Effect of coordinate noncommutativity on the mass of a particle in a uniform field and the equivalence principle

TL;DR

This paper investigates how coordinate noncommutativity affects a particle's mass and the equivalence principle in a rotationally invariant noncommutative space, providing exact calculations and solutions to potential violations.

Contribution

It introduces a method to analyze the impact of noncommutativity on particle mass and addresses the violation of the equivalence principle in such spaces.

Findings

Noncommutativity influences particle mass in uniform fields.

The equivalence principle can be violated in noncommutative space.

A proposed solution restores the equivalence principle in this context.

Abstract

We consider the motion of a particle in a uniform field in noncommutative space which is rotationally invariant. On the basis of exact calculations it is shown that there is an effect of coordinate noncommutativity on the mass of a particle. A particular case of motion of a particle in a uniform gravitational field is considered and the equivalence principle is studied. We propose the way to solve the problem of violation of the equivalence principle in the rotationally invariant noncommutative space.