The Boundary Condition in the Classical Derivation of the BBR

Abstract

The classical derivation of the black body radiation (BBR) spectrum by Boyer was based on an equilibrium mechanism such that in the absence of thermal radiation particles in a container can gain kinetic energy from the random electromagnetic zero point field (ZPF) radiation. Their loss of that energy was to be by means of their collisions with the walls of the container. Theoretically, energy dissipation through collisions with the walls might lead to a divergent kinetic energy value for the particles. This is because the box can be taken large enough to minimize the collisions probability, and that can lead to a particle’s indefinite growth in energy. Furthermore, a derivation of a general phenomenon such as the BBR should be possible without relying on the walls boundary of a box. Therefore, a new boundary condition is proposed here which is related to relativistic effects. It is shown that with the new boundary condition one may still recover the BBR spectrum. A discussion is presented that shows how the new boundary condition is indeed responsible for energy dissipations.