I wrote the other day about how shocked I was to learn that the leading proponents of the “semi-classical school” (which by my reckoning should actually be called the hemi-semi-classical school) had such poor physical intuitions. If they knew what I knew about things like the crystal radio, they could never come up with such misguided ideas as using the size of an atom to estimate the capture cross-section of the photo-electric effect.
Actually, they shouldn’t even need to understand the crystal radio for that. When you study inelastic collisions in Grade Eleven, it’s perfectly obvious that the greatest momentum transfer occurs between two particles of comparable mass. When one is very much lighter than the other (as is the case for a “photon” colliding with an electron) there is very little energy transferred to the larger particle. The absorption of light is clearly a bulk phenomenon that is not concentrated on a single atom, so the atomic cross-section has no place in any such calculation.
Anyhow, when I read Scully’s misguided explanation of these things, it got me thinking again. It had been probably ten years since I first started going on the internet to argue the case for classical light in discussion groups like sci.physics. I’d challenge anyone who said that the photo-electric effect proved that light was made of particles. And whenever I got into a discussion, there were these two self-appointed guardians of the truth who always showed up to put me in my place. Either Jim Carr or Mati Meron would jump in and say something to the effect of “even if you can explain the photo-electric effect, you can’t explain the Compton effect”. It didn’t matter that I wasn’t trying to explain the Compton effect. The fact that I had no explanation for it made whatever I said about the photo-electric effect, in their eyes, irrelevant.
It did no good to challenge them to meet me head on and argue the photo-electric effect. It was always “even if you are correct…”, never an actual admission that I was in fact correct. I would never get anywhere until I explained how the Compton effect worked without photons.
And then it happened! I guess it was reading that article by Scully that got me riled up or something, but I was out walking in the forest one day when it came to me in a flash. The Compton effect was much easier to explain than the photo-electric effect! The mathematics are identical to one of the most familiar examples from first-year physics, the well-known case of the infinite square well.
Think about it: in the square well, you have standing waves of charge, which can be written as two travelling waves going in opposite directions. It means that if you have a single electron in the superposition of two states, one travelling to the left and one travelling to the right, that the electric charge distribution will consist of many parallel sheets.
You can see right away how such a charge distribution must interact with a classical electromagnetic wave. In general, there will be no net interaction. But in the special case when the wavelength of the light is equal to the wavelength of the momentum, something very interesting happens. There need only be the slightest reflection off any given sheet: the reflection from the second sheet will be perfectly in phase with the reflection from the first sheet, as will the reflections from all subsequent layers. In very short order the power of the incident light wave will be completely reflected. And that is just what you find in the Compton effect.
Of course, to get total reflection you have to analyze the experiment in a center-of-mass reference frame. In the ordinary lab reference frame you only get fractional reflection. But the rules are well known whereby you transform the calculation from one reference frame to the other, and the net result is total reflection in the center-of-mass frame. And the reason why it has to work is obvious: in quantum mechanics, wavelength is the the measure of momentum; and in the C-O-M frame, the wavelength of the light is equal to the wavelength of the electron. That’s when the interaction suddenly becomes ultra-strong.
I was ecstatic when I put all this together, and not only because I finally had an answer for my tormentors from the internet forums. This was much bigger! If I had actually found a classical explanation for the Compton Effect, this would surely overturn the whole paradigm upon which the Copenhagen Interpretation of quantum mechanics was built. Was my analysis correct? It was so obvious that I could hardly doubt it. Had anyone else come up with it before me? The idea was laughable. Surely if such an explanation had ever been proposed in the past, it would be widely known. On the contrary: in all the popular accounts, the Compton effect was hailed as the third “nail in the coffin” that laid to rest the classical theory of electromagnetism once and for all. (The other two “nails” being the black body spectrum and the photo-electric effect.)
My readers will undoubtedly be surprised and disappointed to learn that I was not, after all, awarded the Nobel Prize for this amazing discovery. The sad story of how this happened will be left for a future posting.