Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-07-18
Int.J.Theor.Phys.47:1512-1532,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
23 pages, Few changes and added references in v2
Scientific paper
10.1007/s10773-007-9592-y
We investigate the possibility of assigning consistent probabilities to sets of histories characterized by whether they enter a particular subspace of the Hilbert space of a closed system during a given time interval. In particular we investigate the case that this subspace is a region of the configuration space. This corresponds to a particular class of coarse grainings of spacetime regions. We consider the arrival time problem and the problem of time in reparametrization invariant theories as for example in canonical quantum gravity. Decoherence conditions and probabilities for those application are derived. The resulting decoherence condition does not depend on the explicit form of the restricted propagator that was problematic for generalizations such as application in quantum cosmology. Closely related is the problem of tunnelling time as well as the quantum Zeno effect. Some interpretational comments conclude, and we discuss the applicability of this formalism to deal with the arrival time problem.
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