The nonrelativistic limit of the Magueijo-Smolin model of deformed special relativity

TL;DR

This paper investigates the nonrelativistic limit of a deformed special relativity model, revealing deviations in mass definitions and CPT symmetry, with potential experimental implications.

Contribution

It provides a detailed analysis of the nonrelativistic limit of the Magueijo-Smolin DSR model, clarifying mass and velocity concepts and highlighting CPT symmetry breaking.

Findings

Rest mass differs from inertial mass in the nonrelativistic limit.

CPT invariance is broken due to mass differences between particles and antiparticles.

Predicted effects are near current observational limits.

Abstract

We study the nonrelativistic limit of the motion of a classical particle in a model of deformed special relativity and of the corresponding generalized Klein-Gordon and Dirac equations, and show that they reproduce nonrelativistic classical and quantum mechanics, respectively, although the rest mass of a particle no longer coincides with its inertial mass. This fact clarifies the meaning of the different definitions of velocity of a particle available in DSR literature. Moreover, the rest mass of particles and antiparticles differ, breaking the CPT invariance. This effect is close to observational limits and future experiments may give indications on its effective existence.