dorsal/arxiv
View SchemaToy Model for a Relational Formulation of Quantum Theory
| Authors | David Poulin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505081 |
| URL | https://arxiv.org/abs/quant-ph/0505081 |
| DOI | 10.1007/s10773-006-9052-0 |
| Journal | Int.J.Theor.Phys. 45 (2006) 1189 |
Abstract
In the absence of an external frame of reference physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is to demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental level, from which the original "non-relational" theory emerges in a semi-classical limit. According to this thesis, the non-relational theory is therefore an approximation of the fundamental relational theory. We propose four simple rules that can be used to translate an "orthodox" quantum mechanical description into a relational description, independent of an external spacial reference frame or clock. The techniques used to construct these relational theories are motivated by a Bayesian approach to quantum mechanics, and rely on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, there is no need for a "collapse of the wave packet" in our model: the probability interpretation is only applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of "spin networks" introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semi-classical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.
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"abstract": "In the absence of an external frame of reference physical degrees of freedom\nmust describe relations between systems. Using a simple model, we investigate\nhow such a relational quantum theory naturally arises by promoting reference\nsystems to the status of dynamical entities. Our goal is to demonstrate using\nelementary quantum theory how any quantum mechanical experiment admits a purely\nrelational description at a fundamental level, from which the original\n\"non-relational\" theory emerges in a semi-classical limit. According to this\nthesis, the non-relational theory is therefore an approximation of the\nfundamental relational theory. We propose four simple rules that can be used to\ntranslate an \"orthodox\" quantum mechanical description into a relational\ndescription, independent of an external spacial reference frame or clock. The\ntechniques used to construct these relational theories are motivated by a\nBayesian approach to quantum mechanics, and rely on the noiseless subsystem\nmethod of quantum information science used to protect quantum states against\nundesired noise. The relational theory naturally predicts a fundamental\ndecoherence mechanism, so an arrow of time emerges from a time-symmetric\ntheory. Moreover, there is no need for a \"collapse of the wave packet\" in our\nmodel: the probability interpretation is only applied to diagonal density\noperators. Finally, the physical states of the relational theory can be\ndescribed in terms of \"spin networks\" introduced by Penrose as a combinatorial\ndescription of geometry, and widely studied in the loop formulation of quantum\ngravity. Thus, our simple bottom-up approach (starting from the semi-classical\nlimit to derive the fully relational quantum theory) may offer interesting\ninsights on the low energy limit of quantum gravity.",
"arxiv_id": "quant-ph/0505081",
"authors": [
"David Poulin"
],
"categories": [
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"doi": "10.1007/s10773-006-9052-0",
"journal_ref": "Int.J.Theor.Phys. 45 (2006) 1189",
"title": "Toy Model for a Relational Formulation of Quantum Theory",
"url": "https://arxiv.org/abs/quant-ph/0505081"
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