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?

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    $\begingroup$ The "sum over all possible paths" is really the natural language version of what the path integral does. Asking what "reality" computes is not really a sensible question. Asking how we compute this in practice is too broad since that is a large part of what quantum field theory is about. $\endgroup$ – ACuriousMind Aug 21 '15 at 20:39
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    $\begingroup$ I'm under the impression that causality is still respected, meaning there is no contribution from point A to points outside of A's lightcone. However I don't recall seeing a proof of this. $\endgroup$ – adipy Aug 21 '15 at 20:43
  • $\begingroup$ It would be nice if either of you could formulate an answer. I think @ACuriousMind's answer helps with both the last question of me and also with the model aspect, and adipy's comment is also interesting, since it deals with the Alpha Centauri part. Maybe someone else with some kind of proof or reference could weigh in on this. $\endgroup$ – Arne Aug 22 '15 at 17:34

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