Measurement of time of arrival in quantum mechanics

Y. Aharonov, J. Oppenheim, S. Popescu, B. Reznik, and W. G. Unruh
Phys. Rev. A 57, 4130 – Published 1 June 1998
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Abstract

It is argued that the time of arrival cannot be precisely defined and measured in quantum mechanics. By constructing explicit toy models of a measurement, we show that for a free particle it cannot be measured more accurately then ΔtA1/Ek, where Ek is the initial kinetic energy of the particle. With a better accuracy, particles reflect off the measuring device, and the resulting probability distribution becomes distorted. It is shown that a time-of-arrival operator cannot exist, and that approximate time-of-arrival operators do not correspond to the measurements considered here.

  • Received 15 September 1997

DOI:https://doi.org/10.1103/PhysRevA.57.4130

©1998 American Physical Society

Authors & Affiliations

Y. Aharonov1, J. Oppenheim2,*, S. Popescu3,†, B. Reznik4,‡, and W. G. Unruh2,§

  • 1School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, IsraelDepartment of Physics, University of South Carolina, Columbia, South Carolina 29208
  • 2Department of Physics, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada V6T 1Z1
  • 3Isaac Newton Institute, Cambridge University, 20 Clarkson Road, Cambridge CB3 OEH, United KingdomBRIMS, Hewlett-Packard Laboratories, Bristol BS12 6QZ, United Kingdom
  • 4Theoretical Division, T-6, MS B288, Los Alamos National Laboratory, Los Alamos, New Mexico 87545

  • *Electronic address: jono@physics.ubc.ca
  • Electronic address: sp230@newton.cam.ac.uk
  • Electronic address: reznik@t6-serv.lanl.gov
  • §Electronic address: unruh@physics.ubc.ca

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Vol. 57, Iss. 6 — June 1998

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