  The description of spontaneous symmetry breaking that underlies the
connection between classically ordered objects in the thermodynamic limit and
their individual quantum mechanical building blocks is one of the cornerstones
of modern condensed matter theory and has found applications in many different
areas of physics. The theory of spontaneous symmetry breaking however, is
inherently an equilibrium theory, which does not address the dynamics of
quantum systems in the thermodynamic limit. Here, we will use the example of a
particular antiferromagnetic model system to show that the presence of a
so-called thin spectrum of collective excitations with vanishing energy -one of
the well-known characteristic properties shared by all symmetry-breaking
objects- can allow these objects to also spontaneously break time-translation
symmetry in the thermodynamic limit. As a result, that limit is found to be
able, not only to reduce quantum mechanical equilibrium averages to their
classical counterparts, but also to turn individual-state quantum dynamics into
classical physics. In the process, we find that the dynamical description of
spontaneous symmetry breaking can also be used to shed some light on the
possible origins of Born's rule. We conclude by describing an experiment on a
condensate of exciton polaritons which could potentially be used to
experimentally test the proposed mechanism.
