The Common Logic of Quantum Universe-Part II: The Case of Quantum Gravity

@article{65826,
   author = {Tessarotto, Massimo and Cremaschini, Claudio},
   article_number = {2},
   doi = {http://dx.doi.org/10.1007/s10701-022-00548-y},
   keywords = {Quantum mechanics; Quantum gravity; Quantum logic; Principle of non-contradiction},
   language = {eng},
   issn = {0015-9018},
   journal = {Foundations of Physics},
   title = {The Common Logic of Quantum Universe-Part II: The Case of Quantum Gravity},
   url = {https://link.springer.com/article/10.1007/s10701-022-00548-y},
   volume = {52},
   year = {2022}
}

TY  - JOUR
ID  - 65826
AU  - Tessarotto, Massimo - Cremaschini, Claudio
PY  - 2022
TI  - The Common Logic of Quantum Universe-Part II: The Case of Quantum Gravity
JF  - Foundations of Physics
VL  - 52
IS  - 2
SP  - "39-1"-"39-37"
EP  - "39-1"-"39-37"
SN  - 00159018
KW  - Quantum mechanics
KW  - Quantum gravity
KW  - Quantum logic
KW  - Principle of non-contradiction
UR  - https://link.springer.com/article/10.1007/s10701-022-00548-y
N2  - 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.
ER  - 

TESSAROTTO, Massimo a Claudio CREMASCHINI. The Common Logic of Quantum Universe-Part II: The Case of Quantum Gravity. \textit{Foundations of Physics}. 2022, roč.~52, č.~2, s.~''39-1''-''39-37'', 37 s. ISSN~0015-9018. Dostupné z: https://dx.doi.org/10.1007/s10701-022-00548-y.