I read "The Quantum Universe (Cox & Forshaw)" that a particle can be measured at a given position at a given time, and in another galaxy one second later. The probability of such event may be small but still non zero. As he explains, this would be due to the fact that the wave function propagate in the universe instantly, as opposed to a water wave that propagate at a finite speed.
This is striking me because from what I remember from quantum physics, the wave function does propagate at a finite speed. So if a particle is detected somewhere at time $t$, the wave function collapse and starts spreading at time $t$.
Am I missing something here?