Here is the most notorious "that can't be legal" result in physics. A photon is split into an entangled pair: the signal flies through a double slit to a screen; its idler twin flies off to a detector where you decide — possibly after the signal already hit the screen — whether to record which slit it went through or to erase that knowledge. When you erase, an interference pattern appears. Choosing now seems to reach back in time and change what the photon did. Run it and watch — then watch the catch that dissolves the paradox.