Authors: Carlos Castro
Superluminal particles are studied within the framework of the Extended Relativity theory in Clifford spaces (C-spaces). In the simplest scenario, it is found that it is the contribution of the Clifford scalar component π of the poly-vector-valued momentum which is responsible for the superluminal behavior in ordinary spacetime due to the fact that the effective mass M = (see paper) is imaginary (tachyonic). However, from the point of view of C-space, there is no superluminal (tachyonic) behavior because the true physical mass still obeys M2 > 0. Therefore, there are no violations of the Clifford-extended Lorentz invariance and the extended Relativity principle in C-spaces. Furthermore, to lowest order, there is no contribution of terms involving powers of the Planck mass (1/m2P ) indicating that quantum gravitational effects do not play a role at this order. A Born's Reciprocal Relativity theory in Phase Spaces leads to modified dispersion relations involving both coordinates and momenta, and whose truncations furnish Lorentz-violating dispersion relations which appear in Finsler Geometry, rainbow-metrics models and Double (deformed) Special Relativity. These models also admit superluminal particles. A numerical analysis based on the recent OPERA experimental findings on alleged superluminal muon neutrinos is made. For the average muon neutrino energy of 17 Gev, we find a value for π = 119.7 Mev that, coincidentally, is close to the mass of the muon mμ = 105.7 Mev.
Comments: 13 pages, submitted to Physics Letters B
[v1] 9 Oct 2011
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