Abstract

Time arises in the theory of gravity through the semiclassical approximation of the gravitational part of the solution of the Wheeler-De Witt equation in the manner shown by Banks (SCAG). We generalize Banks' procedure by grafting a Born-Oppenheimer type approximation onto SCAG. This allows for the feedback of matter onto gravity, wherein the latter is driven by the (quantum) mean energy-momentum tensor of matter. The wave function is nonvanishing in classically forbidden configurations of gravity. In SCAG this is described by the evolution of matter in imaginary time. This is interpreted as an inverse temperature, and the norm of the matter wave function, no longer conserved for these gravitational configurations, is a partition function. A simple cosmological model is worked out to illustrate these ideas. In this model it is shown that the temperature of the matter which emerges into the classically permitted region is the inverse bounce time of the bounce executed by the system in the forbidden region (behind the horizon).Time present and time past are both perhaps present in time future. And time future contained in time past. If all time is eternally present All time is unredeemable.—T. S. Eliot, “Burnt Norton,”Four Quartets, 1943.