Research Profile

by Roberto Lalli

Werner Heisenberg

Nobel Prize in Physics 1932
"for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen".

Werner Heisenberg is arguably one of the most enigmatic figures in the history of 20th century physics. An extremely brilliant student in late Wilhelmine and Weimar Germany, already in his twenties he made path-breaking contributions to the formulation, development and physical interpretation of quantum mechanics. Heisenberg’s foundational contributions to the formulation of matrix mechanics in his 1925 paper “Quantum-theoretical re-interpretation of kinematic and mechanical relations,” (“Über die Quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen”) and his 1927 formulation of the uncertainty principle that bears his name (also called indeterminacy principle) gained Heisenberg the 1932 Nobel Prize in Physics. The Prize was actually awarded in 1933, the same year in which the German National Socialist Workers’ Party came to power in Germany. Heisenberg’s decision to stay in his home country under Hitler’s rule and his wartime participation in the Uranverein (Uranium Club)—as the German nuclear weapon project was informally called—are still cause of deep disagreement between commentators and historians. In the aftermath of World War II, Heisenberg became a central figure in the complex process of cultural and political (re-)construction of West Germany. Heisenberg assumed various positions of responsibility in the organization of the research system and in the reconfiguration of its connection to the political sphere (e.g., as director of the Max Planck Institute for Physics), which made him an important actor in the shaping of the network of scientific institutions and scientific advisory bodies in West Germany until the early 1970s.
Heisenberg’s scientific and human trajectory has been at the centre of many attentive studies, which have underlined how the name of the quantum principle he discovered could be applied to the difficulties in interpreting Heisenberg’s actions in their historical context. (Historian of physics David C. Cassidy played with this double sense by entitling what might be considered Heisenberg’s definitive biography Uncertainty: The Life and Science of Werner Heisenberg). Some of these studies have made it clear how Heisenberg’s life might be instructive to think over general themes such as the moral responsibility of scientists, the relevance of science policy in an increasingly technological world, and the broader role of science in the cultural and political spheres. In 1998, some of these aspects also found a place in modern theatre, when the playwright Michael Frayn drew on an episode of Heisenberg’s life—his wartime encounter with his master and friend Niels Bohr in occupied Copenhagen during which they discussed the possible military employment of nuclear energy—to address themes such as the complex master-disciple relationship, the unsettled correlation between intentions and actions, and the limits of human knowledge with respect to past events in the play Copenhagen. As a matter of fact, that episode and the contrasting recollections of the historical actors seriously affected the friendship between Heisenberg and Bohr in the postwar period and is still cause of historical controversies.
The ambiguity surrounding some of Heisenberg’s actions during the Third Reich, however, cannot affect the fact that Heisenberg was undoubtedly one of the most important theoretical physicists of the 20th century who made enormous contributions to the establishment of one of the building blocks of our current physics knowledge: quantum mechanics.

Heisenberg at the Juncture Between Old Quantum Theory and Quantum Mechanics
Werner Heisenberg was born in Würzburg on December 5, 1901, in a family belonging to the German educated middle class (Bildungsbürgertum), which considered culture as a mean for the cultivation of the self. Heisenberg embraced the idealistic stances of the family he belonged to by looking at science from a broader cultural perspective often related to philosophical considerations. Since his childhood, he showed himself an extremely talented student with a passion for mathematics and natural sciences. In 1910, his family moved from Würzburg to Schwabing—a suburb of Munich—after the appointment of Werner’s father as professor of Byzantine philology at the University of Munich. There, Werner Heisenberg and his older brother Erwin attended the eminent Maximilian Gymnasium.
In 1920, at the age of eighteen, Heisenberg graduated from that institution and the same year entered the University of Munich, where he was soon admitted at the seminar on theoretical physics held by Arnold Sommerfeld. With Sommerfeld, the University of Munich was at the time one of the major centres in theoretical physics, strongly involved in the development of quantum theory. As student, Heisenberg was able to grasp the major theoretical problems of quantum physics and to make original contributions to its development. The German academic system allowed brilliant students to rapidly enter the phase of research and gain a doctoral degree in a time as short as three years. And this Heisenberg did. Under Sommerfeld’s supervision and in an environment that kept together talented young physicists (including Wolfgang Pauli, with whom Heisenberg would have a long-lasting and intense intellectual relationship), Heisenberg made use of his creativity to solve theoretical problems of the Bohr-Sommerfeld theory of atomic structure.
