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The British Society for the Philosophy of Science

Origin and Concept of Relativity (II) Author(s): G. H. Keswani Source: The British Journal for the Philosophy of Science, Vol. 16, No. 61 (May, 1965), pp. 1932 Published by: Oxford University Press on behalf of The British Society for the Philosophy of Science Stable URL: http://www.jstor.org/stable/686136 Accessed: 19/05/2009 07:24 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=oup. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org.

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ORIGIN AND CONCEPT OF RELATIVITY(II)* G. H. KESWANI S WhatdidPoincare, Lorentz,atldEinsteinthemselves say aboutthe Authorship oftheTheory ? Pomcarelived for aboutsevenyearsafterthe publicatlon of Einstem's paperbutnowhere didhe creditElnstein withthediscovery of the theoryof relatlv1ty.On the contrary, he statedoftenthat Lorentzwasthe discourerer. Indeedat one placein the yearI9I2 whilementiomng someothercontributlon of Einsteln he spokeat the verysameplacelof' leprmapederelatlvlte deLorere , andhesaldso repeatedly.Andthere1Sareason forthls. Lorentz wastheiirst to use L.T.E.to explain thenullresults of expenments undertaken to discover the absolutemotlonof the earth,althoughhe did not explicitly enunaatetheprmapleof relativlty, m hlsmemoirof I904. Indeed, L.T.E.formthevehsclemwhlchtheprinclple of relauvlty movesand establishes itS dommlon in theworldof physlcswherever highvelocltlesareencountered. Of course,Pomcare waswellawareof Emstem's workandm the yearI9I I spokemglowmgwordsabouthlmwhenPomcare wasasked to glvehlsopimonof Einstem fora certasn appointment,2 butat no placedidhe attribute theicory of relatlvlthr to Einstenl.We may mentlona corroboraisve episode narrated by Mao; Born.3 Irla keture on relatlvity glvenby Pomcare m I909, at whiclsBornwaspresent, Polncare didnotsomuchasmentlon thenameof Einsteln although he mentloned othernamesandin factgaveMaxBomthelmpresslon that he wasrecording Lorentz's work. WhilePoincare considered Lorentz asthediscoverer, Lorentz himselfnevermadeanyclaimto dlediscovery.However, he sometlmes * Paroc I appearedin the prewownumber.

1Oeuvres deHenriPoincard, =, Gauth Villars,Pans,s954,p. 68o,alsoseepp. 6S44Ss. Pomcarediedm I912. Inwhatfollowswe referto thlsvolumeasOeuvres. 2 CarlSeelig,AIbert Einstem, StaplesPress,ntltsh wans.,I956, p. I34 8 MaxBorn,Phystcs anMy Generation, PergamonPress,sgS6,p. tg2 I9


G. H. KESWANI

solely. Einstem andsometlmes wlththediscovery Pomcare credited phySlCS, tO mathematlCal ofPoincare onthecontributlons Commenting hesaldm theyearI9I4: parmolen I904 qUl donnerent publiees ' Cefurentcesconslderatlons , quede l'electron sur1sdynaml lieua Pomcared'ecrlresonMemolre dontJevlensde monnoma la transformatlon danslequelil a attache se a ce proposquela memetransformatlon parler.Je dolsremarquer trouvedejadansunartlcledeM.Volgtpublieen I887 et queJen'alpas des tlrede cet artificetoutle partlpossible.Eneffet,pourcertames la Jen'alpasmdique danslesformules, qwentrent physlques grandeurs le mleux.' Celaete faltparPolncareet qulconv1ent transformatlon ensuiteparMM. Einsteinet Minkowskt.'l

de desequatlons parfalte aobtenuunemsarlance aucontralre, ' Pomcare, termes de relatlv1te'', et il a formule" le postulat l'electrodynamlque, a employer.'2 qu'il a ete le prem1er

onemwhlcheach of self-abnegatlon, spectacle a strange Wewltness hlsownclalmandcreditstheother. renounces llame Emstem's mentloned Lorentz Butlater,on manyoccaslons, expenon theMichelson-Morley at a conference only.Forexample, MillerandKennedy mentheldatMtWilsonm I927 whereMichelson, sald: werepresent,Lorentz3 the of thetlmewasalsonecessary.SoI mtroduced ' A transformatlon of refsystems diSerent for different 1S whlch tlme of local conceptlon erencewhlcharem motlon relatlve to eachother. ButI neverthought Also seep. 689. 687. Afterquotmg thls passage approvmgly, ReneDugas, op. at.,

