Sommerfeld: Atomic Structure

An English edition to Atomic Structure and Spectral Lines by Arnold Sommerfeld was published by Methuen & Co in 1919. Below we give the title page, the English translation of an extract from the Preface to the German edition, and Sommerfeld's Retrospect of the Development of Electrodynamics:

Atomic Structure and Spectral Lines
Arnold Sommerfeld

Methuen & Co Ltd
36 Essex Street W C

Preface (Extract)

After the discovery of spectral analysis no one trained in physics could doubt that the problem of the atom would be solved when physicists had learned to understand the language of spectra. So manifold was the enormous amount of material that had been accumulated in sixty years of spectroscopic research that it seemed at first beyond the possibility of disentanglement. An almost greater enlightenment has resulted from the seven years of Röntgen spectroscopy, inasmuch as it has attacked the problem of the atom at its very root, and illuminates the interior. What we are nowadays hearing of the language of spectra is a true "music of the spheres" within the atom, chords of integral relationships, an order and harmony that become ever more perfect in spite of the manifold variety. The theory of spectral lines will bear the name of Bohr for all time. But yet another name will be permanently associated with it, that of Planck. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious on which Nature plays her music of the spectra, and to the rhythm of which she regulates the structure of the atoms and nuclei.

September, 1919

§ 1. Retrospect of the Development of Electrodynamics

In the first half of the nineteenth century Electrodynamics consisted of a series of disconnected elementary laws. Formed analogously to Newton's Laws of Gravitation, they asserted the existence of direct action at a distance, which, starting from the seat of an electric charge or of magnetism and leaping over the intervening space was supposed to act at the seat of a second electric or magnetic charge.

Opposed to this there arose in the second half of the nineteenth century a view which followed the course of the continuously extended electromagnetic field from point to point and moment to moment; it was called the "Field Theory" in contradistinction to the "Theory of Action at a Distance." It was propounded by Faraday, worked out by Maxwell, and completed by Heinrich Hertz. According to this view the electromagnetic field is represented by the course, in space and time, of the electric and magnetic lines of force. Maxwell's equations teach us how electric and magnetic lines of force are linked with one another, how magnetic changes at any point of the field call up electrical forces, and how electric currents are surrounded by magnetic forces. The intervening medium, even if non-conducting, is supposed to have a certain transparency (permeability) and receptivity (dielectric capacity) towards magnetic and electric lines of force; hence at every point of space it influences the distribution of the electromagnetic field according to its constitution at that point.

The greatest triumph of this view occurred when Hertz succeeded in connecting light, the phenomenon of physical nature with which we are most familiar, with electromagnetism, which was at that time the most perplexing phenomenon. After Maxwell had already surmised that light was an alternating electromagnetic field (he succeeded in calculating the velocity of light from purely electrical measurements made by Kohlrausch), Hertz produced his "rays of electric force," which, just like light, are reflected, refracted, and brought to a focus by appropriate mirrors, and which are propagated in space with the velocity of light. The electric waves produced by Hertz had a wave-length of several metres. From them an almost unbroken chain of phenomena leads by way of heat rays and infra-red rays to the true light rays, whose wave-lengths amount to only fractions of ??. The greatest link in this chain came later as a direct result of Hertz's experiments, namely, the waves of wireless telegraphy, whose wave-length have to be reckoned in kilometres. (Nauen {A German radio transmitter] sends out waves having a wave-length of 12 kilometres, or 71/2 miles); the smallest and most delicate link is added at the other end of the chain, as we shall see, in the form of Röntgen rays, and the still shorter ??-rays which are of a similar nature; likewise the ultra- ?? - or cosmic radiation.

Hertz died on 1st January 1894, at the age of thirty-seven years. It would be natural to conclude that the later years of his short life and the work of his followers were occupied with the development of his wave experiments and of his theory of electromagnetic fields. But the last experimental paper by Hertz, "Concerning the Passage of Cathode Rays through Thin Metallic Layers" (1891), already pointed in a new direction.

The field theory had diverted attention from the origin of lines of force, and had chiefly served to illuminate their general course in a regular distribution of the field. The next question was to study the singitlarities of the field, the charges. The best conditions for doing so are offered by cathode ray tubes, which have a very high vacuum exceeding that of the so-called Geissler tubes (which were investigated by Plücker and Hittorf). Here we have electricity in a pure form, unadulterated by ordinary matter, and, in addition, moving in a straight line at an extremely high speed; cathode rays are corpuscular rays of negative electricity. It is true that Hertz as well as his eminent pupil Lenard first clung to the opposite view, namely, that the rays were undulatory in character; but Hertz had recognised the important value of the investigation of cathode rays for the future. Thus he had in this way helped personally in attracting workers from the field of physical knowledge just opened up by him towards pioneer work in a new field. In the sequel, the greatest interest became centred not in the propagation of the lines of force but in the charges, as the origin of these lines of force. The original theory of Maxwell which had been perfected by Hertz retained its significance for phenomena on a large scale, such as those of electrotechnics and wireless telegraphy, and gave an easy means of determining the mean values of the electrical phase quantities (i.e. quantities that define the state of the field). But to render possible deeper research leading to a knowledge of elementary phenomena a deepened view became necessary. Maxwell's Electrodynamics had to give way to Lorentz's Dynamics of the Electron; the theory of the continuous field became replaced by the discontinuous theory, that of the atomicity of electricity. So the theory of action at a distance and the theory of action through fields was succeeded by the atomistic view of electromagnetism, the theory of electrons.

JOC/EFR July 2008

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