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Oxford University Press eBooks

Crisis: The End of the Bohr Model

Helge Kragh

Published May 17, 2012• 0 citations
Publisher

Abstract

Failed attempts to understand the anomalous Zeeman effect contributed to the feeling of crisis that by 1924 characterized parts of the physics community. The solution proposed by W. Heisenberg’s ‘core model’ only raised other problems. Another indication was the state of radiation theory and the uncertain relationship between wave theory and the light quantum, a problem that resulted in the controversial BKS (Bohr–Kramers–Slater) theory of 1924. In the wake of this theory, H. Kramers and Heisenberg constructed a formal theory of dispersion that did not rely on electron orbits but only on observable quantities, in agreement with the ‘quantum mechanics’ programme of M. Born. The development culminated with Heisenberg’s paper of August 1925, which marks the end of the Bohr model and the beginning of quantum mechanics. The chapter reconsiders the crisis and the reasons for it, in particular the role of experimental anomalies.

DOI
10.1093/acprof:oso/9780199654987.003.0008

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Failed attempts to understand the anomalous Zeeman effect contributed to the feeling of crisis that by 1924 characterized parts of the physics community. The solution proposed by W. Heisenberg’s ‘core model’ only raised other problems. Another indication was the state of radiation theory and the uncertain relationship between wave theory and the light quantum, a problem that resulted in the controversial BKS (Bohr–Kramers–Slater) theory of 1924. In the wake of this theory, H. Kramers and Heisenberg constructed a formal theory of dispersion that did not rely on electron orbits but only on observable quantities, in agreement with the ‘quantum mechanics’ programme of M. Born. The development culminated with Heisenberg’s paper of August 1925, which marks the end of the Bohr model and the beginning of quantum mechanics. The chapter reconsiders the crisis and the reasons for it, in particular the role of experimental anomalies.
Abstract This chapter covers the history of dispersion theory starting from the classical theories of the late nineteenth century, involving charged harmonic oscillators with resonance frequencies at the absorption frequencies of the dispersing materials to account for anomalous dispersion, the phenomenon that the index of refraction decreases rather than increases with frequency around the absorption frequencies. It then covers dispersion theories formulated in the context of the old quantum theory, in which the link between radiation frequencies and orbital frequencies is severed. Drawing on these efforts, especially by Ladenburg and Reiche in the early 1920s, and using Bohr’s correspondence principle and other ingredients of the old quantum theory, Kramers found a successful quantum formula in late 1923. He only published a full treatment of his new dispersion theory in a paper with Heisenberg in early 1925. This paper played a key role in laying the foundations of matrix mechanics.
Abstract The discovery of the Compton effect at the end of 1922 was a decisive event in the transition to the new quantum mechanics of 1925‐1926 because it stimulated physicists to examine anew the fundamental problem of the interaction between radiation and matter. I first discuss Albert Einstein's light‐quantum hypothesis of 1905 and why physicists greeted it with extreme skepticism, despite Robert A. Millikan's confirmation of Einstein's equation of the photoelectric effect in 1915. I then follow in some detail the experimental and theoretical research program that Arthur Holly Compton pursued between 1916 and 1922 at the University of Minnesota, the Westinghouse Lamp Company, the Cavendish Laboratory, and Washington University that culminated in his discovery of the Compton effect. Surprisingly, Compton was not influenced directly by Einstein's light‐quantum hypothesis, in contrast to Peter Debye and H.A. Kramers, who discovered the quantum theory of scattering independently. I close by discussing the most significant response to that discovery, the Bohr‐Kramers‐Slater theory of 1924, its experimental refutation, and its influence on the emerging new quantum mechanics.
This article discusses the history of quantum physics, beginning with an analysis of the process through which a community of quantum theorists and experimentalists came into being. In particular, it traces the roots and fruits of Max Planck’s papers in irreversible processes in nature. It proceeds by exploring the origin and subsequent development of Niels Bohr’s so-called ‘planetary model’ of the atom, focusing on the extension of the model by Arnold Sommerfeld and members of his school as well to Bohr’s use of his principles of correspondence and adiabatic invariance. It also considers the post-war years, as the problems of atomic spectroscopy sparked the development of new methodological approaches to quantum theory. Finally, it offers a history of the two distinct new forms of quantum mechanics put forward in the mid-1920s: Werner Heisenberg, Max Born, and Pascual Jordan’s matrix mechanics, and Erwin Schrödinger’s wave mechanics.
‘At the present state of science it does not seem possible to avoid the formal character of the quantum theory which is shown by the fact that the interpretation of atomic phenomena does not involve a description of the mechanism of the discontinuous processes […]. On the correspondence principle it seems nevertheless possible to […] arrive at a consistent description of optical phenomena by connecting the discontinuous effects occurring in atoms with the continuous radiation field […]’. This announced a turning point in atomic physics research; for the first time there were reasons to assert that discontinuity was not in itself incompatible with the theory's descriptive content, and rational solutions were provided that related a whole set of phenomena dependent on the radiation properties of matter to the continuous picture of the radiation field. This was the conclusion arrived at in a new paper by Bohr which took up and developed the hypothesis put forward by the American physicist John Slater that ‘the atom, even before a process of transition between two stationary states takes place, is capable of communication with distant atoms through a virtual radiation field’ was taken up and developed. The article, ‘The Quantum Theory of Radiation’, signed by Bohr, Kramers and Slater, was published in the Philosophical Magazine in January 1924. Slater had arrived in Copenhagen at the end of the preceding year with the idea that his hypothesis might lead to very different theoretical results.
The development of quantum mechanics in the early twentieth century marked one of the most profound conceptual revolutions in physics. Beginning with Planck's quantization of radiation and Einstein's interpretation of the photoelectric effect, followed by Bohr's atomic model, and later formalized by Heisenberg and Schrödinger, the theory provided a new description of nature—one in which probability amplitudes replaced deterministic trajectories. Within this framework, microscopic systems such as atoms, electrons, and photons are characterized by wavefunctions and operators rather than by points in phase space.
The exclusion principle was the final outcome of Pauli's struggle to understand some spectroscopic anomalies in the early 1920s: doublets were observed in the spectra of alkali metals, singlets and triplets in the spectra of the alkaline earths, and even more anomalous patterns were observed when chemical elements were placed in an external magnetic field (anomalous Zeeman effect and Paschen–Back effect). These anomalous spectra challenged the old quantum theory, and prompted a radical theoretical change (Section 2.1). From 1920 to 1924 Alfred Landé, Werner Heisenberg, and Niels Bohr were all engaged in trying to save the traditional spectroscopic model (the so-called atomic core model) and to reconcile it with the observed anomalies. The impasse was solved only with Pauli's introduction of a fourth degree of freedom for the electron, and the consequent demise of the atomic core model (Section 2.2). What Pauli called the ‘twofoldness’ [ Zweideutigkeit ] of the electron's angular momentum was soon reinterpreted as the electron's spin (Section 2.3). Pauli's exclusion rule was announced in this semi-classical spectroscopic context that characterized the revolutionary transition from the old quantum theory to the new quantum theory around 1925. The prehistory of Pauli's exclusion principle Atomic spectra and the Bohr–Sommerfeld theory of atomic structure The existence of spectral lines had been known to scientists since the beginning of the nineteenth century when Wollaston and Fraunhofer first observed the dark absorption lines in the spectrum of the Sun.