113.

Since a wholly new element, entirely unrelated to the fundamental principles of electrodynamics, enters into the range of investigation with the introduction of probability considerations into the electrodynamic theory of heat radiation, the question arises at the outset, whether such considerations are justifiable and necessary. At first sight we might, in fact, be inclined to think that in a purely electrodynamical theory there would be no room at all for probability calculations. For since, as is well known, the electrodynamic equations of the field together with the initial and boundary conditions determine uniquely the way in which an electrodynamical process takes place, in the course of time, considerations which lie outside of the equations of the field would seem, theoretically speaking, to be uncalled for and in any case dispensable. For either they lead to the same results as the fundamental equations of electrodynamics and then they are superfluous, or they lead to different results and in this case they are wrong.

In spite of this apparently unavoidable dilemma, there is a flaw in the reasoning. For on closer consideration it is seen that what is understood in electrodynamics by "initial and boundary" conditions, as well as by the "way in which a process takes place in the course of time," is entirely different from what is denoted by the same words in thermodynamics. In order to make this evident, let us consider the case of radiation in vacuo, uniform in all directions, which was treated in the last chapter.

From the standpoint of thermodynamics the state of radiation is completely determined, when the intensity of monochromatic radiation ${𝖪}_{\nu }$ is given for all frequencies $\nu$. The electrodynamical observer, however, has gained very little by this single statement; because for him a knowledge of the state requires that every one

of the six components of the electric and magnetic field-strength be given at all points of the space; and, while from the thermodynamic point of view the question as to the way in which the process takes place in time is settled by the constancy of the intensity of radiation ${𝖪}_{\nu }$, from the electrodynamical point of view it would be necessary to know the six components of the field at every point as functions of the time, and hence the amplitudes $C_n$ and the phase-constants ${\theta }_n$ of all the several partial vibrations contained in the radiation would have to be calculated. This, however, is a problem whose solution is quite impossible, for the data obtainable from the measurements are by no means sufficient. The thermodynamically measurable quantities, looked at from the electrodynamical standpoint, represent only certain mean values, as we saw in the special case of stationary radiation in the last chapter.

We might now think that, since in thermodynamic measurements we are always concerned with mean values only, we need consider nothing beyond these mean values, and, therefore, need not take any account of the particular values at all. This method is, however, impracticable, because frequently and that too just in the most important cases, namely, in the cases of the processes of emission and absorption, we have to deal with mean values which cannot be calculated unambiguously by electrodynamical methods from the measured mean values. For example, the mean value of $C_n$ cannot be calculated from the mean value of $C_n^2$, if no special information as to the particular values of $C_n$ is available.

Thus we see that the electrodynamical state is not by any means determined by the thermodynamic data and that in cases where, according to the laws of thermodynamics and according to all experience, an