Equivalence between Lorentz and Einstein

Albert Einstein is considered the greatest physicist of the 20th century, with his greatest paper being his 1905 special relativity paper. To justify this fame, much has been written to try to distinguish the work from previous relativity papers by others.

An excellent new paper on this subject has just been posted by Pablo Acuña, titled On the Empirical Equivalence Between Special Relativity and Lorentz's Ether Theory. As with other scholars, he finds bizarre and contrived reasons for favoring Einstein and it is fascinating how he deals with the basic facts.

Lorentz's papers were published in 1892, 1895, 1899, and 1904. These papers were widely read, and he got the 1902 Nobel Prize for his electron theory, as it was called at the time. Lorentz had certain conceptual gaps that were filled by Poincare.

Lorentz presented all these results — the coordinate transformations and the length - contraction hypothesis — in a more systematic and structured way in his 1895 Attempt of a Theory of Electric and Optic Phenomena in Moving Bodies. This work rapidly became a central point of discussion for the scientific community of the time. Henri Poincaré introduced observations and criticisms that were important for its further development. He complained that the explanations for the negative results of ether-drift experiments of first and second order the theory provided were two different and logically disconnected parts of the theory. In 1900 he stated that "the same explanation must be found for the two cases, and everything tends to show that this explanation would serve equally well for the terms of higher order and that the mutual destruction of these terms will be rigorous and absolute" (Poincaré 1900, p. 172)4.

A second important contribution of Poincaré on Lorentz‘s theory was to elucidate that `local time‘ was not only a mathematical tool, as Lorentz originally conceived, but that it contained a physical meaning. In a contribution for a volume celebrating the 25th anniversary of Lorentz‘s doctorate, Poincaré explained his point by means of an illustration that strikingly resembles Einstein‘s method for the synchronization of clocks.

If you consider Lorentz electron theory (aka Lorentz aether theory) as understood by Poincare, it was mathematically and observationally equivalent to Einstein's 1905 theory. That was the consensus of physicists of the day, who sometimes called it the Lorentz-Einstein theory in 1906, and the consensus of scholars today. Acuna says "the expression Lorentz-Einstein theory was common before Minkowski‘s famous conference of 1908", and "began to disappear" in 1909, as it was superseded by the spacetime geometry formulation.

After this outline of the development of Lorentz‘s theory, we can clearly see that the theory which is empirically equivalent to special relativity is not the one that Lorentz formulated in 1904. The amendments and contributions that Poincaré introduced in his 1906 work and the observations and criticisms that he leveled ca. 1900 must be considered to really obtain the predictive equivalence. In other words, the case of empirical equivalence at issue concerns Einstein‘s theory and a conceptual reconstruction that we could call the Lorentz-Poincaré theory.

Next the paper turns to non-empirical reasons for favoring Einstein.

In The Logic of Scientific Discovery, Karl Popper offered a definition of ad hoc hypotheses within the context of his falsificationist framework. A hypothesis is called ad hoc if it is unfalsifiable, that is, if the 14 hypothesis does not entail any predictions that could put it `at risk‘. He mentioned the Lorentz-Fitzgerald length-contraction as a paradigmatic example of an ad hoc hypothesis—and this judgment became very influential regarding the epistemological assessment of Lorentz‘s theory. As we saw above, the LorentzFitzgerald contraction was originally introduced with the specific goal of providing an account for the negative result of the Michelson-Morley experiment. If this were the only empirical prediction for which the hypothesis is logically relevant, then it would clearly qualify as ad hoc in Popper‘s sense. Since Popper stated as a methodological principle that the introduction of new hypotheses in a given theory is allowed only if such hypotheses increase the degree of falsifiability of the theory, then the ad-hocness of length contraction is reason enough, according to Popper, to dismiss Lorentz‘s theory and favor special relativity:

An example of an unsatisfactory auxiliary hypothesis would be the contraction hypothesis of Fitzgerald and Lorentz which had no falsifiable consequences but merely served to restore the agreement between theory and experiment—mainly the findings of Michelson and Morley. An advance was here achieved only by the theory of relativity which predicted new consequences, new physical effects, and thereby opened up new possibilities for testing, and for falsifying, the theory. (Popper 2002, pp. 62-3).

Adolf Grünbaum (1959) showed that this view was mistaken. ...

