|
Rational and Empirical Origins of Special Relativity |
|
|
|
I made my soul familiar with her extremity, |
|
That at the last it should not be a novel agony. |
|
Emily Dickinson |
|
|
|
It’s a curious fact that the discovery of special relativity is regarded by some people as an example of the superiority of empiricism over rationalism, and by others as an example of the superiority of rationalism over empiricism. For the first group, the most striking feature of special relativity, especially as expounded by Einstein, was it’s rejection of any conceptual elements (e.g., the ether, absolute time) that had no empirical content. The lesson of special relativity, according to these people, is that we must insist on operational meanings for all the terms of our theoretical constructions. On the basis of this interpretation the logical positivist philosophers of the Vienna Circle touted special relativity as an exemplar of their philosophy. Physicists too were inspired by what they saw as the strict empiricism of Einstein’s special relativity. For example, the young Heisenberg established “a basis for theoretical quantum mechanics founded exclusively upon relationships between quantities which in principle are observable”. As Heisenberg recalled, he was inspired and emboldened to take this approach by the example Einstein had set in founding special relativity, rejecting things (such as the ether) that were in principle not observable. (Heisenberg said, in describing the origins of quantum mechanics, “There was this very famous point of Einstein that one should only speak about those things which one can observe...”) To this day, special relativity is often presented as a positivist house-cleaning, dispensing with metaphysical notions and replacing them with good operationally-based representations of verifiable facts. These accounts often stress the role of the Michelson-Morley experiment in the origin of special relativity. |
|
|
|
But there is another – completely different – view of the origin of special relativity. Einstein’s original paper on special relativity does not actually mention the Michelson-Morley experiment by name (although it mentions the failed attempts to detect the ether wind), and in fact Einstein always seemed to minimize the empirical motivations for the theory. He proposed two principles (or, as he sometimes referred to them, postulates), without dwelling at length on the origins or justifications for these principles, and from them proceeded to derive all of special relativity. (Of course, much of the content of the theory actually derives from the definitions in terms of which Einstein’s postulates are expressed.) Now, in point of fact, both of Einstein’s principles had strong empirical motivations, but he took for granted that his readers were well aware of the fact that no violation of the principle of relativity had ever been observed (despite many ingenious attempts), that the state of motion of the putative ether had never been detected, and that the speed of light seems to be independent of the speed of the source, a proposition supported by all the empirical successes of Maxwell’s equations and the wave theory of light. |
|
|
|
In addition to the sensible assumption that his readers were already aware of the empirical situation, Einstein had another reason for not linking his deliberations too closely or explicitly to any particular experiments. His main criticism of Lorentz’s theory was its apparent reliance on “ad hoc” hypotheses, especially the hypothesis of length contraction to reconcile his (Lorentz’s) theory with the Michelson-Morley experiment. (Einstein never seems to have acknowledged Lorentz’s later “explanation” for the contraction, perhaps because it relied on the “molecular force hypothesis”, which is arguably just a disguised version of the contraction hypothesis. It’s also worth noting that as late as 1909 Poincare was still citing the contraction hypothesis as one of the foundations of Lorentz’s theory, as discussed below.) Not surprisingly, then, Einstein sought to derive his theory from very general principles with broadly-based empirical foundations, and would have wanted to avoid the appearance of being guided by any specialized or peculiar empirical facts. He also sought to avoid basing his theory on any detailed models of the fundamental constituents of matter, which he considered premature. In fact, he didn’t even take Maxwell’s equations as given, since he had already become convinced that they didn’t have absolute validity (since they don’t account for the photo-electric effect, etc.). |
|
|
|
