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- Title
On Superluminal Particles and the Extended Relativity Theories.
- Authors
Castro, Carlos
- 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>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=105.7 MeV.
- Subjects
SUPERLUMINAL effect; PARTICLES (Nuclear physics); RELATIVITY (Physics); CLIFFORD algebras; NEUTRINOS; MASS transfer; TOPOLOGICAL spaces; NUMERICAL analysis
- Publication
Foundations of Physics, 2012, Vol 42, Issue 9, p1135
- ISSN
0015-9018
- Publication type
Article
- DOI
10.1007/s10701-012-9659-3