TESSAROTTO, Massimo and Claudio CREMASCHINI. The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity. Entropy. 2020, vol. 22, No 11, p. "1209-1"-"1209-25", 25 pp. ISSN 1099-4300. Available from: https://dx.doi.org/10.3390/e22111209.
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Basic information
Original name The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity
Authors TESSAROTTO, Massimo (380 Italy, belonging to the institution) and Claudio CREMASCHINI (380 Italy, belonging to the institution).
Edition Entropy, 2020, 1099-4300.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10308 Astronomy
Country of publisher Switzerland
Confidentiality degree is not subject to a state or trade secret
WWW URL
RIV identification code RIV/47813059:19630/20:A0000061
Organization unit Institute of physics in Opava
Doi http://dx.doi.org/10.3390/e22111209
UT WoS 000592759200001
Keywords in English covariant quantum gravity; Heisenberg indeterminacy principle; Heisenberg inequalities; quantum probability density function; deterministic limit
Tags FÚ, FÚ2020, RIV21
Tags International impact, Reviewed
Changed by Changed by: Mgr. Pavlína Jalůvková, učo 25213. Changed: 23/3/2021 22:09.
Abstract
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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