Subsequent to Einstein’s 1905 papers, others (e.g., Ignatowski, Minkowski, etc.) attempted to show that special relativity actually could have been discovered by purely rationalistic reasoning – at least if we accept as given the approximate validity of the physics of Newton. Indeed, it can be shown by simple algebra that relatively moving inertial coordinate systems (i.e., systems of space and time coordinates in terms of which the equations of Newtonian mechanics hold good at least quasi-statically) must be related to each other by transformations of the form x’=(x−vt)γ, t’=(t−vx/k2)γ where γ =(1−v2/k2)−1/2 and k is a constant with units of speed. With a suitable choice of units we can normalize the value of k, so there are really only three qualitative possibilities: k equals −1, 0, or +1. With k = −1 the manifold of space and time would have a Euclidean metric, which is clearly unrealistic. With k = 0 we get Galilean relativity. With k = +1 we get Minkowski spacetime, which is the spacetime of special relativity, from which it follows that k equals the invariant speed of any massless energy. This could have been known to Newton, in the sense that no new empirical information beyond what was known to Newton would have been necessary to make these rational deductions. |
|
|
|
Of course, as a matter of historical fact, no one made these deductions until empirical findings forced them upon us. When the Lorentz transformations finally made their appearance, it wasn’t initially as the relationship between inertial coordinate systems, but merely as the relationship between a class of coordinate systems in terms of which Maxwell’s equations (and the generic wave equation) retain their form. In view of this, one might argue that the discovery of the Lorentz transformation (for electromagnetism) was therefore empirical, since the laws of electromagnetism were painstakingly inferred from the careful experimental work of Coulomb, Ampere, Oersted, Faraday, and others. However, we should keep in mind that those laws, handed down to Maxwell by his experimentalist predecessors, were not Lorentz invariant. Maxwell added a crucial term, which he called the displacement current, to Ampere’s law, and only with this additional term do the equations become Lorentz covariant. This is also the term that causes Maxwell’s equations to have wavelike solutions, so that electromagnetic waves are possible. But Maxwell’s addition of this term was not empirically motivated. According to his own account, he added the term because it was suggested by a (rather crude) mechanistic model of the electromagnetic field. Thus one could argue that the motivation for the concept of the displacement current, which led to the discovery of Lorentz covariance for electromagnetism (which hinted at the possibility of Lorentz covariance for everything else), was rational rather than empirical. (Incidentally, Einstein’s friend Besso once commented that the discovery of relativity had proven the superiority of speculation (rationalism) over empiricism, but Einstein disagreed, saying that no useful and profound theory had ever been found purely speculatively, but he added that the closest case was Maxwell’s displacement current.) |
|
|
|
Even if we believe that the Lorentz invariance of electromagnetism was discovered empirically, this does not imply that anything else is Lorentz invariant. Admittedly during the early 1900s some physicists entertained the possibility of an electromagnetic world view, i.e., the idea that ultimately all phenomena are electromagnetic. If this were true, then of course the Lorentz covariance of electromagnetism would indeed imply the Lorentz covariance of everything else – by definition. Hence we would have complete relativity based on the Lorentz transformation. But it is not true, and in fact most people knew it was not true even at the time. Maxwell’s equations are linear, and hence cannot lead to stable configurations, so some other forces must exist to balance the electromagnetic forces in stable configurations of matter. Also gravity is quite dis-similar to electromagnetism in important ways (e.g., all gravitational “charges” attract). We now know that only a small fraction of an electron’s inertia is due to electromagnetic induction. Therefore, the Lorentz invariance of electromagnetism provides no warrant at all for the belief that, for example, inertial coordinate systems are related by Lorentz transformations. |
|
|
|
This is why, in Lorentz’s proof of his “theorem of corresponding states” his finds it necessary to simply assume (postulate) that all the unknown forces responsible for maintaining the stability of matter, and the forces of real mechanical inertia (not just the apparent inertia due to electromagnetic induction) are Lorentz covariant. |
|
|
|
To the assumptions already introduced, I shall add two new ones, namely (1) that the elastic forces which govern the vibratory motions of the electrons are subjected to the relation 300 [i.e., Lorentz covariance], and (2) that the longitudinal and transverse masses m’ and m” of the electrons differ from the mass m0 which they have when at rest in the way indicated by equation 305, [which] contains the assumptions required for the establishment of the theorem [of corresponding states]. |
|
|
|
