"Because when the box is in thermal equilibrium, there can never be any electric field at the walls for it would shake the charge in the wall around, changing the temperature, contradicting the claim that the box is in thermal equilibrium."
This argument just doesn't sit right with me. Thermal equilibrium does not mean that it's absolutely forbidden for the temperature in a system to locally fluctuate. Its like saying, when the box with gas is in thermal equilibrium, there are no collisions between the molecules anymore... Thermal equilibrium merely means that every degree of freedom is on average giving away as much energy as it is absorbing.
The book by Robert Eisberg and Robert Resnick, "Quantum Physics" has this to say:
"We assume for simplicity that the metallic-walled cavity filled with electromagnetic radiation is in the form of a cube of edge length a, as shown in Figure 1-3. Then the radiation reflecting back and forth between the walls can be analyzed into three components along the three mutually perpendicular directions defined by the edges of the cavity. Since the opposing walls are parallel to each other, the three components of the radiation do not mix, and we may treat them separately. Consider first the x component and the metallic wall at x = O. All the radiation of this component which is incident upon the wall is reflected by it, and the incident and reflected waves combine to form a standing wave. Now, since electromagnetic radiation is a transverse vibration with the electric field vector E perpendicular to the propagation direction, and since the propagation direction for this component is perpendicular to the wall in question, its electric field vector E is parallel to the wall. A metallic wall cannot, however, support an electric field parallel to the surface, since charges can always flow in such a way as to neutralize the electric field. Therefore, E for this component must always be zero at the wall. That is, the standing wave associated with the x-component of the radiation must have a node (zero amplitude) at x = O. The standing wave must also have a node at x = a because there can be no parallel electric field in the corresponding wall. Furthermore, similar conditions apply to the other two components; the standing wave associated with the y component must have nodes at y = 0 and y = a, and the standing wave associated with the z component must have nodes at z = 0 and z = a. These conditions put a limitation on the possible wavelengths, and therefore on the possible frequencies, of the electromagnetic radia- tion in the cavity."
Particularly this part: "A metallic wall cannot, however, support an electric field parallel to the surface, since charges can always flow in such a way as to neutralize the electric field. Therefore, E for this component must always be zero at the wall."
Well, then how can it emit any radiation? Clearly, metal objects outside of a box can also emit thermal radiation so doesn't that contradict the idea that "E for this component must always be zero at the wall"?
What should happen is that the emitted wave, once reflected, is reflected again from the surface that originally emitted it. This, however, will never cancel the resulting standing wave completely, even ad infinitum.
Maybe what is happening is that although the frequencies that don't create standing waves with nodes at the edges never die down, they also do not grow bigger and bigger after each reflection, whereas the frequencies that do create standing waves with nodes at the edges have their amplitudes increased, due to constructive interference, as a result of every reflection, overshadowing the other frequencies in amplitude.
This leads to my second question though: the intensities that we'd observe coming from this box are highly amplified due to these reflections and are therefore different from those emitted from normal thermally radiating surfaces.
This final point could be easily resolved if somebody could confirm that the spectra of the box and that of a regular surface only differ by a constant factor that takes into account how often the waves are reflected and with what ratios. I have seen no mention of such constant anywhere however.
All these questions about this whole experiment have been plaguing me for over two years now. I hope that somebody can help me finally make this intuitive and straightforward. Physics is not satisfactory to me when I'm not really trying to step into the shoes of the people that first did the experiments and the calculations to think it through to a point where I can see why they did everything the way they did. Any insights would be much appreciated!