eminar
H eisenberg entered the University of Munich in the fall of 1920.
Between the start of his studies in Munich and his appointment as professor of theoretical physics in Leipzig seven years later, quantum physics underwent a profound transformation, from what Max Born called disorder in 1920 to the orderly system that Born and Heisenberg pronounced complete in 1927. 1
While still a student and junior lecturer, Heisenberg was a prominent member of the small cast of talented physicists that performed this transformation. His role arose from the felicities of location, colleagues, and timing, in addition to his own extraordinary abilities. During those seven years, Heisenberg studied and lectured at three major quantum research centers — Munich, Gottingen, and Copenhagen — under three leading quantum theorists of the day: Arnold Sommerfeld, Max Born, and Niels Bohr. He also studied and worked with some of the brightest young physicists of the day: Pauli, Jordan, Dirac, Wentzel, Kramers.
The profound inadequacy of quantum theory in resolving the riddles of the atom was just coming to light in Munich when Heisenberg began his studies. Through his teachers and colleagues, Heisenberg became acquainted with particular problems and with various attempts to resolve them. This groundwork was vital in facilitating his own contributions over the coming years.
Those contributions were fundamental. They included the pivotal breakthrough to quantum mechanics in 1925, participation in the development of the complete quantum mechanics apparatus from 1925 to 1927, and perhaps Heisenberg’s most famous achievement of all — his
formulation of the principle of uncertainty, or indeterminacy, in 1927, Heisenberg’s contribution to the “Copenhagen interpretation” of quantum mechanics. Although it remained controversial, quantum mechanics and the Copenhagen interpretation of its formalism completed the quantum revolution first ignited by Planck, Einstein, Ehrenfest, Bohr, and others during the first decade and a half of the century. It has formed the basis of research on the atomic scale to this day.
By the turn of the twentieth century, understanding of the workings of the physical world had reached a culmination in the classical mechanics of motion and force, derived from the work of Newton and his successors, and in the classical electrodynamics of electricity, magnetism, and light, based on the contributions of Maxwell, Hertz, and Lorentz at the end of the nineteenth century. In the same year that Einstein offered a revision of classical electrodynamics in his special theory of relativity (1905), he offered a profound and not readily accepted challenge to the classical electromagnetic wave theory of light with his hypothesis of “light quanta” — tiny, discrete bundles of light energy, each behaving like an independent particle and carrying identical amounts of energy.
Atoms, meanwhile, attracted increasing attention and — thanks again to Einstein — soon gained acceptance as real entities. Efforts to comprehend the structure of atoms and to account for their known properties led in 1913 to a quantum theory of the atom propounded by Bohr and extended thereafter by Bohr, Sommerfeld, and others. Bohr’s model combined quantum elements, such as light quanta and discrete energies, with classical mechanics and electrodynamics. Although the resulting Bohr-Sommerfeld quantum theory of the atom enabled accounts of an astonishing array of atomic phenomena, the theory itself remained for many theorists a puzzling combination of classical and quantum notions that only somewhat seemed to work.
After World War I, improved experimental techniques and more sophisticated quantitative analyses began to illuminate more and more areas in which the theory seemed to work less and less satisfactorily. The limitations of the Bohr-Sommerfeld quantum theory of the atom and possible ways to overcome them or to revise the theory engaged quantum physicists throughout the early twenties. Heisenberg fully participated in these analyses and, after 1923, in the efforts to replace the by then inadequate quantum theory with a new quantum mechanics. The new mechanics and its Copenhagen interpretation, achieved by the end of 1927, were combined with other innovations —such as electron spin and the exclusion principle —to enable at last a consistent, self
contained theory of processes on the atomic scale. In opening up the realm of the atom, quantum mechanics enabled entirely new and profound advances in understanding all aspects of the physical world, from nuclei and quarks to the big bang — which had profound implications for the world in which we live, from philosophy to the technology of nuclear reactors, atomic bombs, semiconductors, and superconductivity. Heisenberg played a leading role in many of these developments from the very moment in the fall of 1920 that, as an 18-year-old student, he entered the University of Munich.
Heisenberg’s work and studies continued to parallel the upheavals of Germany’s social unrest. The military defeat in World War I and the collapse of the monarchy galvanized many Germans, especially young people. The Versailles peace treaty, imposed on Germany at the end of the war, blamed the defeated nation for the war and exacted oppressive reparations to the victors. At the same time, the new Weimar constitution imposed democracy on the already traumatized nation — all of which awakened violent nationalistic and antirepublican sentiments among many Germans, some of whom were now violently anti-Semitic as well. According to one count, 376 political murders were committed in Germany between 1919 and 1922, 354 of which were carried out by right-wing assassins. Between 1919 and 1924, 12 different federal cabinets governed in Berlin, of which only one came to power through normal electoral processes. 2 In the midst of such upheaval, inflation wracked the German economy, reaching astronomical proportions just as Heisenberg received his doctorate in 1923.
