Sommerfeld, Arnold Johannes Wilhelm

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(b. Königsberg, Prussia [later Kaliningrad, Russia], 5 December 1868; d. Munich, Germany, 26 April 1951), theoretical physics, quantum theory. For the original article on Sommerfeld see DSB, vol. 12.

Paul Forman’s and Armin Hermann’s thoughtful and detailed portrayal of Sommerfeld’s career does not need major revisions (see DSB). However, the historical research since that essay has resulted in a deeper understanding of the boundary zones between physics and mathematics at the turn from the nineteenth to the twentieth century, so that Sommerfeld’s case may be better evaluated in larger contexts. New source material concerning his early career displays in great detail the contingent and fragile nature of the nascent discipline of theoretical physics; for the later period, Sommerfeld’s scientific correspondence reveals his dominant role for the spread of this discipline.

Although best known for the relativistic extension of Niels Bohr’s atomic model, Sommerfeld’s career should not be regarded with a focus on relativity and quantum theory alone. Physics was not his initial calling. For more than a decade of his beginning academic life, Sommerfeld traversed disciplinary boundaries between mathematics, physics, and technology: During his study at the university of his home town, Königsberg, his favorite discipline was mathematics; he graduated with a doctoral dissertation in mathematics and a state examination that qualified him to teach mathematics, physics, chemistry, and mineralogy at the high school (Gymnasium) level. During a five-year sojourn at the University of Göttingen, from 1892 to 1897, he acquired the qualification to present lectures at universities (venia legendi) with a dissertation on the “mathematical theory of diffraction.” In 1897 he became professor of mathematics at the mining academy (Bergakademie) in Clausthal. Three years later he accepted a position as professor of mechanics at the technical university (Technische Hochschule) in Aachen. In 1906 he became a professor of theoretical physics at the University of Munich, which became his lifelong academic home.

Work at Göttingen The emergence of theoretical physics has been largely perceived as a specialization from its mother-discipline, physics, pursued by low-ranking professors as a transient activity in the beginning of their career. However, Sommerfeld’s approach to theoretical physics, as well as the early career of other theorists, such as Max Born, and the physical work of mathematicians such as David Hilbert, Henri Poincaré, and Hermann Minkowski—all among Sommerfeld’s frequent correspondents—indicate a stronger role for mathematics in this process of disciplinary formation during the crucial period between the 1890s and World War I. Local traditions, such as those at Cambridge and Göttingen, have been described in great detail with regard to the enticements and constraints of developing new research agendas. From this perspective, Sommerfeld’s academic maturation in Göttingen deserves a renewed interest. While he was Felix Klein’s assistant in the mathematics institute at Göttingen University, Sommerfeld’s specialty was designated as “physical mathematics”—a mathematical subfield that used physics as a tool for mathematics rather than the other way around. With this orientation, Sommerfeld became an expert in physical differential equations and complex functions (potential theory). He regarded Klein as his role model.

Although his early scientific papers appear disparate from the perspective of physics, because they addressed phenomena in such diverse areas as optics, electromagnetism, and x-rays, they are coherent with respect to their underlying mathematical approach. When Sommerfeld was called as professor of mechanics to Aachen in 1900, he embraced technology in addition to physics as an opportunity to display and interpret Klein’s tendencies. At the same time, another Kleinian legacy brought him into closer contact with physics: As an editor of the physics volumes of the Encyclopedia of Mathematical Sciences, Sommerfeld traveled together with Klein to England, for example, in order to invite leading representatives of contemporary physics to review their field for the encyclopedia. His correspondence with encyclopedia authors reveals how he occasionally developed new research problems based on contemporary themes from a wide range of subjects. Thus, he combined mathematical versatility with an awareness of the actual research front in physics. When he was considered as a candidate for the chair of theoretical physics at the university in Munich, the committee found Sommerfeld’s approach attractive because it attempted to bring to bear “the new knowledges of the theory of functions to solve various physical problems” (Eckert and Pricha, 1984, p. 112).

