# Pauli, Wolfgang

# PAULI, WOLFGANG

(*b*.Vienna, Austria, 25 April 1900; *d*. Zurich, Switzerland, 14 December 1958)

*physics.*

Wolfgang Pauli’s father, a distinguished and original scholar, was professor of colloid chemistry at the University of Vienna and was also named Wolfgang. Thus his son, in his early work, called himself Wolfgang Pauli, Jr. The child was baptized a Catholic, his godfather being Ernst Mach, the physicist and critical philosopher. Pauli went to school in Vienna. Toward the end of his high school studies he became acquainted with Einstein’s general theory of relativity, which at that time was completely new. He read it secretly during dull classroom hours. He was truly proficient in higher mathematics, for he had previously studied Jordan’s *Cours d’ analyse* in the same manner. Einstein’s papers had made a deep impression on him. It was, he said, as if scales had fallen from his eyes; one day, so it appeared to him, he suddenly understood the general theory of relativity.

After finishing high school Pauli decided to study theoretical physics. He went to Arnold Sommerfeld in Munich, who was then the most imposing teacher of theoretical physics, in Germany or elsewhere. Many outstanding theoreticians were his pupils, including Heisenberg and Bethe. Here Pauli further perfected his analytical skills, which he later again and again masterfully put to use. Felix Klein was then publishing the *Encyklopädie der mathematischen Wissenschaften*, a monumental compilation that was to examine the current state of science from all sides. Leading scholars—mathematicians and physicists—were contributors. Klein had requested Sommerfeld to write an article on relativity theory for the Encyklopädie. Sommerfeld ventured to entrust the task to Pauli, who although scarcely twenty years old had published several papers on the subject. (Sommerfeld revealed admirable courage and insight in letting a student in his fourth semester write this important article.)

Pauli soon completed a monograph of about 250 pages, which critically presented the mathematical foundations of the theory as well as its physical significance. He took thorough account of the already very considerable literature on the subject but at the same time clearly put forth his own interpretation. Despite the necessary brevity of discussion, the monograph is a superior introduction to the special and general theories of relativity; it is in addition a first-rate historical document of science, since, together with H. Weyl’s *Raum, Zeit, Materie*(“Space, Time, and Matter”), it is the first comprehensive presentation of the mathematical and physical ideas of Einstein, who himself never wrote a large work about his theory.

Sommerfeld was elated by this performance and wrote to Einstein that Pauli’s article was “simply masterful”—and so it has remained to the present day. Pauli showed here for the first time his art of presenting science, which marks everything he wrote.

In Sommerfeld’s institute Pauli also became acquainted with the quantum theory of the atom. He wrote in his Nobel lecture:

While, in school in Vienna, I had already obtained some knowledge of classical physics and the then new Einstein relativity theory, it was at the University of Munich that I was introduced by Sommerfeld to the structure of the atom, somewhat strange from the point of view of classical physicist, accustomed to the classical way of thinking, experienced when he came to know of Bohr’s “basic postulate of quantum theory” for the first time.

It is a modest expression when Pauli speaks of “some knowledge of classical physics and the… Einstein relativity theory.” This must be taken into account to understand what it means for a “physicist, accustomed to the classical way of thinking, “ to experience a shock from Bohr’s postulate. There were, to be sure, few students scarcely twenty years of age who had penetrated the classical way of thinking as deeply as Pauli had. At this age the shock must have been great.

In 1922 Pauli obtained the doctorate with the thesis “Über das Modell der Wasserstoffmolekülions”. Soon thereafter he began to work on the anomalous Zeeman effect. as he reports in his Nobel lecture, these studies finally culminated in the discovery of the exclusion principle, announced in “Ueber den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren” (*Zeitschrift für physik.***31** [1925], 765). The markedly complicated title shows that here Pauli had solved an intricate problem. Landzé, Sommerfeld, and Bohr among others believed, particularly in the case of the alkali metals, that the atomic core around which the valence electron moved possessed an angular momentum and that this was the cause of the magnetic anomaly. Why the atomic core should possess a halfintegral angular momentum and a magnetic moment was, to be sure, unclear. Even more incomprehensible was the situation regarding the alkaline earths which possess both a singlet and a triplet system; these two systems should also be explained from the properties of the core. Indeed, the core should always possess the same electron configuration; but in the two cases it would interact differently with the valence electrons. No one could say how this would happen; and Bohr spoke of a *Zwang*, or constraint, which had no mechanical analogue. Now because the core, the closed noble gas configuration, should possess such peculiar properties, it was further believed that the core could not be characterized by the quantum numbers of the individual electrons: the “permanence of the quantum numbers” would have to be given up.

