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@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.
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