Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme

Details Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme Approaching the Problem of Time with a Combined Semiclassical-Records-Histories Scheme

2012-04-13

arxiv.org/abs/1204.2868v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26 pages, 4 figures

Scientific paper

I approach the Problem of Time and other foundations of Quantum Cosmology using a combined histories, timeless and semiclassical approach. This approach is along the lines pursued by Halliwell. It involves the timeless probabilities for dynamical trajectories entering regions of configuration space, which are computed within the semiclassical regime. Moreover, the objects that Halliwell uses in this approach commute with the Hamiltonian constraint, H: [H, O] = 0. This approach has not hitherto been considered for models that also possess nontrivial linear constraints, Lin. This paper carries this out for some concrete relational particle models (RPM's). If also [Lin, O] = 0 - the Kuchar observables condition - the constructed objects are Dirac observables. Moreover, this paper shows that the problem of Kuchar observables is explicitly resolved for 1- and 2-d RPM's. Then as a first route to Halliwell's approach for nontrivial linear constraints that is also a construction of Dirac observables, I consider theories for which Kuchar observables are formally known, exemplifying this with the relational triangle. As a second route, I apply an indirect method that generalizes both group-averaging and Barbour's best matching. For conceptual clarity, my study involves the simpler case of Halliwell 2003 top-hat window functions. I leave the elsewise-improved case of smoothed-out window functions of Halliwell 2009 for a subsequent Paper II. Finally, I provide comments on Halliwell's approach and how well it fares as regards the various facets of the Problem of Time and as an implementation of QM propositions.

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