Conditional probabilities in Ponzano-Regge minisuperspace
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We examine the Hartle-Hawking no-boundary initial state for the Ponzano-Regge formulation of gravity in three dimensions. We consider the behavior of conditional probabilities and expectation values for geometrical quantities in this initial state for a simple minisuperspace model consisting of a two-parameter set of anisotropic geometries on a $2$-sphere boundary. We find dependence on the cutoff used in the construction of Ponzano-Regge amplitudes for expectation values of edge lengths. However, these expectation values are cutoff independent when computed in certain, but not all, conditional probability distributions. Conditions that yield cutoff independent expectation values are those that constrain the boundary geometry to a finite range of edge lengths. We argue that such conditions have a correspondence to fixing a range of local time, as classically associated with the area of a surface for spatially closed cosmologies. Thus these results may hint at how classical spacetime emerges from quantum amplitudes.
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The Ponzano-Regge model has been used to study conditional probabilities and the emergence of quasiclassical behavior, but the cut-off dependence of these results makes their physical significance unclear.
“The model has been used to study conditional probabilities and the emergence of quasiclassical behavior in quantum gravity [223], but the cut-off dependence of these results makes their physical significance unclear.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [223]
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Cites
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Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
- Authors
- Petryk, R., & Schleich, K.
- Affiliations
- University of British Columbia (CA)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2003-01-21
- Volume
- 67
- Issue
- 2
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W1964141544
- Cited by
- 4
- References
- 2
- FWCI
- 0.40
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Natural Sciences and Engineering Research Council of Canada
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- Ponzano-Regge model, minisuperspace, conditional probability, three-dimensional quantum gravity, anisotropic geometry, cutoff dependence, emergent spacetime, quantum gravity
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