The British Society for the Philosophy of Science

Origin and Concept of Relativity (II)Author(s): G. H. KeswaniSource: The British Journal for the Philosophy of Science, Vol. 16, No. 61 (May, 1965), pp. 19-32Published by: Oxford University Press on behalf of The British Society for the Philosophy ofScienceStable URL: http://www.jstor.org/stable/686136Accessed: 19/05/2009 07:24

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available athttp://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unlessyou have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and youmay 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 athttp://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 printedpage of such transmission.

JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with thescholarly community to preserve their work and the materials they rely upon, and to build a common research platform thatpromotes the discovery and use of these resources. For more information about JSTOR, please contact support@jstor.org.

Oxford University Press and The British Society for the Philosophy of Science are collaborating with JSTOR todigitize, preserve and extend access to The British Journal for the Philosophy of Science.

http://www.jstor.org

G. H. KESWANI

S What did Poincare, Lorentz, atld Einstein themselves say about the Authorship of the Theory ?

Pomcare lived for about seven years after the publicatlon of Einstem's paper but nowhere did he credit Elnstein with the discovery of the theory of relatlv1ty. On the contrary, he stated often that Lorentz was the discourerer. Indeed at one place in the year I9I2

while mentiomng some other contributlon of Einsteln he spoke at the very same placel of' le prmape de relatlvlte de Lorere , and he sald so repeatedly. And there 1S a reason for thls. Lorentz was the iirst to use

L.T.E. to explain the null results of expenments undertaken to discover the absolute motlon of the earth, although he did not explicitly

enunaate the prmaple of relativlty, m hls memoir of I904. Indeed, L.T.E. form the vehscle m whlch the princlple of relauvlty moves and establishes itS dommlon in the world of physlcs wherever high velo- cltles are encountered.

Of course, Pomcare was well aware of Emstem's work and m the year I9I I spoke m glowmg words about hlm when Pomcare was asked to glve hls opimon of Einstem for a certasn appointment,2 but at no

place did he attribute the icory of relatlvlthr to Einstenl. We may mentlon a corroboraisve episode narrated by Mao; Born.3 Irl a keture on relatlvity glven by Pomcare m I909, at whicls Born was present, Polncare did not so much as mentlon the name of Einsteln although he mentloned other names and in fact gave Max Bom the lmpresslon that he was recording Lorentz's work.

While Poincare considered Lorentz as the discoverer, Lorentz him- self never made any claim to dle discovery. However, he sometlmes

* Paroc I appeared in the prewow number. 1 Oeuvres de Henri Poincard, =, Gauth Villars, Pans, s954, p. 68o, also see pp.

6S44Ss. Pomcare died m I912. In what follows we refer to thls volume as Oeuvres. 2 Carl Seelig, AIbert Einstem, Staples Press, ntltsh wans., I956, p. I34 8 Max Born, Phystcs an My Generation, Pergamon Press, sgS6, p. tg2

I9

ORIGIN AND CONCEPT OF RELATIVITY (II)*

G. H. KESWANI

credited Pomcare wlth the discovery and sometlmes Einstem solely. Commenting on the contributlons of Poincare tO mathematlCal phySlCS,

he sald m the year I9I4:

' Ce furent ces conslderatlons publiees par mol en I904 qUl donnerent lieu a Po mcare d' ecrlre son Memolre sur 1s dynaml que de l ' electron , dans lequel il a attache mon nom a la transformatlon dont Je vlens de parler. Je dols remarquer a ce propos que la meme transformatlon se trouve deja dans un artlcle de M. Volgt publie en I887 et queJe n'al pas tlre de cet artifice tout le partl possible. En effet, pour certames des grandeurs physlques qw entrent dans les formules, Je n'al pas mdique la transformatlon qul conv1ent le mleux. ' Cela ete falt par Polncare et ensuitepar MM. Einstein et Minkowskt.'l

' Pomcare, au contralre, a obtenu une msarlance parfalte des equatlons de l'electrodynamlque, et il a formule " le postulat de relatlv1te'', termes qu'il a ete le prem1er a employer.'2

We wltness a strange spectacle of self-abnegatlon, one m whlch each renounces hls own clalm and credits the other.

