Classical Limit and Quantum Logic

Losada, Marcelo; Fortín, Sebastián; Holik, Federico

doi:10.1007/s10773-017-3579-0

Cited by 11 publications

(15 citation statements)

References 43 publications

(27 reference 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%

“…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%

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Dynamics of algebras in quantum unstable systems

Losada

Fortín

Gadella

et al. 2018

Int. J. Mod. Phys. A

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We introduce a dynamical evolution operator for dealing with unstable physical process, such as scattering resonances, photon emission, decoherence and particle decay. With that aim, we use the formalism of rigged Hilbert space and represent the time evolution of quantum observables in the Heisenberg picture, in such a way that time evolution is non-unitary. This allows to describe observables that are initially non-commutative, but become commutative after time evolution. In other words, a non-abelian algebra of relevant observables becomes abelian when times goes to infinity. We finally present some relevant examples. * All authors contributed equally to this manuscript.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 91%

Dynamics of algebras in quantum unstable systems

Losada

Fortín

Gadella

et al. 2018

Int. J. Mod. Phys. A

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“…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%

Truth Values of Quantum Phenomena

Bolotin

2018

Int J Theor Phys

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In the paper, the idea of describing not-yet-verified properties of quantum objects with logical many-valuedness is scrutinized. As it is argued, to promote such an idea, the following two foundational problems of many-valued quantum logic must be decided: the problem of choosing a proper system of many-valued logic and the problem of the emergence of bivalence from logical many-valuedness. Difficulties accompanying solutions of these problems are discussed. Introducing logical many-valuedness in quantum mechanicsThe argument claiming that quantum theory could not be comprehended on the grounds of classical two-valued logic is rather straightforward and goes like this.Let us consider a typical quantum interference experiment where a quantum particle being released from a source is absorbed by a screen after passing through a two-slit barrier 1 . Suppose that immediately behind that barrier are placed two which-way detectors able to verify (e.g., by way of clicking) the particle's passage through a corresponding slit. Let X 1 denote the proposition of the click of the detector placed behind slit 1 such that X 1 is true (denoted by "1") if the detector clicks and X 1 is false (denoted by "0") if the detector does not. Let X 2 in an analogous manner denote the proposition of the signal from the detector placed behind slit 2.Assume that the propositions X 1 and X 2 are in possession of not-yet-verified truth values -i.e., ones existing before the detectors can click -that are merely revealed by the act of verification of the particle's passage.Within the given assumption, let us accept that such values of the propositions X 1 and X 2 are either 1 or 0. Accordingly, exclusive disjunction on these values of X 1 and X 2 can be decided by * Email : arkadyv@bgu.ac.il 1 In the present paper, rather than being strictly restricted to spatially arranged slits, quantum interference is considered generally for any set of perfectly distinguishable alternatives.

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“…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%