Classical counterexamples to Bell’s inequalities

Abstract

This paper shows that a classical system containing a conventional yes/no decision-making component can behave like a quantum system of spin measurements in many ways (although it lacks a wave function) when, in principle, there are no deterministic decision procedures to govern the decision making, and when probabilistic decision procedures consistent with the system are introduced. Most notably, the system violates Bell's inequalities. Moreover, since the system is simple and macroscopic, its similarities to quantum systems arguably provide an insight into quantum mechanics and, in particular, EPR experiments. Thus, from the qualitative correspondences, $\mathrm{decisions}\ensuremath{\leftrightarrow}\mathrm{quantum}$ measurements and the impossibility of deterministic decision $\mathrm{procedures}\ensuremath{\leftrightarrow}\mathrm{quantum}$ noncommutativity, we conclude that the violation of Bell's inequalities in quantum mechanics does not require the existence of an unknown nonclassical nonlocality. It can merely be a result of local noncommutativity combined with nonlocalities of the classical type. The proposed classical decision-making system is a nonquantum theoretical construct possessing complementarity features in Bohr's sense.