An End to the Controversy

A recent book by J. Ginoux offers “an end to the controversy” regarding the discovery of special relativity. Not surprisingly, this has led to a flurry of controversy, with numerous back-and-forth communications being posted, notably between Ginoux and G. Weinstein. Below are some comments on Ginoux’s latest reply to Weinstein, using his ordering of the topics.

1. The Physical Meaning of the Lorentz Transformation

Poincare’s review of Lorentz’s 1904 article was published in June of 1905, presenting what he later named the Lorentz transformation. Lorentz had presented it in a fragmented form, since he implicitly began with a Galilean transformation, X = x−vt, T = t, and then applied the further transformation x’ = γX, t’ = t/γ – γvX where γ = 1/√(1−v²), so the overall transformation is x’ = (x−vt)γ, t’ = (t−vx)γ as written by Poincare. The question is whether this mathematical transformation represented the same thing, physically, to Lorentz and Poincare as it did to Einstein in his 1905 paper. Weinstein says they meant physically different things, and Ginoux responds by asking how they differ mathematically. This needs some clarification.

The physical meaning of a given mathematical equation depends not just on the form of the equation but on the meanings that we associate with the terms of the equation.  For a trivial example, consider the equation A=BC, which one author might use to describe the physical relationship between the force A, the mass B, and the acceleration C, while another might use it to represent the physical relation between the voltage A, the current B, and the resistance C. Obviously the relations F=ma and V=IR have very different physical meanings, despite being mathematically of the same form.

In the case of the Lorentz transformation, all the parties tacitly took x,t to be a standard system of inertial coordinates (i.e., a system of coordinates in terms of which the equations of Newtonian mechanics hold good, at least in the low speed limit), but there is some lack of clarity in what Lorentz and Poincare took x’,t’ to represent physically. Yes, by construction they are coordinates in terms of which Maxwell’s equations of electromagnetism take their usual homogeneous and isotropic form, but this doesn’t imply that they are standard inertial coordinates, which are defined in terms of the behavior of mechanical inertia. Lorentz explicitly admitted (later) that his failure to realize this was the chief reason for his failure to discover special relativity. Likewise, in later public lectures, Poincare credited Einstein’s 1905 paper for this crucial insight (which we know from the testimony of someone who attended one of those lectures). Even Minkowski’s 1908 paper credits Einstein as the first to recognize the real physical significance of the transformed coordinates. Furthermore, Lorentz, Poincare, and even Minkowski were still devoted to the idea that all physics could ultimately be reduced to electromagnetism, even though they all (as after-thoughts) acknowledged the possibility that other forces, including even ”inertial forces”, if not electromagnetic in origin, would need to be assumed to transform in the same way as electromagnetic forces. From this they could have realized that the transformed coordinates were indeed nothing but standard inertial coordinates… but they didn’t. We shouldn’t judge them too harshly, because even today it’s very difficult for people to grasp this when they are first exposed to it, and many never do, even among those who are superficially well-versed in relativity.

In summary, it isn’t that the parties were using mathematically different relations (aside from Lorentz’s mistake with the current density), it’s that the physical meanings that they attached to the terms in the equations were different. To the ends of their lives, both Poincare and Lorentz continued to express their preference for the “old” way of thinking, in which there is a single “true” absolute simultaneity, regardless of the practical difficulty of identifying it. Poincare held to the view that the subject was fundamentally a matter of convention, until Einstein pointed out the actual (measurable) path-dependence of proper time.  It’s also worth noting that although Poincare had recognized in his 1898 article on “The Measure of Time” that different methods of synchronization could yield different simultaneities, he did not discuss the possibility that a single method could yield different simultaneities for different frames of reference, and he certainly never imagined that inertial simultaneity was relative – let alone that the elapsed proper time between two events was path-dependent – despite the fact that both he and Lorentz were in possession of all the facts necessary to reach that conclusion. The facts were necessary, but not sufficient. 

