Generalized Minkowski spacetime with geometric algebra

TL;DR

This paper develops a geometric algebra framework for Minkowski spacetime that naturally incorporates spin, helicity, and electromagnetic phenomena, leading to new insights into time, magnetic monopoles, and the structure of physical laws.

Contribution

It introduces a generalized eight-dimensional Minkowski spacetime using Clifford algebra, deriving electromagnetic laws and properties purely from geometric principles without physical assumptions.

Findings

Incorporates spin and helicity directly into spacetime

Derives Maxwell's equations from geometric algebra

Provides a new explanation for the non-existence of magnetic monopoles

Abstract

We begin from the generalised eight-dimensional Minkowski spacetime structure, previously developed in Clifford geometric algebra $ C\ell(\Re^3) $. We propose that this is the correct algebraic representation for physical three-dimensional space. We find that this representation incorporates spin and helicity directly into spacetime, in a Lorentz invariant manner. From this foundation, based on purely algebraic arguments, we derive Minkowski spacetime, the properties of electromagnetic radiation and Maxwell's equations. These results being achieved all without physical arguments, showing that these physical laws are actually purely geometric effects. This approach also leads to a generalization of complex mass and proper time. Several insight about time are produced, including an arrow of time, which ultimately becomes a five-dimensional property. We also provide a new argument explaining the non-existence of magnetic monopoles. We suggest that the rotational freedoms, inherent in three-dimensional physical space are an important aspect of nature, not properly addressed in physics, as they are not incorporated within the spacetime background, as achieved in this paper.