We should stress that these were in no way deductions or derivations. Lorentz merely postulated these things, as the necessary conditions in order for motion relative to the ether to be perfectly undetectable. In other words, he merely postulated the principle of relativity. Nevertheless, he wrote in his 1909 book |
|
|
|
I cannot speak here of the many highly interesting applications which Einstein has made of this principle. His results concerning electromagnetic and optical phenomena agree in the main with those which we have obtained, the chief difference being that Einstein simply postulates what we have deduced... from the fundamental equations of the electromagnetic field. |
|
|
|
This statement has often been misinterpreted. Considering that, as we’ve just seen, Lorentz himself merely postulated the Lorentz covariance of mechanical inertia and all the forces responsible for the stable configurations of objects, he cannot plausibly be claiming to have deduced special relativity – and indeed he is not. Lorentz is speaking here specifically about “results concerning electromagnetic and optical phenomena”, which of course can be deduced from the equations of the electromagnetic field – but this is not special relativity. The essence of special relativity is that all forms of energy (including kinetic energy) have inertia, and hence mechanical inertia is Lorentz invariant, and hence the coordinate systems that are related by Lorentz transformations are nothing other than the inertial coordinate systems of Newton and Galileo, which are what have always been regarded as the true measures of space and time. This cannot possibly be “deduced from the equations of electromagnetic field”, because inertia is not an electromagnetic phenomenon. Of course, Lorentz did not claim otherwise. He said specifically that he was referring to electromagnetic and optical phenomena, and he can rightly claim to have deduced the Lorentz invariance of these phenomena from Maxwell’s equations. But, again, this is not special relativity. |
|
|
|
As Einstein later said, the key insight of special relativity is that the significance of the Lorentz transformation transcended its connection with Maxwell’s equations, and concerned the fundamental nature of space and time. (This is what Lorentz could have been referring to when he mentioned the “highly interesting applications which Einstein has made” of the principle of relativity.) Einstein’s statement, too, has often been misinterpreted, as if he was invoking some metaphysical concepts of “true” space and time. Again, the meaning as it was understood by his contemporaries, is that special relativity identifies the coordinate systems related by Lorentz transformations as none other than the inertial coordinate systems. These were (and still are) the default measures of space and time that have been used implicitly throughout history. Whether we call these the “true” measures of space and time is a matter of convention, but they are indisputably the inertial measures, which were considered to be the true” measures prior to the advent of special relativity, i.e., they are what we have always meant by “space and time”. It was a shock to discover that the loci of simultaneity of these systems are mutually skewed. This was “the step” that everyone rightly attributed to Einstein. For example, Minkowski wrote “The credit of first recognizing clearly that the time of the one electron is just as good as that of the other, that is to say, that t and t’ are to be treated identically, belongs to A. Einstein”. (Poincare had previously argued that we have no direct sense of simultaneity, and had even noted that Lorentz’s local time exhibited the synchronization corresponding to the assumption that the speed of light has the value c in all directions. However, this does not amount to a recognition of the fact the mechanical inertia is isotropic in those same coordinates, something that can only be properly understood in terms of the inertia of all forms of energy, which Poincare did not understand, as explained below.) |
|
|
|
As noted above, after deducing the Lorentz covariance of electromagnetism, Lorentz went on to postulate the Lorentz covariance of every other physical phenomena (including mechanical inertia), just as Einstein did, so one might wonder why Einstein is credited with the discovery of special relativity. In the 1909 book “The Theory of Electrons”, Lorentz described what he called “effective coordinates” and “effective time”, etc., and then he commented that these concepts “have prepared us for a very interesting interpretation of the above results, for which we are indebted to Einstein”. He then notes that two relatively moving observers |
|
|
|
...would be alike in all respects. It would be impossible to decide which of them moves or stands still with respect to the ether, and there would be no reason for preferring the times and lengths measured by the one to those determined by the other, nor for saying that either of them is in possession of the “true” times or the “true” lengths. This is a point which Einstein has laid particular stress on... |
|
|
|
