TIME AND PROBABILITY IN QUANTUM COSMOLOGY

A time function, an exactly conserved probability measure, and a time-evolution equation (related to the Wheeler-DeWitt equation) are proposed for quantum cosmology. The time-integral of the probability measure is the measure proposed by Hawking and Page. The evolution equation reduces to the Schrödinger equation, and probability measure to the Born measure, in the WKB approximation. The existence of this "Schrödinger-limit", which involves a cancellation of time-dependencies in the probability density between the WKB prefactor and integration measure, is a consequence of laplacian factor ordering in the Wheeler-DeWitt equation. © 1990.