Comment on ``Time-like flows of energy-momentum and particle trajectories for the Klein-Gordon equation''

Abstract

Horton, Dewdney, and Nesteruk [quant-ph/0103114] have proposed Bohm-type particle trajectories accompanying a Klein-Gordon wave function psi on Minkowski space. From two vector fields on space-time, W^+ and W^-, defined in terms of psi, they intend to construct a timelike vector field W, the integral curves of which are the possible trajectories, by the following rule: at every space-time point, take either W = W^+ or W = W^- depending on which is timelike. This procedure, however, is ill-defined as soon as both are timelike, or both spacelike. Indeed, they cannot both be timelike, but they can well both be spacelike, contrary to the central claim of [quant-ph/0103114]. We point out the gap in their proof, provide a counterexample, and argue that, even for a rather arbitrary wave function, the points where both W^+ and W^- are spacelike can form a set of positive measure.