Bell’s inequality is a necessary condition for the existence of a classical probabilistic model for a given set of correlation functions. This condition is not satisfied by the quantum-mechanical correlations of two-spin systems in a singlet state. We give necessary and sufficient conditions, on the transition probabilities, for the existence of a classical probabilities model. We also give necessary and sufficient conditions for the existence of a complex (respectively real) Hilbert space model. Our results apply to individual-spin systems hence they need no «locality» assumption. When applied to the quantum-mechanical transition probabilities, they prove not only the necessity of a nonclassical probabilities model, but also the necessity of using complex rather than real Hilbert spaces.

Accardi, L., Fedullo, A. (1982). On the statistical meaning of complex numbers in quantum mechanics. LETTERE AL NUOVO CIMENTO DELLA SOCIETÀ ITALIANA DI FISICA, 34(7), 161-172 [10.1007/BF02817051].

On the statistical meaning of complex numbers in quantum mechanics

ACCARDI, LUIGI;
1982-01-01

Abstract

Bell’s inequality is a necessary condition for the existence of a classical probabilistic model for a given set of correlation functions. This condition is not satisfied by the quantum-mechanical correlations of two-spin systems in a singlet state. We give necessary and sufficient conditions, on the transition probabilities, for the existence of a classical probabilities model. We also give necessary and sufficient conditions for the existence of a complex (respectively real) Hilbert space model. Our results apply to individual-spin systems hence they need no «locality» assumption. When applied to the quantum-mechanical transition probabilities, they prove not only the necessity of a nonclassical probabilities model, but also the necessity of using complex rather than real Hilbert spaces.
1982
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
University of Salerno preprint May (1981)
Accardi, L., Fedullo, A. (1982). On the statistical meaning of complex numbers in quantum mechanics. LETTERE AL NUOVO CIMENTO DELLA SOCIETÀ ITALIANA DI FISICA, 34(7), 161-172 [10.1007/BF02817051].
Accardi, L; Fedullo, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/81190
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