State, Statistics and Quantization in Einsteins 1907 Paper Plancks Theory of Radiation and the Theory of Specic Heat of Solids Peter Enders Senzig, Ahornallee 11, D-15712 Knigs Wusterhausen, Germany; enders@dekasges.de Abstract Einsteins paperPlancks theoryof radiation and the theory of specic heat of solids[Ann. Phys. 22, 180 (1907)] is famous for that it marks the beginning of the quantum theory of solids. In contrast to classical statistics, a simple quantum oscillator model of lattice vibrations yields a decreasing specic heat with decreasing temperature, in agreement with the then few experimental nd- ings. This brought him the attention of Nernst who became one of the driving forces to attract Einstein to Berlin. Less known is, however, that this paper contains two other fundamental insights. First, it shows that the di/erences between classical and quantum statistical distribution functions is related to the energetic spectra of systems rather than to the (in)distinguishability of par- ticles. Second, the problem of quantization is (indirectly) formulated as the problem to select the set of quantum states out o/ the set of classical states. Such an approach allows to satisfy the requirements to any quantization posed by Schrdinger from the very beginning. Nevertheless, this paper has found much less attention than most other pioneering contributions by Einstein. It is hoped that the revival of these thoughts will help to overcome some of the still present di¢ culties in the interpretation of quantum mechanics as well as to provide a dynamical solution to Gibbs paradox within classical statistical mechanics. 1 Introduction Albert Einstein (1879-1955) 1 was the rst to took Max Plancks (1858-1947) quantum hypothesis seriously, and he was believing in the existence of universal physical laws. His e/orts to realize his visions culminated in his annus mirabilis 1905 the centenary of which has been celebrated in the World Year of Physics 2005. Corresponding to the experimental material, he sought for applications of quantum theory rst in the eld of light-matter interaction [12][13], where he found the rst explanations of Stokes rule, of the external photo e/ect (the main point in the reasoning for awarding him the Nobel prize [15]) and of the photo-ionization of gases. His seminal paper Plancks theory of radiation and the theory of specic heat of solids[14] published two years later founded the quantum theory of solids; it was the rst to apply the quantum hypothesis to ponderable matter [37]. Again, Albert Einstein took an atomistic position in 1 The bibliographical and historical details have been taken from [37][64][44][43] and the Wikipedia. 1