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In Frauchiger-Renner's paper, the authors propose a thought experiment which suggests that taking QM together with certain natural assumptions, one arrives at a contradiction. They go on to say that Many Worlds Interpretation throws out the assumption:

"I am certain $x =\xi$ at time $t$" implies "I deny $x \neq \xi$ at time $t$"

It is true that getting rid of the above assumption does permit the results of the experiment, but that assumption seems true by definition of equality. Further, it is my understanding of many worlds that in a given "branch", things are consistent. That is in any given "world", the assumption above holds, while in general, or universally, every possible outcome happens. Thus I don't think MWI discards the above assumption in a way that can explain the experiment. Where I am confused?

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  • $\begingroup$ Does the Many World theory actually try to argue why each "branch" has a consistent story? I am not sure. Actually, the argument of Frauchiger and Renner is problematic, as explained very well in this paper: arxiv.org/abs/1809.08070 $\endgroup$ – Luke Dec 7 '18 at 11:45
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    $\begingroup$ I just came across the video of Renner's more recent talk where he more or less says what you are saying and also presents a simplified version of the experiment: video.ethz.ch/speakers/its/2018/autumn/colloquium.html. I also updated my answer with it. $\endgroup$ – Daniel Mahler Feb 2 at 1:41
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Further, it is my understanding of many worlds that in a given "branch", things are consistent. That is in any given "world", the assumption above holds, while in general, or universally, every possible outcome happens. Thus I don't think MWI discards the above assumption in a way that can explain the experiment.

I believe you are correct. Renner also said as much in a recent talk. Here is the recording. He also presents a simplified version of the experiment using computers to downplay any consciousness woo woo.

I am currently writing up an explanation of a simplified version of Frauchiger & Renner's thought experiment that also shows that their principle S, the one you quote, is irrelevant. If a theory agrees with standard QM it rejects their principle C (Consistency), but that is nowhere nearly as serious as it sounds. The failure of their Consistency principle is a consequence of the necessity of negative probabilities in Wigner functions.

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