Pauli now proposed that the magnetic anomaly be understood as a result of the properties of the valence electron: in it appears, as he wrote, “a classically nondescribable two-valuedness in the quantum-theoretic properties of the electron.” The atomic core, on the other hand, possesses no angular momentum and no magnetic moment. This assumption meant that the “permanence of the quantum numbers, “ Bohr’s *Aufbauprinzip*, could in principle be described by quantum numbers. In addition to the already known *n*, *l*, and *m*, one now needed a fourth, which is denoted today by the spin quantum number *s*. After such a strong foundation was laid, Pauli went on to study the structure of the core, which had previously been considered by E. C. Stoner (*Philosophical Magazine*, **48** [1924], 709).Pauli was able to explain Stoner’s rule by means of his famous exclusion principle:

There can never be two or more equivalent electrons in an atom, for which in a strong field the values of all the quantum numbers

n,k,_{1}kand_{2}mare the same. If an electron is present, for which these quantum numbers (in an external field)have definite values, then this state is “occupied”.

In this formulation the atom is first considered in a strong external field (Paschen-Back effect), since only then can the quantum numbers for single electrons be defined. However, on thermodynamic grounds (the invariance of the statistical weights during an adiabatic transformation of the system) the number of possible states in strong and weak fields must, as Pauli observed, be the same. Thus the number of possible configurations of the various unclosed electron shells could now be ascertained.

The discovery of the exclusion principle builds the crowning conclusion to the old quantum theory based on the correspondence principle, which Pauli described in *Handbuch der Physik*, XXIII (1926). When the article was published, new developments had already occurred; in rapid succession the fundamental work of Heisenberg, Dirac, and Schrödinger appeared, leading to a proper, mathematically consistent quantum mechanics.

Following Dirac’s precedent, Jordan, Heisenberg, and Pauli developed the relativistic quantum electrodynamics. This theory occupied physicists for a good twenty years before it became clear that, in spite of all the doubts and disappointments, one of the most precise physical theories had been discovered. Disappointment and doubt had arisen primarily from the following circumstances: It was known for a long time that in the quantum theory of light and the electron, the Sommerfeld fine structure constant *e ^{2}/hc = α* plays an exceptional role: α is a dimensionless quantity and has the value 1/137. In it three areas of theoretical physics are symbolically united: electromagnetism, which is represented by

*e;*relativity, represented by

*c;*and quantum theory, represented by

*h.*It was therefore believed that if a relativistic quantum electrodynamics was successfully developed, it would at the same time yield a theory of α Thereby, so it was further hoped, a natural solution would be found for the problem of the infinite self-energy of the electron, an insurmountable problem in the classical electron theory. These hopes have not been fulfilled.

In order to accommodate the new developments, Pauli wrote an article on wave mechanics for the second edition of the *Handbuch der Physik* (XXIV, pt.1 [1933]), “Die allgemeinen Prinzipien der Wellenmechanik.” A student at the time, the author well remembers meeting Hermann Weyl on the street and his saying, “What Pauli has written on wave mechanics is again completely outstanding!” This judgment of a connoisseur is still valid today: the same article, twenty-five years later, was used unchanged in the new handbook (1958). Pauli’s presentation was thoroughly modern and well thought out, considering that such articles frequently become outdated after only a few years.

While the work on the Pauli principle and the first *Handbuch* article—“the Old Testament”—was done in Hamburg, the second article—“the New Testament”—was written in Zurich. After finishing his thesis under Sommerfeld’s guidance, Pauli had gone to Göttingen as an assistant to Max Born. Here he met Niels Bohr, who invited him to Copenhagen. From there he soon went to Hamburg, where he held an assistantship under Wilhelm Lenz and gave his inaugural lecture as *Privatdozent.* In 1928 the Swiss Board of Education appointed him Debye’s successor as professor at the Eidgenössische Technische Hochschule, where he remained until his death in 1958. At the same time Schrödinger had left the University of Zurich, where wave mechanics was developed, and he was succeeded by Gregor Wentzel. Both professors were very young and brought a rich and active scientific life to Zurich. For many years Pauli and Wentzel organized a seminar together, in which the more important new work from practically all areas of theoretical physics was critically discussed.

