Finslerian spaces possessing local relativistic symmetry

TL;DR

This paper introduces generalized Lorentz transformations within Finslerian spaces, providing a potential solution to ultra-high energy cosmic ray anomalies by describing anisotropic space-time symmetries beyond Minkowski space.

Contribution

It proposes a new class of Lorentz transformations acting on Finslerian spaces with local anisotropy, extending relativity theory beyond isotropic Minkowski space.

Findings

Generalized Lorentz transformations maintain group properties and velocity addition laws.

Finslerian spaces with broken isotropy serve as the geometric framework for these transformations.

Potential physical effects of space-time anisotropy are suggested for experimental search.

Abstract

It is shown that the problem of a possible violation of the Lorentz transformations at Lorentz factors $\gamma >5\times 10^{10} ,$ indicated by the situation which has developed in the physics of ultra-high energy cosmic rays (the absence of the GZK cutoff), has a nontrivial solution. Its essence consists in the discovery of the so-called generalized Lorentz transformations which seem to correctly link the inertial reference frames at any values of $\gamma .$ Like the usual Lorentz transformations, the generalized ones are linear, possess group properties and lead to the Einstein law of addition of 3-velocities. However, their geometric meaning turns out to be different: they serve as relativistic symmetry transformations of a flat anisotropic Finslerian event space rather than of Minkowski space. Consideration is given to two types of Finsler spaces which generalize locally isotropic Riemannian space-time of relativity theory, e. g. Finsler spaces with a partially and entirely broken local 3D isotropy. The investigation advances arguments for the corresponding generalization of the theory of fundamental interactions and for a specific search for physical effects due to local anisotropy of space-time.