Monday, May 12, 2014

Philosopher searches for Poincare's mistake

University of Chicago philosophy professor Howard Stein writes Physics and Philosophy Meet: the Strange Case of Poincaré:
Poincaré is a pre-eminent figure: as one of the greatest of mathematicians; as a contributor of prime importance to the development of physical theory at a time when physics was undergoing a profound transformation; ...

Let me begin with a remark about the culminating event, Poincaré’s memoir of 1905/6 on the dynamics of the electron. I am by no means the first one to comment on that paper: there is a well known controversy over the question whether or not it deserves to be considered as containing a statement of the special theory of relativity -- and if not, why not? -- i.e., the question, how does Poincaré’s theory differ from Einstein’s? That such a controversy should be possible at all is certainly a little odd; so prima facie, the case is strange. But I have not seen it pointed out just how strange; I know of nothing like it in the entire history of physics. There have been many instances of work inadequately appreciated at first, on account of what might be called philosophical preconceptions or prejudices; but here we have to deal with a great work by a great scientist and philosopher of science whose own author failed to appreciate its true worth.
It is very strange, and that is why I wrote a book on the subject, How Einstein Ruined Physics.

Everyone likes to credit Einstein for relativity. His theory was really essentially the same as Lorentz's but they can explain away Lorentz by saying that he did not have the entire theory. Explaining away Poincare is tougher because he had all the formulas, principles, interpretations, etc. On paper, Poincare went well beyond Einstein. So the only way to explain away Poincare is to somehow argue that he did not understand what he wrote.

As Stein explains, historians such as Arthur I. Miller have refused to credit Poincare largely because he was not bold enough in claiming credit for himself. And when discussing points like the aether, Poincare makdes philosophical points that seem maddening to others. Sometimes he says the aether does not exist, and other times he says that it is a useful convenience.

Some physicists find Poincare's view hard to square with relativity, which is supposedly based on the absence of the aether. But Poincare was more of a mathematician, and clearly understood that a concept can be convenient and useful, even if it is not directly measurable. So Poincare was correct.

Even if you do not agree with Poincare'd philosophy, it is very strange not to credit him for one of the greatest advances in the history of science, just because he was modest or of an idiosyncratic philosophy.

Stein starts be quoting Poincare's famous 1905/6 relativity paper. In the introduction, Poincare explains that he is presenting a reformulation of Lorentz's theory, with two views. The Lorentz view is that "there is nothing in the world that is not of electromagnetic origin." Then relativity can be understood as originating in Maxwell's equations, and universally applicable because electromagnetism is also.

In this Lorentz view, the FitzGerald contraction of a measuring rod results from the molecules of the rod being held together by electromagnetic forces, and motion distorting those forces.

The second view is that relativity theory is "something that derives from our methods of measurement." That is, the Lorentz transformations say something about how we measure space and time, and are not just a property of electromagnetism. This is the modern view.

Poincare boldly makes an analogy to the revolution that took us from Ptolemy to Copernicus. He was boldly declaring himself to be the new Copernicus, with a revolutionary view of space and time. Einstein never said that he had a spacetime theory until well after Minkowski bodly endersed the spacetime view in 1908.

At the end of the introduction, Poincare credits Lorentz and says that it all could be disproved by experiment. For this, Miller and others argue that Poincare lacked originality and confidence, and so should not be credited. Miller is wrong.

I quote Stein's translation of Poincare, so you can decide for yourself:
We cannot content ourselves with formulas simply juxtaposed which agree only by a happy chance; it is necessary that these formulas come as it were to interpenetrate one another. The mind will not be satisfied until it believes itself to grasp the reason of this agreement, to the point of having the illusion that it could have foreseen this.

But the question can be presented from still another point of view, which a comparison will help to explain. Let us imagine an astronomer earlier than Copernicus, reflecting upon the system of Ptolemy; he will notice that one of the two circles, epicycle or deferent, of each of the planets is traversed in the same time. This cannot be by chance, there is therefore among all the planets I know not what mysterious bond.

But Copernicus, by simply changing the coordinate axes that are regarded as fixed, makes this appearance vanish; each planet describes only one circle and the times of revolution become independent ... .

There may here be something analogous; if we admit the postulate of relativity, we shall find in the law of gravitation and in the electromagnetic laws a common number which is the velocity of light; and we shall continue to find it in all the other forces, of whatever origin -- which can be explained in two ways only:

Either there is nothing in the world that is not of electromagnetic origin.

