998681545,
0.032476454973220825,
-0.01006672065705061,
-0.031177593395113945,
0.0032333387061953545,
0.040960364043712616,
-0.024524541571736336,
0.03430281952023506,
0.01525863353163004,
-0.037046730518341064,
0.008594609797000885,
0.06064336746931076,
-0.008068897761404514,
0.006893254816532135,
0.027757447212934494,
-0.009186040610074997,
0.017607955262064934,
-0.0013021603226661682,
0.10545690357685089,
0.053008873015642166,
-0.0131727559491992,
-0.008542046882212162,
0.05198561027646065,
0.025954868644475937,
-0.013973006047308445,
0.013107706792652607,
-0.02077571675181389,
-0.018351607024669647,
0.014243239536881447,
0.0034169061109423637,
0.013930839486420155,
-0.0670219138264656,
-0.012945025227963924,
0.02455286681652069,
-0.05346713587641716,
0.023217493668198586,
0.043313831090927124,
-0.011633152142167091,
0.025754563510417938,
-0.03834517300128937,
-0.05187429487705231,
-0.010101175867021084,
0.011703641153872013,
0.01928425207734108,
0.01522035337984562,
-0.0447758287191391,
-0.01656252145767212,
-0.015788348391652107,
-0.0423458106815815,
0.03990791738033295,
-0.014754334464669228,
0.0329672209918499,
0.0907813012599945,
0.009547521360218525,
0.014507157728075981,
-0.05444246903061867,
-0.04556075483560562,
0.0750151053071022,
-0.01720491796731949,
-0.03300376236438751,
-0.03256145119667053,
0.024643616750836372,
0.05360875651240349,
-0.001714177429676056,
0.0032021943479776382,
-0.03279811143875122,
-0.0012195188319310546,
0.002461473923176527,
-0.004629215225577354,
-0.014487272128462791,
0.009095926769077778,
-0.051383569836616516,
-0.03250517696142197,
-0.009164037182927132,
0.016005616635084152,
0.004799206741154194,
0.05618838220834732,
0.0304917823523283,
0.02347608096897602,
-0.0023600775748491287,
-0.02131492644548416,
0.0552661158144474,
-0.01938849687576294,
-0.0034698278177529573,
-0.09122749418020248,
-0.018534114584326744,
0.049555178731679916,
-0.03939687833189964,
0.01741933450102806,
-0.045933470129966736,
0.008531630970537663,
0.013999363407492638,
-0.02043917402625084,
0.01984807848930359,
-0.008250786922872066,
-0.04154685139656067,
0.05309082940220833,
0.01629624515771866,
-0.004513280466198921,
0.0549900121986866,
0.01471792533993721,
-0.015765149146318436,
0.0023987512104213238,
-0.014101564884185791,
0.0075952401384711266,
-0.0023051314055919647,
-0.03222440183162689,
-0.003413352882489562,
-0.010579034686088562,
0.0037426010239869356,
-0.017024822533130646,
0.10465214401483536,
0.045809727162122726,
0.014180593192577362,
-0.03803642839193344,
-0.002310720970854163,
0.026678340509533882,
0.017146557569503784,
0.02756754867732525,
-0.04698178917169571,
0.003423029789701104,
-0.016743062064051628,
0.04069241136312485,
-0.05161982774734497,
-0.03978040814399719,
0.09105002135038376,
-0.02931847609579563,
-0.026221483945846558,
-0.01448014285415411,
-0.020359808579087257,
-0.05438420549035072,
-0.004090520087629557,
-0.05569133907556534,
0.037010446190834045,
0.08199544996023178,
0.010355554521083832,
0.0548529326915741,
0.046407636255025864,
-0.02189599722623825,
-0.04563514515757561,
-0.04322678968310356,
-0.012478365562856197,
0.04354613646864891,
-0.004447040148079395,
0.03376340493559837,
0.03772105276584625,
-0.0066953073255717754,
-0.03423842415213585,
-0.0018766074208542705,
0.01806432567536831,
-0.01776854135096073,
0.005468330346047878,
0.0027891192585229874,
0.04426531121134758,
0.017010398209095,
-0.006027637515217066,
0.025223296135663986,
-0.00226295436732471,
-0.08471964299678802,
0.006644515786319971,
-0.01297062635421753,
0.013178966008126736,
0.007051039021462202,
-0.028544001281261444,
-0.007399145048111677,
0.024314185604453087,
-0.04219939559698105,
0.03240439295768738,
0.01281655952334404,
0.01366756297647953,
-0.03930037096142769,
-0.05339821055531502,
-0.012128674425184727,
0.023140400648117065,
-0.01507847011089325,
-0.020166883245110512,
0.05002950131893158,
-0.00972689688205719,
-0.00813958141952753,
0.010389112867414951,
-0.03309975191950798,
0.03357452154159546,
0.04400750249624252,
-0.0606251023709774,
0.007661405019462109,
0.006174986716359854,
-0.023619143292307854,
-0.02149280346930027,
-0.04430922120809555,
0.05007561668753624,
-0.021630894392728806,
0.033252082765102386,
-0.022729121148586273,
-0.03558187931776047,
0.031064920127391815,
-0.022916162386536598,
0.04347863793373108,
-0.01914612390100956,
-0.019135013222694397,
0.09301172941923141,
-0.012970115058124065,
-0.04422643780708313,
0.014283307828009129,
0.04224153235554695,
0.02372286655008793,
-0.05376939848065376,
0.018719449639320374,
-0.05450351908802986,
0.003240464022383094,
0.029021913185715675,
0.017526179552078247,
-0.044869907200336456,
-0.00838121771812439,
-0.02615644596517086,
-0.01174220722168684,
-0.051119614392519,
0.003435893449932337,
0.039957400411367416,
-0.016472650691866875,
-0.07479832321405411,
0.0016867941012606025,
-0.03396103158593178,
0.07109478116035461,
-0.028114615008234978,
-0.10135545581579208,
-0.013985707424581051,
-0.028248615562915802,
0.002592226257547736,
-0.09536924213171005,
-0.01763961836695671,
-0.02700713276863098,
-0.015696117654442787,
-0.005317127797752619,
0.06162028759717941,
-0.028403664007782936,
0.08607909828424454,
0.008757330477237701,
-0.012157448567450047,
0.028136804699897766,
0.00975758396089077,
0.03826424479484558,
0.004083138890564442,
-0.05826263502240181,
-0.0738711953163147,
0.045749492943286896,
-0.08976798504590988,
-0.02735489420592785,
0.030650991946458817,
0.04587619751691818,
-0.016610153019428253,
0.06250608712434769,
-0.011800921522080898,
0.013790182769298553,
0.030643854290246964,
0.02527616359293461,
0.05274074897170067,
0.0361405648291111,
-0.016679171472787857,
-0.09061682969331741,
-0.038788773119449615,
-0.016948310658335686,
-0.02886686660349369,
0.015557712875306606,
-0.030147485435009003,
0.02206341363489628,
0.014077980071306229,
-0.012065320275723934,
-0.008948760107159615,
-0.04513969272375107,
-0.05527208745479584,
0.12219297140836716,
0.05906340107321739,
0.004678504075855017,
0.07559141516685486,
0.04997285455465317,
0.029364097863435745,
-0.02230038493871689,
0.019917979836463928,
0.07154615968465805,
0.003622499294579029,
-0.029583826661109924,
0.029250890016555786,
-0.03992269188165665,
-0.03860403224825859,
0.026892367750406265,
0.02159036695957184,
-0.03176373988389969,
0.01497294194996357,
-0.038028303533792496,
0.018463779240846634,
-0.023482119664549828,
0.00020903135009575635,
-0.007475561462342739,
-0.0048953150399029255,
-0.03842831775546074,
-0.03800245746970177,
-0.003021038370206952,
-0.008698317222297192,
0.10207414627075195,
0.05292672663927078,
-0.06863066554069519,
-0.01325182057917118,
-0.02350803092122078,
0.02149287983775139,
-0.0056404187344014645,
0.07494857907295227,
-0.01820679008960724,
-0.012435412034392357,
0.028318550437688828,
0.037247657775878906,
0.05112576484680176,
-0.04543602839112282,
0.0038858086336404085,
-0.04317881539463997,
-0.012591589242219925,
0.02024945616722107,
0.03300779312849045,
0.039907876402139664,
0.0367412231862545,
-0.03583229333162308,
0.052122343331575394,
-0.010011189617216587,
0.028777306899428368,
0.01783166266977787,
0.0024612005800008774,
-0.021312208846211433,
0.002205761382356286,
-0.02482614852488041,
-0.012976573780179024,
0.00564966443926096,
0.030304064974188805,
-0.033876609057188034,
-0.046536076813936234,
-0.05713395029306412,
0.08415548503398895,
-0.00740330945700407,
0.06142403185367584,
0.020631933584809303,
-0.0585089772939682,
0.04200228303670883,
0.057692550122737885,
-0.021181635558605194,
0.015636183321475983,
-0.011788463220000267,
0.04144250601530075,
0.009709029458463192,
-0.05133838206529617,
-0.013182278722524643,
-0.03205394372344017,
-0.07181236147880554,
0.037747129797935486,
-0.07213596254587173,
0.04649937525391579,
0.048474617302417755,
0.026721419766545296,
0.013166154734790325,
0.029718803241848946,
0.001360018621198833,
0.06965529918670654,
-0.0011640016455203295,
0.016198979690670967,
-0.052295129746198654,
0.025351181626319885,
0.0184743981808424,
-0.03696082904934883,
0.016764461994171143,
0.047393303364515305,
0.00742087047547102,
0.038262948393821716,
0.03563287854194641,
-0.006848466582596302,
0.03249518945813179,
-0.0036645110230892897,
-0.00020034279441460967,
0.030389737337827682,
-0.05935585871338844,
0.07861866801977158,
-0.03889106959104538,
0.020104389637708664,
0.013063587248325348,
-0.020319804549217224,
0.004319564905017614,
0.013065504841506481,
-0.020099449902772903,
0.029682176187634468,
0.062251169234514236,
0.000032323958294000477,
-0.037981387227773666,
-0.045692261308431625,
0.020008007064461708,
0.014189541339874268,
-0.00731646828353405,
-0.021838530898094177,
0.019443931058049202,
-0.009639854542911053,
-0.005882317200303078,
-0.01463920809328556,
0.04808605834841728,
-0.03249511867761612,
0.010090626776218414,
0.0318918414413929,
-0.03766896575689316,
-0.010108302347362041,
0.014166664332151413,
0.023548221215605736,
0.04832526668906212,
0.01812555082142353,
-0.045450013130903244,
-0.09679991006851196,
-0.01452604215592146,
-0.0012642440851777792,
0.008829952217638493,
-0.013087896630167961,
0.027815064415335655,
-0.016712455078959465,
-0.06572998315095901,
0.005346558056771755,
0.034610673785209656,
0.025572746992111206,
0.04526330903172493,
-0.05442242696881294,
0.020019369199872017,
-0.00612651789560914,
0.010258573107421398,
0.023972399532794952,
-0.053402386605739594,
-0.0033109672367572784,
0.04088960960507393,
-0.0477791465818882,
0.06689496338367462,
0.004886919632554054,
0.045675016939640045,
0.007067766040563583,
0.0690046027302742,
0.02105369232594967,
-0.003064497373998165,
0.01750745065510273,
-0.06567694991827011,
0.009127307683229446,
-0.018295463174581528,
-0.004522337112575769,
-0.02957105077803135,
0.04811698943376541,
0.012316645123064518,
0.021907219663262367,
0.00931898970156908,
-0.11058755218982697,
0.07287593185901642,
0.02064855769276619,
-0.023757092654705048,
0.0014005377888679504,
-0.031455960124731064,
0.06608368456363678,
0.023133236914873123,
-0.0382118783891201,
-0.033308904618024826,
0.0016720256535336375,
0.028948171064257622,
-0.0023582959547638893,
-0.031346049159765244,
-0.021249771118164062,
0.04309862107038498,
0.019862283021211624,
-0.012981324456632137,
-0.029689060524106026,
-0.003406527219340205,
0.010365971364080906,
0.008522587828338146,
-0.024041296914219856,
0.042569298297166824,
-0.012568733654916286,
0.0012989068636670709,
-0.005995872896164656,
0.026706775650382042,
0.0157272107899189,
-0.03693905472755432,
0.0248270146548748,
-0.07686947286128998,
0.0316464826464653,
-0.060502488166093826,
0.053978778421878815,
0.0008589301723986864,
-0.011844370514154434,
0.023897508159279823,
0.08592844754457474,
-0.016527114436030388,
-0.018691018223762512,
-0.05076027289032936,
-0.031682323664426804,
0.03376803547143936,
0.04786650836467743,
-0.001177775557152927,
0.011022587306797504,
-0.05616544559597969,
-0.015174047090113163,
-0.01805172488093376,
-0.0037830136716365814,
0.018540719524025917,
0.04429111257195473,
-0.011091744527220726,
0.006807833444327116,
-0.04819329455494881,
-0.0028127499390393496,
0.040934398770332336,
-0.05785515904426575,
-0.027039235457777977,
-0.03248468413949013,
0.008868212811648846,
0.022345954552292824,
-0.07495273649692535,
-0.022570353001356125,
0.03698514401912689,
0.01749119721353054,
0.02505919151008129,
-0.03726967051625252,
0.0709524005651474,
0.04357706010341644,
0.00549172842875123,
-0.02670084498822689,
-0.0578661784529686,
0.035394612699747086,
0.0025709113106131554,
0.009470222517848015,
0.048829738050699234,
-0.06039367988705635,
-0.05000204220414162,
-0.021691350266337395,
-0.05738149583339691,
0.04337289184331894,
0.04336393252015114,
0.017622925341129303,
-0.019148096442222595,
-0.0041605629958212376,
-0.027832765132188797,
-0.014132305979728699,
0.008088590577244759,
-0.05106152221560478,
0.004976409021764994,
-0.04647147282958031,
-0.011561996303498745,
-0.008771746419370174,
-0.019077708944678307,
0.043580733239650726,
-0.0433516688644886,
-0.003517232136800885,
-0.002568313619121909,
-0.03240884840488434,
-0.006359665188938379,
0.0496567003428936,
0.02433984912931919,
-0.05111465975642204,
-0.03991252928972244,
-0.017386138439178467,
0.0018296117195859551,
-0.047529835253953934,
0.0034157554619014263,
0.0030887010507285595,
-0.025996869429945946,
-0.09888068586587906,
0.00030812463955953717,
0.002890252508223057,
-0.04304717108607292,
0.07328305393457413,
0.028480328619480133,
0.005327171646058559,
0.018784042447805405,
-0.02984275296330452,
0.02469419129192829,
0.04142289236187935,
-0.0013920094352215528,
-0.02829141728579998,
0.07640390843153,
0.036577168852090836,
-0.0049477629363536835,
0.0008141986327245831,
-0.010911411605775356,
-0.01070356648415327,
-0.009607658721506596,
-0.01734214648604393,
-0.01068042777478695,
0.06226933375000954,
0.02269565872848034,
0.013403144665062428,
0.008854882791638374,
0.019423844292759895,
0.0008519843104295433,
-0.05150463059544563,
0.06522056460380554,
0.03886877000331879,
0.022705677896738052,
0.025839807465672493,
0.011387291364371777,
-0.03492249920964241,
0.028624998405575752,
-0.018252575770020485,
0.02688649296760559,
-0.00017430935986340046,
0.0005640833405777812,
-0.016681000590324402,
-0.026516977697610855,
-0.018640778958797455,
-0.04777193441987038,
0.0701531320810318,
0.03725976496934891,
-0.04023738577961922,
-0.006009790580719709,
-0.0016170117305591702,
-0.028129637241363525,
-0.07481063902378082,
0.00964184757322073,
-0.04316111281514168,
-0.017674816772341728,
-0.06144776940345764,
0.04268335923552513,
-0.01898450404405594,
-0.021882399916648865,
-0.03825286403298378,
0.0009351916378363967,
-0.02665269933640957,
-0.057108595967292786,
-0.04765099659562111,
0.01577487587928772,
-0.02277284860610962,
0.012660345993936062,
-0.004136784002184868,
0.04143280163407326,
-0.02497177943587303,
-0.09066027402877808,
0.04607311636209488,
-0.037169698625802994,
0.006476818583905697,
0.02385712042450905,
-0.05195082724094391,
-0.013633805327117443,
-0.013101274147629738,
-0.030733510851860046,
0.001999305095523596,
0.031721021980047226,
0.04899701476097107,
-0.012433068826794624,
0.007824964821338654,
0.03773711621761322,
0.010783931240439415,
-0.009526608511805534,
0.0017419051146134734,
0.020041845738887787,
0.026930175721645355,
0.009757001884281635,
0.008279445581138134,
0.02432573027908802,
-0.01119238045066595,
-0.009626486338675022,
0.011536773294210434,
-0.036045271903276443,
0.013049758970737457,
0.027393722906708717,
0.03269169479608536,
0.005119635723531246,
0.012781530618667603,
-0.055225081741809845,
0.025629641488194466,
-0.03756597265601158,
-0.027805838733911514,
-0.04757484421133995,
0.032513801008462906,
0.030360521748661995,
0.023058690130710602,
0.02737908996641636,
-0.02453700266778469,
0.013149188831448555,
0.0313216857612133,
0.04664871469140053,
0.0014093144563958049,
0.007145749870687723,
-0.03710440173745155,
-0.07852676510810852,
-0.059052854776382446,
-0.04363274946808815,
-0.03008701466023922,
-0.033328767865896225,
-0.01301630586385727,
-0.07122048735618591,
-0.007903601042926311,
-0.03006645292043686,
-0.030010255053639412,
0.051862381398677826,
0.03739146515727043,
-0.05741456151008606,
-0.037478357553482056,
-0.02852511592209339,
0.020142482593655586,
0.01944442093372345,
-0.010317059233784676,
0.043330952525138855,
-0.0034674303606152534,
0.039810970425605774,
0.055858008563518524,
-0.022059356793761253,
0.008121466264128685,
-0.016537830233573914,
-0.020704234018921852,
0.003603451419621706,
0.042705804109573364,
-0.004855316132307053,
0.0022253806237131357,
-0.06640991568565369,
-0.05495551973581314,
0.08016751706600189,
0.06799701601266861,
-0.04697892442345619,
-0.05152292922139168,
0.01545643713325262,
-0.04545295983552933,
-0.0026465498376637697,
0.06774702668190002,
-0.015094393864274025,
-0.002588429721072316,
0.0022303895093500614,
-0.04679971560835838,
-0.02941078692674637,
-0.014578888192772865,
-0.013486125506460667,
0.012744108214974403,
-0.02752990834414959,
0.0037251259200274944,
0.016048720106482506,
0.0021202550269663334,
-0.014540192671120167
] |
<p>I have an 80 mm <a href="http://en.wikipedia.org/wiki/Refracting_telescope" rel="nofollow">refractor</a> telescope on a tripod, but it shakes on every touch. It's very hard to see via 6 mm (x120) ocular. Even a little wind causes the image to become too unsteady. </p>
<p>How can I make my tripod more steady?</p>
|
g2485
|
[
0.0058344583958387375,
0.04112071916460991,
-0.019052758812904358,
-0.04589195176959038,
0.0288276094943285,
0.015691274777054787,
0.03895319998264313,
0.006206288002431393,
0.06120830774307251,
0.024766672402620316,
0.08818411827087402,
-0.004742125049233437,
0.0321156345307827,
0.03530454263091087,
0.04780992120504379,
0.025958774611353874,
0.05535838380455971,
-0.014824481680989265,
0.058884501457214355,
0.04654485732316971,
0.02809046022593975,
-0.014085578732192516,
-0.05750410631299019,
-0.01361136045306921,
0.05381748080253601,
0.04818679392337799,
-0.043484754860401154,
-0.00040162596269510686,
-0.026760565117001534,
0.026276055723428726,
0.012147926725447178,
-0.03439725935459137,
-0.02800343930721283,
-0.018874764442443848,
0.01321798749268055,
0.039539434015750885,
0.050069816410541534,
0.08074536919593811,
0.013206136412918568,
-0.01699884422123432,
-0.00043909018859267235,
-0.0324460007250309,
0.005999621469527483,
0.039379093796014786,
0.03428204357624054,
-0.03786151483654976,
0.014164047315716743,
-0.06292611360549927,
-0.05737590789794922,
-0.015445608645677567,
0.01926741935312748,
-0.008872254751622677,
0.03963808715343475,
-0.03187674283981323,
-0.027392681688070297,
0.012170900590717793,
-0.04093281924724579,
0.036683339625597,
0.02339271269738674,
-0.04058465734124184,
-0.019102126359939575,
-0.06644362211227417,
-0.02623307704925537,
0.04045993834733963,
0.0014383795205503702,
-0.03524239361286163,
-0.0484221950173378,
-0.01143980398774147,
0.07135341316461563,
0.034632012248039246,
-0.016122523695230484,
-0.005999675951898098,
-0.020372141152620316,
0.010018017143011093,
-0.1046179011464119,
-0.04280770197510719,
-0.01718079298734665,
-0.017224939540028572,
-0.013105535879731178,
-0.02440028265118599,
0.001844075508415699,
0.014051580801606178,
-0.004660449456423521,
-0.013399600982666016,
-0.0073958202265203,
-0.015516147017478943,
0.013979945331811905,
0.012048688717186451,
0.036960385739803314,
0.004894176498055458,
0.03532131016254425,
-0.021986452862620354,
0.031444475054740906,
0.0757904201745987,
0.11554581671953201,
-0.0027419147081673145,
-0.037041209638118744,
0.07972365617752075,
-0.010993020609021187,
-0.004042960237711668,
-0.021988993510603905,
-0.01771083101630211,
0.004006092436611652,
0.0327015146613121,
0.015002232044935226,
-0.024738643318414688,
-0.03535088896751404,
-0.015013468451797962,
0.004089853726327419,
-0.0014077038504183292,
-0.07921367883682251,
-0.06187869608402252,
0.003061668248847127,
-0.05942532420158386,
-0.03135935589671135,
-0.045568209141492844,
0.003982509020715952,
0.034621067345142365,
-0.02856271155178547,
0.058491919189691544,
-0.008931255899369717,
-0.02626441791653633,
-0.06371606141328812,
0.03327199071645737,
-0.0003157315659336746,
-0.005673047620803118,
0.034433864057064056,
-0.017534978687763214,
0.028621455654501915,
0.004905973561108112,
0.0023177238181233406,
0.0014255107380449772,
-0.023276783525943756,
-0.007278157398104668,
-0.027722446247935295,
0.05369112268090248,
0.0030163475312292576,
-0.02011706680059433,
-0.012034646235406399,
0.015367054380476475,
0.021323569118976593,
-0.04017971456050873,
0.06980963051319122,
-0.01645798049867153,
-0.026637470349669456,
0.015858283266425133,
-0.006034679710865021,
0.047119248658418655,
0.10071069747209549,
-0.024379028007388115,
0.031808506697416306,
0.051299016922712326,
0.007446113042533398,
-0.004122356418520212,
-0.009619306772947311,
-0.049602314829826355,
0.06756825745105743,
0.04253054037690163,
0.03476329147815704,
-0.04515090957283974,
0.038188543170690536,
-0.026885157451033592,
-0.010433360934257507,
-0.030597977340221405,
0.010515175759792328,
0.05825699120759964,
0.018145322799682617,
0.015060563571751118,
-0.007841753773391247,
-0.021886568516492844,
-0.05812591686844826,
0.01306248176842928,
0.011184600181877613,
0.005047486629337072,
-0.019025694578886032,
-0.012040426023304462,
0.027967533096671104,
0.022149378433823586,
-0.03204159066081047,
0.044393692165613174,
0.024697577580809593,
-0.02568693272769451,
-0.02198781445622444,
-0.04149436205625534,
-0.0006641475483775139,
0.02055743709206581,
0.023434273898601532,
0.014597246423363686,
0.002879222622141242,
0.044467464089393616,
0.032249774783849716,
-0.04397422820329666,
-0.026659775525331497,
0.050403863191604614,
0.016944048926234245,
-0.03985404595732689,
-0.0024223793298006058,
-0.034977927803993225,
-0.03009755164384842,
0.024428224191069603,
0.007099021691828966,
0.018757706508040428,
0.029617000371217728,
0.008280478417873383,
-0.026515187695622444,
-0.03703039512038231,
-0.025783788412809372,
0.05088334158062935,
-0.029334625229239464,
-0.02666030451655388,
0.024196946993470192,
0.008778709918260574,
-0.0009688973659649491,
0.020098024979233742,
-0.03857060894370079,
-0.016851911321282387,
0.02177828922867775,
-0.04471968859434128,
-0.023877926170825958,
0.04829977825284004,
0.007523402106016874,
0.037018537521362305,
-0.0035829339176416397,
0.030714401975274086,
-0.005498925223946571,
-0.01559765450656414,
-0.014666191302239895,
0.03838852420449257,
0.06908225268125534,
0.02409236505627632,
-0.05544893071055412,
-0.028259675949811935,
0.03620414808392525,
0.02695552259683609,
0.017467813566327095,
-0.0465099923312664,
-0.01098165288567543,
0.028430150821805,
-0.06870879977941513,
0.0022315718233585358,
0.03164084255695343,
0.004948024172335863,
-0.005737368483096361,
-0.11160950362682343,
-0.041812218725681305,
0.05431892350316048,
0.015132985077798367,
0.04451565071940422,
0.03573361039161682,
0.007079568691551685,
0.09350551664829254,
-0.008715296164155006,
-0.0006196033209562302,
-0.035695869475603104,
-0.04371964558959007,
0.04923160746693611,
-0.08297883719205856,
0.03377096727490425,
-0.024305744096636772,
0.010343723930418491,
0.0194990374147892,
0.017374062910676003,
0.01233840174973011,
-0.03558440878987312,
-0.0509236603975296,
0.0297547634691,
-0.023817962035536766,
0.05205471068620682,
-0.00176330900285393,
0.05213895067572594,
0.03485142067074776,
0.02789759449660778,
0.05143284425139427,
-0.010023838840425014,
-0.04245208203792572,
0.009955361485481262,
-0.0008506636368110776,
0.0033793116454035044,
0.024053258821368217,
0.024895967915654182,
0.011988190934062004,
0.004872061312198639,
0.033823464065790176,
-0.02001483552157879,
-0.001667628763243556,
-0.0008685513166710734,
0.009968372993171215,
0.02564447559416294,
-0.01740621030330658,
-0.04717126116156578,
-0.05865123122930527,
0.030165035277605057,
-0.012416341342031956,
-0.01716950535774231,
-0.000449126964667812,
0.010055460967123508,
0.00782924797385931,
0.02406361885368824,
0.030137881636619568,
0.0792466476559639,
0.0117280138656497,
-0.019570665434002876,
0.004649990703910589,
-0.0070043765008449554,
-0.003926874604076147,
-0.009172742255032063,
-0.008558499626815319,
-0.04486884921789169,
0.02788364514708519,
0.018019620329141617,
0.0372513048350811,
0.03200637176632881,
-0.002900774125009775,
0.036614663898944855,
0.013645182363688946,
0.04878578707575798,
-0.009635396301746368,
-0.014858751557767391,
0.05454893410205841,
0.029056211933493614,
-0.004846050404012203,
-0.006115148775279522,
-0.024924883618950844,
0.000466870580567047,
0.04470245912671089,
-0.012189583852887154,
0.02618158981204033,
0.032297566533088684,
-0.01176685281097889,
0.0058021643199026585,
0.06794898957014084,
0.03777100145816803,
-0.04746585711836815,
-0.00929701142013073,
-0.019804539158940315,
0.023039354011416435,
-0.0039673144929111,
-0.031645189970731735,
0.013203109614551067,
-0.013074665330350399,
-0.04695802181959152,
0.0013741307193413377,
-0.019332120195031166,
-0.07185736298561096,
-0.010530934669077396,
0.009950351901352406,
0.018651548773050308,
-0.019859852269291878,
0.012124045751988888,
-0.058010902255773544,
0.05210323631763458,
0.05352222919464111,
0.03985189273953438,
-0.005832814145833254,
0.013975249603390694,
-0.016265451908111572,
-0.0029851875733584166,
0.06511659920215607,
0.00796457938849926,
-0.043776996433734894,
-0.008411423303186893,
0.023724671453237534,
-0.05733204260468483,
-0.029535911977291107,
-0.01364821381866932,
-0.03001677617430687,
0.009037347510457039,
0.042031534016132355,
-0.0375482402741909,
0.04086412489414215,
-0.05266653001308441,
-0.08976027369499207,
-0.04741312190890312,
-0.034069642424583435,
-0.009448998607695103,
0.009991457685828209,
0.06435879319906235,
-0.007198381703346968,
0.0185841117054224,
0.009687522426247597,
0.008239701390266418,
-0.02635909803211689,
-0.020262623205780983,
-0.005573241971433163,
0.0267045795917511,
0.03548567369580269,
0.01742371916770935,
-0.06643634289503098,
0.0659855529665947,
-0.005730928387492895,
0.06598116457462311,
-0.08315042406320572,
0.05561046302318573,
0.015311038121581078,
0.03414304926991463,
-0.047888170927762985,
0.028124351054430008,
-0.03473840653896332,
-0.031857382506132126,
-0.005970291793346405,
0.009873087517917156,
0.035561200231313705,
0.03281034529209137,
-0.014280207455158234,
-0.06071408838033676,
-0.01588277332484722,
0.016894245520234108,
0.04485436528921127,
-0.02920635975897312,
0.01277833804488182,
-0.0052771614864468575,
-0.048489801585674286,
0.029551764950156212,
-0.040562164038419724,
0.02952573448419571,
0.018265144899487495,
0.022220758721232414,
0.026504410430788994,
0.02432534098625183,
-0.01952509954571724,
-0.04241129010915756,
0.059022583067417145,
0.02013969235122204,
-0.03365126997232437,
-0.01839377172291279,
0.04723279923200607,
0.026863817125558853,
0.005311703309416771,
-0.0006430347566492856,
-0.0018037175759673119,
0.0265340656042099,
-0.015860406681895256,
0.04059440642595291,
0.02496160939335823,
0.026326598599553108,
0.04382488876581192,
0.02066192217171192,
-0.03713330999016762,
0.02103162556886673,
0.022020254284143448,
-0.0024539593141525984,
0.01289278082549572,
-0.046365443617105484,
-0.026909543201327324,
-0.031063109636306763,
0.08634380251169205,
-0.010089564137160778,
-0.022431088611483574,
-0.05035020411014557,
0.013423098251223564,
-0.06567535549402237,
-0.054978836327791214,
0.0045265210792422295,
-0.0029516711365431547,
-0.001082120114006102,
0.04733381047844887,
-0.03180692344903946,
0.0070050377398729324,
0.006857027765363455,
-0.019978517666459084,
-0.03238319978117943,
0.04768724367022514,
0.007159684784710407,
0.012876283377408981,
-0.010265696793794632,
-0.04496314004063606,
-0.04545406252145767,
-0.0462680384516716,
-0.014176194556057453,
-0.02850281074643135,
-0.028934534639120102,
0.009668032638728619,
0.017624666914343834,
0.0007384014897979796,
-0.06114749610424042,
-0.017012720927596092,
0.0009414353989996016,
0.0063183302991092205,
-0.026064997538924217,
0.01938839629292488,
-0.017516210675239563,
0.04311845824122429,
0.09079496562480927,
-0.016357554122805595,
-0.02134101092815399,
-0.10109829157590866,
0.0038983183912932873,
0.0307448823004961,
0.009664617478847504,
-0.0336630679666996,
-0.0598609559237957,
-0.03953543305397034,
-0.00043275795178487897,
-0.04451892152428627,
0.0003237853816244751,
0.007723261136561632,
0.0024613894056528807,
-0.00015966042701620609,
0.021873727440834045,
0.05932120606303215,
0.021313054487109184,
-0.04610421136021614,
-0.07533065974712372,
-0.009321372956037521,
-0.01555322390049696,
-0.051544275134801865,
-0.040733225643634796,
-0.06198078393936157,
0.04239838570356369,
0.08740226179361343,
-0.030296407639980316,
0.035500120371580124,
0.09410231560468674,
0.02329760231077671,
-0.004798460751771927,
-0.011374571360647678,
0.01590932533144951,
0.030156219378113747,
-0.044978946447372437,
-0.018082264810800552,
0.02787015028297901,
-0.07738488912582397,
-0.002564722904935479,
-0.029500901699066162,
-0.018712176010012627,
0.03339949995279312,
-0.006633691489696503,
0.006341505330055952,
-0.03625890985131264,
-0.032974883913993835,
0.05336868762969971,
-0.05122249573469162,
0.019189145416021347,
-0.012043949216604233,
-0.007923584431409836,
0.006570508703589439,
0.005025248974561691,
0.011150723323225975,
-0.06389953941106796,
0.008676758036017418,
-0.016894254833459854,
0.060310959815979004,
0.029105771332979202,
0.024788806214928627,
-0.003234902396798134,
-0.003766167676076293,
0.018463563174009323,
0.03198304772377014,
0.08546316623687744,
0.0006895407568663359,
0.022689728066325188,
0.07514877617359161,
0.003792925039306283,
0.010800686664879322,
-0.0472949780523777,
-0.011965920217335224,
-0.029796062037348747,
-0.031223131343722343,
-0.013524646870791912,
-0.04557746648788452,
0.030488066375255585,
0.024704601615667343,
0.03975211828947067,
0.021543752402067184,
-0.04564812406897545,
-0.006729227025061846,
-0.04237222298979759,
0.0001943176903296262,
0.04355822503566742,
0.00014492031186819077,
-0.04713793471455574,
0.042430330067873,
-0.05002877116203308,
-0.0055656093172729015,
0.032845769077539444,
0.04302902892231941,
-0.09680470079183578,
0.046857092529535294,
-0.015766385942697525,
0.017829669639468193,
-0.06839493662118912,
0.040797751396894455,
-0.008796688169240952,
-0.05817063897848129,
-0.032840438187122345,
-0.05362454429268837,
-0.03886091709136963,
-0.008438404649496078,
-0.004431985318660736,
-0.022915195673704147,
-0.02803078293800354,
0.03955942019820213,
-0.028394557535648346,
-0.016471976414322853,
0.0012473383685573936,
0.016443384811282158,
-0.05579925701022148,
0.0718325823545456,
-0.02267792820930481,
0.06051831692457199,
-0.0019434791756793857,
-0.020037760958075523,
0.04636525735259056,
0.03142629563808441,
-0.04028080776333809,
-0.057087622582912445,
-0.016393249854445457,
0.011741666123270988,
0.0675649419426918,
0.009560110978782177,
0.07529324293136597,
0.012149767950177193,
-0.007576788775622845,
0.0027683707885444164,
-0.04812956228852272,
-0.01028868742287159,
-0.04562695324420929,
-0.017069969326257706,
-0.03626076504588127,
-0.05536902695894241,
0.014861932955682278,
0.011369142681360245,
-0.005846766754984856,
0.013986623845994473,
-0.05736559256911278,
-0.03735676035284996,
-0.03700011968612671,
-0.01661819964647293,
0.026504911482334137,
-0.09436873346567154,
0.010561954230070114,
-0.006399133242666721,
-0.03688979893922806,
0.048044051975011826,
0.01411361899226904,
0.0542687326669693,
-0.07971606403589249,
-0.0036658847238868475,
0.004724359139800072,
0.012031021527945995,
0.03115997090935707,
0.04880378022789955,
0.015684504061937332,
0.022750249132514,
-0.01708156242966652,
-0.021471358835697174,
0.006772584747523069,
0.01954016461968422,
-0.01148518081754446,
-0.021769696846604347,
0.021504005417227745,
-0.05909828096628189,
-0.010864670388400555,
0.03979327902197838,
-0.042921677231788635,
0.05786324292421341,
-0.0015126998769119382,
0.0330001637339592,
-0.003955414053052664,
0.020466212183237076,
-0.01828911155462265,
-0.056094877421855927,
-0.027220724150538445,
-0.036474645137786865,
-0.0037752180360257626,
0.01522430032491684,
-0.0394306480884552,
0.03733326494693756,
-0.009695452637970448,
0.02882547676563263,
-0.0221539493650198,
-0.04489792510867119,
-0.07079990953207016,
0.008881913498044014,
0.0361342579126358,
-0.011251947842538357,
0.03131162375211716,
-0.026106536388397217,
-0.004129862878471613,
0.013017947785556316,
-0.01433536410331726,
0.011198495514690876,
0.047955822199583054,
-0.011395752429962158,
-0.007850298658013344,
0.03762827441096306,
-0.006471910048276186,
0.058829400688409805,
0.1053212583065033,
-0.05485258996486664,
-0.0031824689358472824,
0.09206845611333847,
-0.027218928560614586,
-0.03541354835033417,
-0.05240509286522865,
-0.030488772317767143,
-0.0059036328457295895,
-0.03893379122018814,
0.01567946933209896,
-0.06324451416730881,
-0.061527375131845474,
0.002380960388109088,
0.028575895354151726,
0.05201982706785202,
0.03559403494000435,
-0.005269145593047142,
-0.08818058669567108,
-0.04913591220974922,
0.018352573737502098,
0.04509282857179642,
0.029580604285001755,
-0.02853255905210972,
-0.058080535382032394,
0.01265949197113514,
-0.009306475520133972,
0.0246839988976717,
0.004741388373076916,
0.014778634533286095,
-0.0716787576675415,
0.0039070905186235905,
-0.05781617760658264,
0.021158406510949135,
0.010432839393615723,
-0.05290435254573822,
0.05740535259246826,
-0.0321475975215435,
0.026108896359801292,
-0.041468545794487,
-0.03177756443619728,
-0.025397857651114464,
0.06522024422883987,
0.016697095707058907,
-0.04771040007472038,
-0.05674207583069801,
0.020165596157312393,
0.02713293768465519,
0.0029028572607785463,
-0.08453024923801422,
0.00304429535754025,
0.014709651470184326,
0.039794065058231354,
-0.03996299207210541,
-0.08683180809020996,
0.006324307527393103,
0.018234863877296448,
0.02378956414759159,
0.024977009743452072,
0.02744254656136036,
0.03950005769729614,
0.0042946599423885345,
0.0093431007117033,
0.0367850586771965,
0.03955675661563873,
-0.04388738423585892,
-0.045127030462026596,
-0.029629793018102646,
0.0269831120967865,
-0.047345519065856934,
0.007381462026387453,
0.011741196736693382,
0.013863101601600647,
0.01016382034868002,
0.032859161496162415,
-0.005006986670196056,
-0.012763739563524723,
-0.010805650614202023,
-0.02702704630792141,
-0.02305450104176998
] |
<p>I'm not an expert but I've come to understand that the universe is expanding at enormous speed. That means that all of the visible galaxies are moving away from us at great speed. </p>
<p>I also came to understand that, eventually (in many many years), all the galaxies and all of the rest of the objects outside our own galaxy will move so far away from us that it will be impossible for us to look (or measure) them.</p>
<p>This means that eventually our entire observable universe will be our own galaxy and it will be impossible for us to measure anything else, and scientific measurements at that point in time will not correspond to the actual reality... because data will show that other galaxies don't exist.</p>
<p>But I have two questions regarding this phenomena:</p>
<ol>
<li><p>How is it that the light won't reach us anymore? Is the expansion happening at greater speed than light itself, making it impossible for it to ever reach anything?</p></li>
<li><p>If scientific measurements, at that point in time, will prove to be wrong, because they will show that galaxies don't exist (while they actually do exist), doesn't that mean that something similar could be happening right now as well? We could be measuring something about the universe that we're <em>dead</em> sure about, but it won't be the actual reality.</p></li>
</ol>
|
g2486
|
[
0.016167012974619865,
0.06808329373598099,
0.00039182917680591345,
0.010975135490298271,
0.0169202983379364,
0.03793085366487503,
-0.029763419181108475,
0.00413869135081768,
0.018312674015760422,
-0.04406071454286575,
0.029594840481877327,
0.0034004610497504473,
0.04051581025123596,
0.024934038519859314,
0.02889946848154068,
-0.025915667414665222,
0.06641119718551636,
-0.04899194464087486,
0.004637193866074085,
0.005486379377543926,
0.002562817418947816,
-0.011042892932891846,
0.046677276492118835,
-0.07899484783411026,
-0.07375340908765793,
-0.041647929698228836,
0.026928994804620743,
-0.024481670930981636,
0.03320269286632538,
-0.02173704095184803,
0.015298145823180676,
-0.04868496209383011,
0.01883842423558235,
-0.030112670734524727,
0.051360536366701126,
-0.024604832753539085,
-0.011142384260892868,
-0.015059992671012878,
0.07018598914146423,
-0.015816742554306984,
-0.0323343425989151,
0.01424261461943388,
0.010462857782840729,
-0.03786620870232582,
0.07916105538606644,
0.03373020142316818,
-0.03112810105085373,
0.015502951107919216,
0.08769916743040085,
-0.02085932344198227,
-0.04774085432291031,
-0.020777316763997078,
0.005826920736581087,
0.08120147138834,
-0.0023616051767021418,
0.004891256336122751,
0.028191443532705307,
-0.035246096551418304,
0.04117745906114578,
-0.004543091636151075,
-0.0033994896803051233,
-0.0012644351227208972,
0.057623352855443954,
0.015241564251482487,
0.036485593765974045,
-0.017796235159039497,
-0.03521488606929779,
-0.04377645626664162,
0.04047003388404846,
-0.01114121824502945,
0.0037108459509909153,
-0.008663046173751354,
-0.05339058116078377,
-0.05739269778132439,
-0.05831439793109894,
0.045009080320596695,
0.02510417252779007,
-0.017575012519955635,
-0.001743445754982531,
0.02244613505899906,
-0.044624704867601395,
-0.01872894912958145,
-0.0419439859688282,
0.017177889123558998,
0.02808307483792305,
-0.004153547342866659,
-0.042772457003593445,
0.020590074360370636,
0.01705390401184559,
0.024513186886906624,
0.04821961745619774,
-0.0035326697397977114,
0.0738803893327713,
-0.028744399547576904,
-0.03864824399352074,
-0.0378042571246624,
-0.03163257613778114,
0.04086212068796158,
-0.022666754201054573,
-0.007333095651119947,
-0.03085736185312271,
0.010347742587327957,
0.0055785770528018475,
0.008774579502642155,
-0.00920726079493761,
-0.033945757895708084,
0.015284179709851742,
-0.014659261330962181,
-0.0026723055634647608,
-0.03513813018798828,
-0.03284564986824989,
-0.03020613081753254,
-0.018184462562203407,
-0.015445319004356861,
-0.027625586837530136,
-0.01719697378575802,
0.007606299594044685,
0.05308287963271141,
0.01950971409678459,
0.01051871944218874,
0.06289537250995636,
0.04206305369734764,
0.03636670485138893,
-0.02010907605290413,
-0.006570806261152029,
-0.02356160432100296,
0.03352637216448784,
0.04604034125804901,
0.01747700572013855,
-0.017437933012843132,
0.019952446222305298,
0.06069907918572426,
-0.05811520665884018,
0.08266521990299225,
0.0061415694653987885,
-0.013388155028223991,
-0.03238675743341446,
0.010916529223322868,
0.007587080355733633,
0.039362676441669464,
0.03772138059139252,
-0.07375269383192062,
0.013840852305293083,
-0.03676023334264755,
-0.015790635719895363,
-0.011169916950166225,
-0.009586593136191368,
0.012750418856739998,
-0.020658941939473152,
-0.0494784377515316,
0.018826058134436607,
0.0734676793217659,
-0.01105553936213255,
-0.026419933885335922,
-0.0401301346719265,
0.0077702938579022884,
0.01905236765742302,
-0.006990802474319935,
0.002687608590349555,
-0.03273257613182068,
0.01831832155585289,
-0.034216590225696564,
-0.025701556354761124,
0.016340387985110283,
-0.02684592455625534,
0.044299762696027756,
-0.015521588735282421,
-0.05479086935520172,
0.02627951093018055,
-0.0023864679969847202,
-0.07476069778203964,
0.003086279146373272,
0.024059809744358063,
0.04886329546570778,
0.0022226967848837376,
0.05965457856655121,
0.045271001756191254,
-0.02299746870994568,
-0.11236853897571564,
0.012917867861688137,
-0.0172700434923172,
-0.07219408452510834,
-0.010510710999369621,
-0.03050066903233528,
0.0036304709501564503,
-0.04461550712585449,
-0.02995394729077816,
-0.03752392530441284,
0.0067352126352488995,
0.008851082995533943,
-0.016829077154397964,
-0.03632090613245964,
0.04158920422196388,
0.0097603565081954,
-0.03277317434549332,
-0.013015924021601677,
0.029613588005304337,
-0.018086010590195656,
-0.030844682827591896,
-0.044935908168554306,
0.007328636012971401,
0.03748072683811188,
-0.025430068373680115,
-0.009049768559634686,
0.03834198787808418,
-0.04112960025668144,
-0.02333167940378189,
0.03318919986486435,
0.03488343209028244,
0.014087521471083164,
0.012323345057666302,
-0.0653408095240593,
-0.012991045601665974,
-0.017559757456183434,
0.02382505312561989,
0.021606212481856346,
-0.01698625087738037,
0.01817028410732746,
0.015094729140400887,
0.02439764142036438,
0.03740344196557999,
-0.010214957408607006,
0.04054230451583862,
-0.03482701629400253,
0.01842091605067253,
-0.023951144888997078,
-0.07221157103776932,
-0.02598269097507,
0.026775944977998734,
0.041584793478250504,
-0.06194739416241646,
-0.013238622806966305,
0.07422523200511932,
-0.011850548908114433,
-0.002810308476909995,
0.02590220794081688,
-0.02484934963285923,
-0.002082879887893796,
0.024660078808665276,
0.025169597938656807,
0.03741027042269707,
-0.06295551359653473,
-0.034440428018569946,
0.02050536312162876,
0.05880202353000641,
-0.08310120552778244,
0.05626910179853439,
-0.0562339685857296,
-0.036548350006341934,
0.022130925208330154,
0.0657212883234024,
0.03371944651007652,
0.004516448825597763,
-0.02394205518066883,
-0.030224300920963287,
0.00182129698805511,
0.037172626703977585,
0.07282961159944534,
-0.0649024099111557,
0.0054063862189650536,
-0.00782516598701477,
0.037395019084215164,
0.01726888120174408,
-0.018673080950975418,
-0.03451799601316452,
0.0018423954024910927,
-0.03752199560403824,
0.0004508060810621828,
-0.05575037747621536,
-0.01714576594531536,
-0.00548052042722702,
0.002442823024466634,
0.003822148311883211,
0.01231204904615879,
0.054661378264427185,
0.03961386904120445,
-0.0042314971797168255,
-0.033432669937610626,
0.061833009123802185,
-0.01630338467657566,
-0.03322618082165718,
-0.002065061591565609,
-0.07283450663089752,
-0.01264912448823452,
0.008890490047633648,
-0.05509829521179199,
-0.009135812520980835,
-0.01616521179676056,
0.03748933970928192,
-0.019879985600709915,
0.01726561412215233,
0.017768939957022667,
0.01770280860364437,
0.01692497357726097,
-0.04436545446515083,
0.0742647796869278,
-0.049634527415037155,
0.02994018979370594,
0.008451606146991253,
-0.06166011840105057,
0.03451624512672424,
-0.048038508743047714,
0.01708252727985382,
-0.027432231232523918,
0.05248943343758583,
0.03220594301819801,
-0.02880791947245598,
-0.014059514738619328,
0.033731020987033844,
-0.051951389759778976,
0.004823922645300627,
0.025574441999197006,
-0.004922128282487392,
0.01748771034181118,
0.026440123096108437,
0.041240740567445755,
-0.013688702136278152,
0.05115702375769615,
0.044656865298748016,
0.027433080598711967,
0.03249569982290268,
-0.015212783589959145,
-0.0654938668012619,
-0.03918224573135376,
0.05370437353849411,
-0.049321871250867844,
-0.02822762355208397,
-0.03159797936677933,
-0.059576258063316345,
0.016451328992843628,
0.014131477102637291,
0.017339900135993958,
0.015347872860729694,
-0.012702789157629013,
-0.04729202389717102,
0.0224288497120142,
0.005590172950178385,
0.02236836589872837,
0.0638534426689148,
0.005582853686064482,
-0.016884194687008858,
-0.011819426901638508,
-0.045687321573495865,
0.04332536458969116,
-0.035258229821920395,
0.012865491211414337,
-0.025426216423511505,
-0.03956390917301178,
-0.022167272865772247,
-0.014876025728881359,
0.07894796133041382,
0.028066564351320267,
-0.013606523163616657,
-0.022584453225135803,
0.004021763801574707,
0.036115724593400955,
0.03321154788136482,
0.0024432255886495113,
0.08017795532941818,
-0.02807939611375332,
-0.008279845118522644,
0.003173121018335223,
0.04470466822385788,
-0.03622216358780861,
-0.03575194254517555,
-0.03864382579922676,
0.013434872962534428,
-0.015224605798721313,
0.006827109027653933,
0.022169820964336395,
0.0026758459862321615,
-0.02617662027478218,
-0.045845773071050644,
0.029540177434682846,
0.07033847272396088,
0.007290406618267298,
0.0395258292555809,
0.018230760470032692,
-0.02639220841228962,
0.04700498282909393,
0.021349217742681503,
0.0631856843829155,
0.03753437101840973,
-0.012107409536838531,
0.030653351917862892,
0.022318556904792786,
-0.04913627356290817,
-0.0659920871257782,
-0.02488080970942974,
-0.04421267285943031,
0.08408414572477341,
-0.03140658512711525,
0.022527242079377174,
0.0026462979149073362,
0.024387771263718605,
-0.08002136647701263,
-0.01242850348353386,
0.009193055331707,
0.0658213421702385,
-0.01733667589724064,
-0.002930006943643093,
0.014096599072217941,
-0.00465066684409976,
-0.013538866303861141,
-0.03334859758615494,
-0.0221723560243845,
0.013954607769846916,
0.0021655408199876547,
0.0171897504478693,
-0.0358712300658226,
0.008284249342978,
0.003927056211978197,
-0.00453179283067584,
-0.044560208916664124,
0.017432263121008873,
0.025499751791357994,
0.004329442046582699,
-0.05465550348162651,
-0.014469461515545845,
0.019999565556645393,
0.011413183994591236,
0.025931373238563538,
0.024412386119365692,
-0.013585088774561882,
-0.040181566029787064,
0.058555856347084045,
-0.016545599326491356,
-0.07031811773777008,
-0.006965723354369402,
0.02233419194817543,
0.02024470642209053,
0.04608357325196266,
0.055817168205976486,
0.09604193270206451,
0.026959728449583054,
0.03252103179693222,
0.006847139913588762,
0.07379937916994095,
0.007241864688694477,
0.023545369505882263,
0.0579858124256134,
-0.007253178395330906,
0.0012410735944285989,
0.07471716403961182,
0.005443682428449392,
0.06205344200134277,
-0.07031813263893127,
-0.007251461036503315,
-0.020551014691591263,
0.0008516083471477032,
-0.025114383548498154,
0.06023741513490677,
0.0053029246628284454,
0.008739893324673176,
-0.005116520449519157,
-0.04350489377975464,
0.016293177381157875,
0.04079145938158035,
0.02013908326625824,
0.03221061825752258,
-0.05808321759104729,
0.07156693190336227,
0.029996216297149658,
0.013538572937250137,
0.052934180945158005,
-0.01576826348900795,
-0.03468262776732445,
-0.066472128033638,
-0.040878623723983765,
0.017023641616106033,
-0.09305907040834427,
0.007408153265714645,
0.044881850481033325,
0.03205706551671028,
-0.04250181466341019,
0.009415775537490845,
-0.05106668174266815,
-0.0025503390934318304,
-0.03554031252861023,
-0.03292553871870041,
-0.029799407348036766,
-0.03453976660966873,
0.052110705524683,
-0.03951268270611763,
-0.027081862092018127,
0.055454567074775696,
-0.011085433885455132,
0.027981771156191826,
-0.020490283146500587,
0.002006193855777383,
0.04756823927164078,
-0.023346755653619766,
0.03509102761745453,
0.028259271755814552,
-0.04099709540605545,
0.04081939533352852,
-0.008281241171061993,
0.007637813221663237,
-0.024307316169142723,
-0.01414532121270895,
0.009096762165427208,
0.06673647463321686,
-0.032847896218299866,
-0.055392082780599594,
0.002931260969489813,
0.05016140639781952,
0.023531030863523483,
-0.026524042710661888,
0.017357030883431435,
0.0031765673775225878,
0.024054892361164093,
0.03177957609295845,
0.010496004484593868,
-0.018071483820676804,
0.018841110169887543,
-0.065760038793087,
0.020445510745048523,
-0.00323655316606164,
0.034814439713954926,
-0.03553377091884613,
-0.0940980464220047,
-0.006752272602170706,
0.034206390380859375,
-0.0055558932945132256,
0.06894619762897491,
0.007103988900780678,
-0.02487003244459629,
0.031655699014663696,
0.08246926218271255,
-0.011256195604801178,
0.08169930428266525,
0.008461683057248592,
0.012626499868929386,
-0.07866086810827255,
-0.03010556660592556,
0.05777810513973236,
0.01636650785803795,
-0.04553887993097305,
-0.01473420299589634,
-0.011373508721590042,
0.03503992781043053,
-0.001795241143554449,
-0.0005494868964888155,
0.10366526246070862,
-0.008016487583518028,
0.041938524693250656,
0.02143346145749092,
-0.0048456802032887936,
0.04830572381615639,
-0.013311853632330894,
-0.015017243102192879,
-0.015641402453184128,
-0.0289588775485754,
0.04495459794998169,
-0.04067262262105942,
0.029916023835539818,
0.058739323168992996,
0.00620355224236846,
-0.07147994637489319,
-0.02781309187412262,
0.038882359862327576,
0.007981732487678528,
-0.022031797096133232,
-0.018550200387835503,
0.0014775831950828433,
-0.027642054483294487,
0.03397511690855026,
-0.02906814217567444,
0.02984829619526863,
0.04716666042804718,
-0.011978608556091785,
0.011406459845602512,
0.013445713557302952,
-0.010624738410115242,
0.0009060814045369625,
0.04536553844809532,
-0.001468804432079196,
0.009212189354002476,
-0.020502589643001556,
0.003176966914907098,
-0.011996692977845669,
0.008686628192663193,
0.043878547847270966,
-0.0054072607308626175,
0.033323656767606735,
0.010650007985532284,
0.01279291883111,
0.0036327557172626257,
0.08136497437953949,
-0.07077985256910324,
0.009753920137882233,
0.003062301082536578,
-0.0012005924945697188,
-0.07637391984462738,
-0.06431201100349426,
-0.06279692053794861,
-0.005277514457702637,
-0.10498395562171936,
-0.042092081159353256,
-0.01812104880809784,
-0.049708545207977295,
-0.046185653656721115,
0.07958676666021347,
-0.04331743344664574,
0.030547579750418663,
-0.01298086903989315,
-0.03380201756954193,
-0.0006794132059440017,
0.10366557538509369,
-0.05410653352737427,
0.01170576922595501,
0.020002810284495354,
0.04405900835990906,
0.03110446408390999,
0.025021405890583992,
-0.06357713788747787,
0.052293140441179276,
-0.0360424630343914,
0.008937709033489227,
0.024588579311966896,
0.018955865874886513,
-0.030003633350133896,
0.01610572636127472,
0.024182775989174843,
-0.034133415669202805,
0.03346667438745499,
-0.045068416744470596,
-0.0005132080405019224,
0.006811259314417839,
0.036034658551216125,
0.024364233016967773,
0.0009864425519481301,
0.04730840399861336,
0.01519034430384636,
0.04009177163243294,
0.03295274078845978,
0.007328013423830271,
0.021035989746451378,
0.03660067170858383,
-0.049346473067998886,
0.015100670978426933,
0.010767610743641853,
0.0024560594465583563,
-0.04014915972948074,
-0.0013435248984023929,
0.01956866681575775,
-0.002069536130875349,
-0.040667977184057236,
-0.054687418043613434,
-0.00020704713824670762,
-0.0021121245808899403,
-0.08230609446763992,
-0.003567261854186654,
-0.00834051426500082,
-0.020344167947769165,
0.009152062237262726,
-0.00030757326749153435,
-0.049008458852767944,
-0.05648847296833992,
-0.04032745212316513,
-0.037950851023197174,
-0.04888924956321716,
-0.026079505681991577,
-0.02487300895154476,
-0.010976629331707954,
0.030417028814554214,
-0.009569132700562477,
-0.0746760442852974,
0.013090400956571102,
-0.03908582404255867,
0.03154537454247475,
-0.02823418565094471,
-0.03929499536752701,
-0.047837357968091965,
0.025414342060685158,
0.011860695667564869,
-0.06446029990911484,
0.011270899325609207,
0.04140112176537514,
-0.0091173080727458,
-0.022669365629553795,
0.05928492546081543,
-0.015383929014205933,
0.06136538088321686,
-0.02395021729171276,
0.0476720817387104,
-0.02678157389163971,
-0.00743818748742342,
-0.04260861501097679,
-0.029765119776129723,
-0.005798281170427799,
-0.025646330788731575,
-0.02667596936225891,
0.012008240446448326,
0.05663646385073662,
0.00036910208291374147,
-0.012649822048842907,
0.022634463384747505,
-0.014374414458870888,
-0.02864975482225418,
-0.01363796554505825,
-0.00738271651789546,
-0.0073569281958043575,
-0.01437442284077406,
0.008448014035820961,
-0.011745073832571507,
-0.022837864235043526,
0.0032053955364972353,
0.017495371401309967,
0.023002270609140396,
0.004258631728589535,
0.060845959931612015,
-0.006059909239411354,
-0.038371242582798004,
0.012150204740464687,
-0.032264240086078644,
0.020903734490275383,
-0.03984379395842552,
-0.01958346553146839,
-0.02824278548359871,
-0.023377347737550735,
0.0009606356034055352,
-0.01216565165668726,
-0.04379250481724739,
-0.006919861305505037,
0.027798710390925407,
0.05254346504807472,
0.03576347976922989,
-0.02312452346086502,
-0.016461189836263657,
0.008709752932190895,
0.008391862735152245,
-0.002440220909193158,
-0.03782939910888672,
-0.06677727401256561,
0.05986609309911728,
-0.029321718961000443,
-0.012763811275362968,
-0.05883267894387245,
-0.00382356159389019,
-0.026326024904847145,
-0.012852183543145657,
0.0011047882726415992,
0.054766517132520676,
0.01800798624753952,
-0.0748421847820282,
0.022198211401700974,
0.043214473873376846,
-0.008963440544903278,
0.026780378073453903,
-0.01591586507856846,
0.09159687161445618,
-0.00422070873901248,
0.06175018846988678,
0.01030215248465538,
-0.0388958677649498,
-0.03683962672948837,
-0.02894849143922329,
-0.008975274860858917,
-0.0165538489818573,
0.0057278284803032875,
-0.010698161087930202,
-0.0003367026220075786,
0.02388109639286995,
-0.002558707958087325,
-0.07003343850374222,
-0.06778957694768906,
0.01972239278256893
] |
<p>If general relativity is the newest model of Gravity which is so far been proven. Does it still have any anomalies such as the <a href="http://physics.stackexchange.com/q/26408/2451">problem</a> of Mercury's orbit during Newtonian gravity period?</p>
<p>If so are there other types of physics to be discovered?</p>
|
g2487
|
[
0.015011271461844444,
0.07119828462600708,
0.015108348801732063,
0.010089666582643986,
0.01605254039168358,
0.07103268057107925,
0.04760421812534332,
-0.024721745401620865,
-0.047819770872592926,
0.006031778175383806,
0.06563055515289307,
-0.04695795848965645,
-0.01706881634891033,
-0.01676982268691063,
-0.01866050809621811,
-0.02160627394914627,
0.047896601259708405,
-0.0515119694173336,
0.014852720312774181,
0.03955361992120743,
0.04763663932681084,
-0.034360770136117935,
0.03639376908540726,
-0.008703935891389847,
0.026634899899363518,
0.0055607156828045845,
0.03462750092148781,
0.004525011871010065,
-0.016684841364622116,
-0.01313955057412386,
0.014146903529763222,
-0.05549526959657669,
0.03347443789243698,
-0.05697338655591011,
-0.026460399851202965,
-0.051975004374980927,
0.027865611016750336,
0.012178812175989151,
0.0009401574498042464,
0.004305445123463869,
0.0010110670700669289,
-0.001270623761229217,
-0.08539216965436935,
0.00323697691783309,
0.022470859810709953,
-0.025988519191741943,
-0.021491898223757744,
0.009311615489423275,
0.03749523684382439,
-0.04296422377228737,
-0.02175757847726345,
0.05584859848022461,
0.027212923392653465,
-0.06642813235521317,
-0.004936964251101017,
0.043627556413412094,
0.004736959468573332,
0.02420094422996044,
0.04042536020278931,
-0.009176656603813171,
0.009464122354984283,
0.024515578523278236,
0.0658537968993187,
-0.014749794267117977,
-0.04586832970380783,
0.026243750005960464,
-0.050760384649038315,
0.0012536158319562674,
0.022743703797459602,
-0.008953043259680271,
0.05136478692293167,
0.017083419486880302,
0.016445038840174675,
0.015742715448141098,
-0.024384140968322754,
0.025281913578510284,
0.01672704517841339,
0.017376216128468513,
-0.044446587562561035,
-0.012128489091992378,
-0.02443188615143299,
0.027802033349871635,
0.007883448153734207,
-0.03332696482539177,
0.09660828113555908,
-0.035365305840969086,
-0.024043826386332512,
0.05864064767956734,
-0.008089778013527393,
0.07384762167930603,
0.029591912403702736,
-0.0285072922706604,
0.06807399541139603,
-0.002930206013843417,
-0.003978912252932787,
0.018302109092473984,
-0.01617908850312233,
0.0980929508805275,
0.001101061818189919,
0.03213677927851677,
-0.009699351154267788,
0.0600590817630291,
0.03199678286910057,
0.0004116453346796334,
0.046985775232315063,
-0.009745561517775059,
0.027597161009907722,
0.0132278548553586,
0.0009873388335108757,
-0.018952270969748497,
-0.025634583085775375,
0.028462544083595276,
0.01368018239736557,
-0.003138067666441202,
-0.057927146553993225,
-0.010816352441906929,
0.03187638893723488,
-0.05857181176543236,
0.015324469655752182,
0.02952989563345909,
-0.026942700147628784,
0.028968878090381622,
-0.012507281266152859,
0.047618597745895386,
-0.07025783509016037,
0.003912478685379028,
0.016998227685689926,
0.017185719683766365,
0.019846662878990173,
-0.01291080005466938,
0.020491797477006912,
0.033108144998550415,
0.013338414952158928,
0.05100174993276596,
0.009385156445205212,
-0.04875699803233147,
0.0825822502374649,
0.03566000983119011,
0.010534465312957764,
0.002349979244172573,
0.02161283977329731,
-0.03893018513917923,
0.05019376799464226,
0.016052819788455963,
0.046856947243213654,
0.01836298406124115,
0.01017245464026928,
0.0968736931681633,
0.016918588429689407,
0.03359007462859154,
-0.04479803144931793,
0.05778302997350693,
0.03546437621116638,
-0.06734910607337952,
-0.010310236364603043,
-0.03614246845245361,
-0.09045194089412689,
-0.0011042167898267508,
0.009670781902968884,
-0.02404855564236641,
0.05450672656297684,
-0.026496263220906258,
0.02015601471066475,
0.039597317576408386,
-0.05307285487651825,
0.052523549646139145,
-0.05020846426486969,
-0.0549176000058651,
0.0038140183314681053,
-0.019534830003976822,
-0.07999642193317413,
-0.0061731114983558655,
0.006564243696630001,
0.07071347534656525,
0.04290018230676651,
0.004390615038573742,
0.009253659285604954,
-0.037258848547935486,
0.002749290317296982,
0.015421601012349129,
0.018219396471977234,
-0.06645270437002182,
-0.027407528832554817,
-0.009361677803099155,
-0.03589528053998947,
-0.03022684156894684,
0.02423618547618389,
-0.044094253331422806,
-0.08008747547864914,
0.005637361668050289,
-0.03261003643274307,
-0.009604932740330696,
-0.015344365499913692,
-0.01710040494799614,
0.024204345420002937,
-0.04229516535997391,
0.0044650062918663025,
-0.0154416523873806,
-0.04153117164969444,
0.09074724465608597,
-0.013056998141109943,
0.05850089341402054,
-0.01238766685128212,
-0.0051817139610648155,
-0.0019166981801390648,
-0.004203442949801683,
0.01970302313566208,
-0.05167042091488838,
0.056005679070949554,
0.036174189299345016,
0.027959054335951805,
-0.05263194441795349,
0.07768064737319946,
-0.017914894968271255,
-0.02313327044248581,
-0.010605858638882637,
0.035065729171037674,
0.04294783994555473,
0.009545257315039635,
0.030944164842367172,
0.023043310269713402,
0.033231470733881,
-0.03064490482211113,
0.05286644399166107,
0.018329523503780365,
-0.011975456960499287,
-0.029102468863129616,
0.021137768402695656,
0.01898166909813881,
0.015684355050325394,
0.010606487281620502,
0.043585117906332016,
-0.029624884948134422,
-0.019927050918340683,
0.07213585078716278,
0.023658985272049904,
0.02125157229602337,
-0.050914496183395386,
0.022895358502864838,
0.0046232640743255615,
-0.03032877668738365,
0.03940601646900177,
-0.04862187057733536,
-0.05239288881421089,
0.05073218047618866,
-0.01876019686460495,
-0.015789039433002472,
-0.0023767061065882444,
0.03071570210158825,
0.043112773448228836,
0.01587834767997265,
0.004869591910392046,
-0.03951412811875343,
0.003882498247548938,
0.004797382280230522,
0.028576241806149483,
-0.025797784328460693,
0.07815667241811752,
-0.08544271439313889,
-0.05236872285604477,
0.03166395053267479,
-0.0387122817337513,
0.0023637856356799603,
0.013844171538949013,
-0.05648663640022278,
-0.02630443498492241,
-0.06849140673875809,
-0.024564310908317566,
-0.06507302820682526,
-0.001443613087758422,
-0.0027076222468167543,
0.009897539392113686,
-0.0038296065758913755,
0.048700232058763504,
-0.06868880987167358,
0.0518663115799427,
-0.010205433703958988,
-0.0018925375770777464,
0.019114580005407333,
-0.007472470868378878,
-0.04932153597474098,
-0.022356553003191948,
-0.04485488682985306,
-0.011705189943313599,
0.01570407673716545,
-0.031890202313661575,
-0.0077964444644749165,
0.011601175181567669,
-0.023566288873553276,
0.02265169844031334,
0.021892957389354706,
0.03747537359595299,
0.044688500463962555,
0.026752617210149765,
-0.056324686855077744,
0.04325336590409279,
-0.018247397616505623,
0.005197334103286266,
-0.03436851501464844,
-0.018670346587896347,
0.03255927935242653,
-0.050093818455934525,
-0.019110044464468956,
0.060218725353479385,
0.019636329263448715,
-0.03781243413686752,
-0.02141779474914074,
0.01201909501105547,
0.029869673773646355,
-0.0370391383767128,
0.016090454533696175,
0.06619727611541748,
-0.017850738018751144,
0.045243989676237106,
-0.010678652673959732,
-0.00788203626871109,
-0.0040389858186244965,
0.0134328193962574,
-0.023905066773295403,
-0.01134906243532896,
0.000010398882295703515,
-0.04894327372312546,
-0.034783922135829926,
-0.05986172333359718,
0.06466396898031235,
0.06491675227880478,
-0.03382282704114914,
-0.020326711237430573,
-0.00972080510109663,
0.032116569578647614,
0.012551451101899147,
-0.03429093584418297,
-0.037487369030714035,
0.000022392474420485087,
0.019964393228292465,
0.009478870779275894,
-0.006686464883387089,
0.018597563728690147,
0.05969454348087311,
0.023739228025078773,
0.044006675481796265,
0.02048441208899021,
-0.0021701008081436157,
-0.005334018729627132,
-0.014059409499168396,
0.006535871420055628,
-0.016435228288173676,
-0.0029057152569293976,
0.026872307062149048,
0.05132246017456055,
-0.012070881202816963,
-0.03181029483675957,
0.024893078953027725,
-0.04138999432325363,
-0.019733790308237076,
-0.005455334205180407,
0.024480804800987244,
0.012712143361568451,
0.009492351673543453,
-0.04133603349328041,
-0.08266820013523102,
-0.031750697642564774,
-0.017791075631976128,
0.06696084141731262,
0.04994507133960724,
0.016835801303386688,
0.03771074488759041,
-0.019355740398168564,
0.0271377582103014,
-0.034382518380880356,
0.04580526798963547,
0.020897923037409782,
0.03744132071733475,
-0.038436174392700195,
0.06417806446552277,
-0.014711915515363216,
0.017027322202920914,
0.03253024443984032,
0.017349978908896446,
-0.016262533143162727,
0.03816433995962143,
-0.009128034114837646,
0.007389761507511139,
0.05258125811815262,
0.010419134050607681,
-0.02085079438984394,
-0.009139206260442734,
-0.03916284069418907,
-0.009732103906571865,
-0.07993125170469284,
-0.011728933081030846,
0.04767204076051712,
0.00486403563991189,
0.021690480411052704,
-0.01494264230132103,
0.010845164768397808,
-0.0020611677318811417,
-0.0092553049325943,
0.027033155784010887,
0.01447231974452734,
-0.0016573522007092834,
-0.01704644411802292,
-0.049641095101833344,
0.06679613143205643,
-0.06253919005393982,
-0.011994685977697372,
0.026914386078715324,
0.007556953001767397,
-0.0027099137660115957,
0.023242162540555,
0.030651705339550972,
0.043757788836956024,
-0.06261126697063446,
-0.05692121386528015,
0.03098527155816555,
0.02304409258067608,
-0.012371107935905457,
-0.00726336520165205,
0.011975718662142754,
-0.016959670931100845,
0.04171530529856682,
0.09894513338804245,
0.01789383590221405,
0.00693243695423007,
0.0029536292422562838,
0.01698194071650505,
0.023537976667284966,
-0.03576694801449776,
-0.02898584119975567,
-0.035175200551748276,
0.018338965252041817,
-0.05901108309626579,
-0.016978807747364044,
0.04147407039999962,
-0.020903954282402992,
0.03281167894601822,
-0.017178663983941078,
-0.014303803443908691,
-0.0006752318004146218,
0.014434495009481907,
0.09282919764518738,
0.03272927179932594,
-0.002087353030219674,
0.020570963621139526,
-0.0025015822611749172,
0.05958213284611702,
0.030309190973639488,
0.010630490258336067,
-0.025411365553736687,
0.05846839398145676,
-0.02550840750336647,
-0.01647513173520565,
0.009608864784240723,
0.017363132908940315,
-0.027715511620044708,
-0.06187910586595535,
-0.02529100514948368,
0.057763032615184784,
-0.040954217314720154,
0.06362176686525345,
-0.04267840459942818,
-0.061988718807697296,
0.0394352450966835,
0.07272408902645111,
-0.01627524383366108,
-0.08924165368080139,
-0.041923828423023224,
-0.018893776461482048,
-0.09384366869926453,
-0.07918357104063034,
-0.02664502151310444,
-0.005504576954990625,
0.03646575286984444,
0.02680295892059803,
-0.0026240369770675898,
-0.04380957782268524,
0.014245342463254929,
-0.00464896485209465,
-0.0070909722708165646,
-0.026283465325832367,
-0.039108093827962875,
0.0004539035726338625,
0.003604613710194826,
0.047924675047397614,
0.012095274403691292,
0.032471079379320145,
-0.038037125021219254,
-0.02396697923541069,
-0.03458767756819725,
-0.07536107301712036,
0.03589073196053505,
-0.025828033685684204,
0.024297624826431274,
-0.016471462324261665,
-0.022027095779776573,
0.016666945070028305,
-0.03597607463598251,
0.0012490194058045745,
0.006992224138230085,
-0.00702845212072134,
-0.014465763233602047,
0.06411199271678925,
0.03807014226913452,
-0.03760542720556259,
0.015324479900300503,
0.06632345914840698,
-0.027031976729631424,
-0.004280015826225281,
-0.04887174069881439,
0.013278242200613022,
-0.0364203006029129,
-0.0154243353754282,
-0.061874136328697205,
0.0077337054535746574,
0.0326269268989563,
-0.02887818031013012,
0.02884070947766304,
-0.04676268994808197,
-0.0077921440824866295,
-0.07246039062738419,
-0.06145600229501724,
-0.0170265045017004,
0.06135455518960953,
0.009167484007775784,
0.0758591890335083,
0.021122338250279427,
-0.024017758667469025,
-0.0002965494350064546,
0.00547582283616066,
-0.01434795930981636,
0.030035804957151413,
-0.022375470027327538,
0.04447987675666809,
0.018811581656336784,
0.030744191259145737,
-0.01992274634540081,
0.01581033691763878,
0.019666817039251328,
0.06124721094965935,
-0.024150697514414787,
-0.060130879282951355,
-0.0016193963820114732,
-0.0033889799378812313,
0.008581212721765041,
-0.020150581374764442,
-0.028367212042212486,
-0.07251720130443573,
0.038510482758283615,
0.02343021333217621,
-0.0986027866601944,
-0.018992893397808075,
0.016063034534454346,
-0.032852381467819214,
0.07866884768009186,
-0.06971614807844162,
0.023005835711956024,
-0.04928532987833023,
-0.061134036630392075,
-0.005837189499288797,
0.019367927685379982,
0.003208179259672761,
0.017959097400307655,
0.05811331048607826,
-0.048648130148649216,
-0.014295467175543308,
0.01460032444447279,
0.002379455603659153,
-0.03393876180052757,
0.056653231382369995,
0.0003875899128615856,
-0.04803384840488434,
0.025035973638296127,
-0.03366243839263916,
0.01758071780204773,
-0.011752870865166187,
-0.08352622389793396,
-0.010059687308967113,
0.006326145026832819,
-0.055801521986722946,
-0.014416641555726528,
0.012065023183822632,
0.0034738746471703053,
0.04275551810860634,
-0.013349635526537895,
-0.04637477919459343,
0.03984437882900238,
-0.05292005464434624,
-0.004639852792024612,
-0.009733697399497032,
-0.024253658950328827,
-0.05827329307794571,
-0.05166416987776756,
-0.03308869153261185,
-0.008347238413989544,
-0.07253025472164154,
0.0193670354783535,
-0.0011223729234188795,
0.005916350521147251,
-0.03012581542134285,
0.013373779132962227,
-0.0008709504618309438,
-0.04399378225207329,
0.09165021777153015,
0.007994952611625195,
0.005639577284455299,
0.004758108872920275,
-0.04898146167397499,
0.01214980985969305,
-0.0005564510356634855,
0.016469664871692657,
0.05183638259768486,
0.005048059392720461,
-0.0035407389514148235,
0.024421343579888344,
-0.05455928295850754,
-0.03000907599925995,
0.04712773486971855,
-0.004059370141476393,
-0.04707486927509308,
0.009072463028132915,
0.015924576669931412,
0.009220747277140617,
-0.02800854668021202,
-0.03788849711418152,
-0.008001147769391537,
0.03120199777185917,
-0.051691893488168716,
0.015877557918429375,
0.01628876104950905,
0.010525785386562347,
0.018914122134447098,
0.012976482510566711,
-0.05253879353404045,
0.02661266177892685,
0.04720478877425194,
0.021888813003897667,
-0.0411863699555397,
0.03966474533081055,
0.03936566784977913,
-0.022203870117664337,
0.026989910751581192,
-0.0785437747836113,
-0.00231167976744473,
-0.030092595145106316,
-0.02028932236135006,
0.02492917701601982,
0.025325018912553787,
0.007601042278110981,
-0.019062314182519913,
-0.009580523706972599,
0.013886985369026661,
-0.019074497744441032,
0.014821582473814487,
-0.009241554886102676,
-0.009961331263184547,
0.005226296838372946,
0.009853542782366276,
0.014532302506268024,
0.06817884743213654,
-0.03135855123400688,
0.0023956988006830215,
0.020293353125452995,
0.007148802746087313,
0.059602852910757065,
0.0046413918025791645,
0.011755101382732391,
0.0076874252408742905,
-0.0984925925731659,
-0.01376156322658062,
0.03910807520151138,
-0.009852482937276363,
-0.03298695385456085,
-0.01996852084994316,
-0.016808001324534416,
0.02883979305624962,
0.010168103501200676,
-0.010376454330980778,
-0.06832479685544968,
0.009236015379428864,
-0.030296344310045242,
-0.02626718021929264,
0.06836234033107758,
-0.009037076495587826,
0.0627821832895279,
-0.00009776367369340733,
0.015879034996032715,
0.017300719395279884,
-0.005620586685836315,
0.0020496381912380457,
-0.016438575461506844,
0.02576005831360817,
0.044594183564186096,
0.016023339703679085,
-0.01272759959101677,
-0.002004854381084442,
-0.03403354808688164,
-0.019054412841796875,
0.02800011821091175,
0.013738644309341908,
-0.04413355514407158,
-0.016903899610042572,
0.007890952751040459,
-0.02864333987236023,
-0.03395543992519379,
-0.019551480188965797,
0.0039177206344902515,
-0.04431748390197754,
-0.02261260710656643,
-0.0289827361702919,
0.054847683757543564,
0.02464865893125534,
0.040282946079969406,
0.025689924135804176,
0.008722435683012009,
0.01937679387629032,
0.011163940653204918,
-0.08327475190162659,
-0.045153941959142685,
0.02528686635196209,
-0.09675592184066772,
-0.015985531732439995,
-0.050324346870183945,
-0.04219631850719452,
-0.04006631299853325,
-0.07927235960960388,
-0.02065134420990944,
0.002941354876384139,
-0.0012301955139264464,
-0.010995973832905293,
-0.08536907285451889,
0.018341923132538795,
-0.028100360184907913,
-0.04598243907094002,
0.0252822432667017,
-0.0031552501022815704,
-0.0011345897801220417,
0.018806762993335724,
-0.09994780272245407,
-0.0011161800939589739,
0.0145207978785038,
0.010694516822695732,
-0.021170783787965775,
0.058829326182603836,
-0.012167287059128284,
0.042621809989213943,
-0.001077312626875937,
-0.03971261903643608,
0.0391165055334568,
0.04856858029961586,
-0.007434467785060406,
-0.05913316830992699,
0.029987838119268417,
0.03395111858844757,
0.023464346304535866,
-0.018868766725063324,
0.005361275281757116,
-0.0060785431414842606,
0.01543243695050478,
-0.002491338411346078,
0.033834412693977356,
0.044100210070610046,
0.0154542475938797,
0.03937458619475365,
-0.02478082850575447,
0.01914849504828453,
0.0016351127997040749,
0.029120931401848793,
-0.0009782303823158145
] |
<p>We can see that when a charge sphere is at rest & we are to put it in motion with any desired velocity than we will have to apply the same force for a longer time as if it were applied to the identical uncharged sphere to put it in motion with the same desired velocity.Here the due to electromagnetic fields associated with the charged sphere are responsible for this fact & by methods of integration we find that the additional inertial property gained by the body due to its charge can be given by a simple function of universal constants charge of the body and its radii.I have varified that in linear as well as planar or 3d motion we can apply normal mechanics by adding this factor of additional inertial property in its actual mass.so in one way we can say that the particle show more inertia without any external interference to it so its inertial mass is increased.And I have read that all experiments till today show that inertial mass and gravitational mass are completely identical.so due to charge on any body its gravitational mass is also changed affected or not ?</p>
|
g2488
|
[
0.055148184299468994,
0.006042498629540205,
0.007082143798470497,
0.01301087811589241,
0.09196989238262177,
0.04676118865609169,
0.04192293435335159,
0.003852312220260501,
-0.023119382560253143,
0.02736697904765606,
-0.012762554921209812,
0.002753384644165635,
-0.018990887328982353,
0.01415938325226307,
-0.04083698242902756,
0.009689963422715664,
0.09165067225694656,
0.00170964899007231,
-0.0290248841047287,
0.053841471672058105,
0.05288742482662201,
0.0439629852771759,
0.00561912776902318,
-0.009744682349264622,
-0.06568459421396255,
0.03502287715673447,
0.0339055135846138,
0.008886036463081837,
0.01635322906076908,
-0.036209870129823685,
0.037600304931402206,
-0.031619295477867126,
-0.014901228249073029,
-0.0514252744615078,
-0.014262411743402481,
-0.03266013041138649,
0.059243373572826385,
-0.006401962134987116,
-0.021937577053904533,
0.019340863451361656,
-0.017409563064575195,
-0.023052433505654335,
0.025518953800201416,
0.04341606795787811,
0.02707301266491413,
0.0010052877478301525,
0.04842120409011841,
0.04658731073141098,
-0.014818605035543442,
-0.03252982348203659,
-0.0576191246509552,
0.010161648504436016,
-0.015338476747274399,
-0.032257989048957825,
-0.0005047080921940506,
0.020193049684166908,
0.026380617171525955,
-0.028284654021263123,
0.011630682274699211,
0.07147785276174545,
0.0110904136672616,
-0.026902886107563972,
0.00034936959855258465,
0.020907757803797722,
0.0033340041991323233,
-0.04557875916361809,
-0.07424840331077576,
0.004789122845977545,
-0.04213846102356911,
0.003681176109239459,
0.005747287999838591,
-0.041865669190883636,
-0.07444562017917633,
-0.04245606064796448,
0.006762676872313023,
-0.016504669561982155,
0.06292121112346649,
0.008000657893717289,
-0.0008482509292662144,
-0.03795349597930908,
-0.03156186640262604,
-0.012904233299195766,
0.06579172611236572,
0.006544151343405247,
0.10068797320127487,
-0.06032932177186012,
-0.01900096982717514,
-0.020290395244956017,
-0.006164503283798695,
-0.017578396946191788,
0.03276742622256279,
-0.03126908466219902,
0.027722224593162537,
0.03597007319331169,
-0.05433786287903786,
-0.04855063557624817,
-0.002385270083323121,
0.058071937412023544,
-0.0001450063136871904,
0.02253107726573944,
-0.03442307561635971,
-0.016464926302433014,
0.032494474202394485,
0.0576416440308094,
0.030246378853917122,
-0.0016740162391215563,
0.031405944377183914,
0.02805403806269169,
-0.003259293269366026,
-0.010463079437613487,
-0.027626952156424522,
-0.06981956958770752,
0.005618183873593807,
-0.015382492914795876,
-0.05738665163516998,
-0.055901333689689636,
0.06882992386817932,
-0.015819022431969643,
-0.011229305528104305,
0.022226892411708832,
-0.018382294103503227,
0.03707221522927284,
-0.006841528229415417,
0.015242782421410084,
-0.045465242117643356,
-0.013528524897992611,
0.011306855827569962,
0.03723540157079697,
-0.012427167035639286,
-0.034608256071805954,
0.011038826778531075,
0.0188734233379364,
-0.03911007568240166,
0.009991742670536041,
-0.01811446249485016,
0.0038459361530840397,
0.023559292778372765,
-0.0062462822534143925,
-0.01219740230590105,
-0.003996196668595076,
-0.00420248182490468,
-0.030576102435588837,
0.04056562855839729,
0.013641133904457092,
-0.04753789305686951,
0.05394107103347778,
-0.012518922798335552,
-0.022367892786860466,
0.00037155402242206037,
0.06524284929037094,
0.015596521086990833,
0.03902652487158775,
0.0659380704164505,
-0.022027548402547836,
0.0749669149518013,
-0.015909582376480103,
0.0054863616824150085,
0.041322533041238785,
-0.006737142335623503,
-0.010112673044204712,
0.025874312967061996,
0.03842375427484512,
0.0455249585211277,
0.010815536603331566,
-0.04431780427694321,
0.045096248388290405,
-0.005643744021654129,
-0.01437202375382185,
-0.018427317962050438,
-0.12700974941253662,
-0.040914200246334076,
-0.03190677985548973,
-0.016369257122278214,
0.0435490757226944,
-0.015067529864609241,
-0.016738377511501312,
-0.023793356493115425,
-0.04814944043755531,
0.006266979966312647,
-0.016910314559936523,
-0.05033428594470024,
-0.0006341035477817059,
-0.015137109905481339,
-0.05332223325967789,
-0.052975572645664215,
0.02487346902489662,
0.00913054309785366,
0.029692525044083595,
-0.058405421674251556,
0.029489196836948395,
-0.07470735162496567,
0.013978123664855957,
-0.03002244047820568,
0.051786068826913834,
-0.0026931818574666977,
-0.0017482686089351773,
0.045989736914634705,
0.059415366500616074,
-0.052041731774806976,
0.03812982514500618,
-0.024134019389748573,
0.036814238876104355,
-0.005485386587679386,
-0.04339509457349777,
0.04201515391469002,
-0.055511925369501114,
-0.005757677834481001,
-0.04148184880614281,
0.05548359826207161,
0.008592577651143074,
0.05617718771100044,
0.021724535152316093,
0.026916950941085815,
-0.018360259011387825,
0.00047334551345556974,
0.03129858896136284,
-0.021855993196368217,
-0.027672987431287766,
-0.0005578238051384687,
-0.06298091262578964,
-0.06409985572099686,
-0.0006456480477936566,
0.029755285009741783,
0.035419683903455734,
-0.0011720076436176896,
-0.03904173895716667,
-0.0367690846323967,
0.010007146745920181,
0.016858816146850586,
0.009083401411771774,
-0.004653761629015207,
0.05582673102617264,
0.010066460818052292,
0.0030883471481502056,
0.032962214201688766,
-0.003485526889562607,
-0.08065342903137207,
-0.011006657965481281,
0.016406530514359474,
-0.02439923956990242,
-0.026926713064312935,
0.017425891011953354,
-0.019590366631746292,
-0.021466899663209915,
0.0014415908372029662,
-0.042333897203207016,
0.002499653957784176,
0.0050965272821486,
-0.0266036968678236,
0.02511887438595295,
0.01615285873413086,
0.01482160110026598,
-0.012521801516413689,
-0.03512899950146675,
0.05614291504025459,
0.0023663975298404694,
-0.05414426699280739,
0.017649464309215546,
-0.03581232577562332,
-0.06525847315788269,
-0.006059813778847456,
-0.02022302895784378,
0.0127930399030447,
0.008904491551220417,
-0.09220132231712341,
0.005775324068963528,
-0.023064756765961647,
0.03909264877438545,
0.01662532426416874,
-0.018835583701729774,
-0.032037537544965744,
0.11240124702453613,
0.034153860062360764,
0.047502074390649796,
-0.02115003764629364,
0.02643662504851818,
-0.01000357698649168,
-0.00040997029282152653,
0.007817169651389122,
-0.053514961153268814,
-0.009262660518288612,
0.031202489510178566,
-0.0865619033575058,
-0.0067779673263430595,
-0.006824468728154898,
-0.0168505497276783,
-0.014278094284236431,
-0.059978801757097244,
-0.03417966887354851,
-0.04287617653608322,
0.019400062039494514,
0.03243693336844444,
0.06668097525835037,
-0.019640835002064705,
0.024402381852269173,
0.06851089000701904,
0.021739650517702103,
-0.018974626436829567,
-0.025496000424027443,
0.008780403062701225,
0.02266944758594036,
-0.052965737879276276,
-0.01408396102488041,
0.021558016538619995,
0.00297147617675364,
0.07869936525821686,
-0.025081228464841843,
-0.01624787226319313,
0.020798232406377792,
0.0060123261064291,
-0.03356077894568443,
0.047744911164045334,
-0.03663188964128494,
0.025016942992806435,
-0.04133954271674156,
0.0010014667641371489,
-0.03420703858137131,
0.005928177386522293,
-0.027672186493873596,
0.001005358062684536,
-0.008932419121265411,
-0.04037683457136154,
0.011374284513294697,
-0.024913903325796127,
0.0032092935871332884,
0.03610503301024437,
-0.0015760110691189766,
0.004941685125231743,
-0.009950397536158562,
-0.03305463492870331,
0.008730028755962849,
-0.013881517574191093,
0.007330853492021561,
-0.0012767642037943006,
-0.01391624379903078,
-0.007153591141104698,
0.031938791275024414,
0.007546673994511366,
0.09556186944246292,
0.011981874704360962,
0.04020688310265541,
-0.010159536264836788,
-0.10368917137384415,
0.002968196989968419,
-0.07801128178834915,
0.009538811631500721,
-0.0024172975681722164,
-0.060890257358551025,
0.007361072115600109,
0.006438316777348518,
0.011474927887320518,
0.0014466713182628155,
0.03332792967557907,
-0.0024223218206316233,
0.01674896664917469,
-0.001949053374119103,
0.07049257308244705,
0.05323895812034607,
-0.08030985295772552,
-0.027945950627326965,
0.011443065479397774,
-0.03556593134999275,
0.028588727116584778,
0.04197552427649498,
0.024613624438643456,
0.031719814985990524,
-0.0246895682066679,
0.03613172471523285,
-0.028235025703907013,
-0.026926076039671898,
-0.025000398978590965,
-0.02227238193154335,
0.005167677998542786,
-0.04091930389404297,
0.026631206274032593,
-0.004691048990935087,
0.03461017087101936,
0.03999360650777817,
-0.01253348309546709,
-0.05422455444931984,
0.053756263107061386,
0.03891623765230179,
0.024428891018033028,
0.0020178796257823706,
-0.0021092332899570465,
0.022672956809401512,
-0.020489096641540527,
0.03226862847805023,
0.052957288920879364,
-0.009273435920476913,
-0.009905489161610603,
-0.061037469655275345,
0.008349061012268066,
-0.022916648536920547,
0.06902024894952774,
-0.03771205618977547,
0.001021061441861093,
-0.11061451584100723,
0.10317116230726242,
-0.04000278562307358,
0.01263746153563261,
0.009490407072007656,
-0.0063629369251430035,
-0.001462903106585145,
-0.01757116988301277,
0.015907444059848785,
0.09684886038303375,
-0.05251462385058403,
0.015925433486700058,
-0.04990382492542267,
0.00650231447070837,
-0.03380892425775528,
-0.010398116894066334,
-0.013036984018981457,
0.004534840118139982,
0.014630698598921299,
-0.014370580203831196,
0.03351477161049843,
-0.03297843411564827,
0.04704166203737259,
0.022916804999113083,
0.062045663595199585,
0.032753996551036835,
-0.009743183851242065,
0.00009657583723310381,
0.05547160282731056,
0.08194614201784134,
-0.01808350719511509,
-0.02621912769973278,
-0.0020477145444601774,
0.0044112494215369225,
0.036785420030355453,
0.011986041441559792,
0.01981799118220806,
-0.05628933757543564,
-0.0028290420304983854,
0.008921992965042591,
0.06735966354608536,
-0.021288592368364334,
0.010184097103774548,
0.0667870044708252,
0.07443811744451523,
0.01656978763639927,
-0.0840093120932579,
-0.020254233852028847,
0.0478975884616375,
-0.02046702802181244,
-0.011376063339412212,
-0.015924394130706787,
-0.013822441920638084,
-0.016988597810268402,
-0.018154453486204147,
-0.014365420676767826,
-0.006852724589407444,
-0.012265359051525593,
-0.0008888221345841885,
-0.019241169095039368,
-0.029979748651385307,
-0.06491425633430481,
-0.017382698133587837,
-0.04509180039167404,
0.02722533978521824,
0.03093568980693817,
0.0029896851629018784,
0.01570412702858448,
-0.0017207164783030748,
-0.044570308178663254,
-0.017387719824910164,
-0.05783060938119888,
0.024722451344132423,
0.031483035534620285,
0.047988131642341614,
0.01672755368053913,
-0.05144378915429115,
0.03490649163722992,
-0.03521110489964485,
0.04387423396110535,
-0.0034252814948558807,
0.010841436684131622,
-0.04136594757437706,
-0.012671561911702156,
-0.034846555441617966,
0.0064338454976677895,
0.008669295348227024,
-0.028716808184981346,
0.013808254152536392,
-0.03191576153039932,
0.03133264183998108,
-0.001961985370144248,
-0.03137560561299324,
0.020659983158111572,
-0.0344422347843647,
0.010582035407423973,
-0.024576859548687935,
0.04827352613210678,
0.09636444598436356,
-0.03943295031785965,
-0.010920330882072449,
-0.02235483191907406,
-0.005769006907939911,
-0.022378642112016678,
-0.04156786948442459,
0.00701730465516448,
0.015295459888875484,
0.00795209314674139,
0.044949378818273544,
-0.0017836426850408316,
0.022914765402674675,
-0.04828773811459541,
0.024211924523115158,
-0.042227573692798615,
0.08163042366504669,
0.019380157813429832,
0.018317406997084618,
-0.029031699523329735,
0.06301016360521317,
-0.012187441810965538,
-0.02041127160191536,
0.04748319461941719,
-0.023855317384004593,
0.06628696620464325,
-0.025741133838891983,
0.08638328313827515,
-0.02197108417749405,
0.0417451374232769,
0.040436290204524994,
0.050790876150131226,
-0.058021847158670425,
0.049547117203474045,
0.04329283908009529,
-0.021364977583289146,
-0.06878530979156494,
0.0021715951152145863,
-0.049722928553819656,
-0.030600812286138535,
-0.06360404938459396,
-0.0015696788905188441,
0.04538804292678833,
0.056142836809158325,
-0.014082886278629303,
-0.0005221096216700971,
-0.09320288896560669,
0.050481319427490234,
0.034463219344615936,
-0.021552706137299538,
-0.005661265458911657,
-0.04895052686333656,
-0.013104889541864395,
0.05665508657693863,
-0.07185424119234085,
-0.05427934601902962,
0.02157672680914402,
-0.006828138139098883,
-0.0037953488063067198,
-0.015963861718773842,
0.0312696136534214,
-0.025567537173628807,
0.0009152955026365817,
-0.05362902581691742,
0.002529502846300602,
0.024485262110829353,
-0.024844402447342873,
0.03607829660177231,
0.012148183770477772,
0.0038132001645863056,
-0.07226542383432388,
0.02366105653345585,
-0.05477922037243843,
0.058784496039152145,
-0.020231636241078377,
-0.01794249191880226,
-0.011712866835296154,
-0.004969217348843813,
-0.018177736550569534,
0.027659855782985687,
0.013136803172528744,
-0.014977408573031425,
0.03414818271994591,
-0.02801542729139328,
-0.005940825678408146,
0.022048093378543854,
-0.010558104142546654,
0.05312073603272438,
-0.029949823394417763,
-0.005325686652213335,
0.027308549731969833,
-0.03490832448005676,
-0.021970245987176895,
0.048793286085128784,
-0.045489925891160965,
-0.01194640714675188,
-0.04494661092758179,
-0.006791511084884405,
-0.03497278690338135,
-0.06220511719584465,
-0.010462411679327488,
-0.019831102341413498,
-0.013390645384788513,
0.027203457430005074,
0.03219727426767349,
0.034216590225696564,
-0.04840803146362305,
0.04234347864985466,
-0.014173938892781734,
0.038043901324272156,
0.0324421189725399,
-0.0268767848610878,
-0.07784735411405563,
0.016301343217492104,
-0.004605794791132212,
-0.057376064360141754,
-0.04233568534255028,
0.009766800329089165,
0.01974658854305744,
-0.047912031412124634,
-0.027734706178307533,
-0.019939623773097992,
0.028501830995082855,
-0.003962888848036528,
-0.025682762265205383,
-0.034574951976537704,
-0.0025541887152940035,
0.030638108029961586,
0.019102608785033226,
0.0319465808570385,
-0.027515660971403122,
-0.05900134518742561,
0.04802227392792702,
-0.021312087774276733,
0.003644956974312663,
-0.03814241662621498,
0.028354240581393242,
-0.003961335401982069,
0.04140409454703331,
0.05159831792116165,
0.02674141153693199,
0.06401071697473526,
0.0325547456741333,
0.011180059053003788,
-0.006336076185107231,
-0.00014796406321693212,
0.04337061569094658,
0.015378064475953579,
0.040443647652864456,
-0.12116517871618271,
-0.00022197699581738561,
0.0507105328142643,
-0.006582458503544331,
-0.009859705343842506,
0.011272383853793144,
-0.04918739199638367,
0.02252262271940708,
0.04433697089552879,
0.08594352006912231,
-0.013926300220191479,
-0.02545776404440403,
0.043117839843034744,
0.005787059664726257,
0.03483080491423607,
-0.0751200020313263,
-0.02352026291191578,
0.04998934268951416,
-0.0002732682041823864,
-0.009604468010365963,
-0.014268078841269016,
0.011456574313342571,
0.012230304069817066,
-0.061791397631168365,
-0.01101338304579258,
0.030552763491868973,
0.02986067533493042,
-0.012141715735197067,
0.007580817211419344,
0.009917010553181171,
-0.004603467881679535,
0.007628893479704857,
-0.016329273581504822,
0.041004035621881485,
-0.026521380990743637,
0.02462267316877842,
0.005581291858106852,
0.04501018673181534,
-0.010122391395270824,
0.055866677314043045,
-0.024495435878634453,
0.006776407361030579,
-0.03103276528418064,
0.013501987792551517,
-0.020682336762547493,
0.02332206629216671,
0.005715744569897652,
0.0189521461725235,
0.0027347696013748646,
0.032761070877313614,
-0.05709073692560196,
0.008398408070206642,
0.030718756839632988,
0.059785157442092896,
0.030264681205153465,
-0.046488866209983826,
-0.060260578989982605,
-0.06309504061937332,
0.032141607254743576,
-0.03508733958005905,
0.03917061910033226,
0.03442629799246788,
-0.057301875203847885,
-0.012430435046553612,
-0.038737498223781586,
0.0592881441116333,
0.05618174001574516,
-0.02116396836936474,
-0.0011602344457060099,
0.025084728375077248,
0.02971942536532879,
0.016096167266368866,
0.0255298912525177,
0.026986490935087204,
0.002585483016446233,
-0.012870808131992817,
-0.0330355167388916,
-0.026432065293192863,
0.03542497754096985,
-0.07126957178115845,
0.0009458897984586656,
-0.044744376093149185,
-0.03224312514066696,
-0.0006020099972374737,
0.04529919847846031,
-0.04601270332932472,
-0.007294689770787954,
-0.037491731345653534,
-0.002671779366210103,
0.0006789008621126413,
-0.009886924177408218,
0.045231692492961884,
0.00383981061168015,
-0.011157909408211708,
-0.026338016614317894,
-0.0040168119594454765,
0.026471568271517754,
-0.03291366994380951,
-0.017739450559020042,
-0.007536445278674364,
-0.028528641909360886,
0.007894081063568592,
0.016391964629292488,
0.05329334735870361,
0.0602010153234005,
0.07136252522468567,
0.004769755527377129,
-0.015176978893578053,
-0.08820611983537674,
-0.005112525075674057,
-0.002518151653930545,
-0.025937777012586594,
-0.013933070935308933,
0.02830522134900093,
-0.02246398665010929,
0.0013640039833262563,
0.02443503960967064,
-0.014249253086745739,
0.015843477100133896,
-0.015237980522215366,
0.02144567109644413,
-0.038577236235141754,
0.01974647119641304,
0.029304619878530502
] |
<p>So it's Thanksgiving here in the states and an odd combination of things are on my mind. In the past day, I've</p>
<ul>
<li>Brined a turkey whole, skin on</li>
<li>Taken a long epsom salt bath</li>
</ul>
<p>(Same thing, right? What a turkey! Haha.)</p>
<p>Anyways, it got me wondering, can a long salt water bath increase water retention? It's basically the same process as <a href="http://en.wikipedia.org/wiki/Brining" rel="nofollow">brining meat</a>:</p>
<blockquote>
<p>Salt is added to cold water in a container, where the meat is soaked usually six to twelve hours [making] cooked meat moister by hydrating the cells of its muscle tissue before cooking, via the process of osmosis</p>
</blockquote>
<p>I'm sure we've all experienced dry, shriveled or even cracking skin (called <a href="http://en.wikipedia.org/wiki/Xeroderma" rel="nofollow">xeroderma</a> when chronic), which can <a href="http://www.medicinenet.com/dry_skin/page6.htm#what_are_some_home_remedies_for_dry_skin" rel="nofollow">apparently be improved by warm baths or showers</a>. And here is where I'm in danger of leaving the bounds of rigorous science: can you cause or worsen <a href="http://en.wikipedia.org/wiki/Water_retention_%28medicine%29" rel="nofollow">water retention</a> by soaking in a salt water bath? How much water can the skin take on? If you weighed yourself regularly and rigorously, would you be able to perceive a difference in weight before and after such a bath?</p>
<p>If it doesn't occur, what makes human skin different in this regard from poultry skin? Would brining not be effective if the body cavity of the bird weren't opened and vacated? (Brining and marinating of course works perfectly well on skinless cuts of meat.)</p>
|
g2489
|
[
0.057331763207912445,
0.0581444650888443,
0.0015707053244113922,
-0.03772907331585884,
0.006433920934796333,
-0.027105621993541718,
-0.00133916933555156,
0.01849299669265747,
0.015282719396054745,
-0.050511691719293594,
-0.004320614505559206,
0.0917680561542511,
0.06304242461919785,
0.05423910170793533,
-0.043241966515779495,
-0.037777747958898544,
0.05551184341311455,
-0.035680267959833145,
-0.016030117869377136,
0.0076522668823599815,
-0.0422348715364933,
0.020967643707990646,
0.03011033684015274,
0.0156436525285244,
-0.05808252468705177,
-0.010223671793937683,
-0.013150643557310104,
0.05948822572827339,
0.006713154260069132,
0.014522777870297432,
-0.08229033648967743,
-0.0723230242729187,
-0.06268035620450974,
0.0006874236278235912,
-0.021201057359576225,
-0.03240220993757248,
0.011518728919327259,
-0.0008238127920776606,
-0.013366783037781715,
-0.01470610499382019,
0.04052155464887619,
0.02235732600092888,
0.07144162058830261,
0.013247638009488583,
0.002012495882809162,
0.04526069760322571,
-0.019511912018060684,
-0.04496299475431442,
-0.0006959825986996293,
0.0022356505505740643,
0.022060232236981392,
-0.03995280712842941,
0.008959531784057617,
0.017250504344701767,
-0.03150634840130806,
-0.07598938047885895,
-0.033292077481746674,
0.008543701842427254,
0.022966325283050537,
-0.006567919626832008,
0.020617054775357246,
-0.047415073961019516,
-0.007181653752923012,
-0.0004337847058195621,
-0.00939452089369297,
-0.005193097051233053,
-0.03808083385229111,
0.06323499977588654,
0.02861381135880947,
0.04529598355293274,
0.015645090490579605,
-0.08377274870872498,
-0.06464076787233353,
-0.03364221379160881,
-0.05903209000825882,
0.04462726041674614,
0.016483213752508163,
0.005970532540231943,
0.07231844961643219,
0.033300139009952545,
-0.010497245006263256,
0.019439484924077988,
-0.037818774580955505,
0.014764353632926941,
-0.06016714498400688,
0.025304770097136497,
-0.03671920299530029,
-0.061872176826000214,
0.050709087401628494,
0.0455578938126564,
0.002823905786499381,
-0.014467218890786171,
-0.00013954607129562646,
0.05679547041654587,
-0.0020959461107850075,
0.0032513702753931284,
0.04613432660698891,
0.032426606863737106,
-0.06788226217031479,
-0.012785754166543484,
0.015028722584247589,
-0.030753014609217644,
0.04051273316144943,
-0.019370868802070618,
-0.03471927344799042,
0.03270737826824188,
0.08319252729415894,
0.003825961612164974,
-0.021489925682544708,
-0.008170312270522118,
-0.07260019332170486,
-0.03717169165611267,
-0.0336754284799099,
0.001106533920392394,
-0.003692350583150983,
0.0208428967744112,
0.011078367941081524,
0.021220771595835686,
-0.06691101938486099,
-0.03330948203802109,
0.027760686352849007,
0.03062034770846367,
0.011806800030171871,
-0.03965122625231743,
-0.04616205394268036,
0.04434230178594589,
-0.024464620277285576,
-0.003633566200733185,
0.08326569199562073,
0.013520017266273499,
-0.046916618943214417,
0.05764976516366005,
0.001485844375565648,
0.018115311861038208,
0.0064381929114460945,
0.02791014313697815,
-0.045192789286375046,
-0.02408665232360363,
0.023223988711833954,
-0.059657011181116104,
0.0027037695981562138,
-0.037626489996910095,
-0.043893709778785706,
0.07411377131938934,
0.0033109458163380623,
0.002940801903605461,
-0.04239123314619064,
0.004264784976840019,
0.004986397456377745,
0.02988034300506115,
0.02145722322165966,
0.017639555037021637,
-0.011036737821996212,
0.04804277792572975,
0.003473812248557806,
0.030539650470018387,
-0.015018913894891739,
-0.019416553899645805,
-0.006276499480009079,
0.041171953082084656,
0.04158705845475197,
0.03941551595926285,
0.062411144375801086,
0.04345521330833435,
-0.05313711613416672,
-0.007532188203185797,
0.022504068911075592,
-0.04272298142313957,
-0.03288885951042175,
-0.019681628793478012,
0.001279133022762835,
0.003701143665239215,
-0.03369801491498947,
0.011260153725743294,
-0.03552769124507904,
0.035576410591602325,
0.03457900509238243,
-0.06734780222177505,
-0.010588482022285461,
-0.05792735889554024,
-0.06139082834124565,
0.04536592960357666,
-0.0011213936377316713,
-0.02519475296139717,
0.046765413135290146,
0.041146405041217804,
0.035847608000040054,
-0.0225459486246109,
-0.060790788382291794,
-0.05109252780675888,
-0.009292436763644218,
0.03335144743323326,
0.04242691025137901,
0.0060377176851034164,
-0.00721790362149477,
-0.015328478999435902,
-0.016707049682736397,
-0.009928502142429352,
-0.011482922360301018,
0.0010628348682075739,
-0.017464274540543556,
-0.020952079445123672,
-0.06902370601892471,
-0.0035214656963944435,
-0.008141685277223587,
-0.013929515145719051,
-0.03369741141796112,
-0.06141984090209007,
-0.011530191637575626,
-0.027020789682865143,
-0.014284737408161163,
0.04336061328649521,
0.0058733089827001095,
-0.03606736287474632,
0.03785775229334831,
0.01038221176713705,
0.024716593325138092,
0.03319796919822693,
-0.020540712401270866,
-0.035075593739748,
0.032498668879270554,
0.010813639499247074,
-0.021258259192109108,
0.01846883073449135,
0.023991277441382408,
-0.006648911163210869,
-0.07696995884180069,
-0.05406288430094719,
-0.06263948976993561,
0.04409992694854736,
0.007640073075890541,
0.006506538949906826,
0.058418601751327515,
-0.07850809395313263,
-0.003408232005313039,
-0.007728819735348225,
0.016275987029075623,
0.011225638911128044,
0.0181540846824646,
0.0032694584224373102,
0.02408703789114952,
-0.02625209465622902,
-0.04468462988734245,
0.030216705054044724,
-0.04308700188994408,
0.0032369366381317377,
-0.03758610039949417,
-0.02359055168926716,
0.030095117166638374,
-0.010908110998570919,
-0.012396272271871567,
0.04472411051392555,
-0.0024206284433603287,
-0.04590333625674248,
-0.003585481783375144,
0.03134164214134216,
-0.00901053287088871,
-0.003720354288816452,
-0.05052485316991806,
-0.014913604594767094,
-0.05517764016985893,
-0.002118324628099799,
0.019083186984062195,
0.06349394470453262,
-0.03421320766210556,
0.020102545619010925,
-0.06936164200305939,
0.03810843452811241,
0.010150779038667679,
0.017519831657409668,
0.03981168568134308,
0.007278277073055506,
0.004950980190187693,
0.03193250298500061,
-0.05201539024710655,
-0.0024531083181500435,
-0.03345600143074989,
0.01932552643120289,
-0.006761675700545311,
-0.05465038865804672,
-0.009761382825672626,
-0.023939356207847595,
-0.024418193846940994,
0.05491185188293457,
0.00014175026444718242,
0.009299186989665031,
-0.004597327671945095,
0.007010591682046652,
0.012399238534271717,
0.005804234184324741,
0.023320861160755157,
0.019643103703856468,
0.030299663543701172,
0.016099249944090843,
-0.0226911511272192,
0.012270752340555191,
0.007590372581034899,
-0.012630123645067215,
-0.028011290356516838,
-0.01006650272756815,
0.009956343099474907,
0.008876820094883442,
-0.00788538996130228,
0.0046219490468502045,
0.009327130392193794,
0.020353564992547035,
-0.09467249363660812,
0.020842060446739197,
0.07941090315580368,
-0.01819148100912571,
0.04018205776810646,
-0.00011753704166039824,
-0.07202084362506866,
-0.011132659390568733,
-0.004129983950406313,
-0.006638690363615751,
-0.019392121583223343,
0.01763802208006382,
0.056669626384973526,
-0.029790319502353668,
0.029255354776978493,
0.028123125433921814,
-0.017106035724282265,
-0.00794315617531538,
0.0561409555375576,
0.014468680135905743,
-0.019136564806103706,
0.10006730258464813,
-0.0418909452855587,
-0.001959710381925106,
0.013076981529593468,
0.015019530430436134,
0.04706362262368202,
-0.030899301171302795,
0.008821548894047737,
0.022192640230059624,
0.030201051384210587,
-0.005715508479624987,
0.0024733119644224644,
-0.026529891416430473,
0.014031566679477692,
-0.10244511812925339,
0.008088188245892525,
-0.06669650971889496,
0.0413997657597065,
0.03914260119199753,
-0.01895814575254917,
-0.028939081355929375,
-0.03380679339170456,
0.00042307176045142114,
0.02189994789659977,
0.02090051956474781,
-0.03504372760653496,
0.006682987324893475,
-0.005521440878510475,
0.04418976977467537,
0.018784185871481895,
0.05808853730559349,
0.002835072809830308,
0.019993551075458527,
0.009685737080872059,
-0.023185957223176956,
-0.025180546566843987,
-0.0579276978969574,
-0.02521573193371296,
0.014878122135996819,
0.07149209082126617,
0.05545593053102493,
-0.029457872733473778,
-0.023071130737662315,
-0.028394486755132675,
-0.005518108606338501,
-0.038457222282886505,
0.07093355804681778,
0.05167056620121002,
0.07871802896261215,
0.015266378410160542,
0.044760026037693024,
0.007692588493227959,
0.04643111303448677,
-0.009313925169408321,
0.0035158346872776747,
-0.017576422542333603,
0.020964691415429115,
-0.032711829990148544,
-0.02641788125038147,
-0.005691488739103079,
0.025041062384843826,
0.06052696332335472,
-0.042172592133283615,
0.047769561409950256,
0.008739558979868889,
0.013654856942594051,
0.011205330491065979,
-0.03170877695083618,
-0.03078630194067955,
0.026228483766317368,
-0.0015709396684542298,
0.0033171488903462887,
0.02230261266231537,
0.04589265212416649,
0.0035925402771681547,
0.010272396728396416,
0.03784108906984329,
-0.03527269512414932,
-0.02458345890045166,
0.047414183616638184,
0.03846854344010353,
-0.09165813773870468,
-0.06031300500035286,
0.026677174493670464,
-0.012742999009788036,
-0.007083640433847904,
-0.023383384570479393,
-0.06785864382982254,
0.07796154171228409,
-0.010798964649438858,
-0.006348724011331797,
-0.007836220785975456,
-0.03767084702849388,
-0.0006466331542469561,
-0.009286878630518913,
-0.04851893335580826,
0.05662638321518898,
0.005237624514847994,
0.0247664637863636,
-0.03410360962152481,
-0.07642052322626114,
0.05842066928744316,
-0.02875344827771187,
0.016598956659436226,
0.004247577395290136,
0.03610265627503395,
0.05373990535736084,
0.005867930594831705,
0.03539478778839111,
-0.05016854777932167,
-0.018892426043748856,
0.009040677919983864,
0.02150803618133068,
-0.0013798711588606238,
0.009019536897540092,
0.016147179529070854,
0.019973887130618095,
0.04864002764225006,
-0.0338435135781765,
-0.03520868346095085,
-0.021149711683392525,
0.02818957529962063,
0.012935755774378777,
-0.023507578298449516,
0.033136941492557526,
0.030505338683724403,
-0.04620411992073059,
0.007719262037426233,
0.03337918594479561,
0.022624585777521133,
-0.03404129669070244,
-0.010446760803461075,
0.026477592065930367,
-0.004229398909956217,
-0.014878218062222004,
-0.01937238872051239,
0.021694036200642586,
0.013422329910099506,
-0.05398552864789963,
0.08210571110248566,
-0.04400739446282387,
-0.06724300980567932,
0.029165523126721382,
0.03355775028467178,
0.05675828829407692,
0.04418725520372391,
0.039489760994911194,
-0.01257872674614191,
-0.02877531573176384,
0.0495215505361557,
-0.021421711891889572,
-0.0011605690233409405,
0.0016089671989902854,
0.029329171404242516,
0.04041847959160805,
-0.024057812988758087,
0.05834543704986572,
-0.04841380566358566,
-0.007398271467536688,
0.010883989743888378,
0.06195729970932007,
-0.06831007450819016,
-0.027439266443252563,
-0.046479471027851105,
-0.03560619428753853,
0.041336189955472946,
0.04502163454890251,
0.0006436888361349702,
0.010149888694286346,
-0.03060830757021904,
-0.026372388005256653,
-0.017080865800380707,
-0.006457967683672905,
0.020144455134868622,
0.032409973442554474,
0.03299850970506668,
-0.03158925473690033,
0.04346266761422157,
0.01562967337667942,
0.0019520384958013892,
-0.0026210593059659004,
-0.010722431354224682,
0.043729592114686966,
-0.021483005955815315,
-0.03303522244095802,
-0.053833067417144775,
-0.07066507637500763,
0.08852844685316086,
-0.016115719452500343,
-0.009057443588972092,
-0.015155618079006672,
0.03194007650017738,
0.01542352233082056,
0.04559966176748276,
0.02006227895617485,
-0.012190930545330048,
0.02412424422800541,
-0.035165563225746155,
-0.0045223962515592575,
-0.08010366559028625,
0.03531329706311226,
0.0196201354265213,
0.04838435724377632,
0.05514610931277275,
0.058231011033058167,
-0.01781684160232544,
0.06703519821166992,
-0.01864771731197834,
-0.026282982900738716,
-0.051572516560554504,
0.03146689012646675,
-0.00645035644993186,
0.015792636200785637,
0.04167928174138069,
0.07312162220478058,
0.05975722894072533,
0.07615592330694199,
0.03745725378394127,
-0.07315079122781754,
0.01782926544547081,
-0.06849939376115799,
-0.0036193944979459047,
0.045133352279663086,
-0.05621900036931038,
-0.01568988710641861,
-0.016468601301312447,
-0.02926304191350937,
0.0037232842296361923,
-0.02758684754371643,
0.0362384095788002,
-0.005544428247958422,
0.060101255774497986,
-0.01817926950752735,
0.08604080975055695,
0.031130867078900337,
0.045099593698978424,
-0.0028371145017445087,
0.011536753736436367,
0.011062904261052608,
0.0024254873860627413,
-0.029444750398397446,
0.06700113415718079,
0.055231478065252304,
-0.056316860020160675,
0.005712216719985008,
0.03557097539305687,
-0.028892306610941887,
-0.01558044832199812,
0.029781972989439964,
-0.02287168987095356,
-0.03460827097296715,
-0.009751617908477783,
0.00037729114410467446,
-0.011086727492511272,
-0.01326652243733406,
-0.03928206115961075,
-0.010656489059329033,
-0.07327475398778915,
0.017621953040361404,
-0.018157577142119408,
-0.02700617164373398,
0.07610683888196945,
0.04539501294493675,
0.014329829253256321,
0.013636035844683647,
0.004037906881421804,
-0.010941076092422009,
0.020296260714530945,
-0.02862006425857544,
0.012784130871295929,
0.022123122587800026,
-0.04688822105526924,
0.015128814615309238,
0.01970955729484558,
-0.020786462351679802,
0.03016861528158188,
-0.00822899304330349,
-0.036143507808446884,
0.03824787214398384,
0.024076983332633972,
0.0038264768663793802,
-0.0017590756760910153,
-0.03667091578245163,
-0.032458771020174026,
0.009869418106973171,
0.011168090626597404,
-0.0692206472158432,
-0.041517697274684906,
-0.08731763809919357,
-0.01261531375348568,
0.011914067901670933,
0.01962333731353283,
0.022871587425470352,
0.021423807367682457,
-0.06568105518817902,
0.019186481833457947,
0.008940992876887321,
0.04697033762931824,
0.00508194649592042,
-0.016819043084979057,
0.05366900935769081,
0.00497753731906414,
-0.012933535501360893,
-0.019356325268745422,
0.011283011175692081,
-0.044632166624069214,
0.006391058675944805,
-0.033994078636169434,
0.0010555005865171552,
-0.03870069608092308,
0.008453971706330776,
-0.01030076202005148,
0.03881020471453667,
-0.028167732059955597,
0.034850578755140305,
-0.0013158483197912574,
0.01089658122509718,
-0.08537497371435165,
0.033363472670316696,
0.025985511019825935,
0.01977197267115116,
-0.04976894333958626,
-0.012456461787223816,
0.01745225489139557,
0.04912750795483589,
-0.08022331446409225,
0.004243636038154364,
0.04424994811415672,
0.0013206454459577799,
-0.05428103730082512,
0.007944544777274132,
-0.017320051789283752,
0.014559770002961159,
-0.012310797348618507,
0.0377945713698864,
0.06446807831525803,
-0.009766904637217522,
-0.0003597088798414916,
0.013003533706068993,
-0.01919846050441265,
-0.04429817199707031,
-0.011645765975117683,
0.03166142851114273,
0.020071372389793396,
-0.017380090430378914,
-0.016739429906010628,
-0.005021119490265846,
0.07437532395124435,
0.026790490373969078,
0.061468061059713364,
0.021174544468522072,
-0.012976046651601791,
0.003310305066406727,
0.036339037120342255,
-0.022320466116070747,
0.007718787528574467,
0.01949693262577057,
-0.050745803862810135,
-0.004658240359276533,
-0.0454992800951004,
0.008727668784558773,
0.06092091649770737,
-0.014118674211204052,
0.013245122507214546,
0.015038751997053623,
-0.032958123832941055,
0.07666769623756409,
0.02331710420548916,
-0.029177166521549225,
0.0019949779380112886,
0.015132994391024113,
0.03754623606801033,
-0.06276816129684448,
-0.0014197941636666656,
0.008957989513874054,
0.009345153346657753,
-0.0012311117025092244,
0.038750335574150085,
0.025556229054927826,
-0.06808646768331528,
-0.0010166646679863334,
-0.049820370972156525,
-0.004961485508829355,
-0.05004475265741348,
-0.047023043036460876,
-0.01149988267570734,
0.012509632855653763,
0.026062998920679092,
-0.07142835110425949,
-0.003510076552629471,
-0.008916693739593029,
-0.03342774510383606,
-0.03903929144144058,
-0.02198917418718338,
-0.014636481180787086,
-0.011175069957971573,
-0.07994645833969116,
0.013976342044770718,
0.0011010029120370746,
-0.05682302266359329,
-0.013253800570964813,
-0.017016669735312462,
0.0132091473788023,
0.014985165558755398,
-0.044724829494953156,
-0.020529689267277718,
-0.006641028448939323,
0.07358618825674057,
-0.00420454191043973,
0.09886524826288223,
0.05728801339864731,
0.0005589531501755118,
-0.009938524104654789,
0.03491368517279625,
-0.0037860244046896696,
0.015196030959486961,
-0.04521862789988518,
0.015908030793070793,
-0.012979188933968544,
-0.012754704803228378,
0.06968888640403748,
0.04664014279842377,
0.013253523968160152,
-0.02187233231961727,
-0.083160899579525,
-0.0708736851811409,
-0.0008722490747459233,
-0.021812740713357925,
-0.01426019798964262,
-0.02521025575697422,
-0.0147621538490057,
0.0607118122279644,
-0.0224832221865654,
0.04240987449884415,
-0.007632587105035782,
-0.017794940620660782,
-0.017209695652127266,
-0.053877539932727814,
-0.04519512504339218,
0.02969665266573429,
-0.053942978382110596
] |
<p><strong>Question:</strong></p>
<p>Will this work as I've shown it here, more or less, or will the iron cylinder being hollow produce results not shown? </p>
<p><strong>Topic:</strong></p>
<p>I'm experimenting with magnetic fields and have been testing electromagnets. For a specific device that I'm interested in engineering, I'll need to look at the effects of a hollow iron tube wrapped by a standard charged wire coil. The reason that it needs to be hollow is that other machinery will need to fit down the center of the device.</p>
<p>This is what I'm expecting from this:</p>
<p><strong>Model 1:</strong></p>
<p><img src="http://i.stack.imgur.com/Nobbo.png" alt="enter image description here"></p>
<p>In this model, the poles originate from the edges of the cylinder. </p>
<p>Another possibility that I thought might occur would be this model:</p>
<p>Model 2:</p>
<p><img src="http://i.stack.imgur.com/DGdo6.png" alt="enter image description here"></p>
<p>Here, the poles originate from the object's true center. </p>
<p><strong>Are either of these models accurate? If not, what's the answer?</strong> </p>
|
g2490
|
[
0.012086458504199982,
-0.04558195918798447,
0.005020839162170887,
-0.021675555035471916,
0.06593713164329529,
0.02686784602701664,
0.02350310981273651,
0.020434968173503876,
-0.039585333317518234,
0.01020756084471941,
-0.06573700159788132,
0.02531365305185318,
0.0021187353413552046,
-0.059152208268642426,
-0.017536472529172897,
0.023734474554657936,
0.046615228056907654,
0.0018232165602967143,
-0.003163879504427314,
-0.009538887068629265,
0.005321399308741093,
0.03604814037680626,
0.028635963797569275,
-0.016425324603915215,
-0.00841740146279335,
-0.007990223355591297,
-0.022598376497626305,
0.03988361731171608,
-0.013833947479724884,
-0.04538219794631004,
-0.02145417034626007,
0.009668566286563873,
0.07571448385715485,
-0.03145141527056694,
-0.0839211717247963,
0.01684562861919403,
0.006375858560204506,
0.059922266751527786,
-0.020394960418343544,
-0.02062319964170456,
-0.011133157648146152,
-0.009285996668040752,
0.03798263892531395,
-0.02048889361321926,
-0.00471036322414875,
-0.032475851476192474,
-0.016698431223630905,
0.027342114597558975,
-0.02160273678600788,
-0.013105977326631546,
-0.017512835562229156,
-0.01645740680396557,
0.036607954651117325,
0.007544819265604019,
0.008753434754908085,
0.019601469859480858,
-0.010619020089507103,
0.016476791352033615,
0.043768271803855896,
0.029148166999220848,
-0.015663787722587585,
0.040471065789461136,
-0.020442631095647812,
-0.010516691021621227,
-0.022851454094052315,
0.06243618577718735,
-0.025237981230020523,
-0.04346165806055069,
0.030895264819264412,
0.00883150938898325,
0.004893998149782419,
-0.02944355271756649,
-0.019331011921167374,
-0.05966631695628166,
-0.045826446264982224,
0.04829518124461174,
0.02197296917438507,
0.003807506989687681,
0.043540287762880325,
-0.02275921031832695,
-0.07247745990753174,
0.00773800490424037,
-0.056242648512125015,
0.07978950440883636,
0.048615097999572754,
0.010797793045639992,
-0.031925421208143234,
0.016426609829068184,
0.019936054944992065,
0.0275370255112648,
0.007046259008347988,
0.03906642273068428,
0.0027876365929841995,
0.00872090458869934,
0.03854876384139061,
-0.024038169533014297,
0.02636791206896305,
0.06028882786631584,
-0.024726849049329758,
0.017348339781165123,
0.0015151766128838062,
-0.02586626075208187,
-0.029481448233127594,
0.05698598921298981,
-0.04527993127703667,
0.013885810039937496,
0.039046864956617355,
0.03795536234974861,
-0.010497331619262695,
-0.015558948740363121,
-0.057454004883766174,
-0.032260533422231674,
-0.1131659522652626,
0.03853476047515869,
-0.04902954772114754,
-0.03606889024376869,
0.06358440965414047,
0.001084541785530746,
-0.010245195589959621,
0.04118118807673454,
0.073324054479599,
-0.014337795786559582,
0.048694197088479996,
0.0807223692536354,
-0.023789353668689728,
-0.046785324811935425,
-0.053758151829242706,
-0.016154836863279343,
-0.01609085313975811,
-0.007300843950361013,
-0.019495315849781036,
-0.05228154733777046,
0.004484042525291443,
0.01621980406343937,
0.044103868305683136,
0.02884732559323311,
-0.05116204544901848,
-0.009548069909214973,
0.03971458971500397,
0.010967021808028221,
0.013470444828271866,
-0.056499917060136795,
0.021695734933018684,
-0.04227086529135704,
0.00021033121447544545,
-0.02636166289448738,
0.061601459980010986,
-0.050825897604227066,
0.08233601599931717,
0.035952307283878326,
-0.034415677189826965,
0.040602631866931915,
-0.007647352758795023,
0.0016999337822198868,
-0.06818768382072449,
0.016359219327569008,
-0.005587910767644644,
-0.030609969049692154,
0.09288937598466873,
-0.013189154677093029,
0.003083452582359314,
-0.04321368411183357,
0.04672975093126297,
-0.008410468697547913,
-0.0011098276590928435,
-0.00836159847676754,
0.0070669143460690975,
-0.03499002009630203,
0.06223702430725098,
-0.056408416479825974,
-0.05474457889795303,
-0.01949005387723446,
0.06437674164772034,
0.07854647189378738,
-0.0174262672662735,
-0.006216798909008503,
0.07943810522556305,
-0.03717806190252304,
0.03500011935830116,
0.022601071745157242,
-0.024208854883909225,
0.005299852695316076,
-0.021673591807484627,
-0.0007890777778811753,
-0.03805143013596535,
0.012558704242110252,
0.0066559771075844765,
0.039067741483449936,
-0.028820130974054337,
-0.02714977040886879,
-0.06503316015005112,
-0.003920919261872768,
0.02258135937154293,
0.023784659802913666,
-0.03511962294578552,
-0.03383218124508858,
0.03396625444293022,
-0.03563424199819565,
-0.01677767187356949,
-0.027082281187176704,
0.01113081257790327,
0.006788249127566814,
0.0731559544801712,
0.05683128535747528,
-0.014787837862968445,
-0.07015318423509598,
0.009058116003870964,
-0.03822975605726242,
0.04065725579857826,
0.036283332854509354,
0.03718886524438858,
0.07382069528102875,
0.0032177474349737167,
0.06289514899253845,
-0.0013608898734673858,
-0.03229893371462822,
0.007857524789869785,
0.0760098472237587,
-0.06100260838866234,
0.017333105206489563,
0.04792705923318863,
-0.002791621955111623,
0.015730658546090126,
-0.053194813430309296,
-0.00598781555891037,
-0.016167009249329567,
0.06262645870447159,
-0.001540142111480236,
-0.03407181799411774,
-0.044804371893405914,
-0.001049855025485158,
-0.04444574937224388,
0.031312957406044006,
-0.06778720021247864,
0.09135982394218445,
-0.03156737610697746,
-0.020060453563928604,
-0.0542457289993763,
-0.03965646028518677,
-0.020794935524463654,
-0.019728275015950203,
-0.029520343989133835,
0.018325598910450935,
-0.05696578696370125,
0.002708081156015396,
0.022734152153134346,
-0.0017639093566685915,
-0.00863280426710844,
0.024615034461021423,
0.04018554463982582,
0.001661826390773058,
0.050480637699365616,
0.0005204990739002824,
0.043597497045993805,
-0.014981199987232685,
-0.010091358795762062,
-0.0014125112211331725,
0.01292499154806137,
-0.060662105679512024,
-0.03733263537287712,
-0.02315802313387394,
-0.062042247503995895,
-0.0014902678085491061,
0.07696980983018875,
-0.058167748153209686,
-0.04063456133008003,
-0.04378671944141388,
-0.08888623863458633,
0.0007877589087001979,
0.0420527309179306,
-0.079522505402565,
0.08767814189195633,
-0.0009037573472596705,
0.04607208073139191,
0.028240982443094254,
-0.00007217028905870393,
-0.026541445404291153,
0.03962717205286026,
0.005287629086524248,
0.004556533880531788,
-0.010740093886852264,
0.018199829384684563,
-0.0007730019860900939,
0.03990734741091728,
-0.022736957296729088,
-0.001635800232179463,
-0.05790349096059799,
-0.00483077485114336,
-0.008514191955327988,
0.029001809656620026,
-0.05217472091317177,
0.01864253543317318,
0.08688423782587051,
-0.019193332642316818,
-0.004067892674356699,
0.040220387279987335,
0.016856007277965546,
-0.02559378743171692,
-0.012629050761461258,
0.02496861107647419,
0.009640838950872421,
0.031028522178530693,
-0.02477356232702732,
0.02956235036253929,
0.019732555374503136,
-0.03352014720439911,
0.0028883477207273245,
-0.043655138462781906,
0.03521481528878212,
-0.030386820435523987,
-0.02516035921871662,
0.014242510311305523,
0.06554367393255234,
-0.015328090637922287,
-0.022218840196728706,
0.016039667651057243,
-0.05454785004258156,
-0.0015486418269574642,
0.05804711580276489,
0.04689612612128258,
-0.008473891764879227,
-0.036765746772289276,
-0.0075102741830050945,
0.012323306873440742,
0.010936555452644825,
-0.015911774709820747,
0.01178586296737194,
-0.011034583672881126,
-0.019806765019893646,
0.0055218711495399475,
0.005988252814859152,
0.04983620345592499,
-0.01883423700928688,
-0.0332571305334568,
-0.009762285277247429,
-0.004207596182823181,
-0.03588034212589264,
0.04970245063304901,
-0.03883910924196243,
0.0012505135964602232,
-0.035648100078105927,
-0.04932461306452751,
0.04662957787513733,
-0.07852757722139359,
0.03311675786972046,
0.05597732961177826,
-0.04794229939579964,
-0.007744451053440571,
0.05034420266747475,
0.004665892105549574,
0.08913969993591309,
0.03041831962764263,
0.01406764704734087,
-0.006910426542162895,
0.038532841950654984,
-0.022406162694096565,
0.027708103880286217,
0.033706702291965485,
0.014938256703317165,
-0.0011121126590296626,
0.04903337359428406,
-0.025512075051665306,
0.02492184191942215,
-0.07478953897953033,
0.013101214542984962,
-0.009033378213644028,
0.052983228117227554,
0.03890019655227661,
0.03241291269659996,
-0.013355505652725697,
-0.018808037042617798,
0.030847422778606415,
-0.03926054760813713,
0.03730543330311775,
0.05664617568254471,
0.007238191086798906,
0.0012177842436358333,
0.03913947194814682,
-0.038317300379276276,
0.006583026144653559,
-0.0038277371786534786,
0.02423928678035736,
-0.03189646452665329,
0.024302814155817032,
-0.0204376969486475,
-0.008925930596888065,
0.03241320326924324,
0.006204493809491396,
-0.027967317029833794,
-0.008834927342832088,
-0.029219133779406548,
0.011410458013415337,
-0.03207264840602875,
0.00978364609181881,
-0.01762527972459793,
-0.024657117202878,
-0.012392504140734673,
-0.030194252729415894,
0.004969610366970301,
-0.02658895216882229,
0.02708032727241516,
0.002615206176415086,
-0.007749505341053009,
0.025121347978711128,
0.0076593924313783646,
-0.047281231731176376,
-0.017242982983589172,
-0.010986801236867905,
-0.03137720376253128,
0.0073159243911504745,
-0.012256568297743797,
-0.021862739697098732,
-0.013100010342895985,
-0.06081872433423996,
0.10484188795089722,
-0.020569656044244766,
-0.0038512512110173702,
-0.009848925285041332,
-0.03933066874742508,
-0.07824878394603729,
0.06509576737880707,
0.025598209351301193,
-0.016360735520720482,
-0.010562051087617874,
-0.025925900787115097,
-0.005025445483624935,
-0.015377653762698174,
-0.02202620916068554,
-0.01221547182649374,
-0.024411052465438843,
-0.04657421261072159,
-0.01595698483288288,
0.021578088402748108,
0.0014349909033626318,
-0.01719049923121929,
0.02907194383442402,
-0.0553058385848999,
-0.0033152836840599775,
0.014574326574802399,
0.01123714353889227,
0.006173606030642986,
0.049128707498311996,
0.043272100389003754,
-0.02269696071743965,
-0.04144727438688278,
0.014496192336082458,
