  In the Schroedinger equation, time plays a special role as an external
parameter. We show that in an enlarged system where the time variable denotes
an additional degree of freedom, solutions of the Schroedinger equation give
rise to weights on the enlarged algebra of observables. States in the
associated GNS representation correspond to states on the original algebra
composed with a completely positive unit preserving map. Application of this
map to the functions of the time operator on the large system delivers the
positive operator valued maps which were previously proposed by two of us as
time observables. As an example we discuss the application of this formalism to
the Wheeler-DeWitt theory of a scalar field on a Robertson-Walker spacetime.
