Hidden Measurements, Hidden Variables and the Volume Representation of Transition Probabilities

Author： Oliynyk Todd  

Publisher： Springer Publishing Company

ISSN： 0015-9018

Source： Foundations of Physics, Vol.35, Iss.1, 2005-01, pp. : 85-107

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Abstract

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 serves as a generalization of it for dimensions n .≥ 3 We also show how to construct a hidden variables scheme based on hidden measurements and we discuss how joint distributions arise in our hidden variables scheme and their relationship with the results of Fine [J. Math. Phys. 23 1306 (1982)].

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