6 Sommerfeld’s Atombau und Spektrallinien
A textbook is commonly perceived as a didactic tool dedicated to achieving the goals of curricula in teaching institutions. This definition may be regarded in an operational sense, with an eye to the actual uses in practical teaching, or with a focus on the author’s intentions (Bertomeu-Sánchez et.al. 2005, 223). In neither regard did Arnold Sommerfeld’s Atombau and Spektrallinien (1919) start out as a textbook. Its first edition was intended to popularize atomic physics for non-professionals. It was only in the course of its subsequent editions that it eventually transformed into one of the most renowned quantum textbooks in the twentieth century.
The story of Atombau und Spektrallinien, therefore, suggests a broader notion of a textbook. Rather than a singular event transforming past results of research into didactic lessons, a textbook may be a process—subject to change within its environment as much as the research for which it is accounting. Atombau und Spektrallinien entails an evolution of intentions, uses, and perceptions. Its author, Sommerfeld, was one of the architects of modern theoretical physics and a charismatic teacher who trained numerous quantum theorists (Eckert 1993; Seth 2010). He involved his talented students, among them prodigies like
The first four editions of Atombau und Spektrallinien (Sommerfeld 1919; 1921; 1922; 1924) and a wave-mechanical supplementary volume (Sommerfeld 1929) mirror the transformation of quantum and atomic physics during this crucial decade after the First World War. In 1931 Sommerfeld published the fifth edition of what he now named volume 1 of Atombau und Spektrallinien. The wave-mechanical supplement became volume 2. Like the pre-quantum-mechanical editions of volume 1, the “wave-mechanical” part would be subject to revision, adaptation, and extension. Sommerfeld dedicated a good deal of his energies during the 1930s to this effort. When he finally published the second edition of volume 2 in 1939, its size had more than doubled from 352 to 819 pages. If we ignore the minor changes added in subsequent editions, the process that lay behind Atombau und Spektrallinien extended over more than two decades. The results of this process comprise a series of pre- and post-quantum-mechanical editions that stand out as unique within the physics textbook literature (see table 6.1).
|Atombau und Spektrallinien|
|1st edition||1919||550 pages|
|2nd edition||1921||583 pages|
|3rd edition||1922||764 pages|
|4th edition||1924||826 pages|
|Atombau und Spektrallinien I|
|5th edition||1931||734 pages|
|6th edition||1944||734 pages|
|Atombau und Spektrallinien II|
|Wellenmechanischer Ergänzungsband||1929||352 pages|
|2nd edition||1939||819 pages|
|3rd edition||1944||819 pages|
6.1 The chronology of editions of Atombau und Spektrallinien (1919–1944).
Despite this ongoing gestation, Atombau und Spektrallinien was already praised in 1923 as “the bible of the modern physicist.”1 These and other assessments of the early editions suggest that it was not the final result—the two–volume edition from the 1930s—but the entire process of its development, particularly on the eve of quantum mechanics during the early 1920s, which made Atombau und Spektrallinien a classic of modern textbook literature.
This chapter is concerned only with the first four editions of Atombau und Spektrallinien, published before the advent of quantum mechanics. The focus is on its conception, birth, growth, and reception, that is, the evolution that characterizes this textbook as the embodiment of a process extending from the First World War until the eve of quantum mechanics. The post-quantum-mechanical phase concerning the further transformation of the fourth into a fifth edition (1931) and the addition of a wave-mechanical supplementary volume (1929–1939) is left to a sequel.
