It is shown that a lack of knowledge about the measurements of a physical system gives rise to a nonclassical probability calculus for this physical system. It is also shown that the nonclassical probability calculus of quantum mechanics can be interpreted as being the result of a lack of knowledge about the measurements. Examples are given of macroscopic real systems that have a nonclassical probability calculus. A macroscopic real system that has a quantum probability calculus is also given, and more specifically a model for the spin of a spin‐ 1/2 particle is constructed. These results are analyzed in light of the old hidden variable problem.
Topics
Quantum probability
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L. Accardi, Rend. Sem. Mat. Univ. Politech. Torino 1982, 249.
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D. Aerts, “A possible explanation for the probabilities of quantum mechanics and example of a macroscopical system that violates Bell inequalities,” in Recent Developments in Quantum Logic, edited by P. Mittelstaedt and E. W. Stachow, in Grundlagen der Exakten Naturwissenschaften, band 6 (Wissenschaftverlag, Bibliografisches Institut, Mannheim, 1985).
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© 1986 American Institute of Physics.
1986
American Institute of Physics
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