1 Oeuvres,p. 68S. 2 Oeuvres,p.

theRublcon alonecrossed thatEinstem ttmust beemphaslsed ' Indeed, p.649,remarks, '. To thlsdistsctlon asapostulate qualified of whatPomcare aprmaple bymakLng had thatPomcare we must addthecomment andTweedledee Tweedledum between ' ' or ' law' rathermoreoftenthantheword' postulate usedtheword' prmclple (p. and,more,thatmhlsongmalpaperof I905, Einsteln to relatlvlty whenreferrmg becalled of whlchwillhereafter (thepurport 38)sald,' WewillralsethlsconJecture maknglittle ")to thestatus ofapostulate. . .', obvlously of Relanuty the" Prlnaple '. ' and' postulate thewords' pnnclple htmselfbetween distmctlon thetheoryof the alsodiscussed I928, 68, 385-388.Theconference 3 Astrophys.J., to be expected.It 1S trulysutprlsmg andtheresults experlment Michelson-Morley but mtiS rent; yetastowhat1S to beexpected opmlon thatthere1S nosettled wlthrelatlvlty. conslstetlt a nullresult1S,of course, 20


ORIGIN

AND

CONCEPT

OF RELATIVITY

thatthlshadanythmg to do wlthrealtlme. Thlsrealtlmeformewas still represented by theolderclasslcal notlonof anabsolute tlme,whlch s lndependent of anyreference to speclal Samesof coordinates.There exlstedformeonlyonetruetlme. I consldered mytlmetransformatlononlyasaheurlstlc workmg hypothesls.So,thetheory ofrelativity is reatly solelyEinsteln's work. 'Askedif I conslderthlscontractlon as a realone,I shotlldanswer " yes". It1S asrealasanythmgwe canobserve.' Up to theend(I928) Lorentz wasreluctant to glveuptheconceptlOllof absolute spaceandtlme. Whlttakerl recalls this. We now entera crltlcalstagem our mqulry.Einsteln, ma letterwrittenonlytwo monthsbeforehlsdeathmJuly,I955, hasleft on recordthathe knewnothmgaboutPomcare's workandthathe knewof onlytwo papers of Lorentz published muchearlier, beforehe wrotehlsownpaperm Igo5. We reproduce thlsletter2below: ' There1S no doubt,thatthespeclaltheoryof relatlvlty, if we regard ltS development m retrospect, wasrlpefor discovery m I905. Lorentz hadalready observed thatfor theanalysls of Maxwell's equatlons the transformatlons whlchlaterwereknownby hlsnameareessentlal, and Pomcare hadpenetrated evendeepermtotheseconnectlons.Concernsng myself,I knewonly Lorent7's lmportant workof I895 "La theoneelectromagnetlque de Maxwell"and" Versuch emerTheorle derelektnschen undoptlschen Erschemungen mbewegten Korpern "but not Lorentz's laterwork,nor the consecutlve mvestlgatlons of Pomcare.Inthlssensemyworkof I905 wasindependent. Thenew feature of it wastherealizatlon of thefactthatthebearlng of theLorentz transformatlon transcended ltS connectlon wlthMaxwell's equatlons and wasconcerned wlththenatureof spaceandtlmem general.A further newresultwasthatthe" Lorentz mvanance " 1S a general conditlon for anyphyslcal theory Thlswasformeof partlcular lmportance because I hadalready prevlously foundthatMaxwell's theorydidnotaccount forthemlcrostructure of radiatlon andcould,therefore, havenogeneral validity.' Respectfully, we mustsubmitas follows. It appearsthatEinstelnwasrecording frommemory. The two

papersof Lorentzwerenot bothpublished in I895 butin I892 and 1 E. T. Whlttalcer,A Historyof the Theories ofAethaandElectricity (I900I926), Thomas Ndson, Ig^3, p. 36 2 Max Born, op. Clt.,p. I94 2I