But later, on many occaslons, Lorentz mentloned Emstem's llame only. For example, at a conference on the Michelson-Morley expen- ment held at Mt Wilson m I927 where Michelson, Miller and Kennedy were present, Lorentz3 sald:

' A transformatlon of the tlme was also necessary. So I mtroduced the conceptlon of local tlme whlch 1S different for diSerent systems of ref- erence whlch are m motlon relatlve to each other. But I never thought

1 Oeuvres, p. 68S. Also see p. 689. 2 Oeuvres, p. 687. After quotmg thls passage approvmgly, Rene Dugas, op. at.,

p. 649, remarks, ' Indeed, tt must be emphaslsed that Einstem alone crossed the Rublcon by makLng a prmaple of what Pomcare qualified as a postulate '. To thls distsctlon between Tweedledum and Tweedledee we must add the comment that Pomcare had used the word ' prmclple ' or ' law ' rather more often than the word ' postulate ' when referrmg to relatlvlty and, more, that m hls ongmal paper of I905, Einsteln (p. 38) sald, ' We will ralse thls conJecture (the purport of whlch will hereafter be called the " Prlnaple of Relanuty ") to the status of a postulate . . .', obvlously makng little distmctlon htmself between the words ' pnnclple ' and ' postulate '.

3 Astrophys.J., I928, 68, 385-388. The conference also discussed the theory of the Michelson-Morley experlment and the results to be expected. It 1S truly sutprlsmg

that there 1S no settled opmlon yet as to what 1S to be expected m tiS rent; but a null result 1S, of course, conslstetlt wlth relatlvlty.

20

ORIGIN AND CONCEPT OF RELATIVITY

that thls had anythmg to do wlth real tlme. Thls real tlme for me was still represented by the older classlcal notlon of an absolute tlme, whlch s lndependent of any reference to speclal Sames of coordinates. There exlsted for me only one true tlme. I consldered my tlme transforma- tlon only as a heurlstlc workmg hypothesls. So, the theory of relativity is reatly solely Einsteln's work.

'Asked if I conslder thls contractlon as a real one, I shotlld answer " yes ". It 1S as real as any thmg we can observe.'

Up to the end (I928) Lorentz was reluctant to glve up the concep- tlOll of absolute space and tlme. Whlttakerl recalls this.

We now enter a crltlcal stage m our mqulry. Einsteln, m a letter written only two months before hls death m July, I955, has left on record that he knew nothmg about Pomcare's work and that he knew of only two papers of Lorentz published much earlier, before he wrote hls own paper m Igo5. We reproduce thls letter2 below:

' There 1S no doubt, that the speclal theory of relatlvlty, if we regard ltS

development m retrospect, was rlpe for discovery m I905. Lorentz had already observed that for the analysls of Maxwell's equatlons the transformatlons whlch later were known by hls name are essentlal, and Pomcare had penetrated even deeper mto these connectlons. Concern- sng myself, I knew only Lorent7's lmportant work of I895 "La theone electromagnetlque de Maxwell" and " Versuch emer Theorle der elektnschen und optlschen Erschemungen m bewegten Korpern "- but not Lorentz's later work, nor the consecutlve mvestlgatlons of Pomcare. In thls sense my work of I905 was independent. The new feature of it was the realizatlon of the fact that the bearlng of the Lorentz transformatlon transcended ltS connectlon wlth Maxwell's equatlons and was concerned wlth the nature of space and tlme m general. A further new result was that the " Lorentz mvanance " 1S a general conditlon for any physlcal theory Thls was for me of partlcular lmportance because I had already prevlously found that Maxwell's theory did not account for the mlcrostructure of radiatlon and could, therefore, have no general validity.'

