Abstract

Bell's theorem is 50 years old. There still remains a controversy about its implications. Much of this controversy has its roots in confusion regarding the premises from which the theorem can be derived. Some claim that a derivation of Bell's inequalities requires just a locality assumption and nothing more. Violations of the inequalities are then interpreted as a ‘non-locality’ or ‘quantum non-locality’. We show that such claims are unfounded and that every derivation of Bell's inequalities requires a premise—in addition to locality and freedom of choice—which is either assumed tacitly, or unconsciously, or is embedded in a single compound condition (such as Bell's ‘local causality’). The premise is equivalent to the assumption of the existence of additional variables which do not appear in the quantum formalism (in the form of determinism, joint probability for outcomes of all conceivable measurements, ‘additional causes’, ‘hidden variables’, ‘complete description of the state’ or counterfactual definiteness, etc). A certain irony is that perhaps the main message of the violation of Bell's inequalities is that our notion of locality should be based on an operationally well-defined no-signalling condition, rather than on local causality.

This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.