Measurement events relative to temporal quantum reference frames
- URL: http://arxiv.org/abs/2308.10967v1
- Date: Mon, 21 Aug 2023 18:26:12 GMT
- Title: Measurement events relative to temporal quantum reference frames
- Authors: Ladina Hausmann, Alexander Schmidhuber, Esteban Castro-Ruiz
- Abstract summary: We compare two approaches to the Page-Wootters formalism to clarify the operational meaning of evolution and measurements.
We show that for non-ideal clocks, the purified measurement approach yields time non-local, non-unitary evolution.
- Score: 49.1574468325115
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The Page-Wootters formalism is a proposal for reconciling the
background-dependent, quantum-mechanical notion of time with the background
independence of general relativity. However, there has been much discussion
regarding the physical meaning of the framework. In this work, we compare two
consistent approaches to the Page-Wootters formalism to clarify the operational
meaning of evolution and measurements with respect to a quantum temporal
reference frame. The so-called "twirled observable" approach implements
measurements as operators that are invariant with respect to the Hamiltonian
constraint. The "purified measurement" approach instead models measurements
dynamically by modifying the constraint itself. While both approaches agree in
the limit of ideal clocks, a natural generalization of the purified measurement
approach to the case of non-ideal, finite-resource clocks yields a radically
different picture. We discuss the physical origin of this discrepancy and argue
that they describe operationally distinct situations. Moreover, we show that,
for non-ideal clocks, the purified measurement approach yields time non-local,
non-unitary evolution and implies a fundamental limitation to the operational
definition of the temporal order of events. Nevertheless, unitarity and
definite temporal order can be restored if we assume that time is discrete.
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