Or else this part which is as it were common to all physical phenomena is a mere appearance, something that derives from our methods of measurement. ... In this theory, two equal lengths are, by definition, two lengths that light takes the same time to traverse.

Perhaps it would suffice to renounce this definition, for the theory of Lorentz to be as completely overthrown as Ptolemy’s system was by the intervention of Copernicus. If this happens some day, it will not prove that the effort made by Lorentz was useless; for Ptolemy, whatever one thinks of him, was not useless to Copernicus.

Therefore I have not hesitated to publish these few partial results, even though at this very moment the whole theory might seem placed in danger by the discovery of the magnetocathodic rays.
I never understood the reference to "magnetocathodic rays". Stein tracks it down, and it was some sort of magnetic monopole idea that died several years later. Poincare is not expressing any opinion about these rays, except to say that new observations could disprove the theory. Miller and others have made the silly argument that this showed that Poincare lacked confidence in the theory.

As you can see, Poincare was presenting a very modern and correct view.

Stein goes on to quibble with some of Poincare's philosophy, and to claim this sheds light on the strangeness of Poincare not getting credit. Poincare's biggest mistake, according to Stein, was to not take the theory seriously enough. As a result, he was more interested in explaining the existing experimental data than in predicting new experiments.

As an example, Stein says that Poincare tried to find a relativistic gravity theory compatible with Newton while Einstein (10 years later) tried to explain the anomalies in Mercury's orbit. The example is not so convincing because Poincare first used relativity to partially explain that Mercury anomaly, and Einstein got the idea from Poincare.

If this seems like a weak and muddled conclusion, Stein admits that when presenting his this this thesis, listeners do not get the Poincare mistake. In Stein's words:
The basic mistake that I ascribe to Poincaré is that of seeing the significance of theoretical work as residing essentially and exclusively in its function in organizing knowledge (putative as well as real): that is, organizing the “real generalizations” -- which count as presently claimed knowledge, although it is always possible that they may later fail experimental test. ...

And this is the crucial difference, as I see it, between Poincaré’s relation to the special theory of relativity and Einstein’s. Both of them discovered this theory -- and did so independently. So far as its mathematical structure is concerned, Poincaré’s grasp of the theory was in some important respects superior to Einstein’s. But Einstein “took the theory seriously” in the sense that he looked to it for NEW INFORMATION about the physical world -- that is, in Poincaré’s language, he regarded it as “fertile”: as a source of new “real generalizations” -- of empirically testable consequences.
For this, Einstein is the world's greatest genius was just a misguided fool? No, Stein's analysis just makes the common view look stranger. Devising theories to explain experiments is not a mistake.

Another new philosophy paper carefully distingsuishes the Lorentz constructive view from the spacetime view. In A Case for Lorentzian Relativity, Daniel Shanahan writes:
For the student of physics, there comes a moment of intellectual pleasure as he or she realizes for the first time how changes of length, time and simultaneity conspire to preserve the observed speed of light. Yet Einstein's theory (1) provides little understanding of how Nature has contrived this apparent intermingling of space and time. The language of special relativity (SR) may leave the impression that the Lorentz transformation (the LT) describes actual physical changes of space and time. Thus we have Minkowski's confident prediction that,
Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows and only a kind of union of the two will preserve an independent reality (2).
... Indeed the Minkowski metric should itself be seen as a kind of illusion, and as a consequence rather than the cause of this change in matter. But to entertain these thoughts is to embark upon a process of reasoning, associated primarily with Lorentz, that became unfashionable following Einstein's famous paper of 1905 (1). Lorentz had sought to explain the transformation that bears his name on the basis of changes that occur in matter as it changes velocity. This was, it is suggested, an idea before its time. ...

In what follows, the distinction drawn will be between Einstein's SR (ESR) and what we will call Lorentzian SR (LSR). This is not to diminish the contributions of others, but it was Lorentz in particular who sought to explain SR from underlying physical processes, as will be the objective below. Once the form of the LT was known, all else in SR then followed, including the composition of velocities, the group theoretic properties of the transformation, and the invariance of Maxwell's equations. It may be argued that with these refinements (largely due to Einstein and Poincaré), ESR and LSR are essentially equivalent. They cannot be distinguished, mathematically or empirically, through the privileged frame that was supposed by Lorentz, but declared "superfluous" by Einstein (1). It would seem that any such frame is rendered undetectable by the covariance of the LT. Nor can ESR and LSR be distinguished by supposing that in ESR, though not in LSR, the LT describes a transformation of spacetime. As we have seen, the LT must be explained in either case by changes occurring in matter as it is accelerated from one inertial frame to another. Historically, the two approaches are distinguished by the assumptions made by Einstein in justifying the LT. His confident assertion of these "postulates" gave impetus to the recognition and development of SR.
This is mostly accurate, but it makes more sense to distinguish LSR from Minkowskian SR. Poincare was the first to formulate the spacetime view, as an alternative to LSR, and Minkowski was the first to unequivocally adopt it. After Minkowski, the leading European physicists also adopted it, and eventually Einstein did also.

