Werner Carl Heisenberg (5 December 1901, Würzburg – 1 February 1976, Munich) – German theoretical physicist, one of the founders of quantum mechanics, Nobel Prize in Physics (1932), a member of several academies and scientific societies around the world.
Heisenberg is the author of a number of fundamental results in quantum theory: he laid the foundations of matrix mechanics, formulated the uncertainty relation, applied the formalism of quantum mechanics to the problems of ferromagnetism, the anomalous Zeeman effect and others. Later he actively participated in the development of quantum electrodynamics (Heisenberg – Pauli theory) and quantum field theory (S-matrix theory), in the last decades of his life he attempted to create a unified field theory. Heisenberg belongs to one of the first quantum mechanical theories of nuclear forces; during the Second World War he was the leading theorist of the German nuclear project. Several works are also devoted to cosmic ray physics, turbulence theory and philosophical problems of natural science. Heisenberg played a major role in the organization of scientific research in postwar Germany.
The Young Years (1901-1920)
Werner Heisenberg was born in Würzburg into the family of August Heisenberg, professor of medieval and modern Greek philology, and Annie Wecklein, daughter of the director of the Maximilian Gymnasium in Munich. He was the second child of the family, his older brother Erwin (1900-1965) later became a chemist. In 1910, the family moved to Munich, where Werner attended school, excelling in mathematics, physics and grammar. His studies were interrupted in the spring of 1918, when he and other 16-year-olds were sent to a farm to do auxiliary work. During this time he became seriously interested in philosophy, reading Plato and Kant. After the end of World War I, the country and the city found themselves in an uncertain situation, with power shifting from one political group to another. In the spring of 1919, Heisenberg served for a time as a vestryman, helping the troops of the new Bavarian government who had entered the city. He then took part in a youth movement whose members were dissatisfied with the existing order of things, the old traditions and prejudices. Here is how Heisenberg himself recalled one of the meetings of such young people:
Many speeches were made whose pathos would seem foreign to us today. Which is more important, the fate of our people or the fate of all mankind; whether the sacrificial death of the fallen is meaningless in defeat; whether young people have the right to shape their own lives according to their own ideas of values; which is more important, loyalty to themselves or the old forms that have ordered human life for centuries–all these things were talked about and argued about with passion. I was too hesitant on all issues to take part in this debate, but I listened to it again and again…
His main interest at this time, however, was not politics, philosophy or music (Heisenberg was a gifted pianist and, as Felix Bloch recalls, could spend hours playing the instrument), but mathematics and physics. He studied them mostly independently, and his knowledge, which went far beyond the school course, was especially noted in the final examinations of the gymnasium. During his long illness, he read Hermann Weill”s book Space, Time and Matter, was impressed by the power of mathematical methods and their applications, and decided to study mathematics at the University of Munich, where he enrolled in the summer of 1920. However, mathematics professor Ferdinand von Lindemann refused to make the newcomer a member of his seminar, and on his father”s advice Heisenberg turned to the well-known theoretical physicist Arnold Sommerfeld. He immediately agreed to admit Werner to his group, where the young Wolfgang Pauli was already working, who soon became a close friend of Heisenberg.
Munich – Göttingen – Copenhagen (1920-1927)
Under the guidance of Sommerfeld Heisenberg began to work in the mainstream of the so-called “old quantum theory”. Sommerfeld spent the winter of 1922-1923 at the University of Wisconsin (USA), recommending his student to work in Göttingen under Max Born. Thus began a fruitful collaboration between the two scientists. It should be noted that Heisenberg had already visited Göttingen in June 1922 during the so-called “Bohr Festival”, a series of lectures on new atomic physics given by Niels Bohr. The young physicist even managed to get acquainted with the famous Dane and talk to him during one of his walks. As Heisenberg himself later recalled, this conversation had a great influence on the formation of his views and approach to solving scientific problems. He defined the role of various influences in his life as follows: “I learned optimism from Sommerfeld, mathematics from Göttingen, and physics from Bohr.
Heisenberg returned to Munich for the summer semester of 1923. By this time he had prepared his dissertation on some fundamental problems of hydrodynamics. This topic was suggested by Sommerfeld, who thought that a more classical topic would simplify the defense. However, in addition to the thesis, an oral examination in three subjects was necessary for the Ph.D. degree. Particularly difficult was the test in experimental physics, to which Heisenberg had not paid much attention. In the end he could not answer any of Professor Wilhelm Wien”s questions (on the resolving power of the Fabry-Perot interferometer, the microscope, the telescope and the principle of the lead battery), but thanks to the intercession of Sommerfeld he still received the lowest grade, enough to be awarded the degree.
In the fall of 1923, Heisenberg returned to Göttingen with Born, who secured an additional assistant position for him. Born described his new employee as follows:
He looked like a simple peasant boy, with short, blond hair, clear lively eyes, and a charming expression. He performed his assistant duties more earnestly than Pauli, and was a great help to me. His incomprehensible quickness and keen comprehension always allowed him to get through a tremendous amount of work without much effort.
In Göttingen the young scientist continued his work on the theory of the Zeeman effect and other quantum problems, and the following year he underwent the habilitation procedure, receiving the official right to give lectures. In the fall of 1924, Heisenberg came to Copenhagen for the first time to work under Niels Bohr. He also began to work closely with Hendrik Kramers, writing a joint paper on quantum dispersion theory.
In the spring of 1925 Heisenberg returned to Göttingen and over the next few months made decisive progress in constructing the first logically coherent quantum theory – matrix mechanics. Later the formalism of the theory was perfected with the participation of Born and Pascual Jordan. Another formulation of the theory – wave mechanics – was given by Erwin Schrödinger and stimulated both appearance of numerous concrete applications and deep elaboration of physical foundations of the theory. One of the results of this activity was Heisenberg”s uncertainty principle, formulated in early 1927.
