Quantizing time: Interacting clocks and systems
This article generalizes the conditional probability interpretation of time in which time evolution is realized through entanglement between a clock and a system of interest. This formalism is based upon conditioning a solution to the Wheeler-DeWitt equation on a subsystem of the Universe, serving a...
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2019-07-01
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Series: | Quantum |
Online Access: | https://quantum-journal.org/papers/q-2019-07-08-160/pdf/ |
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doaj-eb9b8adc4dfa453b8adb570a26dbf0fd2020-11-25T00:03:58ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2019-07-01316010.22331/q-2019-07-08-16010.22331/q-2019-07-08-160Quantizing time: Interacting clocks and systemsAlexander R. H. SmithMehdi AhmadiThis article generalizes the conditional probability interpretation of time in which time evolution is realized through entanglement between a clock and a system of interest. This formalism is based upon conditioning a solution to the Wheeler-DeWitt equation on a subsystem of the Universe, serving as a clock, being in a state corresponding to a time $t$. Doing so assigns a conditional state to the rest of the Universe $|\psi_S(t)\rangle$, referred to as the system. We demonstrate that when the total Hamiltonian appearing in the Wheeler-DeWitt equation contains an interaction term coupling the clock and system, the conditional state $|\psi_S(t)\rangle$ satisfies a time-nonlocal Schrödinger equation in which the system Hamiltonian is replaced with a self-adjoint integral operator. This time-nonlocal Schrödinger equation is solved perturbatively and three examples of clock-system interactions are examined. One example considered supposes that the clock and system interact via Newtonian gravity, which leads to the system's Hamiltonian developing corrections on the order of $G/c^4$ and inversely proportional to the distance between the clock and system.https://quantum-journal.org/papers/q-2019-07-08-160/pdf/ |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Alexander R. H. Smith Mehdi Ahmadi |
spellingShingle |
Alexander R. H. Smith Mehdi Ahmadi Quantizing time: Interacting clocks and systems Quantum |
author_facet |
Alexander R. H. Smith Mehdi Ahmadi |
author_sort |
Alexander R. H. Smith |
title |
Quantizing time: Interacting clocks and systems |
title_short |
Quantizing time: Interacting clocks and systems |
title_full |
Quantizing time: Interacting clocks and systems |
title_fullStr |
Quantizing time: Interacting clocks and systems |
title_full_unstemmed |
Quantizing time: Interacting clocks and systems |
title_sort |
quantizing time: interacting clocks and systems |
publisher |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
series |
Quantum |
issn |
2521-327X |
publishDate |
2019-07-01 |
description |
This article generalizes the conditional probability interpretation of time in which time evolution is realized through entanglement between a clock and a system of interest. This formalism is based upon conditioning a solution to the Wheeler-DeWitt equation on a subsystem of the Universe, serving as a clock, being in a state corresponding to a time $t$. Doing so assigns a conditional state to the rest of the Universe $|\psi_S(t)\rangle$, referred to as the system. We demonstrate that when the total Hamiltonian appearing in the Wheeler-DeWitt equation contains an interaction term coupling the clock and system, the conditional state $|\psi_S(t)\rangle$ satisfies a time-nonlocal Schrödinger equation in which the system Hamiltonian is replaced with a self-adjoint integral operator. This time-nonlocal Schrödinger equation is solved perturbatively and three examples of clock-system interactions are examined. One example considered supposes that the clock and system interact via Newtonian gravity, which leads to the system's Hamiltonian developing corrections on the order of $G/c^4$ and inversely proportional to the distance between the clock and system. |
url |
https://quantum-journal.org/papers/q-2019-07-08-160/pdf/ |
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AT alexanderrhsmith quantizingtimeinteractingclocksandsystems AT mehdiahmadi quantizingtimeinteractingclocksandsystems |
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