The term Heisenberg uncertainty relation is a name for not one but three distinct trade-off relations which are all formulated in a more or less intuitive and vague way in Heisenberg's seminal paper of 1927 [1]. These relations are expressions and quantifications of three fundamental limitations of the operational possibilities of preparing and measuring quantum mechanical systems which are stated here informally with reference to position and momentum as a paradigmatic example of canonically conjugate pairs of quantities:
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(A)
It is impossible to prepare states in which position and momentum are simultaneously arbitrarily well localized. In every state, the probability distributions of these â–º observables have widths that obey an uncertainty relation.
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(B)
It is impossible to make joint measurements of position and momentum. But it is possible to make approximate joint measurements of these observables, with inaccuracies that obey an uncertainty relation.
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(C)
It is impossible to measure position without disturbing momentum, and vice versa. The inaccuracy of the position measurement and the disturbance of the momentum distribution obey an uncertainty relation.
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Primary Literature
Heisenberg, W.: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik 43, 172–198 (1927).
Shull, C.: Single-slit diffraction of neutrons, Physical Review 179, 752–754 (1969).
Kaiser, H., S.A. Werner, E.A. George: Direct measurement of the longitudinal coherence length of a thermal neutron beam. Physical Review Letters 50, 560–563 (1983).
Klein, A.G., G.I. Opat, W.A. Hamilton: Longitudinal coherence in neutron interferometry. Physical Review Letters 50, 563–565 (1983).
Nairz, O., M. Arndt, A. Zeilinger: Experimental verification of the Heisenberg uncertainty principle for fullerene molecules. Physical Review A 65, 032109/1-4 (2002).
Scully, M.O., B.G. Englert, H. Walther: Quantum optical tests of complementarity. Nature 351, 111–116 (1991).
Storey, E.P., S.M. Tan, M.J. Collet, D.F. Walls: Path detection and the uncertainty principle. Nature 367, 626–628 (1994). Complementarity and Uncertainty. Nature 375, 368 (1995).
Dürr, S., T. Nonn, G. Rempe: Origin of quantum-mechanical complementarity probed by ‘which-way’ experiment in an atom interferometer. Nature 395, 33–37 (1998). Dürr, S., G. Rempe: Can wave-particle duality be based on the uncertainty relation? American Journal of Physics 68, 1021–1024 (2000).
Secondary Literature
Jammer, M.: The Philosophy of Quantum Mechanics (Wiley, New York, 1974).
Busch, P., T. Heinonen, P.J. Lahti: Heisenberg’s uncertainty principle. arXiv:quant-ph/0609185.
Falkenburg, B.: Particle Metaphysics (Springer, Berlin, 2007) 296–311.
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Busch, P., Falkenburg, B. (2009). Heisenberg Uncertainty Relation (Indeterminacy Relations). In: Greenberger, D., Hentschel, K., Weinert, F. (eds) Compendium of Quantum Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70626-7_86
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