Lorentz also mentions “a remarkable reciprocity that has been pointed out by Einstein”, i.e., the fact that clocks at rest in one frame run slow in terms of the time coordinate of the other frame, and vice versa. Finally, in a lengthy footnote added to the 1915 edition, Lorentz admitted that he had regarded the local time as “no more than an auxiliary mathematical quantity”, whereas Einstein showed that the local time was nothing other than the time coordinate of an inertial coordinate system. (This goes far beyond Poincare’s tautological observation that coordinates in which the equations of electromagetism are invariant are also coordinates we would construct using electromagnetic signals.) Because of admissions like that, along with his explicit statement that special relativity really was Einstein’s creation, it has been difficult to claim Lorentz as the founder of special relativity. However, the argument is often made that Poincare deserves that credit, because although he ostensibly was just describing Lorentz’s work, he (Poincare) actually went well beyond Lorentz, and gave Lorentz’s theory a profound interpretation that fully anticipated Einstein’s insights (or so it is claimed). It’s interesting to examine Poincare’s writings – before, during, and after 1905 – to determine what he knew and when he knew it. |
|
|
|
From the standpoint of the debate between empiricism and rationalism, Poincare presents a mixed example. He was certainly attentive to current experimental results, and indeed he apologized for even exploring the consequences of the relativity postulate at a time when experiments may well have proven it wrong (“...at this very moment the discovery of cathode-magneto rays seems to threaten the entire theory”). But as a mathematician he was also very adept at rationalistic developments. Indeed his Palermo paper, written in the summer of 1905 (though not published until the following year) begins with the stated goal of evaluating the consequences of the postulate of complete relativity. Note again that this was “merely postulated” at the start, and was not in any way “deduced”. He says in the introduction that “Whether or not this postulate, which up to now agrees with experiment, may later be corroborated or disproved by experiments of greater precision, it is interesting in any case to ascertain its consequences”. Thus he is presenting purely rationalist deductions from a tentatively proposed postulate. Poincare’s deliberations were even less “constructive” than Lorentz’s, who at least had done some (arguably) constructive work on the electromagnetic side (albeit based on Maxwell’s rationalist displacement current), but Poincare was explicitly expounding what he called a theory of principle. (Einstein is often credited with the classification of theories into constructive theories and principle theories, but this classification was actually described in earlier writings of Poincare.) For example, during the course of the Palermo paper, Poincare exploits the group property for coordinate transformations to immediately deduce the scale factor that Lorentz had labored to derive. Poincare also noted the quadratic invariants of the space and time intervals, and the fact that the Lorentz transformation was formally a hyperbolic rotation (or a circular rotation if we use an imaginary time coordinate). |
|
|
|
In view of all this, should we conclude that Poincare had discovered special relativity by 1905, and that Einstein contributed nothing new? Most scholars have concluded that we should not, although their reasons vary. Pais argued that Poincare never understood special relativity, and as proof of this he points to the fact that Poincare continued to say (even as late as 1909) that “the new mechanics” was based on three hypotheses, the first two being the relativity principle and the principle that no body can exceed the speed of light (which Pais identifies with Einstein’s two postulates), but then he says |
|
|
|
One needs to make a third hypothesis, much more surprising, much more difficult to accept, one which is of much hindrance to what we are currently used to. A body in translational motion suffers a deformation in the direction in which it is displaced... However strange it may appear to us, one must admit that the third hypothesis is perfectly verified. |
|
|
|