6.2 Popular Lectures
We have to look at Sommerfeld’s pedagogy to lay open the roots of Atombau und Spektrallinien. Although the later success of Sommerfeld’s school tends to glorify its haphazard beginnings (Eckert 1999; Seth 2010, chap. 2), the list of his early disciples bears testimony to flourishing pedagogical activity. (Among these numbered
In addition to the lectures, students in the Munich “nursery of theoretical physics,” as Sommerfeld used to call his institute, were trained for future careers in research and teaching through seminars and colloquia. The seminar was, at first, only a forum where students were presented with problems related to the theme of the main lecture.2 Eventually, the seminar acquired the research orientation about which Sommerfeld’s later students reported enthusiastically in their recollections (i.e., Bethe 2000). The pedagogical activity that offered the closest contact with current research themes, before the First World War, was the regular Munich Wednesday Colloquium.3 Here Sommerfeld’s advanced students could present results from their doctoral work and discuss them with advanced students from Wilhelm Röntgen’s institute. Occasionally, the Munich theorists invited speakers from other universities to present their most recent papers in an informal environment. On 15 July 1914, for example,
In summer 1916, when Sommerfeld published his extension of
How little Sommerfeld perceived these popular lectures as the seed for a textbook on theoretical physics is evident from the explicit emphasis on “without mathematical deduction.” Although he must have already thought about publishing a book during the course of the first of these public lecture series, in the winter semester of 1916/17, he did not have physicists in mind as his readers. “This semester I held a popular lecture on atomic structure and spectral lines,” he wrote to
The audience was about 80 people, among them 12 colleagues, mainly chemists, medical scientists, and philosophers. I intend to publish it as a book. I had so much fun that I will try to lecture on relativity in the next semester also popularly, i.e., without mathematics, only conceptually presented.6
Sommerfeld also presented popular lectures for soldiers at the western front in January 1918. Unfortunately no records are preserved from these presentations; in a letter to his wife,
To address an audience of non-physicists may have been an exciting challenge when restricted to a few lectures, a museum exhibition, or a speech to soldiers about “peace physics”—but when it came to writing a book it also involved a sacrifice. Sommerfeld could not give as much space to his own recent achievements in atomic theory as he might have wished, had he envisaged theoretical physicists as his readership. Such advanced subjects as the fine structure theory were curtailed for the benefit of a broader exposition of subjects like radioactivity, X-rays, or the periodic system. He was well aware of this self-imposed limitation. “I am now writing a half-popular general presentation of the field and have repressed my own curiosity,” he confided in December 1918 to a colleague with whom he otherwise exchanged his most recent results concerning the theory of X-ray spectra.12
But he did not entirely abstain from presenting research that had not yet had enough time to be generally accepted—all the more when it originated from his own institute. One recent accomplishment in which he took particular pride was the theoretical derivation of selection rules obtained without recourse to additional assumptions by
The writing of Atombau und Spektrallinien, therefore, lasted less than a year, from early summer 1918 to the spring of 1919. If we take the first mention of the book at the end of the winter semester 1916/17 as its inception, we may add a two-year stretch of popular lectures as a gestation. Neither the war nor the ensuing revolutionary turmoil seems to have had an impact on the transformation of the popular, wartime lectures into a semi-popular textbook. Sommerfeld, however, like most of his colleagues, was far from untouched by these events. Politically he may be characterized by and large as national-liberal.16 His lectures at the front involved close contact with leading military officials and chauvinistic cultural propaganda. After his trip to Belgium in January 1918, Sommerfeld praised, in a newspaper article, the transformation of Ghent University into a German university as “the most effective and seminal trait of German politics in Belgium which tackled the problem at its root, the root of the common Germanic culture.”17 After the war, during the short-lived Soviet government in Munich in the spring of 1919 (to which the press often attached the epithet “Jewish”), Sommerfeld wrote in a moment of anger at the Munich revolutionary unrest to the right-wing
It appears at Vieweg. I had also negotiated with Teubner and Springer. Teubner was not at all accommodating and seems to be in economic troubles. Springer was very tempting, but I did not trust his business practices and am becoming more and more anti-semitic in view of the Jewish-political mischief.18
Otherwise the turbulent times during which the book project was carried out left no traces. Up to the last moment, Sommerfeld continued to add recent results that seemed pertinent to the proofs.19 In the preface, dated 2 September 1919, Sommerfeld emphasized once more that his book was an attempt to popularize its subject matter and its inception lay in popular lectures given during the war. That the last two of the six chapters, where he reviewed his fine-structure theory,
6.3 First Reactions
By the end of October 1919, the book was printed.20 The very first reactions signaled that Atombau und Spektrallinien would be a success.
This was not the only political allusion in the flood of positive, and often euphoric, reactions.
