## 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

**Unique-IP document downloads:** 205 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*