> a billiard ball entering a wormhole that leads to a closed time-like curve must always meet its older self coming out of the wormhole. What’s more, the resulting collision always prevents the ball entering the wormhole in the first place. In other words, the billiard ball would simply bounce off the entrance to a closed time-like curve.
I thought what Kip Thorne proved is that you can always find an "exit" angle such that the ball that travels back in time glances its previous self, knocking it into the wormhole at an angle that will produce that exit angle. The contradiction only happens if you assume the ball goes straight into the wormhole and then calculate that it will glance itself and not go straight into the wormhole. But there is always a consistent solution as well. Though as I recall there are or can be multiple (infinitely many?) solutions and no clear way to favor one over another.
I thought what Kip Thorne proved is that you can always find an "exit" angle such that the ball that travels back in time glances its previous self, knocking it into the wormhole at an angle that will produce that exit angle. The contradiction only happens if you assume the ball goes straight into the wormhole and then calculate that it will glance itself and not go straight into the wormhole. But there is always a consistent solution as well. Though as I recall there are or can be multiple (infinitely many?) solutions and no clear way to favor one over another.