In other words, we can’t rightly attribute the discovery of a concept to a person purely based on the fact that they were in possession of all the facts necessary to recognize the concept. After all, Newton was arguably in possession of all the facts necessary to discover special relativity. The principle of inertia, by itself, logically implies (as can be shown by grade school algebra) that standard inertial coordinates must be related by Euclidean, Galilean, or Lorentzian transformations, and, as Minkowski later observed, the Lorentzian group is more “mathematically intelligible” than the Galilean group (as we’ve discussed elsewhere), so “the thought might have struck some mathematician, fancy free, that natural phenomena do not possess invariance under the Galilean group, but rather under the Lorentzian group. Such a premonition would have been an extraordinary triumph for pure mathematics.” Moreover, by the 1850’s with the establishment of the principle of conservation of energy (in all of its many forms) by the experiments of Joule, et al, the theory of special relativity became logically unavoidable. Nevertheless, it was not really grasped as a clear and distinct fact (rather than a peculiar attribute of electromagnetism) until Einstein’s 1905 papers.

2.  Reliability of First Hand Testimony

Ginoux asks how we know the statements of Einstein (or, presumably, anyone else) are true.  In particular, can we trust Einstein’s statement that he had not seen Lorentz’s 1904 paper, nor Poincare’s 1905 review, prior to writing his 1905 EMB paper? Questions like this are of particular interest to people who believe that the papers of Lorentz and Poincare contained everything of value in Einstein’s paper, leaving us with only the question of whether Einstein stole it or found it independently. On the other hand, for people who see in Einstein’s paper a fundamentally new and more profound conceptual framework for the entirety of physics, extending far beyond anything to be found in the papers of Lorentz and Poincare, the question of whether Einstein had previously seen the (much less insightful) papers of Lorentz and Poincare prior to writing his own paper is not particularly important.

In any case, Einstein’s paper itself mentions that it had already been shown to the first order that the same laws of electrodynamics are valid for all frames for which the equations of mechanics hold good. This is a reference to what was shown in Lorentz’s 1895 paper (which Einstein acknowledged having read), whereas in the 1904 paper Lorentz attempts to extend the result to all orders (though not entirely successfully, e.g., regarding the current density). When Einstein’s paper was re-printed in 1913 along with Lorentz’s 1895 and 1904 papers, a footnote on this “first order” sentence was added, to say “The preceding memoir by Lorentz [i.e., the 1904 paper] was not at this time known to the author”.

Needless to say, this mere assertion does not prove with that Einstein had not seen Lorentz’s 1904 paper, nor Poincare’s 1905 review of it, although the timing of the latter would have been difficult. (There’s no mention of Lorentz’s 1899 paper, in which he first attempted to extend relativity to all orders.) Nevertheless, the statement in Einstein’s paper about first-order results is consistent with him not having seen Lorentz’s 1904 paper (or any review of it). We also know that, to the end of his life, Einstein continued to say that Lorentz introduced length contraction as an ad hoc assumption, which was true in 1895, but overlooks the fact that Lorentz gave the underlying constructive explanation for that contraction (at least for objects governed by electromagnetism) in his 1904 paper. Oddly, even in Einstein’s survey article of 1907 he still does not appear to have read Lorentz’s 1904 paper.  He continues to reference just the 1895 paper.  As Einstein once said when discussing Galileo’s disregard of Kepler’s ideas, creative people are sometimes not very receptive.

In the same paragraph of his 1905 paper where he mentioned the first order results, Einstein referred to “the unsuccessful attempts to discover any motion of the earth relatively to the light medium”, which presumably referred to all such experiments, including Michelson and Morley, with which he was certainly familiar, because Lorentz’s 1895 paper (that Einstein acknowledged having read) was entitled “Michelson’s Interference Experiment”, and it was devoted to Lorentz’s analysis of that experiment. Despite this, Einstein later remarked at least once that he didn’t recall if he had been aware of Michelson’s experiment when he wrote his 1905 paper (admittedly an odd thing to say). He claimed the first-order experiments were sufficient motivation, so it wasn’t necessary to wait for second, third, and fourth order confirmations. However, in other discussions he cited Michelson’s result as important in the development of special relativity.

