Time-travel is a common plot element in science fiction. It's one rife with paradoxes. A few very notable examples can be found in the Terminator franchise. In the original movie, Kyle Reese goes back in time to stop The Terminator, sent from the future by the evil machines, from killing Sarah Connor, so that she can give birth to John Connor, who will lead a successful human resistance against the machines. The paradox arises when we learn that Kyle Reese is also John Connor's father -- but then how did John Connor get there to lead the resistance in the first place?!
In the second movie, The Terminator is now a good guy (Arnold was too marketable a star at that point to make him the enemy), who thwarts an attempt by a different time-traveling terminator to kill a now teenage John Connor. Also in this movie, The Terminator destroys a chip that paved the way for the technological advances leading to the takeover by the machines (which was left by behind by the original bad Terminator). But in so doing, wouldn't he have eliminated the very technology that created him, and thus wouldn't he disappear instantly after having done that? (In the movie, he does not disappear, but instead dramatically destroys himself immediately after destroying the chip -- or maybe he has Sarah destroy him, because he's programmed not to destroy himself; either way, he gets melted in some sort of industrial lava).
These paradoxes are things I've wrestled with before, and I came up with a way to think about time and reality that will resolve them. As always, these are probably not original ideas. I'm sure if I Googled it I could find a dozen websites laying out these ideas better than I could. But I'm not going to Google it. I thought of it on my own, so I'm going to write it up on my own. Also, I'm certainly not claiming this is how our physical universe actually works. I'm just saying this is how movies could resolve their time-travel paradoxes -- and, who knows, maybe there are some that do this that I've never seen.
The gist of the idea is to think of time as comprised of discrete moments and the universe being comprised of discrete particles. At any given moment t, we are in some state of reality based on the location (and other physical properties) of all the particles in the universe. At the next moment t+1, we move to a new state in which at least one particle has changed it's location. However, in addition to "reality", the state we are actually in, we also have billions and billions of "potential realities" that could have happened if a particle did something different than it actually did. So we have one potential reality for possible every movement (within the laws of physics) of every particle in the universe.
For example, in the diagram, our reality is, say, blue, but if at least one particle had done something different, then we might have been on the red track or the green track or one of the orange tracks or one of the googols of other tracks not pictured. Those other tracks don't actually exist, but they could have existed, if a particle (or particles) had done something different.
What determines which state is the next part reality? How the particles know where to go next? How we actually travel through time? Good question. Maybe it's random chance (God does play dice); maybe it's a divine hand; or, most intriguing to me, maybe we determine it -- maybe that's what free will is. Our collective self-governance determines the next state of reality. For the sake of resolving movie paradoxes, however, it doesn't really matter.
Thinking of time and the universe in this way, can instantly eliminate almost all time-travel paradoxes. For example, in T2, once the terminators go back in time, their presence changes the state of the universe at that moment, thus putting us in a new reality (because some particles are in a different place). So, say, the red track is now reality, and the blue track -- the one in which the machines take over -- is now a potential reality. The goal now for the good guys is to make sure the machines also don't take over in the red reality. (That is, in actual reality, which would be very close to the old (blue) reality since only a little bit has change.) The Terminator succeeds by destroying the bad terminator (John lives), and the chip, making the human-enslaving technology now nonexistent in the new (red) reality. And since he destroyed it in the red reality, not in the blue reality, in which he was created (which is now only a potential reality), he's not preventing his own existence. He was made in the blue reality and "jumped" backwards to the red reality, where he lives, until he destroys himself a few minutes later. Paradox resolved!
(Although, one thing that bothers me about this is that it seems like it can create energy out of nothing. Every time a time-traveler comes back to a certain moment, they are new energy in reality that wasn't there before. I think you can resolve this, by saying that time travel works by swapping energy from the two states. So if somebody goes from state S021 to state S0 in the diagram above, an equal amount of energy must be swapped from S0 to S021, somehow. That's what time travel is: an exchange of energy between moment-states.)
Resolving how Kyle Reese can be John Connor's father is a bit more difficult, but it still can be done. Here's how. Say, Kyle was born in the blue reality, and there is no John Connor. For some reason, he goes back in time, makes sweet love to Sarah Connor, and she births John Connor, and all of this happens in the red reality. Then, for other unknown reasons, Kyle goes forward into the future of the red reality (theoretically possible for real!). He ends up in the middle of the robot apocalypse, but his own son, who is now his age, successfully leads the human rebellion. So the machines send The Terminator back in time to kill Sarah, and so Kyle goes back in time to stop him and knock-up Sarah again, and all this happens in, say, the green reality -- The Terminator is this story. There we go! Air-tight! That is, until I think of a logical flaw in bed, unable to sleep, at 2 am tomorrow morning.
Until next time...