By today’s standards facilities at both schools were at that time rather limited. At the Technical University, Pauli was the only lecturer for theoretical physics, and students specializing in this field were practically nonexistent. But Pauli—in contrast to Wentzel at the university—did have an assistantship at his disposal. This was a research position, and he always filled it with someone who had already attained the doctorate. These assistants became his true pupils: R. Kronig, Rudolf Peierls, H. B. G. Casimir, and V. F. Weisskopf were his assistants during his first ten years in Zurich, and all were scholars who later became well-known in the field.

Pauli was never what one would call a good lecturer. He mumbled to himself, and his writing on the blackboard was small and disorganized. Above all, though, he had the tendency during the lecture to think over the subject at hand—which, as Wilhelm Ostwald remarked in *Great Men,* hinders teaching. And so his lectures were difficult to understand—but nevertheless his students were fascinated and greatly stimulated. On the whole he radiated a very strong personal force. One was immediately impressed by his sharp and critical judgment. In discussions he was in no way willing, and perhaps completely unable, to accept unclear formulations. He seemed hard to convince, or he reacted in a sharply negative manner. Thereby he forced his partner in discussion to selfcriticism and to a more logical organization of his thoughts. If, however, one succeeded in convincing Pauli of an idea, then at the same time one’s own thoughts were brought to a greater clarity. In this sense he was a truly Socratic teacher who helped in the birth of the ideas of others.

The great influence that Pauli exerted on students and colleagues cannot be ascribed to his imposing critical understanding alone. Nor did the respect that one had for him originate solely from his often caustic way of jumping at his discussion partner, which put many into disarray. Such attacks, although occasionally malicious, were not intended to be mean and had a humorous, ironic side. It was the daemon of the man that one sensed. Theoretical physics surely appears quite rational, but it rises from irrational depths. And so it rests on a daemonic background that can lead to serious conflicts. Pauli had experienced and endured this deep within himself. He had, as few others, earnestly endeavored to master this conflict rationally. Since mathematics and theoretical physics are creations of the human soul, and since they come out of the structure of the soul, he took up the ideas of C. G. Jung in order to better understand the meaning of scientific activity. The results of these efforts are numerous essays and lectures, and particularly his study “Der Einfluss archetypischer Vorstellungen auf die Bildung naturwissenschaftlicher Theorien bei Kepler.” It appeared—and Pauli attached importance to this—in the book *Naturerklärung und Psyche* (1952), which he published with C. G. Jung.

It appears that Pauli’s colleagues did not always understand how earnestly he wrestled with the philosophical foundations of science and how strongly he experienced their irrational origin. But in some obscure manner they felt it and realized it in outward experiences. These experiences took form in the strange phenomena known as the “Pauli effect”: Pauli’s mere presence in a laboratory would cause all sorts of misfortunes. So believed critical scholars, such as Otto Stern, who was friendly with Pauli, and so Pauli himself believed. The great impression that his personality made on all who came in contact with him can be correctly assessed only when this mysterious side of his complex being is taken into account.

One of Pauli’s most significant accomplishments in physics while in Zurich is the neutrino hypothesis. With it he correctly explained the continuous β spectrum, at that time ver puzzling. In a lecture before the Naturforschende Gesellschaft in Zurich in 1957 he presented the history of this discovery. Niels Bohr was of the opinion that in the case of β decay the conservation of energy should be only statistically valid. If this were conceded, then the conservation of angular momentum and the statistical laws for particles of spin 1/2 would be violated. In the early days of the development of atomic theory, Bohr was ready to sacrifice the *Aufbauprinzip* and the permanence of the quantum numbers and to introduce a mechanically unexplainable *Zwang;* and he was now also prepared to give up the classical conservation laws. He was always “ready and willing” to discover the unexpected in the realm of atomic dimensions. Pauli, on the other hand, resolved only with great difficulty to let fall natural laws that had previously been confirmed everywhere. Just as he held on to the permanence of the quantum numbers in his theory of the closing of shells in atoms, which led him to the exclusion principle, so it appeared to him right to retain the conservation laws. Thus he proposed in a letter of 4 December 1930 to Lise Meitner and associates “the continuous β-spectrum would be understandable under the assumption that during β-decay a neutron is emitted along with the electron…”

Since the letter was written before Chadwick had discovered the neutron in the nucleus, the discussion here involved another particle, which Fermi then christened “neutrino.” At the Solvay Congress in 1933, Pauli again extensively justified his proposal, which was published in the Congress report. Shortly thereafter, in 1934, Fermi worked out his theory of β decay, which, in spite of unsolved basic difficulties, has been confirmed amazingly well.

