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Not that Poincaré had any objection to experimental work. On the contrary, he believed in experimental results and mathematical rigour. "Explanations are what we lack the least," he once said. What would he have made of String Theory? The Higgs boson? Dark matter? We still need his epistemological scepticism, combined with huge mathematical ability. He believed the universe to be truly intelligible, but also that we can never know what it is "truly" like. He was sceptical of what we call space, or even space-time, and this was before quantum theory, before we fully realised that space-time cannot be infinitely divisible. He even talked of an "atom of time", and believed in the primacy of processes and relationships, rather than some nebulous space in which they take place, and used the concept of symmetry (mathematically speaking: group theory) in preference to that of space. How interesting, then, that symmetry has been the guiding hand in studying interactions unknown in Poincaré's time, the strong and weak nuclear forces, which along with electromagnetism have given us the three quantum forces of the so-called Standard Model of elementary particles.

If space is an illusion, where then does it come from? Poincaré located our intuition of space in our nervous impulses. He would have loved modern brain-imaging techniques, partical accelerators, computers and on the centenary of his death last year some writers referred to this great polymath as "the last universalist". I fervently hope not, but where do we find another like him?

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Physict
June 21st, 2016
6:06 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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