I read an explanation somewhere that the way these time loops work has to do with branching timelines or something like that. Like, basically, any choice you make starts a new universe where you made one choice differently, and since the situations in the time loops are so dangerous, all the universes will end in death except the one where you made the right choice. So you save yourself because all the other yous are dead. Huh...that made more sense before I tried to explain it. I wish I remembered where I read the original theory, which was much more coherent....
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