It is not difficult, though, to demonstrate that the length-contraction hypothesis is not ad hoc in Popper‘s sense. ...

Besides Popper‘s, though, there remain two senses in which the length-contraction hypothesis might be accused of ad-hocness. First, it was cooked up with the only and specific goal of solving one single experimental difficulty. This is true, but as we just saw, further development of the theory connected the hypothesis with unexpected empirical results. In this sense, the length-contraction hypothesis is on an analogous stand with Planck‘s quantum of energy hypothesis — which was introduced with the only and specific goal of providing an account for the observed spectrum of black-body radiation — and in neither of the two cases this sense of ad-hocness could be invoked to reject the corresponding hypothesis, of course. Moreover, one could ask what is wrong with ad hoc hypotheses—in the sense of cooked up hypotheses—in themselves. Even if a hypothesis is helpful in providing an explanation for one single experimental result, it does contribute to enlarge the scope and fruitfulness of the corresponding theory24.

The second remaining sense of ad-hocness that could be attributed to the length-contraction hypothesis is that it was a sort of rabbit in the hat maneuver, that is, that the contraction was postulated without a justified physical underpinning. In this case, the ad-hocness accusation boils down to an accusation of implausibility. We saw above that Lorentz did propose a plausibility argument for his length-contraction hypothesis, and the fact that the same argument had been already envisioned by Fitzgerald bestows Lorentz‘s with good credentials. Moreover, the eventual fulfillment of the main goal of the electromagnetic worldview program—namely, the reduction of all physics to electromagnetism—would have provided the generalized contraction hypothesis with firm physical foundations.

I agree with this. It is silly to argue that Einstein's approach was somehow better because it was less ad hoc.

A second non-empirical feature that could be used in order to make a choice favoring Einstein‘s theory is given by the aesthetic-mathematical virtues that characterize special relativity. Actually, these features did play a historically relevant role in the matter26. Consider, for example, the following passage included in Max von Laue‘s 1911 textbook (the first ever published) on special relativity:

Though a true experimental decision between the theory of Lorentz and the theory of relativity is indeed not to be gained, and that the former, in spite of this, has receded into the background, is chiefly due to the fact that, close as it comes to the theory of relativity, it still lacks the great simple universal principle, the possession of which lends the theory of relativity an imposing appearance. (Quoted in Schaffner 1974, p, 74)

Minkowski‘s introduction in 1908 of the four-dimensional formalism in which the theory can be expressed was a crucial factor regarding the general judgment about the mathematical simplicity of special relativity. Scott Walter (2010) has offered a historical survey of the early reception of Minkowski‘s work in connection with the acceptance of special relativity. He shows that Laue‘s specific reasons to embrace Einstein‘s theory in terms of simplicity was given—in spite of its difficult visualizibility in intuitive terms — by the mathematical elegance and simplicity that the four-dimensional formulation allowed:

Laue considered Minkowski space-time as an "almost indispensable resource" for precise mathematical operations in relativity. He expressed reservations, however, about Minkowski‘s philosophy, in that the geometrical interpretation (or "analogy") of the Lorentz transformation called upon a space of four dimensions: "[A] geometric analogy can exist only in a four-dimensional manifold. That this is inaccessible to our intuition should not frighten us; it deals only with the symbolic presentation of certain analytical relationships between four variables". One could avail oneself of the new four -dimensional formalism, Laue assured his readers, even if one was not blessed with Minkowski‘s space-time intuition, and without committing oneself to the existence of Minkowski‘s four-dimensional world‘ (Walter 2010, p. 17).27

I agree that the 1908 Minkowski space-time view is aesthetically superior, but that view owes much more to Lorentz (and Poincare) than to Einstein. I document this in my book, How Einstein Ruined Physics. Other scholars ignore this.

Poincare's 1905 paper was based on Lorentz, not Einstein, and introduced the following crucial concepts. He (1) combined space and time into a 4-dimensional spacetime, (2) gave it a non-Euclidean geometry using a metric and symmetry group, and (3) recast electromagnetic variables and equations as covariant under that geometry. These are the essential ideas in Minkowski's 1908 paper, and his previous 1907 paper cites Poincare as the source. Minkowski also cites Einstein, but got nothing significant from him. Einstein rejected these ideas until after Minkowski became popular.

