Conversations seem to occur on several levels simultaneously. There's a level of literal truth. There are also multiple dimensions of politics. (What I call "micro" and "macro," in a way analogous to the application to economics.) There's even a meta-level that consists of just trying to overwhelm people with verbiage.

Well, I note in a comment somewhere, that it would have to be a version of Amelia who was rather ditsy about time.

It doesn't preclude scenario B. It just makes it unlikely.

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.

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.

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.

I am going to have to accuse you of making a grave Mind Projection

Apparently Black Holes preserve information. There are other connections to physics and information theory, Such as the theoretical computers that can use ever smaller quantities of energy, so long as all of their operations are reversible. Given that, it doesn't seem unreasonable that there would be an information theoretic component to the rules of magic. My formulation doesn't require a human mind. If I talk about minds or arbiters, or use language suggesting that then that's just lazy writing on my part.

I only saw the 91-92 thread and didn't think it fit there. Other threads that I found were marked as superseded.

All information is probabilistic, Bayesian.

Is there a rigorous argument for this, or is this just a very powerful way of modeling the world?

The problem here is that even if Scenario A and Scenario B are indistinguishable, Amelia's words still constitute Bayesian evidence on which Dumbledore can update his beliefs.

In my formulation, that's "side information." Really, my gedankenexperiment doesn't work unless Amelia Bones happens to be very ditzy concerning time.

I'm inclined to believe that whatever intelligence is behind capital-T Time is enforcing an intuitive definition of information, in the same way that brooms work off of Aristotelian mechanics.

So then, this is a limitation in the "interface" that the Atlantean engine is following. I think my hypothesis is testable.

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?