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On Bell-Type Inequalities in Quantum Logics

  • Jarosław Pykacz
Part of the Fundamental Theories of Physics book series (FTPH, volume 24)

Abstract

Bell-type inequalities are studied within the framework of quantum logic approach. It is shown that violation of Bell’s inequalities indicates that pure states are not dispersion-free, whenever they are Jauch-Piron states which is true both in classical and in quantum mechanics. This result completes the results obtained by Santos [4] who has shown that violation of Bell’s inequalities implies that a lattice of propositions for a physical system is not distributive. Connections between Jauch-Piron properties of states, non-dispersive character of pure states and distributivity of a logic are studied and it is shown that if a logic is finite the former two properties imply the latter.

Keywords

Physical System Pure State Classical Mechanic Boolean Algebra Triangle Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bell JS On the Einstein Podolsky Rosen paradox Physics 1 195 1964Google Scholar
  2. 2.
    A. Aspect, P. Grangier, and G. Roger, Phys.Rev.Lett.47 460 (1981)CrossRefGoogle Scholar
  3. 2.A
    Aspect A. Dalibard J. Roger G. Phys.Rev.Lett. 42 1804 1982CrossRefADSMathSciNetGoogle Scholar
  4. 3.
    Aerts, D. The One and the Many, Ph.D.Thesis,Vrije Universiteit Brussel, 1980; ‚The physical origin of the EPR paradox’ in Open Questions in Quantum Physics, G.Tarozzi and A. van der Merve, Eds., 33-50,D.Reidel, Dordrecht, 1985.Google Scholar
  5. 4.
    Santos E. The Bell inequalities as tests of classical logicPhysics LeTters A 115 8 363 1986CrossRefADSMathSciNetGoogle Scholar
  6. 5.
    Beltrametti, E. and Cassinelli, G. The Logic of Quantum Mechanics Addison-Wesley Reading 1981zbMATHGoogle Scholar
  7. 6.
    Pykacz,J. ‚On the geometrical origin of Bell’s inequalities′ , to be published in Problems in Quantum Physics, World Scientific,Singapore.Google Scholar
  8. 7.
    Mackey G W The Mathematical Foundations of Quantum Mechanics Benjamin New York 1963zbMATHGoogle Scholar
  9. 8.
    Ruttimann GT Jauch-Piron states Journal of Mathematical Physics 18 2 189 1977CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Jarosław Pykacz
    • 1
  1. 1.Institute of MathematicsUniversity of GdańskGdańskPoland

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