Implications of Lorentz covariance for the guidance equation in two-slit quantum interference

Peter Holland and Chris Philippidis
Phys. Rev. A 67, 062105 – Published 20 June 2003
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Abstract

It is known that Lorentz covariance fixes uniquely the current and the associated guidance law in the trajectory interpretation of quantum mechanics for spin-12 particles. In the nonrelativistic domain this implies a guidance law for the electron which differs by an additional spin-dependent term from that originally proposed by de Broglie and Bohm. In this paper, we explore some of the implications of the modified guidance law. We bring out a property of mutual dependence in the particle coordinates that arises in product states, and show that the quantum potential has scalar and vector components, which implies the particle is subject to a Lorentz-like force. The conditions for the classical limit and the limit of negligible spin are given, and the empirical sufficiency of the model is demonstrated. We then present a series of calculations of the trajectories based on two-dimensional Gaussian wave packets which illustrate how the additional spin-dependent term plays a significant role in structuring both the individual trajectories and the ensemble. The single packet corresponds to quantum inertial motion. The distinct features encountered when the wave function is a product or a superposition are explored, and the trajectories that model the two-slit experiment are given. The latter paths exhibit several new characteristics compared with the original de Broglie–Bohm ones, such as crossing of the axis of symmetry.

  • Received 3 December 2002

DOI:https://doi.org/10.1103/PhysRevA.67.062105

©2003 American Physical Society

Authors & Affiliations

Peter Holland*

  • Green College, University of Oxford, Woodstock Road, Oxford OX2 6HG, England

Chris Philippidis

  • Science Studies Centre, University of Bath, Bath BA2 7AY, England

  • *Email address: peter.holland@green.ox.ac.uk
  • Email address: c.philippidis@bath.ac.uk

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Vol. 67, Iss. 6 — June 2003

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