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Complementarity in the Bohr-Einstein Photon Box

Dieks, Dennis and Lam, Sander (2007) Complementarity in the Bohr-Einstein Photon Box. [Preprint]

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    Abstract

    The photon box thought experiment can be considered a forerunner of the EPR-experiment: by performing suitable measurements on the box it is possible to ``prepare'' the photon, long after it has escaped, in either of two complementary states. Consistency requires that the corresponding box measurements be complementary as well. At first sight it seems, however, that these measurements can be jointly performed with arbitrary precision: they pertain to different systems (the center of mass of the box and an internal clock, respectively). But this is deceptive. As we show by explicit calculation, although the relevant quantities are simultaneously measurable, they develop non-vanishing commutators when calculated back to the time of escape of the photon. This justifies Bohr's qualitative arguments in a precise way; and it illustrates how the details of the dynamics conspire to guarantee the requirements of complementarity. In addition, our calculations exhibit a ``fine structure'' in the distribution of the uncertainties over the complementary quantities: depending on when the box measurement is performed, the resulting quantum description of the photon differs. This brings us close to the argumentation of the later EPR thought experiment.


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    Item Type: Preprint
    Keywords: Quantum mechanics, complementarity, Bohr, Einstein, photon box, EPR
    Subjects: General Issues > Thought Experiments
    Specific Sciences > Physics > Quantum Mechanics
    Depositing User: Dennis Dieks
    Date Deposited: 22 May 2007
    Last Modified: 07 Oct 2010 11:15
    Item ID: 3349
    URI: http://philsci-archive.pitt.edu/id/eprint/3349

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