C. Castro: On Superluminal Particles and the Extended Relativity Theories


On Superluminal particles and the Extended Relativity theories,
by Carlos Castro, Center for Theoretical Studies of Physical Systems,
Clark Atlanta University, Atlanta, Georgia. 30314, perelmanc@hotmail.com
October, 2011, submitted to Phys. Letts B

Abstract
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.

Full paper (PDF) available for download at: http://www.vixra.org/abs/1110.0028

Source: Email by C. Castro, czarlosromanov_at_yahoo.com, 2011/10/11 17:30

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