Pais argues that length contraction is a consequence of the first two postulates, and since Poincare didn’t realize this, he did not know special relativity. A defender of Poincare could reply that this third hypothesis, or something like it, actually is needed if we understand that Poincare’s light speed limitation hypothesis was different than Einstein’s light speed postulate. Recall that Einstein said his light speed postulate was “apparently irreconcilable” with the relativity postulate, and many subsequent readers agreed. This was the postulate that people found “difficult to accept”, and yet Poincare says in his presentation that it is the third postulate on length contraction (not his light speed limitation postulate) that is surprising and difficult to accept. This might seem strange, because there is nothing like a speed limitation in Newtonian physics. How could this not be regarded as a surprising hypothesis? The explanation is that, like Lorentz, Poincare continued to believe (incorrectly, as we now know) that all inertial mass was electromagnetic in origin. (In the 1915 edition of his book on electron theory, Lorentz still says “it will be best to admit Kaufmann’s conclusions... that the negative electrons have no material mass at all”.) It can be shown that the field energy of electromagnetic self-induction does indeed go to infinity as the speed of the charged particle approaches the speed of light. This is the basis of Poincare’s assertion that “no body can attain a velocity higher than that of light”, which he explains (in 1908) by describing an electron moving through a hypothetical non-viscous fluid comprising the ether, and needing to impart infinite energy into the ether flow field to reach the speed of light. He does not say that the speed of light is independent of the speed of the source (and we should remember that emission theories of light were being considered at that time), nor does he note any apparent conflict between his light speed limitation postulate and his relativity postulate. Thus the content of Poincare’s light speed limitation postulate was quite different than the content of Einstein’s light speed postulate. Poincare’s postulate was not sufficient to serve as the foundation of a complete “kinematics” based on the Lorentz transformation. Just as Poincare said, some additional hypothesis was needed, and his hypothesis of length contraction (active, not just passive) served this purpose. This hypothesis (together with the others) implies that the speed of light, as measured by rulers and clocks at rest in any inertial frame, will have the same value, whereas we cannot conclude this purely from Poincare’s first two postulates, which differ from Einstein’s two postulates, even though they look superficially similar. |
|
|
|
Nevertheless, Poincare’s writings do reveal that he had not grasped the essence of special relativity. The reason is related to his light speed limitation postulate, which was still founded on the purely electromagnetic world view. This is strange, because at various times Poincare himself pointed out that there must be other forces at work in the stable configurations of matter. Indeed he postulated a universal pressure to oppose the electromagnetic forces and hold the parts of a charged particle together, leading to the deformations required by Lorentz’s theory, provided the pressure is assumed to be suitably Lorentz covariant. Also, both Poincare and Lorentz made statements to the effect that all inertial mass was electromagnetic – or, if not, then all inertial mass transforms in the same way as electromagnetic mass – but they usually seemed to disregard the caveat, and certainly failed to appreciate its significance. As noted above, Lorentz was still saying the electron probably has no “material mass” at all, even as late as 1915. Kaufmann’s results are best remembered today for how they seemed to slightly favor Abraham’s theory over Lorentz’s, but almost everyone agreed that the results indicated that all the electron’s mass was electromagnetic. Only gradually did people realize that Einstein’s theory of relativity (as distinct from Lorentz’s or Poincare’s) undermined that conclusion. |
|
|
|
The essential fact of special relativity that Poincare missed is the inertia of energy. Now, people familiar with the history of the subject may be surprised by this, because it is often said that Poincare anticipated the relation E = mc2 in his contribution to the Lorentz Festschrift in 1900. It is true that Poincare discussed the inertia of electromagnetic energy in that paper, but the paper also reveals (as do his subsequent writings) that he did not understand the inertia of energy in the sense of special relativity. The subject came up in Poincare’s discussion of the principle of action and reaction. Poincare had previously written (and Lorentz agreed) that Lorentz’s theory violated this principle. The reason was that Lorentz’s ether was perfectly stationary, not influenced by the motions of ponderable bodies, and hence could not convey momentum. But, as Maxwell had already shown, if a body emits an electromagnetic wave in a particular direction (e.g., with a parabolic mirror) it will recoil in the opposite direction, and likewise when that pulse of electromagnetic energy is absorbed by some other object (assuming it is), that receiving object will recoil in the opposite direction. Hence the law of reaction is satisfied for the completed transaction, but since the light requires some amount of time to travel from emitter to absorber, the reaction is delayed, so there is (at least) a temporary violation. Of course, this assumes that the energy in transit has no momentum, but this is what Poincare thought must be the case for Lorentz’s theory, since the ether was immobile. |
