I'm following this derivation of the Rayleigh-Jeans law:
There are a few points that I don't quite understand, and I would appreciate help in understanding them:
In part 2, it is mentioned that the electric field at the walls must be zero, or otherwise electric field would impart energy to the cavity walls and lose energy itself. But why is this required? I thought that "thermal equilibrium" in this situation means the radiation and cavity are at the same temperature; so I thought the wall would be continuously absorbing some amount of radiation, only to re-radiate it and lose the gained energy again.
It is mentioned that the energy of one mode is $kT$. This is the result of applying the equipartition theorem, which states that every degree of freedom has an energy $1/2kT$. So apparently every mode has two degrees of freedom. Do these correspond to two possible polarizations of light? But from other sources I've found out that the ultraviolet catastrophe arises from the idea that every mode has this energy $kT$. But why does every mode have this energy? Would this mean that the degrees of freedom are acctually the numbers $n_x$, $n_y$, $n_z$?
- And why do we even apply equipartition theorem to radiation? I understand that for an ideal gas, $1/2kT$ is the energy per degree of freedom, but neither the radiation nor the cavity are ideal gasses. I don't even see what it means for radiation to have temperature $T$.
I would very much appreciate help in understanding this derivation.