Poincaré’s Relativistic Physics: Its Origins and NatureVol. 7 (2005) Poincaré’s Relativistic Physics 269 and for that reason it has attracted extensive historical and philosophical

268

Poincaré’s Relativistic Physics: Its Origins and Nature

Shaul Katzir*

Henri Poincaré (1854–1912) developed a relativistic physics by elevating the empirical inability todetect absolute motion, or motion relative to the ether, to the principle of relativity, and its math-ematics ensured that it would be compatible with that principle. Although Poincaré’s aim and the-ory were similar to those of Albert Einstein (1879–1955) in creating his special theory of relativ-ity, Poincaré’s relativistic physics should not be seen as an attempt to achieve Einstein’s theory butas an independent endeavor. Poincaré was led to advance the principle of relativity as a conse-quence of his reflections on late nineteenth-century electrodynamics; of his conviction that physicsshould be formulated as a physics of principles; of his conventionalistic arguments on the natureof time and its measurement; and of his knowledge of the experimental failure to detect absolutemotion. The nonrelativistic theory of electrodynamics of Hendrik A. Lorentz (1853–1928) of 1904provided the means for Poincaré to elaborate a relativistic physics that embraced all known phys-ical forces, including that of gravitation. Poincaré did not assume any dynamical explanation ofthe Lorentz transformation, which followed from the principle of relativity, and he did not seek todismiss classical concepts, such as that of the ether, in his new relativistic physics.

Key words: Henri Poincaré; Hendrik A. Lorentz; Albert Einstein; principle of relativi-ty; electrodynamics; physics of principles; Lorentz transformation; simultaneity; mea-surement of time.

Inroduction

The electrodynamics of bodies moving at high velocities attracted considerableattention at the beginning of the twentieth century, and various theories were proposedfor it. All of the theories were based on Maxwell’s equations, but rested on differentgrounds and led to distinctly different solutions. Albert Einstein (1879–1955) based histheory on the principle of relativity and the constancy of the speed of light, meaning bythe former that all phenomena depend only on motion relative to matter and not rel-ative to the electromagnetic ether. Two other physicists, Alfred Bucherer (1863–1927)and Henri Poincaré (1854–1912), also used the principle of relativity in their investiga-tions. Bucherer, however, did not accept the Lorentz transformation, while Poincarédid. Poincaré’s theory thus was more similar to Einstein’s theory of special relativity,1

Phys. perspect. 7 (2005) 268–2921422-6944/05/030268–25DOI 10.1007/s00016-004-0234-y

* Shaul Katzir teaches in the Graduate Program in History and Philosophy of Science, Bar IlanUniversity.

Vol. 7 (2005) Poincaré’s Relativistic Physics 269

and for that reason it has attracted extensive historical and philosophical attention,which has generally been directed at trying to establish which aspects of special rela-tivity Poincaré anticipated. I believe, by contrast, that Poincaré’s work should not beseen as an attempt to formulate special relativity, but as an independent attempt toresolve questions in electrodynamics. The superiority of Einstein’s theory over Poin-caré’s was not evident around 1905.

Edmund T. Whittaker opened the debate about Poincaré’s contribution to specialrelativity with his provocative claim that special relativity had been discovered by Poin-caré and Hendrik A. Lorentz (1853–1928) already in 1904.2 A decade later, GeraldHolton analyzed Poincaré’s theory, pointing out the thematic differences betweenPoincaré’s and Einstein’s work that had prevented Poincaré from creating special rel-ativity.3 Stanley Goldberg and Camillo Cuvaj followed Holton in identifying differ-ences between Poincaré’s and Einstein’s concepts and advancing further reasons forPoincaré’s failure to create special relativity.4 Arthur I. Miller later published a detailedstudy of Poincaré’s major paper of 1905, “On the Dynamics of the Electron,”5 and in asubsequent paper concluded that Poincaré

was involved in the grandiose research program known as the electromagneticworld-picture in which Lorentz’s electromagnetic theory is the fundamental theoryfor all matter in motion. Consequently, mechanics would be deduced from Lorentz’selectromagnetic theory, and subsequently the rest of physics.6

Other historians and philosophers, however, have disputed the claims of Holton,Goldberg, and Miller. Jerzy Giedymin concluded that Poincaré had indeed discoveredthe main components of special relativity, although he did not analyze the develop-ment of Poincaré’s work in detail.7 Eli G. Zahar, on the basis of a “rational recon-struction” of Poincaré’s work, also claimed that Poincaré had discovered special rela-tivity.8 Olivier Darrigol adopted a different approach, examining Poincaré’s contribu-tions to electrodynamics and the role that the principle of relativity played in them.9

Finally, Peter Galison investigated Poincaré’s and Einstein’s involvement in the tech-nology of time and distance measurements and their relationships to the concept ofsimultaneity.10

I will avoid viewing Poincaré’s work through the lens of Einstein’s theory of specialrelativity and concentrate on his engagement with the principle of relativity, which wascentral to his view of physics in general and of electrodynamics in particular, between1895 and 1905. Poincaré’s physics, in other words, was a relativistic physics, one thatdenied in principle that there is any observable difference between a stationary systemand one moving uniformly with respect to it. Late nineteenth-century electrodynamicsadmitted differences between a system at rest and one in motion relative to the ether,and hence the principle of relativity in mechanics could have been maintained ifmotion relative to the ether was regarded as relative motion. Poincaré, however, in hisnew interpretation of electrodynamics considered such motion to be absolute motion,and was convinced that to adapt the principle of relativity to it required the adjustmentof current physical concepts. I claim that the principle of relativity guided Poincaré’sthinking, and because of his commitment to it he deliberately elaborated a relativisticphysics.

Shaul Katzir Phys. perspect.270

I will first discuss the development of Poincaré’s thought on the principle of relativ-ity after 1895 and then, in light of that development, analyze Poincaré’s major paper of1905, “On the Dynamics of the Electron.” The sources of Poincaré’s thought on theprinciple of relativity were the current theories of electrodynamics, the known experi-mental evidence, the general role that principles played in Poincaré’s physics and phi-losophy, and his physical and philosophical considerations on space and time. Poin-caré’s development of his theory thus displays an alternative path to a relativisticphysics, and since it is better documented than Einstein’s, it may help us to reconstructEinstein’s as well.* In any case, my discussion of Poincaré’s thought on the principle ofrelativity after 1895 will lay the groundwork for my subsequent discussion of his 1905paper, which disagrees with those who maintain that Poincaré was committed to theelectromagnetic worldview and advanced a constructive theory of electrodynamics.Instead, I see in the general role that Poincaré assigned to principles in physics anexplanation of the special way in which he presented his study. In my concluding sec-tion, I will comment on the physical significance of Poincaré’s new theory of electro-dynamics, how the Lorentz transformation was involved in it, and on the role that Poin-caré assigned to the ether in it.

Poincaré’s Development of the Principle of Relativity, 1895-1905

First Statements

Henri Poincaré (figure 1) introduced the principle of relativity in 1895 in connectionwith a critical examination of current theories of electrodynamics:

Experiment has revealed a group of phenomena that can be summarized as follows:It is impossible to detect the absolute movement of matter, or better, the relativemovement of ponderable matter in relation to the ether; all that one can find evi-dence of is the movement of ponderable matter in relation to ponderable matter.

The suggested theories [of electrodynamics] account well for this law, but on twoconditions:1. One has to neglect dispersion and various other secondary phenomena of the

same type.2. One has to neglect the square of the aberration.Now, this is not enough; the law also seems to be true without these restrictions, aswas proved by a recent experiment by Mr. Michelson.11

Poincaré noted that current theories of electrodynamics accounted only for phenome-na of first order in v/c, where v is the velocity of the moving matter and c is the speedof light, such as the ether-drag experiment of Hippolyte Fizeau (1819–1896) of 1851.12

* Darrigol has already discussed some of the work of Poincaré and others (notably Lorentz) toelucidate the electrodynamic origins of special relativity; see Darrigol,“electrodynamic origins”(ref. 1).

Poincaré concluded that the failure of current theories of electrodynamics, such asLorentz’s electron theory, to conform fully to the principle of relativity constituted alacuna in them,* which he connected to another shortcoming, their failure to conformto the principle of action and reaction.

[The] impossibility to find evidence for the relative movement of matter withrespect to the ether, and the indisputable equivalence of action and reaction with-out allowing for the action of matter on ether, are two facts whose connection seemsevident.

Perhaps the two lacunas will be filled at the same time.13

Fig. 1. Henri Poincaré (1854–1912). Source: Poincaré, Dernières Pensées (ref. 82), frontispiece.

* That Poincaré did not refer here to Lorentz’s length-contraction conjecture of 1892 to accountfor the null result of Michelson’s experiment indicates that Poincaré was dissatisfied withLorentz’s conjecture as an explanation of the principle of relativity.