Thus the chain of relativity development is Maxwell 1860-1880, to Lorentz 1892-1904, to Poincare 1905, to Minkowski 1908, to Laue textbook 1911. No one has ever been able to give a convincing argument that Einstein played an important role in either the development of special relativity or in the popular acceptance of it. Einstein's reasoning did influence a few people like Max Planck in 1906, but that reasoning was obsolete by 1908.

Acuna discusses other contrived reasons for preferring Einstein.

After this review and critical assessment of Janssen‘s arguments, we can now consider the best possible formulation of what he regards as a reason to prefer special relativity. Recall that the basic idea is that in Lorentz‘s theory the fact that all the laws of physics are Lorentz-invariant remains as an unexplained coincidence; whereas in special relativity Lorentz-invariance gets naturally explained by the specific kinematics of space-time. For the reasons mentioned above, this explanation cannot be taken either as causal or as constructive. If it is an explanation at all, it has to be an explanation of principle.

When philosophers discuss distinctions between Lorentz and Einstein theories, they usually put a modern interpretation on the theories that were not necessarily articulated in 1905. For example, Acuna discusses the applicable symmetry groups but neither Lorentz nor Einstein mentioned them. It is sometimes said that Lorentz wanted a constructive theory where the contraction is caused by electromagnetic forces, and Einstein wanted a non-causal spacetime theory.

Lorentz said:

Einstein simply postulates what we have deduced, with some difficulty and not altogether satisfactorily, from the fundamental equations of the electromagnetic field. By doing so, he may certainly take credit for making us see in the negative result of experiments like those of Michelson, Rayleigh and Brace, not a fortuitous compensation of opposing effects but the manifestation of a general and fundamental principle. Yet, I think, something may also be claimed in favour of the form in which I have presented the theory. {Lorentz 1916, but from 1906 lectures]

I read this as saying that Einstein's difference was one of presentation, not substance. Lorentz derived a theorem from Maxwell's equations, and Einstein took a shortcut by just postulating the theorem.

Einstein was not opposed to Lorentz's constructive approach, but had difficulty understanding it:

So, first to the question of whether I consider the relativistic treatment of, e.g, the mechanics of electrons as definitive. No, certainly not. It seems to me too that a physical theory can be satisfactory only when it builds up its structures from elementary foundations. The theory of relativity is not more conclusively and absolutely satisfactory than, for example, classical electrodynamics was before Boltzmann had interpreted entropy as probability. If the Michelson-Morley experiment had not put us in the worst predicament, no one would have perceived the relativity theory as a (half) salvation. Besides, I believe that we are still far from having satisfactory elementary foundations for electrical and mechanical processes. I have come to this pessimistic view mainly as a result of endless, vain efforts to interpret the second universal constant in Planck‘s radiation law in an intuitive way. I even seriously doubt that it will be possible to maintain the general validity of Maxwell‘s equations for empty space. [1908 letter to Sommerfeld]

The truth is that there was very little difference between the views of Lorentz and Einstein.

Another common argument is the allegation that Lorentz believed in the aether.

The problematic status of the ether is another feature that has been typically considered as a reason to dismiss Lorentz‘s theory and to embrace special relativity. Usually, the ether is held to be problematic chiefly because it is undetectable. Since there is no possible observation that directly indicates the reality of the ether, we should simply apply Occam‘s razor and pick the most economic theory. Adolf Grünbaum, for example, has argued along this line: ...

Two objections can be leveled against this view. First, it is awkward to state that there was no physical foundation in order to postulate a preferred inertial ether frame. ...

Second, and more importantly, the automatic rejection of unobservable entities as a normative principle is debatable. ...

These remarks are enough in order to show that the standard arguments regarding the problematic status of the ether in Lorentz‘s theory are not compelling. However, there is a different perspective from which the ether can be questioned anyway. The real problem with it relies on the fact that, after Poincaré showed that the Lorentz coordinate transformations are symmetric, the ether became not only directly unobservable, but also empirically superfluous — a hypothesis is superfluous if it is logically irrelevant for the derivation of the empirical consequences of the theory it belongs to44.

After rejecting all the other reasons, Acuna ultimately gives two reasons for favoring Einstein over Lorentz. First he notes that Lorentz himself wrote papers about how his electron theory was not compatible with emerging quantum ideas of Planck and others. Second, general relativity built on Minkowski's spacetime geometry, and not Lorentz's formulation.