Politics in and around the University of Munich tilted precariously to the right during the early 1920s. The trauma of the Munich soviet experience led to the creation of secret civilian armies in Bavaria to resist what they regarded as “Bolshevism.” The authorities placed the city under a permanent state of emergency to suppress every left-wing tendency. Right-wing extremism flourished unchecked in Munich, especially within the “nonpartisan” secret armies. It burst into Bavarian politics during the Kapp putsch. When Captain Ehrhardt’s free corps brigade, which had earlier helped to suppress the Munich soviet, was ordered to disband as part of the German demobilization, his troops, now in Berlin, joined with other units and seized control of the government. A communist revolt erupted in the Ruhr in response, prompting the dispatch of Bavarian volunteers — among them Werner’s brother, Erwin — to suppress it. Gustav Kahr, president of Upper Bavaria, took over the Bavarian government at the insistence of the secret armies. Hoffmann and his Social Democratic regime, whom the victors over the Munich
soviet had restored to power in 1919, withdrew from office, never to return to power in Bavaria. Hoffmann’s successor, Kahr, instituted an even more ruthless suppression of political opposition, preparing to declare Bavarian independence at his earliest opportunity.
When workers rallied to the socialist regime in Berlin, ending the putsch, many of the putschists headed for the fertile fields of separatist Bavaria, a magnet for right-wing fanatics throughout the Reich. When not soldiering, many of the zealots were university students, if only in name. The University of Munich quickly became a stronghold of rightwing extremism. 3
The university administration openly encouraged its fanatical students. During the height of their power, the soviet leaders had aggressively attempted to subject the elite institution to proletarian rule. Armed student revolutionaries had seized control of the university, taken the rector hostage, and set up a revolutionary council to dictate university policy. The university senate promptly closed the institution and sent the faculty into hiding. 4 When the restored Hoffmann regime proclaimed Bavaria a social democratic republic in 1919, the move was denounced almost universally by the monarchical faculty. When in 1920 the courts sentenced Graf Arco to death for assassinating Eisner, the university rector himself joined his students in a demand of clemency for Arco that did not stop short of threatening violence. The threat succeeded. Max Weber, then a professor of sociology, attempted to defend a socialist student who opposed the demand, only to find his lectures constantly disrupted. 5
The dire political and economic situation, combined with horrendous overcrowding at the university, contributed immensely to student fanaticism during the early 1920s. In the fall of 1920, when Werner entered the University of Munich, it had a student population of 6879, 62 percent of whom were Bavarian. A year later, 9659 students were enrolled, only 52 percent of whom were Bavarian. 6 Many students came from middle-class families who were among those hardest hit by inflation. During Werner’s first semester, in the winter of 1920-1921, a counselor discovered that an astonishing 61 percent of the students existed on a monthly income that was below the minimum cost of living for a Munich student. 7 The lowest paid unskilled worker at the university earned more than the minimal living costs of a student — a circumstance that further embittered the already resentful students.
Although Heisenberg suffered a certain amount of economic difficulty, he was far better off than most. He was one of a small number (2.3 percent) of male Bavarian students who lived at home and avoided
boarding expenses. His father’s income, moreover, was not seriously threatened by inflation until 1923. Professor Heisenberg’s salary was near the top of the civil-servant pay scale (step 12 of 13). It nearly tripled between July 1920 and October 1921, while the mark decreased in value relative to the U.S. dollar by only slightly more than that amount. 8 Even without the added income of seminar fees, the professor’s salary in 1922 was still 4000 marks above the total expenses of an average five-member professorial family in the more expensive city of Berlin. 9
With his elder son studying in Berlin between military stints, the professor found it necessary to put his younger son on a budget. In October 1921, August paid Werner’s way to Jena so that he could attend his first physics conference, a conference at which he briefly met some of the great names in his profession for the first time — among them, Max Planck and Max von Laue, but, to Werner’s dismay, not Einstein, who could not attend. During the conference, Werner decided to impose further on his father’s finances and travel by train to Berlin to visit the Berlin contingent of his youth movement. 10 His parents maintained that they could not afford to give him more. On Werner’s vehement insistence, his parents finally withdrew a sum from a golddollar account set up by Werner’s rich American Uncle Karl to help his German relatives in emergencies. Independent minded and little concerned with parental dilemmas, Werner longed even more keenly for the day when he would not have to rely on family generosity. 11
Weimar scientists, especially atomic scientists, reacted to the worsening economic conditions by developing increasingly innovative strategies to obtain research support for themselves and their students. However, in the political sphere, these same scientists, continuing to eschew politics, reacted to the upheavals of the era by becoming more insular. In keeping with the blame cast on Germany for unleashing the world war, international boycotts of German science followed the war. German scientists withdrew even further from political affairs, stubbornly refusing to allow outside events and pressures to contaminate them or their science. Richard Willstatter, a Munich professor of chemistry, deftly dodged machine-gun bullets on his way home for lunch during the battle of Munich — he refused to let his soup get cold. 12 During the Kapp putsch, Max Born encountered a heavy street battle in Frankfurt; yet, he recalled, “After things had settled a little we went about as if everything were normal.” 13
Heisenberg’s future Munich mentor, Arnold Sommerfeld, managed to complete two of his most significant scientific papers in the midst of this turmoil. He submitted the Sommerfeld-Kossel ring model of the
atom at the height of the soviet republic in April 1919; his spectroscopic magneto-optical splitting rule paper, the inspiration for Heisenberg’s early work on spectroscopy, arrived at the publisher within four days of the Kapp putsch.
