At the End of the Rainbow: Optical Dispersion as the Bridge between the Old Quantum Theory and Matrix Mechanics

Michel Janssen

Optical dispersion, observed in rainbows and prisms, was already studied seriously by Descartes and Newton. A satisfactory theory is hard: it involves the difficult problem of the interaction between light and matter, and Lorentz's elaboration of Maxwell's electrodynamics in the 1890s, two centuries after Newton, was the first to give a reasonable account of dispersion. It was however called into question by Bohr's quantum model of the atom. In the early 1920s the problem of dispersion took center stage. The famous Umdeutung (reinterpretation) paper with which Heisenberg ushered in the era of modern quantum mechanics grew directly out of a quantum theory of dispersion proposed by Kramers, Bohr's right-hand man at the time. Drawing on work by Einstein and Ladenburg, Kramers was able to reconcile Lorentz's theory of dispersion with Bohr's theory of the atom. With hindsight, it was only a small step from Kramers' theory to Heisenberg's matrix mechanics.

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