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International Journal of Theoretical Physics

, Volume 35, Issue 11, pp 2245–2261 | Cite as

Conditional probabilities with a quantal and a kolmogorovian limit

  • Sven Aerts
Article

Abstract

We give a definition for the conditional probability that is applicable to quantum situations as well as classical ones. We show that the application of this definition to a two-dimensional probabilistic model, known as the epsilon model, allows one to evolve continuously from the quantum mechanical probabilities to the classical ones. Between the classical and the quantum mechanical, we identify a region that is neither classical nor quantum mechanical, thus emphasizing the need for a probabilistic theory that allows for a broader spectrum of probabilities.

Keywords

Field Theory Elementary Particle Quantum Field Theory Broad Spectrum Probabilistic Theory 
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. Accardi, L., and Fedullo, A. (1982). On the statistical meaning of the complex numbers in quantum mechanics,Nuovo Cimento,34, 161–173.MathSciNetGoogle Scholar
  2. Aerts, D. (1986). A possible explanation for the probabilities of quantum mechanics,Journal of Mathematical Physics,27, 202.CrossRefADSMathSciNetGoogle Scholar
  3. Aerts, D. (1987). The origin of the non-classical character of the quantum probability model, inInformation, Complexity, and Control in Quantum Physics, A. Blanquiereet al., eds., Springer-Verlag, Berlin.Google Scholar
  4. Aerts, D. (1991). A macroscopical classical laboratory situation with only macroscopical classical entities giving rise to a quantum mechanical probability model, inQuantum Probability and Related Topics, Vol. VI, L. Accardi, ed., World Scientific, Singapore.Google Scholar
  5. Aerts, D. (1995).International Journal of Theoretical Physics,34(8), 1165–1186.CrossRefMATHMathSciNetGoogle Scholar
  6. Aerts, D., and Aerts, S. (1994). Applications of quantum statistics in psychological studies of decision processes,Foundations of Science,1, 85–97.MathSciNetGoogle Scholar
  7. Aerts, D., Durt, T., Grib, A. A., Van Bogaert, B., and Zapatrin, R. R. (1993). Quantum structures in macroscopical reality,International Journal of Theoretical Physics,32, 489.MathSciNetGoogle Scholar
  8. Aerts, S. (1994). A bridge from quantum to classical, The conditional probability for the epsilon model, Graduation Thesis, Free University of Brussels (VUB), University of Antwerp (UIA).Google Scholar
  9. Coecke, B. (1996). Generalization of the proof on the existence of hidden measurements with an infinite set of outcomes,Foundations of Physics Letters, to appear.Google Scholar
  10. Cohen, L. (1986). Joint quantum probabilities and the uncertainty principle, inNew Techniques and Ideas in Quantum Measurement Theory, D. M. Greenberger, ed., New York Academy of Sciences.Google Scholar
  11. Czachor, M. (1992). On classical models of spin,Foundations of Physics,5, 249.MathSciNetGoogle Scholar
  12. Durt, T. (1996).From quantum to classical, a toy model, Ph.D. Thesis, Free University of Brussels.Google Scholar
  13. Foulis, D., and Randall, C. (1972).Journal of Mathematical Physics,1972, 1667.MathSciNetGoogle Scholar
  14. Gudder, S. P. (1984). Reality, locality and probability,Foundations of Physics,14(10), 997–1011.CrossRefMathSciNetGoogle Scholar
  15. Gudder, S. P. (1988).Quantum Probability, Academic Press, New York.Google Scholar
  16. Pitovski, I. (1989).Quantum Probability-Quantum Logic, Springer-Verlag, Berlin.Google Scholar
  17. Von Mises, R. (1919).Mathematische Zeitschrift,4, 1.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Sven Aerts
    • 1
  1. 1.TENA, Free University of BrusselsBrusselsBelgium

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