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Volume 15: Pages 418-421, 2002
The Quantum Connection
Kenneth J. Epstein
6400 N. Sheridan, #2604, Chicago, Illinois 60626 U.S.A.
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 not 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.
Keywords: quantum censorship, temporal censorship, virtual singularity, Koszul connection
Received: June 28, 2002; Published online: December 15, 2008