If each of us had every single one of our written and spoken utterances over our entire lifetime examined and cross-referenced for consistency and freedom from self-interest or bias, I suspect very few of us would be found to have been perfectly consistent and unbiased. These things may interest historians, but for me, the question of what was new in Einstein’s paper, relative to what had been published previously, can be fully determined from examining the technical content of the papers themselves, independent of the chronological order of the papers. Also, I think each participant can be relied on to give their testimony as to their own perceptions of Einstein’s papers. Lorentz, Poincare, Minkowski, and many other contemporary physicists all acknowledged that they believed Einstein’s paper was a watershed. A notable example is Max Born, who later wrote that although he had already been very familiar with the writings of Lorentz, Poincare and Minkowski by the time he first read Einstein’s 1905 paper (which doesn’t strike anyone as implausible), Einstein’s reasoning was a revelation to him, and had a stronger effect on him than any other scientific experience of his life. Many other scientists of the day report similar reactions, and we can certainly give at least some weight to these individuals as to their own personal impressions.

3.  Was Einstein in Communication with Planck

Leopold Infeld reported that Einstein once told him “Before I was thirty, I never met a real physicist”. Einstein was thirty years old in 1909, which is when he finally left the Patent Office position for his first job is academia. Of course, it’s somewhat of an exaggeration, since his professors and even his first wife were nominally “physicists”. The statement is similar to the “no true Scotsman” motif, since it leaves open to interpretation who Einstein regarded as a real physicist. In any case, he obviously communicated with real physicists before 1909, but it’s less clear how extensive Einstein’s communications with real physicists were prior to June of 1905, and in particular whether Einstein would have had access to the most recent writings of Lorentz and Poincare. I personally don’t think it matters very much, since we can learn everything we need to know from the actual papers.

4. The Heuristic Uses of the Luminiferous Ether

Ginoux and Weinstein disagree about what, if any, heuristic use either Einstein or Poincare made of the ether. In my opinion, there is much semantic confusion about this topic, although the semantic confusion is ultimately grounded in conceptual confusion. The word “ether” and similar expressions such as “luminiferous aether” were used by some throughout history to refer to an actual substance with mechanical properties, and for those who regarded it as infinite in extent and all pervasive, and with mutually co-stationary parts, it was natural to regard this unique sub-stratum material as being at (or rather, as defining) absolute rest. Of course, one could just as well imagine this aethereal substance to be in motion in an underlying absolute vacuum of “empty space”, but it was convenient to take the ether as defining absolute rest, or rather, as the frame in terms of which fundamental physical laws take an isotropic and homogeneous form. Now, Lorentz admitted that although his reasoning relied heavily on the ether, he couldn’t really say much about this putative substance, and Poincare said physicists would doubtless one day discard the ether as useless… but was he referring to the hypothetical mechanical substance called ether (that Maxwell imagined), or to the underlying notion of an absolute rest, i.e., an absolute true system of space and time coordinates?  They became agnostic and even skeptical about the existence of an aetheral substance, but throughout their lives Lorentz and Poincare continued to defend the intelligibility of a single true absolute reference system.

I would argue that neither Lorentz, Poincare, nor Einstein ever were entirely clear about this. For example, in Einstein’s 1905 paper he famously didn’t postulate that light propagates at c in terms of every inertial coordinate system, but rather that it propagates at c in terms of one particular inertial coordinate system – which in those days would have been identified as the absolute rest frame – and then he claimed that he could combine this postulate with the relativity principle to deduce that light must have speed c in terms of every inertial coordinate system. This is a problematic maneuver, and modern expositions usually avoid it by simply positing invariant light speed at the start. It is understood that Einstein’s reasoning doesn’t actually work, at least not without adding assumptions that amount to the conclusion. The problem is that we can’t so casually invoke the relativity principle, because (as Lorentz pointed out in private correspondence with Einstein) light need not propagate at the same speed in the other frames, because those other frames might be physically distinct from the “original” frame, simply by virtue of the other frames being in absolute motion.

