A systematic search for a three-velocity gyrodistributive law in special relativity with the lorentz R package

TL;DR

This paper introduces the lorentz R package for relativistic physics, aiming to find a gyrodistributive law in special relativity, but no such law was discovered despite systematic search.

Contribution

The paper presents a new R package for relativistic calculations and uses it to systematically search for a gyrodistributive law in special relativity.

Findings

No gyrodistributive law was found in the searched space.

The package facilitates relativistic computations and law searches.

Systematic search did not yield a new gyrodistributive law.

Abstract

Here I present the lorentz package for working with relativistic physics. The package includes functionality for four-vector transformations, three-velocity addition, and other relativistic processes such as the behaviour of photons. It was designed to facilitate the search for a gyrodistributive law. In special relativity, three-velocities and scalars constitute a gyrovector space with addition $\oplus$ and scalar multiplication $\odot$. Standard vector spaces obey the distributive law $a(x + y) = ax + ay$ for scalar $a$ and vectors $x$, $y$; but no analogous gyrodistributive law for $r\odot (u \oplus v)$ is known. The package was designed to facilitate the search for a gyrodistributive law and includes functionality for four-vector transformations and three-velocity addition, which is noncommutative and nonassociative. I use the package to systematically sweep a large space of potential gyrodistributive laws, without success. The package is available on CRAN, at \url{https://CRAN.R-project.org/package=lorentz}.