The two Bellʼs theorems of John Bell

Abstract

Abstract. Many of the heated arguments about the meaning of "Bell's 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 Bell's 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 Bell's theorems -which I present to explain the relation between Jarrett-completeness, "fragile locality", and EPR-completeness -I maintain that Bell's two versions are the essential ones. Although the two Bell's 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 Bell's 1976 theorem, is motivated implicitly by Reichenbach's 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 Reichenbach's 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, Bell's 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.

Causarum Investigatio and the Two Bell’s Theorems of John Bell

“…The latter, however, deny that there are really two different theorems, claiming that in his 1964 paper Bell used 'locality' to mean LOCAL CAUSALITY, and that from it he derived PREDETERMINATION 3 rather than assuming it. I have argued in depth [4,11] that this is a misrepresentation of what Bell proved in 1964.…”

“…There, one finds the role of natural philosophy defined as causarum investigatio (Fig: 1). The investigation of causes, or, more particularly, of notions of causation, has proven to be a very fruitful way to analyse Bell's theorem, and the disagreements over it [6,7,8,4,5].…”

“…[5], and Ref. [4], each has independent material, they all share some core material, which can be summarized as follows. Bell actually proved two theorems (Sec.…”

A Top-down versus a Bottom-up Hidden-variables Description of the Stern–Gerlach Experiment

“…of "local causality")á la Bell [17] and is compatible with the "non-locality" in a hidden-variables theoriesá la Bohm [17]-cf. (O ′ ), Section 4.…”

“…Therefore different contents of "locality" are naturally linked through the quantum structural studies. Second, on the ontological level, QSS as per Section 2 is in sharp contrast with the reductionistic interpretations of quantum theoryá la Bohm [5,17]. Distinguishing between these two approaches to quantum theory may be seen as an amendment to the tests of the Bell inequalities [17]: one should simultaneously consider more than one composite-system's structure, which leads to the following observation.…”