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All attempts at deriving the born rule in MWI have been shown to be circular in some way. So if it turns out that MWI cannot derive the born rule without some form of circularity, does that mean that the MWI is wrong?

Qmechanic
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  • If euclidean geometry cannot prove the fundamental theorem of calculus, does that mean that euclidean geometry is wrong? – WillO Jul 18 '17 at 18:04
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    @WillO I don't know. What do you think? –  Jul 18 '17 at 18:05
  • It was a rhetorical question, to which I'd have thought the answer was obvious. Let me try again: If general relativity cannot predict the stock market, does that mean that general relativity is wrong? – WillO Jul 18 '17 at 18:06
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    @WillO I'm not sure if the same arguement applies in this case since relativity and the stock market are two totally different subjects. QM is a theory of probability given by the born rule. So if the MWI is right then shouldn't it be able to derive it? –  Jul 18 '17 at 18:10
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    Related: https://physics.stackexchange.com/q/195703/2451 and links therein. – Qmechanic Jul 18 '17 at 18:12
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    @N.V. Better analogy would be - The Copenhagen interpretation can't derive Born rule, does that mean that the Copenhagen interpretation is wrong? – OON Jul 18 '17 at 18:42
  • @ONN Is that even an analogy? I think the point of the analogy was to take it out of the context of QM. Your analogy also uses the Born rule; when the original example also uses it. I get what you're saying; for clarity sake your statement might be better; but it's not really a good analogy. Perhaps they thought bringing it into the math domain could help see their point. Anyways; there's my pedantic rant on quality of analogies. – JMac Jul 18 '17 at 20:03
  • Why the downvotes on this question? I don't necessarily agree with some of the facts that the OP seems to be assuming, but I don't think that's a reason to downvote. –  Jul 23 '17 at 00:28

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A pretty standard presentation of the principles of quantum mechanics is as follows. MWI says

  1. We have a Hilbert space with
  2. unitary evolution of the wavefunction.

The Copenhagen interpretation (CI) adds additional postulates saying that

  1. measurements produce c numbers,
  2. probabilities are given by the Born rule, and
  3. measurement collapses the wavefunction.

All attempts at deriving the born rule in MWI have been shown to be circular in some way.

This just says that postulate 4 is independent of postulates 1-2. Why is that a problem? Actually, CI doesn't "derive" the Born rule, it just states it as a postulate.

So if it turns out that MWI cannot derive the born rule without some form of circularity, does that mean that the MWI is wrong?

Since the postulates of MWI are a subset of the postulates of CI, the only way that MWI can be wrong is if CI is wrong as well.

Note that if you want CI and you take some other rule than the Born rule, you will probably get nonconservation of probability. You can make this more formal using Gleason's theorem. Whether this counts as "deriving" the Born rule is a matter of opinion or preference.