Advertisement

Foundations of Physics Letters

, Volume 8, Issue 5, pp 437–447 | Cite as

Generalization of the proof on the existence of hidden measurements to experiments with an infinite set of outcomes

  • Bob Coecke
Article

Abstract

We generalize Aerts' proof concerning the existence of hidden measurements for experiments withn outcomes to general experiments with an infinite set of outcomes. More specific we prove that, ifɛ is a set of experiments on an entityS with a set of pure states Σ, and alleɛ are such that the outcomes can be represented as a measurable subset of a finite dimensional real space, on which for every initial state of the entity there exists a probability measure, then there exists a hidden measurement representation for this set of experiments.

Key words

quantum probability determinism lack of knowledge hidden measurements 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Aerts,J. Math. Phys. 27, 202 (1986).CrossRefGoogle Scholar
  2. 2.
    D. Aerts,Helv. Phys. Acta. 64, 1 (1991).MathSciNetGoogle Scholar
  3. 3.
    D. Aerts, “A macroscopic classical laboratory situation with only macroscopic classical entities giving rise to a quantum mechanical probability model”, inQuantum Probability and Related Topics, Vol. VI, L. Accardi, ed. (World Scientific, Singapore, 1991).Google Scholar
  4. 4.
    M. Czachor,Found. Phys. Lett. 5, 249 (1992).CrossRefGoogle Scholar
  5. 5.
    D. Aerts, T. Durt, A.A. Grib, B. Van Bogaert, and R.R. Zapatrin,Int. J. Theor. Phys. 32, 489 (1993).CrossRefGoogle Scholar
  6. 6.
    D. Aerts and T. Durt,Found. Phys. 24, 1353 (1994).Google Scholar
  7. 7.
    D. Aerts,Found. Phys. 24, 1205 (1994).CrossRefGoogle Scholar
  8. 8.
    J. Von Neumann,Grundlehren, Math. Wiss. XXXVIII (1932).Google Scholar
  9. 9.
    A.M. Gleason,J. Math. Mech. 6, 885 (1957).Google Scholar
  10. 10.
    S. Kochen and E.P. Specker,J. Math. Mech. 17, 59 (1967).Google Scholar
  11. 11.
    S.P. Gudder,Rev. Mod. Phys. 40, 229 (1968).CrossRefGoogle Scholar
  12. 12.
    G.H. Hardy and E.M. Wright,The Theory of Numbers (Oxford University Press, London, 1938).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Bob Coecke
    • 1
  1. 1.TENA, Free University of BrusselsBrusselsBelgium

Personalised recommendations