To make Einstein’s deduction valid, he needs to stipulate that being in motion relative to the “original” frame doesn’t affect the speed of light in terms of that “moving” frame… but of course this is simply assuming the conclusion.  The confusion is reinforced by mistaken ideas about Maxwell’s equations being defined as “laws of physics” that have been stipulated to take the same form in terms of every standard inertial system. This again just begs the question, since (for example) the dynamical equations for the speed of sound are also “law of physics”, but they apply in a simple homogeneous and isotropic form only in terms of the rest frame of the medium. There’s really no way of reaching the conclusion that light propagates in empty space (note the loaded expression “empty space”) at the same speed in terms of every standard system of coordinates without essentially just stipulating it.  This is tacitly invoking the principle of sufficient reason, and connecting it with the notion of “empty space”, which is being posited to exist (along with the proposition that light propagates in empty space).  It does not follow purely from the principle of relativity and independence from the speed of the source. It’s also important to remember that Einstein had just finished his paper on the photo-electric effect, in which he argued that light, in some contexts, propagates more like Newtonian ballistic particles than like Maxwellian waves, so his conception was more consonant with the idea of propagation in “empty space”.  This is also why it was so crucial for Einstein to show that the energy and the frequency of a “light complex” transform in exactly the same way, consistent with E=hν. Of course, neither Lorentz nor Poincare were dealing with any such considerations.

5. Did Einstein See and Plagiarize Poincare’s 1905 paper?

Ginoux suggests that Einstein may have had access to Poincare’s 1905 review of Lorentz’s 1904 paper prior to submitting his own OMB paper.  Ginoux envisions two possibilities.  First, he thinks Einstein might have gotten a copy of Poincare some time between June 5 and June 30 when Einstein submitted his paper.  Second, he thinks Einstein might have made edits to his paper some time between June 30 when it was initially submitted and September when the paper actually appeared in print. As mentioned above, this is primarily of interest to those who see nothing new in Einstein’s paper, whereas I actually find in Einstein’s paper a very large advance, including the first fairly clear recognition that the coordinate systems related by Lorentz transformations are nothing but standard inertial coordinate systems (not just systems in which Maxwell’s equations take the same form). Likewise the inertia of mass is not due to induction on its electric charge, but due to its energy, which makes it all-encompassing.

The one statement in Einstein’s 1905 paper that I could imagine being prompted by Poincare’s paper is in Section 5, where Einstein derives the velocity composition formula for the one-dimensional (“parallel”) case, and makes the side comment that such transformations necessarily form a group. This single sentence is the only mention of “group” in the paper, and it’s just an observation. Poincare invokes the closure property of groups to argue for assigning a value of unity to Lorentz’s scale factor, though his reasoning was questionable, because the group property doesn’t actually uniquely determine the scale factor. In contrast, Einstein gave valid physical reasoning, based on the physical symmetry, and then observed (correctly) in passing that the transformations obviously form a group. One might wonder why he even mentioned it. However, Felix Klein’s Erlangen program from the late 19^th century, relating group symmetries and geometry, was highly influential and fashionable at the time, so it isn’t too surprising that Einstein might mention it. In any case, no non-trivial group theory is involved in this subject (either for Einstein or Poincare), and the closure property is self-evident for logical consistency, so the off-hand comment is of little significance.

Overall, we know that, already in May of 1905, Einstein wrote to Conrad Habicht that he had drafted a paper on “a modification of the electrodynamics of moving bodies which employs a modification of the theory of space and time”, and he adds “the purely kinematical part of this paper will surely interest you”.  So it seems that the essential content of the paper for purposes of formulating special relativity was already in hand prior to Poincare’s review being published. The idea that Einstein might have made adjustments (such as perfunctorily mentioning groups) at some later time seems unlikely to me, but it wouldn’t be particularly significant if he did. We also can’t categorically rule out the possibility that Einstein saw Lorentz’s 1904, or at least an early synopsis of it in German, but, again, Einstein would hardly have said that previous attempts only applied to the first-order terms had he known that Lorentz’s more recent paper explicitly addressed higher orders.  He can hardly have imagined that, by not mentioning this, it would go unnoticed. It’s also worth keeping in mind that Einstein published five important papers that year, in addition to holding down a “day job” and dealing with family distractions, so his time and energy was limited.

