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Two-Valued Probability Measure on the Pontryagin Space

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Abstract

The well known Kochen-Specker’s theorem is devoted to the problem of hidden variables in quantum mechanics. The Kochen-Specker theorem says: There is no two-valued probability measure on the real Hilbert space of dimension three. In the paper we present an analogy of Kochen-Specker’s theorem in Pontryagin space: A Pontryagin spase H of dimension greater than or equal to three has a two-valued probability measure if and only if H has indefinite rank one: in which case, any such two-valued probability measure on H is unique.

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Authors and Affiliations

  1. Kazan Federal University, Kazan, Russia

    Marjan Matvejchuk & Elena Utkina

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  1. Marjan Matvejchuk
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  2. Elena Utkina
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Correspondence to Marjan Matvejchuk.

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Matvejchuk, M., Utkina, E. Two-Valued Probability Measure on the Pontryagin Space. Int J Theor Phys 54, 4570–4575 (2015). https://doi.org/10.1007/s10773-015-2723-y

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  • DOI: https://doi.org/10.1007/s10773-015-2723-y

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