Length contraction in Very Special Relativity

TL;DR

This paper investigates length contraction within Very Special Relativity (VSR), specifically the HOM(2) subgroup, revealing that VSR predicts different length contraction formulas from SR, with some cases showing similar results.

Contribution

It provides the first detailed calculation of length contraction in VSR, expanding understanding of relativistic effects beyond standard special relativity.

Findings

Length contraction formulas in VSR differ from SR in general.

In many cases, VSR and SR predict similar length contraction.

The study focuses on the HOM(2) subgroup of VSR.

Abstract

Glashow and Cohen claim that many results of special theory of relativity (SR) like time dilation, relativistic velocity addition, etc, can be explained by using certain proper subgroups, of the Lorentz group, which collectively form the main body of Very special relativity (VSR). They did not mention about length contraction in VSR. Length contraction in VSR has not been studied at all. In this article we calculate how the length of a moving rod contracts in VSR, particularly in the HOM(2) version. The results are interesting in the sense that in general the length contraction formulas in VSR are different from SR but in many cases the two theories predict similar length contraction of moving rods.