Ginoux suggests that Einstein stole (plagiarized) the Lorentz transformations, but this seems like a strange accusation, for several reasons.  First, Lorentz himself admitted that Larmor had preceded him in deducing the transformations for electromagnetism years earlier, and Lorentz admitted that he must either have forgotten it or never read Larmor’s paper – which no one finds implausible. Of course, the general form of transformations preserving the wave equation had even earlier been noted by Voigt, which Lorentz also failed to acknowledge until many years later. Second, as discussed above, the form of a mathematical equation and its physical meaning are two different things. When we refer to “the Lorentz transformation” today, we are referring to the equations as the relationship between standard inertial coordinate systems, but for Larmor, Lorentz, and Poincare those equations were just relating coordinate systems in terms of which Maxwell’s equations take the same form.  So, from the standpoint of physics, one could argue that Einstein was the first to discover what is today called the Lorentz transformations.  Third, if Einstein’s intent was to hide Lorentz’s contributions, he certainly did a poor job of it.  In his commissioned survey article of 1907, extensive reference to Lorentz is made, although (as mentioned above) Einstein still refers to the 1895 paper, and still talks about the ad hoc contraction assumption, and so on.  He clearly was not trying to conceal Lorentz’s work, but rather was bringing Lorentz’s work to the forefront, and, as Poincare later said, “it is in the 17th volume of the Annales of Physique 1905 that we find Einstein's work on the principle of relativity considered in a methodical manner”.

6. The Same But Different

In this section Ginoux argues that Einstein was as wedded to the concept of the ether as were Lorentz and Poincare. He accepts that Lorentz and Poincare were indeed thinking in terms of an absolute true reference frame, regardless of whether there is some aethereal substance at rest in that frame, as discussed above, but he contends that Einstein too was committed to the ether. He bases this on Einstein’s 1920 lecture, but of course this contention is completely wrong, because Einstein’s lecture very explicitly denies not only the existence of a substantial ether, but also the existence of a preferred system of reference for the isotropic and homogeneous expression of the (local) laws of physics. In other words, he explicitly re-affirms his rejection of the conception of “ether” and absolute rest frame that Lorentz, Poincare, and the 19^th century Maxwellian physicists harbored, and in its place he simply noted that in general relativity there is at any event in “empty space” (and time) some definite metric and curvature (for example), and hence spacetime has properties, and we are obviously free to re-purpose the word “ether” to refer to spacetime endowed with its metric. But the point is that the metric of spacetime is locally Lorentz invariant, and hence does not possess the sole attribute that characterized what Lorentz and Poincare (and the others) had referred to as the ether.

As an aside, it’s interesting that anti-relativity crackpots invariably try to exploit Einstein’s 1920 article to argue that general relativity “restored the ether”, when in fact that lecture sealed the demise of the ether according to the meaning of the word that those same anti-relativityists espouse.

7. Connection Between Maxwell’s Equations and Special Relativity

Here Ginoux agrees that “the Lorentz transformation, the real basis of the special relativity theory, in itself has nothing to do with the Maxwell theory”, and “we do not know the extent to which the energy concepts of the Maxwell theory can be maintained in the face of the data of molecular physics." Indeed, this is why Einstein chose not to base special relativity on Maxwell’s equations, choosing instead to base it on the generic proposition that massless energy (of which “light” was considered the canonical example) propagates in empty space at an invariant speed in terms of every standard system of inertial coordinates, because he had just weeks earlier finished a paper in which he pointed out that Maxwell’s equations cannot be fundamentally correct, since they do not account for things like the photoelectric effect. (Also, it’s known that classical electrodynamics isn’t even self-consistent, with high accelerations, and even quantum electrodynamics must resort to re-normalization.) On the other hand, it can be shown that Maxwell’s equations are Lorentz invariant, so they provide an important example of how the form of physical laws, to be empirically viable at all, are constrained by this symmetry.  Oddly, Ginoux asks, “Why did Einstein apply the Lorentz transformation to the Maxwell equations in his 1905 article?” Again, Maxwell’s equations are Lorentz invariant, and also clearly match empirical results over a wide range of circumstances, so it’s natural and valuable to “test” the principle of Lorentz invariance on this field theory, and show its implications. This doesn’t imply any commitment to the ultimate correctness of the Maxwell theory.

