QED and light traveling in straight lines

[dEdt]

I tried asking a similar question earlier, but based on the answers I got I wasn't able to convey myself well.

Here's Feynman's argument (at least as I understand it) for why, from a Quantum perspective, light (roughly) travels in straight lines from points A to B:
1) the photon will travel every path from A to B; with every path, there is an associated amplitude, with a phase which depends on the time of travel and frequency alone. The total probability amplitude for a photon traveling from A to B is given by the sum of the individual amplitudes for all the paths
2) the phases of the paths close to the path of least time will be very close to one another; hence, they will all be in roughly in phase and interfere constructively.
3) as such, the greatest contributor to the total amplitude comes from those paths close to the path of least time.
4) Hence, if the paths near the path of least time or blocked, the total amplitude will drop dramatically; blocking other paths will have negligible effects on the total amplitude.
5) The path of least time between A and B is a straight line.

But this doesn't seem like a complete explanation. Suppose we had a laser at A, and a photon detector at B. This explains why the photon counting rate would decrease or go to zero if a barrier were put in the way of the line AB. However, this appears to be unable to explain other features of light-traveling-in-a-straight-line that we commonly observe. For example, if there's some dust, we'll see the lightbeam traveling in straight line. And if the photon detector is our eye-ball instead, we'll see the where the beam is coming from: it traveled from A to B. How can these be explained, from a Quantum perspective?

 

[EWH]

There are lots of photons in the beam, which explains the dust / scattering visibility. The photons go every path, but the A-B path is most likely for any distance along that path. The photon scatters off in some random direction when it hits a dust particle, so you see it come from somewhere along the original A-B path, but there are still lots of photons to be scattered by other dust particles along that path, giving the image of the whole length of the beam and still more photons are left to actually get to B.

The directional sensitivity of the eye is due to the lens mapping different angles to different spots on the retina. This occurs because the phase is advanced by the thicker part of the lens in the center relative to the periphery, (slower propagation in the lens material, so more phase accumulation in thicker bits) which leads to focusing for paths near the optical axis and because the iris excludes paths which are not close to the eye's optical axis. Slightly different angles also have slightly different geometrical phases, which affects the image mapping. It's complicated, but the the whole thing can be worked out in terms of relative phases and alternate paths. Holograms show the phase effects much better.

 

[dEdt]

There are lots of photons in the beam, which explains the dust / scattering visibility. The photons go every path, but the A-B path is most likely for any distance along that path. The photon scatters off in some random direction when it hits a dust particle, so you see it come from somewhere along the original A-B path, but there are still lots of photons to be scattered by other dust particles along that path, giving the image of the whole length of the beam and still more photons are left to actually get to B.

But why are the photons just scattering off the dust particles on the line AB? Shouldn't the probability amplitude for the photons bouncing off any dust particle be the same (I know this isn't true, but isn't it implies by Feynman's logic)?

 

[Born2bwire]

But why are the photons just scattering off the dust particles on the line AB? Shouldn't the probability amplitude for the photons bouncing off any dust particle be the same (I know this isn't true, but isn't it implies by Feynman's logic)?

But the dust motes themselves represent a potential barrier. If you want a very rough way of looking at it, you can rationalize it in the same way that you would in explaining how light would reflect off of a perfect mirror. You just have to realize that light traveling through the air is no longer doing so in a vacuum.

 

[EWH]

Well as you said in your original post, the phases of the waves paths along paths other than A-B cancel each other out. The same argument for the original A-B being the overwhelmingly primary path still holds if we move B closer and closer to A. And the other paths still aren't detected, the phases still cancel out.

When a dust mote is in that A-B path, it acts as if a tiny bit of the screen at B has moved closer to A. And when a bit of dust is a a location that is not in that path, the phases of the light cancel and there is no light for the dust to scatter there.