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Foundations of Physics

, Volume 42, Issue 9, pp 1135–1152 | Cite as

On Superluminal Particles and the Extended Relativity Theories

  • Carlos Castro
Article

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 \(\mathcal{M} = \sqrt{ M^{2} - \pi^{2} }\) 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 M 2>0. Therefore, there are no violations of the Clifford-extended Lorentz invariance and the extended Relativity principle in C-spaces. It is also explained why the charged muons (leptons) are subluminal while its chargeless neutrinos may admit superluminal propagation. 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 the magnitude \(|\mathcal{M } | = 119.7\mbox{~MeV}\) that, coincidentally, is close to the mass of the muon m μ =105.7 MeV.

Keywords

Extended relativity Clifford spaces Finsler geometry superluminal 

Notes

Acknowledgements

We thank M. Bowers for her assistance, to Sergiu Vacaru for discussions and to the referee for offering many suggestions to improve the manuscript and pointing out many important references.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Center for Theoretical Studies of Physical SystemsClark Atlanta UniversityAtlantaUSA

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