This is not true, you are just making a false claim! All of a sudden you have forgotten about the randomness of QED’s paths! The energized electron, at the mirror surface, emits its photon in vast different directions, with varying possibilities. QED’s paths cover vast area, how does QED conveniently ignore all other paths, and just sticks with the optic path!? Isn’t that convenient!?The QED formulation shows that the shortest path is the one that has the high probabilities of detection for the standard setup. That doesn't go into the calculation. It comes out of them.
I am not cheating.
The optic path is selected out *because* it is the shortest path and thereby doesn't have all nearby paths cancel out. All other paths are not shortest so do get canceled out.
In our experiment for detector at Y1 location, the produced path by QED all-path calculation it is an optic path, and it has the shortest path from the source to Y1 location. Although this optic path has different direction and different angle of incident, but QED all-path does not consider this information any way. This optic path from source to Y1 location is different from the other optic path that it is resulted by considering the direction and the angle of incident of the incoming photon. Since you are confused, then you keep making false statements, and false claims!
It seems Donald Trump approach it also has infected our scientists.