Quantum mechanics emerged from a series of challenges to the mechanical worldview. In part, these challenges arose from conflicts between theoretical expectations and novel experimental results. At a deeper level, however, the crisis of mechanics arose from attempts to integrate newly-established physical theories such as electrodynamics and thermodynamics into a coherent mechanical worldview. Conflicts between theories necessitated a reorganization of certain fundamental concepts. Historians of science often stress the revolutionary character of this process. However, not only did a large amount of empirical knowledge remain undisputed, also some theoretical structures persisted and survived the advent of quantum mechanics. Which concepts and theoretical structures of classical physics could be maintained in the new mechanics and could thus serve as a guide for its development?

In my talk, I will discuss the classical roots of wave mechanics, focusing on the role of the optical-mechanical analogy originally formulated by Hamilton in the 1830s. This analogy already played a role in Schrödinger's research in the late 1910s, but only turned into a heuristic tool when he developed de Broglie's ideas about matter waves in late 1925. Only in early 1926 did he understand the full impact of the analogy: Classical mechanics is an approximation to his new undulatory mechanics, just as ray optics is only an approximation to wave optics. This completion of Hamilton's analogy convinced Schrödinger to stick to a realist interpretation of the wave function, in opposition to the emerging mainstream. Drawing on Schrödinger's research notebooks, I will illustrate how the analogy, when transferred from classical to modern physics, persisted as a theoretical structure by undergoing a deep transformation in its role and interpretation. My talk is based on joint research with Christoph Lehner.

The Classical Roots of Schrödinger's Wave Mechanics