In May 1926 Heisenberg moved to Denmark and took up his duties as associate professor at the University of Copenhagen and assistant to Niels Bohr.
Leipzig – Berlin (1927-1945)
The recognition of Heisenberg”s scientific merits resulted in invitations from Leipzig and Zurich for a professorship. The scientist chose Leipzig, where Peter Debye was the director of the Institute of Physics at the university, and in October 1927 he took the post of professor of theoretical physics. His other colleagues were Gregor Wentzel and Friedrich Hund, and his first assistant was Guido Beck. Heisenberg fulfilled many duties in the department, gave lectures in theoretical physics, organized a weekly seminar on atomic theory, which was accompanied not only by intensive discussion of scientific problems, but also by friendly tea parties and sometimes smoothly flowed into table tennis competitions (the young professor played very well and with great gusto). However, as biographers Neville Mott and Rudolf Peierls point out, Heisenberg”s early fame had little or no effect on his personal qualities:
No one would have judged him if he had begun to take himself seriously and become a little pompous after taking at least two crucial steps that changed the face of physics, and after becoming a professor at such a young age, which made many older and less important people feel important, but he remained as he was-unofficial and cheerful in his treatment, almost boyish and possessing a modesty bordering on shyness.
Heisenberg”s first pupils appeared in Leipzig, and a major scientific school soon formed there. At various times Felix Bloch, Hugo Fano, Erich Hückel, Robert Mulliken, Rudolf Peierls, Georg Placzek, John Slater and Edward Teller were members of the theoretical group, Laszlo Tissa, John Hasbrouck van Fleck, Victor Weisskopf, Karl von Weizsäcker, Clarence Zehner, Isidor Rabi, Gleb Vatagin, Erich Bagge, Hans Euler, Siegfried Flügge, Theodor Förster. Theodor Förster, Grete Hermann, Hermann Arthur Jahn, Fritz Sauter, Ivan Supek, Harald Wergeland, Giancarlo Wieck, William Vermillion Houston, and many others. Although the professor usually did not go into the mathematical details of his students” work, he often helped clarify the physical nature of the problem he was studying. Felix Bloch, Heisenberg”s first student (and later Nobel laureate), described the pedagogical and scientific qualities of his mentor as follows
If I have to pick out the only one of his great qualities as a teacher, it would be his extraordinarily positive attitude toward all progress and his encouragement in this regard. …One of Heisenberg”s most striking features was the almost unmistakable intuition he displayed in his approach to a physical problem, and the phenomenal way in which solutions seemed to fall from the sky.
In 1933 Heisenberg was awarded the Nobel Prize in Physics for the previous year with the wording “for the creation of quantum mechanics, the applications of which, among other things, led to the discovery of the allotropic forms of hydrogen. Despite his joy, the scientist expressed bewilderment at the fact that his colleagues Paul Dirac and Erwin Schrödinger received one prize (for 1933) for two, and Max Born was completely ignored by the Nobel Committee. In January 1937, he met a young woman Elisabeth Schumacher (Elisabeth Schumacher, 1914-1998), the daughter of a Berlin professor of economics, and in April he married her. The following year they had twins Wolfgang and Anna-Maria. Altogether they had seven children, some of whom also showed an interest in science: Martin (Martin Heisenberg) became a geneticist, Jochen (Jochen Heisenberg) became a physicist, and Anna-Maria and Verena became physiologists.
By this time the political situation in Germany had drastically changed: Hitler came to power. Heisenberg, who decided to stay in the country, was soon attacked by the opponents of so-called “Jewish physics,” which included quantum mechanics and relativity theory. Nevertheless, throughout the 1930s and early 1940s, the scientist worked fruitfully on the problems of atomic nucleus theory, cosmic ray physics, and quantum field theory. From 1939 he participated in the activities of the German nuclear project as one of its leaders, and in 1942 he was appointed professor of physics at Berlin University and head of the Institute of Physics of the Kaiser Wilhelm Society.
Postwar period (1946-1976)
During Operation Epsilon, ten German scientists (including Heisenberg) who were working on nuclear weapons in Nazi Germany were detained by Allied forces. The scientists were captured between May 1 and June 30, 1945, and transported to Farm Hall, a bugged building in Godmanchester, near Cambridge, England. They were held there from July 3, 1945, to January 3, 1946, to determine how close the Germans were to developing the atomic bomb.
In early 1946 Colonel B. K. Blount, a member of the science department of the British occupation zone military government, invited Heisenberg and Otto Hahn to Göttingen, which was to begin the revival of science in ruined Germany. The scientists paid much attention to organizational work, first within the Council for Science and then the Max Planck Society, which replaced the Kaiser Wilhelm Society. In 1949, after the founding of the FRG, Heisenberg became the first president of the German Research Society, which was to promote scientific work in the country. As head of the Committee on Atomic Physics, he was one of the initiators of the start of work on nuclear reactors in Germany. At the same time Heisenberg opposed the acquisition of nuclear weapons by the Adenauer government. In 1955 he played an active role in the emergence of the so-called Mainau Declaration, signed by sixteen Nobel laureates, and two years later the Göttingen Manifesto of eighteen German scientists. In 1958, he signed an appeal to ban nuclear testing initiated by Linus Pauling and addressed to the Secretary General of the United Nations. A distant result of this activity was Germany”s accession to the Treaty on the Non-Proliferation of Nuclear Weapons.
Heisenberg actively supported the creation of CERN, participating in a number of its committees. In particular, he was the first chairman of the Committee on Science Policy and was involved in determining the direction of CERN”s development. At the same time, Heisenberg served as director of the Max Planck Physical Institute, which in 1958 moved from Göttingen to Munich and was renamed the Institute for Physics and Astrophysics (German Max-Planck-Institut für Physik). He remained at the head of the institute until his retirement in 1970. He used his influence to open new institutes within the Society – the Karlsruhe Research Center (now part of the University of Karlsruhe), the Max-Planck-Institut für Plasmaphysik and the Institute for Extraterrestrial Physics. In 1953, he became the first postwar president of the Alexander von Humboldt Foundation, aimed at promoting foreign scientists who wanted to work in Germany. Holding this post for two decades, Heisenberg ensured the autonomy of the Foundation and its structure, free from the bureaucratic shortcomings of state institutions.