-0.08247639983892441,
-0.0055808378383517265,
0.03722725436091423,
-0.023694492876529694,
-0.021598363295197487,
-0.009484299458563328,
0.009633203037083149,
0.014721808955073357,
0.03101462312042713,
-0.029756104573607445,
0.046547167003154755,
0.03169699385762215,
0.026015082374215126,
-0.03229823336005211,
-0.034187737852334976,
0.014957369305193424,
-0.016499042510986328,
0.04684137552976608,
0.004205876961350441,
-0.039350204169750214,
-0.0004782827163580805,
-0.04901941120624542,
-0.016212863847613335,
0.011647868901491165,
-0.012580623850226402,
0.021886887028813362,
0.06095847859978676,
-0.026079297065734863,
-0.012649692595005035,
0.04589153453707695,
0.018211565911769867,
-0.0218369010835886,
0.004186822567135096,
-0.016665376722812653,
-0.06848499178886414,
-0.010884763672947884,
0.04728591442108154,
0.02223769761621952,
0.04064434394240379,
0.03637104481458664,
-0.029128560796380043,
0.05616901069879532,
-0.03521907329559326,
-0.016317300498485565,
-0.010898351669311523,
-0.009329480119049549,
-0.005869016516953707,
-0.05207834765315056,
-0.01578574813902378,
-0.004024419002234936,
0.04480436071753502,
-0.019769195467233658,
-0.07817816734313965,
0.015819206833839417,
-0.04400082305073738,
0.027266861870884895,
-0.054951198399066925,
0.011941894888877869,
-0.04034014418721199,
0.04016910120844841,
0.04853006824851036,
-0.00575681496411562,
0.027244972065091133,
-0.02881789021193981,
-0.03793451935052872,
-0.012030374258756638,
0.01687006466090679,
0.002072703093290329,
0.010347114875912666,
0.01918855309486389,
-0.05038357898592949,
0.06669238209724426,
0.017529252916574478,
0.042999472469091415,
0.05248027294874191,
0.004313040059059858,
0.08459846675395966,
-0.046143271028995514,
-0.01166815310716629,
0.026945605874061584,
0.004288533702492714,
-0.028690434992313385,
0.07115820795297623,
0.010297277942299843,
-0.007879378274083138,
0.04777126386761665,
-0.008330858312547207,
-0.01394319161772728,
0.027165425941348076,
-0.03357305750250816,
0.027924956753849983,
0.023610185831785202,
0.009633968584239483,
-0.04112013429403305,
0.03271419182419777,
0.000028695862056338228,
0.06795314699411392,
-0.007114145439118147,
-0.04989487677812576,
-0.01415702048689127,
0.04835424944758415,
0.0027804120909422636,
0.037518665194511414,
0.013140126131474972,
-0.03210330754518509,
0.024242836982011795,
-0.08641563355922699,
-0.011122248135507107,
0.020037367939949036,
0.0046289036981761456,
0.00974363088607788,
-0.04057392105460167,
0.07685515284538269,
-0.05219066143035889,
0.0028382716700434685,
-0.005902562290430069,
-0.005823782179504633,
0.02004224807024002,
0.0012706439010798931,
0.00970508437603712,
-0.03184507414698601,
-0.003326533595100045,
0.036510832607746124,
0.027224069461226463,
0.04597752168774605,
-0.05671919882297516,
0.012808453291654587,
-0.030018744990229607,
0.06370525062084198,
0.0017121752025559545,
-0.04742928594350815,
0.07145479321479797,
0.007451966870576143,
0.019426779821515083,
-0.014386478811502457,
0.02079710178077221,
0.035414110869169235,
0.025757942348718643,
0.07399332523345947,
0.007738535758107901,
-0.054597921669483185,
0.02653277851641178,
0.03127771615982056,
-0.03352582827210426,
-0.04236835613846779,
0.02377084083855152,
0.03935035690665245,
-0.0004233962099533528,
-0.054296039044857025,
-0.036324188113212585,
-0.0013615034986287355,
0.03331393748521805,
-0.05152132734656334,
0.01953705959022045,
-0.006400661543011665,
-0.022465089336037636,
0.01194390095770359,
-0.04681134968996048,
0.06597818434238434,
-0.00962523277848959,
0.00994583684951067,
-0.005742539651691914,
0.00021035528334323317,
-0.039797037839889526,
0.05563047528266907,
0.00586142111569643,
-0.02245645597577095,
0.01766566000878811,
-0.02278701774775982,
-0.046516623347997665,
0.01930347830057144,
-0.03135055676102638,
0.03274782747030258,
0.0357755571603775,
-0.015701930969953537,
-0.008821430616080761,
-0.011390461586415768,
-0.06652757525444031,
-0.02259066328406334,
0.06924449652433395,
-0.05101098492741585,
-0.040424589067697525,
0.02020764909684658,
0.036660343408584595,
-0.054820816963911057,
0.02023445814847946,
-0.011172160506248474,
0.011066615581512451,
0.00566325057297945,
0.08744494616985321,
0.05452931672334671,
-0.02855553850531578,
0.06404700130224228,
0.03929457068443298,
-0.03663346543908119,
0.0514487624168396,
0.025375673547387123,
0.041642896831035614,
-0.07721956819295883,
0.0024033349473029375,
0.03308526799082756,
0.03453705087304115,
-0.009957617148756981,
0.0574297271668911,
0.00714521249756217,
-0.01321165356785059,
-0.05564490705728531,
-0.01683870702981949,
0.0009351929184049368,
-0.047892313450574875,
0.00827066134661436,
-0.01271937694400549,
-0.022083265706896782,
-0.03670979291200638,
-0.0299141313880682,
-0.024032440036535263,
-0.045128658413887024,
-0.055313240736722946,
0.013880605809390545,
-0.010721728205680847,
-0.015946051105856895,
0.015534583479166031,
-0.030454717576503754,
0.032282184809446335,
-0.0023693277034908533,
0.0030301185324788094,
-0.0400177538394928,
-0.007763863541185856,
0.04747477546334267,
-0.04696682468056679,
-0.02708376944065094,
-0.061463721096515656,
-0.024696340784430504,
-0.03661185875535011,
-0.0479910671710968,
-0.0006636994075961411,
0.02362922579050064,
0.004084247630089521,
-0.014369639568030834,
-0.004301914945244789,
-0.021793048828840256,
-0.004230252932757139,
-0.0027720679063349962,
-0.016001813113689423,
0.0264455433934927,
0.03425106406211853,
0.053551085293293,
0.02044575847685337,
-0.015623407438397408,
0.03369681537151337,
-0.02150803431868553,
0.04344562068581581,
0.016417358070611954,
0.012358255684375763,
0.05109889432787895,
0.052731167525053024,
-0.024696746841073036,
0.021147916093468666,
0.06116895377635956,
0.011254613287746906,
-0.038421381264925,
0.024754956364631653,
-0.04985928535461426,
0.01577840745449066,
0.056153833866119385,
0.09246694296598434,
0.0039895074442029,
-0.002454860834404826,
-0.003395704086869955,
0.012280363589525223,
-0.04141782969236374,
-0.010695266537368298,
0.023384148254990578,
-0.0024910280480980873,
-0.09015350788831711,
0.016797859221696854,
0.005547605454921722,
-0.00406415993347764,
-0.019133713096380234,
-0.049773845821619034,
-0.024014024063944817,
0.09612811356782913,
-0.026058435440063477,
0.0043562850914895535,
0.013607536442577839,
-0.05372465401887894,
-0.04483999311923981,
0.044738706201314926,
-0.0024519157595932484,
-0.08723519742488861,
-0.0220883060246706,
-0.007530683651566505,
0.008821056224405766,
-0.06705784052610397,
-0.009194540791213512,
-0.04841884225606918,
0.004330228548496962,
-0.03641919046640396,
-0.03219805657863617,
0.07958370447158813,
-0.043357424437999725,
0.07885853946208954,
0.014156107790768147,
0.007237032521516085,
-0.008176012896001339,
-0.02267920970916748,
-0.023659147322177887,
0.0018847655737772584,
0.01977171003818512,
-0.04542255774140358,
-0.021454349160194397,
0.036472830921411514,
-0.00008112876821542159,
0.033895429223775864,
-0.020218729972839355,
0.013088742271065712,
-0.04793863371014595,
0.002056021708995104,
-0.011583405546844006,
-0.026675745844841003,
-0.026584813371300697,
0.05090641230344772
] |
<p>The pressure cooker is heated at the base to cook the food. The pressure cooker releases steam when the force exerted by pressure exceeds the counterweight, at which point the weight rises up allowing steam to escape. The time to cook is measured by the number of times steam is released.</p>
<p>When food(dry lentils) is kept in a container inside the pressure cooker it does not cook as well as if it were dumped in there directly. The same amount of water is added to the food in both cases, though in the former case there is also some water in the base of the cooker outside the container. In both cases the cooker was allowed to release steam 3 times.</p>
<p>I thought that based on Pascal's law the same pressure would be exerted on the water in the container as it would if kept there directly. Since the temperature is the same, in both cases the food should be completely cooked. However practical results differ. Please suggest a theory which explains this.</p>
|
g2491
|
[
0.04944955185055733,
0.0365072563290596,
0.016101619228720665,
-0.0012698887148872018,
0.01940675638616085,
-0.00504828616976738,
-0.021472694352269173,
-0.030612394213676453,
-0.08015957474708557,
-0.0017170000355690718,
-0.0068250079639256,
0.004210134036839008,
0.020680436864495277,
0.07586416602134705,
0.019153155386447906,
-0.027916554361581802,
0.02767353691160679,
-0.04545892775058746,
-0.03140069171786308,
0.0398213267326355,
-0.0006072959513403475,
0.02533966675400734,
-0.03338836506009102,
-0.07815336436033249,
-0.1130128800868988,
-0.04237770661711693,
0.005188815761357546,
0.03425406664609909,
-0.060843005776405334,
-0.04573005810379982,
-0.023655392229557037,
-0.023551613092422485,
-0.05579901486635208,
-0.04008287563920021,
-0.04291409254074097,
-0.025830697268247604,
0.05745749548077583,
0.02948732115328312,
-0.018624817952513695,
-0.022949334233999252,
-0.02468874305486679,
0.03227769955992699,
-0.011695445515215397,
0.04881265014410019,
-0.02212327904999256,
0.024580322206020355,
-0.04097442328929901,
0.024534087628126144,
-0.007461032830178738,
0.014106136746704578,
0.014411811716854572,
0.00042101056897081435,
-0.03551287576556206,
-0.03812152147293091,
-0.001044546370394528,
-0.00006969254172872752,
-0.0427185595035553,
0.006366767454892397,
0.043416790664196014,
-0.0012717113131657243,
0.011854808777570724,
0.009769435971975327,
0.04420698434114456,
0.015143128111958504,
0.03911425918340683,
-0.0372062511742115,
-0.00241098552942276,
0.027401724830269814,
0.012093347497284412,
0.05054265260696411,
0.0276421457529068,
-0.09604954719543457,
0.018160182982683182,
-0.060314714908599854,
-0.016996067017316818,
0.005394135136157274,
-0.03791143000125885,
-0.050268664956092834,
0.05246596410870552,
-0.003373551880940795,
0.0031309674959629774,
-0.01596456579864025,
0.04378447309136391,
0.0211174339056015,
0.03836009278893471,
-0.039854537695646286,
-0.014476973563432693,
-0.014234579168260098,
-0.039120081812143326,
0.020429830998182297,
-0.011828107759356499,
-0.03649456426501274,
0.07716350257396698,
0.08332321792840958,
0.0040139188058674335,
0.001258106785826385,
-0.006255017593502998,
0.009770319797098637,
-0.013876747339963913,
-0.03041023574769497,
0.09266012161970139,
-0.05174969881772995,
0.0648052915930748,
0.010962172411382198,
-0.026152843609452248,
0.03570324555039406,
0.0705183744430542,
0.049254145473241806,
-0.06690598279237747,
-0.03230702504515648,
-0.0019347220659255981,
-0.02969237230718136,
-0.0730835571885109,
-0.007965752854943275,
0.04386129602789879,
-0.04818282276391983,
0.07987499237060547,
-0.012335478328168392,
-0.015585090033710003,
0.00504986522719264,
0.01785910874605179,
0.016009461134672165,
0.023943042382597923,
0.025447051972150803,
0.04543657600879669,
0.025805514305830002,
0.006630136165767908,
-0.012857889756560326,
0.03666829690337181,
-0.0060220989398658276,
-0.03365589678287506,
0.007779798004776239,
-0.05029274895787239,
0.047557488083839417,
0.04431537538766861,
-0.016515890136361122,
-0.01477959007024765,
0.0268445685505867,
-0.022002898156642914,
-0.048761188983917236,
-0.016785070300102234,
0.026566172018647194,
-0.028795946389436722,
-0.008291435427963734,
0.012818236835300922,
0.02294399030506611,
0.06516280025243759,
0.009478122927248478,
0.023833151906728745,
0.004004375543445349,
0.01139139849692583,
0.05115405097603798,
0.021442603319883347,
0.04772020876407623,
-0.001632301020435989,
-0.01893431693315506,
0.003768978174775839,
-0.01156681589782238,
0.022731905803084373,
0.03018805757164955,
0.034332189708948135,
-0.012739558704197407,
0.010150059126317501,
0.05085097253322601,
-0.09246747940778732,
0.035669825971126556,
0.022221965715289116,
-0.028290122747421265,
-0.014030668884515762,
-0.0659048780798912,
-0.029938263818621635,
0.007218840532004833,
-0.04364253580570221,
0.033675383776426315,
-0.01451126765459776,
0.0009528720984235406,
0.07621708512306213,
0.006882763467729092,
0.009549395181238651,
-0.060433465987443924,
-0.044203490018844604,
-0.000972682551946491,
-0.0017911063041538,
-0.02755969949066639,
-0.0060207960195839405,
-0.008398286066949368,
0.05244719982147217,
0.04569357633590698,
-0.09766264259815216,
0.0026001054793596268,
-0.01767687499523163,
0.017474563792347908,
-0.009094958193600178,
0.09022881090641022,
0.029422301799058914,
-0.051534831523895264,
-0.0035390835255384445,
-0.04305112734436989,
-0.00497288117185235,
-0.045926474034786224,
-0.019095830619335175,
-0.057791173458099365,
0.04474586620926857,
0.035781245678663254,
-0.021436695009469986,
0.015398044139146805,
0.016387391835451126,
0.017957622185349464,
0.01955389603972435,
0.012386666610836983,
-0.07619746029376984,
0.07556087523698807,
-0.00962962955236435,
0.0020774505101144314,
0.0034984606318175793,
0.019644295796751976,
-0.01706339418888092,
0.02341877855360508,
-0.033614546060562134,
0.011536125093698502,
-0.024646172299981117,
0.006580864544957876,
-0.046940114349126816,
0.006572796497493982,
-0.03181048110127449,
-0.005263766273856163,
-0.08282065391540527,
0.011613834649324417,
-0.07031313329935074,
0.028876015916466713,
0.001008540391921997,
-0.01472034864127636,
0.012509595602750778,
0.008093087933957577,
0.00034264486748725176,
-0.01987830363214016,
-0.007008806802332401,
0.011237358674407005,
-0.020300954580307007,
0.038670413196086884,
-0.019071949645876884,
0.021508950740098953,
-0.0021958129946142435,
-0.008231490850448608,
0.02715878374874592,
-0.004952582996338606,
0.0283966064453125,
-0.029526669532060623,
0.04285518452525139,
0.014954425394535065,
-0.0019083154620602727,
0.06602847576141357,
-0.00010405847569927573,
0.011161284521222115,
-0.025518856942653656,
-0.008001177571713924,
-0.006200245115906,
0.0021973252296447754,
-0.07610436528921127,
-0.0393981970846653,
0.011343791149556637,
0.023324595764279366,
0.03324045240879059,
0.05520353466272354,
0.027098974213004112,
-0.017051134258508682,
-0.008721101097762585,
0.004236005712300539,
0.03126605972647667,
-0.005698797758668661,
-0.011755765415728092,
-0.0034415279515087605,
0.04126948118209839,
0.024460922926664352,
0.033738620579242706,
-0.042983073741197586,
0.01494373008608818,
-0.045479316264390945,
0.010794133879244328,
0.009731997735798359,
0.0031148255802690983,
-0.028992177918553352,
-0.01924438774585724,
0.02835770882666111,
-0.013511830009520054,
-0.008321846835315228,
0.011239433661103249,
-0.00031889887759462,
-0.044550079852342606,
-0.026567906141281128,
0.02188924513757229,
0.034434519708156586,
0.007276941556483507,
0.0046272799372673035,
0.01939263567328453,
0.09549735486507416,
0.03783266991376877,
-0.03623645380139351,
0.002060811035335064,
-0.02990797348320484,
0.031886663287878036,
-0.0321471281349659,
-0.021071551367640495,
0.041222985833883286,
0.005321387201547623,
0.017012478783726692,
-0.05191269889473915,
0.0065077077597379684,
-0.052770208567380905,
-0.032839830964803696,
0.0009948688093572855,
0.029108557850122452,
-0.05234859511256218,
-0.0315694734454155,
-0.05079086497426033,
-0.012585015036165714,
-0.05857693403959274,
0.0714043453335762,
-0.0035049072466790676,
0.023672277107834816,
-0.06588207930326462,
0.027345769107341766,
-0.05607185512781143,
-0.026035362854599953,
-0.0016822024481371045,
0.060423269867897034,
-0.03617718815803528,
0.03010902926325798,
0.060495518147945404,
-0.057138778269290924,
0.019464915618300438,
0.039731208235025406,
0.005525627173483372,
-0.05972425639629364,
-0.0429723747074604,
0.03849039226770401,
0.004749285988509655,
0.03244656324386597,
-0.009014515206217766,
0.038805972784757614,
0.023840541020035744,
-0.02032425068318844,
-0.0036582848988473415,
0.01084248535335064,
0.023484183475375175,
0.032797541469335556,
0.04054374247789383,
-0.023091943934559822,
0.017790524289011955,
0.033430032432079315,
0.08910337835550308,
0.001442256267182529,
-0.03202153742313385,
0.02396344393491745,
-0.015531324781477451,
0.020796259865164757,
-0.04995967075228691,
-0.01824597641825676,
0.02047908306121826,
0.015193726867437363,
0.026820695027709007,
-0.0677073523402214,
-0.010942482389509678,
-0.021131927147507668,
-0.024147002026438713,
0.014859306626021862,
0.06028202921152115,
0.021659422665834427,
0.013913786970078945,
-0.024598686024546623,
0.01701946370303631,
-0.04439839720726013,
-0.024301769211888313,
0.013473323546350002,
0.08909187465906143,
-0.005910755135118961,
0.026123203337192535,
-0.032801948487758636,
-0.0062379310838878155,
0.006987611763179302,
0.030530190095305443,
0.00036842518602497876,
-0.01823396049439907,
0.06177399680018425,
0.06396744400262833,
0.01068687904626131,
-0.017203286290168762,
0.06416461616754532,
0.03760622441768646,
-0.04791802912950516,
0.03606567159295082,
-0.02074448950588703,
0.038332562893629074,
0.02990133687853813,
0.03740204870700836,
0.00006702901737298816,
-0.034115202724933624,
-0.035102974623441696,
0.040421728044748306,
-0.0014548598555848002,
0.00904106069356203,
-0.027170568704605103,
0.03393641859292984,
-0.03867846354842186,
-0.039675481617450714,
0.033694230020046234,
0.06328678131103516,
-0.01224557962268591,
-0.061995722353458405,
0.0011974956141784787,
-0.014142758212983608,
0.028641583397984505,
-0.020096590742468834,
0.013162757270038128,
-0.03056173399090767,
-0.03459685668349266,
0.07454255223274231,
0.011590971611440182,
-0.01685853861272335,
0.006001032888889313,
-0.023450931534171104,
0.0022467446979135275,
-0.015994511544704437,
-0.01360708475112915,
-0.007148416247218847,
0.051020413637161255,
0.017237931489944458,
0.015309548936784267,
0.02279743365943432,
-0.02535715512931347,
-0.035844724625349045,
0.03652111068367958,
0.0011678762966766953,
0.011085432954132557,
-0.00808204710483551,
0.01723363995552063,
-0.06452708691358566,
-0.002573885954916477,
-0.061586398631334305,
0.07900132983922958,
-0.015254458412528038,
0.012253998778760433,
-0.0026510118041187525,
0.033355262130498886,
0.039057184010744095,
0.027563586831092834,
0.005310627166181803,
-0.07003980875015259,
0.0034677458461374044,
-0.0921163484454155,
0.011963524855673313,
0.07419013231992722,
-0.026866205036640167,
-0.002095916774123907,
-0.03785302862524986,
0.03247798979282379,
-0.048228345811367035,
-0.014465569518506527,
-0.05535370856523514,
-0.0009985571959987283,
-0.09149957448244095,
-0.029586251825094223,
-0.04446408525109291,
0.042162153869867325,
-0.022530611604452133,
-0.005184235982596874,
-0.006291581783443689,
-0.023832665756344795,
-0.01293722353875637,
0.05319005995988846,
0.03180471807718277,
0.05093225836753845,
0.025530805811285973,
0.00235178554430604,
0.07779952138662338,
0.058733899146318436,
-0.0017037107609212399,
0.02212391421198845,
0.015483030118048191,
-0.05863489583134651,
0.017898641526699066,
-0.04231332615017891,
0.020610131323337555,
0.023827003315091133,
-0.017688199877738953,
-0.012212780304253101,
0.015770230442285538,
-0.03335999324917793,
0.007352977059781551,
-0.054338108748197556,
0.018510619178414345,
-0.015883881598711014,
-0.015918731689453125,
-0.01736140064895153,
0.005309015978127718,
-0.00009877436968963593,
0.020717797800898552,
0.027064794674515724,
0.014611498452723026,
0.024345751851797104,
-0.07693170011043549,
-0.06616392731666565,
0.015948975458741188,
-0.03662499040365219,
-0.0472603365778923,
-0.016100279986858368,
0.02974124439060688,
-0.023046977818012238,
-0.012531157582998276,
0.04582048952579498,
0.07664288580417633,
0.025772714987397194,
-0.04239592328667641,
-0.01648690365254879,
0.04632650688290596,
-0.027106821537017822,
0.0011051174951717257,
-0.017766064032912254,
-0.0003570147673599422,
-0.00551250483840704,
0.039741192013025284,
0.01955343224108219,
-0.021820835769176483,
0.03548877313733101,
0.019327916204929352,
-0.04976116493344307,
-0.0355655737221241,
-0.015558454208076,
-0.0038887839764356613,
0.0073050823993980885,
0.005943428725004196,
0.030497295781970024,
0.05463200807571411,
0.04085106775164604,
-0.03996851667761803,
-0.011514076963067055,
-0.027275698259472847,
0.06794800609350204,
0.07247010618448257,
-0.038181547075510025,
0.006726042367517948,
-0.0075379349291324615,
0.007585657760500908,
0.03003673069179058,
0.008125469088554382,
-0.007751255761831999,
-0.08492378890514374,
-0.0021623801440000534,
0.015114721842110157,
0.021771203726530075,
-0.04568083584308624,
0.10180068761110306,
-0.051434677094221115,
-0.0578073114156723,
0.056915104389190674,
0.007544944062829018,
0.09348003566265106,
-0.00687938928604126,
-0.006145020481199026,
-0.01468852162361145,
-0.02289811335504055,
0.08034206926822662,
0.02880834974348545,
0.039891377091407776,
-0.008887294679880142,
-0.0430104024708271,
-0.043812114745378494,
-0.035271260887384415,
-0.0120937405154109,
0.03348029777407646,
0.008250240236520767,
-0.03847838193178177,
0.027866873890161514,
0.02379985712468624,
-0.035865314304828644,
0.059206634759902954,
-0.008699523285031319,
0.01711251214146614,
0.018485862761735916,
0.0026028119027614594,
0.029020795598626137,
0.03537699952721596,
-0.028444577008485794,
-0.015155811794102192,
-0.020140742883086205,
0.04126165434718132,
-0.025007305666804314,
0.019191734492778778,
0.027992894873023033,
0.02225465513765812,
0.0063791885040700436,
-0.0010336347622796893,
-0.025856569409370422,
0.03371855616569519,
0.05479292571544647,
0.031562741845846176,
0.004624377936124802,
0.024073811247944832,
-0.021061312407255173,
0.014691649004817009,
0.020467156544327736,
0.03780137374997139,
0.09696794301271439,
-0.027777908369898796,
-0.011718095280230045,
-0.018565457314252853,
0.019506430253386497,
-0.019921524450182915,
0.012111086398363113,
0.04015551507472992,
-0.012697805650532246,
0.021158140152692795,
0.0716240331530571,
0.0056883832439780235,
0.026347188279032707,
-0.04515393450856209,
-0.01015127170830965,
-0.01695810817182064,
0.028080405667424202,
0.00913658831268549,
0.013715164735913277,
-0.04532445967197418,
-0.06264268606901169,
-0.05390596017241478,
0.030093582347035408,
-0.011209285818040371,
-0.07763493806123734,
0.012627101503312588,
0.04500621557235718,
-0.02776658535003662,
0.023755624890327454,
-0.06677379459142685,
-0.022335417568683624,
-0.014120441861450672,
-0.02145024575293064,
0.010648960247635841,
-0.021013611927628517,
0.053964145481586456,
-0.01493950467556715,
0.02947237901389599,
-0.07374785840511322,
-0.007551243994385004,
-0.019501319155097008,
0.01966700330376625,
-0.07245802879333496,
0.005428052973002195,
0.07278761267662048,
-0.052603062242269516,
-0.07265090942382812,
-0.020155945792794228,
-0.03804035857319832,
-0.028362538665533066,
-0.03953566774725914,
0.006891004275530577,
-0.018765533342957497,
-0.0001856311719166115,
0.02834612876176834,
0.0056333402171730995,
-0.05939110741019249,
0.007088818587362766,
0.015641378238797188,
-0.006537549197673798,
0.02202054299414158,
0.042224183678627014,
0.03305472806096077,
0.01675022765994072,
-0.004578334279358387,
-0.06578591465950012,
0.016937652602791786,
-0.02488158829510212,
0.04142892360687256,
-0.024994444102048874,
-0.024758687242865562,
-0.04063742607831955,
-0.00208510784432292,
0.04777706786990166,
0.04243345931172371,
-0.015592297539114952,
-0.06636301428079605,
-0.0011081771226599813,
-0.04867500811815262,
-0.05667790770530701,
0.0230146124958992,
-0.01768059842288494,
0.019822439178824425,
0.012169580906629562,
0.004443890880793333,
-0.011136503890156746,
0.03310303017497063,
0.013990828767418861,
0.030899574980139732,
0.030817290768027306,
0.05676857754588127,
0.01365603692829609,
-0.0008475278737023473,
0.03171420469880104,
0.04590511694550514,
-0.004107694607228041,
0.052223045378923416,
-0.0014108994510024786,
0.003424636786803603,
-0.00854884646832943,
-0.018566276878118515,
0.006573124788701534,
0.013486514799296856,
0.04127403721213341,
-0.026835443452000618,
0.03509083762764931,
-0.06552143394947052,
0.0057892329059541225,
0.003600186901167035,
-0.007845583371818066,
0.04041586071252823,
-0.03200415149331093,
0.0037836579140275717,
-0.016383923590183258,
-0.10673005878925323,
-0.04148884862661362,
-0.050437185913324356,
-0.06499561667442322,
-0.02546882815659046,
-0.057053133845329285,
-0.03544788435101509,
-0.033829621970653534,
0.0025694335345178843,
0.012135404162108898,
-0.03942618519067764,
-0.07556966692209244,
0.023635009303689003,
0.03010280802845955,
0.002481705043464899,
-0.002137974603101611,
-0.013704773969948292,
0.032224200665950775,
0.0380832701921463,
0.04516978561878204,
0.10761324316263199,
0.006545646116137505,
-0.021432364359498024,
0.014502459205687046,
-0.015736721456050873,
0.07607465237379074,
0.0026523198466748,
-0.021093375980854034,
-0.009130720049142838,
-0.016111202538013458,
-0.04768751189112663,
0.006202229298651218,
0.0591491274535656,
-0.02008455991744995,
0.029387585818767548,
-0.04899507388472557,
-0.07060426473617554,
-0.03611242398619652,
0.0022621259558945894,
-0.05945871025323868,
-0.016811519861221313,
0.005663658957928419,
0.024366112425923347,
-0.07183198630809784,
-0.007896188646554947,
-0.005078986752778292,
-0.00024369244056288153,
-0.017703957855701447,
-0.0011966099264100194,
0.004780693911015987,
0.007805495522916317,
-0.032642364501953125
] |
<p>Hope this isn't something trivially wrong, I am a beginner in classical mechanics. But anyways, say there is a cube, of side length $a \ \text{cm}$. The volume of the cube is $a^3 \ \text{cm}^3$. If the total mass of the cube is $m \text{ kg}$, the <a href="http://en.wikipedia.org/wiki/Density" rel="nofollow">density</a> of the cube will be $\frac{m}{a^3} \text{kg/cm}^3$. Again, consider the cube as the combination of many square plates of negligible thickness. If the mass of each is $m_2 \ \text{kg}$, their density will be $\frac{m_2}{a^2} \ \text{kg/cm}^2$. Here's the question: we found the density in two ways, and their dimensions don't match. I think I know why this happens- we are finding the density of the cube by integrating the densities of each plate. But how would you answer the following question?</p>
<p>The density of a cube is $X \text{ kg/cm}^3$. Find the density of each square plate.</p>
<p>Again, I am sorry if this is something trivial, I am a novice. :)</p>
|
g2492
|
[
0.11969044804573059,
0.03888007253408432,
-0.0034169077407568693,
-0.020273370668292046,
0.02698875032365322,
0.030147148296236992,
0.010441488586366177,
-0.015826525166630745,
-0.07230457663536072,
-0.013083604164421558,
-0.020796088501811028,
-0.04300275817513466,
-0.004407059401273727,
0.011394498869776726,
0.0023285660427063704,
0.03650946542620659,
0.025164151564240456,
0.04721532762050629,
0.03804957866668701,
0.059413015842437744,
-0.05292261391878128,
-0.0029160475824028254,
0.01016802154481411,
-0.03639954701066017,
-0.027684079483151436,
-0.029363734647631645,
0.014589766971766949,
0.030885372310876846,
-0.036579668521881104,
-0.04235975444316864,
-0.0488332100212574,
0.018400993198156357,
0.055599894374608994,
-0.02390335127711296,
0.056742165237665176,
-0.006127423141151667,
0.028539322316646576,
0.026046695187687874,
-0.043417368084192276,
-0.07467024028301239,
-0.02155391313135624,
-0.03673459589481354,
0.025102099403738976,
0.0272306390106678,
-0.012893683277070522,
0.01345817744731903,
-0.07669183611869812,
-0.017494654282927513,
-0.006207067519426346,
-0.0004406002990435809,
-0.005343007389456034,
0.11046696454286575,
0.029626887291669846,
-0.04438357800245285,
-0.025883348658680916,
0.031318459659814835,
0.055487532168626785,
-0.08282255381345749,
0.03426435962319374,
0.006680649239569902,
0.019233400002121925,
-0.038511138409376144,
-0.008043518289923668,
0.0037842567544430494,
0.08845017850399017,
-0.011168955825269222,
-0.03796667605638504,
0.0333070270717144,
0.005918797105550766,
-0.03899064287543297,
0.002477263333275914,
-0.046931590884923935,
-0.011856190860271454,
-0.022455981001257896,
-0.022033724933862686,
-0.054101377725601196,
0.05348563939332962,
0.037605300545692444,
0.013318759389221668,
-0.009612247347831726,
-0.05012694373726845,
0.004037951119244099,
0.07131199538707733,
-0.014263852499425411,
0.020384034141898155,
-0.002965334104374051,
0.001434057834558189,
-0.022842342033982277,
-0.06181254982948303,
0.024200858548283577,
-0.05099854618310928,
-0.0025971184950321913,
0.02382364124059677,
0.006249298807233572,
-0.041693173348903656,
-0.01551896519958973,
0.007701815105974674,
0.046420272439718246,
-0.021413316950201988,
0.010689044371247292,
-0.0177035853266716,
0.0023860959336161613,
-0.001011153100989759,
-0.023910433053970337,
-0.01773962564766407,
-0.015519406646490097,
0.045964282006025314,
0.01219035405665636,
0.013017409481108189,
0.006471800617873669,
-0.08860248327255249,
-0.027994565665721893,
-0.0014574610395357013,
-0.060532864183187485,
-0.0022435560822486877,
0.0050933388993144035,
0.047518230974674225,
0.009962226264178753,
-0.04814428091049194,
0.04915526509284973,
0.006174898706376553,
0.012310905382037163,
0.028995709493756294,
0.03288411349058151,
0.03463844954967499,
0.0074071562848985195,
0.009122180752456188,
0.09664586931467056,
0.0178335290402174,
-0.010982455685734749,
0.042733509093523026,
0.025148017331957817,
0.004562013782560825,
-0.02914115972816944,
0.018588056787848473,
0.0753050148487091,
-0.05675230920314789,
0.05957089737057686,
-0.04204969108104706,
0.047604918479919434,
-0.04677172377705574,
-0.00905870832502842,
-0.031934309750795364,
-0.0048936414532363415,
0.003939923830330372,
0.0041706012561917305,
-0.07723139971494675,
-0.06343287229537964,
-0.009289171546697617,
0.01977323181927204,
-0.03880104050040245,
0.049174029380083084,
0.018249252811074257,
-0.03969559445977211,
0.003859009360894561,
0.07321905344724655,
0.02290763519704342,
-0.025353150442242622,
0.04233362525701523,
-0.07796535640954971,
0.022824537009000778,
-0.017179569229483604,
0.001688557444140315,
0.018043138086795807,
0.005129829049110413,
0.05706506595015526,
-0.00427887262776494,
-0.04279746860265732,
0.019581517204642296,
-0.05247427150607109,
0.018804995343089104,
-0.04153380170464516,
-0.018163155764341354,
0.020277831703424454,
-0.030122006312012672,
0.019372904673218727,
0.009594511240720749,
-0.021207114681601524,
0.0342174768447876,
-0.0038106455467641354,
-0.0038776618894189596,
0.029089007526636124,
0.04648314416408539,
-0.019674664363265038,
-0.004871301352977753,
0.01599983684718609,
0.08735362440347672,
-0.027522938326001167,
-0.04821645841002464,
0.06386448442935944,
-0.01997431367635727,
-0.016571614891290665,
0.028347419574856758,
0.04869788512587547,
0.001838548807427287,
-0.012944026850163937,
0.05372818186879158,
-0.006940745748579502,
-0.01503918319940567,
-0.058103904128074646,
0.01989590749144554,
-0.0089733200147748,
0.08082510530948639,
0.022328197956085205,
0.024912109598517418,
0.025243379175662994,
0.011268476955592632,
0.0168977789580822,
0.05011773481965065,
0.0071610379964113235,
-0.057598672807216644,
-0.02404663898050785,
-0.01550939679145813,
0.0627138540148735,
-0.021891506388783455,
-0.043779123574495316,
0.009087737649679184,
0.02956942282617092,
-0.06373398005962372,
-0.009001395665109158,
-0.06617596745491028,
0.013635396957397461,
-0.049187105149030685,
-0.006612052209675312,
0.007003625854849815,
-0.0004772832617163658,
0.009993040934205055,
0.0024468975607305765,
-0.02949596755206585,
-0.013586134649813175,
-0.05754661560058594,
-0.02325272746384144,
-0.014917498454451561,
-0.02281983382999897,
0.06891405582427979,
0.06846925616264343,
-0.055267784744501114,
0.011196552775800228,
-0.00547200720757246,
0.023729613050818443,
0.01525150891393423,
-0.014143617823719978,
-0.05530799552798271,
-0.04814748838543892,
0.05858801677823067,
-0.016451677307486534,
-0.0021218580659478903,
-0.024294136092066765,
0.02154272422194481,
0.06844186037778854,
-0.05081367865204811,
0.04236309975385666,
-0.028660455718636513,
-0.010237317532300949,
0.041218411177396774,
0.014704459346830845,
-0.06862599402666092,
-0.002718799514696002,
0.03260861709713936,
-0.048867736011743546,
0.007580174133181572,
-0.013872877694666386,
0.019896680489182472,
0.009117304347455502,
-0.08060458302497864,
-0.01769382320344448,
-0.05465256795287132,
-0.030409110710024834,
0.027298813685774803,
0.05965397134423256,
0.025841161608695984,
0.01818954572081566,
0.0517679788172245,
0.003977017477154732,
0.018127594143152237,
-0.009505823254585266,
-0.009353488683700562,
0.01960657350718975,
0.03244578465819359,
-0.020248886197805405,
0.037058498710393906,
0.03312598541378975,
0.006928866263478994,
0.04871749132871628,
0.03550023213028908,
-0.016032930463552475,
0.011014566756784916,
0.021851569414138794,
0.03141169622540474,
0.0018998566083610058,
0.03941377252340317,
0.007370735052973032,
0.03137829527258873,
-0.01980418898165226,
0.04318459704518318,
0.04058818891644478,
0.01939372718334198,
-0.049750566482543945,
0.008844306692481041,
-0.005936003755778074,
0.03510700538754463,
0.00963674671947956,
0.01763274520635605,
-0.0486447848379612,
0.033259615302085876,
0.029606221243739128,
-0.021281613036990166,
-0.016632314771413803,
0.012073268182575703,
0.010241372510790825,
0.062194135040044785,
0.00771213648840785,
0.036097150295972824,
-0.020290954038500786,
-0.07280556857585907,
0.003300738986581564,
0.02948431856930256,
-0.04463730752468109,
-0.0000024300863969983766,
-0.031540751457214355,
-0.026033230125904083,
-0.026421014219522476,
0.006554003339260817,
-0.015307161025702953,
-0.020857390016317368,
0.06408487260341644,
-0.05453821271657944,
0.029983950778841972,
-0.021360622718930244,
-0.024588437750935555,
-0.0190297681838274,
-0.023207422345876694,
-0.006986670196056366,
-0.04427916929125786,
-0.07626412808895111,
-0.020418645814061165,
0.009540246799588203,
-0.0015050485963001847,
0.054444219917058945,
0.021725483238697052,
0.020803600549697876,
-0.05542153865098953,
0.002646904904395342,
-0.014485133811831474,
-0.062396012246608734,
0.0003445454640313983,
-0.015775587409734726,
0.050495732575654984,
-0.00034770104684866965,
0.04503213241696358,
-0.03290887549519539,
-0.014163745567202568,
0.029600270092487335,
-0.015026258304715157,
-0.038293223828077316,
0.03242657333612442,
0.028850005939602852,
0.009023187682032585,
0.007439068518579006,
-0.019021090120077133,
0.030553989112377167,
-0.04463493078947067,
-0.017980974167585373,
-0.015201997943222523,
-0.01909589022397995,
0.013542493805289268,
0.004011198412626982,
0.061492919921875,
0.0006106236833147705,
0.014608321711421013,
-0.005379782523959875,
-0.08870897442102432,
-0.023868706077337265,
0.043428320437669754,
0.07685922086238861,
-0.056258175522089005,
-0.05195578560233116,
-0.00036219885805621743,
0.033443696796894073,
0.05738263577222824,
0.025044718757271767,
0.026239298284053802,
-0.03347168490290642,
-0.06897670030593872,
-0.0076308054849505424,
-0.00567743880674243,
0.016786938533186913,
-0.009632215835154057,
0.05582772195339203,
-0.004871489480137825,
0.034874942153692245,
0.008181385695934296,
-0.09300686419010162,
0.03911576420068741,
-0.02216794714331627,
-0.03392821550369263,
0.016993723809719086,
-0.021319516003131866,
-0.10087058693170547,
-0.0005613127141259611,
0.01977858692407608,
-0.01225024089217186,
0.0066373310983181,
-0.06205064430832863,
-0.012675709091126919,
0.03060791827738285,
0.017524974420666695,
-0.04476247727870941,
0.059130966663360596,
-0.00982297956943512,
-0.014262016862630844,
-0.047602925449609756,
0.029016273096203804,
-0.07738056033849716,
-0.048951406031847,
0.0028903926722705364,
0.008948823437094688,
0.024204779416322708,
0.00024995391140691936,
0.014171048998832703,
0.015995454043149948,
0.05149175226688385,
-0.11142230778932571,
-0.01702883094549179,
-0.014363694004714489,
-0.0002021918335231021,
0.05847684666514397,
-0.05318382382392883,
0.03439047560095787,
-0.0032304341439157724,
0.006771232467144728,
0.003513757139444351,
0.009592272341251373,
0.06314296275377274,
-0.01769699901342392,
-0.054188311100006104,
0.021141765639185905,
0.03440878540277481,
-0.016751455143094063,
0.016938943415880203,
-0.033085066825151443,
-0.003758851671591401,
-0.057126883417367935,
0.011180799454450607,
0.045296549797058105,
0.012861169874668121,
-0.03376764804124832,
-0.03915887326002121,
-0.021678993478417397,
-0.003492851974442601,
0.010420665144920349,
-0.03375817835330963,
-0.046619564294815063,
-0.021638832986354828,
0.010574458166956902,
0.041634880006313324,
0.041681818664073944,
0.03670452535152435,
-0.007535773795098066,
0.018003245815634727,
0.026314007118344307,
0.007016475312411785,
-0.00414130138233304,
-0.018703561276197433,
-0.009272024966776371,
-0.058073945343494415,
0.005435143131762743,
0.05159032717347145,
-0.08124824613332748,
-0.03723965585231781,
-0.018712252378463745,
0.005960261914879084,
-0.011354810558259487,
0.07008804380893707,
0.021573783829808235,
0.01879662089049816,
0.0002433965273667127,
0.013447617180645466,
-0.016450660303235054,
-0.047263603657484055,
0.019707130268216133,
0.01410299725830555,
0.00913518387824297,
0.05198363587260246,
0.04974381625652313,
0.008651340380311012,
0.006943760439753532,
-0.01810428313910961,
0.010852726176381111,
-0.0026458874344825745,
0.0517851822078228,
-0.021010059863328934,
0.03212666139006615,
0.011997312307357788,
-0.012559369206428528,
-0.035188525915145874,
0.009661131538450718,
-0.033301230520009995,
0.021515952423214912,
0.017260735854506493,
0.005462667904794216,
0.00568415829911828,
0.014294542372226715,
-0.005142079200595617,
-0.034541256725788116,
0.020128464326262474,
0.08244623988866806,
-0.0030314596369862556,
0.03278568014502525,
0.0977676659822464,
0.05386679247021675,
-0.014359886758029461,
0.08259320259094238,
0.020966270938515663,
-0.018587736412882805,
-0.016146942973136902,
0.0039348420687019825,
0.0353015698492527,
0.009505735710263252,
-0.0240835789591074,
0.03750922530889511,
0.010829809121787548,
-0.027937479317188263,
0.0023280573077499866,
0.03583149239420891,
-0.024455495178699493,
-0.04820045456290245,
-0.054624591022729874,
0.001574029098264873,
0.022823024541139603,
-0.0814928486943245,
-0.03740181401371956,
0.037100352346897125,
-0.0012964062625542283,
-0.08040378987789154,
-0.0016193968476727605,
-0.03743565082550049,
-0.011001773178577423,
0.038730014115571976,
-0.0056058550253510475,
0.04932543262839317,
0.003482972038909793,
-0.01441506389528513,
0.03463785722851753,
-0.04403981566429138,
-0.008711072616279125,
-0.027477024123072624,
-0.05834849178791046,
0.04968304559588432,
0.05735906958580017,
-0.054405778646469116,
0.014408527873456478,
-0.03868890926241875,
0.0010785427875816822,
0.031089453026652336,
-0.02443580888211727,
0.009712175466120243,
-0.015026092529296875,
0.005114678759127855,
0.016156025230884552,
0.006547675002366304,
-0.027217671275138855,
0.02054714225232601,
-0.009800074622035027,
0.008596478030085564,
-0.03639410436153412,
0.019439904019236565,
-0.015805866569280624,
0.021160421893000603,
0.0011469792807474732,
-0.01664828509092331,
-0.03983798250555992,
0.05044608935713768,
0.002002582885324955,
0.08615484833717346,
0.07219438254833221,
-0.02665763534605503,
-0.02358209900557995,
-0.002563971094787121,
0.008941125124692917,
0.006018081214278936,
0.0071632880717515945,
-0.009607421234250069,
0.016666924580931664,
-0.010550240986049175,
-0.0019937362521886826,
0.0043333121575415134,
-0.06367776542901993,
0.0039995163679122925,
-0.038918547332286835,
-0.030401451513171196,
-0.005914279725402594,
-0.039604220539331436,
-0.020847920328378677,
-0.0022405933123081923,
0.00944049283862114,
0.020491568371653557,
0.08606259524822235,
-0.026476621627807617,
0.04722823575139046,
0.01577438786625862,
0.030044637620449066,
0.04789251089096069,
-0.016567662358283997,
0.03536466136574745,
-0.04416753351688385,
-0.047859858721494675,
-0.050032712519168854,
-0.049346376210451126,
-0.012966676615178585,
-0.030866893008351326,
0.037932902574539185,
-0.011627277359366417,
-0.015021012164652348,
0.0582289956510067,
-0.018663790076971054,
-0.009957464411854744,
-0.024903690442442894,
0.02113856002688408,
-0.030137671157717705,
0.045009586960077286,
-0.01432542409747839,
-0.044667940586805344,
-0.11069194227457047,
0.042030561715364456,
-0.05798695608973503,
-0.015521429479122162,
-0.035281699150800705,
0.10037580877542496,
0.006058019120246172,
0.04225695878267288,
-0.04885781928896904,
0.037428710609674454,
0.0366438589990139,
0.0037850027438253164,
0.04000088572502136,
-0.033487413078546524,
0.05044885724782944,
0.04332621023058891,
-0.0008057880331762135,
-0.03555329516530037,
0.002345545217394829,
0.010964439250528812,
0.051944147795438766,
-0.018302831798791885,
-0.042770758271217346,
0.016783103346824646,
-0.0017960662953555584,
-0.024570494890213013,
-0.006430373061448336,
0.03428418189287186,
0.08934495598077774,
-0.04730449244379997,
0.014535854570567608,
-0.07047242671251297,
0.014992077834904194,
0.022182894870638847,
0.016839683055877686,
0.010060571134090424,
-0.0033597038127481937,
-0.06906498223543167,
0.00768284359946847,
0.0013982844538986683,
-0.0067621502093970776,
-0.0015644278610125184,
0.00236848765052855,
0.010060695931315422,
-0.018046826124191284,
-0.055811427533626556,
-0.049083031713962555,
0.003058175789192319,
0.03928380459547043,
-0.026756368577480316,
0.036777984350919724,
0.02395182102918625,
0.058511894196271896,
0.04044950008392334,
-0.0102338632568717,
0.054580096155405045,
-0.024259600788354874,
0.03602517768740654,
0.012797646224498749,
-0.04268556460738182,
-0.009708297438919544,
0.0010381323518231511,
0.024304645135998726,
0.012738720513880253,
-0.018997760489583015,
0.013460250571370125,
0.09566756337881088,
-0.016818037256598473,
-0.041027821600437164,
-0.021327806636691093,
0.01017121784389019,
-0.036091528832912445,
0.014779339544475079,
0.023663632571697235,
-0.016430307179689407,
-0.04628005623817444,
0.020165609195828438,
-0.00046754124923609197,
-0.024196097627282143,
-0.00572573347017169,
-0.02028963342308998,
-0.014641967602074146,
-0.033699750900268555,
0.03535265475511551,
0.020589951425790787,
0.0035647470504045486,
0.027801336720585823,
0.0629909485578537,
-0.014485308900475502,
0.0265561044216156,
0.0028910369146615267,
0.0837910994887352,
0.003003408433869481,
-0.025170743465423584,
0.03873451054096222,
0.022528961300849915,
-0.07214835286140442,
-0.09380733221769333,
0.00800404790788889,
-0.02622690424323082,
-0.08196099102497101,
-0.012506702914834023,
0.0022204529959708452,
-0.005927137564867735,
-0.012790968641638756,
-0.016026590019464493,
0.06730136275291443,
-0.025131868198513985,
0.009812218137085438,
-0.012775297276675701,
-0.012859857641160488,
0.0045384070836007595,
-0.006727220024913549,
0.042513713240623474,
0.013569080270826817,
0.010219812393188477,
0.04184231534600258,
-0.01538016926497221,
-0.03376314043998718,
0.002579181920737028,
-0.03487912565469742,
-0.024960467591881752,
-0.04550594836473465,
-0.0486910454928875,
0.07907889783382416,
0.03496015444397926,
-0.04735749587416649,
-0.021352142095565796,
-0.0498308502137661,
-0.008819167502224445,
0.012983978725969791,
0.012606225907802582,
-0.006358178332448006,
0.03970206901431084,
-0.02336571365594864,
-0.03418128937482834,
0.0044204541482031345,
0.02874760515987873,
-0.005003097001463175,
-0.04275214299559593,
-0.0051951282657682896,
0.03392311558127403,
-0.013664993457496166,
-0.013763213530182838,
-0.029698098078370094
] |
<p>I had read somewhere that a star, whose light passes very close to the sun and reaches the earth produces 4 images of the same star (left, right, top and bottom) in a telescope due to gravitational lensing. However, this cannot be possible. Since light from the star passes on all sides of the sun (continuous 360 degrees) and bends to reach the earth, the star should be visible as a continuous ring around the sun. Is there any such star that appears as a continuous ring around the sun due to gravitational lensing? What is the reason for the 4 separate images and not the continuous ring?</p>
|
g48
|
[
-0.0115493293851614,
0.004164217971265316,
0.018836844712495804,
0.0034950997214764357,
-0.006173546425998211,
0.05217248946428299,
-0.0025027801748365164,
-0.023239662870764732,
-0.042946476489305496,
-0.002607201924547553,
0.0302116796374321,
0.04470086842775345,
0.05023062229156494,
-0.008161104284226894,
0.07059267163276672,
0.010852224193513393,
0.060089755803346634,
-0.0986609235405922,
0.010335124097764492,
0.02338239550590515,
0.008713656105101109,
0.07458458095788956,
0.00216036313213408,
0.023976419121026993,
-0.03424740582704544,
0.029566790908575058,
0.03972353786230087,
0.0009006711188703775,
0.0036179744638502598,
-0.022885719314217567,
0.01664028875529766,
-0.039904553443193436,
0.03913453221321106,
-0.04687780141830444,
0.0028453092090785503,
-0.023502275347709656,
0.02356872521340847,
-0.008119838312268257,
0.004141504876315594,
-0.029382405802607536,
0.012203823775053024,
-0.04020661115646362,
-0.013417710550129414,
0.015826711431145668,
0.041077010333538055,
-0.04425215348601341,
-0.002677774056792259,
0.012369793839752674,
0.05820094048976898,
-0.033621881157159805,
0.030962452292442322,
0.023351648822426796,
-0.005927450489252806,
-0.00883175153285265,
-0.019190384075045586,
0.014884380623698235,
0.029991041868925095,
0.016900697723031044,
0.01991409808397293,
-0.015419986099004745,
-0.005626138299703598,
0.041854020208120346,
-0.028654616326093674,
0.009195846505463123,
0.05760810896754265,
-0.014012793079018593,
-0.018985824659466743,
0.015448826365172863,
0.006299399770796299,
0.02335456758737564,
0.01526300236582756,
-0.0030014109797775745,
0.01864396221935749,
-0.012134629301726818,
0.004589783027768135,
-0.02310754731297493,
-0.016185518354177475,
0.006637423299252987,
-0.030243797227740288,
0.03048141486942768,
0.04021584615111351,
-0.003816727316007018,
-0.05936390906572342,
0.022403765469789505,
0.06325090676546097,
-0.03013371303677559,
-0.0008212285465560853,
-0.007885240018367767,
-0.03727879375219345,
-0.04310041293501854,
0.02162431925535202,
0.03365905582904816,
0.001526528038084507,
-0.011828002519905567,
0.013765046373009682,
-0.0037194581236690283,
0.00631302036345005,
0.06280845403671265,
-0.03160278499126434,
-0.0202488973736763,
-0.04541335254907608,
0.03995569422841072,
0.037140268832445145,
0.012898669578135014,
0.011210324242711067,
0.019656067714095116,
0.02313489094376564,
0.03626691550016403,
-0.00730188749730587,
-0.008823077194392681,
-0.018717464059591293,
-0.05984915792942047,
0.06394810229539871,
0.02634999342262745,
-0.1047096997499466,
-0.013841931708157063,
0.05247599631547928,
0.013727078214287758,
0.03941125422716141,
-0.006435910705476999,
-0.0027561774477362633,
0.01750732772052288,
0.009280032478272915,
0.06444878876209259,
-0.06733454763889313,
-0.019467419013381004,
0.05791281536221504,
-0.012040280736982822,
0.026079099625349045,
0.004571703262627125,
-0.04950571432709694,
0.010249209590256214,
-0.001685282215476036,
-0.017195405438542366,
0.041331034153699875,
0.006477683316916227,
-0.013093594461679459,
-0.014357047155499458,
-0.021643484011292458,
0.005473829340189695,
0.029890069738030434,
-0.008137372322380543,
0.04490962252020836,
0.01193320844322443,
-0.03379829600453377,
0.018193785101175308,
-0.015147050842642784,
-0.018378108739852905,
0.00473362673074007,
-0.00468906806781888,
0.022873325273394585,
0.07835306227207184,
0.011660357005894184,
0.011744941584765911,
-0.00841565616428852,
0.009550425224006176,
-0.028263254091143608,
-0.00551836472004652,
-0.004669580142945051,
0.02017524652183056,
0.06429605185985565,
-0.03609660267829895,
-0.0159502811729908,
-0.028830816969275475,
-0.07431052625179291,
0.06824257969856262,
0.0045855604112148285,
-0.03134586289525032,
-0.02043306455016136,
-0.02803746424615383,
-0.0032405266538262367,
-0.03242233768105507,
0.025011103600263596,
-0.023851428180933,
0.00660543330013752,
-0.0313691645860672,
0.06330102682113647,
-0.04085430130362511,
-0.013161343522369862,
0.0457061268389225,
-0.04450175166130066,
-0.012151246890425682,
-0.02047625370323658,
0.00021927093621343374,
0.027964789420366287,
-0.0023447878193110228,
0.00515807094052434,
-0.037883494049310684,
0.0040442668832838535,
0.03323138877749443,
0.0460481159389019,
-0.01890062354505062,
0.005307371262460947,
0.037579674273729324,
0.011654186993837357,
-0.04957791045308113,
0.02245938405394554,
-0.03286194056272507,
-0.012927775271236897,
0.052810266613960266,
-0.016016772016882896,
0.03475123643875122,
0.0304417721927166,
0.015091979876160622,
0.013127165846526623,
0.006753657013177872,
-0.02168395183980465,
0.03309210389852524,
0.029311157763004303,
-0.015422163531184196,
-0.022378310561180115,
-0.057669155299663544,
0.03899329900741577,
0.020746009424328804,
-0.04330289363861084,
-0.02583080716431141,
-0.03613626956939697,
0.01777009293437004,
0.021052848547697067,
0.04070451483130455,
0.00765394838526845,
0.04371843487024307,
0.03650389984250069,
-0.03427717462182045,
-0.045644961297512054,
0.012056085281074047,
-0.010445293970406055,
0.02213401347398758,
0.06550492346286774,
-0.011692930944263935,
-0.04259695112705231,
-0.022731663659214973,
0.025632495060563087,
0.004030164331197739,
0.024598345160484314,
-0.03891626372933388,
-0.009573739022016525,
0.024526312947273254,
-0.022092891857028008,
0.013950685039162636,
-0.015511203557252884,
-0.02082514390349388,
-0.042546167969703674,
-0.04353584721684456,
0.07113618403673172,
0.0003728712035808712,
0.008518434129655361,
0.039783768355846405,
-0.02283576689660549,
0.002494811313226819,
0.02406783401966095,
0.02759466879069805,
0.007342172786593437,
0.01846805214881897,
-0.0037930142134428024,
0.009714075364172459,
-0.03479047864675522,
0.06155535578727722,
-0.018254488706588745,
0.014552625827491283,
-0.03495250269770622,
-0.051975324749946594,
0.03951459378004074,
-0.029692551121115685,
-0.02853775955736637,
-0.006007061339914799,
-0.028601622208952904,
-0.01771894469857216,
0.034839410334825516,
0.04908936843276024,
-0.058425046503543854,
0.014384139329195023,
0.0413895919919014,
0.0028977871406823397,
-0.05085243284702301,
0.03537743538618088,
0.0005654918495565653,
-0.0010849006939679384,
-0.04888179898262024,
0.055633608251810074,
0.06090940907597542,
-0.003207940375432372,
-0.01762082614004612,
-0.02939825877547264,
0.0016599467489868402,
-0.035888999700546265,
-0.0008110211347229779,
0.009948669001460075,
0.030639773234725,
0.0029403045773506165,
0.000984532991424203,
0.01608782447874546,
0.034442901611328125,
0.01000417210161686,
0.0052866386249661446,
0.03969021514058113,
0.03672882169485092,
0.08663103729486465,
-0.03365081176161766,
0.012823617085814476,
-0.0028286564629524946,
-0.04293333739042282,
0.02043570764362812,
0.018256664276123047,
0.031468477100133896,
-0.007387068588286638,
-0.035203829407691956,
-0.0034859527368098497,
-0.007540932856500149,
-0.03781493380665779,
0.031773850321769714,
-0.006583899259567261,
0.02954251319169998,
0.08795581758022308,
0.046259988099336624,
-0.046686962246894836,
-0.04039972275495529,
-0.033267099410295486,
0.018758364021778107,
0.04700377956032753,
0.04489503800868988,
0.06270896643400192,
-0.01971672847867012,
-0.03129994869232178,
-0.00012344305287115276,
0.03964441642165184,
-0.07848727703094482,
-0.006808429956436157,
0.016316711902618408,
-0.039842408150434494,
-0.04800347238779068,
-0.020704397931694984,
-0.07035601139068604,
0.010338176973164082,
0.03510880470275879,
0.06747686117887497,
-0.06212744861841202,
0.008523736149072647,
0.12052346020936966,
0.03678935393691063,
0.013260331936180592,
0.05867183580994606,
-0.08817649632692337,
-0.021916856989264488,
0.00857627298682928,
-0.014436359517276287,
0.0028941654600203037,
-0.009508703835308552,
-0.02046869695186615,
0.008389631286263466,
0.006427127867937088,
-0.007763776928186417,
0.024115750566124916,
-0.04346612095832825,
-0.010682923719286919,
0.04523605853319168,
-0.05498909577727318,
0.042593684047460556,
0.047974005341529846,
-0.08079162985086441,
0.051237571984529495,
0.025090597569942474,
-0.018410827964544296,
0.031853143125772476,
0.036294445395469666,
0.000670040724799037,
0.07843761891126633,
-0.00946984812617302,
0.031676530838012695,
-0.016789330169558525,
0.03599446266889572,
-0.042295463383197784,
-0.03320987895131111,
-0.048688363283872604,
0.04714922234416008,
-0.007919210940599442,
0.019911132752895355,
0.010982070118188858,
-0.03454415872693062,
0.0778028592467308,
0.0075176432728767395,
0.06720393896102905,
0.04195297509431839,
0.01347624883055687,
0.024008136242628098,
-0.03524188697338104,
-0.005387159530073404,
-0.10105112195014954,
-0.011850190348923206,
-0.05793813616037369,
0.057963158935308456,
-0.0736246407032013,
0.055065542459487915,
-0.026653923094272614,
-0.021243587136268616,
-0.043947163969278336,
-0.003549071028828621,
0.00047854933654889464,
0.017563415691256523,
-0.026128515601158142,
0.06663431227207184,
-0.036723542958498,
-0.004774345085024834,
-0.007731049321591854,
-0.0537898950278759,
-0.016548072919249535,
-0.02192322351038456,
0.04666208475828171,
0.007754983846098185,
0.060548387467861176,
-0.006304583046585321,
0.011484895832836628,
-0.007187139708548784,
-0.027373231947422028,
0.12155551463365555,
0.044032055884599686,
0.013660659082233906,
0.02428169548511505,
0.019672734662890434,
-0.036716435104608536,
-0.04621608927845955,
0.05777163803577423,
-0.025267601013183594,
-0.01809677667915821,
0.06251777708530426,
0.09876834601163864,
0.022469641640782356,
-0.027803409844636917,
-0.0596664696931839,
0.061559513211250305,
0.05691933259367943,
0.02466062642633915,
0.023222217336297035,
-0.027127891778945923,
0.0009959718445315957,
0.015762457624077797,
-0.07320805639028549,
0.030804581940174103,
-0.015192304737865925,
0.020799754187464714,
0.026693502441048622,
-0.021469516679644585,
0.048966944217681885,
-0.03054565005004406,
-0.014290669932961464,
0.03503631055355072,
0.010082187131047249,
-0.029693543910980225,
-0.04611143097281456,
-0.015059398487210274,
-0.06253717094659805,
-0.059769824147224426,
-0.04936785623431206,
0.011264118365943432,
-0.026368306949734688,
-0.04460522159934044,
-0.06029363349080086,
-0.036118507385253906,
-0.0009252747404389083,
0.03744858130812645,
0.003356996225193143,
-0.0025309354532510042,
0.013550241477787495,
0.07399702817201614,
0.03670601174235344,
-0.022115344181656837,
-0.05856702849268913,
0.001985111040994525,
0.016271021217107773,
-0.008025206625461578,
-0.021530993282794952,
0.08128390461206436,
0.0032627175096422434,
0.041597794741392136,
-0.04872704669833183,
-0.050479091703891754,
-0.07820255309343338,
0.010057592764496803,
0.03673265501856804,
-0.006648305803537369,
0.0037445947527885437,
-0.013515871949493885,
0.020093604922294617,
-0.02619653381407261,
-0.01262152474373579,
0.06306730955839157,
-0.0021044029854238033,
-0.006910873111337423,
-0.012545723468065262,
0.01581772416830063,
-0.0775638222694397,
-0.08067925274372101,
0.0571458637714386,
-0.05230807512998581,
0.0413612425327301,
-0.04850967973470688,
0.04598649591207504,
-0.022897545248270035,
0.03178605064749718,
0.06673885136842728,
0.02808673493564129,
-0.03622240945696831,
-0.003960549831390381,
-0.0007450693519786,
0.021679464727640152,
0.04757922142744064,
-0.0165361687541008,
-0.040443550795316696,
0.01831095851957798,
0.06702183932065964,
-0.03498188778758049,
-0.011102872900664806,
-0.017865773290395737,
0.023566966876387596,
-0.02776823192834854,
-0.03435669094324112,
-0.03885443136096001,
0.001470277551561594,
0.01158994622528553,
0.0005047914455644786,
-0.030755292624235153,
-0.02962641231715679,
-0.016466842964291573,
0.017993027344346046,
0.08059138804674149,
-0.025725441053509712,
0.002853126497939229,
0.06378105282783508,
-0.0007039703777991235,
-0.038375791162252426,
0.024417517706751823,
-0.008132812567055225,
0.04241856560111046,
-0.005808406509459019,
0.03656686842441559,
-0.03668118640780449,
0.02914426103234291,
0.03409898281097412,
0.00843321904540062,
-0.016535675153136253,
-0.017856266349554062,
-0.02906103804707527,
0.03259427100419998,
0.04879530519247055,
0.0024117070715874434,
-0.0197792649269104,
-0.0069410777650773525,
0.02628706395626068,
-0.0010582961840555072,
-0.010586418211460114,
0.012410982511937618,
0.07155145704746246,
-0.02006351947784424,
0.011346140876412392,
-0.04289684817194939,
0.019794678315520287,
-0.05964318662881851,
-0.003452942706644535,
0.02546166069805622,
-0.06455369293689728,
0.06950652599334717,
-0.023054784163832664,
-0.027681546285748482,
-0.0007943937671370804,
-0.06087660416960716,
-0.06338412314653397,
0.0042443969286978245,
-0.01281373854726553,
0.07676663994789124,
0.021510131657123566,
-0.012741061858832836,
0.0028542298823595047,
-0.026312904432415962,
0.027213329449295998,
0.011208303272724152,
-0.033683355897665024,
-0.004483608994632959,
0.06290074437856674,
-0.027719199657440186,
-0.003461041720584035,
0.05959494411945343,
0.004514642991125584,
-0.012409239076077938,
-0.04925074428319931,
0.031087853014469147,
-0.029240481555461884,
-0.037707068026065826,
-0.04131019860506058,
-0.015448876656591892,
-0.05940369516611099,
-0.024639034643769264,
-0.03533343970775604,
-0.029385391622781754,
0.015031255781650543,
-0.021575668826699257,
0.0008688017842359841,
-0.03871222957968712,
0.09031815826892853,
-0.05943022668361664,
0.002419200260192156,
0.009614834561944008,
-0.022879846394062042,
0.08698832243680954,
0.015146223828196526,
-0.02748360112309456,
0.012285537086427212,
-0.05575747415423393,
-0.03104274906218052,
0.09294974058866501,
-0.00005766322647104971,
0.019131718203425407,
0.023939786478877068,
0.01150078047066927,
0.0216897614300251,
-0.035286836326122284,
-0.018883997574448586,
-0.07508864998817444,
-0.04825802147388458,
0.020837610587477684,
-0.029923008754849434,
0.0030887103639543056,
-0.023014187812805176,
-0.06385792046785355,
-0.013087904080748558,
-0.004437969531863928,
0.03492574766278267,
-0.003448000643402338,
0.008755464106798172,
-0.02720576710999012,
0.03307923302054405,
-0.05968613177537918,
-0.06695765256881714,
-0.05511737987399101,
0.031445495784282684,
0.04939109832048416,
-0.03823210671544075,
-0.04788648337125778,
0.029795410111546516,
-0.003541188081726432,
-0.003051299601793289,
0.003561551682651043,
-0.028100265190005302,
0.02207266353070736,
0.039148543030023575,
0.03903764486312866,
-0.032019130885601044,
-0.01727820374071598,
-0.05918256565928459,
-0.05672505497932434,
0.025687461718916893,
-0.022625278681516647,
-0.016831664368510246,
-0.013138738460838795,
0.03929177671670914,
-0.03995129466056824,
0.031069833785295486,
-0.017890801653265953,
-0.03207607567310333,
-0.008631543256342411,
-0.031509481370449066,
0.004197028931230307,
-0.0025448244996368885,
-0.02234712988138199,
-0.02954191528260708,
-0.013387109152972698,
-0.0173883568495512,
0.06180723011493683,
-0.05656062439084053,
-0.02681448869407177,
0.03828296810388565,
0.04829965904355049,
0.04013359546661377,
0.02467210963368416,
0.019178811460733414,
-0.03293762728571892,
-0.005058269947767258,
-0.01946675032377243,
0.04527873545885086,
-0.003660189686343074,
-0.0378497913479805,
-0.04053831100463867,
0.06023485213518143,
0.030925840139389038,
0.017874129116535187,
-0.018110277131199837,
0.0062062498182058334,
-0.028588570654392242,
-0.007859008386731148,
0.038505956530570984,
-0.04900423064827919,
0.009057117626070976,
0.07310580462217331,
0.03307409584522247,
-0.03266346827149391,
0.008443087339401245,
0.03804458677768707,
0.002960952464491129,
-0.015468352474272251,
-0.0037716301158070564,
-0.013448318466544151,
-0.05235094204545021,
0.027348410338163376,
0.012243028730154037,
-0.07245230674743652,
0.058758076280355453,
-0.014955291524529457,
-0.07739269733428955,
0.05040832236409187,
-0.0027270889841020107,
-0.0117125129327178,
0.06245644763112068,
0.01699719950556755,
-0.06052475422620773,
-0.04017767310142517,
-0.005834177136421204,
-0.014765050262212753,
-0.0442851223051548,
-0.030116060748696327,
0.022800564765930176,
-0.016965828835964203,
-0.05185559764504433,
-0.03808683529496193,
-0.023986075073480606,
-0.03224960342049599,
0.004375888966023922,
-0.014642879366874695,
0.029904525727033615,
-0.04755060374736786,
0.01542738825082779,
-0.018958620727062225,
-0.0007001967751421034,
0.05585057660937309,
-0.06217839568853378,
-0.048150837421417236,
-0.012834606692194939,
-0.02228708751499653,
0.001378027955070138,
-0.05096587911248207,
0.021329697221517563,
0.002594111952930689,
-0.03809370473027229,
-0.07231100648641586,
0.02002866379916668,
-0.0548345223069191,
0.01645773835480213,
0.03385985270142555,
-0.05217374116182327,
-0.015134885907173157,
0.0201561376452446,
-0.03053397685289383,
-0.004593859426677227,
0.08765115588903427,
0.06578194350004196,
0.016213947907090187,
0.006367572117596865,
-0.011568315327167511,
-0.0420292429625988,
0.005473139695823193,
-0.019020790234208107,
-0.03173290193080902,
-0.027106480672955513,
-0.025674765929579735,
-0.0030292950104922056,
-0.02214721217751503,
0.0047489190474152565,
-0.06194033846259117,
0.018075909465551376,
0.02641846239566803
] |
<p>As far as I understand a new pattern of crystal growth has been found experimentally. How does it relate to the known 2D and 3D nucleation and growth of crystals? The dominating theory of crystal growth nowadays is that initiated by Cabrera and Frank. How is the new finding related to what we know so far or is it at odds with what we know and how?</p>
|
g2493
|
[
0.042984556406736374,
0.05666572228074074,
-0.0011122687719762325,
0.02531290054321289,
-0.008225351572036743,
0.06912925094366074,
0.04321371018886566,
-0.024259289726614952,
-0.014436676166951656,
-0.0669131800532341,
-0.0018964182818308473,
-0.04534098133444786,
0.06766759604215622,
-0.024640759453177452,
0.003911727108061314,
0.02323167398571968,
0.03388729318976402,
-0.06038312241435051,
-0.049506738781929016,
0.03811711445450783,
-0.012232476845383644,
0.010419294238090515,
-0.006026524119079113,
0.004171750973910093,
-0.049818478524684906,
0.1005612164735794,
-0.021231621503829956,
-0.03501260280609131,
-0.005580403842031956,
-0.013831072486937046,
0.07480381429195404,
0.025698712095618248,
0.04653988033533096,
-0.006447272375226021,
0.007232150994241238,
-0.040496405214071274,
0.02722250670194626,
0.05247558653354645,
0.023836996406316757,
0.0068082199431955814,
-0.05305640026926994,
-0.011164985597133636,
-0.009146599099040031,
0.02202475816011429,
-0.06568705290555954,
-0.0328141450881958,
-0.04846261814236641,
0.006410015281289816,
-0.03238062560558319,
-0.025405025109648705,
0.000670450332108885,
0.062069300562143326,
0.08424750715494156,
-0.039940811693668365,
-0.009878040291368961,
0.07932231575250626,
0.01870724931359291,
-0.0073347315192222595,
0.09593012928962708,
-0.07707881182432175,
0.014455664902925491,
0.03749101981520653,
0.0336293950676918,
0.005013962276279926,
0.046657029539346695,
-0.030639788135886192,
-0.058946263045072556,
0.007058404851704836,
-0.00955889467149973,
-0.029158396646380424,
-0.03182269632816315,
-0.01761111617088318,
-0.014401990920305252,
-0.00356827094219625,
-0.02910517156124115,
-0.044126205146312714,
0.0553760826587677,
-0.0497300885617733,
-0.026305602863430977,
0.0020381140056997538,
0.0049020275473594666,
-0.02309201844036579,
-0.03420388698577881,
0.02247611992061138,
0.05748216062784195,
0.020572775974869728,
-0.012096166610717773,
0.01262913178652525,
-0.0379134826362133,
0.004063363652676344,
-0.03805571421980858,
0.01653059758245945,
-0.009863137267529964,
-0.006564546842128038,
0.039462413638830185,
0.017032375559210777,
0.009814249351620674,
-0.012835587374866009,
-0.014005433768033981,
0.04239784926176071,
0.0027597935404628515,
-0.0023433840833604336,
0.0465354286134243,
0.01248866505920887,
0.02482754737138748,
0.03672904521226883,
0.010312482714653015,
-0.033075302839279175,
-0.0036707590334117413,
0.06869932264089584,
-0.048636674880981445,
0.015304338186979294,
0.0005548691842705011,
0.0481765940785408,
-0.0042694634757936,
-0.02828257717192173,
0.021407490596175194,
0.04283025488257408,
0.04982178285717964,
0.015773959457874298,
0.03801167383790016,
0.031313732266426086,
0.03308878093957901,
0.05744597688317299,
0.02128187194466591,
0.014740968123078346,
0.021128715947270393,
-0.021377403289079666,
-0.030162762850522995,
0.017458345741033554,
0.037723567336797714,
0.014091169461607933,
-0.02712758630514145,
-0.03520503640174866,
0.0448869913816452,
-0.006861817091703415,
-0.0063149286434054375,
0.030883347615599632,
0.02620835229754448,
-0.004266950301826,
-0.0570688359439373,
0.014111218973994255,
-0.03526562079787254,
0.020118538290262222,
0.017977403476834297,
-0.012353929691016674,
0.01844262331724167,
0.08198373764753342,
-0.014385079964995384,
-0.010226856917142868,
-0.051220666617155075,
0.0408158116042614,
0.014994939789175987,
-0.0867069885134697,
-0.07622276991605759,
0.022812440991401672,
-0.015996776521205902,
-0.018741415813565254,
0.015420441515743732,
0.0006932965479791164,
0.016550136730074883,
-0.0691928043961525,
-0.03227835148572922,
-0.02365020103752613,
-0.03454636409878731,
-0.012582934461534023,
0.027211207896471024,
0.0014323546783998609,
0.007190135773271322,
0.0012804385041818023,
-0.04528813436627388,
0.017852071672677994,
-0.02935664914548397,
0.011327198706567287,
-0.021235277876257896,
0.045238424092531204,
0.06009673327207565,
-0.05598282441496849,
0.08534202724695206,
-0.005459394305944443,
-0.05808408930897713,
-0.043990738689899445,
-0.031311146914958954,
0.00010747562191681936,
0.01986594684422016,
0.01850246824324131,
0.034544702619314194,
-0.017936302348971367,
0.013582763262093067,
0.007973757572472095,
0.0017166966572403908,
-0.03975555673241615,
-0.017397703602910042,
0.038810327649116516,
0.03135927394032478,
0.012721423991024494,
0.0327051505446434,
-0.011916936375200748,
0.0034859355073422194,
0.026132622733712196,
-0.0347311832010746,
0.037026211619377136,
-0.029254449531435966,
-0.009640064090490341,
0.060080934315919876,
0.01460390817373991,
-0.06418123096227646,
-0.00031325488816946745,
0.028653375804424286,
0.04658600315451622,
-0.06489300727844238,
0.015410840511322021,
-0.007792986463755369,
-0.022396616637706757,
0.018981589004397392,
0.006689330097287893,
0.0640021488070488,
0.0024428891483694315,
0.03704645484685898,
0.01717170886695385,
-0.023045150563120842,
0.020936578512191772,
-0.023072153329849243,
0.009086936712265015,
0.05316048115491867,
-0.02066541649401188,
-0.0013249492039903998,
-0.026424430310726166,
0.02552586793899536,
0.031012263149023056,
-0.09565778821706772,
-0.009842422790825367,
0.001948983408510685,
-0.011953507550060749,
0.05752020329236984,
-0.018405873328447342,
-0.07572978734970093,
0.00023692904505878687,
0.012370497919619083,
0.04551641643047333,
-0.015351232141256332,
-0.024654880166053772,
-0.06445775926113129,
-0.0004745592304971069,
0.02215607836842537,
-0.07423875480890274,
0.0568305142223835,
0.00039776015910319984,
-0.045648157596588135,
0.02969973348081112,
0.10279065370559692,
-0.0038057928904891014,
-0.02427416481077671,
-0.00940264668315649,
-0.020863063633441925,
0.00644574873149395,
-0.021552391350269318,
0.060738205909729004,
-0.03921385481953621,
-0.05532743036746979,
0.042196035385131836,
0.006711665540933609,
0.02405863255262375,
-0.02403801493346691,
-0.032583869993686676,
-0.04468102380633354,
-0.004770106170326471,
0.010127529501914978,
-0.05746257305145264,
-0.02938084676861763,
-0.019799496978521347,
0.016716208308935165,
0.0027065712492913008,
-0.017240077257156372,
-0.09249391406774521,
-0.025549594312906265,
0.07198643684387207,
-0.01502959430217743,
0.00690464535728097,
-0.014003592543303967,
-0.029942452907562256,
-0.021624097600579262,
-0.03301239386200905,
0.006029067561030388,
0.004706233274191618,
0.03043362870812416,
0.03213026002049446,
-0.09007660299539566,
0.016831323504447937,
0.026790786534547806,
0.022398101165890694,
-0.023816252127289772,
-0.034174252301454544,
0.039672985672950745,
0.0019436231814324856,
-0.011505312286317348,
0.0110783027485013,
0.00625859759747982,
-0.046417485922575,
0.0385131873190403,
-0.025846382603049278,
-0.06372252106666565,
-0.024491701275110245,
-0.02526998147368431,
0.053095899522304535,
0.04482198506593704,
-0.024908889085054398,
-0.012385500594973564,
-0.012485099025070667,
-0.0465429313480854,
-0.021437179297208786,
0.04579208046197891,
0.017600011080503464,
-0.011350478045642376,
-0.03980998322367668,
-0.028043624013662338,
-0.03211767226457596,
0.10294568538665771,
0.03488452360033989,
-0.015831664204597473,
-0.04342975467443466,
0.010415220633149147,
-0.00022444501519203186,
0.007655804976820946,
0.022047901526093483,
0.02509012632071972,
-0.017630379647016525,
0.018401488661766052,
-0.036360420286655426,
-0.019474102184176445,
-0.0068849800154566765,
-0.02333017811179161,
-0.040488794445991516,
-0.020064860582351685,
0.035733334720134735,
-0.037547897547483444,
0.004660774488002062,
0.058302756398916245,
0.04075487703084946,
-0.008429544977843761,
-0.001343029784038663,
0.03817809000611305,
-0.0484711118042469,
-0.01314111240208149,
0.03595736622810364,
-0.017538337036967278,
-0.056790124624967575,
0.010137970559298992,
-0.03779541701078415,
0.01926415227353573,
0.017261259257793427,
0.006201120093464851,
-0.028391018509864807,
0.04726643115282059,
0.02825634554028511,
0.046558793634176254,
-0.029830124229192734,
0.021309051662683487,
0.003528453642502427,
-0.09061046689748764,
-0.009325244463980198,
0.0007675375090911984,
0.05671914666891098,
0.005384525284171104,
-0.020978646352887154,
-0.0009211615542881191,
0.007661761716008186,
-0.043226711452007294,
0.03457770124077797,
-0.03806200623512268,
-0.0019472204148769379,
-0.07563167810440063,
0.0019838728476315737,
-0.006054847501218319,
0.012691531330347061,
0.05372624471783638,
0.0032070332672446966,
0.021750595420598984,
-0.02766510657966137,
0.014487775973975658,
0.008085300214588642,
0.008958308957517147,
0.018672354519367218,
0.004752364940941334,
-0.06241702288389206,
0.00939883105456829,
-0.09305793046951294,
-0.0017723528435453773,
-0.10203076899051666,
-0.025451181456446648,
0.043507348746061325,
0.03013523295521736,
-0.04260750859975815,
0.01907893642783165,
-0.023495694622397423,
-0.03494725748896599,
0.048253245651721954,
0.0228382870554924,
0.013891288079321384,
-0.02366825006902218,
-0.004306423012167215,
-0.04228391870856285,
-0.06181397661566734,
-0.047770798206329346,
-0.03884895145893097,
-0.011344637721776962,
-0.003471788950264454,
-0.018199089914560318,
0.006592248100787401,
-0.012824046425521374,
0.0340864397585392,
0.026553412899374962,
0.011609354056417942,
-0.060231178998947144,
0.0747096911072731,
-0.03619561344385147,
-0.011137190274894238,
-0.02598947286605835,
0.03939255699515343,
0.021214909851551056,
-0.0007268433109857142,
0.009045877493917942,
-0.029180917888879776,
0.014039075002074242,
0.024961208924651146,
0.05356220528483391,
0.011446774005889893,
-0.04974978789687157,
-0.013235350139439106,
-0.06544919312000275,
0.08046722412109375,
0.01626819744706154,
0.025704436004161835,
0.008763274177908897,
-0.02313266508281231,
-0.00801091454923153,
-0.03473471477627754,
0.07695332169532776,
-0.020867014303803444,
0.03952498361468315,
0.05116252601146698,
0.03606606647372246,
0.01809130795300007,
0.034154411405324936,
0.09048006683588028,
-0.002995067974552512,
-0.009255840443074703,
0.033016305416822433,
0.03387334942817688,
0.03278488665819168,
0.013568473979830742,
0.04905303567647934,
0.030887950211763382,
-0.04339019954204559,
0.036407940089702606,
-0.029741430655121803,
-0.05423791706562042,
0.05675078555941582,
0.01674952730536461,
0.023993149399757385,
-0.03580952063202858,
-0.04375932738184929,
0.05408892035484314,
0.008673942647874355,
0.030469488352537155,
-0.07794798165559769,
-0.021687770262360573,
-0.07610198855400085,
-0.03024175949394703,
-0.019694799557328224,
-0.03562702611088753,
-0.021191533654928207,
0.02689371444284916,
0.019056284800171852,
0.002841176465153694,
-0.10146570950746536,
0.0005709687247872353,
-0.017532698810100555,
0.0635451152920723,
-0.02819075807929039,
0.029043862596154213,
0.03491765633225441,
0.026421625167131424,
0.026525048539042473,
-0.006850890349596739,
0.008561980910599232,
-0.0374094657599926,
-0.002343128900974989,
-0.038523200899362564,
-0.02575235441327095,
0.024708373472094536,
-0.053555164486169815,
0.028241122141480446,
0.09401585161685944,
-0.038519419729709625,
-0.03960812836885452,
0.0555645115673542,
0.03499988839030266,
-0.009272814728319645,
0.03196442872285843,
-0.04892761632800102,
0.07048465311527252,
0.04189569130539894,
-0.02282528206706047,
0.04375026002526283,
0.05116569250822067,
0.0670991837978363,
-0.06047545000910759,
0.009439872577786446,
0.0010711346985772252,
-0.0029176175594329834,
-0.034448157995939255,
0.01467287726700306,
-0.02174273319542408,
-0.0075571537017822266,
-0.04362461343407631,
0.03293482959270477,
-0.03711910545825958,
0.0017276180442422628,
-0.04500024765729904,
-0.044290464371442795,
0.0036868033930659294,
-0.03404572606086731,
-0.07494547218084335,
0.0537431463599205,
0.013554174453020096,
-0.018576858565211296,
0.04463588446378708,
0.04898099973797798,
0.02138517238199711,
-0.03832026198506355,
-0.01391682866960764,
0.02304743602871895,
0.026025282219052315,
-0.0039376504719257355,
0.017569677904248238,
-0.007083620876073837,
0.05798245966434479,
-0.007963745854794979,
-0.0014131112257018685,
0.022333763539791107,
0.031289055943489075,
0.031310949474573135,
0.06934218108654022,
0.01761918142437935,
0.011230790987610817,
0.01587601564824581,
0.026091495528817177,
0.05751176178455353,
-0.009937576949596405,
-0.03923402354121208,
-0.02472214587032795,
0.008815762586891651,
0.026747845113277435,
-0.03421030938625336,
0.01909557916224003,
-0.07463563233613968,
-0.019782675430178642,
-0.01770532876253128,
-0.05607180669903755,
-0.020164871588349342,
0.034973807632923126,
0.03190718963742256,
0.014291943982243538,
-0.0100411307066679,
-0.04108843952417374,
0.00400752667337656,
-0.029288699850440025,
0.058993514627218246,
0.01949218660593033,
0.012102791108191013,
0.03826506435871124,
0.024171141907572746,
0.015844058245420456,
-0.03640631586313248,
-0.015266209840774536,
-0.029358256608247757,
0.000637276389170438,
0.004343261942267418,
0.0012405477464199066,
0.0135509567335248,
0.03171562775969505,
0.010929198004305363,
0.02307792566716671,
0.018953530117869377,
-0.016108348965644836,
0.026796652004122734,
0.01872946135699749,
-0.04937545582652092,
-0.041007284075021744,
-0.04829676076769829,
0.019605696201324463,
-0.0414571575820446,
-0.030627643689513206,
-0.02197081595659256,
-0.022418782114982605,
-0.01262587122619152,
0.020189212635159492,
-0.05217260867357254,
-0.03813773766160011,
-0.005356461741030216,
-0.0011189206270501018,
0.04051539674401283,
-0.020335854962468147,
0.00499895540997386,
0.01261918991804123,
-0.012705875560641289,
0.05652201175689697,
0.0329139344394207,
0.02774677239358425,
0.00918184220790863,
0.020503275096416473,
-0.004705270752310753,
0.014668584801256657,
0.0046446979977190495,
-0.06742867082357407,
0.013462753035128117,
0.01895769126713276,
0.02343122474849224,
0.019912077113986015,
0.03478751331567764,
-0.0008311030687764287,
-0.033106729388237,
-0.05838446691632271,
0.0197126567363739,
0.020437926054000854,
-0.06463459879159927,
-0.049292463809251785,
0.0279505904763937,
0.04465746879577637,
-0.06952451914548874,
-0.04686068743467331,
-0.019992023706436157,
0.09387784451246262,
-0.003670341335237026,
-0.042816270142793655,
0.011123918928205967,
0.040226053446531296,
0.04467669874429703,
-0.050833214074373245,
0.013844529166817665,
-0.029058465734124184,
-0.004070970229804516,
0.004417741671204567,
-0.026276670396327972,
-0.007809382397681475,
-0.01464980561286211,
-0.02038564160466194,
0.007606001105159521,
0.00391734391450882,
-0.007296182215213776,
0.0015399750554934144,
-0.019825831055641174,
-0.027960194274783134,
0.00335528701543808,
0.004170025698840618,
0.000019044793589273468,
0.0019451756961643696,
0.006468769162893295,
-0.0445120632648468,
-0.09555045515298843,
0.052937306463718414,
0.013690982013940811,
-0.020067160949110985,
-0.0006177622708491981,
-0.014950855635106564,
0.007559169549494982,
0.008816969580948353,
-0.0061659743078053,
-0.01436472125351429,
0.00974037405103445,
-0.00974136870354414,
0.014537080191075802,
0.05262283980846405,
-0.0581701323390007,
0.04225803166627884,
0.02597179263830185,
-0.04426056519150734,
0.02155734971165657,
0.010510735213756561,
0.06843101978302002,
0.054671745747327805,
0.039151474833488464,
-0.022661928087472916,
0.001526550273410976,
0.052792344242334366,
-0.0684821829199791,
-0.004565113224089146,
-0.06911943107843399,
-0.03272450342774391,
0.0026186343748122454,
0.0015791498590260744,
0.02887502685189247,
-0.04247472435235977,
0.004860967863351107,
0.010439456440508366,
0.016693327575922012,
0.025477949529886246,
-0.03969237208366394,
0.03631817549467087,
0.001957391621544957,
0.014581738971173763,
-0.062226302921772,
0.031573764979839325,
0.023362133651971817,
-0.0031856915447860956,
0.038379326462745667,
0.016762878745794296,
0.007138226646929979,
-0.037094347178936005,
-0.04240686818957329,
-0.014976633712649345,
0.05367380380630493,
0.004370683338493109,
0.04648391529917717,
0.015584289096295834,
0.02624192088842392,
-0.0425867959856987,
0.0007007668609730899,
0.00406108982861042,
-0.05475246533751488,
-0.04417744278907776,
-0.019530480727553368,
-0.07432624697685242,
0.02882751263678074,
0.008658763021230698,
0.02491176687180996,
0.00853037554770708,
0.022154590114951134,
0.048092376440763474,
-0.00269912788644433,
-0.049739789217710495,
0.023522425442934036,
0.043317049741744995,
-0.04461642727255821,
0.06103019788861275,
0.05723698437213898,
-0.01325584203004837,
-0.020582037046551704,
-0.05334223061800003,
-0.0029716086573898792,
0.06323307007551193,
-0.004677799064666033,
-0.07916063070297241,
-0.02352866902947426,
-0.03450319543480873,
-0.021983901038765907,
0.0705081894993782,
0.05415314435958862,
-0.048643968999385834,
-0.06659293174743652,
-0.002637083176523447,
0.04000076279044151,
0.0033442850690335035,
0.01989266462624073,
-0.02482766844332218,
0.00578330596908927,
0.04981307312846184,
0.000807609932962805,
-0.040998343378305435,
-0.006803659722208977,
0.01729842647910118,
-0.03320857509970665,
-0.06251338869333267,
0.013151834718883038,
0.0161808580160141,
-0.020632857456803322,
-0.006235851440578699
] |
<p>When judging if relativity is important in a given phenomenon, we might examine the number $v/c$, with $v$ a typical velocity of the object. If this number is near one, relativity is important. In optics, we examine $\lambda/d$, with $\lambda$ the wavelength of light involved, and $d$ a typical size-scale for the object interacting with light. If this number is near one, physical optics becomes important. In fluid mechanics we have the Reynolds number, etc.</p>
<p>Can we compute a number to tell roughly when a gas will deviate significantly from the ideal gas law?</p>
<p>For simplicity, you may want to deal only with a monatomic gas, but a more general approach would be welcome.</p>
|
g2494
|
[
-0.0382084883749485,
0.04822596162557602,
-0.0006075856508687139,
-0.01870960183441639,
0.008485927246510983,
-0.06361383199691772,
-0.009800972416996956,
0.02205800823867321,
-0.031586188822984695,
-0.022539548575878143,
0.07694731652736664,
-0.01235125306993723,
0.0680202767252922,
0.013819616287946701,
0.013005487620830536,
-0.03315147012472153,
0.0004982174141332507,
-0.04408091679215431,
0.03932378441095352,
0.003190042218193412,
-0.01935466378927231,
-0.023155013099312782,
0.022071901708841324,
-0.08385808020830154,
0.015135311521589756,
0.015669556334614754,
0.05483842268586159,
-0.001102738082408905,
-0.09138250350952148,
0.0027015581727027893,
0.008693273179233074,
0.006898817606270313,
0.004047849681228399,
-0.05397230386734009,
-0.028103526681661606,
-0.028825554996728897,
0.007358891889452934,
0.0535636730492115,
0.018099864944815636,
-0.031381987035274506,
0.04494659602642059,
-0.003727230243384838,
-0.012891956605017185,
0.011603091843426228,
0.023737041279673576,
0.010613026097416878,
-0.0010297979461029172,
-0.012201645411550999,
0.03650553151965141,
-0.010609302669763565,
0.03149109706282616,
0.05132010951638222,
0.008992830291390419,
0.028500745072960854,
0.047098904848098755,
0.058190446346998215,
-0.013287748210132122,
-0.019080543890595436,
0.05229233205318451,
0.006035394500941038,
0.02345300279557705,
-0.040776610374450684,
-0.019763708114624023,
-0.00925653986632824,
0.02739422768354416,
0.03221755474805832,
-0.04734101518988609,
-0.03158179670572281,
0.005057951435446739,
-0.030364254489541054,
-0.0028235262725502253,
-0.01004247646778822,
0.02685718610882759,
-0.02963598072528839,
-0.11014652252197266,
0.0035389524418860674,
-0.04841320216655731,
0.001279883668757975,
-0.017950888723134995,
0.002811398822814226,
-0.027797872200608253,
-0.014382407069206238,
0.01830807887017727,
0.018865788355469704,
0.07129260152578354,
0.011023993603885174,
0.000056295575632248074,
-0.02951768785715103,
0.04245029762387276,
0.06621620059013367,
0.05990045145153999,
-0.0069326297380030155,
0.07254166901111603,
0.007402854040265083,
0.014950123615562916,
-0.01408430840820074,
0.022380968555808067,
0.05271579697728157,
0.00321446661837399,
0.009967108257114887,
-0.017135491594672203,
-0.004731298424303532,
-0.03588584437966347,
-0.013986600562930107,
-0.031424157321453094,
0.03686051070690155,
0.008127538487315178,
0.05298331752419472,
-0.0030472460202872753,
-0.05050232633948326,
-0.05990369990468025,
-0.03797953203320503,
-0.035173509269952774,
-0.03257810324430466,
-0.06706170737743378,
-0.032445453107357025,
0.03509999066591263,
-0.011058472096920013,
-0.032124511897563934,
0.08193418383598328,
0.00038215049426071346,
0.06556601077318192,
0.07057411968708038,
0.04552850127220154,
0.0037726599257439375,
-0.03642541915178299,
0.0022697323001921177,
-0.0028144826646894217,
0.020270565524697304,
-0.028055155649781227,
0.020611606538295746,
-0.007879837416112423,
0.030282704159617424,
-0.004230870865285397,
-0.06317010521888733,
0.035699114203453064,
0.029028743505477905,
0.040764302015304565,
0.003969689831137657,
-0.002264862647280097,
0.08120337128639221,
-0.03600723296403885,
0.0006035856786184013,
-0.004499156028032303,
-0.04563194513320923,
-0.020141972228884697,
-0.05698850750923157,
0.021865444257855415,
0.0337911993265152,
-0.061267293989658356,
0.017726436257362366,
0.08290183544158936,
0.023159315809607506,
-0.027938492596149445,
-0.02812146209180355,
-0.03549952432513237,
-0.0024711918085813522,
0.01225824374705553,
-0.053510215133428574,
-0.022260861471295357,
0.04800037667155266,
0.003000951139256358,
-0.013638466596603394,
0.01448576059192419,
-0.03644450753927231,
0.005148965399712324,
-0.012806600891053677,
-0.04087906330823898,
-0.0026646461337804794,
-0.022600270807743073,
-0.038687191903591156,
-0.011512053199112415,
0.05750889331102371,
0.0074570574797689915,
0.0003129781689494848,
0.0328637920320034,
0.024782147258520126,
0.019905628636479378,
-0.019828617572784424,
0.04953712224960327,
0.00926718208938837,
-0.07865666598081589,
0.014302102848887444,
-0.04701881855726242,
-0.024133680388331413,
-0.005320449825376272,
0.0023211936932057142,
-0.05375543236732483,
-0.07436567544937134,
0.005001188721507788,
-0.028264962136745453,
0.00417758384719491,
0.011011462658643723,
0.008130415342748165,
-0.05402306467294693,
0.0009599964250810444,
0.020441269502043724,
-0.011284281499683857,
-0.0904063805937767,
0.03382212668657303,
-0.026230424642562866,
0.06674903631210327,
-0.012226023711264133,
0.088896244764328,
-0.026503391563892365,
-0.0008749866392463446,
-0.00039294088492169976,
0.005096179433166981,
-0.0013047681422904134,
0.015969621017575264,
0.03751218691468239,
-0.03281927481293678,
0.011454802006483078,
0.013258062303066254,
-0.02702023647725582,
0.0033235447481274605,
0.036125607788562775,
0.05565353110432625,
0.010537352412939072,
0.06648750603199005,
0.013997725211083889,
0.031272996217012405,
0.05783209949731827,
0.028352657333016396,
-0.020572708919644356,
-0.02534353919327259,
-0.0030440962873399258,
0.01864807866513729,
0.07785703241825104,
0.02608742192387581,
-0.03059295378625393,
0.012664460577070713,
0.03786244988441467,
0.011222454719245434,
-0.002893430180847645,
-0.00018958598957397044,
-0.008919081650674343,
-0.031286586076021194,
0.1053105965256691,
0.034842267632484436,
0.07530605792999268,
-0.03767206892371178,
-0.0374629907310009,
0.028848690912127495,
0.02080545946955681,
-0.008771223947405815,
-0.029194531962275505,
-0.006739601027220488,
-0.0334264300763607,
0.007664633449167013,
-0.006429347209632397,
0.016340063884854317,
0.021680373698472977,
0.022417744621634483,
-0.02047455497086048,
0.06854062527418137,
0.012645845301449299,
0.04216817766427994,
-0.09010054916143417,
0.0171967763453722,
-0.014419789426028728,
-0.03129136934876442,
0.03157975897192955,
-0.016156550496816635,
-0.04071689769625664,
-0.0069803805090487,
0.009891090914607048,
0.06309971958398819,
-0.023760950192809105,
0.0034374992828816175,
0.025038346648216248,
0.011076792143285275,
0.0023796020541340113,
-0.00909064244478941,
0.048023298382759094,
0.017674773931503296,
0.016307836398482323,
-0.026690341532230377,
-0.003479649778455496,
0.01723836176097393,
-0.06347666680812836,
-0.02105610817670822,
-0.07222543656826019,
0.0012573678977787495,
0.030139027163386345,
-0.07041821628808975,
0.045354846864938736,
0.07139510661363602,
0.007080641109496355,
0.04453334957361221,
-0.003967087250202894,
0.0899888426065445,
-0.0363181047141552,
0.030912520363926888,
0.0013984586112201214,
0.015361836180090904,
0.02985450252890587,
0.06448200345039368,
0.03584237024188042,
-0.02304605394601822,
0.022386806085705757,
-0.05156508833169937,
-0.004638290032744408,
0.005588476546108723,
-0.02479195035994053,
-0.016143150627613068,
-0.028795454651117325,
-0.030934367328882217,
0.06713811308145523,
0.010465693660080433,
0.01485802698880434,
0.06279675662517548,
0.031087597832083702,
-0.006202396005392075,
-0.041307929903268814,
0.04864167422056198,
0.01399913989007473,
-0.004234169144183397,
-0.04733695834875107,
0.041072048246860504,
0.01455236691981554,
-0.013747923076152802,
0.02280237153172493,
-0.046886932104825974,
0.0362253375351429,
-0.002050184877589345,
-0.007598993368446827,
-0.05706064775586128,
-0.004938229918479919,
0.06681583821773529,
-0.0033581901807338,
-0.04141099750995636,
-0.02301347814500332,
0.01583014242351055,
-0.024167431518435478,
-0.0356220044195652,
-0.012989985756576061,
-0.028529850766062737,
0.07470453530550003,
0.01846212148666382,
-0.00861779972910881,
-0.018194980919361115,
-0.021032776683568954,
-0.03548230603337288,
-0.016496097669005394,
0.00034182745730504394,
-0.028165029361844063,
0.06805262714624405,
0.0016551072476431727,
-0.06831540912389755,
0.02542305737733841,
-0.06357642263174057,
-0.001314836903475225,
-0.014642756432294846,
0.01947440765798092,
0.021683823317289352,
0.07092850655317307,
0.05508285388350487,
-0.012802723795175552,
-0.058590907603502274,
-0.009211303666234016,
-0.001591566950082779,
-0.017082454636693,
0.009178724139928818,
0.00810917653143406,
-0.03088138811290264,
-0.035421036183834076,
0.04322432726621628,
-0.02181524783372879,
-0.04775536060333252,
-0.018962325528264046,
0.010711925104260445,
-0.02658810466527939,
0.03590119257569313,
-0.006154695060104132,
-0.018294963985681534,
0.042530231177806854,
0.025049667805433273,
-0.0005996085819788277,
-0.025700349360704422,
0.07582751661539078,
0.08340416103601456,
-0.03229864314198494,
-0.014357865788042545,
0.0015729197766631842,
-0.045435771346092224,
-0.04864927753806114,
-0.03671741485595703,
0.03388424590229988,
-0.06387075036764145,
-0.02123565785586834,
-0.03989878669381142,
-0.03759612888097763,
-0.005509661976248026,
0.036055825650691986,
-0.03577065467834473,
0.054421037435531616,
0.020155852660536766,
-0.03103027679026127,
0.05819747596979141,
0.0068952105939388275,
-0.015767667442560196,
0.014147155918180943,
0.027189722284674644,
-0.016342008486390114,
0.018289050087332726,
0.055669620633125305,
-0.03874978795647621,
-0.0009851590730249882,
0.03974141180515289,
0.027988376095891,
-0.032449644058942795,
-0.0288675706833601,
-0.10501894354820251,
0.014227358624339104,
0.027879539877176285,
-0.04956262186169624,
-0.07401543855667114,
0.059626344591379166,
0.02958632819354534,
0.019238634034991264,
0.0706598237156868,
0.00010721500439103693,
-0.01931001991033554,
-0.023618387058377266,
0.01249080989509821,
0.09794675558805466,
0.006158850621432066,
-0.010246418416500092,
-0.05426352471113205,
0.04293270409107208,
0.029118875041604042,
-0.05547748878598213,
0.055486034601926804,
-0.04531668871641159,
0.08664172887802124,
-0.018866412341594696,
0.03075309470295906,
-0.0029675804544240236,
0.0691487044095993,
0.011220389045774937,
0.018852287903428078,
0.031268417835235596,
-0.05451980233192444,
0.009021086618304253,
0.04144393280148506,
-0.05781080573797226,
-0.009111925959587097,
-0.04817305877804756,
0.03222990781068802,
-0.0023424706887453794,
0.005526350811123848,
-0.03308010473847389,
-0.07339101284742355,
0.009441588073968887,
-0.017591780051589012,
-0.07625444233417511,
0.017656642943620682,
0.029293091967701912,
-0.025104759261012077,
-0.049462929368019104,
-0.010870781727135181,
0.02408016286790371,
0.0173786748200655,
-0.000260338798398152,
-0.003965198062360287,
-0.044134657829999924,
0.02776918187737465,
-0.03128725662827492,
0.0007234517252072692,
-0.03758892044425011,
-0.014992428943514824,
0.021457575261592865,
-0.006443703081458807,
-0.023749087005853653,
-0.006471746601164341,
-0.016185246407985687,
0.022127455100417137,
-0.03464076668024063,
-0.08153537660837173,
-0.04540406912565231,
0.002270330674946308,
0.03748500347137451,
0.022853145375847816,
0.006308396812528372,
0.02619459666311741,
-0.03806254267692566,
-0.009663796983659267,
-0.025334205478429794,
-0.016232464462518692,
-0.0007345258491113782,
-0.010912725701928139,
-0.0021055913530290127,
0.009631632827222347,
-0.04831865802407265,
-0.00884032528847456,
0.06765725463628769,
-0.04135961830615997,
0.002618431579321623,
-0.02305474504828453,
-0.08046881854534149,
0.05069587752223015,
-0.008957781828939915,
-0.0161794051527977,
-0.0606645792722702,
0.014442924410104752,
0.02230258844792843,
-0.03912835568189621,
-0.0462198443710804,
0.05665551871061325,
0.014354084618389606,
-0.006215077359229326,
0.047529514878988266,
0.0002459042880218476,
-0.015694471076130867,
-0.06166061758995056,
0.03260812908411026,
0.026370353996753693,
-0.0059429737739264965,
-0.08066898584365845,
-0.007056846283376217,
-0.028999079018831253,
0.01801830343902111,
-0.008486202917993069,
0.009231619536876678,
0.019093774259090424,
0.01119964849203825,
-0.035966791212558746,
0.008090632036328316,
-0.0032790983095765114,
0.02154501900076866,
-0.008222686126828194,
-0.01633511297404766,
-0.008699161931872368,
-0.007937807589769363,
-0.012299562804400921,
0.007529495283961296,
0.027762530371546745,
0.07951837033033371,
-0.007879875600337982,
-0.06115070730447769,
0.05014350637793541,
-0.060646045953035355,
0.06784217059612274,
0.03323466330766678,
-0.011316751129925251,
-0.011062988080084324,
0.04009044170379639,
0.04395332932472229,
-0.024073399603366852,
-0.0007389090023934841,
0.019472600892186165,
0.00046597456093877554,
0.0023907136637717485,
-0.0287264883518219,
0.0178820863366127,
0.006192564964294434,
0.006318435538560152,
-0.02998223900794983,
0.022692423313856125,
0.03564183786511421,
0.025820067152380943,
0.0222974494099617,
0.006281022448092699,
0.004761268384754658,
-0.06286134570837021,
0.024109551683068275,
-0.05085526779294014,
0.026683401316404343,
0.05533311888575554,
-0.06629742681980133,
0.017784621566534042,
0.013591025024652481,
-0.03657074645161629,
0.05530929192900658,
-0.01587037928402424,
-0.028904162347316742,
-0.013435041531920433,
-0.03090212494134903,
0.013227525167167187,
-0.017842616885900497,
0.017554059624671936,
0.04679606482386589,
-0.04416149854660034,
-0.05122513324022293,
-0.01655418984591961,
0.00041587097803130746,
0.0001957544154720381,
-0.020304078236222267,
0.0015185020165517926,
0.029650744050741196,
-0.04527774453163147,
-0.017707763239741325,
-0.060236793011426926,
-0.022265931591391563,
-0.06423667073249817,
-0.00704481964930892,
-0.09141883999109268,
-0.04784109443426132,
0.04911166429519653,
0.015399498865008354,
0.01114184595644474,
-0.012784966267645359,
-0.011692121624946594,
0.0011723508359864354,
0.01827239990234375,
-0.04965561628341675,
0.014460859820246696,
0.005982427392154932,
0.007738546933978796,
0.023017525672912598,
0.014998752623796463,
-0.016036909073591232,
0.06056184321641922,
-0.016484050080180168,
0.0009138231980614364,
0.011065849103033543,
0.05169539526104927,
-0.0053473180159926414,
-0.03283248096704483,
0.03316820412874222,
-0.025925761088728905,
0.014427907764911652,
-0.007604046259075403,
0.03255118429660797,
0.003044840646907687,
-0.03944012150168419,
0.005438328720629215,
0.029280977323651314,
-0.004540521651506424,
0.06318554282188416,
-0.019027093425393105,
-0.00899748969823122,
0.06829868257045746,
0.050420090556144714,
-0.032516807317733765,
-0.11695839464664459,
0.024566296488046646,
0.04967385530471802,
0.039963483810424805,
0.02621203102171421,
-0.017375603318214417,
0.04357323795557022,
0.04589695855975151,
-0.00419143820181489,
-0.02539941295981407,
0.06828221678733826,
-0.01713339239358902,
-0.02898651547729969,
-0.0282454751431942,
-0.0020190884824842215,
-0.05525119975209236,
0.01495243702083826,
0.00751256151124835,
-0.05295485258102417,
0.04833947867155075,
-0.03332330659031868,
-0.005918106064200401,
0.03232652321457863,
-0.11269914358854294,
0.02716120518743992,
-0.0022790743969380856,
0.007919109426438808,
-0.01576315611600876,
-0.020884428173303604,
0.05071282759308815,
-0.002152948873117566,
-0.05770298093557358,
-0.001808193395845592,
-0.03614247962832451,
0.05002859607338905,
0.01110268384218216,
-0.09095489233732224,
0.03352897986769676,
0.035276561975479126,
-0.006606570445001125,
-0.06639660894870758,
0.034957416355609894,
0.040058743208646774,
-0.015194597654044628,
-0.016095321625471115,
0.055277179926633835,
0.0027366841677576303,
-0.011930692009627819,
-0.03510406240820885,
0.028487199917435646,
-0.019827324897050858,
-0.029882963746786118,
-0.01932092010974884,
-0.034272320568561554,
-0.016202427446842194,
-0.033414144068956375,
0.03164020925760269,
-0.028409570455551147,
-0.02668985351920128,
-0.015175148844718933,
0.04628410190343857,
0.037256140261888504,
0.026333706453442574,
0.021361105144023895,
-0.0063699716702103615,
0.04579539969563484,
-0.011931898072361946,
-0.018505796790122986,
-0.024590007960796356,
0.043484918773174286,
-0.016636766493320465,
-0.03175928443670273,
0.006725396029651165,
-0.01688637211918831,
-0.01631610468029976,
0.046206384897232056,
0.007897206582129002,
-0.021284926682710648,
0.017546584829688072,
-0.06291834264993668,
-0.011296887882053852,
-0.03009684756398201,
-0.0021716344635933638,
0.004886550363153219,
-0.017573775723576546,
0.016731219366192818,
0.01031956821680069,
-0.02863164246082306,
-0.018611235544085503,
-0.06296422332525253,
-0.0161802489310503,
-0.020445384085178375,
-0.03076562099158764,
-0.02751336805522442,
-0.03381466120481491,
0.03087538480758667,
-0.06470747292041779,
0.0660676509141922,
-0.030779514461755753,
0.0754217803478241,
-0.00046822885633446276,
0.025964995846152306,
0.010192370042204857,
0.010266315191984177,
-0.012847255915403366,
-0.016025902703404427,
0.05256448686122894,
-0.003070564242079854,
0.023051081225275993,
-0.022624876350164413,
-0.023196110501885414,
0.024934349581599236,
0.02911348268389702,
0.0355636291205883,
-0.02861746959388256,
0.0461624339222908,
0.07560914009809494,
0.02071276865899563,
0.0016160134691745043,
-0.05052793025970459,
-0.015290945768356323,
-0.016294799745082855,
-0.0274905264377594,
-0.01896880567073822,
0.045343104749917984,
0.033346258103847504,
0.023705890402197838,
0.019561242312192917,
-0.015720246359705925,
-0.043727654963731766,
-0.014236174523830414,
0.004249017685651779
] |
<p>Suppose I do two experiments to find the triple point of water, one in zero-g and one on Earth. On Earth, water in the liquid or solid phase has less gravitational potential per unit mass than water in the gas phase. Therefore, the solid and liquid phases should be favored slightly more on Earth than in zero-g.</p>
<p>In a back-of-the-envelope calculation, how does the temperature of the triple-point of water depend on the gravitational acceleration and, if necessary, on the mass of water and volume and shape of container?</p>
<p><b>Edit</b>
Let's say I have a box in zero-g. The box is one meter on a side. It has nothing in it but water. Its temperature and pressure are just right so that it's at the triple point. All the water and ice and steam are floating around the box because it's zero-g.</p>
<p>Now I turn on gravity. The liquid water and ice fall to the bottom of the box, but the average height of the steam remains almost half a meter above the bottom of the box. So when gravity got turned on, the potential energy of the ice and liquid water went down significantly, but the potential energy of the steam didn't. Doesn't this mean that once gravity is turned on, water molecules would rather be part of the ice or liquid phase so that they can have lower energy? Wouldn't we no longer be at the triple point?</p>
<p>Several people have posted saying the answer is "no". I don't disbelieve that. Maybe the answer is just "no". I don't understand why the answer is no. Answers such as "No, because gravity doesn't affect the triple point," or "No, because the triple point only depends on pressure and temperature" simply restate the answer "no" with more words.</p>
|
g2495
|
[
0.043806884437799454,
0.0664726123213768,
0.015601224265992641,
0.024003973230719566,
0.04654881730675697,
0.04478610306978226,
-0.0007271421491168439,
0.02903306856751442,
-0.12991251051425934,
-0.018191758543252945,
0.01756991446018219,
0.02093903347849846,
0.03632816672325134,
-0.004812489729374647,
-0.04107736796140671,
-0.01925104856491089,
0.037054866552352905,
-0.020952429622411728,
-0.007006616797298193,
0.029330633580684662,
0.0022524544037878513,
-0.029914991930127144,
-0.008225628174841404,
-0.07616802304983139,
-0.04218946769833565,
0.0043880390003323555,
0.03124282695353031,
-0.05238892510533333,
-0.06139995902776718,
0.046432964503765106,
-0.027066050097346306,
0.008592686615884304,
-0.0041956910863518715,
-0.03652381896972656,
-0.03997001051902771,
-0.020336594432592392,
0.02571391873061657,
0.04845749959349632,
-0.0587000735104084,
-0.061682019382715225,
0.02991202101111412,
-0.007625539321452379,
-0.009579308331012726,
0.020504850894212723,
0.01846902072429657,
0.019281631335616112,
0.010279008187353611,
0.006280049681663513,
0.045614879578351974,
-0.01370152272284031,
0.026807963848114014,
0.032598886638879776,
0.03962123766541481,
0.012790068052709103,
-0.036416586488485336,
0.03779706731438637,
-0.06327502429485321,
0.0141059635207057,
0.014838967472314835,
0.015936411917209625,
-0.020247943699359894,
0.018342263996601105,
0.0063334801234304905,
-0.0018546463688835502,
0.08793092519044876,
-0.0073171332478523254,
-0.053116001188755035,
0.008055169135332108,
0.0157075896859169,
0.01075868122279644,
0.009432832710444927,
-0.019529446959495544,
-0.09630558639764786,
-0.03656899183988571,
-0.04012306034564972,
-0.000026821615392691456,
-0.012732886709272861,
0.005310342647135258,
0.015919726341962814,
0.01241289172321558,
0.015196011401712894,
0.022984104230999947,
0.03571313992142677,
0.0391404815018177,
0.00004826016811421141,
-0.02695440873503685,
0.041216880083084106,
0.007896698080003262,
-0.04383007436990738,
0.03278378024697304,
-0.050793230533599854,
0.020766714587807655,
0.10119583457708359,
0.039005931466817856,
0.012250755913555622,
0.06138866767287254,
0.05082322284579277,
0.08292405307292938,
0.07131879776716232,
0.05161711201071739,
-0.01691715605556965,
-0.02195754460990429,
0.061841078102588654,
0.007691584527492523,
-0.033871736377477646,
-0.0171456728130579,
0.017224101349711418,
0.02842634730041027,
0.018074948340654373,
-0.055945586413145065,
-0.03942359238862991,
-0.024522660300135612,
-0.034808967262506485,
-0.03769022598862648,
-0.02066786400973797,
-0.009103157557547092,
0.0030346105340868235,
-0.027517175301909447,
0.012143738567829132,
0.04349561408162117,
-0.04604598879814148,
0.04957171902060509,
-0.043855372816324234,
0.11777449399232864,
-0.01992800086736679,
-0.013983618468046188,
-0.025660738348960876,
0.031486254185438156,
-0.013886827975511551,
-0.03031192719936371,
0.004848169162869453,
0.021406443789601326,
-0.07730967551469803,
-0.03595742955803871,
0.0018030466744676232,
0.006483517587184906,
-0.03735866770148277,
0.014822732657194138,
0.0033272826112806797,
0.055669788271188736,
-0.03422071039676666,
0.029106395319104195,
-0.022516662254929543,
-0.01548350416123867,
-0.004885558970272541,
0.047604914754629135,
-0.03795422986149788,
0.022448496893048286,
0.03110768459737301,
0.03264126554131508,
0.009183503687381744,
0.03572306036949158,
0.0498618558049202,
-0.007550387177616358,
0.05601632967591286,
-0.03049745038151741,
-0.049344342201948166,
-0.0145867969840765,
0.03974369168281555,
0.01625574193894863,
0.02920851856470108,
-0.023555994033813477,
0.024160319939255714,
0.0151392612606287,
-0.017426757141947746,
0.03562762588262558,
0.02975221537053585,
-0.03780346363782883,
0.01174088940024376,
-0.024358434602618217,
-0.028176199644804,
0.026847871020436287,
0.0013091970467939973,
0.00863781850785017,
-0.026552826166152954,
-0.005569725763052702,
0.04320342838764191,
-0.06407523155212402,
0.024219216778874397,
-0.0017182898009195924,
-0.033422164618968964,
-0.002734521171078086,
-0.05114085227251053,
-0.061184849590063095,
-0.013877619989216328,
0.0033353613689541817,
0.033723797649145126,
0.04719756916165352,
-0.04366059973835945,
-0.020574867725372314,
0.006573124788701534,
0.03184518590569496,
0.02221268229186535,
-0.01599394716322422,
-0.018047474324703217,
-0.004177486058324575,
0.017265019938349724,
0.016498783603310585,
-0.042725570499897,
0.04524188116192818,
-0.07097069174051285,
0.04578013718128204,
0.007274949923157692,
0.012260066345334053,
-0.021371524780988693,
0.016443951055407524,
0.01923377998173237,
0.031492527574300766,
0.015569440089166164,
-0.0056598070077598095,
-0.049317289143800735,
0.06293445080518723,
0.0070182750932872295,
-0.016437673941254616,
0.0024077838752418756,
0.042144231498241425,
-0.02648581936955452,
-0.038360994309186935,
0.03135186433792114,
-0.0028033216949552298,
-0.07707665115594864,
0.019216934219002724,
-0.017844872549176216,
0.013197301886975765,
-0.03638874739408493,
-0.027587682008743286,
-0.0034335043746978045,
-0.05539948120713234,
0.0024423818103969097,
-0.03175049647688866,
-0.055317413061857224,
0.06503105163574219,
0.04997297376394272,
-0.0698651373386383,
0.0384695939719677,
0.013810932636260986,
-0.04375602304935455,
-0.03264760971069336,
0.033861659467220306,
0.0731799378991127,
-0.00165838364046067,
0.016662312671542168,
-0.06468874216079712,
0.039581049233675,
0.08992518484592438,
-0.031216729432344437,
0.03102491982281208,
-0.026307053864002228,
0.05797727778553963,
0.023523002862930298,
-0.031021064147353172,
0.047707993537187576,
-0.018458351492881775,
0.02222873829305172,
-0.011188658885657787,
0.03188975527882576,
-0.033531304448843,
-0.001653355429880321,
-0.0649719163775444,
-0.01726071909070015,
0.03179887309670448,
-0.06827937066555023,
-0.013397609815001488,
0.007260918617248535,
-0.040526848286390305,
0.031120598316192627,
-0.06474417448043823,
-0.04127433896064758,
-0.008620034903287888,
0.047403376549482346,
0.023445691913366318,
0.03655272722244263,
-0.007698473520576954,
0.04604605585336685,
-0.031940679997205734,
-0.025229737162590027,
-0.0054266261868178844,
-0.020253049209713936,
0.04712992534041405,
-0.04606586694717407,
-0.003166567301377654,
-0.04295558109879494,
-0.035725176334381104,
0.018017584457993507,
0.006235719192773104,
-0.00492947967723012,
-0.02316582202911377,
0.011708141304552555,
-0.01402608584612608,
0.0001987141731660813,
0.017842154949903488,
0.068541519343853,
0.04432688280940056,
0.02990482747554779,
0.000021597046725219116,
-0.007600380107760429,
-0.008929330855607986,
-0.054864417761564255,
-0.05338937044143677,
-0.005707073956727982,
-0.00857103057205677,
0.04244637116789818,
0.0003357608220539987,
0.052279032766819,
-0.0031653176993131638,
0.035682469606399536,
-0.04288173466920853,
-0.06062619015574455,
0.0176992304623127,
-0.013253533281385899,
-0.022456331178545952,
0.014609595760703087,
-0.03951295092701912,
0.005394589621573687,
-0.0714614987373352,
-0.012613382190465927,
-0.053447574377059937,
0.017820246517658234,
0.021982401609420776,
-0.029066890478134155,
-0.0294863972812891,
-0.016632134094834328,
0.003407843643799424,
-0.05105871707201004,
0.0014909764286130667,
0.11406257748603821,
-0.008700143545866013,
0.0115086380392313,
-0.0468217097222805,
0.023754309862852097,
0.009185045957565308,
-0.00434231199324131,
0.017742954194545746,
0.014416683465242386,
0.001963010523468256,
-0.0023899893276393414,
0.04170428216457367,
-0.009769972413778305,
0.04779718443751335,
0.028571872040629387,
0.0018631401471793652,
0.00903452467173338,
-0.021404188126325607,
-0.0015896138502284884,
0.004500140901654959,
0.010829778388142586,
-0.011371462605893612,
-0.00065570417791605,
-0.032293953001499176,
-0.005254928953945637,
0.06293895840644836,
-0.059385035187006,
-0.03203163668513298,
0.0030219699256122112,
0.0006392078357748687,
-0.005149566102772951,
-0.002158842282369733,
-0.018540270626544952,
-0.013112598098814487,
0.044867027550935745,
-0.051350243389606476,
-0.037970881909132004,
0.022955026477575302,
0.006108664907515049,
0.022830668836832047,
-0.027980633080005646,
-0.047311361879110336,
0.01797100529074669,
-0.03441093489527702,
0.022001177072525024,
0.009052085690200329,
-0.0388922393321991,
-0.04111006483435631,
0.03175336867570877,
0.09021831303834915,
-0.06013137102127075,
0.006972690112888813,
-0.027062905952334404,
-0.05545026436448097,
0.06170910596847534,
0.033961810171604156,
-0.05107755586504936,
-0.005382622126489878,
0.04784354194998741,
0.0038388539105653763,
0.007128918543457985,
-0.025010520592331886,
-0.03447321802377701,
0.02269429713487625,
-0.03373738005757332,
0.003166336566209793,
-0.006983350962400436,
-0.019164446741342545,
0.040224019438028336,
0.029897257685661316,
0.06029322370886803,
0.035160183906555176,
-0.012898852117359638,
-0.01860714890062809,
0.03978641331195831,
0.008667263202369213,
-0.032615602016448975,
0.018662575632333755,
-0.016536863520741463,
-0.03324129804968834,
-0.02802060730755329,
0.06654009222984314,
-0.021852856501936913,
-0.05200667306780815,
-0.03401299566030502,
0.0607045479118824,
-0.05342383310198784,
-0.02801341377198696,
-0.04443606734275818,
0.039227064698934555,
-0.07395577430725098,
0.03706914559006691,
-0.01704910770058632,
-0.005681529175490141,
-0.010709256865084171,
0.0564708337187767,
0.007333067711442709,
-0.021260662004351616,
-0.06476736813783646,
-0.05132771283388138,
0.044163696467876434,
0.030730661004781723,
-0.006794758606702089,
-0.04903508350253105,
0.010226741433143616,
-0.006107127759605646,
0.03412352129817009,
0.0034676173236221075,
0.0783776044845581,
0.014362757094204426,
0.09101241081953049,
-0.02429281733930111,
0.009755481965839863,
0.02953535132110119,
0.033635810017585754,
0.05922986567020416,
0.036709014326334,
-0.05120137706398964,
0.0132074523717165,
-0.023282388225197792,
0.07182346284389496,
-0.005289667285978794,
-0.007256160955876112,
0.022749317809939384,
-0.0221959687769413,
-0.06148581579327583,
0.023411111906170845,
-0.04995708167552948,
0.008731940761208534,
-0.03732555732131004,
0.03988885134458542,
-0.026332128793001175,
0.04709063097834587,
-0.020468849688768387,
0.04007609561085701,
-0.036456577479839325,
0.004926248453557491,
-0.013941498473286629,
0.05647434666752815,
0.010740886442363262,
-0.0293872132897377,
-0.02749842405319214,
-0.011675771325826645,
-0.018693512305617332,
-0.031546175479888916,
0.03719820827245712,
0.02613445371389389,
0.055735062807798386,
0.08784304559230804,
0.04922552779316902,
-0.01319716963917017,
0.008677784353494644,
-0.020359722897410393,
0.052721746265888214,
-0.02091320976614952,
-0.01986061967909336,
0.03039485216140747,
0.05853986367583275,
0.02141343243420124,
0.0027849564794451,
0.05605718865990639,
-0.06581658124923706,
0.03216848894953728,
0.035923562943935394,
0.005264734383672476,
0.03355557098984718,
-0.03423553705215454,
0.00041722849709913135,
-0.029958590865135193,
-0.0023556314408779144,
0.02282710000872612,
0.029662933200597763,
0.011767381802201271,
0.0072789182886481285,
0.010460042394697666,
-0.048776693642139435,
0.022637169808149338,
0.044718191027641296,
0.005486310459673405,
-0.0012229059357196093,
0.0453164279460907,
-0.017726391553878784,
-0.0826357752084732,
0.00492637837305665,
0.04749695211648941,
0.005095089320093393,
-0.01780463382601738,
0.0023113908246159554,
0.04744286835193634,
0.07540281116962433,
-0.07614583522081375,
-0.009451854042708874,
-0.027625659480690956,
-0.021534167230129242,
-0.02589561976492405,
0.051597002893686295,
0.0023681726306676865,
0.016596196219325066,
-0.018010467290878296,
0.014676962979137897,
-0.012941964901983738,
-0.05826801434159279,
0.007900428958237171,
0.024724168702960014,
0.013746047392487526,
-0.022085532546043396,
0.03766988590359688,
0.06494248658418655,
0.002593870973214507,
0.017909223213791847,
-0.02219155803322792,
-0.020131103694438934,
0.008434472605586052,
0.11633504927158356,
0.007738076616078615,
-0.02991793490946293,
0.009023021906614304,
-0.0009931724052876234,
0.09378394484519958,
-0.0541226789355278,
0.0001293465174967423,
-0.0778544694185257,
0.008563986048102379,
-0.024343736469745636,
-0.007506525609642267,
-0.026225438341498375,
-0.026120521128177643,
0.011438612826168537,
0.03230256214737892,
-0.02333650551736355,
0.02400628849864006,
-0.009743046946823597,
-0.03293733298778534,
0.009884512983262539,
-0.006741686724126339,
-0.02452205680310726,
0.03564952686429024,
0.027375927194952965,
0.03976801037788391,
0.049456268548965454,
-0.08928569406270981,
-0.02612011879682541,
-0.07112725079059601,
-0.0056738774292171,
0.003150437492877245,
-0.002960098907351494,
0.017468413338065147,
-0.01649503782391548,
-0.043421853333711624,
0.015731845051050186,
-0.0038992136251181364,
-0.0869537964463234,
-0.023688115179538727,
-0.03106049820780754,
-0.00340365176089108,
0.007374907843768597,
0.04473617672920227,
0.018590645864605904,
-0.07399962097406387,
0.041691675782203674,
0.026494000107049942,
-0.03832961618900299,
0.009747711941599846,
0.008824686519801617,
-0.010943370871245861,
-0.026665540412068367,
-0.013895085081458092,
-0.03424817696213722,
-0.020387960597872734,
-0.022298060357570648,
-0.05416039377450943,
0.010889819823205471,
-0.018369579687714577,
-0.05194029584527016,
0.03307871147990227,
0.04593215510249138,
0.04664928838610649,
0.07413209229707718,
-0.024536877870559692,
0.003508110297843814,
-0.04118431359529495,
0.009185204282402992,
-0.01650531403720379,
0.019432440400123596,
-0.0494915209710598,
-0.021654171869158745,
0.02802114188671112,
0.034438081085681915,
-0.012794886715710163,
-0.0045923227444291115,
-0.05680698901414871,
-0.0037497752346098423,
-0.01677769050002098,
-0.0016355073312297463,
0.003525438951328397,
-0.0017450674204155803,
-0.04138953238725662,
-0.0074097877368330956,
-0.09712286293506622,
0.04364516958594322,
0.027448847889900208,
-0.04042280465364456,
0.06659521907567978,
-0.0014361875364556909,
0.00471465615555644,
0.0250987745821476,
0.015837907791137695,
-0.06378678232431412,
0.022748716175556183,
0.003382990136742592,
0.001180202467367053,
-0.016736218705773354,
-0.01563071459531784,
0.04244829714298248,
0.03089595027267933,
-0.0007111363811418414,
-0.004917390178889036,
-0.01186705008149147,
-0.0020150465425103903,
-0.0580679289996624,
0.010586274787783623,
-0.001104450086131692,
-0.04471633583307266,
-0.018251828849315643,
0.0035287924110889435,
0.00161713024135679,
-0.07197624444961548,
-0.004067587200552225,
0.049957871437072754,
-0.032457731664180756,
0.04202280193567276,
0.012574203312397003,
-0.0023600663989782333,
-0.0006392498034983873,
-0.010132034309208393,
-0.08078788965940475,
0.008233618922531605,
-0.022636234760284424,
0.07813431322574615,
-0.022302325814962387,
0.05214117839932442,
0.045653972774744034,
-0.04638725519180298,
0.018846722319722176,
0.03444669768214226,
-0.009950312785804272,
-0.00038274339749477804,
-0.06842424720525742,
-0.010967269539833069,
0.04354686290025711,
-0.000789780227933079,
0.021318983286619186,
-0.03234477341175079,
0.0176407303661108,
0.04332653060555458,
-0.008799617178738117,
0.016234898939728737,
0.004516939166933298,
-0.03670297935605049,
-0.06192654371261597,
-0.048337411135435104,
-0.01812036894261837,
0.03516395017504692,
0.02640809677541256,
-0.011435264721512794,
0.018652930855751038,
0.05637122690677643,
0.04571644589304924,
0.009566767141222954,
-0.04436878859996796,
0.02265034429728985,
0.036402687430381775,
0.030317485332489014,
0.04938077554106712,
-0.009204668924212456,
0.01649503968656063,
-0.030604226514697075,
-0.013954062014818192,
-0.030550047755241394,
0.033993981778621674,
0.06064336746931076,
0.0005786553374491632,
0.00034956936724483967,
-0.02381259948015213,
-0.007681448012590408,
-0.035759277641773224,
0.006650516763329506,
0.034469861537218094,
-0.004923616535961628,
0.03030567057430744,
0.021326517686247826,
-0.057757534086704254,
-0.01629520021378994,
-0.05608915537595749,
-0.07682015746831894,
-0.047954708337783813,
-0.04151923954486847,
-0.026159368455410004,
-0.04334418103098869,
0.009977544657886028,
0.03349200636148453,
-0.0592019259929657,
-0.022822003811597824,
0.05826781317591667,
0.01715240068733692,
-0.04594854637980461,
0.010347837582230568,
0.002662615617737174,
0.020190071314573288,
0.014765994623303413,
0.02842409536242485,
0.018065663054585457,
0.020705394446849823,
-0.024576231837272644,
-0.008321779780089855,
0.02403581142425537,
0.03906016796827316,
-0.0010423525236546993,
-0.038251396268606186,
0.03423847258090973,
-0.014190157875418663,
-0.046920448541641235,
0.059032339602708817,
0.04418584704399109,
-0.04254613071680069,
0.017295988276600838,
-0.02278911881148815,
-0.02021394670009613,
0.004861143417656422,
-0.02074475772678852,
-0.03231391683220863,
-0.01984100230038166,
0.006177486386150122,
-0.028720825910568237,
-0.019535183906555176,
-0.035998713225126266,
0.007030146196484566,
0.0523051954805851,
-0.06040657311677933,
-0.03705110773444176,
-0.005976472049951553,
0.022867253050208092,
0.04930808022618294
] |
<p>I have a horizontal bar on vertical rails and we can consider that does not exist any friction. </p>
<p>Perpendicular to the plane of the rails it exists a magnetic field $B$. </p>
<p>I am asked to find the movement equations and the bar position depending on time. </p>
<p>And I have made some considerations: </p>
<p>I should separate the phenomenon in two parts: first one until the forces are equal and one after. </p>
<p>I'm stuck on finding the equations before the forces get equals. This is what I have done so far: </p>
<p>$$mg-F_{m}=m·a$$ with $F_m$ the magnetic force, with the Ohm Law: $$\epsilon=\frac{I}{R}$$ and with: $$\epsilon=-\frac{d \phi }{dt}=-Bl\frac{dx}{dt}$$
and all together:</p>
<blockquote>
<p>$$mg-\frac{B^2l^2}{R}·\frac{dx}{dt}=m·\frac{dx^2}{dt^2} $$</p>
</blockquote>
<p>So, what now? I am in my first physics course so I am not supposed to be solving this by two order differential equations tools. </p>
<p>I know that I can find the $v_{limit}$ if I make the sum of forces equal to $0$, but that is not enough. I'm really stuck, maybe I should be making some assumptions, but I don't know what! </p>
<p>(I have tried my best with my English language knowledge)</p>
<p>Thank you in advance. </p>
|
g2496
|
[
0.033950045704841614,
0.0688306912779808,
-0.01912156492471695,
-0.017871573567390442,
0.0927676409482956,
-0.00033025004086084664,
0.03585018962621689,
0.007577783428132534,
-0.05491151288151741,
-0.031881820410490036,
-0.018804116174578667,
-0.015076540410518646,
-0.0515427328646183,
-0.020310215651988983,
0.047393523156642914,
-0.0017523769056424499,
-0.019350606948137283,
0.0010982052190229297,
-0.017412180081009865,
-0.0001575187488924712,
0.016308613121509552,
0.041422177106142044,
0.0468946248292923,
-0.004080530721694231,
0.05642744153738022,
-0.025455959141254425,
0.019256481900811195,
-0.03510567545890808,
-0.0400504544377327,
0.013260719366371632,
-0.02995096892118454,
0.000007647704478586093,
0.062360506504774094,
-0.05552862957119942,
0.0009559117024764419,
-0.016751728951931,
0.04511747881770134,
0.01730310544371605,
0.013510634191334248,
-0.014264428988099098,
0.03047250024974346,
-0.058336976915597916,
0.04900826886296272,
-0.017215857282280922,
0.044100768864154816,
-0.03335002809762955,
-0.0575372576713562,
-0.025690311565995216,
-0.013697558082640171,
0.02894044853746891,
-0.0007732327794656157,
0.011060959659516811,
0.07380653917789459,
-0.008115907199680805,
