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.
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.