Respectfully, we must submit as follows. It appears that Einsteln was recording from memory. The two

papers of Lorentz were not both published in I895 but in I892 and

1 E. T. Whlttalcer, A History of the Theories of Aetha and Electricity (I900I926), Thomas Ndson, Ig^3, p. 36

2 Max Born, op. Clt., p. I94

2I

G. H. KESWANI

I895 respectively.l None of these papers, of course, contains L.T.E. or relatluty. Nor do they contam ' Lorentz's theory of the electrodynamlcs of movmg bodies ' m any form that can be regarded as 'in agreementwith the principleofrelatlvity' on the basis of Einstem's ' kinematlcal principles'. The particular reference m Einsteln's paper to Lorentz's work quoted earlier cannot be explained wlthout assuming that Einstein was referrmg to Lorentz's theory propounded m the memolr of I904. Wnting in the year Ig05, having published seven papers dealing wlth problems at the forefront of physics, showmg marked awareness of Lorentz's work on the electrodynamlcs of movlllg bodies, elaborating what he consldered a new and revolutlonary theory of the electrodynamlcs of movmg bodies, and consldermg lt necessary to relate his work to that of Lorentz, did Einstem find it enough to have studied only those papers of Lorentz whlch were published many years agov

As to Pomcare, the evldence is concluslve that Einstem had studied hls Science and Hypothesis, m whlch the prmaple of relatlvlty was first elaborated.

We must again state that Lorentz did not pOSlt L.T.E. only to

establish invariance of Maxwell's equatlons indeed he did not estab- lish complete mvarlance of Maxwell's equations. Lorentz too assumed that m splte of L.T.E. (instead of Galilean equatons of transformatlon), the laws of mechanics were the same m different systems. He sald (p. 27), ' It is clear that the state we have supposed to exlst m the movmg system will really be possible, if in E and );', the products of the mass m and the acceleratlon of an electron are to each other m the same relatlon as the forces....'

We must also submlt that there 1S no reference tO ' Lorentz-mVar-

iance ', l.e. mvarlance of the laws of physlcs under the new transforma- tlon equations in Einsteln's paper of I905. As we pomted out earlier lt

was Pomcare who used the words ' mvariants of Lorentz group ' and related ldeas for the first tlme in a paper published m January I906.

(We are, of course, not mslsting on the use of the t^ord Lorentz in thls context.) However, Einsteln (p. SI) did mentzon that such ' parallel' transformatlons form a group.

It 1S further said that since Maxwell's equations cannot account for micro-phenomena, the notlon of Lorentz-invariance is more general. Tllls 1S certamly true but there is no statement to this effect in Einstemss

1 H. A. Lorentz, Collected Papers, Martlnus NijhoK, The Hague, I936, 2, I64, atd

5, rtspecelvely

22

ORIGIN AND CONCEPT OF RELATIVITY

orlglnal paper. Einstem hlmselfused mvarlance of a macro-phenontenon, the pr1nclple of constancy of veloclty of light, to der1ve L.T.E.

6 Relativity according to Poincare, Lorentz, and Einstein Firstly regarding Polncare's relatlvlty. Pomcare used the phrase

' the law of relatlvlty ' mltlally 1n the context of relatlvlty of space,2 l.e. equlvalence of all pomts m space for descrlptlon of the laws of pllyslcs (' local' effects apart). Thls doctrme, whlch has recelved much less attentloll than the relatlvlty of motion, 1S perhaps equally mportant. How does lt come about that all poults m space are equlva-

lentH3 No experlment wlthm the solar system, whlch as a whole 1S ln

motlon relatlve to the system of the stars, has mdicated that there are diSerences m the laws of physlcs at different locatlons in space or for different directlons. Is lt that m order ' to apply the law of relatlvlty m all ltS rlgour, lt must be applied to the entlre umverse ', as Pomcare4 conJectured? We shall return to thls questlon m a later paper.

As another step toBrards generalisatlon, Pomcare used the term ' the prmaple of relatlvity ' to mclude relativlty of space as well as of um- form motlon. Polncare, however, saw lmrnediately that the prmctple

1 In fact thls prmclple, postulatlng mvanance of the geometry of the wave-surface of electromagnetlc propagatlon (the second postulate), ls a partlcular case of the m- vanance of the wave-equatlon whlch m turn 1S a partlcular case of mvarlance of Maxwell's equatlons.

