Hyper-relativistic mechanics and superluminal particles

TL;DR

This paper proposes a hyper-relativistic mechanics model with modified dispersion relations to account for potential superluminal particles, challenging standard relativity and exploring implications for neutrino motion, Cherenkov radiation, and quantum equations.

Contribution

It introduces a novel hyper-relativistic framework with generalized Lorentz transformations and a modified Dirac equation, extending relativistic mechanics to include superluminal particles.

Findings

Predicts large Lorentz gamma-factors for superluminal neutrinos

Derives generalized Lorentz transformations for hyper-relativistic case

Analyzes properties of Cherenkov radiation in vacuum

Abstract

Recent experiments by OPERA with high energy neutrinos, as well as astrophysics observation data, may possibly prove violations of underlying principles of special relativity theory. This paper attempts to present an elementary modification of relativistic mechanics that is consistent both with the principles of mechanics and with Dirac's approach to derivation of relativistic quantum equations. Our proposed hyper-relativistic model is based on modified dispersion relations between energy and momentum of a particle. Predictions of the new theory significantly differ from the standard model, as the former implies large Lorentz gamma-factors (ratio of particle energy to its mass). First of all, we study model relationships that describe hypothetical motion of superluminal neutrinos. Next, we analyze characteristics of Cherenkov radiation of photons and non-zero mass particles in vacuum. Afterwards, we derive generalized Lorentz transformations for a hyper-relativistic case, resulting in a radical change in the law of composition of velocities and particle kinematics. Finally, we study a hyper-relativistic version of Dirac equation and some of its properties. In present paper we attempted to use plain language to make it accessible not only to scientists but to undergraduate students as well.