When Heisenberg arrived in 1920, Sommerfeld was occupied with the quantum theoretical explanation of the anomalous Zeeman effect—the splitting of the multiplets when a radiation source is placed in a magnetic field. While in 1916 Sommerfeld had been able to derive the normal Zeeman effect—the splitting of singlets into three equally spaced components—the anomalous effect had proven to be much harder to solve. One month after his arrival, Heisenberg was given the task to work on this problem. He made use of the notion of inner quantum number j, which Sommerfeld had recently introduced to account for the spectral patterns of the anomalous Zeeman effect by means of the selection rule Δj = ±1. The approach led Heisenberg to develop a model of complex atoms called the “core model,” according to which the set formed by the nucleus and non-valence electrons acted as a positively-charged spinning rigid core whose quantized angular momentum has to be taken into consideration. The scheme could explain the available empirical data, but only if one assumed half-integral quantum numbers in the calculation—a bold proposal that was initially rejected by the leaders of the field, for the introduction of non-integer quantum numbers lacked any physical justification. Although barely acceptable from the standards of theoretical construction, Heisenberg’s model (published in 1922) had some success to show, including the doublet and triplet line structures, the 1921 Landé rules for the Zeeman effects, and the recently discovered Paschen-Back effect; namely, the transition from the anomalous to the normal Zeeman effect when the intensity of the external magnetic field was sufficiently large.
A fundamental event shaping Heisenberg’s career was his encounter with Niels Bohr in June 1922, when the young Heisenberg went with Sommerfeld to the Bohr Festival—a two-week series of lectures delivered by Bohr at the University of Göttingen. After one of Bohr’s lectures, Heisenberg made a strong impression on the uncontested leader of quantum theory by making detailed criticisms to one of Bohr’s arguments.
When Sommerfeld travelled to the United States in winter 1922-23, Heisenberg transferred to Göttingen to work in the group headed by the German-Jewish mathematician and theoretical physicist Max Born. Göttingen, along with Munich and Copenhagen, was at the forefront in quantum theoretical research. Heisenberg favoured the different and mathematically rigorous approach followed by Born. Under Born’s direction, Heisenberg came to appreciate the relevance of perturbation methods, borrowed from classical celestial mechanics, to address problems concerning the many-body systems in atomic physics. Born and Heisenberg extended the general perturbation techniques recently developed by Born and Pauli to confirm Bohr’s explanation for the closing of shells in the building up of atoms by deriving the phase relations between the motion of electrons in many-electron atoms. The next step was to apply the same approach to the quantum theoretical analysis of the excited helium atom, which however was unsuccessful, for their calculation produced theoretical estimates of the spectral lines very different from their empirical values.
The problem to correctly address the helium (and more complex) atomic structure in the quantum theoretical framework began to be considered one of the most pressing issues of what is now called the old quantum theory. Starting from the helium problem, in some quarters (especially in Göttingen and Copenhagen) theoretical physicists became convinced that a new radical approach to the physical issues of the atomic and molecular structures had to be pursued.

While during his doctoral studies Heisenberg had already made significant contributions to quantum theory, his dissertation concerned a classical problem of hydrodynamics on the equation for stability and turbulence of flowing fluids. Although Heisenberg successfully solved the problems he addressed, his doctoral exam was seriously affected by his poor performance in the oral examination in experimental physics conducted by the 1911 Nobel Laureate Wilhelm Wien. The result was that he passed the exam only with the third of four passing grades, which highly preoccupied the 21-year old Heisenberg, aware of the extremely strong competition in the field of physics. Max Born, however, had already made plans to have Heisenberg habilitate in Göttingen and his decision was unaffected by Wien’s complaints about Heisenberg’s knowledge of experimental physics.