-0.04638468474149704,
0.011779832653701305,
0.0845995768904686,
-0.053243864327669144,
0.030580872669816017,
0.03747866302728653,
0.018263837322592735,
0.005644313991069794,
-0.015260016545653343,
-0.007023652084171772,
0.02065156027674675,
-0.03855994716286659,
-0.06324248015880585,
-0.022698942571878433,
0.04035612568259239,
-0.009547343477606773,
-0.0021276012994349003,
-0.025099731981754303,
0.009556096978485584,
-0.04470380023121834,
-0.06654196232557297,
0.039827872067689896,
0.02262328937649727,
0.00001330693885392975,
0.05505312234163284,
-0.05896487832069397,
-0.04689633846282959,
0.04347430169582367,
0.028466936200857162,
0.041737332940101624,
0.023410962894558907,
-0.04106910899281502,
0.03943246230483055,
0.039198581129312515,
0.0017215535044670105,
0.011354740709066391,
-0.012424430809915066,
-0.01617320068180561,
0.07950285077095032,
0.02249201014637947,
0.04567881301045418,
-0.050722770392894745,
-0.015675460919737816,
0.09475887566804886,
-0.002286650938913226,
-0.024352746084332466,
-0.019764145836234093,
-0.039125364273786545,
-0.038980260491371155,
-0.03618358075618744,
0.044054064899683,
-0.044627200812101364,
0.03571848198771477,
0.028484219685196877,
-0.012643766589462757,
-0.0238807313144207,
-0.014311540871858597,
0.026443220674991608,
-0.07839138805866241,
-0.0316031351685524,
0.025338642299175262,
-0.020784951746463776,
0.033507805317640305,
0.011864951811730862,
-0.009392006322741508,
0.020411282777786255,
0.024431493133306503,
0.0023716199211776257,
0.008549701422452927,
0.07881926745176315,
-0.0025694239884614944,
-0.03400471433997154,
-0.01576867140829563,
0.0574023574590683,
0.04152662307024002,
-0.048671964555978775,
0.015703121200203896,
0.006606807000935078,
0.07876341044902802,
0.00776322279125452,
-0.04607800021767616,
0.04703640565276146,
-0.016266563907265663,
0.02706417627632618,
-0.00041520700324326754,
0.009806745685636997,
-0.01786467432975769,
-0.04536531865596771,
-0.014455530792474747,
-0.049881283193826675,
-0.03202776610851288,
0.03186474367976189,
-0.017730778083205223,
-0.010616176761686802,
0.05920005962252617,
-0.03212493658065796,
-0.007034167181700468,
0.06669659167528152,
-0.043047960847616196,
0.015364149585366249,
0.024917513132095337,
-0.011559687554836273,
0.032521892338991165,
-0.031362175941467285,
0.003316121408715844,
-0.032412778586149216,
0.021168023347854614,
-0.03924287483096123,
0.05254582688212395,
0.014058755710721016,
-0.044986311346292496,
0.04719957336783409,
0.027584463357925415,
0.0011042783735319972,
0.05206716060638428,
-0.011388593353331089,
-0.04438344016671181,
0.00035797542659565806,
0.047704536467790604,
0.08157479017972946,
0.01970006339251995,
0.09134988486766815,
0.003931304439902306,
-0.06219712644815445,
0.010296930558979511,
0.03180865943431854,
0.028673794120550156,
-0.04415039345622063,
0.03643711283802986,
-0.023178864270448685,
0.030760960653424263,
-0.03570908308029175,
0.011032959446310997,
0.07047931849956512,
-0.044275104999542236,
-0.0262141115963459,
-0.02831757441163063,
0.026363352313637733,
-0.024110211059451103,
0.02401745319366455,
-0.044954873621463776,
0.027149273082613945,
-0.005612218286842108,
-0.006435340736061335,
0.013172739185392857,
-0.029876308515667915,
-0.006139816716313362,
0.03409441560506821,
0.06139220669865608,
0.018231119960546494,
0.004056970123201609,
-0.021461892873048782,
0.004686035215854645,
-0.004153227899223566,
0.05999778211116791,
0.007720641326159239,
-0.016413051635026932,
-0.06123782694339752,
-0.014251111075282097,
-0.007708363700658083,
-0.019905848428606987,
-0.07506292313337326,
0.03549382463097572,
0.001972832251340151,
-0.0333235003054142,
0.019567234441637993,
-0.027505097910761833,
0.004516089800745249,
0.02362530492246151,
-0.013158444315195084,
-0.015417791903018951,
-0.042026933282613754,
-0.020863104611635208,
0.009198296815156937,
-0.015901712700724602,
-0.0386984646320343,
-0.014460289850831032,
-0.01084283646196127,
0.026563027873635292,
-0.058153796941041946,
0.04946980997920036,
0.012578139081597328,
0.01666804403066635,
0.005480852909386158,
-0.03265628218650818,
0.014058278873562813,
-0.015533370897173882,
0.035101573914289474,
0.05396389216184616,
-0.02766689658164978,
0.04986579716205597,
-0.008234909735620022,
0.0931522324681282,
0.06348516047000885,
0.019306359812617302,
0.04803952947258949,
0.03920511528849602,
-0.017585063353180885,
-0.02955925650894642,
0.019320562481880188,
-0.025353282690048218,
-0.004148670006543398,
-0.011854950338602066,
0.010438919998705387,
-0.025341294705867767,
-0.08821921050548553,
-0.04204844310879707,
-0.023150289431214333,
0.03303810581564903,
0.068570077419281,
-0.09745065867900848,
-0.028445443138480186,
-0.08820638060569763,
-0.04492750018835068,
0.056584443897008896,
-0.03114571049809456,
-0.04184606671333313,
-0.01728634350001812,
-0.04084327071905136,
0.011109388433396816,
-0.00720951147377491,
-0.038117531687021255,
0.032917238771915436,
0.02122064121067524,
0.01893426850438118,
0.04119305685162544,
0.012153830379247665,
-0.04775526002049446,
0.002424291567876935,
-0.012184925377368927,
0.009693201631307602,
0.055049289017915726,
0.010196429677307606,
0.014342265203595161,
-0.02711600251495838,
0.04738159850239754,
-0.0550418347120285,
0.03297541290521622,
0.0832863599061966,
0.0014788935659453273,
-0.060741689056158066,
0.0453411228954792,
-0.015162033028900623,
-0.039884693920612335,
-0.05846940353512764,
-0.013238065876066685,
0.007846649736166,
-0.005615196190774441,
0.01656961254775524,
0.01984574645757675,
-0.02128995768725872,
-0.03638780862092972,
-0.016118453815579414,
-0.024598045274615288,
0.0560421496629715,
0.02420858107507229,
-0.005553834140300751,
0.03067469410598278,
0.016355736181139946,
-0.04055864363908768,
-0.0007211322081275284,
0.04500287026166916,
0.0019229450263082981,
-0.019762609153985977,
0.0013529462739825249,
0.03177604451775551,
-0.026813501492142677,
-0.08015522360801697,
-0.006439869292080402,
-0.021718110889196396,
0.05317064747214317,
0.005853407550603151,
-0.04890808090567589,
-0.008866693824529648,
-0.033870454877614975,
0.05323086678981781,
0.010736368596553802,
0.059713687747716904,
0.05984054505825043,
-0.014045857824385166,
0.004528543911874294,
-0.03665890917181969,
0.026159923523664474,
-0.0246142391115427,
-0.0036397112999111414,
0.013623976148664951,
-0.023702574893832207,
-0.041278138756752014,
-0.01327615324407816,
0.03932962566614151,
0.011036514304578304,
0.008086536079645157,
-0.007068697363138199,
0.08938400447368622,
-0.002345205517485738,
0.028398005291819572,
-0.0008186727063730359,
-0.0249308031052351,
0.01526570599526167,
0.02702316641807556,
-0.007379903923720121,
0.02620440162718296,
0.02643752656877041,
0.024256033822894096,
-0.008311178535223007,
-0.010912400670349598,
-0.008007013238966465,
-0.028309620916843414,
-0.014717023819684982,
0.038981616497039795,
0.04683220759034157,
0.02448274940252304,
0.024503082036972046,
0.03272921219468117,
-0.008484164252877235,
-0.06353743374347687,
0.05205211415886879,
-0.055010996758937836,
0.014327836222946644,
-0.01620088703930378,
0.015889041125774384,
-0.08066924661397934,
0.015944670885801315,
-0.03532823920249939,
-0.010357062332332134,
0.044944919645786285,
-0.012289959006011486,
0.06805897504091263,
-0.026893431320786476,
0.05386991798877716,
0.019982583820819855,
0.047279201447963715,
-0.005657758563756943,
0.03926968201994896,
0.03766421228647232,
-0.006164747290313244,
0.02376530133187771,
0.01687871292233467,
-0.019874384626746178,
0.011634554713964462,
-0.029244964942336082,
-0.05527816340327263,
0.03660358116030693,
0.03307326138019562,
-0.018688634037971497,
-0.0017447451828047633,
0.05144074186682701,
0.010621788911521435,
-0.020562980324029922,
0.05658090487122536,
-0.06717239320278168,
0.03479611128568649,
0.03566431999206543,
-0.026979362592101097,
0.044410645961761475,
-0.004809251520782709,
0.01871989108622074,
-0.06552380323410034,
-0.05847452953457832,
-0.023985857143998146,
0.042091790586709976,
0.03714701905846596,
0.03068475052714348,
0.049781184643507004,
0.018612636253237724,
-0.024075396358966827,
0.05771157890558243,
0.1211204081773758,
-0.005650129169225693,
-0.09781155735254288,
0.003952972125262022,
0.02356143668293953,
-0.002936246572062373,
0.0033321783412247896,
-0.02355370670557022,
-0.049788374453783035,
-0.04110494628548622,
-0.0068475850857794285,
-0.029054677113890648,
-0.015405572019517422,
-0.06311821192502975,
0.049945104867219925,
-0.04683462157845497,
-0.02899172157049179,
-0.01529780961573124,
0.06234077364206314,
0.014092468656599522,
0.030766619369387627,
0.012059282511472702,
0.016357634216547012,
-0.08372153341770172,
0.05577889084815979,
-0.013878447003662586,
-0.08146442472934723,
-0.04849708452820778,
-0.04514990746974945,
-0.006005348637700081,
0.011177766136825085,
-0.032971519976854324,
-0.014364393427968025,
-0.015934545546770096,
-0.03799789771437645,
-0.005046606529504061,
-0.0005689187673851848,
0.0022067457903176546,
0.0005350174033083022,
0.0037170343566685915,
-0.023150242865085602,
-0.03579237312078476,
-0.008228418417274952,
-0.038096096366643906,
-0.025570573285222054,
0.006097014062106609,
-0.017575053498148918,
-0.034715767949819565,
0.018290415406227112,
0.024815622717142105,
0.01061956211924553,
0.0397077351808548,
0.009983707219362259,
-0.0037057462614029646,
0.015870196744799614,
0.060020092874765396,
-0.0345860980451107,
0.026597347110509872,
-0.00047187114250846207,
-0.0885869637131691,
0.023360291495919228,
0.04916563630104065,
0.011567237786948681,
-0.02097494713962078,
-0.044809047132730484,
-0.01393361110240221,
0.010108630172908306,
0.0356883630156517,
-0.020434685051441193,
-0.011236501857638359,
0.054948121309280396,
-0.06555048376321793,
-0.0020743049681186676,
-0.01596778631210327,
-0.05026310309767723,
-0.056931763887405396,
0.025481412187218666,
-0.03165839612483978,
0.005490065086632967,
-0.03616016358137131,
-0.016404516994953156,
0.005458381958305836,
0.008150344714522362,
0.0035591875202953815,
0.07243874669075012,
0.02761770784854889,
0.01614794135093689,
0.0007017125026322901,
0.041486408561468124,
-0.00959812942892313,
-0.0026232548989355564,
0.01722254604101181,
-0.00851195864379406,
-0.056740470230579376,
-0.006155174691230059,
0.052350003272295,
0.03063313476741314,
-0.06226278096437454,
-0.0017573238583281636,
0.05531585216522217,
-0.0247943215072155,
0.06705299019813538,
-0.030840076506137848,
-0.007308688014745712,
-0.009767708368599415,
-0.06958869099617004,
0.01656377874314785,
-0.024717682972550392,
0.004339085426181555,
0.032810453325510025,
-0.04108623042702675,
-0.006993947550654411,
0.010539352893829346,
-0.008700720965862274,
-0.01324502844363451,
0.07769645750522614,
-0.0676264688372612,
-0.05672285333275795,
0.00569976307451725,
-0.034581806510686874,
-0.026939598843455315,
0.05314153805375099,
-0.009647035971283913,
-0.05550355091691017,
-0.0005561625002883375,
-0.06419370323419571,
-0.04461827501654625,
0.03931298106908798,
-0.022922642529010773,
-0.027630390599370003,
-0.014208587817847729,
-0.02112513780593872,
0.014262363314628601,
0.007398507557809353,
0.027123499661684036,
-0.007740493398159742,
-0.021546129137277603,
0.002163220662623644,
0.029192321002483368,
0.06689444929361343,
-0.04223747178912163,
0.004221841227263212,
-0.002863961039111018,
0.02276831865310669,
-0.007715586572885513,
0.029205456376075745,
0.023174729198217392,
0.048878151923418045,
0.01946389488875866,
-0.019808558747172356,
0.02675427310168743,
-0.05566362291574478,
0.06920889765024185,
0.06774619221687317,
0.03478636220097542,
-0.014695501886308193,
-0.012054198421537876,
-0.044650908559560776,
0.05278724431991577,
0.00047509840806014836,
0.051909539848566055,
-0.027601759880781174,
-0.031191237270832062,
-0.04280097782611847,
0.07381213456392288,
-0.059137552976608276,
-0.058104898780584335,
0.019457347691059113,
-0.05746341496706009,
-0.02146245166659355,
0.014972549863159657,
-0.01778983138501644,
-0.02112155221402645,
0.01559298112988472,
-0.024968165904283524,
0.02044595777988434,
-0.045057136565446854,
0.006614260375499725,
0.05739235132932663,
-0.006654627155512571,
-0.012882781215012074,
-0.017720365896821022,
0.007377288769930601,
0.04857718572020531,
-0.010080800391733646,
-0.02439308352768421,
0.0015712525928393006,
-0.04421728104352951,
-0.019659755751490593,
0.025803091004490852,
0.008597602136433125,
-0.05088694766163826,
-0.00916517898440361,
-0.01089450903236866,
0.007558452896773815,
0.04496701806783676,
0.050256021320819855,
0.04310690984129906,
-0.002436150563880801,
-0.048073019832372665,
-0.017925212159752846,
-0.016249023377895355,
-0.02976464107632637,
0.02856547199189663,
-0.041380856186151505,
-0.0649571493268013,
-0.06561487913131714,
0.012525518424808979,
-0.02528851106762886,
0.0366707369685173,
-0.0499645434319973,
-0.024585844948887825,
0.004511498846113682,
0.01121555082499981,
0.03462584689259529,
0.005833519622683525,
-0.0430450476706028,
0.005788849201053381,
0.016755089163780212,
-0.011038861237466335,
0.002269425895065069,
-0.01687956601381302,
0.02638178877532482,
0.04114501550793648,
0.0000015048848354126676,
0.03651609271764755,
0.016842463985085487,
-0.05688657611608505,
0.022201327607035637,
0.014979413710534573,
-0.017691034823656082,
-0.03159795701503754,
0.0059763239696621895,
-0.058237578719854355,
0.012743202969431877,
0.023919936269521713,
-0.0028802575543522835,
0.04331407696008682,
0.0378919318318367,
-0.031746361404657364,
-0.01099141500890255,
-0.01907808519899845,
0.02078174613416195,
0.004670712165534496,
0.05339159816503525,
-0.05105198174715042,
0.0001846350060077384,
0.0036094519309699535,
-0.03503734990954399,
0.00467783072963357,
-0.031061165034770966,
0.041279375553131104,
0.01588534563779831,
0.016332076862454414,
0.03327389806509018,
-0.010605016723275185,
0.003729948541149497,
0.04405159503221512,
-0.007833183743059635,
-0.041112106293439865,
-0.000717800110578537,
-0.04529237374663353,
-0.04029819741845131,
0.011929197236895561,
0.0523177869617939,
0.0022899708710610867,
-0.0040472326800227165,
0.043705783784389496,
0.018274158239364624,
-0.019969463348388672,
0.048787541687488556,
0.013394908048212528,
-0.04068979620933533,
0.021384555846452713,
-0.052168264985084534,
-0.04454542323946953,
0.024711767211556435,
0.052836742252111435,
-0.020131057128310204,
0.011173592880368233,
-0.0032363873906433582,
-0.038062792271375656,
0.015398346818983555,
-0.02782481350004673,
-0.02310255356132984,
-0.04060543328523636,
-0.03794154152274132,
-0.03939693793654442,
-0.000617933226749301,
-0.0008793692104518414,
0.13205748796463013,
-0.009478271938860416,
-0.0476081557571888,
-0.006194489076733589,
0.04481523111462593,
-0.0855000838637352,
0.0189562626183033,
0.0423889122903347,
-0.02074083499610424,
-0.016407139599323273,
-0.02949366346001625,
-0.04337310045957565,
-0.08421888202428818,
0.010495300404727459,
0.01796150952577591,
-0.027682004496455193,
0.00427586305886507,
0.029773510992527008,
-0.0013933164300397038,
0.008325096219778061,
-0.048510778695344925,
-0.043070510029792786,
0.04450676962733269,
-0.04642548784613609,
0.00689513748511672,
-0.0007290527573786676,
-0.018810894340276718,
0.04074164852499962,
-0.007750401273369789,
-0.002731937449425459,
-0.05629194900393486,
-0.06313574314117432,
-0.025391671806573868,
0.002803587354719639,
0.012061696499586105,
-0.009011475369334221,
0.05647166073322296,
-0.00436036754399538,
0.03770921379327774,
0.0035485427360981703,
0.04876817390322685,
0.009298755787312984,
-0.03309045359492302,
0.042348701506853104,
-0.05467875674366951,
0.019008848816156387,
0.044082336127758026,
0.0618765652179718,
0.029803739860653877,
-0.020678680390119553,
-0.002757727401331067,
-0.034921176731586456,
-0.0026330065447837114,
-0.0011246934300288558,
0.00816948339343071,
-0.020723916590213776,
0.003320166375488043
] |
<p>While reading about the <a href="http://en.wikipedia.org/wiki/Clausius-Clapeyron_equation" rel="nofollow">Clausius Clapeyron equation</a> from the Feynman lectures on Physics, I couldn't understand a few things from its derivation:</p>
<p>Although the argument was pretty clear, when the system consists both gas(vapour) and liquid why would it have constant pressure on heating and increasing volume?? </p>
<p>Second and more fundamental, how can we assign a single pressure value to this composite system in spite of it having two states of matter; wouldnt the pressure in the gas part (on top part of container) be different from that at the bottom or side in the liquid part? On top of this how can this be the vapour pressure (which I think is the pressure of the vapours on the surface of liquid)? </p>
|
g2497
|
[
0.0014229989610612392,
0.003471905365586281,
-0.007048463448882103,
0.008916749618947506,
0.087367482483387,
-0.0007600925164297223,
-0.024653149768710136,
0.01349629182368517,
-0.07766103744506836,
-0.0077298479154706,
-0.025510648265480995,
-0.0014940956607460976,
0.02857343666255474,
0.03206661716103554,
-0.015162098221480846,
-0.008426413871347904,
0.016652770340442657,
-0.03420158848166466,
0.03450676426291466,
0.008956330828368664,
-0.07498882710933685,
0.022410187870264053,
-0.02103978395462036,
-0.08006487786769867,
-0.04472314193844795,
-0.04236393794417381,
0.019617456942796707,
0.0301889106631279,
-0.026731528341770172,
-0.058195434510707855,
-0.03575374558568001,
0.030734410509467125,
0.011480861343443394,
-0.008576853200793266,
0.022391686215996742,
-0.03760839253664017,
0.028575869277119637,
-0.014597764238715172,
0.016295388340950012,
-0.02083161100745201,
-0.013931360095739365,
-0.0030133347027003765,
-0.013470650650560856,
0.012137321755290031,
-0.03902005776762962,
0.021915659308433533,
-0.08584670722484589,
-0.06572793424129486,
-0.02084365487098694,
0.008105827495455742,
0.03177186846733093,
0.02535332180559635,
-0.005973816383630037,
-0.005773666314780712,
-0.015025658532977104,
0.0456659272313118,
0.021063677966594696,
0.04112950339913368,
0.06918881088495255,
0.021749140694737434,
-0.0051535977981984615,
0.03372526168823242,
0.010379570536315441,
0.06984974443912506,
0.04327492043375969,
-0.022834697738289833,
-0.04127165675163269,
0.023358428850769997,
-0.009829740971326828,
0.026602018624544144,
0.061426591128110886,
-0.0446680411696434,
-0.005073281936347485,
-0.06105996295809746,
-0.007934513501822948,
0.009480435401201248,
0.0359048917889595,
-0.00934233982115984,
0.042728241533041,
-0.01450289785861969,
0.02457418292760849,
0.04149368032813072,
0.030448580160737038,
-0.022592848166823387,
0.05520036444067955,
-0.03521563485264778,
-0.06655160337686539,
-0.04919185861945152,
-0.02006770856678486,
-0.011382014490664005,
-0.07428116351366043,
0.05578245222568512,
0.06340215355157852,
0.008786534890532494,
-0.006775818299502134,
-0.0321953222155571,
0.017144089564681053,
0.01719474233686924,
-0.059139449149370193,
0.0037850462831556797,
-0.0013271711068227887,
-0.007621417753398418,
0.03539033979177475,
-0.03537503257393837,
-0.03898368030786514,
0.005564501974731684,
-0.0466139055788517,
0.03166401386260986,
-0.024510957300662994,
-0.04348556697368622,
-0.021491196006536484,
0.05238571763038635,
-0.05740620195865631,
0.05653436481952667,
0.00004995606650481932,
-0.0366811603307724,
0.027900490909814835,
0.01697940193116665,
0.0019749400671571493,
0.02285340242087841,
-0.007609108928591013,
0.06292987614870071,
0.015567745082080364,
0.028407396748661995,
-0.014585002325475216,
-0.022227173671126366,
0.0499434694647789,
-0.017847344279289246,
0.003722753608599305,
-0.002747579710558057,
0.0068037318997085094,
-0.013927765190601349,
0.008939030580222607,
-0.025335116311907768,
0.05626431107521057,
0.04297174513339996,
-0.023104924708604813,
0.005618527997285128,
-0.05270714312791824,
-0.006539587397128344,
0.0075479596853256226,
0.017732705920934677,
-0.024258149787783623,
0.008236899971961975,
0.04468642547726631,
-0.04675102233886719,
-0.0950627401471138,
-0.004062876105308533,
-0.020713062956929207,
-0.02323427051305771,
0.053698260337114334,
0.08495841175317764,
0.06069009751081467,
-0.00543871009722352,
0.023720240220427513,
0.001745432848110795,
0.026220085099339485,
-0.0048330179415643215,
-0.011186491698026657,
0.022836485877633095,
0.03820227459073067,
-0.00702302809804678,
0.003623017342761159,
0.005429481156170368,
-0.06411141902208328,
0.06707875430583954,
-0.06667251139879227,
-0.0429815948009491,
-0.03315609320998192,
0.008347390219569206,
-0.06260707974433899,
0.01698124408721924,
-0.029024120420217514,
0.05635423585772514,
0.04850657656788826,
0.014761907048523426,
0.04010886326432228,
0.012186320498585701,
0.05609455704689026,
0.010629789903759956,
0.012393174692988396,
0.02824549190700054,
0.00412100600078702,
-0.01686888374388218,
-0.020698733627796173,
0.07659389078617096,
0.0009446811163797975,
0.025083379819989204,
-0.08644040673971176,
-0.021330393850803375,
-0.0342407152056694,
0.009162945672869682,
0.008079912513494492,
0.049145251512527466,
0.03473103046417236,
-0.02181398868560791,
-0.005390581209212542,
-0.04393888637423515,
-0.008186166174709797,
-0.029252659529447556,
-0.1302308589220047,
0.028987955302000046,
0.08221742510795593,
-0.018432937562465668,
0.04461041837930679,
0.027566803619265556,
-0.030662840232253075,
0.017443856224417686,
-0.004600658547133207,
-0.02311483956873417,
-0.052236560732126236,
-0.019043060019612312,
0.010928960517048836,
0.005073273088783026,
0.025200216099619865,
-0.007320052478462458,
-0.009573150426149368,
-0.021707206964492798,
0.018287919461727142,
0.025047708302736282,
-0.054117247462272644,
0.009156502783298492,
0.012465325184166431,
0.020637398585677147,
-0.06618179380893707,
-0.0025911866687238216,
-0.0011461761314421892,
0.010050907731056213,
-0.01584962010383606,
0.022488046437501907,
-0.009455830790102482,
0.026944411918520927,
-0.02039141207933426,
-0.04439396411180496,
0.04646892100572586,
0.004042868502438068,
-0.02686591073870659,
0.0027403337880969048,
0.02650345303118229,
0.08822347223758698,
-0.0017914617201313376,
-0.040479034185409546,
0.026966413483023643,
-0.0018924723844975233,
0.018255898728966713,
0.006204111035913229,
-0.0009130020043812692,
-0.048492416739463806,
0.08090012520551682,
-0.026780543848872185,
-0.0309155210852623,
-0.07568738609552383,
-0.08545020967721939,
-0.00852792989462614,
0.03507925570011139,
-0.011085324920713902,
-0.0360354520380497,
0.031562671065330505,
-0.03839747607707977,
-0.052475180476903915,
0.001953704981133342,
-0.005489330273121595,
0.017751948907971382,
0.018545325845479965,
-0.0868152603507042,
0.03604564815759659,
-0.08096443861722946,
0.007957068271934986,
0.039365701377391815,
0.016110757365822792,
0.052378688007593155,
0.06180580332875252,
-0.02564230002462864,
-0.008283672854304314,
0.007014245260506868,
-0.012696197256445885,
0.004862090572714806,
-0.01256188191473484,
0.05986583232879639,
0.015109374187886715,
-0.05324222147464752,
0.001325315097346902,
0.023303130641579628,
0.010669371113181114,
0.0066953012719750404,
-0.005995791405439377,
-0.022393574938178062,
0.005838070530444384,
0.03666922077536583,
0.06023254618048668,
0.0602249875664711,
0.040894147008657455,
-0.009337641298770905,
0.023707466199994087,
-0.02091130055487156,
0.03650277107954025,
0.053013816475868225,
-0.020462267100811005,
0.012624463066458702,
0.019941268488764763,
0.00125278125051409,
-0.0019316580146551132,
0.021247906610369682,
0.011914773844182491,
-0.03398013859987259,
0.03488833084702492,
-0.08691282570362091,
0.01897316798567772,
-0.0027056692633777857,
-0.00984689500182867,
-0.0029822189826518297,
0.013305358588695526,
0.013966787606477737,
-0.016810160130262375,
-0.0026864672545343637,
-0.028334850445389748,
-0.0053875683806836605,
0.02029959298670292,
0.01248855795711279,
-0.013107424601912498,
-0.04646722227334976,
0.03540807217359543,
-0.008575382642447948,
-0.06377021223306656,
0.0810905247926712,
-0.005272901151329279,
-0.038438864052295685,
0.045339327305555344,
-0.03025580756366253,
-0.009792588651180267,
0.03890252858400345,
-0.043483614921569824,
0.007355640176683664,
-0.03449574112892151,
0.0031935253646224737,
-0.0531410351395607,
-0.01971731148660183,
0.022791529074311256,
0.06502848863601685,
0.03068634867668152,
0.011909635737538338,
-0.060738757252693176,
-0.046216946095228195,
0.05940055847167969,
0.009982218034565449,
-0.006187374237924814,
0.04392794519662857,
-0.010525457561016083,
0.04617606848478317,
0.0016068501863628626,
0.0407419390976429,
0.022177360951900482,
0.024052301421761513,
0.03761347755789757,
0.01266599353402853,
-0.005513874348253012,
0.06064126640558243,
0.013959723524749279,
-0.047519613057374954,
0.042963579297065735,
0.007010714616626501,
-0.06637413799762726,
0.043527182191610336,
0.012054596096277237,
0.0012986609945073724,
-0.017394941300153732,
0.0408715195953846,
0.016298461705446243,
-0.012910834513604641,
-0.04528814181685448,
-0.03724709525704384,
0.012320378795266151,
-0.023334769532084465,
-0.005843466147780418,
0.04345133900642395,
-0.05149613693356514,
-0.012264612130820751,
-0.03886440396308899,
-0.041731249541044235,
0.024808205664157867,
0.029473431408405304,
0.018772410228848457,
0.009609989821910858,
0.043430667370557785,
0.0007653736975044012,
0.0027620657347142696,
-0.08647739142179489,
0.021930687129497528,
0.04406458139419556,
-0.08600795269012451,
0.08590110391378403,
-0.02756323479115963,
-0.02040390856564045,
0.04127967357635498,
0.005639877635985613,
0.0034120988566428423,
0.03161794692277908,
-0.05347374826669693,
-0.01841084100306034,
0.024656863883137703,
0.01724964752793312,
-0.03869107738137245,
0.017400961369276047,
-0.06585436314344406,
-0.06602131575345993,
-0.013823327608406544,
0.07222694158554077,
-0.032803259789943695,
-0.00545087642967701,
0.0460343062877655,
0.04126795008778572,
0.029332570731639862,
0.024480892345309258,
0.004717280622571707,
0.032990213483572006,
-0.03445572778582573,
0.026723548769950867,
0.012224509380757809,
0.049487657845020294,
-0.02347271516919136,
-0.03537021204829216,
-0.0010780015727505088,
0.026021257042884827,
-0.015755007043480873,
0.0007577201467938721,
0.006257109809666872,
-0.0010716948891058564,
0.03765159845352173,
-0.01302925031632185,
-0.02043578214943409,
-0.026614271104335785,
-0.004319631028920412,
0.02517828345298767,
0.019175253808498383,
-0.033385660499334335,
0.03663642704486847,
0.006324362941086292,
-0.014792419038712978,
-0.03937067836523056,
0.051657479256391525,
0.04218654707074165,
0.0016646778676658869,
-0.010351031087338924,
-0.03028945066034794,
0.02143588848412037,
0.02100234478712082,
0.01232845988124609,
-0.059744056314229965,
0.011443942785263062,
-0.07538527250289917,
-0.024225352331995964,
0.049466077238321304,
0.012792271561920643,
-0.055156584829092026,
-0.016914939507842064,
-0.005504945293068886,
-0.017775535583496094,
-0.032813750207424164,
0.0516199953854084,
-0.006512261927127838,
-0.057946499437093735,
-0.013700040988624096,
-0.03206227719783783,
0.022573227062821388,
0.024625061079859734,
-0.01550848875194788,
-0.04711467772722244,
-0.030845467001199722,
0.012622815556824207,
0.0009745697025209665,
0.013383368961513042,
-0.002227107062935829,
0.002040455350652337,
0.0317256860435009,
0.06687791645526886,
-0.006422354839742184,
0.015660405158996582,
-0.024268634617328644,
0.01388599630445242,
-0.01608680747449398,
0.02455403469502926,
0.040976401418447495,
0.047308217734098434,
0.02914400026202202,
0.021712884306907654,
0.04228805750608444,
0.000827936630230397,
-0.003408972406759858,
-0.05381833761930466,
0.05745827779173851,
0.025125376880168915,
0.010711968876421452,
0.03067990019917488,
-0.017024504020810127,
0.003275335766375065,
-0.034253597259521484,
-0.023592254146933556,
-0.03377301245927811,
-0.007275482639670372,
0.028479916974902153,
-0.05303202196955681,
0.030967626720666885,
0.04642540588974953,
0.06701129674911499,
0.006569219287484884,
0.03032107837498188,
0.009286729618906975,
-0.030822748318314552,
-0.025239011272788048,
0.05929071828722954,
0.05720236897468567,
0.009749971330165863,
-0.0006859198329038918,
0.0018177421297878027,
-0.006106644868850708,
-0.02984659932553768,
-0.005164532456547022,
-0.0011053394991904497,
-0.013815782964229584,
-0.044630102813243866,
-0.019002603366971016,
0.0031861572060734034,
0.02900092676281929,
-0.03895481675863266,
-0.024211125448346138,
0.022651035338640213,
-0.06489834934473038,
-0.023922685533761978,
-0.00793384201824665,
0.019466636702418327,
-0.05142603814601898,
0.0015420018462464213,
0.0451570600271225,
0.0029749416280537844,
-0.03454684838652611,
-0.04987271502614021,
-0.04536512866616249,
0.05622752755880356,
0.0853409692645073,
0.017494075000286102,
-0.027206076309084892,
-0.08529703319072723,
-0.006529051344841719,
0.04579215496778488,
0.029603049159049988,
0.010607131756842136,
-0.01724260114133358,
-0.021872080862522125,
0.05352769047021866,
-0.016009807586669922,
0.011874618008732796,
-0.012873642146587372,
-0.0012885390315204859,
-0.017736628651618958,
0.048246338963508606,
0.027573544532060623,
-0.008034263737499714,
0.022368798032402992,
0.013370485045015812,
0.00882842019200325,
0.02739146538078785,
0.011676130816340446,
-0.016457095742225647,
0.036332204937934875,
-0.008489156141877174,
-0.04782635346055031,
-0.07420303672552109,
0.005945703946053982,
0.06389398127794266,
0.04391105845570564,
-0.020942330360412598,
0.013667869381606579,
0.06146806478500366,
-0.05984529107809067,
0.016930367797613144,
0.029330085963010788,
-0.026967864483594894,
-0.03416866809129715,
-0.02879255637526512,
0.012802601791918278,
0.0033725483808666468,
-0.007183609995990992,
0.006116572767496109,
-0.01644965261220932,
-0.004238419234752655,
-0.0020732746925204992,
-0.05988871306180954,
-0.055907245725393295,
0.022275378927588463,
-0.001263514393940568,
-0.011881550773978233,
-0.007315438706427813,
-0.03824963793158531,
-0.03755344823002815,
0.006629390642046928,
-0.0008825611439533532,
0.04040653258562088,
0.03960326313972473,
-0.022936353459954262,
0.0020588617771863937,
-0.025640496984124184,
0.015392372384667397,
-0.03915509209036827,
-0.003173637669533491,
-0.03010566160082817,
0.010263461619615555,
0.04146029055118561,
0.0037514965515583754,
-0.020355695858597755,
-0.020227603614330292,
-0.058991946280002594,
0.05040233954787254,
0.011751780286431313,
-0.0498235858976841,
0.08245867490768433,
-0.032820168882608414,
-0.016666796058416367,
0.029938144609332085,
-0.005739279091358185,
0.017787126824259758,
-0.03784893825650215,
-0.05903397500514984,
0.029519835487008095,
-0.0728837326169014,
0.04772603139281273,
0.03954745829105377,
-0.06826525181531906,
0.06952302902936935,
0.061009280383586884,
0.07066486775875092,
0.030289890244603157,
-0.025990355759859085,
0.01730266958475113,
0.023213617503643036,
0.008810021914541721,
-0.03179973363876343,
-0.03624976798892021,
-0.02860201522707939,
0.08652157336473465,
0.032039824873209,
0.015453514643013477,
-0.005644189193844795,
0.08378825336694717,
-0.009976728819310665,
-0.03168879821896553,
0.002519589150324464,
-0.03695112466812134,
-0.03968285024166107,
-0.08066150546073914,
0.07493077963590622,
0.018478183075785637,
-0.0500820130109787,
-0.04454711079597473,
0.09401600062847137,
0.02979976311326027,
-0.0180117916315794,
-0.019350796937942505,
-0.012350708246231079,
0.07085660099983215,
-0.017329828813672066,
-0.0345483124256134,
-0.012714198790490627,
0.0029436303302645683,
0.07532089948654175,
-0.0012719696387648582,
0.03258748725056648,
-0.00917502585798502,
-0.0459132082760334,
0.03302318602800369,
-0.026350952684879303,
-0.026023169979453087,
-0.019196122884750366,
-0.04258099943399429,
0.008673329837620258,
-0.013953369110822678,
0.022995300590991974,
0.037411730736494064,
0.001625681295990944,
0.020886629819869995,
-0.02013428695499897,
-0.042141903191804886,
0.0005389490397647023,
-0.008721698075532913,
0.004447141662240028,
-0.051000580191612244,
-0.0010577577631920576,
0.016221385449171066,
0.01479557529091835,
0.042551878839731216,
-0.0725112184882164,
0.06670253723859787,
-0.03084217570722103,
0.031783148646354675,
0.03829525411128998,
-0.050233110785484314,
0.0554816797375679,
0.028912797570228577,
-0.0003992756537627429,
0.017894988879561424,
-0.024129459634423256,
0.0010912979487329721,
-0.022095443680882454,
-0.056173231452703476,
-0.028986677527427673,
0.0015659085474908352,
0.018796266987919807,
0.03045964427292347,
0.035233937203884125,
-0.030818693339824677,
0.0018874671077355742,
-0.013873082585632801,
0.0016755412798374891,
0.006444054190069437,
0.043536558747291565,
0.07122708112001419,
-0.02558320015668869,
-0.025553584098815918,
0.0367557592689991,
-0.030222008004784584,
0.009058494120836258,
-0.02028150111436844,
-0.04486475884914398,
-0.028173821046948433,
-0.05673465505242348,
0.00200508045963943,
-0.0049082376062870026,
-0.025367889553308487,
-0.06340552866458893,
-0.021955518051981926,
0.01925736293196678,
-0.06510624289512634,
0.025937838479876518,
-0.018866246566176414,
0.011071443557739258,
0.007564842700958252,
0.02101801335811615,
0.07198023796081543,
-0.02555510401725769,
0.017715904861688614,
-0.048486389219760895,
-0.037976182997226715,
-0.009717813692986965,
0.03956558555364609,
-0.027564601972699165,
0.01340071577578783,
-0.0821780413389206,
-0.1378132849931717,
0.04716877639293671,
0.003722052089869976,
-0.03252086415886879,
0.007967754267156124,
-0.0284859761595726,
-0.02239648438990116,
0.005567839369177818,
-0.005731262266635895,
-0.029652735218405724,
-0.012977189384400845,
0.02417735569179058,
-0.02499397285282612,
0.00717888493090868,
-0.01763365976512432,
0.05694389343261719,
0.006929787807166576,
-0.021996039897203445,
0.04190639778971672,
0.00043520942563191056,
-0.02227187156677246,
0.02090637944638729
] |
<p>In <a href="http://arxiv.org/abs/hep-th/0702178" rel="nofollow">this 2007 paper by Alan Guth</a> discussing eternal cosmic inflation, he start's using a value $\phi$ on page 8. My understanding is that $\phi$ is the scalar field representing the dark energy of a "false vacuum" - but then why does $\phi$ appear as the dependent variable of the energy density function $V$?</p>
|
g2498
|
[
0.04693673923611641,
0.017797991633415222,
-0.019723331555724144,
-0.05581843852996826,
0.047277629375457764,
0.0486128106713295,
-0.0020598263945430517,
0.03894927725195885,
-0.09401854127645493,
-0.019201459363102913,
0.0018395395018160343,
0.043427836149930954,
0.018941059708595276,
0.0036302993539720774,
0.07098415493965149,
-0.0022534981835633516,
0.01738911308348179,
0.010113684460520744,
0.040265604853630066,
-0.004051218740642071,
-0.03695311024785042,
-0.01125950925052166,
0.03467673063278198,
-0.04550398886203766,
0.06857414543628693,
-0.05884910747408867,
0.04180747643113136,
-0.03239956125617027,
-0.014952444471418858,
-0.062277935445308685,
0.06137797608971596,
0.07116714119911194,
0.04174894466996193,
-0.02694890648126602,
-0.06017947942018509,
0.011017329059541225,
0.0769897997379303,
0.05296379700303078,
0.05018027126789093,
-0.029123736545443535,
-0.0802920013666153,
0.03710726648569107,
-0.012075402773916721,
0.00664113974198699,
-0.055668968707323074,
0.08222904056310654,
-0.06039450690150261,
0.0011392359156161547,
0.0011505457805469632,
-0.04255649074912071,
0.030415618792176247,
0.04341069236397743,
0.04037827253341675,
0.016950184479355812,
-0.0034440052695572376,
-0.032993052154779434,
0.002574346959590912,
0.0010539873037487268,
0.028612425550818443,
0.07981939613819122,
0.019268382340669632,
-0.042204711586236954,
0.04490690678358078,
-0.0016946102259680629,
0.05913783609867096,
0.012409085407853127,
-0.01916852593421936,
-0.013834361918270588,
-0.05550214648246765,
-0.03310924023389816,
-0.004774364642798901,
-0.06603112071752548,
-0.014386488124728203,
-0.01344781182706356,
-0.014753742143511772,
0.0451008677482605,
0.046278759837150574,
-0.05807330831885338,
0.053656596690416336,
-0.024673309177160263,
-0.012524900026619434,
0.018490072339773178,
0.035281404852867126,
0.006240167189389467,
0.08591614663600922,
-0.02113788202404976,
0.002948764944449067,
-0.03602587804198265,
0.01753229647874832,
-0.020918993279337883,
0.03686347231268883,
0.004059613682329655,
0.007100597955286503,
0.012371483258903027,
-0.01716093346476555,
-0.057984668761491776,
-0.03120356798171997,
0.109990693628788,
-0.016090892255306244,
0.012680614367127419,
-0.007876022718846798,
0.018588658422231674,
0.06749320775270462,
-0.0008002520771697164,
0.022429313510656357,
-0.04322339594364166,
0.017494723200798035,
-0.01682060956954956,
0.02760966494679451,
-0.003972337115556002,
-0.05362165346741676,
-0.006497844122350216,
-0.026791846379637718,
-0.048648808151483536,
-0.024172285571694374,
-0.04183011129498482,
0.041026487946510315,
-0.04932357370853424,
-0.04728527367115021,
0.03208059445023537,
-0.006947990506887436,
-0.019925033673644066,
0.03790430352091789,
0.013401093892753124,
-0.08695171028375626,
-0.01589087024331093,
0.013079055584967136,
-0.038730502128601074,
0.022113317623734474,
-0.05574091523885727,
0.0438673309981823,
-0.026560164988040924,
-0.04080665856599808,
0.035235293209552765,
0.0016987334238365293,
0.004265445284545422,
0.0005293719004839659,
-0.01473974995315075,
-0.0213474128395319,
0.0525706447660923,
-0.005692338105291128,
-0.04576939344406128,
0.009627644903957844,
-0.02411438338458538,
0.004620050545781851,
0.019076183438301086,
0.010815856978297234,
-0.04571688920259476,
0.037489570677280426,
-0.013206103816628456,
0.012819110415875912,
0.0819087028503418,
-0.04481455683708191,
0.0016711773350834846,
0.010827447287738323,
-0.025128480046987534,
0.05080750584602356,
0.03681834787130356,
-0.011559031903743744,
-0.04285866394639015,
0.06769966334104538,
0.05032510682940483,
0.03294925391674042,
-0.030071532353758812,
0.004395117983222008,
0.012336832471191883,
0.04349790886044502,
-0.045025117695331573,
0.0008333997102454305,
0.025226367637515068,
0.0006861128495074809,
0.029288263991475105,
0.019911842420697212,
-0.042580898851156235,
0.046610068529844284,
0.004841254558414221,
0.01568572409451008,
0.03751712664961815,
0.029125744476914406,
0.02583385817706585,
-0.0054858080111444,
-0.03181266784667969,
0.054373614490032196,
-0.01666797325015068,
0.05512015148997307,
0.010839204303920269,
-0.010318229906260967,
-0.0027609216049313545,
-0.03319094702601433,
-0.004106383305042982,
0.013945434242486954,
-0.021712789312005043,
0.02883954532444477,
0.07779587060213089,
0.040276892483234406,
0.016213309019804,
0.013622594065964222,
-0.049722060561180115,
-0.04747425392270088,
0.014733524061739445,
-0.03357219696044922,
0.01989300362765789,
0.08049777895212173,
0.02077261544764042,
0.015149245969951153,
0.0361514538526535,
-0.009615642949938774,
-0.04373984783887863,
0.016850952059030533,
-0.003676492255181074,
0.02819170616567135,
-0.05783301964402199,
-0.004881410859525204,
0.022228313609957695,
0.040169328451156616,
-0.005758460611104965,
-0.03421042487025261,
0.0372888520359993,
-0.010294944047927856,
0.044115327298641205,
-0.07902111858129501,
0.012224255129694939,
0.06730376183986664,
0.033633578568696976,
-0.021516943350434303,
0.012147792614996433,
-0.030294518917798996,
-0.07134782522916794,
-0.009195641614496708,
-0.0482320562005043,
-0.009713788516819477,
0.004797740373760462,
-0.042894311249256134,
0.05059723183512688,
0.056943297386169434,
0.027585983276367188,
-0.014807887375354767,
0.053891561925411224,
0.029261164367198944,
0.02603481337428093,
-0.02647189237177372,
-0.023088708519935608,
0.03707972541451454,
0.02554435096681118,
0.04470394551753998,
-0.012480725534260273,
0.025668548420071602,
-0.009665988385677338,
-0.04251273721456528,
-0.0283214058727026,
-0.012485570274293423,
-0.05246162787079811,
-0.012934968806803226,
0.02158484049141407,
0.005379118025302887,
-0.0002214793930761516,
-0.0384674146771431,
-0.006133975926786661,
0.006458806339651346,
-0.006280615460127592,
0.007391613908112049,
-0.011773284524679184,
0.026828428730368614,
0.01935233548283577,
0.019258413463830948,
-0.026997212320566177,
0.012597344815731049,
0.025453967973589897,
-0.03086758218705654,
-0.03871497884392738,
0.039540521800518036,
0.08108984678983688,
-0.004044590052217245,
-0.008978216908872128,
0.04047830030322075,
0.022410910576581955,
-0.07273180782794952,
0.00219362648203969,
0.0570015124976635,
-0.06702537089586258,
0.021565282717347145,
0.01555043924599886,
-0.008563184179365635,
-0.012195819057524204,
-0.00025193041074089706,
-0.03628663718700409,
-0.02549004927277565,
0.007845625281333923,
-0.00004801236718776636,
-0.03029775060713291,
0.054927680641412735,
0.038412753492593765,
-0.07150517404079437,
0.028191320598125458,
-0.024593548849225044,
0.055441875010728836,
0.0071530407294631,
-0.005084326956421137,
0.005901387892663479,
0.021419718861579895,
0.007677610032260418,
-0.03048204816877842,
-0.03531666472554207,
0.0030177212320268154,
-0.046322934329509735,
0.014452492818236351,
0.010725751519203186,
-0.02279326692223549,
-0.07503127306699753,
-0.00733858160674572,
0.020788028836250305,
0.022720854729413986,
0.015651840716600418,
-0.037030477076768875,
-0.024469245225191116,
0.01643660105764866,
-0.01718238554894924,
-0.004028894938528538,
0.025786178186535835,
0.014537503942847252,
-0.03739013150334358,
-0.025454586371779442,
-0.011832669377326965,
0.02949240803718567,
0.04092828556895256,
0.024598127231001854,
-0.02125696837902069,
-0.022157588973641396,
0.006384020205587149,
-0.03944966942071915,
0.014954241923987865,
-0.03892611712217331,
-0.002398267388343811,
-0.04045577347278595,
-0.035848598927259445,
-0.020094307139515877,
-0.07442235946655273,
0.046687234193086624,
-0.005047221202403307,
0.06887941807508469,
-0.04429590329527855,
0.02135145477950573,
-0.05152083933353424,
0.07169781625270844,
0.027646712958812714,
-0.013255186378955841,
-0.0778779461979866,
0.0010294911917299032,
0.032634537667036057,
0.013019018806517124,
-0.02506595104932785,
-0.01943979039788246,
0.045870453119277954,
-0.01951633393764496,
-0.009016366675496101,
0.030586659908294678,
0.042653560638427734,
-0.05067847669124603,
0.008168657310307026,
-0.026379311457276344,
0.029966086149215698,
-0.039087653160095215,
0.024666156619787216,
0.0396232046186924,
0.0014883492840453982,
0.010877171531319618,
-0.02487201988697052,
-0.009762789122760296,
-0.029517142102122307,
0.004390849731862545,
0.05028301849961281,
-0.045657940208911896,
0.03596324846148491,
0.024965621531009674,
-0.008339454419910908,
-0.09962822496891022,
-0.003778320737183094,
-0.0003138601023238152,
-0.020690323784947395,
0.023074358701705933,
0.03283286094665527,
-0.016023900359869003,
0.015537877567112446,
0.02157251536846161,
0.01741081476211548,
0.0009008575580082834,
-0.038072336465120316,
0.003537598764523864,
0.043530434370040894,
-0.04534279927611351,
0.0177917517721653,
-0.012167234905064106,
-0.029542792588472366,
-0.0008201083983294666,
0.014526222832500935,
0.020704133436083794,
0.05719870328903198,
-0.02112887054681778,
-0.052138809114694595,
0.02269463799893856,
0.021114060655236244,
-0.06044817715883255,
0.04265356808900833,
-0.03532028943300247,
-0.0005333346780389547,
0.039011888206005096,
0.04297472536563873,
-0.05532904714345932,
0.003265458159148693,
-0.05787784606218338,
0.010732755064964294,
-0.026168271899223328,
0.0150840375572443,
-0.03515034168958664,
0.049774352461099625,
-0.03596578538417816,
0.06879409402608871,
0.011091689579188824,
0.0718756914138794,
0.014135311357676983,
0.03894978389143944,
0.04451606422662735,
-0.038082268089056015,
-0.029930943623185158,
-0.024854743853211403,
0.085488460958004,
0.02587820403277874,
0.04455791786313057,
0.005471555981785059,
-0.04029691219329834,
0.03186066076159477,
0.003301967866718769,
0.02101721055805683,
0.029110591858625412,
-0.07387792319059372,
0.05318448692560196,
-0.06728164851665497,
0.0037282812409102917,
-0.05896017327904701,
-0.00946618989109993,
0.09741450846195221,
-0.0016686453018337488,
0.011671260930597782,
0.02310315892100334,
0.019043410196900368,
0.027473626658320427,
0.009919097647070885,
-0.021644558757543564,
0.015492069534957409,
0.02846822328865528,
-0.036462318152189255,
0.0028565144166350365,
0.060904450714588165,
-0.016716966405510902,
0.09777092188596725,
-0.04832879453897476,
0.0029029427096247673,
-0.012313990853726864,
0.006898846477270126,
-0.007020702585577965,
-0.04097083956003189,
0.021899232640862465,
-0.023632902652025223,
0.0016490668058395386,
0.05955158546566963,
0.015148082748055458,
-0.08110247552394867,
-0.022477589547634125,
-0.02856045588850975,
0.02468050643801689,
-0.0011616104748100042,
0.003979380242526531,
0.020297154784202576,
0.004746349528431892,
0.04748620092868805,
0.005921546835452318,
0.011187172494828701,
-0.03468107432126999,
-0.034916602075099945,
-0.013216900639235973,
0.012420154176652431,
-0.010240331292152405,
0.023288318887352943,
0.04211904853582382,
-0.02108079195022583,
0.027722366154193878,
-0.033143263310194016,
-0.018469739705324173,
-0.020074790343642235,
-0.04382247105240822,
0.05446593463420868,
0.055481743067502975,
0.037043601274490356,
0.02678818814456463,
-0.018233846873044968,
-0.02881462126970291,
-0.039277270436286926,
-0.04708831012248993,
0.008625700138509274,
0.0036510464269667864,
-0.04935215413570404,
0.010883727110922337,
-0.03094237484037876,
0.02382863499224186,
-0.008829236030578613,
0.036559704691171646,
0.04846225306391716,
0.005447935312986374,
-0.04032491147518158,
0.00519053777679801,
-0.008167966268956661,
0.027882317081093788,
0.02751683071255684,
0.04176140949130058,
0.010674151591956615,
-0.06604277342557907,
0.016617804765701294,
0.02646595984697342,
-0.014725244604051113,
-0.03006412461400032,
0.03199363499879837,
0.031208939850330353,
0.020228883251547813,
-0.005633807275444269,
0.11180554330348969,
0.00830115657299757,
0.006534993648529053,
-0.08629994839429855,
0.0048448131419718266,
0.004678268451243639,
-0.0052614975720644,
-0.03710193559527397,
0.06640584766864777,
-0.016965065151453018,
-0.01923516020178795,
-0.01978999376296997,
0.0347331203520298,
0.03878014162182808,
0.010825078003108501,
0.00971572007983923,
-0.028954878449440002,
-0.04357816278934479,
-0.049530934542417526,
-0.031670015305280685,
0.0005275567527860403,
0.01748749054968357,
-0.03007538430392742,
-0.001625863485969603,
0.004844063892960548,
-0.03839532658457756,
-0.06722971796989441,
-0.009720772504806519,
0.001266222563572228,
0.03557097911834717,
0.006057416088879108,
-0.00041607703315094113,
0.02195017598569393,
-0.026261795312166214,
-0.03260734677314758,
-0.008572475984692574,
-0.036490559577941895,
0.013980496674776077,
-0.0013826485956087708,
0.031092246994376183,
-0.0013530791038647294,
0.008363292552530766,
0.053114619106054306,
-0.055243801325559616,
-0.0030674119479954243,
-0.06308144330978394,
-0.01339044701308012,
0.012021111324429512,
-0.00009812900680117309,
-0.036195751279592514,
0.015657994896173477,
-0.011972744949162006,
-0.021945862099528313,
-0.092315673828125,
-0.02144673652946949,
-0.015359267592430115,
0.03744299337267876,
-0.028528930619359016,
0.0975407138466835,
-0.07066813111305237,
0.025384603068232536,
-0.01935775764286518,
-0.04663398116827011,
-0.034648653119802475,
-0.03614690154790878,
0.006018649786710739,
-0.014193781651556492,
-0.018941283226013184,
-0.006638370919972658,
0.02015049383044243,
-0.032718364149332047,
-0.0052087134681642056,
-0.06389749050140381,
0.004902366083115339,
-0.05268664285540581,
-0.03802042454481125,
0.014989681541919708,
0.033147163689136505,
0.014426538720726967,
-0.03933403268456459,
0.03303344175219536,
0.0044219535775482655,
-0.038329001516103745,
0.045464739203453064,
-0.04533382132649422,
0.03762604668736458,
-0.032491039484739304,
0.013932540081441402,
-0.033157818019390106,
-0.016374824568629265,
0.02080787904560566,
-0.010106774047017097,
0.04116746038198471,
0.050883304327726364,
-0.02185695804655552,
0.027827957645058632,
0.0033299957867711782,
0.04136732220649719,
0.005633438937366009,
0.012316115200519562,
0.04087812080979347,
-0.018420454114675522,
-0.058491144329309464,
0.030952103435993195,
0.019538890570402145,
0.003920986317098141,
0.018289467319846153,
0.03792871907353401,
0.01879338175058365,
0.056099411100149155,
-0.02617386169731617,
0.026914231479167938,
-0.03389382362365723,
0.06710309535264969,
0.024503465741872787,
0.004620195832103491,
-0.03824648633599281,
-0.005078862886875868,
0.04650135338306427,
-0.06719823181629181,
-0.03471067547798157,
0.06346520036458969,
-0.027387935668230057,
-0.019387634471058846,
-0.025071928277611732,
-0.013693507760763168,
-0.025578800588846207,
-0.015824129804968834,
0.026163285598158836,
-0.026503928005695343,
-0.0066332644782960415,
0.04465358331799507,
-0.019222401082515717,
-0.04717325419187546,
-0.014931567013263702,
-0.052740588784217834,
0.030051270499825478,
-0.031140798702836037,
-0.0008510405896231532,
0.04918469488620758,
-0.0006090819952078164,
0.02211230807006359,
0.005953036714345217,
-0.04009006544947624,
0.06997925043106079,
-0.04432035610079765,
0.0486864410340786,
-0.0414951927959919,
-0.04902728646993637,
-0.03520601987838745,
-0.030139612033963203,
-0.0812753289937973,
-0.062309037894010544,
0.00904147606343031,
0.045447029173374176,
0.012073032557964325,
-0.017426369711756706,
0.02336835488677025,
0.02871675416827202,
-0.03477662801742554,
-0.06605837494134903,
-0.03207404166460037,
-0.04289814457297325,
-0.030393453314900398,
0.016943559050559998,
0.03993874043226242,
-0.02648664079606533,
-0.03789055347442627,
0.009834234602749348,
-0.03168618679046631,
0.019257331266999245,
0.0501294806599617,
0.015857171267271042,
0.030527302995324135,
0.038191474974155426,
0.05249383673071861,
0.08970768004655838,
-0.005097644403576851,
-0.008795453235507011,
0.005647081881761551,
0.02321743220090866,
0.03263063356280327,
0.02902558632194996,
-0.003684825263917446,
-0.054492056369781494,
0.03169780597090721,
0.026577483862638474,
-0.06435549259185791,
-0.009632798843085766,
-0.0021946055348962545,
0.028533348813652992,
0.008409010246396065,
-0.04564724862575531,
-0.03791875019669533,
-0.03149161860346794,
-0.03263691067695618,
0.03483208641409874,
-0.034728728234767914,
-0.051672033965587616,
-0.03990734741091728,
0.050356969237327576,
0.03775304928421974,
-0.054775115102529526,
-0.047884706407785416,
0.007943264208734035,
0.014357256703078747,
-0.09586825221776962,
0.013653547503054142,
0.03573276847600937,
0.0024844969157129526,
-0.032783884555101395,
-0.0036783372052013874,
0.004715939052402973,
0.002191466512158513,
0.07563869655132294,
-0.042827725410461426,
0.0037278751842677593,
-0.02873537503182888,
0.016065552830696106,
-0.030656542629003525,
-0.026562044396996498,
-0.03260277211666107,
-0.06978201866149902,
-0.005580354947596788,
0.05662643909454346,
0.01829177513718605,
-0.006253683473914862,
-0.04936138913035393,
-0.0326252356171608,
0.021349705755710602,
0.016554903239011765,
0.010611367411911488,
0.012835098430514336,
-0.01897682435810566,
-0.019145255908370018,
0.033792249858379364,
-0.014290919527411461,
-0.07115980237722397,
0.013966742902994156,
0.003417078172788024,
0.033941831439733505,
-0.030703533440828323,
0.022896697744727135,
0.008693068288266659
] |
<p>I have some question about interpreting PDG particle cross section data sets' metadata fields. The data sets I'm having questions for are <a href="http://pdg.lbl.gov/2011/hadronic-xsections/hadron.html" rel="nofollow">http://pdg.lbl.gov/2011/hadronic-xsections/hadron.html</a></p>
<p>For example, the data set for p-bar p collision <a href="http://pdg.lbl.gov/2011/hadronic-xsections/pbarp_total.dat" rel="nofollow">http://pdg.lbl.gov/2011/hadronic-xsections/pbarp_total.dat</a></p>
<p>The data set has meta data fields as shown at the top of the .dat file. I have questions about the following metadata fields. Apologies if the questions are silly.</p>
<ul>
<li><p><code>BEAM_MASS</code></p>
<p>Is this the energy of the beam particle w.r.t. lab coordinates?</p></li>
<li><p><code>TARGET_MASS</code></p>
<p>Again, w.r.t. lab coordinates?</p></li>
<li><p><code>THRESHOLD</code></p>
<p>Not exactly sure what this is, but most files has 0 for this value, what's it?</p></li>
<li><p><code>FINAL_STATE_MULTIPLICITY</code></p>
<p>Is this multiplicity from phase space configuration? Could you given a reference or an example so I may check details of the derivation?</p></li>
<li><p><code>PLAB(GEV/C)</code></p>
<p>Momentum of the beam particle w.r.t. lab reference coordinate?</p></li>
<li><p><code>LAB_MIN</code>, <code>PLAB_MAX</code></p>
<p>Minimum and maximum of PLAB? So a data point in the plot will have an x coordinate with uncertainty? how should it be plotted then? It seems in the plot in the PDF the x-coordinate doesn't have "bars" but only the y-coordinate has it. How is the uncertainty of x taken into account?</p></li>
<li><p><code>SY_ER+(PCT)</code>, <code>SY_ER-(PCT)</code>:</p>
<p>What's this? is it visible in the plot at all?</p></li>
<li><p><code>REFERENCE FLAG</code></p>
<p>For example, "ELIOFF 62 PR 128, 869", but what is the last number here? My guess is .</p></li>
</ul>
|
g2499
|
[
0.014294907450675964,
0.007170905824750662,
0.0023839271161705256,
-0.049848783761262894,
0.07190872728824615,
-0.0235317163169384,
-0.04462157189846039,
0.02238491177558899,
-0.026292141526937485,
-0.01043909601867199,
0.009228426031768322,
0.022832514718174934,
0.005151576828211546,
-0.06428366899490356,
-0.017261609435081482,
-0.09100403636693954,
0.054574791342020035,
-0.022728964686393738,
0.05557979270815849,
0.025646556168794632,
-0.0036748782731592655,
0.03591563180088997,
0.039299964904785156,
-0.07470841705799103,
0.03471031039953232,
-0.004474133253097534,
-0.009826110675930977,
-0.024178551509976387,
-0.09727143496274948,
-0.06566023081541061,
0.07242482900619507,
-0.011964717879891396,
0.002342265797778964,
0.003012331435456872,
-0.01641375944018364,
-0.07080154120922089,
-0.0014634536346420646,
0.02962099201977253,
-0.023073380813002586,
0.04632837325334549,
-0.0027480158023536205,
-0.016635458916425705,
0.03628501296043396,
0.020278634503483772,
-0.00927272904664278,
0.009306088089942932,
-0.06256557255983353,
-0.01244942843914032,
-0.014922736212611198,
-0.03270495682954788,
-0.029417600482702255,
0.035372309386730194,
0.013194547034800053,
0.019969752058386803,
0.04070260375738144,
0.04196370765566826,
0.037366822361946106,
0.008002299815416336,
0.04346830025315285,
-0.03126824274659157,
0.047996386885643005,
0.03411978483200073,
0.0029626560863107443,
-0.024351447820663452,
0.04593760520219803,
-0.0016490110429003835,
-0.07817386090755463,
-0.006204999051988125,
-0.08056250214576721,
-0.030625730752944946,
0.02729152701795101,
-0.009663205593824387,
-0.019529592245817184,
0.013315541669726372,
-0.03620271757245064,
-0.05217726528644562,
-0.06985064595937729,
0.027862880378961563,
0.0022217025980353355,
0.008034978061914444,
0.01148325577378273,
0.0062958491034805775,
-0.040116168558597565,
-0.026664232835173607,
0.022362446412444115,
0.04132126271724701,
-0.031233077868819237,
0.014152002520859241,
-0.01333546731621027,
-0.024011217057704926,
0.04143218323588371,
-0.03856870159506798,
0.026051975786685944,
-0.004868650808930397,
-0.0394807830452919,
0.052688874304294586,
-0.0040034400299191475,
0.04334362968802452,
-0.004949840251356363,
0.03736594691872597,
-0.01055834162980318,
0.046257562935352325,
0.005331723485141993,
0.04467371851205826,
-0.03845083341002464,
-0.005471004173159599,
0.04421995207667351,
0.02295529656112194,
-0.004319749306887388,
-0.007494272664189339,
-0.07892262190580368,
0.022925671190023422,
-0.05478714406490326,
-0.014596432447433472,
-0.052267566323280334,
-0.06660885363817215,
0.07067450881004333,
-0.025115082040429115,
-0.048081833869218826,
0.01794772781431675,
0.058869000524282455,
-0.011526248417794704,
0.0382232740521431,
0.026768164709210396,
-0.041941091418266296,
-0.04291462153196335,
-0.022193381562829018,
0.007247039116919041,
0.029912808910012245,
-0.030676882714033127,
-0.04187759757041931,
-0.05783331021666527,
-0.01400948315858841,
0.055717527866363525,
-0.01967603527009487,
-0.04088376834988594,
0.029608121141791344,
0.06194906681776047,
0.025869978591799736,
-0.029320454224944115,
0.01362263411283493,
-0.026792092248797417,
-0.04308519512414932,
-0.09142801910638809,
-0.007385924458503723,
-0.002060180064290762,
-0.034951481968164444,
-0.029085347428917885,
0.05453326553106308,
0.07729464024305344,
0.02832503616809845,
0.05471782013773918,
0.028545096516609192,
-0.0212316382676363,
0.013293254189193249,
-0.012362110428512096,
-0.0013700549025088549,
-0.06073375418782234,
-0.03633485734462738,
-0.013334964402019978,
0.025051528587937355,
0.03258458897471428,
0.029279213398694992,
-0.01221854891628027,
0.02796212024986744,
-0.013396558351814747,
0.024426294490695,
-0.03893027827143669,
0.0052216071635484695,
-0.04714233800768852,
-0.005582004319876432,
0.00030095005058683455,
0.023569324985146523,
-0.01216778066009283,
-0.031565144658088684,
0.0622686930000782,
-0.0030551431700587273,
-0.007379319053143263,
0.035650886595249176,
0.03953590989112854,
-0.017797477543354034,
0.013092371635138988,
0.035121262073516846,
0.019272584468126297,
-0.002024056389927864,
-0.02599223516881466,
0.00040511952829547226,
0.008219028823077679,
-0.026567190885543823,
-0.013298329897224903,
-0.026976224035024643,
-0.034951113164424896,
-0.044441718608140945,
-0.00433537969365716,
0.023420045152306557,
-0.009326557628810406,
-0.012467618100345135,
-0.010987875051796436,
-0.024888789281249046,
0.01736169494688511,
-0.008525758050382137,
0.03591271862387657,
-0.04670412838459015,
0.046204742044210434,
0.00010135719639947638,
-0.0118476003408432,
-0.03396870940923691,
0.0003401933645363897,
-0.029308347031474113,
0.03629467263817787,
0.016545884311199188,
-0.04126300662755966,
0.0008549338090233505,
0.051572300493717194,
-0.03353077545762062,
-0.0011943097924813628,
-0.013409299775958061,
0.023240618407726288,
0.006625221110880375,
0.002009932417422533,
-0.09310062229633331,
-0.018750358372926712,
-0.013253290206193924,
0.020875144749879837,
0.01192884985357523,
0.04727524146437645,
0.020360242575407028,
-0.01938827708363533,
-0.022391170263290405,
0.012322125025093555,
-0.04276895523071289,
0.0295749269425869,
-0.03818045184016228,
-0.007247633766382933,
-0.021092602983117104,
-0.02940402179956436,
-0.02565218321979046,
-0.025362294167280197,
0.005003012716770172,
0.02321476675570011,
0.035834893584251404,
0.0090439198538661,
-0.025525884702801704,
0.024532800540328026,
0.07067625969648361,
-0.0020647537894546986,
0.027081195265054703,
0.02890169806778431,
-0.0251056719571352,
0.02565041184425354,
-0.005712174344807863,
0.028106719255447388,
0.013077504932880402,
0.026130961254239082,
-0.005492296535521746,
-0.08135442435741425,
-0.021073775365948677,
0.012987767346203327,
-0.026142815127968788,
0.01694549061357975,
0.03481592610478401,
0.015521890483796597,
-0.07846946269273758,
0.018877696245908737,
0.01650003157556057,
-0.005980598274618387,
0.03931017965078354,
0.013389027677476406,
0.027533868327736855,
-0.028813136741518974,
-0.024003375321626663,
0.005212096497416496,
0.08696430176496506,
0.01948346570134163,
0.022371690720319748,
0.006235125474631786,
0.03233138099312782,
-0.007714244071394205,
-0.05913778021931648,
-0.057806480675935745,
-0.03776558116078377,
0.007692260667681694,
0.016612756997346878,
0.024846255779266357,
0.032504621893167496,
0.011641060002148151,
0.001166188158094883,
-0.006169192958623171,
-0.009236767888069153,
0.05311267450451851,
0.03431614488363266,
-0.04166082665324211,
0.04180026799440384,
-0.031120385974645615,
-0.03276964649558067,
-0.04909469187259674,
0.010669981129467487,
-0.03647772967815399,
0.05521215498447418,
0.012033837847411633,
-0.030779236927628517,
0.04051731154322624,
-0.035562511533498764,
0.05703171715140343,
0.03628663718700409,
0.0068446057848632336,
-0.037096090614795685,
-0.0028353799134492874,
-0.05196483060717583,
0.02382996864616871,
-0.0005685752839781344,
0.01873762533068657,
0.02275656722486019,
-0.02341240830719471,
0.004727015737444162,
-0.018190205097198486,
-0.02286708354949951,
-0.0025091434363275766,
-0.025114532560110092,
0.06022275611758232,
0.010164719074964523,
-0.038216885179281235,
0.06150718778371811,
-0.024867065250873566,
0.025468068197369576,
0.02365737594664097,
0.0022347192279994488,
0.0074994973838329315,
-0.001477128709666431,
0.0034152143634855747,
0.011508838273584843,
-0.03062182106077671,
0.015731558203697205,
0.02775152586400509,
-0.05190112441778183,
-0.016476592049002647,
-0.05163869261741638,
0.006567792035639286,
-0.015995372086763382,
0.009399333968758583,
0.016936417669057846,
-0.004114235285669565,
0.03348631039261818,
-0.05665162205696106,
0.01155890990048647,
-0.001142428140155971,
0.04665384814143181,
-0.036759153008461,
-0.0026128925383090973,
0.0060656252317130566,
0.013852445408701897,
0.06325089186429977,
-0.016757503151893616,
0.02481417916715145,
-0.03999783843755722,
0.04013853892683983,
-0.012447030283510685,
-0.02302481420338154,
0.00616846326738596,
0.0547838993370533,
-0.03730238974094391,
-0.03707649186253548,
0.04214126616716385,
-0.02933635376393795,
-0.032794270664453506,
0.020605359226465225,
-0.05136491358280182,
0.052262529730796814,
0.03691320866346359,
-0.05868731066584587,
-0.007440974470227957,
-0.051797181367874146,
0.057515814900398254,
0.023573288694024086,
-0.08550738543272018,
-0.05381307378411293,
-0.04033457115292549,
-0.030133021995425224,
0.006609507370740175,
0.03346863389015198,
0.00018508064385969192,
0.06228315457701683,
0.01816437393426895,
0.03732195124030113,
0.015615253709256649,
-0.05384070426225662,
0.006097407080233097,
0.04901742935180664,
0.053810928016901016,
-0.007860608398914337,
0.04517337679862976,
-0.02968837134540081,
-0.1238679438829422,
0.025524595752358437,
0.043332990258932114,
-0.09071724861860275,
-0.013408238068223,
0.061482615768909454,
0.022862054407596588,
0.032999005168676376,
-0.02556961588561535,
0.03215578943490982,
-0.03022622875869274,
-0.05116210877895355,
0.022148264572024345,
-0.04376527667045593,
-0.026946106925606728,
-0.07744506001472473,
0.050012748688459396,
-0.058874163776636124,
0.000010812399523274507,
-0.04357293248176575,
0.03504490107297897,
-0.005740908440202475,
0.019449381157755852,
0.020062431693077087,
-0.00795496441423893,
-0.06144440174102783,
0.0054940530098974705,
0.04798159375786781,
0.03677351400256157,
-0.001736778998747468,
0.04481764882802963,
-0.04507189616560936,
0.07908974587917328,
0.057539407163858414,
0.05116100609302521,
-0.024241026490926743,
-0.025147132575511932,
-0.026469217613339424,
0.08139202743768692,
0.05859261751174927,
-0.017083104699850082,
0.03788735345005989,
-0.030670683830976486,
-0.001287833321839571,
-0.044032398611307144,
-0.04022541269659996,
-0.01788591779768467,
0.041778646409511566,
-0.02345147915184498,
-0.05369796231389046,
-0.003871633904054761,
-0.03951871395111084,
-0.05071769654750824,
0.044589847326278687,
-0.039731819182634354,
0.015898460522294044,
-0.038096506148576736,
0.02953215502202511,
0.012604289688169956,
-0.03968149051070213,
-0.03361036255955696,
-0.010926461778581142,
0.03553175926208496,
0.006625815760344267,
0.05701147019863129,
0.024844277650117874,
-0.02898690663278103,
-0.001633652951568365,
-0.04684380814433098,
-0.04284079745411873,
-0.027673248201608658,
-0.0005975797539576888,
-0.016380133107304573,
0.017975063994526863,
-0.07605040818452835,
-0.039633750915527344,
-0.03694455325603485,
-0.01839470863342285,
-0.020787617191672325,
-0.03172406926751137,
0.007381979376077652,
-0.061360955238342285,
0.025028197094798088,
0.05442965030670166,
-0.052578601986169815,
-0.0010397559963166714,
-0.004226855933666229,
-0.035056088119745255,
-0.02862210012972355,
0.027732331305742264,
0.009537524543702602,
0.033214863389730453,
-0.002343958942219615,
-0.027593346312642097,
0.03333258256316185,
-0.029224280267953873,
0.01597405970096588,
-0.012073910795152187,
-0.04847782850265503,
0.022716306149959564,
0.05344007536768913,
0.03198139742016792,
-0.023555098101496696,
-0.035569917410612106,
0.00038560363464057446,
-0.02713094837963581,
-0.011327765882015228,
0.026830919086933136,
0.018209047615528107,
0.033832453191280365,
0.011828461661934853,
-0.025201277807354927,
-0.07026028633117676,
0.06327907741069794,
0.05599522590637207,
0.016134845092892647,
0.028166135773062706,
-0.06619889289140701,
0.03513120859861374,
0.02140149101614952,
0.018333394080400467,
0.00691733555868268,
-0.040962979197502136,
-0.04326567426323891,
-0.02729591354727745,
0.09430870413780212,
-0.008897489868104458,
-0.0039765196852386,
-0.026015430688858032,
0.06246253475546837,
0.0938294529914856,
0.021021870896220207,
0.016731712967157364,
-0.003978037275373936,
0.04381123185157776,
-0.021578911691904068,
0.011624428443610668,
0.0773637592792511,
0.0012107095681130886,
0.002814867999404669,
0.026569901034235954,
-0.005916914902627468,
-0.026646535843610764,
-0.05536654591560364,
-0.013363858684897423,
0.003555232658982277,
0.081578329205513,
0.019806228578090668,
-0.01333370991051197,
0.006102867424488068,
0.012167733162641525,
0.004909900948405266,
-0.02484639547765255,
-0.04527483880519867,
0.05094096437096596,
-0.023996705189347267,
0.028289465233683586,
-0.02297874540090561,
0.058003805577754974,
0.039224497973918915,
0.03664981946349144,
-0.0175040140748024,
0.003587544895708561,
0.0015609259717166424,
0.069890096783638,
-0.005848133470863104,
0.015352805145084858,
-0.04258795082569122,
-0.012059477157890797,
0.005818346980959177,
-0.00904179085046053,
0.03279762342572212,
0.06099708005785942,
0.01761767826974392,
-0.02192004770040512,
-0.05911063402891159,
-0.004097729455679655,
-0.011449095793068409,
0.013053998351097107,
-0.012797008268535137,
0.007075970526784658,
0.07470685988664627,
0.03540591150522232,
0.06186796724796295,
-0.007257731631398201,
0.036929432302713394,
-0.019410040229558945,
0.005996385123580694,
0.02494213357567787,
0.009648669511079788,
0.0015075342962518334,
-0.040302883833646774,
-0.005587784107774496,
0.02072117291390896,
-0.040972232818603516,
0.01089512649923563,
-0.07248242199420929,
-0.07713908702135086,
-0.07106973230838776,
-0.010504577308893204,
0.09263922274112701,
0.03930244967341423,
-0.0047576092183589935,
0.005462450906634331,
-0.00048395615885965526,
0.0397920235991478,
0.03310060501098633,
-0.012703442946076393,
-0.016240356490015984,
0.04911872372031212,
-0.01615830510854721,
0.0038805862423032522,
0.04061567783355713,
-0.04342854768037796,
-0.03930641710758209,
-0.03870050609111786,
-0.02418319694697857,
0.0161111019551754,
0.00964263267815113,
0.04533853381872177,
-0.05493246018886566,
0.08815400302410126,
0.0067229256965219975,
-0.034046538174152374,
-0.01091067586094141,
-0.007454040925949812,
-0.06817696243524551,
0.06205891817808151,
0.0005022116820327938,
-0.009148743003606796,
-0.010005643591284752,
-0.0004432200803421438,
-0.0479227714240551,
0.004016402177512646,
0.0004252530634403229,
0.026066862046718597,
0.017553893849253654,
-0.025669734925031662,
0.03006605990231037,
0.033741146326065063,
0.022702950984239578,
0.02666502818465233,
-0.04130547493696213,
0.036005277186632156,
-0.04728332906961441,
0.07172271609306335,
0.05705677717924118,
0.023761652410030365,
0.06099706143140793,
-0.0032332665286958218,
-0.006786718964576721,
-0.01496390625834465,
-0.034418985247612,
0.02008702978491783,
-0.027570877224206924,
0.011411657556891441,
-0.05454995110630989,
-0.021407978609204292,
0.020726578310132027,
-0.002859060186892748,
-0.022559508681297302,
0.04489699751138687,
0.03004884533584118,
0.030492188408970833,
-0.010949927382171154,
0.009143004193902016,
-0.0025533984880894423,
0.007175071630626917,
-0.038479793816804886,
-0.03992320969700813,
0.0057249730452895164,
-0.0016353847458958626,
0.02179277129471302,
0.0027757955249398947,
0.02566603384912014,
0.0052094790153205395,
0.05074866861104965,
-0.039170701056718826,
-0.023242967203259468,
-0.02300785295665264,
-0.035357799381017685,
0.02898867055773735,
0.07819081842899323,
0.014249666593968868,
0.007171864155679941,
0.012349658645689487,
-0.02413768693804741,
0.060083337128162384,
-0.006259588059037924,
0.07285995036363602,
-0.03680712357163429,
-0.03734215348958969,
-0.024345437064766884,
-0.032641779631376266,
0.0028204256668686867,
0.022877512499690056,
0.0020078716333955526,
-0.0220915749669075,
-0.006925560999661684,
-0.03230743855237961,
0.04723185673356056,
-0.007248940411955118,
-0.04670127108693123,
-0.02287140116095543,
0.036265093833208084,
0.00047207329771481454,
0.021388160064816475,
-0.03837022930383682,
0.019522706046700478,
-0.013064431957900524,
-0.011742540635168552,
0.01966116577386856,
0.03418521210551262,
-0.0003821246209554374,
0.02040439285337925,
0.01152004674077034,
-0.002450291533023119,
-0.04422792047262192,
-0.07084397226572037,
0.017135409638285637,
0.030604461207985878,
0.011592528782784939,
-0.012565097771584988,
0.061248768121004105,
0.034681469202041626,
0.03068036213517189,
0.008849910460412502,
0.027044344693422318,
0.01964809186756611,
0.024262985214591026,
-0.010716354474425316,
-0.01844489388167858,
0.07378503680229187,
-0.11291755735874176,
-0.04899278283119202,
0.07029448449611664,
0.007355322130024433,
0.025029335170984268,
-0.03882941976189613,
-0.0012259345967322588,
-0.05987978354096413,
-0.00888015329837799,
-0.020236462354660034,
0.009819606319069862,
-0.0062174382619559765,
-0.013667169027030468,
-0.006628996226936579,
-0.0040060305036604404,
0.01812933199107647,
0.017463944852352142,
0.0012307980796322227,
0.02595188282430172,
-0.06182364374399185,
-0.032727666199207306,
-0.04756442457437515,
0.045623451471328735,
0.046674955636262894,
0.007489701267331839,
-0.04081181809306145,
-0.004012614954262972,
0.002962011843919754,
0.0600469745695591,
-0.04689491540193558,
-0.06697463244199753,
0.05991709232330322,
0.07017847895622253,
0.020925957709550858,
-0.00624708691611886,
0.03221871703863144,
-0.0055130175314843655,
0.04844900593161583,
0.06045520678162575,
-0.04657858610153198,
0.007541297003626823,
-0.07373606413602829,
-0.011748196557164192
] |
<p>I'm trying to write N=4 SYM in terms of N=1 superfields. I have the lagrangian</p>
<p>$$\mathcal{L}=\frac{1}{16 k} \int d^2 \sigma \text{Tr} \big[W^a W_a\big]+c.c+\int d^4\theta \text{Tr}\big[\bar{\Phi}^i e^V \Phi^i e^{-V}\big]+\frac{\sqrt{2}}{3}\int d^2\theta \text{Tr}\big[\phi^i [\phi^j,\phi^k]\big]\epsilon_{ijk}+c.c $$</p>
<p>Where the $\Phi^i$ are chiral superfields and V is a vector superfield. In components, this is
all fine except for the Yukawa terms
$$\mathcal{L} \supset i\sqrt{2} f^{ABC} Z^{i\dagger}_A \psi^i_B \lambda_C - \sqrt{2}\epsilon_{ijk} Z^i_A \psi^j_B \psi^k_C+c.c $$</p>
<p>Where $A,B,C$, are $SU(N)$ gauge group indices, $i,j,k$ number my 3 chiral superfields, which have an explicit $SU(3)$ symmetry, the $Z^i_A$ are the complex scalars from my chiral superfields, $\psi^i_A$ are the fermions from my chiral superfields, and the $\lambda_A$ is the fermion from my vector superfield. </p>
<p>The fermions combine into an fundamental $SU(4)$ multiplet $\chi^I=(\psi^i, \lambda)$, and I decompose my complex scalars into real ones in a fundamental $SO(6)$ (isomorphic to $SU(4)$) multiplet, $Z^i=X^a+iX^{a+3}$. I should be able to write the Yukawa terms as</p>
<p>$$\mathcal{L} \supset f^{ABC} X^a_A C^a_{IJ}\chi^I \chi^J +c.c $$</p>
<p>essentially putting the scalars into the antisymmetric matrix representation of $SU(4)$, $X_{IJ}=X_{[IJ]}=X^a_{IJ}X^a$.</p>
<p>So I need to show that the $C^a_{IJ}$ that I have are an invariant symbol of $SO(6)=SU(4)$, and thus my Lagrangian has that R symmetry. Not sure how to do that... a reference I found says they should be related to the $SO(6)$ gamma matrices (<a href="http://arxiv.org/abs/hep-th/0201253">http://arxiv.org/abs/hep-th/0201253</a>, below equation 3.1), but that hasn't been very helpful.</p>
|
g2500
|
[
0.020570965483784676,
-0.010276701301336288,
-0.014985265210270882,
-0.05763861536979675,
0.019056763499975204,
-0.005310427863150835,
0.05759675055742264,
0.08678417652845383,
-0.03799371421337128,
0.005788868758827448,
-0.04707219824194908,
-0.016460517421364784,
-0.0027461678255349398,
0.060765158385038376,
-0.013380404561758041,
0.0014618424465879798,
0.02192855253815651,
0.03481867164373398,
0.009985879063606262,
-0.06709939986467361,
-0.011730662547051907,
-0.00803963653743267,
0.004731465131044388,
-0.0464879535138607,
0.04876787215471268,
-0.044438011944293976,
0.035794779658317566,
-0.0256965234875679,
-0.016795868054032326,
-0.034577954560518265,
0.03495584428310394,
0.028872888535261154,
0.010766358114778996,
-0.023911841213703156,
-0.0035566093865782022,
-0.03181849792599678,
0.05149506404995918,
0.023778513073921204,
0.02218189463019371,
-0.037870217114686966,
-0.01383855938911438,
-0.03099687397480011,
0.05159376934170723,
0.028177272528409958,
-0.01632036082446575,
0.030596943572163582,
-0.0035744851920753717,
0.0018109773518517613,
-0.060621075332164764,
-0.009404391050338745,
0.07994097471237183,
0.0035596308298408985,
0.02962270751595497,
-0.07422419637441635,
-0.03467739000916481,
0.04811249300837517,
0.0020506391301751137,
0.0077024237252771854,
0.015059771947562695,
0.08661994338035583,
-0.008643269538879395,
-0.08926673978567123,
-0.004445718135684729,
0.02043887786567211,
0.08010464161634445,
0.06275512278079987,
-0.0280197411775589,
-0.03209799900650978,
-0.04066173732280731,
-0.03947362303733826,
-0.045197777450084686,
-0.01262060645967722,
0.05517136678099632,
-0.008517595008015633,
-0.0390140525996685,
0.005476886406540871,
-0.013578517362475395,
0.024044247344136238,
-0.028765305876731873,
-0.02265748754143715,
-0.017758391797542572,
-0.008768893778324127,
0.016859719529747963,
0.07334597408771515,
0.007865866646170616,
-0.03800521045923233,
-0.011417108587920666,
-0.00800752080976963,
-0.012409793213009834,
-0.052258361130952835,
0.012667867355048656,
0.014874090440571308,
-0.028180714696645737,
0.01804177835583687,
0.02131073921918869,
0.048668429255485535,
-0.0046911658719182014,
0.025857508182525635,
-0.06094692274928093,
-0.10859125107526779,
-0.015256121754646301,
0.05195261538028717,
0.041636910289525986,
-0.015692848712205887,
-0.034797303378582,
-0.026584917679429054,
0.06481259316205978,
-0.020593363791704178,
0.0077028581872582436,
0.011715440079569817,
-0.031404197216033936,
0.048189662396907806,
-0.047878630459308624,
0.00198399368673563,
-0.03366374596953392,
-0.010730158537626266,
0.003350808285176754,
-0.04245903715491295,
-0.029029566794633865,
-0.014837873168289661,
-0.014792095869779587,
-0.00006428326014429331,
0.023553751409053802,
0.01784980110824108,
0.023973027244210243,
0.023930111899971962,
0.03042306751012802,
0.03904423117637634,
0.04117603227496147,
-0.023923581466078758,
-0.038507264107465744,
-0.053912024945020676,
-0.02006395161151886,
0.04755363613367081,
-0.006120920646935701,
0.030752234160900116,
-0.005428950302302837,
0.04907330870628357,
-0.057188380509614944,
-0.0342818982899189,
0.013484179973602295,
-0.01285050343722105,
0.02412179671227932,
-0.057609762996435165,
-0.004691197071224451,
-0.028687693178653717,
-0.036160316318273544,
-0.09107950329780579,
0.03649749606847763,
-0.0395272895693779,
0.02273685671389103,
0.055210988968610764,
-0.03517953306436539,
-0.0035717885475605726,
0.03366246446967125,
-0.0042373365722596645,
0.03215185925364494,
-0.014151323586702347,
-0.04342471808195114,
-0.018731573596596718,
0.016493452712893486,
-0.03559936583042145,
0.04461895674467087,
-0.002166500547900796,
0.002147109480574727,
0.03498050943017006,
0.06054200604557991,
-0.0206591933965683,
-0.016460368409752846,
-0.020885426551103592,
-0.05300063267350197,
0.06790858507156372,
0.009958134964108467,
-0.008465944789350033,
0.019669728353619576,
0.04839155822992325,
-0.03950335457921028,
-0.03660289943218231,
-0.00043847208144143224,
0.009802896529436111,
-0.01426108181476593,
-0.008221390657126904,
0.01397987175732851,
-0.007333945948630571,
-0.023637447506189346,
0.00769742950797081,
0.0010398883605375886,
0.0344310961663723,
0.008550740778446198,
0.04122764989733696,
0.024789776653051376,
0.055453576147556305,
0.04619758948683739,
0.024301115423440933,
0.02184138260781765,
0.046601053327322006,
0.023351090028882027,
-0.07291049510240555,
-0.034390147775411606,
-0.029312117025256157,
0.04152702912688255,
0.04403073340654373,
-0.04043855145573616,
-0.024309685453772545,
0.04276879131793976,
0.00058522674953565,
-0.06334123015403748,
-0.005845152772963047,
0.015503508038818836,
0.010781392455101013,
-0.03710046038031578,
-0.038828495889902115,
-0.023229563608765602,
0.005933600943535566,
-0.027246281504631042,
-0.022103464230895042,
0.04726231098175049,
-0.015469107776880264,
-0.03803601488471031,
0.056757207959890366,
0.021331604570150375,
-0.010231870226562023,
0.05819431692361832,
0.0297799464315176,
0.015551340766251087,
0.03744000568985939,
-0.00255796336568892,
0.027476057410240173,
0.052230775356292725,
-0.05037013068795204,
-0.07971745729446411,
0.024426184594631195,
0.02406337857246399,
-0.062247708439826965,
-0.031227603554725647,
-0.0014271134277805686,
-0.039824265986680984,
0.028034640476107597,
0.02154133841395378,
0.04645978659391403,
0.008394848555326462,
0.015163025818765163,
0.026167962700128555,
0.008797354996204376,
0.0342760905623436,
0.06250230222940445,
0.04065871983766556,
-0.002961757592856884,
-0.05324104428291321,
0.02401003986597061,
-0.03562571108341217,
0.006434440612792969,
-0.04023168608546257,
-0.00947253406047821,
0.008976727724075317,
-0.04121655970811844,
0.054757583886384964,
-0.0028111108113080263,
-0.014454757794737816,
-0.011299870908260345,
0.007835173979401588,
-0.0013438955647870898,
-0.036094631999731064,
0.015201602131128311,
-0.04464758560061455,
-0.02248627506196499,
0.008764239028096199,
-0.01542855054140091,
0.007994950748980045,
-0.0012688142014667392,
-0.0916394367814064,
0.03231944143772125,
0.057212866842746735,
-0.01033960934728384,
-0.05056498199701309,
0.004610902164131403,
-0.046339184045791626,
-0.010794469155371189,
0.03317904472351074,
-0.008895899169147015,
-0.02616959996521473,
0.017237963154911995,
0.03413761407136917,
-0.008602538146078587,
0.03902716934680939,
-0.06866699457168579,
-0.004352103918790817,
0.033688999712467194,
-0.017050348222255707,
0.055438004434108734,
0.018184151500463486,
0.06101008877158165,
0.032044894993305206,
-0.016381293535232544,
-0.03827057033777237,
0.013956200331449509,
-0.024146782234311104,
-0.0027552915271371603,
0.041203536093235016,
0.021537670865654945,
0.035577598959207535,
0.027110973373055458,
0.019301539286971092,
-0.0013800740707665682,
0.009079789742827415,
-0.027658507227897644,
-0.03817176818847656,
0.0037125148810446262,
0.0474388413131237,
-0.08236132562160492,
-0.05198408663272858,
-0.03847607597708702,
0.04355239495635033,
-0.023647500202059746,
-0.043131597340106964,
-0.0151973282918334,
0.008845129050314426,
-0.027852080762386322,
0.0524541400372982,
-0.010750369168817997,
-0.0621994212269783,
-0.03211987391114235,
0.05184517428278923,
0.00215123756788671,
-0.03254032880067825,
0.018250498920679092,
-0.019107233732938766,
-0.0018783898558467627,
-0.021701574325561523,
-0.031555671244859695,
-0.04340625926852226,
-0.047440558671951294,
0.04094112291932106,
0.03261953592300415,
-0.03442497178912163,
0.06263864785432816,
-0.11479087918996811,
-0.08262229710817337,
-0.009575070813298225,
-0.07848742604255676,
-0.07180523872375488,
-0.016383497044444084,
-0.07335186749696732,
-0.01951044611632824,
0.0037113227881491184,
0.015228907577693462,
-0.02829018607735634,
-0.016584498807787895,
-0.022370774298906326,
-0.011736609041690826,
-0.057902973145246506,
0.05876589193940163,
0.06361351162195206,
-0.03860236331820488,
0.04363115131855011,
-0.010817919857800007,
0.033846210688352585,
0.016098057851195335,
-0.040733493864536285,
-0.0035195599775761366,
0.024508144706487656,
0.04152807965874672,
-0.032799575477838516,
0.013421288691461086,
-0.01114011649042368,
0.06462348252534866,
-0.02949182316660881,
-0.006977975368499756,
-0.0015620311023667455,
0.059247903525829315,
0.03722634166479111,
-0.004057880491018295,
-0.0018165326910093427,
0.005621629301458597,
-0.056306153535842896,
-0.10750334709882736,
-0.013322367332875729,
-0.003750435309484601,
0.0003489083028398454,
-0.011802504770457745,
0.011256743222475052,
-0.021291358396410942,
0.005709674675017595,
-0.006449106615036726,
0.029017087072134018,
0.03139467537403107,
-0.0024564943742007017,
0.026900187134742737,
-0.03345474228262901,
0.007169559597969055,
0.0008337398758158088,
-0.00231315940618515,
-0.046568091958761215,
0.0055664354003965855,
-0.0004943529493175447,
0.009173574857413769,
0.015547506511211395,
0.03559272363781929,
-0.08784020692110062,
0.007453848607838154,
-0.002823886927217245,
0.014922704547643661,
0.07242519408464432,
-0.019437219947576523,
-0.027461830526590347,
-0.02145296521484852,
0.02626929059624672,
-0.009995441883802414,
0.05197293683886528,
0.02230466715991497,
-0.017469927668571472,
-0.001071227714419365,
0.10268176347017288,
-0.017459459602832794,
0.05623691901564598,
0.010033594444394112,
-0.029428893700242043,
-0.05919238552451134,
0.01053116749972105,
-0.03254394233226776,
0.025267746299505234,
-0.0234743170440197,
0.045505765825510025,
0.007944467477500439,
0.09104610979557037,
0.010727514512836933,
0.03834686800837517,
0.04045844078063965,
-0.0036955256946384907,
0.06720911711454391,
0.0011096292873844504,
0.02135668322443962,
-0.03599031642079353,
0.019335921853780746,
-0.06931862235069275,
-0.012917846441268921,
-0.08800806850194931,
-0.0012995980214327574,
0.037629932165145874,
0.07149820029735565,
0.04126426577568054,
0.036072637885808945,
0.015310168266296387,
-0.09000825136899948,
0.012592058628797531,
0.016053281724452972,
-0.04044941067695618,
0.029161851853132248,
0.007855018600821495,
-0.00826205313205719,
0.0009506443748250604,
0.016705257818102837,
-0.003272941568866372,
0.010928478091955185,
0.03861594200134277,
-0.01746528036892414,
-0.010449985973536968,
-0.0005493384669534862,
0.014415932819247246,
0.027713168412446976,
-0.024981064721941948,
-0.06007714569568634,
-0.010415096767246723,
-0.0531579963862896,
0.07003849744796753,
0.008591307327151299,
-0.06103428080677986,
0.03296942263841629,
0.03105751797556877,
-0.04725376144051552,
0.04309922829270363,
-0.05224403366446495,
-0.05104442313313484,
-0.08375289291143417,
-0.002068229718133807,
0.006188459228724241,
-0.06872361898422241,
-0.007259859703481197,
-0.015929432585835457,
0.0409536212682724,
0.027049195021390915,
-0.0058369566686451435,
0.002633248455822468,
0.011658268049359322,
0.041360337287187576,
-0.03388870134949684,
0.03915547952055931,
-0.05456775426864624,
-0.07361765205860138,
-0.006785012315958738,
-0.030163900926709175,
-0.04993226006627083,
-0.004352770745754242,
0.016348931938409805,
-0.008879014290869236,
0.06629815697669983,
0.025290468707680702,
-0.034277498722076416,
-0.007433097809553146,
0.05923644080758095,
-0.042988844215869904,
0.07911521196365356,
0.006373281590640545,
0.04612541198730469,
0.005924344062805176,
0.009734475053846836,
0.09452425688505173,
0.0016644191928207874,
-0.005917571950703859,
0.023338481783866882,
0.06334540247917175,
-0.025546902790665627,
0.007342782337218523,
-0.02221691980957985,
-0.028354482725262642,
-0.011231462471187115,
0.0005566510371863842,
0.006309194955974817,
-0.004456927068531513,
-0.08445001393556595,
-0.004165965598076582,
0.005666184704750776,
-0.023555681109428406,
-0.02490083873271942,
0.019622724503278732,
0.0486195906996727,
-0.055431537330150604,
-0.028338659554719925,
0.05713442713022232,
-0.044186968356370926,
0.014879572205245495,
0.008649862371385098,
0.02681683748960495,
-0.00976675283163786,
0.09806674718856812,
-0.039619773626327515,
0.02122863009572029,
-0.030601276084780693,
0.028822127729654312,
0.026280660182237625,
-0.006230818573385477,
-0.03232821077108383,
-0.013867940753698349,
0.020069804042577744,
-0.026515375822782516,
0.010718491859734058,
0.007711540441960096,
-0.007456987630575895,
-0.003316326532512903,
0.005246749147772789,
-0.02180899679660797,
0.02255990169942379,
-0.012951262295246124,
-0.010068954899907112,
-0.014418870210647583,
-0.006736173760145903,
-0.024149393662810326,
-0.024643056094646454,
-0.0054693142883479595,
0.039546795189380646,
-0.014824367128312588,
0.014861228875815868,
0.01245002169162035,
0.010534791275858879,
-0.0008184794569388032,
0.004454330075532198,
-0.012456930242478848,
-0.06859485059976578,
0.03430052474141121,
0.034936580806970596,
-0.005277819000184536,
0.0465286523103714,
-0.016896530985832214,
-0.027302425354719162,
0.011138279922306538,
0.018401842564344406,
0.024477584287524223,
0.008110159076750278,
-0.02287355624139309,
0.01848636381328106,
-0.011072286404669285,
-0.045055925846099854,
0.013869608752429485,
-0.06251749396324158,
-0.005275755189359188,
0.059586770832538605,
-0.05723349750041962,
-0.025857098400592804,
0.005084335338324308,
0.017657170072197914,
0.022512655705213547,
0.0243481807410717,
-0.012205353938043118,
0.05875919386744499,
0.0009258452337235212,
0.04779433459043503,
-0.038821741938591,
0.04497173801064491,
-0.0017210431396961212,
-0.016097933053970337,
0.05946456268429756,
-0.025209499523043633,
0.04658100754022598,
-0.07188577950000763,
0.0032462915405631065,
0.057803571224212646,
-0.050776995718479156,
0.017110386863350868,
0.009830265305936337,
-0.016732318326830864,
0.053141411393880844,
0.01902623660862446,
0.021924765780568123,
0.0762806311249733,
0.05350011959671974,
-0.012942496687173843,
0.04123383387923241,
0.04460129514336586,
-0.012722658924758434,
0.025132350623607635,
0.037442661821842194,
0.04837154597043991,
-0.05274619534611702,
-0.028002368286252022,
0.004021074622869492,
0.030918888747692108,
-0.041905567049980164,
0.0010749908396974206,
0.020150240510702133,
0.002917882753536105,
0.04523108899593353,
-0.034309543669223785,
0.06444510072469711,
0.02271491102874279,
0.0020444015972316265,
0.012398503720760345,
-0.02985997311770916,
0.06295210868120193,
0.002512814709916711,
0.022036941722035408,
-0.01285477727651596,
0.051038239151239395,
0.006249825470149517,
-0.04526081681251526,
-0.019685089588165283,
-0.02471090294420719,
0.0032711951062083244,
0.004988332744687796,
-0.03276630491018295,
-0.004826445132493973,
0.06536118686199188,
-0.00031534882145933807,
-0.021841026842594147,
-0.034891508519649506,
-0.05127285420894623,
-0.03302280977368355,
-0.012873485684394836,
-0.005436253733932972,
0.030327223241329193,
-0.01513429544866085,
-0.014635320752859116,
-0.0013171541504561901,
-0.017145011574029922,
-0.05734097957611084,
0.011550399474799633,
0.09305576235055923,
0.010787957347929478,
0.004428686574101448,
0.07251141965389252,
-0.0102233262732625,
-0.05256492272019386,
0.025573326274752617,
0.018863072618842125,
0.030675075948238373,
0.0021851526107639074,
-0.03277929499745369,
0.047632355242967606,
0.04376760497689247,
0.022085202857851982,
-0.014037900604307652,
-0.030501876026391983,
0.02163793332874775,
0.015169897116720676,
0.021195096895098686,
-0.041540589183568954,
0.008248426020145416,
0.010709432885050774,
0.034695468842983246,
-0.001037732232362032,
0.039728421717882156,
0.0384700708091259,
0.008509728126227856,
-0.03642083704471588,
-0.03172239288687706,
-0.05043746531009674,
-0.020562415942549706,
0.01819036900997162,
0.0024255921598523855,
0.02250804752111435,
0.04417122155427933,
-0.007859889417886734,
-0.0006151910056360066,
-0.047404270619153976,
-0.01215960644185543,
0.02955866977572441,
0.015636393800377846,
-0.05898956581950188,
-0.03470653295516968,
-0.0032144172582775354,
-0.004980334080755711,
-0.03259437158703804,
0.03399841859936714,
-0.00966909620910883,
0.05213312432169914,
0.04705005884170532,
0.038523972034454346,
-0.014903147704899311,
0.010471909306943417,
0.004363293759524822,
-0.021023547276854515,
-0.0050109070725739,
0.02751028537750244,
-0.012921003624796867,
-0.04298952594399452,
-0.037327349185943604,
-0.08756141364574432,
0.025898540392518044,
0.016485823318362236,
0.04023157060146332,
-0.01938180811703205,
-0.04397718608379364,
0.014057135209441185,
-0.08188636600971222,
0.09069350361824036,
-0.034218765795230865,
-0.00340531044639647,
-0.02387036196887493,
-0.07352373003959656,
0.04105182737112045,
0.0018222065409645438,
-0.005144881084561348,
-0.027877897024154663,
-0.0010560019873082638,
0.02457675337791443,
0.008719267323613167,
-0.031010722741484642,
-0.03017086535692215,
0.002787034260109067,
-0.018525799736380577,
-0.04318533092737198,
0.05568690598011017,
0.019941071048378944,
-0.012918103486299515,
-0.01592297852039337,
0.05512092635035515,
0.012286962009966373,
0.01640957221388817,
-0.02744297683238983,
0.05895184352993965,
-0.002297154627740383,
-0.03804640471935272,
-0.012471805326640606,
0.009279429912567139,
0.05334780737757683,
-0.0063097174279391766,
-0.051503174006938934,
0.01216275803744793,
-0.011083529330790043
] |
<p>Charged pions $\pi^\pm$ decay via an intermediate $W$ to (e.g.) a lepton-neutrino pair. </p>
<p>The pions being scalar (spin-0) particles and the intermediate $W$ having spin 1, how is spin conserved in this interaction?</p>
|
g2501
|
[
0.05975457280874252,
-0.0675414651632309,
-0.017148597165942192,
-0.0011767323594540358,
0.09388288855552673,
0.013558585196733475,
-0.0019018002785742283,
-0.010154256597161293,
0.018479375168681145,
0.012022800743579865,
-0.03717968612909317,
0.06250336766242981,
-0.0290366318076849,
-0.017271872609853745,
-0.022391146048903465,
0.03481826186180115,
0.008956864476203918,
0.0005185881163924932,
0.04697365313768387,
0.005230119917541742,
-0.02567022480070591,
-0.024417797103524208,
-0.00800998229533434,
-0.021818719804286957,
0.027325788512825966,
-0.08414430916309357,
-0.009623924270272255,
0.012813961133360863,
-0.003332110121846199,
0.0029769933316856623,
0.04262678325176239,
0.013096257112920284,
0.007105591706931591,
-0.03323131799697876,
0.0038148853927850723,
-0.09369958192110062,
0.04074201360344887,
-0.030116453766822815,
0.021089978516101837,
0.004992374684661627,
0.013256418518722057,
-0.00002715970913413912,
0.11847657710313797,
-0.0005089527694508433,
0.06632020324468613,
0.010576790198683739,
-0.033513374626636505,
-0.004737013950943947,
-0.015917383134365082,
-0.007667187601327896,
0.021085307002067566,
0.005984372925013304,
0.01869257353246212,
0.0767461284995079,
0.010366476140916348,
-0.03196723386645317,
0.03187175840139389,
-0.07497864216566086,
-0.001551805529743433,
0.06508835405111313,
-0.02155488356947899,
-0.009554329328238964,
0.017976077273488045,
0.030087357386946678,
0.03779800981283188,
-0.06671213358640671,
-0.0776543840765953,
0.006281835027039051,
0.012976094149053097,
0.0323667973279953,
-0.01405891589820385,
0.011393150314688683,
-0.004341721534729004,
-0.043974827975034714,
0.06776469200849533,
0.03876926749944687,
0.023937193676829338,
-0.03619716688990593,
0.016990797594189644,
0.001674080267548561,
-0.06442524492740631,
-0.010984672233462334,
0.009929245337843895,
-0.001597932423464954,
-0.011995247565209866,
-0.04462059959769249,
0.011658906005322933,
-0.03900740668177605,
-0.04563099145889282,
-0.018091930076479912,
0.0132472338154912,
-0.07268725335597992,
0.03203269839286804,
0.026864342391490936,
0.009701401926577091,
-0.041291892528533936,
0.009273174218833447,
0.03585198149085045,
-0.021999286487698555,
-0.030435001477599144,
0.041902415454387665,
-0.018201902508735657,
0.002597058890387416,
-0.021753545850515366,
0.08513069152832031,
0.03181891888380051,
0.03669038787484169,
0.003008106490597129,
-0.029631396755576134,
0.057032693177461624,
0.06506244838237762,
-0.002714684000238776,
-0.037337396293878555,
-0.019012732431292534,
-0.031281307339668274,
-0.016418317332863808,
0.04073880985379219,
0.003983602859079838,
0.054947491735219955,
0.04063006117939949,
0.011733321473002434,
0.01231343112885952,
0.007144335191696882,
0.03776494413614273,
0.0166922714561224,
-0.035025350749492645,
0.04648192226886749,
0.006422239355742931,
0.045559316873550415,
0.034733306616544724,
0.00752875255420804,
-0.02694612741470337,
0.0007711930084042251,
0.05439036712050438,
0.004178585950285196,
0.024682775139808655,
0.057648077607154846,
0.01866842433810234,
-0.0252396073192358,
-0.030252765864133835,
-0.052853718400001526,
-0.03428307920694351,
0.009663625620305538,
-0.07477118074893951,
-0.043148938566446304,
0.04299911484122276,
0.03471154347062111,
-0.07872552424669266,
0.011554168537259102,
0.02543449029326439,
0.0408572256565094,
0.06837163865566254,
0.009704060852527618,
0.034161243587732315,
0.02589525654911995,
-0.05740507319569588,
0.055866289883852005,
-0.026075448840856552,
0.01063223835080862,
0.017068803310394287,
0.04354948177933693,
-0.04022233560681343,
-0.021199963986873627,
0.009582634083926678,
-0.03140511363744736,
-0.028678307309746742,
0.026339951902627945,
-0.08353421092033386,
-0.026812192052602768,
-0.06378549337387085,
-0.014767820946872234,
-0.01288650557398796,
0.016366302967071533,
0.047916460782289505,
0.018746962770819664,
-0.017575789242982864,
-0.060490746051073074,
-0.027577834203839302,
-0.025225264951586723,
0.06057075411081314,
-0.016648409888148308,
0.00957152433693409,
0.01758386194705963,
0.013703406788408756,
0.006130175665020943,
0.03989125415682793,
-0.01940494403243065,
0.06479870527982712,
-0.030316269025206566,
-0.04236773028969765,
-0.0042901118285954,
-0.0032260718289762735,
-0.0083600003272295,
0.021679498255252838,
0.022742891684174538,
0.020129775628447533,
0.03976549953222275,
-0.027349356561899185,
0.007114119362086058,
-0.0075858174823224545,
0.0011611272348091006,
0.03899094834923744,
0.010021692141890526,
-0.006939411628991365,
0.0006422202568501234,
-0.04937601462006569,
-0.011161718517541885,
-0.05400020629167557,
0.0616917684674263,
-0.006533624138683081,
-0.001207748893648386,
-0.016379470005631447,
-0.03175708279013634,
-0.01810857653617859,
-0.03442641347646713,
-0.029390394687652588,
-0.02627735584974289,
0.054077841341495514,
-0.010671566240489483,
0.007806894835084677,
-0.05047144740819931,
-0.06730830669403076,
0.049156177788972855,
0.01488310843706131,
-0.017415504902601242,
0.03358014300465584,
-0.02750305086374283,
0.0051688156090676785,
0.0011060260003432631,
0.06942813843488693,
-0.05708977207541466,
0.002711736597120762,
-0.03290664032101631,
0.014293011277914047,
-0.003612241707742214,
0.02552717737853527,
-0.013120514340698719,
0.013897462747991085,
-0.005166001617908478,
0.023291219025850296,
-0.02967793494462967,
-0.007356320042163134,
-0.028564143925905228,
0.005690444726496935,
0.03994418680667877,
0.0135792326182127,
-0.030212892219424248,
-0.04059956967830658,
-0.05058473348617554,
-0.014517776668071747,
0.020373260602355003,
-0.015371843241155148,
0.013022002764046192,
-0.036182425916194916,
0.03452449291944504,
-0.0622062087059021,
0.04733661562204361,
0.03748108819127083,
-0.04714307561516762,
-0.04751693829894066,
0.010013761930167675,
0.006219789851456881,
-0.037983544170856476,
0.006718259304761887,
0.060236167162656784,
-0.02442236989736557,
0.08458954840898514,
0.019490865990519524,
0.03169465437531471,
-0.0011743016075342894,
-0.057658273726701736,
0.07523895055055618,
-0.02430463396012783,
-0.0017316431039944291,
-0.03840130940079689,
-0.04702194035053253,
0.008725419640541077,
0.003295384580269456,
0.043268341571092606,
-0.06080768257379532,
-0.010894768871366978,
0.0005090267513878644,
0.010687499307096004,
-0.04742450639605522,
0.04322507977485657,
-0.051701270043849945,
-0.02550925500690937,
-0.026016956195235252,
0.0074434466660022736,
-0.011649773456156254,
-0.027437398210167885,
0.006530512124300003,
0.07894228398799896,
-0.07645293325185776,
0.09538985043764114,
0.012432687915861607,
0.01144299004226923,
-0.007372783496975899,
-0.064134880900383,
0.09571760147809982,
0.046741925179958344,
-0.04745391383767128,
0.0035780456382781267,
-0.0453440323472023,
0.0004385898937471211,
0.014252196066081524,
-0.0029111753683537245,
-0.04135770723223686,
-0.03748469799757004,
-0.002159157767891884,
-0.08581655472517014,
0.06653909385204315,
-0.07021994888782501,
0.009101738221943378,
-0.0424235500395298,
-0.023357922211289406,
0.0032316793221980333,
-0.024617183953523636,
-0.006030373740941286,
-0.008565311320126057,
-0.000882203399669379,
0.02301827073097229,
0.08538659662008286,
-0.02964191697537899,
-0.026835937052965164,
0.019146433100104332,
-0.09160491824150085,
-0.03325307369232178,
-0.0428367480635643,
0.004048611037433147,
-0.006212717853486538,
0.01515896711498499,
0.04581281170248985,
-0.020836487412452698,
-0.05079058185219765,
0.02113385871052742,
-0.024225426837801933,
0.02049609087407589,
0.06606200337409973,
-0.03638574108481407,
-0.005723530426621437,
-0.0416293628513813,
-0.055046193301677704,
0.009009013883769512,
0.028038909658789635,
0.018103938549757004,
-0.014087099581956863,
-0.01316780038177967,
0.037908900529146194,
0.028584463521838188,
0.013763165101408958,
0.011052694171667099,
0.017092173919081688,
-0.059816498309373856,
-0.011571794748306274,
-0.045485809445381165,
-0.02362363040447235,
0.048603568226099014,
-0.04477362707257271,
-0.014770247973501682,
0.04489239677786827,
-0.010185124352574348,
0.03894861415028572,
-0.008253345265984535,
-0.02951420471072197,
-0.00032799021573737264,
-0.04811778664588928,
0.0014183562016114593,
0.08036626875400543,
-0.029405582696199417,
-0.007738910615444183,
0.05024321749806404,
-0.04328753426671028,
0.019891129806637764,
-0.02314005233347416,
0.005328258033841848,
0.013094402849674225,
0.03483866900205612,
-0.04606490954756737,
0.03288589417934418,
-0.006263567600399256,
-0.03487037867307663,
-0.03673847019672394,
-0.012031389400362968,
0.01436760276556015,
0.014823546633124352,
0.0008713296847417951,
0.024585822597146034,
-0.016006972640752792,
0.008457902818918228,
0.0035565176513046026,
0.012638280168175697,
0.014920002780854702,
0.011208644136786461,
0.08645879477262497,
-0.0070547848008573055,
-0.0530233308672905,
-0.029923327267169952,
0.016470393165946007,
-0.033160582184791565,
-0.0744805857539177,
0.053450584411621094,
-0.01607987843453884,
-0.0553150400519371,
0.03699290752410889,
-0.019247854128479958,
-0.04787937551736832,
-0.020910928025841713,
0.06288309395313263,
-0.0008823607349768281,
0.030619030818343163,
0.01205588411539793,
-0.024451011791825294,
0.027273716405034065,
-0.04802938178181648,
-0.046616293489933014,
-0.03469112142920494,
-0.022605055943131447,
-0.020637867972254753,
-0.014627085067331791,
-0.01568036898970604,
-0.009831052273511887,
-0.01729622855782509,
0.02765030600130558,
0.05417359620332718,
0.04085925966501236,
-0.03174642473459244,
-0.02504138834774494,
-0.04427263140678406,
-0.049252334982156754,
0.04667849838733673,
0.05459592118859291,
0.020280616357922554,
-0.03651214763522148,
-0.07749419659376144,
0.03436774015426636,
-0.03766895830631256,
-0.011267603375017643,
-0.007567555643618107,
0.08383256942033768,
0.046194564551115036,
0.005890510510653257,
0.019800595939159393,
-0.04376096650958061,
0.03287231922149658,
0.0668516457080841,
-0.01984824612736702,
0.02068544365465641,
0.13834112882614136,
-0.061990976333618164,
-0.023071574047207832,
0.00019736688409466296,
-0.03149188682436943,
-0.03648797422647476,
0.07297118008136749,
-0.013971889391541481,
0.042594265192747116,
0.020358677953481674,
-0.021955281496047974,
0.013537279330193996,
-0.0665283277630806,
0.0213108342140913,
-0.04027809947729111,
0.0068933796137571335,
-0.02783406898379326,
-0.00033880656701512635,
-0.03820996731519699,
0.0032504370901733637,
-0.050540294498205185,
0.02329307049512863,
0.0253747571259737,
-0.008687535300850868,
0.09041135758161545,
-0.022255370393395424,
-0.0005606483900919557,
0.00770358694717288,
-0.052594203501939774,
0.0014302334748208523,
-0.02004363387823105,
0.011862135492265224,
-0.015602508559823036,
0.01847202517092228,
-0.06502142548561096,
0.0035856037866324186,
0.024073902517557144,
-0.012889735400676727,
-0.014825337566435337,
-0.028515081852674484,
0.002644158434122801,
0.001263519749045372,
0.030021434649825096,
0.04334017261862755,
0.02772814780473709,
0.043348006904125214,
0.01742543652653694,
0.02855631150305271,
-0.03677043691277504,
0.0022450112737715244,
0.020763950422406197,
0.01688852161169052,
0.018758954480290413,
-0.08831900358200073,
-0.017754357308149338,
-0.02825753018260002,
0.023087311536073685,
0.040771402418613434,
0.039385825395584106,
0.017469121143221855,
-0.039285965263843536,
0.025495685636997223,
-0.008214214816689491,
-0.007924593985080719,
0.056690189987421036,
0.032390445470809937,
0.009273829869925976,
0.04529065638780594,
0.009279238991439342,
0.012645989656448364,
0.000524548755493015,
-0.009848850779235363,
0.002519847359508276,
0.03203935548663139,
-0.009812166914343834,
0.011748874559998512,
0.00962926261126995,
-0.002897784812375903,
0.02021929807960987,
0.008602514863014221,
0.02461748756468296,
0.029742959886789322,
0.03620966523885727,
-0.05407251790165901,
0.013371921144425869,
0.04691997542977333,
-0.011226244270801544,
-0.05065096542239189,
-0.023725975304841995,
-0.006954284850507975,
0.011531026102602482,
0.043358974158763885,
-0.030031859874725342,
-0.034566350281238556,
0.020561017096042633,
0.06514041870832443,
0.025590814650058746,
0.018877817317843437,
0.002288657007738948,
0.031006237491965294,
-0.016852229833602905,
-0.03624991700053215,
-0.03764999285340309,
-0.007595548871904612,
0.008147219195961952,
-0.007199238985776901,
-0.014135194942355156,
0.03933015465736389,
0.04182175546884537,
-0.0361211858689785,
0.0023765654768794775,
-0.001937015214934945,
-0.014764530584216118,
-0.035919222980737686,
0.032601434737443924,
0.04101981967687607,
-0.004469036590307951,
0.012694615870714188,
0.02794797718524933,
-0.045749373733997345,
0.037722762674093246,
-0.025548439472913742,
-0.019047968089580536,
0.03737008571624756,
-0.06999541074037552,
-0.011767015792429447,
-0.009656050242483616,
-0.04162438213825226,
-0.016688082367181778,
0.05094924196600914,
-0.04203342646360397,
-0.04528346285223961,
0.02296491153538227,
-0.036913249641656876,
0.02225513383746147,
-0.010359260253608227,
0.020784860476851463,
0.0592697449028492,
-0.0017116136150434613,
-0.007092825602740049,
0.08061383664608002,
0.04603245109319687,
0.0019779184367507696,
-0.0006556676817126572,
0.016397420316934586,
-0.010006314143538475,
0.017721664160490036,
0.09212399274110794,
-0.015700405463576317,
-0.000264220405369997,
-0.04836656525731087,
0.021321620792150497,
0.04989638552069664,
0.022263525053858757,
-0.0009398692054674029,
-0.026607293635606766,
0.010356739163398743,
0.028014345094561577,
0.00574681768193841,
-0.04167366400361061,
-0.016738398000597954,
0.0295500997453928,
-0.06771872192621231,
0.015949901193380356,
0.00683401245623827,
-0.04613060876727104,
-0.026195401325821877,
-0.01465549599379301,
0.07422680407762527,
0.03556733578443527,
-0.036872390657663345,
0.005629129242151976,
-0.026664959266781807,
-0.011993110179901123,
-0.04866798594594002,
-0.04764726758003235,
0.005113257560878992,
-0.011605024337768555,
0.039416294544935226,
0.025023365393280983,
0.024630790576338768,
0.007929159328341484,
-0.03753511980175972,
0.017554206773638725,
0.017571400851011276,
0.041436273604631424,
0.014515391550958157,
0.03713736683130264,
0.023809777572751045,
-0.003710376098752022,
0.026004817336797714,
0.06596338748931885,
0.04173983633518219,
0.030292635783553123,
0.021326027810573578,
0.032074831426143646,
-0.10488241165876389,
0.012072204612195492,
-0.028405537828803062,
-0.034627534449100494,
-0.025326896458864212,
0.0013047757092863321,
0.028433380648493767,
0.032965440303087234,
0.020970892161130905,
0.00911763310432434,
-0.01286383531987667,
-0.0282581839710474,
0.013172810897231102,
0.009743860922753811,
-0.01766078919172287,
-0.01701924204826355,
0.010023890063166618,
-0.023157669231295586,
0.007718553300946951,
0.0030064682941883802,
-0.014444399625062943,
-0.005890254862606525,
-0.038086455315351486,
-0.016342025250196457,
0.04628918692469597,
-0.022639065980911255,
-0.035244137048721313,
-0.07763746380805969,
-0.07147064059972763,
0.007386005483567715,
-0.010430482216179371,
-0.05916701629757881,
0.02581491507589817,
-0.05704580619931221,
-0.021374445408582687,
0.00989368837326765,
-0.041599713265895844,
-0.03373884782195091,
-0.00198684586212039,
0.018170824274420738,
-0.0016753798117861152,
0.047470178455114365,
0.004476465750485659,
0.0324343703687191,
-0.02384077198803425,
0.10036125034093857,
-0.042173177003860474,
-0.00565809290856123,
0.057818397879600525,
0.011807810515165329,
-0.030478693544864655,
0.00731609296053648,
-0.023531300947070122,
0.02339138649404049,
-0.033131685107946396,
0.07711563259363174,
0.05652010813355446,
-0.004405505955219269,
0.0649113580584526,
-0.018588196486234665,
0.0022350132931023836,
-0.007543729618191719,
-0.06562313437461853,
-0.039263639599084854,
-0.015614505857229233,
-0.005194120574742556,
0.013254242949187756,
0.012160984799265862,
-0.01226031593978405,
0.019402382895350456,
-0.00013480255438480526,
-0.010872211307287216,
-0.012720773927867413,
-0.007142086047679186,
0.0587468147277832,
0.026303058490157127,
-0.006786178797483444,
0.03700476512312889,
0.012344760820269585,
-0.04646885767579079,
-0.04025696590542793,
-0.060751110315322876,
0.004131542518734932,
0.038228876888751984,
0.03066934645175934,
0.05901098623871803,
-0.025498149916529655,
0.019787617027759552,
-0.06198041886091232,
0.007269719615578651,
0.02140927128493786,
-0.014685030095279217,
0.0023774923756718636,
-0.000782538263592869,
0.019160261377692223,
-0.01952727511525154,
-0.037643544375896454,
-0.0391070619225502,
0.007652631960809231,
-0.029665062204003334,
-0.04223758727312088,
0.049201223999261856,
0.06752909719944,
0.009644083678722382,
-0.004869083873927593,
0.0020070530008524656,
0.04640090838074684,
0.01212968397885561,
-0.041077688336372375,
0.08694058656692505,
0.0004368781519588083,
-0.07470552623271942,
-0.04600062593817711,
0.04616964980959892,
-0.03425721079111099,
0.010577327571809292,
-0.038890667259693146,
-0.009131375700235367,
-0.042364418506622314,
0.016013799235224724,
0.040131594985723495,
-0.024287020787596703,
-0.043360400944948196,
-0.0018829237669706345
] |
<p>Are there any books or articles that describe models for transport in a metal/semiconductor junction where the thickness of the semiconductor is less than the thickness of the depletion/accumulation layer?</p>
|
g2502
|
[
0.03533215448260307,
0.018652556464076042,
-0.013753076083958149,
0.007017903495579958,
0.011797676794230938,
-0.0014646985800936818,
0.025087231770157814,
0.007613528519868851,
-0.01193229015916586,
0.022003445774316788,
0.004451248329132795,
-0.02928263135254383,
0.019088013097643852,
-0.02244277484714985,
0.0374811589717865,
0.019523873925209045,
-0.015805374830961227,
0.012586626224219799,
0.01025906577706337,
0.04780976101756096,
-0.03908153623342514,
0.019095879048109055,
0.02203775756061077,
-0.010533805936574936,
-0.026474840939044952,
0.03215930983424187,
-0.02735123597085476,
-0.031060053035616875,
-0.088957779109478,
-0.05795338749885559,
-0.029454268515110016,
-0.09674129635095596,
-0.029070233926177025,
-0.008310637436807156,
-0.06254582852125168,
0.01374756544828415,
0.022732526063919067,
-0.017629139125347137,
0.02123413048684597,
0.006447724532335997,
0.08388445526361465,
-0.08943422138690948,
0.024411050602793694,
0.012472063302993774,
-0.07325851172208786,
0.014137032441794872,
-0.01427403837442398,
0.007034703157842159,
-0.013765868730843067,
-0.018497783690690994,
-0.042435165494680405,
0.03948504105210304,
0.023638390004634857,
0.015606849454343319,
-0.008048555813729763,
0.0007032841676846147,
-0.07135427743196487,
-0.06545393168926239,
0.0002474768552929163,
-0.0018782003317028284,
-0.02102702111005783,
0.03882567211985588,
-0.0549495667219162,
-0.051745686680078506,
0.047321099787950516,
-0.0464167557656765,
-0.017152976244688034,
-0.035247042775154114,
0.05411975085735321,
-0.05050069838762283,
0.05869487673044205,
0.04193691536784172,
-0.05361954867839813,
-0.0585765540599823,
0.033178020268678665,
0.012857658788561821,
0.0042437659576535225,
0.017305519431829453,
-0.0026626649778336287,
0.01659574545919895,
-0.09952636808156967,
0.011560413055121899,
0.02722676657140255,
0.0037322533316910267,
-0.020151281729340553,
0.019978079944849014,
0.012892886064946651,
-0.015402482822537422,
0.03926710784435272,
0.0067054471001029015,
-0.05024050548672676,
0.01876991055905819,
0.027277568355202675,
-0.08082249015569687,
-0.026698535308241844,
-0.0028271826449781656,
0.0003109128156211227,
0.007026264443993568,
-0.0188924428075552,
0.008372165262699127,
0.02631695568561554,
-0.05047274008393288,
0.011063789017498493,
-0.030999287962913513,
-0.04707445204257965,
0.013542085886001587,
-0.03186849504709244,
0.0018250254215672612,
-0.035912491381168365,
0.06789738684892654,
-0.035155583173036575,
-0.03580957278609276,
-0.052984803915023804,
-0.005452608689665794,
0.07471957802772522,
0.017745008692145348,
-0.045610200613737106,
0.040621623396873474,
0.045629773288965225,
-0.027815021574497223,
0.018862726166844368,
0.044487085193395615,
-0.04776139184832573,
-0.018489426001906395,
0.05478538200259209,
0.009281318634748459,
-0.026180056855082512,
0.04585131257772446,
-0.03233363479375839,
0.018697865307331085,
0.0498795211315155,
-0.02724282070994377,
-0.009993074461817741,
0.04411773756146431,
0.031632326543331146,
-0.00003673429091577418,
0.02260463312268257,
-0.02848537638783455,
-0.031780801713466644,
0.006662219297140837,
-0.024487702175974846,
0.04942023754119873,
-0.07480812817811966,
-0.026084119454026222,
0.009934340603649616,
0.026228642091155052,
-0.0030815971549600363,
0.029669854789972305,
-0.007238509599119425,
-0.02853512018918991,
0.01686934567987919,
0.02603534236550331,
-0.031180312857031822,
-0.060861483216285706,
-0.04333987832069397,
0.002752842614427209,
0.07772484421730042,
-0.09169738739728928,
0.02694852277636528,
-0.022032344713807106,
0.005480811931192875,
-0.023076752200722694,
-0.00905949529260397,
0.04497133195400238,
0.020108768716454506,
-0.015672799199819565,
-0.02658059634268284,
0.0062278141267597675,
0.00943817850202322,
-0.03813089057803154,
0.026087448000907898,
-0.008548334240913391,
0.059998881071805954,
0.09790752083063126,
0.007558137644082308,
0.02019800990819931,
0.03402275592088699,
-0.008073418401181698,
-0.007603614591062069,
-0.005257392302155495,
-0.0077040246687829494,
-0.024195317178964615,
0.06149826571345329,
-0.03679961338639259,
-0.010831436142325401,
-0.019341152161359787,
0.027993446215987206,
-0.01132203359156847,
-0.04721355438232422,
0.058960381895303726,
-0.014348740689456463,
0.033772874623537064,
-0.005613250657916069,
-0.0013291120994836092,
-0.04215052351355553,
0.010753370821475983,
0.05268293246626854,
-0.06833022832870483,
0.02328731119632721,
-0.07027997076511383,
-0.0304771326482296,
0.006866177078336477,
0.040077682584524155,
0.04744809865951538,
-0.014613340608775616,
0.007388464640825987,
-0.08506195992231369,
-0.03444146737456322,
-0.013345442712306976,
-0.025817561894655228,
-0.06957953423261642,
0.018055224791169167,
0.01712917536497116,
0.03040902689099312,
0.0308352243155241,
-0.026062458753585815,
0.004833029117435217,
0.018600501120090485,
0.011185111477971077,
-0.04663082957267761,
-0.03326506167650223,
-0.07921556383371353,
0.0352696068584919,
0.028706207871437073,
-0.03709426894783974,
-0.041162800043821335,
0.07684982568025589,
0.008593354374170303,
-0.02335990220308304,
-0.016154425218701363,
-0.04051804915070534,
0.0030012461356818676,
-0.04142725467681885,
-0.045805394649505615,
0.012778463773429394,
0.0059012374840676785,
-0.00864723976701498,
-0.016437212005257607,
-0.01675601303577423,
0.03241471201181412,
0.019801629707217216,
-0.004287270363420248,
-0.08546362072229385,
0.04785216599702835,
-0.032128091901540756,
-0.058085449039936066,
-0.00892212986946106,
-0.01313825137913227,
0.05964280292391777,
0.01656031422317028,
0.001970612443983555,
-0.04214382544159889,
0.018916893750429153,
-0.022253835573792458,
-0.02285267598927021,
-0.03468559309840202,
0.003150684991851449,
0.04850711300969124,
-0.013424726203083992,
-0.026682259514927864,
-0.002020681044086814,
0.006333394907414913,
-0.022884894162416458,
-0.022312849760055542,
-0.022783391177654266,
0.022110911086201668,
-0.008543777279555798,
-0.06517145037651062,
-0.0026191326323896646,
0.021147357299923897,
-0.01355734933167696,
-0.041015639901161194,
-0.06338316202163696,
0.04537723585963249,
0.10855993628501892,
-0.03740354999899864,
0.04436805099248886,
0.0208597294986248,
0.029047533869743347,
-0.0064374222420156,
-0.011160425841808319,
-0.019434882327914238,
0.004205084405839443,
-0.005789724178612232,
-0.017120040953159332,
-0.024837566539645195,
0.030394650995731354,
0.0025788648054003716,
0.04904351383447647,
0.04806964099407196,
-0.03097609616816044,
-0.017497563734650612,
0.02825421467423439,
0.07377450913190842,
0.06581476330757141,
0.06065494194626808,
-0.028536852449178696,
-0.042714811861515045,
-0.027417726814746857,
-0.001539902645163238,
0.00332977925427258,
-0.028805015608668327,
0.020159631967544556,
-0.01041177287697792,
-0.0028764696326106787,
-0.0008288415847346187,
-0.005429951474070549,
-0.028917411342263222,
0.0115785738453269,
-0.03668871149420738,
0.00011981180432485417,
0.006367215886712074,
0.09192460030317307,
0.027069220319390297,
-0.02626021020114422,
0.012950672768056393,
0.012437859550118446,
0.031711477786302567,
0.018438778817653656,
0.00959029421210289,
-0.020460767671465874,
-0.044783081859350204,
0.02082834020256996,
0.014122752472758293,
-0.02719266526401043,
0.029984069988131523,
0.027458613738417625,
-0.053215790539979935,
-0.04050363600254059,
0.07099422067403793,
0.01510466169565916,
0.011127456091344357,
0.03343556821346283,
-0.018420789390802383,
-0.028032541275024414,
-0.06091669574379921,
0.009393231943249702,
0.03953281044960022,
0.0420403927564621,
0.02473435550928116,
-0.0229794941842556,
0.03416002169251442,
0.021911809220910072,
0.009237335063517094,
-0.016999753192067146,
-0.0069029550068080425,
-0.02758728340268135,
0.05615389719605446,
0.0203601885586977,
-0.07148536294698715,
0.04915820062160492,
0.026484044268727303,
0.006117077078670263,
-0.049294788390398026,
-0.06654118746519089,
0.021617984399199486,
-0.01729334332048893,
0.011620603501796722,
-0.021511361002922058,
0.014668879099190235,
0.045344479382038116,
0.0189206600189209,
0.01164713129401207,
0.016349049285054207,
0.016443561762571335,
0.01432617288082838,
-0.008417535573244095,
0.0631110668182373,
0.02057238295674324,
-0.07692661881446838,
-0.022838346660137177,
0.05825366452336311,
-0.01402513962239027,
0.029000908136367798,
-0.0292892474681139,
-0.04153556004166603,
0.02990209497511387,
0.055554334074258804,
-0.027472134679555893,
0.00403584074229002,
0.03146427497267723,
0.0017071431502699852,
0.0054097664542496204,
-0.008972767740488052,
0.02436407096683979,
-0.024738634005188942,
0.026445472612977028,
-0.005507508292794228,
-0.06028733029961586,
-0.02982320263981819,
-0.004304732196033001,
-0.014596736058592796,
0.012615669518709183,
-0.035927850753068924,
-0.007323823403567076,
-0.0015695741167291999,
0.0340733602643013,
-0.023375386372208595,
-0.009482239373028278,
-0.04708128422498703,
0.03401733562350273,
-0.013891237787902355,
-0.04323436692357063,
0.01319970190525055,
-0.019695628434419632,
0.05184425413608551,
0.00468095438554883,
-0.02401289902627468,
-0.04774107784032822,
0.035475313663482666,
-0.04912087693810463,
-0.047806862741708755,
-0.040492475032806396,
0.041017644107341766,
-0.00039821714744903147,
0.0026992622297257185,
0.00003810941780102439,
0.03949478641152382,
0.0004941245424561203,
0.02699996531009674,
-0.02156291902065277,
0.05580644682049751,
-0.02370433509349823,
0.0212445966899395,
0.07501960545778275,
0.01625867187976837,
-0.027748828753829002,
-0.01137728150933981,
0.06377675384283066,
0.01925954781472683,
-0.06289339810609818,
-0.011127123609185219,
-0.0635024756193161,
0.04507160931825638,
0.0056489333510398865,
0.041957251727581024,
-0.0292966291308403,
0.0677918866276741,
-0.008152439258992672,
0.05404675751924515,
0.04884828254580498,
0.02056197077035904,
0.009543577209115028,
0.029456675052642822,
0.00571644539013505,
0.08180355280637741,
-0.020853111520409584,
-0.012982107698917389,
-0.055914562195539474,
-0.07310020178556442,
-0.062480565160512924,
0.02196115255355835,
-0.034664951264858246,
-0.03239018842577934,
-0.03900595009326935,
-0.024835625663399696,
-0.04486218839883804,
0.06708521395921707,
0.06868509948253632,
-0.00785378459841013,
-0.01774120144546032,
0.0766143873333931,
-0.03194127604365349,
-0.004971022717654705,
-0.07162440568208694,
-0.06714042276144028,
0.010618182830512524,
0.0477185919880867,
-0.03857019916176796,
0.02816857025027275,
-0.03426631912589073,
0.0027985135093331337,
0.07053224742412567,
0.09711341559886932,
0.05623331665992737,
-0.009975858964025974,
0.030466709285974503,
0.012406298890709877,
-0.024241620674729347,
-0.01218987163156271,
0.013940776698291302,
0.04112022742629051,
0.02752269059419632,
0.037060052156448364,
0.02761303260922432,
0.057266850024461746,