G. H. KESWANI

None of these papers,of course,contains theoryof the L.T.E.or relatluty. Nor do theycontam' Lorentz's of movmgbodies' m anyformthatcanberegarded electrodynamlcs onthebasisofEinstem's theprincipleofrelatlvity' as'inagreementwith paper m Einsteln's reference principles'.Theparticular ' kinematlcal assuming wlthout explained be cannot quoted earlier work toLorentz's m the theorypropounded to Lorentz's was referrmg thatEinstein seven memolrof I904. Wntingin theyearIg05,havingpublished of physics,showmg at the forefront papersdealingwlth problems of movlllg workontheelectrodynamlcs ofLorentz's awareness marked theory anewandrevolutlonary whatheconsldered bodies,elaborating lt necessary and consldermg bodies, movmg of electrodynamlcs of the findit enoughto have didEinstem torelatehisworkto thatofLorentz, manyyears whlchwerepublished of Lorentz onlythosepapers studied agov hadstudied thatEinstem isconcluslve theevldence Asto Pomcare, wasfirst of relatlvlty m whlchtheprmaple hlsScienceandHypothesis, elaborated. L.T.E.only to We must againstatethatLorentzdid not pOSlt equatlonsindeedhe didnotestabof Maxwell's invariance establish tooassumed equations.Lorentz ofMaxwell's mvarlance lishcomplete of transformatlon), equatons of Galilean thatm splteof L.T.E.(instead systems.Hesald(p. werethesamem different thelawsof mechanics to exlstm themovmg 27),' Itis clearthatthestatewe havesupposed of themassm if in E and);',theproducts systemwillreallybepossible, areto eachothermthesamerelatlon of anelectron andtheacceleratlon astheforces....' tO ' Lorentz-mVarWemust also submltthatthere1S no reference underthenewtransformaof thelawsof physlcs iance', l.e.mvarlance lt paperof I905. As we pomted out earlier in Einsteln's tlonequations group' and of Lorentz whousedthewords' mvariants wasPomcare I906. m January relatedldeasfor thefirsttlmein a paperpublished in thls Lorentz on theuseof thet^ord (Weare,of course,notmslsting thatsuch' parallel' (p.SI)didmentzon context.) However,Einsteln forma group. transformatlons for cannot account equations saidthatsinceMaxwell's It1S further is moregeneral. thenotlonof Lorentz-invariance micro-phenomena, to thiseffectinEinstemss isnostatement Tllls 1S certamly true butthere I895

respectively.l

1 H. A. Lorentz,CollectedPapers,MartlnusNijhoK,The Hague, I936, 5, rtspecelvely 22

2, I64, atd


ORIGIN

AND

CONCEPT

OF RELATIVITY

Einstem hlmselfused mvarlance of amacro-phenontenon, thepr1nclple of constancy of veloclty of light,to der1ve L.T.E. orlglnal paper.

6 Relativity according toPoincare, Lorentz, andEinstein Firstlyregarding Polncare's relatlvlty.Pomcare usedthe phrase ' thelawof relatlvlty ' mltlally1nthecontextof relatlvlty of space,2 l.e. equlvalence of all pomtsm spacefor descrlptlon of the laws of pllyslcs('local' effectsapart). Thlsdoctrme, whlchhasrecelved muchlessattentloll thanthe relatlvlty of motion, 1S perhaps equally mportant.Howdoeslt comeaboutthatallpoults mspaceareequlvalentH3 No experlment wlthmthesolarsystem, whlchasa whole1S ln motlon relatlve to thesystem of thestars, hasmdicated thatthereare diSerences m thelawsof physlcsat different locatlons in spaceor for different directlons.Islt thatm order' to applythelawof relatlvlty m allltSrlgour,lt mustbe applied to theentlreumverse ', asPomcare4 conJectured? We shallreturnto thls questlon m a laterpaper. Asanother step toBrards generalisatlon, Pomcare usedtheterm' the prmapleof relatlvity ' to mcluderelativlty of spaceaswellasof umformmotlon. Polncare, however, sawlmrnediately thattheprmctple 1Infactthlsprmclple, postulatlng mvanance of thegeometry of thewave-surface of electromagnetlc propagatlon (thesecondpostulate), ls a partlcular caseof themvananceof the wave-equatlon whlchm turn1S a partlcular caseof mvarlance of Maxwell's equatlons. Itcanbeshowneasily thattheassumptlon ofinvanance ofMaxwell's equatlons leads tO L.T.E. (More accurately, theassumptlon of invanance of Maxwell's equatlons leads to awldergroup,nanlely theconformal group. Further assumptlons (e.g.Iineanty) are necessary to extract theLorentz group. We aremdebted to oneof thereferees for thlsremark.)Infact,a muchweakerconditlon of mvanance of thevelouty of an clectromagnetlc pulse,coupledwlth plausible assumptlons basedon the physlcal SItUatlOn, 1S SUiCtt to establish L.T.E.,aswe sU seem a subsequent paper. Anmterestmg questlon 1S: To whatextent doMaxwell's equanons already lmply thelrownmvarlance? Islt, asMaxBorncongectures, thatISorentz trarnformatlon 1S SU1lIltRlllSlC property ofMaxwell's equatlons?(Naturat Philosophy o+Cause andChance, Oxford,I949, p. 27). A superfiaal exammatlon of Maxwell's equatlons onceshowsthatcharge1S already lmpliedto be mvanant, l.e. measure (p)ls mdepelldent of because we at

