Friedrich Hasenöhrl

“ Thus we come to the result: When the volume decreases with velocity according to the previous law, i.e. when the dimensions of matter are contracting in the direction of motion in the ratio
,
then the pressure of every body remains unchanged at adiabatic change of velocity, while the temperature of all bodies decreases in the same measure. Then, no influence of a common translatory motion is observable.
This is in agreement with the contraction hypothesis of H. A. Lorentz, as well as with the theorems derived by Planck from the so called relativity principle. ”

“ In the same way, as the electromagnetic mass is proportional to the static energy of the stationary electron, also the apparent mass caused by radiation is proportional to the energy content of the stationary cavity. Namely, the proportionality factor is in both cases of the same order of magnitude. Now, since the heat content of every body partly consists of radiation energy, then every body must possess such an apparent mass depending on the temperature, and which is added to the mass in the ordinary sense. ”

“ The criterion of equality of temperature is not applicable to bodies of unequal velocity, since we cannot directly bring them in reversible heat exchange, but only with the aid of an auxiliary body which assumes different velocities. Though if we don't set equal to one, then also the entropy of the adiabatic acceleration changes.
Anyway, it is the easiest way to define by equation (8) ; then is a complete differential and the entropy remains constant at adiabatic acceleration. [7]
4. ”

“ Under absolute radiation one understands the energy quantity, which traverses (in unit time) the unit surface of an absolutely resting plane situated perpendicular of the absolute beam direction. This energy quantity is equal to the heat, absorbed by the unit surface of an equally located black plane.
Under total relative radiation we understand the energy quantity, which traverses (in unit time) the unit surface of an (imagined) plane, moving with absolute velocity , and which is oriented perpendicular to the relative beam direction. ”

“ To avoid this difficulty, we want to imagine adiabatic changes of the radiation state in our cavity as of such kind, that a black body is present in the space surrounded at all sides by mirrors, yet whose capacity is so small, that its heat content can be neglected against the energy content of space . ”

“ Of course, upon this foundation one can calculate the values and , when one assumes that a moving body is emanating waves, whose amplitude is the same as in the stationary state, while the density of the radiation energy is inversely proportional to the square of the wavelength. ”

“ Even when we don't set these functions equal to one, we neither come into contradiction with the theorem of the impossibility of a thermal perpetual motion machine, nor with the ordinary definition of temperature which is indeed only related to bodies of same velocity. ”

“ Now, when our system was initially at rest, yet the surfaces and were not hindered to emanate, then the energy density is initially present in , and it is the question, what is happening with the energy quantity when the system is suddenly brought to velocity . The previous consideration indicates that the energy amount has to be completely absorbed by the surfaces and ; no part of it may be transformed into mechanical work. ”

“ With the aid of equations (2) and (10) , momentum and total energy () can be expressed by the state variables of the resting system. (We have to consider here, that equations (1) , (3) , (4) and (5) may not be applied now; they only hold for velocity changes at constant volume.) ”

“ At that occasion, the work 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 , though its temperature is now higher than , and thus it can by itself pass to a body whose temperature is higher than .
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 . ”

“ Now, by generalization of the thought that was first spoken out by Larmor [8] , the same result can be derived from the standpoint of the elastic theory of light, which I would like to show soon.
We consider a light source, moving under the (absolute) angle against the -axis. ”

“ The entropy of a moving body.
We arrived at the result that pressure and temperature assume the values
at isochoric-adiabatic acceleration. plays the role of the inner energy in a system moving with constant velocity.
Let the entropy of the resting system be , that of the moving one can be expressed by . ”

“ In order to calculate the absolute energy flow, i.e. the energy flow through a cross-section imagined as at rest, we have to add the product of the energy density multiplied with the translation velocity, to the relative energy flow in the direction of motion, i.e. ”

“ Since we can also set instead of (within the expression multiplied with the infinitely small magnitude ) it eventually becomes:
Quite analogously it is given:
If we use these equations, it becomes.
or We can determine the first integral by the aid of equation (21) , the second one has the value:
thus it becomes
where is the value, which emerges from when is replaced by (see equation (21) ) . One easily convince oneself, that the bracket expression in the last equation has the value ; thus it becomes:
Our earlier assertion is proven by that. ”

“ Yet the law of reciprocity is always exactly valid for relative rays, i.e., a relative ray can always traverse the same way in both directions; this is a consequence of thermodynamics (see F. Hasenöhrl, Sitzungsber. d. k. Akad. d. Wissensch. zu Wien IIa. 113. p. 493. 1904) ↑ J. H. Poynting, Phil. Trans. ”

“ Compare for instance F. Hasenöhrl, Jahrb. d. Radioaktivität, 2, p. 281 (1905) . ↑ This terminology agrees with the one used in an earlier paper (Ann. d. Phys., 15 [1904] ) . There, and was written instead of and . ”