I am guessing that Acuna had to give some reasons for favoring Einstein, or he would not be able to get his paper published. So he added these silly reasons. It is true that the classical electrodynamics of Maxwell and Lorentz was refined by quantum mechanics, but those equations of Maxwell and Lorentz are still taught and used every day. They are as valid as ever.

Acuna disposes of a couple of general relativity misconceptions also. Some have said that the proof of Einstein's non-ad-hoc and principled thinking is that he went on to create general relativity while being guided by general covariance and ignoring experiment. But in fact he wrote papers rejecting covariance (using a fallacious hole argument), and he was driven by Poincare's use of relativity to explain anomalies in Mercury's orbit.

The inescapable conclusion is that the physicists, historians, and philosophers who idolize Einstein are wrong. They get the facts wrong, and promote a misguided view of what science is all about. The story of Einstein and relativity is one of the most commonly retold stories in the whole history of science, and there is no excuse for contradicting the primary literature.

Acuna has co-authored another paper on Another Look at Empirical Equivalence and Underdetermination of Theory Choice. It says:

Therefore, Lorentz‘s theory is usually considered as EE [empirical equivalence] to Einstein‘s special relativity. This is correct, although some cautious is needed. ... The full equivalence of the theories is obtained only if several crucial amendments and contributions introduced by Henri Poincaré are taken on board.

Lorentz's charge density formula was not quite right, and Einstein's relativistic mass formula was not quite right, and neither had the Lorentz group which was needed to show that the theory made sense. Poincare got everything correct in 1905.

Therefore, in 1906 physics was facing an instance of our problem: there were two predictively equivalent theories and the choice between them was underdetermined by empirical data. We know that in the end Einstein‘s theory won the competition. The historical course of events that led to this victory was rather complex, though. For example, between 1906 and 1909 the scientific community often spoke about the Lorentz-Einstein theory, as the difference between the two rival theories had not been generally recognized. Clarification concerning this rivalry had to wait until Minkowski‘s groundbreaking work (1908). A couple of years later, around 1911, the expression Lorentz-Einstein theory disappeared from the vocabulary of physics, and special relativity was adopted as the main-stream theory.

The expression disappeared because the Poincare-Minkowski non-Euclidean geometry formulation quickly became the dominant theory of relativity, replacing the Lorentz-Einstein theory. No, Einstein's theory did not win. The non-Euclidean geometry version of special relativity won.

Poincare and Minkowski made no use of Einstein's work. Poincare's 1905 paper was written before Einstein's. Minkowski cites Einstein, but only for clearly presenting a couple of Lorentz's ideas.

Einstein used Lorentz's work for the Michelson-Morley consequences, Maxwell's theory, FitzGerald contraction, local time, relativistic mass, and the constant speed of light. Einstein used Poincare for the relativity principle, time synchronization, and the reality of local time.

Thus there are really two observationally equivalent theories. The Lorentz-Einstein theory based on Michelson-Morley, Maxwell's equations, the relativity principle, and the constant speed of light; and the Poincare-Minkowski theory based on the non-Euclidean geometry of spacetime. The non-Euclidean geometry was the paradigm shift, and Einstein completely missed it.

Acuna's Utrecht (Dutch) thesis has more detail. He explains the argument that Einstein did not rely on experiment:

As I mentioned at the beginning of this chapter, there was a time when an essential connection was stated between the Michelson-Morley experiment and SR. That is, the former was thought to have been a direct motivation for Einstein to develop his theory. After the work of historians like Hirosige, Holton, Stachel, Miller and others, this view has finally been shown to be wrong. Einstein?s motivation was not to solve the problem of the ether. ...

After this example of the theoretical asymmetries that do not correspond to the observed phenomena, Einstein briefly refers to “the unsuccessful attempts to discover any motion of the earth relatively to the light medium”, and states that these failed attempts “suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest”78. These two observations are the only reasons that Einstein mentions in his 1905 paper as leading him to the formulation of his relativity principle. That the only specific experiment he mentions is the one of electromagnetic induction and his generic reference to the failed attempts to detect ether-wind effects clearly point out that the Michelson-Morley experiment had no special relevance for the formulation of the theory. After all, this experiment is only one more among the unsuccessful attempts to discover any motion of the earth relatively to the light medium.

