A Relational Formulation of Quantum Mechanics

Abstract Non-relativistic quantum mechanics is reformulated here 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. This idea, combining with the emphasis tha...

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Autor principal:	Jianhao M. Yang
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2018
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/72ed22025ba24999bbd90c8f4f5b9b57
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id	oai:doaj.org-article:72ed22025ba24999bbd90c8f4f5b9b57
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spelling	oai:doaj.org-article:72ed22025ba24999bbd90c8f4f5b9b572021-12-02T15:07:45ZA Relational Formulation of Quantum Mechanics10.1038/s41598-018-31481-82045-2322https://doaj.org/article/72ed22025ba24999bbd90c8f4f5b9b572018-09-01T00:00:00Zhttps://doi.org/10.1038/s41598-018-31481-8https://doaj.org/toc/2045-2322Abstract Non-relativistic quantum mechanics is reformulated here 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. This idea, combining with the emphasis that measurement of a quantum system is a bidirectional interaction process, leads to a new framework to calculate the probability of an outcome when measuring a quantum system. In this framework, the most basic variable is the relational probability amplitude. Probability is calculated as summation of weights from the alternative measurement configurations. The properties of quantum systems, such as superposition and entanglement, are manifested through the rules of counting the alternatives. Wave function and reduced density matrix are derived from the relational probability amplitude matrix. They are found to be secondary mathematical tools that equivalently describe a quantum system without explicitly calling out the reference system. Schrödinger Equation is obtained when there is no entanglement in the relational probability amplitude matrix. Feynman Path Integral is used to calculate the relational probability amplitude, and is further generalized to formulate the reduced density matrix. In essence, quantum mechanics is reformulated as a theory that describes physical systems in terms of relational properties.Jianhao M. YangNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 8, Iss 1, Pp 1-19 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Jianhao M. Yang A Relational Formulation of Quantum Mechanics
description	Abstract Non-relativistic quantum mechanics is reformulated here 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. This idea, combining with the emphasis that measurement of a quantum system is a bidirectional interaction process, leads to a new framework to calculate the probability of an outcome when measuring a quantum system. In this framework, the most basic variable is the relational probability amplitude. Probability is calculated as summation of weights from the alternative measurement configurations. The properties of quantum systems, such as superposition and entanglement, are manifested through the rules of counting the alternatives. Wave function and reduced density matrix are derived from the relational probability amplitude matrix. They are found to be secondary mathematical tools that equivalently describe a quantum system without explicitly calling out the reference system. Schrödinger Equation is obtained when there is no entanglement in the relational probability amplitude matrix. Feynman Path Integral is used to calculate the relational probability amplitude, and is further generalized to formulate the reduced density matrix. In essence, quantum mechanics is reformulated as a theory that describes physical systems in terms of relational properties.
format	article
author	Jianhao M. Yang
author_facet	Jianhao M. Yang
author_sort	Jianhao M. Yang
title	A Relational Formulation of Quantum Mechanics
title_short	A Relational Formulation of Quantum Mechanics
title_full	A Relational Formulation of Quantum Mechanics
title_fullStr	A Relational Formulation of Quantum Mechanics
title_full_unstemmed	A Relational Formulation of Quantum Mechanics
title_sort	relational formulation of quantum mechanics
publisher	Nature Portfolio
publishDate	2018
url	https://doaj.org/article/72ed22025ba24999bbd90c8f4f5b9b57
work_keys_str_mv	AT jianhaomyang arelationalformulationofquantummechanics AT jianhaomyang relationalformulationofquantummechanics
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A Relational Formulation of Quantum Mechanics

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