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 \textit{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