XII Международная студенческая научная конференция Студенческий научный форум - 2020

Werner Karl Heisenberg(5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the key pioneers of quantum mechanics. He published his work in 1925 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 Heisenberg uncertainty principle, which he published in 1927. Heisenberg was awarded the 1932 Nobel Prize in Physics "for the creation of quantum mechanics".

He also made important contributions to the theories of the hydrodynamics of turbulent flows, the atomic nucleus, ferromagnetism, cosmic rays, and subatomic particles, and he was instrumental in planning the first West German nuclear reactor at Karlsruhe, together with a research reactor in Munich, in 1957. He was a principal scientist in the German nuclear weapons program during World War II. He travelled to occupied Copenhagen where he met and discussed the German project with Niels Bohr.

Following World War II, he was appointed director of the Kaiser Wilhelm Institute for Physics, which soon thereafter was renamed the Max Planck Institute for Physics. He was director of the institute until it was moved to Munich in 1958, when it was expanded and renamed the Max Planck Institute for Physics and Astrophysics.

Heisenberg was also president of the German Research Council, chairman of the Commission for Atomic Physics, chairman of the Nuclear Physics Working Group, and president of the Alexander von Humboldt Foundation.

Early years

Werner Karl Heisenberg was born in Würzburg, Germany, to Kaspar Ernst August Heisenberg ,a secondary school teacher of classical languages who became Germany's only ordentlicher Professor (ordinarius professor) of medieval and modern Greek studies in the university system, and his wife, Annie Wecklein.

Heisenberg was raised and lived as a Lutheran Christian. His autobiography starts with the young Heisenberg in his late teenage years, reading Plato's Timaeus while hiking in the Bavarian Alps. Heisenberg recounted the philosophical conversations with his fellow students and teachers on understanding the atom while receiving his scientific training in Munich, Göttingen and Copenhagen.

Habilitation

He studied physics and mathematics from 1920 to 1923 at the Ludwig Maximilian University of Munich and the Georg-August University of Göttingen. At Munich, he studied under Arnold Sommerfeld and Wilhelm Wien. At Göttingen, he studied physics with Max Born and James Franck and mathematics with David Hilbert. He received his doctorate in 1923, at Munich under Sommerfeld. At Göttingen, under Born, he completed his habilitation in 1924 with a Habilitationsschrift (habilitation thesis) on the anomalous Zeeman effect.

Because Sommerfeld had a sincere interest in his students and knew of Heisenberg's interest in Niels Bohr's theories on atomic physics, Sommerfeld took Heisenberg to Göttingen to attend the Bohr Festival of June 1922. 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.

In his youth he was a member and Scoutleader of the Neupfadfinder, a German Scout association and part of the German Youth Movement. In August 1923 Robert Honsell and Heisenberg organized a trip to Finland with a Scout group of this association from Munich.

Heisenberg arrived at Munich in 1919 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."

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. His seminal paper, "Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen" ("Quantum theoretical re-interpretation of kinematic and mechanical relations"), 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.

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. At various times they included Erich Bagge, Felix Bloch, Ugo Fano, Siegfried Flügge, William Vermillion Houston, Friedrich Hund, Robert S. Mulliken, Rudolf Peierls, George Placzek, Isidor Isaac Rabi, Fritz Sauter, John C. Slater, Edward Teller, John Hasbrouck van Vleck, Victor Frederick Weisskopf, Carl Friedrich von Weizsäcker, Gregor Wentzel, and Clarence Zener.

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. In the spring of 1929, he was a visiting lecturer at the University of Chicago, where he lectured on quantum mechanics.

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 paper establishing 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 in MacKinnon, 1977, 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. 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 that it was announced 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 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. Writing in his book The Physicist's Conception of Nature, Heisenberg argued that ultimately we only can speak of the knowledge (numbers in tables) which describe something about particles but we can never have any "true" access to the particles themselves:

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 [sic] 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.

Autobiography and death

In his late-sixties Heisenberg penned his autobiography for the mass market. In 1969 the book was published in Germany, in early 1971 it was published in English and in the years thereafter in a string of other languages. Heisenberg had initiated the project in 1966, when his public lectures increasingly turned to the subjects of philosophy and religion. Heisenberg had sent the manuscript for a textbook on the unified field theory to the Hirzel Verlag and John Wiley & Sons for publication. This manuscript, he wrote to one of his publishers, was the preparatory work for his autobiography. He structured his autobiography in themes, covering: 1) The goal of exact science, 2) The problematic of language in atomic physics, 3) Abstraction in mathematics and science, 4) The divisibility of matter or Kant's antinomy, 5) The basic symmetry and its substantiation, and 6) Science and religion.

Heisenberg wrote his memoirs as a chain of conversations, covering the course of his life. The book became a popular success, but was regarded as troublesome by historians of science. In the preface Heisenberg wrote that he had abridged historical events, to make them more concise. At the time of publication it was reviewed by Paul Forman in the journal Science with the comment "Now here is a memoir in the form of rationally reconstructed dialogue. And the dialogue as Galileo well knew, is itself a most insidious literary device: lively, entertaining, and especially suited for insinuating opinions while yet evading responsibility for them." Few scientific memoirs had been published, but Konrad Lorenz and Adolf Portmann had penned popular books that conveyed scholarship to a wide audience. Heisenberg worked on his autobiography and published it with the Piper Verlag in Munich. Heisenberg initially proposed the title Gespräche im Umkreis der Atomphysik (Conversations on atomic physics). The autobiography was published eventually under the title Der Teil und das Ganze (The part and the whole). An English translation under the title Physics and Beyond: Encounters and Conversations was published in 1971.

Heisenberg died of kidney cancer at his home, on 1 February 1976. The next evening, his colleagues and friends walked in remembrance from the Institute of Physics to his home, lit a candle and placed it in front of his door.

In 1980 his widow, Elisabeth Heisenberg, published Das politische Leben eines Unpolitischen (The Political Life of an Apolitical Person) and characterized Heisenberg "first and foremost, a spontaneous person, thereafter a brilliant scientist, next a highly talented artist, and only in the fourth place, from a sense of duty, homo politicus."

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