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International Journal of Theoretical Physics

, Volume 57, Issue 2, pp 465–475 | Cite as

Classical Limit and Quantum Logic

  • Marcelo Losada
  • Sebastian Fortin
  • Federico Holik
Article

Abstract

The analysis of the classical limit of quantum mechanics usually focuses on the state of the system. The general idea is to explain the disappearance of the interference terms of quantum states appealing to the decoherence process induced by the environment. However, in these approaches it is not explained how the structure of quantum properties becomes classical. In this paper, we consider the classical limit from a different perspective. We consider the set of properties of a quantum system and we study the quantum-to-classical transition of its logical structure. 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. Moreover, we consider systems with many characteristic decoherence times, whose sublattices of properties become distributive at different times.

Keywords

Classical limit Decoherence Non-unitary evolution Quantum logic 

Notes

Acknowledgments

This research was founded by CONICET, ANCyPT, the National University of La Plata and the University of Buenos Aires. The authors want to thank Manuel Gadella and Mario Castagnino for interesting discussions.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Marcelo Losada
    • 1
  • Sebastian Fortin
    • 2
  • Federico Holik
    • 3
  1. 1.CONICETUniversidad de Buenos AiresBuenos AiresArgentina
  2. 2.CONICET - Departamento de FísicaUniversidad de Buenos AiresBuenos AiresArgentina
  3. 3.CONICET - Instituto de FísicaUniversidad Nacional de La PlataLa PlataArgentina

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