Accordingly we now return to the considerations of [sect:135.] Sec. 135 and assume a system of ideal linear oscillators in a stationary field of radiation. In order to make progress along the line proposed, it is necessary to know the elementary dynamical law, according to which the mutual action between an oscillator and the incident radiation takes place, and it is moreover easy to see that this law cannot be the same as the one which the classical electrodynamical theory postulates for the vibrations of a linear Hertzian oscillator.
For, according to this law, all the oscillators, when placed in a stationary field of radiation, would, since their properties are exactly similar, assume the same energy of vibration, if we disregard certain irregular variations, which, however, will be smaller, the smaller we assume the damping constant of the oscillators, that is, the more pronounced their natural vibration is. This, however, is in direct contradiction to the definite discrete values of the distribution densities , , which we have found in [sect:139.] Sec. 139 for the stationary state of the system of oscillators.
The latter allows us to conclude with certainty that in the dynamical law to be established the quantity element of action must play a characteristic part.
Of what nature this will be cannot be predicted a priori; this much, however, is certain, that the only type of dynamical law admissible is one that will give for the stationary state of the oscillators exactly the distribution densities calculated previously.
It is in this problem that the question of the dynamical significance of the quantum of action stands for the first time in the foreground, a question the answer to which was unnecessary for the calculations of the preceding sections, and this is the principal reason why in our treatment the preceding section was taken up first.