1) Each photon is actually spread out in configuration space—I’ll talk about this later—so an infinitesimal error in timing only creates an infinitesimal probability of both detectors going off, rather than a discontinuous jump.
2) Physicists have gotten good at doing things with bloody precise timing, so they can run experiments like this.
Jordan, the three answers to your question are:
1) Each photon is actually spread out in configuration space—I’ll talk about this later—so an infinitesimal error in timing only creates an infinitesimal probability of both detectors going off, rather than a discontinuous jump.
2) Physicists have gotten good at doing things with bloody precise timing, so they can run experiments like this.
3) I didn’t actually perform the experiment.