Ever since 1900, when Planck introduced the new universal constant “h” in the theory of radiation, physicists started to use it to account for physical phenomena, for whose explanation the theories of electrodynamics and mechanics inherited of the 19th century seemed not to suffice. From 1900 until 1925, physicists tried to incorporate “h” in the structure of electrodynamical and mechanical theories by tentatively supplementing them with “quantum” conditions. The problems originated by these attempts led physicists to be increasingly concerned about the relation between the emerging quantum physics and the classical body of knowledge: Was integration between the two ever-differentiating quantum and classical physics eventually possible, or a choice between both should be made?

Discussions on these fundamental questions rarely took place disconnected from the concrete physical problems one attempted to solve. In this paper, I will examine the different answers that Niels Bohr, Arnold Sommerfeld, and Rudolf Ladenburg put forward between 1910 and 1920, in the context of the explanation of optical dispersion. Contrarily to other physical phenomena more commonly discussed in the secondary literature, optical dispersion was consistently considered a paradigmatic example of the success of classical theories in accounting for the interaction between light and matter almost until 1920. Despite the increasing awareness of fundamental conceptual inconsistencies between the quantum postulates and classical physics during the 1910s, certain experimental features of optical dispersion could not be explained by the quantum hypothesis. How to deal then with this phenomenon? Should one seek for conceptual consistency in quantum theory, or should one trust old successful theories in this particular case?

Different answers were provided depending on different agendas. For Bohr a consistent quantum theory came first, at the expenses of explaining the physical mechanism. For Sommerfeld, instead, the classification of phenomena according to physical mechanisms was more important than full consistency. Finally, Ladenburg sought for an integration of optical phenomena through a common interpretation of experimental parameters over a detailed theory of the physical process. The physical characterization of dispersion was in each case different. The boundaries between quantum and classical physics were under negotiation, alongside the criteria to establish them.