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
If it actually existed, then obviously I would subscribe to whatever theory most accurately described how it worked. That’s science.
If you’re asking which theory I would predict is most likely, knowing only that time travel was possible as a starting point, then there are only two that I’m aware of that are logically consistent. Either:
Single fixed timeline, whereby if you go back in time then whatever you do there was already a part of history from the start. You won’t be able to “change” anything because you were always there. This is the approach described by the Novikov self-consistency principle.
Multiple worlds, in which if you go back in time you just end up following a different “branch” of history forward from there.
Any of the models that let you “change your own history” are logically inconsistent and therefore utterly impossible. They just can’t exist, like a square triangle or 1=2. They may be fine for entertaining movie plots but don’t take them seriously.
I just imagine if life is a simulation and everytime someone travel back a new branch created but then coming back to present timeline you have to fix all the merge conflicts.
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?