When Heisenberg returned in Göttingen in October 1923, Born was formulating an approach to quantum physics, which Heisenberg called “discretization of atomic physics”. During his habilitation, Heisenberg again dedicated himself to the problem of the anomalous Zeeman effect. After his first study on the subject, new detailed observations of complex atomic spectra had made the previous theoretical scheme outdated. In 1923, the German physicist Alfred Landé put forward a new phenomenological formula that described fairly well the complex multiplet spectra by making use of the vector model of the atomic core as well as of the half-integral quantum number for the angular momenta of both the atomic core and the electron emitting the spectral line. The new formula of what would be later called the Landé g-factor, however, had serious problems regarding its possible physical interpretation and its consistence within the framework of old quantum theory. Heisenberg attacked the problem from the point of view of the new research program pursued by Born—who aimed at substituting the classical differential equations with quantum discrete difference equations—with the goal of deriving the empirically successful Landé’s formulas. In just one year, Heisenberg elaborated his approach in a series of papers culminating in his habilitation thesis completed by July 1924. Heisenberg had set a series of rules that could describe the available data, and related this rule to a new theoretical framework, which could possibly constitute a new approach to the atomic theory. In summer 1924, at the astonishing age of twenty-two, Heisenberg obtained his habilitation in Göttingen, and could begin his academic career as Privatdozent (lecturer) at the same institution.
Before starting with the new appointment, Heisenberg had the opportunity to spend seven months with Bohr at the recently established Institute for Theoretical Physics of the University of Copenhagen thanks to a postdoctoral fellowship funded by the Rockefeller Foundation. His experience in Copenhagen was the last building block in the scientific formation of the young Heisenberg. There, he appreciated Bohr’s physical insights as well as the intellectually stimulating environment. In Copenhagen, Bohr, along with his assistant Hendrik A. Kramers and the American postdoc John Slater, had developed the theory of radiation known as the BKS theory, which explained atomic radiation by means of the notion of virtual oscillators without introducing the quantum of light. One of the major features of their theory was that it violated classical principles such as the exact energy and momentum conservation laws and causality. For the three physicists, in the interaction between radiation and atoms the conservation of energy and momentum could no longer be considered as precise statements, but only as statistically valid. In March 1924, Kramers made use of the BKS theory to provide a quantum theory of dispersion, which Born would soon consider a hint for the formulation of the new mechanics he was looking for: a new “quantum mechanics,” as Born christened it in a paper published in June 1924. In it, Born extended Kramers’ ideas to the interaction of electrons in a multi-electron atom and showed that the summation rules he formulated were unrelated to the BKS theory, although he employed the notion of virtual oscillators. Born’s paper did not put forward the novel mechanics theoreticians were waiting for, but was an important step in that direction.

When Heisenberg arrived at Copenhagen, one of the main problems was the application of the correspondence principle to the calculation of intensities and polarizations of the spectral lines in connection with the BKS theory. Bohr found it difficult to fully employ the correspondence principle to degenerate states, for which more than one virtual oscillator corresponded with a single harmonic component. The correspondence principle had been considered one of the most useful tools in the quantum theoretical reasoning since Bohr had first formulated it in 1918. While in Copenhagen, Heisenberg was captured by the potential of the correspondence principle as well as by the virtual oscillators program and contributed significantly to the development of this research project. The first step was what he called “the logical sharpening of the correspondence principle.” In November 1924, Heisenberg and Bohr’s new articulation of the correspondence principle to deal with degenerate states allowed them to use the sharpened principle to calculate the intensities and polarizations of fluorescent light and to derive Ornstein’s summation rules.
The next successful application of the sharpened correspondence principle in the BKS theoretical framework was the 1924 Kramers-Heisenberg theory of dispersion relations, which extended the previous theoretical investigation made by Kramers alone—an extension that was motivated also by the need to explain a form of incoherent scattering of light recently predicted by Viennese physicist Adolf Smekal, which is now called the Raman effect after the Indian physicist who confirmed it in 1928. By employing perturbation theory, Heisenberg and Kramers obtained a general formula of the quantum theoretical scattering without unobservable elements related to the orbitals of electrons, but strongly disagreed on some of the central features of the theoretical apparatus and of its physical interpretation as well as on the authorship of the paper. Years later, Heisenberg described the Kramers-Heisenberg dispersion theory as the forerunner of his matrix mechanics formalism, but at the time its connection with the BKS theory made the Kramers-Heisenberg theory problematic. The confirmation of the Compton effect for individual collisions by Walther Bothe and Hans Geiger showing that the conservation laws were exactly valid made the BKS theory untenable. Moreover, in 1924 a relativistic study by Pauli contributed to rule out the atomic core model of multiplet splitting and of the anomalous Zeeman effect. According to Pauli’s demonstration, the atomic core could contribute nothing to the total angular momentum—a reasoning which led Pauli to attribute to the valence electron the two-valuedness earlier attributed to the atomic core, and, later, to the formulation of the exclusion principle that convincingly explained Bohr’s building up principle and the regularities of the atomic table.
