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Quantum-Like Representation of Macroscopic Configurations

  • Andrei Khrennikov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5494)

Abstract

The aim of this paper is to use a contextual probabilistic model (in the spirit of Mackey, Gudder, Ballentine) to represent and to generalize some results of quantum logic on macroscopic quantum-like (QL) behaviour. The crucial point is that our model provides the QL-representation of macroscopic configurations in terms of complex probability amplitudes – wave functions of such configurations. Thus, instead of the language of propositions which is common in quantum logic, we use the language of wave functions which common in the conventional presentation of QM.

Keywords

Contextual probabilistic model complex Hilbert space hyperbolic Hilbert space quantum-like representation 

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References

  1. 1.
    Khrennikov, A.Y.: Contextual Approach to Quantum Formalism. Springer, Berlin (2009)CrossRefzbMATHGoogle Scholar
  2. 2.
    Khrennikov, A.Y.: Ubiquitous Quantum Structure: from Psychology to Finances. Springer, Berlin (2009)Google Scholar
  3. 3.
    Foulis, D.J.: A Half-Century of Quantum-Logic. What Have We Learned? In: Quantum Structures and the Nature of Reality. Einstein Meets Magritte, vol. 7, pp. 1–36. Kluwer, Dordrecht (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Andrei Khrennikov
    • 1
  1. 1.International Center for Mathematical Modeling in Physics and Cognitive SciencesUniversity of VäxjöSweden

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