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stcredzero comments on [HPMOR][Possible Spoilers] Gedankenexperiment: Time Turner Meta-Informational Relativity - Less Wrong
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I don't think the path of a single neutrino could do it. Answer this, from the informational POV of Dumbledore's location in space-time, is path P of that neutrino any less consistent with Scenario A or Scenario B?
I don't think you quite get what I'm saying.
You have given two scenarios that Dumbledore cannot distinguish. This proves that he has incomplete information. It does not prove that he has no infomation. That would require that he be unable to distinguish any two scenarios.
Imagine that Amelia Bones tells Dumbledore everything that happened up until her departure from the future, except the path of some neutrino. Furthermore, thanks to Dubledore's legillimancy, he knows she's telling the truth. Can he distinguish between Scenario C, what actually happened, and Scenario C', which is just like C, except that the neutrino went left instead of right?
Is the inability to distinguish C and C' enough for Dumbledore to be able to go back another six hours? If not, how is distinguishing C and C' different from distinguishing A and B?
No, because if she was able to provide that much information as a conscious communication, she will have provided enough information to have affixed her departure at a specific time.
In any case, there's probably some reason that would make it impossible for her to convey that much information inside 6 hours, anyhow.
How about this:
Scenario A: Amelia Bones comes back from six hours in the future and provides large amounts of evidence of this fact, and of what happens.
Scenario B: Due to quantum randomness, a large number of particles happen to jump into the spot to create a clone of Amelia Bones who believes she is from the future and carries evidence of this.
It is, again, impossible for Dumbledore to tell which of these situations happens. Yet the time turner does not work.
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.