Statistical basis for physical laws; non-relativistic theory

Abstract

We extend the constructions of previous papers, showing the equivalence of quantum mechanics and a classical probability formalism with constraints assuring differentiable probability densities without contradictions, to show that these constructions also yield Maxwell's equations and the Lorentz force. These constructions have already yielded Schroedinger's equation for a charged particle in an electromagnetic field, but here it is shown that this statistical construction provides the basis for gauge conditions and defines a specific gauge for this non-relativistic formalism. These constructions also provide new insight into the relationship of Schroedinger quantum mechanics and a classical diffusion process.