I am currently reading Feynman's popular book on QED "the strange theory of light and matter". I know classical optics quite well, know about Fresnel, Brewster angle and the like.
I also am now used to the concept that QED sums up all the probability amplitudes of all possible propagation paths. And the little clocks are basically the complex phases of the photons. The higher the photon's frequency, the faster the clock ticks.
However I am wondering: if I want to calculate the propagation of light from point A to B which are let's say 1m apart. I now have to calculate all contributions of all possible paths. Even from A to Alpha Centauri back to B. This sounds pretty crazy. But is it correct?
How does reality determine this in a finite amount of time? Or is this simply the model of reality—it "just works" this way?
Also: for practical computations—would I limit the summing to a certain length of paths, if I were to numerically approximate a solution?