Time and classical equations of motion from quantum entanglement via the Page and Wootters mechanism with generalized coherent states

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Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2021-12
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Language
en
Pages
9
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Nature Communications, Volume 12, issue 1
Abstract
We draw a picture of physical systems that allows us to recognize what “time” is by requiring consistency with the way that time enters the fundamental laws of Physics. Elements of the picture are two non-interacting and yet entangled quantum systems, one of which acting as a clock. The setting is based on the Page and Wootters mechanism, with tools from large-N quantum approaches. Starting from an overall quantum description, we first take the classical limit of the clock only, and then of the clock and the evolving system altogether; we thus derive the Schrödinger equation in the first case, and the Hamilton equations of motion in the second. This work shows that there is not a “quantum time”, possibly opposed to a “classical” one; there is only one time, and it is a manifestation of entanglement.
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Funding Information: We thank G. García-Pérez, S .Maniscalco, B. Sokolov, and F. Bonechi for amazing discussions, stimulating questions, and valuable suggestions. C.F. and P.V. also acknowledge the beauty of the Dolomites for inspiration during the Quantum Hiking 2019 international conference. P.V. gratefully acknowledges support from the Kavli Institute for Theoretical Physics @UC Santa Barbara, in the framework of the program Open Quantum System Dynamics, and all the discussions with the participants during the program itself. A. Cuccoli and C.F. acknowledge Fondazione CR Firenze for financial support within project 2018.0951. This work is done in the framework of the Convenzione operativa between the Institute for Complex Systems of the Consiglio Nazionale delle Ricerche (Italy) and the Physics and Astronomy Department of the University of Florence. Publisher Copyright: © 2021, The Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
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Foti , C , Coppo , A , Barni , G , Cuccoli , A & Verrucchi , P 2021 , ' Time and classical equations of motion from quantum entanglement via the Page and Wootters mechanism with generalized coherent states ' , Nature Communications , vol. 12 , no. 1 , 1787 . https://doi.org/10.1038/s41467-021-21782-4