The simple explanation is that Einstein got the relativity principle from Poincare, the induction from Maxwell, and the other experiments from Lorentz. Einstein even uses Poincare's term, "relativity principle". Acuna acts as if Einstein reinvented some of it on his own, but there is no evidence of that.

To get his thesis accepted, Acuna probably had to give an explanation for crediting Einstein, in spite of all the historical evidence that others had all the big ideas first.

Before finishing this section and turning to Einstein?s theory, I will make a brief and general remark about a fascinating and important issue: did Poincare independently discover SR? [special relativity] Some authors state that he did –- Giedymin, Zahar and Whittaker75. The main arguments for this conception are Poincare's analysis of the measurement of time and the determination of distant simultaneity, his amendments on the meaning of the Lorentz transformations, and the fact that he derived some mathematical results from the transformations that clearly prefigure Minkowski's space-time –- he noticed that, so that the transformations can be understood not only as rotations around the y and z-axes, but also around the x-axis and a fourth axis it –- and he also noticed that many physical quantities can be expressed as determined by four components, and that so expressed they remain invariant under Lorentz transformations.

In spite of the many results that Poincare obtained, and in spit e of the many epistemological considerations which resemble some of the ones that Einstein also did; I think that Poincare did not discover SR. Even though he made a step towards it with his right foot, his left foot and his whole body stayed in the core of classical mechanics. His relativistic glimpses are only spots in a non-relativistic backdrop.

Acuna's main arguments are that Poincare followed Lorentz's terminology in saying that clocks measure "local time" instead of "true time", and postulated a pressure (or stress) to hold the electron charge together. Supposedly these show an incorrect ontological belief in the aether, altho no one has ever been able to explain what was incorrect.

Acuna does admit that Poincare proved that his theory did not depend on any aether frame:

Poincare explicitly showed that the correct interpretation of the transformations is symmetrical, i.e., that the relevant velocities involved are the relative ones. This feature was not originally noticed by Lorentz, he interpreted them as asymmetric –- his view of the transformations was such that the transformation to go back to the ether-rest frame delivers uncontracted lengths, for example, whereas Poincare showed that both systems S and S’ determine that the lengths of bodies in (relative) motion get contracted. Curiously, as Janssen points out, Lorentz only saw this via Einstein, not via Poincare; even though he was certainly aware of his work –- Lorentz openly accepted the introduction of the Poincare-pressure, for instance74.

When Lorentz lectured on Einstein's work, this symmetry was described as if it were the main technical breakthru. It is curious that Lorentz did not appreciate Poincare's 1905 theory until years later.

The only way Acuna can credit Einstein is to credit him for Minkowski's formulation:

In addition to the mathematical and structural simplicity of Einstein's theory, its formulation in terms of the four-dimensional language introduced by Minkowski was followed by an evaluation of SR as being a very elegant theory. For example, in his 1911 paper Relativitätsprinzip und Äther, Emil Wiechert made such claim [as quoted by Walter]:

Wiechert wrote that SR theory was “brought by Minkowski to a highly mathematically-finished form.” He continued:

It was also Minkowski who, with bold courage, drew the extreme consequences of the theory for a new spacetime intuition and contributed so very much to the theory's renown.

It was precisely Minkowski's spacetime intuition, or his identification of the extreme consequences of this intuition, that had made the theory of relativity famous in Wiechert's view.132

But as explained above, Minkowski's formulation was based on Poincare's non-Euclidean geometry, and had nothing to do with Einstein. It was Minkowski's formulation that was popular in 1911, not Einstein's.

The radically new approach to physics that Einstein‟s paper contained with respect to the notions of space and time were crucially developed and clarified by the work of Hermann Minkowski. In his famous paper of 1908 Space and Time he elucidated that Einstein‟s theory implied a revolutionary reformation of the meaning of these concepts by the introduction of a four-dimensional manifold that we now call space-time.

Here is that 1908 paper, and Minkowski's earlier 1907 paper. Nowhere does either say that Einstein's theory implies anything.

The main reason for crediting Poincare is not that Poincare published published every crucial idea ahead of Einstein. The main reason is that Poincare discovered the spacetime geometry formulation that became the essence of relativity, and Einstein did not even understand it.