A Relativisfic Model of a Particle-Antiparticle Pair may Break up the E.P.R. Paradox

A special theory of Relativity in the space-like region has been developed by R. Dutheil and A. Rachman (1,2,3,4) with the tensor formalism and using Tachyonic Referential Frames (TR-F). Now two different theories of Relativity built on two different metrics, define two different Lorentz groups which respectively transform two types of referential frames: Ordinary Referential Frames (ORF) for one theory, Tachyonic Referential Frames (TRF) for the other. The both theories of Relativity may describe the same event in the physical space: so they need to be unified. In some previous papers R. Dutheil and G. Nibart have shown that particles having a superluminal velocity, named tachyons [5,6] may exist [7] and do not violate the Causality Principle [8], and according to our reinterpretation principle, the Tachyon Bradyon Identity Principle (TBI Principle) [7] they will always be perceived by any natural observer, using Ordinary Referential Frames (ORF), as being antiparticles having a subluminal velocity. ln the present communication we attempt a unification of the time-like region theory and the space-like region theory into a six-dimensional manifold, where the Lorentz transformations are generalized. Here, the light barrier appears as a mathematical singularity that can be removed by a pure algebraical method which eliminates time coordinates (time and energy) from both four-dimensional theories. ln this new model, time (the function t) is not a coordinate, but it is an "observable" and by definition, it is not reversible. The equation of Klein, Gordon, and Fock can be written in a six dimensional manifold. The Dirac equation can also be written in a six dimensional manifold where it has more conveniently no negative energy solutions. Furthermore, a pair of particles - here a tachyon (i.e. an antiparticle) and a bradyon#can be considered as one unique event in a timeless six-dimensional space. As its wave function may propagate in two different physical ways, we think this new conception of a particle pair will soon break up the E.P.R. paradox.