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Thanks, Matt, that’s helpful.
About Bell and K&S: You’re right that the theorems apply equally to theories in which the wave function is ontic. I should make that clear. They constrain property ascription in Everett, for example. But Everettians can shrug their shoulders – of course you can’t ascribe pre-measurement properties to systems corresponding to their unique outcomes, because measurements typically don’t have unique outcomes. But even if there’s no special obstacle for epistemic views (compared to ontic views), the theorems still constrain epistemic views. What’s more, epistemic views invite the picture (although they don’t mandate it) that the wave function represents our knowledge of pre-existing properties that are revealed on measurement. This is precisely the picture that the theorems make trouble for.
About interference: I confess that I don’t really know what to make of Spekkens’ toy models. Sure, you get interference, but how exactly? You start with a principle about knowledge – that knowing more than half the information is ruled out. But without knowing why that principle holds, it’s hard to judge whether this is really an epistemic view. Bohm’s theory has restrictions on knowledge too, but the way in which those restrictions are brought about involves the wave function pushing the particles around (on a literal reading at least). I’m not sure that Spekkens can simply assert that this kind of restriction on knowledge can arise without the state being a causal entity in some sense. So I guess I’m not convinced yet that Spekkens has shown that you can get interference out of a wave function epistemic theory.
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