The Logic of a Quantum Mechanical System

Veeravalli S. Varadarajan

Felipe Dilho Alves, João Carlos Alves Barata

Quantum mechanics has been subject to logical scrutiny since its inception. The behavior of quantum systems, which are fundamentally dissimilar from classical systems, often appears to point to a logical inconsistency in quantum mechanics, allegedly leading to contradictions in the prediction of experimental measurements--though such contradictions have never materialized. A recent example of this type of inquiry into the logical well-posedness of quantum mechanics is the Frauchiger-Renner Gedankenexperiment, which purports to demonstrate that quantum mechanics is logically inconsistent. In this article, we show that by considering the property of contextuality in quantum systems--as predicted by the Kochen-Specker theorem--the supposed contradiction proposed by Frauchiger and Renner becomes logically inaccessible.

Enrico G. Beltrametti, Gianni Cassinelli, Peter Carruthers

Mituo Taketani, Masayuki Nagasaki

Pitsri Atisoontornkul, Preedeeporn Limcharoeri

Several attempts have been made to establish the logical structure of quantum mechanics on an axiomatic foundation. It has been shown that, whereas the logical structure of the propositional calculus of classical mechanics is that of a Boolean lattice, the logical structure of the propositional calculus of quantum mechanics is non-Boolean. Moreover, a probability model of a quantum system, namely, the quantum probability model, has a mathematical structure completely different from that of the Kolmogorovian probability model, which is the standard probability model of a classical system. These results, which are still controversial, are analysed and put in critical perspective.

Enrico G. Beltrametti, Gianni Cassinelli, Peter Carruthers