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
Time travel wouldn’t be by jumps but by contionous change in perpendicular* time dimension.
So earth wouldn’t escape from your feet as you would move with it, just like you are doing right now with just one dimension.
*time travel would be imposible if you can move only in one direction. ~~Then the 2nd time dimension would need to be under some funky angle (3/4π>α>1/2π and α≠π and α≠0) ~~ i am wrong