The Common Logic of Quantum Universe-Part I: The Case of Non-relativistic Quantum Mechanics

@article{66182,
   author = {Tessarotto, Massimo and Cremaschini, Claudio},
   article_number = {1},
   doi = {http://dx.doi.org/10.1007/s10701-022-00547-z},
   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 I: The Case of Non-relativistic Quantum Mechanics},
   url = {https://link.springer.com/article/10.1007/s10701-022-00547-z},
   volume = {52},
   year = {2022}
}

TY  - JOUR
ID  - 66182
AU  - Tessarotto, Massimo - Cremaschini, Claudio
PY  - 2022
TI  - The Common Logic of Quantum Universe-Part I: The Case of Non-relativistic Quantum Mechanics
JF  - Foundations of Physics
VL  - 52
IS  - 1
SP  - "30-1"-"30-38"
EP  - "30-1"-"30-38"
SN  - 00159018
KW  - Quantum mechanics
KW  - Quantum gravity
KW  - Quantum logic
KW  - Principle of non-contradiction
UR  - https://link.springer.com/article/10.1007/s10701-022-00547-z
N2  - One of the most challenging and fascinating issue in mathematical and theoretical physics concerns the possibility of identifying the logic underlying the so-called quantum universe, i.e., Quantum Mechanics and Quantum Gravity. Besides the sheer difficulty of the problem, inherent in the actual formulation of Quantum Mechanics-and especially of Quantum Gravity-to be used for such a task, a crucial aspect lies in the identification of the appropriate axiomatic logical proposition calculus to be associated to such theories. In this paper the issue of the validity of the conventional principle of non-contradiction (PNC) is called into question and is investigated in the context of non-relativistic Quantum Mechanics. In the same framework a modified form of the principle, denoted as 3-way PNC is shown to apply, which relates the axioms of quantum logic with the physical requirements placed by the Heisenberg Indeterminacy Principle.
ER  - 

TESSAROTTO, Massimo a Claudio CREMASCHINI. The Common Logic of Quantum Universe-Part I: The Case of Non-relativistic Quantum Mechanics. \textit{Foundations of Physics}. 2022, roč.~52, č.~1, s.~''30-1''-''30-38'', 38 s. ISSN~0015-9018. Dostupné z: https://dx.doi.org/10.1007/s10701-022-00547-z.