Is it possible? Well, I don’t think it’s logically impossible at all.
Objectors to time travel point out that going back in time would change the course of the present which would change the traveler herself. If she went back, for example, and accidentally killed her infant self, what would happen to the traveler? Similarly for any alteration induced by the traveler’s presence, given the multiplying effects of chaos.
Seems this objection trades on a mistaken view of time and of time travel. We usually think that time is on a kind of line
from A to B and thence to the future. And time travel is viewed as some person, say, Jay, removing himself from the line and going back to a previous position on the line. So infant Jay at time A grows in time to point B and then decides to time-travel by going back to point A.
But that’s to assume that time A is a kind of permanent place to visit, and to assume that Jay can get out of time and go back to that same place. Both are mistaken. When Jay decides to time travel, Jay is not going back on a line, but, with respect to his personal “timeline”, is going “forward” or continuing in his own time of his life. In this progress of his life, he encounters himself as an infant. He manages to kill that infant. In the future of Jay-the-traveler there will be no youthful Jay, just Jay-the-traveler. But there’s no reason to believe that Jay-the-traveler can’t continue himself. In fact, you’d expect he would. Why wouldn’t he? He’s already there, and time and causality only move forward.
Baby J>—–Grown J>——Grown J kills baby J>——Grown J continues
By point C/A, it’s too late for baby Jay’s death to affect grown Jay causally. He’s already there and he’s moving forward in one and only one world.
The going-back view of time traveling implies a kind of dual time with parallel worlds that are somehow related causally. If you go back and kill your infant self, then, cause-by-effect in time you could never have lived to travel and kill your infant self; hence time travel to the past could be argued to be logically impossible (on the going-back view).
That’s actually a reductio ad absurdum. Suppose time travel to the past were in fact possible. The above objection would say that the possible is logically impossible. That is itself a contradiction. So objectors conclude from logic that time travel is impossible regardless of the facts. That’s for logic to determine facts that are independent of logic.
The reductio misses because there are two premises, not just the one premise “time travel to the past is possible.” The other premise that the reductio can rule out is “there is a causal chain from the reprised time to the new present.” And there’s no reason to believe that.
If time travel to the past is impossible, logic isn’t the reason. The reason, more likely, is that the past doesn’t exist at all. It’s a fiction of memory. There’s no place “the past” that perdures. Time is just change and change is just the things that were that aren’t anymore. Time, as it were, moves only forward, just as motion is always forward, whichever direction it is going. Walking back home at night is moving forward, just in a different direction from the direction you took in the morning. Flipping backward on a video is moving forward, even if it looks funny. The only remnant of the past is its causal consequences for the present and future. Otherwise it isn’t. But if we could come to a place of our past, there would be no contradiction in influencing it (to use Horwich’s important distinction between influencing the past and changing the past), partly because influencing it would only influence the one world in which we are, and partly since there’s no ‘real’ past there to change anyway. We’d just be moving forward with a difference like the world of the movie Groundhog Day. But we’ll never get there, because it’s not there.