Chataignier, Leonardo ORCID: 0000-0001-6691-3695 (2021). Relational observables, reference frames, and conditional probabilities. Phys. Rev. D, 103 (2). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2470-0029

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Abstract

We discuss the construction of relational observables in time-reparametrization invariant quantum mechanics, and we argue that their physical interpretation can be understood in terms of conditional probabilities, which are defined from the solutions of the quantum constraint equation in a generalization of the Page-Wootters formalism. In this regard, we show how conditional expectation values of worldline tensor fields are related to quantum averages of suitably defined relational observables. We also comment on howthe dynamics of these observables can be related to a notion of quantum reference frames. After presenting the general formalism, we analyze a recollapsing cosmological model, for which we construct unitarily evolving quantum relational observables. We conclude with some remarks about the relevance of these results for the construction and interpretation of diffeomorphism-invariant operators in quantum gravity.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Chataignier, LeonardoUNSPECIFIEDorcid.org/0000-0001-6691-3695UNSPECIFIED
URN: urn:nbn:de:hbz:38-566594
DOI: 10.1103/PhysRevD.103.026013
Journal or Publication Title: Phys. Rev. D
Volume: 103
Number: 2
Date: 2021
Publisher: AMER PHYSICAL SOC
Place of Publication: COLLEGE PK
ISSN: 2470-0029
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
QUANTUM-MECHANICS; TIME; EQUATIONS; GRAVITYMultiple languages
Astronomy & Astrophysics; Physics, Particles & FieldsMultiple languages
URI: http://kups.ub.uni-koeln.de/id/eprint/56659

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