Maxwell’s Equations Directly from the Dynamics of Point Particles

Abstract

The Kac Stochastic Model of the Telegraph Equations may be modified to produce Maxwell’s equations in 1+1 Dimensions. This shows that Maxwells’s equations, while usually regarded as field equations governing electromagnetic waves, may also be interpreted as descriptions of ensembles of particles. Thus Maxwell’s equations may be derived in the same way as recent derivations of the Schroedinger and Dirac equations. All three equations have the same features that the’ wave’ aspect of solutions to the equations are produced by ensembles of classical particles, which themselves have no’ wave’ attributes. The model then provides a many-particle simulation of the electromagnetic field in 1+1 dimensions.