Max Planck

“ But the principle of least action is not sufficient for a complete foundation of the dynamics of ponderable bodies; because by itself it provides no replacement - which has proven above to be untenable and which should not be introduced here - for splitting the energy of a body in kinetic and internal energy. On the other hand, such a replacement is in prospect in a complete way for the introduction of another theorem: the "principle of relativity as expressed by H. A. Lorentz [2] and in the most general form by A. Einstein [3] . ”

“ Such a freely moving cavity radiation, separated form outer space by thin rigid reflective walls, provides a good example of a rigid body, whose laws of motion completely differ from those of ordinary mechanics. Although it differs, considered superficially, in no way from other rigid bodies and also possesses a certain inertial mass and obeys the law of inertia, its mass changes significantly with temperature and it also depends in a certain specifiable way from the magnitude of the velocity as well as from the direction of the moving force in respect to the velocity. ”

“ According to the theory developed here, we therefore have to imagine an energy store in the interior of each body, whose amount is so enormous that the usually observed heating and cooling processes, and even quite deep invasive chemical transformations associated with considerable heat effects, changes it by only an imperceptible fraction. This is valid down to the lowest attainable temperatures: for both the specific heat of a body as well as the reaction enthalpy of chemical processes keep up their magnitude close to absolute zero. ”

“ It appears that we can attribute constancy to it before all other quantities: it is what until very recently, even in Hertz's mechanics, was considered to be the fundamental property of matter and therefore is used in almost every physical world system as the first building stone. However, it can now be proven that the mass of each body depends on temperature. Because inertial mass is defined most directly by the kinetic energy. ”

“ The latent energy is quite independent of the temperature and the motion of chemical atoms, [18] its location is therefore to be found within the chemical atom; by its nature it could be of potential nature but just as well be of kinetic nature. For nothing hinders us to accept, which would even be considered very probably especially by the electrodynamic point of view, that within the chemical atoms certain stationary motion processes in the form of standing oscillations take place, associated with none or only small radiation. ”

“ The energy of these oscillations, which can be very substantial, would (as long as the atoms remain unchanged) emerge in no other way than through inertia, by which it opposes to a translational acceleration of the oscillating system, and by the gravitational effect which is apparently in close connection to it. However, the views based on the kinetic theory of gases, which assume the inertial mass as something primarily given and the chemical atoms as rigid bodies or as simple material points, are insufficient for a further development of those ideas ”

“ For every ponderable body contains in its interior a specifiable finite amount of energy in the form of radiant heat, and if the body is imparted a certain velocity, then the heat radiation is also set into motion. As regards moving heat radiation, a separation of energy into internal and progressive energy is quite impossible, although its energy notably depends on the speed of motion ”

“ The last theorem makes it possible to express in a very general way the relation between the values of the temperature and the pressure of an arbitrarily moving body for the two reference frames used by us. We imagine that a moving body with arbitrarily directed velocity is given. The magnitude of velocity for the unprimed frame is q, and q' for the primed frame. If, from the given condition, the body is brought in a reversible, adiabatic and isobaric way to rest for the unprimed reference frame, then its volume has grown from V' to , its temperature from T' to . ”

“ Every change in nature corresponds to a certain number of influence elements which are independent of the reference frame. It is understood that this theorem extends the importance of the principle of least action in a new direction. ”

“ Although the prospect of the realization of such a radical operation appeared to be very low a decennium ago, now due to the discovery of radioactive elements and their transformations it is in close proximity, and in fact the observation of the strong persistence of heat production by radio-active substances gives almost a direct support for the assumption, that the source of that heat is just nothing else than the latent energy of the atoms. ”

“ Given the situation described, by which some views and theorems are stripped of its general nature, hitherto considered to be the strongest support for the usual theoretical considerations of any kind, it must appear as a task of particular importance to single out and especially put into the foreground, those theorems that previously formed the bases of general dynamics, and which also proved absolutely accurate in the light of the results of recent research; for they alone will henceforth be entitled to find use as the foundations of dynamics. ”

“ For, once the momentum is no longer proportional to the velocity, the mass of a body is no longer constant; also we are led to completely different dependencies of mass on velocity, depending on whether we divide momentum G by velocity q, or if we differentiate velocity q, where in this case it is necessary to specify particularly the manner in which the differentiation took place: whether isothermal, adiabatic, etc. Again, a different value for the mass is found in general, if we start from the energy E and differentiate it to . ”

“ But from the standpoint of the general theory we must unconditionally and principally distinguish between such theorems, which can be regarded only as approximations, and those which claim exact validity, because today it is unknown to which consequences the further development of the exact theory will lead us: far reaching revolutions, also in practice, have often enough started with discoveries of almost imperceptibly small inaccuracies within a theory that was previously considered as generally exact. ”

“ With these values we obtain for the energy E, the pressure p and the momentum G of the moving cavity radiation as functions of the independent variables q, V and T, the following expressions:
So, for example, if we impart some acceleration to the cavity radiation, while its volume V is kept constant and no heat is supplied from outside so that also the entropy S remains constant, the temperature T of the radiation is decreased by (2) in the ratio . ”

“ There, H is the kinetic potential of the body as a function of the above-mentioned five independent variables, where the velocity components only occur in combination with q, and is the external moving force acting on the body. ”

“ Comparing this relation with the one found above (21) , it follows that those have no general meaning, but only apply if and , that is, when the process runs isobaric and adiabatic. In fact, this property is characteristically for the process under consideration at that time: the motion of an electrically charged, diathermanous solid body in an evacuated electromagnetic field.
Finally, there may be still room for general relations between the values for the energy of the body, as well as the performed external work, and the supplied heat for both reference systems. ”

“ In accordance to (48) , a large latent energy is connected with a large mass as well. This is well in line with the fact that the radio-active elements have a particularly high atomic weight, and that their bindings belong to those with the highest specific weights.
According to J. Precht [19] 1 gr of radium, when surrounded by a sufficiently thick layer of lead, gives 134.4 · 225 gr = 30240 gr cal per hour. This gives according to (48) a reduction of mass in an hour by
or in a year a reduction of mass around 0.012 mgr. ”

“ Then the body is reduced to cavity radiation, as it was discussed in the previous section. ↑ On the existence of a state equation. see Byk, Ann. d. Phys. (4) 19, p. 441, 1906. ↑ H. Von Helmholtz, Ges. Abh. (Leipzig, J. A. Barth) III, S. 225, 1895. There, the kinetic potential is defined by the opposite sign. ↑ All these relations are also valid for a non-uniformly moving medium in which the velocity continuously varies in magnitude and direction from point to point. In this case, V can be understood as any infinitesimal volume element. ↑ A. Einstein, Ann. d. Phys. ”