Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1996-05-09
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
86 pages, LaTeX (no figures); in this replaced version, some issues in the argumentation are formulated more accurate, referen
Scientific paper
We formulate a ''minimal'' interpretational scheme for fairly general (minisuperspace) quantum cosmological models. Admitting as few exact mathematical structure as is reasonably possible at the fundamental level, we apply approximate WKB-techniques locally in minisuperspace in order to make contact with the realm of predictions, and propose how to deal with the problems of mode decomposition and almost-classicality without introducing further principles. In order to emphasize the general nature of approximate local quantum mechanical structures, we modify the standard WKB-expansion method so as to rely on exact congruences of classical paths, rather than a division of variables into classical and quantum. The only exact mathematical structures our interpretation needs are the space of solutions of the Wheeler-DeWitt equation and the Klein-Gordon type indefinite scalar product. The latter boils down to plus or minus the ordinary quantum mechanical scalar product in the local quantum structures. According to our approach all further structures, in particular the concepts encountered in conventional physics, such as observables, time and unitarity, are approximate. Our interpretation coincides to some extent with the standard WKB-oriented view, but the way in which the conventional concepts emerge, and the accuracy at which they are defined at all, are more transparent. A simpler book-keeping of normalization issues is automatically achieved. Applying our scheme to the Hawking model, we find hints that the no-boundary wave function predicts a cosmic catastrophe with some non-zero probability.
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