ItS

ItS

motlon

(u)

wnte

curlH-(a

+ pU),

forallvaluesof u. 2 H. Pomcare, Sclence andHypothests, Dover,p. 77 3 Einsteen (p.44)usesthewords' homogenaty whlchweattnbute tO space and tsme'. 4 H. Poscard, op.at., p. 77 23


G. H. KESWANI

wasnotaltogether of general validity and,m partlcular, thatlt wasnot true of accelerated motlonorevellof uniform rotatlon. Iftheskywere forevercovered withclouds,saldPo1ncare, andlf wehadnomeansof observmg the stars,we mlght,nevertheless, condudethattheearth tUNlS round, because flattemng at thepolesandFoucault's pendultlm wouldrevealthlsrotatlonal motlon.l No observatlons on thestars needbecarried outtodetermlIle themotlonoftheeartllwlthreference to theabsolute systemof thestars. (Weshallseeln alaterpaperhow thepossibility thatlt 1S thesystemof thestarsthatrotates andtlOt the earthmustbeexcluded.)Therotatlonal mot1on ls,therefore, not relaiive to anyreference frame, butrelatlve onlytoonesystem andoneonly; st is absolute.Theprmc1ple of relatlv1ty 1S not, therefore, generally valid. 'l'hat1S whyPomcare thoughtlt was' battered '. Ponderlng overtheeffects ofrotatlonal motlon,he asked, ' Canathmg turnwlthout turmngwlthrespect to somethmg? '2 Andwhatcouldbethls something,whlch1S, as lt were,everywhere? Ratherfortunately, theyoungEinstem wasnot besetwlththese doubtsabouttheprmclple whenappliedto noll-uniform motlonand launched relatlvlty on ltS trlumphant careerthatwe knowof so well. Ofcourse, hehadto return to Pomcare's mlSg1VlNgS later,butwlththe courage olllya youthcouldpossess, Einsteln sawonlywhatneedhave beenseenthen(I905), a partlal butlnsplrmg V1sl0n.Polncare saw lt complete w1thlongslladows of doubtw Nevertheless, Polncare contmued to developtheprulclple of relativity of uniform motlonof translanon andobtamed almostall the essentlal results beforeEinstem.Occaslonally hepaldlip-servlce to the aether3 whlchhe neverdefinedsuilciently clearly or, at any rate, categorlcally. There1S nottheslightest doubtthatEinsteln (p.38)was thefirstto proclalm unequlvocally thattheaethersoncept 1S superfluousif theprlnclple of relatIvlty 1S to hold(not to mentson Important developments suchastheformula forcompounding velocltses andthe relatlv1stlc theoryof theDopplereffect). Buthe wasableto clotlllS becausehe disregarded (orprobablydid not appreclate) the difficulttes the prlnclpleof relatlvityhadthen(Igo5)to facelf non-unifornl and rotaiional motlonswereconsjdered. H. Pomcare,op. Clt.p. II4 Ibld.,p. II4 3 In the discusslon on pagesI69I72, ibld.,for example,Pomcarecategorlcally demesthe aether,but the remarkat tlle top of page244, ibld.,makeshls posltlon uncertam.Thlsstateof beliefperslsted rlghtup to hls death. 24


ORIGIN

AND

CONCEPT

OF RELATIVITY

Whereas Pomcare andEinstem m thetrldeason relatlvlty nweant morenearlythesamethmg, Lorentz's baslcldeasweredifferent, ashe himselftoldusagamandagam. lIe firmlybelieved ln anaether,the domamof absolute tlmealldabsclute space. MotlonrelatlvetOthjS aethr produced ' real' changes.InI92Ihecompared 1th changein lengthdue tO mOt10n, tO the changeproducedI)y tenlperature. Ehrenfest,2 whosucceeded LorenFz m111S cllalr at Lelden, tells us clearly aboutLorentz's conceptlon of theaetller ' Statlonary aethermeantfor Lorelltz,JUstas lt alreadydid for Inrenesl, statlonary wlth respectto somethlnglike the worldof the fixedstars.'