In spite of his numerous administrative and social responsibilities, the scientist continued his scientific work, focusing in recent years on attempts to construct a unified field theory. Among the members of his Göttingen group at different times were Karl von Weizsäcker, Kazuhiko Nishijima, Harry Lehmann, Gerhart Lueders, Reinhard Oehme, Walter Thierring, Bruno Zumino, Hans-Peter Dürr and others. After his retirement, Heisenberg spoke mainly on general or philosophical questions of natural science. In 1975, his health began to deteriorate, and on February 1, 1976 the scientist died. The famous physicist Eugene Wigner wrote on this occasion:
There is no living theoretical physicist who made a greater contribution to our science than he did. At the same time, he was friendly with everyone, devoid of arrogance, and kept pleasant company.
The old quantum theory
The early 1920s in atomic physics was the time of the so-called “old quantum theory,” which was originally based on the ideas of Niels Bohr, which were developed in the works of Sommerfeld and other scientists. One of the main methods of obtaining new results was the Bohr correspondence principle. Despite a number of successes, many questions have not yet been solved in a satisfactory way, in particular the problem of several interacting particles or the problem of spatial quantization. In addition, the theory itself was inconsistent: Newton”s classical laws could only be applied to the stationary orbits of the electron, while the transition between them could not be described on this basis.
Sommerfeld, well aware of all these difficulties, involved Heisenberg in his work on the theory. His first paper, published in early 1922, dealt with the phenomenological model of the Zeeman effect. This work, which proposed a bold model of the atomic frame interacting with valence electrons and introduced semi-integer quantum numbers, immediately made the young scientist one of the leaders of theoretical spectroscopy. Subsequent papers based on the correspondence principle discussed the widths and intensities of spectral lines and their Zeemanian components. The papers written jointly with Max Born considered general problems of the theory of multi-electron atoms (within the framework of the classical perturbation theory), analyzed molecular theory and proposed a hierarchy of intramolecular motions differing in their energy (molecular rotations and vibrations, electronic excitations), evaluated the values of atomic polarizabilities and concluded that the introduction of half-integer quantum numbers was necessary. Another modification of quantum relations, which consisted in attributing to quantum states of the atom two half-integer values of angular momentum quantum numbers, followed from consideration of the anomalous Zeeman effect (later this modification was explained by the presence of electron spin). This work, at the suggestion of Born, served as the Habilitationsschrift, i.e., the basis for the habilitation received by Heisenberg at the age of 22 at Göttingen University.
A joint work with Hendrik Kramers, written in Copenhagen, contained a formulation of dispersion theory that generalized the recent results of Born and Kramers himself. It resulted in quantum-theoretical analogues of dispersion formulas for the polarizability of the atom in a given stationary state, taking into account the possibility of transitions to higher and lower states. This important work, published in early 1925, was a direct precursor of the first formulation of quantum mechanics.
Creating Matrix Mechanics
Heisenberg was not satisfied with the state of the theory, which required solving each particular problem within classical physics and then translating it into quantum language using the correspondence principle. This approach did not always yield results and largely depended on the intuition of the researcher. Seeking to obtain a rigorous and logically consistent formalism, in the spring of 1925 Heisenberg decided to abandon the former description, replacing it with a description through so-called observable quantities. This idea was influenced by the work of Albert Einstein, who gave a relativistic definition of time instead of the unobservable Newtonian absolute time. (However, as early as April 1926, in a private conversation with Heisenberg, Einstein remarked that it is theory that determines which quantities are observable and which are not.) Heisenberg abandoned the classical notions of the position and momentum of the electron in the atom and considered the frequency and amplitude of oscillations, which can be determined from optical experiment. He managed to represent these quantities as sets of complex numbers and to give a rule for their multiplication, which proved to be noncommutative, and then he applied the developed method to the problem of the anharmonic oscillator. For a particular case of the harmonic oscillator it naturally followed the existence of the so-called “zero-point energy”. Thus, the correspondence principle was included into the very foundations of the developed mathematical scheme.
Heisenberg obtained the solution to this problem in June 1925 on the island of Helgoland, where he was recovering from an attack of hay fever. When he returned to Göttingen, he described his results in an article “On the quantum-theoretic interpretation of kinematic and mechanical relations” and sent it to Wolfgang Pauli. Having secured the latter”s approval, Heisenberg submitted the paper to Born for publication in Zeitschrift für Physik, where it was received on July 29, 1925. Born soon realized that the sets of numbers representing physical quantities were nothing but matrices, and that Heisenberg”s rule of multiplication was the rule of matrix multiplication.
In general, matrix mechanics was received rather passively by the physical community, which was not familiar with the mathematical formalism of matrices and which was scared away by the extreme abstractness of the theory. Only a few scientists paid close attention to Heisenberg”s article. For example, Niels Bohr immediately praised it and declared that “a new era of mutual stimulation of mechanics and mathematics has begun. The first rigorous formulation of matrix mechanics was given by Born and Pascual Jordan in their joint paper “On Quantum Mechanics,” completed in September 1925. They obtained the fundamental permutation relation (quantum condition) for the coordinate and momentum matrices. Heisenberg soon became involved in this research, which culminated in the famous “work of three” (Drei-Männer Arbeit), completed in November 1925. It presented a general method for solving problems within the framework of matrix mechanics, in particular considering systems with an arbitrary number of degrees of freedom, introducing canonical transformations, giving the basics of quantum-mechanical theory of perturbations, solving the problem of angular momentum quantization, discussing selection rules and a number of other issues.
