I never intended to use this blog for random, thinking-out-loud speculations. But I'm afraid that is what it's come down to. I started out three days ago thinking I would make a clear case for the semi-classical picture of the black-body spectrum, but the farther I go the more messed up it gets.
So where are we now?
I've put forward the suggestion that maybe the true black-body spectrum is the old Rayleigh-Jeans distribution, with its ultraviolet catastrophe; and proposed that the reason we avoid the catastrophe is that there is simply no mechanism available in the form of atomic collisions that can effectively drive the high-frequency molecular oscillations needed in turn to excite the high-frequency electromagnetic standing waves. In all modesty I must say it's an intriguing theory, but in the end I can't quite bring myself to believe in it.
The equipartition theorem is not derived on the basis of any particular model of how collisions work. It is hard-core thermodynamics, based on maximizing the entropy of a system. For any mechanical collection of objects, including projectiles, oscillators, and rotators, so long as the energy is somehow quadratic with the motion (as it is in these cases)...the derivation shows that entropy is maximized when the energy is shared equally between all modes. I think I'm summarizing this correctly.
So under my proposal, the system would come to rest in a state of less than maximum entropy. This is a problem, if we believe the entropy calculation is correct. The problem is still perplexing: it is true that the entropy calculation does not rely on any specific mechanism to acheive its result, but should it also not be in physical agreement with a real mechanism which actually does exist? And I have put forward a plausible mechanism to show why the vibrational modes should remain low. What does it all mean?
Suppose I want to achieve the impossible, and redo the entropy calculation itself; suppose I then find that for a real gas, the entropy is maximized by those states I've described with the weak oscillators. I've still got a huge problem. Because my state has to be in thermodynamic equilibrium with a theoretical state made of classically "ideal" oscillators that follow Rayleigh-Jeans. And while I might have a faint hope that the two systems could be in mechanical equilibrium, there is no way they can still be in equilibrium when I include the electromagnetic field. It's a real problem.
Maybe there is a missing term in the entropy calculation which accounts for frequency. I'm damned if I can figure out how that would work.