Magical Me (3)
Back to the second lecture. The issue is the paths photons take when hitting a plane surface. Classical theory advertises the equality of the angle of incidence with the angle of reflection, while QED affirms that a photon can take any path from the source S to a detector D, even if it means going to the extreme ends of the surface and then to the detector, that is following the longest path. But experience tells us that light goes in a straight line, that incidence equals reflection, so , how can we reconcile both these views? The solution is that most paths cancel themselves out, leaving only the paths of least time which are very close to the classical model.
Feynman considers this as a triumph for QED because it arrives at known and accepted conclusions on the basis of the calculations of probabilities, his famous arrows.
The cancellation of the unwanted paths is of course interference in sheep's clothes, even if Feynman consequently speaks of photons and not of waves. But then, as he will argue in his following lectures, in QED electrons can destroy photons which can create electrons (and positrons) which can create photons. So, it is all for the best really.
Gratings are according to him a proof that photons do not only follow the incidence and reflection rule, but can indeed travel all possible paths on their way to the detector. The trick is to cancel cancellation and keep only the photons that bounce off to the right (or all those that bounce off to the left), and that is exactly what a grating does.
Since Feynman, as I already mentioned earlier in another post, jumps indiscriminately from individual photons to light in general, we will have to keep in mind what I will call the Hitachi principle: successive individual impacts by photons, or electrons, have ultimately the same effects as that of a beam (or wave) of light emitting millions of photons, or electrons, at the same time.
Once we do that we start to wonder why there should be any cancellation. When we look at a light beam hitting a surface we can certainly distinguish a path which is more illuminated than others, and which undeniably follows the classical lines. But, at the same time, there are regions surrounding this path which even if less bright, are certainly receiving parts of the beam, until darkness takes over. So, what seems wondrous when considering isolated photons becomes much less strange when the whole scene is taken into account.
Feynman is certainly right to attend his audience to the limitations of the classical view of incidence and reflection. But then he overshoots and makes it seem like the way light behaves cannot be understood by any rational means, only probabilistic calculations.
Real life teaches us that light, even if it goes in straight lines, does not go straight forward only, it spreads in all directions, or at least a cone . This is an empirical fact and is not any stranger than the fact that some rays do move straight forward. The Law of Reflection offers indeed a very limited view which is contradicted by our own perception and experience. We do not need to stand in the same angle as the incident ray to be able to see it. And apparently, neither does a photomultiplier.
On the other hand, Feynman's probabilistic view, whatever its practical merits, is not necessary to give an account of the phenomena of light. We can reject the simplicity of the law of reflection without embracing the irrationality of quantum theory.