Reply #11: This problem troubles most people.

[NNadir]

I was just discussing it with my son who is just entering into the conception of what energy, in particular, light energy, is. (I am introducing him to the first law of thermodynamics in his discussion of his fifth grade geology homework, which involves seismic waves.)

I always try to explain it this way: The particle/wave duality is without physical meaning in the sense that we are trying to impart macroscopic phenomena (massive objects and waves) on atomic scale events. For some type of problems it is convenient to describe light and/or mass as particles. For other types of problems, it is convenient to rely on its wave properties. The problem arises at the intersection of the two and the fact that people have no direct visible experience in the macroscopic world of what this might mean.

Once the photoelectric effect was explained, it was necessary to assume that a photon, the photon being a concept invented by Einstein's explanation, had momentum from conservation of momentum arguments. This momentum has in fact now been measured to some precision. When a photon transfers its energy to an electron, it disappears and no longer exists. I saw an interview with Richard Feynman in which he said he explained this (to his father) as if the photon was a word (ie a sound), it has an effect so long as it exists, but when it no longer exists, it disappears and no one is troubled by it. One can, at a loud concert for instance, actually feel sound pressure, but the sound is, as we all know, actually a wave. Of course one knows that sound pressure is transported in a medium, air, so one is somewhat more comfortable than one is with light, but on some level the analogy holds.

The energy of a photon is given by the relation E = hf = pc, where f is the frequency (usually designated by the greek letter nu). The momentum of light, p, is given by the relationship p = E/c. Since c = lf where l is the wavelength (usually designated by lamda) p = c/l.

Since force is simply the change in momentum dF = dp, the change in momentum induced by the absorption of light or its generation results in a net force on the emitting or absorbing object. One can in fact use solar sails in space, although for my money, ion engines (where the transfer of momentum is much larger) are a better deal.

It may not be satifying to say it this way, but it is "just so."