After introductory surveys of Poincaré’s role in the Dreyfus case and of his “Fourth Geometry,” I turn to the main question. The problem confronting both Poincaré and Einstein was how to reconcile the phenomena of electrodynamics, notably the optical principle of relativity, with the principles of Newtonian mechanics. I show that, on such questions as the existence and role of the ether and the relation between kinematics and dynamics, Poincaré and Einstein held diametrically opposed views. Poincaré did everything to preserve the old viewpoint, while Einstein abandoned the absolute time and proposed a new mechanics.
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