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de Broglie's Pilot-Wave Theory for the Klein–Gordon Equation and Its Space-Time Pathologies

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Abstract

We illustrate, using a simple model, that in the usual formulation the time-component of the Klein–Gordon current is not generally positive definite even if one restricts allowed solutions to those with positive frequencies. Since in de Broglie's theory of particle trajectories the particle follows the current this leads to difficulties of interpretation, with the appearance of trajectories which are closed loops in space-time and velocities not limited from above. We show that at least this pathology can be avoided if one adapts in a covariant form the formulation of relativistic point particle dynamics proposed by Gitman and Tyutin.

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Authors and Affiliations

  1. School of Earth and Environmental Science, University of Portsmouth, Burnaby Building, Portsmouth, PO1 3QL, U.K.

    George Horton & Chris Dewdney

  2. Fachbereich Physik, Universität Oldenburg, D26-111, Oldenburg, Germany

    Ulrike Ne'eman

Authors
  1. George Horton
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  2. Chris Dewdney
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  3. Ulrike Ne'eman
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Correspondence to Chris Dewdney.

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Horton, G., Dewdney, C. & Ne'eman, U. de Broglie's Pilot-Wave Theory for the Klein–Gordon Equation and Its Space-Time Pathologies. Foundations of Physics 32, 463–476 (2002). https://doi.org/10.1023/A:1014865430144

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  • DOI: https://doi.org/10.1023/A:1014865430144

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