Charles Galton Darwin\u2019s 1922 quantum theory of optical dispersion

Benjamin Johnson

doi:10.1140/epjh/e2020-80058-7

Abstract

The quantum theory of dispersion was an important conceptual advancement which led out of the crisis of the old quantum theory in the early 1920s and aided in the formulation of matrix mechanics in 1925. The theory of Charles Galton Darwin, often cited only for its reliance on the statistical conservation of energy, was a wave-based attempt to explain dispersion phenomena at a time between the theories of Ladenburg and Kramers. It contributed to future successes in quantum theory, such as the virtual oscillator, while revealing through its own shortcomings the limitations of the wave theory of light in the interaction of light and matter. After its publication, Darwin’s theory was widely discussed amongst his colleagues as the competing interpretation to Compton’s in X-ray scattering experiments. It also had a pronounced influence on John C. Slater, whose ideas formed the basis of the BKS theory.

Highlights

The European Physical Journal H to add another piece to Darwin’s scientific biography, this article examines his 1922 publication A Quantum theory of Optical Dispersion (Darwin, 1922b, 1923b) as a concrete, but overlooked step in the conceptual development of dispersion theory
The form the quanta took during propagation was not clear. Were they directed with defined energy and momentum or wave-like as they dispersed in free space, as the majority of physicists believed (Stark, 1909a,b)?
Bohr did not find the mathematical or conceptual execution of Darwin’s paper to be satisfactory, as he wrote to his brother Harald on June 12, 1912, but, at a time when his own ideas on atomic structure were nearing fruition, he did not brush it aside without consideration (Mehra 1982a [page 185]). This would not be the only time a daring, but flawed idea of Darwin’s led Bohr to a more progressive position. Throughout this period, Darwin remained a stalwart of classical physical concepts, but he was aware of the controversy stirred by Planck’s derivation of the radiation law (Sanchez-Ron, 1993)

Summary

Introduction

The European Physical Journal H to add another piece to Darwin’s scientific biography, this article examines his 1922 publication A Quantum theory of Optical Dispersion (Darwin, 1922b, 1923b) as a concrete, but overlooked step in the conceptual development of dispersion theory. The harmonic oscillator provided insight and motivation for the final formulation of matrix mechanics in 1925 (Jammer 1966 [page 181]; Mehra 1982c [page 170]; Blum 2017) Throughout this period, Darwin remained a stalwart of classical physical concepts, but he was aware of the controversy stirred by Planck’s derivation of the radiation law (Sanchez-Ron, 1993). Beyond the ideas extending from Planck’s radiation law, Darwin was likely exposed to other perspectives critical of the conservation of energy before he left for war He was a well-known admirer of Henri Poincare’s and translated the French mathematician and physicist’s On The Theory of Quanta into English (Poincare, 1912; Darwin, 1919d).. Like Newton’s laws, and for an analogous reason, the principle of the conservation of energy being based on experiment, can no longer be invalidated by it

Toward non-conservation

Darwin’s 1922 theory of optical dispersion

Reactions to Darwin’s theory

Conclusion