Whatarethephyslcal consequences of postulatlon of SUCI1 anaetller? Arethelawsof physlcs wltlllnvanoussystems movmgunlformly sslth reference to thlsaether different?Ifnot,whatis theuseof postulatlng anaddinonal reference frameof tlleaether; To tlleseandotherquestlons,we shallturnln subsequent papers.It 1Sto be clcarlync)tcd, hovwrever, thataethercact conslstently be postulated lf lt 1Sa111nertlal s+;,stenz andexpenmental results conslstent wlthrelatlvlty willnot tllus l)evlolated.Thequestlon reallyiswhetller lt ls necessary todesoandif arethephys;cal consequences of suchanaethel .3 SO Wllat

7

Mi1lkotvski

Although Einsteln regected thenotlonof theaetheror analesolute frameof reference, derlved L.T.E.,whlcllhadonlyl:cenposlted adhoc by Lorentz earlier, andestablished somenew results ln hls paper of 190s,there evldence thathehadnot yet fullydolnlnated thetlleorarhe 1S

H. A. I orentz, Nature,I92I, I06, 794 C(llectedSetent,ific Paper.s of PaulEllrcwffest, North-HollaIldPub. Co., IgS9, p. 474 3 Yearsago (in 19II) von Laue saxd,' A really experlmentaldeaslon ben7Seen the

2

theoryof Lorentzandthetheoryof relatlvxty ls sndeedno. to be gamed,andthatthe fornler,m splteof thls,llasrecededmtothebaclcgroulld, ls chleflydtteto tllefact,that closeasstcomesto thetlleoryof relatlvlty, lt still lacksthcgreatunlversal prmclple, the possesslon of whlchlendsthetheoryof relatlxrlty anImposlng appearance.' Quoted n MaxJammer,ConcertsoJvSyace, Harvard Unlv Press,I954,p. I42. H. Margenau andR. A. Itlouldmorerecentlywrotcslnlilarly, ' If thelavirs of natureareof thesame formwltll respectto all firames of reference, tllentheyareof thatformm anyclloserl frameof reforence.. . Clearlyxtdoesnot makesenseto speakof settling the matter betweenEinstemandLorentzby experlment. . What1S slgnificant aboutEinstclll's prlnaple1S thatlt 411 be nzantalncd,not thatIt nlustbe mamtamed.'' Relatllty: An EplstemologlcalAppralsal', P11illxsophy of Sc1ellve, I957, 24, 303. 2S


G. H. KESWANI

on Einstem's paper, propollnded. Butbeforevwre crltlcally comment we mustmentlon arevolutlon whlchtumedthetheoryfromltSsomeanel whatturbldbegmnmgs mto clarltyln physlcalmterpretatlon mathematlcal representatlon alike. Themanwhobroughttlus aboutwasMiiowskl. He wentfor thoughhe closely hlsmspiratlon neltherto Lorentznorto Einsteln, waslikely traced andextended Pomcare's lineofthought. Minkowskl not aware ofPomcare's work. Histwlnconceptjon ofa44imensional frompurely space-tlme contsuumandltSmvarlant metncstemmed tensorsm the geometncal roots. Indeedlt washe who mtroduced wayof pretheoryof relatlvlty.So revolutionary was Minkowski's ' Sincethemathematsentatlon andanalysls thatEinsteln 1remarked, I do not understand lt clanshavemvadedthetheoryof relatlvlty, of myselfanymore'. Minkowskl wasthefirsttruemathematician relatlvlty. to Minkowski's way of What1S remarkable 1S thataccordmg presentation ' relatlvlty'becamelessslgnlficant.Thekeywordhere whattheSameof was' invanants ', whlchremamed thesamenomatter of thesewasthe reference mwhlchtheyweremeasured.Theslmplest 1lluniform translatlonal 4Ximenslonal metncof space-tlme. A partlcle ' word-line ', anelement motlondescribes an mvarlant 44imenslonal of whlcllat the' world-pomt ' (x,y, z, t ln anysnertlal frame)1S

dT -v(c2dt2 dx2

d-dZ2)

at the betngphyslcally the(proper) tlmemeasured bya clockstatlonary dr remams the partlcle ltself. Whatever be the frameof reference, differeniial. same. It1S to benoted,however, thatdr1S nota complete worldli?es,|dT,tlle Thus,fortWo worldpomts connected bytwodigerent mtegral of s proper'tlme,doesnothavethesamevalue. However, motion can mtersect m no theworldlillesof two particles m uniform morethanonepomt. elements, so to speak, preMinkowski drewattentlon to theabsoltate nomatter served mthefluxof space-tzme (world) whichdidnotchange wlthoutMinkowski's whattheframeof reference mlghtbe. Indeed, wouldnot ideas,thedevelopment of thegeneraltheoryof relatlvlty later. havebeenpossible, asEinsteln hlmselfacknowledged

