Page:Zur Theorie der Strahlung in bewegten Körpern.djvu/24

 (black) energy reservoir of temperature $$T$$, and a cavity surrounded by mirrors of volume $$v$$. Let the system at first be at rest, and the cavity be in connection with the heat reservoir, so that the radiation energy $$v\epsilon_0$$ is present in the first one. If we now bring the system to velocity $$w$$, then the heat reservoir gives off the heat $$v(\epsilon-\epsilon_0) = v\epsilon_{0}(\varkappa - 1)$$ to the cavity; at the same time, the work $$v\epsilon' = v\epsilon_{0}\tau$$ must be performed. Now we separate the cavity from the heat reservoir by a mirror, and bring the velocity of our system to zero again. At that occasion, the work $$v\epsilon_{0}\tau$$ is gained from the cavity radiation again, so that no work is neither gained nor lost altogether. Yet, the density of true radiation (now the only remaining radiation in the cavity) is still equal to $$\epsilon_{0}\varkappa$$, though its temperature is now higher than $$T$$, and thus it can by itself pass to a body whose temperature is higher than $$T$$.

A new hypothesis is necessary to solve this. Such one would be the assumption, that the emission capacity of a black body changes with the velocity of translation, so that it always caeteris paribus is proportional to $$1/\varkappa$$. Then the density of the true cavity radiation would always have the value $$\epsilon_{0}$$, and our procedure just described, to bring heat to a higher temperature, would be impossible. We must stick to the fact, that this change must be related to the true emission capacity, i.e., the amount of inner energy of the radiating body which is transformed into radiation in unit time. About this quantity we always assumed until now, that it is independent of motion; in case this were incorrect, then this would also be true for our earlier considerations; thus also in our derivation of the radiation pressure. Anyway, this assumption doesn't fit into the framework of the theory presented here. Furthermore, this change also should surely concern (in the same way) the energy quantity emanated in different directions; thus the energy emanated by the elementary oscillations, independent of the orientation