Page-Wootters mechanism: the role of coherence and finite sized clocks
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Biblioteca Digital de Teses e Dissertações da USP |
Texto Completo: | https://www.teses.usp.br/teses/disponiveis/76/76134/tde-22122021-091709/ |
Resumo: | Among the many proposals to approach the concept of time in quantum theory, the Page-Wootters mechanism has attracted much attention in the last few years. Originally, this mechanism explored a stationary pure bipartite non-interacting global system, i.e., a system of interest together with an ancillary clock, to determine how the evolution in time can emerge and an equation of motion can be obtained for a quantum particle conditioned to the measurement of the state of the clock. In this mechanism, time is seen as an inaccessible coordinate and the apparent passage of time arises as a consequence of correlations between the subsystems of a global state. Here we propose a measure that captures the relational character of the mechanism, showing that the internal coherence is the necessary ingredient for the emergence of time in the Page–Wootters model. Connecting it to results in quantum thermodynamics, showing that it is directly related to the extractable work from quantum coherence. In a second step we analyze such a timeless approach to quantum theory but deriving an equation of motion for a mixed state system that evolves according to its gravitationally induced interaction with a non-ideal quantum clock. The interaction considered is known to describe the gravitational decoherence mechanism, and the clock model is the recently proposed quasi-ideal clock, i.e., one constructed to approximate the time-energy canonical commutation relation. As a result of our considerations, we obtained an equation of motion that is non-linear in nature, dependent on the systems initial conditions. |
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Page-Wootters mechanism: the role of coherence and finite sized clocksMecanismo de Page-Wootters: o papel da coerência e relógios finitosCoerência internaEquação não linear de movimentoInternal coherenceNon-linear equation of motionPage-WoottersPage-WoottersQuasi-ideal clockRelógio quase idealAmong the many proposals to approach the concept of time in quantum theory, the Page-Wootters mechanism has attracted much attention in the last few years. Originally, this mechanism explored a stationary pure bipartite non-interacting global system, i.e., a system of interest together with an ancillary clock, to determine how the evolution in time can emerge and an equation of motion can be obtained for a quantum particle conditioned to the measurement of the state of the clock. In this mechanism, time is seen as an inaccessible coordinate and the apparent passage of time arises as a consequence of correlations between the subsystems of a global state. Here we propose a measure that captures the relational character of the mechanism, showing that the internal coherence is the necessary ingredient for the emergence of time in the Page–Wootters model. Connecting it to results in quantum thermodynamics, showing that it is directly related to the extractable work from quantum coherence. In a second step we analyze such a timeless approach to quantum theory but deriving an equation of motion for a mixed state system that evolves according to its gravitationally induced interaction with a non-ideal quantum clock. The interaction considered is known to describe the gravitational decoherence mechanism, and the clock model is the recently proposed quasi-ideal clock, i.e., one constructed to approximate the time-energy canonical commutation relation. As a result of our considerations, we obtained an equation of motion that is non-linear in nature, dependent on the systems initial conditions.Dentre as muitas propostas de como abordar o conceito de tempo na teoria quântica, o mecanismo de Page-Wootters tem atraído muita atenção nos últimos anos. Originalmente, este mecanismo se focou num sistema global bipartido puro, não-interagente e estacionário, constituído de um sistema de interesse junto com um relógio, e buscou determinar como a evolução no tempo pode emergir e uma equação de movimento ser obtida para uma partícula quântica condicionada a medição do estado do relógio nestas circunstâncias. Nesse mecanismo, o tempo é visto como uma coordenada inacessível e a aparente passagem do tempo surge como consequência das correlações entre os subsistemas de um estado global. Aqui propomos uma medida que captura o caráter relacional do mecanismo, mostrando que a coerência interna é o ingrediente necessário para o surgimento do tempo no modelo de Page-Wootters. Conectando-o a resultados em termodinâmica quântica, mostrando que está diretamente relacionada ao trabalho extraível da coerência quântica. Em uma segunda etapa, analisamos essa abordagem atemporal da teoria quântica, mas derivando uma equação de movimento para um sistema de interesse num estado misto que evolui de acordo com sua interação induzida gravitacionalmente com um relógio quântico não ideal. A interação considerada é conhecida por descrever o mecanismo de decoerência gravitacional, e o modelo do relógio é o relógio quase ideal recentemente proposto, construído para aproximar a relação de comutação canônica tempo-energia. Como resultado de nossas considerações, obtivemos uma