The British Society for the Philosophy of Science

Origin and Concept of Relativity (I)Author(s): G. H. KeswaniSource: The British Journal for the Philosophy of Science, Vol. 15, No. 60 (Feb., 1965), pp. 286-306Published by: Oxford University Press on behalf of The British Society for the Philosophy ofScienceStable URL: http://www.jstor.org/stable/686536Accessed: 19/05/2009 07:23

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G. H. KESWANI

I* Introduction

WHATEVER its future, relativity-theory is rightly regarded as one of the greatest intellectual endeavours of man. Yet, sufficient research has not been made into its origins. So far as we are aware, it has not even been established as to who used and discussed the phrase ' The principle of Relativity ' first in the sense in which we understand it in physics today, meaning that only the xelative motion of a body is physically ascertainable, and when.**

In talking of the origins, we mean the special theory. In recent years the question of origins has received attention, pariicularly as a result of a provocative investigation by Whittakerl. After exaniining

t Received 28. iii. 64

* Parts I and 2 of the present paper is about the origin of the special principle of relativity. In subsequent papers we shall deal with the idea of relativity of all motion in general, and with Einstein's theory of gravitation, returning to the principle of relativity of uniform motion in the light of Einstein's theory of gravitation.

** No doubt, Berkeley, Euler, Kant, Leibnitz, Huyghens, Mach and others had discussed and speculated on the question of relativity of motion. What we mean is a discussion of the principle of relativity of motion for electromagnetic phenomena no less than for mechanical phenomena with the experimental background of failures to detect motion relative to the ' luminiferous ' aether. We owe this amplification to one of the referees.

1 (a) E. T. Whittaker, A History of the Theories of Aether and Electricity (I900-

I926), Thomas Nelson, I953. Whittaker seems to suggest that Poincare used the phrase ' The Principle of relativity ' for the first time in the year I904 in an address at St. Louis, ibid. p. 30. As we shall see, Poincare had used the phrase even earlier. Re- garding Whittaker's conclusions, J. L. Synge has remarked that it was denigration of Einstein, adding that this word is a little too strong. ' Whittaker's Contributions to the Theory of Relativity ', Proc. Edin. Math. Soc., I958, 2, part I, 46.

(b) Rene Dugas critically examines some well-known contributions of Lorentz, Einstein, and Poincare. A History of Mechanics, Routledge & Kegan Paul (English translation of I957). Particularly see pp. 64S650.

(c) Provoked by Whittaker's views, Max Born commented briefly on the origins of the theory in an address to a conference on relativity held in Berne in the year I955. The address is reproduced in a book by Max Born entitled: Physics in My Generation, Pergamon Press, I956.

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evidence from vanous sources, Whittaker gave the case for Poincare and Lorentz, almost to the complete exclusion of Einstein's name and in sharp discord with accepted belie? Whittaker referred to the special theory as ' the relativity theory of Poincare and Lorentz ' and Whlttaker was his own man. In the face of rather unpleasant reaction from some quarters, he maintained his judgment even later irl a biographical memoirl of Einstein written on his death in I955

We shall consider the matter in five sections: (a) What exactly was Poincare's contribution prior to the publica-

iion of Einstein's paper of September I905 (submitted for publi- cation on 30th June I905) ? 2

(b) Did Einstein know of Poincare's contribution before the sub- mission of his paper? Which contribution?

(c) Did Einstein know of Lorentz's mernoir3 of April/June, Igo4? (d) What did Poincare, Lorentz, and Einstein themselves say about

the anthorship of the theory?

(d) Gerald Holton refutes the conclusions of Whittaker: ' On the Origins of the Special Theory of Relativity,' Amer. J. Phys., I960, 28, 627.

(e) One of the earliest examinations rather brief was made by W. Pauli, who touched on the question ofthe origins here and there in an article on relativity published in the year I92I and reprinted in English with notes as: Theory of Relativity, Pergamon Press, I958, pp. 3 and 78 particularly. Pauli concluded, ' The formal gaps left by Lorentz's work were filled by Poincare. He stated the relativity principle to be gen- erally and rigorously valid. It was Einstein, finally, who in a way completed the basic formulation of this discipline.'

1 Obituary by E. T. Whittaker in Biographical Memoirs of Fellows of the Royal Society, I955, London, pp. 37-67. This memoir contains little new material bearing on the question of prioritythat is not there in his History, footnote I(a) above, except- ing a remark on p. 42 to the eSect, ' Einstein adopted Poincare's Principle of Relativity (using Poincare's name for it) '.

2 ' On the Electrodynamics of Moving Bodies ', Ann. der Phys., I905, I7, 89I:

English translation in The Principle of Relativity, Dover, to which we shall give references here.

3 ' Electrodynamic Phenomena in a System Moving with any Velocity less than that of Light ', Proc. Acad. Sci. Amsterdam, I904, 6, 809, reproduced in rhe Principle of Relativity, Dover, to which we shall give references here. Lorentz's memoir was presented at the April, I904 meeting of the Academy and its English translation appeared in June I904. Whittaker, op. cit., quotes the year of publication in the text and footnote on p. 3 I, as I903. Holton, ibid., p. 63S, reads a meaning in this slip of Whittaker alleging that, ' Since Whittaker was otherwise very careful with volum- inous citations of references, this repeated slip, which doubles the time interval be- tween the work of Lorentz and of Einstein is not merely a mistake.' However, Whittaker quotes the correct year (I904) on p. 30, footnote 4 and p. S3 footnote I, and obviously, mention of the year I903 elsewhere was only a mistake, pure and simple.

