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stcredzero comments on [HPMOR][Possible Spoilers] Gedankenexperiment: Time Turner Meta-Informational Relativity - Less Wrong
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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.
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.
The most obvious instance of Information Theory/Bayesian Statisics overlapping physics is Thermodynamics and Statistical Mechanics, which both deal with the notion of Entropy (all physical entropy is Shannon Entropy). The Information Problem of black holes is a question of their entropic behaviour, and really, black holes are sort of a grey area of our map of reality.
Your formulation exactly hinges on information, not observables. I read it twice. It is much more likely that the 6 hours is a conceptual limitation and that the HPMOR-verse is consistent if not causal, either by recomputation or being the solution to an equation, and just has time travel built in.
Conceptual limitations are apparent in other branches of magic, and I would hazard a guess that timetravel requires energy correlating to the amount of time jumped back. This would put a practical limit on it too.