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

TL;DR

This paper demonstrates that non-separability does not resolve the issues raised by Bell's theorem, showing that locality principles are unaffected by abandoning separability assumptions.

Contribution

It clarifies that Bell's theorem and locality do not depend on the separability assumption, countering claims that holism can restore locality in quantum mechanics.

Findings

Localised events can be defined without separability.

Bell's locality condition does not rely on separability.

Bell's theorem proof does not assume separability.

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.