equação de movimento que é de natureza não linear, dependente das condições iniciais do sistema.Biblioteca Digitais de Teses e Dissertações da USPPinto, Diogo de Oliveira SoaresMendes, Leandro Raffhael da Silva2021-10-25info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdfhttps://www.teses.usp.br/teses/disponiveis/76/76134/tde-22122021-091709/reponame:Biblioteca Digital de Teses e Dissertações da USPinstname:Universidade de São Paulo (USP)instacron:USPLiberar o conteúdo para acesso público.info:eu-repo/semantics/openAccesseng2024-08-23T13:19:02Zoai:teses.usp.br:tde-22122021-091709Biblioteca Digital de Teses e Dissertaçõeshttp://www.teses.usp.br/PUBhttp://www.teses.usp.br/cgi-bin/mtd2br.plvirginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.bropendoar:27212024-08-23T13:19:02Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP)false |
dc.title.none.fl_str_mv |
Page-Wootters mechanism: the role of coherence and finite sized clocks Mecanismo de Page-Wootters: o papel da coerência e relógios finitos |
title |
Page-Wootters mechanism: the role of coherence and finite sized clocks |
spellingShingle |
Page-Wootters mechanism: the role of coherence and finite sized clocks Mendes, Leandro Raffhael da Silva Coerência interna Equação não linear de movimento Internal coherence Non-linear equation of motion Page-Wootters Page-Wootters Quasi-ideal clock Relógio quase ideal |
title_short |
Page-Wootters mechanism: the role of coherence and finite sized clocks |
title_full |
Page-Wootters mechanism: the role of coherence and finite sized clocks |
title_fullStr |
Page-Wootters mechanism: the role of coherence and finite sized clocks |
title_full_unstemmed |
Page-Wootters mechanism: the role of coherence and finite sized clocks |
title_sort |
Page-Wootters mechanism: the role of coherence and finite sized clocks |
author |
Mendes, Leandro Raffhael da Silva |
author_facet |
Mendes, Leandro Raffhael da Silva |
author_role |
author |
dc.contributor.none.fl_str_mv |
Pinto, Diogo de Oliveira Soares |
dc.contributor.author.fl_str_mv |
Mendes, Leandro Raffhael da Silva |
dc.subject.por.fl_str_mv |
Coerência interna Equação não linear de movimento Internal coherence Non-linear equation of motion Page-Wootters Page-Wootters Quasi-ideal clock Relógio quase ideal |
topic |
Coerência interna Equação não linear de movimento Internal coherence Non-linear equation of motion Page-Wootters Page-Wootters Quasi-ideal clock Relógio quase ideal |
description |
Among the many proposals to approach the concept of time in quantum theory, the Page-Wootters mechanism has attracted much attention in the last few years. Originally, this mechanism explored a stationary pure bipartite non-interacting global system, i.e., a system of interest together with an ancillary clock, to determine how the evolution in time can emerge and an equation of motion can be obtained for a quantum particle conditioned to the measurement of the state of the clock. In this mechanism, time is seen as an inaccessible coordinate and the apparent passage of time arises as a consequence of correlations between the subsystems of a global state. Here we propose a measure that captures the relational character of the mechanism, showing that the internal coherence is the necessary ingredient for the emergence of time in the Page–Wootters model. Connecting it to results in quantum thermodynamics, showing that it is directly related to the extractable work from quantum coherence. In a second step we analyze such a timeless approach to quantum theory but deriving an equation of motion for a mixed state system that evolves according to its gravitationally induced interaction with a non-ideal quantum clock. The interaction considered is known to describe the gravitational decoherence mechanism, and the clock model is the recently proposed quasi-ideal clock, i.e., one constructed to approximate the time-energy canonical commutation relation. As a result of our considerations, we obtained an equation of motion that is non-linear in nature, dependent on the systems initial conditions. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-10-25 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://www.teses.usp.br/teses/disponiveis/76/76134/tde-22122021-091709/ |
url |
https://www.teses.usp.br/teses/disponiveis/76/76134/tde-22122021-091709/ |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
|
dc.rights.driver.fl_str_mv |
Liberar o conteúdo para acesso público. info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Liberar o conteúdo para acesso público. |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.coverage.none.fl_str_mv |
|
dc.publisher.none.fl_str_mv |
Biblioteca Digitais de Teses e Dissertações da USP |
publisher.none.fl_str_mv |
Biblioteca Digitais de Teses e Dissertações da USP |
dc.source.none.fl_str_mv |
reponame:Biblioteca Digital de Teses e Dissertações da USP instname:Universidade de São Paulo (USP) instacron:USP |
instname_str |
Universidade de São Paulo (USP) |
instacron_str |
USP |
institution |
USP |
reponame_str |
Biblioteca Digital de Teses e Dissertações da USP |
collection |
Biblioteca Digital de Teses e Dissertações da USP |
repository.name.fl_str_mv |
Biblioteca Digital de Teses e Dissertações da USP - Universidade de São Paulo (USP) |
repository.mail.fl_str_mv |
virginia@if.usp.br|| atendimento@aguia.usp.br||virginia@if.usp.br |
_version_ |
1809091003092566016 |