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G. H. KESWANI

(e) Did the three Poincare, Lorents, and Einstein-mean the same thing in their ideas on relativity?

In what follows, we shall refer to the above paper of Einstein and the earlier memoir of Lorents, only by the names of the two authors fol- lowed by the pertinent page-number of references 3 and 4.

Throughout, italics have been used by us for emphasis but no attempt has been made to show separately the italics used by other authors themselves.

2 Poincare's Contribution

The idea of relativity of motion had been simmering in Poincare's mind at least since the year I 895 when he said,l ' Et, en effet, l'impossi- bilite de mettre en evidence un mouvement relatif de la matiere par rapport a l'ether....' This is perhaps the earliest conjecture which is the central idea of the relativity of motion, that is, it is impossible to bring into evidence the velocity of a body relative to the aetller or any absolute standard of rest. In the year I899, he said2 similarly:

' je regarde comme tres pro6alD1e que le phenomenes optiques ne depen- dent que des mouvements relatifs des corps materiels en presence, sources luniineuses ou appareils optiques et cela non pas aux quantites pres de l'ordre du carre ou du cube de l'aberration, mais rigoureusement.'

In the year I900 he queried3 again if the aether really existed adding that he believed that experiment could reveal nothing more than relative displacements. In the same year, he very nearly came to name the principle of relativity when he used the equivalent but physically even more descriptive and precise phrase, ' The principle of relative motion ',4

to signify that it is possible to ascertain only the relative motions of bodies.

Soon after, in the yeal I902, he analysed this idea critically and at length, and appalently for the first time used the appellatiolls ' The Law

1 Oeuvres de Henri Poincare, t. ix, Gauthier-Villars, Paris, I954, p. 4I3. Henceforth we shall refer to this volume of Poincare's works as Oeuvres.

2 A Sorbonne lecture of I 899 reproduced in Electricite' et Optique, Gauthier-Villars, Paris, I954, p. 536. Whittaker, op. cit., p. 30, in giving a translation of this passage omits the words ' ou du cube ', an omission of little consequence.

3 Quoted in Whittaker, op. cit., p. 30

4 Oeuvres, pp. 482-483. The words used repeatedly are, ' Le principe du mouve- ment relatif '.

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of relativity' and ' The principle of relativity'l in his book Science et Hypothese.

In liis principle of relative motion2 or the law of relativity or the principle of relativity-he used all these equivalent phrases in I902

Poincare asserted the relativity of positions or displacements as well as of uniform velocities. All points in space are equivalent in respect of the readings that we can take with our instruments3, said Poincare, and thus it is possible to measure relative distances only. A wider principle, that of relative motion, holds when the motion of the movable axes (reference system) is uniform and in a straight line but it is not true when the motion is accelerated or (even uniformly) rotational,4 in support of which Poincare quotes the fact of impact occurring when a train is decelerated, and the phenomena of flattening at the poles of a rotating sphere and the motion of Foucault's pendulum. Regarding time, Poincare remarked 5 in the same book

' There is no absolure time.... Not only have we no direct intuition of the equality of two periods, but we have not even direct intuition of the sinlultaneity of two events occurrirlg at two different places.' These penetrating reflections were followed in September, I904, by

similar reflections in an address delivered by Poincare before the Inter- national Congress of Arts and Sciences at St. Louis in U.S.A.6 We quote from this address at length partly to correct some minor omis- sions in Whittaker's translation, but generally to understand better the processes of Poincare's mind. The pages refer to the English version mentioned in footnote 4.

p. 5 ' The principle of relativity, according to which the laws of phys- ical phenomena should be the same, whether for an observer fixed, or for an observer carried along in uniform movement of transla- tion....'

1 Science and Hypothesis, English trans., Dover, I952 reprint, pp. 76 and 244. In some places, the year of publication of this book is given as I903 . Rene Dugas, ibid. p. 660, gives the year of first publication by Flammarion as I902.

2 Scietlce and Hypothesis, Dover, pp. III-II2

3 Ibid. p 77

4 Ibid. pp. II3-II4. Einstein and others also quote the case of flattening of a sphere into an ellipsoid in the same context. The Foundations of the General Theory of Retativity, Eng. trans. The Principle of Relativity, Dover, p. I I2.

5 Science and Hypothesis, Dover, p. go. Poincare said so earlier in I898; see foot- note, ibid.

6 An English translation of the address by G. B. Halsted appeared in rhe Monist of January I905, I5, No. I, I-24. The original in French was published in Bull. des Sc. Math., I904, 28, 302.

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G. H. KESWANI

It is to be noted that Poincare mentions only uniform translational

motion.

p. I0 ' When the station B perceives the signal from the station A, its clock should not mark the same hour as that of station A at the moment of sending the signal, but this hour augmented by a con- stant representing the duration of the transmission. Suppose, for example, that the station A sends its signal when its clock marks the hour o, and that the station B perceives it when its clock marks the hour t. The clocks are adjusted if the slowness equal to t represents the duration of the transmission, atld to verify it, the station B sends in its turn a signal when its clock marks t. The time pieces are then adjusted. And in fact, they mark the same hour at the same physical instant, but on one condition, which is that the two stations are fixed. In the contrary case the duration of the transmission will not be the same in the two senses, since the station A for example moves forward to meet the optical perturb- ation emanating from B, while the station B flies away, before the perturbation emanating from A. The watches adjusted in that manner do not mark, therefore, the true time, they mark what one may call the local time, so that one of them goes slow on the other. It matters little since we have no means of perceiving it. All the phenomena which happen at A, for example will be late, but all will be equally so, and the observer who ascertains them will not perceive it since his watch is slow; so as the principle of relativity would have it, he will have no means of knowing whether he is at rest or in absolute motion.