Further modifications of matrix mechanics took place along two main lines: the generalization of matrices in the form of operators, carried out by Born and Norbert Wiener, and the representation of the theory in algebraic form (within the Hamiltonian formalism), developed by Paul Dirac. The latter recalled many years later how stimulating the emergence of matrix mechanics had been for the further development of atomic physics:
I have the most compelling reason to be an admirer of Werner Heisenberg. We studied at the same time, were almost the same age, and worked on the same problem. Heisenberg succeeded where I failed. By that time, a huge amount of spectroscopic material had accumulated, and Heisenberg had found the right path in his labyrinth. By doing this, he ushered in a golden age of theoretical physics, and soon even a second-rate student was able to do first-rate work.
The ratio of uncertainties
At the beginning of 1926, Erwin Schrödinger”s work on wave mechanics, which described atomic processes in the familiar form of continuous differential equations and which, as it soon became clear, was mathematically identical with matrix formalism, began to come out of print. Heisenberg was critical of the new theory and, in particular, of its original interpretation as dealing with real waves carrying an electric charge. And even the appearance of the Born”s probabilistic treatment of the wave function did not solve the problem of interpretation of the formalism itself, i.e. clarification of the meaning of the concepts used in it. The need to solve this problem became especially clear in September 1926, after Schrödinger”s visit to Copenhagen, where he in a long discussion with Bohr and Heisenberg defended the continuity of atomic phenomena and criticized the ideas of discreteness and quantum jumps.
The starting point in Heisenberg”s analysis was the realization of the need to adjust classical concepts (such as “coordinate” and “momentum”) so that they could be used in microphysics, just as the theory of relativity had adjusted the concepts of space and time, thus giving meaning to the formalism of Lorentz transformations. He found a way out of the situation by imposing a restriction on the use of classical concepts, expressed mathematically in the form of the uncertainty relation: “the more precisely the position is defined, the less precisely the momentum is known, and vice versa”. He demonstrated his conclusions with a well-known mental experiment with a gamma microscope. Heisenberg presented his results in a 14-page letter to Pauli, who praised them. Bohr, who returned from a vacation in Norway, was not entirely satisfied and made a number of comments, but Heisenberg refused to make changes to his text, mentioning Bohr”s suggestions in a postscript. An article “On the illustrative content of quantum-theoretic kinematics and mechanics” with a detailed statement of the uncertainty principle was received by the editors of the Zeitschrift für Physik on March 23, 1927.
The uncertainty principle not only played an important role in the development of the interpretation of quantum mechanics, but also raised a number of philosophical problems. Bohr linked it with the more general concept of additionality that he was developing at the same time: he interpreted the uncertainty relations as a mathematical expression of the limit to which mutually exclusive (additional) concepts are possible. In addition, Heisenberg”s article drew the attention of physicists and philosophers to the concept of measurement, as well as to a new, unusual understanding of causality proposed by the author: “…in the strong formulation of the law of causality: ”if one knows the present precisely, one can predict the future,” the premise is wrong, not the conclusion. We cannot in principle know the present in all its details.” Later, in 1929, he introduced into quantum theory the term “collapse of the wave packet,” which became one of the basic concepts within the so-called “Copenhagen interpretation” of quantum mechanics.
Applications of quantum mechanics
The emergence of quantum mechanics (first in matrix and then in wave form), immediately recognized by the scientific community, stimulated rapid progress in the development of quantum concepts, solving a number of specific problems. Heisenberg himself in March 1926 completed a joint article with Jordan that gave an explanation of the anomalous Zeeman effect using the Goudsmit and Uhlenbeck hypothesis of electron spin. In subsequent papers, written using the Schrödinger formalism, he considered systems of several particles and showed the importance of symmetry of states considerations for understanding the spectral features of helium (the terms para- and orthohelium), lithium ions, and two-chromium molecules, which led to the conclusion about the existence of two allotropic forms of hydrogen – ortho- and para-hydrogen. In fact, Heisenberg independently arrived at the Fermi-Dirac statistics for systems satisfying the Pauli principle.
In 1928 Heisenberg laid the foundations of the quantum theory of ferromagnetism (Heisenberg model), using the idea of exchange forces between electrons to explain the so-called “molecular field” introduced by Pierre Weiss in 1907. In this case, the key role was played by the relative direction of electron spins, which determined the symmetry of the spatial part of the wave function and thus affected the spatial distribution of electrons and the electrostatic interaction between them. In the second half of the 1940s Heisenberg made an unsuccessful attempt to construct a theory of superconductivity that took into account only the electrostatic interaction between electrons.
Since the end of 1927 the main task that occupied Heisenberg was the construction of quantum electrodynamics, which would take into account not only the presence of a quantized electromagnetic field, but also its interaction with relativistic charged particles. Dirac equation for the relativistic electron, which appeared in early 1928, on the one hand, indicated the right way, but on the other hand it gave rise to a number of problems, which seemed unsolvable – the problem of the electron intrinsic energy, associated with the appearance of an infinitely large addition to the mass of the particle, and the problem of states with negative energy. The research conducted by Heisenberg together with Pauli, reached a dead end, and he abandoned it for a time, taking up the theory of ferromagnetism. It was not until the beginning of 1929 that they were able to go further in constructing a general scheme of relativistic theory, which was outlined in a paper completed in March of that year. The proposed scheme was based on a quantization procedure of classical field theory containing a relativistically invariant Lagrangian. The scientists applied this formalism to a system that included an electromagnetic field and matter waves interacting with each other. In the next paper, published in 1930, they greatly simplified the theory, using symmetry considerations learned from communication with the famous mathematician Hermann Weil. First of all, this concerned the considerations of gauge invariance, which allowed to get rid of some artificial constructions of the original formulation.
