Time and Interpretations of Quantum Gravity

Abstract

In canonical quantization of gravity, the state functional does not seem to depend on time. This hampers the physical interpretation of quantum gravity. I critically examine ten major attempts to circumvent this problem and discuss their shortcomings.

Time Paradox in Quantum Gravity

“…Additionally, the Wheeler-DeWitt equation based on one particular choice of time variable, like Ω in this case, may give a different quantum theory than the same equation based on another choice of the time variable. This is what Kuchař called the multiple choice problem [5].…”

“…Kuchař [5] classified them in three basic approaches. It should be stressed that the boundaries of these interpretations are not clearly defined:…”

“…Its difficulty stands on the fact how to explain quantum dynamics in terms of constants of motion. The existing proposals are ambiguous, since the replacement of the classical global time parameter by an operator is ambiguous and its consequences lead to the multiple choice problem and to the problem of how to construct a Hilbert space [5].…”

“…This brings us to the Hilbert space problem for a relativistic particle. The absence of a privileged oneparticle Hilbert space structure is the source of ambiguities in constructing a unique quantum field theory on a dynamical background [5].…”

“…It is well known that, as a second order functional differential equation, the Wheeler-DeWitt equation presents familiar problems when one tries to turn the space of its solutions into a Hilbert space [5].…”