Years at Munich In Munich, mathematics, technical mechanics, and physics finally merged into theoretical physics as his lifelong profession. Traversing disciplinary boundaries, however, entailed problems. Mathematicians, such as Sommerfeld’s Königsberg professor Ferdinand von Lindemann, and physicists, like those at the University of Leipzig, where Sommerfeld was considered and turned down in 1902 as successor to Ludwig Boltzmann, had mixed feelings about Sommerfeld’s qualification as a theoretical physicist. During his first years in Munich, where he became director of a new institute of theoretical physics, Sommerfeld struggled hard for recognition among physicists. At the same time, during a period when

there were few ordinary chairs for theoretical physics, Sommerfeld’s Munich institute naturally attracted the interest of aspiring theory-minded students. Sommerfeld had to find his own way of teaching theoretical physics. He often chose contemporary problems as subject matter for lecture courses. It took several years before Sommerfeld’s haphazard lectures gradually turned into a regular six-semester sequence of lectures, which was later considered as canonical for teaching theoretical physics. He also granted considerable freedom to his students to pursue their own research interests for doctoral theses. The topics ranged from turbulence in a river to wireless telegraphy and often involved both experimental and theoretical investigations with uncertain prospects of success. Those who mastered the difficulties spread the renown of Sommerfeld’s “nursery” (Pflanzstätte), as he himself called his institute, but at least in one case he was criticized for not caring enough for his doctoral student.

Sommerfeld’s approach in theoretical physics has been described as a “physics of problems”—in contrast to the “physics of principles” of Max Planck, for example (Seth, 2003, p. 8). Sommerfeld’s eagerness to demonstrate the mathematical accessibility of physical problems from many areas made him aware of new challenges and brought him into close contact with contemporary experimental investigations. Shortly before his call to Munich, for example, he exchanged long letters with the experimental physicist Friedrich Paschen, whose recent experiments on gamma rays seemed to verify his ideas on the electron theory. Although this effort of “theoretically experimenting” failed in 1905 (Eckert and Märker, 2000), it was successfully renewed a decade later, when Sommerfeld and Paschen focused their interest on atomic spectra. Sommerfeld made Bohr’s atomic model a subject of his own research not for theoretical reasons but because of its success in determining a spectroscopic quantity (Rydberg’s constant); by extending Bohr’s model Sommerfeld hoped to break new ground in the field of atomic spectroscopy. This time, Paschen’s measurements indeed confirmed Sommerfeld’s theoretical results, which in turn motivated further spectroscopic investigations. During World War I, Sommerfeld and Paschen opened a new chapter of atomic theory by exploring the fine structure of atomic spectra. After the war, a similar collaboration with Manne Siegbahn on x-ray spectroscopy further consolidated the success of this approach.

Barriers to the Nobel Prize It has long been a subject of debate why Sommerfeld was not awarded the Nobel Prize. For more than a decade after he had published his monumental paper “On the Quantum Theory of Spectral Lines” in 1916, Sommerfeld was nominated almost regularly for the Nobel Prize. There were rumors that he was turned down because of “rivalry with Bohr,” as Sommerfeld confided in a letter to a close colleague; he felt hurt by this neglect and argued that “it would have been the only correct and sincere manner to award me in 1923, after Bohr had received the prize in 1922.” (“Jedenfalls wäre es das einzig Richtige u. Anständige gewesen, nachdem Bohr den Preis 1922 erhalten hatte, mir ihn 1923 zu geben”; quoted in Eckert and Märker, 2004, p. 292). As is apparent now from the files of the Nobel archives, he had no chance for the award because the representative of physics on the Nobel committee, Carl Wilhelm Oseen, regarded Sommerfeld’s style of theorizing as not fundamental enough.

Research Program Sommerfeld’s versatile approach toward a variety of physical problems makes it difficult to discern a favorite specialty. Following atomic theory, to which he focused his own and his students’ research for about a decade after 1915, the electron theory of metals became a major object of study. Just as Sommerfeld’s extension of Bohr’s model had opened a route toward quantum mechanics, his semiclassical electron theory (1927) paved the way for the quantum theory of solids.

