The alleged nonlocal character of quantum mechanics is inextricably related to the formulation of the Bell theorem. However, as we shall see, that relation is commonly incorrectly assessed. The departure from the clear line of reasoning that John Bell tried to convey has led to a polarization of part of the scientific community into radical irreconcilable positions. We show how the correct appreciation of Bell's work calls for reinterpreting the usual significance given to the Bell theorem yielding a more rational perspective of the problem. Given the relevance of the Bell-type inequalities in quantum information technology and quantum foundations, further clarification of their relation to the nonlocality conundrum deserves due attention. The exposition is also of didactic value. It shows the problems arising from incorrect inferences and superfluous metaphysical ideas.
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.