When Heisenberg entered university in October 1920, physics was not his first choice. Having been brilliantly successful at high school, he intended to study mathematics and to launch immediately into advanced research. Indeed, Heisenberg's father arranged an appointment with the famous mathematician Ferdinand von Lindemann in the hope that his ambitious son would be admitted into Lindemann's class where he would begin advanced research straight away. But the interview did not go well for young Heisenberg. Lindemann, who was then 68 and partially deaf, barely understood what Heisenberg said. And from what he did understand, he concluded that the young man's unorthodox approach to mathematics was not to his taste. Heisenberg's second attempt to obtain access to advanced study without the usual preliminaries led him to Arnold Sommerfeld, professor of theoretical physics at Munich. Experienced with exceptional students, Sommerfeld, who was then 52, responded differently: "It may be that you know something; it may be that you know nothing. We shall see." Heisenberg could not have found a more appropriate home for his ambitions. Here he met congenial students, like Wolfgang Pauli, then 20 years old and in his fifth semester. Indeed, the names of Sommerfeld's pupils reads like a Who's Who of modern theoretical physicists: Alfred Land?, Peter Paul Ewald, Karl Herzfeld, Gregor Wentzel, Otto Laporte, Adolf Kratzer and Wilhelm Lenz, to name only those with whom Heisenberg became acquainted during his early studies. At the time Sommerfeld was deeply immersed in atomic theory. In 1915 he had extended Bohr's atomic model by taking the theory of special relativity into account and by quantizing both the azimuthal and radial motion of orbiting electrons. A year later, he also quantized the orientation of the electronic orbit. He was able to calculate electronic energies, which gave rise to additional terms in atomic spectra. This fine structure was verified by the spectroscopist Friedrich Paschen with whom Sommerfeld corresponded intensively during the First World War. Sommerfeld's classic treatise Atomic Structure and Spectral Lines, first published in 1919, went through four editions during Heisenberg's time at Munich, indicating the rapid progress being made in atomic theory during those years.
Surrounded by like-minded students and guided by a revered leader, Heisenberg felt as intellectually at home in Sommerfeld's group as he had felt emotionally at home within his Pathfinder group. Sommerfeld soon came to appreciate the talents of his new pupil. In 1922 he made the 21-year-old Heisenberg co-author of two papers on the atomic theory of X-ray spectra and the so-called anomalous Zeeman effect. The splitting of spectral lines in a magnetic field had been observed some 25 years earlier by the Dutch physicist Pieter Zeeman, and was explained by the interaction of the angular momentum of the orbiting electrons with the external field. The observation of additional splitting, however, was a major riddle in the early days of quantum mechanics and was later recognized to be a consequence of the intrinsic angular momentum or "spin" of the electron. In 1921 Sommerfeld agreed that Heisenberg could publish a paper on the anomalous Zeeman effect, although he was sceptical about the physical foundation of Heisenberg's theory. "His Zeeman model generally meets with opposition, particularly with Bohr," Sommerfeld wrote in a letter to Epstein. "But I find its success so enormous that I held back all my reservations with its publication." Heisenberg's model involved half-integer quantum numbers, which he attributed to the atomic core. However, his model did agreed with Land?'s empirical results on the splitting of spectral lines in magnetic fields and, crucially, broke the dogma of integer quantum numbers.
In the summer of 1922 Heisenberg met Niels Bohr for the first time and confronted him with his unorthodox ideas about atoms. The meeting took place during a week of lectures by Bohr in G?ttingen - the "Bohr festival" as is it became known - and transformed Heisenberg into a well known figure within the small community of atomic theorists. But Heisenberg did not specialize in atomic theory and his second publication was about alternating vortices in fluids called K?rm?n vortices. Indeed, Sommerfeld and his pupils repeatedly addressed problems in fluid dynamics, such as the transition from smooth laminar flow to turbulence. It should therefore come as no surprise that Heisenberg's doctoral dissertation was on fluid flow, rather than atomic physics.
