The two Bellʼs theorems of John Bell

Abstract

Many of the heated arguments about the meaning of 'Bellʼs theorem' arise because this phrase can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976.His 1964 theorem is the incompatibility of quantum phenomena with the dual assumptions of locality and determinism.His 1976 theorem is the incompatibility of quantum phenomena with the unitary property of local causality.This is contrary to Bellʼs own later assertions, that his 1964 theorem began with that single, and indivisible, assumption of local causality (even if not by that name).While there are other forms of Bellʼs theorems-which I present to explain the relation between Jarrett-completeness, 'fragile locality', and EPR-completeness-I maintain that Bellʼs two versions are the essential ones.Although the two Bellʼs theorems are logically equivalent, their assumptions are not, and the different versions of the theorem suggest quite different conclusions, which are embraced by different communities.For realists, the notion of local causality, ruled out by Bellʼs 1976 theorem, is motivated implicitly by Reichenbachʼs principle of common cause and explicitly by the principle of relativistic causality, and it is the latter which must be forgone.Operationalists pay no heed to Reichenbachʼs principle, but wish to keep the principle of relativistic causality, which, bolstered by an implicit 'principle of agent-causation', implies their notion of locality.Thus for operationalists, Bellʼs theorem is the 1964 one, and implies that it is determinism that must be forgone.I discuss why the two 'camps' are drawn to these different conclusions, and what can be done to increase mutual understanding.