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The validity of the principle of equivalence in the WKB limit of quantum mechanics

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Foundations of Physics Letters

Abstract

In the context of the causal interpretation of quantum mechanics one can formulate the equation of motion of a quantal particle in the presence of a gravitational field. It is pointed out that, in the WKB limit of high quantum numbers, states exist for which one component of classical equivalence (that all bodies fall at an equal rate independent of their mass) is not recovered, due to quantum effects mediated by the quantum potential.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique CNRS/URA 769, Université P. et M. Curie Institut Henri Poincaré, 11, rue P. et M. Curie, 75005, Paris, France

    P. R. Holland

Authors
  1. P. R. Holland
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Additional information

1. The classical limit of the uncertainty relations is obtained when part of the quantum stress tensor of the Ψ field may be neglected - it is not necessary or necessarily consistent to let h → 0 here either [3].

2. In the relativistic case, one can nevertheless still “geometrize” quantum mechanics in the presence of gravity by introducing metrics that depend on particle characteristics (e.g. Finsler metric). The equation of motion is then a geodesic in this generalized space [8,9].

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Holland, P.R. The validity of the principle of equivalence in the WKB limit of quantum mechanics. Found Phys Lett 2, 471–485 (1989). https://doi.org/10.1007/BF00689814

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  • DOI: https://doi.org/10.1007/BF00689814

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