Pilot-wave theory for a relativistic spin zero particle

摘要

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.