  The quantization of time-reparametrization invariant systems such as general
relativity is plagued by an ambiguity relating to the role of time in the
theory. If one parametrizes observables by the (unobservable) time, and then
relies on the existence of an approximate "clock" degree of freedom to give
physical meaning to the observables, one finds multiple quantum states that
yield the same predictions yet interfere with each other.