In this situation, Heisenberg began looking for a new mechanics that employed only observables without any reference to the underlying mechanical motions of electrons. In his research, he also considered the new spectroscopic line intensity ratio for hydrogen obtained by Ralph Kronig. After his return to Göttingen in April 1925, Heisenberg turned his attention to the calculation of the intensity lines by employing the methodology of the sharpened correspondence principle and the discretization prescriptions used in the quantum dispersion theory, but incurred many difficulties during his pursuit. Heisenberg made the last step towards the breakthrough leading to the foundation of matrix mechanics when he was seeking relief from hay fever in the isle of Helgoland in June 1925. In dealing with the problem of the anharmonic oscillator, Heisenberg got rid of unobservable entities and produced quantum-mechanical equations of motion based on a non-commutative multiplication rule that acted only on in-principle observable properties of radiation emitted and absorbed by an atom. To check whether energy was exactly conserved in his quantum-theoretical scheme—a property that was considered a necessary condition, especially after the Bothe-Geiger scattering experiment—Heisenberg proved that the quantum theoretical re-interpretation of the energy expression for a particular type of anharmonic oscillator was time independent. This demonstration convinced Heisenberg of the validity of the theory he had put forward, and, after Pauli’s blessing, he drafted the mathematically inelegant paper “Quantum-theoretical re-interpretation of kinematic and mechanical relations,” (informally called the Umdeutung paper). The paper launched a new era in theoretical physics by laying the foundations of the novel quantum mechanics theoretical physicists were waiting for to replace the Bohr-Sommerfeld theory of the atomic structure.

Matrix Mechanics, Wave Mechanics and the Uncertainty Principle
After having read Heisenberg’s manuscript, Born soon recognized that Heisenberg’s rule for the multiplication of two quantum-mechanical transition amplitudes was simply a matrix multiplication, which he knew because of his mathematical training in linear algebra. Born’s recognition that matrix calculus could be the long-awaited theoretical tool for addressing the problems of atomic physics was at the origin of a further elaboration of Heisenberg’s theoretical scheme. Along with his new collaborator Pascual Jordan, Born developed the matrix approach to quantum mechanics. Later, Born, Heisenberg and Jordan wrote together a paper, in which they put forward a clear and complete formulation of the new matrix mechanics and of its applications to degenerate and perturbed systems of any number of particles with a preliminary study of the angular momentum. The paper, later baptized Dreimännerarbeit (three-man paper) was soon considered a fundamental breakthrough in the understanding of atomic physics although many complained about the high level of abstraction of the theory. Soon after the publication of the Born-Heisenberg-Jordan paper, Pauli and Dirac successfully employed the matrix formulation of quantum mechanics to derive the Balmer series of the hydrogen atoms. After the introduction of the atomic spin in the scheme to successfully derive the anomalous Zeeman effect in early 1926 (after an initial rejection of the idea of electronic spin when it was proposed, first by Kronig and later by Samuel Goudsmit and George Uhlenbeck), the new quantum mechanics seemed to promise the resolution of the more complex problems of atomic physics.
The year 1926, however, also saw the formulation of an alternative approach to the resolution of atomic physics problems: In a series of articles, the Austrian theoretical physicist Edwin Schrödinger elaborated a completely new formulation of non-relativistic quantum mechanics, called wave mechanics. In his theoretical approach, Schrödinger extended the proposal recently put forward by the French doctoral candidate Louis de Broglie that, under certain condition, matter behaves like waves. Schrödinger’s wave equation describing the propagation of matter waves seemed compelling to most physicists because it was more visualisable than the abstract matrix algebra as well as more easily applicable to actual physical problems. Soon after the publications of Schrödinger’s first paper, matrix mechanics and wave mechanics were understood as two different theories, but Schrödinger and Pauli soon showed that they were mathematically equivalent. After this demonstration, the combination of the two approaches, which were increasingly perceived as different formulations of the same successful quantum mechanical theory, raised mainly interpretational issues that were vividly discussed in meetings as well as individual debates. The controversy was often casted in terms of wave-particle duality, for the central ontological objects of wave mechanics were waves, while Heisenberg pointed out that the particle picture was equally valid in other empirical domains. According to some recollections, a turning point was the 1927 Solvay conference dedicated to quantum mechanics, in which the combination of two new principles put forward by Heisenberg and Bohr was illustrated as providing a persuasive physical interpretation of the new quantum mechanics: Heisenberg’s uncertainly principle and the Bohr’s related complementary principle. The two principles are the core of what was later called the Copenhagen interpretation of quantum mechanics and is still the most widespread physical interpretation of the quantum mechanical formalism. Recent scholarship, however, pointed out that Heisenberg and Bohr did not agree on some essential features of an allegedly unified picture of quantum mechanics. These studies consider the Copenhagen interpretation as a postwar rhetorical construction to promote a shared common view, while the historical actors had in fact held quite different views.