Although Heisenberg and Pauli”s attempt to construct quantum electrodynamics significantly expanded the boundaries of atomic theory by incorporating a number of well-known results, it proved unable to eliminate the divergences associated with the infinite eigenenergy of the point electron. All attempts made later to solve this problem, including such radical ones as space quantization (lattice model), were unsuccessful. The solution was found much later within the framework of renormalization theory.
Beginning in 1932, Heisenberg paid a lot of attention to the phenomenon of cosmic rays, which, in his opinion, provided an opportunity to seriously test theoretical ideas. It was in cosmic rays that Carl Anderson discovered the positron predicted earlier by Dirac (Dirac”s “hole”). In 1934 Heisenberg developed the theory of holes, including positrons in the formalism of quantum electrodynamics. He, like Dirac, postulated the existence of the vacuum polarization phenomenon and in 1936, together with Hans Euler, calculated quantum corrections to Maxwell”s equations associated with this effect (the so-called Heisenberg-Euler Lagrangian).
In 1932, soon after the discovery of the neutron by James Chadwick, Heisenberg proposed the idea of a proton-neutron structure of the atomic nucleus (somewhat earlier it had been independently proposed by Dmitri Ivanenko) and in three articles he tried to construct a quantum-mechanical theory of such a nucleus. Although this hypothesis resolved many difficulties of the previous (proton-electron) model, the origin of electrons emitted in beta decay processes, some features of the statistics of nuclear particles, and the nature of forces between nucleons remained unclear. Heisenberg tried to clarify these issues by assuming the existence of exchange interactions between protons and neutrons in the nucleus, which are similar to the forces between the proton and hydrogen atom that form the hydrogen molecular ion. This interaction, according to the assumption, should be carried out by means of electrons, which are exchanged between neutron and proton, but these nuclear electrons had to be ascribed “wrong” properties (in particular, they should be spinless, i.e. bosons). The interaction between neutrons was described similarly to the interaction between two neutral atoms in a hydrogen molecule. Here, the scientist first expressed the idea of isotopic invariance associated with the charge exchange between nucleons and the charge independence of nuclear forces. Further improvements to this model were made by Ettore Majorana, who discovered the saturation effect of nuclear forces.
After the appearance in 1934 of the theory of beta decay, developed by Enrico Fermi, Heisenberg engaged in its expansion and suggested that the nuclear forces arise due not to the exchange of electrons, but electron- neutrino pairs (this idea was developed independently by Ivanenko, Igor Tamm and Arnold Nordsik). However, the value of such an interaction was much lower than that shown by the experiment. Nevertheless, this model (with some additions) remained dominant until the appearance of Hideki Yukawa”s theory, which postulated the existence of heavier particles, providing the interaction of neutrons and protons in the nucleus. In 1938 Heisenberg and Euler developed methods for analyzing absorption data of cosmic rays and were able to give the first estimate of the lifetime of the particle (“mesotron”, or, as they later said, meson) belonging to the hard component of the rays and at first associated with the hypothetical Yukawa particle. In the following year Heisenberg analyzed the limitations of existing quantum theories of elementary-particle interactions based on the use of perturbation theory, and discussed the possibilities of going beyond these theories in the high energy region attainable in cosmic rays. In this field the birth of multiple particles in cosmic rays is possible, which he considered in the framework of the theory of vector mesons.
Quantum field theory
In a series of three papers written between September 1942 and May 1944, Heisenberg proposed a radical way to get rid of divergences in quantum field theory. The idea of the fundamental length (the quantum of space) prompted him to abandon the description by means of the continuous Schrödinger equation. The scientist returned to the concept of observable quantities, the relations between which should form the basis of the future theory. For the relations between these quantities, to which he unambiguously referred the energies of stationary states and the asymptotic behavior of the wave function in scattering, absorption and emission processes, he introduced (independently of John Wheeler, who did it in 1937) the concept of the S-matrix (scattering matrix), that is, a certain operator transforming the incident wave function into the scattered wave function. According to Heisenberg”s plan, the S-matrix was to replace the Hamiltonian in the future theory. Despite the difficulties of exchanging scientific information under war conditions, the scattering matrix theory was soon picked up by a number of scientists (Ernst Stückelberg in Geneva, Hendrik Kramers in Leiden, Christian Møller in Copenhagen, Pauli in Princeton), who undertook to further develop the formalism and clarify its physical aspects. However, with time it became clear that this theory in its pure form could not become an alternative to the usual quantum field theory, but could be one of the useful mathematical tools within it. In particular, it is used (in modified form) in Feynman”s formalism of quantum electrodynamics. The notion of S-matrix, supplemented with a number of conditions, has taken a central place in formulation of the so-called axiomatic quantum field theory and later in development of string theory.
In the postwar period, with the increasing number of newly discovered elementary particles, the problem arose of describing them with as few fields and interactions as possible, in the simplest case – a single field (then we can talk about “unified field theory”). Beginning about 1950, the problem of finding the right equation describing this single field became the main one in Heisenberg”s scientific work. His approach was based on a nonlinear generalization of the Dirac equation and the presence of some fundamental length (of the order of the classical electron radius) that limited the applicability of conventional quantum mechanics. In general, this direction, immediately faced with the most difficult mathematical problems and the need to accommodate a huge amount of experimental data, was skeptically received by the scientific community and developed almost exclusively in the Heisenberg group. Despite the fact that no success was achieved and the development of quantum theory went mainly along other ways, some ideas and methods, which appeared in the works of the German scientist, played their role in this further development. In particular, the idea of representing the neutrino as a Goldstone particle, arising as a result of spontaneous symmetry breaking, influenced the development of the supersymmetry concept.
