Relational observables, reference frames, and conditional probabilities

Chataignier, Leonardo

doi:10.1103/physrevd.103.026013

Cited by 20 publications

(28 citation statements)

References 47 publications

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“…While completing this manuscript, we became aware of Chataignier [38], which independently extends some results of Höhn et al [7] on the conditional probability interpretation of relational observables and their equivalence with the Page-Wootters formalism into a more general setting. However, a different formalism [37] is used in Chataignier [38], which does not employ covariant clock POVMs and therefore the two works complement one another.…”

Section: Introductionsupporting

confidence: 53%

“…Our proposal is thus to turn the multiple choice problem into a feature by having a multitude of quantum time choices at our disposal, which we are able to connect through quantum temporal frame transformations. This is in line with developing a genuine quantum implementation of general covariance [7,30,31,38,[70][71][72][73][74]. This proposal is part of current efforts to develop a general framework of quantum reference frame transformations (and study their physical consequences [75][76][77][78][79][80][81][82][83][84][85]), and should be contrasted with other attempts at resolving the multiple choice problem by identifying a preferred choice of clock [53] (see [7] for further discussion of this proposal).…”

Section: Introductionsupporting

confidence: 53%

“…This is advantageous for quantum gravity, where classical spacetime coordinates are a priori absent. A quantum version of general covariance should be formulated in terms of dynamical reference degrees of freedom [7,30,31,38,[70][71][72][73][74].…”

Section: Clock-neutral Formulation Of Classical and Quantum Mechanicsmentioning

confidence: 99%

“…Being of odd dimension dim P kin − 1, C is also not a phase space. A proper phase space description can be obtained, e.g., through phase space reduction by gauge-fixing [7,30,31,38,58]. Given a choice of clock function T, we may consider the gaugefixing condition T = const, which may be valid only locally on C. Since F f ,T (τ ) is constant along each orbit generated by C H for each value of τ , we do not lose any information about the relational dynamics by restricting to T = const and leaving τ free.…”

Section: Clock-neutral Classical Theorymentioning

confidence: 99%

“…The quantization of relational observables is non-trivial, especially because Equation (4) may not be globally defined on C, and depends very much on the properties of the chosen clock. Steps toward systematically quantizing relational Dirac observables have been undertaken (e.g., in [7,17,20,37,38]) and part of this article is devoted to further developing them for a class of relativistic models.…”

Section: Clock-neutral Quantum Theorymentioning

confidence: 99%

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Equivalence of Approaches to Relational Quantum Dynamics in Relativistic Settings

2021

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We have previously shown that three approaches to relational quantum dynamics—relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations—are equivalent. Here we show that this “trinity” of relational quantum dynamics holds in relativistic settings per frequency superselection sector. Time according to a clock subsystem is defined via a positive operator-valued measure (POVM) that is covariant with respect to the group generated by its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves Kuchař's criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks.

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Section: Introductionsupporting

confidence: 53%