Before Heisenberg finished his studies at Munich in 1923, he spent six months at Max Born's institute in G?ttingen. Born had just started an ambitious research programme in atomic theory, exploring perturbation methods from celestial mechanics in an attempt to deal with many-body problems in atoms by analogy with those in classical mechanics. This research resulted in a collaboration between Heisenberg and Born on the theory of the helium atom. Born also proposed that Heisenberg should come to G?ttingen as his assistant after finishing his studies in Munich. But Heisenberg's doctoral examination almost resulted in disaster. He could not answer experimentalist Wilhelm Wien's questions about the resolving power of optical instruments and how a storage battery works. Wien only let him pass after Sommerfeld vigorously defended his pupil.
After this traumatic event, Heisenberg was glad to escape to G?ttingen where he focused entirely on atomic theory. Within a few months he had qualified as a lecturer following the publication of a paper in which he modified the rules of quantum theory to address the anomalous Zeeman effect. In September 1924 he interrupted his stay at G?ttingen and went to Copenhagen, where Bohr had invited him as a research associate. In Copenhagen, Heisenberg's research focused on the quantum theory of radiation. Bohr, his Dutch assistant Hendrik Kramers, and a visiting American research fellow, John Slater, had worked out a semi-classical theory, which became known as BKS theory. But the hypothesis soon met with serious difficulties and was abandoned.
According to classical dispersion theory, atoms respond to electromagnetic fields by oscillating at the frequency of the absorbed or emitted radiation. Such a theory, however, could not account for the quantum features of the Bohr atom and the particle-like behaviour of radiation in certain circumstances. The BKS modification of classical dispersion theory was still classical, in as far as it assumed that electromagnetic radiation was wave-like and did not involve quanta, although it did account for quantum jumps.
The remedy was a "virtual radiation field", a sort of ghost field containing the possible frequencies for the quantum transitions of an atom in a given stationary state. Although it violated established physical principles, such as causality and energy conservation, the virtual field suggested a new mathematical framework for connecting the classical and quantum worlds. It therefore became the subject of intense scrutiny by Born and Heisenberg when the latter returned to G?ttingen. This was the conceptual prerequisite from which Heisenberg conceived his quantum mechanics. His decisive contribution to this programme was his paper "On a quantum theoretical re-interpretation of kinematical and mechanical relationships", now considered to be the breakthrough in modern quantum mechanics. Heisenberg's paper marked a radical departure from previous attempts to solve atomic problems by making use of observable quantities only. "My entire meagre efforts go toward killing off and suitably replacing the concept of the orbital paths that one cannot observe," he wrote in a letter dated 9 July 1925. In this respect, his work went far beyond Born's efforts to achieve a discrete quantum analogue of atomic mechanics. Rather than struggle with the complexities of three-dimensional orbits, Heisenberg dealt with the mechanics of a one-dimensional vibrating system - an anharmonic oscillator. And he explored the behaviour of the observable quantities - the radiation frequencies - that, according to the BKS legacy, had emerged from the "virtual oscillators" of an atom. The result was formulae in which quantum numbers were related to observable radiation frequencies and intensities. Born noticed that Heisenberg's formulae could be expressed in a concise manner using matrices. For this reason, the new theory also became known as "matrix mechanics".
