Gyromagnetics of the Electron Clock

The Dirac equation is presented as a complete theory of the electron as a gyromagnetic particle clock with precise physical interpretation for all degrees of freedom. The electron is modeled as a point charge with toroidal zitter and variable zilch. That is to say, the charge oscillates at the speed of light on a torus centered on a circular orbit around its center of mass $\mathbf {z}=\mathbf {z}(t)$ , with an axis at a variable angle $\beta =\beta (\mathbf {z}(t))$ with respect to its spin vector $\mathbf {s}=\mathbf {s}(t)$ . The Dirac wave function $\Psi =\Psi (ct+\mathbf {x})$ has a unique factorization $\Psi =(\rho e^{i\beta })^{\scriptstyle \frac {1}{2}}U$ , where $U=U(ct+\mathbf {x})$ is a spatial rotor with magnetic degrees of freedom, and the quantity $\Psi \widetilde {\Psi }=\rho e^{i\beta }$ specifies an embedding of electron paths in the vacuum, where the zilch function $\beta =\beta (ct+\mathbf {x}-\mathbf {z}(t))$ is a measure of electron energy density. It culminates in a new synthesis of Dirac electron theory with Maxwell’s electrodynamics by identifying zilch as a common factor that binds them together.