2020/07/01 by Philipp A. Hoehn, Philipp A. Höhn, Alexander R. H. Smith +1 · 1 voice · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Observable #POVM #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum dynamics #Quantum mechanics #Quantum operation #Statistical physics #Superselection #Theoretical physics #gr-qc #hep-th #math-ph #quant-ph
paper · pdf · doi:10.3389/fphy.2021.587083
arxiv published 2020/07/01 · arxiv updated 2020/07/01 · openalex publication_date 2021/06/18 · openalex created_date 2021/07/05 · openalex updated_date 2026/07/29
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.