Tenseurs d'impulsion–énergie asymétriques et moment angulaire à six composantes dans le problème des deux impulsions du photon et celui de l'effet magnétodynamique

Abstract

When an asymmetrical momentum–energy tensor Tij is used in the relativistic covariant formulation of the six component angular momentum conservation, and when this formulation is particularized in Newtonian style (initial and final integrals at constant times t and t + dt, origin of point instants simultaneous with t), there is a compensation of terms which substitutes the energy flux T4α for the momentum density Tα4.Three applications of this general result are given.If Tij is the Maxwell–Minkowski tensor, the integrated momentum density D × B is fully replaced by the energy flux E × H, or in other terms, the Minkowski momentum of the photon nhv/c is replaced by the Abraham momentum hv/nrc (n and nr = n cos θ are the refractive indices of the diopter for the directions normal to the equiphase planes and parallel to the extraordinary ray). This is a general solution of the photon two momenta paradox for refringent media.An analogous problem exists for the Fresnel evanescent wave associated with total reflection, in relation to the Goos–Hänchen and Imbert shifts. The solution is identical, but uses the de Broglie and Géhéniau canonical tensor (the Maxwell–Minkowski tensor, being symmetrical in vacuum, cannot be used). A third similar problem is that of the momentum [Formula: see text] 'hidden' in an electric field E = ∂V (Penfield–Haus effect). In terms of densities, the energy flux Vj is seen to appear instead of momentum density qA expected a priori (A, iV: 4 potential, j, iq: current density). In this case, the paradox is solved by using the momentum–energy tensor Akjl or Akjl – (1/2)Aijiδkl. [Translated by the Journal]