Page:Zur Theorie der Strahlung in bewegten Körpern.djvu/25

 of the latter, must be changed by the same amount by motion. Exactly this seems improbable to me. Though the possibility of this hypothesis must be permitted in any case.

However, there is also another possibility for the solution of this contradiction, which is particularly remarkable by the fact, that it is the same one stated by and  to explain the negative result of the experiment of  and. Namely the hypothesis, that the dimensions of matter depend on their absolute velocity.

The apparent contradiction with the second thermodynamic law, at which we arrived, stems indeed from the fact, that the temperature of the true cavity radiation changes at adiabatic change of velocity; or, which is the same, that its density doesn't change. This can of course be achieved by a corresponding change of volume, by which the density of the true radiation changes, so that the temperature stays the same; i.e., that it assumes the value $$\epsilon_0$$ especially in the case, when the cavity comes to rest again.

If we now denote (during the adiabatic velocity change) the variable density of the true radiation by $$\epsilon$$, then $$\epsilon v$$ is the momentary true energy content of the cavity. If the volume is changed, then the radiation performs a work, whose amount depends on the magnitude of the pressure. Although it would be probably no problem, to exactly calculate this work, we nevertheless want to confine ourselves to the precision, which is extended only to order $$\beta^2$$ (incl.). Since (as we want to preface) the considered change of volume is of order $$\beta^2$$, we can confine ourselves to the first term independent of $$\beta$$ when we are stating the pressure; i.e., we set the pressure equal to a third of the density of the total radiation. Since furthermore, the total and true radiation only differ by terms of order $$\beta^2$$ as well, we can set the work performed by the true radiation equal to

$\frac{1}{3}\epsilon dv$