TESSAROTTO, Massimo and Claudio CREMASCHINI. The Common Logic of Quantum Universe-Part II: The Case of Quantum Gravity. Foundations of Physics. 2022, vol. 52, No 2, p. "39-1"-"39-37", 37 pp. ISSN 0015-9018. Available from: https://dx.doi.org/10.1007/s10701-022-00548-y.
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Basic information
Original name The Common Logic of Quantum Universe-Part II: The Case of Quantum Gravity
Authors TESSAROTTO, Massimo (380 Italy, belonging to the institution) and Claudio CREMASCHINI (380 Italy, belonging to the institution).
Edition Foundations of Physics, 2022, 0015-9018.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10308 Astronomy
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
WWW URL
RIV identification code RIV/47813059:19630/22:A0000213
Organization unit Institute of physics in Opava
Doi http://dx.doi.org/10.1007/s10701-022-00548-y
UT WoS 000768838400001
Keywords in English Quantum mechanics; Quantum gravity; Quantum logic; Principle of non-contradiction
Tags FÚ, RIV23
Tags International impact, Reviewed
Changed by Changed by: Mgr. Pavlína Jalůvková, učo 25213. Changed: 31/1/2023 12:00.
Abstract
The logical structure of quantum gravity (QG) is addressed in the framework of the so-called manifestly covariant approach. This permits to display its close analogy with the logics of quantum mechanics (QM). More precisely, in QG the conventional 2-way principle of non-contradiction (2-way PNC) holding in Classical Mechanics is shown to be replaced by a 3-way principle (3-way PNC). The third state of logical truth corresponds to quantum indeterminacy/undecidability, i.e., the occurrence of quantum observables with infinite standard deviation. The same principle coincides, incidentally, with the earlier one shown to hold in Part I, in analogous circumstances, for QM. However, this conclusion is found to apply only provided a well-defined manifestly-covariant theory of the gravitational field is adopted both at the classical and quantum levels. Such a choice is crucial. In fact it makes possible the canonical quantization of the underlying unconstrained Hamiltonian structure of general relativity, according to an approach recently developed by Cremaschini and Tessarotto (2015-2021). Remarkably, in the semiclassical limit of the theory, Classical Logic is proved to be correctly restored, together with the validity of the conventional 2-way principle.
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