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The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity

The subject of this paper deals with the mathematical formulation of the Heisenberg Indeterminacy Principle in the framework of Quantum Gravity. The starting point is the establishment of the so-called time-conjugate momentum inequalities holding for non-relativistic and relativistic Quantum Mechani...

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Autores principales: Tessarotto, Massimo, Cremaschini, Claudio
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7712843/
https://www.ncbi.nlm.nih.gov/pubmed/33286977
http://dx.doi.org/10.3390/e22111209
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author Tessarotto, Massimo
Cremaschini, Claudio
author_facet Tessarotto, Massimo
Cremaschini, Claudio
author_sort Tessarotto, Massimo
collection PubMed
description The subject of this paper deals with the mathematical formulation of the Heisenberg Indeterminacy Principle in the framework of Quantum Gravity. The starting point is the establishment of the so-called time-conjugate momentum inequalities holding for non-relativistic and relativistic Quantum Mechanics. The validity of analogous Heisenberg inequalities in quantum gravity, which must be based on strictly physically observable quantities (i.e., necessarily either 4-scalar or 4-vector in nature), is shown to require the adoption of a manifestly covariant and unitary quantum theory of the gravitational field. Based on the prescription of a suitable notion of Hilbert space scalar product, the relevant Heisenberg inequalities are established. Besides the coordinate-conjugate momentum inequalities, these include a novel proper-time-conjugate extended momentum inequality. Physical implications and the connection with the deterministic limit recovering General Relativity are investigated.
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spelling pubmed-77128432021-02-24 The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity Tessarotto, Massimo Cremaschini, Claudio Entropy (Basel) Article The subject of this paper deals with the mathematical formulation of the Heisenberg Indeterminacy Principle in the framework of Quantum Gravity. The starting point is the establishment of the so-called time-conjugate momentum inequalities holding for non-relativistic and relativistic Quantum Mechanics. The validity of analogous Heisenberg inequalities in quantum gravity, which must be based on strictly physically observable quantities (i.e., necessarily either 4-scalar or 4-vector in nature), is shown to require the adoption of a manifestly covariant and unitary quantum theory of the gravitational field. Based on the prescription of a suitable notion of Hilbert space scalar product, the relevant Heisenberg inequalities are established. Besides the coordinate-conjugate momentum inequalities, these include a novel proper-time-conjugate extended momentum inequality. Physical implications and the connection with the deterministic limit recovering General Relativity are investigated. MDPI 2020-10-26 /pmc/articles/PMC7712843/ /pubmed/33286977 http://dx.doi.org/10.3390/e22111209 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Tessarotto, Massimo
Cremaschini, Claudio
The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity
title The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity
title_full The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity
title_fullStr The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity
title_full_unstemmed The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity
title_short The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity
title_sort heisenberg indeterminacy principle in the context of covariant quantum gravity
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7712843/
https://www.ncbi.nlm.nih.gov/pubmed/33286977
http://dx.doi.org/10.3390/e22111209
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