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I think it should be understood that the concept of "entanglement" is not native to the mathematical formalism of QM, but only comes to us with Einstein's assumption (in the EPR paper) that there is an initial, composite wavefunction that can somehow later split into two simple wavefunctions, and that an observed result of one of these simple wavefunctions will dictate the exact state of the other wavefunction.

But the idea that there was a prior "interaction" that had occurred that led to a composite wavefunction is already a classical, spacetime picture that was never warranted by the formalism of QM itself. That is, the formalism offers no explanation as to how certain theoretical entities (i.e. "particles") may possibly relate to one another. In other words, a single "observable" yields only a single quantity; at no point is there ever any mention of multiplicity.

But for some reason, Einstein was able to get away with making this assumption, because if not, then QM would have been exposed as an exercise in tautological thought. That is, the notion that a simple system (as represented by a wavefunction) can be observed in order to yield a particular result does not offer much in the way of compelling physics. So, the idea of complexity had to be allowed into the picture in order to elevate QM into the pantheon of theories that are understood to be dynamically interactive (i.e. "physical").

Furthermore, the very idea that wavefunctions are capable of joining and splitting relies upon a kind of mathematical metaphysics that is simply not permitted from within the canonical understanding of QM as a mere predictive formalism that can only relate to classical spacetime descriptions by way of the principle of complementarity.

From where I stand, it makes sense to assert that Bell's theorem (and the associated question of particulate "entanglement") is only meaningful when this unwarranted assumption is allowed to remain in effect. That is, the only time that we can even start to speak rigorously about "relations" between "systems" is when we delve into quantum field theory, and when we do this, the mathematical simplicity of pure, formal QM begins to degenerate into complexities that are anything but pleasant to contemplate. In other words, what had previously been a "clean" formalism that is completely described by the application of linear operators on a field of values now becomes an exercise in mathematical "sloppiness" that is known as perturbation theory.

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# Prior interaction as an unwarranted assumption of EPR

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