Path integral implementation of relational quantum mechanics

Abstract Relational formulation of quantum mechanics is based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum mechanics. In a recent paper (Yang in Sci Rep 8:13305, 2018),...

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Autor principal:	Jianhao M. Yang
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/b2b1a5a3ec0d464fb062cfa0b2e22f4e
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spelling	oai:doaj.org-article:b2b1a5a3ec0d464fb062cfa0b2e22f4e2021-12-02T17:32:59ZPath integral implementation of relational quantum mechanics10.1038/s41598-021-88045-62045-2322https://doaj.org/article/b2b1a5a3ec0d464fb062cfa0b2e22f4e2021-04-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-88045-6https://doaj.org/toc/2045-2322Abstract Relational formulation of quantum mechanics is based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum mechanics. In a recent paper (Yang in Sci Rep 8:13305, 2018), basic relational quantum mechanics framework is formulated to derive quantum probability, Born’s Rule, Schrödinger Equations, and measurement theory. This paper further extends the reformulation effort in three aspects. First, it gives a clearer explanation of the key concepts behind the framework to calculate measurement probability. Second, we provide a concrete implementation of the relational probability amplitude by extending the path integral formulation. The implementation not only clarifies the physical meaning of the relational probability amplitude, but also allows us to elegantly explain the double slit experiment, to describe the interaction history between the measured system and a series of measuring systems, and to calculate entanglement entropy based on path integral and influence functional. In return, the implementation brings back new insight to path integral itself by completing the explanation on why measurement probability can be calculated as modulus square of probability amplitude. Lastly, we clarify the connection between our reformulation and the quantum reference frame theory. A complete relational formulation of quantum mechanics needs to combine the present works with the quantum reference frame theory.Jianhao M. YangNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-18 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Jianhao M. Yang Path integral implementation of relational quantum mechanics
description	Abstract Relational formulation of quantum mechanics is based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum mechanics. In a recent paper (Yang in Sci Rep 8:13305, 2018), basic relational quantum mechanics framework is formulated to derive quantum probability, Born’s Rule, Schrödinger Equations, and measurement theory. This paper further extends the reformulation effort in three aspects. First, it gives a clearer explanation of the key concepts behind the framework to calculate measurement probability. Second, we provide a concrete implementation of the relational probability amplitude by extending the path integral formulation. The implementation not only clarifies the physical meaning of the relational probability amplitude, but also allows us to elegantly explain the double slit experiment, to describe the interaction history between the measured system and a series of measuring systems, and to calculate entanglement entropy based on path integral and influence functional. In return, the implementation brings back new insight to path integral itself by completing the explanation on why measurement probability can be calculated as modulus square of probability amplitude. Lastly, we clarify the connection between our reformulation and the quantum reference frame theory. A complete relational formulation of quantum mechanics needs to combine the present works with the quantum reference frame theory.
format	article
author	Jianhao M. Yang
author_facet	Jianhao M. Yang
author_sort	Jianhao M. Yang
title	Path integral implementation of relational quantum mechanics
title_short	Path integral implementation of relational quantum mechanics
title_full	Path integral implementation of relational quantum mechanics
title_fullStr	Path integral implementation of relational quantum mechanics
title_full_unstemmed	Path integral implementation of relational quantum mechanics
title_sort	path integral implementation of relational quantum mechanics
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/b2b1a5a3ec0d464fb062cfa0b2e22f4e
work_keys_str_mv	AT jianhaomyang pathintegralimplementationofrelationalquantummechanics
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Path integral implementation of relational quantum mechanics

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