Towards a Computational Derivation of a Dual Relativity with Forward-Backward Space-Time Shifts

A computational derivation of the Klein-Gordon quantum relativist equation and the Schrôdinger quantum equation with forward and backward space-time shifts was developed in Dubois (1999, 2000). The forward-backward space λ and time t shifts are related to a phase velocity u = λ/t. The ratio v/u, where v is a group velocity, is related to the mass of paticles: for v < u, particles have a real mass and for v = u, there is no mass, as for photons. In this paper, it is shown that this formalism gives rise to a quantum interpretation of the mass in relation with plane waves. Moreover there is a third case for mass of particle: when for v > u, particles have an imaginary mass, as for tachyons. From these considerations, we look at the possibility to develop a dual relativity including these three types of mass.