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arXiv · 1101.4916

On the Semiclassical Approach to Quantum Cosmology

Edward Anderson
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Abstract

The emergent semiclassical time approach to resolving the problem of time in quantum gravity involves heavy slow degrees of freedom providing via an approximately Hamilton-Jacobi equation an approximate timestandard with respect to which the quantum mechanics of light fast degrees of freedom can run. More concretely, this approach involves Born-Oppenheimer and WKB ansatze and some accompanying approximations. In this paper, I investigate this approach for concrete scaled relational particle mechanics models, i.e. models featuring only relative separations, relative angles and relative times. I consider the heavy-light interaction term in the light quantum equation - necessary for the semiclassical approach to work, firstly as an emergent-time dependent perturbation of the emergent-time-dependent Schrodinger equation for the light subsystem. Secondly, I consider a scheme in which the backreaction is small but non-negligible, so that the l-subsystem also affects the form of the emergent time. I also suggest that the many terms involving expectation values of the light wavefunctions in both the (unapproximated) heavy and light equations might require treatment in parallel to the Hartree--Fock self-consistent approach rather than merely being discarded; for the moment this paper provides a counterexample to such terms being smaller than their unaveraged counterparts. Investigation of these ideas and methods will give us a more robust understanding of the suggested quantum-cosmological origin of microwave background inhomogeneities and galaxies.

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Edward Anderson. 2011-01-25. On the Semiclassical Approach to Quantum Cosmology. https://doi.org/10.1088/0264-9381%2F28%2F18%2F185008

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