The Matter-Antimatter Concept Revisited

In this paper, we briefly review the theory elaborated by Louis de Broglie who showed that in some circumstances, a particle tunneling through a dispersive refracting material may reverse its velocity with respect to that of its associated wave (phase velocity): this is a consequence of Rayleigh's formula defining the group velocity. Within his Double Solution Theory, de Broglie re-interprets Dirac's aether concept which was an early attempt to describe the matter-antimatter symmetry. In this new approach, de Broglie suggests that the (hidden) sub-quantum medium required by his theory be likened to the dispersive and refracting material with identical properties. A Riemannian generalization of this scheme restricted to a space-time section, and formulated within an holonomic frame is here considered. This procedure is shown to be founded and consistent if one refers to the extended formulation of General Relativity (EGR theory), wherein pre-exists a persistent field.