The grandfather paradox is well-known and has a good dramatic hook, but it's a rather ineffective controlled experiment. The Polchinski Paradox gives us a time travel paradox based purely on laws of motion, without any of that tiresome free will. Plus, it involves billiards.
Everyone knows the grandfather paradox. You win a trip to go back in time and, while you're there, you accidentally kill your grandfather. Or maybe you intentionally kill him. I don't judge you. For all I know he was a jerk. The point is, he's dead before he had a chance to have kids, and so you can't exist. But if you don't exist, you can't have gone back in time to murder him. How can this paradox be resolved?
The answer is — not by investigating the matter like that! That's a sloppy research method. Joseph Polchinski a physicist, came up with a better way of thinking about the paradox. First, instead of going back in time, find a looped wormhole that goes back in time. Second, shoot billiard balls through that wormhole to see at what angle they come out. Third, calculate a shot that is timed and angled so that, as the new ball goes toward the wormhole, the "old" one that's been sent back in time flies out and knocks the new one off course so that it never enters the wormhole in the first place. Suddenly the myriad complexities of time travel and free will can be substituted with some classical mechanics.
Or not. Solutions to Polchinski's paradox, otherwise known as the billiard ball paradox, have been found. An infinite number of them. Students of Polchinski have found ways for the ball to make its way through the wormhole and hit its younger self enough to alter its course, but not enough to knock it away from the hole. So it's possible that paradoxes simply can't happen in this world. Or maybe they just can't happen in the world of billiards.