Einstein's reasoning in his famous 1905 paper was essentiallly the same as Lorentz's original reasoning, but expressed differently. Whereas FitzGerald, Lorentz, Larmor, Poincare, and Minkowski directly appealed to the Michelson-Morley experiment to deduce the relativity principle and the constant observed speed of light, Einstein said that he was elevated these principles to the status of postulates. Either way, they were deducing the LT from the relativity principle and the constant speed of light.

Lorentz went deeper and provided and electromagnetic explanation. Einstein did not comment on that explanation, as Poincare did.

Here is Shanahan's version of the history:
Briefly first some history. The problem addressed by Lorentz and subsequently Einstein was the speed of light. This emerged as a constant in Maxwell's equations, but if as was generally supposed, light is wave-like, it seemed reasonable to assume that it must be carried by some medium (the "luminiferous aether") at a velocity characteristic of that medium. Thus its velocity relative to an observer should have varied with the motion of the observer through the medium. Experiments of increasing sophistication failed to reveal any trace of that variation.

Several explanations were put forward. It was proposed that the Earth must carry the local aether with it, but a more fruitful suggestion made independently by Fitzgerald (10) and Lorentz (11) was that objects moving through the aether must be somehow shortened along their direction of travel, thereby disguising relative changes in the velocity of light. It was supposed that intermolecular forces must be transmitted at the same velocity as electromagnetic waves, so that movement through the aether would influence the degree of attraction between molecules and thus the separation of those molecules. ...

The LT was already reasonably well known by 1905. There had been significant contributions to its development, not only from Lorentz and Fitzgerald, but also by (among others) Heaviside, Larmor and Poincaré. It was Heaviside's analysis of the disposition of fields accompanying a charged particle (the "Heaviside ellipsoid") that had suggested to FitzGerald the idea of length contraction (12). Larmor had described an early form of the LT and discussed the necessity of time dilation (13). Poincaré had recognized the relativity of simultaneity and had studied the group theoretic properties that form the basis for the covariance of the transformation (14).

But these "trailblazers" (Brown (6), Ch. 4 ) appear to have missed in varying degrees the full significance of the transformation3. It is not only particular phenomena, but all of Nature that changes for the accelerated observer. Lorentz struggled to explain how all aspects of matter could became transformed in equal measure, being discouraged by experimental reports that seemed to show that particles do not contract in the direction of travel (see Brown (6), p. 86). A wider view seems to have been noticed by Poincaré (14), who has been regarded by some as codiscoverer of SR (see, for instance, Zahar (15), and Reignier (16)). But it is not apparent that these earlier investigators saw the changes described by the LT as anything more than mathematical constructs. In his paper of 1905 (1), Einstein simply asserted that the velocity of light, and other properties of Nature, must appear the same for all uniformly moving observers, thereby effecting an immediate reconciliation between Maxwell's equations and classical mechanics.

In 1905, Einstein's approach may have been the only way forward.
Again, this is pretty accurate, but a couple of comments are bizarre. Some historians do claim that Lorentz and Poincare saw the LT as nothing more than mathematical constructs. But this is clearly false, as the Lorentz and Poincare papers are concerned with explaining the Michelson-Morley and other experiments, and directly say that the LT is necessary for those observations.

This is another example of a scholar acknowledging that Poincare had the entire SR theory, but then trying to devalue him by saying that he did not understand what he was doing.

The last claim that Einstein's 1905 paper was the "only way forward" is another common misconception. It is a historical fact that his paper had very little influence in 1905, and papers on SR did not mushroom until after publication of the famous 1908 Minkowski paper, quoted above. The chain of development went from Maxwell to Michelson to Lorentz to Poincare to Minkowski to widespread acceptance to textbooks.

Some people later decided that Einstein's approach had some pedagogical advantages because it allows deriving the LT without discussing actual experiments. But that is not how SR was originally proposed and accepted.

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