TheLibrary of 1 Quotedby A. Sommerfeld m Albert EinsteinPhilosopher-Sclentist, LlvlngPhilosophers, I949, p. I02 26


ORIGIN

AND

CONCEPT

OF RELATIVlTY

It1S snterestig to know whatMinkowskl hlmself thought of the originof theideasassoaated wlthrelativlty-theory. Hehaslefton record 1: ' Thevalidity wsthout excepeon oftheworld-postulate, I liketo tht, thetruenudeusof anelectromagnetlc lmageof theworld,wlllch discovered byLorentz, andfurther revealed byEinstein, nowliesopenmthe fulllightof day.' 1S

8 Criticism ofEinsfein's Paper

Aswe remarked earlier, Einstem wasthefirstto deriveL.T.E.from thepostulates of (i)relatlvlty and(ii)constancy of velocltyof lightm allframes of reference.Lorentz hadonlyassumed theseequatlons, and thoughPomcare clearlysawthattheseequatlons wereconslstent wsth theprmclplW of relauvlty, andapparently alsosawthattheydemanded anupperlimltof velocltles equalto thevelocltyof light,he madeno attemptto derlveL.T.E. Did heconslder thlstrlvlal?We do not know. It appears tO US, however, thatEinstem's ongmalderlvatlon 1S not satlsfactory. Einsteln (pp.44 45),usesvelocitesof lightpropagatlon equalto (c v), (c+v) and utterdisregard of hls own second postulate.Wemustnotethattheseveloclties of light-propagatlon,m Einstem's derlvatlon, arephyslcally measured (i.e.observable) velocltlesandnot certamquantltles m an algebraic calculatlon.It is mterestmg to seeexactlyhow Einstem established L.T.E.andwe, therefore, glvehlsmethodalongwithsomecomment mAppendix A.2 NorwasEinsteln yet m possesslon of the4Qimenslonal concept. Afterdevelopmg Lorentz's equatlons, Einsteln (p.46)usesthemto transformthe sphencalwave-front of lightln one frameglvenby the /(C2

v2)

in

equatlon x2 +y2 into

+,<,2

_s2t2

0

another framemovmgrelatlxre tO thefirstandgets xt2 +yt2

+zw2

c2t2

0

He(p.46)nghtlyconcludes: ' Thewaveunder conslderatton 1S, therefore, no lessa spherlcal wave W1th areloclty of propagatlon c whenorzewed m themovmgsystem.' Butwhenconsidering theenergycontamed wltllmtheexpanding wave-front of lightas observed m the two systems, Einsteln (p. 57) asserts: 1H.Minkowskl, ' Space andTime', ThePrttlclpleofRelativity,DoverPublications, 2 Alsoseethelatter part of foomote I, p. 294,Part I. 3 27

p. 9I


G. H. KESWANI ' Thesphencalsurface vlewedm the movmgsystem surface... '

1S aIl ellipSOldEl

! ellipsold of theexpanding to workouttheequatlon Hethenproceeds Remarks g Concluding

