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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Replying to @sigfpe
I completely agree with you, Dan! People should be arguing about "the collapse of the probability distribution" versus the "many-worlds interpretation of probability theory"? Half the problems with interpreting QM are problems with probability theory. Entanglement is new.
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Replying to @johncarlosbaez @sigfpe
"Entanglement," sadly, is something of a red herring. It's not the existence of indecomposable elements in the tensor product of the state space with itself that matters. The thing to focus on is the structure of the algebra of observables (as superselection rules make clear.)
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Replying to @MathPrinceps @johncarlosbaez
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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Replying to @sigfpe @johncarlosbaez
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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It is certainly correct to say that the crucial distinctive feature of quantum probability is "interference," but it takes some care to say exactly what this word means. I think the best explanation now in existence is due to Itamar Pitowsky: http://bit.ly/2q09gYv
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