Heisenberg began to deal with the fundamental problems of fluid dynamics in the early 1920s, in his first article he made an attempt, following Theodore von Karman, to determine the parameters of the vortex tail that occurs behind a moving plate. In his doctoral thesis he examined the stability of laminar flow and the nature of turbulence on the example of fluid flow between two plane-parallel plates. He was able to show that laminar flow, stable at small Reynolds numbers (below the critical value), at first becomes unstable when this parameter is increased, but at very large values its stability increases (only long-wave perturbations are unstable). Heisenberg returned to the problem of turbulence in 1945 when he was interned in England. He developed an approach based on statistical mechanics, which in many ways was similar to the ideas developed by Geoffrey Taylor, Andrei Kolmogorov, and other scientists. In particular, he managed to show how energy exchange occurs between vortices of different sizes.
Relationship with the Nazi regime
Shortly after Hitler came to power in January 1933, a brutal invasion of established university life by politics began with the goal of “cleansing” science and education of Jews and other undesirable elements. Heisenberg, like many of his colleagues, was shocked by the apparent anti-intellectualism of the new regime, which was bound to weaken German science. At first, however, he was still inclined to emphasize the positive features of the changes taking place in the country. Apparently, the Nazi rhetoric of German renaissance and German culture appealed to him because of its proximity to the romantic ideals shared by the youth movement after World War I. Moreover, as the biographer David Cassidy notes, the passivity with which Heisenberg and his colleagues perceived the changes was probably related to the tradition of viewing science as an institution outside politics.
Attempts by Heisenberg, Max Planck, and Max von Laue to change the policy toward Jewish scientists, or at least mitigate its effects through personal connections and petitions through official bureaucratic channels, were unsuccessful. Since the fall of 1933, “non-Aryans,” women, and people of left-wing persuasion were barred from teaching, and since 1938 prospective lecturers had to prove their political trustworthiness. In this situation, Heisenberg and his colleagues, considering it a priority to preserve German physics, made attempts to replace the vacated positions with German or even foreign scientists, which was negatively received by the scientific community and also did not reach its goal. A last resort was to resign in protest, but Planck dissuaded Heisenberg by pointing out the importance of the survival of physics despite the disaster that awaited Germany in the future.
The desire to maintain their apolitical stance not only prevented Heisenberg and other scientists from resisting the growing anti-Semitism in university circles, but soon put them themselves under serious attack by “Aryan physicists. In 1935, attacks against “Jewish physics,” which included relativity theory and quantum mechanics, intensified. These actions, supported by the official press, were directed by active supporters of the Nazi regime, Nobel laureates Johannes Stark and Philipp Lenard. The resignation of Arnold Sommerfeld, who chose his famous pupil to succeed him as professor at the University of Munich, prompted attacks on Heisenberg, branded by Stark in December 1935 as “the spirit of the Einstein spirit” (Geist von Einsteins Geist). The scientist published a response in the Nazi party newspaper Völkischer Beobachter, calling for more attention to fundamental physical theories. In the spring of 1936 Heisenberg, together with Hans Geiger and Max Wien, managed to collect the signatures of 75 professors on a petition in support of this call. These countermeasures seemed to sway the Imperial Ministry of Education to side with the scientists, but on July 15, 1937, the situation changed once again. On that day, the official SS newspaper Das Schwarze Korps published a major article by Stark entitled “White Jews” in Science (“Weisse Juden” in der Wissenschaft) proclaiming the need to eliminate the “Jewish spirit” from German physics. Heisenberg personally was threatened with being sent to a concentration camp and named “Osiecki of physics. Despite a number of invitations from abroad that came to him at this time, Heisenberg was unwilling to leave the country and decided to negotiate with the government. David Cassidy gave the following picture of this difficult choice:
Had the regime restored his superior status, he would have accepted the compromises that were required, moreover convincing himself of the justice of the new justification: with the personal sacrifice of remaining in his position, he was actually protecting correct German physics from distortion by National Socialism.
Following the chosen course, Heisenberg drafted two official letters – to the Imperial Ministry of Education and to Reichsführer SS Heinrich Himmler – in which he demanded an official reaction to the actions of Stark and his supporters. In the letters he stated that if the attacks were officially approved by the authorities, he would leave his post; if not, he needed protection from the government. Thanks to an acquaintance of the scientist”s mother with Himmler”s mother, the letter reached its addressee, but it took almost another year, during which Heisenberg was interrogated by the Gestapo, his home conversations were tapped and his actions were spied upon, before a positive response was received from one of the highest leaders of the Reich. Nevertheless, the position of professor in Munich was still given to another candidate more loyal to the party.
The start of the uranium project. Trip to Copenhagen
The compromise reached between Heisenberg and the Nazi leadership has been figuratively described by Cassidy as the Faustian bargain. On the one hand, the success against the “Aryan physicists” and the public rehabilitation of the scientist meant recognition of his importance (and that of his colleagues) in maintaining a high level of physics education and scientific research in the country. The other side of this compromise was the willingness of German scientists (including Heisenberg) to cooperate with the authorities and participate in military developments of the Third Reich. The relevance of the latter especially increased with the outbreak of World War II, not only for the army, but also for the scientists themselves, because cooperation with the military served as a reliable protection from conscription to the front. There was another side to Heisenberg”s agreement to work for the Nazi government, expressed as follows by Mott and Peierls:
…It is reasonable to assume that he wanted Germany to win the war. He did not accept many aspects of the Nazi regime, but he was a patriot. Wishing his country to be defeated would have implied far more rebellious views than those he held.
Already in September 1939, the army leadership supported the creation of the so-called “Uranium Club” (Uranverein) for a deeper study of the prospects for the use of uranium nuclear fission, discovered by Otto Hahn and Fritz Strassmann in late 1938. Heisenberg was among those invited to one of the first discussions of the problem on September 26, 1939, where the project plan was drawn up and the possibility of military applications of nuclear energy noted. The scientist was to theorize the operation of the “uranium machine”, as the nuclear reactor was then called. In December 1939, he presented the first secret report with a theoretical analysis of the possibility of obtaining energy through nuclear fission. In this report, carbon and heavy water were proposed as moderators, but since the summer of 1940 it was decided to choose the latter as a more economical and affordable option (the corresponding production was already established in occupied Norway).
