## On Superluminal Particles and the Extended Relativity Theories

**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 m_{μ} = 105.7 Mev.

**Comments:** 13 pages, submitted to Physics Letters B

**Download:** **PDF**

### Submission history

[v1] 9 Oct 2011

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