But even the ivory tower of Sommerfeld’s institute could not protect its members from a collision with the university’s anti-Semites. The issue, which arose during Heisenberg’s second year of studies, was Einstein. Sommerfeld’s students learned of the episode from Sommerfeld’s correspondence with Einstein, which Sommerfeld often read aloud to his seminar. 14 Einstein, well known in Germany as a pacifist, openly supported the Weimar democracy and worked tirelessly in the cause of international understanding and accord. Since his newly confirmed theory of relativity seemed so profound yet so incomprehensible to most lay people, many saw in him a symbol of their own incomprehension of recent events and in the Jews a scapegoat for Germany’s troubled situation. Outspoken, captivating, and Jewish, Einstein made an ideal target for both anti-Semitic and antiscientific hate. In 1920, Einstein’s opponents unleashed an anti-Semitic campaign in Berlin against the man and his theory. 15 They were supported by several prominent experimentalists, including the Nobel laureate Philipp Lenard. Although the sources of their hatred were myriad, Lenard and his colleagues were especially furious at Einstein’s sudden popularity and prestige as a theoretical physicist, which threatened to overshadow them and their field of experimental physics. 16
During the nineteenth century, German physics and German physicists had established their power and prestige mainly in the field of experimental physics, the gathering and analysis of data. Experimental work also required mathematical methods and the framing of general hypotheses, but by the early years of the twentieth century a new professional discipline had emerged, especially in Germany, that focused in a new way on hypothesis, mathematical analysis, and empirically informed theories of natural phenomena — theoretical physics. 17 By the end of World War I, the startling results and successes of professional theorists such as Planck, Laue, and Einstein provided the new field with enormous popular appeal and prestige in Germany, but it still held a secondary professional status behind the established and supposedly more well-grounded discipline of experimental research. Many still held empirical data to be more fundamental than mathematically construed theories. Because of the lower status accorded theoretical work, Jewish
physicists found more opportunities in theoretical physics, but_as
everywhere else in German society —they also encountered anti-Semitism, both before and after World War I. 18
Moderate Weimar physicists usually considered opposition to antiSemitism to be not a moral or an ethical issue but primarily a political one. Such a view apparently arose from the politicization of anti-Semitism in Germany. Anti-Semitism had already become a plank in the platforms of several major political parties, and those who engaged in anti-Semitism often did so for obvious political ends. Because of this, scientists and academics regarded both blatant anti-Semitism and overt opposition to it as too political and therefore to be avoided. While determined opposition therefore failed to develop, implicit anti-Semitism flourished in German academe, at times infecting even Sommerfeld’s institute. 19
Einstein was a special case. While German repute abroad suffered because of the war, Einstein’s international fame reflected favorably on the foreign image of German physics. The grotesque anti-Einstein campaign in Berlin threatened to tarnish that image. Sommerfeld and others, while carefully avoiding political involvement, realized that something had to be done. In 1920, Sommerfeld and several Munich professors formed an Einstein support committee. As their first order of business, they invited him to lecture in Munich. Sommerfeld obtained financing from a sympathetic philanthropist, and Einstein readily accepted, intending to arrive in Munich in November 1921. Heisenberg and his fellow student Pauli, disappointed at having missed Einstein in Jena, eagerly anticipated an encounter with the great man in Munich. 20
The plan unraveled shortly before Einstein’s appearance. An article in a leftist Berlin literary magazine reported an ominous meeting held nearly a year earlier between Sommerfeld and representatives of the Munich student government in the rector’s office. Noting the disruptions of Einstein’s lectures in Berlin, the rector — now suddenly worried about the reputation of his school — demanded assurances that no such disruptions would occur in Munich. The students responded with objections to Einstein’s “person,” prompting Sommerfeld to lecture them on the physicist’s significance — but without success. During the next student government meeting, extremist representatives, especially members of the “Swastika Majority,” refused any assurance against disruption. The article reporting these events appeared just before Einstein’s arrival in Munich. Einstein immediately canceled his appearance. 21 Sommerfeld pleaded with his colleague to reconsider. His colleague absolutely refused. “There is just no other way,” he told the nonJewish Sommerfeld. “That you must feel yourself.” 22 Heisenberg would have to wait three more years before meeting Germany’s foremost theorist.
Sommerfeld and his students stubbornly maintained their insulation, both before and after the Einstein affair. These were talented and intense young scientists consumed by the demanding intricacies of their discipline. It was easy for them to relegate social issues to second place — and they welcomed the opportunity to do so. The arduous work and tantalizing promise of scientific research served as a convenient antidote to social upheaval — as it has for other scientists in similar situations throughout history. 23 Pauli, for instance, entered the university in the winter of 1918-1919, just before the end of the war. The years immediately following witnessed the soviet republic, civil wars in Munich and Vienna, the taking over and closing of the university, rampant inflation, and brutal violence. Yet he notes none of these events in his available correspondence nor in any of his published recollections. Years later, he wrote: “The war was over, with Sommerfeld I was in my right element. What then were the political and economic situations in Germany and Austria to me as a young man?” 24 Insular concentration fostered successful work, which in turn encouraged further insulation.