It can be shown easily that the assumptlon of invanance of Maxwell's equatlons leads tO L.T.E. (More accurately, the assumptlon of invanance of Maxwell's equatlons leads to a wlder group, nanlely the conformal group. Further assumptlons (e.g. Iineanty) are necessary to extract the Lorentz group. We are mdebted to one of the referees for thls remark.) In fact, a much weaker conditlon of mvanance of the velouty of an clectromagnetlc pulse, coupled wlth plausible assumptlons based on the physlcal SItUatlOn, 1S SUiCtt to establish L.T.E., as we sU see m a subsequent paper.

An mterestmg questlon 1S: To what extent do Maxwell's equanons already lmply thelr own mvarlance? Is lt, as Max Born congectures, that ISorentz trarnformatlon 1S

SU1 lIltRlllSlC property of Maxwell's equatlons? (Naturat Philosophy o+Cause and Chance, Oxford, I949, p. 27).

A superfiaal exammatlon of Maxwell's equatlons at once shows that charge 1S

already lmplied to be mvanant, l.e. ItS measure (p) ls mdepelldent of ItS motlon (u)

because we wnte

curl H-(a + pU),

for all values of u. 2 H. Pomcare, Sclence and Hypothests, Dover, p. 77 3 Einsteen (p. 44) uses the words ' homogenaty whlch we attnbute tO space and

tsme '. 4 H. Poscard, op. at., p. 77

23

G. H. KESWANI

was not altogether of general validity and, m partlcular, that lt was not true of accelerated motlon or evell of uniform rotatlon. If the sky were for ever covered with clouds, sald Po1ncare, and lf we had no means of observmg the stars, we mlght, nevertheless, condude that the earth tUNlS round, because flattemng at the poles and Foucault's pendultlm would reveal thls rotatlonal motlon.l No observatlons on the stars need be carried out to determlIle the motlon ofthe eartll wlth reference to the absolute system of the stars. (We shall see ln a later paper how the possibility that lt 1S the system of the stars that rotates and tlOt the earth must be excluded.) The rotatlonal mot1on ls, therefore, not rela- iive to any reference frame, but relatlve only to one system and one only; st is absolute. The prmc1ple of relatlv1ty 1S not, therefore, generally valid. 'l'hat 1S why Pomcare thought lt was ' battered '. Ponderlng over the effects of rotatlonal motlon,he asked, ' Can a thmg turn wlthout turmng wlth respect to somethmg? '2 And what could be thls some- thing, whlch 1S, as lt were, everywhere?

Rather fortunately, the young Einstem was not beset wlth these doubts about the prmclple when applied to noll-uniform motlon and launched relatlvlty on ltS trlumphant career that we know of so well. Of course, he had to return to Pomcare's mlSg1VlNgS later, but wlth the courage ollly a youth could possess, Einsteln saw only what need have been seen then (I905), a partlal but lnsplrmg V1sl0n. Polncare saw lt complete w1th long slladows of doubt w

Nevertheless, Polncare contmued to develop the prulclple of rela- tivity of uniform motlon of translanon and obtamed almost all the essentlal results before Einstem. Occaslonally he pald lip-servlce to the aether 3 whlch he never defined suilciently clearly or, at any rate, categorlcally. There 1S not the slightest doubt that Einsteln (p. 3 8) was the first to proclalm unequlvocally that the aethersoncept 1S super- fluous if the prlnclple of relatIvlty 1S to hold (not to mentson Important developments such as the formula for compounding velocltses and the relatlv1stlc theory of the Doppler effect). But he was able to clo tlllS

because he disregarded (or probably did not appreclate) the difficulttes the prlnclple of relatlvity had then (Igo5) to face lf non-unifornl and rotaiional motlons were consjdered.

H. Pomcare, op. Clt. p. II4

Ibld., p. II4

3 In the discusslon on pages I69I72, ibld., for example, Pomcare categorlcally demes the aether, but the remark at tlle top of page 244, ibld., makes hls posltlon uncertam. Thls state of belief perslsted rlght up to hls death.

