Max Planck

“ If we divide an irreversible process into its elementary constituents, the disorder and along with it the irreversibility vanishes; an irreversible process must remain beyond the understanding of anyone who relies upon the fundamental law: that all properties of the whole must also be recognizable in the parts. ”

“ If an electrodynamic process were to occur in a ponderable medium as in a vacuum, then it would have absolutely no sense to distinguish between field strength and induction. In fact, one can ascribe to the vacuum any arbitrary value of the dielectric constant, as is indicated by the various systems of units. But how is it now with regard to the velocity of propagation of light? This also is not to be regarded as a property of the vacuum, but as a property of electromagnetic energy which is present in the vacuum. Where there is no energy there can exist no velocity of propagation. ”

“ Take the case of a monatomic gas which is not sufficiently attenuated to have the properties of the ideal state; there are here, as pointed out by J. D. van der Waals, two things to consider: (1) the finite size of the atoms, (2) the forces which act among the atoms. Taking account of these involves a change in the value of the probability and in the energy of the gas as well, and, so far as can now be shown, the corresponding change in the conditions for thermodynamic equilibrium leads to an equation of state which agrees with that of van der Waals. ”

“ Above all, we are concerned here with the determination of those quantities which at any place in a medium traversed by heat rays determine the state of the radiant heat. The state of radiation at a given place will not be represented by a vector which is determined by three components; for the energy flowing in a given direction is quite independent of that flowing in any other direction. In order to know the state of radiation, we must be able to specify, moreover, the energy which in the time flows through a surface element for every direction in space. ”

“ This is the reason why one may directly apply the principle of least action to processes other than mechanical, and the result has shown that such applications, as well in electrodynamics as in thermodynamics, lead to the appropriate laws holding in these subjects. Since a representation of a unified system of theoretical physics such as we have here in mind must lay the chief emphasis upon as general an interpretation as possible of physical laws, it is self evident that in our treatment the principle of least action will be called upon to play the principal rôle. ”

“ But I consider the independence from the reference frame not as a solid physical result, but more as a hypothesis, which I consider as promising but not to be established yet. However, we just need to consider whether these relationships actually exist in nature. This we can only learn by experiment, and hopefully the time is not far off when we experience it. ”

“ Since in nature the entropy can only increase, it follows that the state of a physical configuration which is completely isolated, and in which the entropy of the system possesses an absolute maximum, is necessarily a state of stable equilibrium, since for it no further change is possible. ”

“ But since it is, as shown earlier, impossible to separate the energy of the kinetic motion of a body from its internal state, it follows immediately that a constant with the properties of inertial mass may not exist. The reason for this lies again in the internal energy of thermal radiation which contributes to the inertia of a body in a small but determinable way, i.e., by a term which depends on the radiation density or temperature. If, however, we want to define mass rather by momentum than by kinetic energy, namely as the ratio of momentum by velocity, we obtain no different result. ”

“ After I had recognized that the existing theories, including mine, do not meet the requirements, I have asked me the question, if it is possible to be consistent with experience while keeping Maxwell's equations and the principle of equality of action and reaction. This is possible when we rely on the following principle: the ponderomotive force between two systems in relative uniform motion to each other, by consideration of the sign, is the force calculated from the Maxwell-Lorentz equations acting upon a system which is arbitrarily regarded as at rest. ”

“ Now after all the irreversibility in nature thus appears in a certain sense eliminated, it is an illuminating fact that general elementary dynamics has only to do with reversible processes. Therefore we shall occupy ourselves in what follows with reversible processes exclusively. That which makes this procedure so valuable for the theory is the circumstance that all known reversible processes, be they mechanical, electrodynamical or thermal, may be brought together under a single principle which answers unambiguously all questions regarding their behavior. ”

“ A body that has an "independent" volume, i.e. independent of external influences, does not exist in all of nature, and even less in relativity theory. At least I think, that the attempt to make the abstraction of the rigid body (which is so important for ordinary mechanics) also useful for the theory of relativity, does not promise any real success [2] .
The task, to determine the deformation of a somehow accelerated body is therefore essentially a problem of elasticity, in relativity theory and in ordinary mechanics. ”

“ Following the preparatory considerations of the last lecture we shall treat today the problem which we have come to recognize as one of the most important in the theory of heat radiation: the establishment of that universal function which governs the energy distribution in the normal spectrum. The means for the solution of this problem will be furnished us through the calculation of the entropy of a resonator placed in a vacuum filled with black radiation and thereby excited into stationary vibrations. ”

“ For if, while engaged in body and mind in patient and often modest individual endeavor, one thought strengthens and supports us, it is this, that we in physics work, not for the day only and for immediate results, but, so to speak, for eternity. ”

“ As the momentum located in a particular area can only change due to external effects, i.e. according to the theory of direct action only by processes at the surface of that space, the amount of change in unit time is a surface integral which can be described as the total momentum flux in the interior of that space. A major difference, however, to the energy flux is the fact that the energy is a scalar, yet the momentum is a vector. Therefore, the incoming energy in that space is expressed by a single surface integral, and the energy flux is a vector. ”

“ However, inertia and gravitation are in every respect and by all our experience, for the most varied materials and from the lightest to the heaviest, so closely connected with each other that we may seek without concern the origin of these two effects at the same place, namely in the latent energy of the chemical atoms. Assuming that gravity is directly proportional to the latent energy, then the mass depending on temperature is only very slightly larger than the ponderable mass which is quite independent of temperature. ”

“ The capacity for emission and the capacity for absorption of an element of a body depend only upon its own condition and not upon that of the surrounding elements. If, therefore, as we shall assume in what follows, the state of the body varies only with the temperature, then the capacity for emission and the capacity for absorption of the body will also vary only with the temperature. The dependence upon the temperature can of course be different for each wave length. ”

“ In fact, the motions of single atoms are always reversible, and thus far one may say, as before, that the irreversible processes appear reduced to a reversible process, but the phenomenon as a whole is nevertheless irreversible, because upon reversal the disorder of the numerous individual elementary processes would be eliminated. Irreversibility is inherent, not in the individual elementary processes themselves, but solely in their irregular constitution. ”

“ Planck: Abraham is right when he says the main advantage of the sphere theory would be that it would be a purely electrical theory. If this were feasible that would be very nice, for now it is only a postulate. The Lorentz-Einstein theory is based on a postulate, namely that no absolute translation can be demonstrated. It seems that the two postulates can not be united, and now it depends on which postulate is to be preferred. That of Lorentz is more sympathetic to me. It's probably the best thing when work continues in both areas and the experiments eventually give the decision. ”