Authors: Carlos Castro
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 $ \kappa$-deformed Poincare algebras which are essential ingredients in the formulation of DSR.
Comments: 17 Pages. Submitted to Advances in Applied Clifford Algebras
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[v1] 2014-01-31 08:28:30
[v2] 2014-02-23 04:29:23
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