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.
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.