The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity

@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 a Claudio CREMASCHINI. The Heisenberg Indeterminacy Principle in the Context of Covariant Quantum Gravity. \textit{Entropy}. 2020, roč.~22, č.~11, s.~''1209-1''-''1209-25'', 25 s. ISSN~1099-4300. Dostupné z: https://dx.doi.org/10.3390/e22111209.