Billiard-Ball Time Loop: A Self-Consistent Paradox

This simulator builds the classic Polchinski billiard-ball time-travel paradox as a real elastic-collision problem and solves it numerically. A ball heading for one mouth of a wormhole is struck — just before it arrives — by a second ball that is really its own future self, already returned from an earlier trip through the wormhole. Instead of picking a trajectory by hand, the solver runs a damped fixed-point iteration on the struck-ball's velocity until the loop closes: the velocity the ball carries into the wormhole, after being deflected by the collision, must be exactly the velocity that produced the deflection in the first place. Adjust the impact geometry (δ), the wormhole's relative twist (ψ) and launch speed to watch the solver converge on a different self-consistent trajectory each time — a live demonstration that consistent time loops are heavily constrained, not automatically contradictory.