Why light diffracts and was directed to QED by Feynman

[AlanPartr]

A while ago I made a post asking why light diffracts and was directed to QED by Feynman. I have now read the book (or the relevant part at least) and it explains diffraction by the number of possible routes of photons through an aperture as being reduced when the is gap made smaller, and therefore the probability is equalled out less, meaning there is a more substantial chance of a photon arriving at a point other than directly through the gap, i.e. diffraction is observed. I understand that, but Feynman uses the simplification in the book of there being a finite number of paths, but in reality can’t a photon take an infinite number of routes, so regardless of the size of the aperture the paths should always be equalled out shouldn’t they?

 

[Chi Meson]

IF there is no barrier at all (no slits, no gaps to consider) then there are more possible routes for the light to take yet the probability of light taking anything but the "least-time" path approaches zero.

Technically you could say that no matter what the configuration, there are an infinite number of paths (since one point over to the left or to the right is still another path), but we can't add an infinite number of those "amplitude arrows". Instead, we treat it as in an introduction to calculus, and examine a finite number of paths each path differing slightly but significantly from the adjacent one (sort of a "differential"). THe result is the same as if we did add an infinite number of amplitude arrows together since all the possible paths between two of the adjacent "selected" paths would be canceled out somewhere on the "other side" (gosh, that's vague).