Thomas-Wigner rotation via Clifford algebras

TL;DR

This paper presents a pedagogical derivation of the Thomas-Wigner rotation angle using Clifford algebras, making the concept accessible to students with basic special relativity knowledge.

Contribution

It introduces a new, elementary Clifford-algebra-based derivation of the Thomas-Wigner rotation angle, simplifying the understanding of relativistic rotations.

Findings

Derived Macfarlane's formula using Clifford algebras

Provided an accessible pedagogical approach

Clarified the geometric interpretation of the rotation

Abstract

We derive Macfarlane's formula for the Thomas-Wigner angle of rotation using Clifford-algebra methods. The presentation is pedagogical and elementary, suitable for students with some basic knowledge of special relativity; no prior knowledge of Clifford algebras is required.