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I don't understand "perfectly local or perfectly global". My intuition of the Schroedinger equation is that it gives an approximation of the probability amplitude for a system, and that approximation is accurate to the extent that the system is isolated from the rest of the universe. The degree to which it is not accurate is the degree to which it is not isolated. An unentangled hydrogen atom in intergalactic space is fairly isolated; a hydrogen atom participating in an H2 molecule is not; but I argue that there are intermediate - "imperfect" states. And, given the big bang, no subsystem is going to be "perfectly" local because of its (once) proximity to other parts of the system. Nonetheless, our intergalactic hydrogen atom is going to behave indistinguishably close to the "perfectly" local model. Do you mean something else by "perfectly local or perfectly global"?