-0.021706921979784966,
0.0034129845444113016,
-0.012484927661716938,
-0.026228705421090126,
0.048472367227077484,
-0.0782996118068695,
0.01175119262188673,
0.10094986110925674,
-0.0856437236070633,
0.004754696507006884,
0.041017238050699234,
0.05513128265738487,
-0.03238154202699661,
0.04297563433647156,
0.01209245901554823,
-0.008014867082238197,
0.02479129284620285,
0.004491338972002268,
0.0546785444021225,
0.036183036863803864,
0.011750294826924801,
-0.006983650382608175,
-0.02847319096326828,
0.005859313532710075,
-0.0015241613145917654,
0.040895622223615646,
0.015912646427750587,
-0.022677063941955566,
-0.00943178404122591,
-0.008217886090278625,
-0.059776607900857925,
0.03677785024046898,
-0.03030225820839405,
-0.032132819294929504,
-0.024778470396995544,
-0.04831741377711296,
-0.004859724082052708,
0.0037343380972743034,
-0.042520396411418915,
-0.03447026386857033,
-0.0375264436006546,
0.029841873794794083,
0.042478080838918686,
-0.0393267460167408,
0.058213599026203156,
-0.03583327308297157,
-0.0470702163875103,
0.03661230579018593,
0.0301558505743742,
0.0360141396522522,
0.037523459643125534,
0.015207513235509396,
-0.005016871728003025,
0.10165301710367203,
-0.022841371595859528,
-0.026507873088121414,
0.009299424476921558,
0.03979886695742607,
0.05856936424970627,
0.016192324459552765,
-0.027776459231972694,
0.049631498754024506,
0.03197363018989563,
-0.03048420138657093,
0.025505531579256058,
-0.05011740326881409,
-0.04050292447209358,
0.01401743944734335,
-0.029975105077028275,
-0.06402137875556946,
0.04313770681619644,
0.050687022507190704,
0.028333663940429688,
0.0019423289922997355,
-0.007144562900066376,
-0.0013788448413833976,
0.017835194244980812,
-0.002375213662162423,
0.020745443180203438,
0.002542000263929367,
-0.02957814373075962,
0.043904758989810944,
0.0383283756673336,
-0.02558031491935253,
-0.019579986110329628,
-0.035308703780174255,
-0.024874191731214523,
-0.020999658852815628,
-0.011065827682614326,
0.04189394786953926,
-0.004839620087295771,
-0.04423510655760765,
0.029728099703788757,
0.006213726010173559,
0.0007311272202059627,
0.052150797098875046,
-0.008207130245864391,
0.06624407321214676,
0.03295662999153137,
-0.030136408284306526,
-0.0595502108335495,
-0.02471521496772766,
0.026583779603242874,
0.03345446661114693,
0.00016524117381777614,
0.0193680040538311,
0.02300061099231243,
-0.0016879772301763296,
-0.02643778547644615,
-0.023411685600876808,
-0.018601808696985245,
0.006248184479773045,
-0.00038083409890532494,
0.009871866554021835,
0.03580784425139427,
-0.028086021542549133,
0.02576185204088688,
-0.03062949702143669,
0.07892792671918869,
-0.01930498704314232,
0.009309833869338036,
0.028812669217586517,
-0.05972835421562195,
-0.02599702775478363,
0.025167783722281456,
-0.00813880655914545,
0.0002043493586825207,
-0.014131146483123302,
0.03693443536758423,
-0.07199770957231522,
0.0011361435754224658,
0.028441673144698143,
-0.05820037052035332,
-0.03408190980553627,
-0.04211848974227905,
-0.06182568147778511,
0.02691323682665825,
-0.022086547687649727,
0.0035131629556417465,
0.03178972005844116,
0.0005195989506319165,
0.007463803980499506,
0.013111111707985401,
-0.02819432131946087,
-0.005304007790982723,
0.0038265525363385677,
0.0005034580826759338,
-0.013161277398467064,
0.016775887459516525,
0.03843327984213829,
0.011827603913843632,
-0.06528343260288239,
0.021213797852396965,
0.023329423740506172,
-0.0027403407730162144,
0.0104506341740489,
0.060056254267692566,
0.022937379777431488,
0.03710411861538887,
-0.04095154255628586,
-0.0018863343866541982,
0.05064328759908676,
0.004152548033744097,
0.010517462156713009,
0.04384204000234604,
0.021656814962625504,
-0.02198822610080242,
-0.05871560797095299,
0.038733769208192825,
-0.029406515881419182,
-0.002938374876976013,
0.012127728201448917,
0.009393344633281231,
0.05740188807249069,
-0.03347740322351456,
-0.056165337562561035,
0.03369994834065437,
0.036485910415649414,
-0.00881448108702898,
0.06880124658346176,
0.04119846969842911,
-0.03267240151762962,
0.013610458001494408,
-0.057842232286930084,
-0.038443006575107574,
-0.03157288208603859,
-0.020342081785202026,
0.01662362925708294,
-0.030556635931134224,
-0.02725471369922161,
-0.04576459899544716,
0.05366462096571922,
-0.07417444884777069,
-0.06822986900806427,
0.03584202006459236,
0.01662837155163288,
0.061380282044410706,
-0.056426551192998886,
0.0011547424364835024,
-0.015004657208919525,
-0.005456221289932728,
-0.03215799480676651,
0.02617844194173813,
0.09006107598543167,
0.002407435094937682,
-0.010348697192966938,
0.02721581794321537,
0.03935715928673744,
-0.013735189102590084,
-0.0011079736286774278,
-0.04767879471182823,
0.06996120512485504,
0.025208259001374245,
0.0033550432417541742,
-0.01665014773607254,
0.01513898465782404,
-0.0021534112747758627,
-0.01271304301917553,
-0.0434858612716198,
0.002882627537474036,
-0.025013260543346405,
0.028310004621744156,
-0.020948532968759537,
-0.01688222587108612,
0.06884022057056427,
0.04901488870382309,
-0.02452303096652031,
-0.011105374433100224,
0.002878157887607813,
-0.007142293266952038,
-0.07604721188545227,
-0.049344249069690704,
0.015311342664062977,
0.032252222299575806,
-0.01094156876206398,
0.0004978524520993233,
0.010150252841413021,
0.0396522618830204,
0.013385176658630371,
-0.004291831981390715,
0.019325384870171547,
0.03132219985127449,
0.0233061071485281,
0.057513896375894547,
0.011934141628444195,
0.008690382353961468,
-0.027767574414610863,
-0.004233386367559433,
-0.005394452251493931,
-0.02863127551972866,
0.028353851288557053,
0.006713048089295626,
-0.0497344508767128,
0.033672090619802475,
-0.034785136580467224,
-0.050524357706308365,
0.04817265272140503,
0.023516301065683365,
-0.03622271493077278,
0.02055693417787552,
0.021994858980178833,
-0.013309174217283726,
0.005254799034446478,
0.01722176931798458,
-0.02065546065568924,
0.022182298824191093,
0.04658069461584091,
0.009816097095608711,
-0.009685247205197811,
-0.05622248351573944,
0.013144023716449738,
-0.0095845190808177,
-0.02212589420378208,
-0.03729711100459099,
-0.03799653425812721,
-0.07313427329063416,
0.011733749881386757,
-0.03369392454624176,
-0.025529146194458008,
0.006471696309745312,
0.02214869298040867,
-0.027747243642807007
] |
<p>Calculate $r$ vector and $v$ vector in AU and AU/TU respectively for the Halley's comet on September 12, 2014 given:
= 17.9 AU
= 0.967
= 2.8274 rad
Ω = 1.0210 rad
= 1.9513 rad
= 0 rad on February 9, 1986</p>
|
g2503
|
[
0.021783754229545593,
-0.017730196937918663,
-0.0049440995790064335,
-0.04332681745290756,
0.0038271101657301188,
-0.012348834425210953,
0.02415604703128338,
-0.03932508826255798,
0.015833541750907898,
-0.022741766646504402,
0.007059731055051088,
0.028230946511030197,
0.034689027816057205,
-0.023179270327091217,
0.059457927942276,
0.004569849465042353,
0.04309135675430298,
0.012459435500204563,
-0.03986910358071327,
0.0020222472958266735,
0.0037491254042834044,
0.032635774463415146,
-0.0016090725548565388,
-0.019134430214762688,
0.04255176708102226,
-0.020656701177358627,
0.0038474772591143847,
0.020090673118829727,
-0.06032710522413254,
-0.011091701686382294,
0.06329965591430664,
-0.02856922522187233,
0.008035451173782349,
-0.059976473450660706,
-0.02540690079331398,
0.0497874952852726,
0.04133648797869682,
0.025645816698670387,
0.00016206051805056632,
-0.03747175633907318,
-0.03381296619772911,
-0.03950135037302971,
0.04039163142442703,
0.061149027198553085,
-0.06506853550672531,
0.03966737166047096,
-0.023122401908040047,
-0.057582274079322815,
0.039989449083805084,
-0.036965761333703995,
0.04224659502506256,
0.06105280667543411,
-0.0030529119540005922,
-0.05274364352226257,
0.014181667938828468,
0.0602775439620018,
-0.01960168220102787,
-0.04264034703373909,
0.021568642929196358,
0.053747329860925674,
-0.014524099417030811,
0.022732388228178024,
0.004177523776888847,
-0.050658393651247025,
0.03254586085677147,
-0.022451819851994514,
0.014506988227367401,
0.021157650277018547,
-0.04849041998386383,
0.05091428384184837,
0.02157163992524147,
0.0049343714490532875,
-0.002976421033963561,
-0.02025313675403595,
-0.10243602097034454,
-0.01476496271789074,
-0.029068898409605026,
0.010092555545270443,
0.01139110792428255,
-0.007818667218089104,
-0.008687812834978104,
0.005832426715642214,
0.027014419436454773,
0.04173176735639572,
0.04876096919178963,
-0.03745899721980095,
-0.035675764083862305,
0.022349493578076363,
0.03340120613574982,
-0.01883787289261818,
-0.041839659214019775,
-0.047507308423519135,
-0.042448561638593674,
0.05914125218987465,
0.019137857481837273,
-0.021468980237841606,
-0.08230721950531006,
-0.003944236785173416,
-0.028480766341090202,
-0.0012486475752666593,
0.0015904041938483715,
0.008013442158699036,
-0.028406880795955658,
-0.003277574200183153,
-0.008750392124056816,
-0.024472156539559364,
0.006776898168027401,
-0.0302177332341671,
0.00571441650390625,
-0.0382782481610775,
-0.06945675611495972,
-0.05074199661612511,
0.023543843999505043,
-0.0002029704919550568,
0.04000082612037659,
0.02795393206179142,
0.0543149933218956,
-0.04478077217936516,
-0.06949099898338318,
0.04540843516588211,
0.042306479066610336,
0.06147490069270134,
-0.034874964505434036,
0.08255817741155624,
0.023530693724751472,
0.028774026781320572,
0.03927531838417053,
-0.01663202792406082,
0.015053209848701954,
0.023165719583630562,
-0.031882353127002716,
-0.05146462097764015,
0.009077365510165691,
0.031320586800575256,
0.048175182193517685,
-0.04923225939273834,
0.03633864223957062,
-0.023476243019104004,
-0.011929619126021862,
-0.02407732605934143,
0.08731967210769653,
-0.0011480588000267744,
0.0011481958208605647,
-0.04153411462903023,
-0.07191202044487,
0.01702362298965454,
0.017755553126335144,
-0.014547082595527172,
0.011854917742311954,
-0.05630211904644966,
-0.010218930430710316,
0.031924519687891006,
-0.03221568837761879,
0.020227987319231033,
-0.03902897611260414,
0.008742686361074448,
-0.02666947990655899,
-0.002205601194873452,
-0.023358825594186783,
-0.011133553460240364,
0.014109678566455841,
0.042651914060115814,
0.029257090762257576,
-0.0434507392346859,
0.05364314839243889,
0.05690736323595047,
-0.011703409254550934,
-0.017809689044952393,
0.004630988463759422,
0.02093343436717987,
-0.03255974501371384,
-0.011413631960749626,
0.0498579740524292,
-0.031239617615938187,
-0.013071213848888874,
0.02849823236465454,
-0.036567993462085724,
0.02533014677464962,
-0.023468943312764168,
0.09942823648452759,
0.03821184113621712,
-0.059749968349933624,
-0.005107429344207048,
0.021329859271645546,
-0.05330420285463333,
-0.041508790105581284,
0.0029717860743403435,
-0.004511372186243534,
-0.04128158465027809,
0.020454127341508865,
-0.005052610766142607,
0.018625915050506592,
-0.015590104274451733,
0.06943243741989136,
0.005219412501901388,
0.007952558808028698,
0.021666666492819786,
-0.014587056823074818,
-0.07568047940731049,
0.09107795357704163,
0.002331693656742573,
0.0376540943980217,
0.017924129962921143,
0.03177759423851967,
-0.01879481039941311,
0.02513532154262066,
-0.022706400603055954,
0.00762643339112401,
0.00984931644052267,
-0.03710337355732918,
0.009202603250741959,
-0.004671197850257158,
0.015403215773403645,
0.05312418192625046,
-0.03129439800977707,
0.060986172407865524,
0.021326648071408272,
-0.004379425663501024,
0.0161887239664793,
-0.018893476575613022,
-0.018665067851543427,
0.0350278876721859,
-0.020413653925061226,
0.0046815574169158936,
-0.035979099571704865,
0.03404349088668823,
-0.012001627124845982,
0.007746205199509859,
0.07925886660814285,
-0.09210746735334396,
0.07803427428007126,
0.03989517316222191,
-0.04135588929057121,
-0.007879567332565784,
0.013540475629270077,
0.02132093906402588,
0.010296937078237534,
0.04769831895828247,
-0.027631111443042755,
0.0564558207988739,
0.017246928066015244,
0.01871492527425289,
0.006897433660924435,
0.012778276577591896,
0.02104470506310463,
0.003909790888428688,
0.033196497708559036,
-0.0032960176467895508,
-0.0309730414301157,
0.052103400230407715,
-0.04488512873649597,
-0.013829276897013187,
-0.014701428823173046,
0.060137879103422165,
-0.06595326960086823,
0.0246267132461071,
-0.06849101930856705,
0.0187290757894516,
-0.08504363894462585,
0.0156689640134573,
0.015426265075802803,
0.02156725339591503,
-0.015263491310179234,
0.025810416787862778,
-0.01140913087874651,
0.03396490588784218,
0.01815689355134964,
0.003910692408680916,
0.0046564447693526745,
-0.003986469004303217,
0.07576273381710052,
0.05557788163423538,
0.02401711232960224,
0.04294193908572197,
-0.05060561001300812,
-0.041744768619537354,
-0.03251436725258827,
-0.011118808761239052,
-0.009928150102496147,
0.004312997218221426,
0.021349720656871796,
-0.08294586092233658,
0.028716593980789185,
0.07208040356636047,
-0.016880040988326073,
0.020073486492037773,
-0.07125811278820038,
0.05314966291189194,
-0.022540302947163582,
-0.024291766807436943,
-0.06113418936729431,
0.010452096350491047,
-0.03299383819103241,
0.012687798589468002,
0.013698582537472248,
0.08155244588851929,
0.06422900408506393,
0.05649323761463165,
0.03355598449707031,
-0.0719335749745369,
0.061120614409446716,
-0.09050062298774719,
-0.036565475165843964,
-0.04646031931042671,
-0.0030133610125631094,
0.02466541714966297,
-0.048138123005628586,
-0.025684840977191925,
0.00513296015560627,
-0.0503893680870533,
0.02348460629582405,
-0.00978501234203577,
0.027116885408759117,
-0.05039787292480469,
0.015940602868795395,
-0.021232450380921364,
0.025278916582465172,
-0.02803453616797924,
0.007817204110324383,
0.07691004127264023,
-0.0079095009714365,
-0.09058627486228943,
0.013840798288583755,
-0.02675219625234604,
-0.03696207329630852,
0.028200559318065643,
-0.040369149297475815,
0.014463221654295921,
-0.0041761803440749645,
-0.03893072158098221,
-0.057855699211359024,
0.02046162821352482,
0.028483321890234947,
-0.05257849395275116,
-0.025954660028219223,
0.04373309016227722,
0.002211017766967416,
0.042684923857450485,
0.014491700567305088,
0.06254808604717255,
-0.01851203665137291,
0.0008042219560593367,
0.02783380262553692,
0.018845712766051292,
-0.000034708766179392114,
-0.0011322099016979337,
0.011382627300918102,
0.0025582171510905027,
0.0012596490560099483,
-0.006272106897085905,
0.044627297669649124,
0.008667964488267899,
-0.022068677470088005,
-0.04824524372816086,
-0.04553007706999779,
0.03481360524892807,
-0.021811887621879578,
-0.0001803498453227803,
0.020741989836096764,
0.014869053848087788,
0.06848403811454773,
-0.010372000746428967,
-0.011432032100856304,
-0.01692570559680462,
0.005917703732848167,
0.005072268657386303,
-0.014397530816495419,
-0.030566703528165817,
-0.008735423907637596,
-0.025910958647727966,
0.040840595960617065,
-0.012247868813574314,
-0.03913477435708046,
-0.009534409269690514,
0.06918060034513474,
-0.06683840602636337,
0.002525711664929986,
-0.014757601544260979,
-0.007284602150321007,
0.05539378523826599,
0.059981897473335266,
-0.05148143321275711,
0.051554858684539795,
0.009534179233014584,
0.04453152418136597,
0.014781027100980282,
-0.03919707611203194,
-0.006511649116873741,
0.00245205988176167,
-0.07988017052412033,
-0.002364764455705881,
-0.04170169308781624,
0.02859419398009777,
-0.05624425411224365,
0.040704529732465744,
-0.06642825156450272,
0.04871894791722298,
0.04153415188193321,
-0.04177457466721535,
0.005353736691176891,
-0.03282700851559639,
0.021848706528544426,
0.03498740866780281,
-0.005595851689577103,
-0.0036503449082374573,
0.027074087411165237,
-0.016793979331851006,
-0.017207060009241104,
0.0585881806910038,
-0.027475234121084213,
-0.004847832955420017,
-0.00551962573081255,
0.01632029563188553,
-0.007419824134558439,
-0.006659642793238163,
-0.01578134298324585,
-0.016529465094208717,
0.01044523436576128,
0.039503153413534164,
-0.012172306887805462,
-0.010773816145956516,
0.013396428897976875,
0.03547249734401703,
-0.01813947595655918,
-0.01762116327881813,
0.019823873415589333,
-0.023456674069166183,
0.02672356367111206,
0.08063923567533493,
-0.015964943915605545,
0.019556785002350807,
0.034854184836149216,
-0.03921881690621376,
0.031140990555286407,
-0.04556022956967354,
0.08947264403104782,
0.012871569953858852,
0.07717150449752808,
0.023488538339734077,
-0.030365096405148506,
-0.009330383501946926,
0.01615644060075283,
-0.0008960055420175195,
0.01749301142990589,
0.011558611877262592,
-0.0025742147117853165,
0.022928010672330856,
-0.08739607781171799,
0.047833461314439774,
-0.01353214681148529,
0.012029127217829227,
-0.02794881910085678,
0.024505821987986565,
0.01420565601438284,
0.01947855018079281,
-0.0007582104881294072,
-0.040376581251621246,
0.04265943542122841,
0.047470804303884506,
0.061021458357572556,
-0.06012332811951637,
0.06522581726312637,
-0.028450733050704002,
0.031422022730112076,
0.07125908881425858,
-0.05447063222527504,
-0.07757958024740219,
0.017091041430830956,
0.002881369087845087,
-0.011059187352657318,
0.019490282982587814,
0.008231308311223984,
-0.008951593190431595,
-0.04476851224899292,
-0.058748509734869,
-0.04465274512767792,
0.008635937236249447,
-0.04285638406872749,
0.08059806376695633,
-0.004183017183095217,
-0.02780684269964695,
0.022204013541340828,
-0.003571233246475458,
0.038551896810531616,
0.0019384922925382853,
0.0574767179787159,
-0.023173397406935692,
-0.044732239097356796,
-0.0030065265018492937,
0.048551611602306366,
-0.0123674925416708,
0.035712260752916336,
0.020801067352294922,
-0.05352470278739929,
0.02694127894937992,
-0.0031270342878997326,
-0.07092809677124023,
-0.10268703103065491,
-0.008961405605077744,
0.013548140414059162,
-0.0009203606750816107,
0.03186667710542679,
-0.028310274705290794,
-0.03970657289028168,
0.0014726596418768167,
0.056070517748594284,
0.042447831481695175,
0.008878938853740692,
0.028261078521609306,
0.04806545004248619,
0.016927029937505722,
-0.013887000270187855,
0.03986155986785889,
-0.0016470198752358556,
-0.04311246797442436,
0.020336711779236794,
0.030806442722678185,
0.06061460077762604,
-0.021637501195073128,
-0.05243953317403793,
0.05528337508440018,
-0.018143681809306145,
0.03815845772624016,
0.01159049291163683,
-0.008416697382926941,
-0.003283949801698327,
-0.0020260801538825035,
-0.03661743178963661,
-0.00896401610225439,
-0.007411065045744181,
-0.028132429346442223,
-0.060050513595342636,
0.022517159581184387,
0.04922691732645035,
-0.01580771431326866,
-0.02842414565384388,
-0.02251647599041462,
-0.03761838749051094,
0.04508809745311737,
-0.04206765070557594,
-0.01762177236378193,
0.02010277844965458,
0.058569710701704025,
0.02316557802259922,
-0.03940960392355919,
0.005641639232635498,
-0.020902331918478012,
-0.022603150457143784,
0.0077971587888896465,
-0.013773713260889053,
0.0007566164713352919,
-0.01876893639564514,
-0.03767326474189758,
-0.004482917953282595,
-0.05113621801137924,
-0.013196724466979504,
0.02864888869225979,
-0.05049910768866539,
-0.060555268079042435,
0.03581446036696434,
0.020632216706871986,
0.00944564025849104,
-0.002390476642176509,
0.0545668751001358,
-0.05222327634692192,
-0.003021807875484228,
0.029411153867840767,
-0.009394457563757896,
0.027505960315465927,
-0.03766888752579689,
0.017147330567240715,
-0.0015461230650544167,
-0.03985356539487839,
-0.015828685835003853,
0.08375784009695053,
0.027392292395234108,
-0.047745231539011,
-0.026555217802524567,
-0.04562852159142494,
-0.0363541916012764,
0.037948790937662125,
-0.03824205696582794,
0.026169531047344208,
-0.020073475316166878,
-0.06445546448230743,
0.019497504457831383,
-0.02836737595498562,
-0.02355034649372101,
0.006735228002071381,
-0.020193330943584442,
0.01951657049357891,
0.03558321297168732,
-0.021778719499707222,
0.006359428633004427,
-0.02770780585706234,
0.0344664566218853,
-0.06685402244329453,
-0.015444012358784676,
-0.0017394295427948236,
0.011169706471264362,
0.06575419008731842,
0.04297671839594841,
0.07597402483224869,
0.07401017099618912,
0.040989574044942856,
-0.06599638611078262,
-0.026945142075419426,
-0.003716315608471632,
0.009218677878379822,
0.025472957640886307,
0.04064924269914627,
0.004063818603754044,
0.007690201047807932,
0.06447025388479233,
0.021179504692554474,
-0.031279511749744415,
0.04113202169537544,
0.012046284042298794,
-0.043918464332818985,
-0.004676861688494682,
-0.016256609931588173,
0.014385047368705273,
-0.050834912806749344,
0.03695967420935631,
0.03983452916145325,
0.028435979038476944,
-0.0429186075925827,
-0.030244961380958557,
0.0563238225877285,
-0.027728697285056114,
0.03524109721183777,
-0.002940673613920808,
0.07485921680927277,
-0.0045899273827672005,
0.006995137315243483,
-0.006665260065346956,
-0.018093504011631012,
0.026773903518915176,
-0.026840463280677795,
0.03131523355841637,
0.008717244490981102,
-0.028854314237833023,
0.01018165610730648,
-0.031067701056599617,
-0.005784448701888323,
-0.020808912813663483,
-0.004024236463010311,
-0.015409953892230988,
-0.004181318450719118,
-0.0076957582496106625,
0.0279541052877903,
-0.010443163104355335,
-0.009322029538452625,
-0.0281436238437891,
0.02647944912314415,
0.02730192430317402,
0.0054511879570782185,
0.02100735902786255,
0.032839324325323105,
0.03535580635070801,
0.046184465289115906,
0.0235902089625597,
0.023605328053236008,
0.03764262795448303,
0.02032720297574997,
-0.008222829550504684,
-0.011245283298194408,
0.019892124459147453,
0.04232383146882057,
-0.024663636460900307,
0.012420985847711563,
0.028164196759462357,
0.00017426232807338238,
-0.03477523475885391,
-0.0023274587001651525,
-0.018649110570549965,
-0.01766274869441986,
-0.020333707332611084,
-0.056686725467443466,
0.04663563892245293,
-0.019779250025749207,
0.01639283075928688,
-0.03323841840028763,
0.03538099303841591,
-0.0025679252576082945,
-0.00032221199944615364,
-0.017593909054994583,
-0.05080879107117653,
0.03669074922800064,
-0.019451400265097618,
-0.0376543328166008,
0.023471113294363022,
-0.0016241410048678517,
0.032055698335170746,
0.007403559982776642,
0.005355319939553738,
-0.08253825455904007,
-0.019672870635986328,
0.02754339389503002,
0.007371303625404835,
-0.017024260014295578,
0.009634929709136486,
0.015793874859809875,
-0.014422588050365448,
-0.02859734743833542,
0.009341384284198284,
-0.007723683025687933,
0.02964627370238304,
-0.08586941659450531,
-0.05661582201719284,
-0.025806691497564316,
0.021811265498399734,
-0.056153442710638046,
0.018129300326108932,
-0.006697246804833412,
-0.050877150148153305,
0.04499058425426483,
0.016469916328787804,
0.04435020312666893,
-0.0386350154876709,
-0.009878848679363728,
-0.09766066819429398,
0.003919379785656929,
-0.06064717844128609,
0.03360908478498459,
-0.015585921704769135,
-0.033084042370319366,
-0.0193448718637228,
0.05395979434251785,
-0.04492168873548508,
-0.017212362959980965,
0.009493379853665829,
-0.03261295333504677,
-0.028558015823364258,
-0.010131493210792542,
0.034819718450307846,
0.035710033029317856,
-0.05199093744158745,
-0.0005016722716391087,
0.029794085770845413,
0.021904027089476585,
-0.07060053199529648,
0.014812451787292957,
0.04853539541363716,
-0.10448956489562988,
-0.024120407178997993,
-0.04207272082567215,
-0.03232967108488083,
0.009099548682570457,
-0.015144361183047295,
0.016868894919753075,
-0.01921228878200054,
-0.03104637935757637,
0.026159558445215225,
0.020925788208842278,
-0.0049016219563782215,
-0.014771349728107452,
-0.023512953892350197,
-0.001306268386542797,
-0.02525882050395012,
0.018737908452749252,
-0.016149569302797318,
0.0026050677988678217,
0.012450648471713066,
0.07354964315891266,
-0.02849898859858513,
-0.058416418731212616,
-0.01851341314613819
] |
<p>In relation to my question <a href="http://biology.stackexchange.com/questions/10945/isotropicity-of-sarcomere-bands-in-skeletal-muscle-cells">here</a> I wanted to make sure that my physical argument was not flawed. </p>
<p>Anisotropic properties, (especially refractive index) is characteristic of a well-ordered solid (usually crystalline). On the other hand Isotropic properties is indicative of an amorphous solid, i.e lack of well-ordered arrangement (a random arrangement). The question is:- </p>
<blockquote>
<p><strong>Can any composite arrangement of isotropic elements give an
anisotropic system? Can any arrangement of anisotropic elements give an isotropic system?</strong> </p>
</blockquote>
<p>Intuitively, I think, it should not be possible, if isotropicity implies random arrangement (of individually anisotropic components) since any arrangement of random elements should not give a well-ordered system capable of exhibiting anisotropic refractive index. </p>
<p>As for the other part of my question, intuitively, it must be possible, since a random arrangement of anisotropic elements will impart an overall randomness and hence isotropic refractive index. (If I am not mistaken, this is what happens in short-range order amorphous solids, whre individually anisotropic grains are randomly arranged to produce an isotropic solid).</p>
|
g2504
|
[
-0.02419048547744751,
0.02968158759176731,
0.016719454899430275,
0.0011031582253053784,
0.0036127353087067604,
-0.0038232437800616026,
0.005374510772526264,
-0.013185568153858185,
0.006399356760084629,
0.03223874047398567,
0.0427711196243763,
0.024988189339637756,
0.0033245845697820187,
-0.04356137290596962,
-0.03808193281292915,
-0.004506303928792477,
0.06667550653219223,
0.027303187176585197,
-0.009260165505111217,
0.05118224024772644,
-0.08671470731496811,
-0.009892293252050877,
0.011104549281299114,
-0.017501527443528175,
-0.010186809115111828,
0.03105616196990013,
0.03893261030316353,
-0.09568960964679718,
-0.05518070235848427,
-0.016182778403162956,
0.026526784524321556,
-0.010548669844865799,
0.02871408499777317,
-0.009476622566580772,
-0.01756267435848713,
0.011599813587963581,
-0.012422644533216953,
-0.03082551807165146,
0.02935059182345867,
-0.02157128043472767,
-0.0462992861866951,
-0.025662915781140327,
-0.012712625786662102,
-0.05262097716331482,
-0.022360583767294884,
0.049791403114795685,
-0.04857981577515602,
0.051944997161626816,
-0.016408002004027367,
-0.013196064159274101,
0.01705188862979412,
0.045127250254154205,
0.06659257411956787,
-0.01411624439060688,
0.026826541870832443,
0.026224937289953232,
-0.005076512694358826,
0.010631460696458817,
0.061401184648275375,
0.0410153903067112,
0.034883901476860046,
0.040743838995695114,
0.0001638042158447206,
-0.03501438349485397,
0.022633995860815048,
0.03661610931158066,
0.03705228492617607,
0.043949536979198456,
0.02339876815676689,
-0.018780402839183807,
0.028452422469854355,
-0.01660601608455181,
-0.03164496645331383,
-0.02848726511001587,
-0.012176090851426125,
-0.02641703002154827,
-0.019284134730696678,
-0.015553159639239311,
0.007784715387970209,
0.03084954060614109,
-0.0032690970692783594,
-0.017479591071605682,
-0.025059029459953308,
-0.004908998031169176,
0.04293211176991463,
0.011964313685894012,
0.05644240975379944,
-0.039315685629844666,
0.022833865135908127,
0.07708189636468887,
-0.027174947783350945,
0.034023091197013855,
0.060710374265909195,
0.042837079614400864,
0.004865129943937063,
0.03141144663095474,
-0.016073262318968773,
0.04753032699227333,
-0.0959366038441658,
-0.029421834275126457,
0.0019270754419267178,
0.03211003169417381,
-0.005055735353380442,
-0.009373871609568596,
-0.03112432174384594,
0.0032874972093850374,
0.02258278615772724,
0.018343348056077957,
-0.0659312978386879,
-0.021333642303943634,
-0.015577501617372036,
0.023074088618159294,
-0.029132064431905746,
0.016688985750079155,
0.009624456986784935,
0.004669325891882181,
0.08647788316011429,
0.026375148445367813,
0.004354977048933506,
0.03760724142193794,
0.03185350075364113,
0.03166267275810242,
0.07563422620296478,
0.03555348888039589,
-0.0457458533346653,
0.019546320661902428,
0.05543858930468559,
0.041732307523489,
0.05209575220942497,
-0.02914808876812458,
-0.05135373771190643,
-0.023315485566854477,
0.03512493148446083,
-0.048309337347745895,
-0.05937938392162323,
-0.009344634599983692,
0.008165514096617699,
-0.03274223580956459,
0.0005913871573284268,
0.014938641339540482,
-0.0207758117467165,
0.040451765060424805,
-0.040787480771541595,
0.04015049338340759,
-0.06436622142791748,
-0.01169701386243105,
-0.03541849926114082,
0.015006186440587044,
-0.0017469845479354262,
0.052625689655542374,
-0.02601083554327488,
0.024516137316823006,
-0.03169844299554825,
-0.05853090062737465,
0.0164629053324461,
-0.029876364395022392,
-0.0026720401365309954,
0.021123098209500313,
0.01664627157151699,
-0.0024330157320946455,
0.05308673903346062,
0.002001447370275855,
0.0039257630705833435,
-0.025278404355049133,
-0.02456331066787243,
-0.06355036795139313,
-0.028074948117136955,
-0.04438866302371025,
0.042306091636419296,
-0.07994726300239563,
-0.043265391141176224,
0.019329912960529327,
0.017772627994418144,
0.03057548776268959,
-0.026584375649690628,
0.027984416112303734,
0.05224083364009857,
-0.0026742464397102594,
0.04009319841861725,
0.010511498898267746,
-0.034568168222904205,
0.09632466733455658,
-0.04898406192660332,
-0.061558663845062256,
-0.032485589385032654,
0.01714986003935337,
0.04870721325278282,
-0.001346964854747057,
-0.075160913169384,
0.019068680703639984,
-0.006506646517664194,
-0.005659426562488079,
-0.06944910436868668,
0.0899791419506073,
0.010821226052939892,
-0.01935173198580742,
0.009552706964313984,
0.04395795613527298,
-0.045405857264995575,
0.027971912175416946,
0.011790471151471138,
0.01470519881695509,
0.00882610585540533,
0.03537933900952339,
0.007890199311077595,
-0.0002190164668718353,
-0.024121105670928955,
0.04323773831129074,
-0.0012326394207775593,
-0.010083457455039024,
-0.0031270813196897507,
0.003909585531800985,
-0.04106631875038147,
-0.03936140984296799,
0.04052484780550003,
0.00889658834785223,
0.007218371611088514,
-0.04821830242872238,
-0.03020218200981617,
-0.03183123096823692,
0.012763268314301968,
0.007896574214100838,
-0.03741956129670143,
0.016465527936816216,
-0.020671561360359192,
-0.030071385204792023,
-0.0070681083016097546,
0.014723924919962883,
0.0375249944627285,
-0.03613777086138725,
-0.04275514557957649,
0.019696420058608055,
0.04358666390180588,
-0.02921461872756481,
-0.01189641747623682,
0.016138674691319466,
-0.05381001904606819,
0.04128685221076012,
-0.053374335169792175,
-0.025573590770363808,
-0.02290470339357853,
-0.05238236486911774,
0.021586371585726738,
0.003724326379597187,
-0.027576006948947906,
-0.028053043410182,
0.0621209479868412,
-0.014096012338995934,
0.015090154483914375,
0.06033167243003845,
-0.0022022288758307695,
0.025331327691674232,
-0.02715364284813404,
-0.009415880776941776,
-0.000276811420917511,
-0.04178117960691452,
-0.006964464671909809,
0.05242934077978134,
-0.015821930021047592,
0.0038484155666083097,
-0.004341287072747946,
-0.019380351528525352,
0.037765633314847946,
0.003536778734996915,
-0.11161880195140839,
0.061677686870098114,
-0.023589318618178368,
-0.02329191192984581,
-0.004086048807948828,
-0.02383776195347309,
-0.003123113652691245,
0.04212801530957222,
0.06648183614015579,
0.07441945374011993,
-0.00881961826235056,
0.04099883884191513,
-0.008406003937125206,
-0.017208902165293694,
-0.029341721907258034,
-0.001145071815699339,
0.0035100558307021856,
0.003322109580039978,
-0.0321512408554554,
0.033610887825489044,
-0.021400002762675285,
0.055976174771785736,
0.0756138414144516,
-0.03877675160765648,
0.006087201647460461,
0.0402846522629261,
-0.005232209339737892,
0.035761743783950806,
0.05604339763522148,
0.0441349558532238,
-0.012446790933609009,
-0.026770848780870438,
-0.004153232555836439,
-0.0064760600216686726,
-0.054652139544487,
0.06032411381602287,
-0.05735456198453903,
-0.016504336148500443,
0.040183957666158676,
-0.006061644293367863,
-0.027613133192062378,
0.08937361091375351,
-0.07277552038431168,
-0.05845364183187485,
-0.010001695714890957,
0.018496816977858543,
-0.02394193224608898,
0.005908821243792772,
-0.033028725534677505,
0.0069213383831083775,
-0.0014175729593262076,
0.0229579396545887,
-0.06544831395149231,
-0.03243589401245117,
0.004114042967557907,
-0.01854182593524456,
-0.03430444747209549,
-0.0018688421696424484,
0.010611544363200665,
-0.02606833353638649,
-0.008370282128453255,
-0.054700229316949844,
-0.049060381948947906,
0.03898032754659653,
-0.03157641738653183,
-0.013679184019565582,
0.0009491404052823782,
-0.02155306562781334,
0.0004493704764172435,
0.00028353568632155657,
-0.07393596321344376,
-0.02914769947528839,
-0.043390873819589615,
-0.0022865247447043657,
0.02590065449476242,
-0.0397939532995224,
0.05053393915295601,
-0.010323912836611271,
0.001422385685145855,
-0.015572721138596535,
-0.05312679708003998,
0.08235479891300201,
0.06292921304702759,
-0.0421794168651104,
0.03465593233704567,
-0.023713165894150734,
-0.012871477752923965,
-0.004918921738862991,
0.0348949208855629,
-0.03983544185757637,
-0.05901944637298584,
0.01846008561551571,
0.038138825446367264,
0.05488162115216255,
-0.014046822674572468,
-0.03994433954358101,
-0.0026255783159285784,
-0.09392569959163666,
0.007352632470428944,
-0.06523196399211884,
-0.005414700135588646,
0.038065895438194275,
0.01330229640007019,
0.03509313613176346,
0.012271463871002197,
0.022362198680639267,
0.0026512807235121727,
-0.048228174448013306,
-0.01831982098519802,
-0.003091097343713045,
0.012792273424565792,
0.04285352677106857,
0.03086256794631481,
0.028103195130825043,
-0.03532129153609276,
-0.000111200766696129,
-0.018753603100776672,
0.03356165811419487,
0.009555414319038391,
0.012078074738383293,
-0.010902812704443932,
0.032905463129282,
-0.02053731493651867,
-0.04421713203191757,
-0.03378432244062424,
-0.006471291650086641,
0.04689238220453262,
-0.0215406846255064,
-0.05806008726358414,
0.049022216349840164,
-0.013948284089565277,
-0.04635428637266159,
0.005659421905875206,
-0.028333956375718117,
0.03440837189555168,
0.014025427401065826,
0.020543770864605904,
-0.02373087964951992,
-0.06542466580867767,
-0.010183962993323803,
-0.003315095091238618,
0.018632348626852036,
-0.007844015955924988,
-0.030535487458109856,
-0.0891941711306572,
-0.033237893134355545,
0.027722731232643127,
0.008853968232870102,
0.030303914099931717,
-0.04583299160003662,
0.03711211681365967,
0.03399799019098282,
-0.06478609889745712,
0.018812784925103188,
0.0026512795593589544,
0.030148234218358994,
-0.0025060928892344236,
0.04203831031918526,
0.020783429965376854,
-0.0639725998044014,
-0.020441196858882904,
0.05267779901623726,
0.019324442371726036,
-0.0891459658741951,
-0.0008933869539760053,
0.0007455847808159888,
0.029275858774781227,
0.03311546891927719,
0.04066869243979454,
0.008347180671989918,
-0.01250007189810276,
0.04503742977976799,
-0.018219823017716408,
0.005913880653679371,
0.08628123253583908,
0.028972074389457703,
-0.03374463692307472,
-0.015510751865804195,
0.07492432743310928,
-0.01473515946418047,
0.03979819640517235,
-0.0024081456940621138,
-0.001190074603073299,
0.04540763422846794,
-0.06743886321783066,
0.03424595296382904,
0.04046225920319557,
-0.000054185740737011656,
-0.01682458631694317,
-0.04002465680241585,
-0.025421615689992905,
-0.04028226435184479,
-0.03892550989985466,
0.024535473436117172,
0.03299783170223236,
-0.005260133650153875,
0.019536396488547325,
-0.04417219012975693,
-0.03491199389100075,
0.07419244199991226,
-0.02021341770887375,
0.033172398805618286,
-0.003522025654092431,
-0.002487802878022194,
-0.07123357057571411,
0.058855194598436356,
0.01940765604376793,
0.054521530866622925,
0.008237903006374836,
0.018094347789883614,
0.039361052215099335,
-0.025922155007719994,
-0.004362211097031832,
-0.03995296731591225,
-0.05246233567595482,
-0.00268728518858552,
-0.0768778920173645,
0.00551774213090539,
0.02272828482091427,
-0.07087494432926178,
0.026761870831251144,
0.017908966168761253,
-0.06634373217821121,
0.05435553565621376,
-0.06204286962747574,
0.0063634575344622135,
-0.0018762288382276893,
-0.034205857664346695,
0.006793538574129343,
-0.052800655364990234,
0.019905442371964455,
-0.07189017534255981,
0.06569665670394897,
0.03241118788719177,
-0.0034480965696275234,
0.03032078593969345,
-0.033997032791376114,
0.01063233707100153,
0.03676499053835869,
-0.02154715359210968,
-0.0008275970467366278,
0.08091984689235687,
0.02130766212940216,
-0.007994462735950947,
0.026306038722395897,
-0.030729906633496284,
0.011915280483663082,
0.013085667975246906,
0.027394184842705727,
0.01801311783492565,
0.009412766434252262,
0.02772662416100502,
-0.06533388048410416,
0.01137099415063858,
0.022914815694093704,
-0.06552071869373322,
-0.09095057845115662,
0.025530865415930748,
-0.02592380717396736,
-0.04415236413478851,
-0.0798381045460701,
0.010379387997090816,
-0.03053572028875351,
0.0057456460781395435,
-0.04086979106068611,
0.00781815405935049,
0.004929882939904928,
0.0387786403298378,
-0.021773630753159523,
-0.03437664359807968,
-0.010042515583336353,
-0.04142244532704353,
-0.05012588948011398,
0.03788342699408531,
0.011182230897247791,
0.012133815325796604,
-0.009858056902885437,
0.002046051202341914,
0.04760586842894554,
0.08785147964954376,
-0.004660346545279026,
-0.012512678280472755,
-0.010127677582204342,
-0.06363120675086975,
0.004355526529252529,
-0.015380273573100567,
-0.004283557180315256,
0.0651286244392395,
0.010442412458360195,
-0.004963363520801067,
0.016830820590257645,
0.08671960979700089,
-0.04963487759232521,
-0.03451760858297348,
0.005426294170320034,
-0.0349164642393589,
0.04080326855182648,
0.04091116040945053,
-0.003427834017202258,
0.00857026968151331,
0.0361197367310524,
-0.008669434115290642,
0.009233693592250347,
-0.013918984681367874,
0.0027227106038480997,
0.06911498308181763,
0.01430550403892994,
-0.02047898806631565,
0.022904368117451668,
0.03527117520570755,
-0.004185313358902931,
-0.04439171776175499,
-0.05562366172671318,
0.009859082289040089,
0.03829142451286316,
0.0009066984639503062,
-0.00901219341903925,
0.022684162482619286,
0.01009808573871851,
0.053697437047958374,
-0.007140207104384899,
-0.01349641103297472,
0.0019153207540512085,
0.027388405054807663,
0.021553561091423035,
-0.06608740240335464,
-0.05257270485162735,
-0.03318920359015465,
-0.08388271927833557,
0.008135686628520489,
-0.038166265934705734,
-0.011519743129611015,
0.043189503252506256,
0.0902276337146759,
-0.04837172105908394,
0.05353984609246254,
0.037379372864961624,
0.019689690321683884,
0.07344049960374832,
-0.017183419317007065,
0.0062009422108531,
0.012212536297738552,
0.006403182167559862,
0.07147503644227982,
0.028801675885915756,
-0.005909554194658995,
-0.011158127337694168,
0.02791239321231842,
0.009039309807121754,
0.044113803654909134,
0.012110650539398193,
-0.05602005496621132,
-0.06960798799991608,
-0.0003142600180581212,
0.001557476818561554,
-0.0018916469998657703,
0.002661821898072958,
0.005573842208832502,
-0.014820393174886703,
-0.014136644080281258,
-0.0029741465114057064,
0.0396248921751976,
-0.018503723666071892,
0.06207837536931038,
-0.009108132682740688,
0.018931103870272636,
-0.0028387401252985,
-0.023649781942367554,
0.034548819065093994,
0.03095443919301033,
0.03210963308811188,
-0.02469441294670105,
-0.05828295648097992,
0.022832395508885384,
0.03291955590248108,
-0.0030726264230906963,
0.01354264561086893,
0.027790376916527748,
0.08715365827083588,
-0.014191163703799248,
-0.03204815834760666,
0.024678310379385948,
0.09040310233831406,
-0.013304776512086391,
-0.016005931422114372,
-0.021070510149002075,
0.012443698942661285,
0.0022271915804594755,
-0.021458663046360016,
0.00042161851888522506,
0.004508094396442175,
0.03687193617224693,
-0.012115749530494213,
0.0052818190306425095,
0.04816611483693123,
-0.02627434954047203,
-0.0622832290828228,
0.03571280837059021,
-0.04087626561522484,
-0.01030747964978218,
-0.0008519577095285058,
0.02807723544538021,
0.04614170268177986,
-0.030960403382778168,
-0.04271218180656433,
0.00972517766058445,
-0.010908763855695724,
0.011991247534751892,
0.02648049220442772,
-0.03709085285663605,
0.009194117970764637,
-0.011553351767361164,
0.008497231639921665,
-0.016238590702414513,
0.05023231729865074,
0.046870917081832886,
0.03377579525113106,
0.029344068840146065,
0.0016092421719804406,
0.004905917681753635,
-0.025094030424952507,
0.05077217519283295,
-0.027443213388323784,
0.006577569060027599,
0.04098645970225334,
-0.05796508491039276,
-0.015597047284245491,
-0.016207531094551086,
-0.035050176084041595,
-0.0015355914365500212,
-0.05233432725071907,
-0.01414171326905489,
0.01504389476031065,
0.05419196933507919,
-0.029706841334700584,
-0.06377838551998138,
0.030393796041607857,
-0.018851514905691147,
-0.07870686799287796,
-0.002440114039927721,
0.04571646451950073,
-0.05850903317332268,
-0.03723439946770668,
0.020496075972914696,
-0.050386711955070496,
-0.024302896112203598,
-0.013620504178106785,
0.03254437819123268,
0.04798397794365883,
0.010663297027349472,
-0.012298156507313251,
0.0019018447492271662,
-0.0319167859852314,
-0.00746014341711998,
-0.04534710943698883,
0.01242035161703825,
-0.0744994729757309,
-0.04205784946680069,
-0.019103197380900383,
-0.017923295497894287,
-0.010920862667262554,
-0.004979392513632774,
0.04114605113863945,
0.021502504125237465,
0.05026058480143547,
0.040127791464328766,
0.009386665187776089,
-0.025967201218008995,
-0.005231020040810108,
0.04423700273036957,
0.009251669980585575,
-0.00004575449929689057,
0.013932696543633938,
-0.006256421096622944,
-0.0008682854240760207,
-0.00038224775926209986,
-0.005174278747290373,
0.01991068385541439,
-0.0076081170700490475,
-0.04629143700003624,
0.038300156593322754,
0.009000290185213089,
-0.07521654665470123,
-0.017065873369574547,
0.006587013602256775,
-0.01657472550868988,
-0.10634329915046692,
0.030373822897672653,
0.05514213442802429,
-0.003364014904946089,
0.017959346994757652,
0.06272193789482117,
0.03882717713713646,
0.002817153697833419,
0.03192407265305519,
-0.0044373623095452785,
0.0372767336666584,
-0.007319105789065361,
-0.0034111407585442066,
-0.018715491518378258,
-0.006648242939263582,
0.028550658375024796,
-0.04117174819111824,
-0.03478149697184563
] |
<p>What is the transfer matrix size for a strip lattice of width $n$ vertices, with arbitrary $q$??<br>
I am not sure if it is $q^n$ x $q^n$ or something else.</p>
<p>Any reference is also welcome.</p>
|
g2505
|
[
-0.01843813993036747,
0.03683680668473244,
0.000008920343134377617,
-0.05492907389998436,
-0.02450631931424141,
-0.03631804510951042,
-0.04345553368330002,
-0.006276861764490604,
0.017215093597769737,
0.030869893729686737,
-0.003369863610714674,
0.10235349088907242,
0.003963361959904432,
0.01724444143474102,
-0.03753127157688141,
0.02918855845928192,
0.042049773037433624,
0.029522035270929337,
0.022480830550193787,
-0.024664023891091347,
0.004534401930868626,
-0.02737288922071457,
-0.07334771752357483,
-0.09033308923244476,
0.009182706475257874,
-0.040891025215387344,
0.04001550003886223,
-0.023747840896248817,
0.00649585947394371,
0.020330680534243584,
-0.02298649214208126,
0.011209356598556042,
-0.07697165012359619,
-0.05247686058282852,
-0.009229365736246109,
0.04464632645249367,
-0.05368437245488167,
-0.006696675904095173,
0.06338522583246231,
-0.005358380265533924,
-0.05157513916492462,
0.002791713224723935,
-0.012141763232648373,
0.06401656568050385,
0.029835140332579613,
0.00463752169162035,
0.03234225511550903,
0.02489885874092579,
-0.016584711149334908,
0.018709959462285042,
-0.021068304777145386,
0.07425124198198318,
0.0034687647130340338,
0.04023769497871399,
-0.025456441566348076,
0.01602751389145851,
-0.019185123965144157,
-0.009640603326261044,
0.0012014582753181458,
0.07847937941551208,
-0.037213459610939026,
-0.03744383156299591,
-0.010021462105214596,
0.011191618628799915,
0.016848701983690262,
0.08348459750413895,
0.015047268010675907,
0.06761965155601501,
-0.008510013110935688,
0.01874230057001114,
0.01791868358850479,
0.048460137099027634,
0.01655418425798416,
0.012768814340233803,
-0.07165732234716415,
-0.022803375497460365,
0.008535736240446568,
0.02647552080452442,
0.04863819479942322,
0.0024434395600110292,
-0.031117109581828117,
-0.018877394497394562,
-0.05118207260966301,
-0.009554813615977764,
-0.007727809716016054,
0.04440029710531235,
-0.02839159406721592,
-0.006753918249160051,
-0.029236093163490295,
0.07732745260000229,
0.03103923238813877,
0.015792714431881905,
0.07129126787185669,
0.030212469398975372,
-0.04390683397650719,
-0.015705298632383347,
0.04209790378808975,
-0.03291408717632294,
-0.06476488709449768,
0.011247286573052406,
0.021585196256637573,
-0.004981575533747673,
0.037863872945308685,
-0.02366776019334793,
0.035623908042907715,
0.029867874458432198,
0.004056422505527735,
-0.028771910816431046,
0.018695620819926262,
0.09615761041641235,
-0.013010075315833092,
-0.0016437668818980455,
-0.04682246595621109,
0.0011654193513095379,
-0.02311013638973236,
-0.026413574814796448,
0.03836686536669731,
-0.021349510177969933,
-0.012474946677684784,
0.009249348193407059,
0.054490894079208374,
-0.03211497515439987,
0.050491418689489365,
0.0003854515089187771,
0.06522376835346222,
-0.04852382466197014,
0.007004330866038799,
0.039310578256845474,
-0.006226950790733099,
0.0003582042991183698,
0.02844206802546978,
-0.0272680651396513,
0.0036078509874641895,
0.01370006799697876,
-0.020142007619142532,
0.0017920074751600623,
0.03428104892373085,
0.027472330257296562,
-0.038164447993040085,
-0.0004093302122782916,
-0.044151999056339264,
0.00066142447758466,
-0.017051318660378456,
-0.029526621103286743,
0.026898054406046867,
-0.04745282977819443,
-0.020788192749023438,
-0.034680601209402084,
-0.01536038052290678,
-0.04229354485869408,
0.02894355170428753,
0.04537291079759598,
-0.04941761866211891,
-0.02918996475636959,
-0.002092439914122224,
0.01723458804190159,
-0.004497157875448465,
-0.05140559747815132,
0.00972727220505476,
0.011542717926204205,
0.03705483675003052,
0.013020247220993042,
0.012262853793799877,
-0.011134148575365543,
-0.007070724852383137,
-0.0764511376619339,
-0.013439370319247246,
-0.017680391669273376,
-0.03840995207428932,
-0.03704383969306946,
-0.0198858343064785,
-0.0031777818221598864,
0.05260699614882469,
0.00024709413992241025,
-0.022080320864915848,
0.03438977524638176,
0.006441433448344469,
0.01463948655873537,
0.013665388338267803,
-0.0235206987708807,
-0.021167175844311714,
-0.006144831422716379,
0.011964071542024612,
-0.0029010698199272156,
0.03445881977677345,
-0.0022247489541769028,
0.04071833938360214,
-0.03903361037373543,
-0.006179179530590773,
-0.01863633655011654,
0.008289769291877747,
-0.013826909475028515,
0.056142035871744156,
-0.05234520509839058,
0.009898283518850803,
-0.0096096470952034,
0.05401698872447014,
0.00548814469948411,
-0.04685060307383537,
-0.07010888308286667,
0.015409354120492935,
0.03165845945477486,
0.06004152446985245,
-0.0008763403166085482,
0.014598424546420574,
0.023480715230107307,
-0.07522992789745331,
0.010156286880373955,
-0.02462696097791195,
0.04610961303114891,
-0.024443410336971283,
-0.036457281559705734,
0.0015416131354868412,
0.08421199023723602,
0.039696305990219116,
-0.018885863944888115,
-0.032905202358961105,
-0.04423670098185539,
0.08023728430271149,
0.035035472363233566,
-0.04353877902030945,
-0.026701536029577255,
0.011542904190719128,
-0.022247998043894768,
-0.0220227912068367,
0.015833601355552673,
0.02877391129732132,
0.002141261240467429,
0.036767564713954926,
0.054082006216049194,
-0.10519358515739441,
-0.012858920730650425,
-0.025323325768113136,
-0.05171157792210579,
-0.027841515839099884,
-0.02462788298726082,
-0.048520527780056,
0.005372070241719484,
-0.03078014962375164,
-0.014352469705045223,
0.08802003413438797,
-0.02997535467147827,
-0.03976095840334892,
0.03498305007815361,
-0.06228586286306381,
-0.012026665732264519,
-0.03939017280936241,
-0.04434889927506447,
0.01606813073158264,
-0.05726047605276108,
-0.06081761047244072,
-0.03622344508767128,
0.014846490696072578,
0.034013599157333374,
-0.03548043221235275,
0.036223359405994415,
-0.002183328615501523,
-0.03258604183793068,
-0.08071024715900421,
-0.05410214886069298,
0.008350730873644352,
-0.021758751943707466,
-0.011127667501568794,
-0.015103643760085106,
0.01947784796357155,
0.005068071186542511,
-0.0033608516678214073,
0.05336691811680794,
-0.03146735206246376,
0.02564094588160515,
0.03303810581564903,
0.04379737377166748,
0.02541988156735897,
-0.04439225420355797,
0.019567033275961876,
-0.03328719362616539,
0.04428793117403984,
-0.05662092566490173,
-0.034438036382198334,
-0.044991012662649155,
-0.03656302019953728,
-0.02079855464398861,
-0.046630751341581345,
0.025496209040284157,
-0.01500851009041071,
-0.059117238968610764,
-0.01294008083641529,
0.049247607588768005,
-0.04186807945370674,
0.029356151819229126,
-0.07027669250965118,
0.039115842431783676,
0.00025254045613110065,
-0.04164305329322815,
0.017476024106144905,
0.019173281267285347,
0.044472817331552505,
0.014390651136636734,
-0.00163489009719342,
0.05085991322994232,
-0.014449477195739746,
0.005650846287608147,
-0.016981065273284912,
-0.040023189038038254,
0.05867515876889229,
-0.01301655825227499,
-0.026246292516589165,
0.014483096078038216,
-0.053980350494384766,
-0.040459293872117996,
0.01186482235789299,
-0.019231164827942848,
0.04922545701265335,
-0.009871838614344597,
-0.07805361598730087,
-0.0189814493060112,
0.008863870054483414,
-0.013535385020077229,
0.00032529677264392376,
-0.009305641986429691,
0.0062728263437747955,
-0.04974650964140892,
0.05305996909737587,
0.05344075709581375,
-0.02955435775220394,
0.0101348627358675,
-0.04353403300046921,
0.05060765519738197,
0.03835935890674591,
0.024807143956422806,
-0.050800420343875885,
0.03899761289358139,
-0.016946133226156235,
-0.004970299080014229,
-0.03435017541050911,
-0.01618427038192749,
-0.008587000891566277,
0.01313837431371212,
-0.0008018173975870013,
-0.0042762053199112415,
-0.06967832148075104,
0.004623126704245806,
-0.029315918684005737,
-0.007176043000072241,
0.008229262195527554,
0.005253311712294817,
-0.00045328683336265385,
0.02225690893828869,
-0.00960459839552641,
-0.023650536313652992,
0.007192639168351889,
-0.02795269526541233,
-0.00919834803789854,
-0.037810441106557846,
0.014085423201322556,
0.03058776818215847,
-0.06539794057607651,
-0.012751576490700245,
0.031356751918792725,
-0.039937231689691544,
0.02511114813387394,
-0.009533298201858997,
0.07761870324611664,
0.0013647867599502206,
0.0018464281456544995,
0.011326882988214493,
0.005813924130052328,
-0.01757931336760521,
-0.007899655029177666,
-0.035911161452531815,
-0.03853327035903931,
-0.04951348900794983,
-0.036885105073451996,
0.011670513078570366,
-0.03735100477933884,
-0.016042392700910568,
-0.035629693418741226,
-0.024986127391457558,
0.03549811989068985,
0.014947504736483097,
0.000188312929822132,
-0.006872438360005617,
0.025640975683927536,
-0.010043934918940067,
-0.021363329142332077,
-0.04533260315656662,
-0.04816654324531555,
-0.009101424366235733,
-0.007461695000529289,
-0.034431930631399155,
0.018294034525752068,
-0.020357925444841385,
0.004800398834049702,
-0.07803498208522797,
-0.009388742037117481,
0.005036522634327412,
0.03421967476606369,
0.050480861216783524,
-0.03204506263136864,
0.021486835554242134,
0.01581740379333496,
-0.007851207628846169,
-0.046921055763959885,
-0.006123407743871212,
0.004211802966892719,
0.05645860731601715,
0.039168719202280045,
0.05785011500120163,
-0.005693541374057531,
0.022674327716231346,
-0.027421073988080025,
-0.056452978402376175,
0.01476195640861988,
-0.028623344376683235,
0.04578327387571335,
0.0613831989467144,
-0.03402791917324066,
-0.013811456970870495,
0.00039377622306346893,
-0.06436962634325027,
-0.030508028343319893,
0.017554400488734245,
-0.004731450229883194,
0.021804120391607285,
0.06869523972272873,
0.02784292958676815,
-0.00457422761246562,
0.014352899976074696,
0.03037627786397934,
0.03490043804049492,
0.008286455646157265,
0.08865794539451599,
-0.05435173586010933,
0.06196460500359535,
-0.024028245359659195,
-0.01820904202759266,
0.013962222263216972,
0.014294063672423363,
0.001677862135693431,
-0.014691171236336231,
0.05997759476304054,
0.010461687110364437,
-0.01766982302069664,
0.0015642170328646898,
-0.020299173891544342,
-0.012691985815763474,
-0.03035600297152996,
0.0021459783893078566,
-0.02732129395008087,
-0.03493212163448334,
0.08070722967386246,
0.002225128933787346,
-0.02735200710594654,
-0.03902426362037659,
-0.05427589267492294,
0.004668144509196281,
0.033226512372493744,
0.013817809522151947,
0.08557219803333282,
0.06623265147209167,
0.06142894923686981,
0.05223946273326874,
-0.06773872673511505,
0.0036823111586272717,
0.027799390256404877,
0.033268220722675323,
-0.04079781100153923,
0.06185705214738846,
0.011963878758251667,
-0.06274265795946121,
0.029120897874236107,
0.061997562646865845,
-0.013730050064623356,
-0.017214559018611908,
-0.00997955072671175,
0.014804217964410782,
-0.032826200127601624,
-0.030715081840753555,
0.006314284633845091,
-0.015871241688728333,
-0.027691366150975227,
0.03872149810194969,
0.049666572362184525,
-0.0007147711585275829,
0.012083166278898716,
0.017523856833577156,
0.006798967719078064,
-0.024050571024417877,
0.03322545811533928,
-0.02507145144045353,
0.021848417818546295,
-0.02900617942214012,
-0.024677764624357224,
0.044623032212257385,
-0.03774845600128174,
-0.0626300498843193,
-0.01577320136129856,
-0.08177800476551056,
0.02176797017455101,
0.06738428771495819,
0.06204969435930252,
0.07393429428339005,
-0.0027728641871362925,
0.02234553173184395,
0.03138327598571777,
-0.02296905778348446,
0.007222298067063093,
0.001338893547654152,
-0.01528790034353733,
0.04373425990343094,
0.01796717569231987,
-0.006874287500977516,
0.010555244982242584,
-0.040355030447244644,
0.01264907605946064,
-0.0061152358539402485,
-0.044271666556596756,
-0.045373354107141495,
-0.022030143067240715,
0.05068279802799225,
0.007527039386332035,
-0.007055399473756552,
-0.0031220675446093082,
-0.044357094913721085,
-0.05392405390739441,
0.06631726026535034,
-0.03568222001194954,
-0.07334288209676743,
-0.0839528888463974,
-0.019628560170531273,
0.0022199382074177265,
0.05243954807519913,
-0.048931509256362915,
0.018069513142108917,
-0.005266549065709114,
-0.0127507783472538,
0.03374863043427467,
-0.039306897670030594,
-0.019868936389684677,
0.003467922331765294,
0.03030741587281227,
-0.0086576072499156,
-0.03548315539956093,
0.04213247075676918,
-0.006318270694464445,
0.008140279911458492,
-0.00537703325971961,
-0.05440371111035347,
0.029628898948431015,
0.013518918305635452,
0.010719685815274715,
-0.018256058916449547,
-0.026457518339157104,
-0.026688221842050552,
0.011075221002101898,
-0.005792622454464436,
-0.018120624125003815,
0.027155326679348946,
-0.024104638025164604,
0.03749466687440872,
0.05916725844144821,
0.04314078390598297,
-0.02773059532046318,
-0.05902659520506859,
0.0009239940554834902,
-0.038059525191783905,
-0.008612613193690777,
0.018533915281295776,
0.003282923949882388,
0.03597291558980942,
-0.016308488324284554,
-0.035347338765859604,
-0.032841768115758896,
0.029121333733201027,
-0.00020133864018134773,
-0.014251044020056725,
-0.009790775366127491,
-0.017524536699056625,
-0.07834040373563766,
-0.01227858942002058,
0.005935669876635075,
0.011784995906054974,
-0.06670273840427399,
0.023619264364242554,
-0.04381667077541351,
0.040238142013549805,
-0.003126465482637286,
-0.05357711389660835,
0.04825786501169205,
0.01717492938041687,
-0.06484071165323257,
-0.014547199942171574,
0.029042348265647888,
-0.004047073889523745,
-0.0017741251504048705,
-0.006762511096894741,
-0.037790797650814056,
0.015222381800413132,
-0.007244348991662264,
-0.008548001758754253,
0.005372420884668827,
0.015109315514564514,
0.020827440544962883,
0.03347860276699066,
-0.00956649798899889,
0.04567756876349449,
-0.000440073199570179,
0.0012620458146557212,
-0.003558193799108267,
-0.02068771794438362,
0.06966521590948105,
0.03961467370390892,
0.02972760796546936,
-0.00022703161812387407,
0.035539016127586365,
-0.0693812221288681,
0.01488147210329771,
-0.010817845351994038,
-0.019815713167190552,
-0.007484604138880968,
0.00841487105935812,
-0.04334258288145065,
-0.025291165336966515,
0.001750812865793705,
0.06347029656171799,
0.06661008298397064,
-0.012813588604331017,
0.00018935541447717696,
0.023522989824414253,
-0.012028642930090427,
0.033655207604169846,
-0.014649050310254097,
-0.0011784867383539677,
0.042215850204229355,
0.029868952929973602,
0.07524248957633972,
-0.09166298806667328,
-0.00789101142436266,
0.07731927186250687,
0.041523952037096024,
-0.044940363615751266,
0.04536232352256775,
0.016780966892838478,
-0.04784280061721802,
0.08604953438043594,
0.009686660952866077,
0.01246108952909708,
0.030007587745785713,
0.005288679618388414,
0.04143831878900528,
0.06456827372312546,
0.050393182784318924,
-0.07528070360422134,
-0.006251370534300804,
-0.03685593605041504,
0.04215868189930916,
0.02528325282037258,
0.025915248319506645,
0.016241302713751793,
0.004311920143663883,
0.01755605638027191,
-0.028762027621269226,
0.014387083239853382,
0.01441382896155119,
0.029839200899004936,
0.03608952835202217,
0.06677379459142685,
-0.012496762908995152,
-0.038285866379737854,
-0.020427754148840904,
-0.00619445089250803,
-0.013448324985802174,
0.01554094534367323,
0.00922377873212099,
0.006848295219242573,
-0.010567246936261654,
0.017692334949970245,
-0.02075294964015484,
0.007058360613882542,
0.0003271160239819437,
-0.00712665356695652,
-0.060981787741184235,
0.021307028830051422,
0.04258648306131363,
-0.06023644655942917,
0.04676153510808945,
-0.023903686553239822,
0.004901748616248369,
-0.0016444992506876588,
0.008338773623108864,
0.01991296000778675,
-0.0042143650352954865,
-0.0006071348907426,
-0.012696881778538227,
0.012185651808977127,
0.03768044337630272,
-0.01690405048429966,
0.0012732805917039514,
0.02992749959230423,
0.08340981602668762,
0.00308551755733788,
-0.02069428190588951,
-0.005174469668418169,
0.03799986466765404,
-0.0031854931730777025,
0.013625623658299446,
0.0019636317156255245,
-0.008207147009670734,
0.013070084154605865,
-0.08474703878164291,
0.0028790058568120003,
-0.05543123185634613,
0.031079530715942383,
0.0840650200843811,
0.090592160820961,
0.0487048402428627,
-0.028438707813620567,
0.019600603729486465,
0.06380975246429443,
-0.029829837381839752,
0.06064126640558243,
0.004549136385321617,
-0.022285064682364464,
-0.022819356992840767,
-0.04403284564614296,
-0.03262145444750786,
0.006512010470032692,
-0.05404927209019661,
0.023145392537117004,
0.015263509936630726,
0.021264057606458664,
-0.020914165303111076,
-0.046137552708387375,
-0.06040533632040024,
-0.040188271552324295,
0.0538039356470108,
-0.0009613236761651933,
0.01554596796631813,
0.05936301127076149,
0.06757503002882004,
-0.05286914482712746,
0.03328462690114975,
0.03362778574228287,
0.019938074052333832,
0.042173851281404495,
0.020240776240825653,
-0.06901814788579941,
-0.021624188870191574,
0.05105156451463699,
-0.04826373606920242,
-0.09226102381944656,
-0.024141501635313034,
0.03515103459358215,
0.07131560146808624,
-0.005492114461958408,
-0.07278076559305191,
-0.003128600539639592,
0.03389968350529671,
-0.024212760850787163,
-0.0010996304918080568,
-0.03800245374441147,
0.01758795790374279,
0.038200609385967255,
0.060518525540828705,
0.031497783958911896,
-0.002334780292585492,
-0.042585067451000214,
0.010464959777891636
] |
<p>My textbook says talking about Cygnus X-1 (the first black hole to be identified as such) has variations in brightens of the order of 0.01 seconds and that this means that it's dimeter must be on the order of 3000km (=speed of light times 0.01). Why must this be so? The reason I asked is could (if it was not a black hole) it just not have vary active outer layers and be much larger. What the above seems to imply is that the light must be able to travel from one side of the source to the other in the time between differences in intensity. But I can not see why this should be the case. </p>
|
g2506
|
[
-0.02103380672633648,
0.039316326379776,
0.0006333550554700196,
-0.032279349863529205,
0.05975976213812828,
0.01020550262182951,
0.027965014800429344,
-0.013957255519926548,
-0.05027634650468826,
-0.023047421127557755,
0.0016545115504413843,
0.044826384633779526,
0.024319009855389595,
0.023116081953048706,
-0.030960770323872566,
-0.02348901517689228,
-0.023984745144844055,
-0.007519334089010954,
-0.009370537474751472,
0.014685157686471939,
-0.02253791317343712,
0.011596092022955418,
0.0199618861079216,
-0.08028746396303177,
0.007360669318586588,
0.015469145029783249,
0.040839388966560364,
-0.0621032789349556,
-0.024073265492916107,
-0.022113768383860588,
0.06509649753570557,
-0.015422482043504715,
0.04687665402889252,
-0.020358620211482048,
0.026158194988965988,
0.03845212981104851,
-0.01112462766468525,
-0.025778787210583687,
0.04367329925298691,
0.061361804604530334,
-0.025470111519098282,
-0.06154300272464752,
0.019830740988254547,
-0.03356897085905075,
0.012378394603729248,
0.021881213411688805,
-0.010709958150982857,
-0.010270765982568264,
0.030179932713508606,
-0.014968346804380417,
0.008469157852232456,
0.04887119680643082,
0.08150409162044525,
-0.007936704903841019,
0.010023803450167179,
0.05918830633163452,
-0.011149509809911251,
0.005745413713157177,
0.060643602162599564,
0.03788672015070915,
-0.03132793679833412,
-0.03658703342080116,
0.039791397750377655,
0.015310307033360004,
0.02640945091843605,
-0.022423529997467995,
-0.006875152699649334,
-0.07202348858118057,
0.017628196626901627,
-0.019906731322407722,
-0.042271435260772705,
-0.025392120704054832,
-0.011502992361783981,
0.029326776042580605,
-0.017222203314304352,
0.021037856116890907,
0.012119530700147152,
0.012546445243060589,
-0.030990146100521088,
-0.017762279137969017,
-0.02414741925895214,
-0.028363464400172234,
0.017042934894561768,
0.055071428418159485,
0.0948508158326149,
0.04747979715466499,
-0.015459716320037842,
-0.02143942192196846,
0.03016909770667553,
0.03513665124773979,
0.009354687295854092,
-0.026269659399986267,
0.03119288943707943,
0.036717209964990616,
0.040462665259838104,
0.015543666668236256,
-0.01658606342971325,
0.05798223614692688,
0.00541428430005908,
0.03522211313247681,
-0.044509127736091614,
0.029472919180989265,
-0.016367679461836815,
0.053768765181303024,
-0.0015686653787270188,
-0.017643267288804054,
6.775866090436011e-9,
0.011349261738359928,
-0.020335448905825615,
0.010154776275157928,
-0.015183656476438046,
-0.06157257780432701,
-0.017798474058508873,
-0.07598062604665756,
-0.004962798207998276,
0.019654689356684685,
0.024734143167734146,
0.018782058730721474,
-0.014191079884767532,
0.038727983832359314,
0.016911687329411507,
-0.05860891565680504,
0.01489502377808094,
0.03534578159451485,
0.002148184459656477,
-0.020197806879878044,
0.03703749179840088,
-0.001421294524334371,
-0.012738300487399101,
0.01534800510853529,
-0.002445284044370055,
0.020969906821846962,
0.0378032810986042,
0.07913419604301453,
-0.026800736784934998,
-0.0038183548022061586,
0.06719636172056198,
0.05181649327278137,
-0.013069221749901772,
0.043555863201618195,
-0.007032390218228102,
-0.004612171556800604,
0.01834556832909584,
-0.016801582649350166,
0.00479073915630579,
0.0045380257070064545,
-0.010601910762488842,
-0.02009912207722664,
0.013680076226592064,
-0.014780360274016857,
0.05716775357723236,
0.09778232127428055,
0.0017766227247193456,
0.009368556551635265,
-0.05737334117293358,
0.00394531711935997,
0.02698572352528572,
-0.03524134308099747,
-0.08498939126729965,
0.01126235444098711,
0.057776354253292084,
0.008885666728019714,
-0.0003240181540604681,
0.04318687319755554,
-0.04806720092892647,
-0.048309896141290665,
0.0354880653321743,
-0.06819252669811249,
0.013535813428461552,
-0.04876792058348656,
0.0004901636857539415,
0.028480911627411842,
0.03320123255252838,
0.027186939492821693,
0.046403829008340836,
0.004907023627310991,
0.06199819594621658,
-0.021210908889770508,
0.006836033426225185,
0.014056355692446232,
-0.06361587345600128,
-0.020694956183433533,
-0.07004021108150482,
-0.02984292060136795,
0.01845814287662506,
-0.03640409931540489,
0.014689159579575062,
-0.05706818774342537,
-0.05076812952756882,
0.06412862986326218,
0.00942080095410347,
-0.03595597669482231,
-0.007321163546293974,
0.06358159333467484,
-0.012556779198348522,
-0.024399014189839363,
-0.007118849083781242,
-0.017806382849812508,
-0.00295506720431149,
0.043783362954854965,
-0.00870933011174202,
0.03260248154401779,
0.04640265926718712,
0.05177278816699982,
0.004177930764853954,
-0.01137507427483797,
-0.0010832888074219227,
-0.0018808896420523524,
0.03709657862782478,
-0.0022038824390619993,
0.024414749816060066,
-0.03042437694966793,
-0.04297083616256714,
-0.0029129076283425093,
-0.030281780287623405,
-0.03741442784667015,
-0.022672131657600403,
0.07376282662153244,
0.045911792665719986,
0.027498215436935425,
-0.06517120450735092,
0.02255714125931263,
0.083566814661026,
-0.07307194918394089,
-0.07922626286745071,
0.05194636806845665,
0.009534111246466637,
-0.026539577171206474,
0.028570787981152534,
0.04352906718850136,
-0.08214285969734192,
0.031752098351716995,
-0.04371641203761101,
0.031352780759334564,
0.029082041233778,
-0.016190648078918457,
-0.00633746013045311,
-0.03763997182250023,
0.03432229533791542,
0.04906643554568291,
0.01620793156325817,
-0.0196075439453125,
-0.03341003507375717,
-0.03216193988919258,
-0.04312507435679436,
-0.01873955689370632,
-0.007091774605214596,
-0.010457698255777359,
-0.05398999899625778,
0.006189259234815836,
0.02192929945886135,
-0.05150210112333298,
0.0036393627524375916,
-0.0243170578032732,
-0.024226820096373558,
-0.05954824388027191,
0.01754777692258358,
0.001050880760885775,
-0.08646196126937866,
0.008886512368917465,
0.021700419485569,
-0.012474480085074902,
0.02949105203151703,
-0.044492244720458984,
-0.024519745260477066,
-0.004202249925583601,
-0.04796634614467621,
0.01749778725206852,
-0.049660488963127136,
-0.018889376893639565,
-0.05050421878695488,
-0.016028499230742455,
0.03847312554717064,
0.000018887889382313006,
-0.03429539129137993,
0.017438571900129318,
-0.060358449816703796,
-0.0157963577657938,
0.05706692487001419,
0.02005493827164173,
-0.05491689592599869,
0.027667757123708725,
-0.058800406754016876,
-0.02804744243621826,
0.026187526062130928,
-0.012080986984074116,
-0.0012738717487081885,
0.03390389308333397,
-0.041124314069747925,
0.014278188347816467,
-0.039758119732141495,
0.0024105971679091454,
0.028983647003769875,
0.05597439035773277,
0.04618600755929947,
0.025061585009098053,
0.025293869897723198,
0.01807871274650097,
-0.014784576371312141,
0.008027374744415283,
0.019316447898745537,
0.023880230262875557,
0.006504623219370842,
0.054587192833423615,
0.03459944576025009,
0.031908709555864334,
-0.020035725086927414,
0.001023035729303956,
0.012762102298438549,
-0.025095347315073013,
0.04718111455440521,
0.031603433191776276,
-0.028867440298199654,
0.06175106018781662,
0.022996686398983,
-0.0002144268510164693,
0.00498552992939949,
0.05212859436869621,
0.005694214720278978,
0.0020907411817461252,
0.019392244517803192,
-0.008864478208124638,
-0.043025754392147064,
0.0018635145388543606,
0.039440251886844635,
0.027352996170520782,
0.054557617753744125,
-0.04147984832525253,
-0.06809697300195694,
0.05581608787178993,
-0.01107714232057333,
-0.02204156294465065,
-0.05440087616443634,
-0.015773897990584373,
-0.026932628825306892,
-0.025340121239423752,
0.009874079376459122,
0.013533898629248142,
0.04684589430689812,
-0.00379860564135015,
-0.027519144117832184,
-0.0020967447198927402,
-0.07878459244966507,
0.042375434190034866,
0.03247779607772827,
-0.0655289739370346,
-0.03011445887386799,
-0.02456146478652954,
-0.041143935173749924,
0.037972591817379,
0.0027892126236110926,
-0.028734395280480385,
0.0063790082931518555,
-0.02472868002951145,
0.003719808766618371,
0.018458636477589607,
0.009429377503693104,
0.06761730462312698,
0.006036600098013878,
-0.025292038917541504,
0.0006019229767844081,
-0.008348538540303707,
-0.011875906027853489,
0.00713299261406064,
-0.00783422589302063,
-0.022554267197847366,
-0.005208895076066256,
-0.001134777325205505,
0.040437597781419754,
0.048298485577106476,
0.020353449508547783,
0.06353822350502014,
-0.0023432772140949965,
0.05005227029323578,
-0.017299745231866837,
0.0016180613311007619,
0.014414383098483086,
0.023660343140363693,
0.046368278563022614,
0.0121150566264987,
-0.03571629896759987,
-0.019569778814911842,
0.06706233322620392,
-0.051977720111608505,
0.020595455542206764,
0.056626856327056885,
-0.024167196825146675,
-0.030291320756077766,
-0.0018939690198749304,
-0.09025200456380844,
0.018680674955248833,
0.0078573701903224,
-0.02680538408458233,
-0.03582112491130829,
0.012496774084866047,
0.06479790061712265,
0.03132352977991104,
-0.029628010466694832,
-0.003052281215786934,
-0.00004609363531926647,
0.037824977189302444,
-0.007689633872359991,
-0.020458821207284927,
-0.03549972549080849,
-0.0315253809094429,
0.01200372539460659,
0.00012709471047855914,
0.004804336000233889,
0.030387282371520996,
0.01795855164527893,
0.00402104901149869,
0.011834215372800827,
-0.008712073788046837,
-0.01849062740802765,
-0.01111786998808384,
-0.0069489553570747375,
0.04123953729867935,
0.020295483991503716,
0.013272039592266083,
-0.029700802639126778,
0.05996529757976532,
-0.018377501517534256,
-0.016474325209856033,
0.021747175604104996,
0.04042605310678482,
0.06734635680913925,
0.02522291988134384,
0.015124786645174026,
-0.07541928440332413,
0.07734908908605576,
-0.005517912562936544,
-0.015179354697465897,
-0.019922859966754913,
0.026154769584536552,
-0.03801188990473747,
0.0771540105342865,
-0.021291950717568398,
0.009093653410673141,
0.01321979146450758,
0.03819660469889641,
0.043415363878011703,
0.044740211218595505,
-0.0015540700405836105,
-0.04576454311609268,
0.03684983029961586,
0.02396063692867756,
-0.02336297743022442,
0.020984282717108727,
0.04139138385653496,
-0.0017932731425389647,
0.03690572455525398,
-0.013089741580188274,
-0.007396216969937086,
-0.011240337044000626,
0.017304399982094765,
0.01577950268983841,
-0.07001584768295288,
0.00722145289182663,
0.01636078767478466,
0.06083081662654877,
-0.0015384620055556297,
0.004571362864226103,
0.008546962402760983,
0.025213485583662987,
0.000294447730993852,
0.0029229442588984966,
-0.0029619215056300163,
-0.0030118196737021208,
-0.06996915489435196,
0.025603970512747765,
-0.0077075595036149025,
0.04790549352765083,
0.012796985916793346,
0.030922723934054375,
-0.001489305286668241,
0.04921676963567734,
-0.059462472796440125,
-0.04635123163461685,
-0.06001492217183113,
0.014998162165284157,
-0.02014702372252941,
-0.030287018045783043,
0.043350741267204285,
0.03055834211409092,
0.06208980828523636,
0.047860175371170044,
-0.036618221551179886,
0.03549988940358162,
-0.01674617826938629,
-0.012861843220889568,
0.03919605538249016,
0.029147770255804062,
0.001897306414321065,
0.006296295672655106,
-0.0110018877312541,
-0.018313709646463394,
0.06491421163082123,
-0.02517293021082878,
0.04125003144145012,
-0.024380745366215706,
-0.04548375681042671,
0.03944609686732292,
0.021578587591648102,
-0.021076377481222153,
-0.01095427293330431,
0.07960064709186554,
0.03086966462433338,
-0.012028813362121582,
-0.01231224462389946,
0.013085710816085339,
-0.06843695044517517,
-0.00786539912223816,
-0.005522533319890499,
0.04396120458841324,
0.03844796493649483,
-0.08687825500965118,
0.043002836406230927,
-0.001998507184907794,
0.07612955570220947,
0.006979331374168396,
-0.05006982758641243,
-0.010793891735374928,
0.034659381955862045,
0.016179321333765984,
-0.006343516521155834,
0.016561100259423256,
-0.05933672934770584,
-0.035497866570949554,
0.025337377563118935,
-0.033486753702163696,
0.023384878411889076,
0.03918988257646561,
0.031803060322999954,
-0.04003194347023964,
0.012527640908956528,
-0.009965430945158005,
0.060557637363672256,
-0.0007802261388860643,
0.03217649832367897,
0.009060225449502468,
-0.05189498886466026,
-0.05026610940694809,
-0.014423259533941746,
-0.006578986532986164,
0.021161865442991257,
-0.0035922217648476362,
-0.04507121816277504,
0.010640923865139484,
-0.009263676591217518,
-0.09646224230527878,
0.00927697028964758,
-0.017300818115472794,
0.008644506335258484,
0.06393775343894958,
-0.04816560819745064,
0.05455555021762848,
-0.011183122172951698,
-0.03227017819881439,
-0.03867138549685478,
-0.08554796874523163,
0.027323003858327866,
-0.03239144757390022,
-0.004210184793919325,
0.005238741636276245,
0.017028678208589554,
-0.09763728082180023,
0.01481211744248867,
0.0001409018732374534,
0.046867113560438156,
0.02865898609161377,
-0.010450363159179688,
-0.04675823822617531,
-0.01200883649289608,
0.024037573486566544,
0.06894870102405548,
-0.02889963798224926,
0.020404310896992683,
-0.020367108285427094,
-0.06397123634815216,
-0.019827717915177345,
0.008067619055509567,
0.03181636333465576,
-0.0396408885717392,
-0.042101554572582245,
0.025044575333595276,
-0.031805746257305145,
-0.0027229569386690855,
0.057526953518390656,
0.010423503816127777,
-0.02366376854479313,
-0.02614394947886467,
-0.016227271407842636,
0.009248001500964165,
-0.05807265639305115,
-0.057895414531230927,
-0.03951767459511757,
-0.0061054411344230175,
0.039180416613817215,
-0.007134870160371065,
-0.06798016279935837,
-0.010100415907800198,
0.02224685810506344,
0.009969156235456467,
0.0012283975956961513,
-0.034993939101696014,
0.009515149518847466,
-0.003478890284895897,
0.024931006133556366,
0.049938783049583435,
0.06060699373483658,
0.058065589517354965,
0.03097461350262165,
-0.07653157413005829,
-0.0158549714833498,
-0.08489279448986053,
-0.01638760417699814,
0.007642631884664297,
-0.01323712058365345,
0.03501918911933899,
-0.012287432327866554,
0.04914992302656174,
0.027671894058585167,
-0.015037776902318,
-0.009806254878640175,
-0.03132358565926552,
0.08187565952539444,
-0.06653514504432678,
0.018379440531134605,
0.026275238022208214,
0.033366404473781586,
0.06997082382440567,
0.012287073768675327,
-0.016188839450478554,
0.007489408366382122,
0.0657171756029129,
-0.012384453788399696,
-0.0568922683596611,
0.009853960946202278,
-0.02608114667236805,
0.009037884883582592,
0.00037927395896986127,
-0.0419076643884182,
0.007991093210875988,
-0.055808376520872116,
0.025828080251812935,
0.06596102565526962,
0.0469232015311718,
0.048381149768829346,
-0.04623695835471153,
0.003955448511987925,
0.01910475268959999,
-0.12957775592803955,
-0.0452444814145565,
0.0006754390196874738,
0.005115171428769827,
0.00013891945127397776,
0.01942942850291729,
0.009554573334753513,
0.029179207980632782,
-0.0418902151286602,
-0.04201095551252365,
-0.012727487832307816,
-0.08976586163043976,
0.024447625502943993,
-0.01122285332530737,
0.002573356730863452,
0.03970537334680557,
-0.08234168589115143,
-0.008396144956350327,
-0.011906537227332592,
-0.026373466476798058,
0.0034600505605340004,
-0.020483525469899178,
-0.08855370432138443,
-0.006054267752915621,
-0.033677879720926285,
-0.018033519387245178,
0.00825335644185543,
0.06349552422761917,
0.000003991523044533096,
0.027338078245520592,
0.008258880116045475,
0.006207529921084642,
0.0019492412684485316,
-0.035798080265522,
0.06065322458744049,
-0.08962409943342209,
-0.05625571683049202,
0.06694640219211578,
-0.05394821614027023,
0.030024614185094833,
-0.046184711158275604,
-0.035053856670856476,
-0.05363577604293823,
0.016415702179074287,
0.01867150329053402,
0.0032547146547585726,
0.023766010999679565,
0.008513972163200378,
-0.04300685599446297,
-0.05657079443335533,
-0.06898974627256393,
-0.023243466392159462,
-0.024576442316174507,
-0.014817342162132263,
-0.05293518677353859,
-0.03528352826833725,
-0.012390147894620895,
-0.03456990793347359,
-0.013591764494776726,
-0.002415786264464259,
0.020339172333478928,
0.027260050177574158,
-0.031527984887361526,
-0.02610352635383606,
-0.028914030641317368,
-0.01951221562922001,
-0.0356287844479084,
-0.05300803482532501,
0.021791065111756325,
0.030307289212942123,
0.03949011117219925,
-0.011503859423100948,
-0.03182157874107361,
-0.01883145608007908,
-0.08352813869714737,
0.014286101795732975,
-0.012975059449672699,
-0.0010447388049215078,
0.01625221036374569,
0.004755736794322729,
0.041588228195905685,
-0.02048097364604473,
-0.0068920995108783245,
-0.06595487892627716,
0.018794333562254906,
0.029307404533028603,
-0.0169290192425251,
-0.06535564363002777,
0.004296665079891682,
-0.023135317489504814,
0.0017659232253208756,
0.03988006338477135,
0.004406125750392675,
-0.003937695175409317,
-0.031770575791597366,
0.020529745146632195,
0.009100775234401226,
0.06910325586795807,
0.01269450318068266,
0.00719549972563982,
0.017446069046854973,
0.0019813436083495617,
-0.016638705506920815,
0.020659346133470535,
0.030622193589806557,
-0.03210865706205368,
-0.015833960846066475,
-0.08028056472539902,
-0.002221939619630575,
-0.059229422360658646,
0.0004725441103801131,
0.04293127357959747,
0.011881295591592789,
0.02045562118291855,
0.015021144412457943,
-0.018757373094558716,
-0.014399516396224499
] |
<p><strong>Context</strong>: Solid state physics. Monoatomic linear chain.</p>
<p><strong>Question</strong>: To prove that the total momentum of the chain is zero.</p>
<p><strong>Attempted solution</strong>: I consider the sum:</p>
<p>\begin{align*}
p = \sum_{n=1}^{N} m \dot{u_n}
\end{align*}</p>
<p>where $u_n$ is the displacement from the equilibrium position of the $n$-th atom. The displacement is given by the formula:</p>
<p>\begin{align*}
u_n = u_0 \exp\left[-i\left(\omega t \pm k n a\right)\right]
\end{align*}</p>
<p>where $k$ is the wavevector, $n$ is the $n$-th atom and $a$ is the distance between atoms. If I substitute the above formula to the first sum, I get a result of the form:</p>
<p>\begin{align*}
p \sim \sum_{n=1}^{N} \exp(i k n a)
\end{align*}</p>
<p>I wonder, how could I prove that this is always zero ? If I treat it as the sum of a geometric series with $\alpha_1=\exp(ika)$ and $\lambda=\exp(ika)$, I still get a result that isn't necessarily zero.</p>
<p>\begin{align*}
S_{1\to N} = \alpha_1 \frac{\lambda^N-1}{\lambda - 1} = e^{ika} \frac{e^{ikNa}-1}{e^{ika}-1}
\end{align*}</p>
<p>If I further require that the first and last atoms are fixed, then $\exp(ikNa) = \exp(ika)$ and $S_{1\to N} = \exp(ika)$. Then</p>
<p>\begin{align*}
p = -i\omega u_0 m \exp(-i\omega t) \exp(ika) = -i\omega m \underbrace{u_0 \exp\left[-i(\omega t - k a)\right]}_{u_1} = -i \omega m u_{1} = 0
\end{align*}</p>
<p>since we assumed that the 1st atom is fixed. Does this sound correct ?</p>
|
g2507
|
[
0.025729859247803688,
0.005198788363486528,
0.0070586432702839375,
-0.05265916883945465,
0.0642741471529007,
-0.0035775683354586363,
0.0091136759147048,
0.0032280462328344584,
0.0033478166442364454,
0.021897178143262863,
-0.05102114379405975,
-0.012743289582431316,
-0.050960637629032135,
-0.03608489781618118,
0.0037869249936193228,
0.02995145693421364,
0.051663562655448914,
-0.027214089408516884,
0.0008134702802635729,
0.0009449772187508643,
-0.04074004665017128,
0.03281746432185173,
-0.04075923189520836,
-0.10577768087387085,
0.021548321470618248,
-0.00252725463360548,
-0.02626970037817955,
-0.02704009786248207,
-0.07895983010530472,
0.008683660067617893,
0.018397869542241096,
-0.025811033323407173,
0.048654504120349884,
-0.037185877561569214,
-0.02508142590522766,
-0.0019046656088903546,
0.06420046091079712,
-0.011874604970216751,
0.0651441290974617,
-0.020178183913230896,
0.018761418759822845,
0.01614951156079769,
-0.003884212113916874,
0.04217144474387169,
0.004893274512141943,
-0.018804881721735,
-0.038341205567121506,
0.019703907892107964,
0.004246508702635765,
0.01695057563483715,
0.009114964865148067,
0.046207111328840256,
-0.004496230278164148,
-0.05101475492119789,
-0.06795243918895721,
0.07567628473043442,
-0.025822287425398827,
-0.02648215927183628,
0.010294649749994278,
0.03566356375813484,
-0.012538725510239601,
-0.030711783096194267,
0.024159874767065048,
-0.004114793613553047,
0.018231820315122604,
0.01160729955881834,
-0.06472714245319366,
0.030097773298621178,
0.03835051879286766,
-0.008342423476278782,
0.02498948574066162,
-0.036796435713768005,
0.04715024679899216,
0.01748063415288925,
-0.02964680828154087,
-0.039967287331819534,
-0.0033745327964425087,
0.02148395963013172,
0.041424673050642014,
-0.02671676129102707,
-0.06555163115262985,
-0.0199228897690773,
0.04296603798866272,
-0.03193419799208641,
-0.003441363340243697,
-0.02344219759106636,
0.00802002102136612,
0.026290515437722206,
-0.020018605515360832,
0.021090084686875343,
0.043205369263887405,
0.05324830487370491,
0.00931096076965332,
0.012073199264705181,
0.002444050507619977,
-0.06258819997310638,
-0.029327640309929848,
0.08800864964723587,
0.032209377735853195,
-0.028254404664039612,
-0.01414100918918848,
0.03584453463554382,
-0.016943225637078285,
0.005620848853141069,
0.0428742989897728,
-0.02064628154039383,
0.01748654991388321,
0.010977515019476414,
0.008638816885650158,
0.007140621542930603,
-0.03476710617542267,
-0.015217332169413567,
-0.005578227806836367,
-0.04879201203584671,
-0.0642097145318985,
-0.016065482050180435,
0.05144600197672844,
-0.028293602168560028,
-0.010721860453486443,
0.045878369361162186,
-0.04793403670191765,
-0.004118725191801786,
-0.0006690569571219385,
0.07870003581047058,
-0.01242087408900261,
-0.03258608654141426,
-0.03489511087536812,
0.025857556611299515,
0.04415058344602585,
0.0066304318606853485,
-0.04362369328737259,
-0.014416897669434547,
-0.011788585223257542,
0.02153908647596836,
-0.0523400716483593,
-0.009811891242861748,
-0.023031091317534447,
0.03594345599412918,
0.008771006017923355,
0.06008151173591614,
0.006571215111762285,
-0.08658671379089355,
-0.004838824272155762,
-0.015223839320242405,
0.008784789592027664,
-0.012929127551615238,
0.0017076506046578288,
-0.024909956380724907,
0.0664670318365097,
0.01412484422326088,
-0.020975105464458466,
0.07270056754350662,
-0.022476274520158768,
0.04261443391442299,
0.047256357967853546,
-0.025700556114315987,
0.03555581346154213,
-0.01481634471565485,
0.027286600321531296,
-0.008166790008544922,
0.03043450601398945,
-0.02437753416597843,
-0.01621355675160885,
-0.006942283362150192,
-0.03151184320449829,
0.003340934868901968,
0.05529240518808365,
-0.05861375480890274,
0.018647613003849983,
-0.0002447442675475031,
-0.035425927489995956,
0.029429253190755844,
-0.011121430434286594,
-0.0011803272645920515,
0.045790255069732666,
-0.006769150961190462,
0.011243839748203754,
-0.0024183783680200577,
0.018307257443666458,
-0.01757759228348732,
0.029309336096048355,
-0.02809116244316101,
0.04204205051064491,
0.009741893038153648,
0.008769960142672062,
0.013589112088084221,
0.023285361006855965,
0.040958892554044724,
-0.07914979755878448,
-0.0023608626797795296,
-0.002480195602402091,
0.07016552984714508,
-0.020976053550839424,
0.00024615207803435624,
-0.05581232160329819,
0.011414861306548119,
0.035505544394254684,
-0.06795012950897217,
-0.02759491093456745,
-0.01548546552658081,
0.04353464022278786,
0.046556875109672546,
0.0111484844237566,
0.012482182122766972,
0.015983382239937782,
0.021461566910147667,
0.01170828565955162,
-0.05139812082052231,
0.0034175270702689886,
0.02272222563624382,
-0.02056114748120308,
-0.021322987973690033,
-0.093406543135643,
0.03794853016734123,
-0.015754789113998413,
-0.04899883270263672,
0.050975896418094635,
-0.023661619052290916,
0.00010068254778161645,
0.01193117443472147,
-0.01107805222272873,
-0.011231307871639729,
-0.019920557737350464,
0.017657041549682617,
-0.04420307278633118,
-0.008670120500028133,
0.029018059372901917,
-0.009424916468560696,
-0.0024855893570929766,
0.05332443118095398,
-0.04543158411979675,
0.05155864730477333,
0.026476498693227768,
-0.028317147865891457,
0.07652493566274643,
0.02577211521565914,
-0.01705099456012249,
0.0067325253039598465,
-0.01262158527970314,
0.05582807585597038,
0.006087545771151781,
-0.01891724392771721,
-0.09584930539131165,
-0.05246935412287712,
0.07995457947254181,
-0.03640080615878105,
0.04164616018533707,
0.005732106976211071,
0.038177113980054855,
-0.05243026837706566,
0.0465642549097538,
-0.017464272677898407,
-0.024422530084848404,
-0.017117250710725784,
0.029613444581627846,
-0.0386849008500576,
-0.008710606023669243,
0.031271304935216904,
0.00020596150716301054,
-0.035021644085645676,
0.0378752276301384,
-0.060455676168203354,
0.011005138047039509,
0.005187987349927425,
-0.09961595386266708,
0.02292877994477749,
-0.07221827656030655,
-0.022438321262598038,
-0.014572827145457268,
0.008113808929920197,
-0.017636319622397423,
0.04651252180337906,
0.028358513489365578,
0.06922938674688339,
-0.04469704627990723,
0.03055841103196144,
0.008176231756806374,
-0.0034936824813485146,
0.054117508232593536,
0.02536092698574066,
-0.024656200781464577,
0.11173340678215027,
-0.04642162099480629,
0.027375733479857445,
0.034580718725919724,
-0.06293805688619614,
0.006948492024093866,
0.012904085218906403,
0.03894678130745888,
-0.026157286018133163,
0.010155134834349155,
0.054074086248874664,
0.1067083328962326,
0.047402866184711456,
-0.017031656578183174,
0.10179238766431808,
0.014049825258553028,
-0.05178023874759674,
0.026508761569857597,
0.0019237896194681525,
-0.026905590668320656,
0.0870959535241127,
-0.01508889440447092,
0.020022263750433922,
0.07274704426527023,
0.07931321859359741,
-0.009660144336521626,
-0.04846378415822983,
-0.00247776391915977,
0.025530051440000534,
-0.0030607564840465784,
0.07745804637670517,
0.015591118484735489,
-0.026267990469932556,
-0.03290171176195145,
0.045293644070625305,
0.02453669346868992,
-0.03655007854104042,
-0.004132409114390612,
-0.0025279601104557514,
0.002577891107648611,
-0.03294842690229416,
0.023832740262150764,
0.005497177131474018,
0.014595182612538338,
0.003257489763200283,
-0.05412648990750313,
0.005113336257636547,
-0.059823859483003616,
-0.0033044160809367895,
0.00012464098108466715,
0.017722172662615776,
0.02489369548857212,
-0.018680620938539505,
-0.025416038930416107,
-0.030209217220544815,
-0.027616912499070168,
0.004860627464950085,
-0.0017602567095309496,
0.010704873129725456,
-0.0565049946308136,
0.008978175930678844,
-0.026679981499910355,
-0.0012581581249833107,
0.03772380203008652,
0.00513262115418911,
-0.028372719883918762,
0.07592354714870453,
-0.0247179102152586,
-0.0265986118465662,
0.02047865465283394,
0.02768521010875702,
-0.04276527464389801,
0.015480955131351948,
-0.030897239223122597,
0.02712010033428669,
0.04035899415612221,
0.004168327432125807,
0.030327439308166504,
-0.04613308608531952,
0.0350828655064106,
-0.032395269721746445,
-0.002787463366985321,
0.005733951926231384,
0.0013526714174076915,
-0.004784296732395887,
-0.03133608028292656,
0.021851234138011932,
0.011950553394854069,
0.020098702982068062,
-0.007647584192454815,
-0.03636793792247772,
0.00030099140712991357,
-0.03724277764558792,
-0.026371026411652565,
-0.04996372386813164,
-0.019184377044439316,
0.010364130139350891,
-0.04900573939085007,
0.05737417936325073,
0.07419959455728531,
-0.01346540730446577,
0.005131105426698923,
0.029223104938864708,
-0.012354576028883457,
0.021687190979719162,
-0.04735612869262695,
-0.017256001010537148,
-0.00976797565817833,
0.012116766534745693,
-0.00014784178347326815,
0.010283030569553375,
0.03290359675884247,
0.014322159811854362,
0.021046841517090797,
-0.019422244280576706,
0.02112841233611107,
-0.02096378430724144,
-0.08025709539651871,
0.010241062380373478,
-0.029001682996749878,
0.020343640819191933,
-0.011285931803286076,
-0.028023913502693176,
0.028929436579346657,
0.013046086765825748,
0.00676879333332181,
0.024154329672455788,
-0.002216068096458912,
-0.014284001663327217,
-0.03215283900499344,
-0.006993790622800589,
-0.021055923774838448,
-0.07164420932531357,
-0.010295742191374302,
0.026479411870241165,
0.0013536537298932672,
-0.008453465066850185,
-0.00906743761152029,
-0.03994650021195412,
0.02773284912109375,
0.05301577225327492,
-0.03148956969380379,
-0.0409250371158123,
0.05235525593161583,
0.023752780631184578,
0.013957610353827477,
0.030275283381342888,
0.05029316619038582,
0.009371873922646046,
-0.07337260246276855,
0.0032420079223811626,
0.028859738260507584,
0.03936136141419411,
-0.04213113710284233,
0.021456042304635048,
0.024797309190034866,
0.033396925777196884,
0.013064829632639885,
0.03148987889289856,
0.03513536602258682,
0.048015397042036057,
-0.004310695454478264,
0.01468585804104805,
-0.044884100556373596,
0.04679124429821968,
-0.021975159645080566,
-0.06974378228187561,
-0.022783992812037468,
0.004240693524479866,
0.01170939952135086,
0.021790653467178345,
-0.02720699831843376,
-0.0015103892656043172,
-0.018827548250555992,
-0.017220675945281982,
-0.08935514837503433,
0.055819444358348846,
-0.03870860114693642,
0.04555608332157135,
-0.014473047107458115,
-0.021537350490689278,
0.03477306663990021,
-0.013009228743612766,
0.03536590188741684,
-0.027037743479013443,
-0.014356151223182678,
0.044551994651556015,
-0.05505731701850891,
-0.004864283837378025,
0.02236262895166874,
-0.007675565779209137,
0.014361918903887272,
0.03176393732428551,
-0.03748238459229469,
-0.03505098819732666,
-0.049542639404535294,
0.020188720896840096,
0.029990412294864655,
-0.05475401505827904,
-0.035743214190006256,
0.02254169061779976,
-0.04253571480512619,
-0.017549334093928337,
0.05167222023010254,
0.015435856766998768,
-0.026583753526210785,
-0.024331673979759216,
0.012609806843101978,
0.016585983335971832,
0.043155062943696976,
0.006853820756077766,
-0.005124600604176521,
-0.06300128996372223,
-0.042094409465789795,
0.0041463118977844715,
-0.01605306752026081,
0.014668624848127365,
0.005671205930411816,
0.05708308890461922,
-0.051020942628383636,
0.0290126521140337,
0.025782344862818718,
-0.017388373613357544,
0.010577943176031113,
-0.007079444359987974,
0.012955312617123127,
0.04759591817855835,
-0.009919794276356697,
-0.005869380198419094,
0.008943445980548859,
0.05263933166861534,
-0.02775406278669834,
0.043810248374938965,
0.05255521088838577,
-0.009840977378189564,
0.025548482313752174,
-0.019573206081986427,
-0.038362566381692886,
-0.0019035948207601905,
-0.01339857280254364,
-0.009950781241059303,
0.0026917578652501106,
-0.03400241583585739,
0.020403776317834854,
-0.04333119094371796,
-0.022753922268748283,
-0.028795761987566948,
-0.01828264258801937,
0.07083556056022644,
-0.005985255353152752,
0.008830787613987923,
-0.05265793204307556,
-0.05389949679374695,
-0.026994192972779274,
-0.01859319768846035,
-0.017843952402472496,
0.046326588839292526,
-0.030913719907402992,
-0.00838383473455906,
-0.035848524421453476,
-0.0517120398581028,
0.032814886420965195,
0.047170281410217285,
-0.05158334597945213,
-0.03076554648578167,
0.0014491114998236299,
-0.04424246773123741,
0.04447801411151886,
-0.07700226455926895,
-0.04555194079875946,
0.036576978862285614,
-0.0863838642835617,
-0.04716125503182411,
0.010055433958768845,
0.002018079161643982,
-0.04278245568275452,
-0.04385253041982651,
-0.03573564440011978,
-0.010086008347570896,
0.03881451115012169,
0.05214312672615051,
-0.0035832927096635103,
-0.029625337570905685,
0.04645756259560585,
0.0348268561065197,
-0.023576930165290833,
-0.0038904298562556505,
0.05586055666208267,
0.048382095992565155,
-0.0018745228881016374,
0.022140022367239,
0.043376319110393524,
0.004090262111276388,
-0.007354141212999821,
0.043042052537202835,
-0.055243104696273804,
-0.030458413064479828,
-0.049400005489587784,
0.012142989784479141,
-0.0725235641002655,
0.020621148869395256,
-0.00479911407455802,
-0.040487632155418396,
-0.01077570952475071,
-0.012666153721511364,
-0.005557378754019737,
-0.06950677931308746,
0.04937917739152908,
0.03284835070371628,
-0.030533134937286377,
0.017729895189404488,
-0.042961474508047104,
-0.02549748681485653,
-0.007369548082351685,
-0.030435366556048393,
0.03438623622059822,
-0.02721789851784706,
-0.034754134714603424,
0.06368033587932587,
-0.0032281000167131424,
-0.00813494622707367,
0.0649205818772316,
-0.03961240500211716,
-0.010731394402682781,
0.025850750505924225,
-0.021594783291220665,
0.0409395806491375,
-0.02619693987071514,
-0.0005824198015034199,
-0.029875271022319794,
0.07272204756736755,
0.032648637890815735,
-0.00002978734664793592,
0.019560230895876884,
-0.03506487235426903,
0.05456717312335968,
0.04963164031505585,
-0.0051595126278698444,
-0.04095068573951721,
0.0001576676149852574,
0.006873437203466892,
-0.026744188740849495,
0.012032250873744488,
0.03234906494617462,
0.018793152645230293,
-0.055432796478271484,
0.026801006868481636,
0.07586450129747391,
0.0365847647190094,
0.028139788657426834,
0.04200362041592598,
0.016081763431429863,
0.01050317008048296,
-0.05580612272024155,
0.09888765215873718,
-0.020836399868130684,
0.054765939712524414,
0.052699699997901917,
0.025438666343688965,
-0.002034586388617754,
0.02994653210043907,
0.011590172536671162,
-0.023540841415524483,
-0.056634608656167984,
0.0001859986368799582,
0.0005077238311059773,
-0.013125184923410416,
-0.11384525150060654,
-0.06042113155126572,
0.02569473162293434,
-0.0033727120608091354,
-0.01713866926729679,
0.06865837424993515,
-0.052649859338998795,
-0.0008985726162791252,
-0.035267699509859085,
-0.019218524917960167,
0.014989262446761131,
-0.03209137171506882,
0.006230538245290518,
-0.02915804646909237,
0.016943221911787987,
-0.0648704320192337,
-0.02348652482032776,
0.05281839147210121,
0.007360533345490694,
-0.02231197990477085,
-0.03116065263748169,
-0.020103413611650467,
0.023812100291252136,
-0.06367327272891998,
-0.06866800785064697,
0.0248712170869112,
0.04980076849460602,
-0.0007740825531072915,
0.004697374068200588,
0.046279728412628174,
-0.05735910311341286,
-0.05039997771382332,
-0.0017988631734624505,
0.0656786859035492,
-0.003507891669869423,
0.01990855485200882,
0.015787387266755104,
-0.0012751903850585222,
0.004625058267265558,
0.06850714236497879,
-0.024124547839164734,
-0.014172117225825787,
0.026669319719076157,
0.04474584013223648,
0.012040133588016033,
-0.04259016364812851,
0.0039011051412671804,
0.006488046608865261,
-0.0004996928619220853,
0.05182255804538727,
0.030364586040377617,
-0.03311512619256973,
-0.005267220549285412,
-0.013580190017819405,
-0.032644111663103104,
0.05738161876797676,
0.05212054029107094,
-0.02842874266207218,
0.026984212920069695,
-0.022077014669775963,
0.019068298861384392,
-0.004786396864801645,
0.03755183890461922,
-0.054792676120996475,
0.0007588838343508542,
-0.00368962693028152,
0.10199163109064102,
-0.029062168672680855,
-0.027374742552638054,
0.041026804596185684,
0.0034343351144343615,
-0.008683724328875542,
-0.011386753991246223,
0.06028083339333534,
0.009150871075689793,
-0.049468994140625,
-0.0750226154923439,
-0.026090947911143303,
-0.009202162735164165,
0.007868978194892406,
0.056035175919532776,
0.0125449039041996,
-0.010924119502305984,
-0.029345007613301277,
-0.047893572598695755,
0.01056958269327879,
-0.026538945734500885,
-0.055546779185533524,
-0.0065235234797000885,
-0.05034932866692543,
0.010849392972886562,
0.057614777237176895,
-0.06530489027500153,
-0.03662881255149841,
0.024302810430526733,
-0.0009680252987891436,
0.048402898013591766,
-0.03899252042174339,
-0.017686860635876656,
0.08053942024707794,
0.046286504715681076,
-0.0640823170542717,
-0.0001163868946605362,
0.026806099340319633,
0.00546666607260704,
0.029384292662143707,
0.028006933629512787,
-0.03893373906612396,
0.03242872282862663,
-0.011608242057263851,
0.010637801140546799,
0.036358434706926346,
-0.04713365435600281,
0.0028663394041359425,
-0.010567417368292809,
-0.00040241231909021735,
0.03767574578523636,
-0.04615077003836632,
0.0012204209342598915,
-0.0047810194082558155
] |
<p>In the solution of Schrödinger Equation for harmonic oscillator why the distance between peaks of the probability distribution function decreases when n increases?</p>
<p>Is there a good reason for it or is it just the consequence of solving the Schrödinger Equation?</p>
|
g2508
|
[
0.019940152764320374,
0.02510075829923153,
-0.010872981511056423,
-0.017113294452428818,
0.04383831098675728,
0.02933277003467083,
0.005293266847729683,
0.07107137888669968,
-0.027652572840452194,
-0.03470365330576897,
-0.02240564301609993,
0.01258517149835825,
0.020827123895287514,
0.06813176721334457,
0.0030893851071596146,
-0.02064136415719986,
0.03157312795519829,
0.01005627866834402,
-0.050068143755197525,
0.005386766977608204,
-0.08227284252643585,
0.000044036056351615116,
-0.00401323614642024,
-0.03866274282336235,
-0.007760563399642706,
-0.05456318333745003,
-0.038613416254520416,
-0.005267839413136244,
-0.007971519604325294,
0.04092509672045708,
-0.038380105048418045,
0.035186219960451126,
0.051661912351846695,
-0.012115808203816414,
-0.00783687736839056,
0.034250251948833466,
0.06231221929192543,
-0.0033825174905359745,
0.03534271568059921,
-0.016498779878020287,
0.025695079937577248,
-0.05445518717169762,
0.036556944251060486,
-0.060474693775177,
0.013727630488574505,
-0.04792593792080879,
-0.017343128100037575,
0.07664802670478821,
-0.004380915779620409,
-0.005502905696630478,
0.010229061357676983,
-0.0021849286276847124,
0.0307205431163311,
0.03136662021279335,
0.052832040935754776,
-0.0051932730711996555,
-0.003593395696952939,
-0.03719241917133331,
-0.0012856292305514216,
0.06628378480672836,
0.008207753300666809,
0.027829080820083618,
0.00013991628657095134,
0.029669035226106644,
0.029754500836133957,
-0.047936659306287766,
-0.02367137372493744,
-0.0017311160918325186,
0.03972873464226723,
-0.0013321960577741265,
-0.021373748779296875,
-0.03659729287028313,
-0.049237821251153946,
-0.04763435572385788,
0.012266441248357296,
-0.005950387567281723,
0.007047169841825962,
0.0020673335529863834,
0.022274432703852654,
0.08172076940536499,
-0.03557471185922623,
-0.006261005531996489,
0.03135579451918602,
0.0010473831789568067,
-0.006642157677561045,
0.03444608673453331,
0.04220927506685257,
0.012157315388321877,
-0.03197769075632095,
0.052603378891944885,
0.004082167986780405,
-0.030085492879152298,
0.04084393382072449,
-0.0407584086060524,
-0.019119445234537125,
-0.00430013332515955,
-0.07366810739040375,
0.05271550267934799,
-0.0006738626980222762,
-0.004483045544475317,
-0.019169462844729424,
-0.007452785037457943,
0.1010226309299469,
0.001631929655559361,
-0.021369438618421555,
0.007352401502430439,
0.012582275085151196,
0.05905362591147423,
-0.02896771766245365,
0.012501692399382591,
-0.05301842838525772,
-0.014810426160693169,
-0.007309690583497286,
-0.04143630340695381,
-0.009004171937704086,
-0.0187288299202919,
0.03505504131317139,
-0.015038389712572098,
0.02891799621284008,
-0.013121473602950573,
-0.016316311433911324,
0.000491910323034972,
-0.023008856922388077,
0.004329910967499018,
-0.029895180836319923,
0.01755836233496666,
0.029438428580760956,
-0.0025349364150315523,
0.037109293043613434,
-0.017087578773498535,
0.0075130704790353775,
0.0464538037776947,
-0.038899462670087814,
0.058284658938646317,
0.02256837859749794,
0.031352970749139786,
0.013426549732685089,
0.024826684966683388,
0.0049651567824184895,
0.027160897850990295,
0.008119397796690464,
-0.008520790375769138,
0.07225149869918823,
-0.07675492763519287,
-0.008030818775296211,
-0.03468148037791252,
0.00030161550967022777,
-0.05693305283784866,
-0.05426829308271408,
-0.04117957875132561,
-0.03913591057062149,
-0.025331858545541763,
-0.00893775001168251,
-0.04669897258281708,
-0.0052636186592280865,
-0.009920471347868443,
0.03930941969156265,
0.05616508424282074,
-0.0006142806960269809,
-0.021012453362345695,
0.008548544719815254,
-0.019561024382710457,
0.03554566949605942,
0.011371093802154064,
-0.033757179975509644,
0.073990099132061,
-0.027811529114842415,
-0.04553477466106415,
-0.019296245649456978,
0.016475845128297806,
0.0382855199277401,
-0.019061114639043808,
-0.015432684682309628,
0.03282081335783005,
0.02974521741271019,
0.06487221270799637,
0.07037561386823654,
-0.021039338782429695,
-0.001329579041339457,
0.05699997395277023,
-0.0008682464249432087,
-0.0585189014673233,
0.010680376552045345,
-0.07418473064899445,
-0.00021557207219302654,
0.018188821151852608,
0.018459053710103035,
-0.026386817917227745,
-0.0749773234128952,
0.005874085705727339,
0.01206953451037407,
-0.04545104131102562,
-0.02095310389995575,
-0.027279336005449295,
-0.0012991639086976647,
-0.003337751142680645,
-0.009752919897437096,
-0.04517021402716637,
-0.03991226479411125,
-0.020434647798538208,
-0.01931179314851761,
0.013029446825385094,
0.05344242602586746,
0.0022976198233664036,
-0.004096501041203737,
0.009790319949388504,
-0.02507508173584938,
0.022950930520892143,
-0.02199696935713291,
0.003497589146718383,
-0.0523206926882267,
-0.01888817735016346,
-0.01732739247381687,
0.022974710911512375,
-0.008660119958221912,
-0.006364212837070227,
0.031118543818593025,
-0.03805830329656601,
0.018546003848314285,
0.0609690397977829,
0.008239512331783772,
-0.04428902640938759,
0.014668932184576988,
0.008254929445683956,
0.023538218811154366,
0.041977159678936005,
-0.0055085537023842335,
-0.055258214473724365,
-0.06044752523303032,
0.0459875613451004,
-0.05272739753127098,
-0.02894837222993374,
0.004657466430217028,
0.014678857289254665,
0.01508694514632225,
-0.007907997816801071,
0.007681356742978096,
-0.050905026495456696,
-0.03595208376646042,
-0.0015742358518764377,
-0.022998690605163574,
-0.040792666375637054,
-0.015013453550636768,
0.017348535358905792,
0.021913399919867516,
-0.01053436566144228,
-0.03440733626484871,
-0.07383372634649277,
-0.014382501132786274,
-0.010605026967823505,
0.04815074801445007,
0.05260426923632622,
0.04012373089790344,
-0.016599763184785843,
-0.03410842642188072,
-0.04081142321228981,
-0.02433786354959011,
0.01062465738505125,
0.02386442944407463,
-0.07719781994819641,
-0.07987766712903976,
0.021030696108937263,
0.029131412506103516,
-0.02568650059401989,
0.005117824301123619,
0.01893383264541626,
-0.04258596524596214,
0.02348943054676056,
0.017612027004361153,
-0.02408604510128498,
-0.014774230308830738,
0.04512236639857292,
0.025046242401003838,
0.08456125855445862,
-0.007071312051266432,
0.006045572459697723,
-0.0043111685663461685,
0.0038428455591201782,
0.039373189210891724,
0.006476809270679951,
-0.002306165173649788,
0.015664121136069298,
-0.05919955298304558,
-0.014870448969304562,
0.009644784033298492,
-0.07159820199012756,
0.04256630316376686,
-0.017651187255978584,
0.03248583897948265,
-0.015806585550308228,
-0.006728098727762699,
-0.020819196477532387,
0.029488351196050644,
0.00037827237974852324,
0.010867833159863949,
0.04107304662466049,
0.044235751032829285,
-0.04167944937944412,
0.012626650743186474,
0.04138162359595299,
-0.017127543687820435,
-0.010021846741437912,
-0.00495177460834384,
-0.007531543727964163,
0.03450249880552292,
0.05902126803994179,
-0.01793038286268711,
0.04524814710021019,
-0.041616082191467285,
-0.01815897226333618,
0.0016015585279092193,
0.012590702623128891,
0.020508838817477226,
-0.015115774236619473,
-0.01970011182129383,
-0.002744311233982444,
-0.06194980815052986,
0.044733475893735886,
0.026541775092482567,
-0.037917930632829666,
0.0002734133740887046,
-0.07640696316957474,
-0.07262562960386276,
-0.04466361925005913,
0.018376553431153297,
-0.000549292890354991,
-0.024376746267080307,
0.015065766870975494,
0.029903890565037727,
-0.013029184192419052,
0.02205408737063408,
0.00065345544135198,
0.05677584186196327,
-0.01773075759410858,
-0.02158559113740921,
0.0024160698521882296,
-0.003236419288441539,
0.0032547423616051674,
0.025205111131072044,
0.042045366019010544,
0.0453958623111248,
-0.018781907856464386,
-0.06184407323598862,
0.004910270683467388,
-0.019856076687574387,
0.015333753079175949,
-0.029379360377788544,
0.006253804545849562,
0.008471842855215073,
-0.019670333713293076,
-0.006341741420328617,
-0.036833759397268295,
0.004599205683916807,
-0.015412678010761738,
-0.0030019828118383884,
-0.00952325388789177,
-0.026057669892907143,
-0.02212553098797798,
-0.0049079726450145245,
0.007844879291951656,
0.02408614009618759,
-0.0327502116560936,
0.01245583314448595,
0.06696740537881851,
-0.00498755881562829,
0.010994701646268368,
0.010994930751621723,
0.05893901363015175,
-0.00922288466244936,
-0.09055890887975693,
-0.02214508131146431,
-0.010596441105008125,
0.006097040139138699,
0.007340718060731888,
0.06752857565879822,
-0.02748839370906353,
0.008279399015009403,
0.025256650522351265,
-0.015993280336260796,
0.013730796054005623,
0.029403097927570343,
-0.06391141563653946,
-0.010915981605648994,
-0.04881666600704193,
0.05656290799379349,
-0.012506955303251743,
-0.01731199398636818,
-0.04436632618308067,
-0.008933779783546925,
-0.03985867649316788,
-0.0409584641456604,
-0.058826081454753876,
-0.05060989782214165,
0.024907242506742477,
-0.025117194280028343,
0.015110468491911888,
0.004218979738652706,
0.07131875306367874,
-0.005211342591792345,
0.08159687370061874,
-0.06722055375576019,
-0.05222422629594803,
-0.024289090186357498,
0.024335119873285294,
0.018204493448138237,
0.0181512963026762,
0.07842732965946198,
0.004307249560952187,
-0.03062187135219574,
-0.003297623945400119,
-0.036557700484991074,
-0.02060297690331936,
-0.012634554877877235,
-0.07772170007228851,
0.005976417567580938,
-0.06252682209014893,
0.10309550911188126,
0.00331394886597991,
-0.0007221141713671386,
0.023012857884168625,
0.0017356264870613813,
0.01746082492172718,
-0.0026938847731798887,
0.011210433207452297,
-0.01659213751554489,
-0.04660638049244881,
0.04163249954581261,
0.011794648133218288,
-0.0033817340154200792,
-0.02836337685585022,
-0.006388278678059578,
0.053591761738061905,
0.02240150049328804,
-0.0004817074222955853,
-0.006103560794144869,
0.03285808116197586,
0.02911900170147419,
-0.004145831800997257,
-0.045889247208833694,
-0.0007934478926472366,
0.060588911175727844,
0.025937145575881004,
0.009105365723371506,
0.009941368363797665,
0.04241735860705376,
0.03171972185373306,
-0.0029322796035557985,
-0.028623174875974655,
-0.016102008521556854,
0.01448784489184618,
-0.010292650200426579,
0.0002059988910332322,
0.01924768276512623,
-0.008980145677924156,
0.06388917565345764,
-0.05298696830868721,
-0.04491685330867767,
0.0209927000105381,
0.048430442810058594,
0.06564684212207794,
-0.01543199922889471,
0.019894644618034363,
-0.07319307327270508,
-0.04834628850221634,
0.03307843208312988,
0.0009625892853364348,
-0.028684841468930244,
-0.03422114998102188,
-0.009667585603892803,
0.025866974145174026,
-0.0012082301545888186,
0.029487038031220436,
0.09820156544446945,
-0.01468592882156372,
0.008150916546583176,
-0.01091038528829813,
-0.022935815155506134,
0.0028374134562909603,
0.001654075225815177,
-0.06987351179122925,
0.010240290313959122,
-0.030291613191366196,
0.05527225509285927,
0.012708174996078014,
-0.0346381813287735,
-0.0042311823926866055,
-0.01294649112969637,
-0.06611761450767517,
0.044589921832084656,
-0.06605642288923264,
0.04551714286208153,
0.010557076893746853,
0.03968951478600502,
0.06367576122283936,
0.03395174816250801,
-0.02777050994336605,
0.047814566642045975,
0.0378468856215477,
0.0004000104090664536,
-0.0320415124297142,
-0.04181234911084175,
0.024428484961390495,
-0.015984786674380302,
0.00007033131259959191,
-0.01238956954330206,
0.05476512014865875,
0.025493254885077477,
-0.006676713470369577,
0.01571361906826496,
-0.0045880465768277645,
0.052968580275774,
0.010273374617099762,
0.033316582441329956,
0.019740095362067223,
-0.0008079215767793357,
-0.03688981756567955,
-0.0409117229282856,
0.09205572307109833,
-0.004654945805668831,
0.004783968441188335,
0.0888209119439125,
0.000889965333044529,
0.020048458129167557,
-0.0436280332505703,
0.05019940808415413,
0.01540382020175457,
-0.07987357676029205,
0.016380170360207558,
0.024453748017549515,
-0.012386136688292027,
0.013875101692974567,
0.03418254479765892,
0.07011054456233978,
-0.003454296151176095,
0.017698192968964577,
0.004341511055827141,
-0.0015191707061603665,
-0.010327494703233242,
-0.03214634209871292,
-0.016836434602737427,
-0.005963684059679508,
-0.04463314265012741,
-0.015491485595703125,
0.04229319840669632,
0.043204523622989655,
-0.03069193661212921,
-0.028553983196616173,
0.02850840799510479,
0.03860250860452652,
-0.01791071705520153,
0.013638676144182682,
0.004445227328687906,
-0.051862504333257675,
-0.010627729818224907,
-0.04266458377242088,
0.06105229631066322,
0.07475709170103073,
0.012453076429665089,
-0.0066545442678034306,
0.025338903069496155,
0.04594160243868828,
-0.04882308468222618,
-0.04852350428700447,
0.04681944474577904,
0.043994512408971786,
-0.00017754333384800702,
-0.02619604580104351,
0.03598443791270256,
0.03644995018839836,
0.007273385301232338,
-0.01259792223572731,
-0.0269960667937994,
0.013406860642135143,
0.04965820908546448,
0.028302544727921486,
0.019248850643634796,
-0.03507324680685997,
-0.09256491810083389,
-0.023022055625915527,
-0.0492757223546505,
-0.0683891773223877,
0.007974928244948387,
0.014621919952332973,
-0.04198506474494934,
-0.04073755443096161,
0.05663358047604561,
0.008953321725130081,
-0.03051167167723179,
0.09238248318433762,
0.012080526910722256,
0.015346369706094265,
-0.028462940827012062,
0.08217837661504745,
-0.047070153057575226,
0.013423537835478783,
-0.06788712739944458,
0.039144497364759445,
-0.006375091150403023,
-0.06266455352306366,
0.004524214193224907,
0.025667794048786163,
-0.04692927375435829,
0.06834875047206879,
0.03417573869228363,
-0.021434791386127472,
0.029033813625574112,
-0.0031837972346693277,
0.0054801153019070625,
0.010467689484357834,
0.03572724759578705,
0.0476665161550045,
0.06541118770837784,
0.08471516519784927,
0.022412460297346115,
0.024756573140621185,
-0.021238232031464577,
0.058115046471357346,
0.024333566427230835,
-0.057445138692855835,
0.03291650116443634,
0.03489076346158981,
0.013673157431185246,
-0.03465409576892853,
0.03981290012598038,
0.026143698021769524,
0.02809794805943966,
-0.013879229314625263,
-0.06686558574438095,
0.06880389899015427,
-0.008452731184661388,
0.041854098439216614,
0.05557037517428398,
-0.016549916937947273,
0.07204669713973999,
-0.03551647812128067,
-0.020089643076062202,
-0.04006068408489227,
-0.04621146619319916,
0.005039759445935488,
0.01738128624856472,
-0.049957651644945145,
-0.011768922209739685,
0.09616071730852127,
-0.032654520124197006,
-0.06179383024573326,
0.03220144659280777,
0.06301435083150864,
0.049128297716379166,
-0.08755486458539963,
0.010190103203058243,
0.04270642623305321,
-0.0236912090331316,
-0.05118909478187561,
0.0010663514258340001,
0.05604542791843414,
-0.0017788629047572613,
-0.014790138229727745,
-0.004156095441430807,
0.0020506796427071095,
-0.04397697374224663,
-0.029807567596435547,
-0.07189047336578369,
-0.027107195928692818,
-0.01957952044904232,
0.0018703744281083345,
0.08020532131195068,
0.0419287383556366,
-0.027531621977686882,
-0.057378605008125305,
-0.0403125174343586,
0.012983824126422405,
-0.008792729116976261,
-0.048887234181165695,
-0.041202690452337265,
0.03762810304760933,
0.0350935235619545,
-0.02064593881368637,
-0.02731054462492466,
-0.04139389470219612,
-0.033572494983673096,
0.0019392863614484668,
-0.021552514284849167,
-0.03390827029943466,
-0.08182571828365326,
0.029171735048294067,
0.06047416105866432,
-0.089176245033741,
-0.0023084008134901524,
-0.002578654093667865,
0.02416159212589264,
-0.021627921611070633,
-0.022498954087495804,
-0.04364790394902229,
-0.056259434670209885,
0.013311290182173252,
0.03568003699183464,
0.003401883877813816,
0.03483593091368675,
0.015291002579033375,
0.020306628197431564,
-0.02910231612622738,
-0.052184097468853,
0.05013224855065346,
-0.010431061498820782,
-0.04294328764081001,
0.013188604265451431,
-0.012424536049365997,
-0.02877814508974552,
-0.006004613358527422,
-0.02810298465192318,
0.05173417180776596,
-0.04463852196931839,
-0.028563182801008224,
0.014022121205925941,
-0.014541822485625744,
0.05442553013563156,
0.032287660986185074,
0.03630458936095238,
-0.019331948831677437,
-0.016273243352770805,
0.014730215072631836,
0.002079436555504799,
0.05125396326184273,
-0.03450450673699379,
-0.04381071776151657,
-0.0043174815364181995,
0.024773305281996727,
-0.016919637098908424,
-0.030967313796281815,
-0.04677996039390564,
0.005796689540147781,
0.014764667488634586,
0.004898667801171541,
-0.007170084863901138,
-0.006944732274860144,
-0.02909143641591072,
-0.003993709571659565,
0.033649154007434845,
0.03464465215802193,
-0.016024716198444366,
0.0038668035995215178,
-0.0341799259185791,
0.0540834441781044,
-0.012850029394030571,
-0.03986867517232895,
-0.036009687930345535,
0.0102999834343791,
-0.014381688088178635,
0.054053038358688354,
-0.009268051944673061,
-0.03487660363316536,
0.007887449115514755,
-0.03298777714371681,
0.09385333210229874,
0.02573024481534958,
-0.0830438956618309,
0.01978953182697296,
0.020935194566845894,
0.008009754121303558,
-0.05864853039383888,
0.05559653043746948,
-0.039463166147470474,
-0.026052886620163918,
-0.022067176178097725,
0.028154153376817703,
-0.026632094755768776,
-0.04848009720444679,
-0.019540848210453987
] |
<p>Given complete knowledge of the precise state of every property of every particle and energy phenomenon existing in our universe for a given infinitely small frame of time, is it possible to completely determine the status of every property of every particle and energy phenomenon existing in the succeeding time frame?</p>
<p>This situation assumes that there are no restrictions towards the access of any information, particularly particle states, existing in the universe.</p>
<p>How can this situation be mathematically modeled?</p>
|
g49
|
[
0.033519066870212555,
-0.000316716730594635,
0.0032219139393419027,
-0.001530173933133483,
-0.0020624599419534206,
-0.040597569197416306,
-0.021969765424728394,
0.03499162569642067,
-0.0024161706678569317,
-0.05449148267507553,
0.022347912192344666,
0.0003271938185207546,
-0.00012291262100916356,
0.004590562079101801,
-0.03273233398795128,
-0.0020877092611044645,
0.038397204130887985,
-0.0160030797123909,
0.012390229851007462,
0.03498917073011398,
0.046480245888233185,
0.02428588643670082,
0.024298647418618202,
-0.01750941388309002,
-0.05744367837905884,
-0.03466092422604561,
0.03408266231417656,
-0.04326124116778374,
-0.021347863599658012,
0.006850272882729769,
-0.00867877621203661,
-0.06469390541315079,
0.037125978618860245,
0.019649285823106766,
0.04426036402583122,
-0.042674124240875244,
0.037318501621484756,
-0.018266087397933006,
-0.006257589440792799,
-0.007979093119502068,
0.03640158101916313,
0.010601864196360111,
0.004477099049836397,
-0.03249988332390785,
0.00832755770534277,
0.030251160264015198,
0.020996222272515297,
-0.01742851734161377,
-0.009783156216144562,
-0.05947991460561752,
-0.032560382038354874,
-0.0056355055421590805,
-0.0017909687012434006,
-0.0051866378635168076,
0.02983890101313591,
0.002608231035992503,
0.037954289466142654,
-0.03287999704480171,
0.09849199652671814,
-0.0237435232847929,
0.019550446420907974,
0.019452277570962906,
0.0012284987606108189,
0.042197246104478836,
0.019418764859437943,
-0.0040783872827887535,
-0.05599687620997429,
0.006459701806306839,
0.02162870205938816,
-0.020214082673192024,
0.001019588322378695,
-0.034118060022592545,
-0.033123575150966644,
-0.03883169963955879,
-0.01811329647898674,
0.05831291526556015,
-0.003188234521076083,
0.0022646705619990826,
0.029210371896624565,
0.03760369122028351,
-0.046050965785980225,
0.0033884032163769007,
0.09924623370170593,
-0.031333666294813156,
0.003905092366039753,
-0.038510359823703766,
0.0098739517852664,
0.0037250786554068327,
-0.00458259554579854,
0.027466408908367157,
-0.02773142233490944,
0.011856019496917725,
0.04676905274391174,
-0.013418413698673248,
0.06672389805316925,
0.033232711255550385,
-0.045747123658657074,
0.058058857917785645,
0.0016694576479494572,
-0.014082849957048893,
-0.010941064916551113,
-0.014908459037542343,
-0.01368458941578865,
-0.04577908292412758,
0.016443215310573578,
-0.009786799550056458,
-0.009017636999487877,
-0.01676814816892147,
0.03867868334054947,
-0.014028538018465042,
-0.04383835196495056,
0.016980929300189018,
-0.03001699224114418,
0.03644810989499092,
-0.09734586626291275,
-0.027725204825401306,
0.058738574385643005,
0.015389801934361458,
-0.06672032177448273,
0.03310370817780495,
-0.08109450340270996,
0.03927386552095413,
-0.0019387137144804,
0.06337220221757889,
-0.04678450897336006,
0.024375474080443382,
-0.020171234384179115,
0.03791201487183571,
0.009620101191103458,
-0.030058175325393677,
0.02174779586493969,
-0.01794031448662281,
-0.012264087796211243,
0.03620845079421997,
-0.03982158750295639,
-0.03252186253666878,
0.008389809168875217,
0.019600458443164825,
0.023486759513616562,
0.024088390171527863,
-0.015877772122621536,
-0.018389489501714706,
-0.03992065414786339,
0.035134442150592804,
-0.010984973050653934,
0.012794019654393196,
-0.028552765026688576,
0.006868211552500725,
0.01021880004554987,
0.002549524651840329,
0.018646880984306335,
0.09477847069501877,
-0.013201337307691574,
-0.013761909678578377,
0.054808810353279114,
-0.00649356609210372,
-0.013447271659970284,
0.0010047337273135781,
-0.05103352665901184,
-0.014212848618626595,
0.02973179705440998,
0.008758949115872383,
0.03338279947638512,
-0.029132017865777016,
-0.014779597520828247,
0.03591327741742134,
-0.034820038825273514,
-0.05888151749968529,
0.007227099966257811,
-0.04412827640771866,
-0.06745828688144684,
-0.006965920329093933,
0.0014545316807925701,
0.0186971053481102,
0.012898917309939861,
0.04022320359945297,
0.034924257546663284,
