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

被引：0
作者：
Massimo Tessarotto
Claudio Cremaschini
机构：
[1] University of Trieste,Department of Mathematics and Geosciences
[2] Silesian University in Opava,Research Center for Theoretical Physics and Astrophysics, Institute of Physics
来源：
Foundations of Physics | 2022年 / 52卷
关键词：
Quantum mechanics; Quantum gravity; Quantum logic; Principle of non-contradiction;
D O I：
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摘要：
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.
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