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Equivalence of approaches to relational quantum dynamics in relativistic settings

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arxiv 2007.00580 v1 pith:DIY3NKX4 submitted 2020-07-01 gr-qc hep-thmath-phmath.MPquant-ph

Philipp A. Hoehn , Alexander R. H. Smith , Maximilian P. E. Lock This is my paper · ORCID
classification gr-qchep-thmath-phmath.MPquant-ph
keywords quantumclockrelationalrelativisticdynamicsobservablesapproachesconditioning
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We have previously shown (arXiv:1912.00033) 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. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves Kucha\v{r}'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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Cited by 8 Pith papers

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