Four-space formulation of Dirac's equation

Abstract

Dirac's equation is reviewed and found to be based on nonrelativistic ideas of probability. A 4-space formulation is proposed that is completely Lorentzinvariant, using probability distributions in space-time with the particle's proper time as a parameter for the evolution of the wave function. This leads to a new wave equation which implies that the proper mass of a particle is an observable, and is sharp only in stationary states. The model has a built-in arrow of time, which is associated with a restriction to positive-energy solutions. The usual solution for a Coulomb field is retained, though it now implies a slightly different charge distribution. The conventional nonstationary solutions become invalid. The new formulation appears to offer a resolution of difficulties that have been associated with Dirac's equation. It also predicts the occurrence of virtual pairs at a level that may be experimentally testable, and suggests a mechanism for self-cancellation of the vacuum energy.