The principles of relativity and of action and reaction were part and parcel of mechan-ics. Poincaré’s discussion of them in the context of electrodynamics shows that heviewed them as general principles of physics. Moreover, he regarded both as dealingonly with observable entities. The equivalence of action and reaction could be retainedin Lorentz’s theory if the reaction of the ether were taken into account. The principleof relativity could be valid if motion relative to the ether were regarded as relativemotion. Poincaré rejected these solutions. Instead, by requiring the validity of both inelectrodynamics, Poincaré concluded that current theories of electrodynamics wereinadequate.

Five years later, in a lecture at the International Congress of Physics in Paris in 1900,Poincaré reiterated his view that current theories of electrodynamics were in conflictwith the principle of relativity, in whose validity he now seemed to be more confident.According to the theories, he said, “one might expect to see precise methods givingpositive results” for determining the absolute motion of the Earth through the ether,but he believed that “such a hope is illusory.”14 Contrary to expectations, experimentsin neither first-order nor second-order in v/c had detected the motion of the Earththrough the ether. Lorentz had suggested two explanations for this failure, his famouscontraction hypothesis and his concept of corresponding states (see below). Yet, Poin-caré concluded,

this is not enough; who does not feel that this is still to leave to chance too great arôle? Would not that also not be a chance, this singular coincidence which broughtit about that a certain circumstance should come just in the nick of time to destroythe terms of the first order, and that another circumstance, wholly different, but justas opportune, should take upon itself to destroy those of the second order? No, it isnecessary to find an explanation the same for the one as for the other, and theneverything leads us to think that this explanation will hold good equally well for theterms of higher order, and that the mutual destruction of these terms will be rigor-ous and absolute.15

A few months later, Poincaré returned to the principle of relativity in a thorough studyof the principle of action and reaction in Lorentz’s electrodynamics. “As Lorentz’s the-ory shows,” he wrote, “the so-called principle of relative motion was verified onlyimperfectly. This is due to a compensation of effects.”16 In Lorentz’s theory, he point-ed out, terms of second order in v/c had to be neglected; a “local time” instead of thereal time had to be used; different values for the energy in different frames of refer-ence had to be introduced; and an electromagnetic force that exists only in a movingframe of reference had to be assumed. Lorentz’s theory, therefore, conflicted with theprinciple of relativity, and Poincaré once again saw a close connection between thatprinciple and that of action and reaction. Now, however, he showed that the principleof action and reaction could be deduced from the principle of relativity and the princi-ple of conservation of energy.

According to Lorentz’s theory the principle of [action and] reaction does not applyto matter alone and the principle of relative motion does not apply to matter alone


either. The important point is that there is an intimate and necessary connectionbetween these two facts.

It thus will be enough to establish experimentally one of these two [facts] for theother to be established ipso facto.17

Poincaré actually considered the possibility of abandoning both of these principles, butconcluded that their conflict with Lorentz’s theory required physicists,* as he hadclaimed in 1895, “to profoundly modify all of our ideas on electrodynamics.”18

A New Concept of Time

In explaining and elaborating Lorentz’s theory in 1900, Poincaré gave new meaningespecially to Lorentz’s concept of “local time,” which Poincaré claimed was the timemeasured by moving clocks:

I suppose that observers placed at different points set their watches by means ofoptical signals; that they try to correct these signals by the transmission time [of lightbetween them], but that, ignoring their [common] translatory motion and thusbelieving that the signals travel at the same speed in both directions, they satisfythemselves with crossing the observations, by sending one signal from A to B, thenanother from B to A. The local time t’ is the time indicated by watches set in thismanner.

If c is the speed of light, and v the translation [velocity] of the Earth, which I sup-pose to be parallel to the positive x axes, one has t’ = t – vx/c2.19

Poincaré’s expression here neglects higher-order terms in v/c and is identical toLorentz’s, but Poincaré’s physical interpretation of the local time t’ is completely dif-ferent from Lorentz’s: “Lorentz had in mind only a convenient auxiliary transforma-tion, not at all a revision of the concept of time.” Lorentz did not attribute physical real-ity to the local time t’ prior to 1909, he did not regard it as the time measured byclocks.20 Poincaré attributed physical reality to the local time t’, which was a novel andsignificant step, but he devoted only the above words to it, not even explaining how toderive the above expression.21 Poincaré thus seems to have regarded the synchroniza-tion of clocks by means of light signals as a straightforward idea requiring no furthermathematical or physical elaboration,** probably because he had already explainedthis synchronization procedure, although only for observers at rest, two years earlier ina philosophical paper on “The Measurement of Time.”22

* Poincaré did not think that Lorentz’s theory required that the principle of action and reactionhad to be changed, and certainly not rejected. He insisted on the importance of this principle.For a detailed discussion, see Darrigol, “Poincaré’s Criticism” (ref. 9), pp. 17–31.

** Other physicists provided this elaboration:Emil Cohn (1854–1944) explained that the new timevariable is the time measured by clocks in 1904; Max Abraham (1875–1922) followed suit inearly 1905;and Albert Einstein (1879–1955) did the same a few months later; see Darrigol,“elec-trodynamic origins” (ref. 1), pp. 300–301.


In his paper of 1898 on “The Measurement of Time,” Poincaré adopted a conven-tionalistic approach to the concept of time. He ignored qualitative psychological time,asserting that we have no intuitive knowledge of it. Two difficulties then arise: how todefine the equality of two intervals of time, and how to define the simultaneity of twoevents. The first difficulty arises from our lack of “direct intuition of the equality of twointervals of time,”23 a difficulty that had been known at least since the time of Williamof Ockham (ca. 1285–1349) and had been restated thereafter in different versions bymany philosophers and physicists, including some of Poincaré’s contemporaries.24

Poincaré denied that the equality of two intervals of time can be defined objectively,concluding that such equality can be defined only conventionally: Two equal intervalsof time could be defined by reference to the daily rotation of the Earth, the monthlyrevolution of the Moon, or in some other way.25

Poincaré’s discussion of the simultaneity of two events was more original andstemmed from his view that the synchronization, and therefore the temporal order oftwo events, can be defined only by means of signals of finite speed. He opened his dis-cussion by questioning the meaning of the claim that the Nova of 1572 occurred afterColumbus’s discovery of America in 1492, since at least two hundred years had elapsedbefore its light had reached the Earth, so that the resident of a nearby planet wouldhave observed it long before Columbus arrived in America. The temporal order ofthese two events is thus a matter of convention, and for us to say that Columbus’s dis-covery of America preceded the Nova in an absolute sense requires us to conceive ofa supreme intelligence that sees and classifies everything temporally just as we do.Since, however, all past, present, and future events would be known to such a supremeintelligence, and since Poincaré saw time in the Aristotelian tradition as a manifesta-tion of change, he concluded that such a supreme intelligence “would have no time”and thus, even if such a being existed, it would be impenetrable to us. We thereforemust find other means to define the temporal order of events. One promising waymight be to invoke causality, but this would be circular, since we customarily definecausality by invoking the temporal order of cause and effect. Moreover, every phe-nomenon in principle involves an infinite number of causal factors, so there is no one-to-one correspondence between cause and effect. To Poincaré, the latter was not ahypothetical situation, since he had shown how it emerged in a three-body systemunder gravitational attraction – a problem that was one of his areas of expertise.26

Time as defined by the temporal order of events therefore depends upon whichevents are familiar to us, and that is different for different people in different loca-tions. Remote events are perceived by observers by means of light signals, which alsoare used to define simultaneous events. Light signals therefore play a central role indefining time and its measurement, which to Poincaré was connected to his concep-tion of and philosophical reflections on geometry and space. Poincaré’s famous claimthat geometry is an experimental science meant to him that Euclidean geometry isbased upon human experience and thus on the linear propagation of light.27 His dis-cussion of time thus can be seen as an extension of his reflections on geometry andspace.

To Poincaré, however, the measurement of time was not merely an abstract philo-sophical issue. As a member of the French Bureau of Longitude since 1892, he was


immersed in the problem of the measurement of longitude, which rested on the syn-chronization of clocks by means of telegraphic signals.This practical problem also stim-ulated his philosophical reflections on time, as did astronomical practice.28 Anastronomer, Poincaré wrote, has to begin

by supposing that light has a constant velocity, and in particular that its velocity isthe same in all directions. That is a postulate without which no measurement of thisvelocity could be attempted.29

Poincaré’s statement was not the first formulation of the light postulate of special rel-ativity, as some have claimed,30 but was a convention that he adopted in his definitionof simultaneity. Measurements of longitude involved the use of electrical signals intelegraph wires, and Poincaré now referred to the fastest known signal, that of light. Tohim, the postulate that the speed of light is the same in all directions was a conventionthat depends upon the formulation of physical laws; if those laws were different, thespeed of light would not be the same in all directions (even in the ether). The questionof the simultaneity of events thus cannot be separated from the problem of the mea-surement of time. We can define simultaneous events as those whose impressionsarrive at an observer at the same time, or as those whose signals left their points of ori-gin at the same time and traveled to an observer at the speed of light.

