The Odd Couple: Boltzmann, Planck and the Application of Statistics to Physics (1900-1913) Massimiliano Badino ∗ Abstract In the last forty years a vast scholarship has been dedicated to the reconstruction of Planck’s theory of black-body radiation and to the historical meaning of quantization. Since the introduction of quanta took place for combinatorial reasons, Planck’s under- standing of statistics must have played an important role. In the first part of this paper, I sum up the main theses concerning the status of the quantum and compare the ar- guments supporting them. In the second part, I investigate Planck’s usage of statistical methods and the relation to Boltzmann’s analogous procedure. I will argue that this way of attacking the problem is able to give us some interesting insights both on the theses stated by the historians and on the general meaning of Planck’s theory. 1 Introduction: A vexed problem In his epoch-making paper of December 1900 on blackbody radiation,(Planck 1900b)(Planck 1958, 698-706) for the first time Max Planck (1858-1947) made use of combinatorial argu- ments. Although it was a difficult step to take, a real “act of desperation” as he would later call it, Planck pondered it deeply and never regretted it. As he wrote to Max von Laue (1879-1960) on 22 March 1934: “My maxim is always this: consider every step carefully in advance, but then, if you believe you can take responsibility for it, let nothing stop you.”(Heilbron 1986, 5). The difficulty involved in this step was the adoption of a way of reasoning that Planck had been opposing for a long time: Ludwig Boltzmann’s (1844-1906) statistical approach. However, Planck’s application of statistics to the particular problem of finding the spectral distribution of cavity radiation seems to bear only partial resemblance to Boltzmann’s original arguments and the opinions of the scholars are split about the interpretation of the relation between Planck’s and Boltzmann’s procedure. For discussion’s sake, I sort out three basic kinds of outlooks, which I term the discon- tinuity thesis, the continuity thesis and the weak thesis. According to the discontinuity thesis Planck worked from the very beginning with discrete elements of energy. As early as 1962, Martin Klein, in a series of seminal papers(Klein 1962) (Klein 1963) (Klein 1964) (Klein 1966), argued explicitly that in December 1900 Planck introduced the quantization of energy even ∗ Max-Planck-Institut für Wissenschaftsgeschichte and Fritz-Haber-Institut der Max Planck Gesellschaft Boltzmannstrasse 22, 14195 Berlin, Germany. E-mail: mbadino@mpiwg-berlin.mpg.de 1