24

ORIGIN AND CONCEPT OF RELATIVITY

Whereas Pomcare and Einstem m thetr ldeas on relatlvlty nweant more nearly the same thmg, Lorentz's baslc ldeas were different, as he himself told us agam and agam. lIe firmly believed ln an aether, the domam of absolute tlme alld absclute space. Motlon relatlve tO thjS aeth r produced ' real ' changes. In I92I he compared 1 th change in length due tO mOt10n, tO the change produced I)y tenlperature. Ehrenfest,2 who succeeded LorenFz m 111S cllalr at Lelden, tells us clearly about Lorentz's conceptlon of the aetller

' Statlonary aether meant for Lorelltz, JUst as lt already did for Inrenesl, statlonary wlth respect to somethlng like the world of the fixed stars.'

What are the physlcal consequences of postulatlon of SUCI1 an aetller? Are the laws of physlcs wltllln vanous systems movmg unlformly sslth reference to thls aether different? If not, what is the use of postulatlng an addinonal reference frame of tlle aether; To tllese and other ques- tlons, we shall turn ln subsequent papers. It 1S to be clcarly nc)tcd, hovwrever, that aether cact conslstently be postulated lf lt 1S a11 1nertlal s+;,stenz and expenmental results conslstent wlth relatlvlty will not tllus l)e vlolated. The questlon really is whetller lt ls necessary to de so and if SO Wllat are the phys;cal consequences of such an aethel .3

7 Mi1lkotvski

Although Einsteln regected the notlon of the aether or an alesolute frame of reference, derlved L.T.E., whlcll had only l:cen poslted ad hoc by Lorentz earlier, and established some new results ln hls paper of 190s, there 1S evldence that he had not yet fully dolnlnated the tlleorarhe

H. A. I orentz, Nature, I92I, I06, 794

2 C(llected Setent,ific Paper.s of PaulEllrcwffest, North-HollaIld Pub. Co., IgS9, p. 474 3 Years ago (in 19II) von Laue saxd, ' A really experlmental deaslon ben7Seen the

theory of Lorentz and the theory of relatlvxty ls sndeed no. to be gamed, and that the fornler, m splte of thls, llas receded mto the baclcgroulld, ls chlefly dtte to tlle fact, that close as st comes to the tlleory of relatlvlty, lt still lacks thc great unlversal prmclple, the possesslon of whlch lends the theory of relatlxrlty an Imposlng appearance.' Quoted n MaxJammer, ConcertsoJvSyace, Harvard Unlv Press, I954, p. I42. H. Margenau and R. A. Itlould more recently wrotc slnlilarly, ' If the lavirs of nature are of the same form wltll respect to all firames of reference, tllen they are of that form m any clloserl frame of reforence. . . Clearly xt does not make sense to speak of settling the matter between Einstem and Lorentz by experlment. . What 1S slgnificant about Einstclll's prlnaple 1S that lt 411 be nzantalncd, not that It nlust be mamtamed.' ' Relatl lty: An Eplstemologlcal Appralsal ', P11illxsophy of Sc1ellve, I957, 24, 303.

2S

G. H. KESWANI

propollnded. But before vwre crltlcally comment on Einstem's paper, we must mentlon a revolutlon whlch tumed the theory from ltS some- what turbld begmnmgs mto clarlty ln physlcal mterpretatlon anel mathematlcal representatlon alike.

The man who brought tlus about was Miiowskl. He went for hls mspiratlon nelther to Lorentz nor to Einsteln, though he closely traced and extended Pomcare's line ofthought. Minkowskl was likely not aware of Pomcare's work. His twln conceptjon of a 44imensional space-tlme contsuum and ltS mvarlant metnc stemmed from purely geometncal roots. Indeed lt was he who mtroduced tensors m the theory of relatlvlty. So revolutionary was Minkowski's way of pre- sentatlon and analysls that Einsteln 1 remarked, ' Since the mathemat- clans have mvaded the theory of relatlvlty, I do not understand lt

myself any more'. Minkowskl was the first true mathematician of relatlvlty.

