Entwined paths in 3+1 dimensions and the Dirac Equation

Garnet Ord

This is an extension of an ontological model for the Dirac equation from 1+1 to 3+1 dimensions. The extension is simply to embed the original physical model in a three dimensional Euclidean space relative to an arbitrary orthogonal frame. The result is a form of the Dirac equation in which the Pauli matrices represent unit vectors in the background frame. This suggests that, in a sense, the Dirac equation is essentially one-dimensional on scales above the Compton wavelength, and that zitterbewegung models may be constructed using very simple geometries.