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 probabilistic model. We also give necessary and sufficient conditions for the xistence 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 probabilistic model, but also the necessity of using complex ather than real Ililbert spaces.

On the Statistical Meaning of Complex Numbers in Quantum Mechanics

FEDULLO, Aniello
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 probabilistic model. We also give necessary and sufficient conditions for the xistence 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 probabilistic model, but also the necessity of using complex ather than real Ililbert spaces.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/1551396
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 73
  • ???jsp.display-item.citation.isi??? ND
social impact