The simultaneity of two events, or the order of their succession, the equality of twodurations, are to be so defined that the enunciation of the natural laws may be assimple as possible. In other words, all these rules [for determining absolute time], allthese definitions are only the fruit of an unconscious opportunism.31

Two years later, in 1900, Poincaré concluded that Lorentz’s theory suggested that theuse of “true” regular time does not lead to the simplest laws of Nature, and that the useof “local time” instead is more convenient. Moreover, clocks that are synchronized bymeans of light signals in a system that obeys Lorentz’s equations would show not the“true” regular time but the “local time.”

The Role of Principles in Physics

Most physicists did not share Poincaré’s concern about the fate of the principles of rel-ativity and of action and reaction in Lorentz’s electrodynamics.32 Poincaré’s interest intheir fate was rooted in his general conviction of the central role of principles inphysics, which led him to attribute increasing importance to the principle of relativity.33

To Poincaré, the principles of physics are abstractions and generalizations of physicallaws, and are both the basis and aim of physical research. They are constraints on allphysical theories, rather than independent axioms as in geometry.* Poincaré’s physics

* Poincaré’s use of the term “principle” differed from that of some of his contemporaries, espe-cially in Germany, who took a “principle” to mean a fundamental assumption in a particulartheory.To Poincaré, such a fundamental assumption, even one as general as the theory of grav-itation or of electricity, was not a “principle.”


thus was a “physics of principles,” as Darrigol has called it.34 These principles reflecttrue relations (rapports vrais) between physical quantities with no need for specificphysical hypotheses.

In 1904 Poincaré gave a lecture at the Congress of Arts and Science in St. Louis, Mis-souri, in which he observed that the new physics of principles had replaced the oldphysics of central forces.

[Investigators] gave up trying to penetrate into the detail of the structure of the uni-verse, to isolate the pieces of this vast mechanism, to analyse one by one the forceswhich put them in motion, and were content to take as guides certain general prin-ciples which have precisely for their object the sparing us this minute study.…

[The universe] is also a machine, much more complicated than all those of indus-try, and of which almost all the parts are profoundly hidden from us; but in observ-ing the movement of those that we can see, we are able, by aid of this principle [ofconservation of energy], to draw conclusions which remain true whatever may bethe details of the invisible mechanism which animates them.35

Since the true mechanism of the universe will remain hidden from us, there is no pointin suggesting hypotheses as to what it might be. The principles of physics offer a way toavoid hypothetical assumptions. In rejecting any attempt to discover the hidden mech-anism of the universe, Poincaré thus dismissed the mechanical worldview and focusedon the principles of physics, which are rooted in the long history of physical theory.

Most of Poincaré’s contemporaries did not assign such a central role to the principlesof physics. While Poincaré regarded them as a substitute for the mechanical worldview,some physicists continued to espouse the mechanical worldview; others preferred theelectromagnetic worldview;36 and still others embraced phenomenological theories.Thus, Poincaré’s “physics of principles” was a programmatic proposal, an attempt tointerpret current physics, not a description of the views of his contemporaries. His aimwas to unite all of physics in a structural manner through its principles, not to constructthe whole of physics on the basis of a single force. The same principle could describesimilar properties of distinctly different forces, such as the electromagnetic and gravita-tional forces. He thereby distanced himself from the electromagnetic worldview.37

To Poincaré, although the principles of physics originate in experience, they are notmerely generalizations of experimental facts; each is a kind of definition – a convention– that a single experiment could neither confirm nor refute. Physical theory is flexibleenough to admit an additional hypothesis that could resolve a specific contradiction;38

an additional hypothesis thus might not place any constraint on physical theories. Itmight, however, conflict with a principle of physics, and if the theoretical modificationsthat were required to maintain the principle were too extensive, it had to be aban-doned;39 a principle that is immune to contradiction is useless. Conversely, the modifi-cations of the principles of relativity and of action and reaction that would be requiredto include the ether seemed to Poincaré to be too extensive. He never provided clearcriteria, however, for retaining or rejecting a principle; that was a subjective judgmentbased upon the current state of knowledge.

By 1904 Poincaré had concluded that most of the accepted principles of physics wereno longer valid, because they had been contradicted by recent experiments and theo-

ries. Only the principle of relativity and the principle of least action remaineduntouched,40 and he had changed his view on the epistemological origins of the former.Four years earlier, he had written that the principle of relativity, “which was unneces-sary a priori, was verified a posteriori.”41 Now, in his lecture in St. Louis, he claimed that“the principle of relativity … not only is confirmed by daily experience … but it isimposed in an irresistible way upon our good sense.…”42 Nevertheless, current elec-trodynamic theories entailed that the principle of relativity should be interpreted asincluding both matter and the ether. That interpretation, to Poincaré, would deprivethe principle of relativity of meaning.

Indeed, experience has taken upon itself to ruin this interpretation of the principleof relativity; all attempts to measure the velocity of the earth in relation to the etherhave led to negative results. This time experimental physics has been more faithfulto the principle than mathematical physics.43

Poincaré’s words suggest that in addition to the null result of the Michelson-Morleyexperiment, which he mentioned, he also may have had in mind more recent experi-ments, such as the one carried out by Frederick T. Trouton (1863–1922), which showedthat the failure to detect motion relative to the ether was not limited to optical phe-nomena.* To explain these experimental results, Poincaré noted, “was not easy, and ifLorentz has gotten through it, it is only by accumulating hypotheses.”44 Poincaré wasreferring here to Lorentz’s new theory, which he had published only a few months ear-lier, and which accounted for all of these experiments. As noted above, Poincaré hadcriticized Lorentz’s earlier first-order theory and contraction hypothesis of 1892 fortheir lack of coherence and for their conflict with the principle of relativity. Poincaré’scriticism had now stimulated Lorentz to reformulate his theory.

Lorentz’s Theory of 1904

Lorentz’s electrodynamic theory of 1904 has been discussed extensively in the histori-cal literature,45 so I will only sketch its central feature here, namely, Lorentz’s intro-duction of the concept of “corresponding states” between a moving frame and the“true” frame of the stationary ether. Lorentz (figure 2) showed that the variables in thetwo corresponding states transformed according to the now-famous Lorentz transfor-mation equations, which accounted for all of the experimental null results that hadbeen found in the attempts to detect the motion of the Earth relative to the ether.Lorentz’s theory, however, did not preclude the possibility of detecting this motion. In

* Following a suggestion of George F. FitzGerald (1851–1901),Trouton in 1902 tried to detect animpulse on a charging and discharging condenser moving with the Earth. He assumed that amagnetic field would be generated when a moving condenser was charged, the energy of whichwould come from the condenser’s kinetic energy, so that the condenser would recoil. A yearlater, he and Henry R. Noble carried out a more sensitive experiment to detect the same effectby looking for a turning couple on a charged and oscillating condenser. See Janssen,“Lorentz’sether theory” (ref. 46), pp. 19–29; “Reconsidering” (ref. 46), pp. 439–441.



it Maxwell’s equations in the moving frame are identical to those in the stationaryether frame only for the charge-free case, so with electrical charges present the relativemotion should be detectable, in contradiction to the principle of relativity. This was noproblem for Lorentz, since he did not require that his theory be compatible with theprinciple of relativity, but only with the experimental results; he even stated that therelative motion should be observable in a more delicate version of Trouton’s experi-ment.46 Had Lorentz intended to produce a relativistic theory, he would have had nodifficulty in modifying his expressions for the variables in the corresponding state ofthe moving frame accordingly.*

Fig. 2. Hendrik A. Lorentz (1853–1928). Credit: Algemeen Rijksarcheif, The Hague. Courtesy ofAmerican Institute of Physics Emilio Segrè Visual Archives.

* Roberto Torretti has pointed out that Lorentz’s theory contradicts the principle of relativity,which follows directly from Lorentz’s equation for the displacement in the corresponding states,but Torretti does not regard Lorentz as being indifferent to the principle of relativity; see RobertoTorretti, Relativity and Geometry (Oxford: Pergamon Press, 1983), p. 85.

