The Quantum Connection.

The time problem of quantum cosmology is solved by noting that the probability of a geometro-dynamic system being in a given region of superspace is proportional to the amount of time that it spends there, and that this relates the cosmic time t to the wave-function Ψ of the universe. The singularity problem of classical cosmology is solved by showing how the Wheeler-DeWitt equation converts classical singularities to virtual states in which the energy density does hot diverge. The covariance problem of canonical quantum gravity is solved by a Hilbert space affine connection (the quantum connection) in terms of which the quantum-mechanical derivative is a covariant derivative, and the Schrödinger equation is the condition that the state vector be covariant constant. [ABSTRACT FROM AUTHOR]