Pilot-wave theory for a relativistic spin zero particle

Abstract

In the usual approach to the pilot-wave theory for a spin zero particle one starts with the Klein–Gordon equation, which is the relativistic generalization of the Schrodinger equation. This approach encounters several difficulties including superluminal motion and particle trajectories that move backwards in time. In this paper, I start with the relativistic classical Hamilton–Jacobi equation and introduce the quantum potential in a way that avoids the preceding difficulties. Particle trajectories are time-like or null and are future-pointing. The wave equation satisfied by the field is a nonlinear generalization of the Klein–Gordon equation.