Heisenberg found his own escapes. “My first two years at Munich University were spent in two quite different worlds: among my friends of the youth movement and in the abstract realm of theoretical physics,” he wrote. “Both worlds were so filled with intense activity that I was often in a state of great agitation, the more so as I found it rather difficult to shuttle between the two.” 25 Heisenberg literally did shuttle between the two. During the warmer months of the summer semester, he usually camped out with his boys in the mountains at night, then hiked to the nearest train station early the next morning, arriving in Munich in time for Sommerfeld’s 9:00 A.M. lecture. Constantly moving between the worlds of physics and youth conveniently left him little time for anything else.
When he left the Max-Gymnasium in the summer of 1920, Heisenberg still planned to study pure mathematics. Fresh from his brilliant Abitur, the ambitious young man intended to launch immediately into an advanced research seminar leading to a doctoral degree. Having passed the Abitur, students were automatically admitted to the lectures and exercise sessions of the German university of their choice. Most students attended local universities, trying for either a doctorate or a Diplom, the equivalent of an American master’s degree (not available then in Munich). To obtain a degree, one had to be accepted by a professor into his seminar. There the student learned the fundamentals of research while working on an independent project. Rather than requiring the general education courses, examinations, and semester
grades of American schools, the German university quickly introduced its students to focused independent research through early study with working specialists. Once in a seminar, the student completed a thesis project under the direction of a professor, who solicited faculty members in related fields for their written opinion on the result. Final approval of the thesis and a grade for the entire study were conferred at the final oral examination. The new graduate was now qualified to teach at a gymnasium. A university teaching career, however, required an even higher degree: the habilitation, or qualification, which entailed additional research, oral examination, and approval of the faculty.
Shortly after recovering from his bout with typhoid in the summer of 1920, Heisenberg had his father arrange an appointment for him with the mathematician Ferdinand von Lindemann, a colleague of the elder Heisenberg. Lindemann seemed an ideal candidate for the role of Werner’s “doctor father,” as advisors are called in German. He was well known in Werner’s intended field of number theory for his proof of the transcendence of n and was codirector of the university’s mathematicalphysical seminar, composed of four professors and one assistant. It was not a seminar in the sense of a study group but rather an administrative unit, somewhat like an American department. The seminar was designed to train future gymnasium teachers of mathematics and physics in the fundamentals of their field and in basic research. 26 Presumably, a good researcher would make a good teacher. In 1920, Willy Wien, the newly arrived professor of experimental physics, codirected the seminar with Lindemann. Their two colleagues were Aurel Voss, professor of mathematics, and — in fourth place in the pecking order — the professor of theoretical physics, Arnold Sommerfeld. 27
As a favor to August Heisenberg, Lindemann agreed to meet with Werner—but only as a favor. The old gentleman, a longtime chairman of the university’s administrative committee, was two years from retirement. He had little patience with first-year students who intruded on him in his office — and none at all with audacious novices who demanded immediate admission to advanced research. The interview ended in disaster.
As Heisenberg recalled it later, Lindemann received him in a dimly lit office, seated behind a desk on which his pet poodle perched. When Werner began to speak, the poodle barked so loudly that the partially deaf professor could barely understand him. Finally, Lindemann asked his young visitor which textbooks he had studied. After mentioning Bachmann’s Zablentheorie , Heisenberg volunteered that he had just finished Weyl’s Raum-Zeit-Materie. Lindemann, looking for an excuse
and perhaps unsympathetic to Weyl’s contamination of pure mathematics with physics, abruptly closed the interview with the remark: “In that case you are completely lost to mathematics.” 28
Stunned by his first rejection, the 18-year-old returned to his father to seek alternatives. They considered the three remaining seminar professors. Wien, now an experimentalist, would not do, and between Sommerfeld and Voss, the former was the more likely choice, since he and August were already well acquainted. The slightly built, balding, broadly moustached Sommerfeld, who always stood so erect that he looked, in Pauli’s words, like a Hussar officer, had served as dean of the science faculty during the previous summer semester. During the coming year, he would serve as senator from his faculty. 29 These duties had already brought him into frequent contact with Professor Heisenberg, the university representative to the German Hochschullehrerbund (College Teachers Association). Father and son decided to try Senator Sommerfeld.
The physicist proved much more sympathetic than his elderly colleague. His office was well lit and devoid of poodles, and its less imperious occupant gladly received eager students of all levels. Unlike Lindemann, he was elated — and amazed — to learn that Heisenberg had read Weyl. “You are much too demanding,” he told his visitor, with good reason. Obviously impressed, the perceptive Sommerfeld admitted Werner provisionally to his research seminar. “It may be that you know something; it may be that you know nothing. We shall see.” 30 Heisenberg was on his way into theoretical physics.
