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kilobug comments on Harry Potter and the Methods of Rationality discussion thread, February 2015, chapter 109 - Less Wrong
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Time travel isn't fully computable, but that doesn't mean it can't be approximated, that you can't make hacks giving the impression of time travel to people inside the simulation.
It might even be possible that attempts to abuse time travel (like the one done by Harry at the beginning when he tried to factorize primes using the Time-Turner) raise an alert in the simulation, freezes the simulation until an operator manually inputs an acceptable solution ("don't mess with time" being the solution hand-crafted by the operator).
Depends on what kind of time travel and what kind of universe. Heck, even classical newtonian real-valued physics is not computable (but is computable to arbitrary precision). If the information content of the universe is finite (like, it is a grid of finite many cells, each of them could be in only finite many states, and time is discrete as well), then time travel is computable - you just have to store the information for the past 6 hours and brute-force consistent stable loops.