Whatever the actual differences between Bohr’s and Heisenberg’s interpretational frames, the two principles they put forward were broadly accepted and played a central role in freezing the interpretational debate on quantum mechanics. Younger physicists approached quantum mechanics as a successful theoretical apparatus, which was the necessary foundation for any further development of physical knowledge. Heisenberg’s role in this process was the formulation of the uncertainty principle in 1927, when he was Bohr’s assistant at Copenhagen.

In his intellectual dialogue with Schrödinger, Heisenberg had introduced the idea that the function describing the behaviour of a multitude of electrons should show certain symmetry properties in dependence of their permutation and showed that Pauli’s exclusion principle led to the conclusion that the wave function had to be anti-symmetric when two electrons exchanged their position. The procedure Heisenberg developed in 1926 of taking into consideration the “exchange interactions” effects led him to predict the parahydrogen and orthohydrogen molecules, which would be discovered in 1929. In the meanwhile, Born had made an important contribution to the interpretation of wave mechanics by proposing a statistical interpretation of the wave function in his July 1926 paper on atomic scattering. Born interpreted the quantity ψ*ψ as the density of probability in a scattering transition—a reading that soon met with widespread success in addressing the problems of atomic collisions. Even though Born’s probabilistic interpretation of the wave function clarified many physical aspects of quantum mechanics, it also implied the explicit abandonment of determinism for atomic processes. With Born’s probabilistic interpretation and the further development of the transformation theory by Dirac and Jordan, the very understanding of concepts such as position and momentum of particles in the quantum mechanical framework could not be easily related to their classical meanings. Heisenberg answered this issue by making use of a famous thought experiment for the determination of the position of an electron by means of an imaginary gamma-ray microscope, with which he addressed the problem of non-commutative quantities in quantum mechanics. After sending his manuscript to Bohr, who did not approve completely of the reasoning contained therein and suggested some modifications, Heisenberg published the paper “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik,” (“On the Perceptual Content of Quantum Theoretical Kinematics and Mechanics”) which contained the first formulation and the demonstration of the now famous uncertainty relation for position and momentum, which was later formulated in the following way:
where x is the measurement of the position and p is the measurement of the linear momentum. In words, the principle states that in quantum mechanics, there is a fundamental limit to the accuracy with which a pair of complementary variables referring to the same object, such as its position and momentum, could be measured simultaneously. For example, the more precisely the observer knows the position of a particle, the more vague is his knowledge of its momentum. Whatever the following controversial issues of the deep physical meaning of quantum mechanics, the introduction of the uncertainty relation, along with the later formulation of the principle of complementarity by Bohr, was understood as an important step toward a physical understanding of the quantum mechanical formalism and its widespread acceptance by physicists. In the 1927 Solvay conference, Bohr and Heisenberg presented quantum mechanics as a complete theory—a view that at the time was accepted by the majority of physicists, although with notable exceptions such as Einstein, Schrödinger and de Broglie. Heisenberg was first nominated for the Nobel Prize in 1928, probably in connection with the formulation of the uncertainty relation. The discovery of the parahydrogen and orthohydrogen molecules in 1929, predicted by Heisenberg three years before, was recognized as a major event in the motivation of the 1932 Nobel Prize in Physics awarded to Heisenberg. The prize was indeed given “for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen.” The 1932 Prize was actually awarded the following year. In the 1933 Nobel Prize ceremony, Heisenberg was awarded together with two other founding fathers of quantum mechanics: Schrödinger and Dirac, who shared the 1933 Nobel Prize in Physics “for the discovery of new productive forms of atomic theory.” On various occasions, Heisenberg showed some regrets that he received a full prize, while two other giants as Schrödinger and Dirac had to share one. Moreover, he complained that the contributions of Born, Jordan and Kramers had been neglected. A historical scrutiny about the procedures of the Nobel Prize Committee, however, showed that neither Born, nor