Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-11-07
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
A number correspondents indicated it was not obvious from its abstract page that this article is a large Review. So I declare
Scientific paper
Most readers' main interest in this article will be its reviews of the problem of time (POT) in quantum gravity (QG) in Secs 11, 16. Namely, that `time' in GR and in ordinary QM are mutually incompatible notions, which is problematic in trying to put these 2 theories together to form a theory of QG. I also establish relational particle models (RPM's) as useful for the study of the POT and of quantum cosmology (QC). I also unlock RPMs' configuration spaces, classical dynamics and QM in simple concrete examples. I use these to further our understanding of the histories, records, semiclassical, naive Schrodinger interpretation and hidden time strategies toward resolving the POT, alongside considering Halliwell's combination of the first 3. My relational whole-universe models are comparable to minisuperspace in amount of resemblance to full GR, but with a number of different resemblances including various midisuperspace-like ones which render RPM's appropriate as POT models. One point of view is that the best one can currently do as regards QG is to compare multiple such toy models, each of which allows for a different range of calculations that are too difficult to substantially complete for GR. This article is then the RPM counterpart of Ryan's book on minisuperspace models or Carlip's on 2+1 GR, as regards each of these arenas being rendered open to detailed study. Other results covered include suitable variational techniques for relational physics, a novel critique of operator-ordering in QC, reduced versus Dirac quantization, and qualitative issues concerning structure formation, uniform states and closed-universe effects in QC. Finally, this article contributes to the debate of what is relationalism and background independence, which has remained of interest in theoretical physics from Newton versus Leibniz through to foundational issues in today's leading candidates for QG.
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