Following Heisenberg's breakthrough, quantum mechanics took shape at an amazingly rapid pace. Born, together with his new assistant Pascual Jordan, reshaped Heisenberg's work into a systematic matrix formulation, highlighting the relationships between "conjugate variables", such as momentum and position, and energy and time. In quantum mechanics, these relationships became commutation relations between conjugate matrices. Meanwhile Paul Dirac, quite independently from the G?ttingen group, presented quantum mechanics in a new language of operators. In Zurich, Erwin Schr?dinger took a different approach and in 1926 developed wave mechanics - another form of quantum mechanics, which was found to be equivalent to the matrix method. In 1926 Heisenberg succeeded Kramers as Bohr's assistant in Copenhagen. Having been raised in Sommerfeld's school and collaborated with Born, Heisenberg was familiar with the guiding spirits of quantum theory like few others. Working in Bohr's institute, he formulated the principle of uncertainty in March 1927, thereby laying the foundation of what became known as the Copenhagen interpretation of quantum mechanics. Soon afterwards in October 1927, at the age of 26, he became professor for theoretical physics at the University of Leipzig. Within a few years, Heisenberg established Leipzig as a new centre of modern theoretical physics, together with another Sommerfeld pupil, Peter Debye, who held the chair for experimental physics, and Friedrich Hund, who became extraordinary professor for theoretical physics in 1929. By the early 1930s a new generation of theorists - such as Felix Bloch, Rudolf Peierls, Edward Teller, Victor Weisskopf and Carl Friedrich von Weizs?cker - had spread the gospel of the new "Heisenberg school". Students and research fellows from all over the world were attracted to Leipzig, including Ettore Majorana from Italy, Laszlo Tisza from Hungary, and Seishi Kikuchi, Shin-Ichiro Tomonaga and Satoshi Watanabe from Japan. Many of them earned their first academic laurels under Heisenberg's tutelage by applying quantum mechanics to solid-state physics, then a primary target for solving old problems with a new tool. Heisenberg himself paid some tribute to the emerging quantum-mechanical theory of solid-state physics by solving the riddle of ferromagnetism, but his main interest was in exploring new areas, rather than applying established methods. He focused, in particular, on the emerging new field of high-energy physics - which in the era before particle accelerators meant cosmic rays and nuclear physics - where the ideas of relativistic quantum field theory could be compared with experimental observations (see Brown and Rechenberg in further reading). The world is ugly, but the work is beautiful
"It is a pity," Heisenberg wrote to Sommerfeld in February 1938, "that in a time when physics makes such wonderful progress and it is a pleasure to contribute to its further development, one becomes involved in politics again and again." To keep himself aloof of politics was no longer possible after Hitler's rise to power in 1933. Although Heisenberg, like many Germans, probably regarded Hitler's nationalist zeal with some sympathy, he was appalled at the crudity of the regime when it came to practical measures, such as the purge of non-Aryan colleagues from universities. In this situation, Heisenberg asked the grand old man of German science, Max Planck, for advice. Planck persuaded him that the physics profession would be better protected by quiet efforts behind the scenes than by open protest. "Planck has spoken - I think I can pass this on to you - with the head of the government," Heisenberg wrote to Born, a Jew, in June 1933 after Planck had visited Hitler, "and obtained the assurance that nothing will be undertaken beyond the new civil service law that will impede our science." Although Born had not been officially dismissed, he had left G?ttingen and was ready to emigrate. Even if he had been allowed to stay because of a special regulation that exempted the dismissal of Jews who had served in the First World War, Born saw no future for his children in Germany. "I would like to ask you not to make any decisions yet," Heisenberg advised his former mentor, "but to wait and see how our country looks in the autumn." Born ignored Heisenberg's plea and emigrated to the UK where he stayed for 17 years before returning to Germany in 1953. This "wait and see" strategy became a characteristic of Heisenberg's reaction to politics. In 1935 he came closest to an open protest against the Nazi authorities when colleagues from the Leipzig philosophical faculty were dismissed in a second wave of purges. Heisenberg and others were dismayed, and expressed their disapproval at a faculty meeting. The only consequence of this background protest was a formal reprimand for the dissenters by the regional head of the Reich; the dismissals remained in force.Appalled at politics once more, Heisenberg's reaction was again