We investigate whether the collapse of the quantum state of a single photon split between two space-like separated places takes a nonvanishing time. We realize this by using a source of heralded single photons, then splitting the resulting single photon state and letting it propagate over distances much larger than the experimental time resolution times the speed of light c . We find no additional delay within our accuracy and set a lower limit for the speed of collapse of the quantum state to 1550 c .