Quaternions and Special Relativity

TL;DR

This paper presents a quaternionic algebraic reformulation of Special Relativity, demonstrating that real linear quaternions can address transformation issues without requiring complexification, thus offering a new mathematical perspective.

Contribution

It introduces a quaternionic framework for Special Relativity using real linear quaternions, challenging the necessity of complexification in the theory.

Findings

Real linear quaternions resolve transformation issues in 3+1 spacetime

Quaternionic algebra provides an alternative to complexified formulations

Simplifies the mathematical structure of Special Relativity

Abstract

We reformulate Special Relativity by a quaternionic algebra on reals. Using {\em real linear quaternions}, we show that previous difficulties, concerning the appropriate transformations on the $3+1$ space-time, may be overcome. This implies that a complexified quaternionic version of Special Relativity is a choice and not a necessity.