Göttingen, Copenhagen and Leipzig From 1924 to 1927, Heisenberg was a
Privatdozent at Göttingen, meaning he was qualified to teach and examine independently, without having a chair. From 17 September 1924 to 1 May 1925, under an International Education Board
Rockefeller Foundation fellowship, Heisenberg went to do research with
Niels Bohr, director of the Institute of Theoretical Physics at the
University of Copenhagen. On 7 June, after weeks of failing to alleviate a severe bout of
hay fever with aspirin and cocaine, Heisenberg retreated to the pollen-free
North Sea island of
Helgoland to focus on quantum mechanics. His seminal paper, "
Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen" ("Quantum theoretical re-interpretation of kinematic and mechanical relations") also called the
Umdeutung (reinterpretation) paper, was published in September 1925. He returned to Göttingen and, with
Max Born and
Pascual Jordan over a period of about six months, developed the
matrix mechanics formulation of
quantum mechanics. On 1 May 1926, Heisenberg began his appointment as a university lecturer and assistant to Bohr in Copenhagen. It was in Copenhagen, in 1927, that Heisenberg developed his
uncertainty principle, while working on the mathematical foundations of quantum mechanics. On 23 February, Heisenberg wrote a letter to fellow physicist
Wolfgang Pauli, in which he first described his new principle. In his paper on the principle, Heisenberg used the word "
Ungenauigkeit" (imprecision), not uncertainty, to describe it. In 1927, Heisenberg was appointed
ordentlicher Professor (professor ordinarius) of theoretical physics and head of the department of physics at the
University of Leipzig; he gave his inaugural lecture there on 1 February 1928. In his first paper published from Leipzig, Heisenberg used the
Pauli exclusion principle to solve the mystery of
ferromagnetism. At 25 years old, Heisenberg gained the title of the youngest full-time professor in Germany and professorial chair of the Institute for Theoretical Physics at the University of Leipzig. He gave lectures that were attended by physicists like
Edward Teller and
Robert Oppenheimer, In early 1929, Heisenberg and Pauli submitted the first of two papers laying the foundation for relativistic
quantum field theory. Also in 1929, Heisenberg went on a lecture tour of China, Japan, India, and the United States. On 19 August 1929 Heisenberg arrived together with
Paul Dirac with the
Graf Zeppelin LZ 127 at its first round-the-world flight at
Tokyo. In 1928, the British
mathematical physicist Paul Dirac had derived his
relativistic wave equation of quantum mechanics, which implied the existence of positive electrons, later to be named
positrons. In 1932, from a
cloud chamber photograph of
cosmic rays, the American physicist
Carl David Anderson identified a track as having been made by a
positron. In mid-1933, Heisenberg presented his theory of the positron. His thinking on Dirac's theory and further development of the theory were set forth in two papers. The first, "Bemerkungen zur Diracschen Theorie des Positrons" ("Remarks on Dirac's theory of the positron") was published in 1934, and the second, "Folgerungen aus der Diracschen Theorie des Positrons" ("Consequences of Dirac's Theory of the Positron"), was published in 1936. In these papers Heisenberg was the first to reinterpret the
Dirac equation as a "classical"
field equation for any point particle of
spin ħ/2, itself subject to quantization conditions involving anti-
commutators. Thus reinterpreting it as a (quantum) field equation accurately describing electrons, Heisenberg put matter on the same footing as
electromagnetism: as being described by relativistic quantum field equations which allowed the possibility of particle creation and destruction. (
Hermann Weyl had already described this in a 1929 letter to
Albert Einstein.)
Matrix mechanics and the Nobel Prize Heisenberg's
Umdeutung paper that established modern quantum mechanics has puzzled physicists and historians. His methods assume that the reader is familiar with
Kramers-Heisenberg transition probability calculations. The main new idea,
non-commuting matrices, is justified only by a rejection of unobservable quantities. It introduces the non-
commutative multiplication of
matrices by physical reasoning, based on the
correspondence principle, despite the fact that Heisenberg was not then familiar with the mathematical theory of matrices. The path leading to these results has been reconstructed by MacKinnon, and the detailed calculations are worked out by Aitchison and coauthors. In Copenhagen, Heisenberg and
Hans Kramers collaborated on a paper on dispersion, or the scattering from atoms of radiation whose wavelength is larger than the atoms. They showed that the successful formula Kramers had developed earlier could not be based on Bohr orbits, because the transition frequencies are based on level spacings which are not constant. The frequencies which occur in the
Fourier transform of the classical
sharp series orbits, by contrast, are equally spaced. But these results could be explained by a semi-classical
virtual state model: the incoming radiation excites the valence, or outer, electron to a virtual state from which it decays. In a subsequent paper, Heisenberg showed that this virtual oscillator model could also explain the polarization of fluorescent radiation. These two successes, and the continuing failure of the
Bohr–Sommerfeld model to explain the outstanding problem of the anomalous Zeeman effect, led Heisenberg to use the virtual oscillator model to try to calculate spectral frequencies. The method proved too difficult to immediately apply to realistic problems, so Heisenberg turned to a simpler example, the
anharmonic oscillator. The dipole oscillator consists of a
simple harmonic oscillator, which is thought of as a
charged particle on a spring, perturbed by an external force, like an external charge. The motion of the oscillating charge can be expressed as a
Fourier series in the frequency of the oscillator. Heisenberg solved for the quantum behavior by two different methods. First, he treated the system with the virtual oscillator method, calculating the transitions between the levels that would be produced by the external source. He then solved the same problem by treating the anharmonic potential term as a perturbation to the harmonic oscillator and using the
perturbation methods that he and Born had developed. Both methods led to the same results for the first and the very complicated second-order correction terms. This suggested that behind the very complicated calculations lay a consistent scheme. So Heisenberg set out to formulate these results without any explicit dependence on the virtual oscillator model. To do this, he replaced the Fourier expansions for the spatial coordinates with matrices, matrices which corresponded to the transition coefficients in the virtual oscillator method. He justified this replacement by an appeal to Bohr's correspondence principle and the Pauli doctrine that quantum mechanics must be limited to observables. On 9 July, Heisenberg gave Born this paper to review and submit for publication. When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices, which he had learned from his study under
Jakob Rosanes at
Breslau University. Born, with the help of his assistant and former student
Pascual Jordan, began immediately to make the transcription and extension, and they submitted their results for publication; the paper was received for publication just 60 days after Heisenberg's paper. A follow-on paper was submitted for publication before the end of the year by all three authors. Up until this time, matrices were seldom used by physicists; they were considered to belong to the realm of
pure mathematics.
