Choice of the best geometry to explain physics

TL;DR

This paper explores how choosing the right geometric framework, specifically 5D spacetime with monogenic functions, can unify and simplify the fundamental equations of physics like relativity and quantum mechanics.

Contribution

It demonstrates that monogenic functions in 5D spacetime can generate key physics equations, offering a new unifying geometric perspective.

Findings

Monogenic functions generate special relativity line element.

They derive the Dirac equation of quantum mechanics.

Provides a new geometric approach to fundamental physics.

Abstract

Choosing the appropriate geometry in which to express the equations of fundamental physics can have a determinant effect on the simplicity of those equations and on the way they are perceived. The point of departure in this paper is the geometry of 5-dimensional spacetime, where monogenic functions are studied. Monogenic functions verify a very simple first order differential equation and the paper demonstrates how they generate the line interval of special relativity, as well as the Dirac equation of quantum mechanics. Monogenic functions act as a unifying principle between those two areas of physics, which is in itself very significant for the perception one has of them. Another consequence is the possibility of studying the same phenomena in Euclidean 4-dimensional space, providing a different point of view to physics, from which one has an unusual and enriching perspective.