Special relativity with an arbitrary invariant limiting velocity of a particle

TL;DR

This paper develops a generalized special relativity theory allowing for an arbitrary invariant limiting velocity, extending the canonical hyperboloid model, and explores implications for superluminal particles like neutrinos.

Contribution

It introduces a generalized Lorentz framework based on hyperboloids for any limiting velocity, broadening the scope of special relativity beyond the speed of light.

Findings

Generalized Lorentz transformations for arbitrary limiting velocities.

Rest mass of space-like particles remains real in GSTR.

Implication that neutrinos could be superluminal with velocities exceeding light speed.

Abstract

It is shown that a generalized special theory of relativity (GSTR) with an arbitrary limiting velocity of a particle different or equal to the speed of light in vacuum can be constructed from the canonical equation of the 4-dimensional hyperboloid of revolution. In particular, when the limiting velocity equals the speed of light, the special theory of relativity (STR), which corresponds to the equation of the equilateral hyperboloid of revolution, is recovered. The generalized Lorentz transformations for any values of the speed limit for both the time-like and the spice-like regions in the coordinate and momentum spaces and in the general parametric form were obtained. It was established that the inversion of time (energy) axis under the (generalized) Lorentz transformations is forbidden. In the GSTR, the rest mass of a space-like particle is real. Our results strongly suggest that the muon neutrino in the OPERA experiment might most likely be a time-like or a light-like superluminal particle, whose limiting velocity may exceed the speed of light in vacuum, rather than a superluminal space-like particle (tachyon) with a speed limit equal to speed of light for which the rest mass $m=117.1^{+11.0}_{-10.5}$ MeV$/c^{2}$.