|
|
|
The reason Poincare is often (wrongly) credited with discovering the inertia of energy is because in this paper he went on to note that in order to salvage the law of reaction (and also the uniform motion of the center of mass of an isolated system) we would need to imagine a fictitious fluid that conveyed the energy E in accordance with the Poynting vector, and we would need to assign momentum E/c (consistent with Maxwell’s equations) and mass E/c2 to this energy. Here is what he wrote in 1900: |
|
|
|
We can consider the electromagnetic energy as a fictional fluid which travels through space in conformance with Poynting’s law. We just need to realize that the fluid is not indestructible... it is this which prevents us from considering our fictional fluid as a sort of “real” fluid. The momentum of the proper matter plus that of our fictional fluid is represented by a constant vector... However, we do not have the right to conclude that the center of gravity of the system formed by the matter and our fictional fluid is moving linearly and uniformly; and that is because the fluid is not indestructible [since it can be converted into non-electrical energy]... We must then consider the system formed not only by the matter and electromagnetic energy, but also the non-electrical energy... But we must assume that the non-electrical energy remains at the point where the transformation (from electrical energy) takes place, and is not subsequently carried along with the matter at that location. There is nothing in this convention that should shock us, as we’re only discussing a mathematical fiction. If one adopts that convention, then the movement of the center of gravity of the system will remain linear and uniform. |
|
|
|
The fact that electromagnetic waves carry momentum was already known to Maxwell, so this was not original to Poincare. The most troubling (or at least puzzling) part of this quote, for those who would credit Poincare with discovering the inertia of energy, is the claim that “we must assume that the non-electrical energy remains at the point where the transformation takes place”. He hastens to assure us that we shouldn’t be shocked by this “convention”, because it’s just a fiction in any case, but this clearly won’t do if we really want to credit Poincare for the general inertia of all forms of real energy. What’s needed is a statement that the non-electrical energy, in whatever form, carries with it (wherever it goes) the same momentum. Indeed when Einstein addressed this same subject in 1906 (where he actually cited Poincare, albeit only to say he would not base himself on Poincare’s work), the whole point was to explain that the energy in any form whatsoever must carry the momentum and equivalent mass. In contrast, Poincare says the non-electrical energy must remain at the point where the transformation takes place (in terms of the absolute rest frame of the ether?), and then essentially admits that this doesn’t make sense, but it doesn’t matter because it’s just a fiction. |
|
|
|
One might think that perhaps by 1905 Poincare’s views would have been clarified on this, but we find as late as 1908 (in his book Science and Method) him saying still that Lorentz’s theory violates the principle of reaction “at least if we do not consider the ether, but only the electrons which are alone observable” (his emphasis). The words in italics are clearly suggesting that we should not consider unobservable elements in our theory. Indeed he commented in his St. Louis lecture in 1904 how unsatisfactory it is to attribute effects to an undetectable entity. Ironically, Poincare is often credited with abolishing the unobservable ether – saying the ether will no doubt one day be discarded as useless – and yet he is also credited with the discovery of the inertia of energy, citing the above statement in which he specifically relies on the ether as the only conceivable way in which the violation of momentum conservation can be avoided. Later in the same section of Science and Method he compares the emission and absorption of light with the transfer of momentum caused by firing a projectile from a cannon. |
|
|
|
In the case of the cannon, the recoil is the natural result of the equality of action and reaction. The cannon recoils because the projectile on which it has acted reacts upon it. But here [with light emitted from a lamp] the case is not the same. What we have fired away is no longer a material projectile; it is energy, and energy has no mass – there is no counterpart. It is true that if the energy emanating from the lamp happens to reach a material object, this object will experience a mechanical thrust, and this will be equal to the recoil of the lamp... but this compensation is always late, [and] it never occurs at all if the light, after leaving the source, strays in the interstellar spaces without ever meeting a material body... |
|
|
|
