Non-separability does not relieve the problem of Bell's theorem

Abstract

This paper addresses arguments that "separability" is an assumption of Bell's theorem, and that abandoning this assumption in our interpretation of quantum mechanics (a position sometimes referred to as "holism") will allow us to restore a satisfying locality principle. Separability here means that all events associated to the union of some set of disjoint regions are combinations of events associated to each region taken separately. In this article, it is shown that: (a) localised events can be consistently defined without implying separability; (b) the definition of Bell's locality condition does not rely on separability in any way; (c) the proof of Bell's theorem does not use separability as an assumption. If, inspired by considerations of non-separability, the assumptions of Bell's theorem are weakened, what remains no longer embodies the locality principle. Teller's argument for "relational holism" and Howard's arguments concerning separability are criticised in the light of these results. Howard's claim that Einstein grounded his arguments on the incompleteness of QM with a separability assumption is also challenged. Instead, Einstein is better interpreted as referring merely to the existence of localised events. Finally, it is argued that Bell rejected the idea that separability is an assumption of his theorem.

26 pages main body, 33 total. v2: several references and comments added, many minor revisions made, appendix B significantly revised

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Cited by in corpus (8)

• Understanding quantum mechanics: a review and synthesis in precise language
• A histories perspective on characterising quantum non-locality
• How to account for quantum non-locality: ontic structural realism and the primitive ontology of quantum physics
• On the concept of Bell's local causality in local classical and quantum theory
• Bell's Theorem, Accountability and Nonlocality
• A separable, dynamically local ontological model of quantum mechanics
• On the meaning of locality: the overlapping assumptions
• Bell's local causality is a d-separation criterion