Novel Physical Consequences of the Extended Relativity in Clifford Spaces

Abstract

Novel physical consequences of the Extended Relativity Theory in C-spaces (Clifford spaces) are explored. The latter theory provides a very different physical explanation of the phenomenon of “relativity of locality” than the one described by the Doubly Special Relativity (DSR) framework. Furthermore, an elegant nonlinear momentum-addition law is derived in order to tackle the “soccer-ball” problem in DSR. Neither derivation in C-spaces requires a curved momentum space nor a deformation of the Lorentz algebra. While the constant (energy-independent) speed of photon propagation is always compatible with the generalized photon dispersion relations in C-spaces, another important consequence is that these generalized photon dispersion relations allow also for energy-dependent speeds of propagation while still retaining the Lorentz symmetry in ordinary spacetimes, while breaking the extended Lorentz symmetry in C-spaces. This does not occur in DSR nor in other approaches, like the presence of quantum spacetime foam. We conclude with some comments on the quantization program and the key role that quantum Clifford-Hopf algebras might have in the future developments since the latter q-Clifford algebras naturally contain the κ-deformed Poincare algebras which are essential ingredients in the formulation of DSR.