Finsler space-time in light of Segal's principle

TL;DR

This paper explores the stability of the ISIM(2) symmetry group in very special relativity, proposing that Finsler space-time may provide a more accurate framework due to its relation to Segal's principle.

Contribution

It introduces the idea that Finsler space-time, aligned with Segal's principle, offers a more stable symmetry structure than ISIM(2) in very special relativity.

Findings

ISIM(2) symmetry is unstable under small algebraic deformations.

Finsler space-time aligns with Segal's principle, providing a stable alternative.

Very special relativity remains a good approximation due to small deformation parameters.

Abstract

ISIM(2) symmetry group of Cohen and Glashow's very special relativity is unstable with respect to small deformations of its underlying algebraic structure and according to Segal's principle cannot be a true symmetry of nature. However, like special relativity, which is a very good description of nature thanks to the smallness of the cosmological constant, which characterizes the deformation of the Poincare group, the very special relativity can also be a very good approximation thanks to the smallness of the dimensionless parameter characterizing the deformation of ISIM(2).