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| related topics |
| {field, particle, equation} |
| {let, theorem, proof} |
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Comment on ``Time-like flows of energy-momentum and particle
trajectories for the Klein-Gordon equation''
Roderich Tumulka
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0202140
- categories:
- quant-ph
- comments:
- 3 pages, no figures; in the 2nd version a minor mistake has been
corrected; conclusions remain unaltered
- doi:
- 10.1088/0305-4470/35/37/401
- arxiv_id:
- quant-ph/0202140
- journal_ref:
- J. Phys. A: Math. Gen. 35 (2002) 7961-7962
- created:
- 2002-02-25
- updated:
- 2002-04-30
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