The null subspace of G(4,1) as source of the main physical theories

Abstract

It is the author's belief that a perfect theory will eventually be formulated, where geometry and physics become indistinguishable, so that the complete understanding of space properties, together with proper assignments between geometric and physical entities, will provide all necessary predictions. The author intends to show that GR and Quantum Mechanics (QM) can be seen as originating from properties of the null subspace of 5-dimensional space with signature (-++++), together with its associated geometric algebra G(4,1). Besides generating GR and QM, the same space generates also 4-dimensional Euclidean space where dynamics can be formulated and is quite often equivalent to the relativistic counterpart. Euclidean relativistic dynamics resembles Fermat's principle extended to 4 dimensions and is thus designated as 4-Dimensional Optics (4DO). In this presentation the author uses G(4,1) with imposition of the null displacement length condition and derives the method to transpose between the metrics of GR and 4DO; this transition is proven viable for stationary metrics. It is hopeless to apply Einstein type equations in 4DO, for the simple reason that a null Ricci tensor always leads to a metric diverging to infinity. The author uses geometric arguments to establish alternative equations which are solved for the case of a stationary mass and produce a solution equivalent to Schwarzschild's metric in terms of PPN parameters. As a further development, the author analyses the case of a monogenic function in G(4,1). The monogenic condition produces an equation that can be conveniently converted into Dirac's, with the added advantage that it has built in standard model gauge group symmetry.