Unhappily, that does not suffice, and complementary hypo- theses are necessary; it is necessary to admit uniform contraction in the sense of the motion.'

Poincare describes the method of synchronisation of clocks at rest (within a system) and in discussing this method when applied to two clocks in relative motion comes to the conclusion that one ofthe clocks goes slower and notwithstanding tliis finds the principle of relativity valid for the systems attached to the two clocks. He also asserts that it is then necessary to assume that bodies in motion undergo contraction.

p. I6 ' From all these results, if they are confirmed, would arise an entirely new mechanics, which would be, above all, characterised by this fact, that no velocity could surpass that of light . . .'

Whittakerl quotes this passage somewhat differently making the

1 E. T. Whittaker, op. cit. p. 3I. The French version in Bull. des Sc. Math. I904,

28, 3I6, reads as, ' De tous ces resultats, s'ils se confirmaient, sortirait une mechanique 290

ORIGIN AND CONCEPT OF RELATIVITY

statement of the ideas categorical. His rendering reads: ' From all these resxlts theremust arise an entirelynewkind of dynamics . . .'

The original French version shows that Halsted's translation is accurate.

p. I9 ' Shollld we not also endeavour to obtain a more satisfactory theory of the electrodynamics of bodies in motion? Let us take, therefore, the theory of Lorentz, turn it in all senses, modify it little by little and perhaps every thing will arrange itself.'

p. 23 ' Perhaps likewise, we should construct a whole new mechanics, that we only succeed in catching a glimpse of, where inertia increasing with the velocity, the velocity of light would become an impass- able limit '

Here again Whittaker'sl version ' a new mechanics, where, the inertia increasing with the velocity, the velocity of light would become a limit that could not be exceeded ' is not qualified by Poincare's reservation2 ' that we only succeed in catching a glimpse of', which is contained in the original address in the middle of the sentence.

The address contained no mathematics; it was a popular lecture, rather philosophic and reflective. Although the principle of relativity was succinctly enunciated, Poincare obviously had some doubts still. Notice the ' perhaps' mentioned twice and the persistent mood of retraction at a feeling of insufficiency of the proposed doctrine. The philosophic mood and the autonomous power of words no doubt made it possible fol him to carry his formulation to a point that it came to be verified. Buthe himselfhad misgivings, definitely. His insight and eloquence carried him with an impulse which he could not yet fully sustain. It is significant that for about nine months he did not give a mathematical form to his principle of relativity but there were good reasons for this hesitancy.

In support of this thesis, the following additional pessimistic re- marks made in the St Louis address may be noted. As before, the pages refer to the English version in The Monist.

entierement nouvelle qui serait surtout caracterisee par ce fait qu'aucune vitesse ne pourrait depasser celle de la lumiere, . . . '

1 E. T. Whittaker, op. cit. p. 3I

2 H. Poincare, Bull. des Sc. Math., I904, 28, 324. The words are, ' Peut-etre aussi devons-nous construire toute une Mecanique nouvelle que nous ne faisons qu'entre- voir, ou, l'inertie croissant avec la vitesse, la vitesse de la lumiere deviendrait une imite infranchissable.'

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G. H. KESWANI

p. g ' We come to theprinciple of relativity: this not only is confirmed by daily experience, not only is it a necessary consequence of the hypothesis of central forces, but it is imposed in an irresistible way upon our good sense, and yet it also is battered.'

p. I7 ' In the midst of so many ruins what remains standing? The principle of least action is hitherto intact . . .' (In his address Poincare commented on various principles such as the principle of relativity bUt seemed to think that this principle did not remain standing.)

We must, however, take note of the following. (a) ' The principle of relativity' was mentioned in the address

and clearly defined; a new mechanics in which the rrelocity of light could not be surpassed was predicted.

(b) The method of synchronisation of clocks with light-signals was described.

(c) A more satisfactory theory of ' the electrodynamics of moving bodies' was considered necessary and it was ex- pected that this could be secured by some modification to Lorentz's theory.

However, it was not long before Poincare published a definitive paper. InJune I905 and still before the appearance of Einstein's paper in September, Ig05, Poincarel published a paper entitled ' Sur la dynamique de l'electron ' in which he established complete covariance of Maxwell's equations under a Lorentz transformation, including the correct transformation formulae for the case when the space, for which Maxwell's equations are given, is occupied by electric charges. Lorentz (p. I 5) had not succeeded in establishing covariance of Maxwell's equa- tiOtlS involving charge-density. In this respect Poincare's paper was a continuation of Lorentz's memoir of I904 in which lle proposed the new (Lorentz) transformation equations for space and time. But more than this, Poincare immediately recognised the comlection between his principle of relativity and the transformation equations of Lorentz and remarked,2 ' Lorentz a cherche a completer et a modifier son hypothese de faSon a la mettre en concordance, avec le postulat de l'impossibilite complete de la determination du mouvement absolu.' He saw tllat the Lorentz transformation equations meant that it was impossible to determine absolute motion. It was in this very paper that he named the transformation equations after Lorentz. Henceforth we shall refer

H. Poincare, Cosnptes Rendus, I905, I40, I504

2 Ibid. p. I 504. Oeuvres, p. 489 292

ORIGIN AND CONCEPT OF RELATIVITY

to these equations as L.T.E. (Lorentz transformation equations). The assertion that L.T.E. form a group also occurs here for the first time. Incidentally, Poincare suggested in this paper that gravitational effiects are propogated with the velocity of light: indeed he talked of gravita- tional waves !

