Symmetry and Evolution in Quantum Gravity

Abstract

We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory makes predictions that are distinct from Wheeler-DeWitt cosmology. Furthermore, the local symmetry principle - and corresponding observables - of the theory have a direct interpretation in terms of a conventional gauge theory, where the gauge symmetry group is that of spatial conformal diffeomorphisms (that preserve the spatial volume of the Universe). The global evolution is in terms of an arbitrary parameter that serves only as an unobservable label for successive states of the Universe. Our proposal follows unambiguously from a suggestion of York whereby the independently specifiable initial data in the action principle of General Relativity is given by a conformal geometry and the spatial average of the York time on the spacelike hypersurfaces that bound the variation. Remarkably, such a variational principle uniquely selects the form of the constraints of the theory so that we can establish a precise notion of both symmetry and evolution in quantum gravity.

29 pages. 1 table (version accepted to Foundations of Physics)

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Cited by in corpus (11)

• Time Remains
• Bouncing Unitary Cosmology I: Mini-Superspace General Solution
• Superpositions of the cosmological constant allow for singularity resolution and unitary evolution in quantum cosmology
• Schrodinger Evolution for the Universe: Reparametrization
• Bouncing Unitary Cosmology II: Mini-Superspace Phenomenology
• Reassessing the problem of time of quantum gravity
• Big Bang Singularity Resolution In Quantum Cosmology
• Lagrangian Formulation for Particle Interpretations of Quantum Mechanics: Single-Particle Case
• Regarding the `Hole Argument' and the `Problem of Time'
• $\Psi$-Epistemic Quantum Cosmology?
• Gauge and Metaphysics of Spacetime