Sur la Dynamique de l'Électron. Offprint from: Rendiconti del Circolo Matematico di Palermo, vol. 21, no. 1, December 1906

THE SPECIAL THEORY OF RELATIVITY. First edition, extremely rare separately-paginated offprint, of this crucial paper in the development of the special theory of relativity, in which Poincaré showed that the Lorentz transformations form a group and that the Maxwell-Lorentz electromagnetic theory is invariant under this 'Lorentz group' (when augmented by space and time translations, it becomes what is now known as the 'Poincaré group'). "The development of mathematics in the nineteenth century began under the shadow of a giant, Carl Friedrich Gauss; it ended with the domination by a genius of similar magnitude, Henri Poincaré. Both were universal mathematicians in the supreme sense and both made important contributions to astronomy and mathematical physics . Poincaré was active in the discussions concerning Lorentz's theory of the electron from 1899 on; Poincaré was the first to observe that the Lorentz transformations form a group . and many physicists consider that Poincaré shares with Lorentz and Einstein the credit for the invention of the special theory of relativity" (DSB). "In 1905, 1906 and 1908 Poincaré published three important papers on the dynamics of the electron. Of these, the first is a note in the Comptes Rendus [submitted 5 June] that summarizes the second paper [submitted 23 July, 1905, the offered paper], in which Poincaré introduced the Lorentz group" (Gray, pp. 361-362). In these papers "Poincaré mentions the negative result of Michelson's experiment and concludes that 'this impossibility to prove absolute motion appears to be a general law of nature.' He then sets out to demonstrate that the transformations of the electromagnetic field equations, which he calls 'the Lorentz transformations,' form a group. But there is more: he closes his article by wondering about the effect of the Lorentz transformations on forces in general and in particular on gravitation. It is a question that Einstein would not ask until 1907 and which would lead him to general relativity. In that same article, Poincaré assumes that gravitation propagates 'at the speed of light' and introduces the idea of a 'gravitational wave' . the Frenchman lays the foundations of a theory of gravitation that, in his own words, 'would not be altered under the group of Lorentz transformations,' that is to say, it would be 'Lorentz invariant.' Moreover, in the same article Poincaré introduces time as a fourth imaginary coordinate as well as the four-dimensional approach, which Minkowski would make precise in 1908 without mentioning Poincaré" (Eisenstaedt, p. 35). "Poincaré undoubtedly discovered many of the ideas that now form our mental picture of the theory of special relativity and associate with the name of Einstein. In his analysis of the relativistic nature of investigations into space and, above all, time, he discussed how different observers can compare time measurements by exchanging light signals, he called for a new physics in which the speed of light is an impassable limit, and he came up with the Lorentz group - all of this independently of Einstein and mostly before him. He was indeed well ahead of Einstein in speculating about a truly relativistic theory of gravity" (Gray, p. 368). Poincaré's paper was the first to demonstrate the power of symmetry or invariance principles in physics. "One hundred years after Poincaré proposed the symmetry principle for all physical laws under uniform relative motion, symmetry principles in physics have transcended both kinetic and dynamic properties and are at the very heart of our understanding of the universe" (Hsu & Zhang, p. xxii). We have located three institutional copies (Deutsches Museum, Max Planck Institut, Rice University). No copies in auction records. "When in the early 1890s Hertz and Heaviside perfected Maxwell's electrodynamics of moving bodies, they noted that it was incompatible with Fresnel's theory of aberration, but decided to postpone further study of the relation between ether an.…