We shall now consider from the standpoint of pure electrodynamics the processes that take place in a vacuum, which is bounded on all sides by reflecting walls and through which heat radiation passes uniformly in all directions, and shall then inquire into the relations between the electrodynamical and the thermodynamic quantities.
The electrodynamical state of the field of radiation is determined at every instant by the values of the electric field-strength and the magnetic field-strength at every point in the field, and the changes in time of these two vectors are completely determined by Maxwell's field equations [eqn:(52)] (52), which we have already used in [sect:53.] Sec. 53, together with the boundary conditions, which hold at the reflecting walls. In the present case, however, we have to deal with a solution of these equations of much greater complexity than that expressed by [eqn:(54)] (54), which corresponds to a plane wave. For a plane wave, even though it be periodic with a wave length lying within the optical or thermal spectrum, can never be interpreted as heat radiation. For, according to [sect:16.] Sec. 16, a finite intensity of heat radiation requires a finite solid angle of the rays and, according to [sect:18.] Sec. 18, a spectral interval of finite width. But an absolutely plane, absolutely periodic wave has a zero solid angle and a zero spectral width. Hence in the case of a plane periodic wave there can be no question of either entropy or temperature of the radiation.