Thus the postwar political-ideological climate contributed to the transformation of Sommerfeld’s book from a mere exposition of scientific facts into a classic of its time. Of course, there was also a true need for educating physicists on the recent developments in atomic physics. A whole generation of students was returning to the universities, hungry for mental as much as physical nourishment, and eager to absorb the new scientific knowledge about atoms that had been developing so quickly while they were in the trenches.26 Atombau und Spektrallinien offered this knowledge at the right time in a condensed and easily accessible manner. Within a few weeks, the need for a second edition became apparent. “Vieweg informs me today,” Sommerfeld wrote to
Given the euphoric response that Sommerfeld received in numerous letters, from his colleagues it is hardly astonishing that the public reception of Atombau und Spektrallinien was equally favorable. The reviewer in the Physikalische Zeitschrift recommended this “excellent opus” for every physicist interested in atomic physics simply as “indispensable” (Bergwitz 1920, 223–224). In the Physikalische Berichte, the review organ of the physics community, it was predicted that Atombau und Spektrallinien would exert “the deepest effect as a compendium, tool, and guide to further development” (Kossel 1920, 536–537). Another glowing review appeared in Springer’s Naturwissenschaften. The book is
[of] such a pervasive power that every reader with an interest in science must feel swept along and made a docile follower of the author into the new world which was opened up to a large extent by his scientific intuition and that of his disciples. (Franck 1920, 423–424)
Even though many will not follow the guide up to the highest peaks there are enough lookout points within effortless reach from which the sight is rewarding. In particular the first four chapters, which cover more than half of the book, may claim to be broadly understandable. Their reading will be particularly useful for the chemist. (Franck 1920, 423–424)
For the physicist, the book deserved “the greatest interest in all its parts,” not the least because the author had the courage to present “here and there theoretical and experimental material which perhaps will not prove sustainable in the course of further research.” In this manner he reached “to the farthest outposts of atomic research” (Franck 1920, 423–424).
The praise was not limited to private letters and book reviews. When
The favorable reception of Atombau und Spektrallinien was only occasionally accompanied with critical remarks.
[S]ome things in such a way that the layperson must think that everything is in order; but that is often not the case, for example the molecular models of H2 etc., furthermore the whole theory of X-ray spectra.
Landé, at least, has told me recently that everything is in disorder here. Wouldn’t it be good to emphasize the doubts a little more?31
He also blamed Sommerfeld for being too lokalpatriotisch, for example when he gave preference to
6.4 The Second and Third Editions
The second edition was as short-lived as the first. A few months after its appearance, Sommerfeld wrote to
After releasing the second edition with only minor changes, it was clear to Sommerfeld that he would have to make a considerable effort to adapt the third edition to the current state of atomic knowledge. Besides
I do not have the power to do this and am content with the details of the quantum magic in the spectra. Here there are the ‘inner quantum numbers’ which interest me. I have no idea what they mean but they unravel the composed triplets (and doublets).39
With the “inner quantum numbers” and other ad hoc concepts introduced to explain spectroscopic data, Sommerfeld’s atomic theory became more empirical. The new approach seemed particularly appropriate in accounting for the
By that point, in January 1922, he had finished the revisions for the third edition. The excitement about the most recent advances is also manifested in his preface to this edition:
I attach particular importance to the introduction of the inner quantum numbers (chap. VI, § 5), and to the systematic arrangement of the
anomalous Zeeman effects (chap. VI, § 7). The regularities that here obtain throughout are primarily of an empirical nature, but their integral character demands from the outset that they be clothed in the language of quanta. This mode of explanation, just like the regularities themselves, is fully established and is unique. Even at the present early stage it has shown itself in many respects to be fruitful and suggestive.42
In terms of personalities, the indisputable main character of the book was
for the friendly attitude with which you regarded my work and that of my collaborators. During the last years I have often felt scientifically very lonely, under the impression that my tendencies to develop the principles of quantum theory systematically to the best of my ability have been received with very little understanding. For me this is not a matter of a didactic trifle but a sincere effort to obtain an inner connection such that one can hope to create a valid fundament for further construction. I understand very well how little things are yet resolved, and how clumsy I am with expressing my thoughts in an easily accessible manner. All the more I was pleased to see a change of your attitude in the new edition of your book.46
By and large, the third edition was praised as a new accomplishment—and a glimpse at a rapidly-evolving subject. “Everywhere one becomes aware about the progress,”
[A]nd at the same time the systematic rounding of the ideas developed by yourself. Admittedly even now one can not yet speak of an accomplishment of quantum theory as in classical theories. Even the immensely productive
