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