EHRENFESTS PRINCIPLE AND THE PROBLEM OF TIME IN QUANTUM-GRAVITY

We elaborate on a proposal made by Greensite and others to solve the p roblem of time in quantum gravity. The proposal states that a viable c oncept of time and a sensible inner product can be found from the dema nd for the Ehrenfest equations to hold in quantum gravity, We derive a nd discuss in detail exact consistency conditions from both Ehrenfest equations as well as from the semiclassical approximation. We also dis cuss consistency conditions arising from the full field theory. We fin d that only a very restricted class of solutions to the Wheeler-DeWitt equation fulfills all consistency conditions. We conclude that theref ore this proposal must either be abandoned as a means to solve the pro blem of time or, alternatively, be used as an additional boundary cond ition to select physical solutions from the Wheeler-DeWitt equation.