Sommerfeld’s approach to his science and his relations with his colleagues typified the state of German theoretical physics in the early years of the quantum revolution. Like most theorists of his generation (he was then 52), Sommerfeld began his career in mathematics. Coincidentally, he was born in Konigsberg, East Prussia, the site of the first mathematical-physical seminar in Germany, which originated the Central European branch of theoretical physics. Sommerfeld had attended the local gymnasium with the cousins Willy and Max Wien, both of whom became physicists. In 1886, Sommerfeld began studying mathematics at his local university, attending the mathematical-physical seminar, directed by professor of mathematics Ferdinand von Lindemann. But, like many other mathematicians, he became intrigued with the mathematical physics of William Thomson (Lord Kelvin), as outlined in his attempted mechanical comprehension of Maxwell’s electromagnetic field equations. Sommerfeld promptly switched from Lindemann’s number theory to Kelvin’s mathematical physics — the study of mathemati
cal applications to physics — and wrote his doctoral dissertation on the subject under Paul Volkmann, professor of mathematical physics in Konigsberg. 31 Doubtless Sommerfeld saw something of himself in Heisenberg.
Still a mathematician, in 1893 Sommerfeld headed for Gottingen, the capital of German mathematics. There he fell under the influence of the famous mathematician Felix Klein, a superb teacher and administrator who at the time pursued a program for mathematizing science and establishing institutes for applied mathematics. 32 Thirteen years later Sommerfeld began teaching theoretical physics in Munich.
Physics research in Munich derived from the university’s instrument collection, its “physical cabinet,” consisting of experimental apparatus and the professor who used it. In 1892 the cabinet moved into the new Physics Institute, which was headed until 1920 by Wilhelm Rontgen, the discoverer of X rays, who had previously taught at the University of Wurzburg. Rontgen’s successor at Wurzburg was Willy Wien, Sommerfeld’s old school chum. Wien again succeeded Rontgen at Munich, just as Heisenberg entered the university.
Professor Wien was proof of the respect experimental physics commanded in Munich. The Nobel prize-winning Wien, then 55 years old, would not leave Wurzburg unless granted special concessions. He got everything he demanded, despite the grim economics of the day. He received a fat salary, four assistants, three technicians, and six-figure grants to expand and retool the institute. 33 By contrast, Sommerfeld’s institute consisted of a lecture hall, three rooms, a modest laboratory, one assistant, and one technician. It was located on the ground floor and basement level of the university building, two floors directly beneath August Heisenberg’s office. Aside from seminar fees, the institute received the modest sum of 2000 marks per year to purchase apparatus and to maintain a small library. 34
Although Sommerfeld’s chair and quarters were located in the university, they were administered as the state’s scientific instrument collection, its mathematical-physical cabinet. Hence there were two professors of physics, two independent experimental laboratories, and two very different schools of thought as to how physics should be defined and taught. The university’s physics professor handled experimental physics; the conservator of the state’s cabinet pursued mathematical physics with a parallel university appointment. Boltzmann had occupied the position until 1894. In 1905, Rontgen, interested in electron theory, appointed Sommerfeld to the post, over the strenuous objections of Sommerfeld’s former mentor, Ferdinand von Lindemann. 35
On arriving at the university in 1906, Sommerfeld divested the cabinet of most of its outmoded apparatus and gave it a new name reflecting its new primary focus: Institute for Theoretical Physics. It quickly became a leading center of research in the new relativity and quantum theories. Sommerfeld was reportedly the first professor in the world to lecture regularly on both subjects, and he enjoyed world renown as one of the best and most stimulating teachers of the era. His institute produced a steady stream of first-rate theorists — the largest number of doctorates in the field until the 1930s. Einstein was amazed at its fruitfulness and, prompted by a report on Heisenberg, wrote to Sommerfeld in 1922: “What especially impresses me about you is that you have produced so much young talent, like stamping them out of the ground. That is something entirely unique. You must be able to activate and to cultivate the minds of your pupils.” 36
What particularly distinguished Sommerfeld as a teacher and researcher was not so much the brilliance of his physical insight but rather, as Born put it, his “logical and mathematical penetration of established or problematic theories and the derivation of consequences that might lead to their confirmation or rejection.” 37 Sommerfeld combined this talent with an inspiring teaching style and a gradual selection process that served to weed out the weaker pupils. The institute’s Munich location helped to ensure a steady supply of talent for the program.
As the state’s conservator of apparatus, Sommerfeld was still obliged to allow at least some experimental research — work that he relegated to assistants whom he banished to the dark basement. Despite their lowly status, theorists Max von Laue and the outcasts made at least one major discovery: proof that X rays exhibit electromagnetic wave behavior. Laue received the 1914 Nobel prize for his discovery, and Sommerfeld’s institute received generous grants to continue the research — thereafter in broad daylight.
By the time Heisenberg joined the institute, theory once again eclipsed experiment. Sommerfeld focused his theoretical interests on two topics: hydrodynamics and quantum spectroscopy. His interest in hydrodynamics arose with the financial support of the Isar Company in Munich, which had been contracted to channel the Isar River. Work on quantum spectroscopy grew out of Sommerfeld’s concern with the modification of his quantum atomic model in the light of new and puzzling data. To Heisenberg’s extraordinarily good fortune, Sommerfeld’s institute was unique. It was one of only a handful of institutes for theoretical physics in Germany and one of only two or three that performed research on quantum theory. Moreover, it was the only one at that time concerned with theoretical quantum spectroscopy.