What 1S remarkable 1S that accordmg to Minkowski's way of presentation ' relatlvlty' became less slgnlficant. The keyword here was ' invanants ', whlch remamed the same no matter what the Same of reference m whlch they were measured. The slmplest of these was the 4Ximenslonal metnc of space-tlme. A partlcle 1ll uniform translatlonal motlon describes an mvarlant 44imenslonal ' word-line ', an element of whlcll at the ' world-pomt ' (x, y, z, t ln any snertlal frame) 1S

dT -v(c2dt2 dx2 d-dZ2)

betng physlcally the (proper) tlme measured by a clock statlonary at the partlcle ltself. Whatever be the frame of reference, dr remams the same. It 1S to be noted, however, that dr 1S not a complete differeniial. Thus, for tWo world pomts connected by two digerent world li?es, |dT, tlle mtegral of s proper' tlme, does not have the same value. However, the world lilles of two particles m uniform motion can mtersect m no

more than one pomt.

Minkowski drew attentlon to the absoltate elements, so to speak, pre- served m the flux of space-tzme (world) which did not change no matter what the frame of reference mlght be. Indeed, wlthout Minkowski's ideas, the development of the general theory of relatlvlty would not have been possible, as Einsteln hlmself acknowledged later.

1 Quoted by A. Sommerfeld m Albert Einstein Philosopher-Sclentist, The Library of Llvlng Philosophers, I949, p. I02

26

ORIGIN AND CONCEPT OF RELATIVlTY

It 1S snterestig to know what Minkowskl hlmself thought of the origin of the ideas assoaated wlth relativlty-theory. He has left on record 1:

' The validity wsthout excepeon of the world-postulate, I like to tht, 1S the true nudeus of an electromagnetlc lmage of the world, wlllch discovered by Lorentz, andfurther revealed by Einstein, now lies open m the full light of day.'

8 Criticism of Einsfein's Paper As we remarked earlier, Einstem was the first to derive L.T.E. from

the postulates of (i) relatlvlty and (ii) constancy of veloclty of light m all frames of reference. Lorentz had only assumed these equatlons, and though Pomcare clearly saw that these equatlons were conslstent wsth the prmclplW of relauvlty, and apparently also saw that they demanded an upper limlt of velocltles equal to the veloclty of light, he made no attempt to derlve L.T.E. Did he conslder thls trlvlal? We do not know.

It appears tO US, however, that Einstem's ongmal derlvatlon 1S not satlsfactory. Einsteln (pp. 44 45), uses velocites of light propagatlon equal to (c v), (c+v) and /(C2 v2) in utter disregard of hls own second postulate. We must note that these veloclties of light-propag- atlon, m Einstem's derlvatlon, are physlcally measured (i.e. observable) velocltles and not certam quantltles m an algebraic calculatlon. It is mterestmg to see exactly how Einstem established L.T.E. and we, therefore, glve hls method along with some comment m Appendix A.2

Nor was Einsteln yet m possesslon of the 4Qimenslonal concept. After developmg Lorentz's equatlons, Einsteln (p. 46) uses them to trans- form the sphencal wave-front of light ln one frame glven by the equatlon

x2 +y2 +,<,2 _s2t2 0

into another frame movmg relatlxre tO the first and gets xt2 +yt2 +zw2 c2t2 0

He (p. 46) nghtly concludes: ' The wave under conslderatton 1S, therefore, no less a spherlcal wave W1th areloclty of propagatlon c when orzewed m the movmg system.'

But when considering the energy contamed wltllm the expanding wave-front of light as observed m the two systems, Einsteln (p. 57) asserts:

1 H. Minkowskl, ' Space and Time ', The Prttlclple of Relativity, Dover Publications, p. 9I 2 Also see the latter part of foomote I, p. 294, Part I.

3 27

G. H. KESWANI

' The sphencal surface vlewed m the movmg system 1S aIl ellipSOldEl

surface... '

He then proceeds to work out the equatlon of the expanding ellipsold !

g Concluding Remarks

The one concluslon to be drawn 1S that each one of us stands on the shoulders of others and only thus can even a genlus see farther than others. The development of relatlvity-theory also conforms to thls.

It was Pomcare, first and foremost, who talked of relatlvlty of dis- placements or space and ofthe prmclple of relatlve motlon for umform translatlon, and of varlous novel ldeas assoclated wlth the theory of relatlvlty. However, he notlced that the prmclple was not true of non- umform motlon. It was possible to find absolute effects due to non- uniform motlon. Pomcare did not, therefore, categorlcally reJect the concept of tlle aether or an absolute frame of reference. Although he was consequently beset wlth doubts, he contmued to develop the prln- clple of uniform relatlve motlon and lt was he who recogmsed the con- nection between the prmclple of relatlv1ty and Lorentz transformatlon equatlons, poslted earlier by Lorentz.

