Locality, Independence and the Pro-liberty Bell

1 Huw Price 2 Bell's Theorem requires the assumption that the values of hidden variables are statistically independent of future measurement settings. This Independence Assumption (IA) is normally taken for granted, though Bell himself sometimes considered relaxing it, as a way of defending locality. On balance he regarded such a move as even less attractive than non-locality, however—this despite the fact that he himself believed that non-locality conflicts with the orthodox interpretation of Special Relativity—for he thought that if we gave up IA we would have to abandon the belief that we are free. Few other commentators pay any explicit attention to the possibility of giving up IA. I'm not sure whether this is because Bell's concerns about freedom are widely shared, or simply because IA seems too obvious to challenge. At any rate, it is this unconventional path that I want to talk about here. The main point of the paper is to distinguish two quite different ways of giving up IA, which tend to be confused. I confused them myself for a long time, and as I'll explain, I think that others have, too, including Bell himself. But the – 2 – World-line of photon World-line of polarizer A B C Figure 2 two proposals are really quite different. One of them, I think, is rightly dismissed; which means that unless we notice that there is an alternative, it is easy to make the mistake of thinking that IA cannot seriously be challenged. Approached from the right metaphysical perspective, however, the alternative looks like not only a serious possibility, but a very plausible hypothesis. In this case, however, it is easy to overlook the fact that this hypothesis is not what others who have considered rejecting IA have had in mind. I think that discussion of IA has been conducted at cross purposes, and my aim in this paper is to sort things out. What are these two ways of challenging IA? Let's think first about IA itself, in terms of a simple example. Consider a photon approaching a polarising screen: IA is the assumption that the state of the photon is independent of the orientation of the polariser. If we assume that the setting of the polarizer is already fixed as the photon approaches, we can represent this assumption in terms of a simple world-line diagram, as in Figure 1. IA amounts to the assumption that the …