Generalized Minkowski spacetime with geometric algebra

• Published in: arXiv.org 2024-09
• Main Authors: Chappell, James M, Berkahn, David L, Abbott, Derek
• Format: Article
• Language: English
• Subjects: Mathematical analysis; Relativism; Relativistic effects; Relativity; Spacetime
• ISSN: 2331-8422

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.