That was exactly what Poincaré did in the first letter he wrote to Lorentz after hesaw Lorentz’s new theory. Unlike Lorentz, Poincaré was convinced that the principleof relativity had to be preserved, and hence he regarded the Lorentz transformationequations not as mathematical transformations, as Lorentz had, but as physical trans-formations. He thus derived from them expressions for the charge density in the mov-ing frame. To Poincaré, that represented only a technical correction of a mathematicalerror that Lorentz had made.47

Poincaré’s Subsequent View of the Principle of Relativity

With that correction, Poincaré then regarded Lorentz’s theory as satisfying the princi-ple of relativity, and he presented Lorentz’s results as such in his lecture in St. Louis in1904. He recognized only three hypotheses in Lorentz’s theory: the hypothesis of “localtime,” the contraction hypothesis, and the hypothesis that forces, “whatever be theirorigin, gravity as well as elasticity, would be reduced in a certain proportion.…”48

Lorentz had not mentioned the third hypothesis, and Poincaré did not regard theLorentz transformation as a hypothesis, probably because he saw it as following fromthe first two hypotheses, from which the physical transformations of the coordinatescould be derived.

Poincaré emphasized Lorentz’s concept of local time, regarding it as Lorentz’s “mostingenious idea.” Yet, instead of adopting Lorentz’s view of local time as an auxiliarymathematical variable, Poincaré presented his own physical interpretation of it, whichhe had already suggested four years earlier. In comparing the old “classical” conceptsof time and velocity with the new ones, Poincaré declared that when two observersmove relative to each other, “the transition [of light] would not be the same in the twodirections.” To adjust their watches, however, the two observers had to assume the con-stancy of the speed of light in each of their reference frames, so that “watches adjustedin that manner do not mark … the true time; they mark what one may call the localtime, so that one of them goes … [slower than] the other.”49 But there is no way todetermine which watch lags behind the other one, since all phenomena lag together.Thus, one is left with the local time and the assumption that light is transmitted at aconstant speed with respect to the local frame: “True time” is inaccessible in the newrelativistic physics. Moreover, Poincaré recognized the crucial role that the speed oflight plays in the new concept of time that followed from his understanding of the prin-ciple of relativity. He thus asked:

What would happen if one could communicate by non-luminous signals whosevelocity of propagation differed from that of light? If, after having adjusted thewatches by the optical procedure, one wished to verify the adjustment by the aid ofthese new signals, then would appear divergences which would render evident thecommon translation of the two stations.50

Poincaré’s question was not merely a rhetorical one. Current physical theory admittedsignals faster than the speed of light, and Pierre Simon Laplace (1749–1827) had con-cluded that the speed of the gravitational force was at least a million times faster than



that of light. Poincaré thus recognized that his new interpretation of the principle ofrelativity required a modification of the theory of gravitation: Gravitational forceshould transform like electromagnetic forces (his third hypothesis) and should notpropagate at a speed faster than that of light.Thus, the principle of relativity, which firstemerged in mechanics, now revealed the need to modify both electrodynamic andgravitational theory.

Poincaré therefore recognized by 1904 that the admission of the principle of relativ-ity into physics required significant changes in current physical theories and concepts.He also recognized the significance of light signals in his new relativistic physics. On apractical level, he understood the importance of the Lorentz transformation as a phys-ical space-time transformation that linked two observers moving relative to each other.That mass varied with velocity – a necessary consequence of his new relativistic theory– had already been confirmed qualitatively by Walther Kaufmann (1871–1947) in hisexperiments with high-speed electrons between 1901 and 1903.51 Poincaré, however,insisted that the principle of relativity requires that all mass, not only electromagneticmass, must vary in the same manner.52 Poincaré introduced these revolutionary con-cepts in the midst of what he viewed as a “crisis of mathematical physics” that hademerged owing to the contradictions that had been found between the principles ofphysics and experimental observations. “From all these results,” Poincaré concluded, “ifthey are confirmed, would arise an entirely new mechanics, which would be, above all,characterized by this fact, that no velocity could surpass that of light, any more than anytemperature could fall below the zero absolute.”53 To Poincaré, this new mechanics wasnot Lorentz’s theory. Instead, Lorentz’s theory should be surpassed, first by makingelectrodynamics fully compatible with the principle of relativity, and second by discov-ering further consequences of the principle of relativity. Poincaré now took on this lat-ter task himself by studying the implications of his new relativistic mechanics.

“On the Dynamics of the Electron”

Its Structure and Content

Poincaré (figure 3) read a preliminary report of his study, “On the Dynamics of theElectron,” to the Paris Académie des Sciences on June 5, 1905, which he then expand-ed into a long paper by July, which was published in 1906.54 This was one of Poincaré’srare research papers on electrodynamics (his paper of 1900 on the principle of actionand reaction in Lorentz’s theory was another one). In his present paper, Poincaréexplored the consequences of the principle of relativity in kinematics, dynamics, elec-trodynamics, and gravitation. This principle, that all physical laws in moving and sta-tionary frames of reference are identical, and Maxwell’s equations, are the only twopremises he assumed; all other characteristics of his new relativistic physics, such as theconstancy of the speed of light, follow from them.* Each part of electrodynamic theo-

* Since Poincaré’s new relativistic theory therefore depends upon the validity of Maxwell's equa-tions, it is not as general as Einstein’s special theory of relativity, which assumes only the prin-ciple of relativity and the constancy of the speed of light.

ry has to conform to these two premises, while other physical theories, such as gravita-tional theory, have to conform only to the principle of relativity, so that this principleplays the central role in physical theory. It rested on the experimental failure, from theexperiments of Augustin Fresnel (1788–1827) through those of Albert A. Michelson(1852–1931) to those up to that point in time, to detect the motion of the Earth throughthe ether. “Apparently, the impossibility to produce experimental evidence for theabsolute motion of the Earth,” Poincaré asserted, “is a general law of nature; we arenaturally inclined to accept this law, which we will call the Postulate of Relativity, andaccept it without restriction.”55 In contrast to Einstein, who denied the existence ofabsolute motion, Poincaré denied the possibility to detect it, and hence denied that itplayed any role in physical theory.

To Poincaré, in accordance with his general view of principles in physics, the princi-ple of relativity was a constraint on physical theory. Instead of deducing consequencesfrom it, he used it mainly to confirm or refute various hypotheses according to whetherthey agreed or disagreed with it, and if the latter were the case for a given hypothesis,that was sufficient reason to reject it. Thus, he used the principle of relativity to showthat a given hypothesis is necessary, possible (as in gravitational theory), or unattain-

Fig. 3. Henri Poincaré (1854–1912). Credit: Cliché Henri Manuel. Courtesy of American Institute ofPhysics Emilio Segrè Visual Archives, Physics Today Collection.



able (as in the case of Max Abraham’s electron hypothesis, which stood in contradic-tion to it).*

Poincaré introduced the Lorentz transformation, according to which “two systems,one stationary the other in translation, become the exact image of each other,”56 intohis theory without deriving it. To him its justification was that it was compatible bothwith the principle of relativity and with Maxwell’s equations, which are invariant undera Lorentz transformation.** He further demonstrated that a Lorentz transformationforms a mathematical group, thereby making its reciprocity evident,57 and allowinghim to use it as the mathematical basis for deriving the transformations of other phys-ical magnitudes such as velocity and volume, and from them the transformations ofcharge density, electric current, electric and magnetic fields, and electromagneticforce.58 In these derivations Poincaré deviated from Lorentz’s nonrelativistic results of1904, which from Poincaré’s relativistic perspective were mistaken. Poincaré’s deriva-tion of the transformation of electromagnetic force involved the peculiarities of elec-trodynamics, yet it should be valid for any force, since he argued that all forces, fromwhatever their origins, are affected similarly.59

Poincaré thus regarded the consequences of the principle of relativity as not beingrestricted to mechanics and electrodynamics but to include Newtonian gravitationaltheory, which is in conflict with it and would permit the propagation of gravitationalforce at speeds faster than the speed of light. To prevent that possibility, Poincaré con-structed a gravitational theory that was compatible with the principle of relativity – aLorentz covariant theory, to use modern terminology – according to which the gravita-tional force propagates like the electromagnetic force at the speed of light, undergoesa Lorentz transformation, and coincides with Newtonian gravitational theory at lowvelocities. He assumed that gravitational mass is constant, which made his gravitation-al theory analogous to electrodynamic theory with constant charge. He did not find aunique gravitational force; instead, he derived two different expressions for the gravi-tational-force law from a general mathematical expression from which theoretically aninfinite number of different laws could be derived. To choose among them, he said,required more accurate observational data.60 Poincaré’s relativistic theory of gravita-tion, in sum, was an integral part of his relativistic physics, which now included allknown forces. Only a gravitational force that transforms like the electromagnetic forceand propagates at the speed of light could ensure the failure to detect motion relativeto the ether.