Einsteln knew of the ploneermg ldeas of Polncare and probably Lorentz's transformatlon equatlons, but unfortunately he did not say ln hls orlgmal paper what was strlctly lus own contributlon; there 1S no reference to any prevlous work at all exceptmg a general reference to Lorentz's theory of electrodynamlcs. But Einsteln did not only advance the subJect analytlcally and derlve L.T.E. not m a satlsfactory way, though but he was also the first to reJect the aether-concept un- equlvocally, thus becommg the first true believerm the creed of relatlvlty, ltS prophet. The prophet had, however, apparently pa1d no heed to the uncertalntles expressed by Pomcare the doubter, then. It was a blessmg that he did not.

To measure the relatlve contributlons to the prmclple of relatluty, we m1ght quote Max Born 1:

' Einstem's work was the keystone to an arch whlch Lorentz, Polncare and others had built and whlch was to carry the structure erected by Minkowskl. I thlnk lt 1S wrong to forget these other men.... '

and we mlght add what every mason knows; the keystone could be placed ollly when the rest ofthe arch was there and the falsework ofthe aether could be removed only after the whole arch was complete.

Max Born, Physics in My Generation, Pergamon Press, I9S6, p. I95

28

ORIGIN AND CONCEPT OF RELATIVITY

But that 1S not the only story. The problem of non-uniforln motlon had yet to be tackled and the very prmclple of relatlvlty sub- Jected to a more cntlcal examinatlon, as we shall see. All thmgs must

change and nlan must contmue

.... to hope 611 hope creates From ltS own wreck the tllmg lt contemplates.

P. B. Shelley, Prometheus Unbound

BI8, South Extenslon (Part II), New Delhl, I6 India

APPENDIX A

Einstein's Original Derivation of L. T.E.

We first reproduce Einstem's demonstratlon and then bnefly comment

on lt. (The Principle of Relativity, Dover, pp. 43-46) To any system of values x, y, z, , whlch completely defines the place

and tlme of an event mthestatlonarysystem[K], therebelongsasystemof values {,77, C, , determmmg that event relatlvely to the [movlng] system k, and our task 1S now to find the system of equatlons connectmg these quantltles.

In the first place lt 1S clear that the equatlons must be linear on account of the propertles of homogenelty whlch we attribute to space and tlme.

If we place x' x vt, lt ls clear that a pomt at rest m the system k must have a system of values x', y, z, mdependent of tlme. We first define T as a functlon of x', y, z and t. To do tiS we have to express ln equatlons that T 1S nothmg else than the summary of the data of clocks at rest ln system k, whlch have been sSrnchronlzed according to the rule glVen m % I.

From the orlgm of system k let a ray be emltted at the tlme z0 along the X-axls to x', and at the tlme r1 be reflected thence to the orlgln of the co-ordinates, arrlvmg there at the tlme T2; we then must have i (z0 +T2)

1, or, by msertmg the arguments of the functlon z and applymg the prmclple of the constancy of the veloclty of light m the statlonary system.

r (o, o, o, t)+T(o, o, o, t+ _ + + ) -(x', o, o, t+-).

Hence, lf x' be chosen mEimteslmally small,

i(c-v+c+v)at =ax' +c-vuat

29

G. H. KESWANI

aT v aT or ax'+c2 v2 at ?

It is to be noted dlat lIlstead of the ongln of the co-ordinates wc mlght have chosen any other pOlXlt for the pomt of origm ofthe ray, and the equatlon JUSt obtallled 1S therefore valid for all values of x', y, z.

An analogous conslderatloapplied to the axes of Y and Z-It being borne m mmd that light 1S always propagated along these axes, when vlewed from the statlonary system, wlth the veloaty /(C2 v2),

glves us

aT aT - =O, - - O.

by az

Since T 1S a linear functlon, lt follows Som these equatlons that / v \

T -a tt ) where a 1S a functlon +(v) at present uTllcnown, and where for brevlty lt 1S assumed tMt at the orlgm of k, z o, when t - o.

