A Multivector Description of Spacetime

Jamees Chappell -- U of Adelaide

A central aspect of the natural world is the presence of just three degrees of translational freedom. This is confirmed by the presence of exactly five regular solids, which only occurs in three dimensions. Three spatial dimensions also leads to the expectation of inverse square force laws, which for gravity and electromagnetism, has indeed been experimentally verified to very high precision. These preliminary observations regarding the nature of physical space provides a general conceptual structure within which to describe physical processes. The formalism of Clifford’s geometric algebra (GA) of three dimensions Cl(R3) is therefore natural to adopt as a mathematical framework to describe this space. The appropriateness of this choice of Cl(R3) is confirmed by the fact that Minkowski spacetime is found to be embedded as a four-dimensional subspace, within the eight-dimensional space of Cl(R3) [1, 2]. This shows that Minkoswki spacetime is a natural consequence of three spatial dimensions described by Cl(R3) [1].