  We study the reparametrization invariant system of a classical relativistic
particle moving in (5+1) dimensions, of which two internal ones are
compactified to form a torus. A discrete physical time is constructed based on
a quasi-local invariant observable. Due to ergodicity, it is simply related to
the proper time on average. The external motion in Minkowski space can then be
described as a unitary quantum mechanical evolution.