onthe to bedrawn1S thateachoneof usstands Theoneconcluslon than of othersandonlythuscanevena genlusseefarther shoulders to thls. alsoconforms of relatlvity-theory others. Thedevelopment of diswhotalkedof relatlvlty firstandforemost, ItwasPomcare, motlonforumform of relatlve orspaceandoftheprmclple placements wlththe theoryof andof varlousnovelldeasassoclated translatlon, wasnottrueofnonthattheprmclple henotlced relatlvlty.However, effectsdueto nonto findabsolute motlon. It waspossible umform the reJect categorlcally therefore, did not, motlon. Pomcare uniform he frameof reference.Although oranabsolute concept of tlleaether theprlnto develop hecontmued besetwlthdoubts, wasconsequently theconmotlonandlt washewhorecogmsed relatlve clpleof uniform andLorentztransformatlon of relatlv1ty theprmclple nectionbetween byLorentz. posltedearlier equatlons, andprobably ldeasof Polncare knewof the ploneermg Einsteln he didnotsayln but unfortunately equatlons, transformatlon Lorentz's there1S no lusowncontributlon; paperwhatwasstrlctly hlsorlgmal to reference a general workatallexceptmg to anyprevlous reference But Einstelndid not only Lorentz'stheoryof electrodynamlcs. andderlveL.T.E. notma satlsfactory analytlcally thesubJect advance untheaether-concept firstto reJect also the but he was though way, ofrelatlvlty, thecreed thefirsttruebelieverm thusbecommg equlvocally, pa1dno heedto had,however,apparently ltS prophet.Theprophet thedoubter,then. It wasa by Pomcare expressed theuncertalntles thathedidnot. blessmg of relatluty, to theprmclple contributlons therelatlve To measure we m1ghtquoteMaxBorn1: ' Einstem'swork was the keystoneto an archwhlchLorentz,Polncare erectedby and othershad builtand whlchwas to carrythe structure Minkowskl. I thlnklt 1S wrongto forget theseothermen.... '

couldbe andwe mlghtaddwhateverymasonknows;thekeystone ofthe falsework and the was there ofthe arch the rest ollly when placed onlyafterthewholearchwascomplete. aethercouldberemoved Max

PergamonPress, I9S6, Born,Physicsin My Generation,

28

p. I95


ORIGIN

AND

CONCEPT

OF RELATIVITY

But that1S not the only story. The problemof non-uniforln motlonhadyetto be tackled andtheveryprmclple of relatlvlty subJected to a more cntlcal examinatlon, as we shall see. Allthmgs must changeandnlanmustcontmue .... to hope611hopecreates From ltS own wreck the tllmg lt contemplates. P. B. Shelley,PrometheusUnbound BI8, SouthExtenslon(PartII), New Delhl, I6 India

APPENDIX A

Einstein's Original Derivation ofL.T.E.

Wefirstreproduce Einstem's demonstratlon andthenbneflycomment on lt. (ThePrinciple ofRelativity, Dover,pp.43-46) Toanysystemof valuesx, y, z, , whlchcompletely defines theplace andtlmeof aneventmthestatlonarysystem[K], therebelongsasystemof values {,77,C,, determmmg thateventrelatlvely to the[movlng] system k, andourtask1S nowto findthesystemof equatlons connectmg these quantltles.

Inthefirstplacelt 1Sclearthattheequatlons mustbelinear on account of thepropertles of homogenelty whlchweattribute to spaceandtlme. If we placex' x vt,lt ls clearthata pomtatrestmthesystemk musthavea systemof valuesx', y, z, mdependent of tlme. We first defineT asafunctlon ofx', y, z andt. To dotiS wehaveto express ln equatlons thatT 1Snothmgelsethanthesummary of thedataof clocksat restln systemk, whlchhavebeensSrnchronlzed according to therule glVen

m % I.

Fromtheorlgmof systemk leta raybeemltted atthetlmez0along theX-axlstox',andatthetlmer1bereflected thenceto theorlglnof the co-ordinates, arrlvmg thereat thetlmeT2; wethenmusthavei (z0+T2) 1, or,bymsertmg thearguments of thefunctlon z andapplymg the prmclple of the constancy of the velocltyof lightm the statlonary system. r (o,

o, o, t)+T(o,

o, o, t+

_

+

+

)

-(x',

Hence,lf x' bechosenmEimteslmally small, i(c-v+c+v)at

=ax' +c-vuat 29

o, o, t+-).


G. H. KESWANI

aT v aT ax'+c2 v2at ?

or

It is to be noteddlatlIlstead of theonglnof theco-ordinates wc mlghthavechosenanyotherpOlXlt forthepomtoforigmoftheray,and theequatlon JUSt obtallled 1S therefore validforallvaluesof x', y, z. An analogous conslderatloapplied to the axesof Y andZ-It beingbornem mmdthatlight1S alwayspropagated alongtheseaxes, whenvlewedfromthestatlonary system,wlththeveloaty /(C2

glves

v2),

us

aT -

by

SinceT 1S a

linear

aT

=O,

-

- O.