Jordan, nor Kramers had been nominated the year in which Heisenberg received the prize. The Nobel Prize’s rules prevent awarding scientists that were not nominated within the year under consideration, and the Nobel Prize Committee acted with respect to the recommendations of the nominators. This event shows that Heisenberg was broadly considered as the principal creator of matrix mechanics by the leading physicists of the time. A different discourse concerns the unequal treatment between Heisenberg and Schrödinger. Since 1929, many nominators stated that Heisenberg and Schrödinger should either be awarded together, or, even better, that they should both receive one full prize as the initiators of quantum mechanics. The decision of the Physics Section of the Nobel Committee to delay awarding the Prize was due to the radical novelty of the quantum mechanical theoretical framework—which was not easily accepted in conservative milieus—and the fact that an empirically founded relativistic formulation of quantum mechanics was still lacking. The experimental discovery of the positron by Carl Anderson in 1932, predicted in Dirac’s relativistic wave equation formulated in 1928 was considered the great empirical discovery that confirmed the entire theoretical apparatus. This discovery changed the attitude of the Physics Section of the Nobel Prize Committee towards quantum mechanics. The prizes for Heisenberg and Schrödinger were unfrozen, but by then, Dirac was also considered worthy of the Nobel Award, which he shared with Schrödinger.

Extending and Applying Quantum Mechanics
Heisenberg’s intellectual achievements during the year 1925-1927 alone could have given him a place in the pantheon of modern physics. But he did much more. His efforts to extend quantum mechanics to the treatment of electrodynamics and to apply it to nuclear and solid-state physics also had considerable impact on the evolution of theoretical physics. On the academic side, his achievements gained him the chair of theoretical physics at the University of Leipzig in 1927, at the age of twenty-six. There, he built a department which attracted many talented students and postdocs eager to work with Heisenberg, including Felix Bloch, Edward Teller, Rudolf Peierls, Isador Rabi, and Ettore Majorana. With Heisenberg, the Leipzig Physical Institute became the centre in which the foundations of the quantum-mechanical theory of metals were established, especially with the doctoral dissertation written by Bloch. Heisenberg had a fundamental role in this process. Not only did Heisenberg become a valid guide to young researchers, but he also made active contributions to the quantum theory of solids.
Even before being appointed as ordinary professor in Leipzig, Heisenberg had got interested in the problem of solid-state physics and in the phenomenon of ferromagnetism. In 1928, he put forward an explanation of ferromagnetism by making use of Pauli exclusion principle and of his earlier work on the exchange interaction for the electrons’ wave function in the helium atom. The symmetric properties of spin alignments of electrons had an influence on the spatial distribution of electrons and, hence, on their electrostatic interactions. Employing group theoretical methods, Heisenberg was able to show that particular alignments of electronic spins were energetically favoured under certain conditions and drew some conclusions concerning the atomic configuration and the dependence of the ferromagnetic phenomenon on temperature.
The task of creating a relativistic quantum mechanical theory of the interaction between matter and the electromagnetic field was undertaken as early as 1925, before major problems of the new quantum mechanics had been solved. After the creation of quantum mechanics, quantum theoretical physicists saw in quantum electrodynamics the next theoretical step in the direction of a complete theory of elementary interactions. In 1927, Dirac studied the interaction between an atom in an excited state and an electromagnetic field by applying the perturbation theory to isolated systems. This approach laid the foundations of quantum electrodynamics and introduced the procedure of “second quantization” of a continuous space-time field.
This approach was further developed by Jordan and other theoretical physicists who applied the procedure of second quantization to matter fields. In 1929, Heisenberg and Pauli further developed the Lagrangian field theoretical approach to quantum electrodynamics in a two-part article that is still the basis of modern quantum field theory. In the paper, Heisenberg and Pauli put forward a method for the quantization of any field. Although their approach was promising, fully relativistic quantum electrodynamics was plagued with the problems of the infinities, in particular of the self-energy of electrons, which were solved only in the late 1940s by means of the renormalization techniques.
