Causarum Investigatio and the Two Bells Theorems of John Bell

Bells theorem 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 joint assumptions of Locality and Predetermination. His 1976 theorem is their incompatibility with the single property of Local Causality. This is contrary to Bells own later assertions, that his 1964 theorem began with the assumption of Local Causality, even if not by that name. Although the two Bells theorems are logically equivalent, their assumptions are not. Hence, the earlier and later theorems suggest quite different conclusions, embraced by operationalists and realists, respectively. The key issue is whether Locality or Local Causality is the appropriate notion emanating from Relativistic Causality, and this rests on ones basic notion of causation. For operationalists the appropriate notion is what is here called the Principle of Agent-Causation, while for realists it is Reichenbachs Principle of common cause. By breaking down the latter into even more basic Postulates, it is possible to obtain a version of Bells theorem in which each camp could reject one assumption, happy that the remaining assumptions reflect its weltanschauung. Formulating Bells theorem in terms of causation is fruitful not just for attempting to reconcile the two camps, but also for better describing the ontology of different quantum interpretations and for more deeply understanding the implications of Bells marvellous work.