Time, measurement and information loss in quantum cosmology

A framework for a physical interpretation of quantum cosmology appropriate to a nonperturbative hamiltonian formulation is proposed. It is based on the use of matter fields to define a physical reference frame. In the case of the loop representation it is convenient to use a spatial reference frame that picks out the faces of a fixed simplicial complex and a clock built with a free scalar field. Using these fields a procedure is proposed for constructing physical states and operators in which the problem of constructing physical operators reduces to that of integrating ordinary differential equations within the algebra of spatially diffeomorphism invariant operators. One consequence is that we may conclude that the spectra of operators that measure the areas of physical surfaces are discrete independently of the matter couplings or dynamics of the gravitational field. Using the physical observables and the physical inner product, it becomes possible to describe singularities, black holes and loss of information in a nonperturbative formulation of quantum gravity, without making reference to a background metric. While only a dynamical calculation can answer the question of whether quantum effects eliminate singularities, it is conjectured that, if they do not, loss of information is a likely result because the physical operator algebra that corresponds to measurements made at late times must be incomplete. Finally, I show that it is possible to apply Bohr’s original operational interpretation of quantum mechanics to quantum cosmology, so that one is free to use either a Copenhagen interpretation or a corresponding relative state interpretation in a canonical formulation of quantum cosmology.