Author:
Höhn Philipp A.,Smith Alexander R. H.,Lock Maximilian P. E.
Abstract
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.
Funder
Okinawa Institute of Science and Technology Graduate University
Simons Foundation
Foundational Questions Institute
John Templeton Foundation
Natural Sciences and Engineering Research Council of Canada
Dartmouth College
Österreichischen Akademie der Wissenschaften
Austrian Science Fund
Subject
Physical and Theoretical Chemistry,General Physics and Astronomy,Mathematical Physics,Materials Science (miscellaneous),Biophysics
Cited by
26 articles.
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