Poincaré’s New Mechanics

After having recalled the circumstances with which Poincaré introduced the principle of relativityPrinciple of relativity at the Saint Louis congress in 1904, an original analysis of the three letters he wrote to LorentzLorentz, Hendrik Antoon concerning his theory of electronsLorentz (Theory of electrons) will restore the chronological order of his publications. It will be shown that Poincaré’s memoir entitled “Sur la dynamique de l’électron” (On the dynamics of the electron), submitted on the 23rd July 1905 to the Rendiconti del Circolo Matematico di PalermoRendiconti and not published until December 1906, was actually written in May 1905. The note Poincaré presented to the members of the Académie des SciencesAcadémie des Sciences on 5th June 1905 was merely a summary. An analysis of these letters and publications will show that, as early as May 1905, Poincaré was already in possession of the transformation to which he gave Lorentz’s name, which enabled him to establish the new relativistic velocity addition lawRelativistic velocity addition law, and that he had already laid the foundations of a New MechanicsThe New Mechanics, soon to be known as the Special theory of relativityspecial theory of relativity.