Deformation of nonrelativistic space-time and forces noticed by noninertial observer

TL;DR

This paper explores how noncommutative space-time and noninertial transformations influence forces on a nonrelativistic particle, showing that noncommutativity effects can be replicated by suitable noninertial frames.

Contribution

It demonstrates that force modifications due to noncommutative space-time can be equivalently produced by noninertial transformations in classical nonrelativistic mechanics.

Findings

Noncommutative space-time induces additional force terms.

Noninertial transformations can generate similar force effects.

Equivalence between noncommutativity effects and noninertial frames.

Abstract

We consider the nonrelativistic particle moving on noncommutative space-time in the presence of constant force $\vec{F}$. Further, following the paper M. Daszkiewicz, C.J. Walczyk, Phys. Rev. D 77, 105008 (2008); arXiv: 0802.3575 [math-ph], we recall that the considered noncommutativity generates additional force terms, which appear in the corresponding Newton equation. We demonstrate that the same force terms can be generated by the proper noninertial transformation of classical nonrelativistic space-time.