Soon after, Poincare enlarged this short paper into a longer one by the same name. This second paper,l written inJuly, Igo5, was, how- ever, published inJanuary I906, after the publication of Einstein's paper. The connection between the postulate of relativity and L.T.E. was here reiterated, the conception of the Lorents group was further developed, the term ' invariants du groupe de Lorents ' was used 2 for the first time and (x, y, z, +/ I t) were regarded as co-ordinates in a 4-dimensional manifold.

For the sake of historical interest we may mention a third paper by the same name, published by Poincare 3 in I908 in which he compared the principle of relativity to a ' pri1ciple of equivalence ', introducing this phrase also apparently for the first time.

To summarise: As far back as I895, Poincare the innovator had conjectured that it is impossible to detect absolute motion. In I900 he introduced ' The principle of relative motion ' which he later called by the equivalent terms ' The law of relativity' and ' The principle of relativity' in his book Science and Hypothesis published in I902. He furtller asserted in this book that there is no absolute time and that we have no intuition of the ' simultaneity ' of two ' events '4 (mark the words) occurring at two diSerent places. In a lecture given in I904,

Poincare reiterated the principle of relativity, described the method of synchronisation of clocks with light signals, urged a more satisfactory theory of the electrodynamics of moving bodies based on Lorents's ideas and predicted a new mechanics characterised by the rule that the

1 H. Poincare, ' Sur la dynamique de l' electron ', Rendiconti del Circolo tnatematico di Palerno, I906, 2I, I29. Oeuvres, p. 494. ' Paris, juillet I905 ' iS mentioned at the end of the paper.

2 Oeuvres, p. 54I

3 Oeuvres, p. 567. Einstein later used this phrase in a somewhat different sense. 4 The notion of an ' event ' as characterised by a given instant of time, a particular

place and a physical occurrence then-and-there is indeed even older. Years earlier Robert Browning lamented !

Never the time and the place And the loved one all together.

(Never the Time and the Place)

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G. H. KESWANI

velocity of light cannot be surpassed.l This was followed inJune I905

by a mathematical paper entitled 4 Sur la dynamique de l'electron ' in which the connection between relativity (impossibility of detecting absolute motion) and the Lorents transformation given by Lorentz a year earlier was recognised.

In point of fact, therefore, Poincare was not only the first to enun- ciate the principle, but he also discovered in Lorentz's work tlle neces-

1 Poincare's postulate that the velocity of light cannot be surpassed, at once leads to the correct velocity-addition formula, etc. This postulate means that c, the velocity of light compounded with a velocity v (< c) in the same direction is c itself. (In fact this is true whatever the direction of v).

The most general formula for the resultant of any two velocities v1 and v2 may be put in the form:

+(V1, V2)X (V1 + V2)-

It is to be noted that this is an algebraic form and no assertion is made yet re- garding the maximum observable velocity.

When vl = c, the above postulate demands that 0(c, v2)x(c+v2)= c

ie- vl=s c+ V2 I + V2/C

Now the required formula for the composition of any two velocities v1 and v2 in the same direction must be symmetrical in v1 and v2 and + must reduce tO I/(I/ + V21C) or I/(I + V1/C) when v1 = c or v2 = c respectively. Obviously then,

I + V1V2/C2

and the resultant of v1 and v2 is V1 + V2

I + V1V2/C2

which gives a smaller value than the classical (vl + v2) when vl and v2 are in the same . ,

( .lrectlon.

E. T. Whittaker uses a somewhat different method to the same purpose and then derives L.T.E. from the formula for the composition of two velocities. From Euclid to Eddington, Cambridge, I949, pp. 49-50, 6I-62.

To the question whether velocities higher than c can ' occur ' (within the frame- work of the special theory), P. W. Bridgman's answer is an emphatic Yes. A Sophisti- cate's Pris1ler of Relativity, Wesleyan Univ. Press, I962, p. I08. He writes, ' Of course, if both velocities were measured in the same frame, the classical simple addition form- ula for relative velocities will continue to hold. In particular, in the stationaryframe the velocity of a particle moving to the left with velocity o 75 c relative to a particle moving to the right with velocity o 75 c is I vS C, as it always has been and always will be, despite frequent statements that relative velocities higher than c do not occur. Such a relative velocity can be obtained by calculation, not by direct physical measurement. If we stationed a measuring apparatus on the particle moving to the left with velocity o 75 c and with it measured the velocity of the particle moving to the right with velocity o 75 c we would obtain something less than c. In fact, we would obtain o g6 c.'

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ORIGIN AND CONCEPT OF RELATIVITY

sary mathematical formulation of the principle. All this happened before Einstein's paper appeared.

There is one difference that must be noted. Although Poincare stated his ideas on the relativity of motion clearly, he had some doubts when the principle was applied to accelerated motion. There were diSlculties, no doubt, which seemed to demand an absolute frame. Could he then reject the aether outright?

Yet these doubts and diflilculties can take away little from his contri- butions which stand independently of his doubts. We should not for- get tliat he was exploring realms of thought never conceived before. It appears to us that thosel who consider that Poincare failed to take the decisive step, have not fully valued his contribution and have been severe in their judgment. He took the required step but looked round and saw that there were serious difficulties still; there was a hesitancy but one that comes from a fullness of knowledge. After all Poincare knew then more than anyone else what exactly were the stakes.

