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stcredzero comments on [HPMOR][Possible Spoilers] Gedankenexperiment: Time Turner Meta-Informational Relativity - Less Wrong
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It's very possible for to distinguish the two situations. The same probabilistic mechanism that determines the arrow of time precludes scenario B. Also, it's not really that Dumbledore is actually doing the distinction. It's more if he could do it.
It doesn't preclude scenario B. It just makes it unlikely. The same could be said about the original scenario A. It's possible that Amelia Bones was mistaken about when she came back, but it's unlikely. The probability is more extreme, but the information is still there.
I have a "Many Worlds/QM" style interpretation of time turner mechanics. Basically, all of the possible interpretations of the information+metainformation you have transmitted via time turner "exists" or is in a kind of superposition, until receiving information precludes them. Making Scenario B overwhelmingly unlikely is precluding it.
How unlikely does it need to be to be precluded? The given Scenario A is pretty unlikely.
Well, I note in a comment somewhere, that it would have to be a version of Amelia who was rather ditsy about time.