8. The Title of Einstein’s Paper

Ginoux notes that Poincare in his Saint Louis address asked “Shouldn't we also strive for a more satisfactory theory of the electrodynamics of moving bodies?", and he points out that the title of Einstein’s 1905 paper is “On the Electrodynamics of Moving Bodies”.  Indeed, we saw above that Einstein used this phrase in his letter to Conrad Habicht. I haven’t delved deeply enough into Ginoux’s texts to know what significance he attaches to this. I personally would note that Einstein used the same symbol (β) for the “gamma” factor that Lorentz used in his 1904 paper. There’s also the amusing irony in a patent examiner saying he can delegate the “literature search” to Planck. But, again, the content of the papers themselves isn’t altered by any such considerations of mutual awareness.

9. Isolating Lorentz’s Scale Factor

Ginoux repeats the mistake made by A. I. Miller, thinking that the consolidation of unknown factors in Einstein’s 1905 derivation of the Lorentz transformation has some substantive significance.  It does not.  This has long ago been thoroughly explained in the literature, and Miller’s misunderstanding has been resolved.  The consolidation of factors is exactly what any reasonably astute person would do at that point in the derivation, to simplify the expressions, but it has no substantive content, and in no way entails any “foreknowledge” of the result.

10. The Veiled Resolution

Here Ginoux notes that he “never wrote or claimed that Poincare discovered the theory of special relativity”, and indeed that his book (ending the controversy) concludes with the words “So it's hard to understand why, for over seventy years, many scientists and historians of science have stubbornly tried to make Poincare the father of relativity, in spite of himself.”

I suspect the confusion here is due to combining Ginoux’s historical account with his own personal understanding of physics. This is a difficulty that many in Ginoux’s position have faced, namely, they undertake a two-pronged task of showing that (1) Einstein stole credit for a great scientific discovery, and (2) the thing that Einstein is credited with is actually garbage.  This is a somewhat conflicted dual thesis. It is ironic after seeing strenuous labors to prove that Einstein’s paper was plagiarized, to then be told that his paper was completely wrong. The strategy that is usually adopted is to argue that Poincare (and Lorentz) developed a true and great theory – which is not special relativity – and then Einstein stole the results of this great theory and re-packaged and mangled it into a false theory, what is today called special relativity, of which Poincare disapproved to the end of his life. To determine whether this is Ginoux’s approach, and to learn “the end of the controversy”, the reader will need to purchase Ginoux’s book.

11. Long and Tedious Derivation of Velocity Composition

The dispute here seems to be whether Einsteins 1905 derivation or Poincare’s 1906 derivation of the velocity composition formula is more elegant and/or economical. I’d say Einstein’s derivation is fine… although if someone wants to criticize Einstein for lack of succinctness, we can point to his derivation of the Lorentz transformation itself, which really is quite overly elaborate.  It isn’t surprising at all that when he was transcribing a copy of that paper as dictated by Helen Dukas many years later, he stopped her periodically and asked “Did I really write that?  Ach, I could have said that more simply”. More significant than economy of expression, though, is the fact that the “v” in the formula meant different things to Poincare than to Einstein.  To Einstein, those are the actual velocities in terms of the respective standard systems of inertial coordinates, whereas to Poincare they are the parameters of the Lorentz transformation, representing the dx’/dt’ expressions, which were not clearly identified as the actual velocities in inertial coordinates. So, I would argue that Einstein’s paper originated the velocity composition formula, as well as the other relativistic relations, with the full understanding of the actual physical meanings of the variables.

