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I would be very interested to hear your talk, so do send me a link if it’s recorded, etc. I hear what you are saying about the local density matrices, but presumably you can appreciate that there are further (subtle and challenging) questions. For example, if the local density matrix doesn’t exhaust the ontology, then it is hardly persuasive to say “the theory is local because interventions over there do not affect the density matrix over here”. And (as I have written about elsewhere) I think there are real questions about whether the local density matrices even capture the part of the ontology that I think you have in mind when you say that it is/captures “ALL what is in a particular location”. One of the crucial things that is real (in the sense of being there in the wave function) is that there are connections between terms in the local density operator over here, and the one over there. (That is, a certain “piece” of the density operator over here is, so to speak, “in the same world/branch” as a certain other “piece” of the density operator over there.) But, sort of by construction, the collection of local density operators leave precisely these connections out, and hence what they omit is in some sense exactly the thing that (in the context of other theories) causes problems for nonlocality. So the whole argument seems a bit like a swindle.
And then I really just don’t have any idea how I’m supposed to understand mathematical operators (associated with spacetime regions) as describing some physical “stuff”. If you tell me tables are made of particles, that makes sense as a possibility. Or a constellation of spacetime-point “flashes” — OK, that’s weird, but I can comprehend it. Or maybe a table is a table-shaped region in which some field has a different value from the background value. OK, yes, that makes sense as a possibility. But if you tell me a table is made out of mathematical operators that act on states in some abstract Hilbert space, I literally don’t know what you mean; I don’t understand what in the world it could mean for a table to be made of such things.
But maybe this is off-topic for this thread. =)
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