Poincare goes on to describe Hertz’s competing theory, which he says satisfies the principle of reaction (because Hertz’s ether moves in response to material objects), but he notes that Hertz’s theory is ruled out by Fizeau’s experiment. He concludes, “We must accordingly adopt Lorentz’s theory, and consequently give up the principle of reaction (his emphasis)”. With that, he also gives up any claim to discovering the inertia of energy. Poincare admitted only two kinds of inertia, the apparent inertia of a charged particle due to electromagnetic induction, and the actual inertia of material substances (if such things exist). Since electromagnetic waves have no charge and no mass, and the ether is perfectly immobile, he couldn’t conceive of them having momentum. Poincare was not alone in remaining wedded to the electromagnetic world view. For example, the conclusion of Minkowski’s famous 1908 lecture is “The validity without exception of the relativity postulate, I like to think, is the true nucleus of an electromagnetic image of the world, which, discovered by Lorentz and further revealed by Einstein, now lies open in the full light of day.” It’s worth noting that Minkowski had seen Einstein’s papers only in 1907, and it’s evident from this quote that he (Minkowski) still conceived of relativity in purely electromagnetic terms. To be fair, Lorentz conceived of relativity in the same way, and the title of Einstein’s paper, “On the Electrodynamics of Moving Bodies” tended to encourage the idea that Einstein’s view was just a further elaboration of what we now know is an erroneous conception of relativity. |
|
|
|
Like Poincare, Lorentz too struggled with conceiving of massless energy (such as of an electromagnetic field) as a “real thing”, writing in 1915 that |
|
|
|
The flow of energy can, in my opinion, never have quite the same distinct meaning as the flow of material particles... It might even be questioned whether the transfer of electromagnetic energy takes place in the way indicated by Poynting’s law... all depends on the hypotheses which we make concerning the internal forces in the system, and it may very well be that a change in these hypotheses would materially alter our ideas about the path along which the energy is carried |
|
|
|
Indeed, as many freshmen physics students know, by changing between the Coulomb gauge and the Lorentz gauge we can disguise the actual causal flow of energy (which has an interesting analogy in the impossibility of localizing gravitational field energy in general relativity due to the gauge freedom), but this just shows the difficulty that Lorentz and other physicists of the time had in adapting themselves to the relativistic concept of mass-energy equivalence. (It’s true that Hasenohrl considered the increase in apparent mass of a cavity containing electromagnetic radiation, but he did not clearly deduce the correct proportionality, and he certainly didn’t articulate the fact that all forms of energy have inertia – a fact that emerges so naturally, and with the correct proportionality, from Einstein’s conception of special relativity.) |
|
|
|
There’s an interesting and significant parallel between Poincare’s view of momentum transfer and the view of many physicists in those days of quantum phenomena. Recall that Planck and others had inferred that energy (and momentum) is emitted and absorbed only in discrete amounts, but they did not believe that the energy was actually quantized in transit. Planck wrote to Einstein in 1907 |
|
|
|
Does the absolute vacuum (the free ether) possess any atomistic properties? Judging by your remark that the electromagnetic state in a region of space is determined by a finite number of quantities, you seem to answer this question in the affirmative, while I would answer it, at least in line with my present view, in the negative. For I do not seek the meaning of the quantum of action (light quantum) in the vacuum but at the sites of absorption and emission, and assume that the processes in the vacuum are described exactly by Maxwell’s equations. At least, I do not yet see any compelling reason to abandon this assumption, which seems to me the simplest for the time being, and which also expresses the contrast between ether and matter in a characteristic manner. |
|
|
|
Just as Poincare imagined that the momentum recoil was applied to the emitting body at the emission of a light pulse, and to the absorbing body at the reception of a light pulse, but that the momentum had no mode of existence in the free ether between those two events, so Planck imagined that the quantum aspects of radiation applied only to the emission and absorption events, and not to the propagation of the radiation in the free ether between those two events. Indeed this is more than just an analogy, because Einstein’s conception of radiation in terms of photons, and his willingness to question the unlimited validity of Maxwell’s equation, was just as important for his relativity theory as for his ideas on the light quantum. |
|
|