IMO the main objection to MWI here applies just as much to classical probability theory. Until I understand why classical probability works I find it hard to worry about QMhttps://twitter.com/logicians/status/1053293445643624448 …
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I agree that entanglement isn't new in QM as probability has tensor product spaces too. QM's extra feature is that two states with large norms can sum to a state with a small norm aka interference
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Well, strictly speaking, the norms of all quantum states are always equal to 1. Which means that it is misleading (though still very common) to speak of "adding" or "superposing" them. Again, the point is to focus on the observables. They determine which states are pure/mixed.
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The phenomena that people associate with the word "entanglement" all trace back, ultimately, to the assumption that the center of the algebra of observables consists only of multiples of the identity. What counts as pure, and what counts as mixed, depends upon what is observable.
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