Rudolf Ladenburg and the first quantum interpretation of optical dispersion

Abstract

In 1921, the experimental physicist Rudolf Ladenburg put forward the first quantum interpretation of optical dispersion. Theoretical physicists had tried to explain dispersion from the point of view of quantum theory ever since 1913, when Niels Bohr proposed his quantum model of atom. Yet, their theories proved unsuccessful. It was Ladenburg who gave a breakthrough step toward our quantum understanding of dispersion. In order to understand Ladenburg’s step, I analyze Ladenburg’s experimental work on dispersion prior to 1913, the reasons why the first theories of dispersion after 1913 were not satisfactory, and Ladenburg’s 1921 proposal. I argue that Ladenburg’s early experimental work on dispersion is indispensable to understand his 1921 paper. The specific kind of experiments he performed before 1913, the related interpretative problems, and the way he tried to solve them, led him reapproach the dispersion problem in 1921 in a way that was completely different from the way theoretical physicists had done it before.

Application of Einstein’s Methods in a Quantum Theory of Radiation

“…When Bohr introduced his theory of electron orbitals he immediately recognized the possibility that the discrete lines of atomic spectra are related to the discrete lines in dispersion phenomena [3]. Other researchers, in particular Debye and Sommerfeld, were also inspired by that possibility and a series of papers appeared that tried to explain the discrete and continuous properties of dispersion by introducing classically inspired modifications of the electron orbitals [2,4,5]. However, when experiments revealed that the characteristic frequencies of anomalous dispersion coincide with the frequencies of the spectral lines it was evident that orbiting electrons could not account for both and a complete break from classical theory was necessary.…”

“…However, when experiments revealed that the characteristic frequencies of anomalous dispersion coincide with the frequencies of the spectral lines it was evident that orbiting electrons could not account for both and a complete break from classical theory was necessary. Ladenburg was the first to suggest how the new quantum theory would appear by following Einstein's reasoning leading to the A and B coefficients [5][6][7]. This enabled him to equate two theoretical expressions, the energy absorbed/emitted by N classical resonators and the energy absorbed/emitted by N 0 quantum atoms.…”

“…By obtaining a statistical balance between classical and quantum mechanical energy exchange he satisfied the conservation of energy, but not that of momentum. Four years later Kramers reinterpreted Ladenburg's results by using the Bohr model of the atom as a multiply periodic system of virtual oscillators [2,5,8,9]. In that model a quantum mechanical variable X is described with a classical Fourier series, where A(n, nτ) is the quantum analog of the classical amplitude, n indicates the electron orbital number, and τ assumes integral values to denote positive or negative transitions [9].…”

Albert Ladenburg (1842-1911) – The Distinguished German Chemist and Historian of Chemistry of the Second Half of the XIX Century (To the 110th Anniversary of His Death)

“…He drowned in a sailboat accident on Lake Müggel. [35][36] His third son, Rudolf, became a German-American atomic physicist. 37 In 1905, he has had to undergo amputation of the right leg.…”