12. Do Einstein’s Personal Flaws Discredit His Scientific Ideas?

Ginoux notes some well-known disreputable and embarrassing episodes in Einstein’s personal life, and contends that they discredit Einstein’s scientific works, and that, in view of these episodes, Einstein’s word on any subject is not to be trusted.  I don’t think this is a valid line of reasoning, because none of these personal facts affect the actual content of the scientific papers, which show the great insights and advances compared with those of his predecessors. Also, from a methodological standpoint, to apportion credit to people for intellectual achievements based on how well they behaved in the worst moments of their personal lives, we would need to know the worst things done by each of the other individuals (Lorentz, Poincare, Planck, Minkowski, etc.) during their lives.  As far as I know, the private love letters, etc., of these other individuals have not all been published. But this is not a sensible approach anyway. Ginoux says “I believe it is impossible to dissociate the man from his work”, and since he finds Einstein to have been a flawed individual, he thinks Einstein should be disqualified from getting credit for his works (or perhaps we must judge that there is no value in Einstein’s papers on the grounds that he was a flawed person). But the whole issue of who gets credit for things (especially when all the candidates are long deceased) is not very significant. Who really cares, today, whether Newton or Leibniz discovered calculus, except for nationalists wanting to advocate for their respective countries and their favorite sons?

13. Is the Ether Superfluous or Obsolete?

Ginoux and Weinstein discuss whether Einstein really meant “superfluous”, or something more like “obsolete”.  As discussed above, the word “ether” originally meant (to the Maxwellians and their descendants) an actual material substance, whose rest frame was conventionally regarded as “absolute rest”, in terms of which the equations describing electromagnetic phenomena took their isotropic and homogeneous form. With the failures to find any trace of such a substance (and for other reasons as well), this was gradually repudiated, but like the Cheshire Cat that gradually disappeared until nothing was left but his smile, the putative “absolute rest” frame continued to be prominent in the thinking of researchers like Lorentz and Poincare. By showing that the phenomena do not exhibit any attributes that single out any particular local rest frame, Einstein dispensed with this last vestige of the Maxwellian notion, but in fact his reasoning does not just rely on being superfluous (with connotations of being optional), he actually needs to banish it positively, to deploy the principle of sufficient reason when he argues about the indifference of physical phenomena of isolated systems to state of motion in “empty space”. Strictly speaking, Einstein should have explicitly stated this, i.e., his reasoning requires that the ether (substance or preferred frame) be denied, in favor of “empty space”, indifferent to states of motion for isolated systems. Many years later, circa 1917, Lorentz and Einstein were still debating about this (in friendly terms of course). Lorentz referred to a universal spirit that might apprehend the universe in an absolute instant, and argued that we shouldn’t assume it makes no physical difference how an isolated system is moving relative to that “true” frame.

14.  Is Relativity Sufficient?

Ginoux makes the (unfortunately common) mistake of thinking that the principle of relativity implies the existence of a finite invariant speed in terms of standard inertial coordinates. That is plainly not true, as shown by the fact that Newtonian physics in Galilean relativity fully satisfy the principle of relativity, but there is no finite invariant speed. As is well known, in units with c equal to 1 for convenience, all we can infer from the principle of relativity alone (well, along with homogeneity, isotropy, memorylessness, etc.) is that standard inertial coordinate systems are related by a transformation of the form x’ = (x−vt)γ, t’ = (t−kvx)γ where γ = 1/√(1−kv²) and k is a constant. If k=0 this is the Galilean transformation, and if k=−1 it is the Euclidean transformation. If k=1 it is the Lorentz transformation. So, we need to establish the value of k, which can be done in numerous ways. For example, the bound energy E contributes rest mass m=kE, so in the Galilean case energy doesn’t contribute to the inertial mass of a body, but in special relativity k=1 and so E=m.  (In conventional units, k = 1/c², so Galileo and Newton can be forgiven for thinking k=0.) This is all clear from Einstein’s treatment of the subject, but it is far beyond what Lorentz or Poincare had realized. To be fair, even Einstein had to follow up with a second paper, to emphasize the inertia of energy, which is crucial for any actual understanding of the subject.  In any case, the answer to the question “Is relativity sufficient?” is No. Some other principle is required, and Einstein (in the EMB paper) chose to stipulate that massless energy (e.g., light) propagates in “empty space” at the invariant speed c, which must be assigned a numerical value for the Lorentz transformation to actually represent what it purports to represent.  (The problematic maneuver he used was discussed up above.)  Again, since Einstein knew Maxwell’s equations were not fundamentally valid, he chose to isolate a minimal necessary and sufficient condition, which has outlasted Maxwell’s equations (when they were superseded by QED, which is also Lorentz invariant).