* Perhaps because Poincaré used the principle of relativity as a constraint on his theory and notas starting point to deduce consequences from it, Miller regarded it as secondary to Poincaré’sspecific assumptions,which were rooted in Lorentz’s electron theory; see Miller,“Poincaré”(ref.6), p. 77. However, the assumptions of Poincaré’s theory, for example, the Lorentz transforma-tion (including both time dilatation and length contraction), depend logically on their compat-ibility with the principle of relativity (and with Maxwell’s equations).

** Poincaré first applied the Lorentz transformation directly to Maxwell’s equations and then usedthe principle of least action to show, more generally, that the action integral is invariant undera Lorentz transformation; see Poincaré, “Sur la dynamique” (ref. 54), pp. 489–501, 510–513.

Poincaré also employed the principle of relativity to decide among current theoriesof electrodynamics, and at the same time showed that the principle of least action wasapplicable to electrodynamics.61 He studied the so-called Langevin waves,* “a particu-larly elegant form of the formulas that define the electromagnetic field produced by asingle electron,”62 but his main concern was to examine current hypotheses on the vari-ation of the mass and shape of the electron at high velocities.** He thus invoked theprinciple of relativity to decide among the rival hypotheses that followed from the elec-tron theories of Lorentz, Bucherer, and Max Abraham (1875–1922). He showed thatLorentz’s electron theory was the only one of the three that was compatible with theprinciple of relativity, which therefore served as arbiter among them. He also foundthat the structures of the electron that followed from all of the theories except Abra-ham’s required a supplementary nonelectromagnetic potential to maintain the electronagainst electrostatic repulsion. He concluded:

Hence Lorentz’s hypothesis is the only one compatible with the impossibility ofdetecting absolute motion; admitting this impossibility one has to admit that theelectrons in motion contract so that they become oblate spheroids [ellipsoïdes derévolution] of which two axes stay constant; it is necessary therefore to admit … theexistence of a supplementary potential proportional to the volume of the elec-tron.63

Poincaré showed that this supplementary potential, which became known as the “Poin-caré stress,”64 was compatible with the principle of relativity, proving that it is invari-ant under a Lorentz transformation. This potential thus resolved an internal contradic-tion in Lorentz’s theory of 1904.65

Poincaré’s reliance on the principle of relativity to decide among current theories ofelectrodynamics did not imply that he embraced the electromagnetic worldview,according to which all forces in Nature are electromagnetic in origin – an ontologicalstance that conflicted with his physics of principles. If Poincaré had been committed tothe electromagnetic worldview, he would have embraced Abraham’s electron theory,which did not require the existence of a supplementary nonelectromagnetic potential.Instead, by embracing Lorentz’s theory, Poincaré chose to embrace the principle of rel-ativity instead of the electromagnetic worldview.66 Moreover, he suggested that theadditional nonelectromagnetic potential might be connected to another nonelectro-magnetic potential, the gravitational potential, since both are proportional to the restmass. This was yet another manifestation of his misgivings about the electromagneticworldview. “There are forces,” Poincaré wrote, “that one cannot attribute to an elec-tromagnetic origin, for example gravitation.”67

* Paul Langevin (1872–1946) divided the electromagnetic field of an electron into two waves, onedue to its velocity, the other to its acceleration. Poincaré showed that these waves transformaccording to the Lorentz transformation, which enabled him to calculate the wave due to itsvelocity using the wave in its rest system. See Miller, “Study” (ref. 5), pp. 264–266.

** Miller gives a step-by-step analysis of these sections in Poincaré’s paper; see Miller, “Study”(ref. 5), pp. 266–301.



The Physical Meaning of the Lorentz Transformation

Poincaré introduced the Lorentz transformation as being between a stationary and amoving system. Yet, throughout his paper he used it to transform between two movingsystems. He did not differentiate, moreover, between the two systems in his mathe-matical treatment: Since the Lorentz transformation forms a group, it applies to anytwo uniformly moving systems, thus from one moving frame of reference, like the lab-oratory frame, to another, like the electron rest frame, neither of which is identical tothe ether frame. Poincaré, in other words, did not abandon the concept of the ether, buthe did not assign to it the role of a preferred frame of reference in a Lorentz transfor-mation from one system to another. Time also plays a role similar to that of the spatialcoordinates, as Poincaré emphasized in the four-dimensional formalism that he intro-duced. He did not distinguish between the time before and after a Lorentz transfor-mation, nor did he mention Lorentz’s “local time.” The Lorentz transformation trans-forms all mechanical coordinates, replaces the classical Galilean transformation, andexpresses the contraction of lengths and the dilation of time.

Poincaré applied the Lorentz transformation to a sphere, showing how it changedinto an ellipsoid, and to an electron, showing how it contracted,68 thus applying it toboth a rigid body and to an imaginary surface in space. In 1904 Lorentz had suggestedthat such contractions are produced by physical changes in the forces between parti-cles of matter “in quite the same way as the electric forces.…”69 Poincaré, however, aswe have seen, was reluctant to accept such hidden mechanisms and had claimedalready in 1900 that the transformation of time derives from the measurement oflength by means of light signals propagating at a constant speed. The speed of light,which appears in different parts of his theory, thus seems to be the key to his thoughtson the origin of the Lorentz transformation and hence on his new relativistic physics.

The constant and finite speed of light, appearing as it did in both electrodynamicsand gravitation, apparently required a dynamic explanation.

If the propagation of the [force of gravitational] attraction is at the speed of light,that cannot be just pure luck, but has to be due to a function of the ether; it will benecessary to search for the nature of this function, and to connect it to the otherfunctions of the fluid.70

Still, Poincaré suggested “another perspective” based upon a historical analogy:

…Copernicus, in a simple change of the coordinates’ axis regarded as fixed, causedthis appearance [of the common motion of the epicycles and deferents] to fade....

Here it is possible that there would be some analogue; if we admit the relativitypostulate, we will find in the law of gravitation and the electromagnetic laws a com-mon number, the speed of light; and we will find it again in all of the other forces ofwhatever origin, which can be explained only in two ways:

Either everything in the world is of electromagnetic origin [which he had shownwas not the case].*

Or this component [the speed of light], which is so to speak common to all phys-ical phenomena, is only an appearance, something that is due to our methods of

measurement. How do we measure? By transporting objects regarded as invariablesolids against others, one would answer; but this is no longer true in the present the-ory if the Lorentz contraction is accepted. In this theory two equal lengths are, bydefinition, two lengths that light traverses in the same time.71

Poincaré’s new relativistic physics thus was based upon measurement.** Lengths aredefined by means of light signals. To Poincaré, the Lorentz transformation is closelylinked to our methods of measurement.

Poincaré’s definition of length may appeal to modern readers, but he himselfremarked that someday it might have to be abandoned, and with it Lorentz’s entiretheory:

Maybe it will be sufficient to give up this definition [of measurement of length bymeans of light signals] to overthrow Lorentz’s theory just as the system of Ptolemywas by the intervention of Copernicus. If such a day arrives, it will not prove thatLorentz’s effort was useless; for Ptolemy, whatever people think, was not useless forCopernicus.72

Cuvaj has claimed that Poincaré was envisioning here an Einstein who someday wouldoverthrow Lorentz’s classical theory of mechanics,73 which may be true with respect tothe concept of space, but Einstein introduced the Lorentz transformation similarly, bydefining length by means of light signals, although he used rods (that is, solids) for themeasurement of lengths.74 Poincaré’s words should be seen instead as a historical-philosophical observation on the nature of scientific change: He held a gradualist viewthat entailed both the transitory nature of scientific theories (a theme he later repeat-ed in popular addresses75) and their continuity. Just as classical physics was replaced bya new relativistic physics, so that physics probably also would be replaced someday.

Poincaré’s realization that a relativistic physics is linked to the definition of lengthby means of light signals did not mean that the Lorentz contraction originated in ourmethods of measurement. As he wrote in 1907, “we have no way of knowing whetherthis deformation be real.” We “have no way of knowing whether it is the magnitude [oflength] or the instrument which has changed”;76 both possibilities have the same phys-ical significance. Poincaré therefore did not dismiss the possibility of a dynamicalchange in length, but he also did not seek a dynamical explanation for it. Neither doeshis position dismiss Einstein’s view that there is no need to explain the origin of the

* Miller omitted the word “Either” in this sentence, as though Poincaré had stated that “every-thing in the universe is of electromagnetic origin.” This allowed Miller to support his interpre-tation of Poincaré's theory. See Miller, “Poincaré” (ref. 6), p. 81.

** Many readers seem to have missed the important point that to Poincaré the Lorentz transfor-mation was closely linked to our methods of measurement. Among those who referred to thispassage, Zahar did not realize that Poincaré had dismissed the first, electromagnetic alterna-tive; see Zahar, “Poincaré's Independent Discovery” (ref. 8). Giedymin did not explain Poin-caré’s views on the origin of the Lorentz transformation; see Giedymin, Science and Conven-tion (ref. 7), p. 186. Darrigol connected Poincaré’s view here only to his conventionalism, claim-ing that Poincaré probably did not consider revising the concept of time;see Darrigol,“Poincaré’sCriticism” (ref. 9), pp. 36–37.