After his rehabilitation by the Nazi leadership, Heisenberg was allowed to lecture not only in Germany but also in other European countries (including the occupied ones). From the point of view of the party bureaucrats, he was to serve as the embodiment of the prosperity of German science. Mark Walker, a well-known expert on the history of German science of this period, wrote on the subject:
It is obvious that Heisenberg was working for Nazi propaganda unwittingly, perhaps even unknowingly. However, it is equally clear that the relevant National Socialist officials used him for propaganda purposes, that his activities were effective in this regard, and that his foreign colleagues had reason to believe that he was promoting Nazism… Such foreign lecture trips, perhaps more than anything else, poisoned his relationships with many foreign colleagues and former friends outside Germany.
Perhaps the most famous example of such a trip was a meeting with Niels Bohr in Copenhagen in September 1941. The details of the conversation between the two scientists are not known, and its interpretations differ greatly. According to Heisenberg, he wanted to know the opinion of his teacher on the moral aspect of creating new weapons, but because he could not speak openly, Bohr misunderstood him. The Dane gave a very different interpretation of the meeting. He got the impression that the Germans were working intensively on the uranium topic, and Heisenberg wanted to find out what he knew about it. Moreover, Bohr believed that his guest had invited him to cooperate with the Nazis. The Danish scientist”s views were reflected in draft letters first published in 2002 and widely discussed in the press.
In 1998, a play by English playwright Michael Frayn “Copenhagen” premiered in London, dedicated to this not fully clarified episode in the relationship between Bohr and Heisenberg. Its success in Britain and then on Broadway stimulated discussions among physicists and historians of science about the role of the German scientist in creating the “bomb for Hitler” and the content of the conversation with Bohr. It has been suggested that Heisenberg wanted to communicate through Bohr to Allied physicists not to proceed with nuclear weapons or to focus on a peaceful reactor, as German scientists did. According to Walker, Heisenberg communicated “three things in the conversation: 1) the Germans are working on the atomic bomb; 2) he himself is ambivalent about this work; 3) Bohr should cooperate with the German Science Institute and with the occupation authorities. It is therefore not surprising that the Dane, having moved to England and then to the United States in the fall of 1943, supported the rapid development of the nuclear bomb in these countries.
Attempts to create a reactor
By early 1942, despite the shortage of uranium and heavy water, various groups of scientists in Germany were able to conduct laboratory experiments that gave encouraging results in terms of building a “uranium machine. In particular, in Leipzig, Robert Döpel was able to achieve a positive increase in the number of neutrons in the spherical geometry of the arrangement of uranium layers, proposed by Heisenberg. In total, the uranium problem in Germany was worked on by 70-100 scientists in various groups, not united by a single leadership. Of great importance for the fate of the project had a conference organized by the Military Scientific Council in February 1942 (one of the lectures was Heisenberg). Although this meeting recognized the military potential of nuclear energy, but in view of the current economic and military situation in Germany, it was decided that its use in a reasonable time (about a year) will not be achieved, and therefore this new weapon would not be able to influence the course of the war. Nevertheless, nuclear research was deemed important for the future (both militarily and peacefully) and it was decided to continue to fund it, but overall leadership was transferred from the military to the Imperial Research Council. This decision was confirmed in June 1942 at a meeting of scientists with Armaments Minister Albert Speer, and the main goal was to build a nuclear reactor. As Walker points out, the decision not to move the work to the industrial level was key to the fate of the entire German uranium project:
Despite the fact that up to this point American and German research ran parallel to each other, the Americans soon surpassed the Germans… Comparing the work carried out since the winter of 1941
In July 1942, in order to organize the work on the “uranium machine,” the Institute of Physics in Berlin was returned to the Kaiser Wilhelm Society, and Heisenberg was appointed head of the Institute (he was also appointed professor at Berlin University). Since Peter Debye, who had not returned from the United States, remained formally the director of the institute, the title of Heisenberg”s position was “director at the institute. Despite the shortage of materials, in the following years several experiments were conducted in Berlin with the goal of obtaining a self-sustaining chain reaction in nuclear boilers of various geometries. This goal was almost achieved in February 1945 in the last experiment, which was already evacuated, in a room carved out in a rock in the village of Heigerloh (the institute itself was located nearby, in Hechingen). It was here that the scientists and the installation were captured by the secret Alsos mission in April 1945.
Shortly before American troops arrived, Heisenberg rode his bicycle to the Bavarian village of Urfeld, where his family was based and where he was soon found by the Allies. In July 1945, he was interned at Farm Hall, near Cambridge, among the ten major German scientists involved in the Nazi nuclear project. The physicists, who were there for six months, were under constant surveillance and their conversations were recorded with hidden microphones. These recordings were declassified by the British government in February 1992 and are a valuable document on the history of the German nuclear project.
Shortly after the end of the world war, a heated discussion began about the reasons for the failure of German physicists to build the atomic bomb. In November 1946, Die Naturwissenschaften published an article by Heisenberg on the Nazi nuclear project. Mark Walker highlighted several characteristic inaccuracies in the German scientist”s treatment of the events: downplaying the role of physicists closely associated with military circles and who made no secret of this (emphasis on the experimental error that led to the choice of heavy water (rather than graphite) as a moderator, although this choice was primarily driven by economic considerations; obscuring German scientists” understanding of the role of the nuclear reactor in producing weapons-grade plutonium; attributing the meeting of scientists with Minister Speer a decisive role in realizing the impossibility of building nuclear weapons before the war was over, even though this had been recognized earlier by the army leadership who had decided not to industrialize the research and not to waste valuable resources on it. In the same article Heisenberg first appeared a hint that the German physicists (at least from Heisenberg”s entourage) controlled the progress of work and on moral grounds tried to steer it away from the development of nuclear weapons. However, as Walker notes,
first, not only did Heisenberg and his entourage not control the German effort to master nuclear energy, but they could not have done so if they had even tried, and second, thanks to the decision of the Army authorities in 1942 and the general situation in the war, Heisenberg and other scientists working on the nuclear problem never faced the difficult moral dilemma that arises at the thought of making nuclear weapons for the Nazis. Why would they risk trying to change the direction of research if they were sure they could not influence the outcome of the war?
