Bell's theorem without hidden variables

H. Kummer, R. G. McLean

Pavel Vyacheslavovich Kurakin, Георгий Геннадьевич Малинецкий

T. E. Phipps

A. David. Boozer

We clarify the meaning of Bell's theorem and its implications for the construction of hidden variable theories by considering an example system consisting of two entangled spin-1/2 particles. Using this example, we present a simplified version of Bell's theorem and describe several hidden variable theories that agree with the predictions of quantum mechanics. These example theories clarify some subtle points, which are often misunderstood, regarding what it is that Bell's theorem actually establishes. \n

Aleksandr V. Belinskii

Andrea Aiello

Bell's theorem proves the incompatibility between quantum mechanics and local realistic hidden-variable theories. In this paper we show that, contrary to a common belief, the theoretical proof of Bell's theorem is not affected by counterfactual reasoning. Then, we demonstrate that the experimental verification of this theorem may be affected in an unknowable way by our ignorance about the probability distribution of the hidden variables. Our study is based on the standard theory of random variables, and lays the groundwork for a critical rethinking of Bell's theorem and its consequences.