Les structures fines de l'électromagnétisme classique et de la relativité restreinte (The fine structures of Classical Electromagnetism and Special Relativity)

Abstract

One of us (Y.P.) has shown the existence of a longitudinal component in the propagation of light waves on the basis of the kinematics underlying Poincaré's ellipse. We show how this statement agrees with the electromagnetic theory. We recall that the second of us supports the existence of a "fine structure" of Electromagnetism that is, the co-existence of two theories, one based on the fields (Heaviside-Hertz) and the other on the potentials (Riemann-Lorenz). The existence of two different kinematics (the "fine structure" of Special Relativity : Einstein or Poincaré) corresponds to these two formulations of Classical Electromagnetism. With this goal in mind, we prove the relativistic covariance of the Helmholtz decomposition of the vector potential. This one translates into a generalized compensation for all directions of propagation, on the basis of the tangent to Poincaré's ellipse, between the scalar potential and the longitudinal component of the vector potential. The adoption by Poincaré of the Lorenz gauge condition (with longitudinal and temporal components) is in contrast with the Einsteinian photon and the Einsteinian kinematics with only transversal components compatible with the choice of the "completed" Coulomb gauge condition (transverse gauge).