What's a good reference for this classical picture Feynman's talking about? I have a mathematics background but am trying to educate myself a little about physics.  At the beginning of Feynman's QED book (not the popular one) is the following:

Suppose all of the atoms in the universe are in a box.  Classically the box may be treated as having natural modes describable in terms of a distribution of harmonic oscillators with coupling between the oscillators and matter.

I guess this is something that physicists learn, but I have never heard of it.  What is Feynman talking about and where can I learn more about it?  The Wikipedia article on harmonic oscillators gives no indication that physicists do this.
 A: This is a way of giving systematic meaning to the radiation continuum in the context of a set of discrete states.
You assume some set of boundary conditions on the EM fields where they hit the box {1}, derive a set of allowed modes in terms of the geometry of the box {2}, then allow the box to expand without limit. Thus you arrive at a continuum of allowed modes.

{1} Say $E = M = 0$ at the boundary as if the box were a very good conductor.
{2} If the fields go to zero at the sides of the box then a half-integer number of wavelengths must fit, so only some wavelengths are allowed.
A: I just purchased Feynman's Thesis, which provides some insight on how Feynman saw the world, and provides some context here.  One of the key issues Feynman was trying to reconcile in his Lagrangian approach was how to describe quantum mechanics without rely on a field defined by harmonic oscillators, from page 5:

In particular, the problem of the equivalence in quantum mechanics of direct interaction and interaction through the agency of an intermediate harmonic oscillator will be discussed in detail.  The solution of this problem is essential if one is going to be able to compare a theory which considers field oscillators as real mechanical and quantized systems, with a theory which considers the field as just a mathematical construction of classical electrodynamics required to simplify the discussion of the interaction between particles.

So we have to understand that Feynman viewed matter as something different than the harmonic oscillator. Since mass is a parameter for a simple harmonic oscillator, we can see that in his discussion, Feynman didn't necessarily view matter as being the same thing as mass.  I suspect, matter would be viewed as the tangible reality that we are familiar with, and quantum harmonic oscillators are the abstract entities that we use to describe behavior, so it is some way necessarily to map, or couple, the real to the abstract.
