A stochastic model of Maxwell's equations in 1+1 dimensions

Abstract

We show that the random walk model due to Mark Kac which underlies the telegraph equations may be modified to produce Maxwell's field equations in 1+1 dimensions. This provides the field equations with a representation in terms of classical particles. It also establishes the Kac model as a strong conceptual link between the diffusion, telegraph, and Maxwell equations, and suggests that recent simulations of the Schrodinger and Dirac equations are analogous to Maxwell's equation in terms of interpretation.