I think time travel to the past would be impossible given the grandfather paradox. If you’d traveled back in time you’d have to in essence create your own pocket dimension or a whole new timeline to exist in by doing so.

Then there’s the whole notion of all events in your timeline leading up to the point where you travel backward, so once you end up in the past, nothing would change because everything had to have happened to lead you to traveling backward to begin with.

If you cause a timeline to split by traveling backward so that one branch can accommodate you suddenly being there, what would happen to the doomed branch?