In 1932, the discovery of the neutron by the English physicist James Chadwick opened the age of nuclear physics. Heisenberg soon made an impact on the future theoretical development on the forces binding the nucleus together under the hypothesis that the atomic nuclei consisted of protons and neutrons. In a three-part paper on the n-p model of the nucleus, he hypothesized that neutrons and protons were attracted by exchange forces due to the sharing of one electron in analogy to the model describing the interaction in the ionized hydrogen molecule. In Heisenberg’s model, the attraction between two neutrons depended instead on the exchange of two electrons. This nuclear theoretical scheme entailed that the neutron was a sort of proton-electron composite, although he did not explicitly address the problem of the neutron structure. The explicit analysis of the presence of electrons in the nuclear structure would have comported several problems about conservation laws and nuclear properties, such as nuclear spin. In using the exchange force model, Heisenberg introduced the isospin operator as a formal device to describe the change of status between proton and neutron depending on the emission or absorption of one electron—an operator that has since been a fundamental part of the theoretical apparatus for the description of strong nuclear forces.

“White Jew”
The very same year in which Heisenberg received his Nobel Award, Hitler was appointed Chancellor of Germany and began establishing the Nazi dictatorship. Among the dramatic consequences of the transformed political context, the German scientific sector suffered tremendously. Jewish scholars were soon forced to leave their positions in state institutions, like universities and research institutes, or were barred from new appointments. The result was that within a few months many outstanding scientists (including Einstein, Born, Bloch, Eugene Wigner, Hans Bethe, James Franck, Walter Heitler, Fritz London, and Otto Stern) pursued their academic career in other countries. Obviously, the quality of German science was very much affected by this enormous loss of first-rate scientific manpower.
Moreover, the coming to power of the Nazi party favoured those ideologically driven experimental physicists who opposed the recent advancements of theoretical physics. Headed by the Nobel Laureates Philipp Lenard and Johannes Stark, those physicists grouped in a movement called Deutsche Physik, whose aim was to re-establish an empirical scientific tradition, which, according to them, had been abandoned under the influence of an unspecified Jewish tendency for abstract reasoning. Modern theoretical physics, and its pillars relativity and quantum mechanics, was the main target of their hate campaign built over nationalistic sentiments. The political and cultural changes during the Third Reich created a fertile environment for these kinds of thoughts. The main exponents of the Deutsche Physik movement were given a certain degree of power, although the number of physicists really involved in the movement remained limited. German theoretical physicists were constantly under attack, and, among them, Heisenberg became the main target of Stark’s criticisms. In the heated and politically charged debate over new academic appointments and research project funding, Heisenberg came to be called “White Jew.” In this stressful and, even, dangerous situation, Heisenberg decided to stay in Germany. He had to be involved in debates on the evolution of physics and defend theoretical physics in political settings, such as the S.S. newspaper Das Schwarze Korps. In this process, he rehabilitated himself before the regime. During World War II, Heisenberg was involved in some politically charged events aimed at promoting German culture by giving lectures in occupied territories and played a preeminent role in the German nuclear weapon project, although he was never the leader of an organized endeavour, as is sometimes incorrectly stated. The Uranverein (Uranium Club) never became a well-organized and massive military-scientific-industrial effort such as that which led the United States to build the first nuclear weapons in 1945. By June 1942, German politicians decided that no major efforts would be undertaken towards the construction of nuclear weapons because it was understood that success could not be possibly achieved before the end of the war. Since then, the efforts were directed principally toward the construction of a nuclear reactor, which, however, was not realized before Germany surrendered in May 1945.
The dramatic political events from 1933 to 1945 and his involvement in the Uranverein had a strong impact on Heisenberg’s scientific production. After having been one of the major leaders of the field, he found himself somewhat marginalized by major advances accomplished in the United States, which was rapidly supplanting Germany as the leading country in physics research. He continued, however, to offer deep reflections about quantum electrodynamics, cosmic rays, and nuclear physics. To overcome the difficulties emerging in the quantum field theory of electromagnetic interactions, in 1938 Heisenberg proposed the introduction of the quantization of space and the related concept of fundamental length. Heisenberg hoped that the quantization of space would determine the high-energy properties of elementary particles and that the fundamental length would play a central role in a future fundamental theory along with Planck’s constant h and the velocity of light c.