az

functlon, lt followsSom theseequatlons that /

v

\

T -a tt ) wherea 1S a functlon +(v)at present uTllcnown, andwhereforbrevlty lt 1S assumed tMt at theorlgm of k,z o, whent - o. Withthehelpof tiS resultweeasJydetere thequantlties {, , 4 byexpressing m equatlons thatlight(asrequlred bytheprmapleof the constancy of theveloatyof lightX m combmatlon wlththeprmapleof relaavity)1S MSO propagated th veloaty c whenmeasured m the movmgsystem. Fora rayof lightemlttedat thetlmeX o in the directlon of themcreastng gt

ore-aXt

{-CT

ca_u2x)@

Buttheraymovesrdatlvelyto theimttalpomtof k,whenmeasured in thestatlonary system,wlththeveloaty c v, so that x c-v

If we msertdusvalueof t m dleequatlon for{, we obtaxn {

aC2_V2X-

Inananalogous manner we find,byconsidermg raysmovmgalongthe twootheraxes,that / -

when v(Y

V

,\

v2X)

cT-aftf-c2

H)-,x'=o.

3o


ORIGIN AND CONCEPT OF RELATIVITY

Thus n

V2)Y md 4

2

av(

a(c2-v2)

forx' ltS value,we obtam Substitutmg z +(v),B(tvx/c2). t-i(v),B(x vt), 72- g9(V)y 4-+(v)z,

where (I

p

V2/c2)'

of v.' functlon and+ 1Satlasyetunknown thereis an +(v)is latershownto be equalto unity. Incidentally, notatonalslip. The functlona ajooveis alsocalled inconsequental +(v)butin fact I

ff (C2_)

+(V)

V2/C2), i.e. a (I of light-propagausedvelocitles Einsteln earlier, Aswe mentloned overtly, andyet got the tlOllequalto (c-v), (c+v) and(C2-) for L.T.E. The steps correct end result,the usualexpresslons thedemone?ectandapparently compensating takenhavea curiously theresult. wasdnventowards stratlon to theabovedemonfigure,we hope,corresponds Theannexed alongie x andf happegs we consider strat3on.Inthiscomment axesotlly. k (6.Q.g,) K (xty,z,)

,,

We-

'

=ZZVt

O b_

themog Einstein mtroduces K must point at rest in ie system

b

x' _ x-vt sothat: ' a coKrdinate havea system of valuesx', y, z inde

of tlme'. pendent 3 *

V

X

3I


H. KES WANI

G

5t,as A rayleavestheonglno of Kat ame r0, travelsa distance ofKattlmer2. totheorigino mK,mtlme(r1 -T2) andreturns measured ofconstancy ofthevelocity oflightinthemovtheprinclple Applylng relatlonshlp: wrltesehecorrect K,Einstem mgsystem t1

=

i(to+72)*

tO the corresponding or arrival However,thetlmes of departure systemKareglvenasfollows, inthestatlonary t!:lree eventsasmeasured oftheveloclty of collstancy theprmc1ple ' applymg agam,lt 1S asserteds system': oflightln thestatlonary x

x

t, t+ c

x

+ - .

andt+ c

v

v

c+v

to thetlal point (orlglI) ' theraymovesrelatlvely Thestatement, system (K),wlththeveloclty m thestatlonary of K wherlmeasured (c-v), etc.' 1S phySlCauy d?lCdt to foHow. Wecaot meanmgfUly to a pointof one inertlal system relat1ve speakof veloatyof a light-ray (K). u1another systenl (theorigmof K) butaslt (veloaty)is measured asfollows:x' issomelength(measured seemsto proceed Theargunaent rays systemK) whlchtheoutgoingandreturmng n the statlonary (c-v) and(c+v) relatlveto theorlgmof the traverse wlth veloclty K,thequotlents-and + bemgthecorrespollding movulgsystem ts operatlonally m K. The procedure as measured tlmelntervals, th thesecondpostulate. IlOt m confornalty vagueandcertamly are,n1Emstenl's It 1S t0 be notedthat(c v),(c+v)andV(C2_v2) m K andnotascertaln of light-rays asvelocltles consldered exposltlon, process. ln allalgebralc quantltles usedthe word 'event', he did althoughEinstelll Incldentally, not use the 44imenslonalspace-tlmeconcept.For a slmilar NobelPrize Winnersitl Physics remarksee. N. H. de V. Heathcote, New York,I9^3,p. I95). The latter concept was due (Schuman, andwasfurther earlier mtlllS paper, (I906), asweremarked to I'omcarc by Minkowskl.In 44imentndependently, apparently delreloped, X tlme. 1S nottlme buta/-I tllefourthcoKrdinate s1onal space-t1me,

32


Origin and concept of relativity ii[1]  
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