Non-separability Does Not Relieve the Problem of Bell’s Theorem
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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.
KeywordsNon-locality Bell’s theorem Separability Holism
The author would like to thank Michel Buck for pointing out a useful quote from Bell, Fay Dowker and Rafael Sorkin for many conversations about causality and relativity, and especially to Harvey Brown for pointing to previous work on separability such as that of Healey. Thanks are also due to Travis Norsen and Rob Spekkens for edifying discussions of an earlier version on the manuscript. This work was made possible through the support of a grant from the John Templeton Foundation.
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