The other side of the debate was represented by Sam Goudsmit, who served at the end of the war as scientific director of the Alsos mission (in earlier times he and Heisenberg had been quite close friends). In an emotional dispute that lasted several years, Goudsmit argued that the obstacle to success in Germany was the lack of organization of science in a totalitarian society, but he actually accused the German scientists of incompetence, believing that they did not fully understand the physics of the bomb. Heisenberg strongly objected to the latter claim. According to Walker, “the damage to his reputation as a physicist probably bothered him more than the criticism for serving the Nazis.
Later, Heisenberg”s thesis of “moral resistance” was developed by Robert Jung in his bestseller “Brighter than a Thousand Suns,” where it was actually argued that German scientists consciously sabotaged the work on new weapons. Later, this version was also reflected in Thomas Powers” book. On the other hand, Goudsmit”s idea of the incompetence of the physicists brought to the fore under the Nazis was picked up by General Leslie Groves, head of the Manhattan Project, and later expressed by Paul Lawrence Rose in his book. According to Walker, who saw the economic difficulties of the war years as the main reason for the failure, both opposing theses were far from historically accurate and reflected the needs of the time: Heisenberg”s thesis was to restore German science and rehabilitate scientists who collaborated with the Nazis, while Goudsmit”s claim served to justify the fear of Nazi nuclear weapons and the Allies” efforts to build them. Mott and Pyerls also effectively shared the view that technical difficulties were crucial and that it was impossible for Germany to make such a great effort under the prevailing circumstances.
Both opposing points of view (about sabotage and incompetence) are not fully confirmed by the recordings of conversations of German physicists made during their internment in Farm Hall. Moreover, it was in Farm Hall that they were first confronted with the question of why they failed, because until the bombing of Hiroshima they were sure that they were far ahead of the Americans and the British in nuclear developments. During the discussion of this problem, Karl von Weizsäcker first expressed the very idea that they did not build the bomb because “they did not want to. As historian Horst Kant notes, this makes sense, because Heisenberg and Weizsäcker themselves, unlike the participants of the Manhattan Project, did not devote all their time to nuclear development. In particular, Heisenberg just in 1942-1944 was actively developing the theory of the S-matrix, and perhaps just did not feel much interest in purely military research. Hans Bethe, who was head of the theoretical department at Los Alamos Laboratory during the war, also concluded from the Farm Hall films that Heisenberg was not working on the atomic bomb. The debate continues to this day and is far from over, but Cassidy thinks it is safe to consider Heisenberg with a high degree of certainty
…not as a hero or a cruel villain, but as a deeply talented, educated man who unfortunately found himself helpless in the terrible circumstances of his time, for which he, like most people, was completely unprepared.
Throughout his life Heisenberg paid particular attention to the philosophical foundations of science, to which he devoted a number of his publications and speeches. In the late 1950s he published Physics and Philosophy, a text of the Gifford Lectures at the University of St. Andrews, and ten years later his autobiographical work Part and the Whole, described by Karl von Weizsäcker as the only Platonic dialogue of our time. Heisenberg was introduced to Plato”s philosophy as a student at the classical gymnasium in Munich, where he received a quality education in the humanities. In addition, he was greatly influenced by his father, an important philosophical scientist. Throughout his life Heisenberg maintained an interest in Plato and other ancient philosophers, and even believed that “one can hardly make progress in modern atomic physics without knowing Greek philosophy. In the development of theoretical physics in the second half of the twentieth century he saw a return (on a different level) to some of Plato”s atomistic ideas:
If we want to compare the results of modern particle physics with the ideas of any of the old philosophers, Plato”s philosophy seems most adequate: the particles of modern physics are representatives of symmetry groups, and in this respect they resemble symmetrical figures of Plato”s philosophy.
Heisenberg considered symmetries determining properties of elementary particles, not the particles themselves, as something primary, and one of the criteria of truth of the theory aimed at finding these symmetries and associated conservation laws, he saw in its beauty and logical consistency. The influence of Plato”s philosophy can also be traced in the earlier works of the scientist on quantum mechanics. Another source of inspiration for Heisenberg the thinker was the work of Immanuel Kant, especially his concept of a priori knowledge and his analysis of experimental thinking, reflected in the interpretation of quantum theory. Kant”s influence can be traced both in Heisenberg”s modification of the meaning of causality and in his view of the observability of physical quantities, which led to the establishment of the uncertainty principle and the formulation of the measurement problem in microphysics. Heisenberg”s early work on quantum mechanics was indirectly influenced by the positivist ideas of Ernst Mach (through the writings of Einstein).
In addition to Einstein, Heisenberg”s philosophical views were profoundly influenced by his friendship and collaboration with Niels Bohr, who paid special attention to the interpretation of theory, clarifying the meaning of the concepts used in it. Heisenberg, whom Wolfgang Pauli at first called a pure formalist, soon assimilated Bohr”s ideology and in his famous work on uncertainty relations made a significant contribution to the redefinition of classical concepts in the microcosm. Later he was not only one of the main actors in the final formation of the so-called Copenhagen interpretation of quantum mechanics, but also repeatedly referred to the historical and conceptual analysis of modern physics. The philosopher Anatoly Akhutin singled out the idea of the boundary in the broad sense (the concept of an organizing center around which a unified picture of the world and science is built; the problem of going beyond existing knowledge and building a new picture of reality (“steps beyond the horizon”) as the main motives in Heisenberg”s reasoning.
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