La cinématique relativiste sous-jacente à lʹellipse de Poincaré

What is the Lorentz transformation (LT) of a spherical wavefront (a set of simultaneous events)? According to Einstein (1905) the LT produces a spherical wavefront whilst according to Poincaré (1908) the LT produces an ellipsoidal wavefront (the events are no longer simultaneous). What is the LT of a plane wavefront (a set of simultaneous events)? According to Einstein the LT is a space transversal (to the direction of propagation) plane wavefront. According to Poincaré, the LT is a non transversal spacetime wavefront (the tangent plane to the ellipsoid). We show that this contrast between Einsteinʹs and Poincaréʹs theory of wavefronts is not connected with the electromagnetic fields but with electromagnetic potentials. Poincaréʹs explicit choice is the Lorenz gauge while Einsteinʹs implicit choice is the transverse gauge. In other words, the convention of synchronization of clocks with light signals is not the same. We show that Poincaréʹs elongated ellipse in the system of the source is not only a direct explanation of the null result of Michelsonʹs experiment but also a direct explanation of the non null Sagnacʹs experiment. The fruitless historical polemics of priority between Poincaré and Einstein has been replaced by a very current scientific problematic about the best implementation of simultaneity in the GPS system. To cite this article: Y. Pierseaux, C. R. Physique 8 (2007).