-0.04214909300208092,
0.01678985357284546,
0.021548273041844368,
0.01135381031781435,
-0.0365481823682785,
0.042381949722766876,
0.04654945433139801,
-0.031076451763510704,
-0.028866000473499298,
0.01063173171132803,
-0.0006617307662963867,
0.009667159989476204,
-0.0013618530938401818,
0.0028039508033543825,
0.020400408655405045,
-0.013496635481715202,
-0.02013567090034485,
0.028771549463272095,
-0.044598255306482315,
0.06669214367866516,
-0.027732569724321365,
-0.06378082931041718,
-0.03320242464542389,
0.012881295755505562,
0.06694013625383377,
-0.02495332807302475,
0.04642363265156746,
0.027484053745865822,
0.0009068786166608334,
0.04246627539396286,
0.043002981692552567,
-0.00601287093013525,
0.0418715700507164,
0.07478495687246323,
-0.029331371188163757,
-0.01320986170321703,
0.02528354711830616,
-0.02693118155002594,
-0.018067460507154465,
0.015066311694681644,
-0.029715681448578835,
0.03179109841585159,
-0.017696745693683624,
-0.0391370989382267,
0.016875209286808968,
0.041470013558864594,
0.03965483605861664,
-0.021403664723038673,
0.02870352938771248,
-0.0687020868062973,
0.006715854164212942,
-0.015138782560825348,
0.06438753753900528,
-0.0657029002904892,
0.017836758866906166,
0.011292200535535812,
-0.0009189715492539108,
0.039180368185043335,
0.02574228309094906,
-0.0027132155373692513,
-0.010216521099209785,
0.012213720940053463,
0.016315409913659096,
-0.020561421290040016,
-0.024822719395160675,
-0.02083682082593441,
0.017565743997693062,
0.023319819942116737,
-0.061316028237342834,
0.005126334726810455,
-0.007656344212591648,
-0.011124709621071815,
-0.019616637378931046,
-0.0026626926846802235,
-0.042221955955028534,
-0.015762275084853172,
0.022663509473204613,
0.01020228210836649,
-0.052016887813806534,
0.031618788838386536,
0.046142321079969406,
-0.067478708922863,
-0.040322307497262955,
0.020007247105240822,
-0.040480874478816986,
0.02986578829586506,
0.009772178716957569,
0.017679251730442047,
-0.030504291877150536,
0.0032952975016087294,
0.00022370395890902728,
-0.08762062340974808,
0.01251475140452385,
0.029310783371329308,
-0.0006810937193222344,
-0.012886198237538338,
0.089216448366642,
-0.025920124724507332,
0.022856352850794792,
-0.03390035033226013,
-0.025525148957967758,
0.009078885428607464,
-0.03264330327510834,
-0.059112098067998886,
-0.01085026003420353,
-0.05525335296988487,
0.009712347760796547,
0.0071150255389511585,
-0.07844354212284088,
-0.009960830211639404,
-0.007601235993206501,
-0.008644652552902699,
-0.0007459560292772949,
-0.02208460122346878,
0.030019890516996384,
0.031313635408878326,
0.010197922587394714,
-0.09732111543416977,
0.05813725292682648,
-0.0544218048453331,
-0.022100510075688362,
-0.01053044106811285,
-0.003725830465555191,
0.035954032093286514,
-0.04828596115112305,
0.016040878370404243,
-0.05404176563024521,
-0.034321244806051254,
0.04051563888788223,
-0.04625951498746872,
0.01756557822227478,
0.008115892298519611,
-0.019640278071165085,
-0.06329839676618576,
0.040481336414813995,
0.013802088797092438,
0.02547057718038559,
0.007890353910624981,
0.030420055612921715,
0.03451455384492874,
0.013590981252491474,
-0.0034235334023833275,
0.02294030785560608,
0.013279201462864876,
0.03382684662938118,
0.044348448514938354,
-0.025040840730071068,
0.04907916858792305,
-0.027209926396608353,
-0.05771311745047569,
-0.0315355584025383,
-0.09452167898416519,
0.02041521668434143,
0.04134780168533325,
-0.05261373519897461,
0.03148683160543442,
-0.013242959976196289,
-0.0060732606798410416,
-0.029460100457072258,
-0.06607278436422348,
-0.07021451741456985,
0.05191008001565933,
0.0021079375874251127,
0.0174409206956625,
-0.01846141554415226,
-0.029777439311146736,
0.05428885295987129,
0.01651933044195175,
0.04053455591201782,
-0.042262230068445206,
-0.0030079898424446583,
0.03507966920733452,
-0.019595619291067123,
0.03812118247151375,
0.016348956152796745,
0.0005028892774134874,
-0.019595462828874588,
0.024172130972146988,
0.0662628784775734,
0.034184299409389496,
0.03166469186544418,
0.05165954306721687,
-0.0014649051008746028,
-0.024165615439414978,
-0.058079905807971954,
0.05339613929390907,
-0.006818375084549189,
0.00645783357322216,
0.00909496285021305,
-0.0009800144471228123,
-0.013710657134652138,
0.010879749432206154,
-0.0037495577707886696,
0.019729891791939735,
-0.04454923793673515,
-0.032802436500787735,
0.007603663485497236,
0.028473176062107086,
-0.021304752677679062,
0.025829875841736794,
-0.07809333503246307,
-0.08022313565015793,
0.019791798666119576,
0.04274722561240196,
0.02662694826722145,
0.03051784448325634,
0.03253992646932602,
0.039654940366744995,
0.06622721999883652,
-0.02652445062994957,
-0.01389690488576889,
-0.003986585885286331,
-0.021895350888371468,
0.07583646476268768,
-0.14133496582508087,
0.014715926721692085,
-0.004926167894154787,
0.012216517701745033,
-0.0451383963227272,
0.012147285975515842,
-0.037002794444561005,
0.062027838081121445,
0.020711271092295647,
-0.03088444657623768,
0.026836445555090904,
0.01372241135686636,
0.0016335727414116263,
0.03404855355620384,
0.05229134112596512,
-0.0038355581928044558,
-0.023805001750588417,
0.01865316741168499,
-0.05881033465266228,
0.04431157559156418,
0.043198250234127045,
-0.0064841038547456264,
-0.042585425078868866,
-0.004885152913630009,
0.013163751922547817,
-0.01883672922849655,
-0.11057621240615845,
0.03401541709899902,
0.04537124186754227,
0.03664078190922737,
-0.014493194408714771,
0.005493316799402237,
-0.04195421189069748,
0.011464174836874008,
0.06264455616474152,
-0.008501448668539524,
0.00700797326862812,
-0.0391075573861599,
0.020650070160627365,
0.04848251864314079,
0.022820651531219482,
0.05873841792345047,
0.05364982411265373,
-0.030065618455410004,
0.005608271807432175,
-0.04084591194987297,
0.005216563120484352,
0.008305291645228863,
0.028782283887267113,
0.0584794282913208,
-0.00409251032397151,
-0.0040725115686655045,
0.021207718178629875,
-0.036510907113552094,
0.10056173801422119,
-0.06927430629730225,
-0.04046826437115669,
-0.0021127962972968817,
-0.0071026976220309734,
-0.02208884432911873,
-0.005796556826680899,
-0.11519910395145416,
-0.02024480141699314,
-0.02811109833419323,
-0.016169222071766853,
-0.0401826947927475,
0.06287766247987747,
0.013979814946651459,
0.002896081656217575,
-0.06641034781932831,
-0.03026638925075531,
-0.002872243756428361,
0.05066898092627525,
0.03820409998297691,
0.028845636174082756,
-0.0740821361541748,
0.03408467769622803,
-0.0957004502415657,
0.01163252629339695,
0.017919786274433136,
-0.007250235415995121,
0.08301850408315659,
0.04369264096021652,
-0.038617800921201706,
-0.03162932023406029,
-0.042821254581213,
-0.0330977626144886,
0.00832070130854845,
0.052115436643362045,
-0.04748852550983429,
0.0403069444000721,
0.0284586064517498,
0.05939151346683502,
0.0005425694980658591,
0.02342054434120655,
-0.024295136332511902,
0.006992482580244541,
-0.06415003538131714,
-0.018061306327581406,
-0.009407516568899155,
0.03736595809459686,
0.05598682537674904,
-0.0013195812935009599,
0.012891999445855618,
-0.0394023060798645,
-0.03606468811631203,
-0.034127142280340195,
-0.016129381954669952,
0.030717311426997185,
-0.013109535910189152,
-0.00673528341576457,
0.035272061824798584,
0.013510328717529774,
0.003294191090390086,
0.01528764609247446,
0.03491262346506119,
-0.024509718641638756,
-0.03764449059963226,
-0.020404372364282608,
-0.04528074339032173,
0.06435173004865646,
-0.04763554781675339,
0.046660516411066055,
0.008701075799763203,
-0.020712951198220253,
-0.026175957173109055,
0.03335891291499138,
-0.045841578394174576,
-0.06404107064008713,
-0.0051263668574392796,
0.02705252915620804,
0.0648253932595253,
0.0013587698340415955,
-0.0017664601327851415,
0.014662531204521656,
-0.019456233829259872,
0.02843495085835457,
0.022331714630126953,
0.019256211817264557,
0.0410357266664505,
0.013012675568461418,
-0.023492835462093353,
-0.032635416835546494,
0.029838651418685913,
-0.015274490229785442,
0.007519618142396212,
-0.012269805185496807,
0.02065693959593773,
0.032843757420778275,
-0.018794961273670197,
-0.024431660771369934,
0.022176915779709816,
0.021532773971557617,
0.004321446642279625,
-0.036387667059898376,
-0.025479400530457497,
0.05864625424146652,
0.023533495143055916,
-0.06645406782627106,
0.0023259350564330816,
0.01601334847509861,
0.022550152614712715,
0.008965400978922844,
-0.035762038081884384,
0.03486425057053566,
0.054459813982248306,
-0.0005922873970121145,
-0.04785356670618057,
-0.0411314032971859,
0.020250391215085983,
0.04412280395627022,
0.030808869749307632,
-0.02072419598698616,
-0.01139131747186184,
0.026445360854268074,
0.022521208971738815,
-0.05353648588061333,
0.03274709731340408,
0.03508345037698746,
0.03346193954348564,
0.03138419985771179,
0.014418387785553932,
-0.016957998275756836,
-0.01839161477982998,
-0.029316775500774384,
-0.006659859791398048,
-0.010153122246265411,
-0.028643645346164703,
-0.015549235977232456,
0.000027384830900700763,
0.02794671431183815,
0.04238447546958923,
0.04304875433444977,
0.058998946100473404,
0.08350857347249985,
-0.029945677146315575,
0.006920975632965565,
0.018329396843910217,
0.03950777277350426,
0.025523485615849495,
-0.03447944298386574,
-0.0000681191377225332,
-0.015368158929049969,
-0.036570366472005844,
0.03428830951452255,
0.02037743106484413,
-0.03785339742898941,
-0.02331378683447838,
0.028502965345978737,
-0.011532063595950603,
-0.04156886041164398,
0.020778624340891838,
-0.049321167171001434,
0.0454498715698719,
0.043929073959589005,
-0.038504812866449356,
0.037816353142261505,
0.013157430104911327,
-0.0351700596511364,
-0.04944021627306938,
-0.013918688520789146,
0.04481378570199013,
-0.013237937353551388,
-0.019208423793315887,
-0.06759192794561386,
0.037019260227680206,
0.026365913450717926,
-0.027283519506454468,
-0.05915841832756996,
-0.0020030499435961246,
0.038355909287929535,
0.03569474071264267,
-0.01975693553686142,
0.04375793784856796,
0.001594537403434515,
-0.06228213384747505,
0.07580088824033737,
0.02053142338991165,
0.01701474003493786,
0.05899813026189804,
0.008656363002955914,
0.0549323596060276,
0.02298489399254322,
-0.003978218883275986,
0.030282195657491684,
-0.008759853430092335,
0.03913014754652977,
0.00399242015555501,
-0.020091723650693893,
0.02263384684920311,
0.01807643473148346,
0.030888034030795097,
0.014285885728895664,
-0.05043516680598259,
-0.05557787045836449,
0.02957458421587944,
-0.021726863458752632,
-0.004734627902507782,
-0.022020699456334114,
0.018711712211370468,
-0.007722306530922651,
-0.0027034797240048647,
0.020357461646199226,
-0.04220962896943092,
-0.014109690673649311,
-0.02752074785530567,
-0.03514830395579338,
0.04026169329881668,
-0.1043342649936676,
0.04935114085674286,
-0.007748499047011137,
0.010262846015393734,
-0.051728665828704834,
-0.024554934352636337,
0.03470369055867195,
0.03886902332305908,
-0.12067074328660965,
0.02881697751581669,
-0.04658934846520424,
0.041017379611730576,
-0.02730695717036724,
-0.01801869459450245,
0.0126262241974473,
0.004491908010095358,
-0.03341319039463997,
-0.05482836067676544,
0.04194384440779686,
0.0371328704059124,
0.02148694358766079,
0.0008676103316247463,
0.042088065296411514,
0.016040317714214325,
0.033268582075834274,
-0.02810634858906269,
0.04629794508218765,
-0.023342370986938477,
-0.0008903151610866189,
-0.05259125307202339,
-0.014767533168196678,
-0.03289834037423134,
-0.00885323341935873,
0.047451045364141464,
-0.09421452134847641,
0.008650608360767365,
-0.013998226262629032,
0.05104505270719528,
0.005227833054959774,
0.00490002753213048,
-0.04396713525056839,
-0.00919551495462656,
-0.019122349098324776,
0.04187416285276413,
-0.019749443978071213,
0.0006557581364177167,
-0.045217860490083694,
-0.04047219082713127,
-0.014797039330005646,
-0.008986257016658783,
0.08965063095092773,
0.024814395233988762,
0.02887696400284767,
-0.010401973500847816,
0.0342772975564003,
-0.01927410066127777,
0.013236084021627903,
-0.026090053841471672,
-0.007779696956276894,
0.04964665323495865,
0.0002785146061796695,
-0.04060899093747139,
-0.02684788592159748,
-0.037187181413173676,
-0.01907438226044178,
0.020503390580415726,
0.0030378459487110376,
-0.07142970710992813,
0.002721308497712016,
-0.015027492307126522,
-0.02599644474685192,
0.0322953462600708,
-0.003346455516293645,
0.005634581204503775,
-0.019870225340127945,
-0.023444777354598045,
0.08500893414020538,
-0.02973455749452114,
-0.057557012885808945,
-0.0283993948251009,
-0.02767534740269184,
-0.09030400216579437,
-0.07086776942014694,
0.015602636151015759,
0.022109493613243103,
0.05278573930263519,
-0.07352470606565475,
-0.0310940183699131,
-0.0034440276212990284,
0.04775134101510048,
-0.0002834259357769042,
-0.06461967527866364,
-0.011926870793104172,
0.0302619356662035,
0.018353518098592758,
0.000774484477005899,
0.009922577999532223,
0.04108291119337082,
-0.010918552055954933,
-0.009139809757471085,
0.05392969027161598,
0.010425126180052757,
0.021548928692936897,
0.010841074399650097,
0.008907850831747055,
-0.021929308772087097,
-0.04199220985174179,
0.03494855388998985,
0.017846491187810898
] |
<p>If right in the centre of the Earth would be like a hole and I could teleport right there, what would happen to me? Would I explode, implode? My own theory is that maybe I would levitate because since I'm right in the middle, the gravity wouldn't affect me...</p>
<p>What do you guys think? </p>
|
g50
|
[
0.008265513926744461,
0.02365880459547043,
0.024360138922929764,
0.01651167683303356,
-0.034947484731674194,
0.07117772102355957,
-0.02830050140619278,
0.028210680931806564,
-0.008729314431548119,
-0.04029380902647972,
0.008487825281918049,
-0.01361403614282608,
-0.015024214051663876,
-0.029281681403517723,
0.013131740503013134,
-0.017368149012327194,
0.05053902789950371,
-0.010926474817097187,
0.02116435021162033,
-0.031698986887931824,
-0.01309826411306858,
-0.0772104486823082,
-0.025881638750433922,
-0.006805548444390297,
-0.04920991510152817,
0.03301887586712837,
0.03576542064547539,
0.01334920059889555,
-0.05406692996621132,
-0.015601225197315216,
0.02297349087893963,
-0.021750595420598984,
-0.020277738571166992,
-0.09557141363620758,
-0.056491319090127945,
-0.03193575516343117,
-0.029332106932997704,
0.01426156610250473,
0.011513863690197468,
-0.01423204317688942,
-0.016922958195209503,
-0.07990354299545288,
-0.06364374607801437,
-0.05827287957072258,
-0.007326600607484579,
-0.0014397313352674246,
0.03212343901395798,
0.02228604629635811,
0.03874140977859497,
-0.015130707062780857,
-0.036860980093479156,
0.009754988364875317,
0.013743097893893719,
-0.0013804876944050193,
-0.009202617220580578,
-0.019624145701527596,
0.025095000863075256,
-0.0454680398106575,
0.022658856585621834,
-0.0024153708945959806,
-0.03087776154279709,
0.021170957013964653,
-0.029228582978248596,
-0.016096165403723717,
0.03519705310463905,
0.02910727821290493,
-0.05012425035238266,
0.04885797202587128,
0.0007576347561553121,
0.014023548923432827,
0.05628892034292221,
-0.037025466561317444,
-0.041233234107494354,
-0.06802365928888321,
-0.02055952697992325,
0.07264406234025955,
0.011324736289680004,
0.04036775603890419,
0.050385355949401855,
-0.037117257714271545,
-0.023745097219944,
-0.013903312385082245,
0.03444438427686691,
-0.03663404658436775,
-0.01763581484556198,
-0.06915394216775894,
-0.02057011052966118,
-0.035749949514865875,
-0.01648031733930111,
0.01263243518769741,
0.04100523144006729,
-0.03746738284826279,
0.023709120228886604,
0.02367292530834675,
-0.0017915322678163648,
-0.050058089196681976,
0.00936321821063757,
0.08736240863800049,
-0.014006713405251503,
-0.011150481179356575,
-0.010237248614430428,
-0.02575157769024372,
-0.006945131812244654,
0.0036339617799967527,
-0.015454037114977837,
0.004480298608541489,
0.05884524807333946,
-0.05344323813915253,
0.04560757428407669,
-0.021840322762727737,
0.043061744421720505,
-0.0030626824591308832,
-0.0054998816922307014,
-0.005760625470429659,
-0.01691063866019249,
0.00684782350435853,
0.045031819492578506,
-0.0634598657488823,
0.08524207770824432,
0.01635192520916462,
0.040176521986722946,
0.030109090730547905,
0.01090736873447895,
0.044218551367521286,
-0.005597448907792568,
0.03233463689684868,
-0.007512220181524754,
-0.03411981835961342,
-0.023378515616059303,
0.03367362171411514,
-0.021231310442090034,
0.0035039465874433517,
-0.06581996381282806,
0.02195766195654869,
0.024582507088780403,
0.024553479626774788,
-0.02568025328218937,
0.002020273357629776,
-0.010179905220866203,
-0.027438413351774216,
-0.018620193004608154,
-0.016176899895071983,
0.022413505241274834,
0.021641170606017113,
-0.028677836060523987,
-0.047741614282131195,
-0.018924174830317497,
0.03525744378566742,
0.004791637416929007,
-0.018607478588819504,
0.00856468454003334,
-0.005076905246824026,
0.001850688480772078,
-0.01483454741537571,
0.05831904709339142,
0.024255292490124702,
0.04014800488948822,
0.029144287109375,
-0.028194816783070564,
-0.033472832292318344,
0.004230032674968243,
-0.024261023849248886,
0.0426781065762043,
0.022253135219216347,
-0.06901954859495163,
0.018903350457549095,
0.06476213037967682,
-0.04377336800098419,
0.05908694118261337,
0.016046904027462006,
-0.034374285489320755,
0.03735804557800293,
0.0058404915034770966,
0.02303308993577957,
-0.008673923090100288,
-0.001240480924025178,
-0.013876435346901417,
-0.007859652861952782,
0.006991671398282051,
-0.05975968763232231,
0.049527861177921295,
-0.016156991943717003,
-0.025651991367340088,
-0.031087534502148628,
0.008286949247121811,
-0.05707857385277748,
0.04320993274450302,
0.07455851137638092,
-0.07088855654001236,
-0.014633545652031898,
0.05265891179442406,
-0.04639820381999016,
-0.008929600939154625,
0.009087123908102512,
-0.06385808438062668,
-0.0706210508942604,
0.03582819178700447,
0.01725972630083561,
-0.04996665194630623,
0.04127691313624382,
0.016943061724305153,
0.03295939788222313,
0.048916034400463104,
0.019706357270479202,
-0.04139826446771622,
0.0529291145503521,
-0.038356807082891464,
0.009995706379413605,
-0.02359115332365036,
-0.03242345526814461,
0.08366820216178894,
-0.035874493420124054,
0.003588285529986024,
0.03642809018492699,
-0.054128579795360565,
0.02123120054602623,
-0.04153472185134888,
0.016313932836055756,
-0.0246368870139122,
0.05504918470978737,
0.03223252296447754,
-0.048111509531736374,
0.0024730886798352003,
-0.06133709102869034,
0.06551199406385422,
-0.0451202318072319,
-0.05146079137921333,
-0.020598702132701874,
0.06540835648775101,
-0.05287720635533333,
-0.00986639317125082,
0.03585496544837952,
0.049459248781204224,
-0.02754088304936886,
0.051413387060165405,
0.07912160456180573,
-0.02037498913705349,
0.015567868016660213,
-0.015323501080274582,
-0.021286293864250183,
0.003339208895340562,
0.003100163768976927,
0.002475634915754199,
0.005775817669928074,
0.06005461886525154,
-0.0397217832505703,
0.08097951859235764,
-0.0043630413711071014,
-0.01721208170056343,
-0.03176587447524071,
0.023061947897076607,
-0.03985011950135231,
-0.0775175392627716,
0.017099369317293167,
0.0001101165617001243,
-0.0024658197071403265,
-0.02342950738966465,
0.0718868225812912,
-0.012130540795624256,
-0.015175863169133663,
-0.046859338879585266,
-0.015442771837115288,
0.02188759297132492,
-0.014441725797951221,
-0.11384393274784088,
0.034638699144124985,
0.02136341668665409,
0.025621164590120316,
-0.02598606050014496,
0.016457581892609596,
-0.06591226905584335,
0.05729776620864868,
-0.025350451469421387,
0.0758073478937149,
0.010596532374620438,
-0.009158746339380741,
-0.024150751531124115,
-0.04842395335435867,
0.0000559053587494418,
-0.013869596645236015,
0.02412763610482216,
0.045372750610113144,
0.012476226314902306,
0.030629383400082588,
0.026619110256433487,
-0.03338455408811569,
-0.03836256265640259,
0.020392125472426414,
0.001618536887690425,
0.037861842662096024,
0.06717226654291153,
-0.0392259880900383,
0.07925096899271011,
0.05695300176739693,
0.03197555989027023,
0.0005853510810993612,
-0.027533622458577156,
-0.036648910492658615,
-0.041773468255996704,
-0.013616248965263367,
0.012372845783829689,
-0.05202219635248184,
0.06364161521196365,
0.040383175015449524,
-0.08428575098514557,
0.008055415004491806,
0.02032182365655899,
0.014097446575760841,
0.022485021501779556,
-0.004625505767762661,
-0.04330839589238167,
0.05883912369608879,
-0.04083791375160217,
0.020494528114795685,
0.038320720195770264,
-0.017913280054926872,
0.0031579823698848486,
-0.020781125873327255,
0.06874687969684601,
-0.018602246418595314,
-0.028118297457695007,
0.019350899383425713,
0.02558799833059311,
0.032633114606142044,
0.019542714580893517,
0.041044704616069794,
-0.07094878703355789,
-0.0004526931152213365,
-0.04777177795767784,
-0.0639023631811142,
-0.049141962081193924,
-0.029759498313069344,
-0.07851433753967285,
-0.010577909648418427,
-0.015265470370650291,
0.0308784581720829,
0.06182365119457245,
0.045213278383016586,
0.030436431989073753,
0.012383322231471539,
0.012932508252561092,
-0.0117183243855834,
-0.004586127121001482,
-0.007233062759041786,
0.05795798823237419,
0.0026166951283812523,
0.04204482585191727,
0.0331217460334301,
0.01993134617805481,
0.014001237228512764,
0.034330472350120544,
-0.03935721889138222,
0.014216658659279346,
-0.030133286491036415,
0.0022223987616598606,
0.0011990584898740053,
-0.042893942445516586,
-0.00992494821548462,
-0.025228220969438553,
0.009115888737142086,
-0.03498236462473869,
0.026373086497187614,
-0.0136949447914958,
-0.030472205951809883,
-0.0008251019171439111,
0.023523222655057907,
-0.016817059367895126,
-0.031552642583847046,
-0.014622490853071213,
0.013955557718873024,
0.02187839150428772,
0.03618054464459419,
-0.04401950538158417,
-0.007333913818001747,
0.03200250491499901,
-0.043913573026657104,
0.06810510903596878,
-0.05593767762184143,
-0.03908666595816612,
-0.0006634388118982315,
-0.012599248439073563,
-0.04508325457572937,
0.0006371343624778092,
0.04954839125275612,
0.000801054120529443,
0.006333824247121811,
0.0032035885378718376,
-0.028936322778463364,
0.016536401584744453,
0.019987208768725395,
0.06107200309634209,
-0.047616325318813324,
0.03994029015302658,
0.004999907687306404,
0.02081495337188244,
0.023698514327406883,
-0.010238731279969215,
0.002036344725638628,
-0.003437563544139266,
-0.011053948663175106,
0.08198093622922897,
0.02495126985013485,
-0.0061931852251291275,
0.009769073687493801,
0.00044211288332007825,
-0.04586780071258545,
-0.0012759888777509332,
-0.006410042755305767,
-0.013035724870860577,
-0.0033321313094347715,
0.07756227254867554,
0.01557245198637247,
-0.00909397378563881,
-0.033913034945726395,
0.06178702041506767,
0.012481855228543282,
0.04078913480043411,
0.016307711601257324,
-0.03380347043275833,
0.05887385457754135,
0.04718282073736191,
0.06095349043607712,
0.02491902746260166,
-0.027095217257738113,
0.008159131743013859,
-0.004073127638548613,
0.02344495803117752,
-0.03356367349624634,
-0.023262346163392067,
0.044419847428798676,
-0.03760591521859169,
0.039080824702978134,
0.0008785065729171038,
-0.02403249591588974,
-0.007378550712019205,
-0.017071668058633804,
-0.028985394164919853,
-0.0018022528383880854,
0.04324701055884361,
-0.014186165295541286,
0.04510169103741646,
0.009251129813492298,
0.030530646443367004,
0.013556824997067451,
-0.04035131260752678,
0.03606453165411949,
-0.007086181081831455,
-0.024764614179730415,
0.06452096998691559,
-0.04053346812725067,
-0.051633406430482864,
0.024922767654061317,
-0.07377607375383377,
-0.0323711559176445,
-0.018480919301509857,
0.00027111289091408253,
0.02772568166255951,
0.034086357802152634,
-0.02871769666671753,
-0.024574903771281242,
-0.04420895874500275,
0.026904957368969917,
0.01650834083557129,
-0.008388240821659565,
0.01879485510289669,
0.014913195744156837,
-0.009371071122586727,
-0.061487238854169846,
-0.006132923066616058,
-0.04775216802954674,
0.01163438055664301,
-0.021538665518164635,
-0.017281314358115196,
0.053929124027490616,
0.028431106358766556,
0.018922314047813416,
-0.04703874513506889,
-0.04482003673911095,
0.010751252993941307,
-0.06726989150047302,
-0.0163879431784153,
-0.001247187377884984,
0.00028394770924933255,
-0.014456360600888729,
-0.005075812805444002,
0.00947886984795332,
-0.04986809939146042,
0.0064118243753910065,
-0.02663322165608406,
0.009024951606988907,
-0.007826811634004116,
-0.08287477493286133,
-0.042908862233161926,
-0.033658746629953384,
-0.0026503950357437134,
0.02744770050048828,
-0.026523221284151077,
0.01359730213880539,
-0.04930372163653374,
-0.0068291230127215385,
-0.0007056746399030089,
-0.011927319690585136,
0.028789596632122993,
0.022302838042378426,
-0.024034129455685616,
0.0007686259341426194,
-0.005071751307696104,
0.05360277369618416,
-0.014257465489208698,
0.014629945158958435,
-0.0299641452729702,
0.004694746341556311,
-0.09268558770418167,
-0.005543723702430725,
0.014100823551416397,
-0.009646918624639511,
-0.04102056473493576,
0.010066653601825237,
0.02661517821252346,
0.06949114054441452,
-0.0399898923933506,
-0.024699050933122635,
-0.00047250677016563714,
0.02662886306643486,
0.024189166724681854,
0.048962656408548355,
-0.05022907629609108,
0.05322279408574104,
-0.0025911484844982624,
-0.031613539904356,
-0.035814739763736725,
0.013768011704087257,
0.054386381059885025,
-0.04175249859690666,
-0.010405112989246845,
0.0001798311568563804,
0.043653521686792374,
0.006151801906526089,
0.10301700234413147,
-0.06571304053068161,
-0.027140995487570763,
-0.019899677485227585,
-0.05561007186770439,
0.02119952253997326,
-0.010180321522057056,
-0.00022895658912602812,
-0.11699758470058441,
0.03112143464386463,
0.06687697768211365,
-0.03825802728533745,
-0.015800900757312775,
0.020159045234322548,
0.027141207829117775,
0.024785690009593964,
0.003010322107002139,
0.028780758380889893,
-0.01049446128308773,
0.05318295955657959,
0.008212853223085403,
-0.03308490291237831,
0.02847614698112011,
0.028121517971158028,
-0.0056198639795184135,
0.002134696813300252,
-0.026224561035633087,
0.0205442626029253,
0.0053528062999248505,
-0.02645331248641014,
0.03324425593018532,
0.017882036045193672,
0.006801092065870762,
0.0267751794308424,
-0.02483394183218479,
0.025823138654232025,
-0.015385289676487446,
-0.02855919487774372,
0.030437815934419632,
0.02546161226928234,
-0.02922610007226467,
-0.001441767904907465,
0.043059248477220535,
0.007704760413616896,
0.06374592334032059,
0.00865895301103592,
-0.016489306464791298,
0.031315382570028305,
-0.04012977331876755,
0.003347915830090642,
0.05299975350499153,
-0.05104634910821915,
-0.06558326631784439,
0.041683703660964966,
0.0035372793208807707,
-0.017852479591965675,
-0.008056455291807652,
0.004209333565086126,
0.024582816287875175,
-0.005804379936307669,
-0.016205687075853348,
0.07260496914386749,
0.0009230406139977276,
-0.00954188872128725,
0.025413397699594498,
0.046824365854263306,
0.0036825730931013823,
0.026473551988601685,
0.011024894192814827,
0.0014799450291320682,
-0.005656122229993343,
0.008293040096759796,
0.06873311847448349,
0.008837210014462471,
0.032833367586135864,
-0.0028408486396074295,
-0.022824902087450027,
0.05597366765141487,
0.012725960463285446,
-0.02720498852431774,
0.09043506532907486,
0.028444554656744003,
0.01742464490234852,
0.004072180949151516,
-0.08527795970439911,
-0.03376292064785957,
-0.04362337663769722,
-0.002447092439979315,
-0.033469103276729584,
0.025381164625287056,
0.010069970041513443,
-0.03999662026762962,
-0.02198988012969494,
0.01320599764585495,
0.02241375669836998,
0.010446262545883656,
0.0005382114322856069,
0.015468678437173367,
-0.0033009641338139772,
-0.07108353823423386,
-0.013366986066102982,
0.016278591006994247,
0.0292501263320446,
-0.015164386481046677,
0.015582729130983353,
-0.041183650493621826,
-0.025591833516955376,
0.0715731605887413,
-0.01237756758928299,
-0.034187234938144684,
-0.021399566903710365,
0.011525359004735947,
-0.019537726417183876,
-0.023480461910367012,
-0.0064667691476643085,
-0.007987666875123978,
0.002710819710046053,
-0.02200906351208687,
-0.005738851148635149,
0.02402680180966854,
-0.0032383461948484182,
-0.06890305131673813,
-0.015262375585734844,
-0.024091046303510666,
-0.004967475775629282,
-0.03230201452970505,
-0.002435201546177268,
0.026485824957489967,
0.042440857738256454,
0.0036485877353698015,
-0.010673495009541512,
0.02077021449804306,
-0.029455261304974556,
0.02680508978664875,
-0.07564322650432587,
0.06491844356060028,
-0.028103403747081757,
0.05322449654340744,
-0.05314753204584122,
-0.013853208161890507,
-0.022186478599905968,
0.09990443289279938,
-0.0076232957653701305,
0.003415255108848214,
-0.007749664597213268,
0.004113448783755302,
-0.04585220292210579,
0.025835832580924034,
0.049690742045640945,
0.0516679510474205,
-0.055316515266895294,
-0.04593250900506973,
0.03200264275074005,
0.03662285953760147,
0.02697947807610035,
-0.04306117445230484,
-0.051366858184337616,
0.004819595720618963,
0.01104392297565937,
0.039682090282440186,
0.015631385147571564,
-0.05256839841604233,
-0.020017391070723534,
-0.004982616752386093,
-0.019847150892019272,
-0.06993727385997772,
0.022986488416790962,
0.0012241185177117586,
-0.007071890868246555,
0.06025693938136101,
-0.08740440011024475,
0.08352907001972198,
0.11573249846696854,
0.040289610624313354,
0.05291016399860382,
0.04988481104373932,
0.001633638166822493,
0.02829034999012947,
-0.011595473624765873,
0.03125333786010742,
0.001012051128782332,
0.020579421892762184,
-0.022165467962622643,
0.018182754516601562,
-0.006213176995515823,
-0.01616533473134041,
-0.06637747585773468,
0.0819542184472084,
-0.0690883994102478,
0.016818324103951454,
0.016593702137470245,
-0.05876621603965759,
0.030870748683810234,
0.050088949501514435,
0.017052600160241127,
0.007238402031362057,
0.02200319990515709,
0.009484471753239632,
0.01729804463684559,
-0.07297886162996292,
-0.011759741231799126,
-0.01274294126778841,
-0.014437882229685783,
-0.008546111173927784,
-0.0017347080865874887,
0.023354502394795418,
0.019016684964299202,
0.011297011747956276,
-0.018193483352661133,
0.027878887951374054,
-0.058470603078603745,
-0.04183027893304825,
0.07354045659303665,
-0.04154042899608612,
0.007866933010518551,
0.04054762050509453,
0.01990405283868313,
-0.02164372056722641,
-0.041022881865501404,
0.007680372800678015,
-0.025806520134210587,
-0.017297742888331413,
-0.018442491069436073,
-0.026742324233055115,
0.0437694787979126,
-0.010062324814498425,
-0.06640228629112244,
-0.01884668879210949,
0.026011355221271515,
0.027139486744999886
] |
<p>I am appreciating particle physics and I read about mesons. In quark's model, mesons are pairs of quark-antiquark. Now I think that in general matter-antimatter annihilate and so I don't understand how meson could be possible. Why don't a couple up-antiup annihilates? </p>
<p>Thank you!</p>
|
g2509
|
[
-0.032488223165273666,
0.013059714809060097,
0.02272862009704113,
-0.012320095673203468,
0.06543807685375214,
0.0527581125497818,
-0.04727381467819214,
0.03587494045495987,
0.011752251535654068,
-0.013884367421269417,
0.01883716881275177,
0.023578541353344917,
-0.01090939249843359,
-0.025340722873806953,
-0.029997529461979866,
0.012531897984445095,
0.018775248900055885,
0.012006500735878944,
0.0402933806180954,
0.005805087275803089,
-0.03784732520580292,
-0.045963089913129807,
0.028760328888893127,
-0.029387541115283966,
-0.0778382420539856,
0.012464414350688457,
0.0028940571937710047,
-0.028279054909944534,
-0.014385353773832321,
0.056932128965854645,
-0.013160488568246365,
-0.05751485377550125,
0.013462611474096775,
-0.08479955792427063,
0.02565547451376915,
-0.04809168353676796,
0.09190701693296432,
-0.04545632377266884,
0.02777162939310074,
-0.0325394831597805,
0.026277154684066772,
-0.017966926097869873,
-0.019775962457060814,
-0.0294776801019907,
0.0050242505967617035,
0.03277415409684181,
-0.0019494201987981796,
-0.011874997988343239,
-0.005761533509939909,
-0.05102868750691414,
0.027259066700935364,
0.006990631110966206,
0.0722595676779747,
0.03450389951467514,
0.025307824835181236,
-0.00021274514438118786,
-0.011407313868403435,
-0.054154958575963974,
0.09693202376365662,
0.019350284710526466,
-0.04474120959639549,
-0.008152887225151062,
0.03173784911632538,
-0.02747800014913082,
0.05334975942969322,
-0.020012736320495605,
0.030591005459427834,
0.04124075546860695,
0.026857610791921616,
0.03605665639042854,
0.008013688959181309,
-0.008673401549458504,
-0.006192890927195549,
-0.03583090379834175,
0.05596468225121498,
0.015567248687148094,
-0.027321232482790947,
-0.004600493237376213,
0.011673525907099247,
-0.030476508662104607,
-0.028705285862088203,
0.013684555888175964,
0.06731126457452774,
-0.07541773468255997,
0.023136604577302933,
-0.05826014652848244,
-0.02575859986245632,
-0.002073562005534768,
-0.04843199998140335,
-0.026357317343354225,
0.033936407417058945,
-0.0002194881089963019,
-0.011661682277917862,
0.00022808057838119566,
0.012539238668978214,
-0.03733983263373375,
-0.013207316398620605,
0.05315234139561653,
-0.06509257107973099,
0.035952623933553696,
-0.025163108482956886,
0.010004010982811451,
0.07416709512472153,
0.009991162456572056,
0.018402252346277237,
-0.008520162664353848,
0.022322971373796463,
0.01107528991997242,
0.044079650193452835,
0.05192162096500397,
-0.056600168347358704,
0.04777729511260986,
-0.041835930198431015,
-0.010249851271510124,
-0.02298164553940296,
0.026336051523685455,
0.03847863897681236,
-0.02411961555480957,
0.006423519924283028,
0.060616880655288696,
-0.03078875131905079,
0.03004472330212593,
-0.028602151200175285,
-0.018887337297201157,
-0.07876027375459671,
-0.09831862896680832,
0.02383076772093773,
0.017782384529709816,
-0.009435406886041164,
-0.012749270536005497,
0.06381403654813766,
-0.05697939917445183,
-0.02110820636153221,
0.024685487151145935,
0.03018893301486969,
0.03512336686253548,
0.010314722545444965,
0.051531512290239334,
0.0270635224878788,
0.0024916992988437414,
-0.02917362190783024,
-0.006205765064805746,
-0.01080811396241188,
0.0229379553347826,
-0.024844322353601456,
-0.0014559336705133319,
-0.04599536955356598,
-0.017645282670855522,
-0.06947736442089081,
0.0944860428571701,
0.042622845619916916,
0.07964441925287247,
0.001640218892134726,
-0.024802742525935173,
0.026030831038951874,
-0.011253061704337597,
0.01728801615536213,
-0.0011353505542501807,
-0.026370655745267868,
-0.022426016628742218,
0.04463120922446251,
0.014150475151836872,
-0.04502822831273079,
0.0027919765561819077,
-0.08774173259735107,
0.02703714184463024,
0.024278948083519936,
-0.062027543783187866,
0.0065581900998950005,
0.0054250615648925304,
-0.01872408390045166,
0.006361199077218771,
0.003912339452654123,
0.0592421293258667,
0.049236830323934555,
0.014326403848826885,
-0.01908898912370205,
0.023837462067604065,
-0.021389111876487732,
-0.01772969402372837,
0.07908710092306137,
0.027053773403167725,
0.020272957161068916,
0.008359160274267197,
0.012750493362545967,
-0.0333656407892704,
-0.014193943701684475,
0.06132205203175545,
0.04153015464544296,
0.05515294522047043,
0.0203024223446846,
-0.010277736000716686,
-0.0249642264097929,
-0.01768711768090725,
0.07252844423055649,
-0.046348586678504944,
-0.030106356367468834,
0.012345612980425358,
0.032051436603069305,
0.05455401539802551,
-0.036298349499702454,
-0.056075070053339005,
-0.034723181277513504,
-0.063287653028965,
0.06588579714298248,
-0.011983349919319153,
-0.00475451722741127,
0.024832306429743767,
0.07673719525337219,
-0.01793421246111393,
-0.011513150297105312,
-0.02296529896557331,
-0.004964214749634266,
-0.005198467988520861,
-0.02834954485297203,
-0.03241322562098503,
0.012543167918920517,
0.017618414014577866,
-0.05380239337682724,
-0.0014541378477588296,
-0.03842959180474281,
-0.04031718522310257,
0.045970797538757324,
-0.01759161427617073,
-0.007551831193268299,
0.030680106952786446,
0.0264767836779356,
0.0021282616071403027,
-0.017234912142157555,
-0.00485519552603364,
-0.05825240537524223,
0.05679592862725258,
0.019284771755337715,
-0.03243657574057579,
0.04699791967868805,
0.017325829714536667,
0.016551969572901726,
0.018474500626325607,
-0.027295023202896118,
-0.032511964440345764,
-0.04417795315384865,
-0.019812440499663353,
-0.013302024453878403,
0.003651749575510621,
0.01797366701066494,
-0.01081801112741232,
-0.009909246116876602,
-0.025842517614364624,
-0.07711678743362427,
-0.005969909951090813,
0.062024232000112534,
-0.008518101647496223,
-0.08770214766263962,
-0.042002007365226746,
-0.010833733715116978,
-0.002067441353574395,
-0.011779000982642174,
0.025397535413503647,
-0.02508709393441677,
-0.006461494602262974,
-0.01059217844158411,
-0.01814490742981434,
-0.007275703828781843,
0.020497392863035202,
-0.0647379606962204,
0.046314697712659836,
-0.024159297347068787,
0.03152858093380928,
-0.03892901539802551,
0.042605090886354446,
-0.019202278926968575,
0.04845869541168213,
-0.005748939234763384,
0.04365978017449379,
-0.01975122280418873,
0.031931910663843155,
0.014072097837924957,
-0.0034981141798198223,
0.07470609992742538,
-0.024975640699267387,
-0.017571203410625458,
0.09001895040273666,
-0.0408833846449852,
-0.03457384184002876,
0.04792005568742752,
-0.016767900437116623,
-0.02645941823720932,
0.019258365035057068,
-0.02298559807240963,
-0.03655967488884926,
-0.0030098725110292435,
0.005999058019369841,
0.04307576268911362,
-0.021886516362428665,
0.03513141721487045,
-0.004935163073241711,
-0.0007270649075508118,
-0.030798306688666344,
-0.03509007394313812,
0.022348584607243538,
-0.001042426098138094,
-0.016031840816140175,
0.008303324691951275,
-0.03882276266813278,
0.006908958312124014,
-0.0014481424586847425,
-0.03976232931017876,
0.04462248831987381,
-0.06526488065719604,
0.04971536993980408,
0.0280567929148674,
0.12373950332403183,
-0.05939135700464249,
0.021944411098957062,
-0.0027628373354673386,
-0.03311292082071304,
0.01992236264050007,
0.019457293674349785,
0.03514016419649124,
-0.059695202857255936,
-0.002828324679285288,
-0.03213117644190788,
-0.0014230194501578808,
-0.07117567956447601,
0.007515416014939547,
-0.040139034390449524,
-0.12632176280021667,
-0.006288554519414902,
-0.05182904750108719,
-0.007479408755898476,
0.049339283257722855,
-0.008548618294298649,
0.02485939860343933,
0.046064577996730804,
-0.09713443368673325,
0.022308390587568283,
0.03528563305735588,
0.0008507796446792781,
0.006256739143282175,
0.0572921447455883,
0.01431724801659584,
-0.0018168198876082897,
-0.00439807353541255,
0.008595961146056652,
-0.05079711973667145,
0.08450111001729965,
0.03942913934588432,
0.0013291429495438933,
0.06256286054849625,
-0.040003109723329544,
0.034674741327762604,
0.06797633320093155,
0.10403947532176971,
-0.001637256471440196,
-0.048994001001119614,
0.0010120407678186893,
0.068841852247715,
0.010972363874316216,
0.0353202298283577,
-0.02278738282620907,
0.006609566975384951,
0.0345107801258564,
0.04811903461813927,
0.025278162211179733,
-0.007656244095414877,
-0.03300175070762634,
-0.07019315659999847,
-0.028665348887443542,
0.04696248471736908,
-0.010569368489086628,
0.016228538006544113,
-0.02147289738059044,
-0.03667667135596275,
0.0037971879355609417,
0.008052149787545204,
-0.020016832277178764,
0.026560019701719284,
0.027004774659872055,
0.004341697786003351,
-0.0023579043336212635,
0.03644826263189316,
-0.00306826364248991,
0.04043376445770264,
0.003350494196638465,
0.030940962955355644,
0.054517097771167755,
-0.032250192016363144,
-0.02496740221977234,
-0.011188337579369545,
-0.024894898757338524,
0.028356876224279404,
-0.017572779208421707,
-0.0382128544151783,
-0.018947815522551537,
-0.031056052073836327,
-0.04367990046739578,
-0.006109064910560846,
-0.04106109216809273,
0.032044392079114914,
0.023481804877519608,
-0.04830466955900192,
0.003985289949923754,
-0.025196734815835953,
-0.06494838744401932,
0.007069836836308241,
-0.016474036499857903,
-0.013580922968685627,
-0.02886083908379078,
0.016222011297941208,
-0.032874178141355515,
0.01276638638228178,
0.06370387226343155,
-0.00336317322216928,
-0.02524876780807972,
-0.007875718176364899,
-0.00045722335926257074,
-0.024072326719760895,
0.03046313486993313,
-0.0056321462616324425,
0.020895259454846382,
0.010862368158996105,
0.032734815031290054,
0.013443060219287872,
-0.0017685429193079472,
-0.0012999954633414745,
0.06525310128927231,
-0.026956219226121902,
-0.01743646338582039,
0.040206968784332275,
-0.020195141434669495,
0.040105048567056656,
-0.023178212344646454,
0.0022101830691099167,
-0.03506392240524292,
-0.013390845619142056,
0.0010202217381447554,
-0.010977819561958313,
0.03384540602564812,
0.027278661727905273,
0.0004035515303257853,
0.05022037774324417,
0.002602699911221862,
0.03286058083176613,
-0.04809486120939255,
0.06381193548440933,
-0.025997748598456383,
-0.05248115584254265,
0.029561839997768402,
-0.045122452080249786,
-0.05830642580986023,
-0.01990867592394352,
-0.017728211358189583,
-0.03661945462226868,
-0.08253603428602219,
0.01054613757878542,
-0.02273530885577202,
0.005295588169246912,
0.0007100525544956326,
-0.004460781347006559,
0.09592678397893906,
-0.05051621049642563,
-0.005855710711330175,
0.06628841906785965,
0.0048010204918682575,
0.039725612848997116,
-0.0012682288652285933,
-0.0193299800157547,
-0.02146909572184086,
-0.0452820286154747,
0.004066502675414085,
0.004801964852958918,
-0.0006006424664519727,
-0.010646347887814045,
0.01180306263267994,
0.03525503724813461,
-0.047777313739061356,
0.01267204713076353,
0.008972126990556717,
0.03624000400304794,
-0.03282640129327774,
0.021219875663518906,
-0.00006615086749661714,
0.006193442735821009,
-0.03025653213262558,
-0.043364427983760834,
0.010188700631260872,
-0.04426146298646927,
0.04217161610722542,
-0.0146341472864151,
0.01282410603016615,
-0.007321543525904417,
0.006671737413853407,
0.03569165989756584,
-0.02151511237025261,
0.013035186566412449,
0.02445046603679657,
-0.03712756186723709,
0.002967446343973279,
0.001125389477238059,
-0.019018804654479027,
-0.014187430962920189,
-0.05614480376243591,
0.002393047558143735,
0.004278119653463364,
0.01914907991886139,
0.05873802676796913,
0.0728449746966362,
-0.05530693754553795,
-0.021024027839303017,
-0.03437357395887375,
0.038536760956048965,
-0.02403424121439457,
0.007058408111333847,
0.026566598564386368,
0.0013022293569520116,
0.07662693411111832,
0.018217355012893677,
0.06676016747951508,
0.023470040410757065,
-0.04208730161190033,
-0.020875822752714157,
-0.0026572574861347675,
-0.007373780477792025,
0.027237433940172195,
-0.040947623550891876,
0.021574145182967186,
-0.05182194337248802,
0.015071781352162361,
0.05677041411399841,
0.032255128026008606,
0.0456882007420063,
0.015533394180238247,
-0.03850267454981804,
0.01357289869338274,
-0.021817250177264214,
-0.0496077686548233,
-0.005638721864670515,
0.048392001539468765,
-0.02089550532400608,
-0.06954795122146606,
-0.002926525892689824,
-0.05483610928058624,
0.02168823406100273,
0.05488424375653267,
-0.06039843708276749,
-0.031076448038220406,
-0.07139464467763901,
-0.006872972939163446,
0.04962477460503578,
0.004565704148262739,
-0.061078380793333054,
-0.05079158768057823,
0.016178743913769722,
-0.04875703901052475,
0.020387019962072372,
0.008499400690197945,
0.01690593734383583,
-0.000639854755718261,
0.02478865720331669,
-0.03426518663764,
-0.013185598887503147,
0.014111513271927834,
-0.0016248465981334448,
0.03542385995388031,
0.04499023035168648,
-0.027752600610256195,
-0.017722446471452713,
0.0018051682272925973,
-0.03014451451599598,
-0.047095902264118195,
0.037141911685466766,
0.05548182129859924,
0.00849662534892559,
0.02429955266416073,
-0.017110217362642288,
0.009270783513784409,
0.020026467740535736,
0.003411714220419526,
-0.051982682198286057,
-0.021604904904961586,
0.08113747090101242,
0.05225100368261337,
-0.020190317183732986,
0.002887321636080742,
-0.01580834574997425,
0.03664150834083557,
-0.018684474751353264,
0.02568080462515354,
0.04826325550675392,
0.05674735829234123,
-0.06361089646816254,
-0.01094446424394846,
-0.031884487718343735,
0.031784381717443466,
0.003159316722303629,
0.056188736110925674,
0.006229948252439499,
0.01139840018004179,
-0.01932959072291851,
-0.01859443262219429,
0.0274773258715868,
-0.018864372745156288,
-0.044750869274139404,
0.031324028968811035,
0.025715284049510956,
0.06608057767152786,
-0.009753492660820484,
0.030150962993502617,
0.016217878088355064,
0.0010794083354994655,
-0.0013821612810716033,
0.005437243264168501,
-0.002158030867576599,
0.04581020399928093,
-0.018235400319099426,
-0.08785548806190491,
-0.021831918507814407,
0.001993553014472127,
-0.04455511271953583,
0.02039751037955284,
0.07915706187486649,
0.0006765890284441411,
0.00966808944940567,
-0.06427790969610214,
0.0016218482051044703,
0.02093825489282608,
0.015930604189634323,
0.0796625018119812,
0.05871891230344772,
0.00247713434509933,
-0.02917330525815487,
-0.022493598982691765,
0.05144721642136574,
-0.018067263066768646,
-0.03092075139284134,
0.0721794068813324,
0.0049766721203923225,
0.016678182408213615,
-0.01644405536353588,
0.012984104454517365,
-0.008022475987672806,
0.053091272711753845,
0.04976029694080353,
-0.04199448972940445,
-0.0274067185819149,
0.04028854891657829,
0.047921836376190186,
-0.03657989948987961,
-0.020936835557222366,
-0.003228041110560298,
-0.010155308060348034,
-0.003427107585594058,
-0.01690950058400631,
-0.027158770710229874,
-0.00714805768802762,
0.005068277940154076,
0.007680665701627731,
-0.005847376771271229,
0.05529752001166344,
-0.0071502267383039,
0.041238099336624146,
-0.019087165594100952,
-0.0057454598136246204,
-0.04578227177262306,
0.056369636207818985,
-0.04049873724579811,
0.010804657824337482,
-0.006581291556358337,
0.03612975776195526,
-0.021349864080548286,
-0.045548561960458755,
-0.015761425718665123,
-0.0292313564568758,
-0.015123055316507816,
-0.005324272438883781,
-0.03178808093070984,
0.0011098639806732535,
0.05851408839225769,
0.015287752263247967,
-0.04520735517144203,
0.002988810883834958,
-0.041843000799417496,
0.04276495799422264,
-0.011549683287739754,
0.004377600271254778,
0.06869792938232422,
0.046183355152606964,
0.03134097903966904,
-0.018374623730778694,
-0.004992710892111063,
0.0271404217928648,
-0.028048815205693245,
0.040062569081783295,
-0.0029596583917737007,
-0.013356098905205727,
0.014821652323007584,
-0.03396688029170036,
-0.014889628626406193,
-0.02035280503332615,
-0.03244643285870552,
0.036358676850795746,
-0.031081121414899826,
-0.010201581753790379,
-0.045622147619724274,
-0.015870351344347,
-0.02280462719500065,
0.03898914158344269,
-0.014269544743001461,
-0.006846172735095024,
-0.03992975875735283,
-0.02117316424846649,
0.004527076613157988,
0.050637517124414444,
0.038527753204107285,
0.02762134186923504,
-0.0519743338227272,
-0.04076416417956352,
0.0335233174264431,
-0.028916457667946815,
-0.0021527318749576807,
-0.025833653286099434,
-0.0033010211773216724,
-0.0002907465968746692,
-0.02251460775732994,
0.0032742947805672884,
-0.017693309113383293,
0.045039188116788864,
0.0526006817817688,
-0.06799445301294327,
0.0012540004681795835,
-0.04148915410041809,
0.0005242135957814753,
-0.07635143399238586,
-0.002933662151917815,
-0.0007098467322066426,
-0.02635050006210804,
-0.0335734598338604,
0.011472305282950401,
0.0030337534844875336,
0.0282933060079813,
-0.05531761050224304,
-0.05105259269475937,
0.03115246631205082,
0.0472969114780426,
0.0032017563935369253,
-0.09383515268564224,
-0.005092571023851633,
0.001739058643579483,
0.00958937220275402,
-0.023633530363440514,
0.05142444744706154,
-0.007502109277993441,
-0.044648073613643646,
-0.005642380099743605,
0.07207000255584717,
-0.010256686247885227,
0.05642775818705559,
0.04572663456201553,
-0.05783461779356003,
-0.021295908838510513,
-0.03078744001686573,
0.013791567645967007,
-0.06024227291345596,
-0.02702927030622959,
0.0014457013458013535,
-0.011918404139578342,
-0.04876654967665672,
-0.04261007159948349
] |
<p>Linear antenna directed along z, photons (EM waves) propagate along x. Momentum of photons have only x component. Why electrons in antenna have z component of momentum?</p>
|
g2510
|
[
-0.016688866540789604,
-0.02582172304391861,
-0.01462096069008112,
0.012837236747145653,
0.05561531335115433,
0.03855887055397034,
0.07079451531171799,
0.03987664729356766,
0.03907575458288193,
-0.03725674748420715,
0.04943312332034111,
0.05988417565822601,
0.014525598846375942,
-0.013059329241514206,
-0.034365564584732056,
-0.028362592682242393,
0.08166144788265228,
0.07566885650157928,
0.019764110445976257,
0.019515343010425568,
0.030657369643449783,
0.017054783180356026,
-0.0060515133664011955,
-0.05108719691634178,
0.00036474879016168416,
0.02134154550731182,
0.003038169117644429,
-0.02181125245988369,
-0.02558877505362034,
-0.02028135396540165,
0.03874282166361809,
-0.0013080406934022903,
0.025267496705055237,
-0.0154371727257967,
-0.06246563792228699,
-0.05558456853032112,
0.009694241918623447,
0.039218783378601074,
0.006239797919988632,
0.03469531238079071,
-0.038158118724823,
-0.040913429111242294,
-0.07846364378929138,
0.015316377393901348,
0.007418774999678135,
-0.004693426191806793,
-0.005206996574997902,
0.036520570516586304,
-0.0025732750073075294,
-0.05592444911599159,
-0.034618034958839417,
0.021619869396090508,
0.023130444809794426,
-0.017953144386410713,
0.035778507590293884,
0.01811210624873638,
-0.02867877669632435,
0.0053523266687989235,
0.08843649923801422,
0.043626077473163605,
0.008001045323908329,
0.02498943917453289,
-0.03761571645736694,
0.010416468605399132,
0.027668233960866928,
-0.012256556190550327,
-0.02080342173576355,
-0.043092697858810425,
-0.04540707543492317,
-0.008500961586833,
0.02310904674232006,
-0.05053574591875076,
-0.017481455579400063,
-0.01691577024757862,
0.01800079457461834,
0.008003543131053448,
-0.058954160660505295,
-0.02309240587055683,
-0.022297857329249382,
0.03425487503409386,
-0.008162185549736023,
-0.018098026514053345,
0.04203513264656067,
-0.020068515092134476,
0.07288604974746704,
0.031735967844724655,
0.019428675994277,
-0.021709103137254715,
-0.06886202841997147,
-0.09741638600826263,
0.059771038591861725,
-0.02281065471470356,
0.007089332211762667,
0.049892961978912354,
-0.017507554963231087,
-0.04819341376423836,
-0.05113068222999573,
0.013770237565040588,
0.05793687701225281,
-0.04869624972343445,
0.021358752623200417,
0.066156305372715,
-0.03151288256049156,
0.039331987500190735,
0.01075145322829485,
-0.06352382153272629,
-0.03141575679183006,
-0.020681126043200493,
0.0022239438258111477,
0.0023335451260209084,
-0.015969276428222656,
-0.024304276332259178,
-0.05728532746434212,
-0.0460880808532238,
-0.012778985314071178,
0.003184852423146367,
0.09640657901763916,
-0.07516007125377655,
0.010378154926002026,
0.026594413444399834,
0.026318680495023727,
-0.026167938485741615,
-0.005775136407464743,
0.04597127065062523,
-0.015312675386667252,
0.04664504900574684,
0.029812807217240334,
0.009158090688288212,
0.02632424794137478,
0.006935672834515572,
-0.0013595883501693606,
0.006936810910701752,
-0.049594681710004807,
-0.02032635547220707,
-0.014299741946160793,
-0.07317910343408585,
-0.01909480430185795,
0.008488720282912254,
-0.02501298300921917,
0.03663640841841698,
0.014524471946060658,
-0.0347195528447628,
0.03002002462744713,
-0.09872271865606308,
-0.0032966388389468193,
-0.02160702273249626,
-0.02892821654677391,
-0.001775974640622735,
0.03774035722017288,
0.018100770190358162,
-0.00495330523699522,
0.03488646075129509,
-0.006756230257451534,
-0.04949794337153435,
0.010653022676706314,
-0.04066448286175728,
0.06367264688014984,
-0.02281215973198414,
0.007976217195391655,
0.019200190901756287,
0.007902293466031551,
0.05144113674759865,
0.04253438115119934,
-0.029188403859734535,
-0.01980319805443287,
-0.042830463498830795,
-0.03488690033555031,
-0.08578699827194214,
-0.03468294441699982,
0.009579060599207878,
0.010249076411128044,
-0.030969426035881042,
-0.021597174927592278,
-0.025050412863492966,
0.015389428474009037,
0.08577366918325424,
-0.005366113502532244,
0.024533724412322044,
0.07970921695232391,
-0.008626655675470829,
-0.03973422944545746,
-0.005348037462681532,
0.036967162042856216,
0.03074074722826481,
0.024384034797549248,
-0.014146331697702408,
-0.02027936838567257,
0.06866733729839325,
-0.07356487959623337,
-0.04853544011712074,
0.011604984290897846,
0.04517299681901932,
-0.012032650411128998,
0.042749885469675064,
-0.02767859399318695,
-0.04437395930290222,
0.0009035179973579943,
-0.023915648460388184,
0.0112924100831151,
0.04736154153943062,
0.024435512721538544,
0.029362628236413002,
0.010514909401535988,
0.01159972045570612,
0.03966343775391579,
-0.07220561802387238,
-0.029363399371504784,
-0.006825719494372606,
0.02020740881562233,
-0.020876707509160042,
0.046234484761953354,
-0.056517187505960464,
0.0012270280858501792,
0.015406414866447449,
0.01413433812558651,
-0.08375340700149536,
0.01470994297415018,
0.037166010588407516,
-0.005134739447385073,
0.01865043304860592,
-0.04695063829421997,
-0.035109102725982666,
-0.010536928661167622,
-0.03634871914982796,
-0.0555337518453598,
0.025271495804190636,
0.023742878809571266,
-0.018071195110678673,
-0.0035601910203695297,
0.06569621711969376,
-0.0009159734472632408,
0.033318232744932175,
0.012047155760228634,
-0.012237057089805603,
0.033223506063222885,
-0.027854084968566895,
0.00003709015072672628,
0.038696955889463425,
0.0015153426211327314,
-0.02266843058168888,
0.006623799446970224,
0.05299517512321472,
0.020587073639035225,
-0.00532385241240263,
0.04710915684700012,
-0.029027307406067848,
0.04831033572554588,
0.0073542604222893715,
-0.030737480148673058,
-0.02486310340464115,
0.04011329635977745,
-0.021794883534312248,
-0.005014575086534023,
0.03100091777741909,
-0.03839236497879028,
-0.08647594600915909,
-0.017367130145430565,
0.026895659044384956,
-0.05613906309008598,
-0.003986729774624109,
-0.019844451919198036,
0.02086653932929039,
-0.03547282516956329,
-0.02713426947593689,
-0.05792822688817978,
0.012633739970624447,
-0.017454279586672783,
0.015086033381521702,
-0.008982973173260689,
-0.020554939284920692,
-0.029977459460496902,
0.05218745395541191,
0.006778657902032137,
0.024906190112233162,
0.04060275852680206,
-0.04967240244150162,
0.025702066719532013,
-0.02696261741220951,
-0.015173902735114098,
-0.06351925432682037,
0.03176869451999664,
0.039578940719366074,
0.0017948686145246029,
-0.025444602593779564,
0.025817206129431725,
-0.06447816640138626,
0.03004768118262291,
-0.018136367201805115,
-0.03945477306842804,
0.011383767239749432,
-0.07153412699699402,
-0.019726643338799477,
0.0392027422785759,
-0.042735755443573,
0.013447069562971592,
0.016878021880984306,
0.10229694098234177,
-0.02703983522951603,
-0.0340624637901783,
0.032511621713638306,
0.021105477586388588,
-0.00385696510784328,
0.02037298120558262,
-0.06745056062936783,
0.08636253327131271,
0.05648694187402725,
-0.03576679527759552,
-0.0058447918854653835,
0.016460824757814407,
0.0028741543646901846,
0.009407663717865944,
0.03966257721185684,
-0.002863003173843026,
0.012902365997433662,
-0.02393164671957493,
0.02586078643798828,
-0.05379026010632515,
0.002733809407800436,
-0.036123715341091156,
0.03132441267371178,
-0.020004035905003548,
-0.021610302850604057,
0.011864492669701576,
-0.031234486028552055,
0.02848161570727825,
0.008598420768976212,
-0.01156551018357277,
0.033169716596603394,
0.004160773474723101,
0.008797664195299149,
0.00975519698113203,
0.01450661476701498,
0.0013349571963772178,
0.03229158744215965,
0.06755688041448593,
-0.028378253802657127,
-0.03849244862794876,
0.051156651228666306,
-0.004403508733958006,
-0.030008986592292786,
-0.003886530641466379,
-0.004755042493343353,
-0.04869484528899193,
-0.007168247830122709,
0.007012707181274891,
0.007834560237824917,
0.008047367446124554,
0.00958262849599123,
0.005894368514418602,
-0.024263253435492516,
-0.050893139094114304,
-0.013590284623205662,
0.007688697427511215,
0.016414590179920197,
-0.0628884881734848,
0.05583995580673218,
0.03597958758473396,
-0.046376802027225494,
0.03738372400403023,
-0.010852755978703499,
0.01201184093952179,
0.003537149168550968,
0.02514474466443062,
-0.03337163105607033,
-0.02516215667128563,
0.04357821121811867,
-0.011475238017737865,
0.06803751736879349,
0.0009886885527521372,
-0.006384182721376419,
-0.01966988667845726,
-0.07985398918390274,
-0.0343826487660408,
-0.006514302454888821,
-0.039920710027217865,
-0.04942293465137482,
-0.0134136276319623,
0.007785771507769823,
-0.03476967290043831,
0.00925374310463667,
-0.03092006780207157,
0.007100943475961685,
0.03957825154066086,
0.021956877782940865,
0.02172909490764141,
-0.026799414306879044,
0.02520676515996456,
0.054510701447725296,
0.011002223938703537,
0.02242892049252987,
0.039596524089574814,
-0.03626855090260506,
0.04606258124113083,
0.0330619290471077,
0.020326076075434685,
-0.04022509604692459,
0.005809563212096691,
-0.031368911266326904,
0.05143023654818535,
0.02049889974296093,
0.01421789824962616,
0.04044555127620697,
0.007259911857545376,
0.007925506681203842,
0.02249322272837162,
0.08519017696380615,
0.026759032160043716,
-0.012492534704506397,
-0.015088199637830257,
-0.04986674338579178,
0.02702094428241253,
0.05259064957499504,
0.07601134479045868,
-0.006050954572856426,
-0.018716320395469666,
0.01304850447922945,
-0.0007921851356513798,
-0.02944904938340187,
0.02118535339832306,
-0.018762726336717606,
0.046293262392282486,
0.07042939960956573,
0.022229596972465515,
-0.009956995956599712,
-0.0025691946502774954,
0.05090368539094925,
0.037463199347257614,
0.009504502639174461,
-0.01988348364830017,
0.001336679677478969,
-0.004043271765112877,
0.021658405661582947,
0.017581190913915634,
0.013929611071944237,
-0.04263313114643097,
0.007983909919857979,
-0.005801382940262556,
0.021067684516310692,
0.06385789811611176,
0.05627372860908508,
0.1167517900466919,
-0.041285790503025055,
0.0066413492895662785,
-0.028140049427747726,
-0.023063136264681816,
0.05801910161972046,
0.026547718793153763,
-0.012709592469036579,
-0.06786758452653885,
0.058458685874938965,
-0.004411187022924423,
0.03063913621008396,
-0.0173097662627697,
-0.06390979140996933,
0.038542427122592926,
0.029738664627075195,
-0.006350223440676928,
-0.007330665364861488,
0.04262498393654823,
0.017902186140418053,
-0.042539082467556,
-0.02310960926115513,
-0.023161916062235832,
0.01035682950168848,
0.06775450706481934,
-0.028497228398919106,
-0.0346013642847538,
0.00046402550651691854,
-0.050106413662433624,
0.0011042180703952909,
0.050973162055015564,
0.04040413722395897,
0.03338455408811569,
0.03878885507583618,
0.02550334669649601,
-0.03021162934601307,
-0.06873264908790588,
-0.036103904247283936,
-0.06962525844573975,
-0.007630727719515562,
-0.0413726270198822,
-0.06350819766521454,
-0.031128227710723877,
-0.05047036334872246,
-0.011998926289379597,
-0.0742056593298912,
-0.04397232085466385,
0.0431734099984169,
0.021039383485913277,
-0.05945057421922684,
-0.018154283985495567,
-0.016263294965028763,
-0.06684292107820511,
-0.0743463858962059,
-0.033238887786865234,
0.0004078074707649648,
-0.03953750804066658,
-0.0029511789325624704,
0.03545157238841057,
-0.014909736812114716,
0.015554358251392841,
-0.008210083469748497,
-0.037301111966371536,
0.02840922400355339,
-0.02718324400484562,
-0.0026945460122078657,
0.051635149866342545,
-0.012086765840649605,
-0.03434087708592415,
0.02729261852800846,
-0.016644850373268127,
0.0037247524596750736,
0.03886723890900612,
-0.02848227322101593,
0.011974651366472244,
-0.04751436784863472,
-0.03541237860918045,
0.00938295666128397,
-0.012735393829643726,
0.020970961079001427,
0.040181078016757965,
-0.002521473215892911,
-0.004915586672723293,
-0.08490633964538574,
0.044846951961517334,
0.006271533202379942,
-0.07837232202291489,
-0.03259088471531868,
0.015046847052872181,
0.025576403364539146,
0.06481440365314484,
0.038109343498945236,
0.03732758387923241,
-0.04999624937772751,
-0.006501717492938042,
-0.050335101783275604,
0.11839170008897781,
0.03478647768497467,
-0.03023608773946762,
-0.04273970052599907,
0.013691694475710392,
-0.06704361736774445,
0.055055540055036545,
0.08080100268125534,
0.010896444320678711,
-0.00029718890436924994,
0.008693791925907135,
-0.006480589974671602,
-0.007699033711105585,
-0.0478542260825634,
0.01572195068001747,
-0.023717474192380905,
0.01319046039134264,
0.012902035377919674,
-0.01910308562219143,
-0.003919127397239208,
-0.013200204819440842,
0.009157760068774223,
-0.03797687217593193,
-0.03371847793459892,
0.062396757304668427,
0.05575981363654137,
0.022817155346274376,
0.00033505281317047775,
-0.029883652925491333,
0.0017258318839594722,
-0.011300677433609962,
-0.014180578291416168,
0.0035098358057439327,
0.0333242304623127,
-0.015076165087521076,
0.010725305415689945,
-0.01589382253587246,
0.05767836794257164,
-0.0360201820731163,
0.02923320047557354,
0.028402486816048622,
-0.02882632613182068,
-0.09608747810125351,
-0.0020194395910948515,
0.03847791627049446,
0.031012210994958878,
-0.013331778347492218,
-0.03469492867588997,
-0.020846037194132805,
0.018893584609031677,
-0.06090440973639488,
-0.02502545155584812,
0.08097205311059952,
-0.009762930683791637,
-0.05248524993658066,
0.03936391323804855,
0.029843300580978394,
-0.015479737892746925,
-0.059689875692129135,
-0.02358080819249153,
0.028983214870095253,
0.000930401380173862,
0.026843030005693436,
0.042445167899131775,
0.02103813737630844,
-0.038476672023534775,
-0.024015460163354874,
0.05294543877243996,
0.043536700308322906,
0.0432153046131134,
0.037241529673337936,
-0.03895357996225357,
0.022742804139852524,
-0.00011746492964448407,
0.0058489288203418255,
0.01393552403897047,
0.02139962650835514,
-0.02429196797311306,
0.018621373921632767,
-0.022227667272090912,
-0.02415228635072708,
0.024418391287326813,
-0.03708867356181145,
0.022292915731668472,
-0.030317243188619614,
-0.008806710131466389,
-0.09431196004152298,
0.03273877874016762,
0.006699031684547663,
0.01803605444729328,
0.003779425984248519,
0.0855027288198471,
0.021249404177069664,
-0.011589308269321918,
-0.026537708938121796,
0.027476850897073746,
0.0018984404159709811,
-0.0390232652425766,
-0.032941125333309174,
0.029796168208122253,
0.023328006267547607,
0.013237114064395428,
-0.029094558209180832,
-0.0114371869713068,
0.035426583141088486,
0.06053543463349342,
0.03261918947100639,
-0.0016489808913320303,
-0.005786939058452845,
0.06180863454937935,
-0.0022511358838528395,
0.011527149006724358,
-0.04662613570690155,
-0.0049988445825874805,
-0.013318541459739208,
-0.026754230260849,
0.03066440299153328,
0.023200245574116707,
0.009661847725510597,
-0.01700627990067005,
0.01118427887558937,
0.015427596867084503,
0.023198416456580162,
-0.006313451565802097,
-0.08270807564258575,
-0.04387954995036125,
0.04532679170370102,
0.0015529812080785632,
-0.0001076850458048284,
0.0005618311697617173,
-0.004244912415742874,
-0.04234997555613518,
0.02042011171579361,
0.011078868061304092,
-0.041960716247558594,
-0.04471353814005852,
0.008343186229467392,
-0.04243374615907669,
-0.007928558625280857,
0.010139473713934422,
-0.027315886691212654,
-0.00815134309232235,
-0.026613693684339523,
0.03501944616436958,
0.011939645744860172,
0.03795896843075752,
-0.016983231529593468,
-0.054304108023643494,
0.006116279400885105,
-0.038322970271110535,
-0.010443311184644699,
-0.014161922037601471,
0.004355627112090588,
-0.02460486814379692,
0.004036095459014177,
0.02291245386004448,
0.0713919922709465,
-0.037349533289670944,
0.0018302049720659852,
0.051301922649145126,
-0.01734384521842003,
0.06301160156726837,
-0.015739211812615395,
0.018281126394867897,
0.00001202345265483018,
0.010862037539482117,
0.029348153620958328,
0.011722872965037823,
0.05630053952336311,
0.02961834892630577,
-0.00036072623333893716,
-0.04968014359474182,
-0.006161951459944248,
-0.04887780547142029,
-0.08018828183412552,
-0.003896851558238268,
0.028865672647953033,
-0.00682160584256053,
-0.007794373668730259,
0.09801846742630005,
0.012398923747241497,
0.06341277062892914,
-0.004553057253360748,
0.013225734233856201,
0.01430569775402546,
0.011151802726089954,
0.008833938278257847,
-0.007122145965695381,
-0.025898225605487823,
-0.05126068368554115,
0.022022005170583725,
0.000038404665247071534,
0.06179248169064522,
0.007172788958996534,
0.004776447545737028,
-0.02324903942644596,
-0.037881601601839066,
-0.027266494929790497,
-0.05059534311294556,
-0.03963261842727661,
-0.019759779796004295,
0.0356358103454113,
0.023371947929263115,
0.019371839240193367,
0.008786129765212536,
-0.0765877217054367,
-0.0021479721181094646,
-0.02925955504179001,
0.03286305442452431,
0.004893295932561159,
-0.022346897050738335,
-0.024580296128988266,
0.06619078665971756,
0.03805828467011452,
-0.058732595294713974,
-0.01221171673387289,
-0.0474509671330452,
0.04770416021347046,
0.011777572333812714,
0.010165054351091385,
-0.04669692739844322,
0.02350764535367489,
0.047821976244449615,
-0.026653140783309937,
0.007042411714792252,
0.035834234207868576,
0.02075621858239174,
-0.03901134058833122,
-0.040652111172676086,
-0.019206658005714417,
-0.05150710046291351,
0.04043081775307655
] |
<p>The rate at which time passes is relative depending on speed and the gravity as predicted in general relativity. This theory has been tested by scientists by comparing two identical atomic clocks, one on Earth the other on a rocket speeding at escape velocity. The initially synchronised clocks measured different amounts of time when the rocket returned. </p>
<p>Given the current scientific definition of time rate, </p>
<p>"The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom",</p>
<p>does this mean that 1) the above definition is only true on the surface of an object with Earths mass and 2) the fundamental properties of sub-atomic particles change on the speeding rocket so the rate at which electrons of the caesium 133 atom oscillate between the two energy levels is different?</p>
|
g2511
|
[
0.06215018033981323,
0.06948507577180862,
0.017505083233118057,
0.026428576558828354,
0.039336200803518295,
0.05926944687962532,
0.04964793473482132,
0.012217660434544086,
-0.012667783536016941,
0.020388701930642128,
0.05884502828121185,
0.0024577644653618336,
0.011253098025918007,
0.0013334915274754167,
0.015270539559423923,
-0.02026808075606823,
0.10603104531764984,
-0.05361885949969292,
0.027130160480737686,
0.058304186910390854,
0.04616689309477806,
0.03650708124041557,
-0.05547794699668884,
-0.03021457977592945,
-0.012562373653054237,
-0.02986859902739525,
-0.01820191740989685,
-0.037771064788103104,
-0.06300704926252365,
0.004848314914852381,
0.019643394276499748,
-0.04395211860537529,
0.03452536463737488,
-0.012379560619592667,
0.03374013304710388,
-0.042273059487342834,
-0.0006819246336817741,
0.042165596038103104,
-0.00042407994624227285,
0.0062070428393781185,
0.01644500344991684,
0.009370879270136356,
-0.00820920616388321,
-0.06392274051904678,
0.04999750852584839,
-0.0006393959047272801,
-0.03358830511569977,
-0.019016219303011894,
0.03662868216633797,
-0.015359868295490742,
-0.01312074065208435,
0.08562914282083511,
-0.017109740525484085,
0.015699636191129684,
-0.03329453989863396,
-0.014343908056616783,
0.02190772257745266,
-0.024745335802435875,
0.07154161483049393,
0.03289632499217987,
0.02621559612452984,
-0.02326708287000656,
0.04124420881271362,
0.024398531764745712,
0.0755324438214302,
0.030602123588323593,
-0.04158039018511772,
0.013009504415094852,
0.03054722584784031,
0.003749180119484663,
-0.010663633234798908,
-0.0148319061845541,
-0.09666003286838531,
-0.04065684601664543,
-0.013998696580529213,
-0.02023233473300934,
0.012214958667755127,
-0.05031576752662659,
0.0033637313172221184,
0.03139251843094826,
-0.04084892198443413,
0.00766207417473197,
-0.015469257719814777,
0.05308644473552704,
0.07450632005929947,
-0.01937025971710682,
-0.02701244130730629,
0.0292873103171587,
0.018899552524089813,
0.003652973333373666,
-0.0038518146611750126,
-0.07187886536121368,
0.02996518835425377,
0.008685316890478134,
-0.048390891402959824,
-0.010676074773073196,
-0.03041931800544262,
0.0870734378695488,
-0.006739683914929628,
0.030186280608177185,
-0.025063395500183105,
-0.014482525177299976,
-0.0004735360271297395,
-0.02079158090054989,
0.003939520101994276,
-0.019380468875169754,
-0.050367262214422226,
-0.06444405019283295,
0.026819871738553047,
-0.025030385702848434,
0.030204875394701958,
-0.047043830156326294,
-0.004748247098177671,
0.03522029146552086,
0.015151681378483772,
-0.04976796731352806,
-0.0015312876785174012,
-0.06180331110954285,
-0.05714248865842819,
-0.013950655236840248,
0.017988288775086403,
0.04110601544380188,
-0.03736598789691925,
0.017098603770136833,
0.002981761936098337,
0.01975238509476185,
0.00922824814915657,
-0.05095050111413002,
-0.011784679256379604,
0.043787553906440735,
-0.025486450642347336,
-0.0006968790548853576,
0.016395261511206627,
0.034516505897045135,
-0.061594925820827484,
0.004809119272977114,
0.05693819001317024,
0.018951907753944397,
-0.007472477853298187,
-0.014269650913774967,
0.020920466631650925,
-0.04340430349111557,
0.04643457010388374,
-0.03226374089717865,
-0.03373861685395241,
0.05285593494772911,
-0.05368705466389656,
0.08624299615621567,
-0.009059533476829529,
-0.024319931864738464,
-0.01799600012600422,
0.053401969373226166,
0.037257783114910126,
-0.00522640673443675,
-0.030150102451443672,
0.003145860740914941,
-0.036924779415130615,
0.03404731675982475,
-0.03982742875814438,
0.06471497565507889,
0.06437105685472488,
-0.006389881484210491,
-0.0039626192301511765,
0.012517856433987617,
-0.036632638424634933,
0.033141449093818665,
0.025065956637263298,
-0.043411485850811005,
-0.021659070625901222,
-0.04153065383434296,
-0.05772336199879646,
-0.028631513938307762,
-0.0017407600535079837,
-0.006950384937226772,
-0.014390240423381329,
0.0014551541535183787,
0.0890798419713974,
-0.04605098441243172,
-0.027285730466246605,
-0.0094467643648386,
0.0016506622778251767,
-0.08707921952009201,
-0.043978095054626465,
-0.007330577354878187,
0.0034068007953464985,
-0.004813709296286106,
0.01444157026708126,
-0.009635944850742817,
-0.04188407585024834,
0.022884061560034752,
-0.01395940687507391,
-0.056388821452856064,
-0.01453439425677061,
-0.006305815652012825,
-0.03210765868425369,
-0.031960126012563705,
0.02611299604177475,
-0.0004169384192209691,
0.013025700114667416,
0.017855258658528328,
-0.026619721204042435,
0.02615109272301197,
0.010860628448426723,
-0.004282173700630665,
0.090178944170475,
-0.04186181351542473,
-0.02592424303293228,
0.010676763020455837,
0.06973027437925339,
0.03674401342868805,
0.0691281408071518,
0.03212296590209007,
0.028464272618293762,
0.023954050615429878,
-0.014327382668852806,
0.027751276269555092,
-0.0036644740030169487,
-0.006002576090395451,
0.018758410587906837,
0.040367238223552704,
0.017208945006132126,
0.0065185269340872765,
0.05665947124361992,
-0.027276135981082916,
0.012297829613089561,
-0.035312019288539886,
-0.04630344733595848,
-0.015407862141728401,
0.01793483830988407,
0.0038721661549061537,
-0.00283216149546206,
0.021664749830961227,
-0.04657779633998871,
-0.04130556061863899,
0.01700381189584732,
0.03644287958741188,
0.0012432035291567445,
-0.013131783343851566,
0.00475676916539669,
-0.026966677978634834,
0.017195820808410645,
-0.03159307688474655,
-0.0423571914434433,
-0.03855788707733154,
0.005302902311086655,
-0.07186855375766754,
0.01208842545747757,
-0.015552018769085407,
-0.006705319043248892,
-0.013037453405559063,
0.015148784033954144,
-0.053439002484083176,
-0.10493665188550949,
0.04114623740315437,
0.003067776095122099,
-0.01945592649281025,
-0.04645082727074623,
0.035794638097286224,
-0.08827400952577591,
-0.01524127833545208,
0.00046558791655115783,
-0.009609522297978401,
0.03899374231696129,
0.012126704677939415,
-0.04521160200238228,
-0.06277266889810562,
-0.015757838264107704,
0.07924564182758331,
0.002329417271539569,
-0.048254042863845825,
-0.03913039341568947,
-0.03613361716270447,
-0.030038004741072655,
0.048363663256168365,
-0.07725830376148224,
-0.024656588211655617,
0.02033184841275215,
-0.07541615515947342,
-0.021304786205291748,
0.03546689823269844,
-0.03813626244664192,
-0.015139274299144745,
-0.04538854956626892,
-0.002778406487777829,
0.03750943765044212,
-0.024421870708465576,
-0.024923056364059448,
0.02828395739197731,
0.001530757755972445,
0.04015519842505455,
-0.025723416358232498,
0.039726220071315765,
0.06431194394826889,
0.052816107869148254,
0.018618131056427956,
0.058133821934461594,
0.08323100209236145,
-0.008723550476133823,
-0.037889521569013596,
0.05519266054034233,
0.07720468938350677,
-0.04861367866396904,
-0.0048066540621221066,
0.03712783753871918,
-0.009461025707423687,
0.0004792246036231518,
-0.005687551107257605,
-0.012946097180247307,
0.0038559564854949713,
0.011228423565626144,
0.0057770307175815105,
0.017233703285455704,
0.054707080125808716,
-0.001901008072309196,
-0.0006975374417379498,
-0.0048082382418215275,
-0.05621717870235443,
0.04067316651344299,
0.0051373764872550964,
-0.012068976648151875,
0.006079091690480709,
0.040324609726667404,
-0.03584105893969536,
-0.021411854773759842,
-0.029266895726323128,
0.006450886372476816,
0.016435721889138222,
-0.014707347378134727,
-0.05541760474443436,
0.01064177043735981,
-0.015196576714515686,
0.04289792850613594,
-0.07216541469097137,
0.004235900938510895,
-0.04766667261719704,
0.02731751650571823,
0.01334358099848032,
0.02463477849960327,
0.009437997825443745,
0.04158037155866623,
0.030435416847467422,
0.05382464826107025,
-0.01763249933719635,
0.03133557364344597,
0.021399645134806633,
0.026689184829592705,
-0.0418778657913208,
0.012244975194334984,
-0.048318151384592056,
0.021102819591760635,
0.06024203449487686,
0.020294010639190674,
-0.002301865490153432,
0.0007412134436890483,
-0.023908143863081932,
0.05016789957880974,
-0.000005030957254348323,
0.033670324832201004,
-0.026492664590477943,
-0.024147503077983856,
0.034010183066129684,
-0.013067610561847687,
0.03993413224816322,
0.031253959983587265,
-0.0112473014742136,
0.02031368389725685,
-0.022930731996893883,
0.029740262776613235,
0.05537055805325508,
-0.022887244820594788,
-0.023479418829083443,
0.015948286280035973,
0.024098236113786697,
0.006133403163403273,
0.06670039892196655,
-0.05975686013698578,
0.06059422343969345,
-0.03875424340367317,
-0.06243915110826492,
-0.01559421420097351,
0.007260709069669247,
-0.024882638826966286,
-0.009120340459048748,
-0.02519083209335804,
0.05124760791659355,
-0.016177736222743988,
-0.032714344561100006,
-0.06399881094694138,
-0.025332575663924217,
-0.08065929263830185,
0.011879218742251396,
-0.022777128964662552,
-0.07023413479328156,
0.025557110086083412,
-0.0037205596454441547,
0.0025122500956058502,
0.007934142835438251,
0.021808627992868423,
0.0675521269440651,
0.020895246416330338,
0.0028333349619060755,
0.07363834977149963,
-0.06843387335538864,
-0.0107998326420784,
-0.01721970923244953,
0.033940430730581284,
0.0024382146075367928,
-0.04438149929046631,
-0.01053688209503889,
0.017929380759596825,
-0.014640321023762226,
0.012885205447673798,
-0.0645238533616066,
0.023700105026364326,
-0.03930722549557686,
-0.02942139096558094,
0.02020706981420517,
0.02272125892341137,
0.03619703650474548,
0.017122160643339157,
-0.0043197013437747955,
0.07773809880018234,
0.040107399225234985,
-0.04025210812687874,
0.02236533910036087,
0.03925883397459984,
0.06495441496372223,
0.06579872220754623,
0.0032905000261962414,
0.0015782777918502688,
0.048082903027534485,
0.029458921402692795,
-0.0054436661303043365,
0.06378234922885895,
-0.06421592086553574,
0.0622820146381855,
0.018245680257678032,
0.009337479248642921,
0.02836182340979576,
0.023776765912771225,
0.04794015362858772,
-0.009192810393869877,
-0.006207611411809921,
0.029926804825663567,
-0.03330927714705467,
0.07230520248413086,
-0.016276046633720398,
-0.08395329117774963,
0.016269057989120483,
-0.048094797879457474,
-0.0019562016241252422,
0.05981472507119179,
-0.027965690940618515,
0.03168720379471779,
-0.05595143884420395,
-0.07179833203554153,
-0.04205041751265526,
0.021753475069999695,
0.0417572446167469,
0.004613954108208418,
-0.08294826000928879,
0.036446381360292435,
0.025569550693035126,
-0.0023455482441931963,
-0.031129371374845505,
0.011133044958114624,
-0.04251130670309067,
-0.027055583894252777,
-0.03198320418596268,
-0.01679866760969162,
0.02520902082324028,
-0.08439120650291443,
0.003082695882767439,
0.015689095482230186,
0.0045824069529771805,
-0.03532915562391281,
0.023330433294177055,
0.014975360594689846,
0.023082103580236435,
-0.0166194885969162,
-0.06630793958902359,
0.007304718717932701,
-0.02116129733622074,
0.0038322105538100004,
0.006361319683492184,
0.012808066792786121,
-0.010259789414703846,
-0.007512738462537527,
0.007599471136927605,
-0.06125521659851074,
0.03731865808367729,
-0.02396995574235916,
0.004592070821672678,
-0.028594452887773514,
0.003730031894519925,
-0.0010030221892520785,
0.0501101054251194,
0.02414574660360813,
0.03461071848869324,
0.0034711554180830717,
-0.07286221534013748,
0.017686069011688232,
-0.009781848639249802,
0.010136078111827374,
-0.00483956653624773,
0.046011779457330704,
0.005178600084036589,
-0.00125251489225775,
0.003052819287404418,
0.01740110293030739,
-0.04694215580821037,
0.040697693824768066,
-0.03988875448703766,
0.0056861634366214275,
-0.02806161530315876,
-0.027803074568510056,
0.02935739792883396,
-0.011333851143717766,
0.03700322285294533,
-0.05022232234477997,
-0.030115166679024696,
0.015767676755785942,
0.10657364875078201,
0.06096487119793892,
0.04900031164288521,
-0.01176405418664217,
-0.04151270166039467,
0.014743680134415627,
-0.023968406021595,
0.031694453209638596,
-0.009518913924694061,
-0.02925948239862919,
-0.000885728164575994,
0.004417011048644781,
0.0010171668836846948,
-0.02173631452023983,
-0.006649666465818882,
-0.002850875724107027,
0.02683865837752819,
-0.0459519624710083,
-0.07843532413244247,
-0.00983628910034895,
0.005983364302664995,
0.02896103821694851,
-0.014402602799236774,
0.03276483342051506,
-0.08064081519842148,
0.011808134615421295,
0.022348638623952866,
-0.032505594193935394,
0.022567151114344597,
-0.013306490145623684,
0.003725160611793399,
0.016374431550502777,
0.013682237826287746,
0.10874197632074356,
0.03591509163379669,
0.018396755680441856,
-0.04191930964589119,
0.005924778059124947,
0.0042102281004190445,
0.047924041748046875,
0.10412583500146866,
0.014637235552072525,
0.017821038141846657,
-0.09467554837465286,
-0.008327668532729149,
-0.0597664937376976,
0.041168585419654846,
0.020845649763941765,
-0.016005270183086395,
-0.030612779781222343,
-0.015137760899960995,
-0.004813808482140303,
-0.037431586533784866,
-0.009921575896441936,
-0.01625208929181099,
-0.05693991854786873,
-0.072168730199337,
-0.031129993498325348,
0.030057381838560104,
-0.018760668113827705,
-0.02206459827721119,
-0.018321558833122253,
-0.037428323179483414,
-0.006343695800751448,
0.016169073060154915,
-0.01054808497428894,
-0.02689403109252453,
-0.07856478542089462,
0.0286061093211174,
-0.023281732574105263,
-0.02299697883427143,
-0.03777638077735901,
-0.054587025195360184,
0.0045453207567334175,
-0.04963025450706482,
-0.0257741529494524,
0.006467830389738083,
0.05865515395998955,
0.026351017877459526,
-0.040357090532779694,
0.007629010826349258,
0.005261920392513275,
0.053219690918922424,
0.02540195733308792,
-0.04798378422856331,
-0.022193221375346184,
0.04013575240969658,
0.0004822732589673251,
0.005950849037617445,
0.03090604394674301,
0.02589963935315609,
0.045456890016794205,
-0.04421784728765488,
0.01594197191298008,
0.020675750449299812,
0.032307423651218414,
0.015729058533906937,
-0.03536349534988403,
0.02822648175060749,
0.03148474916815758,
0.03552605211734772,
0.005775498691946268,
0.028741270303726196,
0.01277958508580923,
-0.009207434020936489,
0.002903550397604704,
0.03163855895400047,
-0.002442712429910898,
0.015978101640939713,
-0.04583677276968956,
-0.0162776131182909,
0.017481228336691856,
0.05064593255519867,
0.03196609765291214,
0.030799055472016335,
-0.0014581650029867887,
-0.008779916912317276,
-0.009797991253435612,
-0.023598216474056244,
0.018693028017878532,
0.018147200345993042,
0.005564686842262745,
-0.06932906806468964,
-0.02976602129638195,
0.053496986627578735,
-0.014200815930962563,
-0.020876655355095863,
-0.024823753163218498,
-0.0605812668800354,
-0.010504002682864666,
-0.05096687749028206,
0.05165237933397293,
0.05103130266070366,
-0.02730529010295868,
0.016921935603022575,
0.03639337047934532,
0.044589653611183167,
-0.06277146190404892,
-0.07173314690589905,
0.005243309773504734,
-0.019392119720578194,
0.002442397177219391,
-0.025052739307284355,
0.0382123626768589,
-0.029555488377809525,
-0.10009273886680603,
-0.02128486894071102,
-0.03377464413642883,
-0.004033769480884075,
0.023079339414834976,
0.021894000470638275,
0.009444231167435646,
-0.00827688816934824,
0.03970353677868843,
-0.050509292632341385,
-0.02496664971113205,
0.005440137814730406,
-0.020308177918195724,
0.005011397413909435,
0.0415063314139843,
-0.004265286959707737,
0.05853809043765068,
-0.03115146979689598,
0.04771783575415611,
-0.03003905713558197,
-0.020237958058714867,
-0.02196149155497551,
-0.052155155688524246,
0.02875593490898609,
0.03286353126168251,
0.022715739905834198,
0.0386836864054203,
0.01132279820740223,
-0.01735847443342209,
-0.0016669859178364277,
0.0376068651676178,
0.03004571609199047,
0.01965527981519699,
-0.02253204770386219,
0.04011058434844017,
0.02030276693403721,
0.023686211556196213,
-0.005016484297811985,
0.03765786066651344,
0.022508397698402405,
-0.0332152396440506,
-0.04825355112552643,
-0.04178373143076897,
0.009375769644975662,
0.027450745925307274,
0.04069468379020691,
0.0035444090608507395,
-0.004579775035381317,
-0.018056508153676987,
-0.04127346724271774,
-0.03408738225698471,
-0.003900340758264065,
-0.015137617476284504,
0.04012031480669975,
-0.07475221157073975,
0.0036178715527057648,
-0.05723179131746292,
0.02830428071320057,
0.00856543704867363,
0.01054784283041954,
-0.06939151138067245,
0.03798344358801842,
-0.03109312802553177,
0.02923651412129402,
0.014911167323589325,
0.010148282162845135,
0.02198309451341629,
-0.01680700294673443,
0.05226045101881027,
0.011375809088349342,
-0.02186061628162861,
-0.03753380477428436,
-0.0023677463177591562,
0.0046929470263421535,
-0.021683627739548683,
-0.018204161897301674,
0.04541843384504318,
0.010223019868135452,
-0.008767358027398586,
0.016549337655305862,
-0.007158563006669283,
-0.009206533432006836,
-0.030678866431117058,
0.030901949852705002,
0.02999930828809738,
-0.02118806540966034,
0.04376568645238876,
0.05341837927699089,
-0.02627181075513363,
0.007406212389469147,
-0.015260180458426476,
-0.02020462043583393,
-0.03529403358697891,
-0.0155870970338583,
0.025937648490071297,
0.02542179264128208,
-0.060320138931274414,
0.01593908853828907,
-0.06930248439311981,
0.006416057236492634,
-0.002197511726990342
] |
<p>I'm working on a research project involving absorption spectra of particulates in solution. I was curious if someone could clarify or direct me to a resource that explains broadening mechanisms <em>specifically</em> for absorption spectra. For example, the oft-cited Heisenberg and Doppler broadening effects both make sense to me in the context of emission spectra, but I don't see the mechanism by which they would be influential in absorption spectra. But I also can't find a source to verify this, since emission and absorption spectra are often lumped together in the familiar statement "the absorption spectrum is simply the inverse of the emission spectrum"</p>
<p>Thanks very much for any advice.</p>
|
g2512
|
[
0.01545181218534708,
0.02804686315357685,
0.004813484847545624,
0.0004776196728926152,
0.0021874154917895794,
0.08357912302017212,
0.0296770129352808,
0.05308115854859352,
0.015436223708093166,
-0.0006247124983929098,
0.0263105109333992,
-0.03201289847493172,
0.08200210332870483,
0.05689047649502754,
-0.027193421497941017,
-0.016436908394098282,
0.0725598931312561,
0.031197339296340942,
-0.028591981157660484,
0.05280128866434097,
-0.0198622178286314,
-0.020660748705267906,
-0.0691879540681839,
-0.048035748302936554,
-0.0920727476477623,
0.023788893595337868,
-0.025788074359297752,
0.02408129721879959,
0.05276298150420189,
-0.04917329549789429,
-0.05234285444021225,
-0.008723228238523006,
-0.021313076838850975,
0.046248000115156174,
0.02869098260998726,
0.001684946590103209,
0.05079428479075432,
0.03697415813803673,
-0.03196822479367256,
0.02867303043603897,
0.017144877463579178,
-0.01755034178495407,
0.03544066473841667,
0.06200674548745155,
-0.010242811404168606,
-0.0022841282188892365,
-0.0663089007139206,
0.01395449973642826,
0.011311566457152367,
-0.04537017270922661,
0.004042692948132753,
-0.023174380883574486,
0.015154539607465267,
0.010530699975788593,
0.002658956218510866,
-0.012558729387819767,
-0.023231234401464462,
-0.009059546515345573,
0.00977387372404337,
-0.006096330936998129,
0.004198748152703047,
0.03486527502536774,
-0.007432838436216116,
-0.0038963828701525927,
0.02052484080195427,
-0.017597775906324387,
-0.024060772731900215,
-0.027923105284571648,
0.00805758312344551,
-0.01556658186018467,
0.04130803793668747,
0.021351436153054237,
-0.11151046305894852,
-0.04140159860253334,
-0.02164153940975666,
-0.05597800016403198,
-0.04867279529571533,
0.021861257031559944,
0.046625662595033646,
-0.008434169925749302,
-0.013705383986234665,
0.011537346057593822,
-0.013545678928494453,
0.013513127341866493,
0.0518387071788311,
0.04422219470143318,
-0.03534067049622536,
0.006070879753679037,
0.00482881348580122,
-0.019278530031442642,
0.028694188222289085,
-0.0609346404671669,
0.025039367377758026,
-0.0391881987452507,
-0.01916131190955639,
-0.002246328629553318,
0.04411519318819046,
0.03682245314121246,
-0.039306651800870895,
0.009004996158182621,
-0.002281478838995099,
-0.011496352963149548,
-0.024657681584358215,
-0.004841457586735487,
0.018299613147974014,
0.04481545463204384,
0.057179391384124756,
0.0003223754174541682,
-0.0034641737584024668,
-0.012166477739810944,
-0.04132566228508949,
-0.029469741508364677,
-0.03285418823361397,
-0.018187863752245903,
-0.05102024972438812,
-0.0340455062687397,
0.055000584572553635,
0.03875935077667236,
-0.056154605001211166,
0.025837862864136696,
0.07912899553775787,
0.06004784628748894,
0.01061889249831438,
0.009865755215287209,
0.0007229059119708836,
0.015172593295574188,
0.011391200125217438,
0.01014329306781292,
0.006480166222900152,
0.026320084929466248,
0.02399170584976673,
-0.03125733882188797,
0.017729194834828377,
0.03856199234724045,
0.0038074480835348368,
0.023911375552415848,
-0.001749386196024716,
0.021096527576446533,
-0.005786143243312836,
-0.02947274222970009,
0.04443954676389694,
0.016537092626094818,
0.03221317008137703,
-0.0262615829706192,
-0.03379586711525917,
0.0016662322450429201,
-0.019092733040452003,
-0.03952648490667343,
0.024283969774842262,
-0.03275195136666298,
0.01687399484217167,
0.0480034202337265,
0.07761232554912567,
-0.04521246999502182,
0.047473836690187454,
-0.02157636545598507,
0.030258245766162872,
-0.04275115579366684,
0.018083801493048668,
0.0718463659286499,
-0.016960980370640755,
0.02074321173131466,
-0.0850183367729187,
0.007922669872641563,
-0.032272472977638245,
0.009324152022600174,
-0.0030393493361771107,
-0.06481252610683441,
-0.027483992278575897,
-0.03555731847882271,
0.006671924144029617,
-0.019897134974598885,
0.01966211572289467,
0.0865333303809166,
0.021565282717347145,
0.10154081881046295,
0.057777829468250275,
-0.0628228560090065,
0.007573344744741917,
0.055753063410520554,
-0.02853219024837017,
-0.026724370196461678,
-0.033230312168598175,
-0.054713815450668335,
0.057230882346630096,
-0.0017998159164562821,
0.029154818505048752,
0.013998416252434254,
-0.07924587279558182,
0.02361820638179779,
-0.0005012775072827935,
-0.03951134532690048,
-0.004916345700621605,
0.004110371228307486,
-0.03686537221074104,
-0.0416894368827343,
0.03669126704335213,
-0.035069793462753296,
-0.03980739414691925,
-0.01730319671332836,
-0.06210840865969658,
0.0158774983137846,
0.003391259117051959,
0.045061465352773666,
0.08757232129573822,
0.052624236792325974,
-0.021189207211136818,
-0.018197212368249893,
0.02583165094256401,
-0.014739076606929302,
-0.030604327097535133,
-0.013770139776170254,
0.06051851809024811,
0.009939554147422314,
0.02992383763194084,
0.02158210054039955,
-0.06009439006447792,
-0.0020650015212595463,
0.046716004610061646,
0.0597006119787693,
-0.046655211597681046,
-0.04802153632044792,
-0.041960638016462326,
0.015339072793722153,
-0.006096638739109039,
-0.010922325775027275,
0.010847902856767178,
-0.0005175225669518113,
-0.015288393013179302,
0.018083304166793823,
-0.0797160342335701,
-0.003233840921893716,
-0.02741166763007641,
-0.01939205639064312,
0.0559273436665535,
-0.03192101791501045,
0.020498139783740044,
-0.026865920051932335,
0.018724139779806137,
-0.0033522602170705795,
0.0011435486376285553,
-0.04178791120648384,
-0.002608638256788254,
-0.0149995731189847,
-0.007829435169696808,
-0.009637991897761822,
-0.006572252605110407,
-0.04147399589419365,
0.0003812869545072317,
-0.05934775620698929,
-0.014011676423251629,
-0.003641752991825342,
0.022939175367355347,
-0.002745971316471696,
0.012271764688193798,
-0.026363270357251167,
-0.03850948065519333,
0.05402587726712227,
0.0016050408594310284,
-0.04209833964705467,
-0.016817763447761536,
0.03997131437063217,
-0.0216620285063982,
0.011647572740912437,
-0.013992064632475376,
0.022642793133854866,
-0.033421386033296585,
-0.003766934387385845,
0.008937551639974117,
-0.005504540633410215,
0.022300099954009056,
0.02689887396991253,
-0.04174036905169487,
0.02458248846232891,
0.0230304766446352,
0.028834069147706032,
0.04098714515566826,
-0.022867271676659584,
0.06730716675519943,
0.005054275505244732,
-0.07207205146551132,
-0.08165013045072556,
-0.06747431308031082,
-0.04663311690092087,
0.06581626832485199,
0.04573945328593254,
0.012581543996930122,
0.02226148545742035,
-0.026421980932354927,
-0.009695135988295078,
-0.01693437620997429,
0.004785133991390467,
0.02348872274160385,
-0.009392214938998222,
-0.04001316800713539,
0.013973086141049862,
0.02722303569316864,
-0.03773811459541321,
-0.019795231521129608,
-0.0005280175828374922,
0.0009230210562236607,
0.013486846350133419,
0.012867460958659649,
0.007858780212700367,
0.013810278847813606,
0.008288273587822914,
-0.07767995446920395,
-0.02577454224228859,
0.02879878506064415,
0.05752061679959297,
-0.08002059906721115,
-0.03235812857747078,
-0.0162385031580925,
0.05420359596610069,
0.019673282280564308,
0.012959563173353672,
-0.07393234223127365,
-0.007918627932667732,
0.04170814901590347,
-0.028729217126965523,
-0.0025923261418938637,
-0.032817430794239044,
0.0005236275610513985,
-0.034749481827020645,
0.007107472978532314,
-0.0610470287501812,
-0.0016330467769876122,
-0.018001627177000046,
-0.02175617776811123,
-0.0032846590038388968,
-0.009919928386807442,
-0.0455615408718586,
0.021092921495437622,
-0.013184629380702972,
-0.028975777328014374,
-0.006224648095667362,
-0.03796539828181267,
0.005245176609605551,
0.01570919342339039,
0.020987560972571373,
0.04998417943716049,
-0.031230753287672997,
-0.05731944739818573,
-0.02857191488146782,
-0.0708153173327446,
-0.00497022969648242,
0.0011939076939597726,
0.01662532612681389,
-0.002700627548620105,
-0.05546724796295166,
0.036011770367622375,
0.020905038341879845,
-0.03720490261912346,
-0.01251212041825056,
-0.022655798122286797,
-0.02758212760090828,
0.056632839143276215,
0.01103273220360279,
0.053938128054142,
0.03582145646214485,
-0.017832020297646523,
-0.023100953549146652,
0.025601571425795555,
0.022574501112103462,
-0.016878630965948105,
0.025925474241375923,
0.05121912807226181,
0.02224159985780716,
0.020495178177952766,
0.015177684836089611,
-0.009624666534364223,
0.041053567081689835,
-0.04152993857860565,
0.022080563008785248,
-0.021010788157582283,
0.004358117002993822,
0.035638194531202316,
0.08069425076246262,
0.018571188673377037,
0.01656968519091606,
-0.014161608181893826,
0.030660653486847878,
-0.036876387894153595,
0.0436072014272213,
-0.022944113239645958,
-0.036566901952028275,
-0.045470286160707474,
0.06277822703123093,
-0.0357636958360672,
-0.016839327290654182,
0.02418999932706356,
-0.004814949352294207,
-0.04067658632993698,
0.009641028009355068,
0.004704610910266638,
-0.04198706895112991,
-0.06335780024528503,
-0.03258359059691429,
-0.005596050526946783,
0.09862632304430008,
0.020517999306321144,
0.019181281328201294,
-0.033838748931884766,
0.02177341654896736,
0.0037786890752613544,
0.04959624260663986,
0.020657282322645187,
-0.03385872021317482,
-0.05262640118598938,
-0.02542879618704319,
-0.00442975340411067,
0.03188334405422211,
-0.07201861590147018,
-0.021974198520183563,
0.005537764169275761,
0.051444243639707565,
-0.02289162576198578,
-0.07545936852693558,
0.03070487640798092,
-0.039811886847019196,
-0.034816157072782516,
-0.04054553434252739,
-0.015654008835554123,
0.04098368063569069,
-0.01965734176337719,
0.07648603618144989,
-0.03558957204222679,
0.013319602236151695,
0.026487154886126518,
-0.008644645102322102,
-0.00689898943528533,
-0.013151186518371105,
-0.02500489540398121,
-0.006528304889798164,
-0.040988072752952576,
0.03750431537628174,
0.003754277713596821,
0.017285369336605072,
-0.008348113857209682,
-0.02242051623761654,
0.06137245148420334,
0.005880472715944052,
0.005590996704995632,
-0.0008410972659476101,
-0.0046052406542003155,
0.026186851784586906,
-0.03676573187112808,
0.021722985431551933,
-0.001275614951737225,
0.025674698874354362,
0.032819993793964386,
0.03102078102529049,
-0.04840903356671333,
-0.054032567888498306,
-0.029820332303643227,
-0.011958510614931583,
0.04661551117897034,
0.02455180510878563,
0.05485489219427109,
0.011127772741019726,
-0.022540319710969925,
0.02747751586139202,
-0.0047238050028681755,
0.01418023556470871,
-0.0028937896713614464,
0.035994552075862885,
-0.01633336767554283,
0.05372925102710724,
-0.023711079731583595,
0.003979803528636694,
-0.04238080605864525,
-0.013883788138628006,
0.04862697795033455,
-0.04575212672352791,
0.05221160128712654,
-0.010426480323076248,
0.015617821365594864,
-0.07442758232355118,
0.03952166065573692,
-0.05124548077583313,
-0.01877151057124138,
-0.008041173219680786,
0.08197913318872452,
-0.0036055955570191145,
-0.04375096783041954,
0.07454786449670792,
-0.025923924520611763,
0.07179731130599976,
-0.018085673451423645,
-0.07842575758695602,
0.026915261521935463,
0.024198977276682854,
-0.036279112100601196,
-0.028520166873931885,
-0.05297328904271126,
0.013455159030854702,
0.0859479159116745,
-0.03739205375313759,
0.024457702413201332,
-0.012529456987977028,
0.017817353829741478,
-0.051184896379709244,
-0.008907441981136799,
0.059587154537439346,
-0.012144235894083977,
0.030764853581786156,
0.015475488267838955,
0.0024828300811350346,
0.010119209997355938,
-0.020900050178170204,
-0.007332615554332733,
0.006622390355914831,
-0.0359380729496479,
-0.005405917763710022,
-0.07761900871992111,
-0.0007269612979143858,
-0.028257662430405617,
0.03789210692048073,
-0.017545249313116074,
-0.016595978289842606,
-0.031391341239213943,
0.005810304079204798,
-0.02980906330049038,
0.04564351215958595,
0.03929681330919266,
-0.037628062069416046,
-0.031881608068943024,
0.022535407915711403,
0.06122506409883499,
-0.020409321412444115,
0.06790179014205933,
0.03629172593355179,
0.05036535486578941,
0.05093824490904808,
0.0815110057592392,
0.005045040976256132,
-0.012984270229935646,
-0.005279536359012127,
-0.015767903998494148,
0.060803767293691635,
-0.01141780149191618,
-0.006523380987346172,
0.01848931983113289,
0.02012685313820839,
0.015155071392655373,
-0.00430637551471591,
0.036212366074323654,
0.052757132798433304,
0.07583227008581161,
-0.035526011139154434,
-0.010747022926807404,
-0.04286092892289162,
0.025032587349414825,
-0.03184971958398819,
0.005038635339587927,
0.03527871146798134,
0.0016305206809192896,
0.030201740562915802,
0.04587991535663605,
0.006138873286545277,
0.05704275146126747,
0.0215248204767704,
-0.01986246556043625,
-0.04679840803146362,
0.023430094122886658,
-0.007105276454240084,
0.011454170569777489,
0.014310656115412712,
0.007499786093831062,
0.026023019105196,
-0.05539326369762421,
-0.04151580482721329,
0.03390006348490715,
-0.03646920621395111,
0.0052372911013662815,
0.0700768232345581,
0.0004024922091048211,
-0.04216863587498665,
-0.03829964995384216,
-0.030241558328270912,
0.005627249367535114,
-0.017775706946849823,
0.012267275713384151,
-0.017719492316246033,
-0.08223047852516174,
-0.06687058508396149,
-0.017046671360731125,
0.018732747063040733,
0.042701832950115204,
0.006968011613935232,
-0.011940023861825466,
0.006673127878457308,
-0.006027445662766695,
-0.06470206379890442,
0.006007000338286161,
-0.03312747925519943,
-0.036418892443180084,
0.022929714992642403,
-0.059697989374399185,
-0.014100291766226292,
0.03531233221292496,
-0.003413170576095581,
0.053435612469911575,
-0.008464792743325233,
0.019710250198841095,
-0.0891968384385109,
0.016409242525696754,
0.009384498000144958,
-0.03402935341000557,
0.04842096567153931,
-0.029986005276441574,
-0.016665484756231308,
0.01477223914116621,
-0.016585227102041245,
0.021129276603460312,
-0.025379234924912453,
-0.009051930159330368,
0.004381223116070032,
0.0541369803249836,
-0.00331456633284688,
-0.03869996592402458,
-0.08324911445379257,
0.07419741153717041,
-0.02636066824197769,
0.0153445890173316,
0.08823691308498383,
-0.02999749220907688,
-0.02224029414355755,
0.012502318248152733,
-0.032177168875932693,
0.10097253322601318,
-0.033479947596788406,
0.037987928837537766,
-0.004818507935851812,
-0.010627388954162598,
0.03412583842873573,
0.024639619514346123,
-0.037751875817775726,
0.013565268367528915,
0.02121879905462265,
-0.023942865431308746,
-0.002887621521949768,
0.08451719582080841,
0.019986242055892944,
-0.04850348085165024,
0.036264851689338684,
-0.04335598275065422,
0.031380631029605865,
-0.049803197383880615,
0.028692184016108513,
-0.006709323264658451,
-0.057601675391197205,
-0.0541386678814888,
0.05579334497451782,
0.06686844676733017,
0.032081238925457,
-0.034110598266124725,
-0.04099680855870247,
0.07255108654499054,
-0.03128886595368385,
-0.019173694774508476,
-0.0020303772762417793,
-0.0230738315731287,
-0.026968354359269142,
-0.006062248721718788,
0.027683982625603676,
0.07014162838459015,
-0.011894164606928825,
-0.018671561032533646,
0.027526436373591423,
-0.01675114594399929,
-0.02848626673221588,
0.003590555163100362,
-0.059780389070510864,
0.0191469956189394,
-0.012460638768970966,
-0.06331314146518707,
0.03265790641307831,
-0.0328446701169014,
-0.03152282163500786,
0.0015308279544115067,
-0.024279853329062462,
0.008106682449579239,
0.01466446090489626,
-0.054542072117328644,
-0.008843435905873775,
-0.044965021312236786,
0.03737087920308113,
-0.041669316589832306,
-0.02858234941959381,
-0.06330287456512451,
-0.0206290390342474,
-0.011406231671571732,
-0.033411525189876556,
0.011981841176748276,
0.012948761694133282,
0.059685975313186646,
0.008307114243507385,
-0.0005106924218125641,
0.018737759441137314,
-0.005351041443645954,
-0.07355057448148727,
-0.004866657312959433,
0.008712144568562508,
0.02173297479748726,
-0.03448213264346123,
0.020891569554805756,
0.0033356533385813236,
0.02108268439769745,
-0.032381657510995865,
-0.05656518414616585,
-0.04593140259385109,
0.03641112521290779,
0.05602777749300003,
-0.02736460231244564,
-0.016540607437491417,
-0.013883030973374844,
0.014733828604221344,
-0.0016930588753893971,
0.05908573046326637,
-0.021157030016183853,
0.023702209815382957,
0.012689176946878433,
-0.012109429575502872,
-0.0201078150421381,
-0.08553634583950043,
0.007494309917092323,
0.04704070836305618,
-0.004050547257065773,
0.01133764162659645,
-0.006012552417814732,
0.028952615335583687,
-0.0014473828487098217,
-0.05271431431174278,
-0.022709695622324944,
0.017321713268756866,
0.04458499699831009,
0.017087994143366814,
0.012034795247018337,
0.007279297336935997,
0.009458689950406551,
-0.011237445287406445,
0.005217412486672401,
-0.004090624395757914,
-0.050077348947525024,
-0.038279201835393906,
0.027237797155976295,
0.018066413700580597,
0.01812376268208027,
-0.06664953380823135,
-0.03620023652911186,
0.016458280384540558,
0.0412486307322979,
0.07415985316038132,
0.06811337172985077,
0.006057629827409983,
0.02321612276136875,
0.07159922271966934,
-0.015587026253342628,
-0.008224359713494778,
-0.05881834030151367,
-0.0037582148797810078,
0.005175026133656502,
0.03076234459877014,
0.002520096255466342,
0.01318941731005907,
0.0020126064773648977,
0.05818692594766617
] |
<p>When a light beam reaches a dielectric surface, the incident and reflected beams have different intensities depending on polarization. For the so-called Brewster's angle, the reflected light is lineary polarized.</p>
<p>My question is: how does this law work in case of mirror-like surface, when (ideally) all the light is reflected?</p>
|
g2513
|
[
-0.004370004869997501,
0.032365914434194565,
0.007118729874491692,
0.050345513969659805,
-0.032415132969617844,
0.016941331326961517,
0.04476319998502731,
0.04318201541900635,
0.007320750039070845,
0.0263330340385437,
-0.04947451502084732,
0.02178177610039711,
0.04453413560986519,
-0.005660749040544033,
-0.007834099233150482,
0.0025706677697598934,
0.04614846035838127,
0.006883013993501663,
0.04565819725394249,
0.05147009715437889,
-0.051935020834207535,
0.019175324589014053,
-0.011856574565172195,
-0.06778328865766525,
0.010053058154881,
0.026876304298639297,
-0.027455566450953484,
0.012017060071229935,
-0.016376188024878502,
-0.0513860359787941,
-0.014727046713232994,
-0.008279573172330856,
-0.008375456556677818,
0.0009953024564310908,
-0.04039964824914932,
-0.014418437145650387,
-0.01114599872380495,
-0.029170546680688858,
0.03668106347322464,
-0.010639221407473087,
-0.0003767823218367994,
0.05833060294389725,
-0.02847897820174694,
0.04050769656896591,
0.05249287933111191,
-0.06631237268447876,
-0.010871827602386475,
-0.00034298122045584023,
-0.019052229821681976,
-0.012081878259778023,
0.0000254213809967041,
0.028481561690568924,
0.036182302981615067,
-0.05577940493822098,
0.04454578831791878,
0.043125927448272705,
-0.03980492800474167,
-0.0186726413667202,
0.02640383504331112,
0.02926643006503582,
0.04723286256194115,
-0.0025459069292992353,
-0.02881469950079918,
0.05511944368481636,
0.032514698803424835,
-0.04888446629047394,
-0.019836407154798508,
-0.021031787618994713,
0.023779412731528282,
-0.01470032799988985,
0.0053521981462836266,
-0.03800768032670021,
-0.02135147526860237,
-0.08591762185096741,
-0.032370083034038544,
0.00394738232716918,
0.021641496568918228,
0.005148476921021938,
0.023614119738340378,
0.03321262449026108,
-0.015462060458958149,
-0.016330691054463387,
0.0026927851140499115,
0.0037510278634727,
-0.006183223333209753,
0.02882196009159088,
0.03267580270767212,
-0.011748735792934895,
-0.04279465973377228,
-0.031609900295734406,
0.052926044911146164,
-0.0031285379081964493,
0.013283715583384037,
0.006135713774710894,
-0.042109474539756775,
-0.046663105487823486,
0.02351764403283596,
0.0024146013893187046,
-0.07203927636146545,
-0.003297041403129697,
-0.06681787967681885,
-0.00542187737300992,
-0.04035554081201553,
0.016874322667717934,
0.020349692553281784,
-0.024220304563641548,
-0.035250939428806305,
0.019315890967845917,
-0.06519737094640732,
0.045991308987140656,
-0.01613795943558216,
-0.1200924888253212,
-0.040908124297857285,
-0.023090319707989693,
-0.08015386015176773,
-0.021832270547747612,
0.09817588329315186,
-0.0339309498667717,
-0.02391001768410206,
0.10476746410131454,
0.06400858610868454,
-0.016979213804006577,
-0.044684816151857376,
0.09257008880376816,
-0.019612222909927368,
0.0674603059887886,
-0.024749811738729477,
0.005237360950559378,
0.044144775718450546,
-0.009205246344208717,
0.0035888084676116705,
0.0014932259218767285,
-0.021031640470027924,
-0.01661653071641922,
0.017993338406085968,
0.014558598399162292,
-0.00619043642655015,
-0.047262925654649734,
0.020997967571020126,
-0.010527203790843487,
0.006201540119946003,
0.006247666664421558,
-0.0059861899353563786,
-0.00808039028197527,
-0.007726898416876793,
-0.021875247359275818,
-0.02723223716020584,
0.001440507359802723,
0.08922051638364792,
0.005262518767267466,
-0.02262641116976738,
0.0547899454832077,
0.043849050998687744,
-0.0538187250494957,
0.0013061484787613153,
-0.016103755682706833,
-0.0094331419095397,
-0.05646597221493721,
-0.014113149605691433,
-0.031980372965335846,
0.049181386828422546,
-0.044192440807819366,
-0.002644091611728072,
0.022873826324939728,
-0.035478245466947556,
0.027350841090083122,
-0.027498476207256317,
-0.04847143590450287,
0.024677155539393425,
-0.020025791600346565,
-0.0027016361709684134,
0.022747673094272614,
0.020787479355931282,
0.0365479439496994,
0.009873452596366405,
0.038038045167922974,
-0.03671794384717941,
-0.02582395449280739,
0.05107743293046951,
0.032799895852804184,
-0.05325913056731224,
-0.014821546152234077,
-0.004387188702821732,
0.012171115726232529,
-0.019087351858615875,
-0.056736499071121216,
0.016708148643374443,
-0.028695309534668922,
-0.02711697667837143,
0.02620631270110607,
-0.02193175069987774,
0.002401510253548622,
-0.018562933430075645,
0.022037161514163017,
0.01692294143140316,
-0.02152675949037075,
0.06980238854885101,
-0.024076074361801147,
-0.012577258050441742,
-0.038000576198101044,
-0.009317521937191486,
0.07223985344171524,
0.01379207894206047,
0.026996759697794914,
-0.031445443630218506,
-0.008746061474084854,
0.003277355106547475,
-0.014547479338943958,
-0.004928475245833397,
0.011985997669398785,
0.001816334668546915,
-0.009137239307165146,
-0.015455841086804867,
0.027284273877739906,
-0.024725046008825302,
0.043689072132110596,
-0.03234003111720085,
0.02781546488404274,
0.002602868713438511,
0.03219582512974739,
-0.0000132703880808549,
0.050548940896987915,
-0.012830548919737339,
0.02691296860575676,
-0.010074003599584103,
0.008367709815502167,
-0.025159237906336784,
0.030245328322052956,
0.018565857782959938,
0.03249327838420868,
-0.04432390630245209,
-0.08643748611211777,
0.04165711998939514,
0.008519879542291164,
0.040295228362083435,
0.01677728444337845,
-0.03500122204422951,
-0.004898232873529196,
0.03774232417345047,
0.010451423935592175,
-0.029643086716532707,
0.022562991827726364,
-0.032305795699357986,
0.014382581226527691,
-0.04127436503767967,
-0.011327779851853848,
0.023715892806649208,
0.013646945357322693,
0.019437244161963463,
0.04551353305578232,
0.017753543332219124,
0.007698983885347843,
0.01876300573348999,
0.012095795944333076,
-0.01239012461155653,
0.006128573790192604,
-0.0337989404797554,
0.026881717145442963,
-0.031160904094576836,
-0.027109403163194656,
0.019685322418808937,
-0.04015494883060455,
0.0004415714938659221,
0.004213978536427021,
-0.029005266726017,
0.026591213420033455,
0.06001719459891319,
0.014098643325269222,
0.07219290733337402,
0.0301109217107296,
-0.02614075131714344,
0.09807252883911133,
0.04361042380332947,
0.029837092384696007,
0.015765314921736717,
0.030960796400904655,
-0.016016757115721703,
-0.12021943181753159,
-0.030639849603176117,
0.011021248064935207,
-0.07483111321926117,
0.017668021842837334,
-0.07034925371408463,
-0.05368650704622269,
0.027149192988872528,
-0.08022553473711014,
0.06328747421503067,
0.027747081592679024,
-0.03738677129149437,
0.05814782530069351,
-0.05748704820871353,
-0.027451172471046448,
0.013564743101596832,
0.02008858136832714,
-0.012831210158765316,
0.03564626723527908,
0.042431123554706573,
-0.00982950534671545,
-0.0015345185529440641,
0.09054706990718842,
-0.03395175188779831,
-0.0003907509089913219,
-0.047639381140470505,
-0.04894213750958443,
-0.00784448441118002,
0.05075092986226082,
-0.024263251572847366,
-0.09549162536859512,
0.01673826389014721,
0.04706811532378197,
-0.016575081273913383,
0.015310627408325672,
-0.002209101803600788,
0.015421350486576557,
-0.020467622205615044,
-0.002267856616526842,
-0.021057147532701492,
0.007826902903616428,
0.0033637138549238443,
0.04306944087147713,
-0.02063373103737831,
0.013407363556325436,
0.030337637290358543,
0.013753000646829605,
-0.009466499090194702,
-0.01674015261232853,
-0.010201607830822468,
0.04847682639956474,
-0.009490246884524822,
0.032533466815948486,
0.042950525879859924,
0.019420694559812546,
-0.01929151639342308,
-0.009522799402475357,
-0.02046874351799488,
-0.018281521275639534,
-0.03340157866477966,
0.08526047319173813,
0.07393581420183182,
0.02527058683335781,
0.03247048333287239,
0.0025684291031211615,
-0.05967596545815468,
-0.04944850504398346,
0.042760975658893585,
-0.01355744432657957,
-0.02855774573981762,
0.0002730391570366919,
-0.03635126352310181,
0.017270879819989204,
0.03456886112689972,
0.003499215003103018,
0.044654957950115204,
0.04380398988723755,
-0.021893078461289406,
0.010250532068312168,
0.005546262487769127,
0.057457029819488525,
0.0459488146007061,
-0.018248986452817917,
0.01900307834148407,
-0.03044355846941471,
-0.02337469719350338,
-0.01991148851811886,
-0.019876502454280853,
-0.04758135601878166,
0.02424432709813118,
0.02106075920164585,
-0.025179611518979073,
0.0050419894978404045,
-0.015213957987725735,
-0.08486946672201157,
-0.01885673962533474,
0.03568346053361893,
-0.031893644481897354,
-0.015133186243474483,
-0.005312582477927208,
-0.00338366930373013,
-0.027533186599612236,
-0.011683783493936062,
-0.006453783251345158,
0.0638318806886673,
0.038169022649526596,
0.022425122559070587,
-0.004138970281928778,
0.008060510270297527,
-0.028250545263290405,
-0.02867997996509075,
0.06938280165195465,
-0.009301713667809963,
-0.02910173311829567,
-0.01668480597436428,
-0.009293891489505768,
-0.03154868260025978,
0.031644731760025024,
-0.01719740591943264,
-0.0011084252037107944,
-0.04360368102788925,
-0.006167491897940636,
-0.021220242604613304,
0.07494812458753586,
0.08996748179197311,
0.025303572416305542,
0.04376933351159096,
0.0009723857510834932,
-0.030215516686439514,
0.05232687294483185,
-0.009998113848268986,
-0.015418417751789093,
-0.009174245409667492,
-0.020919136703014374,
-0.04659561812877655,
-0.03130066767334938,
-0.06357517838478088,
0.03208645060658455,
0.042592745274305344,
0.007946337573230267,
0.0006026563933119178,
0.052813585847616196,
-0.005798126105219126,
0.01109039131551981,
0.01784530095756054,
0.029204152524471283,
-0.054067667573690414,
0.013449577614665031,
-0.020764676854014397,
0.032460201531648636,
-0.013420091941952705,
0.012747520580887794,
-0.07967325299978256,
-0.009878021664917469,
-0.013756327331066132,
-0.07746398448944092,
-0.01941816322505474,
-0.04436882212758064,
0.002027427311986685,
0.04815993830561638,
0.042310185730457306,
0.013616307638585567,
0.018695911392569542,
0.03634336590766907,
0.013596493750810623,
0.027435781434178352,
-0.03178299963474274,
0.053421638906002045,
0.05135165899991989,
-0.03918255865573883,
-0.04964350908994675,
0.04394920542836189,
-0.0006839900161139667,
-0.06260845810174942,
-0.004699787124991417,
-0.01039984542876482,
-0.08270654082298279,
-0.020353632047772408,
0.008902853354811668,
-0.008665196597576141,
0.055244412273168564,
0.028272969648241997,
0.029426414519548416,
0.0022018456365913153,
-0.02811925858259201,
0.009102290496230125,
-0.050525881350040436,
0.037235621362924576,
0.004627829417586327,
-0.046423427760601044,
0.0037001059390604496,
-0.06458432972431183,
-0.015893887728452682,
-0.026144126430153847,
0.05674322322010994,
0.0015482488088309765,
0.0760645642876625,
-0.049952201545238495,
0.0059896050952374935,
-0.03202610835433006,
-0.04286361485719681,
-0.05516808480024338,
-0.016423894092440605,
-0.001898821210488677,
-0.0641353502869606,
0.02410059981048107,
0.021098867058753967,
-0.0693872720003128,
-0.02134176902472973,
0.002307964488863945,
0.044851649552583694,
-0.02314341999590397,
-0.016173994168639183,
-0.018056560307741165,
-0.007279319688677788,
-0.05615583807229996,
0.03154127672314644,
-0.020095225423574448,
0.07123318314552307,
0.016405243426561356,
0.005360918585211039,
-0.042218971997499466,
0.09686723351478577,
-0.03539619967341423,
-0.005659517832100391,
0.027152717113494873,
0.024848628789186478,
-0.038883425295352936,
0.05366728827357292,
0.05721592530608177,
-0.01792808435857296,
0.018513040617108345,
0.030696094036102295,
0.00008518903632648289,
-0.011395095847547054,
0.02522279880940914,
0.0555117204785347,
-0.020874936133623123,
-0.05999259278178215,
-0.016443515196442604,
0.08250744640827179,
-0.019374007359147072,
0.02716383896768093,
0.010210203938186169,
-0.026381243020296097,
-0.017620686441659927,
-0.017478974536061287,
-0.02188175357878208,
-0.012971363961696625,
-0.02411031536757946,
-0.03263004869222641,
0.03203725814819336,
0.022714782506227493,
-0.008004102855920792,
0.03139824792742729,
0.020912880077958107,
0.0125092389062047,
0.10733350366353989,
-0.06036115810275078,
-0.012752939015626907,
0.03526616469025612,
0.019259599968791008,
0.003306245431303978,
-0.04436282813549042,
0.0422418937087059,
0.0787305161356926,
0.023187361657619476,
0.0751667395234108,
-0.021437572315335274,
0.013413045555353165,
-0.02241167612373829,
0.036352552473545074,
0.035792503505945206,
-0.016911782324314117,
-0.008587324991822243,
0.0008953200886026025,
-0.028235910460352898,
0.01353785302489996,
0.013975965790450573,
-0.03809581696987152,
0.019115025177598,
-0.0008815375040285289,
-0.029792390763759613,
0.09646627306938171,
0.0069073401391506195,
0.043036576360464096,
-0.0703386515378952,
0.01754530891776085,
-0.04737825691699982,
-0.014501413330435753,
-0.007177326362580061,
0.004008020740002394,
-0.03641354665160179,
0.021471969783306122,
-0.062333252280950546,
0.02402702532708645,
-0.02384917065501213,
-0.007380843162536621,
0.054495006799697876,
-0.024213116616010666,
-0.04483996331691742,
-0.00278029078617692,
0.07643108814954758,
0.013317650184035301,
0.0013524318346753716,
0.022242795675992966,
-0.009206952527165413,
-0.03645055368542671,
-0.02128739096224308,
-0.041200608015060425,
-0.041404567658901215,
0.07048643380403519,
-0.07152081280946732,
-0.015863489359617233,
-0.015182937495410442,
0.026907097548246384,
0.003621643176302314,
-0.0045442297123372555,
-0.10368110239505768,
0.02161392569541931,
0.05353306606411934,
0.0013111301232129335,
0.009868040680885315,
0.013773201033473015,
0.03778526559472084,
0.03599858656525612,
-0.0013356187846511602,
0.07367690652608871,
0.010830603539943695,
-0.025419022887945175,
-0.04235852509737015,
0.01858999766409397,
0.054361168295145035,
0.035317059606313705,
0.028927790001034737,
-0.018675077706575394,
0.012943682260811329,
-0.012954247184097767,
-0.02442009747028351,
-0.07896598428487778,
-0.027245571836829185,
-0.006239790469408035,
0.04503783956170082,
-0.02175682969391346,
-0.017399555072188377,
-0.0040116095915436745,
-0.024152196943759918,
0.021484337747097015,
0.010321532376110554,
-0.03183424845337868,
0.030986759811639786,
-0.0047193896025419235,
0.09210310131311417,
0.032425157725811005,
-0.02939312905073166,
-0.010438698343932629,
-0.004073749296367168,
0.04923883453011513,
0.014393423683941364,
-0.028449663892388344,
0.06322713196277618,
0.01569678820669651,
0.021198319271206856,
-0.049025386571884155,
0.08402249217033386,
0.0005328881088644266,
0.0517980121076107,
0.007504894398152828,
0.05519682541489601,
-0.030034061521291733,
-0.058071497827768326,
-0.045710545033216476,
0.0180885661393404,
0.007932478561997414,
-0.02640555240213871,
-0.0036002974957227707,
0.012524547055363655,
-0.019654691219329834,
-0.06421712040901184,
-0.015606111846864223,
0.016302980482578278,
-0.013626395724713802,
-0.03922407701611519,
-0.006605004426091909,
0.02470194362103939,
-0.01352938637137413,
-0.04007737338542938,
0.014065106399357319,
0.015605867840349674,
-0.0034154492896050215,
-0.012909704819321632,
0.020250536501407623,
-0.00925567839294672,
-0.017282765358686447,
-0.0960891917347908,
0.010262624360620975,
0.026823602616786957,
0.0006612676079384983,
0.026851054280996323,
-0.03516608104109764,
0.014272314496338367,
-0.010083337314426899,
0.04017020761966705,
0.025486908853054047,
0.05504746735095978,
-0.0425480380654335,
-0.04423823580145836,
0.030344970524311066,
0.026868365705013275,
-0.0051531665958464146,
-0.004604733549058437,
-0.01369511615484953,
-0.04884877800941467,
-0.02341897413134575,
-0.051459524780511856,
0.03061707317829132,
0.05319344997406006,
-0.008664315566420555,
-0.029316501691937447,
0.02372911386191845,
0.04237445816397667,
-0.02321397140622139,
-0.011585407890379429,
-0.017955901101231575,
-0.01434896420687437,
-0.00872085988521576,
0.017474006861448288,
0.01695984974503517,
-0.03434031084179878,
0.012302374467253685,
-0.05482837185263634,
0.04121202602982521,
0.002519517671316862,
-0.02021169103682041,
0.005243299063295126,
0.048789411783218384,
0.03733733296394348,
0.010473526082932949,
0.008843070827424526,
-0.004096637014299631,
-0.005952260456979275,
0.00033718629856593907,
-0.058801472187042236,
-0.017314430326223373,
-0.006127883680164814,
-0.008582698181271553,
-0.0664936751127243,
-0.013557062484323978,
-0.03519517555832863,
-0.03497479483485222,
-0.017334962263703346,
0.043085984885692596,
0.019678449258208275,
0.0021879032719880342,
0.030657140538096428,
-0.05231863632798195,
