Lorentz Transformations from Reflections:Some Applications

TL;DR

This paper explores how Lorentz transformations can be derived from reflections, demonstrating applications in constructing boosts and understanding Lorentz matrices through Minkowski geometry.

Contribution

It introduces a novel perspective by deriving Lorentz transformations from reflections, providing new geometric insights and methods for constructing boosts and analyzing Lorentz matrices.

Findings

Lorentz boosts can be constructed from hyperplane reflections.

Reflections offer a geometric interpretation of Lorentz transformations.

Applications include understanding V. Moretti's polar decomposition.

Abstract

We point out, by exhibiting two examples and mentioning a third one, that it is sometimes useful to consider Lorentz transformations as generated from hyperplane or line reflections. One example concerns the construction of boosts linking two given 4-vectors, the other one concerns the Minkowski geometric understanding of V. Moretti's polar decomposition of orthochronous Lorentz matrices.