correspondence principle does not yet procure the complete connection to the classical theory.47
6.5 Atombau und Spektrallinien in the United States (1922/23)
In the summer of 1922, Sommerfeld received an invitation from the University of Wisconsin in Madison to lecture there as the Karl Schurz Professor for four months, from September 1922 to January 1923.52 The invitation of a German so shortly after the war was an event that attracted great attention all over the United States. “German Scientist Coming,” the New York Times reported the news on 6 August 1922. “The Karl Schurz Memorial Professorship was founded in 1910 as an exchange professorship with the German universities,” the newspaper informed its readers. “The appointment of Professor Sommerfeld marks its resumption after the interruption caused by the war.” But it was not only this political context—alluding to the pro- and anti-German attitudes taken in the course of US entry into the Great War in 1917—that made the invitation at the University of Wisconsin worth an article in the New York Times. The advances in physics achieved in Europe were being watched with great curiosity and had already resulted in invitations of professors from overseas to several American universities, including
At that time, in autumn 1922, there was still no English translation of Atombau und Spektrallinien available. Those attempting to learn about the recent advances in atomic physics used the third German edition, which had just appeared. But the fame of Sommerfeld’s book preceded the English translation. The news of Sommerfeld’s arrival spread among universities and research laboratories all over the United States, resulting in a flood of invitations to lecture on the subject of his book. “I will be very glad to visit your excellent laboratories at Schenectady and to deliver there a few lectures about Atomic Structure or Spectral Lines,” Sommerfeld responded, for example, to an invitation from the Research Laboratory of General Electric.54 He visibly enjoyed his role as harbinger of a new physics. “Crew is a spectroscopist,” Sommerfeld explained in a letter to
Altogether, Sommerfeld lectured at seventeen locations during his six-month sojourn in the United States. While he was based in Madison for his main stay, at the University of Wisconsin from September 1922 to January 1923, he visited Evanston, Milwaukee, Minneapolis, Ann Arbor, and Urbana. In January, he traveled to California, where
Although Sommerfeld was regarded by some of his American colleagues as “an oracle” with regard to atomic structure and spectral lines, the knowledge transfer accompanying Sommerfeld’s lecture invitations worked both ways. Sommerfeld was particularly interested in “the astrophysical fairyworld of the Mt. Wilson and the first-rate research institution in Pasadena which the energy of Mr. Millikan has created,” as he wrote some months before his visit to his former disciple
The encounter with empirical spectroscopy in America left visible traces—in Sommerfeld’s own research, in his pedagogical practice, and in the forthcoming fourth edition of Atombau und Spektrallinien. After his return to Munich, Sommerfeld continued to discuss spectroscopic details with his American colleagues. “May I ask you to send me the Fe-spectrum from Mt. Wilson,” Sommerfeld wrote to
Besides experimental spectroscopy, the “most interesting” scientific news which Sommerfeld encountered during his American sojourn was “a work by
it would have the consequence that the wave theory of X-rays has to be definitely abandoned. I am not yet totally convinced whether he is right, and I do not know whether I should already speak about his results. I only would like to point out that we may expect eventually a very fundamental new instruction.64
Within a few months, Compton’s experimental result was transformed into the
6.6 The Fourth Edition
Bohr’s theory of the periodic system, Compton’s discovery, much more on inner quanta, magnetons and anomalous Zeeman effects than the third edition. Of course it will contain all we know until now about multiplets. I am glad that my sojourn in Washington bore good fruits in this regard.66
With regard to the
The theory of complex spectra (i.e., the spectra of atoms with more than one valence electron) was a particular highlight of this edition. It forced Sommerfeld irrevocably to abstain from model interpretations of spectral lines. The demise of a visual interpretation in terms of electronic orbits seemed already unavoidable in light of the so-called doublet riddle (Forman 1968). Sommerfeld’s fine structure theory from 1916 had persuasively shown that the doublets observed in X-ray spectra were caused by a relativistic effect, the same effect which caused the fine-structure split of hydrogen lines, but magnified by a factor proportional to the fourth power of the nuclear charge; on the other hand, the optical doublets, like the yellow sodium lines, were interpreted as a magnetic effect, resulting from different orientations of angular momenta. Thus, the doublets of the optical and X-ray spectra were interpreted in terms of different physical models. In April 1924, ultraviolet spectra measured in
Uncertain, however, is the interpretation in terms of a model […] Like with the X-ray spectra it is at present advisable to leave the model interpretation more or less open and to limit oneself, in the main part, to ascertaining the facts quantum-theoretically. (Sommerfeld 1924, 575)
Apart from the wealth of new empirical material, it was this turn toward a model-free approach in atomic theory that rendered the fourth edition peculiar.
