Special Relativity, Einstein Velocity Addition, and Gyrogroups: An Introduction

TL;DR

This paper provides an accessible introduction to special relativity, Lorentz transformations, Einstein velocity addition, and gyrogroups, aiming to serve as educational material for students and non-specialists.

Contribution

It offers a unified, beginner-friendly presentation of advanced concepts like gyrogroups and gyrovector spaces within special relativity.

Findings

Clarifies the mathematical structure of Einstein velocity addition

Introduces gyrogroups and gyrovector spaces in an accessible manner

Serves as a foundational resource for teaching and learning in the field

Abstract

In these notes we give an introductory unified treatment to the topics of special relativity, Lorentz transformations and the Lorentz group, Einstein velocitiy addition, and gyrogroups and gyrovector spaces. An effort has been made to present the material in a manner that is accessible to non-specialists and graduate students, and may even serve as the basis for a graduate course or seminar.