Trinity of relational quantum dynamics
نویسندگان
چکیده
The problem of time in quantum gravity calls for a relational solution. Using reduction maps, we establish previously unknown equivalence between three approaches to dynamics: (1) observables the clock-neutral picture Dirac quantization, (2) Page and Wootters' (PW) Schr\"odinger formalism, (3) Heisenberg obtained via symmetry reduction. Constituting faces same dynamics, call this trinity. In process, develop quantization procedure using covariant positive operator-valued measures which encompass nonideal clocks resolve nonmonotonicity issue realistic reported by Unruh Wald. maps reveal as analog gauge-invariantly extending gauge-fixed quantities. We algebraic properties these observables. extend recent ``clock-neutral'' approach changing temporal reference frames, transforming states, demonstrate clock dependent nonlocality effect. show that Kucha\ifmmode \check{r}\else \v{r}\fi{}'s criticism, alleging conditional probabilities PW formalism violate constraint, is incorrect. They are description gauge-invariant quantity equivalent manifestly evaluation physical inner product. trinity furthermore resolves normalization ambiguity clarifies role entanglement formalism. finally permits us criticism yields wrong propagators showing how give correct transition probabilities. Unlike previous proposals, our resolution does not invoke approximations, ideal or ancilla systems, gauge invariant, easily extends an arbitrary number conditionings.
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ژورنال
عنوان ژورنال: Physical review
سال: 2021
ISSN: ['0556-2813', '1538-4497', '1089-490X']
DOI: https://doi.org/10.1103/physrevd.104.066001