-0.015553885139524937,
0.0011741586495190859,
0.04406147077679634,
0.03509350121021271,
-0.015939587727189064,
-0.02588900364935398,
0.0004626295412890613,
0.019010253250598907,
-0.041339099407196045,
0.032466016709804535,
-0.08595109730958939,
0.040317367762327194,
0.03651464730501175,
-0.0017031006282195449,
-0.05275056138634682,
0.04987649992108345,
-0.007746654096990824,
-0.043690524995326996,
-0.0052839419804513454,
-0.005286602769047022,
0.010191148146986961,
0.07848517596721649,
-0.047319646924734116,
0.014841211028397083,
-0.006202922202646732,
0.05090619996190071,
-0.02273152396082878,
-0.04698372259736061,
-0.003939580172300339,
-0.07468806952238083,
-0.010692034848034382,
-0.011783072724938393,
-0.024622460827231407,
-0.06233067065477371,
-0.0007020705379545689
] |
<p>The question reads as such: "What is the mass of a 1.05 µCi carbon-14 source?"</p>
<p>First I convert to decays/s: $R = 1.05 µCi=3.885 \times 10^4 decays/s$.</p>
<p>The half-life for carbon-14 that we've been using is 5730 years or $T_{1/2}=1.808 \times 10^{11} s$, so $\lambda=\frac{ln(2)}{T_{1/2}}=3.834 \times 10^{-12}s^{-1}$</p>
<p>$R=\lambda N$, so $N=\frac{R}{\lambda}=1.0133 \times 10^{16}nuclei$</p>
<p>Now just to convert to grams: $1.0133 \times 10^{16}nuclei \times \frac{1mol}{N_A} \times \frac{12.011g}{1mol}=2.02 \times 10^{-7}g$. Which unfortunately is the wrong answer. Maybe someone sees a conversion error I made somewhere?</p>
|
g2514
|
[
0.0046610962599515915,
-0.002101671416312456,
0.029846295714378357,
-0.07944534718990326,
0.0644763633608818,
-0.06198212131857872,
0.05170612037181854,
0.013466366566717625,
-0.08482076227664948,
0.021736828610301018,
-0.028851712122559547,
-0.00969784613698721,
-0.03075437620282173,
-0.01410192996263504,
0.06167186424136162,
-0.03905542567372322,
0.04090655967593193,
0.0024040460120886564,
0.016352297738194466,
0.04578116908669472,
-0.07093125581741333,
-0.06148596107959747,
-0.03967561572790146,
-0.06575508415699005,
0.004920865874737501,
-0.04632699862122536,
0.022326262667775154,
0.022236529737710953,
-0.0675973892211914,
0.023276982828974724,
-0.024781694635748863,
-0.03772782161831856,
0.028562691062688828,
-0.005176839418709278,
-0.053750600665807724,
-0.04616910219192505,
-0.006406608037650585,
0.00051956094102934,
-0.01055809948593378,
0.021420584991574287,
0.05102195963263512,
-0.03490763157606125,
0.04868661239743233,
0.01833290234208107,
-0.019682645797729492,
0.038477662950754166,
-0.008874369785189629,
-0.026060232892632484,
0.01637495495378971,
-0.03550561144948006,
0.004724274855107069,
0.049453724175691605,
0.0045091514475643635,
0.07217247039079666,
-0.047293826937675476,
0.03379463404417038,
0.02950240671634674,
-0.025689342990517616,
0.02454744279384613,
0.06361862272024155,
0.07984837889671326,
-0.015242175199091434,
0.011502751149237156,
-0.035065699368715286,
0.054525189101696014,
0.01465859916061163,
-0.0316464826464653,
0.010700451210141182,
0.01712714321911335,
-0.03130310773849487,
-0.012739819474518299,
0.0018825072329491377,
0.024763621389865875,
0.041376743465662,
-0.019252918660640717,
-0.06108849123120308,
0.014415878802537918,
-0.006855903193354607,
0.028852613642811775,
-0.03690928593277931,
-0.04461270198225975,
-0.014668697491288185,
0.007181063294410706,
0.007348043378442526,
0.007611906621605158,
-0.00006185859092511237,
-0.0430685393512249,
0.03145011141896248,
-0.02662034146487713,
0.05219598859548569,
0.053808484226465225,
-0.06772169470787048,
0.021136973053216934,
-0.024870654568076134,
-0.02341403253376484,
-0.012422339990735054,
-0.0012863592710345984,
0.04338105022907257,
0.0029319250024855137,
-0.01668108068406582,
0.03313660994172096,
-0.001588204293511808,
-0.047302186489105225,
0.01671399176120758,
-0.010076009668409824,
0.06797339767217636,
-0.046073198318481445,
-0.011445545591413975,
-0.009866357780992985,
-0.026224227622151375,
-0.04549098387360573,
0.005333737004548311,
-0.0058242641389369965,
-0.005295565817505121,
-0.04847453162074089,
0.00021089236543048173,
0.03556550666689873,
0.004732393193989992,
0.03958095610141754,
0.07266933470964432,
0.010212165303528309,
0.037463586777448654,
0.04210715368390083,
-0.010441891849040985,
-0.021298063918948174,
-0.06685558706521988,
-0.009698035195469856,
0.008588598109781742,
0.048547517508268356,
-0.025748878717422485,
-0.048725027590990067,
-0.00030557235004380345,
-0.011875896714627743,
0.003093355568125844,
-0.002483680611476302,
0.034780148416757584,
-0.008723083883523941,
0.02478448674082756,
-0.032686177641153336,
-0.033176492899656296,
-0.005981349386274815,
-0.06461798399686813,
0.0123862624168396,
-0.003568756626918912,
-0.03342379257082939,
0.04905854910612106,
-0.01610047183930874,
-0.0036164773628115654,
0.036725033074617386,
0.05417834594845772,
0.020064974203705788,
-0.005726099945604801,
0.008947187103331089,
-0.02915559895336628,
0.010168267413973808,
0.0056905923411250114,
-0.027935415506362915,
0.02419724129140377,
-0.04912934824824333,
0.019532443955540657,
-0.011608913540840149,
0.02836810052394867,
-0.02063607983291149,
0.015167329460382462,
-0.035896603018045425,
-0.010044590570032597,
0.017311682924628258,
-0.03546949848532677,
-0.01616031304001808,
-0.030424078926444054,
-0.0195472314953804,
0.025830792263150215,
0.011551860719919205,
-0.004822492599487305,
-0.02020718716084957,
0.013898737728595734,
0.011254060082137585,
0.012190109118819237,
0.04216983914375305,
0.024436671286821365,
0.06754924356937408,
-0.055200736969709396,
0.007177108898758888,
-0.0454845055937767,
0.030554795637726784,
-0.010935093276202679,
0.04190029576420784,
0.013561928644776344,
0.008003195747733116,
-0.000723786186426878,
-0.04439498111605644,
-0.01683228649199009,
-0.01633920520544052,
0.019255174323916435,
-0.00856737419962883,
0.04637650400400162,
0.0261169895529747,
-0.038510747253894806,
0.030019694939255714,
0.05784311145544052,
-0.011872165836393833,
-0.003155537648126483,
-0.012198924086987972,
0.01756841130554676,
0.06070989742875099,
-0.028100445866584778,
0.004938062280416489,
0.015354328788816929,
0.05851965397596359,
-0.04237326234579086,
-0.013698399998247623,
-0.0648944228887558,
-0.00479021156206727,
0.051760103553533554,
-0.03245146945118904,
-0.05060717463493347,
-0.009691833518445492,
0.061937615275382996,
0.052660003304481506,
-0.007432885002344847,
0.010289842262864113,
0.01604229398071766,
0.08904251456260681,
-0.0018170593539252877,
0.05702266842126846,
0.011831770651042461,
-0.01730918325483799,
-0.013013936579227448,
0.015759332105517387,
0.0035776025615632534,
-0.020476633682847023,
0.08103237301111221,
-0.02620762027800083,
-0.01945052482187748,
0.0006937560392543674,
0.01241275668144226,
-0.03379129618406296,
-0.033056944608688354,
-0.012815750204026699,
-0.03393802419304848,
0.021692795678973198,
-0.03103032335639,
-0.057777464389801025,
-0.009484273381531239,
0.025953246280550957,
-0.04678381606936455,
0.02601984515786171,
-0.038973912596702576,
-0.020205959677696228,
0.022488893941044807,
-0.04377049207687378,
0.05030618980526924,
-0.002720875898376107,
0.000025221794203389436,
-0.02320593222975731,
-0.007252266630530357,
-0.0213933028280735,
0.0012057911371812224,
-0.060759708285331726,
0.022347474470734596,
0.025719977915287018,
-0.10067621618509293,
-0.012574591673910618,
-0.03758587688207626,
-0.05080491676926613,
-0.03975334390997887,
-0.028333695605397224,
-0.0344676710665226,
0.04427124932408333,
0.02883538417518139,
0.016936836764216423,
0.013774121180176735,
0.023883258923888206,
0.05811444669961929,
-0.0690164715051651,
-0.00021796183136757463,
0.017830461263656616,
0.07183588296175003,
0.03833547979593277,
-0.030134737491607666,
-0.0578833632171154,
0.01578713022172451,
-0.01955493725836277,
0.010931044816970825,
0.01345351617783308,
-0.03065999038517475,
-0.01568601466715336,
-0.01572619378566742,
0.029306787997484207,
0.018500719219446182,
-0.024304023012518883,
-0.00889288354665041,
0.0166604146361351,
0.026712046936154366,
0.09007997065782547,
0.012807438150048256,
0.07003135979175568,
-0.022328650578856468,
-0.004279422108083963,
-0.009959441609680653,
0.031704649329185486,
0.02460818737745285,
-0.03586938977241516,
-0.05004844442009926,
0.010861708782613277,
0.013072117231786251,
-0.0017241280293092132,
0.01275682169944048,
0.015589320100843906,
-0.006442398298531771,
-0.021635716781020164,
0.02288391999900341,
0.025842618197202682,
-0.025857869535684586,
-0.032471731305122375,
-0.01156629528850317,
0.0006514549604617059,
-0.004653606563806534,
0.011706255376338959,
-0.051823005080223083,
0.013321480713784695,
-0.0431051105260849,
0.03833649307489395,
-0.04402168095111847,
-0.024156425148248672,
0.013773426413536072,
-0.047145090997219086,
-0.019191041588783264,
-0.01656157895922661,
-0.07221096009016037,
0.011192560195922852,
-0.009296417236328125,
-0.010151517577469349,
-0.0007962424424476922,
-0.006769752129912376,
-0.05198448523879051,
-0.03803759068250656,
0.048160575330257416,
0.009712770581245422,
0.006466102786362171,
-0.04012637585401535,
0.04649505391716957,
0.002708186162635684,
0.010781503282487392,
0.06904732435941696,
0.02984449453651905,
-0.06463717669248581,
0.023560233414173126,
-0.016554387286305428,
-0.0069519286043941975,
-0.0025749695487320423,
0.006549967918545008,
-0.04916879162192345,
0.03176167979836464,
-0.004251450300216675,
0.04224828630685806,
-0.01058080606162548,
0.08100401610136032,
0.05089670047163963,
0.011533585377037525,
0.01827423833310604,
-0.07082125544548035,
0.05090724676847458,
0.046993304044008255,
0.0312935970723629,
0.04448655992746353,
-0.004153070040047169,
0.06948277354240417,
0.01635720394551754,
-0.03294229507446289,
-0.027724849060177803,
0.01769639551639557,
0.09183157980442047,
0.015602052211761475,
-0.01934782788157463,
0.0012653939193114638,
-0.027716796845197678,
0.03299371525645256,
-0.014839163050055504,
0.059946849942207336,
0.002135391114279628,
-0.03437340259552002,
-0.035566359758377075,
-0.05726132169365883,
0.00351099856197834,
-0.0030475729145109653,
-0.03107328712940216,
-0.058329202234745026,
0.0017794746672734618,
-0.035758525133132935,
0.010292989201843739,
-0.05049765482544899,
-0.007976983673870564,
0.02461647056043148,
-0.0016569882864132524,
-0.026298359036445618,
0.05804658681154251,
0.006415634881705046,
-0.0012983069755136967,
0.011246515437960625,
-0.016551658511161804,
0.03380698338150978,
0.0611540824174881,
-0.020624658092856407,
0.05014079064130783,
0.08838830143213272,
-0.008661989122629166,
-0.02251765877008438,
0.07859289646148682,
0.015191313810646534,
0.029092904180288315,
0.04094310849905014,
0.02343699149787426,
-0.01807299628853798,
-0.01698962226510048,
-0.03749088943004608,
0.0057669756934046745,
-0.006447287276387215,
0.05754566937685013,
0.010534949600696564,
-0.002397718373686075,
0.01931300386786461,
-0.06612233072519302,
-0.014839018695056438,
-0.0360640250146389,
0.027918919920921326,
0.031492680311203,
-0.02677007205784321,
0.014033307321369648,
-0.017027081921696663,
0.03215821459889412,
0.019830593839287758,
0.03258708119392395,
0.008080227300524712,
-0.07435328513383865,
0.05339887738227844,
0.09424713999032974,
-0.03862129524350166,
0.006511806044727564,
0.027058307081460953,
0.03045649640262127,
-0.025899095460772514,
-0.036109719425439835,
0.019704623147845268,
-0.00709993252530694,
-0.019366074353456497,
-0.03957585617899895,
-0.06097520887851715,
0.011190000921487808,
-0.0036127702333033085,
0.009853526018559933,
0.030728990212082863,
-0.012645427137613297,
-0.049036480486392975,
0.02962486445903778,
-0.023080280050635338,
0.015969404950737953,
0.031427666544914246,
0.014837957918643951,
0.06959856301546097,
-0.04393573850393295,
-0.019797762855887413,
0.05895543098449707,
-0.011634374037384987,
-0.012254517525434494,
0.015096171759068966,
-0.02576717920601368,
0.012121950276196003,
0.029974335804581642,
0.027096249163150787,
-0.04805750399827957,
-0.06351297348737717,
-0.03231097385287285,
-0.05903921276330948,
-0.00467443373054266,
0.05689500644803047,
0.04464997351169586,
0.010405215434730053,
-0.021161606535315514,
0.04473303630948067,
-0.042679861187934875,
-0.02230306901037693,
-0.033438343554735184,
0.03506102412939072,
0.05505567789077759,
0.06779170781373978,
-0.00015912644448690116,
-0.009687509387731552,
0.04274411499500275,
-0.017679015174508095,
0.02684612385928631,
0.07838819175958633,
-0.009552549570798874,
-0.06761910021305084,
0.08998598158359528,
0.02817174606025219,
-0.022701483219861984,
-0.0519220307469368,
0.050143420696258545,
0.041016627103090286,
-0.03066648542881012,
0.05978124216198921,
-0.051913484930992126,
0.06948650628328323,
-0.02636389620602131,
0.04593789577484131,
0.01840728335082531,
0.004864853341132402,
-0.0211784727871418,
0.031031381338834763,
0.01298083458095789,
-0.004952306393533945,
0.06042644381523132,
0.012307765893638134,
0.007617950439453125,
-0.04292748495936394,
0.010412875562906265,
0.09635812044143677,
-0.002619975944980979,
-0.025539539754390717,
0.004898367915302515,
0.02674383856356144,
0.021867193281650543,
0.046240340918302536,
-0.02075410820543766,
-0.040558233857154846,
-0.030516700819134712,
-0.06752119958400726,
0.014561840333044529,
-0.027481554076075554,
0.023551004007458687,
-0.049578581005334854,
0.06067487969994545,
-0.0016506692627444863,
-0.022778186947107315,
0.019303126260638237,
-0.026302039623260498,
-0.04123101755976677,
0.04664811119437218,
-0.0609939880669117,
-0.015823138877749443,
-0.025882743299007416,
0.0084121348336339,
0.08741220086812973,
-0.061868924647569656,
-0.016501830890774727,
0.04365422949194908,
-0.07837457209825516,
-0.03351086005568504,
0.01250207144767046,
0.002428522100672126,
0.032515812665224075,
0.0065668062306940556,
-0.052412282675504684,
0.08820841461420059,
0.04827377200126648,
0.03620606288313866,
0.022941308096051216,
0.006933546159416437,
0.03404338285326958,
-0.042323797941207886,
0.0008998499251902103,
0.0028460919857025146,
0.02191505767405033,
0.04913322627544403,
-0.10203241556882858,
-0.029928436502814293,
-0.06452783942222595,
0.009321046061813831,
-0.025142312049865723,
-0.020204462110996246,
0.04919769614934921,
-0.049119673669338226,
-0.05750786513090134,
0.019235042855143547,
0.02853199653327465,
-0.052475590258836746,
-0.03892815485596657,
0.0148585494607687,
-0.0160138551145792,
0.017100119963288307,
-0.07266997545957565,
0.002765842480584979,
0.012240041978657246,
-0.05378667265176773,
0.0005959115806035697,
-0.03833051025867462,
0.033495452255010605,
-0.005800524726510048,
-0.0386628583073616,
-0.014215373434126377,
0.024737974628806114,
-0.0066900779493153095,
-0.020747093483805656,
-0.0450926311314106,
-0.0243071261793375,
-0.044417571276426315,
-0.04416199401021004,
0.009262479841709137,
0.005836574360728264,
0.09336106479167938,
0.08248741924762726,
0.005255041643977165,
-0.007880978286266327,
0.018265308812260628,
0.023700091987848282,
-0.04824453964829445,
0.02746095508337021,
0.013109719380736351,
0.008952486328780651,
-0.006928620394319296,
0.00347991194576025,
-0.005487586371600628,
0.01896376721560955,
-0.006914334371685982,
-0.05856330692768097,
0.031092599034309387,
0.007182776462286711,
-0.07946303486824036,
0.02985757403075695,
0.054806821048259735,
0.038260478526353836,
0.007367883808910847,
-0.0068452442064881325,
0.03279366344213486,
0.09491610527038574,
0.05168808251619339,
-0.02063761278986931,
0.012925711460411549,
-0.0491567961871624,
-0.02550618164241314,
-0.021122651174664497,
0.004934326279908419,
-0.032875195145606995,
-0.030618946999311447,
0.024436086416244507,
-0.0069819060154259205,
0.007692486047744751,
0.028036504983901978,
0.02968306466937065,
-0.043698377907276154,
-0.07642485201358795,
0.028933202847838402,
0.002073321957141161,
-0.022924551740288734,
0.0034373505041003227,
0.07327800989151001,
0.02036762796342373,
-0.03712188079953194,
0.003207010682672262,
0.02585780620574951,
-0.017224183306097984,
-0.04648444429039955,
0.04493217542767525,
0.0053461091592907906,
-0.023166099563241005,
0.03948712721467018,
0.03759382665157318,
0.0007296346011571586,
-0.05377323180437088,
-0.0730016753077507,
-0.058567192405462265,
-0.01192000973969698,
-0.0018866502214223146,
-0.005083187948912382,
0.040886543691158295,
0.032932184636592865,
-0.01886352337896824,
-0.012567085213959217,
-0.07034887373447418,
-0.024925459176301956,
-0.05001452937722206,
-0.0013501793146133423,
0.00023510557366535068,
0.042631860822439194,
-0.013731900602579117,
-0.05454123392701149,
0.018641885370016098,
0.012927663512527943,
-0.005816709715873003,
-0.023803887888789177,
0.02224668674170971,
-0.03425820171833038,
-0.015832027420401573,
0.015895478427410126,
0.01056146901100874,
-0.06842494755983353,
-0.012041741982102394,
0.006963027641177177,
0.05923392251133919,
-0.017106924206018448,
0.03533615544438362,
0.030443215742707253,
0.0014152709627524018,
-0.07964950054883957,
-0.045855309814214706,
-0.0035279334988445044,
0.01895877718925476,
0.04524044319987297,
0.03672018274664879,
0.013588759116828442,
-0.014385642483830452,
0.0011732291895896196,
0.016246529296040535,
0.01047277171164751,
0.01732219196856022,
-0.06783527135848999,
0.029964672401547432,
-0.0405353344976902,
-0.022400448098778725,
-0.01776980422437191,
-0.011884886771440506,
-0.010362638160586357,
0.014014743268489838,
0.06826034188270569,
-0.0444001667201519,
0.01652243360877037,
-0.05718443542718887,
0.020256416872143745,
-0.05856076627969742,
-0.03889963775873184,
-0.0065928008407354355,
-0.04380333051085472,
-0.018280955031514168,
0.009157108142971992,
-0.08083844184875488,
-0.021626906469464302,
0.021481281146407127,
0.018741372972726822,
0.03549008071422577,
-0.004976864904165268,
0.013277839869260788,
-0.04753277823328972,
-0.022983096539974213,
-0.03124951757490635,
0.008096874691545963,
0.049479033797979355,
-0.0043386006727814674,
0.017223458737134933,
0.029826173558831215,
-0.007429865654557943,
0.0040013426914811134,
0.008952546864748001,
0.0157170332968235,
0.002481675473973155,
-0.009853118099272251,
-0.027245718985795975,
0.05808977037668228,
0.008815143257379532,
-0.07643812894821167,
0.022581441327929497,
0.042111147195100784,
-0.004451249726116657,
0.05220421403646469,
0.04945403337478638,
-0.05649396777153015,
0.02708919160068035,
0.011197873391211033,
-0.0034038505982607603,
0.003016177797690034,
-0.03163629770278931,
0.011875382624566555,
0.006460874807089567,
0.022853193804621696,
0.026923121884465218,
0.02209644392132759,
0.0006633509183302522,
-0.016304930672049522
] |
<p>The magnetic monopoles does not exist which can be shown by $ \int {\vec{B} \cdot d\vec{A}} = 0 $.</p>
<p>But in Faraday's Law of electromagnetic induction, we clearly show the EMF induced is the <em>time rate of change of the magnetic flux</em>, which is $ E = -\frac{d\Phi_B}{dt} = -\frac{d\int{\vec{B}\cdot d\vec{A}}} {dt}$.</p>
<p>Now if $ \int {\vec{B} \cdot d\vec{A}} = 0 $ then shouldn't the induced emf be zero?</p>
|
g2515
|
[
0.020077448338270187,
0.04028313606977463,
-0.009655817411839962,
-0.048971470445394516,
0.11565136909484863,
0.046903081238269806,
0.0712193101644516,
0.07439787685871124,
0.0013762550661340356,
-0.023372003808617592,
-0.08413683623075485,
0.03134426102042198,
-0.010125154629349709,
0.005675534252077341,
-0.0231774915009737,
0.013901655562222004,
-0.007896892726421356,
0.0032230899669229984,
0.03369119018316269,
0.008545520715415478,
-0.019759951159358025,
0.016044436022639275,
0.007950873114168644,
-0.0585077740252018,
0.02068283222615719,
0.018561845645308495,
0.0015895195538178086,
-0.04013930261135101,
0.0043477825820446014,
-0.04396875202655792,
0.008122246712446213,
0.015226278454065323,
0.05042126774787903,
-0.0365976020693779,
0.005123531445860863,
-0.03214597329497337,
0.0034675325732678175,
0.07084845751523972,
0.011648330837488174,
-0.014019516296684742,
-0.0032079482916742563,
0.024607475847005844,
0.03022715076804161,
0.025043081492185593,
-0.009014454670250416,
0.012265818193554878,
0.0030893541406840086,
0.008585128001868725,
-0.03568420186638832,
-0.004488776903599501,
0.0011009160662069917,
0.0044262646697461605,
0.09972267597913742,
-0.04606142267584801,
-0.033732250332832336,
0.01751715876162052,
-0.007962509989738464,
-0.07623116672039032,
0.016023805364966393,
0.0659588947892189,
-0.015708448365330696,
-0.012358766980469227,
0.012457776814699173,
0.019660284742712975,
0.04160022363066673,
0.03012942150235176,
-0.03565558046102524,
-0.048273369669914246,
0.02010670118033886,
0.015354895032942295,
-0.015183939598500729,
-0.04080241918563843,
-0.10439284890890121,
0.028369484469294548,
0.04395611584186554,
0.04128558933734894,
0.06386332213878632,
-0.03534281998872757,
0.014443802647292614,
-0.01259901188313961,
0.002277577295899391,
-0.012975046411156654,
0.003987251315265894,
0.017002735286951065,
0.045642219483852386,
0.0035854147281497717,
0.08409643173217773,
0.012656892649829388,
0.01869458518922329,
-0.013479296118021011,
0.0008244349737651646,
-0.04064454138278961,
-0.008788506500422955,
0.01510802935808897,
0.03970538452267647,
-0.021703558042645454,
0.0469825454056263,
0.07285555452108383,
-0.0554354190826416,
-0.0008316604071296751,
-0.03127417713403702,
0.035271186381578445,
-0.014074175618588924,
0.005354627035558224,
0.008457954041659832,
0.009722606278955936,
0.021239323541522026,
-0.03221778944134712,
-0.020326565951108932,
-0.018348675221204758,
-0.01631574146449566,
0.015274171717464924,
-0.07852688431739807,
0.011692523956298828,
0.012893985025584698,
0.010668979026377201,
0.00458173081278801,
-0.028280513361096382,
-0.04253711923956871,
0.047100719064474106,
0.02212710492312908,
-0.028277702629566193,
-0.044788651168346405,
0.06727349013090134,
-0.024607375264167786,
-0.01072203554213047,
-0.013480925001204014,
0.04991186782717705,
0.09138911962509155,
-0.013944766484200954,
-0.02271050028502941,
-0.024659276008605957,
-0.032077301293611526,
-0.01764349453151226,
-0.003996631596237421,
0.04019100219011307,
0.022379742935299873,
-0.014501860365271568,
-0.014507222920656204,
0.07123874872922897,
-0.051327355206012726,
-0.0480986051261425,
0.030108742415905,
-0.06536781042814255,
-0.033163562417030334,
0.05797813832759857,
0.01741030439734459,
-0.0030916151590645313,
0.06545230001211166,
0.05718417093157768,
0.08021734654903412,
0.09404267370700836,
-0.034219685941934586,
0.02742941491305828,
-0.022899871692061424,
0.033555109053850174,
0.028095627203583717,
0.010719268582761288,
0.01219465583562851,
-0.0021348162554204464,
0.023184312507510185,
0.009741077199578285,
0.03481243550777435,
-0.01869582012295723,
-0.017906054854393005,
0.03377001732587814,
0.07946137338876724,
0.009744896553456783,
0.008727364242076874,
-0.039789337664842606,
-0.0394403301179409,
0.02149777114391327,
0.04440050944685936,
0.02928800694644451,
-0.011432013474404812,
0.02907746471464634,
-0.05250271409749985,
0.0009244753746315837,
-0.0007304769242182374,
-0.0094416169449687,
-0.002565863775089383,
0.027815690264105797,
0.020123055204749107,
-0.05951343849301338,
-0.016794666647911072,
-0.044582635164260864,
-0.044742193073034286,
0.04171319678425789,
-0.08039744943380356,
0.02890418842434883,
-0.08062389492988586,
0.018092354759573936,
-0.006917254533618689,
0.02167823165655136,
0.002619817154482007,
0.01590939424932003,
0.0356878787279129,
-0.03733770549297333,
0.020931662991642952,
0.061151135712862015,
0.00493784761056304,
0.06619342416524887,
0.06753815710544586,
-0.03096034750342369,
-0.0018355244537815452,
-0.016833409667015076,
0.01970173418521881,
-0.02468159794807434,
0.06777698546648026,
-0.012957091443240643,
0.03111875429749489,
0.03524556756019592,
-0.050181567668914795,
0.017535898834466934,
-0.00006593504076590762,
-0.0044607981108129025,
-0.0024307849816977978,
0.03187533840537071,
-0.017585594207048416,
-0.01516579370945692,
0.007896876893937588,
0.01957486756145954,
0.03937043249607086,
-0.007978151552379131,
-0.05822433531284332,
-0.047435905784368515,
-0.03463035076856613,
-0.01364549994468689,
-0.022118311375379562,
-0.02382236160337925,
-0.03550364449620247,
0.0047178263776004314,
-0.044252436608076096,
-0.0015362744452431798,
-0.01576094701886177,
0.03989972919225693,
0.01589292474091053,
-0.05262473225593567,
0.020239122211933136,
0.03451693803071976,
0.00011206887575099245,
-0.030094550922513008,
0.018090052530169487,
-0.006079692393541336,
-0.029048297554254532,
-0.0823301449418068,
0.008140924386680126,
0.011407465673983097,
0.005161845590919256,
0.005009875167161226,
0.02497679926455021,
-0.021098321303725243,
0.05292879045009613,
0.0275854654610157,
-0.04371783509850502,
-0.014051618054509163,
-0.007055874448269606,
0.027885880321264267,
-0.06916700303554535,
-0.03334583342075348,
0.013081870041787624,
0.022580236196517944,
0.0340263731777668,
0.028509657829999924,
-0.09281241148710251,
-0.03913957625627518,
-0.059629302471876144,
0.0034530044067651033,
0.01604592613875866,
-0.01746470481157303,
-0.11664091795682907,
0.020012298598885536,
0.025268616154789925,
0.02864268608391285,
0.019652845337986946,
0.0017154826782643795,
0.03502228111028671,
0.007534431759268045,
-0.0017564097652211785,
-0.004200180526822805,
-0.043737269937992096,
-0.009579531848430634,
-0.02720022201538086,
-0.018991243094205856,
-0.02460581064224243,
-0.0370943583548069,
-0.046365927904844284,
-0.01831258460879326,
-0.026592016220092773,
0.00034321664134040475,
-0.04826224595308304,
-0.0018718147184699774,
0.05263006314635277,
-0.04183477535843849,
-0.002166357822716236,
0.0297861248254776,
0.03966166079044342,
-0.06289553642272949,
-0.0687769427895546,
0.016335295513272285,
0.023433135822415352,
0.021829256787896156,
-0.0076087526977062225,
-0.007848859764635563,
0.04460860788822174,
0.002286286558955908,
0.0025963226798921824,
-0.09713456779718399,
-0.01663968712091446,
0.009877207688987255,
-0.027060164138674736,
0.078068308532238,
0.0044690645299851894,
-0.0444968119263649,
-0.01880127750337124,
0.05214342102408409,
-0.03891510143876076,
0.0464266762137413,
0.053426072001457214,
-0.02148527465760708,
-0.02770952694118023,
-0.07954306155443192,
-0.0018146444344893098,
-0.04413644224405289,
0.04944784194231033,
-0.03968256711959839,
0.014995287172496319,
-0.03327104449272156,
0.026328397914767265,
0.025652287527918816,
0.03087603487074375,
-0.008521518670022488,
0.0016947862459346652,
-0.0058616227470338345,
-0.06019218638539314,
0.020920341834425926,
0.0023031539749354124,
0.029276033863425255,
-0.030032174661755562,
0.041389282792806625,
-0.027898170053958893,
0.014164093881845474,
-0.08457289636135101,
-0.0037284863647073507,
-0.008533511310815811,
0.06973358988761902,
-0.006418748293071985,
0.034505363553762436,
0.02477257139980793,
0.004443158861249685,
0.052012961357831955,
-0.008205095306038857,
0.04567115381360054,
0.030514253303408623,
-0.028576787561178207,
0.0040817963890731335,
0.02141682244837284,
0.025050517171621323,
0.007402507588267326,
-0.021690646186470985,
0.01705244556069374,
0.0002970841887872666,
0.01957881450653076,
0.016093984246253967,
-0.016347801312804222,
0.03960420936346054,
-0.04381310194730759,
0.03851724788546562,
0.048514172434806824,
0.03126869350671768,
-0.03570251166820526,
0.008582557551562786,
-0.016019044443964958,
0.004463160876184702,
0.01678050495684147,
0.006707799155265093,
0.03413333371281624,
0.053339678794145584,
-0.014929492957890034,
0.05518892779946327,
-0.022956470027565956,
0.019247641786932945,
-0.0314030684530735,
0.007256017066538334,
0.03072092868387699,
0.0012974606361240149,
-0.03861669823527336,
0.013508043251931667,
-0.02721169963479042,
-0.01638025976717472,
0.025501543655991554,
0.04220469295978546,
0.04863680899143219,
0.04229116812348366,
-0.024670762941241264,
-0.04373324289917946,
0.00784204714000225,
-0.03081519529223442,
0.06281986832618713,
-0.024017194285988808,
0.06898383051156998,
-0.03592522069811821,
0.004256026819348335,
-0.012472991831600666,
0.01356997899711132,
0.045422788709402084,
0.07261630147695541,
0.008326122537255287,
0.07654944062232971,
-0.06153520196676254,
-0.0479855090379715,
-0.04885953664779663,
-0.014639350585639477,
-0.020650891587138176,
0.014823724515736103,
0.044268898665905,
0.023010453209280968,
-0.03161681815981865,
0.022497529163956642,
-0.0194375179708004,
0.024895844981074333,
-0.019310764968395233,
-0.034771233797073364,
-0.051676563918590546,
0.010531223379075527,
0.040936872363090515,
0.007367108017206192,
-0.001968137687072158,
-0.0072157904505729675,
-0.04911447688937187,
-0.032146964222192764,
0.04239480942487717,
-0.05534087121486664,
-0.016049625352025032,
-0.0375320240855217,
0.09224715083837509,
0.0013049280969426036,
0.019169533625245094,
0.03237869217991829,
0.03234623372554779,
0.0463210828602314,
-0.049332957714796066,
0.09639926254749298,
0.015402121469378471,
0.0078089358285069466,
0.03397895023226738,
-0.08188440650701523,
-0.04089488089084625,
0.01395675353705883,
-0.0030952293891459703,
0.04950881004333496,
0.051338765770196915,
-0.01655443198978901,
-0.02560022659599781,
-0.0017568155890330672,
0.003370063379406929,
-0.0558956116437912,
-0.03191027417778969,
0.01937269978225231,
0.02027234435081482,
-0.10016404092311859,
-0.024266984313726425,
-0.03937213122844696,
-0.001260590273886919,
-0.0011839460348710418,
0.0014057975495234132,
0.014787289313971996,
-0.04762491583824158,
-0.08944720029830933,
-0.06443638354539871,
0.022757794708013535,
-0.0021361911203712225,
-0.015687046572566032,
-0.02134755812585354,
0.02086002007126808,
0.03646678850054741,
0.010939880274236202,
-0.019523223862051964,
0.003929723519831896,
-0.038405172526836395,
-0.0032686565537005663,
-0.045032694935798645,
-0.009129154495894909,
0.013581967912614346,
-0.0042277369648218155,
-0.017050916329026222,
-0.03131509944796562,
0.02566630207002163,
-0.04120676591992378,
-0.08857715874910355,
0.0180452112108469,
0.03929229453206062,
0.0011651181848719716,
-0.07792133837938309,
0.01362335029989481,
-0.019060440361499786,
-0.033754415810108185,
-0.019368577748537064,
-0.0176964420825243,
-0.038602713495492935,
-0.1182200238108635,
-0.0049956925213336945,
-0.07184424251317978,
-0.005740438587963581,
-0.006407549604773521,
0.04704209417104721,
-0.03184724226593971,
-0.009718730114400387,
-0.00817776471376419,
-0.02253129333257675,
-0.02447606809437275,
0.020181767642498016,
0.0014690379612147808,
0.01592385582625866,
0.04475732520222664,
0.027104752138257027,
-0.07536247372627258,
-0.007135360036045313,
0.04040088877081871,
-0.023048367351293564,
0.010393066331744194,
0.024391841143369675,
0.002928262110799551,
-0.055245038121938705,
0.011144590564072132,
0.02342069335281849,
-0.005223861895501614,
-0.029563065618276596,
0.02206605114042759,
0.05328407511115074,
0.022115657106041908,
0.0260302871465683,
-0.021217338740825653,
-0.025822967290878296,
0.0010642544366419315,
-0.017255233600735664,
0.0803132951259613,
-0.013178911060094833,
-0.03400121256709099,
0.006148286629468203,
0.008759727701544762,
-0.03260631486773491,
0.0272815003991127,
-0.026807840913534164,
-0.023207394406199455,
0.015318406745791435,
0.024208271875977516,
-0.028107788413763046,
0.04267951846122742,
-0.03400003910064697,
-0.008537491783499718,
-0.012957141734659672,
0.05564700439572334,
-0.015392386354506016,
-0.005846429616212845,
0.06943976134061813,
-0.051426466554403305,
0.006949665490537882,
-0.0010572208557277918,
-0.07067760825157166,
0.030564486980438232,
0.03958823159337044,
-0.020555930212140083,
0.03413359075784683,
-0.009780637919902802,
-0.02254657633602619,
0.0427846722304821,
0.04164367541670799,
0.05610329285264015,
0.008632835932075977,
0.036968059837818146,
0.024394748732447624,
-0.008291120640933514,
0.014682572335004807,
0.06656903773546219,
-0.022113576531410217,
0.037718765437603,
-0.036827392876148224,
-0.011828416027128696,
-0.026273010298609734,
0.027696801349520683,
0.05280664935708046,
0.06097857281565666,
-0.08257590979337692,
0.01714673638343811,
0.01797599531710148,
-0.022079454734921455,
-0.022417346015572548,
0.03546340391039848,
0.0383555106818676,
-0.02512214332818985,
0.010885280556976795,
0.0037105216179043055,
0.009200646542012691,
-0.0031638205982744694,
-0.036485135555267334,
-0.04107879847288132,
-0.03325977921485901,
0.036781635135412216,
0.04622069001197815,
-0.01854332908987999,
-0.0052825831808149815,
0.03801952674984932,
-0.0028122125659137964,
0.030713466927409172,
-0.03265571966767311,
-0.04106541723012924,
-0.027202077209949493,
-0.022678377106785774,
0.0424753800034523,
0.022834479808807373,
-0.04572765901684761,
-0.06524129211902618,
-0.02367359772324562,
0.004250152036547661,
-0.05698724091053009,
0.023136580362915993,
0.06602644920349121,
0.01704680174589157,
0.10131444782018661,
0.015710745006799698,
-0.06457909196615219,
0.01044001430273056,
0.010230747982859612,
-0.010475052520632744,
0.039930474013090134,
-0.06448585540056229,
0.014588424004614353,
0.037752144038677216,
-0.025096315890550613,
-0.004189766477793455,
-0.006561251822859049,
-0.10224440693855286,
0.019185585901141167,
0.004193834960460663,
-0.0032452496234327555,
0.07619233429431915,
-0.003970394842326641,
0.00033202586928382516,
-0.004637827631086111,
-0.04422545060515404,
0.02739686891436577,
0.05843689292669296,
-0.03943972289562225,
-0.015707679092884064,
-0.019405469298362732,
-0.014610152691602707,
-0.00874982587993145,
-0.021891245618462563,
0.0005725830560550094,
-0.045899488031864166,
0.028065908700227737,
0.007826099172234535,
0.004945696797221899,
-0.05392684414982796,
-0.04280144348740578,
0.022209152579307556,
0.01635761559009552,
0.01635836437344551,
-0.001480378326959908,
0.03187663480639458,
-0.01348601933568716,
-0.05692807585000992,
-0.01795184798538685,
0.05862151086330414,
0.013543523848056793,
-0.001406581257469952,
-0.03097722865641117,
0.02681202068924904,
-0.04313867911696434,
-0.02013348788022995,
-0.014265105128288269,
-0.00022830803936813027,
-0.0003331959305796772,
-0.0014503725105896592,
0.025939228013157845,
0.029076039791107178,
0.0149153433740139,
0.06367722153663635,
0.026476245373487473,
-0.04486120492219925,
0.009457990527153015,
-0.022268328815698624,
-0.005728384479880333,
-0.011525818146765232,
0.03366930037736893,
-0.049394767731428146,
-0.01871856488287449,
0.0014812876470386982,
0.02007492445409298,
0.04001927375793457,
0.01984628476202488,
0.06729131937026978,
0.013980233110487461,
-0.006522845011204481,
-0.00492511410266161,
0.00623472360894084,
-0.042153310030698776,
-0.010933507233858109,
-0.061753448098897934,
0.02946917898952961,
-0.011027227155864239,
-0.03371753916144371,
-0.03498511388897896,
0.009767193347215652,
0.04068072512745857,
-0.00267165363766253,
-0.022497553378343582,
-0.060625188052654266,
0.034650884568691254,
0.03151703625917435,
0.008802826516330242,
0.043036580085754395,
-0.030836131423711777,
0.010891327634453773,
0.012781180441379547,
-0.0740811750292778,
0.030828377231955528,
0.03767726197838783,
-0.034201934933662415,
-0.03891072794795036,
-0.0049858237616717815,
-0.0193039458245039,
-0.052111584693193436,
-0.02457888238132,
-0.028116507455706596,
-0.03109898790717125,
-0.02098119631409645,
0.014108629897236824,
0.00579129857942462,
0.021627657115459442,
-0.034194737672805786,
-0.019169846549630165,
-0.009784447960555553,
-0.08404870331287384,
-0.043191537261009216,
-0.012062990106642246,
0.03374222666025162,
-0.02849256619811058,
0.029744300991296768,
-0.01673441007733345,
-0.017794782295823097,
-0.03495066985487938,
-0.017250793054699898,
0.038691725581884384,
0.03837763890624046,
-0.016000457108020782,
-0.026464637368917465,
0.009607064537703991,
0.0077276648953557014,
0.014640679582953453,
-0.021223159506917,
-0.05783067271113396,
0.01893812231719494,
0.020639119669795036,
0.006819565314799547,
-0.015369883738458157,
0.029241669923067093,
0.04640908166766167,
0.0027709121350198984,
-0.008976966142654419,
-0.0536116361618042,
-0.014404513873159885,
0.025014599785208702,
-0.007156718522310257,
0.020436523482203484,
0.027415702119469643,
0.06564432382583618
] |
<p>The energy of a single planet in a gravitational potential is $$E=\frac{m\dot{r}^2}{2}+\frac{L^2}{2mr^2}-\frac{GMm}{r}$$
And the effective potential energy is defined as the last two terms. Note this satisfies $$F=-\nabla U$$
$$mr^2 \dot{\theta}-\frac{MmG}{r^2}=-\frac{d}{dr}(\frac{L^2}{2mr^2}-\frac{GMm}{r})$$
$$=\frac{L^2}{mr^3}-\frac{GMm}{r^2}$$</p>
<p>Similarly, in quantum mechanics I have encountered the energy of an electron in an electric potential as being
$$E=\frac{\hbar^2}{2mr^2}-\frac{Zq_e^2}{4 \pi \epsilon_0r}$$</p>
<p>With the first term arising from energy due to confinement in a small volume (uncertainty principle).</p>
<p>I'm aware that this question is probably site-pollutingly basic, but:</p>
<ul>
<li>I assume, by analogy, $\hbar$ is the electron's angular momentum (or integer multiples of $\hbar$: it's probably quantised). Does this form for $L_e$hold firm in post-1920/30's quantum mechanics, or is this result as spurious an idea as the Bohr atom model?</li>
<li>If I'm not incorrect, why aren't I? The energy-angular momentum equation is wholly classical, surely electrons behave very differently from this? </li>
<li>To what extent does the electron energy equation hold true, or is it again spurious?</li>
<li>Are there any other analogies exist between the equations that I've missed?</li>
</ul>
|
g2516
|
[
0.006539762485772371,
0.029469944536685944,
-0.002865992719307542,
-0.02317219041287899,
0.035927340388298035,
0.018329953774809837,
-0.003892595646902919,
0.0023524409625679255,
-0.04471667855978012,
0.05652879923582077,
0.03620097413659096,
-0.004596242681145668,
0.01651085540652275,
-0.04155341535806656,
0.028987104073166847,
0.0006528854719363153,
0.08550000190734863,
0.0012320993700996041,
0.01588502712547779,
-0.021369004622101784,
-0.007226269692182541,
-0.008180593140423298,
0.006187860853970051,
-0.028463775292038918,
-0.0033458394464105368,
0.026995405554771423,
0.002079118276014924,
0.003814910538494587,
-0.014725758694112301,
-0.014924371615052223,
0.020632781088352203,
0.004410390742123127,
0.09892085194587708,
-0.06288040429353714,
-0.03244704380631447,
-0.024427611380815506,
0.05511726066470146,
0.030677685514092445,
0.015106790699064732,
-0.042215798050165176,
0.0018688212148845196,
-0.07439415156841278,
-0.0026374822482466698,
-0.005919327028095722,
0.0192058514803648,
0.0032735969871282578,
0.006353620905429125,
-0.02514764480292797,
0.054569218307733536,
-0.029780438169836998,
0.028182566165924072,
0.08599544316530228,
0.07101041078567505,
-0.041695911437273026,
-0.03871055319905281,
0.0637243315577507,
-0.005920019466429949,
-0.01598716899752617,
0.013466049917042255,
0.049776043742895126,
0.04501811042428017,
0.029628556221723557,
-0.050073157995939255,
0.03289376199245453,
0.03683929145336151,
0.011011454276740551,
-0.05565304309129715,
0.02936667762696743,
0.004793524742126465,
-0.039951179176568985,
0.05644356086850166,
-0.06019260734319687,
-0.057384755462408066,
-0.008995253592729568,
-0.014165571890771389,
0.019138067960739136,
-0.0024415659718215466,
-0.027617519721388817,
0.018717046827077866,
-0.012942326255142689,
-0.03850724920630455,
-0.031123317778110504,
0.0046867006458342075,
0.005338920280337334,
0.05062303692102432,
-0.04560326039791107,
0.017570024356245995,
0.021505828946828842,
-0.045471612364053726,
0.005488659720867872,
0.022968579083681107,
-0.077889584004879,
-0.003324819030240178,
-0.03607582300901413,
-0.015416396781802177,
0.02951405756175518,
-0.03936075046658516,
0.04926730692386627,
-0.039471860975027084,
0.00799301452934742,
0.015588836744427681,
0.00453813886269927,
0.03124043717980385,
0.011817042715847492,
0.016159743070602417,
-0.02092096582055092,
-0.01292007602751255,
-0.027028033509850502,
0.0594203844666481,
-0.009699365124106407,
-0.019587254151701927,
0.020659277215600014,
0.02246449515223503,
-0.07749081403017044,
-0.05906199291348457,
0.012944407761096954,
0.10279107838869095,
-0.10739225149154663,
0.017209837213158607,
0.0805332362651825,
0.004073902033269405,
0.08220207691192627,
0.047365639358758926,
0.0634026825428009,
-0.04056147485971451,
-0.011766807176172733,
-0.047114480286836624,
-0.019837932661175728,
0.0560314878821373,
-0.01941252313554287,
-0.017354456707835197,
-0.06785867363214493,
-0.04596798121929169,
-0.03134440258145332,
0.019829608500003815,
0.04367230460047722,
-0.028241682797670364,
0.02754165790975094,
0.00033430734765715897,
-0.016638396307826042,
0.020118823274970055,
-0.05540714040398598,
0.03464418277144432,
-0.0037724440917372704,
-0.04687482491135597,
0.03804609552025795,
-0.018914103507995605,
-0.018557138741016388,
0.055646561086177826,
0.06392529606819153,
-0.013738727197051048,
0.08095123618841171,
0.0020672990940511227,
-0.03009624592959881,
0.01444789208471775,
0.017317190766334534,
0.04479660838842392,
-0.03404776006937027,
0.007451419252902269,
0.03371512144804001,
0.025296935811638832,
-0.015593795105814934,
0.09330976754426956,
-0.006251513492316008,
-0.023875216022133827,
0.039382848888635635,
0.025158803910017014,
-0.016383174806833267,
0.015160518698394299,
0.017587315291166306,
0.01030332874506712,
-0.0443699024617672,
0.054762087762355804,
-0.0024710672441869974,
-0.026388762518763542,
0.04698679968714714,
-0.006520492024719715,
-0.04423438012599945,
-0.05054643750190735,
0.012252951972186565,
0.011322029866278172,
0.011748097836971283,
0.03700700029730797,
-0.02611711621284485,
-0.0060708108358085155,
0.02054433338344097,
0.040186233818531036,
0.05126628279685974,
-0.012218247167766094,
0.0034994580782949924,
-0.019088473170995712,
0.028636924922466278,
0.012257540598511696,
-0.01990940235555172,
-0.010807234793901443,
0.04080480337142944,
0.027865303680300713,
-0.039869438856840134,
-0.028116902336478233,
0.0663449764251709,
-0.04233552888035774,
0.04278305917978287,
0.018982216715812683,
0.02145218476653099,
0.05593736097216606,
0.0017974774818867445,
0.04411884397268295,
-0.01665641739964485,
0.06326641887426376,
-0.04369419813156128,
0.008531852625310421,
-0.0488666370511055,
-0.008692867122590542,
0.0145943658426404,
-0.03322041034698486,
-0.03705865144729614,
-0.04465566202998161,
0.05376623198390007,
-0.03978920355439186,
-0.00411755358800292,
-0.02441573329269886,
-0.008565936237573624,
0.052753154188394547,
-0.020404234528541565,
0.02114776149392128,
0.03475354239344597,
-0.053820136934518814,
-0.03554077073931694,
-0.03800502419471741,
0.016230937093496323,
-0.034226950258016586,
0.05875232070684433,
-0.0025855444837361574,
-0.008860468864440918,
0.012786808423697948,
0.04875379428267479,
-0.020437177270650864,
-0.06587354838848114,
-0.007132528815418482,
0.012035351246595383,
0.024193715304136276,
-0.0067966533824801445,
-0.05360984429717064,
-0.0038057458586990833,
0.07403786480426788,
0.034149929881095886,
0.08517677336931229,
0.004583529196679592,
0.02348889783024788,
0.04952453821897507,
-0.05704683065414429,
-0.0025854180566966534,
-0.045650504529476166,
0.005618150345981121,
-0.02826540917158127,
0.02526017278432846,
-0.023743079975247383,
0.035899873822927475,
-0.06570272892713547,
-0.019676292315125465,
-0.02006084844470024,
-0.05026758834719658,
0.028634769842028618,
0.05598454922437668,
-0.007866323925554752,
-0.007486443035304546,
-0.026575498282909393,
0.012868334539234638,
0.031544070690870285,
-0.029772404581308365,
0.04212753847241402,
0.07612498849630356,
-0.056573573499917984,
0.03746625408530235,
-0.02896774187684059,
-0.033566296100616455,
-0.038748160004615784,
-0.0144294872879982,
0.045885153114795685,
-0.028246143832802773,
-0.04638073220849037,
-0.03927129879593849,
-0.045335132628679276,
0.0580763965845108,
0.02478494681417942,
-0.03257419914007187,
0.01762579195201397,
0.04681159555912018,
0.01654687523841858,
-0.03973736613988876,
-0.01991082727909088,
0.03011837974190712,
0.028915666043758392,
0.025424251332879066,
-0.04091685637831688,
0.0009715526248328388,
0.010191040113568306,
0.012817847542464733,
-0.039780475199222565,
0.024056626483798027,
0.009647585451602936,
0.014701062813401222,
-0.0707947313785553,
0.043748464435338974,
-0.006140825804322958,
0.013314574025571346,
-0.05101591348648071,
-0.03734807297587395,
-0.010193278081715107,
0.010397152975201607,
-0.0386589914560318,
0.055798616260290146,
-0.016036244109272957,
0.03188847377896309,
-0.039292048662900925,
-0.02659137174487114,
-0.037001751363277435,
0.0010196403600275517,
-0.03925338760018349,
-0.05396484583616257,
-0.010738136246800423,
-0.039184942841529846,
0.00013853322889190167,
-0.01739879511296749,
0.02856033481657505,
0.03364361450076103,
-0.0506010502576828,
-0.05036766827106476,
-0.06498438119888306,
0.01812969520688057,
0.01752498559653759,
0.01789957657456398,
0.0019584011752158403,
0.022445855662226677,
-0.011294321157038212,
-0.05730776861310005,
-0.00191821891348809,
0.021320350468158722,
0.04715273901820183,
0.0035001086071133614,
-0.008218985050916672,
0.0129836555570364,
-0.029689159244298935,
-0.01444275863468647,
-0.026799753308296204,
0.0005685354117304087,
-0.018287397921085358,
-0.02149653621017933,
0.009957956150174141,
-0.02462443895637989,
-0.03447935730218887,
-0.025257395580410957,
0.027724020183086395,
0.026561826467514038,
0.022973304614424706,
-0.02510060742497444,
0.014606957323849201,
0.019007248803973198,
0.06731221079826355,
0.04744292423129082,
0.008088464848697186,
0.00214028381742537,
0.02980966866016388,
-0.013743828050792217,
0.0022164497058838606,
-0.016207179054617882,
-0.03659064695239067,
0.014715919271111488,
0.03452127054333687,
-0.028469465672969818,
-0.002551094628870487,
0.008647766895592213,
0.026596570387482643,
0.02702665701508522,
0.03577444702386856,
-0.042744286358356476,
-0.006385736633092165,
-0.008680548518896103,
-0.019088447093963623,
-0.01759544387459755,
0.03452572599053383,
-0.0375637412071228,
0.024476241320371628,
0.08152999728918076,
-0.008053307421505451,
-0.010324422270059586,
-0.042921844869852066,
-0.011296335607767105,
0.03302965313196182,
-0.01220121793448925,
-0.021008003503084183,
-0.05513642728328705,
-0.014194267801940441,
0.04941283166408539,
0.008737084455788136,
-0.002463719341903925,
0.0488680899143219,
-0.0984000638127327,
0.022758696228265762,
0.06801816821098328,
0.007424484472721815,
-0.0014960832195356488,
0.0029221605509519577,
0.02310679666697979,
-0.03277236968278885,
0.021753357723355293,
0.04484812915325165,
-0.04390442371368408,
-0.049847982823848724,
-0.08385390043258667,
0.01823928765952587,
0.022428788244724274,
0.013376102782785892,
-0.024765096604824066,
-0.024121008813381195,
-0.019764449447393417,
-0.014095441438257694,
-0.024266721680760384,
-0.011001242324709892,
0.033493224531412125,
0.005492204800248146,
0.0441625714302063,
0.010745123960077763,
-0.04189833253622055,
-0.03013576939702034,
0.04971669614315033,
0.038568902760744095,
0.027435002848505974,
-0.01571916788816452,
-0.03469080477952957,
0.03841197118163109,
0.027536779642105103,
0.019362030550837517,
0.04155546799302101,
-0.06228822469711304,
0.028058825060725212,
-0.07330912351608276,
0.003387459786608815,
0.016850823536515236,
0.02056410349905491,
0.0897965356707573,
0.05082038789987564,
0.03946148604154587,
0.01645640842616558,
-0.019846327602863312,
0.012948795221745968,
0.0023347348906099796,
0.024705300107598305,
0.01539539359509945,
-0.004973908886313438,
-0.04007678106427193,
-0.058540891855955124,
0.019759656861424446,
-0.013883867301046848,
0.024852784350514412,
-0.052882082760334015,
-0.05690804496407509,
0.009488505311310291,
0.05243181064724922,
0.0035619887057691813,
0.019200993701815605,
0.0008173729875124991,
0.0037482965271919966,
0.0252310149371624,
0.06148771941661835,
-0.026136262342333794,
-0.10993321985006332,
0.006063191685825586,
-0.0433979295194149,
-0.11205469071865082,
-0.0005202239844948053,
-0.03403515741229057,
0.02912236377596855,
-0.021920183673501015,
0.03553232178092003,
0.004658875986933708,
0.014469358138740063,
-0.07144195586442947,
0.00898365955799818,
-0.05551230534911156,
-0.04989033564925194,
-0.013253036886453629,
-0.025380335748195648,
0.07680605351924896,
-0.014429197646677494,
0.021110178902745247,
-0.015870587900280952,
0.010919205844402313,
0.008522383868694305,
0.01366475597023964,
0.02802843041718006,
0.045156825333833694,
-0.026439225301146507,
-0.01456424966454506,
0.04181244596838951,
0.09153462201356888,
-0.02521524392068386,
-0.02773335762321949,
0.0226912684738636,
0.03940584883093834,
-0.035689592361450195,
0.03380764648318291,
-0.0656229704618454,
0.011693229898810387,
0.0366782546043396,
0.03303324803709984,
0.0462954007089138,
-0.028114523738622665,
0.0051007396541535854,
0.004246235825121403,
0.010485442355275154,
-0.0061045242473483086,
-0.04279625043272972,
0.044442351907491684,
0.037536680698394775,
-0.019863953813910484,
-0.029506776481866837,
-0.015972601249814034,
-0.033304087817668915,
-0.03966027870774269,
0.05178285017609596,
0.008081707172095776,
0.025464292615652084,
-0.029053354635834694,
0.046441834419965744,
0.02771737053990364,
-0.055120810866355896,
-0.04741346091032028,
-0.002729238709434867,
0.07852700352668762,
-0.020965345203876495,
-0.019896669313311577,
0.018988708034157753,
0.016621526330709457,
-0.0005086400778964162,
0.017492011189460754,
-0.02844078838825226,
-0.00508508225902915,
0.053070344030857086,
-0.025070641189813614,
0.014397714287042618,
-0.04097016155719757,
0.012222708202898502,
0.011171117424964905,
-0.07047753781080246,
0.014615790918469429,
-0.013378730975091457,
0.0022000735625624657,
0.027082370594143867,
0.00034820003202185035,
-0.020218338817358017,
-0.059202492237091064,
-0.03226466849446297,
-0.00866969209164381,
0.01512612123042345,
0.03535643592476845,
0.03088195249438286,
-0.05161280184984207,
-0.07744813710451126,
-0.020097026601433754,
0.0227799154818058,
0.02040993422269821,
0.056288719177246094,
0.0013949809363111854,
0.030142750591039658,
-0.05052082985639572,
0.040666040033102036,
-0.07216215878725052,
0.007624058984220028,
0.04800857976078987,
-0.032106928527355194,
0.051971685141325,
0.03933389112353325,
-0.051690395921468735,
0.05481038615107536,
0.02441481500864029,
-0.0348820798099041,
-0.03809720650315285,
-0.028319556266069412,
-0.023777928203344345,
0.0036468671169131994,
-0.00417077261954546,
0.02753124199807644,
-0.016238179057836533,
0.00006244193355087191,
0.08456015586853027,
-0.05081505700945854,
-0.06386034190654755,
0.02070811204612255,
-0.05820906534790993,
0.00023068062728270888,
-0.008317934349179268,
0.005617460701614618,
-0.02827160619199276,
-0.04463452100753784,
0.007053046021610498,
0.020010028034448624,
-0.024437883868813515,
-0.043820347636938095,
0.013775989413261414,
0.029655465856194496,
0.03304208442568779,
-0.007318671327084303,
-0.01872817613184452,
0.04428565129637718,
-0.0031202957034111023,
-0.040419213473796844,
-0.017319709062576294,
-0.039206910878419876,
0.030741237103939056,
-0.048139505088329315,
0.03598906844854355,
0.014210903085768223,
0.0021489067003130913,
-0.03731103986501694,
-0.00537683442234993,
-0.002529362216591835,
0.0783512070775032,
-0.018151942640542984,
0.016327740624547005,
0.022401953116059303,
0.0033547603525221348,
0.023739252239465714,
-0.049661360681056976,
0.05877070501446724,
0.010240188799798489,
-0.029641997069120407,
0.019832398742437363,
0.031513091176748276,
-0.022585280239582062,
-0.020662276074290276,
-0.0037122825160622597,
0.04291486367583275,
0.0779108926653862,
-0.02793770283460617,
-0.034452151507139206,
-0.019547495990991592,
-0.030035005882382393,
0.017844559624791145,
0.009474815800786018,
-0.05125207081437111,
-0.0029749833047389984,
0.06255429238080978,
-0.017390942201018333,
-0.045810893177986145,
-0.00547378696501255,
-0.004031707998365164,
0.03335125744342804,
-0.04344189539551735,
-0.01603780873119831,
0.0008464428246952593,
-0.056452080607414246,
0.00915671419352293,
0.01762235350906849,
-0.030826402828097343,
0.003963945433497429,
-0.03469226881861687,
0.052496518939733505,
0.053014714270830154,
-0.052250612527132034,
0.011541186831891537,
-0.009172769263386726,
-0.02223087102174759,
-0.04575701802968979,
-0.004789615981280804,
0.046557117253541946,
-0.00906771793961525,
-0.07692718505859375,
-0.011396863497793674,
-0.0642540231347084,
0.024250607937574387,
-0.01751617342233658,
-0.0172208733856678,
0.030884403735399246,
-0.05098993703722954,
0.015839453786611557,
0.01993265561759472,
-0.007779148407280445,
-0.00026708756922744215,
0.01070063840597868,
0.006075283512473106,
0.05203239619731903,
0.001502766739577055,
0.01389408390969038,
-0.023482123389840126,
-0.032661229372024536,
-0.0217424463480711,
-0.019931044429540634,
-0.03430433198809624,
0.01826322264969349,
0.02059217356145382,
0.04352157562971115,
0.03461926430463791,
0.02408524602651596,
-0.06960337609052658,
-0.01744496449828148,
0.02974935807287693,
0.007839841768145561,
0.030913548544049263,
-0.011164440773427486,
0.003659950103610754,
-0.015537107363343239,
-0.00905483216047287,
-0.022317519411444664,
0.0666249617934227,
0.027592001482844353,
0.006586561910808086,
0.02370624616742134,
-0.06932449340820312,
-0.019211070612072945,
0.05643908679485321,
0.00902668759226799,
0.011820575222373009,
0.020354844629764557,
0.03476628661155701,
-0.04536956548690796,
0.0006134919240139425,
0.06649789214134216,
0.004196783993393183,
-0.017695022746920586,
-0.001501169870607555,
-0.006682675797492266,
0.046290989965200424,
-0.050824496895074844,
0.01662709377706051,
-0.01826563850045204,
-0.014181524515151978,
-0.03082348220050335,
0.09701927751302719,
-0.04342866316437721,
-0.019216682761907578,
-0.009760808199644089,
-0.035010967403650284,
-0.0312713198363781,
-0.03715457022190094,
0.006852248217910528,
0.009582745842635632,
0.003929397091269493,
0.040907122194767,
-0.00952133908867836,
0.038103826344013214,
-0.044435884803533554,
0.05425652489066124,
0.012303164228796959,
-0.04849199950695038,
0.021219950169324875,
-0.06817308813333511,
-0.00514025054872036,
0.0492861308157444,
0.03647296875715256,
-0.0331399105489254,
-0.01885252073407173,
-0.046306367963552475,
0.02461375668644905,
0.07701055705547333,
-0.0628843903541565,
-0.04085475951433182,
0.009824537672102451,
-0.02157418429851532,
0.006163128651678562,
-0.0061809467151761055,
-0.002367034088820219,
0.002964120591059327,
-0.008669471368193626,
-0.02820613607764244,
-0.06829290837049484,
0.012605685740709305,
0.060141656547784805
] |
<p>I have the following question to answer:
a force of160 N stretches a spring 0.050m from its equilibrium position.
A. what is the spring constant of the spring?</p>
<p>The equation for Hooke's Law in my text is F=-kx, where k is the spring constant. So with some simple algebra we can find an equation for k: k = -(f/x). After plugging all my values in I get -3200. </p>
<p>My question: Am I supposed to disregard the negative sign when plugging in value? </p>
|
g2517
|
[
0.01284168753772974,
-0.00009076143760466948,
0.011454869993031025,
0.02347518317401409,
0.010607635602355003,
-0.018786145374178886,
0.013825592584908009,
0.03132076933979988,
-0.036671265959739685,
-0.03338941931724548,
-0.053695596754550934,
0.01016686949878931,
0.006669314112514257,
0.0003638580965343863,
0.06126994267106056,
-0.014671132899820805,
0.03173069283366203,
-0.03232157602906227,
0.019751904532313347,
-0.003172471420839429,
0.011356128379702568,
0.012673500925302505,
-0.035454388707876205,
-0.030117599293589592,
0.04622696712613106,
-0.03637127950787544,
-0.03339071571826935,
0.04288189858198166,
-0.08801091462373734,
-0.05421525612473488,
0.0695481225848198,
-0.030512191355228424,
0.012874861247837543,
-0.07623667269945145,
-0.09638310968875885,
0.030364880338311195,
0.0009606917155906558,
0.03967391327023506,
0.012490191496908665,
0.02776695415377617,
0.032798368483781815,
-0.05369795486330986,
0.01320003904402256,
0.01896466501057148,
0.0114081259816885,
0.010422112420201302,
0.006260562222450972,
0.026219608262181282,
0.031082695350050926,
-0.023759057745337486,
-0.021350853145122528,
-0.0023050683084875345,
0.018128030002117157,
-0.05188654363155365,
0.023474596440792084,
0.054400406777858734,
0.04571151360869408,
-0.03014988824725151,
0.0029304721392691135,
0.05141447111964226,
0.014860427938401699,
-0.010365904308855534,
-0.006735856644809246,
-0.04545445740222931,
0.05075756460428238,
0.020746927708387375,
0.011136469431221485,
-0.0025892797857522964,
-0.03791588917374611,
0.05267755314707756,
-0.03764135017991066,
-0.018460823222994804,
0.040583983063697815,
-0.07753830403089523,
-0.05105120316147804,
0.043022047728300095,
0.04333548620343208,
0.028796570375561714,
-0.024043165147304535,
-0.057583898305892944,
-0.000476664281450212,
0.008769526146352291,
0.04002673551440239,
-0.005679607391357422,
0.04637198522686958,
0.018317708745598793,
0.06752157211303711,
-0.01320316269993782,
0.0161545779556036,
0.0020680874586105347,
0.010476766154170036,
0.020700400695204735,
0.06077263131737709,
-0.04433808475732803,
-0.029849350452423096,
-0.014538570307195187,
0.0005247386870905757,
0.08914340287446976,
0.021586205810308456,
-0.005158587358891964,
0.0016690801130607724,
-0.03972702845931053,
-0.027736563235521317,
-0.0039946832694113255,
-0.0853298231959343,
-0.001858446397818625,
0.021197782829403877,
0.024292536079883575,
0.0023019539657980204,
-0.04355103522539139,
-0.018575549125671387,
-0.041402168571949005,
0.049511294811964035,
-0.041204363107681274,
-0.07235047221183777,
-0.02068943902850151,
0.031350456178188324,
-0.03967899829149246,
0.012582610361278057,
-0.015342076309025288,
-0.007188890594989061,
0.03458748385310173,
0.07796870172023773,
0.026843253523111343,
0.017441503703594208,
-0.09635798633098602,
0.035417892038822174,
0.030829250812530518,
0.01776655949652195,
-0.04076571390032768,
-0.013511190190911293,
-0.026442520320415497,
-0.009596867486834526,
-0.008117896504700184,
-0.015764269977808,
0.07602264732122421,
0.006165585946291685,
-0.01978004164993763,
0.02376975305378437,
0.026683762669563293,
0.018188608810305595,
-0.01202354021370411,
0.04134911298751831,
-0.03333670645952225,
-0.034937214106321335,
0.04166309908032417,
-0.020983410999178886,
-0.04172868654131889,
0.047313008457422256,
0.01747119426727295,
-0.002481857780367136,
0.025560667738318443,
-0.0027459817938506603,
-0.024129295721650124,
0.029965899884700775,
-0.03416067734360695,
0.042334675788879395,
-0.045816607773303986,
-0.0014413157477974892,
0.027924366295337677,
0.03543369844555855,
-0.07056054472923279,
-0.002110684523358941,
0.01392657496035099,
-0.062462903559207916,
0.03917624056339264,
-0.04979199171066284,
0.01194719783961773,
-0.019623888656497,
-0.037693750113248825,
-0.04595822095870972,
0.007225427310913801,
0.02975207380950451,
-0.05777599290013313,
0.015242650173604488,
-0.06008865311741829,
0.00560020562261343,
-0.013205229304730892,
0.017949575558304787,
0.00044647057075053453,
-0.03752349689602852,
0.014769027940928936,
0.013187482953071594,
0.050237592309713364,
-0.026190465316176414,
0.04916992783546448,
0.00994374230504036,
0.029562992975115776,
-0.04591058939695358,
-0.021785294637084007,
-0.015284433960914612,
-0.03713530674576759,
-0.07165718823671341,
0.04565541073679924,
-0.01862204074859619,
-0.050429657101631165,
0.03274035453796387,
-0.01818457432091236,
-0.014291162602603436,
0.007092928979545832,
0.015422849915921688,
0.046224914491176605,
0.008759064599871635,
0.039388544857501984,
0.008562887087464333,
-0.01950840838253498,
0.005984763614833355,
-0.023550407961010933,
0.05633145943284035,
0.004307919181883335,
0.003427678719162941,
-0.03110121376812458,
0.0013332843082025647,
0.061438702046871185,
-0.060776110738515854,
-0.033070072531700134,
0.0047370195388793945,
0.02313932217657566,
0.00916330423206091,
0.04432091489434242,
-0.020548589527606964,
0.035492125898599625,
0.008474753238260746,
-0.018884653225541115,
-0.03499459847807884,
0.018420852720737457,
0.010199960321187973,
-0.031551945954561234,
0.017346573993563652,
-0.0410112626850605,
-0.013842985965311527,
-0.014582275412976742,
-0.054736457765102386,
0.05460812896490097,
0.02673720009624958,
0.07492776215076447,
-0.008767758496105671,
0.02004905231297016,
-0.03709941357374191,
-0.01129115279763937,
0.044534143060445786,
0.007275421638041735,
0.005289743654429913,
-0.029164288192987442,
0.024324027821421623,
0.021980902180075645,
-0.010108200833201408,
0.03425831347703934,
-0.011359475553035736,
0.076204814016819,
0.007103816140443087,
-0.004184426739811897,
0.008855195716023445,
0.05180373042821884,
-0.012285773642361164,
0.016410134732723236,
-0.050926435738801956,
-0.005331771913915873,
-0.0019652866758406162,
-0.02473931573331356,
0.019534282386302948,
-0.028634628280997276,
0.05202890932559967,
0.007096142042428255,
-0.08664406836032867,
-0.013927390798926353,
-0.055467721074819565,
0.0258810892701149,
0.09436498582363129,
0.026945432648062706,
0.014056741259992123,
0.020505862310528755,
-0.03259546682238579,
0.005530201829969883,
0.03621451556682587,
-0.07094577699899673,
-0.04785817116498947,
-0.01557619497179985,
0.004955424461513758,
0.032969001680612564,
0.021386224776506424,
0.004178985022008419,
-0.03568723052740097,
0.008276897482573986,
-0.0005542626022361219,
-0.049135398119688034,
-0.015213585458695889,
0.029324427247047424,
-0.03344644606113434,
0.006547638680785894,
0.003176736645400524,
0.026814939454197884,
0.015144702978432178,
0.011000093072652817,
0.007530592381954193,
0.06805762648582458,
-0.02614433318376541,
-0.05082930251955986,
0.0055670663714408875,
0.05662999674677849,
-0.04766324162483215,
-0.09501204639673233,
0.004913376644253731,
-0.01177379209548235,
0.021231068298220634,
0.005930703599005938,
0.0032126030419021845,
-0.050088297575712204,
0.04863447695970535,
0.055985841900110245,
-0.07559559494256973,
0.0035830901470035315,
0.08114265650510788,
-0.05683073773980141,
-0.0372309647500515,
0.04768726974725723,
-0.02214197814464569,
-0.021846428513526917,
0.007507502567023039,
-0.07578720897436142,
0.042468324303627014,
-0.070198655128479,
0.045615989714860916,
0.021417930722236633,
-0.022075451910495758,
0.014347612857818604,
-0.04677276313304901,
0.013960596174001694,
-0.04890111833810806,
-0.029872532933950424,
-0.03771663084626198,
-0.053122054785490036,
-0.004783716052770615,
0.002455721143633127,
-0.0057534221559762955,
-0.04217894375324249,
0.023365387693047523,
-0.002178709488362074,
0.009792406111955643,
0.045187368988990784,
-0.03708086162805557,
-0.04190986230969429,
-0.028737584128975868,
-0.02056018076837063,
-0.041687414050102234,
-0.03633313253521919,
-0.035365648567676544,
0.05215746909379959,
0.04856176674365997,
-0.03457564115524292,
0.04196152836084366,
-0.021379414945840836,
0.005083013791590929,
-0.03534112870693207,
-0.009230870753526688,
0.010791373439133167,
0.04364044964313507,
-0.00483707943931222,
-0.1033562570810318,
0.014669771306216717,
0.04934098199009895,
-0.05034318193793297,
-0.040561363101005554,
0.054098941385746,
0.005040456540882587,
-0.024890486150979996,
-0.028958819806575775,
0.10230409353971481,
-0.0367228165268898,
-0.007447062060236931,
0.0016202887054532766,
-0.008584641851484776,
0.027708904817700386,
0.04612790420651436,
0.015868721529841423,
-0.06827963143587112,
0.005448201205581427,
0.03605110943317413,
-0.0089526092633605,
0.016744915395975113,
0.014915954321622849,
0.02535977214574814,
-0.02690100483596325,
0.023113125935196877,
0.011272690258920193,
-0.0012715691700577736,
0.013078241609036922,
-0.020340152084827423,
0.02653229795396328,
-0.06740546971559525,
0.03220474347472191,
-0.05375669151544571,
-0.04002697020769119,
0.038793500512838364,
0.021828891709446907,
0.005258731544017792,
-0.025953486561775208,
-0.0011020296951755881,
-0.0516829751431942,
-0.023472081869840622,
-0.0205166507512331,
0.011537287384271622,
0.01174013689160347,
0.037325985729694366,
0.03748669475317001,
0.03486889600753784,
0.044065918773412704,
-0.008883018046617508,
0.028761908411979675,
0.004262982867658138,
0.013122186996042728,
-0.04382673278450966,
-0.018129589036107063,
-0.026776134967803955,
0.02245156466960907,
0.0060516600497066975,
0.06287220120429993,
-0.03762452304363251,
0.03884011134505272,
-0.029177045449614525,
0.0731031596660614,
0.05398107320070267,
-0.02819145657122135,
-0.05949223041534424,
0.0010146781569346786,
0.00785540509968996,
0.008200609125196934,
0.005616418085992336,
0.006600618828088045,
-0.011185829527676105,
-0.10576978325843811,
0.02395937778055668,
0.022666212171316147,
-0.026609405875205994,
-0.06158536672592163,
0.08560719341039658,
-0.011354275047779083,
0.07990147918462753,
-0.05203918740153313,
0.02716517262160778,
-0.041723210364580154,
0.04035084322094917,
0.028624895960092545,
0.003607595805078745,
-0.08724579215049744,
0.005635902285575867,
-0.011259377934038639,
-0.014610915444791317,
-0.03321139141917229,
0.02960861288011074,
-0.02639518678188324,
-0.030770625919103622,
-0.014778238721191883,
-0.03526291251182556,
-0.013494214043021202,
0.05208570510149002,
-0.0548996776342392,
0.034368664026260376,
-0.016090238466858864,
0.002788468962535262,
0.011715162545442581,
0.026750408113002777,
0.008567283861339092,
0.05218665674328804,
0.0438159741461277,
-0.04468312859535217,
-0.00821224320679903,
-0.02984587475657463,
0.019403330981731415,
0.019316626712679863,
0.05848774313926697,
0.017603352665901184,
0.021630531176924706,
0.00681159645318985,
0.02228681370615959,
0.0054381173104047775,
0.0329638347029686,
0.07188167423009872,
-0.01577627658843994,
0.006687142886221409,
-0.017883215099573135,
0.00987061858177185,
-0.014846662059426308,
-0.014039064757525921,
-0.029121702536940575,
0.023353975266218185,
-0.005086804274469614,
0.025231819599866867,
0.010359357111155987,
-0.007259526755660772,
0.07616851478815079,
0.04724657163023949,
0.03383965045213699,
0.028740953654050827,
-0.010671894066035748,
0.029599325731396675,
-0.005019665230065584,
-0.0046577113680541515,
0.008231067098677158,
0.004380512051284313,
-0.054573118686676025,
-0.038703206926584244,
-0.007503504399210215,
0.0354454331099987,
-0.035790786147117615,
0.05862126871943474,
-0.01943303644657135,
0.01682916283607483,
0.04661563038825989,
-0.009945908561348915,
0.04687360301613808,
0.003126091556623578,
0.04267517849802971,
0.0206393264234066,
-0.01487420592457056,
0.010963845998048782,
0.0027700511272996664,
0.015695780515670776,
-0.07403682917356491,
0.037323012948036194,
0.04241013154387474,
0.03833046928048134,
0.06344752758741379,
-0.03468751907348633,
-0.023086728528141975,
-0.004625965375453234,
0.006071754265576601,
-0.044422607868909836,
0.003494885051622987,
-0.015450505539774895,
-0.012362433597445488,
0.0583948940038681,
0.020704343914985657,
-0.01036306656897068,
0.04149171710014343,
-0.04000891000032425,
-0.0133517412468791,
-0.004127878695726395,
-0.009198380634188652,
0.006903366185724735,
-0.008003076538443565,
-0.03292617201805115,
0.08000210672616959,
0.003330598119646311,
-0.08824556320905685,
-0.00639716349542141,
-0.010848332196474075,
0.02235792949795723,
0.008671694435179234,
0.024047208949923515,
-0.029301464557647705,
0.03800132870674133,
-0.05891065672039986,
0.03465154394507408,
0.03265225887298584,
-0.0009207246475853026,
0.02187272533774376,
-0.010399679653346539,
0.0031031023245304823,
0.023943325504660606,
-0.006785287521779537,
0.008912176825106144,
0.014804224483668804,
0.030907273292541504,
0.03864005208015442,
-0.012461662292480469,
-0.001118506072089076,
-0.04228678718209267,
0.05962463095784187,
0.05110538750886917,
0.010918935760855675,
0.012897016480565071,
0.006084198597818613,
0.013620220124721527,
0.015052679926156998,
0.011282361112535,
-0.0631478801369667,
-0.0018995999125763774,
-0.035185594111680984,
0.047447726130485535,
-0.03940384089946747,
-0.029045207425951958,
0.051598045974969864,
-0.06296849250793457,
-0.02865421585738659,
0.0066202860325574875,
-0.003036379348486662,
-0.017074652016162872,
0.025604136288166046,
-0.03421294689178467,
-0.015726758167147636,
0.011651851236820221,
-0.0011065989965572953,
0.04846426472067833,
0.03124198317527771,
-0.040241096168756485,
0.021129963919520378,
-0.03634709492325783,
0.004485153127461672,
-0.027114301919937134,
-0.018506942316889763,
-0.005717298947274685,
0.08368651568889618,
-0.06480475515127182,
0.034186575561761856,
-0.04058530926704407,
-0.007470594719052315,
0.05658998712897301,
-0.04875696823000908,
-0.026593873277306557,
-0.008430802263319492,
0.050584033131599426,
-0.04447115212678909,
0.01051733735948801,
0.03956729173660278,
0.020382318645715714,
0.06291978061199188,
0.041639626026153564,
-0.022899940609931946,
-0.013337792828679085,
0.016418984159827232,
-0.033509451895952225,
0.0047208270989358425,
-0.024925222620368004,
0.026892878115177155,
0.04574063420295715,
-0.0621367022395134,
0.00980182085186243,
-0.026776710525155067,
0.008003437891602516,
0.009490927681326866,
0.038209810853004456,
-0.07898375391960144,
-0.02460821531713009,
0.01740388385951519,
0.07827814668416977,
-0.0029605652671307325,
0.03284204378724098,
0.024016467854380608,
0.09460649639368057,
-0.04330393671989441,
0.015448404476046562,
0.005116129759699106,
-0.00875095184892416,
-0.02964072860777378,
-0.026835553348064423,
0.023417185992002487,
-0.042795054614543915,
-0.07724618911743164,
0.03118789754807949,
0.007629555184394121,
-0.01756940223276615,
-0.008568928577005863,
-0.002143680350854993,
-0.005370753351598978,
0.023668702691793442,
-0.011103268712759018,
0.0195111446082592,
0.03639598935842514,
-0.02666551060974598,
-0.01798173598945141,
-0.02419370599091053,
0.002884254325181246,
0.008547499775886536,
0.0008827360579743981,
0.0883273109793663,
0.009745743125677109,
0.023872174322605133,
0.019542429596185684,
0.01951409876346588,
0.002163957804441452,
-0.0030536865815520287,
0.008177878335118294,
-0.015686791390180588,
-0.03808518871665001,
0.03248697891831398,
-0.0004458663461264223,
0.022978143766522408,
-0.021445637568831444,
-0.04513444006443024,
-0.005499378778040409,
-0.0072852568700909615,
-0.05629933625459671,
-0.03276495635509491,
-0.11614154279232025,
-0.022138798609375954,
0.000057456374634057283,
0.007707701530307531,
0.00955803133547306,
0.026392862200737,
0.010321942158043385,
0.015489415265619755,
0.03617914393544197,
-0.05172676220536232,
-0.00951208546757698,
-0.038474828004837036,
0.009963011369109154,
0.014809520915150642,
0.019118255004286766,
-0.023268116638064384,
0.03847946226596832,
0.004203955177217722,
-0.05626317486166954,
0.011965041048824787,
0.014063731767237186,
0.046018119901418686,
-0.08347642421722412,
-0.04132081940770149,
-0.06825311481952667,
-0.0205962136387825,
0.007448847871273756,
0.025239193812012672,
0.01792341284453869,
-0.02534724958240986,
0.04252972826361656,
0.03518478199839592,
0.025359483435750008,
-0.0011398040223866701,
0.025639869272708893,
-0.0572301410138607,
-0.022117426618933678,
-0.0018849786138162017,
0.019620487466454506,
-0.04288181662559509,
-0.07530470937490463,
-0.030490541830658913,
-0.025788502767682076,
0.023067325353622437,
-0.047575484961271286,
0.03365841880440712,
-0.0387386791408062,
-0.04794596880674362,
0.020295802503824234,
0.03560920059680939,
-0.04907361418008804,
-0.027178850024938583,
0.03449409455060959,
-0.00040224980330094695,
-0.016412978991866112,
0.06486599892377853,
-0.034032538533210754,
-0.03964200243353844,
-0.024703165516257286,
-0.016141662374138832,
0.049616843461990356,
-0.030897391960024834,
-0.044877275824546814,
0.049789298325777054,
0.1222463920712471,
-0.008086198009550571,
0.03726867586374283,
-0.020564990118145943,
0.023425143212080002,
0.011940340511500835,
-0.030710402876138687,
-0.0638105571269989,
-0.024706918746232986,
0.008376975543797016,
0.0416533462703228,
-0.011272872798144817,
-0.03281180188059807,
0.016827475279569626,
-0.02078978531062603,
0.06398382037878036,
0.018720969557762146,
-0.0648345947265625,
-0.02675420232117176,
0.027058329433202744
] |
<p>A proton p collides with a neutron(at rest) n at relatively low-energies and creates a 'deuterium-core' d:</p>
<p>$$p+n->d+\gamma$$</p>
<p>Find the wavelength for the photon as a function of the proton's momentum and the angle that the photon creates with the proton.Do this relativistic.</p>
<hr>
<p>So seems I'm supposed to set up two equations: energy- and momentum-balance.
I tried to set up the relativistic energy equation as function of momentum, but became messy to solve.
Any hint on what this energy equation could look like?</p>
|
g2518
|
[
-0.001280614291317761,
-0.027747878804802895,
0.0017660101875662804,
-0.02219308167695999,
0.06639346480369568,
-0.022784819826483727,
-0.003548875218257308,
0.02972167171537876,
-0.026656772941350937,
-0.026583034545183182,
0.016394464299082756,
0.02002718299627304,
-0.015553477220237255,
-0.019388187676668167,
0.012538145296275616,
0.005002314690500498,
0.03389136865735054,
0.013017206452786922,
-0.016612866893410683,
0.019200649112462997,
-0.026074174791574478,
-0.04155299812555313,
0.01728152111172676,
-0.03780582919716835,
0.000634205702226609,
-0.0014982885913923383,
-0.007724564988166094,
0.009920625016093254,
-0.0681595429778099,
0.022935884073376656,
-0.03932948037981987,
0.015083256177604198,
0.04105311259627342,
0.03403669223189354,
-0.0646018534898758,
0.0008382379892282188,
0.03701525926589966,
0.02921203337609768,
0.02715582773089409,
0.004682160913944244,
-0.04892875254154205,
-0.030657324939966202,
-0.054816484451293945,
-0.02673685923218727,
0.03254593536257744,
-0.025663970038294792,
-0.008259663358330727,
-0.013787331059575081,
-0.012375169433653355,
0.006342594046145678,
-0.035599324852228165,
0.025575673207640648,
0.010706850327551365,
-0.04668278247117996,
0.0007327190251089633,
0.02644817903637886,
0.010979126207530499,
-0.0067545268684625626,
0.025505036115646362,
0.06043163686990738,
0.008540160022675991,
-0.014897236600518227,
0.0034167366102337837,
0.022864757105708122,
0.08821100741624832,
-0.04174381121993065,
0.0011039325036108494,
-0.028866054490208626,
0.03160322830080986,
-0.005349986255168915,
-0.04076727107167244,
-0.05080579221248627,
-0.04042673483490944,
-0.002898265141993761,
0.05679404363036156,
-0.032020844519138336,
0.014878797344863415,
0.011813445948064327,
-0.020618712529540062,
0.052421264350414276,
0.019229527562856674,
0.044510066509246826,
0.07455142587423325,
-0.016380218788981438,
0.0330842025578022,
-0.007654827553778887,
-0.0028972409199923277,
0.007689324207603931,
-0.0569661445915699,
0.012813368812203407,
0.06810665130615234,
0.004844600800424814,
0.031253404915332794,
-0.006315837148576975,
0.02673647180199623,
-0.02287578396499157,
-0.04894208908081055,
0.06847041100263596,
0.01153665129095316,
0.012388341128826141,
0.00007582664693472907,
0.020433997735381126,
0.03746594116091728,
-0.01378438901156187,
0.007519638631492853,
0.016644662246108055,
-0.02576533891260624,
0.004950564820319414,
-0.017488447949290276,
-0.03918865695595741,
-0.07979493588209152,
-0.05966398864984512,
0.015225427225232124,
-0.057441990822553635,
-0.0038313078694045544,
-0.07000318169593811,
0.0344884917140007,
-0.021079866215586662,
0.007954560220241547,
0.10660631954669952,
0.02419867180287838,
0.062251016497612,
-0.041686784476041794,
0.0803651437163353,
-0.010602506808936596,
-0.032061412930488586,
-0.05500861629843712,
0.029951399192214012,
0.06502635776996613,
0.023152418434619904,
0.045944660902023315,
-0.045295365154743195,
-0.041274040937423706,
0.031815625727176666,
0.03484097123146057,
0.027602000162005424,
0.041155919432640076,
0.02430471032857895,
-0.05259012058377266,
-0.009972977451980114,
0.03676827996969223,
0.02620258554816246,
0.015367811545729637,
-0.05046185851097107,
-0.05428195744752884,
0.005004655569791794,
-0.0386316291987896,
-0.027431601658463478,
0.013490788638591766,
-0.01368543691933155,
0.000060716509324265644,
0.04949057102203369,
-0.03195135295391083,
-0.005991257261484861,
0.033083654940128326,
0.035434722900390625,
0.01156434416770935,
-0.053785290569067,
-0.040352366864681244,
-0.002359032165259123,
0.07673057168722153,
-0.03731105104088783,
0.0382002554833889,
-0.0178682804107666,
-0.0034994317684322596,
-0.008570801466703415,
0.030816132202744484,
-0.06527035683393478,
0.005838997196406126,
-0.05268118530511856,
-0.008960746228694916,
-0.06612764298915863,
-0.0016640372341498733,
-0.008433068171143532,
-0.01498100534081459,
0.07353813201189041,
-0.0008702806662768126,
-0.010125510394573212,
-0.026299692690372467,
0.015555206686258316,
0.033201176673173904,
-0.016287820413708687,
0.09664509445428848,
0.018153924494981766,
0.011640580371022224,
-0.038308966904878616,
0.016100294888019562,
0.026672974228858948,
-0.06066686287522316,
0.021289663389325142,
-0.025449838489294052,
0.051973652094602585,
0.02134915627539158,
0.02237119898200035,
0.018341725692152977,
0.04410482197999954,
0.02804541401565075,
-0.05833538994193077,
-0.021181847900152206,
0.10371549427509308,
-0.03454482927918434,
0.04605094715952873,
0.03413505479693413,
0.014112355187535286,
0.027776017785072327,
-0.023056738078594208,
0.046287138015031815,
0.017353860661387444,
0.02683350443840027,
0.009211077354848385,
0.05534055829048157,
-0.013901608064770699,
-0.06075482442975044,
0.014597185887396336,
-0.006791265681385994,
0.011005145497620106,
-0.013631859794259071,
-0.0044150385074317455,
-0.017302094027400017,
-0.009110238403081894,
-0.07443933933973312,
-0.020444877445697784,
0.005912414286285639,
-0.03392954543232918,
-0.033839862793684006,
0.026338836178183556,
-0.07577114552259445,
0.006079265382140875,
-0.013422487303614616,
0.03262249380350113,
-0.02681538462638855,
0.034248899668455124,
-0.0404297299683094,
0.0003087087534368038,
0.0615743063390255,
0.02220764197409153,
-0.02711407095193863,
0.004805510398000479,
0.01050201989710331,
-0.022135302424430847,
-0.022635972127318382,
0.009804189205169678,
-0.03637281805276871,
0.030838195234537125,
0.004976808093488216,
-0.003102597314864397,
0.07822403311729431,
0.010350174270570278,
-0.035415224730968475,
-0.007103771902620792,
0.05833401158452034,
-0.03366389870643616,
-0.04435441270470619,
-0.036363717168569565,
-0.029849879443645477,
-0.07601989805698395,
-0.014827671460807323,
0.035168785601854324,
-0.0996650829911232,
-0.054434336721897125,
-0.024827469140291214,
-0.05243099853396416,
-0.017423665151000023,
0.01292684767395258,
-0.011067239567637444,
-0.029659375548362732,
-0.02441367134451866,
-0.010895533487200737,
0.035810232162475586,
-0.0007622645935043693,
-0.028302310034632683,
-0.010354856960475445,
0.04163150116801262,
0.029368553310632706,
0.019627641886472702,
-0.06548090279102325,
0.019796306267380714,
-0.04832686483860016,
0.01015043631196022,
-0.024202218279242516,
-0.026939237490296364,
0.0157798919826746,
-0.04662570357322693,
0.0019641192629933357,
0.05899042636156082,
-0.06651078164577484,
0.043517209589481354,
0.02211603708565235,
0.012214809656143188,
0.0294489748775959,
-0.009011741727590561,
0.020679792389273643,
-0.0597718209028244,
-0.0032042001839727163,
0.007378214970231056,
0.01273879874497652,
0.07158161699771881,
0.025801537558436394,
-0.0077875880524516106,
-0.025358259677886963,
-0.015322373248636723,
-0.06131546571850777,
-0.02513917349278927,
-0.03136248514056206,
-0.022964438423514366,
-0.0022158885840326548,
-0.05496450513601303,
0.028774302452802658,
0.03640560805797577,
0.006170239299535751,
-0.05077190324664116,
0.061427537351846695,
-0.006147077772766352,
0.03190094232559204,
0.009227034635841846,
-0.012366188690066338,
-0.0037053613923490047,
-0.027729399502277374,
-0.003042038297280669,
0.040868815034627914,
-0.012870343402028084,
-0.030960986390709877,
0.009992198087275028,
0.014049534685909748,
0.011558135971426964,
0.007833744399249554,
-0.042435675859451294,
0.021491026505827904,
-0.060094401240348816,
0.008241395466029644,
0.06241976469755173,
0.03130337595939636,
-0.024516258388757706,
0.043993089348077774,
0.029729461297392845,
0.010163607075810432,
0.0013833403354510665,
-0.013208511285483837,
0.09060264378786087,
0.022625857964158058,
-0.003965818788856268,
-0.013507207855582237,
-0.02504909783601761,
0.02758852392435074,
0.03761354833841324,
-0.05113384872674942,
0.006859713699668646,
-0.007953789085149765,
-0.007679748348891735,
-0.017955830320715904,
-0.04889078438282013,
-0.05249125137925148,
-0.019782040268182755,
-0.0006619564956054091,
0.0012257019989192486,
-0.00029699536389671266,
-0.009278077632188797,
0.06271366029977798,
0.03682135045528412,
-0.011365765705704689,
-0.018095027655363083,
-0.04954180121421814,
-0.01569320075213909,
-0.008680608123540878,
-0.04584546759724617,
-0.04344205558300018,
-0.020321587100625038,
0.008598641492426395,
0.005349266808480024,
-0.01073060929775238,
0.018340209499001503,
-0.05943599343299866,
0.00559304840862751,
-0.043086856603622437,
-0.05370693281292915,
-0.029293393716216087,
0.0319288931787014,
-0.02985919453203678,
-0.03411165252327919,
0.032793622463941574,
0.0005018535885028541,
0.0013193382183089852,
0.05119560286402702,
0.05966220051050186,
-0.030730396509170532,
0.048132263123989105,
-0.03457574173808098,
-0.028990259394049644,
0.07642415910959244,
0.03813963383436203,
0.008120337501168251,
-0.08047971874475479,
-0.0425688736140728,
0.021739257499575615,
0.0014239000156521797,
0.016812598332762718,
-0.004342940635979176,
-0.06111978366971016,
-0.09805091470479965,
0.06361329555511475,
-0.022904377430677414,
0.014268530532717705,
0.03444710001349449,
-0.06753149628639221,
0.013255695812404156,
0.033225785940885544,
0.02147727832198143,
-0.010429967194795609,
-0.03358936309814453,
0.017483312636613846,
0.015223218128085136,
-0.01147370133548975,
0.021783839911222458,
-0.06637237221002579,
-0.030963638797402382,
-0.049746524542570114,
0.03488787263631821,
-0.0241108275949955,
0.017870290204882622,
0.030816759914159775,
-0.014065178111195564,
0.04009171575307846,
0.049754709005355835,
-0.035136908292770386,
-0.004572579637169838,
0.019968649372458458,
0.05216848850250244,
0.007030703127384186,
0.0226573646068573,
0.03947208449244499,
0.05539806932210922,
-0.015616772696375847,
-0.007491783704608679,
0.023389063775539398,
-0.03001931682229042,
0.061377447098493576,
-0.03907598927617073,
-0.013539368286728859,
0.005466322414577007,
0.05005820468068123,
0.08153429627418518,
0.00994801800698042,
0.03874102234840393,
-0.03449251130223274,
0.000517898821271956,
0.09016219526529312,
-0.02562783472239971,
-0.07366669923067093,
-0.0644073337316513,
-0.03607969731092453,
0.03732949122786522,
0.035445403307676315,
-0.019764887169003487,
-0.011271423660218716,
0.009927941486239433,
0.03045203723013401,
-0.028029805049300194,
0.016913970932364464,
0.07883455604314804,
0.03286027908325195,
-0.05629553645849228,
-0.017882170155644417,
0.032304566353559494,
-0.07164521515369415,
0.0746881514787674,
0.015000971034169197,
-0.031152211129665375,
0.016430016607046127,
-0.021002912893891335,
-0.014532037079334259,
0.005363926291465759,
-0.010734843090176582,
0.004788337741047144,
-0.03909093886613846,
0.00414379732683301,
-0.0010826456127688289,
-0.016564106568694115,
0.013048376888036728,
0.038857392966747284,
-0.005991729442030191,
-0.009807764552533627,
-0.01849997229874134,
-0.009086131118237972,
0.04546678438782692,
-0.010222148150205612,
0.034655261784791946,
-0.03951374068856239,
0.03175901621580124,
0.0331086739897728,
-0.018079429864883423,
-0.04591286927461624,
-0.03086857683956623,
-0.025103842839598656,
-0.005251625087112188,
0.07160867750644684,
0.05750185251235962,
-0.010412252508103848,
-0.0019774255342781544,
0.02287748083472252,
-0.00757811451330781,
-0.02808721736073494,
-0.009209119714796543,
-0.04873878136277199,
-0.03331216797232628,
0.005990919657051563,
0.026256445795297623,
0.03314777463674545,
0.055153608322143555,
0.01175190880894661,
0.013099119067192078,
0.016912521794438362,
0.00875107478350401,
0.056709494441747665,
0.02124684676527977,
0.014582676813006401,
-0.013339945115149021,
0.02668817527592182,
0.038448359817266464,
0.01690729521214962,
-0.00312510272487998,
0.03317686542868614,
-0.020425140857696533,
0.039296217262744904,
-0.009466968476772308,
0.06636957824230194,
-0.04886632412672043,
-0.028111349791288376,
-0.017471371218562126,
0.00793010089546442,
-0.0421951487660408,
0.016832949593663216,
-0.04300674796104431,
0.03747764974832535,
0.009633478708565235,
0.008116893470287323,
-0.07415084540843964,
-0.028635552152991295,
0.0013001746265217662,
-0.018876569345593452,
-0.02171872928738594,
0.00249628908932209,
0.04076060652732849,
0.019513646140694618,
0.050752539187669754,
-0.0401989184319973,
-0.02178456448018551,
-0.019171884283423424,
0.027153709903359413,
-0.029534783214330673,
-0.006990182679146528,
0.013849499635398388,
-0.053958047181367874,
0.0015072921523824334,
-0.003278770949691534,
0.007481729611754417,
-0.04140397161245346,
0.0610044039785862,
-0.005518315359950066,
-0.002632938325405121,
-0.032922666519880295,
0.021067775785923004,
-0.02276250347495079,
-0.029674425721168518,
0.07173745334148407,
-0.04674488678574562,
-0.02984393760561943,
-0.0003255610936321318,
-0.07922250032424927,
0.028392400592565536,
-0.07435383647680283,
0.01948561891913414,
0.0004842769994866103,
-0.01863993890583515,
-0.021315492689609528,
0.023306410759687424,
0.05754118412733078,
0.007604630663990974,
0.000007668987564102281,
-0.02819153480231762,
-0.014258956536650658,
0.016132378950715065,
0.04301905259490013,
0.031203968450427055,
0.00586664816364646,
-0.061159443110227585,
0.030413411557674408,
-0.012074158526957035,
-0.029657624661922455,
0.04652871936559677,
-0.003031835425645113,
0.023066170513629913,
0.020040351897478104,
0.0005906690494157374,
-0.030665142461657524,
-0.013872623443603516,
-0.026845671236515045,
0.0399557426571846,
-0.0657973363995552,
-0.07763064652681351,
0.06654893606901169,
0.021502403542399406,
0.011248502880334854,
0.0064273858442902565,
0.03687320277094841,
0.019521372392773628,
-0.0010430552065372467,
-0.057244837284088135,
0.02641524001955986,
-0.002572691300883889,
0.021834582090377808,
-0.024004720151424408,
0.05766955390572548,
-0.009620625525712967,
0.0038803403731435537,
-0.01628374680876732,
-0.020497485995292664,
0.03894536569714546,
0.02888423576951027,
0.02066991478204727,
-0.021777506917715073,
0.024358011782169342,
-0.012389734387397766,
0.013760702684521675,
-0.052705928683280945,
0.06377334892749786,
0.0026717481669038534,
-0.04586373269557953,
0.026710348203778267,
0.005425285082310438,
0.030799580737948418,
0.019973397254943848,
-0.051014941185712814,
-0.004610039293766022,
0.04054047539830208,
-0.007909612730145454,
0.05233385041356087,
-0.058894313871860504,
0.019840585067868233,
0.014631133526563644,
0.020910250023007393,
0.03874822333455086,
0.025905417278409004,
0.04009313881397247,
-0.036841388791799545,
-0.04488655924797058,
0.01224908884614706,
0.029196742922067642,
-0.029290564358234406,
-0.06574968993663788,
0.014352451078593731,
-0.006932886783033609,
-0.02030067890882492,
-0.014957810752093792,
0.021017028018832207,
-0.04671107605099678,
0.034619010984897614,
0.002445794874802232,
0.0017180764116346836,
0.009583773091435432,
-0.04859881103038788,
0.044263806194067,
-0.05965759977698326,
-0.010406605899333954,
-0.027053825557231903,
0.008516550064086914,
-0.0029865202959626913,
0.037989240139722824,
-0.004925111308693886,
0.05318828672170639,
0.00834661815315485,
-0.060856111347675323,
-0.03659466654062271,
-0.040285851806402206,
-0.024122202768921852,
-0.02715112268924713,
0.041739340871572495,
-0.014801658689975739,
0.05838555842638016,
-0.0359966866672039,
-0.03441759943962097,
0.032859254628419876,
0.03654247894883156,
-0.05609783157706261,
-0.07356181740760803,
0.012201023288071156,
-0.005705729592591524,
-0.026659946888685226,
-0.023089950904250145,
0.020847836509346962,
0.07606036961078644,
-0.024705560877919197,
0.019406529143452644,
0.048083625733852386,
-0.009093041531741619,
-0.024921469390392303,
0.017271319404244423,
0.01861104741692543,
0.0332765057682991,
0.03346295654773712,
0.007822833955287933,
0.002707024337723851,
-0.04534662142395973,
0.03632494807243347,
0.011646667495369911,
-0.05413258820772171,
0.058423079550266266,
-0.04329034686088562,
-0.02907482162117958,
-0.0037060054019093513,
-0.03769126906991005,
0.07663410902023315,
-0.02387705072760582,
-0.012610516510903835,
0.014004671946167946,
0.005829564295709133,
0.023291343823075294,
-0.04111763834953308,
0.00011532282951520756,
0.020583946257829666,
0.006143534556031227,
-0.049455974251031876,
-0.07290483266115189,
0.0197740588337183,
-0.027534857392311096,
0.0013355001574382186,
-0.06454228609800339,
-0.015006654895842075,
0.02415037341415882,
0.02763126976788044,
0.06242489069700241,
-0.01976839080452919,
-0.0027422134298831224,
-0.05589906871318817,
-0.008151328191161156,
0.07110778987407684,
-0.06429683417081833,
-0.027010172605514526,
-0.008556596003472805,
0.045948609709739685,
0.03052898682653904,
0.040750231593847275,
-0.10830944031476974,
-0.020973045378923416,
0.008682620711624622,
0.024986354634165764,
-0.021556498482823372,
0.04304672032594681,
0.032144684344530106,
0.1308659464120865,
-0.024654338136315346,
0.05878078192472458,
-0.0006146491505205631,
-0.006573426071554422,
0.016806164756417274,
0.09444061666727066,
-0.0713496208190918,
0.030301017686724663,
0.032051991671323776,
-0.04430181160569191,
-0.043803222477436066,
0.007514786906540394,
-0.03008291684091091,
-0.008216813206672668,
-0.003575209528207779,
0.010533896274864674,
0.029950805008411407,
-0.026612795889377594,
-0.009584125131368637
] |
<p>In Misner, Thorne, Wheeler (henceforth written as "MTW"), "Gravitation", Box 16.4, there's an experimental setup construction (or method) presented by which</p>
<blockquote>
<p>"<i>Each geodesic clock is constructed and calibrated as follows: [...]</i>", where "<i>Those that pass through [event] $\mathcal A$ are calibrated [...] against the [specific timelike] standard interval $\mathcal A B$</i>" and "<i>Any interval $\mathcal P Q$ along the world line of a geodesic clock can be measured by the same method as was used in calibration</i>".</p>
</blockquote>
<p>Regarding importance and motivation of this method it is stated that</p>
<blockquote>
<p>"<i>The Einstein principle that spacetime is described by Riemannian geometry exposes itself to destruction by a "thousand" tests. Thus, from the fiducial interval, $\mathcal A B$, to the interval under measurement, $\mathcal P Q$, there are a "score" of routes of intercomparison, all of which must give the same value for the ratio $\mathcal P Q / A B$.</i>". </p>
</blockquote>
<p>Box 16.4 contains two separate sketches of the setup construction; one concerned with interval $\mathcal A B$, the other equivalently with interval $\mathcal P Q$. Explicitly evident in either sketch are two separate participants ("<i>particles</i>", "<i>timelike world lines</i>") who </p>
<ul>
<li><p>observe pings between each other, and</p></li>
<li><p>both observe one ping to one particular event (event $\mathcal{B}$ in the first setup sketch; or event $\mathcal{Q}$ in the second setup sketch), where</p></li>
<li><p>each participant finds some (integer) number of successive pings to the other as same as the one ping to the "external" event ($\mathcal{B}$, or $\mathcal{Q}$). (The "<i>intercomparison</i>" to be achieved then involves counting those successive pings by the two participants.)</p></li>
</ul>
<p>There are additional "<i>demands</i>" stated (which the two sketches alone don't make explicit); among them that the participants who took part in event $\mathcal A$ (referring to the first sketch), or in event $\mathcal Q$ (referring to the second sketch) are required to have been "<i>freely falling</i>"; and their world lines correspondingly "<i>paths of freely falling particles</i>" and "<i>geodesics</i>".</p>
<p><strong>Question 1</strong>:<br>
Has there at least one such test been carried out already, presumably by "<i>intercomparison</i>" along at least two distinct "<i>routes</i>", by explicitly using the method indicated by MTW ? (i.e. not involving any further "model dependent assumptions" such as in the arguments presented at the end of box 16.4)</p>
<p><strong>Question 2</strong>:<br>
Instead of demanding of the setup(s) that certain participants were "<i>freely falling</i>" and obtaining "<i>a "thousand" tests of the Einstein principle that spacetime is described by Riemannian geometry</i>",<br>
could the described method be explicitly adapted in turn, by assuming "<i>the Einstein principle</i>" as outright valid and by suitably combining sufficiently many (if not "a thousand") of the described setups, to obtain a test of whether (or to which accuracy) a given particle had been "<i>freely falling</i>" (or correspondingly, whether, or to which accuracy, a given timelike world line was "<i>geodesic</i>") ?</p>
|
g2519
|
[
0.05323386564850807,
0.027409180998802185,
-0.0054885344579815865,
0.0003000104916281998,
0.013880519196391106,
0.01812434382736683,
0.03955663740634918,
-0.04549241065979004,
-0.007924223318696022,
-0.004729678854346275,
0.019139310345053673,
-0.035519178956747055,
0.03657936304807663,
0.02520499937236309,
-0.043588679283857346,
-0.00610359339043498,
0.13355903327465057,
0.006321894004940987,
0.03694621101021767,
-0.024929122999310493,
0.016483239829540253,
0.01640172302722931,
-0.006298778112977743,
-0.016910241916775703,
-0.023014850914478302,
-0.04360993206501007,
0.014637522399425507,
-0.03918524459004402,
-0.10637544840574265,
-0.03164880722761154,
0.03626662865281105,
-0.04488781467080116,
0.033075250685214996,
-0.052316129207611084,
-0.024089382961392403,
-0.020136089995503426,
0.005804979708045721,
-0.009488269686698914,
-0.06790122389793396,
0.024883093312382698,
-0.024855777621269226,
-0.018224578350782394,
0.031331516802310944,
0.02170196734368801,
0.038378097116947174,
0.035869959741830826,
-0.0024623489007353783,
0.023722831159830093,
0.039608974009752274,
-0.028885912150144577,
-0.026704205200076103,
0.06479668617248535,
0.05096614733338356,
-0.0022734510712325573,
0.0092371366918087,
0.08488507568836212,
0.0019056169549003243,
-0.010880077257752419,
0.03883792459964752,
0.033276624977588654,
-0.03856319189071655,
0.0016311319777742028,
0.02556956186890602,
-0.05925190821290016,
0.04979219287633896,
0.03027375042438507,
-0.06850039213895798,
-0.035134412348270416,
-0.008744293823838234,
0.005695437081158161,
0.02520325593650341,
-0.056412409991025925,
0.036591701209545135,
-0.03201919421553612,
0.012069832533597946,
0.048063673079013824,
-0.008937999606132507,
-0.018043823540210724,
0.020675618201494217,
0.07606026530265808,
-0.04408369958400726,
0.00021660426864400506,
0.005457606632262468,
-0.008053225465118885,
0.11148878186941147,
-0.03367950767278671,
0.0397002138197422,
0.01656818762421608,
-0.01854707859456539,
0.048246875405311584,
0.003089745994657278,
-0.01536245085299015,
0.035679757595062256,
0.011154974810779095,
-0.027511436492204666,
-0.006216287147253752,
-0.027744775637984276,
0.03564511984586716,
-0.0010343739995732903,
0.04245568811893463,
-0.013000468723475933,
0.02714821696281433,
-0.04028663411736488,
0.004094485659152269,
-0.0022899594623595476,
-0.03439735248684883,
0.031061343848705292,
0.027079656720161438,
0.009076355956494808,
-0.016418926417827606,
0.004713051952421665,
-0.007604841608554125,
-0.008628517389297485,
-0.062199871987104416,
-0.045340538024902344,
-0.0136739332228899,
0.046895842999219894,
0.03514448180794716,
0.004252349957823753,
0.07109937071800232,
-0.02577417716383934,
0.023636354133486748,
-0.015958396717905998,
-0.003626408753916621,
-0.036872271448373795,
0.03132645785808563,
-0.023556524887681007,
0.007647539488971233,
-0.03525733947753906,
0.05185653641819954,
0.008897297084331512,
0.044408682733774185,
-0.03716633468866348,
-0.005725624971091747,
-0.11271823197603226,
0.0053968713618814945,
0.045374199748039246,
-0.014647082425653934,
-0.043718501925468445,
-0.0015369708416983485,
-0.06881336122751236,
-0.02848241850733757,
-0.02110861800611019,
-0.08532834053039551,
0.005224962253123522,
0.06305795162916183,
-0.0035709061194211245,
-0.0011829258874058723,
0.0007604993297718465,
0.043452583253383636,
-0.013541094027459621,
0.048457104712724686,
0.05173885449767113,
-0.06534271687269211,
0.03827536106109619,
-0.005978644825518131,
-0.042890552431344986,
-0.050475988537073135,
0.00636744499206543,
0.032933466136455536,
0.027758058160543442,
-0.016539517790079117,
0.007463837508112192,
0.011691153980791569,
-0.019300535321235657,
0.03865986689925194,
0.016785340383648872,
-0.011418242938816547,
0.04797619208693504,
-0.049305260181427,
-0.05477454513311386,
-0.08360648900270462,
0.04495028406381607,
0.0035838426556438208,
-0.022545741870999336,
0.025839312002062798,
0.020298156887292862,
-0.05836893245577812,
0.010846208781003952,
-0.010414740070700645,
0.028104204684495926,
0.0008630361407995224,
-0.04125656560063362,
-0.02867985889315605,
-0.025978531688451767,
-0.0296255461871624,
0.006194289308041334,
-0.008273218758404255,
0.0010057537583634257,
-0.05714007094502449,
0.03524770215153694,
-0.009519952349364758,
-0.026255693286657333,
0.04309147596359253,
0.03438541665673256,
-0.010484055615961552,
0.0541778989136219,
-0.017108406871557236,
0.005661988630890846,
0.08478272706270218,
0.010212887078523636,
0.05481552332639694,
0.021436724811792374,
-0.005879491101950407,
-0.009875765070319176,
0.010229825042188168,
-0.02165902405977249,
-0.01712852530181408,
-0.03613013029098511,
-0.01754281111061573,
0.07669036090373993,
0.055875979363918304,
0.01166563481092453,
-0.027801066637039185,
-0.032033972442150116,
0.001321192947216332,
0.006698815152049065,
0.011538517661392689,
0.0341285839676857,
0.02563491277396679,
0.024770084768533707,
0.020936453714966774,
0.03662470355629921,
-0.1065259575843811,
0.023441387340426445,
-0.02124880440533161,
-0.06691072136163712,
-0.019072240218520164,
-0.01158007513731718,
0.0071304310113191605,
-0.015877654775977135,
-0.02428886480629444,
-0.02083204686641693,
-0.022790418937802315,
0.04626339673995972,
0.035173896700143814,
-0.00008420950325671583,
0.005135758314281702,
0.040283650159835815,
0.030082903802394867,
0.063627228140831,
-0.04122655466198921,
-0.03931168094277382,
-0.013909216970205307,
-0.005985789466649294,
-0.04413193464279175,
-0.03452145680785179,
0.01027132198214531,
-0.046987589448690414,
0.07910539954900742,
-0.01581766828894615,
-0.016949942335486412,
-0.06653530150651932,
0.03672720864415169,
-0.005206982605159283,
0.01551283523440361,
0.04239106550812721,
0.06561657041311264,
-0.08994805812835693,
0.0282090175896883,
0.011740023270249367,
-0.03138319402933121,
0.007426743861287832,
0.008175321854650974,
0.004898836370557547,
-0.04340839385986328,
-0.011777651496231556,
0.07141482830047607,
-0.050509318709373474,
-0.015134603716433048,
-0.00505709508433938,
0.00936377327889204,
0.04661114513874054,
0.08707410842180252,
-0.05329084023833275,
0.05118454620242119,
0.019925381988286972,
-0.02194639854133129,
0.007656978443264961,
0.03842815011739731,
0.004251730162650347,
0.011448267847299576,
-0.11084087193012238,
0.014483838342130184,
0.06161988899111748,
-0.03261374309659004,
0.008931602351367474,
0.0023399130441248417,
-0.04533474147319794,
0.02521156147122383,
-0.017961816862225533,
0.02055136114358902,
0.018881849944591522,
0.0325121134519577,
-0.04983478784561157,
0.03540759161114693,
-0.0312836617231369,
-0.06656359881162643,
-0.009916243143379688,
-0.004795839544385672,
-0.02328270487487316,
-0.0495210736989975,
0.0264988262206316,
0.04755410552024841,
-0.0038759331218898296,
0.0421098992228508,
-0.005980371031910181,
-0.07039342075586319,
-0.024379728361964226,
-0.02194179780781269,
0.035877715796232224,
0.05193863436579704,
0.03008820302784443,
-0.06887219101190567,
0.005189834628254175,
-0.005987964104861021,
0.02729792147874832,
0.04931791499257088,
-0.025088317692279816,
0.04000154137611389,
0.013328269124031067,
0.04988992586731911,
-0.007404140196740627,
0.0010477656032890081,
0.03651721403002739,
0.014124575071036816,
0.000626951630692929,
-0.0008529258193448186,
-0.06890339404344559,
0.0054816496558487415,
-0.01631534844636917,
0.028792954981327057,
0.03893626108765602,
0.049763210117816925,
0.02310115657746792,
-0.022265717387199402,
0.009772459045052528,
-0.03512486815452576,
0.023591259494423866,
0.050820011645555496,
-0.03321732208132744,
0.018308168277144432,
-0.05384990572929382,
-0.0010470462730154395,
0.0017114615766331553,
-0.011489981785416603,
0.009439158253371716,
0.04104014113545418,
-0.006347958464175463,
-0.022448882460594177,
0.04566304013133049,
0.007831299677491188,
-0.02668793313205242,
-0.05645768344402313,
0.003972205333411694,
-0.00189378228969872,
0.024774130433797836,
0.061299629509449005,
-0.06233270466327667,
-0.0038728448562324047,
0.03519283980131149,
0.0818682610988617,
-0.01750139892101288,
0.02219880186021328,
0.028188027441501617,
0.037422265857458115,
0.0018386151641607285,
0.03897695615887642,
0.041019752621650696,
-0.050793278962373734,
-0.008072561584413052,
0.011325407773256302,
-0.006589935161173344,
0.02675565890967846,
0.041737932711839676,
-0.03091507963836193,
0.04615570977330208,
0.0049212416633963585,
-0.035479556769132614,
0.015617920085787773,
-0.034234967082738876,
0.028473403304815292,
-0.04062839224934578,
-0.02133755013346672,
0.03011108562350273,
-0.005985694006085396,
0.013024557381868362,
-0.032592982053756714,
-0.04345857352018356,
-0.041317835450172424,
0.03780338913202286,
-0.08549804985523224,
-0.028130948543548584,
0.02716705948114395,
-0.001065384945832193,
0.016839567571878433,
-0.035494666546583176,
0.002655874937772751,
0.015739805996418,
0.0010424726642668247,
0.045659128576517105,
0.04483488202095032,
0.03535809367895126,
-0.010117567144334316,
-0.03565598651766777,
-0.04933289811015129,
-0.00837037805467844,
-0.00658319192007184,
0.013440651819109917,
0.04852624237537384,
0.032597616314888,
-0.07672559469938278,
-0.06649512052536011,
-0.08919638395309448,
0.07096727937459946,
-0.014973096549510956,
0.00836279708892107,
-0.01007318589836359,
0.0038881979417055845,
0.014844749122858047,
-0.02058844454586506,
0.054994191974401474,
-0.010919694788753986,
-0.06779985129833221,
0.02575092390179634,
0.04748975858092308,
-0.018065623939037323,
-0.004179355222731829,
-0.046081602573394775,
-0.05195349454879761,
0.015166617929935455,
0.007216969504952431,
-0.03304775431752205,
0.05430670827627182,
-0.04186410829424858,
0.0011210668599233031,
0.022932346910238266,
0.01826593652367592,
0.033598076552152634,
-0.059307996183633804,
-0.012767096050083637,
-0.005300032906234264,
0.008011802099645138,
-0.015507587231695652,
0.05236023664474487,
0.0842573419213295,
-0.04574849456548691,
-0.053322531282901764,
-0.0053686280734837055,
-0.009900186210870743,
0.021397557109594345,
0.006513467989861965,
0.05920812860131264,
0.038044579327106476,
0.023885268718004227,
0.005862129386514425,
-0.001581226591952145,
0.056928351521492004,
-0.019417045637965202,
0.005620025098323822,
-0.03109932690858841,
-0.030322125181555748,
0.02430972270667553,
0.02205701544880867,
0.015444210730493069,
-0.0003711467143148184,
-0.07410839945077896,
-0.07653451710939407,
-0.05773280933499336,
-0.012242265976965427,
0.025338103994727135,
-0.027761613950133324,
0.017590926960110664,
-0.00879871565848589,
-0.012272312305867672,
-0.00004437937241164036,
-0.05235214903950691,
0.03130127117037773,
0.006846236065030098,
-0.05575990304350853,
-0.017407989129424095,
-0.014471577480435371,
-0.04835475981235504,
0.03624272346496582,
0.005655128974467516,
0.03362914174795151,
-0.024427136406302452,
-0.06052028387784958,
0.04590562358498573,
0.011634834110736847,
0.03776131942868233,
-0.0967571958899498,
0.06368856132030487,
-0.01750928908586502,
-0.013219650834798813,
-0.032057955861091614,
0.007469831965863705,
-0.07349947094917297,
-0.0012608109973371029,
-0.04223219305276871,
-0.03671387583017349,
0.04293643683195114,
0.01384379155933857,
-0.01777856983244419,
-0.006643395870923996,
0.004744301084429026,
0.02776890993118286,
0.0003515133576001972,
-0.04425716772675514,
0.03734060004353523,
-0.010877551510930061,
0.001948361867107451,
-0.019318073987960815,
-0.014154978096485138,
0.010876617394387722,
0.019585588946938515,
0.021715287119150162,
-0.009301792830228806,
0.013386096805334091,
-0.10019364953041077,
-0.011622102931141853,
0.0035760782193392515,
-0.0003280981327407062,
0.008880910463631153,
0.020480018109083176,
0.01610039919614792,
-0.05810768902301788,
-0.01715911738574505,
0.009081636555492878,
0.011509188450872898,
0.01137243490666151,
-0.017493942752480507,
0.00033626388176344335,
0.01365917269140482,
0.013056944124400616,
-0.03455047309398651,
-0.0005843873950652778,
0.002296525053679943,
0.08370043337345123,
-0.019728055223822594,
-0.022722406312823296,
-0.04552757740020752,
0.07927902787923813,
0.03770652040839195,
0.03356374800205231,
-0.011763190850615501,
-0.05653863400220871,
0.043403469026088715,
0.022806299850344658,
-0.04382478445768356,
-0.046802449971437454,
-0.015475035645067692,
0.02209331840276718,
0.03408762067556381,
-0.052345991134643555,
0.06889832019805908,
-0.0037848365027457476,
-0.06332678347826004,
-0.026944216340780258,
0.034598059952259064,
-0.01671832613646984,
-0.05600293353199959,
-0.027742767706513405,
0.03206495940685272,
-0.03074670024216175,
-0.06549999117851257,
0.00505048455670476,
-0.008444261737167835,
-0.004559933207929134,
0.00651415204629302,
0.03386666253209114,
-0.009024386294186115,
-0.007251020520925522,
0.014012318104505539,
-0.044632717967033386,
-0.00500344717875123,
-0.018989233300089836,
0.021694660186767578,
-0.012749001383781433,
-0.006814348977059126,
-0.018137497827410698,
-0.001399086439050734,
0.037469588220119476,
-0.019293587654829025,
-0.019790323451161385,
-0.00550942774862051,
-0.0316537544131279,
0.008063612505793571,
-0.04054152965545654,
-0.03304164856672287,
-0.007592204958200455,
-0.011426336131989956,
0.004522582516074181,
-0.03815999627113342,
-0.031858474016189575,
-0.020196720957756042,
0.017394550144672394,
0.028578193858265877,
-0.03937814384698868,
0.02964441478252411,
-0.025945965200662613,
-0.01734275557100773,
0.06631238758563995,
-0.049316611140966415,
0.020026518031954765,
0.005725565832108259,
-0.052900753915309906,
-0.04014475643634796,
0.010973308235406876,
-0.06704245507717133,
0.04048232361674309,
0.06176765635609627,
0.017293274402618408,
0.07515286654233932,
-0.035532716661691666,
-0.004695120733231306,
0.07433349639177322,
-0.007901091128587723,
-0.009263752959668636,
-0.0018200806807726622,
0.10986445844173431,
0.012516209855675697,
0.035464536398649216,
-0.05010627955198288,
0.01945527456700802,
0.0054654027335345745,
0.024226734414696693,
-0.05331169441342354,
-0.023291565477848053,
-0.007907100953161716,
-0.01490628533065319,
0.00873133447021246,
-0.05188243091106415,
-0.012336782179772854,
-0.0422050766646862,
0.013477000407874584,
0.054056890308856964,
0.021633613854646683,
0.03438778966665268,
0.016082247719168663,
0.0067133777774870396,
0.022232521325349808,
0.01608385518193245,
-0.043744128197431564,
-0.0045928750187158585,
0.006633237469941378,
0.025768818333745003,
0.0393611416220665,
0.027655556797981262,
0.024921376258134842,
0.039509404450654984,
0.006410077214241028,
-0.0063718329183757305,
0.04522663727402687,
0.01812608540058136,
0.01609817147254944,
-0.012913220562040806,
0.037029046565294266,
0.046449583023786545,
-0.03988087177276611,
0.011210329830646515,
-0.0250055193901062,
-0.019318874925374985,
-0.038566023111343384,
-0.07600906491279602,
0.01151503436267376,
-0.05416299030184746,
-0.05600873380899429,
0.02168317511677742,
0.013060797937214375,
0.06186689808964729,
-0.0054015773348510265,
-0.02518528886139393,
0.025568442419171333,
0.01906023547053337,
-0.07919283211231232,
0.014816273003816605,
0.0419023334980011,
-0.0077289086766541,
0.02313816174864769,
0.023521093651652336,
0.033770810812711716,
0.02065681852400303,
0.008288164623081684,
-0.006460685282945633,
0.008706250227987766,
0.007002945523709059,
0.007978004403412342,
-0.06691837310791016,
-0.001121053472161293,
0.0186518095433712,
0.074217788875103,
0.000499582092743367,
-0.03773799166083336,
0.037383899092674255,
-0.02046472392976284,
0.07312791049480438,
0.020972859114408493,
0.010888147167861462,
-0.008304503746330738,
0.03264528512954712,
0.0007996677304618061,
0.019216056913137436,
0.00805331114679575,
-0.00979811605066061,
0.0005903914570808411,
-0.009375594556331635,
-0.0014775479212403297,
-0.029869690537452698,
0.004098647274076939,
0.03635682538151741,
0.0563843809068203,
0.003410029225051403,
-0.00753049785271287,
-0.04258762300014496,
0.029239799827337265,
-0.04639488086104393,
-0.025985468178987503,
0.023899374529719353,
-0.003565566847100854,
-0.023398011922836304,
-0.013253915123641491,
-0.03043438121676445,
-0.09827904403209686,
0.045766107738018036,
0.01425950974225998,
0.03638654202222824,
0.01258007436990738,
-0.03003815747797489,
-0.029064754024147987,
0.008163176476955414,
-0.013753773644566536,
-0.025680318474769592,
0.04789033532142639,
0.036279819905757904,
-0.03817320242524147,
-0.007284157909452915,
-0.01287110336124897,
-0.032356154173612595,
0.01948469504714012,
0.005593183916062117,
-0.03616238385438919,
-0.010152507573366165,
-0.018017787486314774,
-0.028437817469239235,
-0.031080519780516624,
-0.0002783005475066602,
0.07299362868070602,
-0.0814334973692894,
-0.03734792023897171,
-0.009286505170166492,
0.004212370608001947,
-0.014492057263851166,
0.024051528424024582,
0.04196973517537117,
-0.03432006016373634,
0.020118562504649162,
-0.024301685392856598,
0.06831377744674683,
-0.022640440613031387,
0.0005528294714167714,
-0.026298174634575844,
0.021375475451350212,
-0.01890362799167633,
-0.0319337360560894,
-0.01961946114897728,
0.0516616515815258,
0.031373001635074615
] |
<p>I'm well aware of transmutation as a way to effectively make radioactive material decay faster, however that isn't really what I mean.</p>
<p>Doing a quick Google search I found references to several theoretical treatises on the subject, and a few references to experiments with, at best, inconclusive results. Among them, there were a few on the quantum anti-zeno effect, which I already knew about, as well as a couple on something called "field enhanced beta decay" and various methods utilizing lasers. Nevertheless, much to my frustration, there was essentially no example I could find with any sort of empirical testing of these effects. So, I suppose I have two questions: </p>
<ol>
<li>How "good" is the physics behind these claims?</li>
<li>Have any of these effects ever been <em>unequivocally</em> observed experimentally?</li>
</ol>
|
g2520
|
[
0.018190089613199234,
0.022088557481765747,
0.026950912550091743,
-0.0038334191776812077,
0.054737456142902374,
-0.03053223341703415,
0.00732007622718811,
0.038890156894922256,
0.013911345042288303,
0.02487845905125141,
-0.00370066799223423,
-0.008646033704280853,
-0.004137699492275715,
-0.03981529548764229,
0.003763708285987377,
-0.01825147494673729,
0.09303107857704163,
0.008010545745491982,
0.006746029015630484,
0.04162507504224777,
0.0018689318094402552,
0.010974041186273098,
-0.03656284138560295,
-0.032693419605493546,
-0.029579536989331245,
-0.008325645700097084,
-0.04253058508038521,
-0.0387892983853817,
0.011495653539896011,
0.025807391852140427,
-0.0034876323770731688,
-0.051549334079027176,
-0.002169726649299264,
-0.03126400336623192,
0.008669650182127953,
-0.013572616502642632,
0.034761566668748856,
-0.030992889776825905,
0.0170302577316761,
0.01831546425819397,
-0.03787238895893097,
-0.0015343145933002234,
0.037512753158807755,
-0.006185857113450766,
-0.00683289160951972,
-0.051903385668992996,
0.004190343897789717,
0.019868342205882072,
-0.0017484062118455768,
-0.04834328219294548,
-0.04496902972459793,
-0.01220230758190155,
0.07840735465288162,
0.08102995902299881,
0.015333589166402817,
-0.00676616420969367,
-0.031710054725408554,
-0.015582744032144547,
0.06954582035541534,
0.00804158952087164,
-0.007631758227944374,
-0.004418045282363892,
0.01267510186880827,
-0.042484939098358154,
0.05892661213874817,
-0.00016329914797097445,
-0.022827962413430214,
0.013276956044137478,
0.024117588996887207,
0.021891577169299126,
0.029094932600855827,
0.03761822357773781,
-0.07286784052848816,
-0.01029361691325903,
0.041026968508958817,
0.02092091739177704,
0.026813052594661713,
-0.0440712496638298,
-0.004648268688470125,
-0.010762056335806847,
-0.09022776782512665,
-0.08416901528835297,
0.01445364486426115,
0.015407448634505272,
0.04270544275641441,
0.004694194532930851,
0.00461302837356925,
0.05779554322361946,
0.021555636078119278,
-0.03697899729013443,
-0.00820272509008646,
-0.030653323978185654,
-0.0008212539250962436,
-0.017898982390761375,
-0.035293031483888626,
0.005733372177928686,
-0.001046414952725172,
0.0348653718829155,
-0.04171767458319664,
0.042280107736587524,
-0.0025883889757096767,
0.012481671757996082,
0.0077541363425552845,
0.012092388235032558,
-0.043137289583683014,
-0.0493115596473217,
0.029227975755929947,
-0.05065527185797691,
-0.0020016729831695557,
0.05334078148007393,
-0.015604862943291664,
0.0009275569464080036,
-0.03689812496304512,
0.0247326772660017,
0.033796072006225586,
-0.03383990377187729,
0.006086293607950211,
0.023565666750073433,
-0.013360288925468922,
-0.00596332224085927,
0.0060548740439116955,
0.07229907810688019,
-0.06961251050233841,
0.015933925285935402,
-0.005223818123340607,
0.00179810740519315,
-0.031395528465509415,
-0.007265091873705387,
0.05058291181921959,
-0.0032068737782537937,
-0.010129346512258053,
0.012688987888395786,
-0.023313120007514954,
0.0510171577334404,
-0.007652907632291317,
0.032893553376197815,
-0.015502660535275936,
0.0020194342359900475,
-0.0018179969629272819,
-0.08394695818424225,
0.05091884732246399,
-0.023723362013697624,
-0.013840693049132824,
0.06282781809568405,
-0.036793120205402374,
0.05193733423948288,
-0.05504872277379036,
0.05445285886526108,
0.0066995397210121155,
0.06235460564494133,
0.0004126780549995601,
-0.03963098302483559,
0.06164062023162842,
-0.04728811979293823,
0.015523224137723446,
0.07266735285520554,
0.027640091255307198,
-0.0453687459230423,
-0.014499864540994167,
0.04148939996957779,
0.007860240526497364,
0.03574802726507187,
-0.021769190207123756,
-0.05129517614841461,
-0.016451215371489525,
-0.041402362287044525,
0.036444347351789474,
0.02160390466451645,
0.005533730145543814,
-0.00450019771233201,
-0.042610447853803635,
0.024860665202140808,
0.009655331261456013,
0.029917728155851364,
0.014904028736054897,
0.0640096515417099,
-0.007656137924641371,
-0.023111552000045776,
-0.0658256784081459,
-0.02475651353597641,
-0.05562852695584297,
-0.014010709710419178,
-0.014746629633009434,
-0.02592865750193596,
0.06309717893600464,
-0.018472665920853615,
-0.02941581793129444,
-0.008185038343071938,
-0.08420494198799133,
-0.0016608075238764286,
-0.01658056676387787,
0.00183616834692657,
0.00786066334694624,
-0.023899924010038376,
-0.0113206896930933,
-0.001926676370203495,
-0.009726686403155327,
0.0012865421595051885,
0.012502355501055717,
0.015387400984764099,
-0.019818497821688652,
-0.0010940034408122301,
0.0033001184929162264,
-0.02477526105940342,
0.06646333634853363,
-0.013882170431315899,
-0.048438411206007004,
-0.015899451449513435,
-0.0034059309400618076,
-0.03285696730017662,
0.04240608215332031,
0.04609287530183792,
0.04911567643284798,
-0.040724363178014755,
-0.00966490525752306,
0.014365901239216328,
0.004753659944981337,
0.06734213978052139,
0.025172367691993713,
-0.004587152041494846,
-0.02317790687084198,
-0.01492643728852272,
0.048408620059490204,
-0.0036734824534505606,
-0.005134627688676119,
-0.011817028746008873,
0.025746114552021027,
-0.01127719134092331,
-0.02157873474061489,
0.0013779421569779515,
-0.06679891049861908,
0.05078267678618431,
0.0004986653802916408,
-0.08681304007768631,
0.0012545562349259853,
0.032772552222013474,
0.007698385044932365,
-0.01772993616759777,
0.06757944077253342,
-0.011051837354898453,
0.04399171099066734,
0.045070163905620575,
-0.12985654175281525,
0.045060254633426666,
0.0347839817404747,
-0.09500702470541,
-0.020053427666425705,
-0.045111920684576035,
0.011818770319223404,
-0.04417180269956589,
0.0006757605588063598,
0.04279804602265358,
-0.08993110805749893,
-0.03471548855304718,
0.005613131448626518,
-0.025461576879024506,
-0.03354409709572792,
0.04662909731268883,
-0.041400130838155746,
0.04056458920240402,
-0.016000475734472275,
0.02717866562306881,
0.010644551366567612,
0.006654947996139526,
-0.007090478204190731,
-0.04289541020989418,
-0.0009670744766481221,
0.02675325609743595,
-0.05128755420446396,
0.011868519708514214,
-0.01427286397665739,
0.018169991672039032,
-0.034527380019426346,
0.07058990001678467,
-0.006855387706309557,
0.0080715985968709,
0.02616480551660061,
-0.043256428092718124,
0.014434556476771832,
-0.013958560302853584,
0.006277757231146097,
-0.004426911938935518,
-0.06339624524116516,
0.06312914192676544,
-0.0017743712523952127,
-0.04460902884602547,
-0.001928845071233809,
-0.046961426734924316,
-0.017829731106758118,
-0.004058167338371277,
-0.030856817960739136,
0.013186936266720295,
0.08065828680992126,
-0.003037982387468219,
-0.015560638159513474,
0.03999811038374901,
0.0445246621966362,
-0.08629561215639114,