During the war Pauli was active at the Institute for Advanced Study in Princeton; but later, after careful consideration, he returned to Zurich. He lived happily with his wife in Zollikon, near great forests that invited meditative strolls. Consistent as he was, he now earned Swiss citizenship.

This article has intentionally avoided giving even an approximately complete review of Pauli’s scientific work, for there is practically no area of theoretical physics in which he did not decisively take part. The aim has been to make clear, in connection with his most important contributions, the manner in which he worked. A last example to be mentioned is his important work on discrete symmetries in field theory. He dedicated it to Niels Bohr on his seventieth birthday under the title “Exclusion Principle, Lorentz Group and Reflection of Space-time and Charge.” Starting from investigations by Schwinger and Löders, Pauli showed that every Lorentz invariant Lagrangian field theory is invariant under the operation CTP, whereas C, T, and P separately do not have to be symmetries of the theory. This study had greatly occupied him, as he occasionally told nee, and I guessed that he had hidden thoughts about the matter which he did not express. So I asked him if in this work there was not in fact another problem between the lines and if he might not say something about it. But he denied my conjecture: he was interested in these symmetries in their own right.

Not much later it was discovered that in weak interactions-for example, in β decay-the parity (P) is not conserved (Lee and Yang, 1956). Pauli was greatly stirred by this discovery. It seemed to him at first extraordinarily repugnant that in nature right and left should not enjoy equal status. But then he realized that the symbolic, to some extent naturalphilosophic, concept which he saw in this symmetry did indeed remain: for as he had made clear one year earlier, CTP must be a valid symmetry if only the natural laws are Lorentz invariant. Thus, guided by his own genius, he had meaningfully prepared for the coming developments.

Just as Pauli received a shock when, as a student, he first became acquainted with the strange laws of quantum theory, so did he receive a shock from the nonconservation of parity. For it was always his hope that physics would indicate the mysterious harmony of God and Nature. This hope was not illusory. Precisely in his most important work he had shown how apparently paradoxical phenomena could be explained through a harmonious extension of the previously confirmed theory. And so theoretical physics since Kepler, Galileo, and Newton appeared to him as a great house the foundations of which, despite many changes, would never be shaken. It was because he felt this way, and because he considered himself a representative of a great tradition, that he reacted so sharply against obscure arguments and superficial speculation. He expressed himself thus concerning his position to a colleague: “In my youth I believed myself to be a revolutionary; now I see that I was a classicist.”

In December 1958, Pauli became violently and seriously ill, and on December 14 he died. At the funeral Viktor Weisskopf said he was “the conscience of theoretical physics.” This is truly the shortest statement that can render the impression which this rare man made on all who knew him.

## BIBLIOGRAPHY

A complete list of Pauli’s books, articles, and studies is *in Theoretical Physics in the Twentieth Century, a Memorial Volume to Wolfgang Pauli* (New York, 1960). Collections include his scientific papers (New York, 1964) and *Aufsätze und Vorträge üiber Physik and Erkenntnistheorie* (Brunswick, 1961).

M. Fierz

# Pauli, Wolfgang

# PAULI, WOLFGANG

The Austrian-Swiss physicist Wolfgang Ernst Pauli was born in Vienna on April 25, 1900, the son of Bertha (Schütz) and Wolfgang Joseph Pauli. His father, originally from Prague, became a professor of chemistry at the University of Vienna in 1922 and was one of the founders of the science of colloid chemistry. Bertha Pauli was a writer, as was her daughter Hertha who was also an actress, and they belonged to the cultural elite of Vienna. The family was originally of Jewish origin, but Wolfgang Sr. became a Catholic, and his son was baptized—his godfather being the famous physicist and philosopher Ernst Mach.

