2017
DOI: 10.1007/s10773-017-3579-0
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Classical Limit and Quantum Logic

Abstract: The more common scheme to explain the classical limit of quantum mechanics includes decoherence, which removes from the state the interference terms classically inadmissible since embodying non-Booleanity. In this work we consider the classical limit from a logical viewpoint, as a quantum-to-Boolean transition. The aim is to open the door to a new study based on dynamical logics, that is, logics that change over time. In particular, we appeal to the notion of hybrid logics to describe semiclassical systems. Mo… Show more

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Cited by 11 publications
(15 citation statements)
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“…In previous works [1][2][3], we have studied the quantum-to-classical transition from the point of view of the algebra of observables of the system. If a quantum system undergoes a physical process such that its behavior becomes classical, then its algebra of observables should undergo a process from a non-Abelian algebra to an Abelian one.…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…In previous works [1][2][3], we have studied the quantum-to-classical transition from the point of view of the algebra of observables of the system. If a quantum system undergoes a physical process such that its behavior becomes classical, then its algebra of observables should undergo a process from a non-Abelian algebra to an Abelian one.…”
Section: Discussionmentioning
confidence: 99%
“…In this work we provide an explicit representation of the time evolution operator for an extensive family of models described by the RHS formalism. We show that, under certain conditions, a commutation process (of the form described in [1][2][3]) is obtained for them. This phenomenon could be of interest for the study of quantum scattering resonances.…”
Section: Introductionmentioning
confidence: 91%
“…To describe the emergence of the logical bivalent limit, one can use clues suggested in the paper [22]. The incompatibility of the projection operatorsP qα andP rβ means that if the system is prepared, say, in the state |Ψ q where all the propositions Q α comes out bivalent, then the truth values of the propositions R β cannot be two-valued in |Ψ q : To be exact,…”
Section: Truth-values Vs Probabilitiesmentioning
confidence: 99%
“…The decoherence approach to the quantum-to-classical transition is based on the Schrödinger picture, in which states evolve over time, while observables and physical properties are taken to be constants. As a result, the structure of quantum properties remains the same for all times: the quantum logic associated with the system does not change [4][5][6][7]. Therefore, in this approach it is not explained how the structure of quantum properties becomes classical.…”
Section: Introductionmentioning
confidence: 99%