Finsler-type modification of the Coulomb law

TL;DR

This paper explores a Finsler geometry-based modification of Maxwell's equations, leading to a Coulomb potential correction and hydrogen energy level splitting, with experimental data constraining the Finsler parameters.

Contribution

It introduces a novel Finslerian framework for modifying Maxwell's equations and computes resulting effects on Coulomb potential and atomic energy levels.

Findings

Finsler metric causes splitting of hydrogen energy levels

Experimental data set bounds on Finsler parameters

Finsler modifications violate local Lorentz invariance

Abstract

Finsler geometry is a natural generalization of pseudo-Riemannian geometry. It can be motivated e.g. by a modified version of the Ehlers-Pirani-Schild axiomatic approach to space-time theory. Also, some scenarios of quantum gravity suggest a modified dispersion relation which could be phrased in terms of Finsler geometry. On a Finslerian spacetime, the Universality of Free Fall is still satisfied but Local Lorentz Invariance is violated in a way not covered by standard Lorentz Invariance Violation schemes. In this paper we consider a Finslerian modification of Maxwell's equations. The corrections to the Coulomb potential and to the hydrogen energy levels are computed. We find that the Finsler metric corrections yield a splitting of the energy levels. Experimental data provide bounds for the Finsler parameters.