Hidden measurements, hidden variables and the volume representation of transition probabilities

Preprint English OPEN
Oliynyk, Todd A.;

We construct, for any finite dimension $n$, a new hidden measurement model for quantum mechanics based on representing quantum transition probabilities by the volume of regions in projective Hilbert space. For $n=2$ our model is equivalent to the Aerts sphere model and ... View more
  • References (12)
    12 references, page 1 of 2

    [1] S.L. Adler, D.C. Brody, T.A. Brun, and L.P. Hughston, “Martingale models for quantum state reduction” J. Phys. A 34, 8795 (2001).

    [2] D. Aerts, “A possible explanation for the probabilities of quantum mechanics” J. Math. Phys. 27, 202 (1986).

    [3] D. Aerts, “The hidden measurement formalism: what can be explained and where quantum paradoxes remain” Int. J. Theor. Phys. 37, 291 (1998).

    [4] D. Aerts, B. Coecke, B. D'Hooghe, and F. Valckenborgh, “A mechanistic macroscopic physical entity with a three-dimensional Hilbert space description” Helv. Phys. Acta 70, 793 (1997).

    [14] M. Czachor, “On classical models of spin” Found. Phys. Lett. 5, 249 (1992).

    [15] A. Fine, “Joint distributions, quantum correlations, and commuting observables” J. Math. Phys. 23, 1306 (1982).

    [16] N. Gisin and C. Piron, “Collapse of the wave packet without mixture” Lett. Math. Phys. 5, 379 (1981).

    [17] K.A. Kirkpatrick, “Classical three-box “paradox”” J. Phys. A 36, 4891 (2003).

    [18] K.A. Kirkpatrick, ““Quantal” behavior in classical probability”Found. Phys. Lett. 16, 199 (2003).

    [19] J.E. Marsden and T.S. Ratiu, Introduction to mechanics and symmetry, Springer-Verlag, 1994.

  • Metrics
Share - Bookmark