Relativistic velocity space, Wigner rotation and Thomas precession

TL;DR

This paper introduces a geometric framework called rapidity space to visualize and compute relativistic effects like Wigner rotation and Thomas precession, based on Lorentz invariance.

Contribution

It develops the concept of rapidity space as a new geometric tool for understanding relativistic velocity transformations and associated phenomena.

Findings

Rapidity space provides a clear geometric visualization of Lorentz boosts.

The approach simplifies calculations of Wigner rotation and Thomas precession.

It offers a unified geometric perspective on relativistic kinematic effects.

Abstract

We develop a relativistic velocity space called \emph{rapidity space} from the single assumption of Lorentz invariance, and use it to visualize and calculate effects resulting from the successive application of non-colinear Lorentz boosts. In particular, we show how rapidity space provides a geometric approach to Wigner rotation and Thomas precession in the same way that spacetime provides a geometrical approach to kinematic effects in special relativity.