dorsal/arxiv
View SchemaComment on ``Time-like flows of energy-momentum and particle trajectories for the Klein-Gordon equation''
| Authors | Roderich Tumulka |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0202140 |
| URL | https://arxiv.org/abs/quant-ph/0202140 |
| DOI | 10.1088/0305-4470/35/37/401 |
| Journal | J. Phys. A: Math. Gen. 35 (2002) 7961-7962 |
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.
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"abstract": "Horton, Dewdney, and Nesteruk [quant-ph/0103114] have proposed Bohm-type\nparticle trajectories accompanying a Klein-Gordon wave function psi on\nMinkowski space. From two vector fields on space-time, W^+ and W^-, defined in\nterms of psi, they intend to construct a timelike vector field W, the integral\ncurves of which are the possible trajectories, by the following rule: at every\nspace-time point, take either W = W^+ or W = W^- depending on which is\ntimelike.\n This procedure, however, is ill-defined as soon as both are timelike, or both\nspacelike. Indeed, they cannot both be timelike, but they can well both be\nspacelike, contrary to the central claim of [quant-ph/0103114]. We point out\nthe gap in their proof, provide a counterexample, and argue that, even for a\nrather arbitrary wave function, the points where both W^+ and W^- are spacelike\ncan form a set of positive measure.",
"arxiv_id": "quant-ph/0202140",
"authors": [
"Roderich Tumulka"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/35/37/401",
"journal_ref": "J. Phys. A: Math. Gen. 35 (2002) 7961-7962",
"title": "Comment on ``Time-like flows of energy-momentum and particle trajectories for the Klein-Gordon equation\u0027\u0027",
"url": "https://arxiv.org/abs/quant-ph/0202140"
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