to retreat. In a letter to his mother in the autumn of 1935 he wrote: "I must be satisfied to oversee in the small field of science the values that must become important for the future. That is the only clear thing left for me to do in this general chaos. The world out there is really ugly, but the work is beautiful." But retreat into science without politics was impossible for the renowned physicist. When Sommerfeld reached retirement age in 1935, Heisenberg was the obvious candidate to succeed him at Munich. But Nazi ideology was now raging in physics too: Johannes Stark and Philip Lenard, both Nobel-prize winners, characterized modern theories like relativity and quantum mechanics as "Jewish physics". Stark complained publicly that although Einstein had left Germany for America, there were still physicists acting in Einstein's spirit. Moreover, he protested that "the theoretical formalist Heisenberg, spirit of Einstein's spirit, is now even to be rewarded with a call to a chair". This was the start of a campaign against Heisenberg and Sommerfeld, which ended in 1939 when Wilhelm M?ller was named as Sommerfeld's successor. M?ller, an aerodynamicist, was branded a "complete idiot" by Sommerfeld. Heisenberg was driven to despair in the course of this struggle. Using private contacts between his and Heinrich Himmler's families, he sought assurance from the Nazis that their official view of him was not the same as that expressed in the campaign waged against him. He even thought of emigrating when the investigation into his case seemed to last forever. Behind the scenes, Heisenberg's case - and the Nazi regime's stance on physics in general - was evaluated differently by different groups. Himmler's power troop, the SS, finally supported Heisenberg and modern theoretical physics for pragmatic reasons, while party leaders and Nazi university representatives emphasized ideology over utility. The fanatics among the physicists - often addressed as one group under the name "Deutsche Physik", despite their diffuse tendencies - had been successful in preventing Heisenberg from succeeding Sommerfeld. But Heisenberg's case marked the beginning of the end for their movement. With the outbreak of the Second World War, the Nazi regime valued the possible uses of physics higher than ideology.
Heisenberg gained government acceptance after the outbreak of the Second World War, and was entrusted by the Ministry of Education with the scientific directorship of the Kaiser Wilhelm Institute of Physics in Berlin, together with Otto Hahn. The institute was under the authority of the Army Ordnance Office because of its central role in co-ordinating a secret war project. Together with other nuclear scientists, who called themselves the Uranium Club, Heisenberg began investigating the possible wartime uses of Hahn's discovery of nuclear fission. Such uses included nuclear reactors for submarine propulsion and the possibility of a new bomb that "surpasses the explosive power of the strongest explosive materials by several orders of magnitude", as Heisenberg argued in an early report in December 1939.
To this day, physicists and historians of physics debate Heisenberg's motivations and role in this effort. His compromises with the Nazi regime - perhaps psychologically explicable in view of his struggle to clear his name - raised doubts about his character. Thousands of pages have been written about "Heisenberg's war", but no consensus has been achieved.
According to one version, championed separately by the journalists Robert Jungk and Thomas Powers, Heisenberg deliberately delayed the project's progress because he abhorred the thought of an atomic bomb in Hitler's hands. But the historian Paul Rose has taken the opposite view. He believes Heisenberg tried hard to build an atomic bomb, but failed because he did not understand the physics properly. Heisenberg's own version was that he and fellow scientists in the Uranium Club were spared the decision because they had not made enough progress due to the circumstances of the war. Meanwhile, Mark Walker has criticized the "black or white" fashion in which this question has been answered. He argues that it was not Heisenberg's competence that dictated the progress of the atomic-bomb project, rather that the Army Ordnance Office lost interest in it in 1942 because the project would not produce results soon enough to influence the outcome of the war. In his study, Nazi Science, Walker provides an answer, which is perhaps as close as one can approach the truth in this entangled matter. "Did the Germans try to build atom bombs?" he asks. On one hand, he argues the Germans did not invest billions of dollars in the construction of huge factories and the development of detonation devices. But they did manufacture substances that were known to be potential nuclear explosives as quickly as possible without hindering the war effort. There is no simple answer, he concludes.
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