He published his work in in a breakthrough paper. In the subsequent series of papers with Max Born and Pascual Jordan , during the same year, this matrix formulation of quantum mechanics was substantially elaborated. He is known for the uncertainty principle , which he published in Heisenberg was awarded the Nobel Prize in Physics "for the creation of quantum mechanics". Heisenberg also made important contributions to the theories of the hydrodynamics of turbulent flows , the atomic nucleus , ferromagnetism , cosmic rays , and subatomic particles.
He was also instrumental in planning the first West German nuclear reactor at Karlsruhe , together with a research reactor in Munich , in He was director of the institute until it was moved to Munich in Heisenberg was raised and lived as a Lutheran Christian. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language" .
Heisenberg arrived at Munich in as a member of the Freikorps to fight the Bavarian Soviet Republic established a year earlier. Five decades later he recalled those days as youthful fun, like "playing cops and robbers and so on; it was nothing serious at all. He received his doctorate in at Munich under Sommerfeld. At the event, Bohr was a guest lecturer and gave a series of comprehensive lectures on quantum atomic physics.
There, Heisenberg met Bohr for the first time, and it had a significant and continuing effect on him. Heisenberg's doctoral thesis , the topic of which was suggested by Sommerfeld, was on turbulence ;  the thesis discussed both the stability of laminar flow and the nature of turbulent flow. The problem of stability was investigated by the use of the Orr—Sommerfeld equation , a fourth order linear differential equation for small disturbances from laminar flow. He briefly returned to this topic after World War II. Heisenberg enjoyed classical music and was an accomplished pianist.
In January , Heisenberg met Elisabeth Schumacher — at a private music recital. Elisabeth was the daughter of a well-known Berlin economics professor, and her brother was the economist E. Schumacher , author of Small Is Beautiful. Heisenberg married her on 29 April.
Fraternal twins Maria and Wolfgang were born in January , whereupon Wolfgang Pauli congratulated Heisenberg on his "pair creation"—a word play on a process from elementary particle physics, pair production. On 1 May , Heisenberg began his appointment as a university lecturer and assistant to Bohr in Copenhagen. It was in Copenhagen, in , 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 , 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 In his first paper published from Leipzig,  Heisenberg used the Pauli exclusion principle to solve the mystery of ferromagnetism. During Heisenberg's tenure at Leipzig, the high quality of the doctoral students and post-graduate and research associates who studied and worked with him is clear from the acclaim many later earned.
In early , Heisenberg and Pauli submitted the first of two papers laying the foundation for relativistic quantum field theory. In , 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 , 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, 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 ,  and the second, "Folgerungen aus der Diracschen Theorie des Positrons" "Consequences of Dirac's Theory of the Positron" , was published in Thus reinterpreting it as a quantum [ clarification needed ] 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 letter to Albert Einstein. Heisenberg's paper establishing quantum mechanics  [a] 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 in MacKinnon, ,  and the detailed calculations are worked out in Aitchison et al.
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 sharp classical 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 by 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.
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 and Born had used them in his work on the lattice theory of crystals in 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.
The development of quantum mechanics, and the apparent 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.
We can no longer speak of the behaviour of the particle independently of the process of observation. As a final consequence, the natural laws formulated mathematically in quantum theory no longer deal with the elementary particles themselves but with our knowledge of them.
Nor is it any longer possible to ask whether or not these particles exist in space and time objectively When we speak of the picture of nature in the exact science of our age, we do not mean a picture of nature so much as a picture of our relationships with nature.
Science no longer confronts nature as an objective observer, but sees itself as an actor in this interplay between man and nature. The scientific method of analysing, explaining and classifying has become conscious of its limitations, which arise out of the fact that by its intervention science alters and refashions the object of investigation.
In other words, method and object can no longer be separated. Shortly after the discovery of the neutron by James Chadwick in , Heisenberg submitted the first of three papers  on his neutron-proton model of the nucleus. As applied in the university environment, political factors took priority over scholarly ability,  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 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.
However, Sommerfeld stayed in his chair during the selection process for his successor, which took until 1 December 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 , 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 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. In this, Heisenberg was called a "White Jew" i. 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. 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 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.
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. 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.
In mid, Heisenberg presented his theory of cosmic-ray showers in two papers. In December , the German chemists Otto Hahn and Fritz Strassmann sent a manuscript to The Natural Sciences reporting they had detected the element barium after bombarding uranium with neutrons and Otto Hahn concluded a bursting of the uranium nucleus;  simultaneously, Hahn communicated these results to his friend Lise Meitner , who had in July of that year fled to the Netherlands and then went to Sweden. However, Heisenberg refused an invitation to emigrate to the United States.
The project had its first meeting on 16 September At a scientific conference on 26—28 February at the Kaiser Wilhelm Institute for Physics, called by the Army Weapons Office, Heisenberg presented a lecture to Reichs officials on energy acquisition from nuclear fission.