Heisenberg’s major endeavour in the wartime period was, probably, the formulation of a different theoretical approach to quantum electrodynamics, which abandoned the Hamiltonian and the state function by describing particle interactions by means of a scattering matrix, later known as S-matrix. The S-matrix theory described the interaction process only through the asymptotic values of the initial and final states, but avoided any discussion of what occurred in the actual interaction. The papers on the S-matrix theory were written during the war, and were soon made obsolete by the success of renormalized field theory in the immediate postwar period. Years later, the S-matrix program re-emerged as the major contender to quantum field theory as the theoretical framework for the understanding and description of particle interactions, until the early 1970s, when several discoveries led to the acceptance of the Glashow-Weinberg-Salam unified theory of electroweak interactions.

Public Figure in the Postwar Reconstruction of West Germany
In July 1945, Heisenberg and nine other leading German physicists who were thought to have been involved in the Uranverein were interned in Farm Hall, England, for six months. The reason for Operation Epsilon, as the plan was called, was that the allied forces wanted to discover how far German scientists had progressed in the pursuit of atomic energy and nuclear weapons by recording their private conversation. The recordings showed that the German project was very far behind the Manhattan Project. In fact, the imprisoned German scientists were greatly surprised, not to say shocked, by the news of the bombs that had destroyed Hiroshima and Nagasaki in early August 1945.
Since Heisenberg had never been member of the Nazi Party and because of his scientific authority, he became a central element in the re-construction of science in West Germany in the postwar period. In the British Zone of Occupation, Heisenberg rapidly became an influential figure in both the process of denazification and in the construction of West Germany in different roles: as scientist, as scientific advisor and as scientific organizer. As director of the Institute of Physics he had an active role in the transformation from the Kaiser Wilhelm Society to the Max Planck Society in 1948 and held the directorship of the Max Planck Institute of Physics and Astrophysics until his retirement in 1970. Adopting various strategies, he tried to influence the scientific program of West Germany through advisory activity, especially related to the nuclear energy program. In these roles, in 1957 he took a strong stance against Germany acquiring nuclear weapons, by signing the Göttingen Manifesto together with other seventeen leading nuclear scientists.
The historian of science, Cathryn Carson has analysed the multifaceted role of Heisenberg’s in the re-construction of West Germany in the public sphere and rigorously described his actions and speeches in the pursuit of building a new scientific tradition in a democratic context out of the ruins of the Third Reich and World War II. These activities were also related to the construction the CERN, of which he acted as member of several committees leading to its establishment. While he was tremendously involved in organizational matters, he did not abandon original research, at a time in which German experimental physics was far behind the United States in several respects. Because cosmic rays research was considerably cheaper than working with new accelerator machines, Heisenberg dedicated himself to this field in the early postwar period in connection with German experimental projects pursued at the institute he directed. Heisenberg also addressed superconductivity, which was one of the major problems in theoretical solid-state physics. In 1947-48, Heisenberg provided a microscopic model involving only the electric interaction between electrons by making use of the concept of energy gap; namely, the view that it a minimum energy was necessary to excite single electrons. Heisenberg’s approach was initially very influential, but was rapidly outdated by the discovery of the isotope effect in 1950, which demonstrated that the isotopic mass had an influence on the transition temperature at which mercury became superconducting. The discovery of the isotope effect meant that the dynamics of the lattice had to be taken into account in an adequate quantum theoretical explanation of superconductivity. This problem was successfully solved only in 1957, when John Bardeen, Leon Cooper and John Schrieffer, proposed a microscopic theory of superconductivity (the BCS theory) that was able to explain all the effects related to the superconductive status and the dependence of the emergence of this phenomenon on temperature.
The major project he pursued in the postwar period, however, was the formulation of a unified field theory of elementary particle interactions. Starting from 1950, he was involved in the attempt to find one equation of a single field with four components and one non-linear term, whose coefficient is the only parameter in the theory. This non-linear field equation should be written in a way that it could explain the emergence of the many particles that had been discovered in cosmic-ray observations and accelerators from 1947 onward. Heisenberg worked on the unified field theory for many years and wrote about twenty articles on it, but failed to win the interest of his fellow physicists. Most theoretical physicists were highly sceptical about Heisenberg’s approach and preferred other research lines, which eventually proved successful in the explanation of elementary particle interactions. When Heisenberg died in 1976, he was undoubtedly considered one of the great physicists of the 20th century, not only as one of the founding fathers of quantum mechanics, but also for his role in the rebuilding of West German and European science in the postwar period.

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