Heisenberg's uncertainty principle

Heisenberg's uncertainty principle Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. Whilst conceptually distinct, these three kinds of uncertainty relations are shown to be closely related formally. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physics Reports Elsevier

Heisenberg's uncertainty principle

Physics Reports, Volume 452 (6) – Nov 1, 2007

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Publisher
Elsevier
Copyright
Copyright © 2007 Elsevier B.V.
ISSN
0370-1573
D.O.I.
10.1016/j.physrep.2007.05.006
Publisher site
See Article on Publisher Site

Abstract

Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. Whilst conceptually distinct, these three kinds of uncertainty relations are shown to be closely related formally. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle.

Journal

Physics ReportsElsevier

Published: Nov 1, 2007

References

  • Complementarity and uncertainty in Mach–Zehnder interferometry and beyond
    Busch, P.; Shilladay, C.R.
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    Folland, G.B.; Sitaram, A.
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    Busch, P.; Heinonen, T.; Lahti, P.
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    Busch, P.; Schonbek, T.; Schroeck, F.
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    Werner, R.F.
  • Positive operator valued measures covariant with respect to an irreducible representation
    Cassinelli, G.; De Vito, E.; Toigo, A.
  • Position and momentum observables on R and on R 3
    Carmeli, C.; Heinonen, T.; Toigo, A.
  • Mathematische Grundlagen der Quantenmechanik
    von Neumann, J.
  • Uncertainty principle for joint measurement of noncommuting variables
    Raymer, M.G.
  • Single-slit diffraction of neutrons
    Shull, C.
  • Zur Kritik der Ungenauigkeitsrelationen
    Popper, K.R.
  • Can quantum-mechanical description of physical reality be considered complete?
    Einstein, A.; Podolsky, B.; Rosen, N.

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