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The photon box thought experiment can be considered a forerunner of theEPR-experiment: by performing suitable measurements on the box it is possibleto ``prepare'' the photon, long after it has escaped, in either of twocomplementary states. Consistency requires that the corresponding boxmeasurements be complementary as well. At first sight it seems, however, thatthese measurements can be jointly performed with arbitrary precision: theypertain to different systems (the center of mass of the box and an internalclock, respectively). But this is deceptive. As we show by explicitcalculation, although the relevant quantities are simultaneously measurable,they develop non-vanishing commutators when calculated back to the time ofescape of the photon. This justifies Bohr's qualitative arguments in a preciseway; and it illustrates how the details of the dynamics conspire to guaranteethe requirements of complementarity. In addition, our calculations exhibit a``fine structure'' in the distribution of the uncertainties over thecomplementary quantities: depending on \textit{when} the box measurement isperformed, the resulting quantum description of the photon differs. This bringsus close to the argumentation of the later EPR thought experiment.

Complementarity in the Bohr-Einstein Photon Box