-0.0437840037047863,
0.04420130327343941,
0.044973570853471756,
-0.04739571735262871,
0.001097214873880148,
0.07171373814344406,
-0.0025556329637765884,
0.02518009953200817,
-0.058698322623968124,
-0.015786606818437576,
0.024550778791308403,
0.01888357289135456,
-0.05186430364847183,
0.02032851241528988,
-0.023095624521374702,
0.03228992223739624,
0.01835084706544876,
-0.03680097684264183,
-0.014424551278352737,
0.024219639599323273,
0.09758666157722473,
-0.022372739389538765,
-0.008511669933795929,
-0.011467638425529003,
0.021862812340259552,
-0.039095189422369,
0.03953738883137703,
-0.01314513385295868,
-0.032549597322940826,
0.0016000912291929126,
-0.06481239944696426,
-0.02181266061961651,
0.029005948454141617,
0.01966954581439495,
-0.013147394172847271,
-0.03409726172685623,
-0.10036628693342209,
-0.022816358134150505,
-0.05647341534495354,
0.07354886829853058,
-0.0060331979766488075,
-0.016489099711179733,
-0.046503763645887375,
-0.008430564776062965,
-0.0145419267937541,
0.048012346029281616,
0.07858826965093613,
0.02992958575487137,
0.011161363683640957,
-0.01710415445268154,
0.010077154263854027,
0.04814201965928078,
0.05704508721828461,
-0.012020385824143887,
0.004397923592478037,
0.020052369683980942,
0.004339509177953005,
0.030577080324292183,
0.01884455606341362,
0.03693155199289322,
0.04783414676785469,
-0.06726929545402527,
-0.029233219102025032,
-0.023062732070684433,
0.10578487813472748,
-0.06215190142393112,
-0.03109551966190338,
0.07545790076255798,
-0.037662193179130554,
0.027914056554436684,
0.031178733333945274,
0.020344050601124763,
-0.020607680082321167,
-0.011401825584471226,
0.013013484887778759,
-0.03602981939911842,
0.00978283304721117,
0.019117455929517746,
0.058770932257175446,
0.04796704277396202,
-0.053257476538419724,
0.05551934242248535,
-0.0104284156113863,
0.021784979850053787,
0.04748329892754555,
-0.002465246943756938,
-0.059310805052518845,
-0.03365710377693176,
-0.04259181767702103,
-0.04365552216768265,
-0.028002731502056122,
-0.009375504218041897,
-0.04659241437911987,
0.006764904595911503,
-0.014237401075661182,
-0.003599294926971197,
0.00026144570438191295,
-0.044057752937078476,
0.02448766864836216,
-0.05652590095996857,
0.03041934035718441,
-0.03603217005729675,
-0.015525920316576958,
0.020495302975177765,
-0.03875424712896347,
0.006355301942676306,
0.01611863449215889,
-0.05820513516664505,
0.02479173056781292,
0.015320053324103355,
-0.005141295492649078,
-0.03065214864909649,
-0.011857669800519943,
0.014336483553051949,
-0.04184957221150398,
-0.06543534994125366,
0.008612805977463722,
0.030567999929189682,
-0.04386892169713974,
-0.02073817327618599,
0.02127193659543991,
0.019830122590065002,
0.0028729815967381,
0.008857439272105694,
-0.04217919334769249,
0.05382221192121506,
0.006634487770497799,
0.04282083362340927,
0.01801050454378128,
-0.03395477309823036,
0.06059880182147026,
-0.05259944871068001,
0.03297373279929161,
0.026460889726877213,
-0.021820010617375374,
0.0363432951271534,
0.024450819939374924,
-0.03433169424533844,
-0.019569747149944305,
0.034420646727085114,
0.035462960600852966,
0.04703661426901817,
0.12619023025035858,
-0.02056792750954628,
0.051365286111831665,
0.053686030209064484,
-0.0026129416655749083,
0.019108517095446587,
-0.0921776294708252,
-0.04659271612763405,
0.028803657740354538,
-0.055456630885601044,
-0.03308776021003723,
0.014114927500486374,
0.008334340527653694,
-0.04491904750466347,
-0.011021517217159271,
-0.04768704995512962,
-0.0013033444993197918,
0.03273395821452141,
0.017465192824602127,
0.05775994062423706,
-0.062169596552848816,
0.012014339677989483,
0.029104940593242645,
0.01259608194231987,
-0.0335475355386734,
-0.001778686186298728,
-0.01577812060713768,
-0.010725700296461582,
-0.028697481378912926,
-0.011041868478059769,
-0.02524733729660511,
-0.048775121569633484,
0.05273623764514923,
0.06529483199119568,
-0.013198187574744225,
-0.10362238436937332,
-0.016619885340332985,
0.011004356667399406,
-0.01639997959136963,
-0.0053181410767138,
-0.06190944090485573,
0.02114354819059372,
0.04717785120010376,
-0.037965837866067886,
-0.029269082471728325,
0.02396567165851593,
-0.09977038204669952,
0.03825100138783455,
0.04906129837036133,
-0.014738425612449646,
0.014328747056424618,
0.005743359215557575,
0.02214895188808441,
-0.06820332258939743,
-0.008758151903748512,
-0.004833745304495096,
0.0177492406219244,
0.01023772731423378,
-0.07464540749788284,
0.022737188264727592,
-0.03917184844613075,
0.03422947973012924,
0.022907884791493416,
-0.0355633869767189,
0.015453046187758446,
0.0119528379291296,
0.06280068308115005,
0.04757346957921982,
-0.04680074006319046,
-0.022039320319890976,
-0.0687742605805397,
0.031028712168335915,
-0.012997427023947239,
-0.003395099425688386,
0.003662057686597109,
0.04392874240875244,
-0.0766393318772316,
0.007808770053088665,
-0.0104387691244483,
-0.08260202407836914,
-0.05486622825264931,
-0.005786361638456583,
-0.0007462473586201668,
0.008760988712310791,
-0.027170268818736076,
0.010503618977963924,
-0.08054081350564957,
0.039108287543058395,
-0.02183864824473858,
-0.004797029308974743,
0.06752768158912659,
-0.008635961450636387,
0.03519121930003166,
0.04298055171966553,
-0.037015676498413086,
0.036373451352119446,
0.014180019497871399,
0.050899237394332886,
-0.04137834906578064,
0.04063662886619568,
0.016649460420012474,
-0.030958278104662895,
0.05945220962166786,
0.05185019597411156,
-0.015349285677075386,
-0.0000550826225662604,
-0.04128759726881981,
-0.00283040595240891,
0.02672828733921051,
-0.023576030507683754,
-0.007287769578397274,
-0.03917635604739189,
0.021429328247904778,
0.017943736165761948,
0.07462756335735321,
0.027389099821448326,
-0.013998959213495255,
-0.03120475262403488,
-0.0016797651769593358,
0.019279692322015762,
0.02554628998041153,
0.0245611984282732,
0.028394170105457306,
-0.0034694138448685408,
0.0342601016163826,
-0.006292402278631926,
0.008487777784466743,
-0.03739182651042938,
0.012665163725614548,
0.054646335542201996,
0.015301935374736786,
0.04111894592642784,
-0.03712795674800873,
-0.006899615284055471,
-0.030364448204636574,
0.004462126642465591,
0.014913939870893955,
-0.06656689941883087,
-0.0362553671002388,
-0.01600513979792595,
0.0038546710275113583,
-0.017192235216498375,
-0.05058789625763893,
-0.0017086121952161193,
-0.01993124932050705,
0.013604591600596905,
-0.04680248722434044,
0.03746980056166649,
-0.04099868983030319,
-0.05050066486001015,
-0.03329608589410782,
-0.003523987252265215,
-0.0007954592583701015,
-0.0299027469009161,
0.012267452664673328,
-0.0024565893691033125,
-0.02646005153656006,
0.0031879181042313576,
-0.008282122202217579,
0.046912550926208496,
-0.030703581869602203,
-0.03254305198788643,
-0.008888592943549156,
-0.0089265750721097,
0.014981758780777454,
0.01896664872765541,
-0.05657542124390602,
0.038884762674570084,
0.03401927649974823,
-0.010668688453733921,
-0.023593423888087273,
-0.012736846692860126,
-0.007257560733705759,
0.0478019043803215,
-0.06789246201515198,
-0.04322599247097969,
0.010453934781253338,
0.015884116291999817,
-0.02388078346848488,
0.030396077781915665,
0.06699792295694351,
-0.046974778175354004,
0.01740065962076187,
0.02479954995214939,
0.007039579562842846,
0.060807742178440094,
-0.016000546514987946,
0.026712657883763313,
0.048673078417778015,
0.023403126746416092,
-0.004204250872135162,
-0.010919015854597092,
0.01484646275639534,
0.010904059745371342,
-0.004266343079507351,
0.03934340551495552,
-0.020433856174349785,
-0.05202504247426987,
0.01627967320382595,
0.004892135038971901,
0.00895573291927576,
0.0035623174626380205,
0.03916046768426895,
-0.03353651612997055,
0.009948424994945526,
0.09346088021993637,
0.027216056361794472,
0.047643229365348816,
-0.018734851852059364,
0.0010667002061381936,
-0.02358936332166195,
0.02457614243030548,
-0.01444390881806612,
0.01835397258400917,
0.016713866963982582,
0.03589198365807533,
0.02583957090973854,
0.042440783232450485,
-0.01748015731573105,
-0.05853375419974327,
0.007143811322748661,
-0.052953049540519714,
-0.0028982541989535093,
-0.029613908380270004,
0.023937053978443146,
-0.00833806861191988,
0.008005346171557903,
0.0068657491356134415,
0.03833764046430588,
-0.009649869054555893,
-0.001655826810747385,
0.008884132839739323,
-0.01362164318561554,
-0.002467220649123192,
0.028771286830306053,
-0.048673488199710846,
-0.002950765658169985,
0.03832804039120674,
-0.005905959289520979,
0.020415829494595528,
-0.018261022865772247,
0.03459198400378227,
0.006965651176869869,
-0.034211453050374985,
-0.0028167287819087505,
0.03681275621056557,
-0.07350539416074753,
0.06448225677013397,
-0.0355316624045372,
0.006812734995037317,
0.013177599757909775,
-0.031666580587625504,
0.018235590308904648,
0.03816452994942665,
-0.011072217486798763,
0.04396739602088928,
-0.022170081734657288,
0.030831921845674515,
0.030129382386803627,
0.017866289243102074,
-0.027201121672987938,
0.02458634413778782,
-0.05464354157447815,
-0.014898035675287247,
0.04288050904870033,
0.03657219931483269,
0.035506412386894226,
-0.00638979347422719,
-0.018587522208690643,
0.01406280416995287,
-0.008258647285401821,
0.05636577680706978,
0.009789889678359032,
-0.05896979570388794,
0.056409552693367004,
-0.02934783510863781,
-0.017013028264045715,
-0.023895135149359703,
0.025751439854502678,
0.045236121863126755,
0.009789898060262203,
0.0574425645172596,
-0.03574713319540024,
-0.013051677495241165,
-0.0024469352792948484,
-0.0057398611679673195,
-0.03769338130950928,
-0.0003805688174907118,
-0.02550584077835083,
0.05815216153860092,
0.03372718021273613,
0.012545320205390453,
-0.045828767120838165,
-0.032713718712329865,
-0.04355637729167938,
0.058666639029979706,
0.05591640621423721,
0.00831837672740221,
-0.03315392881631851,
0.03934164345264435,
0.04675176367163658,
0.00012160157348262146,
-0.02281060628592968,
-0.03358909860253334,
-0.03287995979189873,
-0.0007424732320941985,
-0.02438502572476864,
0.05280974879860878,
-0.04283006116747856,
-0.04430542513728142,
-0.028522305190563202,
0.058741409331560135,
-0.02376055158674717,
0.060427144169807434,
0.03209213539958,
0.010419082827866077,
0.004882773384451866,
-0.001660091569647193,
0.0596177764236927,
0.020540492609143257,
-0.020750759169459343,
-0.0202191062271595,
-0.01804495044052601,
-0.005661369301378727,
-0.05555219203233719,
-0.006253791972994804,
-0.017387917265295982,
0.004702279344201088
] |
<p>I have read that quantum mechanics says that the amount of possible particle configurations is $10^{10^{122}}$ to be exact in the universe. Do we know this figure to be exactly true to the exact figure? Wouldn't we need to know a true theory of quantum gravity to know the exact answer? Is the amount exactly that figure or just an estimate?</p>
|
g2521
|
[
0.00042367257992736995,
0.09091445058584213,
0.0023082084953784943,
-0.07593706995248795,
0.03579527884721756,
-0.049149204045534134,
0.00698850117623806,
0.0014042421244084835,
-0.06848961859941483,
0.009439324028789997,
-0.008442859165370464,
-0.040454015135765076,
-0.02145218476653099,
0.028073294088244438,
-0.0007583435508422554,
0.005208304617553949,
0.04106327146291733,
-0.02121933177113533,
-0.0023700715973973274,
-0.007303284015506506,
0.03372480347752571,
-0.02792751044034958,
-0.006155430339276791,
-0.006233494263142347,
-0.03233252465724945,
0.002528880024328828,
0.007012668531388044,
-0.029733164235949516,
-0.01185026578605175,
-0.017000380903482437,
0.039376042783260345,
-0.001511414535343647,
0.018452472984790802,
-0.034760162234306335,
-0.03374076262116432,
-0.059115637093782425,
0.034342747181653976,
-0.0223049595952034,
0.012845619581639767,
-0.07032076269388199,
-0.0032605852466076612,
-0.021127481013536453,
-0.026393892243504524,
-0.021431896835565567,
-0.010381846688687801,
0.0574474111199379,
0.052270956337451935,
0.02084030956029892,
0.012465202249586582,
-0.029827984049916267,
-0.0426979623734951,
0.018666666001081467,
0.011669833213090897,
0.06357432156801224,
0.013371736742556095,
0.10716739296913147,
0.025394001975655556,
-0.036115437746047974,
0.08137958496809006,
0.026887409389019012,
0.04807860776782036,
-0.002544214017689228,
0.02021067775785923,
0.0328221321105957,
-0.007672740612179041,
-0.006107263267040253,
-0.06147966533899307,
0.023754162713885307,
-0.036059875041246414,
-0.033140573650598526,
0.049690116196870804,
-0.11934919655323029,
0.036658234894275665,
0.02906212955713272,
-0.03593958914279938,
-0.0036164368502795696,
-0.03848251700401306,
0.006922523491084576,
0.014097882434725761,
0.013332274742424488,
0.008685598149895668,
-0.06495378911495209,
0.004302675370126963,
-0.05560708045959473,
0.08323690295219421,
-0.05767050385475159,
0.023967726156115532,
-0.010558582842350006,
-0.011463714763522148,
-0.0007138678920455277,
0.015111492946743965,
0.025046061724424362,
0.03841622173786163,
0.0034218034707009792,
0.042253997176885605,
-0.010078026913106441,
-0.04491589963436127,
0.049210838973522186,
-0.05908871069550514,
0.032668087631464005,
-0.020496994256973267,
0.02952868677675724,
-0.001826748251914978,
-0.010671878233551979,
0.003669802797958255,
0.00018541990721132606,
0.021687865257263184,
0.02808307856321335,
0.05792463570833206,
-0.02600083500146866,
-0.04947013035416603,
0.011628431268036366,
0.01789676398038864,
0.004893514793366194,
-0.12460057437419891,
-0.011702108196914196,
0.06109795346856117,
0.021233150735497475,
0.039105456322431564,
0.06778215616941452,
0.01180499978363514,
0.07083138823509216,
0.04411836713552475,
0.008798548951745033,
-0.03887268900871277,
-0.04269052669405937,
-0.03205236792564392,
-0.003936643246561289,
0.00960521586239338,
0.012393002398312092,
0.03214047849178314,
-0.04074971005320549,
0.026820791885256767,
0.011838200502097607,
-0.05094189941883087,
0.010648418217897415,
0.01933639496564865,
-0.04446091875433922,
0.01169661246240139,
0.033300817012786865,
-0.0009344603749923408,
-0.003350437618792057,
-0.027288097888231277,
0.020752379670739174,
-0.002924819476902485,
0.006342349573969841,
-0.03080274723470211,
0.015555933117866516,
-0.030552096664905548,
0.04433237388730049,
0.047730810940265656,
-0.019825570285320282,
0.01911979354918003,
-0.04408968240022659,
-0.019169867038726807,
-0.07720734924077988,
0.0218121986836195,
0.03518244996666908,
-0.022668858990073204,
0.0636231079697609,
0.04208271577954292,
0.00947479996830225,
-0.0032451357692480087,
0.029896022751927376,
-0.05765524506568909,
-0.005205329041928053,
-0.008553088642656803,
-0.021912304684519768,
-0.016855070367455482,
-0.04640907421708107,
-0.014652224257588387,
-0.002463838318362832,
-0.01863182708621025,
0.05878773331642151,
-0.026960020884871483,
0.04403616487979889,
-0.04367395490407944,
-0.0007883331854827702,
0.02799822948873043,
0.044972460716962814,
0.05977824702858925,
0.007673501502722502,
0.017422955483198166,
0.006518316455185413,
-0.057518891990184784,
-0.03287334740161896,
0.001143470173701644,
-0.012382335029542446,
0.04096733033657074,
0.0011403280077502131,
-0.004527903627604246,
0.0214368999004364,
0.020570531487464905,
-0.00656935153529048,
0.05781969055533409,
0.040056437253952026,
0.07064683735370636,
-0.056582678109407425,
-0.023999642580747604,
-0.003370411926880479,
0.017776042222976685,
0.07433375716209412,
0.027402931824326515,
0.010247886180877686,
0.032727740705013275,
-0.015688369050621986,
0.03534954413771629,
0.069796122610569,
0.012030038982629776,
-0.015908652916550636,
0.038751132786273956,
-0.010933001525700092,
0.09397447854280472,
0.05421074479818344,
-0.031222738325595856,
0.059335168451070786,
0.02227179706096649,
0.007127157412469387,
0.01917290687561035,
0.04616476967930794,
-0.006356972269713879,
0.0011278943857178092,
0.025449084118008614,
0.0629783496260643,
0.002006411086767912,
0.04261798784136772,
-0.04183662310242653,
-0.04896548017859459,
-0.004487069323658943,
0.05643076449632645,
-0.0583517849445343,
0.003703010268509388,
-0.023190872743725777,
0.011121527291834354,
0.00839765090495348,
0.03402620926499367,
-0.051604025065898895,
-0.015670010820031166,
0.0221033226698637,
0.007492954842746258,
0.04851435497403145,
0.006115138530731201,
-0.07669946551322937,
0.025507770478725433,
0.00009193349251290783,
-0.005733999889343977,
0.03069489635527134,
-0.011810262687504292,
-0.04294819012284279,
0.08004889637231827,
0.0031263469718396664,
-0.03394078463315964,
-0.02377418614923954,
0.025675760582089424,
-0.028228064998984337,
0.03835859149694443,
0.005366597790271044,
0.04890596121549606,
-0.038367319852113724,
-0.021467288956046104,
0.009756901301443577,
-0.022936491295695305,
0.026639657095074654,
-0.0009557086159475148,
-0.020100917667150497,
-0.03691912814974785,
-0.039016228169202805,
-0.030614271759986877,
-0.02768819034099579,
0.03129836544394493,
0.062752366065979,
-0.026102010160684586,
-0.02303152158856392,
0.028026528656482697,
0.001929714111611247,
0.0051355017349123955,
-0.0038117263466119766,
0.015555566176772118,
-0.0070826346054673195,
-0.01631239615380764,
-0.05346531420946121,
0.02162184938788414,
-0.0582614429295063,
0.05903259664773941,
0.004691151902079582,
-0.0663389191031456,
-0.030445801094174385,
-0.03707854077219963,
-0.006864319555461407,
0.03465581685304642,
0.005118540488183498,
-0.01599476858973503,
0.01933230087161064,
0.037031155079603195,
-0.03665647283196449,
0.012584911659359932,
-0.005257089156657457,
0.027712000533938408,
-0.014798955991864204,
0.0011878017103299499,
0.025738710537552834,
0.03441956639289856,
-0.03887379914522171,
-0.04002683609724045,
-0.05482270568609238,
0.06917910277843475,
0.013474354520440102,
-0.032227110117673874,
-0.00820629671216011,
-0.06180497258901596,
-0.02537648007273674,
0.06364178657531738,
0.031115686520934105,
0.022890852764248848,
-0.030898837372660637,
0.0017342326464131474,
0.039469391107559204,
0.033055707812309265,
-0.003203689120709896,
-0.05308794230222702,
0.01650908961892128,
-0.0038842372596263885,
-0.010812400840222836,
-0.010457471013069153,
0.06077413633465767,
0.04404417797923088,
-0.05068634822964668,
-0.015098823234438896,
-0.03482363000512123,
-0.04199020192027092,
-0.025314895436167717,
-0.03296973928809166,
-0.02498149685561657,
0.024738257750868797,
-0.02970273606479168,
-0.05378377065062523,
-0.030035385861992836,
-0.01960829831659794,
0.05491210147738457,
-0.01339961402118206,
-0.029911592602729797,
0.02346508577466011,
0.031969573348760605,
0.01940249837934971,
0.021102359518408775,
0.046287424862384796,
-0.07761446386575699,
-0.006888698786497116,
0.022992508485913277,
0.026715688407421112,
0.014497618190944195,
0.000337620556820184,
-0.021824993193149567,
0.0017181584844365716,
0.02260550670325756,
0.030381102114915848,
-0.018338145688176155,
0.0355609655380249,
0.0034554097801446915,
0.020304227247834206,
0.017079299315810204,
-0.06412740051746368,
0.014644315466284752,
0.025740794837474823,
0.048484329134225845,
-0.028673844411969185,
0.0035334331914782524,
0.0032119345851242542,
0.03960061073303223,
-0.012611989863216877,
-0.04348943755030632,
-0.002361586783081293,
-0.033041249960660934,
-0.007388563826680183,
0.05476605147123337,
-0.006876843515783548,
0.022849224507808685,
-0.07895094156265259,
0.010217908769845963,
-0.018523581326007843,
0.0023339150939136744,
0.054204169660806656,
-0.0025479283649474382,
0.039524197578430176,
0.03536280617117882,
0.0207656417042017,
-0.024273594841361046,
-0.04666757211089134,
-0.005763349123299122,
-0.04151076078414917,
-0.0021837186068296432,
-0.06968002021312714,
-0.0428863950073719,
-0.023538170382380486,
-0.023689627647399902,
-0.03116052970290184,
0.036751676350831985,
-0.015133450739085674,
0.028240717947483063,
-0.023882752284407616,
0.04232139140367508,
-0.0188379418104887,
0.004921676125377417,
0.009223990142345428,
0.053373292088508606,
-0.005116580985486507,
0.0260316152125597,
-0.022295333445072174,
0.011975103989243507,
-0.0159236378967762,
0.017383327707648277,
0.06693200767040253,
0.004782559350132942,
-0.036899685859680176,
0.009513755328953266,
0.019120074808597565,
-0.03279225528240204,
-0.0783730298280716,
0.03867773711681366,
-0.01612692140042782,
0.05835079774260521,
0.02369179204106331,
-0.02914387173950672,
-0.014888569712638855,
-0.02070251666009426,
0.061056166887283325,
-0.023847680538892746,
-0.02898239716887474,
-0.0395674891769886,
-0.04954124614596367,
0.04658995568752289,
0.011916570365428925,
0.006400038488209248,
0.05036986246705055,
-0.0727919414639473,
0.037916768342256546,
-0.03186400607228279,
-0.009748805314302444,
-0.020945146679878235,
-0.012176863849163055,
-0.001123141497373581,
0.017442652955651283,
-0.004886508919298649,
-0.013742942363023758,
0.01865234784781933,
-0.02155889756977558,
-0.06145758926868439,
-0.04997437074780464,
-0.039702121168375015,
-0.045207154005765915,
-0.004971409682184458,
-0.020739050582051277,
-0.0517568364739418,
-0.014755898155272007,
-0.04826686903834343,
-0.016108712181448936,
0.006418011151254177,
0.05815919488668442,
-0.01599292643368244,
0.02971484884619713,
-0.06338094174861908,
-0.020691951736807823,
0.06980518251657486,
0.070329949259758,
0.041839953511953354,
0.03075491264462471,
-0.08772862702608109,
0.004457743838429451,
-0.09731078147888184,
-0.014851391315460205,
-0.005973153747618198,
-0.001037949463352561,
0.07726715505123138,
-0.01747230440378189,
-0.029559578746557236,
-0.00145185855217278,
-0.03097565285861492,
-0.04408958554267883,
-0.005866074003279209,
-0.002315304707735777,
-0.0762946605682373,
-0.012883398681879044,
-0.032787952572107315,
0.022863568738102913,
-0.05275977402925491,
0.030289849266409874,
-0.009977363981306553,
0.013087357394397259,
-0.018715914338827133,
-0.02139277197420597,
-0.00843892153352499,
-0.03025057166814804,
0.042573269456624985,
-0.04196846857666969,
0.0097982631996274,
-0.023098299279808998,
-0.034905362874269485,
-0.09286003559827805,
0.02966528944671154,
0.0709558054804802,
-0.003529153997078538,
0.036485910415649414,
0.009335819631814957,
-0.019230233505368233,
-0.05591189116239548,
0.06333864480257034,
0.02410242334008217,
0.03942401707172394,
-0.0040589384734630585,
-0.04806935414671898,
0.005224560387432575,
-0.00708385743200779,
0.010349215939640999,
-0.001946449396200478,
0.036962054669857025,
-0.018954850733280182,
-0.012043981812894344,
0.006041360553354025,
-0.014592021703720093,
0.03458164259791374,
0.012745250947773457,
0.08113368600606918,
0.031534019857645035,
0.0010182643309235573,
-0.016996463760733604,
-0.028013573959469795,
-0.024093149229884148,
0.04240709915757179,
0.015535186044871807,
0.03822989761829376,
0.0259113572537899,
0.030938472598791122,
0.015620691701769829,
-0.03480239585042,
-0.02967177703976631,
0.06858066469430923,
0.024475885555148125,
-0.013331345282495022,
0.07639150321483612,
0.029087767004966736,
-0.01209594402462244,
0.021952008828520775,
-0.008298548869788647,
0.06214755401015282,
-0.006505780387669802,
0.0351949967443943,
-0.08887782692909241,
0.024865910410881042,
0.0483003631234169,
-0.03854710981249809,
-0.06444793194532394,
0.028392504900693893,
-0.033044539391994476,
-0.04438978433609009,
-0.015268469229340553,
0.04924954101443291,
0.0015627011889591813,
-0.008494934998452663,
-0.040416866540908813,
0.030336551368236542,
-0.0022086729295551777,
0.00933671835809946,
-0.009670717641711235,
-0.08004958927631378,
-0.05377255380153656,
0.04774942994117737,
-0.011173032224178314,
-0.022083956748247147,
0.00986724067479372,
-0.008211600594222546,
0.010463984683156013,
0.005874298047274351,
0.012762142345309258,
-0.014823946170508862,
0.03368693217635155,
-0.001766728819347918,
-0.03191104531288147,
-0.042845506221055984,
-0.03526926040649414,
0.0004396549775265157,
0.010451790876686573,
0.02228769101202488,
0.015447184443473816,
-0.04125728830695152,
0.0020020543597638607,
0.1300964206457138,
-0.022336352616548538,
0.008870728313922882,
-0.047769542783498764,
0.049561817198991776,
-0.013694018125534058,
0.015933819115161896,
-0.037403304129838943,
-0.010562768206000328,
-0.007897174917161465,
-0.0015649852575734258,
0.04255952313542366,
0.009133747778832912,
-0.034804075956344604,
-0.02163596823811531,
-0.0032646148465573788,
0.04896363243460655,
0.031082279980182648,
0.005914255976676941,
0.060319092124700546,
0.026015302166342735,
-0.07127469778060913,
0.047452982515096664,
-0.019108671694993973,
0.009067174047231674,
0.01604803279042244,
-0.036747921258211136,
0.008051290176808834,
0.01584826037287712,
0.006214504595845938,
-0.05524280294775963,
0.07380040735006332,
0.05815007537603378,
-0.025115471333265305,
-0.0018083339091390371,
0.05603067949414253,
-0.0021270858123898506,
-0.05097685009241104,
-0.03995119407773018,
-0.01043091993778944,
0.024731053039431572,
0.020100388675928116,
-0.022471582517027855,
0.11571826785802841,
-0.036519043147563934,
0.0073480200953781605,
-0.024126144126057625,
0.04975135251879692,
-0.05481505021452904,
0.0018551822286099195,
0.05316329747438431,
-0.06703303009271622,
-0.00565654132515192,
0.011468689888715744,
-0.0052202008664608,
-0.06941137462854385,
-0.049194421619176865,
0.046895526349544525,
-0.027950093150138855,
-0.019083375111222267,
0.004413567017763853,
0.005549354944378138,
-0.023063145577907562,
-0.0037438063882291317,
-0.01731192320585251,
-0.0035990895703434944,
-0.011548439972102642,
-0.006305962800979614,
0.022722655907273293,
-0.018996326252818108,
0.03230413794517517,
0.00182898691855371,
-0.03399508073925972,
-0.05106240510940552,
-0.08903443813323975,
0.00010396815196145326,
-0.001210458460263908,
-0.017435306683182716,
-0.03454430028796196,
-0.04660273715853691,
0.013984373770654202,
0.026328496634960175,
-0.030750827863812447,
-0.02847033180296421,
-0.011359955184161663,
0.011860867962241173,
-0.009750379249453545,
-0.09904845803976059,
-0.004160088021308184,
0.01828441210091114,
0.004173501394689083,
-0.019426686689257622,
-0.007552037946879864,
0.021644117310643196,
0.04316330701112747,
0.05443281680345535,
0.06585617363452911,
-0.013078054413199425,
0.03396204859018326,
-0.02887064963579178,
0.042786359786987305,
0.02053789421916008,
-0.05674729496240616,
-0.010302715003490448,
0.01508386805653572,
0.010290250182151794,
-0.03755367547273636,
-0.04719744250178337,
-0.006272436119616032,
0.03945164382457733,
0.046018242835998535,
0.028237977996468544,
-0.009209224954247475,
0.09753087908029556,
0.03340906649827957,
0.04386686906218529,
-0.016565626487135887,
-0.037244826555252075,
-0.037622228264808655,
0.028729481622576714,
-0.004599183797836304,
0.0008440618985332549,
0.023863356560468674,
-0.027649838477373123,
0.02685575745999813,
0.022510800510644913,
-0.007739430759102106,
0.00365317240357399,
-0.033604834228754044,
0.024068599566817284,
0.042631879448890686,
-0.01917402260005474,
-0.011668979190289974,
0.019142068922519684,
-0.018530288711190224,
0.03442385420203209,
0.0022353599779307842,
0.005200542509555817,
-0.007285524159669876,
-0.02525409311056137,
-0.006435736082494259,
-0.014948937110602856,
-0.020834235474467278,
-0.02806331403553486,
0.029596099629998207,
0.005707387812435627,
-0.020914260298013687,
0.009095968678593636,
0.013105935417115688,
-0.032975226640701294,
0.006344706751406193,
-0.04225422069430351,
-0.012766704894602299,
-0.029008783400058746,
-0.0010770971421152353,
-0.06109229475259781,
-0.030842522159218788,
0.03508768975734711,
-0.04914833605289459,
-0.026703957468271255,
-0.025675881654024124,
-0.08747949451208115,
0.007354565896093845,
0.06884752959012985,
0.011568314395844936,
-0.02815159596502781,
0.01355742197483778,
0.0034939718898385763,
0.06925275921821594,
0.05264290049672127,
-0.08335074782371521,
0.03419593721628189,
0.009962107054889202,
-0.019217880442738533,
0.02090293914079666,
0.015105416998267174,
0.029747843742370605,
0.04045990854501724,
0.016520394012331963,
0.00878172367811203,
0.015140327624976635,
0.022935252636671066,
-0.014039459638297558
] |
<p>My dad and I have tried to calculate the strength of the explosion if the lid was suddenly freed. We took some measures:</p>
<ul>
<li>Lid mass: $0.7 \textrm{kg}$</li>
<li>Lid surface: $0.415 \textrm{m}^2$</li>
<li>Internal pressure (above external): $ 1\textrm{atm}\approx 100 \textrm{kPa} $</li>
</ul>
<p>Now we are kind of struggling about what to do with these. We'd like to know how to calculate the initial speed, for instance, or any other value that could get us started.</p>
<p>I hope I was clear enough. :)</p>
|
g2522
|
[
-0.0017618685960769653,
0.014196284115314484,
0.006660294719040394,
-0.02712613344192505,
0.004912083502858877,
-0.0063515519723296165,
-0.023269331082701683,
0.04345988482236862,
-0.060337938368320465,
0.011572356335818768,
-0.03464491665363312,
0.0017115107038989663,
0.005882623605430126,
0.013028052635490894,
0.07759268581867218,
0.010541741736233234,
0.06891055405139923,
-0.059515636414289474,
0.00435211043804884,
0.06223156675696373,
0.02788284234702587,
0.01529562845826149,
-0.05873723328113556,
-0.052658867090940475,
-0.0017240188317373395,
-0.016561182215809822,
-0.022785605862736702,
0.04217057302594185,
-0.08254130929708481,
0.023317715153098106,
-0.08846260607242584,
-0.06397535651922226,
-0.020222622901201248,
-0.07026797533035278,
-0.09424354881048203,
0.007489214651286602,
0.01742190308868885,
0.022383451461791992,
-0.033550020307302475,
0.0038603388238698244,
-0.02413150668144226,
-0.02207338623702526,
0.0023818761110305786,
0.0034247825387865305,
-0.015477894805371761,
0.03969384357333183,
-0.06607767939567566,
-0.022812586277723312,
-0.002973046386614442,
0.012983295135200024,
-0.016535403206944466,
0.013728763908147812,
0.031969938427209854,
-0.04234896972775459,
-0.025316692888736725,
0.045436661690473557,
0.009349904954433441,
-0.033036377280950546,
0.03322805464267731,
-0.012281297706067562,
-0.013324673287570477,
-0.07004504650831223,
0.022503094747662544,
-0.09379056096076965,
0.01651710271835327,
0.03116871789097786,
-0.03373821824789047,
0.04553907737135887,
0.033599402755498886,
-0.04025821015238762,
0.04142408445477486,
-0.020655294880270958,
0.0055131386034190655,
-0.017624564468860626,
-0.08116580545902252,
0.05975009500980377,
0.029798714444041252,
0.011725202202796936,
0.014028037898242474,
0.019531359896063805,
-0.042656347155570984,
-0.052114687860012054,
0.045063119381666183,
-0.04325707256793976,
0.012135175056755543,
0.004200602415949106,
-0.054602835327386856,
0.03282955661416054,
-0.028005192056298256,
0.009311305359005928,
0.05945700779557228,
-0.013112056069076061,
0.04703039675951004,
0.005722415167838335,
0.01719849184155464,
-0.008961230516433716,
-0.03457292914390564,
0.017538508400321007,
0.008831379935145378,
0.003199587110430002,
0.01415832620114088,
-0.07063301652669907,
0.030868200585246086,
-0.03587980568408966,
-0.04201902076601982,
0.035870831459760666,
0.030386464670300484,
-0.018390268087387085,
-0.04053743556141853,
-0.019184567034244537,
0.013962799683213234,
-0.038831837475299835,
-0.007691859267652035,
-0.022644879296422005,
0.032529961317777634,
-0.03522618114948273,
0.03486533835530281,
0.015986381098628044,
-0.0061399065889418125,
0.025312695652246475,
0.06128428876399994,
0.06116073578596115,
-0.006524969357997179,
-0.05609932914376259,
0.042810775339603424,
-0.021321740001440048,
0.006546502932906151,
-0.03193037211894989,
0.050259243696928024,
0.0009009712957777083,
0.017476292327046394,
-0.016634007915854454,
-0.029443414881825447,
0.038128770887851715,
0.0734366774559021,
0.051355939358472824,
-0.011677243746817112,
0.04001207649707794,
-0.026288913562893867,
-0.06215789169073105,
-0.020057329908013344,
0.030171556398272514,
-0.013942508026957512,
0.056371722370386124,
0.023077862337231636,
0.03622351959347725,
-0.007443093229085207,
0.058466099202632904,
-0.015543346293270588,
0.022670049220323563,
-0.0011753716971725225,
0.0339462012052536,
0.044743385165929794,
-0.012885035015642643,
-0.009050724096596241,
-0.029667168855667114,
0.06286009401082993,
0.02150018699467182,
-0.027088193222880363,
-0.02274515852332115,
0.02351706102490425,
0.054521262645721436,
0.0036485912278294563,
-0.017732998356223106,
-0.061566680669784546,
0.05685340240597725,
0.048087481409311295,
-0.00923238880932331,
0.038894716650247574,
0.023623879998922348,
-0.030340107157826424,
-0.03351524844765663,
-0.02135859616100788,
0.043394461274147034,
0.0004652599454857409,
0.0019704706501215696,
0.07900039851665497,
-0.0006219758652150631,
-0.04694709926843643,
-0.013232656754553318,
0.02092301845550537,
-0.011346808634698391,
0.06103864684700966,
-0.006947615183889866,
0.016026543453335762,
-0.033114489167928696,
0.05296589806675911,
0.04255278408527374,
-0.045441679656505585,
0.059641193598508835,
-0.009593225084245205,
0.027836855500936508,
0.039207715541124344,
0.019715428352355957,
-0.004047665279358625,
-0.07039856165647507,
0.025555916130542755,
0.014701367355883121,
-0.013159424066543579,
0.015908755362033844,
-0.02178884483873844,
0.011796263046562672,
-0.042073220014572144,
-0.026197822764515877,
-0.03662720322608948,
-0.010583880357444286,
-0.003796258708462119,
0.060432400554418564,
0.010896092280745506,
0.028780238702893257,
-0.008978990837931633,
0.004948456771671772,
-0.02663656324148178,
-0.00953735038638115,
0.062374603003263474,
0.09047754108905792,
-0.026003165170550346,
0.07690083980560303,
0.0039046085439622402,
-0.0045992727391421795,
0.01804283633828163,
0.04432639852166176,
0.05349220708012581,
-0.04508781060576439,
0.006842998322099447,
-0.018583647906780243,
0.024034664034843445,
0.03933176398277283,
0.000803413160610944,
0.027407029643654823,
-0.026284636929631233,
0.02798977680504322,
-0.04588901251554489,
0.005697776563465595,
-0.0024024839513003826,
0.03748646751046181,
0.014975772239267826,
0.012618727050721645,
0.012129750102758408,
0.0418940931558609,
0.005701451096683741,
-0.004930236842483282,
-0.040791045874357224,
-0.003027352038770914,
-0.043000612407922745,
-0.0668300986289978,
-0.004856982734054327,
-0.01599819026887417,
0.02568509615957737,
0.025836721062660217,
-0.02529105730354786,
-0.004305772949010134,
-0.08158448338508606,
-0.042624711990356445,
-0.048015713691711426,
-0.03094054013490677,
-0.03769609332084656,
-0.015794135630130768,
-0.047353263944387436,
-0.04158034175634384,
0.00947867427021265,
-0.014476577751338482,
0.02961145155131817,
-0.015263624489307404,
-0.0751945748925209,
-0.027325527742505074,
0.0044063604436814785,
-0.03999048098921776,
0.01871832087635994,
0.00530215073376894,
-0.0309956856071949,
-0.00006234408647287637,
0.04736306145787239,
0.06405530869960785,
0.04463035613298416,
-0.0767320990562439,
0.01774683967232704,
0.00626749312505126,
-0.0035654748789966106,
0.010158288292586803,
0.012812037952244282,
0.017259912565350533,
-0.0417136587202549,
0.005890933331102133,
-0.011891833506524563,
-0.10091852396726608,
0.02656545862555504,
0.043837014585733414,
0.025089267641305923,
-0.03032618574798107,
0.01188560202717781,
0.04421116039156914,
0.006835784297436476,
0.07751260697841644,
-0.019063536077737808,
0.0725625529885292,
0.05272582918405533,
-0.025082672014832497,
0.0025283487048000097,
-0.05239264294505119,
0.014174801297485828,
-0.036755774170160294,
-0.06156207248568535,
-0.004068099427968264,
-0.06628572195768356,
0.02611396089196205,
-0.0378371886909008,
0.021440261974930763,
0.01663893274962902,
-0.026876449584960938,
0.01891293190419674,
0.054554812610149384,
0.04733043536543846,
-0.036706823855638504,
-0.02481061965227127,
0.003062289208173752,
0.043343257158994675,
0.03185016289353371,
-0.0400812141597271,
0.014204311184585094,
-0.07799609005451202,
-0.03577103093266487,
-0.03189031779766083,
-0.03228309378027916,
-0.01596389152109623,
-0.009456761181354523,
-0.03796081244945526,
-0.000016185287677217275,
0.022015348076820374,
-0.049253128468990326,
0.06056269258260727,
0.07030866295099258,
0.00606056721881032,
-0.03219170868396759,
-0.01817542314529419,
0.009565997868776321,
0.004966242704540491,
0.040511660277843475,
0.019821036607027054,
0.02632606215775013,
0.01087121944874525,
-0.04073503986001015,
-0.05293811857700348,
0.01866506226360798,
-0.025606004521250725,
-0.02320871502161026,
-0.020419327542185783,
-0.04118315130472183,
-0.028304265812039375,
-0.044434111565351486,
0.04859371483325958,
0.025443343445658684,
0.005313691683113575,
-0.01779349148273468,
0.009905225597321987,
0.036600977182388306,
0.058234211057424545,
-0.001960228895768523,
-0.0026817757170647383,
0.033635057508945465,
-0.05561910942196846,
0.002552241086959839,
0.006319346837699413,
0.03788593038916588,
-0.054090466350317,
-0.05021723732352257,
-0.02570176124572754,
0.057502053678035736,
-0.028141191229224205,
0.006043507717549801,
-0.048041932284832,
-0.028143994510173798,
0.008189970627427101,
-0.052260126918554306,
0.004014912992715836,
0.01186396274715662,
0.0544741228222847,
-0.004289249423891306,
-0.019651051610708237,
0.023425037041306496,
0.050942614674568176,
0.011347437277436256,
0.01997433230280876,
-0.015440043993294239,
-0.010109513066709042,
0.034080732613801956,
-0.030486511066555977,
0.027060337364673615,
0.03385837748646736,
-0.04899485781788826,
-0.00043747734162025154,
-0.032423630356788635,
-0.05911742523312569,
0.022086070850491524,
0.025923065841197968,
0.021753378212451935,
0.005879458039999008,
-0.014509039930999279,
-0.07432994991540909,
0.009386804886162281,
0.04151551052927971,
-0.016610918566584587,
0.044744040817022324,
-0.00271608610637486,
-0.009942394681274891,
0.025844981893897057,
0.06053858995437622,
-0.04897207394242287,
0.05151783674955368,
0.014080904424190521,
0.04950273409485817,
-0.02048681117594242,
-0.004619162995368242,
-0.008357170969247818,
-0.018346229568123817,
-0.06346657872200012,
0.03848018869757652,
0.001294259331189096,
-0.0010975170880556107,
0.028909314423799515,
-0.012516479007899761,
-0.016176879405975342,
0.015149212442338467,
-0.016136130318045616,
-0.020293766632676125,
-0.033733852207660675,
0.06158372014760971,
0.022054001688957214,
0.07650243490934372,
-0.03128022700548172,
0.0016125062247738242,
0.005331031046807766,
-0.04159052297472954,
0.0012056085979565978,
0.01698729582130909,
0.003547688713297248,
0.021449366584420204,
0.07970400154590607,
-0.03507731482386589,
0.0131615549325943,
0.004488649778068066,
-0.0014902189141139388,
-0.027053063735365868,
0.09380638599395752,
-0.002618668368086219,
0.05212060362100601,
-0.029149435460567474,
-0.012929302640259266,
-0.018487820401787758,
-0.04643081873655319,
-0.021796170622110367,
0.02166985534131527,
0.007110590115189552,
-0.02953476831316948,
-0.014422877691686153,
0.006167138926684856,
-0.00410196278244257,
0.011077797040343285,
0.06505655497312546,
0.10284586995840073,
-0.04534866660833359,
0.028664331883192062,
0.020238330587744713,
-0.016542699187994003,
0.020354120060801506,
-0.06462876498699188,
-0.008520745672285557,
-0.008853667415678501,
0.008413748815655708,
0.013983373530209064,
0.0181871484965086,
-0.036691609770059586,
0.05732171609997749,
0.007327576633542776,
-0.06301286071538925,
0.013715976849198341,
0.01702454313635826,
-0.009946873411536217,
0.034664977341890335,
-0.030881740152835846,
-0.0025003172922879457,
0.011360704898834229,
-0.033278580754995346,
0.006401954218745232,
0.040850307792425156,
0.05465736985206604,
-0.0307881198823452,
-0.023460566997528076,
-0.02665545605123043,
-0.004050038289278746,
0.003570099361240864,
0.0450250580906868,
-0.015124955214560032,
-0.022783640772104263,
0.007990666665136814,
-0.026649363338947296,
0.0093196677044034,
0.017780641093850136,
-0.02163073420524597,
0.002236396772786975,
-0.06348437815904617,
0.031187644228339195,
-0.023570647463202477,
0.07122725993394852,
-0.054922252893447876,
0.005850282497704029,
-0.045012906193733215,
0.037372760474681854,
0.04295643791556358,
0.02433360181748867,
0.05957707017660141,
-0.005432141944766045,
-0.002701106481254101,
-0.05431203916668892,
0.03292103856801987,
-0.05459989607334137,
0.046769265085458755,
0.05301791429519653,
0.014714572578668594,
0.020471705123782158,
0.036664146929979324,
-0.004566525109112263,
0.06877674162387848,
0.00020172678341623396,
-0.04244270548224449,
-0.006728339474648237,
-0.06684738397598267,
-0.03839772939682007,
-0.024693723767995834,
0.03229504078626633,
-0.0011797123588621616,
-0.016902035102248192,
-0.0062201423570513725,
-0.09162509441375732,
-0.04128023609519005,
0.03806396573781967,
0.033524055033922195,
0.0017604402964934707,
-0.02178889326751232,
-0.04202467203140259,
0.010321095585823059,
0.03095422498881817,
-0.015346521511673927,
0.0569184273481369,
-0.0077393208630383015,
0.032823655754327774,
-0.04874677211046219,
-0.008391637355089188,
0.031808625906705856,
0.05025029927492142,
0.03248228877782822,
0.0038135636132210493,
0.02039523236453533,
0.021581830456852913,
0.07983413338661194,
0.02048756740987301,
-0.004557854030281305,
0.022810962051153183,
-0.02372608706355095,
-0.04344341158866882,
0.01618288643658161,
0.005896245129406452,
0.04457703232765198,
0.06946562975645065,
-0.028255781158804893,
-0.03967057168483734,
-0.03586884215474129,
-0.05093669146299362,
-0.019980283454060555,
-0.008602045476436615,
0.018635204061865807,
-0.0073783001862466335,
0.01542681735008955,
-0.035527899861335754,
0.0409395806491375,
0.03477872908115387,
0.03157421946525574,
-0.008844251744449139,
-0.01114462036639452,
-0.006866843905299902,
-0.015172927640378475,
0.031165137887001038,
0.018316669389605522,
-0.04208260402083397,
-0.07151837646961212,
-0.038945894688367844,
-0.01698511466383934,
0.003834622446447611,
-0.05826239287853241,
-0.08638320118188858,
0.0222880057990551,
-0.008375700563192368,
-0.011539528146386147,
-0.07249948382377625,
-0.019967345520853996,
0.01545519195497036,
-0.006473240442574024,
-0.03862180933356285,
0.044570233672857285,
0.06470448523759842,
-0.01718665100634098,
0.0754876360297203,
0.0113672548905015,
-0.040595486760139465,
0.003756896825507283,
-0.014782777987420559,
0.007562303449958563,
-0.004605066031217575,
-0.03682868182659149,
-0.028103843331336975,
-0.004815870430320501,
0.03454335033893585,
0.012964962050318718,
0.0337882824242115,
0.005913006607443094,
-0.011114668101072311,
0.06257545948028564,
-0.011422987096011639,
0.024910148233175278,
0.004326028283685446,
0.014553990215063095,
-0.009612292051315308,
0.02787284553050995,
-0.07554402947425842,
-0.0010005400981754065,
0.009627489373087883,
-0.05326002836227417,
0.02226586453616619,
0.006018670275807381,
0.0067655048333108425,
0.05309582129120827,
-0.010910245589911938,
0.06463037431240082,
-0.02029077708721161,
-0.029720308259129524,
0.043442972004413605,
0.012333636172115803,
0.06791909039020538,
-0.03891143575310707,
0.012605627998709679,
0.04077453538775444,
-0.018166394904255867,
0.014569465070962906,
0.015456881374120712,
-0.03488500043749809,
0.05142935365438461,
0.004364174325019121,
-0.017789974808692932,
-0.005870969034731388,
-0.007174498401582241,
-0.02400011010468006,
-0.06484802812337875,
-0.033807530999183655,
-0.0009040359873324633,
-0.07540930062532425,
0.007954849861562252,
-0.044055353850126266,
-0.024101583287119865,
-0.03969438001513481,
0.006659301463514566,
-0.007500359322875738,
-0.032324958592653275,
0.05415330082178116,
-0.0797533169388771,
-0.007732320576906204,
0.020150307565927505,
0.02930448390543461,
-0.001462757820263505,
0.0004074493481311947,
-0.06004759669303894,
0.017835300415754318,
-0.002770017832517624,
-0.0708213672041893,
-0.0050172084011137486,
-0.019191384315490723,
0.054664235562086105,
-0.0032953291665762663,
0.012086805887520313,
-0.022329775616526604,
-0.01815156824886799,
-0.08247097581624985,
0.02053460106253624,
-0.05769230052828789,
-0.007437169551849365,
-0.004034431651234627,
0.018239425495266914,
-0.04691651836037636,
-0.009562942199409008,
0.07384384423494339,
0.021667033433914185,
0.01298900879919529,
0.0018581078620627522,
0.0773962140083313,
0.006640826351940632,
-0.06315925717353821,
0.013575105927884579,
-0.003877149196341634,
0.029379887506365776,
0.05690213292837143,
-0.032366733998060226,
-0.005127570126205683,
0.04382937774062157,
0.008376838639378548,
-0.029550226405262947,
-0.03706112131476402,
0.012717864476144314,
0.020068783313035965,
0.04186449572443962,
-0.008153081871569157,
0.01715691015124321,
-0.001574832247570157,
0.005062645301222801,
0.01949917897582054,
-0.03907495737075806,
0.04962786287069321,
-0.01549617201089859,
-0.0029255433473736048,
-0.02278256043791771,
-0.011462715454399586,
0.03788093850016594,
0.03447478637099266,
0.0033795509953051805,
0.014515089802443981,
-0.00399918295443058,
0.014815515838563442,
0.022186942398548126,
-0.018927477300167084,
0.02944006770849228,
-0.04092564806342125,
0.010654550977051258,
0.028599703684449196,
-0.028839198872447014,
-0.012574409134685993,
0.009301584213972092,
-0.01858418434858322,
0.022001933306455612,
0.06490075588226318,
0.007926723919808865,
-0.006443490739911795,
0.05053184553980827,
-0.010682441294193268,
-0.024958088994026184,
-0.015699919313192368,
-0.0048559121787548065,
0.03824172168970108,
-0.050663530826568604,
-0.08762644231319427,
0.051552679389715195,
0.04065261781215668,
-0.009880196303129196,
0.05982594192028046,
-0.0345940887928009,
-0.03794258087873459,
0.022243540734052658,
-0.026612088084220886,
-0.06615053862333298,
-0.09513161331415176,
-0.04005002602934837,
0.04348716139793396,
-0.06959724426269531,
0.008431673981249332,
0.04833725839853287,
0.004830764140933752,
-0.025844115763902664,
0.02603023126721382,
0.04082329198718071,
-0.024341046810150146,
-0.0631694346666336
] |
<p>I'm trying to find the electric field due to an electric dipole $\mathbf{d}$. There are plenty of approaches to doing this online, but I want to do it "my way," which doesn't seem to be working (and I have yet to find this approach in textbooks/online). I start with the potential:</p>
<p>$$ \phi(\mathbf{r}) = \frac{\mathbf{d}\cdot \mathbf{r}}{4\pi\epsilon_0 r^3} = \frac{d\cos\theta}{4\pi\epsilon_0 r^2} $$</p>
<p>And then take the negative gradient to find:</p>
<p>$$ \mathbf{E} = -\nabla \phi = \frac{2d\cos\theta}{4\pi \epsilon_0 r^3} \hat{r} + \frac{d\sin\theta}{4\pi\epsilon_0 r^3}\hat{\theta} $$</p>
<p>But I don't see how to manipulate this into the form that I expect:</p>
<p>$$ \mathbf{E} = \frac{1}{4\pi\epsilon_0}\left[ \frac{3(\mathbf{d}\cdot\hat{r})\hat{r}-\mathbf{d}}{r^3} \right] - \frac{1}{3\epsilon_0}\mathbf{d} \delta^3(\mathbf{r}) $$</p>
<p>Since I haven't done anything mathematically illegal, I don't see why my approach shouldn't get me to the correct answer - but I can't figure out what to do (and I've also been unable to find this derivation online).</p>
|
g2523
|
[
-0.009537698701024055,
0.034560270607471466,
-0.013952739536762238,
-0.03868905082345009,
0.0792178213596344,
0.02708856202661991,
0.06139761209487915,
0.015076929703354836,
0.00018771825125440955,
-0.017194529995322227,
-0.04281937703490257,
-0.009529161266982555,
0.005305559374392033,
-0.007819700986146927,
0.04229090362787247,
0.01076835673302412,
0.05558698996901512,
0.010069957002997398,
0.009373530745506287,
-0.0436558797955513,
-0.03416348248720169,
-0.013122188858687878,
0.03953368216753006,
-0.027252523228526115,
-0.004999355413019657,
-0.0601506233215332,
-0.03334663435816765,
0.009901400655508041,
-0.02989719808101654,
-0.03469768539071083,
-0.05481048673391342,
0.03894346207380295,
0.07022307813167572,
0.003000847762450576,
-0.054646383970975876,
-0.010408995673060417,
0.022427430376410484,
0.06906040757894516,
-0.015100881457328796,
-0.0006285784184001386,
-0.0017684823833405972,
-0.020311277359724045,
0.029016023501753807,
0.06390301138162613,
-0.02933191880583763,
-0.02590429224073887,
-0.032733254134655,
0.0004582634719554335,
-0.044593360275030136,
-0.009319525212049484,
0.013409951701760292,
0.03828886151313782,
0.07583410292863846,
-0.032396189868450165,
-0.04580057039856911,
0.0024850331246852875,
0.05802386254072189,
-0.053382694721221924,
-0.01748211309313774,
0.0018091824604198337,
-0.011655251495540142,
-0.008595732040703297,
0.04090890288352966,
-0.0002977392578031868,
0.027128184214234352,
0.036143459379673004,
-0.02318766340613365,
-0.014128029346466064,
0.0019785917829722166,
-0.04505099728703499,
-0.02471592091023922,
-0.01744551584124565,
-0.011775951832532883,
-0.007281521800905466,
-0.052636321634054184,
0.009918511845171452,
0.025505298748612404,
-0.044198278337717056,
0.05419355630874634,
-0.03928385302424431,
0.0018300850642845035,
-0.016529152169823647,
0.013991954736411572,
0.0044980356469750404,
0.04288243129849434,
-0.009507762268185616,
0.01807890273630619,
0.0310951080173254,
0.004328601993620396,
-0.08125679194927216,
-0.06372933089733124,
0.005406832788139582,
0.004397109150886536,
-0.020953698083758354,
-0.013354691676795483,
-0.02073478139936924,
0.033759698271751404,
0.03788958862423897,
-0.005859635770320892,
-0.030954251065850258,
0.006647077854722738,
0.011748570948839188,
0.025578368455171585,
0.020068136975169182,
-0.07996359467506409,
0.03068060427904129,
0.05924764275550842,
-0.021901892498135567,
0.035662692040205,
-0.022447939962148666,
-0.02459576167166233,
-0.042557794600725174,
-0.031170492991805077,
-0.04464344680309296,
-0.021798932924866676,
-0.012538833543658257,
-0.008252304047346115,
0.006462139543145895,
-0.03629998117685318,
0.07078543305397034,
0.014352277852594852,
-0.017089324072003365,
0.0061661479994654655,
0.036692067980766296,
-0.044149041175842285,
0.0373321995139122,
-0.02408522367477417,
0.02811187133193016,
0.08064953982830048,
-0.03485473245382309,
0.03675229102373123,
-0.012396502308547497,
-0.006768523715436459,
-0.015432127751410007,
0.0025817733258008957,
0.042238522320985794,
-0.025852758437395096,
0.011816298589110374,
0.0061638616025447845,
0.019649282097816467,
0.019463995471596718,
-0.022405501455068588,
0.0026326486840844154,
-0.021761655807495117,
-0.03861676901578903,
0.046278126537799835,
-0.01910436525940895,
-0.030204318463802338,
0.08074980974197388,
0.03659428283572197,
-0.022611219435930252,
0.011435524560511112,
-0.04519011080265045,
-0.012475816532969475,
0.031033238396048546,
-0.016157932579517365,
0.030223017558455467,
-0.01378560159355402,
-0.025885673239827156,
-0.01144382730126381,
0.055593185126781464,
0.00040277509833686054,
-0.022163674235343933,
-0.02007635310292244,
0.010005884803831577,
-0.00963938981294632,
0.04108450189232826,
-0.024433648213744164,
-0.030414024367928505,
-0.029359249398112297,
-0.026853317394852638,
0.02132193185389042,
0.06439798325300217,
-0.005623462609946728,
-0.013315225951373577,
0.051794495433568954,
-0.044524140655994415,
-0.03114989772439003,
0.016262076795101166,
0.07432586699724197,
-0.007570028770714998,
-0.02218862622976303,
0.03976424038410187,
0.040459442883729935,
0.039485398679971695,
-0.011042210273444653,
-0.006525331176817417,
0.03987410292029381,
0.010094521567225456,
-0.009373999200761318,
0.011394565925002098,
0.023775555193424225,
0.041034724563360214,
-0.010393455624580383,
0.0017850016010925174,
0.032313887029886246,
0.026657475158572197,
-0.08707890659570694,
0.06270033866167068,
-0.016778036952018738,
-0.03611534833908081,
0.020116465166211128,
0.054069794714450836,
-0.0008725791703909636,
0.010637196712195873,
-0.02232631854712963,
0.04153954237699509,
-0.02843872830271721,
0.053217723965644836,
0.010492677800357342,
-0.030744725838303566,
-0.028918597847223282,
-0.02163309045135975,
-0.004571069497615099,
-0.05926790460944176,
-0.024941354990005493,
-0.015053938142955303,
0.029306914657354355,
-0.09143625944852829,
0.041549164801836014,
-0.05838264897465706,
-0.0014471105532720685,
0.024103036150336266,
0.018759867176413536,
-0.04870307445526123,
0.022456910461187363,
-0.008997021242976189,
0.0012838762486353517,
-0.050701163709163666,
0.02522408775985241,
-0.06567955017089844,
0.009060547687113285,
-0.01816200092434883,
-0.028921443969011307,
0.04328498989343643,
0.0493277870118618,
-0.04246259108185768,
-0.06361518800258636,
-0.02316652610898018,
0.0007585514103993773,
-0.05672918260097504,
0.0014735768781974912,
0.056064456701278687,
0.0724804624915123,
0.0015889874193817377,
0.0008658443694002926,
0.03945409134030342,
0.07993927597999573,
-0.020227136090397835,
-0.019827617332339287,
0.07990293949842453,
0.02533285692334175,
-0.011588090099394321,
-0.0009702031384222209,
-0.012984059751033783,
-0.01655011996626854,
-0.016494575887918472,
0.04753340780735016,
0.0829734206199646,
-0.02486000955104828,
-0.03360333293676376,
0.01862763799726963,
0.010186229832470417,
0.019800670444965363,
-0.0388040766119957,
-0.02833789400756359,
-0.037152159959077835,
-0.06986180692911148,
0.036709871143102646,
0.0054086726158857346,
-0.040763579308986664,
0.0531264990568161,
0.017238715663552284,
0.025811832398176193,
0.004392281640321016,
-0.05458609014749527,
0.04111115261912346,
-0.024144524708390236,
0.05227439105510712,
0.04170805588364601,
0.07255930453538895,
-0.014475828967988491,
0.05764107406139374,
0.04213915765285492,
-0.01206847932189703,
-0.05931800231337547,
-0.017612934112548828,
-0.020940450951457024,
-0.043922059237957,
-0.011019130237400532,
-0.012888656929135323,
-0.030024249106645584,
0.011338390409946442,
-0.06277801841497421,
-0.002327047288417816,
0.0004037987382616848,
0.056266285479068756,
-0.09491730481386185,
0.033804912120103836,
0.027288148179650307,
0.04448145255446434,
-0.010593055747449398,
-0.01817893795669079,
-0.019312961027026176,
0.0586712621152401,
-0.017524749040603638,
-0.013047503307461739,
0.02342088520526886,
0.02844788320362568,
0.02339080721139908,
0.006121367681771517,
-0.020440394058823586,
0.051815785467624664,
-0.03286292776465416,
-0.013564680702984333,
-0.022543001919984818,
-0.0025389385409653187,
-0.055163510143756866,
0.03148413822054863,
0.010594738647341728,
0.0050458903424441814,
-0.07406935095787048,
-0.040334220975637436,
0.03691316768527031,
0.049467939883470535,
0.026355478912591934,
-0.06067018583416939,
0.027739431709051132,
0.01573895290493965,
-0.08978460729122162,
0.017716482281684875,
-0.04316152632236481,
-0.0011640213197097182,
-0.041854795068502426,
-0.02121148630976677,
-0.029362192377448082,
-0.05067242309451103,
0.03007810190320015,
0.007196597754955292,
-0.06092946231365204,
0.006285892333835363,
-0.0679967850446701,
-0.09653723239898682,
-0.020357545465230942,
-0.02355251833796501,
-0.03353001922369003,
-0.009518483653664589,
0.0563015379011631,
0.04781023785471916,
0.03635247051715851,
-0.02043256163597107,
-0.029714109376072884,
0.006272890605032444,
0.030129216611385345,
0.02768874354660511,
-0.03791964426636696,
0.02018856629729271,
0.05689077451825142,
0.0053523690439760685,
0.05213230103254318,
0.005710719618946314,
-0.025842944160103798,
-0.013167398050427437,
-0.0007723399321548641,
0.019023673608899117,
-0.018478987738490105,
-0.0027539837174117565,
0.012539438903331757,
-0.06904458999633789,
-0.02147909626364708,
0.02357644960284233,
-0.024485288187861443,
0.02944854646921158,
0.020307501778006554,
-0.002116266405209899,
-0.04521326720714569,
-0.037070002406835556,
0.009067554958164692,
-0.04691067710518837,
0.028941884636878967,
-0.02295009046792984,
0.0518115870654583,
0.07814953476190567,
0.0442289337515831,
0.032694220542907715,
0.011740155518054962,
-0.04288506135344505,
0.03974786400794983,
0.01096784882247448,
0.043212179094552994,
-0.05444928631186485,
0.028949620202183723,
-0.008686789311468601,
0.05258241295814514,
-0.046174611896276474,
-0.03485492989420891,
0.02082676626741886,
-0.008563308976590633,
-0.06982941925525665,
0.047478705644607544,
0.027339372783899307,
-0.0037178408820182085,
0.05216869339346886,
-0.007940039969980717,
-0.06865529716014862,
-0.03344324976205826,
0.009238219819962978,
-0.02646680176258087,
0.03842191770672798,
-0.036293286830186844,
-0.04695720598101616,
-0.02956993691623211,
-0.002777797169983387,
-0.007070968858897686,
0.0127800228074193,
0.003941043745726347,
0.07934258878231049,
0.0006413387018255889,
0.06145235896110535,
-0.006241731345653534,
0.009818069636821747,
-0.028180817142128944,
-0.0007973493775352836,
-0.034809354692697525,
0.030284011736512184,
0.05873139202594757,
0.04537457600235939,
-0.013327911496162415,
-0.000652375805657357,
-0.032587599009275436,
-0.018584037199616432,
0.0579008087515831,
-0.03648668900132179,
-0.011191057041287422,
-0.08209001272916794,
0.04183122515678406,
-0.10544287413358688,
-0.0019302915316075087,
-0.01110876351594925,
0.059675998985767365,
0.0440109483897686,
-0.008317501284182072,
0.04030995815992355,
-0.023637358099222183,
-0.015677276998758316,
0.025040773674845695,
-0.036983586847782135,
-0.059360772371292114,
0.03278086706995964,
0.00270711537450552,
0.008130352944135666,
0.006882046815007925,
0.009310480207204819,
0.00584997097030282,
-0.0014226931380107999,
-0.021933844313025475,
-0.02477451041340828,
0.0003342196869198233,
-0.016187138855457306,
0.027605928480625153,
-0.010687782429158688,
-0.004743261728435755,
-0.05676480010151863,
-0.04411283880472183,
0.05728411301970482,
-0.010522267781198025,
-0.059330716729164124,
-0.01803511008620262,
-0.0005356883048079908,
-0.06657801568508148,
-0.009600233286619186,
0.047791074961423874,
-0.00487795053049922,
-0.047744035720825195,
0.011611594818532467,
0.018361404538154602,
0.007107643410563469,
0.012386568821966648,
-0.03326007351279259,
-0.025277534499764442,
0.004422173835337162,
-0.029366299510002136,
0.00667799124494195,
0.0503573901951313,
-0.016952909529209137,
0.027307255193591118,
-0.0006758232484571636,
-0.002365473425015807,
-0.04855106770992279,
-0.06735323369503021,
0.020837293937802315,
0.07615020126104355,
0.041255466639995575,
-0.05308875814080238,
-0.00862841960042715,
0.01013207994401455,
0.002230355516076088,
0.02758129872381687,
-0.0005496990634128451,
-0.022048210725188255,
-0.059936441481113434,
0.02153792791068554,
-0.06377869844436646,
0.042574018239974976,
0.052456166595220566,
0.03684113174676895,
0.06837638467550278,
-0.0016264229780063033,
0.03994403034448624,
-0.020820872858166695,
-0.01976308971643448,
-0.021532459184527397,
0.0385255366563797,
0.03499443084001541,
0.018119854852557182,
-0.010216280817985535,
-0.07090751826763153,
0.03611411154270172,
-0.007654258981347084,
-0.0405157096683979,
0.06869594007730484,
-0.01411300990730524,
0.005107302218675613,
-0.06308133900165558,
0.06291083246469498,
0.007880699820816517,
-0.03381473943591118,
-0.030782733112573624,
0.03237847983837128,
-0.022794893011450768,
-0.01929575763642788,
-0.029725421220064163,
-0.016040829941630363,
0.012786458246409893,
0.00579636637121439,
-0.04138169065117836,
0.007165025919675827,
-0.004438094794750214,
0.003353873500600457,
0.005972625687718391,
0.03779757767915726,
-0.015953626483678818,
0.05150134861469269,
0.001315622590482235,
-0.0200875885784626,
0.014753873459994793,
0.053204458206892014,
-0.03900669515132904,
-0.004313950892537832,
0.0074368673376739025,
-0.0304668378084898,
-0.01924649067223072,
-0.0013770910445600748,
0.0027182414196431637,
0.025620535016059875,
-0.039792031049728394,
-0.02261773683130741,
-0.013894481584429741,
-0.02700228989124298,
-0.01195660512894392,
0.013306207954883575,
-0.0646216943860054,
0.013098742812871933,
0.04378994554281235,
-0.02377070114016533,
0.0005743893561884761,
0.04075736925005913,
0.011384233832359314,
0.024067280814051628,
0.016914833337068558,
0.01815551333129406,
0.0032931941095739603,
-0.02881372533738613,
0.0309697687625885,
0.0032635945826768875,
-0.0020294657442718744,
0.025048349052667618,
0.0015087801730260253,
0.01679881662130356,
0.011002679355442524,
0.02085275761783123,
0.029819006100296974,
0.033132441341876984,
-0.04064994305372238,
-0.03186332806944847,
0.12496832758188248,
-0.037874914705753326,
-0.049063790589571,
-0.007942399941384792,
-0.06171626225113869,
-0.023705001920461655,
0.016810735687613487,
-0.009175004437565804,
-0.014993980526924133,
-0.0003680671798065305,
-0.039363108575344086,
0.029024045914411545,
0.016581906005740166,
0.043362293392419815,
0.05710357427597046,
0.008579240180552006,
-0.009276043623685837,
-0.011294898577034473,
-0.02967703528702259,
0.07207693159580231,
-0.016746902838349342,
0.02747942879796028,
0.013466119766235352,
-0.05178065598011017,
-0.04781576618552208,
0.041972577571868896,
0.03520630672574043,
-0.05866169184446335,
0.001332480343990028,
0.037657156586647034,
0.012586095370352268,
-0.016212861984968185,
0.02399008721113205,
0.022384146228432655,
0.03786146268248558,
-0.02151624672114849,
0.016019485890865326,
-0.013684137724339962,
-0.06587756425142288,
-0.013927615247666836,
0.009914545342326164,
-0.010896841064095497,
-0.024082975462079048,
0.019286110997200012,
0.01941344141960144,
0.02210417576134205,
0.0072824545204639435,
-0.043348781764507294,
0.06656966358423233,
0.014610173180699348,
-0.022661050781607628,
0.04285530000925064,
0.07983043044805527,
0.028371207416057587,
0.04299211502075195,
-0.040927112102508545,
0.024824999272823334,
-0.0075050415471196175,
-0.010414245538413525,
-0.025463344529271126,
0.013052933849394321,
-0.009894177317619324,
0.05088312178850174,
-0.05313273146748543,
0.003754546632990241,
0.09618162363767624,
0.00009179094195133075,
0.012193430215120316,
-0.03134799376130104,
-0.04077935218811035,
-0.010506543330848217,
0.045351117849349976,
0.04818160459399223,
0.013961510732769966,
-0.014400566928088665,
-0.018085362389683723,
-0.06677334010601044,
-0.013493564911186695,
0.00500028021633625,
0.01141160074621439,
0.02368118241429329,
-0.0019129851134493947,
-0.01157402154058218,
0.03307279199361801,
-0.056786950677633286,
0.013018921948969364,
-0.037109002470970154,
0.011658638715744019,
0.049202822148799896,
0.0004891742719337344,
0.0003940480528399348,
0.048829130828380585,
0.026666665449738503,
-0.009173344820737839,
-0.01882123202085495,
-0.029516180977225304,
0.01685304194688797,
-0.003312489250674844,
-0.09903966635465622,
-0.03174209967255592,
-0.005478788632899523,
-0.059355031698942184,
-0.01377960667014122,
-0.009499810636043549,
0.08495604991912842,
-0.0317872017621994,
0.04957804083824158,
-0.020943598821759224,
-0.006726346909999847,
-0.029186761006712914,
0.040700823068618774,
0.052973825484514236,
-0.010068162344396114,
0.07564904540777206,
0.053673628717660904,
0.02340094745159149,
-0.05457357317209244,
0.019067127257585526,
-0.019049912691116333,
-0.02548874169588089,
-0.03264208883047104,
-0.04827868565917015,
-0.020967138931155205,
-0.06854137033224106,
0.012716560624539852,
0.08503632247447968,
-0.009479580447077751,
-0.020715035498142242,
-0.014812509529292583,
0.061429064720869064,
0.071305051445961,
-0.02360067144036293,
0.10865209996700287,
0.001102303504012525,
-0.02525273896753788,
0.011239861138164997,
0.04082072153687477,
-0.03619508072733879,
-0.02386283129453659,
-0.006993488408625126,
0.014325288124382496,
-0.0682452917098999,
-0.03254782781004906,
0.03496736288070679,
-0.0008425326668657362,
-0.004154641646891832,
-0.014091777615249157,
0.0003924737684428692,
0.004272303078323603,
0.0012805702863261104,
0.0019497204339131713,
-0.0372820608317852,
-0.01558609027415514,
0.03578144684433937,
-0.0019500405760481954,
0.012397333048284054,
-0.03718441352248192,
-0.03676706925034523,
-0.06192199885845184,
0.046027254313230515,
-0.01285483781248331,
-0.036215491592884064,
0.01540294848382473,
0.03515651449561119,
-0.003803736064583063,
-0.01690691150724888,
-0.056194234639406204,
-0.023150065913796425,
0.02415747009217739,
0.04632847383618355,
-0.03290865197777748,
0.020640000700950623,
0.012452838942408562,
0.05280936136841774,
0.032906800508499146,
0.0046739354729652405,
-0.05512692779302597,
-0.03413613140583038,
0.08757641911506653,
-0.01682855188846588,
-0.054102666676044464,
-0.000692407542373985,
0.008897383697330952
] |
<p>So, let's say we have a spacecraft in deep space. It activates its rocket engines, to keep it simple. The engine reaction channels exhaust through the aft nozzle, right? How does that chemical reaction actually induce a change in the velocity of the spacecraft? The particles <em>have</em> to push against the geometry of the spacecraft to provide a force. Do they do that and how when their direction vector clearly goes away from the spacecraft?</p>
<p>And here's something else. A pressurized spacecraft opens up an airlock which decompresses the entire deck, would that create a small thrust for the spacecraft and how? Is it the contact hull - air as it is accelerating outwards?</p>
|
g2524
|
[
0.035600196570158005,
0.04984740912914276,
-0.017755206674337387,
0.011216435581445694,
0.022554391995072365,
-0.018237538635730743,
0.004393992014229298,
0.019571738317608833,
-0.024392450228333473,
-0.08317514508962631,
0.0032261647284030914,
0.050588928163051605,
0.07948016375303268,
0.02046104706823826,
0.03719429671764374,
0.02028471976518631,
0.060442812740802765,
-0.041311509907245636,
-0.00537707656621933,
0.0003782682179007679,
0.0035507737193256617,
-0.05035402998328209,
-0.039897918701171875,
-0.045863956212997437,
-0.005771138239651918,
-0.007681748364120722,
0.030743246898055077,
-0.07141369581222534,
0.02610710822045803,
-0.013217058964073658,
0.003809455782175064,
-0.01684720069169998,
0.025355685502290726,
-0.06438631564378738,
-0.036469556391239166,
-0.017793213948607445,
0.004466458223760128,
0.027106670662760735,
-0.0180964432656765,
-0.0363120436668396,
0.0240190289914608,
-0.07032684981822968,
0.005646844394505024,
0.011321436613798141,
-0.01104890275746584,
0.04942215606570244,
-0.07646398991346359,
-0.06762412190437317,
-0.017428306862711906,
0.034044161438941956,
-0.015959791839122772,
0.0006083986372686923,
-0.060274843126535416,
-0.04187699779868126,
-0.001505363266915083,
0.021577417850494385,
-0.003943960182368755,
-0.01347373053431511,
0.08866170793771744,
-0.07823745906352997,
-0.08473297953605652,
0.04112185537815094,
0.02734578400850296,
0.01004358846694231,
0.08186768740415573,
-0.010153512470424175,
-0.03941924124956131,
0.02831839770078659,
0.06761907786130905,
0.036463938653469086,
-0.000432072498369962,
-0.02510136552155018,
-0.050832610577344894,
-0.08336000889539719,
-0.008580108173191547,
-0.017695173621177673,
-0.03548501804471016,
0.006536977831274271,
-0.014867974445223808,
-0.023081164807081223,
0.011734742671251297,
0.016788581386208534,
0.06644916534423828,
-0.0625976175069809,
0.06732926517724991,
0.004704101011157036,
-0.03638840839266777,
-0.02088726870715618,
-0.004582930356264114,
-0.04008806496858597,
-0.0028591679874807596,
0.039791353046894073,
0.028147775679826736,
0.036376290023326874,
-0.019639812409877777,
0.0011897631920874119,
0.027629947289824486,
0.07544994354248047,
0.0004060931096319109,
-0.06153688207268715,
-0.02647664211690426,
-0.0015929860528558493,
0.016517821699380875,
-0.03563861921429634,
-0.001909471582621336,
-0.022157322615385056,
0.03068486787378788,
0.051169440150260925,
0.06040129438042641,
-0.04930838197469711,
-0.012367612682282925,
-0.02990276925265789,
-0.0049681770615279675,
0.020118089392781258,
0.016702258959412575,
-0.04503665864467621,
-0.007349856663495302,
-0.003794469404965639,
-0.0191524438560009,
0.04190604016184807,
-0.005358373746275902,
0.03322404995560646,
-0.05947045236825943,
0.01833242177963257,
-0.00357433850876987,
-0.01203332282602787,
0.015212095342576504,
0.0013383971527218819,
0.009092623367905617,
0.029216133058071136,
-0.012814342975616455,
0.0019823380280286074,
-0.03414972126483917,
-0.002171794418245554,
0.013966472819447517,
-0.025065235793590546,
-0.0735035166144371,
0.00403235899284482,
0.0007573476177640259,
0.006358212325721979,
-0.01599699631333351,
0.009372707456350327,
-0.03718816861510277,
0.016962677240371704,
-0.06754227727651596,
0.018215378746390343,
0.0005367451813071966,
0.03630637004971504,
0.0009047507774084806,
0.02149953879415989,
0.01711060293018818,
0.03181455284357071,
0.039192307740449905,
-0.024259358644485474,
0.024845831096172333,
0.016013460233807564,
0.06267255544662476,
-0.0011580432765185833,
-0.0031611029990017414,
0.017585093155503273,
0.07891156524419785,
-0.02926202304661274,
0.0017641568556427956,
0.01977560855448246,
-0.1351897269487381,
0.02430843934416771,
-0.025643687695264816,
-0.04186388477683067,
0.03361643850803375,
0.011787197552621365,
-0.05006184056401253,
-0.04296242445707321,
0.012465417385101318,
0.05931001156568527,
-0.011074341833591461,
0.025685438886284828,
0.10035593807697296,
0.013216889463365078,
0.023860465735197067,
-0.031922101974487305,
0.013601993210613728,
0.00403680931776762,
0.06861098855733871,
0.009446064941585064,
0.04304618760943413,
-0.012681637890636921,
0.0026397844776511192,
0.04865052551031113,
-0.027359481900930405,
0.021073412150144577,
-0.021651752293109894,
-0.005036559887230396,
0.03546835854649544,
0.05187245085835457,
-0.010349427349865437,
-0.020977472886443138,
-0.024884933605790138,
-0.051215559244155884,
-0.06263624131679535,
0.02589375711977482,
-0.023326326161623,
0.04756633937358856,
0.031098498031497,
0.023129325360059738,
0.032333213835954666,
0.019155554473400116,
0.0018436098471283913,
0.029508594423532486,
0.002808546181768179,
0.030378229916095734,
0.06027188152074814,
0.01640803925693035,
0.010346918366849422,
-0.016893180087208748,
-0.03358195349574089,
0.021061688661575317,
-0.06861386448144913,
-0.02607787400484085,
0.040834296494722366,
-0.041505422443151474,
-0.016051117330789566,
-0.06397976726293564,
0.025802060961723328,
0.019457561895251274,
-0.0154812540858984,
0.017323261126875877,
0.008906734175980091,
-0.044481147080659866,
0.03889103978872299,
0.034797392785549164,
-0.029164861887693405,
0.005888549145311117,
-0.004630105569958687,
-0.055350832641124725,
0.0318053662776947,
0.012515080161392689,
0.02121303789317608,
0.042336441576480865,
-0.03708716109395027,
0.025714339688420296,
0.023777980357408524,
-0.08711481094360352,
-0.03677907586097717,
-0.015223633497953415,
0.03526851907372475,
-0.07104338705539703,
0.0012967282673344016,
0.014328951947391033,
-0.044915951788425446,
-0.028397800400853157,
0.0062087723053991795,
-0.0428113155066967,
-0.019907237961888313,
-0.0057663144543766975,
-0.02945650927722454,
0.023883497342467308,
-0.06424407660961151,
0.075604148209095,
-0.011294488795101643,
-0.05043114721775055,
-0.04236564785242081,
0.02689594216644764,
-0.007569488137960434,
0.044714026153087616,
-0.016997357830405235,
0.03139619529247284,
0.01820523850619793,
0.007703758310526609,
-0.010902661830186844,
0.03283967822790146,
-0.05837045982480049,
0.022772885859012604,
0.03843294084072113,
0.020403746515512466,
-0.004696223884820938,
0.014444631524384022,
0.04797419533133507,
-0.022197561338543892,
-0.0028835430275648832,
0.019367026165127754,
-0.015518487431108952,
0.03192877024412155,
-0.00758192827925086,
-0.025948423892259598,
0.011836777441203594,
0.008036543615162373,
-0.008777749724686146,
0.009789330884814262,
-0.00638347864151001,
-0.06865360587835312,
0.01613185741007328,
-0.033145491033792496,
0.02470344677567482,
0.01617507077753544,
0.014551625587046146,
-0.02092299424111843,
0.054263886064291,
0.0013211761834099889,
-0.02183823101222515,
-0.01998414285480976,
0.017120767384767532,
-0.051414526998996735,
-0.004141023848205805,
0.0025189993903040886,
-0.041096895933151245,
0.038390763103961945,
-0.06491601467132568,
-0.008244888857007027,
-0.06303148716688156,
0.019752515479922295,
-0.02794424444437027,
0.007497227285057306,
0.009277872741222382,
0.030708935111761093,
-0.021676581352949142,
-0.0035236773546785116,
-0.01666218601167202,
-0.002203764161095023,
0.026474550366401672,
-0.01883029006421566,
-0.044978294521570206,
-0.10136813670396805,
-0.023079533129930496,
-0.04921242967247963,
0.05039158836007118,
-0.03161723166704178,
0.03351259231567383,
-0.009302182123064995,
-0.004883948713541031,
-0.0349930040538311,
0.05984881520271301,
0.07210151106119156,
-0.02393687143921852,
-0.06478109210729599,
-0.024637777358293533,
0.03860710561275482,
-0.025221385061740875,
0.049982812255620956,
0.03304097801446915,
0.016301512718200684,
0.0027929411735385656,
-0.028904180973768234,
0.01825355924665928,
0.02475118264555931,
-0.028856167569756508,
0.06909213960170746,
0.060321301221847534,
-0.0041776252910494804,
0.01322280615568161,
-0.013157532550394535,
0.048265282064676285,
0.0008644188055768609,
-0.01569254696369171,
-0.0022450233809649944,
0.013496178202331066,
-0.01628696173429489,
0.004129321314394474,
0.00807146355509758,
0.0033758690115064383,
0.018026478588581085,
0.012814465910196304,
-0.01088671013712883,
-0.07421480119228363,
0.061024393886327744,
-0.001177180907689035,
-0.03393230587244034,
0.035943686962127686,
0.01744934171438217,
-0.021396968513727188,
-0.020581375807523727,
0.02160636894404888,
-0.017766106873750687,
-0.0818009078502655,
0.019536687061190605,
0.03010343573987484,
-0.015218665823340416,
0.009504556655883789,
0.0004038530751131475,
-0.0021138270385563374,
-0.023122545331716537,
0.03991366922855377,
0.07544686645269394,
0.013172421604394913,
-0.015445341356098652,
0.04814416542649269,
0.042110007256269455,
-0.06354302167892456,
-0.008078066632151604,
-0.010598388500511646,
-0.005634992849081755,
0.011095577850937843,
-0.013116246089339256,
-0.028931304812431335,
0.018418684601783752,
0.04450870305299759,
-0.040061019361019135,
-0.0101685905829072,
-0.004355894401669502,
-0.03871675953269005,
-0.01735740527510643,
0.028605222702026367,
0.04866465553641319,
-0.034940529614686966,
0.015849215909838676,
0.0001714121171971783,
0.008368603885173798,
0.012712487019598484,
0.007923142984509468,
-0.008153959177434444,
-0.009497387334704399,
0.03685624152421951,
0.008043886162340641,
-0.03213376924395561,
-0.03998997062444687,
0.0028814775869250298,
0.018841005861759186,
-0.011577172204852104,
0.0303095281124115,
0.009602934122085571,
0.014569705352187157,
-0.027125684544444084,
0.03422463685274124,
0.03540343418717384,
0.022174784913659096,
-0.00007697469845879823,
0.06911269575357437,
0.017940158024430275,
0.007252946496009827,
0.06851140409708023,
-0.005098757334053516,
-0.006185641512274742,
-0.002672297414392233,
0.01494641788303852,
0.035704273730516434,
-0.06582152843475342,
0.043234966695308685,
-0.02319994382560253,
0.06332620233297348,
0.04544563218951225,
0.06648162752389908,
0.024392973631620407,
0.04147350415587425,
0.026121068745851517,
0.02409670129418373,
0.03894863277673721,
0.08663750439882278,
-0.0025256278458982706,
-0.004877407569438219,
-0.033690355718135834,
-0.036347728222608566,
-0.044248562306165695,
0.03117513284087181,
-0.04207178205251694,
0.017474466934800148,
0.003214774653315544,
0.04278387501835823,
-0.04876069724559784,
-0.029619816690683365,
-0.010840438306331635,
-0.011065964587032795,
-0.03464353457093239,
-0.011432845145463943,
0.028029166162014008,
0.03989551216363907,
-0.015274927020072937,
-0.02405461296439171,
0.005043162032961845,
-0.021760959178209305,
0.01209148857742548,
0.02702072262763977,
0.03957176208496094,
-0.0015026938635855913,
-0.002784681972116232,
0.026589112356305122,
0.02791156806051731,
-0.004015072714537382,
0.04268224537372589,
-0.012898297980427742,
0.04045265167951584,
0.009690830484032631,
0.06936472654342651,
0.02590782940387726,
0.004656684119254351,
-0.04485524818301201,
-0.009263908490538597,
0.02060455083847046,
-0.024989107623696327,
-0.036492034792900085,
-0.005548478104174137,
-0.014272155240178108,
-0.013230396434664726,
0.06565076857805252,
-0.09211451560258865,
-0.029409073293209076,
-0.04056601971387863,
0.04341406747698784,
0.03026094101369381,
-0.04289282485842705,
0.014810283668339252,
0.012520231306552887,
-0.04009274020791054,
-0.049773409962654114,
-0.005736319348216057,
0.006846367381513119,
-0.015826277434825897,
-0.060542672872543335,
0.05156230926513672,
-0.0733584389090538,
0.011490740813314915,
-0.018562206998467445,
0.013626661151647568,
0.0345916785299778,
-0.012788456864655018,
0.012587867677211761,
0.025794541463255882,
-0.02876279503107071,
-0.028631541877985,
0.01589842699468136,
0.004412958864122629,
0.02168513648211956,
0.04044641926884651,
-0.01241083163768053,
0.03511299192905426,
-0.019943464547395706,
-0.030387360602617264,
0.02685408852994442,
-0.052127499133348465,
-0.0018895524553954601,
0.00803331844508648,
0.09438178688287735,
-0.05757025629281998,
0.0018727992428466678,
-0.005121226422488689,
0.06341101974248886,
-0.021694950759410858,
-0.04982269927859306,
0.055536508560180664,
0.03549487143754959,
0.04204035550355911,
-0.033763591200113297,
-0.015973981469869614,
0.01617957465350628,
-0.037456318736076355,
0.10495321452617645,
-0.0025255156215280294,
0.028461109846830368,
0.005771588999778032,
0.0413723848760128,
0.012500992976129055,
0.000847952498588711,
-0.05496897175908089,
0.01637575775384903,
0.034132055938243866,
-0.006205507554113865,
-0.03731492906808853,
0.02637256309390068,
-0.022037947550415993,
-0.022147079929709435,
0.015567587688565254,
-0.05281243100762367,
0.009401064366102219,
0.03450814262032509,
-0.0000671049565426074,
-0.055042143911123276,
0.023594094440340996,
-0.00012864988821092993,
-0.030857551842927933,
0.006549831014126539,
0.060944490134716034,
-0.008004694245755672,
0.056876834481954575,
-0.06423845887184143,
-0.0048456997610628605,
-0.044513966888189316,
0.025425972416996956,
-0.058654993772506714,
-0.007497737184166908,
-0.010964704677462578,
-0.09633558243513107,
0.04909704253077507,
0.056496087461709976,
0.002899337559938431,
0.04544099420309067,
-0.020596761256456375,
-0.00900073442608118,
0.0430176816880703,
-0.03332765772938728,
-0.01732214167714119,
0.08954936265945435,
0.050120994448661804,
-0.008096110075712204,
-0.013521309942007065,
-0.04633909463882446,
0.03468376025557518,
-0.07798730581998825,
-0.012030914425849915,
-0.04268474504351616,
0.0561981275677681,
0.0920490100979805,
0.06304929405450821,
0.014790999703109264,
0.0566411092877388,
0.0029659003484994173,
-0.01773257553577423,
0.03562852367758751,
-0.0425906628370285,
0.011041448451578617,
0.0027386494912207127,
0.06244339793920517,
0.016696270555257797,
-0.054945409297943115,
-0.002242941875010729,
-0.00569860590621829,
-0.03226359188556671,
0.020470179617404938,
-0.026816265657544136,
-0.023197928443551064,
-0.02094724215567112,
0.057693883776664734,
-0.007496006321161985,
-0.018942341208457947,
-0.06618142127990723,
0.05895738676190376,
-0.07547585666179657,
0.012493462301790714,
-0.011266626417636871,
-0.05660533532500267,
0.008920415304601192,
0.04151822626590729,
0.010576426982879639,
0.02438110113143921,
-0.01756424829363823,
-0.04852083697915077,
0.010608336888253689,
-0.026479331776499748,
-0.007211774587631226,
0.009630805812776089,
0.06281115859746933,
0.0440555214881897,
0.0158727765083313,
0.0370335578918457,
0.017352601513266563,
-0.05269326642155647,
0.05007454380393028,
-0.04435677081346512,
-0.06308777630329132,
-0.011908928863704205,
-0.03352086618542671,
-0.006523755379021168,
-0.04946066066622734,
-0.05913413316011429,
-0.06706096231937408,
0.005889721214771271,
-0.01282279472798109,
-0.024042867124080658,
0.0378795862197876,
-0.03017444908618927,
-0.029771018773317337,
-0.02221977896988392,
-0.046911340206861496,
0.0296071395277977,
0.0009286791319027543,
-0.050733719021081924,
0.04064296931028366,
0.014991831965744495,
0.024717092514038086,
-0.0069941142573952675,
0.019038010388612747,
0.030344685539603233,
-0.01166931726038456,
0.012655996717512608,
0.013615606352686882,
-0.03929610922932625,
0.05746883526444435,
-0.02182754874229431,
0.028626810759305954,
0.0454099103808403,
0.033242110162973404,
0.04204774647951126,
-0.03225716948509216,
0.04749405384063721,
-0.0063082072883844376,
-0.006465821526944637,
-0.015454431064426899,
-0.02049916982650757,
-0.029189448803663254,
-0.02479160763323307,
0.009761066175997257,
-0.006081439089030027,
-0.040739450603723526,
0.023185495287179947,
0.020414529368281364,
0.020241763442754745,
0.025286126881837845,
0.005570657551288605,
0.023898784071207047,
0.011753935366868973,
-0.004053021315485239,
-0.060573186725378036,
-0.03462369740009308,
0.023056859150528908,
0.03439866006374359,
0.004815596155822277,
0.04124194011092186,
0.019252575933933258,
0.00456956448033452,
0.004042908549308777,
0.0016689334297552705,
-0.0228712260723114,
0.005866517778486013,
-0.037394843995571136,
-0.0271376371383667,
-0.05091041699051857,
0.0010902227368205786,
-0.00009797076927497983,
-0.00648621516302228,
0.01899809017777443,
0.04381453990936279,
0.04118191450834274,
0.06129753589630127,
-0.027580324560403824,
0.010317334905266762,
0.024246523156762123,
0.0027272014413028955,
0.0145501047372818,
-0.05257260799407959,
-0.04096287488937378,
0.01006858516484499,
0.02498483844101429,
-0.030717354267835617,
0.035636041313409805,
-0.012385698966681957,
0.023550663143396378,
0.008387571200728416,
-0.0005195776466280222,
-0.03657672926783562,
0.014114992693066597,
-0.024345852434635162,
-0.044735126197338104,
0.007975402288138866,
-0.01231404673308134,
-0.027192018926143646,
-0.038609035313129425,
0.012640261091291904,
0.03201821446418762,
-0.03147251158952713,
-0.0011045439168810844,
0.08357412368059158,
0.006024773698300123,
-0.037468165159225464,
0.08560208976268768,
-0.028105271980166435,
-0.0026056694332510233,
-0.008591791614890099,
-0.0340050645172596,
-0.06176986172795296,
-0.09099151939153671,
0.017837388440966606,
-0.03469761833548546,
-0.09303159266710281,
0.004645400680601597,
0.07928748428821564,
-0.007535025477409363,
-0.09344328939914703,
-0.0491250716149807,
-0.03699615225195885,
-0.037879157811403275,
-0.006266037467867136
] |
<p>I accept the Big Bang theory. What I can't understand is how there can be a where or when to the Big Bang if space time did not exist prior to it. Did space and time exist prior to the Big Bang? </p>
|
g51
|
[
0.04876141622662544,
0.016053391620516777,
0.026335641741752625,
-0.03597654029726982,
-0.0374491885304451,
0.07934416085481644,
0.036948222666978836,
0.06003725156188011,
-0.045926302671432495,
-0.06448819488286972,
0.00854333583265543,
-0.04872003570199013,
0.007969681173563004,
0.062004540115594864,
-0.01992584392428398,
-0.021774018183350563,
0.03190919756889343,
0.0028105524834245443,
0.0373409129679203,
0.016418905928730965,
-0.02595769800245762,
0.0013338160933926702,
-0.0038472353480756283,
-0.021593989804387093,
-0.09865172952413559,
-0.08834120631217957,
0.021736597642302513,
0.045144084841012955,
0.014418215490877628,
-0.046560756862163544,
0.003143150359392166,
0.029453618451952934,
0.041979603469371796,
-0.08295519649982452,
0.06900306791067123,
-0.06457642465829849,
-0.021362846717238426,
0.018454281613230705,
0.031125051900744438,
-0.020307457074522972,
-0.02345866709947586,
0.007170621771365404,
0.016312001273036003,
-0.04814619570970535,
-0.010534659959375858,
0.03176474943757057,
-0.018628345802426338,
0.013937083072960377,
-0.004295955412089825,
-0.03649049997329712,
-0.045759573578834534,
0.02946311980485916,
0.057907771319150925,
-0.03693964332342148,
0.02591065876185894,
-0.006308674346655607,
0.02120942994952202,
0.011526140384376049,
0.03491351753473282,
0.01985168270766735,
-0.06110731139779091,
0.011647067964076996,
0.07533837109804153,
0.06395930796861649,
0.07421394437551498,
0.03984086588025093,
-0.02549637109041214,
0.007120452355593443,
-0.020256878808140755,
-0.05476541444659233,
0.06892701238393784,
-0.08867128193378448,
-0.028643038123846054,
-0.015795715153217316,
-0.01805049180984497,
0.01851101592183113,
-0.007216316647827625,
0.03292042762041092,
0.004188330378383398,
-0.005590992048382759,
0.03035014122724533,
0.04135178402066231,
-0.012600744143128395,
-0.02950984798371792,
0.05860483646392822,
-0.06280487030744553,
0.00932829175144434,
-0.058685097843408585,
0.01616281270980835,
0.036034807562828064,
-0.03776402026414871,
0.008775457739830017,
0.06843694299459457,
0.04781534895300865,
0.04514474421739578,
-0.015438583679497242,
-0.043507300317287445,
0.10108692944049835,
-0.020528728142380714,
0.019664933905005455,
-0.053901299834251404,
-0.0022584584075957537,
0.009337276220321655,
0.04764535650610924,
-0.0013552348827943206,
-0.05142267420887947,
-0.0020932513289153576,
-0.005888078827410936,
0.01745288446545601,
-0.024329902604222298,
-0.019850824028253555,
0.0003848895721603185,
0.02037755772471428,
0.04911813512444496,
-0.010925515554845333,
0.026558145880699158,
0.02855508029460907,
-0.06774195283651352,
0.010284710675477982,
-0.007231488358229399,
-0.0028081543277949095,
0.01632799208164215,
-0.055856991559267044,
-0.010523726232349873,
-0.07367740571498871,
-0.013811151497066021,
-0.049269288778305054,
-0.013946682214736938,
-0.028003983199596405,
0.011521060019731522,
-0.015721395611763,
0.05155818536877632,
0.013801143504679203,
0.04731259495019913,
-0.011500448919832706,
-0.010025220923125744,
0.028065809980034828,
-0.01355095487087965,
-0.06619902700185776,
0.001414302154444158,
0.01502561941742897,
0.0004977810312993824,
0.022795403376221657,
-0.027148501947522163,
-0.003899451345205307,
0.033451635390520096,
-0.017567742615938187,
-0.03179068863391876,
0.0034255993086844683,
0.028673529624938965,
0.004035910125821829,
0.08722836524248123,
-0.009077455848455429,
0.01951492577791214,
-0.014581524766981602,
0.0029439155478030443,
-0.021563678979873657,
0.024132926017045975,
0.004786282777786255,
0.03721051663160324,
0.018010275438427925,
-0.019782012328505516,
0.011310423724353313,
-0.00763540668413043,
0.007910220883786678,
0.029248742386698723,
-0.03766992688179016,
-0.033350419253110886,
0.01231017243117094,
-0.035903818905353546,
-0.03663260489702225,
0.0038309525698423386,
0.0338374599814415,
0.022413386031985283,
0.024575557559728622,
0.04224289208650589,
-0.02131049707531929,
0.05703223496675491,
-0.02741716429591179,
0.04616342857480049,
-0.006358062382787466,
-0.03357682749629021,
-0.019313929602503777,
0.0064339893870055676,
-0.01615886390209198,
-0.024537820369005203,
0.02891533449292183,
0.011055383831262589,
-0.03792566806077957,
-0.0051491050980985165,
0.02065594121813774,
-0.03025105968117714,
0.04091864451766014,
0.03814845532178879,
0.041453711688518524,
-0.018703017383813858,
0.023376340046525,
0.027006428688764572,
-0.011450032703578472,
0.0056968871504068375,
0.002762279473245144,
0.0017259673913940787,
-0.017843561246991158,
0.004606899805366993,
0.028453832492232323,
0.0009936410933732986,
-0.029145166277885437,
-0.010682717896997929,
0.028127070516347885,
-0.031670235097408295,
-0.027363283559679985,
0.0061547961086034775,
0.001562505611218512,
0.042499709874391556,
-0.02975248359143734,
0.03634710982441902,
-0.01550704799592495,
0.025423826649785042,
-0.026349689811468124,
0.06517636775970459,
-0.014961465261876583,
-0.036316610872745514,
0.009875400923192501,
-0.033352404832839966,
0.01323266513645649,
-0.030941735953092575,
-0.026329215615987778,
0.0006421026773750782,
-0.01346499938517809,
0.056123774498701096,
-0.049683522433042526,
0.006049684248864651,
0.003117056330665946,
0.021710405126214027,
0.004357059486210346,
0.022997209802269936,
0.04722841829061508,
-0.04478064179420471,
-0.01187844481319189,
0.060665108263492584,
-0.0692824199795723,
0.07168605923652649,
-0.014495963230729103,
0.02420402318239212,
0.053523771464824677,
-0.12134581059217453,
0.07242118567228317,
-0.0662631168961525,
0.011822757311165333,
0.029116857796907425,
-0.012404123321175575,
-0.023727940395474434,
-0.029781127348542213,
-0.05509934946894646,
-0.04603011906147003,
0.0029342547059059143,
0.038004253059625626,
0.07476700097322464,
-0.14809666574001312,
-0.039353422820568085,
0.0036040772683918476,
0.01918070949614048,
-0.006309886462986469,
0.023089617490768433,
-0.02603955566883087,
-0.02087208814918995,
-0.019650526344776154,
0.011923102661967278,
-0.012097909115254879,
-0.06559527665376663,
0.02673443965613842,
-0.0348585844039917,
0.04210047423839569,
0.03745022788643837,
-0.010351278819143772,
0.020376216620206833,
0.03430456295609474,
-0.028956374153494835,
0.027796778827905655,
-0.02138170413672924,
0.019012022763490677,
0.006113893818110228,
-0.01997782476246357,
0.02893722802400589,
0.017706487327814102,
0.002895633690059185,
0.023074952885508537,
-0.029302511364221573,
0.014334793202579021,
-0.02184150367975235,
-0.010446940548717976,
0.03127323463559151,
-0.061416953802108765,
0.027437778189778328,
0.019236713647842407,
0.00115193089004606,
-0.029142962768673897,
0.006006675306707621,
-0.001922441879287362,
-0.01667686365544796,
0.014211920090019703,
-0.0002703636127989739,
0.02107454463839531,
-0.03346233814954758,
-0.008024116978049278,
0.01440761424601078,
0.03828318417072296,
0.019338181242346764,
-0.0747828334569931,
-0.025275791063904762,
0.01827325113117695,
0.05576643347740173,
-0.01919141225516796,
0.04373260214924812,
-0.037739284336566925,
0.06189506873488426,
-0.052033431828022,
-0.013402947224676609,
0.08473172783851624,
-0.01718990132212639,
-0.019547104835510254,
0.03174584358930588,
-0.06055834889411926,
-0.026851695030927658,
0.012249712832272053,
-0.0007268696208484471,
-0.030461840331554413,
-0.013886788859963417,
-0.015275120735168457,
0.0010748507920652628,
-0.04869011789560318,
-0.01696048490703106,
0.0016029884573072195,
-0.015684692189097404,
-0.05642203614115715,
-0.02361118420958519,
0.011048772372305393,
0.029663700610399246,
0.014245796948671341,
0.03321497514843941,
0.03773897886276245,
0.07032958418130875,
-0.029781581833958626,
0.06497924774885178,
0.034541018307209015,
0.03344489634037018,
0.05998576059937477,
0.005356719251722097,
0.011322113685309887,
0.024673230946063995,
0.051212746649980545,
0.01027675811201334,
0.0340057797729969,
-0.020639631897211075,
-0.026033123955130577,
0.06040170416235924,
-0.004797431640326977,
0.05065242946147919,
0.050593700259923935,
-0.054550640285015106,
0.026908624917268753,
0.0023552170023322105,
0.048380278050899506,
0.005567180458456278,
0.015559189952909946,
-0.010496214032173157,
0.0041074021719396114,
-0.0038880209904164076,
0.028139621019363403,
0.005515381693840027,
0.05166799575090408,
0.029573962092399597,
0.016890613362193108,
0.009384091943502426,
0.1279425173997879,
-0.062401946634054184,
0.02953902631998062,
0.0614643394947052,
-0.007517825812101364,
0.009351491928100586,
0.022982485592365265,
0.0205919798463583,
-0.0010164458071812987,
0.003824179992079735,
0.00398703757673502,
-0.03782622516155243,
-0.03867558762431145,
0.016207082197070122,
-0.05555951967835426,
-0.01723824441432953,
0.04297008365392685,
-0.035846732556819916,
-0.019572539255023003,
-0.045615725219249725,
0.02914384752511978,
0.028492240235209465,
0.02116154134273529,
-0.003458355087786913,
0.03143112361431122,
-0.08060121536254883,
0.004175597336143255,
0.08810827136039734,
-0.023364095017313957,
-0.025991471484303474,
-0.027376005426049232,
0.07459031045436859,
0.034279465675354004,
-0.05544022098183632,
0.016589075326919556,
-0.017103243619203568,
-0.0022023736964911222,
0.006373818963766098,
-0.06239653751254082,
0.001909007434733212,
-0.023731660097837448,
-0.04093930497765541,
0.04411895573139191,
-0.03172091394662857,
0.052385665476322174,
0.026529531925916672,
-0.013901562429964542,
0.08406362682580948,
0.019005360081791878,
-0.033262815326452255,
0.014780055731534958,
0.0721554234623909,
-0.03988545760512352,
-0.021677128970623016,
-0.012475776486098766,
0.06921873241662979,
-0.023198796436190605,
0.02762490138411522,
-0.01008194126188755,
0.006346244364976883,
-0.04026924818754196,
0.021114466711878777,
-0.04430817440152168,
0.028007615357637405,
0.0017704761121422052,
-0.0762510597705841,
0.029199710115790367,
-0.02460807003080845,
0.01403694599866867,
0.023060262203216553,
-0.044813551008701324,
0.05776386335492134,
-0.04224950447678566,
-0.04037462919950485,
0.026237715035676956,
0.0031380343716591597,
0.03588826209306717,
0.04466455429792404,
-0.007031001150608063,
0.006733250804245472,
-0.06326432526111603,
0.028055397793650627,
0.0013934443704783916,
0.022913189604878426,
-0.004229539539664984,
0.10056968033313751,
-0.06432123482227325,
0.023826615884900093,
0.023495348170399666,
0.04949551075696945,
-0.0027236673049628735,
-0.03046361356973648,
-0.0019171696621924639,
-0.005304176826030016,
0.022093964740633965,
0.016733113676309586,
-0.00393284298479557,
-0.0013662708224728703,
0.021720493212342262,
-0.01666739210486412,
-0.0008614598773419857,
0.007387438789010048,
-0.016974059864878654,
-0.08256926387548447,
0.024906007573008537,
-0.021655678749084473,
0.021585335955023766,
-0.00015653675654903054,
-0.012688039802014828,
0.04413982480764389,
0.003161652944982052,
0.05179007351398468,
-0.007347343023866415,
0.006403516978025436,
0.06927033513784409,
-0.017598014324903488,
-0.0015753870829939842,
-0.02748100832104683,
0.029638906940817833,
0.02303929254412651,
-0.002731579588726163,
-0.0021138451993465424,
-0.019145295023918152,
0.01790647767484188,
-0.014893680810928345,
-0.009037607349455357,
-0.02407258376479149,
0.005504379980266094,
0.03887731581926346,
0.024000901728868484,
-0.02401101216673851,
0.05147469416260719,
-0.027492038905620575,
-0.018373798578977585,
-0.04270469397306442,
0.0062546259723603725,
-0.0019906514789909124,
0.04240064322948456,
-0.052603527903556824,
0.021632153540849686,
0.030939798802137375,
-0.029704822227358818,
0.03997025638818741,
-0.020002784207463264,
-0.03627748787403107,
0.04030878096818924,
-0.11169318854808807,
0.015366798266768456,
0.05007581040263176,
0.03635703772306442,
-0.002372841350734234,
0.007180900312960148,
-0.01125648245215416,
-0.027562281116843224,
0.06591949611902237,
-0.014885899610817432,
-0.034105587750673294,
-0.004369867034256458,
0.0010235150111839175,
0.023346850648522377,
-0.022649459540843964,
0.02513044886291027,
-0.007216308731585741,
-0.02076474018394947,
0.029244564473628998,
-0.08317320048809052,
-0.048188794404268265,
-0.058825280517339706,
0.023966968059539795,
-0.026988383382558823,
0.004471692722290754,
0.051038991659879684,
-0.06337501853704453,
0.05996742099523544,
0.007899012416601181,
-0.07071713358163834,
-0.013726943172514439,
0.02582954242825508,
-0.01503888238221407,
-0.008966830559074879,
-0.05163830146193504,
0.038258813321590424,
-0.005001729354262352,
-0.0308544859290123,
-0.05379076302051544,
-0.03738046810030937,
-0.012078795582056046,
0.02066723257303238,
0.019118711352348328,
0.01881014183163643,
-0.0053618112578988075,
0.012847141362726688,
0.008570109494030476,
-0.0051016779616475105,
0.04376308619976044,
0.00030934251844882965,
-0.05658083036541939,
0.019447334110736847,
-0.05126296728849411,
0.004470247775316238,
0.005395427346229553,
-0.0009546765359118581,
-0.0004769097431562841,
-0.022140812128782272,
-0.025542646646499634,
-0.013725610449910164,
0.004200097639113665,
0.03049207292497158,
0.011138588190078735,
-0.04488198831677437,
-0.0619453601539135,
0.013528694398701191,
0.0036265335511416197,
0.0003538952732924372,
0.006789159495383501,
0.013745967298746109,
0.011139901354908943,
-0.022478628903627396,
-0.0031552989967167377,
-0.01245238445699215,
0.011907829903066158,
0.0424828976392746,
0.0012783319689333439,
0.018096985295414925,
0.0009763778070919216,
-0.032361950725317,
-0.05285698547959328,
-0.04125508666038513,
0.016170553863048553,
0.026172978803515434,
0.06077207997441292,
0.02258128672838211,
0.020087074488401413,
0.027307704091072083,
0.037859950214624405,
-0.0023592091165483,
0.07071543484926224,
0.01581668108701706,
-0.007139713503420353,
0.00916812103241682,
0.023187384009361267,
-0.0267097819596529,
-0.009836290962994099,
-0.03253636509180069,
-0.014547315426170826,
0.0026425509713590145,
0.07556577026844025,
0.013121013529598713,
-0.04049968346953392,
0.0325675867497921,
0.021784106269478798,
-0.01885186694562435,
-0.04034881666302681,
0.043604522943496704,
0.03415660560131073,
0.010343251749873161,
-0.005119551904499531,
-0.05214483663439751,
0.019493330270051956,
0.01016443781554699,
-0.03125099092721939,
0.03902014344930649,
0.026874858886003494,
0.011994434520602226,
-0.046072084456682205,
0.012497317977249622,
0.037118855863809586,
-0.010839796625077724,
0.022468242794275284,
0.015795590355992317,
-0.05016366392374039,
-0.017637282609939575,
0.019737455993890762,
-0.016357852146029472,
-0.03382827341556549,
-0.06819126754999161,
-0.0048028151504695415,
-0.0653383731842041,
-0.02507617324590683,
-0.054679375141859055,
0.00608280673623085,
-0.042210906744003296,
-0.014425280503928661,
0.028782743960618973,
-0.013154927641153336,
-0.10437115281820297,
-0.019166292622685432,
-0.021724307909607887,
-0.07316971570253372,
0.04666939377784729,
0.0707303062081337,
0.008979760110378265,
0.008598360233008862,
-0.028217755258083344,
0.009081943891942501,
-0.0003839036507997662,
-0.05826190859079361,
-0.0029383220244199038,
0.007005472667515278,
0.0053065442480146885,
-0.06377279758453369,
-0.03140260651707649,
-0.007779679726809263,
0.0456741601228714,
-0.019442971795797348,
0.033572614192962646,
-0.06443828344345093,
0.06564464420080185,
-0.04232040047645569,
0.044769514352083206,
0.004366280045360327,
0.012852663174271584,
0.02114816941320896,
-0.0237194262444973,
-0.043667785823345184,
-0.00023490558669436723,
-0.03497155010700226,
-0.049917709082365036,
-0.03692245855927467,
-0.06654327362775803,
0.04970855265855789,
-0.07083828747272491,
0.05467034876346588,
-0.048118118196725845,
-0.06330171227455139,
-0.06641992926597595,
-0.00657712621614337,
-0.05393926799297333,
-0.007964322343468666,
-0.005739601794630289,
-0.02522849664092064,
0.05830005183815956,
0.015162213705480099,
0.03062267228960991,
-0.11496303975582123,
-0.005450551863759756,
0.004384043160825968,
0.03509010002017021,
0.013232098892331123,
0.0038151799235492945,
-0.02503158710896969,
-0.016075173392891884,
-0.046684183180332184,
0.03185524418950081,
0.0048383018001914024,
-0.04308949038386345,
0.023192431777715683,
-0.06597727537155151,
0.0008466534200124443,
-0.049862321466207504,
0.0017616619588807225,
-0.010413208045065403,
-0.0013186057331040502,
0.0019875383004546165,
-0.011326001957058907,
-0.02849280647933483,
0.0057756174355745316,
0.008365701884031296,
-0.012911520898342133,
0.020538339391350746,
-0.04481181129813194,
0.05267299339175224,
-0.05060820281505585,
-0.034052763134241104,
-0.010780243203043938,
0.013238323852419853,
0.01597471535205841,
-0.003725409973412752,
-0.03199481591582298,
0.03614142909646034,
-0.03174081817269325,
0.004256822634488344,
0.0029339450411498547,
0.03627493232488632,
0.03579340875148773,
-0.017764417454600334,
-0.003590199863538146,
0.007184465881437063,
0.019116241484880447,
-0.011971637606620789,
0.06980561465024948,
-0.03145419433712959,
0.016771627590060234,
0.014132619835436344,
0.04341694712638855,
-0.022780798375606537,
0.033291809260845184,
0.012205423787236214,
0.03819958493113518,
-0.013112083077430725,
0.01424900721758604,
0.024109728634357452,
-0.024490689858794212,
-0.08305685222148895
] |
<p>How strong would have to be nuclear explosion on exo-planet that orbits some other star for it to be detectable outside of that system.<br>
Or it would be impossible due to amount <a href="http://www.neatorama.com/2008/03/22/trivia-solar-energy-1-trillion-1-megaton-atom-bombs-per-second/#!8m5ue" rel="nofollow">of radiation coming from that star</a>?<br>
Could the angle at which radiation would go out of that system be indicator, or light interference would make it impossible? </p>
<p><strong>Update:</strong>
Atmospheric nuclear explosions produce a unique signature, often called a "double-humped curve": a short and intense flash lasting around 1 millisecond, followed by a second much more prolonged and less intense emission of light taking a fraction of a second to several seconds to build up. The effect occurs because the surface of the early fireball is quickly overtaken by the expanding atmospheric shock wave composed of ionised gas. Although it emits a considerable amount of light itself it is opaque and prevents the far brighter fireball from shining through. As the shock wave expands, it cools down becoming more transparent allowing the much hotter and brighter fireball to become visible again.</p>
<p><a href="http://en.wikipedia.org/wiki/Vela_%28satellite%29" rel="nofollow">No single natural phenomenon is known to produce this signature.</a> </p>
<p>Could this be used to identify or "double-humped curve" would be of no help in space due to radio pollution, of many double humped curves produced by stars?</p>
|
g2525
|
[
0.004583597648888826,
0.06596960872411728,
0.007667836267501116,
0.01481629814952612,
0.02061150036752224,
0.03995455056428909,
-0.04741581156849861,
-0.0008228907827287912,
0.046845197677612305,
-0.0301971398293972,
-0.05291092023253441,
0.06769847124814987,
0.07654156535863876,
0.02796826884150505,
0.035163361579179764,
-0.05096525698900223,
0.0912451297044754,
-0.10231006890535355,
0.02548752911388874,
0.11129697412252426,
0.015469071455299854,
0.002647619228810072,
0.016136091202497482,
-0.004290690645575523,
-0.027704685926437378,
0.041035886853933334,
0.012405055575072765,
-0.005621969234198332,
-0.013031517155468464,
-0.06481659412384033,
-0.010291900485754013,
-0.03543519973754883,
0.041540078818798065,
-0.023150207474827766,
-0.0491878017783165,
-0.05773209035396576,
-0.05385264381766319,
-0.019032243639230728,
0.01312191877514124,
0.03990025445818901,
-0.083870068192482,
-0.03372137248516083,
0.041593294590711594,
0.04251251742243767,
0.02880864590406418,
-0.027674661949276924,
0.025359775871038437,
0.030546633526682854,
0.04357002675533295,
-0.023846158757805824,
-0.026032451540231705,
0.005666855722665787,
-0.015066963620483875,
-0.01708667166531086,
-0.006317815277725458,
0.03825083747506142,
0.00500128511339426,
-0.008951953612267971,
0.07171876728534698,
-0.034060366451740265,
-0.01724565401673317,
0.06284856796264648,
0.0028354062233120203,
-0.03849188610911369,
0.05007834732532501,
-0.015889283269643784,
-0.11061184853315353,
-0.03166121616959572,
0.009439016692340374,
-0.03143351152539253,
0.03595847636461258,
-0.014263706281781197,
-0.051895610988140106,
-0.05067376792430878,
-0.0014738484751433134,
0.02530667558312416,
-0.02618497982621193,
0.015863412991166115,
-0.013836242258548737,
0.059825580567121506,
0.012063493020832539,
-0.03322400152683258,
-0.03067372925579548,
-0.01599937304854393,
0.06328670680522919,
-0.038513828068971634,
-0.019258487969636917,
-0.021184157580137253,
-0.009869715198874474,
-0.05532519146800041,
0.04028702154755592,
0.031756091862916946,
-0.022048231214284897,
-0.002936476608738303,
0.014463432133197784,
0.03698010370135307,
-0.008807338774204254,
0.02799232490360737,
-0.06273908913135529,
0.015621958300471306,
-0.02257128432393074,
-0.054350778460502625,
-0.009478213265538216,
-0.029594678431749344,
0.015377135016024113,
-0.03623392432928085,
0.008423537947237492,
-0.04432641342282295,
-0.002101303543895483,
-0.02497527003288269,
-0.02843308076262474,
-0.04023931175470352,
0.01592566817998886,
-0.011642485857009888,
-0.023730583488941193,
-0.031486447900533676,
0.033014051616191864,
-0.06391793489456177,
-0.0241183340549469,
0.07540343701839447,
0.0555100180208683,
-0.006422257516533136,
-0.03220212087035179,
0.05037802457809448,
-0.02954309806227684,
-0.05124220252037048,
0.03881663829088211,
-0.03578843176364899,
-0.020452629774808884,
-0.04926396533846855,
-0.03502009063959122,
0.011584128253161907,
-0.00940689630806446,
0.03546423092484474,
0.04251929000020027,
-0.004810204729437828,
-0.012113185599446297,
-0.010885347612202168,
-0.02967393584549427,
-0.015642326325178146,
0.05503450706601143,
0.04279385134577751,
0.02551729418337345,
0.014847984537482262,
-0.015128858387470245,
0.012546438723802567,
-0.0194779634475708,
0.01925961673259735,
0.002535418374463916,
-0.00003945931894122623,
0.0017717843875288963,
0.018702678382396698,
0.010708946734666824,
-0.0030658335890620947,
-0.0015064799226820469,
0.030161747708916664,
-0.006110161542892456,
-0.004023107700049877,
-0.06823430210351944,
0.005077663343399763,
0.0416138656437397,
0.005139332730323076,
0.014857087284326553,
-0.010336405597627163,
-0.026941826567053795,
0.004559863358736038,
0.015943650156259537,
-0.00623580627143383,
0.0041496651247143745,
-0.027205806225538254,
-0.026721110567450523,
-0.00008962870924733579,
0.0817498043179512,
-0.017931878566741943,
-0.022261979058384895,
-0.01972508430480957,
0.07123474031686783,
-0.013313406147062778,
-0.01255626231431961,
0.009025517851114273,
-0.02711048722267151,
0.002269851742312312,
-0.026537375524640083,
0.03812496364116669,
-0.007773427292704582,
-0.09366444498300552,
0.012430530041456223,
0.004533487372100353,
-0.03455382585525513,
0.04081432893872261,
-0.011769212782382965,
-0.04968494176864624,
0.01830575056374073,
0.009402449242770672,
0.009126043878495693,
-0.02872079238295555,
-0.011885978281497955,
-0.018631352111697197,
-0.018628409132361412,
-0.011520436964929104,
0.010684087872505188,
0.04993535205721855,
-0.005230449605733156,
-0.007509852293878794,
0.028243640437722206,
0.0018423988949507475,
0.005063523538410664,
0.025248724967241287,
-0.008505582809448242,
0.010754388757050037,
0.02337540127336979,
-0.033258672803640366,
0.003859907854348421,
0.020250556990504265,
0.03182217851281166,
-0.03918176889419556,
0.007718902081251144,
-0.03259832784533501,
0.02044140361249447,
0.006207705475389957,
0.039355162531137466,
0.04123811051249504,
0.01501661166548729,
-0.049435585737228394,
-0.034114059060811996,
0.0037069199606776237,
-0.03356277570128441,
0.010741138830780983,
0.010914805345237255,
-0.004207872785627842,
-0.041715070605278015,
0.008678026497364044,
-0.0034957705065608025,
-0.003820433747023344,
-0.01059959176927805,
-0.010275959968566895,
0.06450550258159637,
-0.029031673446297646,
-0.006891224067658186,
0.02881774865090847,
-0.006485076155513525,
-0.07715124636888504,
-0.04990662261843681,
0.014449558220803738,
0.04668491333723068,
-0.05620567500591278,
-0.02194269560277462,
0.030110469087958336,
-0.030980927869677544,
-0.026947326958179474,
0.0005603604367934167,
0.04812784120440483,
-0.018552515655755997,
0.04444093629717827,
0.01272584032267332,
-0.04413075000047684,
-0.014615627937018871,
0.041080448776483536,
-0.09704020619392395,
-0.06936102360486984,
-0.0009174318984150887,
-0.015365468338131905,
-0.0017616079421713948,
0.0018742926185950637,
-0.002254321239888668,
-0.012090450152754784,
-0.04623537138104439,
0.03599745035171509,
-0.02142898179590702,
-0.05851651728153229,
-0.03188963606953621,
0.012241773307323456,
-0.03561890870332718,
0.05068476125597954,
-0.021506957709789276,
0.07843752205371857,
-0.00440997164696455,
0.009587389416992664,
0.013792463578283787,
0.0031139818020164967,
0.0044784219935536385,
0.0731482282280922,
-0.01603228785097599,
0.026934031397104263,
0.008601988665759563,
-0.013170513324439526,
0.04920137673616409,
0.05041231960058212,
0.018266985192894936,
-0.000744482094887644,
0.0064383926801383495,
-0.0537307970225811,
0.008219488896429539,
0.016562188044190407,
-0.08209449052810669,
0.013018322177231312,
0.03978739678859711,
0.02664773352444172,
0.0629630908370018,
-0.02081863395869732,
0.04692351445555687,
-0.054876409471035004,
-0.06085081771016121,
0.010318503715097904,
-0.022545697167515755,
-0.028157565742731094,
-0.037332192063331604,
-0.04677470400929451,
0.00961698591709137,
0.025140373036265373,
-0.0046860589645802975,
0.06867537647485733,
0.001315916539169848,
0.037110745906829834,
-0.01235266961157322,
-0.0072802333161234856,
-0.009954935871064663,
0.04525269940495491,
0.011501755565404892,
0.06969372928142548,
-0.009655989706516266,
-0.014808837324380875,
0.009198038838803768,
0.00662262924015522,
-0.0243668332695961,
-0.07421892881393433,
0.04728927090764046,
-0.060495954006910324,
-0.015464797616004944,
-0.04137415438890457,
0.008155809715390205,
0.0015569670358672738,
-0.004712793044745922,
-0.0010591165628284216,
-0.06906601786613464,
0.020233217626810074,
-0.025463439524173737,
0.0771542340517044,
0.014966215938329697,
0.0706619992852211,
-0.015367516316473484,
0.02882435731589794,
-0.04237756133079529,
-0.040889885276556015,
-0.0018089660443365574,
0.023881670087575912,
0.020253347232937813,
-0.03059137612581253,
-0.03384103253483772,
-0.05215523764491081,
0.037413451820611954,
-0.041353438049554825,
0.027303779497742653,
-0.035738978534936905,
0.0496557243168354,
0.004244372248649597,
0.08995763212442398,
0.0064513199031353,
0.035938333719968796,
-0.035069290548563004,
0.0166819728910923,
-0.02276979386806488,
0.011700663715600967,
-0.034129250794649124,
0.022420121356844902,
0.038745809346437454,
0.008117984980344772,
0.003426873590797186,
0.03383384272456169,
0.00553597416728735,
-0.016463352367281914,
-0.019235022366046906,
0.012261753901839256,
-0.004322552587836981,
0.011113869957625866,
-0.021776221692562103,
0.0563877671957016,
-0.005063470918685198,
-0.03654458373785019,
0.07878203690052032,
0.026043254882097244,
-0.01636919379234314,
0.02745530940592289,
0.045388806611299515,
0.022127076983451843,
0.0018775796052068472,
-0.013691172935068607,
-0.02046840824186802,
0.058272235095500946,
0.004787910729646683,
0.03677084296941757,
-0.102370485663414,
-0.06651440262794495,
0.02707507088780403,
-0.0026914665941148996,
-0.014300938695669174,
0.031873129308223724,
0.009597409516572952,
-0.03846392408013344,
0.013495971448719501,
0.025567764416337013,
0.009848533198237419,
0.04344255477190018,
-0.06714064627885818,
-0.066440150141716,
-0.0317523218691349,
-0.0019534360617399216,
0.011380383744835854,
-0.030409395694732666,
-0.04483023285865784,
0.05261166766285896,
0.01935332641005516,
-0.02508837729692459,
0.006927358452230692,
-0.012780633755028248,
0.004097786732017994,
0.011595974676311016,
0.029934391379356384,
0.03291306644678116,
0.013006063178181648,
-0.03491371124982834,
0.03533799201250076,
0.012575817294418812,
0.025798432528972626,
-0.01706504635512829,
0.03376200795173645,
0.04368114098906517,
0.032354604452848434,
0.02394736371934414,
0.04383178427815437,
-0.00673428550362587,
-0.0048439339734613895,
-0.00946867186576128,
0.01917712576687336,
-0.057682838290929794,
0.050084616988897324,
-0.03529338538646698,
0.06228179857134819,
0.0130805978551507,
0.0766165629029274,
0.0704377293586731,
-0.06397338211536407,
0.0020107096061110497,
0.052083875983953476,
0.03285903483629227,
0.06600508093833923,
0.041527509689331055,
-0.01904797926545143,
-0.020220274105668068,
-0.02297280542552471,
-0.07895900309085846,
-0.042211588472127914,
0.009663162752985954,
0.004531098064035177,
-0.011403268203139305,
-0.019886145368218422,
-0.01783696562051773,
0.023448491469025612,
-0.0009253681637346745,
0.02074805088341236,
-0.0010374272242188454,
-0.00766378128901124,
0.09801998734474182,
0.00021854853548575193,
0.055637557059526443,
-0.016290104016661644,
-0.10563816130161285,
-0.040861111134290695,
0.022815357893705368,
0.0076590185053646564,
-0.06671641767024994,
0.025693869218230247,
0.048131491988897324,
0.005470877978950739,
-0.040650103241205215,
-0.020121419802308083,
-0.015573276206851006,
-0.02587287500500679,
-0.0015431733336299658,
0.010273040272295475,
0.027666155248880386,
-0.003423733403906226,
-0.01578151248395443,
0.043655913323163986,
0.009776313789188862,
0.05047190561890602,
-0.013104814104735851,
0.03655897080898285,
0.046481210738420486,
-0.00040419562719762325,
-0.025501882657408714,
-0.02024640329182148,
0.017381584271788597,
-0.017500372603535652,
0.011497207917273045,
-0.04149046167731285,
0.03869126737117767,
-0.04457472637295723,
-0.03255334869027138,
0.023092743009328842,
-0.0553252138197422,
0.007504264824092388,
-0.026729606091976166,
0.05833115428686142,
0.01319972239434719,
-0.03731181100010872,
0.028444012627005577,
-0.02334590256214142,
0.05953926593065262,
-0.008156868629157543,
-0.010781520046293736,
-0.0004795782151632011,
-0.013111899606883526,
-0.020818565040826797,
-0.010515422560274601,
0.00517335906624794,
-0.05217134952545166,
0.04043580964207649,
-0.014377175830304623,
-0.13788636028766632,
-0.02867126651108265,
-0.019590331241488457,
-0.010353893972933292,
0.019264928996562958,
0.06506745517253876,
-0.01952022686600685,
-0.013049687258899212,
-0.02838817611336708,
-0.004975622054189444,
0.038576867431402206,
0.022519392892718315,
0.0018783760024234653,
-0.0362589955329895,
0.006510292645543814,
0.038634780794382095,
-0.03997863456606865,
0.02414708025753498,
0.033931389451026917,
0.013270947150886059,
-0.009019685909152031,
-0.01545313186943531,
-0.056220587342977524,
0.01892988197505474,
0.030850930139422417,
0.013539011590182781,
-0.016898278146982193,
-0.053729474544525146,
-0.015495555475354195,
0.037412118166685104,
-0.012136266566812992,
0.0256341602653265,
0.05082567408680916,
0.03896675258874893,
0.010518277995288372,
0.050163667649030685,
0.01218664925545454,
0.04254550114274025,
0.046524565666913986,
0.010659487918019295,
-0.03828465938568115,
0.018432991579174995,
0.0236448273062706,
0.03410593047738075,
0.06907755881547928,
0.004019195679575205,
-0.0008435404160991311,
-0.007822788320481777,
-0.028067130595445633,
0.058660391718149185,
-0.020674677565693855,
0.011895236559212208,
0.03395938128232956,
-0.020161841064691544,
0.003378988476470113,
0.04525359347462654,
0.0021544736810028553,
0.03464323282241821,
0.027319250628352165,
-0.025234803557395935,
0.03678658604621887,
0.019459206610918045,
0.030757270753383636,
0.039481088519096375,
-0.02323903515934944,
-0.008743110112845898,
-0.016198087483644485,
0.014862913638353348,
0.025232207030057907,
-0.01966412365436554,
-0.07548931241035461,
0.03552264720201492,
-0.07201524823904037,
0.014563493430614471,
-0.05117638036608696,
-0.09206343442201614,
-0.025317510589957237,
-0.07206768542528152,
0.05953095480799675,
-0.0023454783950001,
0.0027273339219391346,
-0.01657339744269848,
0.036429911851882935,
0.03911333531141281,
-0.009311998263001442,
-0.011524517089128494,
-0.00575163122266531,
-0.027557753026485443,
0.022762056440114975,
-0.007195393554866314,
-0.05827655270695686,
-0.01074381172657013,
0.05364701524376869,
-0.0014675547135993838,
0.01577102765440941,
-0.05895136296749115,
-0.04376697167754173,
-0.029601583257317543,
-0.0012145417276769876,
-0.014432955533266068,
0.054176315665245056,
0.029363783076405525,
0.023428985849022865,
0.0358918160200119,
-0.00030863439314998686,
0.02769051492214203,
-0.03308428078889847,
-0.03567274287343025,
0.02822260931134224,
0.053403109312057495,
0.016314316540956497,
0.029253540560603142,
0.02846384607255459,
0.0092829754576087,
0.0062837195582687855,
0.0007591612520627677,
0.04349448159337044,
0.04863208532333374,
0.027456168085336685,
0.017801275476813316,
-0.028467267751693726,
-0.02062799222767353,
-0.00837939977645874,
0.021291133016347885,
-0.0015637344913557172,
-0.0013113283785060048,
0.04327120631933212,
-0.010503099299967289,
-0.0027987195644527674,
0.02308676578104496,
-0.0028603756800293922,
-0.019446877762675285,
-0.09307298809289932,
-0.0217603612691164,
-0.01076450850814581,
-0.007387043442577124,
0.08465255051851273,
0.001794773736037314,
0.0036507155746221542,
-0.0005074986256659031,
-0.07063775509595871,
0.04119609668850899,
0.01072754431515932,
-0.01842610165476799,
-0.050281982868909836,
0.0672731027007103,
-0.035745684057474136,
0.08632835745811462,
-0.06698457151651382,
-0.035714879631996155,
-0.03304631635546684,
0.029615379869937897,
-0.0060510821640491486,
-0.015616192482411861,
-0.04924982786178589,
0.002622302621603012,
0.021564096212387085,
-0.020080016925930977,
-0.02454354614019394,
0.03289557620882988,
0.014762835577130318,
0.017842285335063934,
0.04673571139574051,
0.02075507864356041,
-0.013031329959630966,
-0.013621012680232525,
0.018887091428041458,
-0.03666610270738602,
0.01319387648254633,
0.04261164739727974,
0.04798585921525955,
-0.031207846477627754,
0.054667845368385315,
0.04917632043361664,
-0.03500860556960106,
-0.015250476077198982,
0.01888967677950859,
-0.009591737762093544,
-0.013228329829871655,
0.031006954610347748,
-0.07840093225240707,
-0.024138716980814934,
0.04748633876442909,
0.04119878262281418,
-0.06414539366960526,
0.0036102149169892073,
0.04440419003367424,
0.022364076226949692,
0.05145496129989624,
-0.01993042603135109,
0.02947384864091873,
0.046166371554136276,
-0.0030938475392758846,
0.03511447459459305,
0.01061109360307455,
-0.0031418900471180677,
-0.020321810618042946,
-0.02960679493844509,
-0.013078471645712852,
0.07062789797782898,
0.019284563139081,
-0.05015750229358673,
-0.05134018883109093,
-0.05421685054898262,
-0.02561701089143753,
0.006873829755932093,
-0.019663136452436447,
-0.006136407610028982,
0.0358203649520874,
0.035381387919187546,
-0.06544051319360733,
-0.010488626547157764,
0.0357220396399498,
0.004141009878367186,
-0.06508178263902664,
-0.09343622624874115,
-0.034336477518081665,
0.015851551666855812,
-0.02098214253783226,
-0.088218554854393,
-0.007992034777998924,
0.01157053280621767,
-0.04965977743268013,
0.017727041617035866,
-0.01553838700056076,
0.006308124400675297,
-0.043719641864299774,
-0.014582160860300064,
0.043101683259010315,
0.02380349300801754,
-0.014589661732316017,
0.03883105888962746,
-0.033542826771736145,
0.008844565600156784,
0.013362656347453594,
0.03178983926773071,
-0.016430558636784554,
-0.09632374346256256,
-0.010758878663182259,
-0.0001992213656194508,
-0.043025288730859756,
-0.042073238641023636,
0.01597534865140915,
0.03447099030017853,
-0.026460392400622368,
0.005649914965033531,
-0.06962288916110992,
-0.0058853160589933395,
-0.032339297235012054
] |
<p>I am presently in my senior year and I am considering fluid mechanics for my thesis.