15. More on the Velocity Composition Formula

Ginoux complains that Weinstein says “Poincare's formula… is not a relativistic velocity addition law since it is written in an algebraic form based on group theory”.  In response, Ginoux comments “This is ridiculous!”  I would say it isn’t ridiculous, it’s actually correct. As discussed above, the values in Poincare’s formula that we naturally see as ordinary velocities were not really seen as ordinary velocities by Poincare. When I say “ordinary velocity” I mean dx/dt where x and t are a standard system of inertial coordinates, not just a set of parameters in terms of which Maxwell’s equations are invariant. It was really in Einstein’s paper that the full physical significance of the Lorentz transformation, transcending its connection with Maxwell’s equations and electrodynamics, became clear. That’s why Einstein placed the derivation of that transformation ahead of the discussion of electrodynamics, which of course was completely foreign to the approach of Lorentz and Poincare.  Ginoux rightly points out that Einstein’s comment about the transformations forming a group is sort of out of the blue, and not actually relevant to Einstein’s discussion, although it’s equally true that Poincare didn’t make any non-trivial use of group theory in his derivation. They are really just referring to the closure property, i.e., the composition of two transformations is also a transformation. It doesn’t take any sophisticated group theory to assert this. I would say (as noted previously) it was just fashionable in the wake of Klein’s Erlangen program to always identify groups and symmetries.

16.  Did Poincare Correct Lorentz’s Charge Density?

There seems to be some dispute between Weinstein and Ginoux about Poincare’s correction of the charge density in Lorentz’s paper.  Lorentz thanked Poincare for making that correction, and also for not “reproaching” him for the mistake. Also, in Einstein’s 1905 paper he got the charge density correct as well.  There’s really no disagreement about this.

17.  Originality and Donkeys

Ginoux and Weinstein have exchanged words about each other’s originality, etc. This doesn’t interest me, since it’s well known that there is only one place to turn for the full, clear, correct, and infinitely insightful analysis of the early works on this subject. (Modesty prevents me from citing it.) But I would offer one comment:  Ginoux says “I am sad to see that Mrs. Weinstein, having no more arguments to oppose me, is reduced to insulting me by quoting a letter from Einstein to Grossmann and comparing me with a donkey". I think we can “put an end to this controversy” right away, because the quotation in question had Einstein telling Grossman that God made the donkey (i.e., Einstein himself) with a thick skin, so criticisms didn’t bother him. By quoting this, Weinstein wasn’t calling Ginoux a donkey, she was calling herself a donkey, with a thick skin. It was a self-deprecating joke… at least, that’s how I read it.

18. More Disputation

Here Ginoux expresses displeasure with Weintein’s approach, as she has done toward his approach.  No real content.

19. Poincare’s Final Word

Weinstein concluded her communication with a reproduction of the introduction to Poincare’s final lecture (July 1912), in which he shows that he regards Einstein’s contribution in Volume 17 of the Annals of Physics 1905 as the first methodical treatment of special relativity.  This somewhat undermines the commonly stated idea that Poincare never credited Einstein for special relativity.  We also have the testimony of at least one person who attended one of Poincare’s last lectures, who came away filled with excitement with the idea that someone named Albert Einstein (a name he had never heard before) had originated “mighty new currents of thought”.

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