Poincare regarded relativity to be ollly empirically true of uniform motion, but not absolutely true; it was not altogether impossible for it to be violated by some yet unknown experiment.2 Talking of the

We submit that the first part of the above statement is somewhat misleading. It is not physically meaningful to speak of the velocity of a particle (moving to the left) retative to another particle (moving to the right) but as it (the velocity) ' occurs ' in the frame in which the observer is stationary. Thus the figure I5 C calculated above is a number arising in an algebraic process, but not a result of possible physical measure- ments. (Bridgman admits this.)

The picture in Bridgman's mind appears to have been something as follows: I can see two particles flying apart with a velocity o 75 c relative to me; so do I not see them getting apart at a relative velocity of I5 c? The answer is: No; one or the other particle is moving away from me with velocity o 75 c, which is physically true, but there is no meaning in an assertion about the velocity of a particle relative to another particle but as this relative velocity of the two particles occurs in a third frame.

1 Principally, we have in mind the remarks of R. Taton, Reason and Chance in ScientHc Discovery, English trans., Hutchinson, I957, paragraph entitled, ' Poincare and the theory of relativity ', pp. I34-I35. We should like to say that the judgments in the paragraph mentioned are not explicitly related to specific observations on the contributions of Poincare and Einstein but are only generalisations, apparently based

. * . On some personal 1mpresslons. 2 Such a view was held also by H. A. Lorentz apparently up to the end. He said,

' The question whether the principle of relativity holds or not must be decided by experiment.' Lectures on TheoreticatPhysics, vol. 3, Macmillan, London, I93I, p. 255.

H. Bondi, similarly, remarked recently, ' Thus special relativity is not something that absolutely must be true; it is merely the statement that for a large range and variety of experiments, the preferred velocity is irrelevant '. Proc. Roy. Soc. (A), I962, 270, 3II.

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possibility of detecting the absolute motion of the earth he said,l ' Will this ever be accomplished? I do not think so, and I shall explain why; and yet it is not absurd....'

3 Was Einstein aware of Poincare's Work?

Einstein (p. 3 8) introduces the novel key-phrase, ' The principle of relativity ', in the very beginning of his paper exactly in the words used by Poincare earlier in Science and Hypothesis and in his St Louis address. Are we to regard this as a marvellous concurrence? ' Relativity ' was a word then little used in physics, but Einstein uses it without an explana- tion.

And that brings us to the question whether Einstein was aware of Poincare's earlier works. It is certain that he was. He had drunk deep at Poincare's Science et Hypothese and for this we have tlle independent testimony of Carl Seelig,2 Einstein's biographer. The pages given below refer to footnote 2, p. 296. Einstein had read the above book in the company of Solovine and Conrad Habicht under the auspices of a private gathering called ' Olympia' in Berne before Solovine left Berne in I905 and Habicht earlier, in I904.

p. 57 ' After a while Solovine suggested that they should read useful books together of an evening.... In addition to these programmes included ..., Henri Poitlcare's La science et L'Hypothese.... In 19?S Solovine left Berne for Paris where he was employed from I909-I9 as secretary and collalDorator on the Revue Philo-

. , sop l1que.... p. 59-60 ' Before Conrad HalDicht was elected in 1904 to the post of mathe-

matics and physics teacher in the Protestant Educational Institute in Schiers (Graubunden)....'

p. 6I ' The role played by " Olympia " as they christened their private academy, during Einstein's first years ils Berne, cannot be under- estimated in its influence and intellectual itnportance. For among the books digested during these regular evenings of discussion and reading, those which made a lasting impression upon him were works of Ernst Mach, He>ri Poincare's La Science et l'hypothese- Conrad Habicht finally produced this long-awaited book from a book- shop....'

b a letter dated 6th March I905, to Habicht:

1 Science 1ld Hypothesis, Dover, p. I7I

2 Carl Seelig, Albert Einstein, Staples Press, English trans., I956

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ORIGIN AND CONCEPT OF RELATIVITY

p. 75 ' The fourth study is still a mere concept: the electrodynamics of moving bodies by the use of a modification of the theory of space and time. The purely kinematispart ofthis work will undoubtedly interest you.'

Obviously Poincare's book Science et Hypothese was read together by Einstein, Habicht, and Solovine before the publication or writing of Einstein's paper of I905.

The exact date when this book was read at the ' Olympia' is not given by Seelig (it is hardly to be expected) but there is little doubt left by the chronology that it was before Einstein wrote his own paper. Einstein was svell aware of Poincare. The private academy of which Einstein, Solovine and Habicht were members had been anxiously waiting for Poincare's Science et Hypothese.

It is, therefore, correct to assume that Einstein learnt the principle of relativity from Poincare.l

We may note that Einstein, in his paper of I905 used the method of synchronisation of clocks within a system exactly as Poincare did earlier in I904 and used in a hardly different form Poincare's postulate that the velocity of light cannot be surpassed.

There are some curious things about Einstein's paper. For example, why did he call his paper, ' On the electrodynamics of moving bodies ' ? In a sense this subject electrodynamics of moving bodies was very much in the air at the time Einstein wrote his paper. However, the title of Einstein's paper cannot be regarded as exactly or even largely representative of its thesis. The fulfilment of the theory of electro- dynamics of moving bodies in reality became possible only through Minkowski7s later work. In the words of Sommerfeld2:

1 Of course, Einstein had great respect for Poincare. In fact, at one place, he adopted a curiously reverent attitude towards Poincare.