Lorentz transformation and thereby length contraction and time dilation, just as inNewtonian mechanics there was no need to explain the Galilean transformation. Heprobably thought that there was no need to seek some hidden source of the Lorentzcontraction, since that had no physical significance. The definition of length by meansof light signals can be preserved no matter whether the magnitude of length or theinstrument changes. To Poincaré, the justification of the Lorentz transformation origi-nated neither in the method of measurement of length nor in a real contraction rela-tive to the ether, but in its agreement with the principle of relativity. He was commit-ted to the principle of relativity, not to the ontological nature of the new relativisticlaws of physics such as the Lorentz transformation.

The Role of the Ether

If a dynamical explanation for the Lorentz transformation were to be found in the out-come of some process, that process should occur in the ether. Poincaré’s indifference tosuch a dynamical explanation did not mean that he denied the existence of the ether inhis new relativistic physics, just that the ether played no role in his theory. The princi-ple of relativity negates only the theoretical possibility of detecting the ether, not thatof its existence. Others who worked on relativity at the beginning of the last century,such as Hermann Minkowski (1864–1909), Max Planck (1858–1947), Gustav Mie(1868–1957), and David Hilbert (1862–1943), also upheld the existence of the ether(although they regarded it as four-dimensional). To Poincaré (figure 4), the ether wasundetectable but was still a useful concept. He was indifferent to ontological questionssuch as the reality of the ether, but he did not regard the ether as superfluous. As heexplained in 1900:

We know the origin of our belief in the ether. If light reaches us from a distant star,during several years it was no longer on the star and not yet on the earth; it mustthen be somewhere and sustained, so to speak, by some material support.77

Yet, he had also declared in 1898 and again in 1900 that:

It matters little whether the ether really exists; that is the affair of metaphysicians.The essential thing for us is that everything happens as if it existed, and that thishypothesis is convenient for the explanation of phenomena.… [No] doubt, some daythe ether will be thrown aside as useless.78

That day, however, had not yet arrived, nor did Poincaré’s novel use of the principle ofrelativity change his mind on this question: The ether remained as the locus of electro-magnetic fields, in particular of light waves, and of the gravitational field.79

Today, space or space-time in physics plays the role of Poincaré’s ether, but to Poin-caré space by itself was meaningless: Space in his philosophy was convenientlydefined by material bodies, but had no inherent properties, not even that of volume,80

so space cannot carry forces or waves. Without the ether, action at a distance wouldbe unavoidable, yet the ether has no mechanical properties. In particular, Poincaréattributed no material properties to the ether, as can be seen from his attitude on the


action of ether on matter as expressed in his paper of 1900 on the principle of actionand reaction: He preferred to reject that principle instead of applying it to both etherand matter, a position he also embraced later.81 If he accepted the notion that radia-tion carries momentum, he thought that it was not the usual kind of momentum asso-ciated with matter. He continued to refer to the ether as the carrier of electromag-netic interactions; for example, he considered the ether as the seat of the electromag-netic resonators in Planck’s quantum theory.82 His discussions involving the conceptof the ether were inconsistent: At times he referred only to the ether, at other timesonly to electromagnetic fields or waves; both seem to have denoted the same thing tohim.

Poincaré’s retention of the concept of the electromagnetic ether reveals that histhought was rooted in turn-of-the-century electrodynamics. He constructed a new rel-ativistic physics based upon electrodynamic theory, but he did not attempt to modifyclassical physics more than seemed to be necessary to include in it the experimentallyvalidated principle of relativity. He wished to preserve the concepts of classical physics.This also was evident in his treatment of the concepts of space and time. Regarding thelatter, he followed Lorentz and continued to employ the terms “true time” and “localtime” (later “apparent time”), but to him “local time” was the time marked by clocks,while “true time” had no physical meaning; it could be identified with the time of theether frame, but it had no special properties and was undetectable. Poincaré also called

Fig. 4. Henri Poincaré (1854–1912). Credit: American Institute of Physics Emilio Segrè VisualArchives.


for the preservation of the concepts of classical physics in his popular addresses. Theycontinued to be those employed in daily life and technology,84 and knowledge of themwas necessary for the understanding of his new relativistic physics.

Conclusions

Poincaré’s paper of 1905,“On the Dynamics of the Electron,” was the culmination of hisefforts to uphold the principle of relativity and to incorporate it into physics, althoughhe discussed it later in the classroom and in popular addresses. In his paper, he con-structed a new relativistic physics that applied to all forces known at the time, those ofelectromagnetism and gravitation, and that ensured the impossibility of detectingabsolute motion, that is, motion relative to the ether. In his commitment to the princi-ple of relativity, he rejected the electromagnetic worldview. Yet, his new relativisticphysics originated in electromagnetic theory. He reinterpreted the principle of relativi-ty to exclude effects of motion relative to the ether, and to keep Maxwell’s equationsinvariant under a transformation that turned out to be a Lorentz transformation. Poin-caré’s particular view of physics as a physics of principles, which was connected to hisphilosophy of physics, impelled him to elevate the empirical inability to detect motionrelative to the ether to the status of a principle, the principle of relativity, which he usedto critically examine current theories of electrodynamics and to modify accepted phys-ical laws and concepts, such as that of time. His work in combining the measurement oflongitudes with the synchronization of clocks promoted his philosophical analysis of theconcept of time, which helped to give shape to a new meaning of that concept.

In Poincaré’s new interpretation of electrodynamics, the validity of the principle ofrelativity rested on the experimental failure to detect the motion of the Earth withrespect to the ether. The central role that principles played in his quest for a relativis-tic physics suggests that Einstein may have been similarly directed in creating his spe-cial theory of relativity. Both Poincaré and Einstein were committed to theories ofprinciple rather than to constructive theories. Lorentz’s theory of moving charges,especially in its version of 1904, though nonrelativistic, supplied a basis to Poincaré onwhich he constructed a new and rigorous relativistic physics. He was agnostic on onto-logical questions raised by his new relativistic physics, including those involving spaceand time. To Poincaré, the principle of relativity was the sole basis and justification forhis new relativistic physics. He formulated no independent theory, but only used theprinciple of relativity to show how current theories of electrodynamics and gravitationhad to be modified to be compatible with it. Lorentz’s theory and Newton’s theoryremained as the fundamental bases of electrodynamics and gravitation.

Acknowledgments

My paper originated in my M.A. thesis, which I wrote at Tel Aviv University under thesupervision of Ido Yavetz and also of Jürgen Renn of the Max Planck Institute for theHistory of Science in Berlin, where I carried out part of my research for it. I thank eachof them for their help, as well as Leo Corry, who commented on an earlier draft of mypaper, and Anne Sartiel, who eliminated some of the awkward phrasing in it. I also

thank the anonymous referees for their helpful comments on my paper, and Roger H.Stuewer for his thoughtful and careful editorial work on it.

References

1 Olivier Darrigol, “The electrodynamic origins of relativity theory,” Historical Studies in the Physi-cal and Biological Sciences 26 (1996), 241–312.

2 Edmund T. Whittaker, A History of the Theories of Aether and Electricity. Vol. 2. The Modern The-ories (New York: Tomash Publishers and American Institute of Physics, 1987), pp. 27–77.

3 Gerald Holton, “On the Thematic Analysis of Science: The Case of Poincaré and Relativity,” inL’aventure de l’esprit. Mélanges Alexandre Koyré. Vol. II (Paris: Hermann, 1964), pp. 257–268.

4 Stanley Goldberg, “Henri Poincaré and Einstein’s Theory of Relativity,” American Journal ofPhysics 35 (1967), 934–944; “Poincaré’s Silence and Einstein’s Relativity: The Role of Theory andExperiment in Poincaré’s Physics,” British Journal for the History of Science 5 (1970), 73–84;Camillo Cuvaj, “A History of Relativity: The Role of Henri Poincaré and Paul Langevin,” Ph.D.Dissertation, Yeshiva University, 1970.

5 Arthur I. Miller, “A Study of Henri Poincaré’s ‘Sur la Dynamique de l’Électron’,” Archive for His-tory of Exact Sciences 10 (1973), 207–328.

6 Arthur I. Miller, “Why did Poincaré not formulate Special Relativity in 1905?” in Jean-LouisGreffe, Gerhard Heinzmann, and Kuno Lorenz, ed., Henri Poincaré: Science et philosophie, Con-grès International, Nancy, France, 1994 (Berlin: Akademie Verlag and Paris : Albert Blanchard,1996), pp. 69–100; quotation on p.77.