However, it would be misleading to sum up his contributions only as a hinge between classical and modern physics—a transition that deserves critical analysis on its own. The editors of Sommerfeld’s collected works sorted his published articles into thirteen categories: mathematics, mechanics, electrodynamics, electron theory and relativity, statistical mechanics, electron theory of metals, electromagnetic waves, atomic structure and spectral lines, quantum mechanics, elementary processes, x-ray diffraction, x-ray Bremsstrahlung-spectrum, and popular writings. The same versatility is mirrored by those who grew up in the “Sommerfeld school,” a lineage that was regarded with high esteem among the first generations of twentieth-century theoretical physicists. By comparison with Planck and Albert Einstein, who have been characterized as the authority and the genius, respectively, of German theoretical physics in the first decades of the twentieth century, Sommerfeld was labeled as the teacher of the discipline. “Schools” in science, often called “research schools,” “thought collectives,” “invisible colleges,” or otherwise, have been discerned as crucial for the formation of new specialties. The “Sommerfeld school” played such a role for the emergence of theoretical physics. However, the character of Sommerfeld’s school differs from that of a thought collective: Versatility rather than a common style or focus on a specific subject matter was characteristic for the pupils as much as for their teacher. Peter Debye and Werner Heisenberg, for example, represented rather different styles of theorizing, although they were both Sommerfeld pupils and later even colleagues at the same university in Leipzig. During World War II, when some of Sommerfeld’s pupils were involved in the German and in the British-American atomic bomb and radar projects, little hinted at their common descent from the Munich “nursery.”

It is worth mentioning, however, that not only in Germany but all around the world theoretical physicists felt connected in one way or another with Sommerfeld’s school. Sommerfeld was an ambitious missionary of his discipline and spread the gospel of new research results throughout the world. His book Atombau und Spektrallinien went through many editions and was translated in many languages. He was invited as a guest lecturer to many countries and welcomed foreign students in his institute. His ties with physics in the United States were confirmed in 1949, when the American Association of Physics Teachers chose Sommerfeld as the recipient of its Oersted Medal “in recognition of your contribution to the broad field of the teaching of physics both directly here and elsewhere and through students who have worked with you” (Eckert and Märker, 2004, p. 632). To award this distinction to a German so shortly after World War II also shows that American physicists counted Sommerfeld among the few German scientists who were untainted with regard to Nazi affiliations. Sommerfeld was known for his strong national feelings during and after World War I, but he was cured from nationalism when he experienced the National Socialists’ rise to power. After his retirement in 1935, the succession of Sommerfeld’s chair turned into a tug-of-war with an anti-Semitic faction of fanatics, who regarded modern theoretical physics as Jewish. Although recent historical research calls for a more refined view of what is generally labeled as the “German Physics movement”—the fanatics did not act as one group and did not represent the regime’s views on science policy—the tug-of-war ended with a victory for Sommerfeld’s enemies and ruined the reputation of his former institute within a few years.

In order to overcome his depression about this decline, in the 1940s Sommerfeld actualized his long-held intent to edit his lecture courses. Like Atombau und Spektrallinien, which was celebrated as the “bible of atomic physics,” Sommerfeld’s six volumes of Vorlesungen über theoretische Physik became a textbook classic of his discipline. “We are proud that we can do our share to distribute your ‘Lebenswerk’ throughout English-speaking countries,” his American publisher announced in December 1948, referring to the forthcoming appearance of the English translation of volume 6, Partial Differential Equations in Physics, Sommerfeld’s favorite lecture course. It must have been a great relief for the eighty-year-old theorist to see his life’s work thus acknowledged worldwide— when his Munich “nursery” was in ruins, physically as much as intellectually.


Most of Sommerfeld’s publications have been reprinted (see original DSB article). A selection of Sommerfeld’s scientific correspondence has been edited in two volumes.


Arnold Sommerfeld: Wissenschaftlicher Briefwechsel, Band 1: 1892–1918. Edited by Michael Eckert and Karl Märker. Berlin, Diepholz, Munich: Deutsches Museum, GNT-Verlag, 2000.

Arnold Sommerfeld: Wissenschaftlicher Briefwechsel, Band 2: 1919–1951. Edited by Michael Eckert and Karl Märker. Berlin, Diepholz, Munich: Deutsches Museum, GNT-Verlag, 2004.

“Arnold Sommerfeld (1868–1951), Wissenschaftlicher Briefwechsel.” Leibniz Computing Centre of the Bavarian Academy of Sciences and Humanities. Available from A survey of Sommerfeld’s correspondence.


Corry, Leo. “David Hilbert and the Axiomatization of Physics.” Archive for the History of Exact Science 51 (1997): 83–198.

Eckert, Michael. “Propaganda in Science: Sommerfeld and the Spread of the Electron Theory of Metals.” Historical Studies in the Physical and Biological Sciences 17, no. 2 (1987): 191–233.

