TITLE:
Physics in Geometric Algebra Cl3,0
AUTHORS:
Jesús Sánchez
KEYWORDS:
Geometric Algebra, Eight Dimensions, Dirac Equation, Gravitation, E8 Theory
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.4,
April
24,
2025
ABSTRACT: In this paper, we will show how Geometric Algebra expands the three spatial dimensions into entities of 8 degrees of freedom. It is also explained that one of these degrees of freedom (the trivector) can be considered to be the time (so no ad-hoc extra dimension is necessary). The square of the trivector is negative, solving this way the issue of the negative signature of the time (not necessary any ad-hoc metric indicating this, it is a property of time that appears naturally). Also, we will show that we can try to prove this experimentally looking for the electromagnetic trivector, an entity that should exist according to GA. Also, some comments regarding the similarities with E8 theory are given. Mainly that E8 theory considers 8 dimensions, exactly the same, emerging naturally in this paper. But not only that, also some similarities regarding how gravity can be understood, and others are presented.