Heisenberg was also fortunate in the timing of his entry into Sommerfeld’s teaching program. Like mathematics and other sciences, physics was part of the philosophical faculty, which required of doctoral candidates a minimum of only six semesters (three years) of study. Sommerfeld accordingly arranged the topics of his main lecture in a six-semester cycle, starting with classical mechanics. If a student entered in midcycle, he could either learn the material out of sequence or spend his first semesters on mathematics and required minors while waiting for the cycle to begin again. Heisenberg entered the program just at the start of a cycle, in the winter semester of 1920-1921. Sommerfeld had spent the previous year teaching a tiresome series of make-up semesters for war veterans and free corps volunteers. 38
Sommerfeld designed his teaching program to satisfy a variety of needs. While Heisenberg studied under him, he offered five main lectures (one each semester for four hours a week) covering nearly all of classical theoretical physics. For advanced students, he taught contemporary nonclassical physics in a special lecture on current research. He also conducted the research seminar for doctoral candidates and gave an occasional public lecture on modern theories to raise money for the institute. The main lectures were attended by as many as 80 to 100 students from a variety of scientific fields. Students of chemistry and medicine who attended Sommerfeld’s lectures on atomic models in 1916-1917 encouraged him to write his famous textbook Atombau und Spektrallinien (Atomic Structure and Spectral Lines), which was for a generation the “bible of the modern physicist.” 39
At each lecture, Sommerfeld assigned homework problems to be turned in during the weekly one-hour Ubung (exercise) sessions. An assistant corrected the problems and discussed them with the students during the exercise, which Sommerfeld himself often attended. No grades were given; a student’s work spoke for itself. Heisenberg recalled turning in such long and complicated solutions that Sommerfeld’s assistant complained. 40
The assistant was probably Peter Paul Ewald, who held the post when Heisenberg arrived. Ewald remembered Sommerfeld as a “true doctor father.” 41 He took a personal interest in his charges, treated them with dignity, and gave them sympathetic fatherly counsel. He set an example for them as a hard-working, intensely active researcher — yet he was always accessible. Heisenberg was often in Sommerfeld’s office for an hour or two each morning during his last semesters. On Sundays, Sommerfeld would invite institute members to accompany him on daylong outings in the countryside. Winter weekends were often spent with other physicists skiing at Willy Wien’s country cottage in Mittenwald
near the Austrian border. When students felt the pinch of economic inflation, Sommerfeld dipped into his own pocket to help them out. Werner, too, benefited from Sommerfeld’s generosity, further increasing his admiration for his mentor. 42
The stimulation and selection process began early in Sommerfeld’s institute. It was his strategy to involve students at once with research and institute affairs, both to encourage and to test them. The professor, as Werner called him, gave his beginning pupils minor tasks, such as checking his calculations, analyzing newly received data, and correcting galley proofs of articles. Advanced students assisted with revisions of Atombau or with articles for Klein and Sommerfeld’s multivolume Encyclopedia of Mathematical Sciences. It was in this work that Pauli’s famous article on relativity theory, still considered one of the best summaries of the subject, first appeared. 43 Heisenberg recalled that Sommerfeld would often motivate a bright pupil by handing him a small problem with the remark, “Well, I can’t solve this problem; now you try it.” Based on performance of these tasks and in the exercise sessions, Sommerfeld assessed his pupils’ suitability for admission to advanced training.
Sommerfeld offered his two-hour special lecture each semester on a topic that he was currently researching but had not yet fully grasped. When once asked how he could lecture on a subject he did not understand, Sommerfeld replied: “If I knew something about it, I wouldn’t lecture on it!” 44 The object was to enable pupils and teacher to grapple with a current problem together and, in the process of searching for a solution (successfully or not), to arrive at a systematic comprehension of the subject. The communal effort made these sessions particularly stimulating. Sommerfeld prepared the special lecture in advance, but he usually tried to rederive the results at the chalkboard without referring to his notes. One can imagine the animated discussions that must have occurred when a derivation didn’t work out. Throughout Heisenberg’s studies in Munich, Sommerfeld devoted the special lecture each semester to the major atomic physics problem of the day: quantum spectroscopy. Young Werner was captivated.
Advanced study at the institute revolved around the research seminar, which was attended by all advanced students, assistants, lecturers, and the occasional precocious beginner. Heisenberg was one such beginner; before him, Pauli had also attended during his first semester. Both managed to survive the weeding out that the course entailed. Sommerfeld devoted each semester’s seminar to a current field of research. Each attendee was given a small problem to solve or a large article to study,
and the results were presented to the seminar for critical review. A successful performance was required for permission to write a dissertation on the subject. Heisenberg obviously did well, for his dissertation and several of his first papers grew out of his early seminar projects.
Sommerfeld put his precocious new pupil to the test from the very start. Within a few weeks of Heisenberg’s arrival, Sommerfeld requested that he analyze some new data on the anomalous Zeeman effect in spectroscopy, and that he report to the seminar on a recent publication on quantum theory by Niels Bohr’s assistant, H. A. Kramers. Both of Heisenberg’s reports provoked long controversies at the institute. But in the quality of his work, Heisenberg proved himself worthy of the master’s tutelage.