———. “Theoretical Physicists at War: Sommerfeld Students in Germany and as Emigrants.” In National Military Establishments and the Advancement of Science and Technology: Studies in the 20th Century History, edited by Paul Forman and José M. Sánchez-Ron. Boston: Kluwer Academic, 1996.

———. “Mathematik auf Abwegen: Ferdinand Lindemann und die Elektronentheorie.” Centaurus 39 (1997): 121–140.

———. “Mathematics, Experiments, and Theoretical Physics: The Early Days of the Sommerfeld School.” Physics in Perspective1 (1999): 238–252.

———. “The Emergence of Quantum Schools: Munich, Göttingen, and Copenhagen as New Centers of Atomic Theory.” Annalen der Physik10, no. 1–2 (2001): 151–162.

———. “The Practical Theorist: Sommerfeld at the Crossroads of Mathematics, Physics, and Technology.” Philosophiae Scientiae 7, no. 2 (2003): 165–188.

———. “Die Deutsche Physikalische Gesellschaft und die ‘Deutsche Physik.’” In Physiker zwischen Autonomie und Anpassung: Die Deutsche Physikalische Gesellschaft im Dritten Reich, edited by Dieter Hoffmann and Mark Walker. Berlin/Weinheim: Wiley-VCH, 2007.

———, and Willibald Pricha. “Boltzmann, Sommerfeld und die Berufungen auf die Lehrstühle für theoretische Physik in Wien und München, 1890–1917.” Mitteilungen der Österreichischen Gesellschaft für Geschichte der Naturwissenschaften4 (1984): 101–119.

Eckert, Michael, et al. Geheimrat Sommerfeld: Theoretischer Physiker; Eine Dokumentation aus seinem Nachlass. Munich: Deutsches Museum, 1984.

Friedman, Robert Marc. The Politics of Excellence: Behind the Nobel Prize in Science. New York: Times Books, 2001

Geison, Gerald L. “Scientific Change, Emerging Specialties, and Research Schools.” History of Science 19(1981): 20–40.

Greenspan, Nancy Thorndyke. The End of the Certain World: The Life and Science of Max Born; The Nobel Physicist Who Ignited the Quantum Revolution. New York: Basic Books, 2005.

Hoddeson, Lillian, Gordon Baym, and Michael Eckert. “The Development of the Quantum-Mechanical Electron Theory of Metals: 1928–1933.” Reviews of Modern Physics59 (1987): 287–327.

Jungnickel, Christa, and Russell McCormmach. Intellectual Mastery of Nature. 2 vols. Chicago: University of Chicago Press, 1986.

Litten, Freddy. Mechanik und Antisemitismus: Wilhelm Müller (1880—1968). Munich: Institut für Geschichte der Naturwissenschaften, 2000.

Rowe, David E. “Klein, Hilbert, and the Göttingen Mathematical Tradition.” Osiris 5 (1989): 189–213

———. “Mathematical Schools, Communities, and Networks.” In The Cambridge History of Science, vol. 5, The Modern Physical and Mathematical Sciences, edited by Mary Jo Nye. Cambridge, U.K.: Cambridge University Press, 2003.

Servos, John W. “Research Schools and Their Histories.” Osiris8 (1993): 2–15.

Seth, Suman. “Principles and Problems: Constructions of Theoretical Physics in Germany, 1890–1918.” Ph.D. diss., Princeton University, Princeton, 2003.

Staley, Richard. “Max Born and the German Physics Community: The Education of a Physicist.” Ph.D. diss., Cambridge University, Cambridge, U.K., 1992.

———. “On the Co-Creation of Classical and Modern Physics.” Isis96 (2005): 530–558.

Walter, Scott. “Minkowski, Mathematicians, and the Mathematical Theory of Relativity.” In The Expanding Worlds of General Relativity, edited by Hubert Goenner, et al. Einstein Studies, no. 7. Boston: Birkauser, 1999

———. “Henri Poincaré and the Theory of Relativity.” In Albert Einstein: Chief Engineer of the Universe, edited by Jürgen Renn. Weinheim, Germany: Wiley-VCH, 2005.

Warwick, Andrew. Masters of Theory: Cambridge and the Rise of Mathematical Physics. Chicago: University of Chicago Press, 2003.

Michael Eckert

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