Relativistic combination of non-collinear 3-velocities using quaternions

@article{Berry2020RelativisticCO,
title={Relativistic combination of non-collinear 3-velocities using quaternions},
author={Thomas Berry and M. Visser},
journal={arXiv: General Relativity and Quantum Cosmology},
year={2020}
}

Quaternions have an (over a century-old) extensive and quite complicated interaction with special relativity. Since quaternions are intrinsically 4-dimensional, and do such a good job of handling 3-dimensional rotations, the hope has always been that the use of quaternions would simplify some of the algebra of the Lorentz transformations. Herein we report a relatively nice result for the relativistic combination of non-collinear 3-velocities. If we work with the relativistic half-velocities $w… Expand