Gustav Mie had used them in a paper on electrodynamics in 1912 and Born had used them in his work on the lattice theory of crystals in 1921. While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics. In 1928, Albert Einstein nominated Heisenberg, Born, and Jordan for the
Nobel Prize in Physics. The announcement of the Nobel Prize in Physics for 1932 was delayed until November 1933. It was at that time announced that Heisenberg had won the Prize for 1932 "for the creation of quantum mechanics, the application of which has,
inter alia, led to the discovery of the
allotropic forms of hydrogen".
Interpretation of quantum theory The development of quantum mechanics, and the apparently contradictory implications in regard to what is "real" had profound philosophical implications, including what scientific observations truly mean. In contrast to Albert Einstein and
Louis de Broglie, who were realists who believed that particles had an objectively true momentum and position at all times (even if both could not be measured), Heisenberg was an anti-realist, arguing that direct knowledge of what is "real" was beyond the scope of science. In his book ''The Physicist's Conception of Nature
, Heisenberg argued that ultimately one only can speak of the knowledge
(numbers in tables) which describes something about particles but they can never have any "true" access to the particles themselves: on his neutron-proton model of the nucleus. After Adolf Hitler came to power in 1933, Heisenberg was attacked in the press as a "White Jew" (i.e. an Aryan who acts like a Jew). Supporters of Deutsche Physik'', or German Physics (also known as Aryan Physics), launched vicious attacks against leading theoretical physicists, including Arnold Sommerfeld and Heisenberg. even though its two most prominent supporters were the
Nobel Laureates in Physics Philipp Lenard and
Johannes Stark. There had been many failed attempts to have Heisenberg appointed as a professor at a number of German universities. His attempt to be appointed as successor to Arnold Sommerfeld failed because of opposition by the
Deutsche Physik movement. On 1 April 1935, the eminent theoretical physicist Sommerfeld, Heisenberg's doctoral advisor at the
University of Munich, achieved
emeritus status. However, Sommerfeld stayed in his chair during the selection process for his successor, which took until 1 December 1939. The process was lengthy due to academic and political differences between the Munich Faculty's selection and that of the
Reich Education Ministry and the supporters of
Deutsche Physik. In 1935, the Munich Faculty drew up a list of candidates to replace Sommerfeld as ordinarius professor of theoretical physics and head of the Institute for Theoretical Physics at the University of Munich. The three candidates had all been former students of Sommerfeld: Heisenberg, who had received the
Nobel Prize in Physics;
Peter Debye, who had received the
Nobel Prize in Chemistry in 1936; and
Richard Becker. The Munich Faculty was firmly behind these candidates, with Heisenberg as their first choice. However, supporters of
Deutsche Physik and elements in the REM had their own list of candidates, and the battle dragged on for over four years. During this time, Heisenberg came under vicious attack by the
Deutsche Physik supporters. One attack was published in
Das Schwarze Korps, the newspaper of the
SS, headed by
Heinrich Himmler. In this, Heisenberg was called a "White Jew" who should be made to "disappear". These attacks were taken seriously, as Jews were violently attacked and incarcerated. Heisenberg fought back with an editorial and a letter to Himmler, in an attempt to resolve the matter and regain his honour. At one point, Heisenberg's mother visited Himmler's mother. The two women knew each other, as Heisenberg's maternal grandfather and Himmler's father were rectors and members of a Bavarian hiking club. Eventually, Himmler settled the Heisenberg affair by sending two letters, one to SS
Gruppenführer Reinhard Heydrich and one to Heisenberg, both on 21 July 1938. In the letter to Heydrich, Himmler said Germany could not afford to lose or silence Heisenberg, as he would be useful for teaching a generation of scientists. To Heisenberg, Himmler said the letter came on the recommendation of his family and he cautioned Heisenberg to make a distinction between professional physics research results and the personal and political attitudes of the involved scientists.
Wilhelm Müller replaced Sommerfeld at the University of Munich. Müller was not a theoretical physicist, had not published in a physics journal, and was not a member of the
German Physical Society. His appointment was considered a travesty and detrimental to educating theoretical physicists. The three investigators who led the SS investigation of Heisenberg had training in physics. Indeed, Heisenberg had participated in the doctoral examination of one of them at the
Universität Leipzig. The most influential of the three was
Johannes Juilfs. During their investigation, they became supporters of Heisenberg as well as his position against the ideological policies of the
Deutsche Physik movement in theoretical physics and academia. ==German nuclear weapons program==