Heisenberg’s first-semester registration form indicates that, despite his audacity and ambition in immediately entering Sommerfeld’s seminar, his father had probably advised restraint: Werner had prudently protected himself in the event of failure by signing up for five hours of mathematics lectures and exercises conducted by Artur Rosenthal but for only one hour of theoretical physics — the exercise session following the main lecture. This meant that Heisenberg was in fact a guest auditor in Sommerfeld’s seminar and main lecture and could withdraw promptly into mathematics should he prove unsuitable for physics. By the second semester, such caution was no longer necessary. Sommerfeld had admitted him without reservation to the program, and Heisenberg filled in his next registration form with all of Sommerfeld’s offerings. 45
Since students in the mathematical-physical seminar were required to take Wien’s course in experimental physics, Heisenberg, like Pauli before him, also registered for the five-hour lectures in experimental physics (mechanics and optics) his first semester. 46 As a second-semester physics student, he registered, as required, for Wien’s tortuous eighthour beginner’s practicum, or laboratory. Heisenberg continued to study mathematics with the aged Rosenthal and his colleagues Pringsheim and Voss — but he avoided Lindemann. Mathematics and astronomy were his two minor subjects, and in each he was expected to register for lectures, exercises, and one seminar. Already rejected by Lindemann, Heisenberg soon discovered that he had lost interest in Lindemann’s abstract number theory but had gained interest in Rosenthal’s “visualizable” geometry. The budding number theorist was ripening into a theoretical physicist.
Heisenberg’s decision to study theoretical physics rather than mathematics caused his father no little concern. 47 Public interest in the relativity and quantum theories was certainly strong, as was demonstrated by
the large audiences at popular lectures such as Sommerfeld’s. Nevertheless, employment opportunities seemed meager. Mathematics and experimental physics were well-established disciplines that could lead to any number of jobs in industry and gymnasiums, but professional careers in theoretical physics were still restricted to university chairs, all of which were already occupied. 48 Although academic positions would increase during the next decade, Professor Heisenberg knew that his son would have to do extremely well, particularly on the doctoral and habilitation exams, to obtain a full professorship and thus achieve the goal the family had set for him. And while Werner’s abilities were keen, other problems loomed. Personal and professional differences were already arising between Sommerfeld and his new and more powerful colleague, Wien. Both were required to sit on the doctoral committee for physics students, and both had to agree on a single physics grade for each candidate.
One historian has argued that, while German physicists vociferously asserted their apolitical stance, they nevertheless polarized into professional camps corresponding roughly to their political temperaments. 49 Such factionalism was rife in every area of professional activity: societies, journals, financial institutions, appointments, and research preferences. Although there were obvious exceptions, conservatives, such as Wien, were usually experimentalists in senior positions who tended to be skeptical about the quantum and relativity theories, usually lived outside Berlin, and frequently contributed to the long-running Annalen der Physik (Annals of Physics), the leading German physics journal. Moderates, like Sommerfeld, were mainly theoreticians and were usually younger than experimentalists. They supported the quantum and relativity theories, either lived in Berlin or were closely allied with Berlin physicists, and frequently wrote for the newly established Zeitschrift fur Physik (Journal for Physics). Sommerfeld, who had helped to found the Zeitschrift in 1920, differed from Wien, a longtime editor of the Annalen, on nearly every point.
Although Wien did not dismiss theoretical physics — he had, in fact, once done theory himself—he simply regarded experimental work as more fundamental. Any doctoral candidate in physics had to convince Wien of his mastery of experimental techniques. Moreover, Wien insisted on a traditional, rigid program of study, leading gradually to advanced work. This method was the very opposite of Sommerfeld’s habit of confronting his pupils early with research, while simultaneously feeding them the fundamentals. By omitting courses outside their major and minor fields, bright students, such as Pauli and Heisenberg, could
obtain doctorates under Sommerfeld in as few as three years. The rapid schedule might leave gaps in a student’s knowledge, but, to Wien’s horror, Sommerfeld assumed students could fill them in themselves. Wien soon discovered that Heisenberg’s training did in fact leave him with serious gaps in his learning, but not apparently with any regrets. Years later, Heisenberg told a group of young people that, regardless of the many years now required to obtain a doctorate in physics, they should be doing original research by the age of 24. 50
With such fundamental differences between the two Munich physicists, the final doctoral examinations could easily deteriorate into a pedagogical wrangle. To forestall problems, Sommerfeld ordered his pupils to enroll again in one of Wien’s laboratory courses before the final orals. Pauli, who took the course in 1921, apparently did not encounter much difficulty with Wien, but Heisenberg — who suffered the course with ill-concealed scorn — did. His father’s anxiety over potential trouble is apparent in a remark he made when Werner visited Gottingen for a semester in 1922, a year before his final orals: “How have Herr Professor Born and the other gentlemen received you? Please don’t neglect the experimental physics!” 51
In addition to his formal training, Heisenberg could credit his rapid advancement under Sommerfeld to the stimulus of an extraordinary group of colleagues and companions. Their names read like a Who’s Who of their generation. When Heisenberg arrived, the principals included lecturers Karl Herzfeld and Wilhelm Lenz, assistant Peter Paul Ewald, and students Gregor Wentzel, Wolfgang Pauli, and Karl Bechert. Otto Laporte arrived in 1921 from Born’s Frankfurt institute to continue his studies with Sommerfeld, and Adolf Kratzer habilitated in 1921 and served as lecturer thereafter. Outside the institute, Heisenberg met Hans Kienle, an assistant at the astronomical observatory who became a close associate, and the mathematician Robert Sauer, a fellow student in Rosenthal’s lectures. As had Werner’s brother Erwin, Sauer entered into a fierce competition with Heisenberg, and in vying with each other to solve the problems presented, they left the other students far behind.
