> So, is choosing the path that takes the shortest time like a standing wave?

Note that photons don't take the shortest path; they take a variationally stationary path (not necessarily the shortest one). My suspicion is that this is because all the possible photon states are coherent along and immediately nearby that path, whereas if the path is not variationally stationary then it interferes with nearby paths. I've done very little variationally physics, however, so take this with a grain of salt.