My theory of time travel

In a post about the externalities of time travel, Tyler Cowen writes,

I believe no one understands the underlying science much at all. But there is some chance that the old science fiction movies are correct and that by time-traveling you alter the course of history, thereby obliterating the universe we used to have. I’ll count that as a net negative, while noting there is some chance we end up with a better universe.

I don’t understand the underlying science (is there any?) at all, but that will not stop me from opining on this subject.

I’m going to assume that time travel happens within only one universe, not across quasi-identical universes like in a certain Michael Crichton novel. The old science fiction time travel trope is that someone goes back in time and kills, say, their great grandfather, creating an intertemporal paradox. My theory is that the universe operates in a kind of reflective equilibrium that makes these paradoxes impossible. Let’s suppose that you time traveled and caused one of these paradoxes. The paradox would obliterate that state of the universe, not in the sense that that state of the universe is destroyed, but in the sense that it is never allowed to come into being. It is not, as Tyler claims, a state “we used to have,” even if we could come up with a non-time-biased way of saying that (note that it is in the past tense).

Intertemporal paradoxes cannot exist, just as interspatial paradoxes cannot exist (they can’t exist, right?). Therefore, our ability to move about through time is going to be limited. How limited? For the answer to that, we must turn to Bryan Caplan’s testicle-jiggling theory of causation. If anything even slightly different happened in the distant past from what actually did happen, then somewhere along the line, one of our male ancestors would have scratched himself or changed his gait and, due to the multitude of sperm from which we emerged, someone else would have been born in our place.

Since virtually any move backward in time would cause a paradox, I conclude that backwards time travel is not possible. The imperative to avoid paradoxes is what makes time’s arrow go in only one direction. To get back to Tyler’s original question—should we tax or subsidize research into time travel—the answer is clear: if backwards time travel is impossible, we should tax it so that no one wastes valuable resources exploring a dead end.

Forward time travel is trickier, but I will note that I have a mental sketch of a novel in which a character deposits money in a bank and travels forward several hundred years to collect it with massive interest. There is a wrinkle in the plan, of course.