Symmetry and Evolution in Quantum Gravity

Foundations of Physics 44 (3):305-348 (2014)

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 contains an evolution equation distinct from standard 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
Keywords Gauge symmetry  Quantum gravity  Problem of time  Canonical quantization  Variational principles  quantum cosmology
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s10701-014-9789-x
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 46,179
Through your library

References found in this work BETA

Change in Hamiltonian General Relativity From the Lack of a Time-Like Killing Vector Field.J. Brian Pitts - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 47:68-89.
Quantum Gravity.Claus Kiefer - 2004 - Oxford University Press UK.
The Role of Time in Relational Quantum Theories.Sean Gryb & Karim Thébault - 2012 - Foundations of Physics 42 (9):1210-1238.
Mach's Principle and the Structure of Dynamical Theories.Julian B. Barbour & Bruno Bertotti - 1982 - Proceedings of the Royal Society, London:295--306.
Scale-Invariant Gravity: Particle Dynamics.Julian B. Barbour - 2003 - Classical and Quantum Gravity 20:1543--70.

View all 11 references / Add more references

Citations of this work BETA

Time Remains.Sean Gryb & Karim P. Y. Thébault - 2016 - British Journal for the Philosophy of Science 67 (3):663-705.

View all 6 citations / Add more citations

Similar books and articles

Frequently Asked Questions About Shape Dynamics.Henrique Gomes & Tim Koslowski - 2013 - Foundations of Physics 43 (12):1428-1458.
Gauge Symmetry Breaking in Gauge Theories—in Search of Clarification.Simon Friederich - 2013 - European Journal for Philosophy of Science 3 (2):157-182.
Making the Case for Conformal Gravity.Philip D. Mannheim - 2012 - Foundations of Physics 42 (3):388-420.
Quantum Gravity on a Quantum Computer?Achim Kempf - 2014 - Foundations of Physics 44 (5):472-482.
Symmetry and Gauge Freedom.Gordon Belot - 2002 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (2):189-225.
Minimal Length in Quantum Gravity and the Fate of Lorentz Invariance.Amit Hagar - 2009 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 40 (3):259-267.
Quantum Concepts in Space and Time.Roger Penrose & C. J. Isham (eds.) - 1986 - New York ;Oxford University Press.

Analytics

Added to PP index
2013-11-10

Total views
26 ( #355,736 of 2,285,616 )

Recent downloads (6 months)
3 ( #419,091 of 2,285,616 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature