arXiv:quant-ph/0202140 · Journal of Physics A Mathematical and General

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

Roderich Tumulka

Published Sep 5, 2002• 2 citations

Abstract

Horton et al ( 2000 J. Phys. A: Math. Gen. 33 7337 ) have proposed Bohm-type particle trajectories accompanying a Klein–Gordon wavefunction ψ on Minkowski space. From two vector fields on space–time, W + and W − , defined in terms of ψ, they intend to construct a time-like 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 time-like. This procedure, however, is ill-defined as soon as both are time-like, or both space-like. Indeed, they cannot both be time-like, but they can well both be space-like, contrary to the central claim of Horton et al . We point out the gap in their proof, we provide a counter example, and we argue that, even for a rather arbitrary wavefunction, the points where both W + and W − are space-like can form a set of positive measure.

DOI: 10.1088/0305-4470/35/37/401

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