The Heisenberg Indeterminacy Principle in the Context of
Covariant Quantum Gravity

J 2020

The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity

TESSAROTTO, Massimo and Claudio CREMASCHINI

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

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10308 Astronomy

Country of publisher

Switzerland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

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

Abstract

V originále

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.

Citovat

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.

@article{49261,
   author = {Tessarotto, Massimo and Cremaschini, Claudio},
   article_number = {11},
   doi = {http://dx.doi.org/10.3390/e22111209},
   keywords = {covariant quantum gravity; Heisenberg indeterminacy principle; Heisenberg inequalities; quantum probability density function; deterministic limit},
   language = {eng},
   issn = {1099-4300},
   journal = {Entropy},
   title = {The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity},
   url = {https://www.mdpi.com/1099-4300/22/11/1209},
   volume = {22},
   year = {2020}
}

TY  - JOUR
ID  - 49261
AU  - Tessarotto, Massimo - Cremaschini, Claudio
PY  - 2020
TI  - The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity
JF  - Entropy
VL  - 22
IS  - 11
SP  - "1209-1"-"1209-25"
EP  - "1209-1"-"1209-25"
SN  - 10994300
KW  - covariant quantum gravity
KW  - Heisenberg indeterminacy principle
KW  - Heisenberg inequalities
KW  - quantum probability density function
KW  - deterministic limit
UR  - https://www.mdpi.com/1099-4300/22/11/1209
N2  - 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.
ER  -

TESSAROTTO, Massimo and Claudio CREMASCHINI. The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity. \textit{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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