The loop of relativistic velocities as a deformation of the menhir loop

TL;DR

This paper introduces a novel algebraic loop structure for relativistic velocity composition, simplifying calculations in special relativity and providing a more elegant mathematical framework compared to traditional methods.

Contribution

It presents an isomorphic algebraic loop on division algebras that streamlines relativistic velocity calculations, offering a new, more elegant formulation.

Findings

Simplifies relativistic velocity calculations

Provides an isomorphic algebraic loop structure

Enhances mathematical elegance in special relativity

Abstract

The algebra of the relativistic composition of velocities is shown to be isomorphic to an algebraic loop defined on division algebras. This makes calculations in special relativity effortless and straightforward, unlike the standard formulation, which consists of a rather convoluted algebraic equation. The elegant appearance of the new formula brings about an additional value.