ddd123 said:
Anyway there is a line of research that shows a different link between entanglement and spatial issues:
http://www.nature.com/news/the-quantum-source-of-space-time-1.18797 .
Wow, that's really a nice article, thank you. The way I interpret what it is saying is that it takes the AdS/CFT duality (which says that gravity in a 3D "bulk" under some conditions will act like a conformal field theory (without any gravity) on the 2D boundary of the bulk) and extends it to saying that the connectivity of space in the bulk is dual to the entanglement in the CFT on the boundary. If we think of connectivity of space as important for concepts like nonlocality, and if we interpret entanglement as fundamentally an issue about the holism of systems, then the article seems to be suggesting that our discussion about nonlocality vs. holism has an interesting duality as well: nonlocality in the bulk is dual to holism on the boundary. Put differently, the idea in the article is that the space in the bulk is in some sense "due to" entanglement on the boundary, such that space is "made of entanglement", as they like to say. That certainly puts our discussion into an interesting new light-- it would say that nonlocality and holism, though not the same thing any more than gravity and quantum mechanics are the same thing, do share a deep connection in that we get one when we look in the bulk, and we get the other when we look in the boundary.
The way I interpret all this is that the concept of the "parts" of a system is not a fundamental truth of how systems work, rather it is an idealization that works well when the entanglement in the holistic system is decohered enough to get away with treating the system as if it were made of parts. Similarly, the concept of "locality", i.e., that the parts can only enforce correlations in measurements by propagating subluminal signals, is also not a fundamental truth, it is an idealization that works well when, again, the entanglement on the boundary is sufficiently decohered. What all this means is, the limitation of not going faster than c, and the distinctions between spacelike and timelike separations, are not fundamental laws, they are just what happens in the bulk when entanglements on the boundary get decohered.
The key point of all this, in this interpretation, is that we could frame Gell-Mann's objection in the following terms. The reason it is "wrong" to say that entanglement is enforced by influences between the parts of the system is that it reverses the way we should be thinking about it. We should be saying that the idealization that systems are made of parts, and the idealization that those parts have different locations in spacetime, both work when entanglement breaks down. As such, entanglement does not need to be explained, it is the default state of things-- it is the concepts of parts and propagating influences that need to be explained, and those concepts only emerge when entanglement is broken. Perhaps you can think of "parts" and "influences" as the kind of behaviors that emerge when the symmetry associated with entanglement is
broken, a symmetry about the unity (or holism) of systems. It really turns entanglement, and holism, on its ear to say that it is their
absence that requires understanding, not their presence. So we don't need to explain why all electrons are indistinguishable, that's a symmetry-- we need to explain why we get away with imagining that they are different, and that they occupy different locations in space. It seems that somehow, all the motion we perceive through space might be traced back to changing coherences in the entanglements on the boundary. It's then not the nonlocality of entanglement that we need to understand, it is the origin of locality as that entanglement evolves that we need to understand.