Of the three nonlaboratory institute rooms, with their creaky wooden floors, high ceilings, and drab interiors, Sommerfeld used one for himself and designated another the seminar room, a forum where the select five to ten advanced students met daily to discuss and debate various problems and papers. Each student had his own desk. When the newly graduated Wentzel replaced Ewald as assistant in 1921, Sommerfeld appointed Pauli, a younger recent graduate, to the post of deputy assistant. Among his duties was the correction of Heisenberg’s home
work. Indicative of the position he would take in physics, Deputy Assistant Pauli’s desk was perched on a small platform, from which he could oversee everyone’s work.
On or off his perch, Pauli proved to be the most influential and vocal of the seminar members and especially so for Heisenberg. Young Pauli had come to Sommerfeld from Vienna even more advanced in the study of physics than was Heisenberg. He arrived in Munich with a paper on general relativity ready for the printer. Although only a year older than Heisenberg, Pauli was already in his fifth semester when Heisenberg first met him in 1920. Like Heisenberg, Pauli was the well-bred son of a university professor, and in their personalities they had much in common. Both were sensitive, naive, adolescent, personally insecure but academically confident, enormously ambitious, and thoroughly dedicated to theoretical physics. The similarities ended there. Outwardly, Heisenberg was quiet and friendly, at once retiring and almost recklessly daring — in life and in science — while Pauli was outspoken, aggressive, carefully systematic, and often devastatingly critical. The virtuous Werner loved the purity of the outdoors, youthful games, and the sunshine of long summer days. Pauli preferred city nightlife, risque cabarets, and the pubs and coffeehouses of Weimar Schwabing. Heisenberg rose early in the morning, worked intensively throughout the day, and often sank into depression during long winter nights. Pauli haunted the cabarets in the evenings, worked feverishly until dawn, then slept until noon, missing his morning lectures. Sommerfeld tolerated Pauli’s behavior since he was a mere deputy. But Pauli obviously annoyed Born, whom Pauli assisted in Gottingen beginning in 1921. Pauli left Gottingen for a new institute in Hamburg after only one year, hungering for city nightlife. “He can’t stand life in a small town,” wrote Born. 52
Although Heisenberg and Pauli were together in Munich for only two semesters, the two physicists —so opposite and yet so similar—formed a close professional friendship that lasted the rest of their lives. That association, recorded in their voluminous correspondence, is one of the most important in modern physics. Their admiration for each other as physicists persisted, 53 and each was significant, perhaps crucial, to the other’s work. Although they never became close personal friends —they used the polite, collegial “sie” (“you”) form of address (the familiar form is “du,” used in families and among close friends) until as late as 1927 — Pauli functioned for Heisenberg in ways remarkably similar to those of Werner’s older brother. Pauli was more advanced in physics and offered Heisenberg brotherly advice on research. But as colleague and grader of homework, he could also issue ruthless criticism that
pushed the insecure yet ambitious Werner to try even harder. Heisenberg once told an interviewer: “Pauli had a very strong influence on me. I mean Pauli was simply a very strong personality. ... He was extremely critical. I don’t know how frequently he told me, ‘You are a complete fool,’ and so on. That helped a lot.” 54
As noted earlier, Pauli apparently was also partly responsible for converting Heisenberg to the study of atoms. Having read Einstein and Weyl, Heisenberg at first considered work on relativity after abandoning number theory. During his first semester, he solicited Pauli’s opinion of his prospects. Pauli was not optimistic. As author of the then definitive summary of relativity theory, he warned Heisenberg that research opportunities in the field would be meager. But Pauli was also the author of a dissertation on the quantum theory of the ionized hydrogen molecule that proved a failure in the agreement between theory and experiment. He could therefore assure his colleague that research in quantum atomic physics was wide open. 55
If Pauli was Heisenberg’s “brother” at the institute, Sommerfeld was his “father.” Werner, rebellious toward his real father yet still searching for new authorities to replace the old, put his education and early career completely in Sommerfeld’s hands. When Sommerfeld left to lecture in America for a semester in 1922-1923, he sent Heisenberg to Born in Gottingen. They had all agreed that Werner would return to Munich to complete his doctorate. During Heisenberg’s visit, Born discovered that he needed a new assistant and hoped that Heisenberg might return to Gottingen to habilitate, after receiving his doctorate. When Born asked him about his future plans, Heisenberg responded: “I don’t have to decide that! Sommerfeld decides that!” Born had to apply to Werner’s guardian for permission to allow him to habilitate in Gottingen. 56 Werner had become by then a valuable commodity.
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