  If time is described by a fundamental process rather than a coordinate, it
interacts with any physical system that evolves in time. The resulting dynamics
is shown here to be consistent provided the fundamental period of the time
system is sufficiently small. A strong upper bound T_C < 10^{-33}s of the
fundamental period of time, several orders of magnitude below any direct time
measurement, is obtained from bounds on dynamical variations of the period of a
system evolving in time.