While replying to the criticism of various contributors to the volume Albert Einsteitl Philosopher Scientist, The Library of Living Philosophers, I949 (see p. 677), Einstein puts the arguments about the question, whether geometry can be considered verif1able or falsifiable from the physical point of view, in the form of a discussion between Poincare and Reichenbach. However, after proceeding with the discussion irl this manner for a while in a purely scientific spirit, Einstein recoils from the idea of Poincare being included in this voluntarily chosen pair in imaginary debate with the sudden remark, ' The conversation cannot be continued in this fashion because the respect of the present writer for Poincare's superiority as thinker and author does not permit it; in what follows, therefore, an anonymous non-positivist is substituted for Poincare '.

2 A. Sommerfeld, Electrodyala>lics, Academic Press, I952, p. 280

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G. H. KESWANI

' Even H. A. Lorents did not quite attain the final form in his papers in the Enzyklopadie (I903), particularly not for magnetizable lDodies. Einstein called his paper of I905 " On the electrodynamics of moving bodies " and indicatedin this mannera principal goalofhis theoryofrela- tivity; however he does not enter upon the general structure of the equations for ponderable bodies but confines himself instead to the equations arising for the isolated electron. Minkowski in I908, at long last in full possession of the principle of relativity, was the first to solve the problem completely'.

Poincare, however, had indicated earlier that a satisfactory formul- ation of the electrodynamics of moving bodies was connected with the problem of the aether or the concept of relativity.

We let this matter rest there partly in the realm of conjecture.

4 Was Einstein aware of Lorentz's Memoir of 1904?

Einstein had published seven papers, all in Annalen der Physik-a leading journal of physics during the period I9OI-5 and before the publication of the relativity paper and was definitely well in touch with current ideas in physics, but as Max Bornl points out, there is a conspicious peculiarityaboutthis relativit,y-paper. ' Thestriking point is that it contains not a single reference to previous literature. It gives you tlle impression of quite a new venture. But that is, of course, as I have tried to explain, not true.'

We can, therefore, hope to trace the connection with previous work only from the text of the paper but before we do that let us see what exactly was the contribution made in the I904 memoir of Lorentz.

It is sometimes said that Lorents put forward L.T.E. to establish covariance of Maxwell's equations.2 This was only a part of Lorentz's programme. He devised these equations primarily to show that the transformations for space and time were such as to give a null result of various aether-drift experiments3: that is how these equations origin-

1 Max Born, Physics in My Generatiorl, Pergamon Press, I956, p. I93

2 For example see: J. Jeans, The Mathematical Theory of Electricity and Magnetism, Cambridge, I960, p. 600

3 As Lorentz himself pointed out years ago, similar equations were given by W. Voigt in I887 so that the form of the wave equation

a2+ a2+ a20_I a2+ aX2 + ay2 + aZ2- C2 at2 X

remained the same for a moving system. Rene Dugas, op. cit. p. 468, therefore, suggests that they should be called Voigt-Lorentz transformation equations.

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ORIGIN AND CONCEPT OF RELATIVITY

ated with Lorentz (pp. II-I3 and 29). He then showed that the mass of an electron increases with velocity (p. 24), applied the equations for mass-variation to an analysis of the experimental data forelectrons then available and conjectured that masses of all particles are influenced by a translation in the same manner. This part of the work, surely, cannot be regarded as a mere attempt to find equations of transforma- tion from one co-ordinate system to another such that the form of Maxwell's equations remains unchanged.

Indeed Einstein also established the formulae for the variation of mass with velocity for the case of an electron only, but with his char- acteristic physical insight, he (p. 63) immediately saw, '. . . these results as to the mass are valid for all ponderable material points, because a ponderable material point can be made into an electron (in our sense of the word) by the addition of an electric charge, no matter how small '. (And we could now say, no matter how big !) How simple ! The analysis was not dependent on the magnitude of the charge of an elec- tron and the formulae are, therefore, true of all masses, whatever their charge.

Incidentally, Einstein (pp. 62-63) got incorrect expressionl for the ' transverse mass ', [mO/(I-v2lc2)] instead of [mO/(I v2/c2)2]. But for the ' longitudinal mass ' he gave the correct expression [mO/(I v2/c2)2]. Lorentz gave correct expressions for both.

We now come to the question whether Einstein knew of Lorentz's memoir of I904. There is no definite evidence but there is a significant remark in Einstein's paper (p. 60) to the effect:

' Since asfollowsfrom the theorem of addition of velocities-the vector (ux, uyX uz) is nothing else than the velocity of the electric charge, measured in the system K, we have the proof that, on the basis of our kinematic principles, the e]ectrodynamic foundation of Lorentz'stheoryof the electro- dynamics of moving bodies is in agreement with the principal of relativity.'

