Exploring Lorentz Violation in Spacetime through Universal Finsler Geometry

TL;DR

This paper proposes that Finsler geometry intrinsically characterizes the universe's structure, leading to new modified dispersion relations and insights into Lorentz violation across particles, consistent with existing observations.

Contribution

It introduces the novel hypothesis that Finsler structures are an intrinsic property of the universe, deriving new dispersion relations and analyzing their implications for Lorentz violation.

Findings

Lorentz violation scales are proportional to particle masses

Derived new modified dispersion relations

Aligns with phenomenological Lorentz violation observations

Abstract

Finsler geometry serves as a fundamental and natural extension of Riemannian geometry, providing a valuable framework for investigating Lorentz violation in spacetime. Previous studies have treated the Finsler structures associated with different particles as distinct entities. In this paper, we propose a novel hypothesis suggesting that the Finsler structure may represent an intrinsic property of the universe itself. Under this assumption, we derive a series of modified dispersion relations that have not been previously explored, and we analyze their implications. Our findings indicate that the scales of Lorentz violation for massive particles are proportional to their masses. Furthermore, we demonstrate that this hypothesis aligns well with existing phenomenological results regarding Lorentz violation observed in photons, neutrinos, and electrons.