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Relational observables, reference frames, and conditional probabilities

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arxiv 2006.05526 v2 pith:ZAMTSHAG submitted 2020-06-09 gr-qc hep-thquant-ph

Leonardo Chataignier This is my paper · ORCID
classification gr-qchep-thquant-ph
keywords quantumobservablesrelationalconditionalconstructiondefinedformalismframes
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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 how the 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.

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Cited by 3 Pith papers

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  1. Dressed Subsystems in Classical Gravity

    physics.class-ph 2025-01 conditional novelty 7.0 of 10

    Internally dressed subsystems, whose boundaries are located by fields within the region, are exactly those whose observables close under Poisson brackets in generally covariant theories.

  2. Cosmological perturbations meet Wheeler DeWitt

    hep-th 2024-12 conditional novelty 6.0 of 10

    The semiclassical Wheeler-DeWitt wavefunction matches the perturbation-theory wavefunction of cosmology up to a specific phase and normalization, verified in exponential-potential and slow-roll mini-superspace models.

  3. Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy

    hep-th 2024-12 accept novelty 6.0 of 10

    Gravitational subregion entropy is observer-dependent: different quantum clocks produce different von Neumann algebras and different entropy functionals for the same global state.

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