Einstein did not say exactly which theory or work of Lorentz he meant but it is clear that the theory in question was in accord with the principle of relaiivity, and this on the basis of Einstein's kinematical principles. It is to be noted again that Einstein was not claiming any significant advance but only an agreement. Now, none of the theories of Lorentz published by him before his memoir of I904 was in agree- ment with the principle of relativity but the basic equations (L.T.E.) of the memotr of I904 were strictly in accord with the principle of

1 See footnotes by A. Somlnerfeld, The Principle of Relativity, Dover, p. 63, and Rene Dugas, op. cit. p. 482

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G. H. KESWANI

relativity (further remarks on this will follow in subsequent papers). Therefore, could Einstein have had in his mind any other theory of Lorentz than the one propounded a year earlier? He knew of ' Lorentz's theory of the electrodynamics of moving bodies ', he him- self was putting forward a new theory also of the electrodynamics of moving bodies (the title of his paper) involving ' a modification of the theory of space and time ', as he put it in a letterl to his friend Habicht written on 6th March I905. It is hardly likely that it could be an old theory of Lorentz which might, after all, have been superseded by a later theory of Lorentz, who was still alive and at the height of his intellectual powers. Moreover, this theory of Lorentz was to be in agreement with the principle of relativity on the basis of Einstein's new ' kine- matical principles', and we shall now show that Einstein did indeed establish such an agreement viewed in relation to Lorentz's memoir of I904. On account of lack of these ' kinematical principles ' Lorentz had been able to establish covariance of Maxwell's equations only partially. To be more precise, it was because Lorentz had not dis- covered the correct formula for compounditlg velocities that he got transformed equations of Maxnvell in a form which is not fully the same as for the ' stationary ' system. Of course, this formula follows from L.T.E., which were already in the possession of Lorentz in the year I904.

Before we proceed further, we may, however, remark that at the very beginning of his paper (p. 37) Eillstein made a statement leaving the impression that the previous workers had ' shown to the first order of small quantities, (that) the same laws of electrodynanzics and optics will be valid for all frames of reference for which the equations of mechanics hold good ' but his statement on p. 60 quoted above does not claim any advance in so far as the order of accuracy goes. This state- ment asserted only an agreement. As a matter of fact, Lorentz himself remarked at the beginning of his memoir (p. I5) that his transformation equations were valid for small values of v so that 1, a function of v, diflRered from unity ' no more than by a quantity of the second order ', but he himself removed this limitation when he showed (Lorentz, p. 27) that I was indeed equal to unity, always.

Incidentally, both Lorentz (p. I4) and Einstein (p. 44) carried out the ' Lorentz transformation ' in two stages, the first one being a transition to the ' moving ' axes. We have therefore, replaced x by (x-Vt) in Lorentz's formulae (p. I4). Also, both first arrive at the more general

Carl Seelig, op. cit. p. 75; also quoted earlier in tlle present paper.

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ORIGIN AND CONCEPT OF RELATIVITY

form of transformation x'-pI(x- vt) or :+(v) (x vt), etc. and show by diSerent methods (p. 27, 47) that I or +(v) must be unity. We have taken I I.

As usual, Lorentz (p. I3) took Maxwell's equations for electric charge in empty space moving with velocity u (components uZ, ug, uz) referred to the ' fixed ' or ' stationary ' system of co-ordinates as:

div E-p, div H-O

curl H =-(at +pu), curlE - c at '

where, E-- electric field strength, H magnetic field strength, and p volume-density of electric charges.

Let the components of velocity of the electric charges as measured in the 'moving' system be ux, uy and ux and the velocity of the 'moving' system itselfwith reference to the ' stationary ' system be v in the direc- tion of U$. Using the transformation equations (we have used more or less the same notation as used in Einstein's paper):

(i) x'-:(x vt), y'-y, z'-z, t' - :(t vxlc2)l LTE where -(I V2/C2)-i; J * *

(ii) p Fpt,F2(UX V)-tXx>pHy Uy:Ux-tlz;

and (iii) X' - X, L' = L,

y' _ (Y vN/c), M - (M+vZ/c), Z' :(Z+vM/c), N' :(N vY/c);

where (X, Y, Z) and (L, M, N) are the spatial components of the electric and magnetic field strengths respectively in the stationary frame (S), the corresponding quantities in the moving frame (S') being (X', Y', Z') and (L', M', N'), Lorentz (p. I5) showed that the transformed equations are:

div' Et = (I- X2 ) p', div' H = o, Primed symbols div', etc., mean ;>Ec that differentiation is carried out

curl' H' = - (a, +ptu'), curl' E' with respect to x', r' and z'.

I DH'

C Dt

It is obvious that the form of Maxwell's equations is unaltered if p'-O, i.e. when space under consideration is charge-free but the transformed equation

div E (I 62)p

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G. H. KESWANI

for the case when charge is present, is not of the same form as the cor- responding equation for the ' stationary' system. Lorentz did not, therefore, establish complete co-variance of Maxwell's equations. As we shall see, Lorentz's equations for transforming p, ux, uq, and uz were not correct, because he did not investigate the kinematic consequences of his (Lorentz) transformation equations. In particular, he did not secure the velocity-addition formula, though this is implied in L.T.E., which is required when transformation of Maxwell's equations for the case of moving electric charges is under consideration.

In the paper, ' Sur la dynamique de l'electron ' (the first mentioned shorter paper published inJune I905), Poincare discovered the following cortect equation for transforming the charge-density, so as to leave the form of Maxwell's equations unchanged under his transforrnation equation for charge taken along with Lorents's equations for transforming E, H, x, r, Z and t. (However, Poincare did not elaborate any proof.)

pt p (I _ X ) p

Einstein proceeded as follows. He first considered the two equa- tions for empty space in the ' stationary ' system:

-- curl H and ---curl E. c at c at

Written in Cartesian form these are: X aN bM IaL aY az

, etc

c at ay az ' c at flaz ay Referred to the ' moving ' system of axes, these are transformed by L.T.E. alone into:

I abtXt - a t {:(N vY)}- aa,{:(M+ 8 z)}, etc.

This result is easily established as follows: Iax Iraxat ax ax)

obvlouslyc at ci at at + ax at 3

I { aX*F+ X*v }

F { aX + aX} aX aY az

Now a + > + a -o in charge-free empty space.

