Classical electrodynamics from the motion of a relativistic fluid

Abstract

We show that there exists a choice of gauge in which the electromagnetic 4-potential may be written as the difference of two 4-velocity vector fields describing the motion of a two-component space-filling relativistic fluid. Maxwell's equations are satisfied immediately, while the Lorentz force equation follows from the interactions of sources and sinks. The usual electromagnetic quantities then admit new interpretations as functions of the local 4-velocities. Electromagnetic waves are found to be described by oscillations of the underlying medium which can therefore be identified with the `luminiferous aether'. The formulation of electrodynamics in terms of 4-velocities is more general than that of the standard 4-potential in that it also allows for a classical description of a large class of vacuum energy configurations. Treated as a self-gravitating fluid, the model can be explicitly identified with Nelson's stochastic formulation of quantum mechanics, making it a promising candidate as the classical field theory unifying gravitation, electromagnetism and quantum theory which Einstein had sought.