On Some Novel Consequences of Clifford Space Relativity Theory

Abstract

Some of the novel physical consequences of the Extended Relativity Theory in C-spaces (Clifford spaces) are presented. In particular, generalized photon dispersion relations which allow for energy-dependent speeds of propagation while still retaining the Lorentz symmetry in ordinary spacetimes, while breaking the extended Lorentz symmetry in C-spaces. We analyze in further detail the extended Lorentz transformations in Clifford Space and their physical implications. Based on the notion of “extended events” one finds a very different physical explanation of the phenomenon of “relativity of locality” than the one described by the doubly special relativity framework. We finalize with a discussion of the modified dispersion relations, rainbow metrics and generalized uncertainty relations in C-spaces which are extensions of the stringy uncertainty relations.