From the Rainbow to the Structure of Atoms

Abstract

AbstractThe optical rainbow is nowadays of much use, in the laboratory and in industry, in the field of optical characterization. However, the geometrical optics interpretation of the optical rainbow generates a caustic singularity which is a clue that something is wrong, and that a more fundamental theory (in practice, wave optics, or Maxwell's equations) is required to explain the optical rainbow and to accurately enough interpret experiments. There also exists a mechanical rainbow in classical mechanics, also leading to a singularity, implying that classical mechanics is wrong too. To smooth out this singularity, we have to turn to a wave mechanics. By lifting the Hamilton‐Jacobi formulation of classical mechanics to a wave mechanics and looking to a time evolution equation, we may reach Schrödinger's equation. We therefore establish a beautiful connection between the rainbow in the sky, and the structure of atoms, in the sky and on earth.