Elementary analysis of the special relativistic combination of velocities, Wigner rotation, and Thomas precession

TL;DR

This paper offers an accessible introduction to how velocities combine in special relativity, covering Wigner rotation and Thomas precession with varying levels of complexity for different learners.

Contribution

It provides an elementary, intermediate, and advanced explanation of relativistic velocity addition, Wigner rotation, and Thomas precession, making these concepts more accessible.

Findings

Clarifies velocity combination in special relativity

Explains Wigner rotation and Thomas precession qualitatively and quantitatively

Provides educational resources for different learning levels

Abstract

The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most familiar tools of special relativity, in arguments presented at three differing levels: (1) utterly elementary, which will suit a first course in relativity; (2) intermediate, to suit a second course; and (3) advanced, to suit higher level students. We then give a summary of useful results, and suggest further reading in this often obscure field.