[HPMOR][Possible Spoilers] Gedankenexperiment: Time Turner Meta-Informational Relativity

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.

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.

Given no other information to strictly verify, any supposed time-traveled conversation is indistinguishable from someone not having time-traveled at all and making the information up. The true rule must depend on the actual truth of information acquired, and the actual time such information came from. Otherwise, the rule is inconsistent. It also looks at whether your use of time travel actually involves conveying the information you gained; whether such information is actually transferred to the past, not merely whether it could be. Knowing that Amelia Bones has some information about 4 hours in the future will only restrict your time travel if you would transmit that information to the past - if you would act significantly differently knowing that than you would have otherwise. If you act the same either way, then you are not conveying information.

In short, the rule is that you cannot convey information more than 6 hours into the information's relative past, but that does not necessarily mean that you cannot go to a forbidden part of the past after learning it. It merely means that you cannot change your mind about doing so after learning it. Worth noting: if you plan on going to the past, and then receive some information from 6 hours in the future that changes your mind, you have conveyed information to the past. I'm not sure how that is handled, other than that the laws of the universe are structured as to never allow it to happen.

All information is probabilistic, Bayesian. Two scenarios, A & B, may have identical effects, but if the relevant probability ratios are different, then observing this effect can still give you information. If Amelia Bones tells Dumbledore that she's come from six hours in the future, then his objective Bayesian probability (given the information that he possesses) that she'll survive the next six hours goes up, even though it doesn't rise to 100%. And all information is like this; objective Bayesian probability is never quite 100%.

Consider Scenario C, in which Amelia Bones travels back in time, does not have additional information about it, and tells Dumbledore. This is distinguishable from Scenarios A and B, and this possibility is eliminated. It still conveys some information. All you've shown is that Dumbledore did not have all the information. There are still two possible scenarios. This would be true if he was told about everything except the path of a single neutrino. If that's all that's necessary to keep time turners from breaking, how could they have possibly figured out they break?

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

Physics, to be believable should never talk about "information." I know from study that most of modern physics have this property, and I know EY knows from the QM sequence and the Epistemology 101 sequence.

Special and General Relativity might talk about "observers" and "observables," but these are very distinct from the "information" discussed in Bayesian Stats.

Bayesian stats (i.e. non-omniscient Agents) is the only place you are ever allowed to talk about "information," (Thermodynamics is applying agents to physics).

An observable in relativity is usually taken to mean something you can slap a unit on and call it a day. Mass of bodies, relative velocities, energy, etc.

The thing to note here, is that, from the informational point of view of Dumbledore, provided he doesn't have some additional side-channel information, Scenario A and Scenario B are indistinguishable.

For Dumbledore, sure. Are the scenarios really indistinguishable for the whatever-it-is that keeps histories consistent and, presumably, enforces the six-hour rule? If not, Dumbledore has an obvious means of distinguishing between the scenarios: Attempt to travel six hours into the past, in steps of one hour, precommitting to telling someone what Amelia told him. In scenario B, the third hop will fail; in A, only the sixth.

That only really works if Bones is perfectly unreliable, though - if she's more likely to come back under certain circumstances, there's information.

At a guess, I would say data below a certain (low) threshold is allowed, and time travellers don't try to deduce such things in case they pass said threshold.

For that matter, Amelia could be wild-guessing when she tells you about something that will happen six hours from now. It doesn't make sense that if she came back six hours and tells you something it would be any different than if she came back one hour and told you the same thing, or said the same thing without any time travel involved.

Downvoted for not keeping MOR stuff in the MOR threads.