Some ideas are:
- You branch off into another timeline and your actions make no difference to the previous timeline
- You’ve already taken said actions but just didn’t know about it so nothing changes
- Actions taken can have an effect (so you could suddenly erase yourself if you killed your parents)
- Only “nexus” or fixed events really matter, the timeline will sort itself out for minor changes
- something else entirely
But what if: https://en.wikipedia.org/wiki/Square_triangular_number
Slightly more seriously (but only slightly), what if what we see as Heisenberg uncertainty and probabilistic wave/particle weirdness is actually the result of multiple overlaid timelines caused explicitly by time travel, and if time travel wasn’t possible, the universe wouldn’t have those properties?