Gravitation and cosmology with York time

Abstract

[Shortened abstract:] In this thesis we investigate a solution to the `problem of time' in canonical quantum gravity by splitting spacetime into surfaces of constant mean curvature parameterised by York time. We argue that there are reasons to consider York time a viable candidate for a physically meaningful notion of time. We investigate a number York-time Hamiltonian-reduced cosmological models and explore some technical aspects, such as the non-canonical Poisson structure. We develop York-time Hamiltonian-reduced cosmological perturbation theory by solving the Hamiltonian constraint perturbatively around a homogeneous background for the physical (non-vanishing) Hamiltonian that is the momentum conjugate to the York time parameter. We proceed to canonically quantise the cosmological models and the perturbation theory and discuss a number of conceptual and technical points, such as volume eigenfunctions and the absence of a momentum representation due to the non-standard commutator structure. We propose an alternative, wavefunction-free method of quantisation based on an ensemble of trajectories and a dynamical configuration-space geometry and discuss its application to gravity. We conclude by placing the York-time theories explored in this thesis in the wider context of a search for a satisfactory theory of quantum gravity.

PhD thesis, 195 pages, 6 figures, 1 table; heavily draws on text overlap with: arXiv:1406.2036, arXiv:1407.4005, arXiv:1507.01556, arXiv:1507.08975, arXiv:1511.03320, arXiv:1606.01801

References in corpus (16)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School)
• Quantum Theory and Determinism
• Constraints and gauge transformations: Dirac's theorem is not always valid
• The Quantum Measurement Problem: State of Play
• Quantum Mechanics as Classical Physics
• De Broglie-Bohm Guidance Equations for Arbitrary Hamiltonians
• Shape Dynamics. An Introduction
• An answer to the Wallstrom objection against Nelsonian stochastics
• What About Quantum Theory? Bayes and the Born Interpretation
• Nonlocality, No-Signalling and Bell's Theorem investigated by Weyl's Conformal Differential Geometry
• Solving the Quantum Nonlocality Enigma by Weyl's Conformal Geometrodynamics
• Remarks on geometry and the quantum potential
• Ab initio derivation of the quantum Dirac equation by conformal differential geometry: the "Affine Quantum Mechanics'"
• Hamilton-Jacobi Many-Worlds Theory and the Heisenberg Uncertainty Principle
• Quantum Computing in the de Broglie-Bohm Pilot-Wave Picture