  The "problem of time" in canonical quantum gravity refers to the difficulties
involved in defining a Hilbert space structure on states -- and local
observables on this Hilbert space -- for a theory in which the spacetime metric
is treated as a quantum field, so no classical metrical or causal structure is
present on spacetime. We describe an approach -- much in the spirit of ideas
proposed by Misner, Kuchar and others -- to defining states and local
observables in quantum gravity which exploits the analogy between the
Hamiltonian formulation of general relativity and that of a relativistic
particle. In the case ofminisuperspace models, a concrete theory is obtained
which appears to be mathematically and physically viable, although it contains
some radical features with regard to the presence of an "arrow of time". The
viability of this approach in the case ofinfinitely many degrees of freedom
rests on a number of fairlywell defined issues, which, however, remain
unresolved. As a byproduct of our analysis, the theory of a relativistic
particle in curved spacetime is developed.
