People don't understand quantum mechanics because they think that energy can only come in descrete lumps. This was an early interpretation of the old quantum mechanics, that has become solidly entrenched in the collective psyche even at the very highest levels. It is wrong and misleading in almost every instance where it is applied. The most imporant example of its misuse is in the case of emission and absorption of radiation between atoms.
Everything that atoms do in the context of thermal radiation can be understood by analyzing them as tiny antennas that work exactly the same as classical radio antennas. This is not some kind of crackpot idea: I know exactly what crackpot ideas are because I've taken a crackpot test and scored 155 on it. Seriously, I know exactly what I'm saying and I can back it up. If you understand this about atoms and radiation then all of quantum mechanics starts to make a little more sense.
The first thing you need to do is throw away the old planetary model of the atom. That was invented in 1915 by Bohr, and it became obsolete in 1926 when Schroedinger came along. Unfortunately, the image of the Bohr atom is burned into everyone's brain, thanks in no small measure to the efforts of the school system. The electron cloud of Schroedinger's atom is a vague and fuzzy concept for most people. Fortunately, there are some good animations of it available. I had a really nice one from the University of Saskatchewan website that I linked to last year in my article on the crystal radio, but as I check it out right now it's giving me a hard time over my browser. So I'm not sure if it works. Here's another guy selling applets that make the same point; even if you don't buy it, you can see some nice animations on the web page. The point is that in quantum mechanics there is such a thing as a charge density, and if you take an atom in any kind of superposition of pure states, then you get an oscillating charge density. That's what you see in the applets, and there's nothing controversial about it.
The stumbling block for many people is the idea that you have an atom in a superposition of pure states. I can't count the number of times people have told me this is nonsense...people who should know better. They say a hydrogen atom, for example, is either in the ground state or the first excited state...never half and half. If it is in the presence of thermal radiation, it may absorb a photon and instantly jump from the lower state to the higher state, or it may emit a photon and jump the other way. That's the old "quantum leap" made popular by Neils Bohr, and made obsolete by the Schroedinger Equation. Or it should have been made obsolete, except that the proponents of the Copenhagen School adapted it to the new Schroedinger atom. Schroedinger developed his theory to show that there was a sensible way for the atom to make a smooth transition from one state to the other, and he was appalled when his theory was hijacked to support the quantum leap.
It's true that the Copenhagen school cobbled together a workable interpretation whereby only pure states exist, but the point is it's not a necessary interpretation. What people don't realize is that there is no experimental way to distinguish between the Copenhagen model of discreet states and quantum leaps, versus the Schroedinger model of mixed states and continuous transitions. This point was made really well by people who know all about these things in a stackexchange.com discussion which I link to in this article. The fact that you can analyze everything in terms of pure states and quantum leaps doesn't mean that you have to analyze it that way.
So what does the universe look like in Schroedinger's picture? Every atom is in some mixture of pure eigenstates, and if you look at the applets I mentioned earlier, it's easy to see that the charges are oscillating. As oscillating charges, they ought to radiate according to the classical laws of antenna theory; and that's where I hit the second wall. "Even if you're right about the oscillating charges..." (notice how they start with "even if", not even admitting what is clearly a mathematical consequence of the theory), "even if you're right about that, you're not allowed to use Maxwell's Equations to calculate the resulting radiation."
Not allowed? Why the hell not? There are two possibilities. Either you get the wrong answer for the black body radiation field, or you get the right answer. If you can show me that you get the wrong answer, then the game is over and I have to pack up my marbles and go home. But what if you get the right answer? Then what becomes of your quantization of energy into discrete lumps? Either way, it has nothing to do with what I'm supposedly allowed to do.
Let's leave it there for now. I'll come back to this before long. But I think I've also left some unfinished business about the theory of evolution...