With the help of tiS result we easJy detere the quantlties {, , 4 by expressing m equatlons that light (as requlred by the prmaple of the constancy of the veloaty of lightX m combmatlon wlth the prmaple of relaavity) 1S MSO propagated th veloaty c when measured m the movmg system. For a ray of light emltted at the tlme X o in the directlon of the mcreastng gt

{-CT or e-aXt ca_u2x)@

But the ray moves rdatlvely to the imttal pomt of k, when measured in the statlonary system, wlth the veloaty c v, so that

x

c-v

If we msert dus value of t m dle equatlon for {, we obtaxn

{ aC2_V2X-

In an analogous manner we find, by considermg rays movmg along the two other axes, that

/ V ,\ - cT-aftf-c2 v2X)

when v(Y H)-,x'=o.

3o

ORIGIN AND CONCEPT OF RELATIVITY

Thus

n av( 2 V2)Y md 4 a(c2-v2)

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

where

p (I V2 /c2)'

and + 1S atl as yet unknown functlon of v.' +(v) is later shown to be equal to unity. Incidentally, there is an

inconsequental notatonal slip. The functlon a ajoove is also called +(v) but in fact

+(V) ff (C2_) I

i.e. a (I V2/C2),

As we mentloned earlier, Einsteln used velocitles of light-propaga- tlOll equal to (c-v), (c+v) and (C2-) overtly, and yet got the correct end result, the usual expresslons for L.T.E. The steps taken have a curiously compensating e?ect and apparently the demon- stratlon was dnven towards the result.

The annexed figure, we hope, corresponds to the above demon- strat3on. In this comment we consider happegs along ie x and f axes otlly.

k (6.Q.g,) K (xty,z,)

We- ,,

O =ZZVt ' V b b_ X

Einstein mtroduces the mog coKrdinate x' _ x-vt so that: ' a point at rest in ie system K must have a system of values x', y, z inde pendent of tlme '.

3I 3 *

G H. KES WANI

A ray leaves the ongln o of K at ame r0, travels a distance 5t, as measured m K,m tlme (r1 - T2) and returns to theorigino of K at tlmer2. Applylng the princlple of constancy ofthe velocity of light in the mov- mg system K, Einstem wrltes ehe correct relatlonshlp:

t1 = i(to+72)*

However, the tlmes of departure or arrival corresponding tO the t!:lree events as measured in the statlonary system K are glven as follows, agam, lt 1S asserteds ' applymg the prmc1ple of collstancy ofthe veloclty of light ln the statlonary system ':

x x x

t, t+ and t+ - + - . c v c v c+v

The statement, ' the ray moves relatlvely to the tlal point (orlglI)

of K wherl measured m the statlonary system (K), wlth the veloclty (c-v), etc.' 1S phySlCauy d?lCdt to foHow. We caot meanmgfUly speak of veloaty of a light-ray relat1ve to a point of one inertlal system (the origm of K) but as lt (veloaty) is measured u1 another systenl (K). The argunaent seems to proceed as follows: x' is some length (measured n the statlonary system K) whlch the outgoing and returmng rays

traverse wlth veloclty (c-v) and (c+v) relatlve to the orlgm of the

movulgsystem K, thequotlents-and + bemg the correspollding

tlme lntervals, as measured m K. The procedure ts operatlonally vague and certamly IlOt m confornalty th the second postulate.

It 1S t0 be noted that (c v), (c+v) and V(C2_v2) are, n1 Emstenl's exposltlon, consldered as velocltles of light-rays m K and not as certaln quantltles ln all algebralc process.

Incldentally, although Einstelll used the word 'event', he did not use the 44imenslonal space-tlme concept. For a slmilar remark see. N. H. de V. Heathcote, Nobel Prize Winners itl Physics (Schuman, New York, I9^3, p. I95). The latter concept was due to I'omcarc (I906), as we remarked earlier m tlllS paper, and was further delreloped, apparently tndependently, by Minkowskl. In 44imen- s1onal space-t1me, tlle fourth coKrdinate 1S not tlme but a/-I X tlme.

32