(translation into Russian) M.Planck, Izbrannye Trudy, Nauka, M. (1975) 251.
(translation into English) The Old Quantum Theory, ed. by D. ter Haar, Pergamon Press (1967) 82.
Gentlemen: when some weeks ago I had the honour to draw your attention to a new formula which seemed to me to be suited to express the law of the distribution of radiation energy over the whole range of the normal spectrum,1 I mentioned already then that in my opinion the usefulness of this equation was not based only on the apparently close agreement of the few numbers, which I could then communicate, with the available experimental data, footnoteVerh. Dtsch. Phys. Ges. Berlin 2,
237 (1900) but mainly on the simple structure of the formula and especially on the fact that it gave a very simple logarithmic expression for the dependence of the entropy of an irradiated monochromatic vibrating resonator on its vibrational energy. This formula seemed to promise in any case the possibility of a general interpretation much rather than other equations which have been proposed, apart from Wien's formula which, however, was not confirmed by experiment. Entropy means disorder,
and I thought that one should find this disorder in the irregularity with which even in a completely stationary radiation field the vibrations of the resonator change their amplitude and phase, as long as considers time intervals long compared to the period of one vibration, but short compared to the duration of a measurement. The constant energy of the stationary vibrating resonator can thus only be considered to be a time average, or, put differently, to be an instantaneous average of the
energies of a large number of identical resonators which are in the same stationary radiation field, but far enough from one another not to influence each other. Since the entropy of a resonator is thus determined by the way in which the energy is distributed at one time over many resonators, I suspected that one should evaluate this quantity in the electromagnetic radiation theory by introducing probability considerations, the importance of which for the second law of thermodynamics was first
of all discovered by Mr. Boltzmann. This suspicion has been confirmed; I have been able to derive deductively an expression for the entropy of a monochromatically vibrating resonator and thus for the energy distribution in a stationary radiation state, that is, in the normal spectrum. To do this it was only necessary to extend somewhat the interpretation of the hypothesis of "natural radiation'' which is introduced in electromagnetic theory. Apart from this I have obtained other relations which
seem to me to be of considerable importance for other branches of physics and also of chemistry.
Related references More (earlier) information appears in M. Planck, Verhandl. Dtsch. phys. Ges. 2 (1900) 202;
See also M. Thiesen, Verhandl. Dtsch. phys. Ges. 2 (1900) 67;
F. Kurlbaum, Ann. Physik 65, 759 (1898);
F. Richarz, Annalen der Physik. Leipzig 52 (1894) 397;
P. Drude, Annalen der Physik. Leipzig 1 (1990) 578;
L. Boltzmann, Sitzungsber. Akad. Wess. Wien 76, 373 (1900);
J.J. Thomson, Phil. Mag. 46 (1898) 528;
O. Lummer and E. Pringsheim, Verhandl. Dtsch. phys. Ges. 2 (1900) 176;
L. Boltzmann, Sitzungsber. Akad. Wess. Wien 76, 428 (1877);
O.E. Mayer, Die Kinetische Theorie der Gase, 2nd ed., (1899) 337;
Analyse data from O. Lummer and E. Pringsheim, Verhandl. Dtsch. phys. Ges. 2 (1900) 174;
O. Lummer and E. Jahnke, Annalen der Physik. Leipzig 3 (1900) 288;
H. Rubens and F. Kurlbaum, Sitzungsber. Akad. Wiss. Berlin (1900) 929;
Quantum hypothesis and explanation of the black body radiation spectrum. Beginnings of the quantum era in physics.