Quantum Physics and Classical Physics—In the Light of Quantum Logic

Article

Abstract

In contrast to the Copenhagen interpretation we consider quantum mechanics as universally valid and query whether classical physics is really intuitive and plausible. We discuss these problems within the quantum logic approach to quantum mechanics where the classical ontology is relaxed by reducing metaphysical hypotheses. On the basis of this weak ontology a formal logic of quantum physics can be established which is given by an orthomodular lattice. By means of the Solèr condition and Piron's result one obtains the classical Hilbert spaces. However, this approach is not fully convincing. There is no plausible justification of Solèr's law and the quantum ontology is partly too weak and partly too strong. We propose to replace this ontology by an ontology of unsharp properties and conclude that quantum mechanics is more intuitive than classical mechanics and that classical mechanics is not the macroscopic limit of quantum mechanics.

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References

  1. Busch, P. (1998). Can unsharp objectification solve the measurement problem. International Journal of Theoretical Physics 37, 241–47.MATHMathSciNetCrossRefGoogle Scholar
  2. Busch, P. (1985). Indeterminacy relations and simultaneous measurements in quantum theory. International Journal of Theoretical Physics 24, 63–92.MathSciNetCrossRefADSGoogle Scholar
  3. Busch, P., Lahti, P., and Mittelstaedt, P. (1996). The Quantum Theory of Measurement, 2nd. edn., Springer-Verlag, Heidelberg.Google Scholar
  4. Dalla Chiara, M. L. (1995). Unsharp quantum logics. International Journal of Theoretical Physics 34, 1331–1336.MATHMathSciNetCrossRefGoogle Scholar
  5. Dalla Chiara, M. L., Cattaneo, G. and Giuntini, R. (1993). Fuzzy-intuitionistic quantum logic. Studia Logica 52, 1–24.MathSciNetGoogle Scholar
  6. Dalla Chiara, M. L. and Giuntini, R. (1994). Partial unsharp quantum logics. Foundation of Physics 24, 1161–1177.MathSciNetGoogle Scholar
  7. Foulis, D. J. (1960). Baer^*—Semigroups. Proceedings of the American Mathematical Society 11, 648–654.Google Scholar
  8. Foulis, D. J. and Bennett, M. K. (1994). Effect algebras and unsharp quantum logics. Foundation of Physics 24, 1331–1352.MathSciNetGoogle Scholar
  9. Giuntini, R. (1990). Brower–Zadeh logic and the operational approach to quantum mechanics. Foundation of Physics 20, 701–714.MathSciNetGoogle Scholar
  10. Giuntini, R. and Greuling, H. (1989). Towards a language of unsharp properties. Foundation of Physics 20, 931–935.MathSciNetGoogle Scholar
  11. Kant, I. (1929). Critique of Pure Reason, N. K. Smith, trans., Macmillan, New York, p. B600.Google Scholar
  12. Mittelstaedt, P. (1978). Quantum Logic, D. Reidel, Dordrecht.Google Scholar
  13. Mittelstaedt, P. (1987). Language and Reality in Quantum Physics, World Scientific, Singapore, pp. 229–250.Google Scholar
  14. Mittelstaedt, P. (1998). The Interpretation of Quantum Mechanics and the Measurement Process, Cambridge University Press, Cambridge, UK.Google Scholar
  15. Piron, C. (1976). Foundations of Quantum Physics, W.A. Benjamin, Reading, MA.Google Scholar
  16. Solèr, M. P. (1995). Characterisation of Hilbert Spaces by Orthomodular Lattices. Communications in Algebra 23(1), 219–243.MATHMathSciNetGoogle Scholar
  17. Stachow, E. W. (1980). Logical foundation of quantum mechanics. International Journal of Theorerical Physics 19, 251–304.MATHMathSciNetADSGoogle Scholar
  18. Stachow, E. W. (1984). Structures of quantum language for individual systems. In Recent Developments in Quantum Logic, P. Mittelstaedt and E.-W. Stachow, eds., BI-Wissenschaftsverlag, Mannheim, pp. 129–145.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.University of CologneGermany

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