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Henri Poincaré: So far ahead of his time that we are still catching up

This Standpoint column gives scientists a forum to express their ideas publicly, though doing so is not easy. Among those who were good at it was the great French scientist Henri Poincaré — not to be confused with his cousin Raymond Poincaré, who was President of France during the First World War. Henri died in 1912 before that war, and if I could reincarnate one figure from the past to comment on modern scientific ideas and breakthroughs, it would be him.

Poincaré arrived at the main ideas of Relativity Theory before Einstein, foreseeing the gravitational implications that emerged later, and a putative 1970s textbook on relativity by a top Princeton mathematician was never published when it was seen to downplay Einstein's role relative to Poincaré's. In fact the two men's work was independent and as the French physicist Louis de Broglie wrote, "he left to Einstein the glory of seeing all the consequences of relativity and, in particular . . . the true physical character of the relationship the principle of relativity establishes between space and time". Why? De Broglie gives an answer in a 1954 address, available on YouTube: it was "without doubt his a little too hypercritical turn of mind, due to his having first been a pure mathematician, that was the cause". 

These quotations appear in Henri Poincaré: A Scientific Biography by Jeremy Gray (Princeton, £24.95). It is full of the mathematical, physical and metaphysical ideas of a man who was not only a dispassionate observer of the world around us, but of our way of understanding it. Epistemology was a vital subject for him and one of his favourite questions was, "How do we know that?" As a disinterested observer he was even called in to examine the Dreyfus case, and completely demolished the "proof" that the handwriting of the main incriminating document was that of the accused. It wasn't.

Henri Poincaré, born in 1854, could already talk at nine months, and during his fourth year at the Lycée (13-14 years) his teacher called at the Poincaré house to say that the boy would be a mathematician. When his mother, who rather liked mathematics, appeared not unduly surprised, the teacher added, "I mean to say, a great mathematician."

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Physict
June 21st, 2016
5:06 AM
This article is flat out WRONG. Poincaré was confused on several points. (See the discussion on Wikipedia regarding "mass energy equivalence".) He could never get the mechanical relations straight, since he could not figure out that E=mc2E=mc2. Einstein followed Poincaré closely in 1905, he was aware of Poincaré's work, but he derived the theory simply as a geometric symmetry, and made a complete system. Einstein did share the credit with Lorentz and Poincaré for special relativity for a while, probably one reason his Nobel prize did not mention relativity. Pauli in the Encyclopædia Britannica article famously credits Einstein alone for formulating the relativity principle, as did Lorentz. Poincaré was less accomodating. He would say "Einstein just assumed that which we were all trying to prove" (namely the principle of relativity). (I could not find a reference for this, and I might be misquoting. It is important, because it shows whether Poincaré was still trying to get relativity from Maxwell's equations, rather than making a new postulate—I don't know.) Special relativity was ripe for discovery in 1905, and Einstein wasn't the only one who could have done it, although he did do it best, and only he got the E=mc2E=mc2 without which nothing makes sense. Poincaré and Lorentz deserve at least 50% of the credit (as Einstein himself accepted), and Poincaré has most of the modern theory, so Einstein's sole completely original contribution is E=mc2E=mc2. Poincare was looking for a "mechanical" explanation of why the speed of light "appeared" constant in all reference frames. In other words, Poincare did not even believe in relativity in the Einsteinian sense. He believed that there was a preferred frame at a fundamental level. What Einstein did was to raise the "problem" of the speed of light appearing constant in all reference frames to the level of a postulate. This is what Poincare means when he says "Einstein just assumes that which we were all trying to prove". I think Poincare didn't really understand what Einstein had done -- space and time were fundamentally woven together in Einstein's theory. In Poincare-Lorentz's theory, space and time are separate, but only appear to be woven together -- there is a preferred frame where simultaneity of spacially separated events is absolute. I would also like to add -- and this part is just speculation -- that I believe we would still not have special relativity today if it hadn't been for Einstein. I believe we would still be working in the framework of Lorentz-Poincare, where Lorentz Invariance is achieved at an observational level, but fundamentally the theory has a preferred reference frame. Looking at comments on what Einstein had that Poincaré didn't have, beyond the mass-equivalence stroke; where Einstein argued that a light pulse which is spherical in one inertial frame, is spherical in every inertial frame. According to Poincaré, a light pulse that is spherical in the above mentioned privileged frame is an elongated ellipsoid in every other inertial frame. The difference in description is due to that fact that Einstein recognized the relativity of spatio-temporal coordinates, when Poincaré did not. And, the aberration constant, Poincaré didn't derive it, Einstein did.

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