How is the many worlds interpretation (MWI) of QM consistent with the probabilistic interpretation of the wave function (given by Born's interpretation)? For example, say a particle has a 90% chance of ending up in state 1 after a measurement, and a 10% chance of ending up in state 2. How does our consciousness "know" to end up in the universe where the particle is in state 1 much more often than the universe where it's in state 2? I mean, surely it should be completely random which world our experience happens to fall into, meaning that the probabilities should have been 50-50, corresponding to the two possible worlds?
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1$\begingroup$ How is this a question about physics? $\endgroup$– Prof. LegolasovMay 22, 2021 at 18:28
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1$\begingroup$ Unpopular opinion but MWI is magic, not science. So youre gonna have contradictions. $\endgroup$– Señor OMay 22, 2021 at 19:28
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2 Answers
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Since my comment was a bit long, I'll post this as an answer.
Your point here is commonly brought up as a critique of MWI. If the wavefunction/quantum state is all that is needed to describe reality, then there must be a derivation of the Born rule from the dynamics of QM alone. No consensus has been reached as to whether the Born rule has been derived. This issue has sometimes been dubbed as the incoherence problem. See this page and this page for more info.
Also, you may be interested in Sean Carroll's idea of self-locating uncertainty, and David Deutsch's decision theory approach. These two approaches attempt to answer your question, so you should look into them. And again, not everyone agrees that these approaches are satisfactory.
answered May 22, 2021 at 18:59
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$\begingroup$ Wow, I actually didn't know that there was so much discussion about this issue. Anyways, thanks for the recommendations. $\endgroup$– User3141May 22, 2021 at 21:56
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1$\begingroup$ There is also Zurek’s idea of einvariance, which is less closely tied to MWI but is along the same lines. (For the record, I am an MWI supporter but don’t buy the einvariance argument.) $\endgroup$ Jun 22, 2021 at 3:12
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1$\begingroup$ I also want to comment on this: “…then there must be a derivation of the Born rule from the dynamics of QM alone.” Many people believe this, and obviously everyone would like to see this in an “ultimate” theory. But it is an unfair burden to place this on MWI but not on other interpretations. In Copenhagen, Born’s rule is just an extra axiom. For the time being, it could also be so in MWI. The only strong mathematical motivation for it in both cases is Gleason‘s theorem, although it is unsatisfying from the perspective of physics. $\endgroup$ Jun 22, 2021 at 3:17
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One problem presented by your question is that there is not a single many worlds interpretation, but a variety, some of which are more open to criticism than others.
If you consider an extreme interpretation which assumes that there is a continual branching in which everything in every universe is repeatedly replicated in yet more universes, our consciousness included, then there will be instances of you in universes in which only the more improbable sequences of events have ever happened. Physicists conducting experiments in those branches must find very puzzling results.
The other problem is that the interpretations are just that- interpretations, and there are at present no decisive physical tests of their validity.
answered May 22, 2021 at 19:22
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1$\begingroup$ "Physicists conducting experiments in those branches must find very puzzling results." Probably not - they will just do what experimental physicists do in our universe - discard the results and repeat until they get answers which make sense. $\endgroup$– isometryMay 22, 2021 at 21:19
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$\begingroup$ They cannot, if they exist in the branch in which regardless of how many times they repeat the experiment, they always get the least likely result! $\endgroup$ May 22, 2021 at 21:43
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$\begingroup$ @MarcoOcram Isn't this related to the quantum immortality idea? I suppose one way of testing the interpretation would be to voluntarily attempt to kill yourself, and seeing that you survive every time. Not sure if that's something you'd wish to do though, or if anyone would believe you even if it succeeded :) $\endgroup$– User3141May 22, 2021 at 22:00
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$\begingroup$ It's all a bit hypothetical, but perhaps what happens is that every time you branch there are ever increasing instances of your consciousness. The one you are aware of as you read this is just one of an endless number of copies. You might therefore be one of the unlucky copies that does die! $\endgroup$ May 22, 2021 at 22:08
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1$\begingroup$ Excuse my flippancy. You might have detected that I have a distaste for the more extreme versions of MWI. $\endgroup$ May 23, 2021 at 6:48