7 Jerzy Giedymin, Science and Convention: Essays on Henri Poincaré’s Philosophy of Science andthe Conventionalist Tradition (Oxford: Pergamon Press, 1982).

8 E.G. Zahar, “Poincaré’s Independent Discovery of the Relativity Principle,” Funamenta Scientiae4 (1983), 147–175.

9 Olivier Darrigol, “Henri Poincaré’s Criticism of Fin De Siècle Electrodynamics,” Studies in Histo-ry and Philosophy of Modern Physics 26 (1995), 1–44.

10 Peter Galison, Einstein’s Clocks and Poincaré’s Maps: Empires of Time (New York: Norton, 2003).11 Henri Poincaré,“A propos de la théorie de M. Larmor,” L’Eclairage électrique 5 (October 5, 1895),

5–14; reprinted in Œuvres de Henri Poincaré, Vol. 9 (Paris: Gauthier-Villars, 1954), pp. 395–426;quotation on p. 412.

12 Ibid., p. 395. For a recent discussion, see Jan Frercks, “Fizeau’s Research Program on Ether Drag:A Long Quest for a Publishable Experiment,” Physics in Perspective 7 (2005), 35–65.

13 Ibid., p. 413.14 H. Poincaré,“Relations entre la Physique Expéimentale et la Physique Mathématique,” in Ch.-Éd.

Guillaume et L. Poincaré, ed., Rapports présentés au Congrès International de Physique réuni aParis en 1900 sous les Auspices de la Société Française de Physique. Tome I (Paris: Gauthier-Vil-lars, 1900), pp. 1–29, quotation on p. 22; reprinted in Henri Poincaré, La Science et l’Hypothèse(Paris: Ernest Flammarion, 1902), quotation on p. 201; translated by George Bruce Halsted as Sci-ence and Hypothesis in H. Poincaré, The Foundations of Science (Lancaster, Penn.: The SciencePress, 1946), quotation on p. 147.

15 Poincaré, “Relations” (ref. 14), pp. 22–23; Science and Hypothesis (ref. 14), pp. 147–148.16 Henri Poincaré, “La Théorie de Lorentz et le Principe de Réaction,” Archives néerlandaises des

Sciences exactes et naturelles 5 (1900), 252–278; reprinted in Œuvres (ref. 11), pp. 464–488; quota-tion on p. 483.

17 Ibid., p. 488. Poincaré’s italics; my translation of the first paragraph follows Darrigol, “Poincaré’sCriticism” (ref. 9), p. 26.

18 Ibid., Poincaré’s italics.19 Ibid., p. 483. Owing to a misprint in the first paragraph, the local time t’ was printed erroneously

as t. I also changed Poincaré’s symbol V to c for consistency in notation. My translation of the firstparagraph follows Darrigol, “Poincaré’s Criticism” (ref. 9), p. 28.

20 Russell McCormmach, “H. A. Lorentz and the Electromagnetic View of Nature,” Isis 61 (1970),459–497; quotation on p. 470. Michel Heinrich Paul Janssen, “A comparison between Lorentz’s



ether theory and special relativity in the light of the experiments of Trouton and Noble,” Ph.D. Dis-sertation, University of Pittsburgh, 1995, pp. 250–263.

21 For a reconstruction of Poincaré’s argument, see Darrigol, “Poincaré’s Criticism” (ref. 9), p. 28.22 Henri Poincaré, “La mesure du temps,” in La Valeur de la Science (Paris: Ernest Flammarion,

1970), pp. 41–54; translated by George Bruce Halsted as “The Measure of Time,” in The Value ofScience in Poincaré, Foundations (ref. 14), pp. 223–234. For a discussion of some aspects of this arti-cle, particularly of the synchronization of clocks, see Galison, Einstein’s Clocks (ref. 10), pp.187–191; Goldberg, “Poincaré” (ref. 4) pp. 939–940; and Cuvaj, “History of Relativity” (ref. 4), p.77. My interpretation of the philosophical aspects of Poincaré’s paper is closer to Galison’s.

23 Poincaré, “mesure” (ref. 22), p. 43; “Measure” (ref. 22), p. 224. Poincaré’s italics.24 Galison, Einstein’s Clocks (ref. 10), p. 314.25 Poincaré, “mesure” (ref. 22), pp. 43–47; “Measure” (ref. 22), p. 224–226.26 Ibid., pp. 48–52; 226–228; Galison, Einstein’s Clocks (ref. 10), pp. 62–66.27 Giedymin, Science and Convention (ref. 7), p. 3; Poincaré, Valeur (ref. 22), pp. 166–167; Value (ref.

22), pp. 236–237.28 Galison, Einstein’s Clocks (ref. 10), especially pp. 174–191.29 Poincaré, “mesure” (ref. 22), p. 52; “Measure” (ref. 22), p. 232. Poincaré’s italics.30 Cuvaj, “History of Relativity” (ref. 4), pp. 73,77; Jules Leveugle,”Poincaré et la relativité,” La jaune

et la rouge (Avril 1994), 30–51, especially 39.31 Poincaré, “mesure” (ref. 22), p. 54; “Measure” (ref. 22), p. 234. Poincaré put these words in quota-

tion marks to emphasize them.32 Darrigol, “electrodynamic origins” (ref. 1), pp. 276–277.33 Poincaré’s philosophy of science in connection with the development of his relativity theory has

been much discussed; see, for example, Goldberg, “Poincaré” (ref. 4); Miller, “Study” (ref. 5), pp.233–245; Giedymin, Science and Convention (ref. 7), pp. 149–195; and Zahar, “Poincaré’s Indepen-dent Discovery” (ref. 8). However, the role of principles in Poincaré’s physics, and more impor-tantly in the development of his relativity theory, has not been emphasized sufficiently, except byDarrigol, who elaborates their roles in Poincaré’s work on electrodynamics; see Darrigol, “Poin-caré’s Criticism” (ref. 9). I follow Giedymin in my interpretation of Poincaré’s conventionalisticphilosophy.

34 Darrigol, “Poincaré’s Criticism” (ref. 9), p. 10.35 Jules Henri Poincaré, “The Principles of Mathematical Physics,” translated by George Bruce Hal-

sted in Howard J. Rogers, ed., Congress of Arts and Science Universal Exposition, St. Louis, 1904,Vol. I (Boston and New York: Houghton, Mifflin and Company, 1905), pp. 604–622, quotation on606; reprinted in Katherine R. Sopka, ed., Physics for a New Century (New York: Tomash Publish-ers and American Institute of Physics, 1986), pp. 281–299; quotation on p. 283; French version inValuer (ref. 22), quotation on p. 126; translated slightly differently in Value (ref. 22), quotation onp. 300. I take all quotations from the first English translation above.

36 McCormmach, “Lorentz” (ref. 20).37 This is in contrast to Poincaré’s alleged commitment to the electromagnetic worldview as ascribed

to him by some historians; see Holton, “Thematic Analysis” (ref. 3); Goldberg, “Poincaré” (ref. 4);and Miller, “Study” (ref. 5).

38 H. Poincaré, “La Mécanique classique,” in Science et l’Hypothèse (ref. 14), pp. 110–134; translatedas “The Classic Mechanics,” in Science and Hypothesis (ref. 14), pp. 92–106.

39 Poincaré, “Principles of Mathematical Physics” (ref. 35), pp. 606–607; 283–284; Valeur (ref. 22), pp.145–146; Value (ref. 22), pp. 299–302.

40 Ibid.41 Poincaré, “Théorie de Lorentz” (ref. 16), p. 483.42 Poincaré, “Principles of Mathematical Physics” (ref. 35), p. 610; 287; Valeur (ref. 22), p. 132; Value

(ref. 22), p. 305.43 Ibid., p. 611; 288.44 Ibid.45 H.A. Lorentz, “Electromagnetic phenomena in a system moving with any velocity smaller than

that of light,” Koninklijke Akademie van Wetenschappen te Amsterdam. Proceeding of the Sec-

tion of Sciences 6 (1904), 809–831; reprinted in Collected Papers, Vol. 5 (The Hague: MartinusNijhoff, 1937), pp. 172–197. For his later formulation, see H.A. Lorentz, The Theory of Electronsand its Applications to the Phenomena of Light and Radiant Heat (Leipzig: B.G. Teubner, 1909;second edition, 1916). For discussions, see McCormmach, “Lorentz” (ref. 20), pp. 481–484; andJed Z. Buchwald, From Maxwell to Microphysics: Aspects of Electromagnetic Theory in the LastQuarter of the Nineteenth Century (Chicago: University of Chicago Press, 1985), pp. 250–254.For Lorentz’s treatment of moving bodies, see Tetu Hirosige, “Electrodynamics before the The-ory of Relativity, 1890–1905,” Japanese Studies in the History of Science 5 (1966), 1–49; “TheEther Problem, the Mechanistic Worldview, and the Origins of the Theory of Relativity,” His-torical Studies in the Physical Sciences 7 (1976), 3–82; and Janssen “Lorentz’s ether theory” (ref.20).

