It's well known that in quantum mechanics, a generic mixed state can be decomposed into pure states in infinitely many different ways.

While this property is kind of understandable if quantum states are viewed more like probability functions, it is kind of mysterious why it should be so in MWI.

Why is it so philosophically? It would seem more likely from an a priori philosophical standpoint that for MWI, different classical probability distributions over ontologically real wavefunctions ought to be empirically distinguishable. But yet, that's not the case if they end up with the same mixed density state.

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    $\begingroup$ Quantum states are NEVER to be viewed as probability distributions, not even in standard Copenhagen. MWI is just total intellectual nonsense, both philosophically and scientifically. The question of state purity, on the other hand, is irrelevant to nature. Any possible superposition of a QM system evolves EXACTLY the same way, at least to any measurable precision. Folks who are obsessed with the preparation of pure or mixed states are basically chasing their own tails, at least for the purpose of analyzing the structure of QM. $\endgroup$ – CuriousOne Dec 20 '14 at 6:12
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    $\begingroup$ @CuriousOne: I also think that MWI is an intellectual nonsense, but can you convince? People get enthusiasm about phantasy. To hold what you said, you have to prove it, not just to say it. Also, beware of the Bohm interpretation that indeed works with probability distributions extracted from the absolute square of the wave-function. $\endgroup$ – Sofia Dec 20 '14 at 18:45
  • $\begingroup$ @Sofia: I don't have to prove that god doesn't exist, either. I can just declare the notion patently absurd and then let the folks who propose such nonsense slug it out while I use my time for better things. Will my decision to keep my brain a nonsense-free zone convince the religious? Nope. Do I care? Nope. Bohm basically replaces one magical postulate with another one. I assume the result is technically equivalent, but I have never spent time on it. Unless there is new physics in any one of these mind games (to the best of my knowledge there isn't), I couldn't care less. $\endgroup$ – CuriousOne Dec 20 '14 at 18:52
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    $\begingroup$ @CuriousOne: I am on your side. But you see, we are exposed to all sort of facts that contradict our classical everyday experience. What can be a better example than the effects of the entanglements which contradict local HV? This is why some people go so far and talk of many worlds. I only said that by telling them that it is a nonsense, it won't convince them. If someone tells you a statement, you would like a proof, won't you? That's all that I said. And the proof is, probably, (I didn't bother with MWI myself) that MWI solves none of the problems of the QM. $\endgroup$ – Sofia Dec 20 '14 at 19:28
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    $\begingroup$ @CuriousOne: this is not a talk that can be effective through comments. It is a very profound talk. If you would like to open a chat room, I would be glad to chat with you on this. The most brilliant minds spent years after years on this issue. My teacher (and friend) told me once that he doubts whether human logic is sufficient for understanding the nature. Just to tell you some part from this difficulty, even accepting non-locality we don't solve the problem of the entanglements. Bohm's interpretation is non-local. I work on proving it as wrong. $\endgroup$ – Sofia Dec 21 '14 at 10:09

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