The model conceptions are now in a fundamental crisis. I guess it will finally end in a further radical accentuation of the contradiction between classical and quantum theory. As becomes particularly clear from
Millikan’s and Landé’s findings concerning the representation of the optical alkali doublets by relativistic formulae, it will hardly be possible to maintain the notion of definite distinct orbits of electrons in the atom. When we speak in terms of models we use a language that is not sufficiently adequate to the simplicity and beauty of the quantum world. For this reason I found it so nice that your presentation of the complex structure is entirely free of all model prejudices.68
Pauli argued from the perspective of a theorist who was primarily interested in the foundations of quantum theory, but experimental spectroscopists also had reasons to welcome the new edition. Atombau und Spektrallinien is “the bible of the practical spectroscopists,”
Others regarded the ever-growing empirical material in Sommerfeld’s Atombau with mixed feelings—and added a dose of sober restraint to the praise. The reviewer in the Physikalische Zeitschrift (Georg Joos), for example, found it “regrettable, but apparently unavoidable” that since the appearance of the third edition “all hopes in model calculations were frustrated.” But he acknowledged that the gain of “arithmetic laws in the complex structure of the spectra” compensated the abandonment of “atomic mechanical speculations” (Joos 1925, 424).
Within only five years after the appearance of its first edition, Atombau und Spektrallinien experienced manifold transformations. The size increased considerably (from 550 to 862 pages). The popular character receded in favor of a growing exposition of expert knowledge. According to the review quoted above, it assumed “more and more the character of a handbook,” although the reviewer considered it “still well readable for the scientifically educated non-professional.”
For the professional quantum theorist, the transformations from the first to the fourth editions were even more striking: Atombau und Spektrallinien presented an evolving body of knowledge about quanta and atoms, which was used at the same time as an indicator of the forefront of research for those who contributed to this process. Numerous physicists recalled that they experienced their first encounter with quantum theory through Atombau und Spektrallinien.72
The fourth edition, which saw the explicit demise of “model prejudices,” may be regarded as opening the door for Pauli’s exclusion principle and the spin concept. Few other textbooks displayed to such an extent their own content as subject to change.
Quantum mechanics did not end this process of transformation. In 1929, Sommerfeld published the Wellenmechanischer Ergänzungsband which was subsequently labeled Atombau und Spektrallinien II. The story of this second volume is beyond the scope of this chapter, but it is worth mentioning here that it also underwent fundamental transformations. Unlike Atombau und Spektrallinien I, it was conceived from the very beginning as a physics textbook, without any aspirations to popularity among non-professionals. But this did not prevent an increase in size between the first and the second edition (published in 1939) from 351 to 820 pages. Furthermore, the second volume shared with the first volume the feature of having been a group effort: Sommerfeld explicitly thanked his disciples
Over the years, other textbooks became available which dealt with one or another subfield of quantum physics in a more appropriate manner than the latest available edition of Atombau und Spektrallinien. For a physicist of the post-quantum-mechanical era, the historical legacy transmitted through the subsequent editions might appear more of a burden than a virtue. Nonetheless, a good deal of this material was regarded as worth knowing far beyond the initial publication of a new edition, so that later textbooks referred to Atombau und Spektrallinien as a basis from which one could embark in a new direction, and to which one could safely return whenever a detail demanded closer inspection. This longevity would be difficult to understand if Atombau und Spektrallinien had merely been a depository of settled knowledge from the pre-quantum-mechanical era.
Abbreviations and Archives
|AEA||Albert Einstein Archives, Hebrew University, Jerusalem|
|AHQP||Archive for History of Quantum Physics. American Philosophical Society, Philadelphia|
|AIP-NBL||American Institute of Physics, Niels Bohr Library, College Park, MD|
|Bancroft Library||University of California, Berkeley|
|Birge Papers||Bancroft Library|
|Caltech||Caltech Archives, California Institute of Technology, Pasadena|
|Churchill Archives Centre||Churchill College, Cambridge|
|DMA||Deutsches Museum, Archive, Munich|
|Meitner Papers||Churchill Archives Centre|
|NBA||Niels Bohr Archive, Copenhagen|
|NBS||National Bureau of Standards|
|NLP||National Liberal Party|
|Private collection, Munich||The owner of this collection wants to remain anonymous|
|Private collection, Warsaw||The owner of this collection wants to remain anonymous|
|RANH||Rijksarchief in Noord-Holland, Haarlem|
|SBPK||Staatsbibliothek Preußischer Kulturbesitz, Berlin|
|SUB||Staats- und Universitätsbibliothek, Göttingen|
|Theodore von Kármán Papers||Caltech|
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