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
I think it would be like the first one, except instead of you going back to that time, you would be making a copy of that time to traverse to from your time, similar to how moving a file between devices causes it to be copied.
A relevant quote from a physicist is “some will say it’s easier to predict the future than the past, since a single effect can have multiple possible causes but a single cause can only have one possible effect.”