46 Janssen, “Lorentz’s ether theory”, pp. 17–62; “Reconsidering a Scientific Revolution: The Case ofEinstein versus Lorentz,” Physics in Perspective 4 (2002), 421–446, especially 439–441. Lorentz’s 1904paper was reprinted in H.A. Lorentz, A. Einstein, H. Minkowski and H. Weyl, The Principle of Rel-ativity: A Collection of Original Memoirs on the Special and General Theory of Relativity (New York:Dodd, Mead and Company, 1923), pp. 11–34, but its last section (§14, pp. 194–197) on Trouton’sexperiment was omitted, which may account for it being neglected by many historians.

47 For a facsimile of Poincaré’s letter to Lorentz in 1904, see Arthur I. Miller, “On Some OtherApproaches to Electrodynamics in 1905,” in Harry Woolf, ed., Some Strangeness in the Proportion:A Centennial Symposium to Celebrate the Achievements of Albert Einstein (Reading, Mass.: Addi-son-Wesley, 1980), pp. 66–91; on pp. 76–78.

48 Poincaré, “Principles of Mathematical Physics” (ref. 35), p. 612; 289; Valeur (ref. 22), pp. 133–134;Value (ref. 22), p. 307.

49 Ibid., p. 611; 288; pp. 133–134; p. 307.50 Ibid., p. 612; 289; p. 134; p. 308.51 Miller, “Study” (ref. 5), pp. 212–213; 229.52 Poincaré, “Principles of Mathematical Physics” (ref. 35), p. 615; 292; Valeur (ref. 22), pp. 138; Value

(ref. 22), p. 311.53 Ibid., p. 616; 293; p. 139; p. 312.54 Henri Poincaré, “Sur la dynamique de l’électron,” Comptes rendus hebdomadaries des séances de

l’Académie des Sciences 140 (1905), 1504–1508; “Sur la dynamique de l’électron,” Rendiconti delCircolo matematico di Palermo 21 (1906), 129–176; reprinted in Œuvres (ref. 11), pp. 494–550.Since the former paper is too brief to be of help in reconstructing Poincaré’s thought, I focus onthe latter paper in my discussion.

55 Poincaré, “Sur la dynamique” (ref. 54), p. 495.56 Ibid.57 Ibid., pp. 513–515.58 Ibid., pp. 498–503.59 Ibid., p. 496.60 Ibid., pp. 538–550. On Poincaré’s theory of gravitation see Shaul Katzir, “Poincaré’s Relativistic

Theory of Gravitation,” in Jean Eisenstaedt und Anne J. Kox, ed., The Universe of General Rela-tivity (Basel: Birkhäuser, 2005), pp. 15–37.

61 Ibid., pp. 503–510. Karl Schwarzschild (1873–1916) anticipated Poincaré by three years in demon-strating how to formulate electrodynamics using the principle of least action; see Hirosige, “Elec-trodynamics” (ref. 45), p. 30.

62 Poincaré, “Sur la dynamique” (ref. 54), p. 515.63 Ibid., p. 535.64 For the history and significance of the “Poincaré stress,” see Miller, “Study” (ref. 5), pp. 280–301;

Camillo Cuvaj, “Henri Poincaré’s Mathematical Contributions to Relativity and the PoincaréStresses,” American Journal of Physics 36 (1968), 1102–1113; and Galina Granek,“Poincaré’s Con-tributions to Relativistic Dynamics,” Stud. Hist. Phil. Mod. Phys. 31B (2000), 15–48, especially39–44.

65 Poincaré, “Sur la dynamique” (ref. 54), pp. 525–538.66 Janssen, “Lorentz’s ether theory” (ref. 20), pp. 225–227.



67 Poincaré, “Sur la dynamique” (ref. 54), p. 538. Miller, who views Poincaré’s theory as a contribu-tion to the electromagnetic worldview, seems not to have taken into account his treatment of grav-itation; see Miller, “Poincaré” (ref. 6); “Study” (ref. 5).

68 Poincaré, “Sur la dynamique” (ref. 54), pp. 499, 522–525.69 Lorentz, “Electromagnetic phenomena” (ref. 45), p. 183; Lorentz’s italics. Cuvaj and Goldberg

claim that Poincaré shared Lorentz’s position; see Cuvaj, “History of Relativity” (ref. 4), p. 99;Goldberg, “Poincaré” (ref. 4), pp. 942–943.

70 Poincaré, “Sur la dynamique” (ref. 54), p. 497.71 Ibid., pp. 497–498.72 Ibid., p. 498.73 Cuvaj, “History of Relativity” (ref. 4), p. 159.74 Albert Einstein, “Zur Elektrodynamik bewegter Körper,” Annalen der Physik 17 (1905), 891–921,

especially 895–900; reprinted in John Stachel, ed., The Collected Papers of Albert Einstein. Vol. 2.The Swiss Years: Writings, 1900–1909 (Princeton: Princeton University Press, 1989), pp. 276–306,especially 280–285.

75 H. Poincaré, “La mécanique nouvelle,” Revue Scientifique 47, No. 6–2e semestre (7 Août 1909),170–177, especially 170; “La mécanique nouvelle,” in Henri Poincaré, Sechs Vorträge über aus-gewählte Gegenstände aus der reinen Mathematik und mathematischen Physik (Leipzig and Berlin:B.G. Teubner, 1910), pp. 51–58, especially p. 52.

76 Henri Poincaré, Science et méthode (Paris: Ernest Flammarion, 1947), p. 100; translated by GeorgeBruce Halsted as Science and Method in Foundations of Science (ref. 14), pp. 359–546; on p. 416.

77 Poincaré,“Relations” (ref. 14), p. 21; reprinted in Science et l’Hypothèse (ref. 14), p. 199; Science andHypothesis (ref. 14), p. 146.

78 Poincaré, Science et l’Hypothèse (ref. 14), pp. 245–246; Science and Hypothesis (ref. 14), p. 174; alsoquoted in Darrigol, “Poincaré’s Criticism” (ref. 9), p. 19.

79 Poincaré, “Sur la dynamique” (ref. 54), p. 497.80 Poincaré, Science et l’Hypothèse (ref. 14), Chapter IV; translated as “Space and Geometry” in Sci-

ence and Hypothesis (ref. 14), pp. 66–80.81 Poincaré, “Théorie de Lorentz” (ref. 16), pp. 464–488; “Principles of Mathematical Physics” (ref.

35), pp. 612–614; 289–291; Valeur (ref. 22), pp. 134–137; Value (ref. 22), pp. 308–310. For a discus-sion, see Darrigol, “Poincaré’s Criticism” (ref. 9), pp. 17–19, 23–32.

82 Henri Poincaré, “Les Rapports de la Matière et de l’Éther,” in Société Française de Physique, LesIdées Modernes sur la Constitution de la Matière Conférences faites en 1912 (Paris: Gauthier-Vil-lars, 1913), pp. 357–370, especially pp. 355–356; reprinted in Dernières Pensées (Paris: Ernest Flam-marion, 1913), pp. 195–220, especially pp. 211–212; translated by John W. Bolduc as “The Relationsbetween Matter and Ether,” in Henri Poincaré, Mathematics and Science: Last Essays (DernièresPensées) (New York: Dover, 1963), pp. 89–101, especially 96–97.

83 Kenneth F. Schaffner has claimed that Poincaré recognized only the impossibility of universalsimultaneity and not the dilation of time, which is contradicted by Poincaré’s explicit claim that theequality of two durations is a convention and by his use of the “local time,” which shows that timedilates in his relativity theory; see Kenneth F. Schaffner,“Space and Time in Lorentz, Poincaré, andEinstein: Divergent Approaches to the Discovery and Development of the Special Theory of Rel-ativity,” in Peter K. Machamer and Robert G. Turnbull, ed., Motion and Time Space and Matter:Interrelations in the History of Philosophy of Science (Columbus: Ohio State University Press,1976), pp. 464–507.

84 Henri Poincaré, “La Dynamique de l’Électron,” Revue générale des Sciences pures et appliquées 19(1908), 386–402; reprinted in Œuvres (ref. 11), pp. 551–585, especially pp. 585–586; “mécaniquenouvelle,” in Sechs Vorträge (ref. 75), p. 58.

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Poincaré’s Relativistic Physics: Its Origins and NatureVol. 7 (2005) Poincaré’s Relativistic Physics 269 and for that reason it has attracted extensive historical and philosophical