An Alternative Mathematical Model For Special Relativity

TL;DR

This paper introduces a novel mathematical framework using pseudo-complex dimensions to model special relativity, potentially offering new insights into space-time structure.

Contribution

It proposes a unique algebraic model with three pseudo-complex dimensions, distinct from existing models, to describe special relativity.

Findings

Mathematical model compatible with Einstein's theory

Uses non-commutative, non-associative algebraic structures

Introduces a new elementary mathematical object

Abstract

We present a mathematical model for a physical theory that is compatible with Einstein's Special Relativity Theory. Our model consists of three pseudo-complex dimensions, representing three real dimensions of space, dual to what could be interpreted as three real dimensions of time. We use the term "pseudo-complex", since the mathematical object representing each paired space-time coordinate in our model, is a two-dimensional space over $\mathbb{R}$ whose multiplication makes it into a non-commutative non-associative algebra. We have been unable to find records of this very elementary mathematical object in the literature.