What area of research of fluid mechanics which is purely analytical and very mathematical since I am an applied mathematician can I look into.
NOTE 1: I am from a 3rd world country and the academic standard is low.
NOTE 2: Please provide references that I can consider.</p>
|
g2526
|
[
0.06506142020225525,
0.016594965010881424,
0.018514547497034073,
-0.020822318270802498,
-0.002757855923846364,
0.016413142904639244,
0.0023775154259055853,
-0.015910135582089424,
0.001533330068923533,
-0.02059355191886425,
0.06334404647350311,
0.004756153095513582,
0.02957565151154995,
0.01250514853745699,
-0.050181735306978226,
-0.025461772456765175,
-0.02549368515610695,
0.027699504047632217,
-0.025231486186385155,
-0.013936983421444893,
-0.01826845481991768,
0.045315150171518326,
0.024760078638792038,
0.0190400630235672,
-0.02424696274101734,
-0.021143851801753044,
0.009130221791565418,
0.016415070742368698,
-0.018531793728470802,
0.04218997806310654,
0.005559561774134636,
-0.06243013218045235,
0.03437482565641403,
-0.0484936386346817,
-0.03377668187022209,
-0.0047396100126206875,
-0.019976170733571053,
0.06231206655502319,
-0.00538941053673625,
-0.02612689882516861,
-0.0018437834223732352,
-0.011162268929183483,
0.0026149966288357973,
0.045783631503582,
0.02050149440765381,
-0.017823655158281326,
-0.01830955222249031,
-0.05097507685422897,
0.007858497090637684,
0.008074392564594746,
0.02113126404583454,
-0.003717590356245637,
0.004495986271649599,
-0.07829371839761734,
-0.004520032089203596,
0.021065492182970047,
0.03900717943906784,
0.013909838162362576,
0.008198277093470097,
-0.02253304049372673,
0.00032235647086054087,
0.03133734315633774,
-0.047918692231178284,
0.0003070628736168146,
0.015985695645213127,
-0.06740279495716095,
-0.04209422320127487,
-0.03649180382490158,
-0.030148880556225777,
0.002630598144605756,
-0.005349151324480772,
-0.06641533970832825,
0.024044489488005638,
0.007591978181153536,
0.0071138665080070496,
0.03279583528637886,
0.030618838965892792,
-0.0286677535623312,
0.0580434687435627,
-0.05094720795750618,
-0.0023567911703139544,
0.01692369394004345,
-0.0016372911632061005,
-0.0025604902766644955,
0.079178087413311,
-0.05639639496803284,
-0.03561996668577194,
-0.002877376042306423,
0.00109748519025743,
-0.03239786997437477,
-0.03703835606575012,
0.035534802824258804,
0.025114631280303,
-0.03462402895092964,
0.011159640736877918,
0.0009200413478538394,
0.01614963635802269,
0.03230511024594307,
-0.010975761339068413,
-0.0033289294224232435,
0.009106768295168877,
0.0008728652610443532,
-0.005640141665935516,
0.03249018266797066,
0.04420233145356178,
0.0029022283852100372,
-0.022862572222948074,
0.08781694620847702,
0.024561075493693352,
-0.015471513383090496,
-0.022945495322346687,
-0.017216941341757774,
-0.11388996988534927,
0.010075921192765236,
-0.03214200586080551,
0.034833043813705444,
-0.009381039068102837,
0.020007647573947906,
0.03890572488307953,
0.07138361781835556,
0.003645616816356778,
0.043199796229600906,
0.032800786197185516,
0.04520667716860771,
-0.0046685258857905865,
0.019906850531697273,
0.018959924578666687,
0.032034073024988174,
0.007578462362289429,
-0.005924566183239222,
0.08645398914813995,
-0.03376586362719536,
-0.021470539271831512,
-0.062316082417964935,
0.01140339020639658,
-0.0038686792831867933,
-0.059774622321128845,
0.011118647642433643,
0.05780761316418648,
-0.0062384530901908875,
0.0685228779911995,
-0.028192289173603058,
0.016330910846590996,
-0.00252935360185802,
0.0023030785378068686,
-0.02644067071378231,
0.0062574767507612705,
0.07112524658441544,
-0.03523273766040802,
-0.0059122550301253796,
-0.011445763520896435,
0.03548186644911766,
0.0025339224375784397,
-0.0684039369225502,
-0.014218858443200588,
0.024600546807050705,
-0.027248404920101166,
0.018454600125551224,
-0.002978314645588398,
-0.01631392166018486,
-0.011790374293923378,
0.011739710345864296,
0.0033179372549057007,
0.02538962848484516,
-0.07661178708076477,
0.02916436456143856,
-0.10756367444992065,
-0.07489572465419769,
0.03948251157999039,
0.015152198262512684,
-0.05096236616373062,
-0.029994569718837738,
-0.0005819942452944815,
-0.00027529761428013444,
0.05060446262359619,
-0.018484411761164665,
0.030757257714867592,
-0.016446970403194427,
0.05550219491124153,
0.01699771359562874,
-0.01323961466550827,
-0.005248811561614275,
-0.00018711369193624705,
-0.04344191774725914,
-0.05850464478135109,
0.0162538830190897,
0.04853633791208267,
0.03608426824212074,
-0.10396773368120193,
-0.0037320463452488184,
0.003594666952267289,
0.0221586674451828,
0.01997353322803974,
0.008674169890582561,
0.015112246386706829,
-0.04333098977804184,
0.02620844915509224,
-0.021297642961144447,
-0.06835301965475082,
-0.022710060700774193,
0.05393090471625328,
0.0028611929155886173,
0.011792265810072422,
0.04051137715578079,
0.01967448927462101,
0.02680264599621296,
0.027183478698134422,
0.013595919124782085,
0.027365634217858315,
0.01434605848044157,
0.01020335964858532,
0.02903514727950096,
0.05573688820004463,
0.03167190030217171,
0.019238393753767014,
-0.02437649480998516,
-0.01938382349908352,
-0.004084444139152765,
-0.020651744678616524,
0.0023310487158596516,
0.02930847369134426,
-0.014424852095544338,
-0.051409974694252014,
0.04119236022233963,
-0.03492261841893196,
0.0188074242323637,
-0.03037163056433201,
0.002635597251355648,
-0.016811203211545944,
0.035517264157533646,
-0.07124824821949005,
-0.04055272415280342,
0.0853995531797409,
-0.020154567435383797,
0.06805973500013351,
0.018197301775217056,
-0.03867945820093155,
0.015325254760682583,
0.017392808571457863,
0.029700350016355515,
-0.008230791427195072,
0.07624967396259308,
-0.026047097519040108,
-0.005009581800550222,
-0.011546768248081207,
-0.014559643343091011,
0.05032620206475258,
0.043686024844646454,
0.06428512185811996,
-0.012002687901258469,
0.023038823157548904,
-0.060155365616083145,
-0.029559392482042313,
0.07811538130044937,
-0.04308434948325157,
-0.021688660606741905,
-0.005542099941521883,
0.01865345425903797,
0.01284799538552761,
0.02983769215643406,
-0.04838310554623604,
0.015875833109021187,
0.021853534504771233,
-0.017745371907949448,
-0.014319836162030697,
0.04141175001859665,
-0.10595681518316269,
0.012241937220096588,
-0.007238262332975864,
0.012384235858917236,
0.047082480043172836,
0.05576684698462486,
-0.010859226807951927,
0.014925487339496613,
-0.018716169521212578,
0.05202940106391907,
0.018488653004169464,
-0.0018114990089088678,
-0.0051646484062075615,
-0.02018064633011818,
0.010272582061588764,
-0.04215296357870102,
0.03135263919830322,
0.020673958584666252,
-0.01949634961783886,
-0.0016565965488553047,
-0.021692665293812752,
0.027718136087059975,
-0.028253978118300438,
-0.03069865144789219,
-0.03911148011684418,
-0.007310354150831699,
-0.06789809465408325,
-0.0635313168168068,
-0.005782055668532848,
0.08681637048721313,
0.0871528685092926,
-0.033610131591558456,
0.0010364921763539314,
0.03228513523936272,
-0.0025816629640758038,
0.009697490371763706,
-0.023035012185573578,
0.018748195841908455,
0.021670565009117126,
-0.021024785935878754,
-0.01699415035545826,
-0.05038755387067795,
0.019776184111833572,
0.015653321519494057,
0.0029402056243270636,
-0.01843271777033806,
-0.007869981229305267,
-0.02746340073645115,
-0.04965362325310707,
0.06130494922399521,
0.013502744026482105,
-0.013326453976333141,
0.05072692036628723,
0.06397286802530289,
-0.02811010554432869,
-0.07140864431858063,
0.035737086087465286,
0.0005711238482035697,
0.06001150235533714,
0.0071518863551318645,
0.013680740259587765,
-0.0013239708496257663,
-0.036831896752119064,
-0.02701904997229576,
-0.018457863479852676,
-0.017468247562646866,
0.00158375920727849,
-0.049016304314136505,
-0.024647848680615425,
-0.0153313297778368,
-0.012746840715408325,
-0.00848009530454874,
0.03531375154852867,
-0.09238223731517792,
0.042382191866636276,
-0.02826465293765068,
0.06004024296998978,
-0.08161669969558716,
-0.04423246905207634,
0.02809167467057705,
-0.05327113717794418,
0.040111083537340164,
0.06025872379541397,
0.01941729709506035,
0.02157321199774742,
0.019992761313915253,
0.053079113364219666,
-0.0587688647210598,
-0.003756688442081213,
-0.0017017803620547056,
0.0553218275308609,
0.024376245215535164,
0.007534431293606758,
0.014900355599820614,
-0.03675456345081329,
-0.021115373820066452,
-0.023289203643798828,
0.019600791856646538,
0.017873134464025497,
0.04653223976492882,
0.017461739480495453,
-0.00156423170119524,
-0.04896035045385361,
-0.048563070595264435,
0.007898002862930298,
-0.03915102779865265,
0.0003359813126735389,
0.03616794943809509,
-0.012876777909696102,
-0.05348081514239311,
-0.07735811918973923,
0.021931776776909828,
-0.06196212396025658,
0.01508953608572483,
0.05379508063197136,
0.03232850879430771,
0.010401041246950626,
0.024929549545049667,
0.014620407484471798,
-0.029703110456466675,
-0.05206103250384331,
0.03695029020309448,
0.04304637759923935,
-0.045490097254514694,
0.08220034092664719,
-0.028223492205142975,
-0.028383692726492882,
0.00644844863563776,
-0.004617984872311354,
-0.017514120787382126,
0.0036096544936299324,
0.027669692412018776,
0.04481956735253334,
0.054133884608745575,
0.03407533839344978,
-0.01665571518242359,
-0.04752165079116821,
0.051962196826934814,
-0.007645146921277046,
-0.03471554443240166,
0.013670460321009159,
-0.01769624650478363,
0.004868853371590376,
-0.024241117760539055,
0.03466201573610306,
-0.05477559566497803,
-0.0006509215454570949,
-0.04104498028755188,
0.010591750964522362,
-0.016007760539650917,
-0.06694158911705017,
0.012892287224531174,
0.027151789516210556,
0.0056328014470636845,
0.042799435555934906,
0.004786417353898287,
-0.08226922154426575,
0.012413582764565945,
0.005465921480208635,
-0.0116455452516675,
0.05480802431702614,
0.006391074974089861,
-0.02495533600449562,
0.05098021402955055,
0.014721157029271126,
0.018010245636105537,
-0.029712297022342682,
0.023088840767741203,
-0.012305987998843193,
-0.023303555324673653,
0.06746294349431992,
-0.005063767544925213,
0.01062717940658331,
-0.016884559765458107,
-0.021881239488720894,
0.028879314661026,
-0.006623908411711454,
0.02520122565329075,
-0.04083714634180069,
0.08235609531402588,
-0.02538938820362091,
-0.05230791121721268,
-0.04874842241406441,
0.04229527711868286,
-0.05330977216362953,
0.012185454368591309,
0.008827993646264076,
0.024502795189619064,
-0.10868776589632034,
0.00534616457298398,
-0.003824310377240181,
-0.039202652871608734,
-0.006792164873331785,
0.05655055120587349,
0.043905794620513916,
-0.005254090763628483,
-0.014477366581559181,
0.023370256647467613,
0.022158438339829445,
-0.027940629050135612,
0.012768671847879887,
0.03806407004594803,
-0.06537246704101562,
-0.09581375122070312,
-0.007841523736715317,
0.03809954971075058,
0.033892083913087845,
-0.04261726140975952,
-0.00020525076251942664,
-0.04143022745847702,
-0.016148274764418602,
-0.038470327854156494,
0.004760508891195059,
-0.010647562332451344,
-0.0114166010171175,
0.014241466298699379,
0.026473646983504295,
0.04819701984524727,
0.02181379869580269,
-0.03155423700809479,
0.006653208751231432,
0.03938141092658043,
-0.023661784827709198,
-0.04439892992377281,
0.024115292355418205,
0.05028920993208885,
0.05327221751213074,
-0.028292685747146606,
-0.05496669188141823,
-0.07977946847677231,
0.0007467548712156713,
0.005840566474944353,
0.030581098049879074,
-0.012977092526853085,
-0.01887081377208233,
0.021473955363035202,
-0.0383334681391716,
0.009117350913584232,
0.00160208682063967,
0.0378117635846138,
-0.0012191444402560592,
-0.0401315800845623,
-0.024368345737457275,
0.06662923842668533,
0.03562578558921814,
-0.03943628445267677,
0.006113630253821611,
0.03269236907362938,
0.058665718883275986,
0.0007556438795290887,
0.05254329741001129,
0.00568346818909049,
-0.004054591525346041,
0.008385526947677135,
0.030961237847805023,
-0.03546096384525299,
0.007085119839757681,
0.011123529635369778,
0.042541563510894775,
-0.05408276617527008,
-0.028468091040849686,
0.012439501471817493,
-0.0132716353982687,
0.006599242798984051,
-0.037000931799411774,
0.010303213261067867,
-0.0007207754533737898,
0.04296659305691719,
-0.06743994355201721,
-0.02782917022705078,
-0.04252389445900917,
-0.01406797207891941,
0.05136274918913841,
0.013839743100106716,
-0.028928296640515327,
-0.04693078249692917,
0.011635219678282738,
0.08497527986764908,
0.0057728830724954605,
0.06785070151090622,
0.013902252539992332,
0.04509374126791954,
0.10341544449329376,
-0.07008427381515503,
-0.0780639722943306,
0.044983141124248505,
0.02785915695130825,
-0.01525167841464281,
0.02328532747924328,
-0.04226178303360939,
-0.027106821537017822,
-0.014735815115272999,
0.001617132918909192,
0.027270231395959854,
0.0076194703578948975,
0.004303347319364548,
0.0074792238883674145,
-0.04443022981286049,
-0.01076319720596075,
-0.01641412451863289,
-0.035845059901475906,
0.006104988045990467,
0.051270000636577606,
0.002847225870937109,
-0.06757433712482452,
-0.009710973128676414,
-0.04797416180372238,
0.019676830619573593,
0.09401349723339081,
0.04395892843604088,
-0.021087517961859703,
-0.003478319151327014,
-0.008511443622410297,
-0.046185046434402466,
0.037050291895866394,
0.025874577462673187,
0.04785696417093277,
-0.03885175660252571,
0.006168256513774395,
0.06943856924772263,
-0.02169926092028618,
0.0025643890257924795,
-0.01960015669465065,
-0.004974364303052425,
-0.027035949751734734,
0.02504293993115425,
-0.03698680177330971,
0.012261361815035343,
0.010010815225541592,
-0.027779117226600647,
0.05362078174948692,
0.023418685421347618,
0.011983069591224194,
-0.027048198506236076,
-0.014883753843605518,
0.008268089033663273,
-0.016862021759152412,
-0.0260901041328907,
0.010146417655050755,
0.0577867329120636,
0.048590779304504395,
-0.003902653930708766,
-0.04002901166677475,
-0.008994904346764088,
-0.0011660718591883779,
0.0318429060280323,
0.0001814438874134794,
0.013391631655395031,
-0.018803497776389122,
-0.06360705196857452,
0.02286267839372158,
-0.026498189195990562,
0.0038480039220303297,
-0.09591926634311676,
0.01925022155046463,
-0.013483619317412376,
-0.007337967865169048,
-0.04664182290434837,
0.02927987463772297,
0.013579838909208775,
-0.09208326786756516,
0.060872383415699005,
0.06044857203960419,
-0.0020563595462590456,
0.05724634230136871,
-0.017298514023423195,
-0.01584646850824356,
0.00393939483910799,
0.002607684349641204,
-0.013727814890444279,
-0.007867613807320595,
-0.02114153653383255,
0.05722900480031967,
0.013499119319021702,
-0.02684449590742588,
0.05318167060613632,
-0.012394538149237633,
-0.015536503866314888,
-0.0224564541131258,
-0.043653350323438644,
-0.024837225675582886,
-0.04152102395892143,
-0.03847432881593704,
0.01896725594997406,
0.03353666141629219,
0.009759449400007725,
-0.034974973648786545,
-0.037414390593767166,
-0.05399834364652634,
0.018732404336333275,
0.028883183375000954,
-0.06542502343654633,
0.05776945501565933,
-0.01816161349415779,
-0.029147742316126823,
0.04744494706392288,
0.019740238785743713,
-0.0035886485129594803,
0.007208597846329212,
0.03938985615968704,
0.021222421899437904,
-0.06910788267850876,
0.0059127239510416985,
0.0016811159439384937,
0.06011427566409111,
-0.028649084270000458,
-0.045650992542505264,
-0.016014548018574715,
0.0019833201076835394,
-0.01259218342602253,
-0.00952079240232706,
-0.026452861726284027,
0.008542613126337528,
0.02872917242348194,
0.021494830027222633,
0.007407505530864,
0.01531567145138979,
-0.02942238561809063,
-0.011004741303622723,
-0.0034939104225486517,
0.0033552704844623804,
-0.05303825065493584,
0.011497273109853268,
-0.013946745544672012,
-0.035449180752038956,
0.024095429107546806,
0.024945663288235664,
-0.07049895823001862,
-0.0033690310083329678,
0.024566983804106712,
0.0009963817428797483,
0.030096249654889107,
0.04935671016573906,
0.021880503743886948,
-0.01314278319478035,
-0.010709932073950768,
0.05302373319864273,
-0.015230565331876278,
-0.0332675501704216,
0.01627810299396515,
0.011015867814421654,
0.017958808690309525,
0.007067009806632996,
0.04538721591234207,
-0.030802365392446518,
0.013926567509770393,
0.0914880782365799,
-0.0144765954464674,
0.026635948568582535,
-0.007765175774693489,
-0.03018847480416298,
-0.012343539856374264,
0.017813771963119507,
-0.017475437372922897,
0.02425757795572281,
-0.050879113376140594,
0.024460721760988235,
-0.03168557956814766,
-0.06566335260868073,
-0.0006613032310269773,
-0.03354864567518234,
-0.004241156857460737,
-0.04239002987742424,
-0.03065146505832672,
-0.02612479217350483,
-0.036491040140390396,
0.009754431433975697,
0.03084815852344036,
-0.1275154948234558,
-0.027191121131181717,
0.08730288594961166,
-0.03384283557534218,
-0.001813470502384007,
0.04964417219161987,
0.033096056431531906,
-0.016467079520225525,
-0.002735341899096966,
-0.03020027093589306,
-0.015329699963331223,
-0.0560840368270874,
-0.0366881899535656,
0.009638752788305283,
0.04395384341478348,
-0.02004929445683956,
0.0412781648337841,
0.03233344852924347,
0.006615216378122568,
0.02524949237704277,
-0.005494794808328152,
-0.07073947787284851,
0.009704876691102982,
0.06681911647319794,
0.006262106355279684,
-0.038946252316236496,
0.044737547636032104,
-0.007201137952506542,
0.02269003912806511,
0.03837576508522034,
-0.009517769329249859,
-0.0035137636587023735,
0.0032839695923030376,
-0.03536832705140114
] |
<p>Here is a drawing of the circuit that is confusing me:
<img src="http://i.stack.imgur.com/Kag3r.png" alt="enter image description here"></p>
<p>I don't quite understand how batteries work in this diagram. If a battery has a negative and positive terminal, there must be a barrier preventing them from neutralizing one another, so how can the potential from either negative terminal ever make it through the top half of the circuit without passing through a battery?</p>
|
g2527
|
[
0.0027609646786004305,
0.03874331712722778,
-0.01449658814817667,
0.054468829184770584,
0.0383317656815052,
0.05304202809929848,
0.029401687905192375,
0.0238802507519722,
-0.014406483620405197,
-0.01668691821396351,
0.005021128803491592,
0.015381010249257088,
0.017273692414164543,
-0.0047075096517801285,
0.06985519081354141,
0.02029074728488922,
0.04586440697312355,
0.012760826386511326,
0.09295760095119476,
0.04646311700344086,
-0.02611539512872696,
0.0356161892414093,
-0.08370690792798996,
-0.006110841874033213,
-0.07197648286819458,
-0.021950840950012207,
-0.005887260660529137,
-0.015802456066012383,
-0.03134754300117493,
-0.025122178718447685,
-0.010042114183306694,
-0.002461848082020879,
0.0610380545258522,
0.005354155320674181,
-0.035986654460430145,
0.038036637008190155,
0.014953099191188812,
-0.022382522001862526,
-0.03607358783483505,
0.03160538151860237,
-0.026395682245492935,
0.0258927159011364,
0.059224020689725876,
-0.05773838981986046,
-0.029806513339281082,
-0.027130503207445145,
0.005252297502011061,
0.0021054723765701056,
-0.024485258385539055,
-0.0755222961306572,
-0.01638087071478367,
-0.018663808703422546,
-0.032801553606987,
0.014942372217774391,
0.004054421093314886,
0.003094844054430723,
0.04672218859195709,
-0.028864992782473564,
0.020640019327402115,
0.02494819462299347,
0.01650809496641159,
0.04364925995469093,
0.023792950436472893,
0.0811852291226387,
0.06699902564287186,
-0.011218774132430553,
-0.025834351778030396,
0.02059878781437874,
0.009059312753379345,
0.0193348191678524,
0.024205980822443962,
-0.0007385058561339974,
-0.04041949287056923,
-0.03014224022626877,
0.026001986116170883,
0.04245389252901077,
0.07373272627592087,
-0.03291429206728935,
0.03682048246264458,
0.00790024921298027,
-0.06325574964284897,
-0.08177771419286728,
0.017700498923659325,
0.01398906484246254,
0.07569322735071182,
0.018580978736281395,
0.02241997793316841,
-0.04805471748113632,
-0.0939372256398201,
0.010725392960011959,
-0.013714013621211052,
0.03926553949713707,
0.08036154508590698,
-0.019889848306775093,
-0.014095968566834927,
0.01297803595662117,
0.013611539267003536,
0.022564517334103584,
-0.0037749262992292643,
0.0005006531719118357,
0.05640539899468422,
0.0004475710156839341,
0.02855709008872509,
0.018501270562410355,
-0.044869594275951385,
0.02773689478635788,
0.002812705934047699,
-0.048667602241039276,
0.010299930348992348,
0.010884413495659828,
-0.07473684102296829,
-0.04580840840935707,
-0.0179999228566885,
-0.04647044464945793,
0.05422268807888031,
0.04681681469082832,
0.07088754326105118,
-0.028740301728248596,
0.0017044171690940857,
-0.06626047194004059,
-0.0255487859249115,
0.09313520044088364,
0.014628663659095764,
-0.05810998007655144,
-0.05089990049600601,
0.015021055936813354,
0.01192435622215271,
-0.014735793694853783,
0.046138644218444824,
0.024396993219852448,
0.05300493165850639,
0.007891918532550335,
-0.03234564885497093,
0.03406674042344093,
0.07228247821331024,
0.010511393658816814,
0.04005247354507446,
-0.033598244190216064,
-0.018497643992304802,
0.0009423575247637928,
-0.015364501625299454,
-0.030122965574264526,
-0.013644745573401451,
0.03008604794740677,
-0.0007693023653700948,
0.008648375980556011,
-0.02169349230825901,
0.011318208649754524,
-0.00028386933263391256,
-0.0005608986248262227,
0.06452066451311111,
0.050775691866874695,
0.01036573201417923,
-0.05746246501803398,
0.03853383660316467,
-0.04988657683134079,
0.12124795466661453,
0.04862907901406288,
0.039727043360471725,
0.027494344860315323,
0.03857295215129852,
0.026013555005192757,
-0.025905944406986237,
-0.046659138053655624,
-0.07014043629169464,
-0.035317182540893555,
0.04128247871994972,
-0.04080129787325859,
-0.01747794821858406,
0.022486407309770584,
-0.03681882843375206,
0.004175507463514805,
0.009523558430373669,
0.05272204056382179,
0.04440619423985481,
0.06371522694826126,
0.0016264497535303235,
0.03730347007513046,
0.01988796330988407,
0.007097935304045677,
-0.049455676227808,
-0.06122007220983505,
0.01512094121426344,
0.01404848787933588,
-0.03260217234492302,
-0.03801478073000908,
-0.003810506546869874,
0.05765916779637337,
-0.06027969345450401,
-0.013997756876051426,
-0.016040276736021042,
-0.023181874305009842,
-0.04534993693232536,
-0.004092659335583448,
-0.06359405070543289,
-0.02300853841006756,
0.045325614511966705,
-0.04438486322760582,
0.0711531937122345,
-0.05517122149467468,
-0.04264412075281143,
0.015429859980940819,
0.040489017963409424,
0.05763789638876915,
0.04047585651278496,
-0.026073716580867767,
-0.008665543980896473,
-0.006801340263336897,
0.028590848669409752,
-0.018282489851117134,
-0.0917666107416153,
0.036452606320381165,
0.022140560671687126,
-0.014852524735033512,
-0.024494027718901634,
-0.04641105234622955,
-0.047213610261678696,
0.02613224647939205,
-0.04462112858891487,
-0.027653725817799568,
-0.012360862456262112,
-0.028647037222981453,
0.002082937629893422,
-0.03547822684049606,
-0.018902000039815903,
0.08296672999858856,
0.01929341070353985,
-0.03520617261528969,
-0.07486934959888458,
0.002333356998860836,
-0.048848021775484085,
-0.0041614314541220665,
-0.03488725423812866,
-0.07106655836105347,
-0.0162753127515316,
0.06170937791466713,
-0.00023449742002412677,
0.03727399557828903,
-0.020302269607782364,
-0.05631376802921295,
0.03445069491863251,
-0.008496333844959736,
0.05674653500318527,
0.08845624327659607,
0.03557465225458145,
-0.03923128545284271,
0.021191105246543884,
0.01372167281806469,
-0.04029370844364166,
0.02939416840672493,
0.010266406461596489,
-0.04963420331478119,
-0.01534399762749672,
0.02385837212204933,
-0.03645731881260872,
-0.03205123543739319,
-0.03754240646958351,
-0.013401180505752563,
-0.0049687959253787994,
-0.03457224369049072,
0.011419369839131832,
-0.014365848153829575,
-0.001243474893271923,
0.04344542324542999,
-0.05529234558343887,
-0.04813935607671738,
-0.017453612759709358,
-0.020607231184840202,
0.033377502113580704,
-0.03798237070441246,
-0.02609778195619583,
0.05046151578426361,
-0.004183582030236721,
-0.05410825088620186,
0.009325545281171799,
-0.016898036003112793,
-0.006882397457957268,
-0.05890245363116264,
0.05886141583323479,
-0.016724994406104088,
0.038291122764348984,
0.03262663260102272,
0.008947632275521755,
0.022061139345169067,
0.008054460398852825,
-0.025335071608424187,
0.04183414578437805,
0.015498131513595581,
0.013325410895049572,
0.002208339050412178,
-0.01014528889209032,
-0.009849539957940578,
0.06732945889234543,
-0.008183635771274567,
0.047562770545482635,
-0.03488779440522194,
0.003081778297200799,
-0.053912945091724396,
-0.06123599410057068,
-0.050516705960035324,
-0.04358169808983803,
0.008868522942066193,
-0.005923161748796701,
-0.012325577437877655,
-0.006790689192712307,
0.010617529042065144,
-0.0007645838777534664,
0.008338605053722858,
0.021343838423490524,
0.07692737877368927,
-0.048415686935186386,
-0.018649520352482796,
0.06255047023296356,
-0.03593903034925461,
0.02169235609471798,
-0.009854570962488651,
-0.03694712370634079,
0.015224653296172619,
-0.02238144911825657,
0.0116538992151618,
0.0022604395635426044,
-0.005522301886230707,
-0.0005358507623896003,
0.049052417278289795,
0.02843346633017063,
0.007045059464871883,
0.003492987947538495,
-0.020665369927883148,
-0.05104755237698555,
-0.013081267476081848,
0.04589741677045822,
0.04994463548064232,
-0.013702094554901123,
0.011156432330608368,
0.010730150155723095,
-0.004146624822169542,
-0.006197704467922449,
0.03341275826096535,
-0.024907931685447693,
-0.05457805097103119,
0.0033872928470373154,
-0.019139211624860764,
-0.038906924426555634,
-0.030243530869483948,
-0.001254821545444429,
-0.018553541973233223,
-0.0026705777272582054,
0.025488926097750664,
0.023167455568909645,
-0.05479064956307411,
0.007826573215425014,
-0.002834827871993184,
0.03016062267124653,
0.001252976362593472,
-0.04338548704981804,
0.03906460478901863,
-0.05707036331295967,
0.03029746562242508,
-0.06392839550971985,
0.07248391211032867,
-0.006850192788988352,
0.04688955470919609,
0.06372898817062378,
-0.004852584097534418,
0.040185000747442245,
-0.023433974012732506,
-0.021329212933778763,
0.005731387063860893,
0.0007193359197117388,
-0.030036047101020813,
0.022857781499624252,
-0.005899571347981691,
-0.026337429881095886,
0.01840365305542946,
0.04774816706776619,
-0.07424691319465637,
0.021096015349030495,
0.034728944301605225,
-0.025432024151086807,
0.06909067183732986,
-0.0022542206570506096,
-0.05384330824017525,
0.04831301420927048,
-0.05869922414422035,
0.0722300335764885,
0.01920413039624691,
-0.005961368326097727,
0.009320016950368881,
-0.025574084371328354,
-0.013978284783661366,
-0.06285460293292999,
0.03427907079458237,
-0.021600041538476944,
-0.017710555344820023,
0.011070492677390575,
0.012125263921916485,
0.0010383116314187646,
0.014531067572534084,
-0.020757555961608887,
0.0016259138938039541,
0.01697530783712864,
0.10041119158267975,
-0.031466491520404816,
-0.04674110934138298,
0.0022678386885672808,
-0.012133829295635223,
0.010319426655769348,
-0.024770408868789673,
0.006973270792514086,
-0.019031573086977005,
0.0008516638772562146,
0.01211779285222292,
-0.0397590734064579,
-0.02508719451725483,
0.020798850804567337,
0.011745401658117771,
0.05523928254842758,
0.06894242018461227,
0.0055001298896968365,
0.061644360423088074,
0.013723389245569706,
0.05433604493737221,
0.018514782190322876,
-0.03806609660387039,
0.018783045932650566,
0.025630677118897438,
0.02485579065978527,
-0.016124987974762917,
0.03299934044480324,
-0.01068079937249422,
-0.03312545269727707,
0.06570328027009964,
-0.016712838783860207,
0.01118532381951809,
-0.04581623524427414,
0.042691413313150406,
-0.08899006247520447,
0.0715266764163971,
0.04310443252325058,
0.045692604035139084,
0.08774001896381378,
-0.03744147717952728,
-0.028573980554938316,
-0.03185610473155975,
-0.013405591249465942,
0.005806659813970327,
-0.05228041112422943,
0.0038345090579241514,
0.0069863805547356606,
-0.049322158098220825,
-0.04188857227563858,
0.016428543254733086,
-0.058069370687007904,
-0.08711110800504684,
-0.04992399737238884,
0.0015921854646876454,
0.007872817106544971,
0.02880329079926014,
0.021258527413010597,
0.008542768657207489,
-0.03134015202522278,
-0.012073197402060032,
-0.005175032652914524,
-0.012544788420200348,
0.04908724129199982,
-0.011777320876717567,
0.025477712973952293,
-0.00020918025984428823,
0.0006017478881403804,
0.0120930140838027,
0.007269833702594042,
0.025713035836815834,
-0.017071176320314407,
0.0630824863910675,
-0.0050323703326284885,
-0.049702923744916916,
0.046532079577445984,
0.025817357003688812,
-0.07202070951461792,
-0.013944901525974274,
-0.0005099985864944756,
0.04485463723540306,
-0.030256113037467003,
0.011912894435226917,
-0.016693098470568657,
0.03814539685845375,
-0.0026501945685595274,
0.022091099992394447,
-0.08281056582927704,
-0.007568588480353355,
0.0215899795293808,
0.0102732228115201,
0.027357693761587143,
0.009313344955444336,
0.014372414909303188,
0.011196982115507126,
0.05783078446984291,
0.052190084010362625,
-0.021997369825839996,
-0.015425099059939384,
-0.03406881168484688,
-0.06478707492351532,
0.006833408493548632,
0.05558895692229271,
-0.00915311649441719,
0.03662578761577606,
-0.010717320255935192,
-0.01785016432404518,
-0.004373237956315279,
-0.030456634238362312,
-0.07468269765377045,
-0.055937666445970535,
-0.06672611832618713,
0.0662064179778099,
0.019801316782832146,
0.016522834077477455,
-0.11153674870729446,
-0.05495178699493408,
-0.026690464466810226,
-0.022900115698575974,
0.02312982641160488,
-0.007534767966717482,
0.005068203900009394,
-0.047536399215459824,
0.009668036364018917,
-0.020902583375573158,
-0.04805362969636917,
-0.028435099869966507,
0.007008340675383806,
0.025097453966736794,
-0.04256320372223854,
0.03937658295035362,
-0.010064435191452503,
0.038520295172929764,
-0.012550003826618195,
-0.0521983839571476,
0.04357624799013138,
-0.04074200615286827,
0.0389992855489254,
0.017521295696496964,
0.05800297111272812,
-0.018300486728549004,
-0.0017742301570251584,
0.07367264479398727,
-0.04369428753852844,
-0.041127853095531464,
-0.029657969251275063,
-0.05679630488157272,
-0.05198973789811134,
0.009613619185984135,
-0.00031508677056990564,
0.012685906141996384,
-0.00800554919987917,
0.026482971385121346,
0.009630813263356686,
0.01226132083684206,
-0.006349281873553991,
-0.042270686477422714,
0.02471226640045643,
-0.06940380483865738,
0.03699637949466705,
0.049927402287721634,
0.024952460080385208,
0.05836450308561325,
0.04488544911146164,
-0.010130548849701881,
-0.021711744368076324,
0.03662264719605446,
0.014240765012800694,
0.035857219249010086,
0.05088092386722565,
-0.002444862388074398,
0.0030009469483047724,
-0.03539392724633217,
0.023717600852251053,
0.0638841837644577,
-0.05023244768381119,
-0.019395355135202408,
0.019468257203698158,
0.018732629716396332,
-0.005602405872195959,
0.022756271064281464,
-0.00014918242231942713,
-0.08058146387338638,
0.011984937824308872,
-0.01115912850946188,
-0.030597975477576256,
-0.06476487964391708,
-0.02622651308774948,
-0.01854880526661873,
-0.028173383325338364,
-0.0435309037566185,
0.018176091834902763,
-0.032619815319776535,
0.037573713809251785,
-0.0492435023188591,
-0.010540441609919071,
0.008563975803554058,
0.021806154400110245,
0.005124547053128481,
0.018526675179600716,
0.014740963466465473,
-0.03046383149921894,
0.008249902166426182,
0.02521269954741001,
0.02990739978849888,
0.01302450243383646,
0.005545101594179869,
0.005370094906538725,
0.02572747878730297,
0.012385640293359756,
0.03095540963113308,
-0.014402853325009346,
-0.029423683881759644,
0.002251739613711834,
-0.019300395622849464,
-0.006323909852653742,
0.021951885893940926,
-0.002933008596301079,
0.07062923908233643,
-0.01936601847410202,
-0.012218218296766281,
0.003929977770894766,
0.07171469926834106,
0.04640475660562515,
-0.003494800301268697,
0.018327752128243446,
0.009347978048026562,
-0.0038205343298614025,
-0.037719957530498505,
-0.02144412137567997,
0.006258324254304171,
-0.01556215900927782,
-0.009396449662744999,
0.019055413082242012,
-0.0074607934802770615,
-0.04042435437440872,
-0.003992234822362661,
0.029867451637983322,
-0.04055987671017647,
-0.015421334654092789,
0.028529589995741844,
-0.04035698622465134,
0.08124709129333496,
-0.0007038618205115199,
-0.04236605018377304,
0.03470296785235405,
-0.018693795427680016,
-0.040914516896009445,
-0.0014221190940588713,
-0.011020581237971783,
-0.0005792969022877514,
-0.10153578966856003,
0.05163063481450081,
0.006540242116898298,
0.014100706204771996,
0.01555712055414915,
-0.017673393711447716,
0.02275390550494194,
-0.017828863114118576,
0.014834989793598652,
-0.03442053124308586,
-0.03326395899057388,
0.027304867282509804,
0.02595638483762741,
0.07565979659557343,
0.009576519951224327,
0.015301899053156376,
-0.01370448712259531,
-0.038717348128557205,
-0.007140936329960823,
-0.03270547464489937,
0.041364528238773346,
0.05704798921942711,
-0.030539756640791893,
-0.02103651873767376,
0.009686054661870003,
0.02613031305372715,
0.012398450635373592,
-0.042002275586128235,
0.024637676775455475,
-0.0296191219240427,
-0.03727329149842262,
-0.015168878249824047,
-0.02664744295179844,
-0.001739843050017953,
0.022354692220687866,
-0.005634061060845852,
-0.034440696239471436,
-0.010662217624485493,
0.041189033538103104,
-0.007823975756764412,
0.025755304843187332,
0.04736228287220001,
-0.01151355542242527,
0.029978768900036812,
0.022325972095131874,
0.018035683780908585,
0.02576190046966076,
0.028343863785266876,
0.01576780155301094,
-0.02021520771086216,
0.010962693020701408,
0.042977601289749146,
0.02205078862607479,
-0.025355134159326553,
-0.040834713727235794,
-0.008084376342594624,
-0.0740617886185646,
-0.020437566563487053,
0.02246975153684616,
0.05139033496379852,
-0.028984421864151955,
-0.01049325242638588,
-0.008922915905714035,
-0.016587676480412483,
-0.018923701718449593,
-0.0006431802175939083,
-0.015765871852636337,
0.022890321910381317,
-0.02834009937942028,
0.017057612538337708,
-0.005361570045351982,
-0.059081126004457474,
-0.03116009011864662,
-0.028022952377796173,
0.019551679491996765,
0.00787251815199852,
-0.009096982888877392,
0.04023926332592964,
-0.03423243761062622,
0.008119669742882252,
-0.021283332258462906,
0.01173579040914774,
-0.015956658869981766,
-0.015597652643918991,
-0.029482701793313026,
-0.023519184440374374,
0.05841628462076187,
0.003625195939093828,
0.014729254879057407,
-0.04146374389529228,
-0.008911523036658764,
-0.0648103654384613,
0.011141962371766567,
0.001606497447937727,
-0.08009621500968933,
-0.004656106233596802,
0.02290005050599575,
-0.001844892743974924,
0.04446849599480629,
-0.006461391691118479,
-0.05477812513709068,
0.02060014009475708,
0.074761301279068,
-0.04538760706782341,
-0.01934751495718956,
0.059906620532274246,
-0.02861522138118744,
-0.0018047713674604893,
0.0034751342609524727,
-0.04062562435865402,
-0.004033364355564117,
-0.009898591786623001,
0.0031959612388163805,
-0.007004403043538332,
-0.012609384953975677,
-0.014673285186290741
] |
<p>This is about a step in a derivation of the expression for the relativistic Doppler effect.</p>
<p>Consider a source receding from an observer at a velocity $v$ along the line joining the two. Light is emitted at frequency $f_s$ and wavelength $\lambda_s$. The frequency $f_0$ and wavelength $\lambda_0$ received by the observer will be different.</p>
<p>Some textbooks now argue that the wavelength received by the observer is given by $\lambda_0=(c+u)T_0$, where $T_0$ is the time period of the wave in the observers frame. The argument given is that the successive "crests" will be an extra distance $uT_0$ apart due to movement of the source. Upon relativistically transforming the time period in the source frame to the observer frame, the correct result $f_0=f_s\sqrt{\frac{c-u}{c+u}}$ is obtained.</p>
<p>But the argument for the wavelength seems reminiscent of the classical Doppler effect for sound. Is it really applicable here through this argument? And is there a way to show the same result for $\lambda_0$ mathematically?</p>
|
g2528
|
[
0.023229973390698433,
-0.0010914328740909696,
0.01628127135336399,
-0.024006487801671028,
0.07932408154010773,
0.032145608216524124,
0.03661058470606804,
0.0130893774330616,
-0.031411249190568924,
-0.0001350475213257596,
-0.027288805693387985,
0.027811290696263313,
0.009398053400218487,
0.0463273786008358,
0.0019315957324579358,
-0.051157284528017044,
0.036071550101041794,
-0.048429425805807114,
-0.014693452045321465,
0.03135067969560623,
-0.019487574696540833,
-0.008850708603858948,
-0.00642606383189559,
-0.03784823790192604,
-0.03186493739485741,
0.002413765760138631,
0.02196810394525528,
-0.009984293952584267,
-0.05829399451613426,
0.0351068452000618,
0.010082458145916462,
-0.021328125149011612,
0.06531280279159546,
0.008920827880501747,
0.021235043182969093,
-0.012441507540643215,
-0.010837060399353504,
0.021230312064290047,
-0.0014096098020672798,
0.04237886145710945,
0.008502746000885963,
0.034604061394929886,
-0.03326694667339325,
-0.03493422642350197,
0.040117695927619934,
-0.013723776675760746,
-0.0166939627379179,
-0.03047754615545273,
-0.0029235570691525936,
-0.03373848646879196,
-0.011253057979047298,
0.01924264244735241,
-0.0039959861896932125,
0.06436695903539658,
0.012381752952933311,
0.06129101291298866,
0.003866905579343438,
-0.014300571754574776,
0.07055478543043137,
0.044343817979097366,
0.024329399690032005,
-0.0058042509481310844,
-0.011082837358117104,
0.002179922303184867,
0.0441773347556591,
0.0038558542728424072,
0.0024803117848932743,
0.009950332343578339,
0.0037879764568060637,
-0.0035086493007838726,
-0.014347301796078682,
-0.062213506549596786,
-0.05276523157954216,
-0.0024943312164396048,
0.015450594946742058,
-0.010255438275635242,
0.0016341833397746086,
-0.04165145754814148,
-0.017765643075108528,
-0.011059711687266827,
-0.030849188566207886,
-0.01876157708466053,
0.014609841629862785,
0.05457891523838043,
0.037947192788124084,
0.001392837380990386,
0.04663494974374771,
0.080643430352211,
-0.029351994395256042,
-0.021959634497761726,
0.007013545837253332,
-0.058366190642118454,
0.04637322574853897,
-0.001594162080436945,
-0.015217392705380917,
-0.03420400619506836,
-0.07898176461458206,
0.01827811636030674,
0.01971367932856083,
0.006844961550086737,
-0.009373500011861324,
0.02773849479854107,
0.03153896704316139,
0.02777078188955784,
0.0013092425651848316,
-0.051172271370887756,
-0.020415455102920532,
0.028553958982229233,
-0.03452497348189354,
-0.05200941115617752,
-0.03125717118382454,
-0.11316075921058655,
0.026744140312075615,
-0.01450488343834877,
-0.06630726158618927,
-0.07125475257635117,
0.016180401667952538,
-0.0007306774496100843,
-0.01607002690434456,
0.0714121013879776,
-0.015179917216300964,
0.0237579382956028,
-0.03132563829421997,
0.11045435816049576,
0.020486315712332726,
-0.005381169728934765,
0.015956131741404533,
-0.012964176945388317,
0.030948037281632423,
0.05053829029202461,
0.018545210361480713,
0.024943150579929352,
0.04547503590583801,
-0.008932406082749367,
0.03300251066684723,
0.01633298583328724,
0.08296623080968857,
0.009152240119874477,
0.0333101749420166,
0.02524302899837494,
0.10662433505058289,
-0.01727599836885929,
0.06029042601585388,
-0.12840262055397034,
-0.036197252571582794,
0.04726703464984894,
-0.0006492301472462714,
-0.04750562459230423,
0.07716259360313416,
-0.04276124760508537,
-0.010277196764945984,
0.028573613613843918,
-0.03913649544119835,
0.046190131455659866,
-0.03617554157972336,
0.03502444550395012,
-0.02189677022397518,
-0.008888520300388336,
-0.039289526641368866,
0.023192835971713066,
0.08288569748401642,
-0.04059046506881714,
0.0290677547454834,
-0.013991902582347393,
-0.016887275502085686,
0.04348461329936981,
-0.02843347378075123,
-0.07286667078733444,
-0.018820278346538544,
-0.07256492972373962,
-0.004248171579092741,
0.007489638868719339,
-0.021161485463380814,
0.04896796867251396,
0.00602257763966918,
0.04384739324450493,
0.057646285742521286,
0.0066261193715035915,
-0.06556996703147888,
0.019159400835633278,
-0.04915735870599747,
-0.0366959385573864,
0.015041746199131012,
-0.057983629405498505,
0.02778886817395687,
-0.03127153217792511,
-0.02203567884862423,
-0.03038516640663147,
-0.07478582113981247,
-0.0046737282536923885,
-0.03481785207986832,
-0.017396381124854088,
-0.001235680771060288,
0.010267811827361584,
-0.020706268027424812,
0.02917618863284588,
-0.023019902408123016,
0.004791941959410906,
-0.023344123736023903,
0.04393739253282547,
-0.014080584980547428,
0.01663581281900406,
0.017776014283299446,
-0.033912062644958496,
0.01903422363102436,
0.029586270451545715,
0.0031667754519730806,
-0.029352741315960884,
-0.022231487557291985,
0.013073846697807312,
0.06294247508049011,
-0.04838372766971588,
-0.03357711061835289,
0.03536301478743553,
-0.03366367891430855,
0.013926000334322453,
0.013219648972153664,
-0.033606790006160736,
0.009943198412656784,
0.03373830392956734,
-0.05786342918872833,
0.06005348637700081,
0.041727956384420395,
-0.048520948737859726,
0.026729486882686615,
-0.018466489389538765,
-0.008535884320735931,
-0.00617132568731904,
0.020588628947734833,
0.022848935797810555,
0.013119729235768318,
0.03418286517262459,
-0.04687583073973656,
-0.02196131832897663,
0.029839465394616127,
0.016270559281110764,
0.02625466138124466,
0.01045566238462925,
-0.004793600644916296,
0.019731488078832626,
0.04477096349000931,
-0.03643782436847687,
-0.07285556942224503,
-0.027190597727894783,
0.03668670356273651,
-0.01068364642560482,
0.04835447669029236,
0.0011427992722019553,
0.017851995304226875,
-0.023578034713864326,
0.07023540139198303,
-0.0073165385983884335,
0.008965077809989452,
0.0074326712638139725,
0.015191156417131424,
-0.009973663836717606,
0.02660631574690342,
0.06538237631320953,
-0.08060366660356522,
-0.06584998220205307,
-0.049345191568136215,
0.017005447298288345,
0.03546636179089546,
-0.031637392938137054,
0.0014184840256348252,
-0.0015303936088457704,
-0.0019755575340241194,
0.06155566871166229,
-0.024474456906318665,
-0.04420104995369911,
-0.0186479315161705,
0.03467268869280815,
0.041497137397527695,
0.045524608343839645,
-0.027481794357299805,
0.021495399996638298,
-0.007615063805133104,
-0.010040638968348503,
0.016168393194675446,
0.009853371419012547,
-0.02832805924117565,
-0.015317757613956928,
-0.07214458286762238,
-0.02098935842514038,
0.04224131628870964,
-0.0751475840806961,
0.029305553063750267,
0.02550596557557583,
0.007638994138687849,
-0.014071209356188774,
-0.009706229902803898,
0.04654783383011818,
0.004441391211003065,
0.010979841463267803,
0.021210085600614548,
0.013695808127522469,
0.07829828560352325,
-0.019439231604337692,
-0.0012926011113449931,
0.04091227799654007,
0.011191131547093391,
-0.03735814243555069,
-0.038951557129621506,
-0.022960035130381584,
-0.017679503187537193,
-0.014311201870441437,
-0.04052713140845299,
-0.04901731014251709,
0.05038309842348099,
-0.04561487212777138,
0.03295980393886566,
0.03061223402619362,
0.027608171105384827,
-0.0035605153534561396,
0.0077334619127213955,
0.011986089870333672,
-0.04504469037055969,
-0.012051771394908428,
-0.0155451325699687,
0.029101630672812462,
0.03267533704638481,
-0.018186742439866066,
-0.04351554811000824,
0.004140934441238642,
0.037583015859127045,
-0.02759426273405552,
-0.01606256142258644,
0.03346753492951393,
-0.07485974580049515,
0.0033664056099951267,
0.020965365692973137,
-0.010696078650653362,
-0.016633646562695503,
-0.019605156034231186,
0.010098065249621868,
-0.04335751384496689,
-0.00696094986051321,
0.02711615525186062,
0.05448615178465843,
0.07411862909793854,
0.03944879025220871,
-0.00022391535458154976,
-0.044627174735069275,
0.026911897584795952,
0.02527787536382675,
0.048505328595638275,
0.053660813719034195,
0.022016379982233047,
-0.030162757262587547,
-0.06138782948255539,
0.010590191930532455,
-0.029927855357527733,
-0.01315295323729515,
-0.039204005151987076,
0.023359665647149086,
-0.013800907880067825,
0.06068846210837364,
-0.00021292787278071046,
0.030514108017086983,
-0.016440194100141525,
0.013791995123028755,
-0.03051965869963169,
-0.02312103658914566,
-0.01335182599723339,
0.031090106815099716,
-0.04458285868167877,
0.00004641097621060908,
0.057628095149993896,
0.0404021218419075,
-0.003691705409437418,
-0.01428566500544548,
-0.027467546984553337,
-0.020784026011824608,
0.024763057008385658,
-0.044376350939273834,
-0.06327886879444122,
0.03145599737763405,
-0.003590043867006898,
0.00237409514375031,
0.053315311670303345,
0.022073259577155113,
0.0359354168176651,
-0.040143322199583054,
0.026848062872886658,
0.001257339958101511,
-0.04335039481520653,
-0.038490768522024155,
-0.04220719635486603,
0.04006356745958328,
-0.07440178841352463,
0.015969181433320045,
-0.02449069544672966,
-0.004391403403133154,
-0.009067270904779434,
0.03205948695540428,
0.013630477711558342,
0.01203758455812931,
0.02198008820414543,
-0.032871074974536896,
0.03783921152353287,
0.0002910196199081838,
-0.013421162031590939,
-0.012536990456283092,
0.020937252789735794,
-0.09659229964017868,
0.021167388185858727,
0.043210893869400024,
-0.04157876595854759,
-0.06022258847951889,
0.023483850061893463,
-0.04366806894540787,
-0.050927985459566116,
-0.08372566103935242,
-0.05510030686855316,
0.0086970878764987,
0.03173235058784485,
0.049603499472141266,
-0.026491181924939156,
0.03496364876627922,
0.06547698378562927,
-0.016793686896562576,
0.042372092604637146,
0.04688328504562378,
0.009540813975036144,
0.001884750323370099,
0.07936394959688187,
0.024523863568902016,
-0.0029361434280872345,
-0.02284797839820385,
-0.061728689819574356,
0.04432690516114235,
-0.010958799161016941,
-0.04807819053530693,
-0.008551248349249363,
-0.052131861448287964,
0.07265379279851913,
0.004653197713196278,
0.0223359614610672,
-0.006452924106270075,
-0.023915085941553116,
-0.024336352944374084,
-0.06022629886865616,
0.032182540744543076,
-0.00795182678848505,
-0.025170963257551193,
0.06919537484645844,
-0.04720424860715866,
-0.05720573291182518,
-0.03191286325454712,
-0.03840859606862068,
-0.04062037169933319,
0.08034635335206985,
-0.007160316687077284,
0.016256367787718773,
0.04898212477564812,
-0.017107389867305756,
-0.024985553696751595,
-0.00454214122146368,
0.05379078537225723,
-0.019146863371133804,
-0.03073456697165966,
0.0152902128174901,
0.03613991662859917,
-0.0287922453135252,
0.026320839300751686,
0.016271159052848816,
-0.02460223250091076,
-0.029188435524702072,
-0.04873749613761902,
0.02308845706284046,
-0.00014840131916571409,
-0.036396730691194534,
-0.020110798999667168,
-0.031071389093995094,
-0.009432772174477577,
-0.01764919050037861,
-0.033374760299921036,
0.012250810861587524,
0.02887321449816227,
-0.050198424607515335,
-0.018532855436205864,
-0.07253596931695938,
0.02863844856619835,
0.0007898882031440735,
-0.007812641561031342,
0.03747827932238579,
-0.023130269721150398,
-0.013152187690138817,
0.03552159667015076,
-0.038057103753089905,
0.043276380747556686,
-0.04316901043057442,
-0.04850431904196739,
-0.017738614231348038,
0.05022943764925003,
0.06856467574834824,
0.054430801421403885,
-0.042717088013887405,
-0.0008375110919587314,
-0.03153533115983009,
-0.057041317224502563,
0.07407929748296738,
0.04555130749940872,
0.05286064371466637,
-0.02155071496963501,
0.03015095368027687,
0.05109509080648422,
0.003272501053288579,
-0.01214507408440113,
0.04168049991130829,
0.010006782598793507,
-0.023441990837454796,
0.006390327587723732,
-0.0007180253160186112,
0.02430364303290844,
-0.056931957602500916,
0.01539373304694891,
0.0034040487371385098,
-0.01439639087766409,
-0.061847880482673645,
0.015198147855699062,
-0.014993513002991676,
-0.004284919239580631,
-0.017450321465730667,
-0.005363473668694496,
0.0028529611881822348,
-0.0225643552839756,
0.006479673087596893,
-0.010529300197958946,
-0.05699366331100464,
0.013023904524743557,
0.016197513788938522,
0.02771734446287155,
0.053157877177000046,
0.059901025146245956,
-0.02223243936896324,
-0.0149070480838418,
-0.046085428446531296,
-0.06262440979480743,
-0.03418038412928581,
-0.06571730226278305,
-0.009692595340311527,
0.011784638278186321,
0.049060702323913574,
-0.017863964661955833,
-0.0026432496961206198,
-0.04525318369269371,
0.03273600712418556,
0.030402811244130135,
0.013327116146683693,
-0.0407935231924057,
-0.01810944266617298,
0.012400531210005283,
0.02109963819384575,
0.009265507571399212,
-0.013149494305253029,
0.00046684383414685726,
-0.017773456871509552,
-0.044585827738046646,
-0.05223044753074646,
0.017789311707019806,
0.027823181822896004,
0.005036052316427231,
0.05397599935531616,
-0.023410623893141747,
-0.002171454718336463,
0.029565081000328064,
-0.034688953310251236,
0.07897808402776718,
0.006466469261795282,
-0.0008748997352086008,
-0.0455855131149292,
-0.07449383288621902,
-0.017606964334845543,
-0.02439199946820736,
0.06154773011803627,
0.027054160833358765,
-0.0727977305650711,
-0.015417346730828285,
-0.007851026020944118,
-0.04848117381334305,
0.00947560090571642,
-0.025750868022441864,
-0.020782824605703354,
-0.07519715279340744,
0.0005434672930277884,
-0.005049472209066153,
0.0058011142536997795,
0.04015146940946579,
0.038378193974494934,
0.0012761832913383842,
-0.05798600614070892,
-0.014716160483658314,
-0.011459424160420895,
-0.05247850716114044,
-0.039369210600852966,
0.0045831771567463875,
0.003377455985173583,
0.011790089309215546,
0.06069190427660942,
-0.0034805703908205032,
0.0007835409487597644,
0.09060121327638626,
-0.02200905978679657,
0.0063875578343868256,
0.01820809580385685,
-0.04472189396619797,
0.031044218689203262,
0.06017008796334267,
-0.013057173229753971,
0.012846427038311958,
0.04984356090426445,
0.03737272694706917,
0.005606340244412422,
-0.014027940109372139,
0.00043307265150360763,
-0.007521485909819603,
0.018560586497187614,
0.01273274328559637,
0.02083839662373066,
0.11860232800245285,
-0.0358307845890522,
0.00947626680135727,
-0.03417365998029709,
-0.057163551449775696,
0.06026988476514816,
-0.05037100613117218,
0.0006087191868573427,
0.042354829609394073,
-0.0011969737242907286,
0.055043548345565796,
-0.05296238511800766,
-0.028326556086540222,
0.04115740954875946,
0.0226239413022995,
0.036202892661094666,
-0.0014361146604642272,
0.0049964068457484245,
0.01469737384468317,
0.009704631753265858,
0.043906211853027344,
0.029787395149469376,
0.012517916038632393,
-0.0039404029957950115,
-0.04255334660410881,
-0.028752408921718597,
0.07291678339242935,
-0.014046115800738335,
-0.05569973215460777,
-0.01435092929750681,
-0.04670120030641556,
-0.017573406919836998,
-0.010051915422081947,
0.07665540277957916,
-0.04183433577418327,
-0.014858036302030087,
-0.025270603597164154,
0.018077172338962555,
-0.009376815520226955,
-0.058600254356861115,
-0.00957202073186636,
-0.07277590781450272,
-0.06091184914112091,
0.011251069605350494,
-0.027683474123477936,
0.03612739220261574,
0.0587618388235569,
-0.03455046936869621,
-0.024639666080474854,
0.039331063628196716,
0.04194531589746475,
-0.09425456076860428,
0.028625238686800003,
-0.014435891062021255,
-0.03910231962800026,
0.00008557081309845671,
-0.033664677292108536,
0.028224442154169083,
-0.025146665051579475,
-0.008451440371572971,
0.016785740852355957,
0.052021175622940063,
0.006677156314253807,
-0.08015675097703934,
-0.012459303252398968,
0.053712449967861176,
-0.021815290674567223,
-0.02612064965069294,
0.007420358248054981,
-0.017732487991452217,
-0.02376583032310009,
0.03761107847094536,
-0.025699220597743988,
-0.015694694593548775,
-0.00380868767388165,
-0.01366389449685812,
0.048745278269052505,
0.028037289157509804,
-0.04245231673121452,
0.050976745784282684,
0.0020567597821354866,
-0.02180122584104538,
-0.003872261382639408,
0.03383927792310715,
0.03814543038606644,
0.014658065512776375,
-0.0220363549888134,
-0.0022058638278394938,
0.004024369642138481,
0.038749419152736664,
0.0420016273856163,
0.008320227265357971,
0.02162018045783043,
0.001496239798143506,
-0.030127886682748795,
-0.024182988330721855,
-0.0321369506418705,
0.059350065886974335,
-0.004930485505610704,
-0.030184278264641762,
-0.00022094699670560658,
-0.04793420806527138,
-0.02433805540204048,
-0.06958221644163132,
0.0221011471003294,
0.006785952486097813,
0.01657566800713539,
-0.02534553036093712,
-0.01268362533301115,
-0.00858328677713871,
0.03779737651348114,
0.031154833734035492,
-0.03501113876700401,
-0.013073084875941277,
-0.013194241560995579,
0.022160079330205917,
0.018803713843226433,
0.0561523362994194,
-0.006029999349266291,
0.027757229283452034,
0.03054727241396904,
-0.01716604270040989,
-0.03705691546201706,
0.012959185987710953,
0.017117412760853767,
-0.04723534733057022,
0.06331534683704376,
-0.02463461644947529,
0.03200288861989975,
-0.014798321761190891,
0.056430965662002563,
0.048835497349500656,
-0.025765186175704002,
0.028349684551358223,
0.06437606364488602,
-0.005850299261510372,
0.013371993787586689,
-0.010852172039449215,
-0.02662740647792816,
-0.006024012807756662,
-0.0022966694086790085,
0.013184338808059692,
0.006790864281356335,
-0.035525038838386536,
-0.0047168610617518425,
0.006733347196131945,
-0.01931435987353325,
0.008479015901684761
] |
<p>I am reading Wald for the interior solutions of a static spherical metric. Assume it to be of the form
$$ds^2 = -f(r)dt^2 + h(r)dr^2 + r^2 ( d{\theta^2} \sin^2{\theta}d{\phi^2})$$</p>
<p>Wald states: For a perfect fluid tensor $T_{ab}= \rho u_a u_b + P ( g_{ab}+ u_{ab})$</p>
<blockquote>
<p>In order to be compatible with the static symmetry of space time, the
four velocity of the fluid should point in the direction of the static
killing vector $\xi^a$</p>
</blockquote>
<p>i.e. $u^a=-(e_0)^a=-f^{\frac{1}{2}}(dt)^a$</p>
<p><strong>EDIT: It also seems $(e_0)_a=f^{\frac{1}{2}}(dt)_a=f^{-\frac{1}{2}}(\frac{\partial}{\partial t})_a$. Please could someone tell, why this is so?</strong></p>
<ol>
<li><p>First, why is the the static killing vector $\frac{\partial}{\partial t}$ equal to $-f^{\frac{1}{2}} dt$?</p></li>
<li><p>Second, why is the velocity, along the killing time vector? What would happen if there is a component perpendicular to it? Does this mean, the fluid doesn't move through space?</p></li>
</ol>
|
g2529
|
[
0.014397703111171722,
-0.017362194135785103,
-0.027725009247660637,
-0.004949405789375305,
0.05134941264986992,
0.023137202486395836,
0.03593377023935318,
0.015335717238485813,
-0.07487285137176514,
-0.00037635990884155035,
-0.005888341926038265,
-0.013802227564156055,
0.05771941319108009,
-0.023424839600920677,
-0.008221437223255634,
-0.017083527520298958,
-0.005157322622835636,
0.0038200756534934044,
-0.004074789118021727,
-0.01364243682473898,
-0.022019602358341217,
0.005906967446208,
0.01252230815589428,
-0.0035181851126253605,
0.06011805683374405,
-0.007285088766366243,
0.08983229845762253,
-0.03387068957090378,
-0.06357051432132721,
-0.027229050174355507,
0.08193007856607437,
0.05459963157773018,
-0.031797878444194794,
-0.04680041968822479,
-0.02118903025984764,
-0.020462917163968086,
0.007490778807550669,
0.003802333492785692,
0.012717250734567642,
-0.04960678145289421,
0.013534469529986382,
-0.03422464057803154,
0.04390016943216324,
0.010105347260832787,
0.008856123313307762,
-0.039961040019989014,
-0.01768632046878338,
-0.029347693547606468,
-0.04660265892744064,
-0.05801239609718323,
-0.035370904952287674,
-0.027138760313391685,
-0.0027157620061188936,
-0.076021209359169,
0.0009760327520780265,
-0.021482111886143684,
-0.038293879479169846,
-0.005913119297474623,
-0.0031413822434842587,
0.03541921451687813,
-0.023795591667294502,
-0.06736923009157181,
0.00029075617203488946,
-0.054859619587659836,
0.04982216656208038,
-0.057613324373960495,
-0.011427152901887894,
-0.0067397477105259895,
0.027688179165124893,
0.06809097528457642,
0.04206714406609535,
-0.014234732836484909,
-0.01678583025932312,
-0.060428064316511154,
-0.022627124562859535,
0.047845374792814255,
0.014259358868002892,
0.0014579829294234514,
0.041664302349090576,
-0.05918460339307785,
-0.03923358768224716,
0.019096655771136284,
-0.0015570272225886583,
0.013348703272640705,
0.06439213454723358,
0.000018366448784945533,
0.02631709724664688,
0.021436884999275208,
-0.046042636036872864,
0.0008897751686163247,
-0.011092502623796463,
0.008903800509870052,
0.01855423115193844,
0.03052353858947754,
-0.02016194351017475,
-0.01425967738032341,
-0.04673868790268898,
0.0991506576538086,
-0.019471662119030952,
-0.013434705324470997,
0.03482682257890701,
0.0343204103410244,
0.00792479794472456,
0.006365663837641478,
0.04365535080432892,
-0.015319162048399448,
0.06376749277114868,
0.06486135721206665,
-0.009218931198120117,
-0.03933081403374672,
0.0057377442717552185,
-0.0030766024719923735,
-0.035222891718149185,
0.008081706240773201,
0.01792212948203087,
-0.004297574050724506,
0.062339507043361664,
-0.03634355962276459,
0.010418194346129894,
0.04722290113568306,
0.02466823160648346,
0.03205196559429169,
-0.00760626932606101,
0.03562683239579201,
0.0037993118166923523,
-0.006173471454530954,
0.008023984730243683,
0.012834210880100727,
0.02754485420882702,
0.0146187674254179,
0.015221919864416122,
0.03191246837377548,
0.018923016265034676,
0.029375437647104263,
0.00499007711187005,
0.032006364315748215,
-0.0029990742914378643,
0.040026791393756866,
-0.021576955914497375,
-0.04093275964260101,
-0.03725744038820267,
0.019726742058992386,
0.02092788554728031,
0.0315619632601738,
-0.02783139795064926,
0.007353904191404581,
0.00929439440369606,
-0.03266172111034393,
0.08188619464635849,
-0.028934510424733162,
0.01825680211186409,
0.10162834078073502,
0.00004673628063756041,
0.023100007325410843,
0.0050538987852633,
-0.009917483665049076,
0.04026645049452782,
-0.008503442630171776,
0.010943802073597908,
-0.010017402470111847,
0.0701211541891098,
0.018620392307639122,
0.010843119584023952,
0.0023077160585671663,
-0.03942321985960007,
0.04120942950248718,
-0.022693630307912827,
0.0015703232493251562,
0.04258357360959053,
-0.036250971257686615,
-0.06357491761445999,
0.027142317965626717,
0.02067575976252556,
0.06684161722660065,
0.0039488887414336205,
-0.03338318318128586,
-0.08609587699174881,
-0.001909908838570118,
-0.030274441465735435,
0.03231751173734665,
-0.045722149312496185,
-0.07094533741474152,
0.047097302973270416,
-0.0208978820592165,
0.018429279327392578,
0.008351072669029236,
0.0009424576419405639,
0.0001555538474349305,
-0.03359296917915344,
0.02567065693438053,
0.011279772035777569,
-0.007179827429354191,
-0.0006908715586178005,
0.08999655395746231,
0.040058527141809464,
0.0242330189794302,
0.0062117124907672405,
-0.05160488188266754,
-0.09174854308366776,
0.024447157979011536,
-0.024182897061109543,
0.050153717398643494,
-0.022991877049207687,
0.017415832728147507,
0.00976681336760521,
0.028910163789987564,
-0.03855076804757118,
0.006719937548041344,
0.050369538366794586,
0.04259977862238884,
0.01502334512770176,
0.01761770062148571,
-0.036942258477211,
0.01963512971997261,
0.011867301538586617,
-0.0004657955141738057,
0.01775699108839035,
0.04578453302383423,
-0.03550374507904053,
-0.004062902648001909,
-0.010066477581858635,
-0.017874369397759438,
-0.02310275286436081,
-0.006521363276988268,
-0.022215593606233597,
-0.010555313900113106,
-0.07120121270418167,
-0.012608724646270275,
-0.0004675934906117618,
-0.008457384072244167,
-0.045188892632722855,
-0.02086530067026615,
0.056276172399520874,
-0.01142831239849329,
0.06640869379043579,
0.02910400554537773,
0.021357337012887,
-0.022905264049768448,
0.0013526137918233871,
0.0009965054923668504,
-0.02468670904636383,
-0.015871943905949593,
-0.03470569849014282,
-0.003283307421952486,
0.059223826974630356,
0.018279826268553734,
0.06080269813537598,
-0.050481658428907394,
-0.0041588773019611835,
0.01790408231317997,
0.020299701020121574,
-0.015508696436882019,
-0.029569031670689583,
0.01252526044845581,
-0.019689589738845825,
-0.028975410386919975,
-0.015957297757267952,
0.04480335861444473,
-0.08314364403486252,
-0.012389768846333027,
-0.058972299098968506,
0.011869433335959911,
-0.014940634369850159,
0.011640781536698341,
-0.07812721282243729,
0.04067507013678551,
-0.019816100597381592,
0.06563791632652283,
0.07786265015602112,
0.019107114523649216,
-0.005039822310209274,
0.11132650822401047,
0.0014734624419361353,
0.07584899663925171,
-0.04833268001675606,
0.04532545804977417,
0.01451195776462555,
0.01766960509121418,
-0.022750545293092728,
0.03590528666973114,
-0.040663328021764755,
0.05049519240856171,
-0.036568231880664825,
0.015706781297922134,
0.028942909091711044,
-0.06268351525068283,
0.025697018951177597,
0.06486556679010391,
-0.03750332444906235,
0.03830791264772415,
0.02207954041659832,
0.07269435375928879,
0.0010755532421171665,
-0.016745295375585556,
0.06992702931165695,
0.05208737775683403,
0.006388739682734013,
-0.0345032773911953,
-0.01839246228337288,
0.006589118856936693,
-0.028231294825673103,
0.005714245140552521,
-0.01553899422287941,
0.0022174916230142117,
-0.008815913461148739,
-0.029410414397716522,
-0.05870266258716583,
-0.06435950100421906,
-0.06527066975831985,
-0.008894180878996849,
0.07300682365894318,
0.026754315942525864,
-0.01642155461013317,
-0.04724152386188507,
-0.05122791975736618,
0.005613765213638544,
-0.0933888852596283,
-0.0283463466912508,
-0.0379316471517086,
0.0031367125920951366,
0.020043162629008293,
0.037068501114845276,
0.00619921600446105,
0.00029645717586390674,
0.035647567361593246,
-0.018194012343883514,
0.009378693997859955,
0.005348538514226675,
-0.08211960643529892,
0.01825224794447422,
-0.012024225667119026,
0.039765626192092896,
0.054536011070013046,
0.03870854899287224,
-0.06603925675153732,
-0.014641878195106983,
-0.08097851276397705,
0.04424222186207771,
0.017364341765642166,
-0.00688864616677165,
-0.019819600507616997,
-0.028574196621775627,
-0.044131018221378326,
-0.01520063728094101,
-0.040263403207063675,
0.0011927274754270911,
-0.012059331871569157,
0.0217824075371027,
-0.0037377653643488884,
0.0329604372382164,
0.05617448687553406,
-0.005378867965191603,
-0.02024710550904274,
-0.05668057128787041,
-0.010507519356906414,
0.027676358819007874,
0.08388498425483704,
0.049890805035829544,
-0.011100738309323788,
0.020376713946461678,
0.009577466174960136,
-0.02049502544105053,
-0.0157881248742342,
0.009594688192009926,
0.02323118969798088,
-0.010168944485485554,
0.036080580204725266,
-0.02204810455441475,
-0.025222986936569214,
-0.004628806374967098,
0.038556307554244995,
0.008627478033304214,
-0.045361027121543884,
0.04857984557747841,
0.033576153218746185,
0.011739572510123253,
-0.010648306459188461,
0.012965172529220581,
-0.04601185396313667,
0.02460423856973648,
0.0610201470553875,
-0.05784007906913757,
-0.02442118152976036,
0.013434477150440216,
0.045160625129938126,
0.019427092745900154,
-0.11053376644849777,
0.0013659701216965914,
0.01620050147175789,
-0.07078754156827927,
0.06958217918872833,
-0.03203703463077545,
0.02986021526157856,
-0.04862934723496437,
-0.012057620100677013,
-0.013003107160329819,
0.0032356600277125835,
0.05702456459403038,
-0.04074092209339142,
-0.013224340975284576,
0.0037993600126355886,
0.014199625700712204,
-0.05633567273616791,
-0.0017441775416955352,
-0.0010983822867274284,
0.023121505975723267,
-0.01541361678391695,
-0.044362183660268784,
0.016665279865264893,
-0.045046161860227585,
0.025905322283506393,
0.013197558932006359,
0.012693891301751137,
-0.08112652599811554,
0.03291279822587967,
0.015193535946309566,
-0.013125719502568245,
0.011986082419753075,
-0.011498344130814075,
-0.006964121945202351,
0.0225689560174942,
-0.026331380009651184,
-0.013139164075255394,
-0.018281899392604828,
0.012705327942967415,
0.011573524214327335,
0.06966444849967957,
-0.01187534537166357,
0.00011501317931106314,
-0.0402505062520504,
0.007317547686398029,
-0.02093742974102497,
0.009081339463591576,
0.05562381073832512,
-0.029363149777054787,
0.021488714963197708,
-0.050717346370220184,
0.03936304524540901,
-0.048004090785980225,
0.0032900047954171896,
0.024065431207418442,
-0.01011388748884201,
0.02071048505604267,
-0.028994886204600334,
-0.0069063282571733,
0.03153528645634651,
0.010775609873235226,
-0.03848551586270332,
-0.01269531436264515,
-0.04099077358841896,
-0.026231521740555763,
0.0486244298517704,
0.01626831851899624,
-0.024086961522698402,
-0.007417355198413134,
-0.022972440347075462,
-0.03049846924841404,
0.04329976066946983,
-0.04942076653242111,
0.02213101089000702,
-0.0824110358953476,
-0.009413959458470345,
0.05529722198843956,
-0.003184105269610882,
0.05218883603811264,
-0.018993495032191277,
0.015321046113967896,
-0.028174281120300293,
-0.05133296549320221,
-0.02667689137160778,
0.025883397087454796,
0.057735178619623184,
-0.008838598616421223,
0.034508880227804184,
-0.03182920068502426,
0.03837762400507927,
-0.00483776954934001,
-0.02770400606095791,
0.03530816733837128,
-0.09285968542098999,
0.016954192891716957,
-0.019552113488316536,
0.04305539280176163,
-0.007853006944060326,
0.011739537119865417,
-0.028229055926203728,
-0.027867648750543594,
-0.019994480535387993,
-0.036493852734565735,
-0.027608681470155716,
-0.008179495111107826,
0.004117617849260569,
-0.02179834246635437,
0.02470771037042141,
-0.0320071242749691,
0.07920344918966293,
0.0030360608361661434,
-0.06922212243080139,
-0.020732294768095016,
0.008638259023427963,
-0.09201379865407944,
-0.05179566517472267,
0.061793889850378036,
0.015308360569179058,
0.025186091661453247,
0.03693236783146858,
0.09471293538808823,
-0.01227925531566143,
-0.057015836238861084,
0.0469558909535408,
0.04815606400370598,
0.019016975536942482,
0.03723030909895897,
0.006400474347174168,
0.014004907570779324,
-0.004223091062158346,
0.0008308705873787403,
-0.028930312022566795,
0.014560374431312084,
0.008451144210994244,
-0.0018117136787623167,
0.006496858317404985,
0.011499485932290554,
0.0231697466224432,
0.028313765302300453,
0.012595906853675842,
-0.034456316381692886,
0.008211525157094002,
-0.047699764370918274,
0.009998922236263752,
-0.016689583659172058,
0.02431390807032585,
0.009968223050236702,
0.012001519091427326,
-0.00857751164585352,
-0.08739758282899857,
0.009035863913595676,
0.004919618368148804,
0.05352930724620819,
-0.044564783573150635,
-0.0347510427236557,
-0.06291905790567398,
-0.011851460672914982,
0.03875843435525894,
-0.08411652594804764,
0.03934691101312637,
0.03885171189904213,
-0.04180005565285683,
-0.035998787730932236,
-0.03132116422057152,
-0.05339590832591057,
0.060403186827898026,
-0.044776469469070435,
-0.021402984857559204,
0.009667237289249897,
0.0082786176353693,
0.0005426074494607747,
-0.007110506761819124,
-0.06237054988741875,
-0.08148586750030518,
0.015334250405430794,
-0.00968953873962164,
-0.017303794622421265,
0.012574808672070503,
0.01415804959833622,
-0.022445790469646454,
-0.032736606895923615,
-0.0008812436717562377,
0.023522932082414627,
0.0022567168343812227,
-0.017004739493131638,
0.02810312993824482,
0.021762661635875702,
-0.02549527771770954,
0.03092597797513008,
0.04621955752372742,
-0.052318647503852844,
0.011310198344290257,
-0.06974147260189056,
0.04579596966505051,
-0.03384717181324959,
-0.0320289209485054,
0.04666171595454216,
-0.06163186579942703,
0.010615570470690727,
-0.0070227691903710365,
-0.04702280834317207,
0.022167595103383064,
0.035907141864299774,
0.0031940911430865526,
-0.04808720946311951,
0.014338784851133823,
0.0035647281911224127,
-0.016555093228816986,
0.02619262970983982,
0.06667348742485046,
0.010638127103447914,
0.00227247248403728,
-0.03259749710559845,
-0.01604079082608223,
-0.014117888174951077,
0.04481259360909462,
0.02747410163283348,
0.024020656943321228,
-0.02723269909620285,
0.007410823367536068,
-0.04827823489904404,
-0.07583942264318466,
-0.006166103761643171,
0.03578047454357147,
0.03640339896082878,
0.07901456207036972,
-0.026416340842843056,
-0.008068548515439034,
-0.02203323319554329,
-0.05097093805670738,
0.0015077422140166163,
0.0029210138600319624,
0.0030739777721464634,
-0.02255607768893242,
0.029163986444473267,
0.00859742984175682,
-0.008042476139962673,
-0.06982564926147461,
0.06829284131526947,
-0.006147623993456364,
-0.04745640978217125,
-0.0006258642533794045,
-0.03153158351778984,
0.025548236444592476,
0.06960549205541611,
-0.030593784525990486,
-0.038017384707927704,
-0.010207178071141243,
-0.010688521899282932,
-0.027802273631095886,
-0.01885453797876835,
0.026015358045697212,
0.013971787877380848,
0.0587833933532238,
0.024922901764512062,
0.07413219660520554,
0.047229647636413574,
-0.02841079980134964,
-0.05090492218732834,
0.025303291156888008,
0.030116699635982513,
-0.018026893958449364,
-0.05305041745305061,
0.022650383412837982,
0.026802534237504005,
-0.03989002853631973,
-0.023320430889725685,
0.029046017676591873,
-0.013450085185468197,
-0.01705608330667019,
-0.033157024532556534,
0.03387945517897606,
0.02308928221464157,
0.018500205129384995,
0.01522753480821848,
0.011089514940977097,
0.004657801706343889,
0.020746391266584396,
0.002814088948071003,
0.043665267527103424,
0.02252775803208351,
-0.020177770406007767,
0.07001528888940811,
-0.0016993120079860091,
0.01738681085407734,
0.039727795869112015,
0.02942551113665104,
0.057585012167692184,
0.018394453451037407,
0.029276488348841667,
0.0040169935673475266,
0.033831458538770676,
0.04555690661072731,
-0.004451541695743799,
-0.005746003240346909,
0.04790875315666199,
0.0004685123567469418,
0.006310887169092894,
-0.06783940643072128,
-0.020860932767391205,
0.008193408139050007,
-0.034560710191726685,
0.024003665894269943,
0.005207264330238104,
0.05002116039395332,
0.035169098526239395,
-0.01816396974027157,
0.035319749265909195,
-0.0304268728941679,
-0.019564267247915268,
0.040935955941677094,
0.011679373681545258,
-0.061872683465480804,
0.026644136756658554,
0.003528999863192439,
-0.04543724283576012,
0.029049362987279892,
-0.007745209615677595,
-0.011087133549153805,
-0.011240622960031033,
0.005779841914772987,
-0.03529300540685654,
0.05647546425461769,
0.02914794534444809,
0.02176165208220482,
0.0396672822535038,
0.04878421127796173,
-0.03948601335287094,
-0.028283586725592613,
-0.028089605271816254,
-0.05984598770737648,
0.005758912302553654,
0.051346760243177414,
-0.03880332410335541,
-0.02954002097249031,
-0.01037648692727089,
0.039388708770275116,
-0.03865152224898338,
-0.059648461639881134,
-0.01898060366511345,
0.00420030765235424,
0.006602154113352299,
0.031353551894426346,
-0.0012149864342063665,
-0.057865630835294724,
-0.023257236927747726,
-0.03869166970252991,
0.05556101351976395,
0.002893272787332535,
0.02566058747470379,
0.0012194178998470306,
-0.04899601265788078,
0.022769201546907425,
0.02329261042177677,
0.02206038124859333,
-0.05706365406513214,
-0.012400166131556034,
-0.00737142376601696,
-0.013128319755196571,
-0.040909748524427414,
-0.024574685841798782,
0.021578332409262657,
0.030351050198078156,
-0.007243741303682327,
0.10432219505310059,
0.03986836597323418,
-0.040786173194646835,
0.0021342746913433075,
0.006631867028772831,
-0.046182822436094284,
0.04181891307234764,
-0.057408787310123444,
0.009484377689659595,
-0.056941866874694824,
-0.016043540090322495,
-0.020133525133132935,
0.018220720812678337,
0.030849946662783623,
-0.011952083557844162,
-0.052558783441782,
-0.03418853506445885,
0.028331009671092033
] |
<p>I'm reading the QFT textbook by Weinberg. In volume one chapter 10 page 451, at the lower part of the page he says,</p>
<blockquote>
<p>Now, because $\Pi^*_{\mu\nu}(q)$ receives contributions only from one-photon-irreducible graphs, it is expected not to have any pole at $q^2=0$.</p>
</blockquote>
<p>$\Pi^*_{\mu\nu}(q)$ is the sum of all one-photon-irreducible graphs, with the two external photon propagators omitted.</p>
<p>Weinberg states it within one sentence as if it's self-explanatory, but I cannot understand why it is true. Is there something simple I missed? </p>
<p><strong>Update:</strong> I think what Weinberg had in mind was Luboš Motl's answer, that why he's so brief. In addition Peskin & Schroeder used the same reasoning in page 245:</p>
<blockquote>
<p>...the only obvious source of such a pole would be a single-massless-particle intermediate state, which cannot occur in any 1PI diagram</p>
</blockquote>
<p>However P&S also put a footnote immediately after:</p>
<blockquote>
<p>One can prove that there is no such pole, but the proof is nontrivial. Schwinger has shown that, in two spacetime dimensions, the singularity in $\Pi$ due to a pair of massless fermion is a pole rather than a cut; this is a famous counterexample to our argument. There is no such problem in four dimensions.</p>
</blockquote>
<p>Thus my original question stands justified. I'd be grateful if one can give a reference that elaborates P&S's footnote. Of course explanations by any SE user himself/herself are even more welcomed. </p>
|
g2530
|
[
0.04611138999462128,
0.03996399790048599,
0.002328135771676898,
-0.0348966084420681,
0.03776881471276283,
0.014608951285481453,
0.049934323877096176,
0.03968793898820877,
0.030191125348210335,
-0.00833092350512743,
-0.03686562180519104,
0.028746675699949265,
-0.014945348724722862,
0.025127554312348366,
-0.009394189342856407,
-0.025428948923945427,
0.03028068132698536,
0.020421842113137245,
0.043089546263217926,
-0.004186796024441719,
-0.06402196735143661,
0.00046269333688542247,
0.02188553288578987,
-0.06811650097370148,
-0.011042824946343899,
-0.030723072588443756,
0.06659822165966034,
-0.058209747076034546,
0.00011835597251774743,
0.00647393986582756,
0.03992608189582825,
-0.02557065337896347,
0.016918493434786797,
-0.043718237429857254,
-0.015907132998108864,
-0.03568291664123535,
0.063639335334301,
0.014293719083070755,
0.014324726536870003,
-0.01307537592947483,
-0.048037465661764145,
0.008868644945323467,
0.027535971254110336,
-0.04802092909812927,
-0.0058770552277565,
-0.0021740247029811144,
0.002081845188513398,
0.021040724590420723,
-0.009778428822755814,
0.006661508698016405,
-0.0012048347853124142,
-0.0034317004028707743,
0.09510021656751633,
-0.00899478979408741,
0.02386409416794777,
0.04461243748664856,
0.008115680888295174,
-0.036616239696741104,
0.06409908086061478,
0.060891203582286835,
-0.048488304018974304,
0.050265077501535416,
0.07857431471347809,
-0.001934471190907061,
0.020627055317163467,
0.001279480871744454,
-0.08115527778863907,
-0.04731281101703644,
-0.022298837080597878,
0.019253825768828392,
-0.024480832740664482,
-0.08049958199262619,
-0.00189962238073349,
0.017035555094480515,
0.031162826344370842,
0.08839204162359238,
-0.008741854690015316,
-0.023851314559578896,
0.002070927992463112,
0.04732976481318474,
-0.06991858035326004,
-0.028017131611704826,
-0.004258851055055857,
0.0036777593195438385,
0.07356107980012894,
0.011956584639847279,
0.013258563354611397,
-0.02477976307272911,
-0.0257258340716362,
0.008730549365282059,
0.013181709684431553,
0.027146192267537117,
0.009567713364958763,
-0.02791721560060978,
0.04474393650889397,
-0.025385424494743347,
0.006567621137946844,
0.06731114536523819,
-0.052705068141222,
0.06931322067975998,
-0.014828825369477272,
0.06460560858249664,
0.01703675277531147,
0.011266651563346386,
-0.026435060426592827,
-0.012939412146806717,
0.07049292325973511,
-0.037686560302972794,
-0.02688288502395153,
0.023860644549131393,
-0.048594843596220016,
-0.005781218875199556,
-0.03418349102139473,
-0.020178785547614098,
-0.05737384781241417,
0.020942503586411476,
0.12642580270767212,
-0.056642793118953705,
0.04330941289663315,
0.10863161832094193,
0.013087522238492966,
-0.04254571348428726,
0.053204067051410675,
0.11210005730390549,
0.005466761067509651,
0.001233985647559166,
0.018262045457959175,
0.028202960267663002,
-0.013666404411196709,
0.008690514601767063,
-0.009743125177919865,
-0.019594086334109306,
-0.044652603566646576,
0.030729850754141808,
-0.002049293601885438,
-0.015613037161529064,
-0.0005717307212762535,
-0.01569686457514763,
0.047627389430999756,
0.012996050529181957,
-0.01953369565308094,
-0.002983119571581483,
-0.06917500495910645,
-0.013223460875451565,
-0.02375197783112526,
-0.009261729195713997,
0.03251709043979645,
-0.023167205974459648,
0.028215544298291206,
0.021443186327815056,
0.04207422956824303,
0.06845709681510925,
-0.03255465254187584,
-0.006146558560431004,
0.02936292439699173,
-0.003483016975224018,
0.05557909980416298,
-0.01670876517891884,
-0.0341368168592453,
-0.005537832621484995,
0.03966815769672394,
-0.01196175254881382,
0.0024325745180249214,
-0.03459139168262482,
-0.040296271443367004,
-0.00263303704559803,
0.006213105283677578,
-0.07384943217039108,
-0.06864474713802338,
-0.08155979961156845,
-0.022660179063677788,
-0.04850305616855621,
0.02696513570845127,
0.02252030000090599,
0.028997648507356644,
0.009329179301857948,
0.015589677728712559,
-0.0018674425082281232,
-0.06082252785563469,
0.06961646676063538,
-0.023497050628066063,
0.036803387105464935,
0.008723256178200245,
0.009416955523192883,
-0.03446903079748154,
-0.02874600887298584,
-0.04775824770331383,
0.07912041246891022,
-0.008135868236422539,
-0.003958798944950104,
-0.03897927701473236,
-0.0033270453568547964,
-0.005175441037863493,
0.047494735568761826,
-0.0006427994812838733,
0.02378384955227375,
-0.019085807725787163,
-0.046388980001211166,
0.0017048160079866648,
0.029033880680799484,
-0.018265599384903908,
0.03447062894701958,
0.023914262652397156,
-0.018082762137055397,
-0.004074819851666689,
0.015784962102770805,
-0.02111586555838585,
-0.02380014955997467,
0.07644087821245193,
-0.05298258364200592,
0.04210063815116882,
-0.03275902196764946,
0.008582902140915394,
0.03543794900178909,
-0.010986328125,
-0.07203958183526993,
-0.0107627734541893,
-0.04435042664408684,
-0.005119680892676115,
-0.007900787517428398,
0.018265163525938988,
-0.040492866188287735,
0.01896893046796322,
-0.0007695252425037324,
0.006752598565071821,
0.02172061987221241,
-0.02539847604930401,
-0.06851156055927277,
-0.06616783887147903,
0.018051261082291603,
-0.09056636691093445,
-0.04582766070961952,
-0.05684015154838562,
0.020720534026622772,
0.03983287140727043,
-0.006982664577662945,
-0.010110286064445972,
-0.0018534079426899552,
0.03624158725142479,
-0.02197602204978466,
0.04645523428916931,
-0.07160819321870804,
-0.04250748082995415,
0.02090393379330635,
0.030164038762450218,
-0.05620608478784561,
0.041527580469846725,
0.00361176417209208,
-0.030752696096897125,
0.032342150807380676,
0.0492224395275116,
-0.0008571394137106836,
0.05977797880768776,
0.06988848745822906,
-0.016790522262454033,
-0.03170640766620636,
0.048283811658620834,
0.06279133260250092,
-0.03381570801138878,
-0.03456363081932068,
-0.026367062702775,
-0.06528908014297485,
-0.0420355461537838,
-0.0008153863018378615,
-0.02785107120871544,
0.003783823922276497,
0.0020240822341293097,
0.010282178409397602,
0.014519699849188328,
-0.03945904225111008,
-0.08331184834241867,
0.06211446225643158,
0.03284713625907898,
0.0026100485119968653,
-0.010459432378411293,
-0.002214925829321146,
0.0171571783721447,
0.03873360529541969,
0.02582859806716442,
0.017285404726862907,
0.01902158185839653,
0.01379279512912035,
-0.01738918200135231,
0.03697441145777702,
0.030177494511008263,
-0.037942368537187576,
-0.01706005074083805,
0.003242364851757884,
-0.04491038993000984,
-0.013418400660157204,
-0.0649779886007309,
-0.03326432779431343,
0.04894886910915375,
-0.01866389438509941,
0.017628489062190056,
0.014123904518783092,
-0.02888929843902588,
-0.013563728891313076,
-0.013019992969930172,
0.007313071750104427,
0.019944174215197563,
0.02061016485095024,
0.012276355177164078,
-0.02908468060195446,
0.030284175649285316,
0.008355952799320221,
-0.05039907246828079,
-0.057664014399051666,
-0.053753823041915894,
0.03319563716650009,
-0.012074935249984264,
0.05835013836622238,
-0.010620060376822948,
-0.01175595447421074,
-0.015440233051776886,
0.003703787922859192,
-0.04021235182881355,
0.06269516795873642,
-0.015791216865181923,
-0.01544521376490593,
-0.03718138113617897,
0.023882035166025162,
-0.00743267172947526,
0.020617851987481117,
0.057478997856378555,
-0.015866437926888466,
-0.03818775340914726,
0.010879826731979847,
-0.022322004660964012,
0.024382928386330605,
0.04104871675372124,
-0.004935602657496929,
-0.001650721300393343,
-0.04388308897614479,
-0.08806109428405762,
-0.04350946843624115,
-0.037676870822906494,
0.052313536405563354,
0.009933673776686192,
0.04690980538725853,
-0.07144293934106827,
-0.026988493278622627,
-0.09941734373569489,
-0.015191011130809784,
0.031017422676086426,
0.01164090447127819,
-0.005620416719466448,
0.010798756964504719,
0.023042092099785805,
0.0036502948496490717,
0.01152891293168068,
0.05590926855802536,
0.017088565975427628,
0.036979883909225464,
0.004546823911368847,
0.015495378524065018,
-0.0427163690328598,
0.018068481236696243,
0.01077170018106699,
0.0358593687415123,
0.025328651070594788,
-0.0037351795472204685,
0.045456212013959885,
0.017238473519682884,
0.014235394075512886,
0.02625620923936367,
-0.034834519028663635,
-0.04370264708995819,
0.03672609105706215,
0.007690355181694031,
0.021117882803082466,
-0.017562130466103554,
-0.046978674829006195,
0.07692292332649231,
0.0009967671940103173,
-0.03597574681043625,
0.009387018159031868,
0.0010140547528862953,
-0.06144087016582489,
0.05825088918209076,
0.04503309354186058,
-0.02349819429218769,
0.04660436511039734,
0.044858504086732864,
0.028865881264209747,
0.07504052668809891,
-0.04669903963804245,
-0.009071807377040386,
-0.0438917875289917,
0.011833039112389088,
0.02855725586414337,
-0.011341617442667484,
0.021232018247246742,
0.018408481031656265,
0.01183221023529768,
-0.02168566733598709,
-0.0034497519955039024,
-0.0259700920432806,
0.016557849943637848,
0.024006381630897522,
-0.03466615080833435,
-0.0272055733948946,
-0.013056488707661629,
-0.04060302674770355,
0.03812732174992561,
-0.02547079138457775,
0.010419701226055622,
-0.033879198133945465,
0.03758459538221359,
-0.03444639965891838,
-0.034699901938438416,
0.05138012394309044,
0.010356133803725243,
-0.02774793840944767,
0.06056215986609459,
-0.01802239753305912,
-0.012524288147687912,
-0.06891022622585297,
0.018084412440657616,
-0.01156948134303093,
-0.03413863852620125,
-0.003004200989380479,
-0.022894926369190216,
-0.029082199558615685,
0.06914593279361725,
0.03744867444038391,
-0.033875662833452225,
0.03134209290146828,
-0.03243662789463997,
-0.011279499158263206,
-0.012446057982742786,
0.04387225955724716,
-0.02118086814880371,
-0.007691364269703627,
-0.03387709707021713,
0.02697969786822796,
-0.033621300011873245,
0.0336800180375576,
0.004759363364428282,
-0.003424114780500531,
0.08331010490655899,
-0.022415490821003914,
0.030747925862669945,
0.025855688378214836,
0.03544187545776367,
0.0022674689535051584,
-0.039328206330537796,
0.0020311602856963873,
0.008114386349916458,
-0.011847241781651974,
-0.015137352049350739,
-0.01996452361345291,
0.019460376352071762,
-0.0384354405105114,
0.011805941350758076,
-0.02159949392080307,
-0.009072571061551571,
0.049973975867033005,
-0.012070765718817711,
0.021556518971920013,
-0.04584140703082085,
-0.023389795795083046,
-0.0035058779176324606,
0.023162120953202248,
0.0020290925167500973,
-0.007479592226445675,
-0.10680820047855377,
0.022107599303126335,
-0.07134081423282623,
-0.07563362270593643,
0.013313638046383858,
0.03942551091313362,
0.040804989635944366,
-0.03254483640193939,
-0.020734712481498718,
-0.009700840339064598,
-0.004808916710317135,
0.01168388593941927,
-0.056522224098443985,
-0.027700034901499748,
0.024025700986385345,
-0.03007436916232109,
0.014588620513677597,
-0.017115110531449318,
0.04560205340385437,
0.028165750205516815,
-0.03567591682076454,
-0.025446221232414246,
-0.015847288072109222,
-0.010986970737576485,
-0.001802796614356339,
0.00033033941872417927,
0.05038010701537132,
0.013846045359969139,
-0.05165499821305275,
0.012260477058589458,
-0.03644749894738197,
-0.028254592791199684,
0.004685441963374615,
-0.02570260874927044,
-0.04648821800947189,
0.051559265702962875,
0.006695801392197609,
-0.0176700409501791,
0.028475340455770493,
-0.002698325552046299,
0.039905328303575516,
-0.03266844153404236,
0.023245608434081078,
-0.015591823495924473,
0.020832372829318047,
-0.03725415840744972,
0.02681891620159149,
0.011136358603835106,
0.042510587722063065,
0.03691598400473595,
-0.015998084098100662,
-0.04621085152029991,
0.005033448804169893,
-0.09462805092334747,
-0.004686878994107246,
0.023678628727793694,
-0.04472235590219498,
0.0009477542480453849,
0.07197083532810211,
0.0590999610722065,
-0.01869109459221363,
-0.05319051444530487,
-0.012387336231768131,
0.04379479959607124,
0.05669126287102699,
0.013268064707517624,
0.006654702126979828,
0.03724709153175354,
0.015926126390695572,
-0.009400290437042713,
0.060225460678339005,
-0.045385561883449554,
-0.009972608648240566,
-0.0011156682157889009,
-0.047175198793411255,
-0.013414382003247738,
0.004520014394074678,
0.05873110890388489,
0.015399775467813015,
-0.01128876581788063,
0.037488777190446854,
0.019810348749160767,
0.014235181733965874,
-0.02199544385075569,
-0.00449629919603467,
-0.040988266468048096,
0.024123061448335648,
0.007548734545707703,
-0.04900757223367691,
0.03737194091081619,
0.007767331786453724,
-0.01218497846275568,
-0.02696939930319786,
-0.041914768517017365,
-0.00017892150208353996,
0.014607694000005722,
0.030643697828054428,
-0.015213842503726482,
-0.034278422594070435,
-0.03839431703090668,
0.02206885814666748,
-0.047512564808130264,
0.027480943128466606,
-0.03746568411588669,
0.012858809903264046,
0.08105958253145218,
0.024526918306946754,
0.045120853930711746,
-0.016956428065896034,
0.0191947128623724,
0.01737101562321186,
-0.000028162330636405386,
-0.03350936248898506,
0.008452209644019604,
-0.03692559152841568,
0.07065851241350174,
0.02295423112809658,
-0.006379110738635063,
0.040697041898965836,
0.025489306077361107,
-0.07421674579381943,
0.004200965631753206,
0.04445769637823105,
0.04260724410414696,
-0.04775559902191162,
0.011168173514306545,
-0.02618379518389702,
0.00004077740231878124,
-0.006559865549206734,
-0.0029789768159389496,
0.02005596272647381,
0.030101554468274117,
-0.04558129608631134,
-0.03602513298392296,
0.045732297003269196,
0.017104415223002434,
0.04248301312327385,
0.005408564116805792,
0.022327043116092682,
0.07999125868082047,
-0.020906951278448105,
-0.019804976880550385,
0.011561927385628223,
-0.00647790776565671,
0.013478606007993221,
0.02654561586678028,
-0.038820330053567886,
-0.05345231294631958,
0.0092525165528059,
-0.07508448511362076,
-0.0077882008627057076,
0.03653313219547272,
-0.08367159217596054,
-0.006089425645768642,
0.05437531694769859,
-0.052484624087810516,
0.01773005723953247,
-0.04926063492894173,
0.061116427183151245,
0.06260894984006882,
0.019912943243980408,
-0.012109474278986454,
0.0718899518251419,
-0.01269072387367487,
-0.03883372247219086,
-0.02275131084024906,
-0.02259308286011219,
0.017785998061299324,
-0.0200679711997509,
-0.015496969223022461,
0.018221164122223854,
-0.005305711179971695,
0.06818835437297821,
0.025508176535367966,
-0.0012552577536553144,
0.02286783792078495,
0.046279218047857285,
0.017659906297922134,
-0.0507112592458725,
0.007941302843391895,
-0.0016930425772443414,
0.037410590797662735,
-0.05898306891322136,
-0.007868429645895958,
0.063318632543087,
0.02476920746266842,
-0.01738715171813965,
-0.02449464052915573,
-0.0007762197055853903,
-0.04377608001232147,
0.006528152618557215,
0.016773410141468048,
0.012268105521798134,
-0.036845479160547256,
-0.04743693396449089,
-0.025261078029870987,
-0.03249690681695938,
0.01960228942334652,
-0.030888352543115616,
0.03747277334332466,
0.02220354788005352,
-0.017302878201007843,
0.05393180623650551,
0.009816166944801807,
-0.0005535523523576558,
-0.07379574328660965,
-0.00024126606876961887,
0.016664957627654076,
-0.002713480731472373,
-0.00394876254722476,
0.04675716534256935,
0.004275319632142782,
0.009736175648868084,
-0.028197860345244408,
-0.026611285284161568,
0.03185385838150978,
0.015359577722847462,
-0.03173043951392174,
-0.07036688923835754,
-0.012912231497466564,
0.003141912631690502,
-0.008546926081180573,
0.02502993308007717,
0.04206065461039543,
0.0012853023363277316,
0.02352890931069851,
0.008695398457348347,
-0.026712417602539062,
0.0022953031584620476,
0.01585487648844719,
0.003939090762287378,
0.03555237501859665,
-0.03105488233268261,
0.02206132374703884,
0.02535475417971611,
-0.057974111288785934,
-0.05479777231812477,
-0.0004145301354583353,
0.013965685851871967,
0.014760388061404228,
0.04901428520679474,
-0.024145500734448433,
0.004178598057478666,
0.012221315875649452,
0.022730931639671326,
0.004545450210571289,
-0.034194331616163254,
-0.00318125169724226,
0.060944605618715286,
-0.00735348230227828,
-0.038412075489759445,
0.020704809576272964,
0.07575833797454834,
-0.0006340285181067884,
-0.07809033244848251,
-0.030302299186587334,
-0.07305137813091278,
-0.05015415698289871,
-0.05790651962161064,
-0.0022560968063771725,
0.06803423911333084,
-0.014703750610351562,
0.03220232576131821,
0.0273280031979084,
0.027764325961470604,
-0.007258810102939606,
-0.04013509675860405,
-0.011177820153534412,
-0.06212972104549408,
-0.041126299649477005,
-0.05439988896250725,
0.005188710521906614,
0.02147640660405159,
-0.030222922563552856,
-0.04399457573890686,
-0.010996043682098389,
-0.019742203876376152,
0.007432253565639257,
-0.041317589581012726,
-0.006991404574364424,
-0.004086451139301062,
0.008058265782892704,
0.010678941383957863,
0.024261269718408585,
-0.05699242278933525,
-0.01511603593826294,
-0.05684354156255722,
0.0597989447414875,
0.08293858915567398,
-0.07571233808994293,
0.03241679072380066,
-0.003133629448711872,
0.018369929865002632,
-0.007200838997960091,
-0.006892829202115536,
-0.008960519917309284,
0.012079563923180103,
0.04037868231534958,
-0.029617303982377052,
0.004833598155528307,
0.024639684706926346,
0.01963636465370655
] |
<p>A cylinder of mass M and radius R is in static equilibrium as shown in the diagram. The cylinder
rests on an inclined plane making an angle with the horizontal and is held by a horizontal string
attached to the top of the cylinder and to the inclined plane. There is friction between the cylinder
and the plane. What is the tension in the string T?</p>
<p><img src="http://i.stack.imgur.com/aHsY6.png" alt="Sketch of the problem"></p>
<p>Ans:
$$T =Mg\sin(\theta)/(1 + \cos(\theta))$$</p>
<p>I'm having trouble arriving at this solution.
I first look at the forces.
I set my $x$-axis such that the Force of friction is parallel with the x-axis.</p>
<p>So my forces are:</p>
<p>$F_T$ = Force of Tension<br>
$F_f$ = Force of friction<br>
$F_N$ = Normal Force<br>
$F_g$ = Force of Gravity</p>
<p>Since the cylinder is not moving. The forces and torques equal zero and balance.</p>
<p>Forces in the X direction: </p>
<p>$$0 = F_f + F_g\cos(\theta) - F_T*\cos(\theta)$$</p>
<p>Forces in the $y$ direction:</p>
<p>$$0 = F_N - F_g\sin(\theta) + F_T\sin(\theta) $$
$$F_T\sin(\theta) = F_g\sin(\theta) - F_N$$</p>
<p>$$F_T = (F_g\sin(\theta) - F_N)/\sin(\theta)$$</p>
<p>I'm not sure if I'm setting up my forces correctly. Can someone help? </p>
|
g2531
|
[
0.00679882662370801,
0.030219873413443565,
0.006035584025084972,
-0.03519833832979202,
0.0350109301507473,
0.01976577565073967,
0.054020386189222336,
-0.07185064256191254,
-0.06792161613702774,
0.041101738810539246,
-0.01250927709043026,
-0.010310741141438484,
-0.03991437330842018,
-0.05117484927177429,
0.07269779592752457,
0.08683145046234131,
0.05357842147350311,
0.017163047567009926,
0.023026788607239723,
-0.013237630017101765,
0.02546398900449276,
-0.01482531987130642,
-0.033515509217977524,
-0.02062368579208851,
0.06555503606796265,
-0.009001272730529308,
0.0031679761596024036,
0.02974734455347061,
0.007588038686662912,
-0.016268344596028328,
-0.01686086319386959,
0.013773568905889988,
0.038421835750341415,
0.016983719542622566,
-0.018506117165088654,
-0.007094365078955889,
0.03471868485212326,
0.0223691388964653,
0.043136171996593475,
-0.045736074447631836,
-0.047049351036548615,
-0.05351188778877258,
0.004461462143808603,
-0.02008988708257675,
0.009230092167854309,
-0.05004590377211571,
-0.0010362564353272319,
0.015749545767903328,
-0.01650206930935383,
-0.00514727458357811,
0.021130984649062157,
0.01423424668610096,
0.003425598843023181,
-0.0572042241692543,
-0.06307577341794968,
0.023250630125403404,
0.05674157664179802,
-0.01739802584052086,
0.004792428109794855,
0.05023116618394852,
-0.037381697446107864,
-0.023994898423552513,
0.028664372861385345,
-0.018919652327895164,
0.012838667258620262,
-0.038969047367572784,
-0.021368663758039474,
0.014896528795361519,
0.007137698121368885,
0.018270790576934814,
-0.04000554606318474,
-0.01806442253291607,
0.03296685963869095,
-0.04374753311276436,
-0.12131454050540924,
-0.02291199564933777,
0.03517579287290573,
-0.03019554726779461,
-0.01056059543043375,
-0.06634460389614105,
-0.01527880597859621,
0.05536282807588577,
0.026134058833122253,
0.0008938704850152135,
0.04008335620164871,
-0.05835367739200592,
0.051255255937576294,
0.024117114022374153,
-0.06858283281326294,
0.0338173471391201,
0.04001088812947273,
0.013533461838960648,
0.052371494472026825,
0.02618454396724701,
0.05346636101603508,
-0.03311287611722946,
-0.016185157001018524,
0.1021418496966362,
0.0007134818588383496,
-0.03177499771118164,
-0.004840437322854996,
-0.008866806514561176,
-0.018093090504407883,
-0.00895637460052967,
0.01976655051112175,
0.01913934201002121,
0.009210018441081047,
0.06668936461210251,
-0.039431001991033554,
0.0019318853737786412,
-0.026157962158322334,
0.040445517748594284,
-0.04572610557079315,
-0.06511655449867249,
0.007024766877293587,
-0.08237677067518234,
0.016416119411587715,
0.031435996294021606,
0.0013160242233425379,
0.011851634830236435,
-0.04121938347816467,
0.02128925733268261,
0.018897775560617447,
0.03782571107149124,
-0.019260721281170845,
-0.049515895545482635,
-0.008926414884626865,
0.020715463906526566,
0.031026005744934082,
-0.07290323078632355,
-0.024174891412258148,
0.0017377497861161828,
0.028544554486870766,
0.0008780667558312416,
0.018587151542305946,
0.03919754922389984,
-0.08045421540737152,
-0.05147230997681618,
0.027903394773602486,
0.0002842382527887821,
-0.03254717215895653,
-0.0029256916604936123,
-0.01177341490983963,
-0.0004768881481140852,
-0.025408171117305756,
0.007770997006446123,
-0.010295243933796883,
0.023304015398025513,
0.041601259261369705,
-0.023160697892308235,
0.026233170181512833,
0.05009806901216507,
-0.016227778047323227,
-0.02896081656217575,
-0.01877802610397339,
-0.02271457202732563,
0.044702041894197464,
-0.04105321690440178,
-0.022329501807689667,
0.003613591194152832,
0.0209027249366045,
-0.05697565898299217,
0.06381743401288986,
-0.04552541673183441,
-0.06341664493083954,
0.03286203369498253,
-0.027436254546046257,
-0.008262853138148785,
0.034029241651296616,
-0.016985706984996796,
-0.029515091329813004,
-0.015397269278764725,
0.00932646356523037,
0.005417407490313053,
-0.021083513274788857,
0.014884011819958687,
0.03759540617465973,
-0.027678698301315308,
0.036974839866161346,
0.005069532431662083,
0.02266056090593338,
-0.03371753916144371,
0.05922490730881691,
0.014510346576571465,
-0.03842655196785927,
0.023329444229602814,
0.023307353258132935,
-0.027072908356785774,
-0.0486767552793026,
0.02601260505616665,
-0.013548201881349087,
0.016171438619494438,
-0.013407111167907715,
-0.005826094653457403,
-0.030118918046355247,
-0.0030971302185207605,
0.022346623241901398,
-0.067134790122509,
0.024480272084474564,
0.039994701743125916,
0.010898387059569359,
0.018577372655272484,
0.004539602901786566,
0.012160757556557655,
-0.01348706055432558,
-0.03159444034099579,
0.044557277113199234,
-0.040404681116342545,
0.02252017892897129,
0.037099819630384445,
0.002098768251016736,
0.019997281953692436,
-0.007111548911780119,
-0.007350665517151356,
-0.016273133456707,
-0.041879694908857346,
0.03165038302540779,
0.021882247179746628,
0.008189701475203037,
-0.011817560531198978,
0.026540597900748253,
-0.03629067540168762,
-0.003744154004380107,
-0.051513589918613434,
-0.044809337705373764,
-0.04295353963971138,
-0.017772261053323746,
-0.01328074000775814,
-0.014441588893532753,
0.02443026192486286,
-0.029054386541247368,
-0.04158385843038559,
0.0407380647957325,
0.02178375795483589,
0.03356928378343582,
0.041840191930532455,
-0.0011429805308580399,
0.009072106331586838,
-0.023804640397429466,
0.04685624688863754,
-0.016325414180755615,
0.028171135112643242,
-0.020395569503307343,
-0.03430923819541931,
-0.0004352461255621165,
0.034689560532569885,
0.03329441696405411,
0.01660863496363163,
0.04627572000026703,
0.06220627576112747,
0.04472685977816582,
-0.01507230382412672,
-0.033881694078445435,
0.03501024469733238,
0.018682273104786873,
-0.03705580532550812,
-0.0671006441116333,
0.00244162674061954,
-0.02751929499208927,
-0.038023579865694046,
-0.024505537003278732,
-0.012808426283299923,
0.03264840319752693,
0.04736877232789993,
-0.08861800283193588,
-0.01696152612566948,
-0.03556114062666893,
-0.049439914524555206,
0.03464100882411003,
-0.009772601537406445,
-0.022845016792416573,
-0.0414249524474144,
-0.06671049445867538,
0.014624161645770073,
-0.023645170032978058,
0.003754490055143833,
-0.012650773860514164,
0.007931740954518318,
-0.027063816785812378,
0.014236373826861382,
0.08101101964712143,
0.0175870843231678,
0.015105917118489742,
0.009590580128133297,
0.02375134639441967,
-0.003102498361840844,
0.020249363034963608,
0.017394352704286575,
0.0171708632260561,
0.019022585824131966,
0.0025468829553574324,
0.03814390301704407,
0.05576859787106514,
-0.02109578065574169,
0.021669944748282433,
0.05382755026221275,
-0.017981937155127525,
-0.04081280902028084,
-0.04139583557844162,
0.0026746641378849745,
-0.07029858976602554,
0.014916152693331242,
0.03590431436896324,
0.017667103558778763,
0.007680442649871111,
-0.048004064708948135,
0.01711261086165905,
-0.024335788562893867,
0.036333389580249786,
0.010440201498568058,
-0.03872595354914665,
-0.009079661220312119,
0.04242759570479393,
-0.06822394579648972,
-0.025358369573950768,
0.04641931876540184,
0.019069520756602287,
0.01211435068398714,
-0.0338725671172142,
-0.0014588654739782214,
-0.04056491330265999,
-0.05237407609820366,
0.01203075423836708,
0.02922067791223526,
-0.027294375002384186,
0.04524121433496475,
-0.050752900540828705,
-0.0226019024848938,
-0.047252267599105835,
0.016704801470041275,
0.025580886751413345,
0.013500257395207882,
0.030381198972463608,
-0.048730671405792236,
-0.00200484786182642,
-0.009938458912074566,
0.021183425560593605,
-0.03793712705373764,
-0.04167798161506653,
0.016093282029032707,
-0.015249974094331264,
0.00552519503980875,
0.012561345472931862,
-0.013124394230544567,
-0.039764922112226486,
-0.010345470160245895,
-0.010456796735525131,
0.04477916285395622,
0.05135053023695946,
-0.012110322713851929,
0.03410068526864052,
-0.028282100334763527,
0.03863776475191116,
-0.02832302637398243,
0.03685580566525459,
0.02983662858605385,
0.005368419922888279,
-0.00024203934299293905,
-0.09594804793596268,
-0.0036890313494950533,
0.060181546956300735,
-0.018482228741049767,
-0.037716519087553024,
0.06146874651312828,
0.04380924627184868,
-0.012699253857135773,
-0.021210966631770134,
0.06078484281897545,
0.022753305733203888,
-0.03445620462298393,
0.004074555821716785,
0.014280099421739578,
-0.021734263747930527,
-0.01837332919239998,
0.029452824965119362,
-0.05181607976555824,
0.03167286142706871,
-0.06113462895154953,
0.019576668739318848,
0.05792558193206787,
0.015222751535475254,
-0.0036348020657896996,
-0.09007689356803894,
0.03690536320209503,
0.01919337920844555,
0.061711668968200684,
-0.014848162420094013,
0.05048651620745659,
0.04356927052140236,
0.05378473922610283,
0.0215758103877306,
-0.050326764583587646,
-0.014501473866403103,
0.03741806745529175,
-0.0002775123866740614,
0.0216789860278368,
0.02281913347542286,
0.03444486856460571,
-0.039225898683071136,
-0.08564390987157822,
0.050391435623168945,
0.006097643170505762,
0.010291757993400097,
0.03688644617795944,
-0.03139442205429077,
0.07482519745826721,
-0.020077021792531013,
-0.02402373030781746,
0.016872143372893333,
0.001991726690903306,
0.0818435400724411,
0.0063089909963309765,
-0.031068606302142143,
0.03744867071509361,
0.048549823462963104,
0.03234260529279709,
-0.008915840648114681,
0.018697859719395638,
-0.002191738225519657,
-0.03439582884311676,
0.011753753758966923,
0.1100059524178505,
0.0008558005793020129,
-0.0342455618083477,
-0.02458745241165161,
-0.024402828887104988,
-0.01251285057514906,
0.03996259346604347,
0.030148539692163467,
-0.027357948943972588,
-0.07081647217273712,
-0.04397108778357506,
0.0058896481059491634,
-0.04170092195272446,
-0.020580878481268883,
0.06913149356842041,
-0.0032178291585296392,
-0.08265971392393112,
-0.03421097248792648,
0.04634749889373779,
0.0354660265147686,
0.049958664923906326,
-0.0026068836450576782,
-0.03489386662840843,
-0.03291037306189537,
-0.012723091058433056,
-0.020526690408587456,
-0.027750536799430847,
0.0032113755587488413,
-0.04233323037624359,
-0.03420211374759674,
-0.034917641431093216,
0.01747598499059677,
-0.025696972385048866,
-0.05672546476125717,
0.01619572751224041,
-0.025488002225756645,
0.07108574360609055,
-0.003156609134748578,
-0.028431179001927376,
0.01186828687787056,
-0.01862644962966442,
-0.008936602622270584,
-0.023288609459996223,
0.017272328957915306,
0.01991007663309574,
0.01339874230325222,
0.013493130914866924,
0.01702152192592621,
-0.006920306943356991,
0.022528555244207382,
0.001563557772897184,
0.052697036415338516,
-0.029075952246785164,
-0.03952205553650856,
0.018154168501496315,
-0.0031950545962899923,
0.00488826259970665,
0.0744808092713356,
-0.015937767922878265,
-0.05144622549414635,
0.062344711273908615,
0.03223885968327522,
0.010384438559412956,
0.06521281599998474,
-0.058696623891592026,
0.02481011673808098,
0.0014838543720543385,
-0.018805433064699173,
-0.009776316583156586,
0.01331933680921793,
0.026636043563485146,
-0.05674360692501068,
-0.026766007766127586,
-0.02010943740606308,
-0.008013329468667507,
-0.015424654819071293,
-0.027219606563448906,
0.01827206276357174,
0.003043221775442362,
-0.0271201953291893,
0.033675529062747955,
-0.0023177824914455414,
0.005643458571285009,
-0.025907229632139206,
0.006927368696779013,
0.042034346610307693,
0.006896679289638996,
0.01793447881937027,
0.10564908385276794,
-0.01188377384096384,
-0.01270200777798891,
0.05607760325074196,
0.021355703473091125,
-0.02980578877031803,
-0.004337057936936617,
0.060196392238140106,
-0.006878893822431564,
0.003886515973135829,
0.04959745332598686,
0.051500897854566574,
0.02855377458035946,
0.017801910638809204,
-0.030141230672597885,
-0.00926518440246582,
0.010006158612668514,
-0.022007685154676437,
0.0555640384554863,
-0.03858814761042595,
0.010450326837599277,
-0.031039848923683167,
0.006916980259120464,
0.025560248643159866,
-0.03581320121884346,
0.043898146599531174,
-0.03270687907934189,
-0.004572360310703516,
-0.04959993436932564,
0.026405083015561104,
-0.05312572792172432,
-0.022049564868211746,
-0.03909176215529442,
0.013299827463924885,
0.004886386916041374,
-0.03660412132740021,
0.019542288035154343,
-0.09025749564170837,
-0.006167537532746792,
0.03686609864234924,
0.015955043956637383,
-0.0309873316437006,
0.062453996390104294,
-0.08029073476791382,
0.06888698041439056,
-0.0365089476108551,
0.015391524881124496,
0.018475914373993874,
-0.045363206416368484,
0.004549342207610607,
0.006897635757923126,
0.04263106733560562,
0.015387133695185184,
-0.008961830288171768,
0.030777616426348686,
-0.010020522400736809,
0.013567195273935795,
0.01970217004418373,
0.007151870522648096,
0.0010679763508960605,
0.011409462429583073,
0.010314869694411755,
0.03245270252227783,
-0.021460765972733498,
0.031227070838212967,
0.06798657774925232,
0.03269072249531746,
-0.1002620980143547,
0.004244966432452202,
-0.019322196021676064,
0.05670682713389397,
-0.00983036682009697,
0.04168001562356949,
0.01259127352386713,
-0.03650260716676712,
-0.03165557608008385,
0.037845563143491745,
-0.07802849262952805,
-0.064534991979599,
0.05545809119939804,
-0.07190913707017899,
-0.06660348176956177,
0.05467631295323372,
0.006476764101535082,
0.04429832473397255,
0.01393767911940813,
-0.026125459000468254,
0.0036357473582029343,
0.06251568347215652,
0.011390645056962967,
0.0449911430478096,
0.041422098875045776,
0.07864294946193695,
0.04567483440041542,
-0.012502964586019516,
0.04418778792023659,
-0.04515758901834488,
0.018969876691699028,
0.035634011030197144,
-0.01282347273081541,
-0.015444466844201088,
0.056890957057476044,
0.04144446924328804,
-0.044728901237249374,
0.044308848679065704,
-0.024483345448970795,
0.019297106191515923,
0.03153996914625168,
0.006659911945462227,
-0.014523821882903576,
-0.011370876803994179,
-0.007799168117344379,
0.04004386439919472,
0.016153883188962936,
-0.041215624660253525,
0.036924395710229874,
-0.049791961908340454,
-0.08328337222337723,
-0.009279374964535236,
0.03622474521398544,
-0.024725398048758507,
0.013649473898112774,
0.0027389200404286385,
0.0008488490129821002,
0.003104730974882841,
-0.03856946900486946,
0.02036125212907791,
-0.023681724444031715,
-0.0016151440795511007,
0.026937410235404968,
0.09050250053405762,
-0.008958517573773861,
0.031212443485856056,
0.016275476664304733,
-0.0643216222524643,
0.0062982612289488316,
-0.007362754084169865,
0.0205534677952528,
-0.01043667085468769,
-0.06594549864530563,
0.03162765875458717,
-0.013833161443471909,
-0.06161082908511162,
-0.045030929148197174,
0.054791297763586044,
-0.007838333025574684,
0.0032560741528868675,
-0.01990705356001854,
-0.022251781076192856,
0.015141620300710201,
-0.003991789650171995,
-0.03853300213813782,
0.0640316754579544,
0.008288858458399773,
0.013442722149193287,
-0.019109956920146942,
0.04166726768016815,
0.02967737428843975,
0.0016073191072791815,
-0.011136465705931187,
0.0459476001560688,
-0.004376781638711691,
-0.011165737174451351,
0.009400347247719765,
-0.019504515454173088,
0.00013921306526754051,
0.036721475422382355,
0.021054338663816452,
-0.00412030890583992,
-0.04193669557571411,
0.02505350485444069,
-0.01438363827764988,
-0.027233237400650978,
-0.013943185098469257,
-0.019934087991714478,
-0.00396100664511323,
-0.01330673135817051,
0.04563631862401962,
0.026041818782687187,
-0.06514831632375717,
0.007043101359158754,
0.01791602000594139,
0.08795735239982605,
-0.07999961078166962,
-0.03337717056274414,
0.026840250939130783,
-0.040587347000837326,
-0.025035133585333824,
0.07675285637378693,
0.06688947975635529,
0.004867137409746647,
0.010266107507050037,
-0.02312854677438736,
-0.04059867933392525,
0.024448541924357414,
-0.02443625219166279,
-0.01617985963821411,
-0.06332716345787048,
-0.023947592824697495,
-0.02770286612212658,
0.013456369750201702,
0.0402655228972435,
0.015519000589847565,
-0.00015526614151895046,
0.01326369121670723,
0.057983141392469406,
0.04487021267414093,
-0.07357876747846603,
0.026268232613801956,
-0.014065084978938103,
-0.027962321415543556,
-0.0799127146601677,
0.012592187151312828,
0.06241779029369354,
-0.10175367444753647,
-0.0836963802576065,
-0.018716007471084595,
-0.03570615127682686,
-0.001829387154430151,
-0.00131161417812109,
-0.015791572630405426,
-0.009447994641959667,
-0.02570069581270218,
0.027880923822522163,
0.038965675979852676,
0.024788418784737587,
-0.028424551710486412,
0.011462779715657234,
-0.036257293075323105,
0.005511793307960033,
0.010237847454845905,
-0.02732532098889351,
-0.059104420244693756,
-0.041522543877363205,
-0.03316916525363922,
0.06441625207662582,
0.0027097943238914013,
-0.039711833000183105,
0.058080874383449554,
0.004214209038764238,
0.02589796669781208,
0.003198767313733697,
-0.014686035923659801,
-0.009053301066160202,
-0.03882382810115814,
-0.0001107730931835249,
-0.0795871764421463,
0.0034733035136014223,
-0.005656607914716005,
0.025616683065891266,
-0.04872150346636772,
-0.017182836309075356,
-0.00872632022947073,
-0.0400068573653698,
-0.029438504949212074,
0.048267610371112823,
0.01609703153371811,
-0.013482713140547276,
-0.026457130908966064
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.