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On the Weak Measurement of Velocity in Bohmian Mechanics

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Abstract

In a recent article (Wiseman in New J. Phys. 9:165, 2007), Wiseman has proposed the use of so-called weak measurements for the determination of the velocity of a quantum particle at a given position, and has shown that according to quantum mechanics the result of such a procedure is the Bohmian velocity of the particle. Although Bohmian mechanics is empirically equivalent to variants based on velocity formulas different from the Bohmian one, and although it has been proven that the velocity in Bohmian mechanics is not measurable, we argue here for the somewhat paradoxical conclusion that Wiseman’s weak measurement procedure indeed constitutes a genuine measurement of velocity in Bohmian mechanics. We reconcile the apparent contradictions and elaborate on some of the different senses of measurement at play here.

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Authors and Affiliations

  1. Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstr. 39, 80333, Munich, Germany

    Detlef Dürr

  2. Departments of Mathematics, Physics and Philosophy, Hill Center, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, NJ, 08854-8019, USA

    Sheldon Goldstein

  3. Dipartimento di Fisica dell’Università di Genova and INFN sezione di Genova, Via Dodecaneso 33, 16146, Genova, Italy

    Nino Zanghì

Authors
  1. Detlef Dürr
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  2. Sheldon Goldstein
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  3. Nino Zanghì
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Correspondence to Sheldon Goldstein.

Additional information

This paper is dedicated to Jürg Fröhlich on the occasion of one of his birthdays.

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Dürr, D., Goldstein, S. & Zanghì, N. On the Weak Measurement of Velocity in Bohmian Mechanics. J Stat Phys 134, 1023–1032 (2009). https://doi.org/10.1007/s10955-008-9674-0

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  • DOI: https://doi.org/10.1007/s10955-008-9674-0

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