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ORIGIN AND CONCEPT OF RELATIVITY

Putting Bx / aY azA ax z aN aMX

-+ l and - c , . I , aX < ay az y at ay az y

we have I DX raN aM vbY vaz)

_ -R - o

cat' r ay az c ay c azj

j { ay ( 6 ) aZ ( 6 )} @

Again- -, and- , from L.T.E. ay ay az az

*@ C att ayt{(N CY)} az{(M+CZ)}@

On the basis of equivalence oftwo inertial systems, Einstein (p. 53) identified these equations with the following corresponding equations assumed to

be of the same form for the ' moving ' system: I ax' aNt aMt I aL' ay' az' c att = ayt Bz' 'c at' azt ay, ,etc.,

and got the transformation equations for the electric and magnetic field strengths as:

X' X, L'-L'

Y' :(Y cN), M :( c )

Z' :(Z+-M), N'-:(N - Y).

(More correctly X' +(v)X, etc., but considering the inverse transformation from X' to X etc., as Einstein pointed out, obviously 0(v)-I.)

Lorents (p. I4-IS) gave the same results, implicitly assuming that Maxwell's equations should have the same form in the ' moving ' system.

Einstein (p. sg-60)further considered the equations for the transfor- mation of charge-density, p, and current, pu, with the assistance of (i) the above equations for transforming E (components X, Y, Z) and H

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G. H. KES WANI

(components L, M, N), (ii) the equation ax + a Y + az = p and (iii) his

newly discovered (p. 50) formulae for compoundi1ng velocities,1 viz. Ux-(USC V)l(I U2V/C2), etc.

In charge-occupied space, the previous two sets of Maxwell's equations in the ' stationary ' system are:

ISaX ) aN aMIaL aY az

l-+uZp3 etc.

Assuming that the equations for the transfornlation of E and H are of the same form for charge-occupied space as for charge-free space, we further pro- ceed thus:

IaX I rax at ax ax) _ . X

c at' c at * at' ' ax * at'

ct t + ax } I ax aN aM uZp (Maxwell's equation for the ' station-

Now - <

cat by az c tary ' system. ax f aY az)

and --p t-+-t ax ( aN aM ay azl -a - <cb ca uZp+vp va va S

* c at'+ c(UZ-8) p ={ay(N_vy)_ a (M+vz)}

Putting X = X', F (N _ v y) = N' : (M + v z) = M' as fior

charge-free space, we have I (axt ) aNt aMt ( a a a a Q v_+s(u- v)pt-ay az tay ay az az3

If this equation has to have the same form as the one for the ' stationary ' system, clearly

uXp'-F(ux v)p.

As stated above, Einstein (p. 50) had shown earlier in his paper that UX - (UX-V)/(I UJCI}/C2).

1 This formula and that for the Doppler eSect may be regarded as the principal contribution of Einstein to relativistic mechanics. To say this is neither to deny that this is an important contribution nor to imply that there is no other contribution.

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ORIGIN AND CONCEPT OF RELATIVITY

Einstein (p. 60) therefore concluded that

p -- :(I Ux8/62) p.

It is easily verified that the remaining Maxwell's equations are trans- formed covariantly by L.T.E. taken along with the above equations for transforming the components of E, H, p and u.

We thus see that Lorents succeeded only partly in establishing co- variance of Maxwell's equations. His equations for transforming E and H were correct and, given the correct kinematical equation for corupounding velocities, his analysis also leads to correct and complete covariance of Maxwell's equations. Armed with the formula, based or) L.T.E., for compounding velocities, Einstein completed Lorentz's analysis for the transformation of Maxwell's equations a1ld remarked that on the basis of his kitlematics not fully developed by Lorentz but following from his equations (L.T.E.) the electrodynamic theory as propounded by Lorentz (p. I4-I5) was in agreement with the principle of relativity. This remark of Einstein exactly defines the advance made by him on Lorentz's theory given in the preceding memoir. And is this union of Lorentz's equations and the principle of relativity not a marriage of the ideas of Lorentz and Poincare? The odds are that Einstein solemnised this marriage. We need not go into the question why the priest did not make it public. Moreover, the priest revealed secrets of physical harmony which had never been dreamt before. Einstein's work cannot be regarded as mere bringing-together of two previous works; it appeared so soon after tlle two and he struck out in so many new directions that it is probable that he was only looking for some confirrrsation of his audacious ideas before publishing them.

We nzentioned a little earlier the formulae for longitudinal and transverse mass of an electron given by Lorentz (p. 24! and Einstein (p. 63). Einstein used the same terrninology as Lorentz and said (p. 62), ' Taking the ordinary point of view we now inquire as to the " longi- tudinal" and " transverse" mass of an electron.' Whose w-as this ordinary point of view?

Now Max Abraharnl had still earlier used the terms ' longitudinal ' and ' transverse ' for the masses of an electron with reference to the direction of it motion but he gave incorrect expressions for these masses evell in his paper of I903, preceeding Lorentz's memoir.

However, Einstein neither refers to the corrections to Abraham's

Max Abraham, ' Prinzipien der Dynamik des Elektrons ',Annalen der Physik, I903,

I0, I S?

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G. H. KESWANI

formulae, nor explains the small discrepancy between his formula and that of Lorentz for the transverse mass. Perhaps this can be cleared up. We may add that the diSerence between Lorentz's and Einstein's for- mulae for the transverse mass is such as may go tmdetected.

(To be concluded)

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