In high school, Pauli was an outstanding student, with a strong interest in mathematics and astronomy. In 1918, he enrolled at the University of Munich, Germany, to study with Arnold Sommerfeld, a famous expert on relativity and atomic physics and the teacher of future Nobel Prize winners, including Werner Heisenberg and Hans Bethe. Pauli completed his Ph.D. in only three years, writing a dissertation on the quantum theory of the hydrogen molecule ion. In 1920, while still a student, Pauli wrote a 250-page article on relativity for the 1921 *Encyclopedia of Mathematical Physics* at Sommerfeld's request. It was highly praised by Einstein and is still regarded as a major treatise on the subject.

## The Exclusion Principle

After receiving his Ph.D., Pauli spent a year at the University of Göttingen, with James Franck and Max Born. He then worked for a year at Copenhagen with Niels Bohr, who had originated the quantum theory of the atom. It was at this time that he first took up the problem of the Zeeman effect, the splitting of spectral lines in the presence of a magnetic field, which was a subject of major interest because it seemed to be an insoluble problem in the Bohr-Sommerfeld quantum theory that dominated atomic physics. This theory, an extensive elaboration of Bohr's 1913 hydrogen model, placed the atomic electrons in classical orbits that were restricted by a general set of quantum conditions. For example, angular momenta and their vector components were restricted to being integer multiples of ħ = *h* /2π, where *h* = 6.63 × 10^{-34} J/s is Planck's constant.

However, the number of atomic states in a magnetic field was double the number that the theory predicted. In the simple case of sodium, for example,

there is one electron outside of a closed shell of electrons (the core) that Bohr-Sommerfeld theory predicts should have zero angular momentum. To account for the extra atomic states, it was proposed that the core should instead have an angular momentum of ½ħ, an idea that Pauli rejected. His solution was to say that the electron itself has a "non-classically describable two-valuedness," so that it was not the core but the external valence electron that was responsible for the doubling of the number of atomic states

This was a suggestion of the greatest importance, for it played an essential role in explaining the periods in Mendeleev's table of chemical elements. Bohr had already made a start in this direction with his building-up principle, which asserted that in passing from one atom in the table (characterized by the atomic number *Z,* or number of electrons) to the next one, the inner electrons kept the same quantum numbers. However, to complete this picture, Pauli's new two-valuedness was needed: each set of the old quantum numbers labeled not one, but two states. The new form of the principle became known as the Pauli Exclusion Principle, and it was for this discovery that Pauli was awarded the Nobel Prize in Physics in 1945.

## Quantum Mechanics and Quantum Electrodynamics

In 1925 Heisenberg, Pauli's close friend and collaborator, replaced the Bohr-Sommerfeld orbit theory with a new quantum mechanics from which the modern theory of physics and chemistry has originated. Pauli, however, was the first to apply Heisenberg's theory to a real physical problem, namely, the hydrogen atom, which he solved completely. Meanwhile, also in 1925, two young Dutch physicists, Samuel Goudsmit and George Uhlenbeck, identified Pauli's quantum number as belonging to electron spin. That is, every electron has an intrinsic spin angular momentum of ½ħ, and an associated intrinsic magnetic moment *e* ħ/*mc* , which can take up one of two orientations in a magnetic field. Pauli resisted this rotating electron interpretation for almost a year, but in March 1926 he wrote to Bohr that he would "capitulate completely" (Mehra and Rechenberg 1982, p. 709). He then applied the spin and the exclusion principle to explain the magnetic properties of normal metals (paramagnetism) and thus initiated in 1927 a new research field, the quantum electron theory of metals.

In that same year, the English quantum theoretician Paul Dirac made a quantum theory of the electromagnetic field and also a relativistic generalization of the wave function, introduced by the Austrian physicist Erwin Schrödinger in his version of quantum mechanics. Dirac's theory predicted the existence of a positive electron (positron) that could be produced together with an ordinary negative electron, providing enough energy was available (at least 2*mc*^{2}, with *m* being the electron mass and *c* the velocity of light). Pauli and Heisenberg then wrote two important papers providing a relativistic treatment of the interaction between radiation and matter. They discovered important difficulties in their theory, which had to wait until the late 1940s for a satisfactory resolution. Problems of quantum field theory, as it came to be called, occupied Pauli for the rest of his life, especially the relation between spin and quantum statistics, which is crucial for the collective behavior of identical particles (whether they form shells, for example, or collapsed states, as in a laser).

As professor at the Swiss Federal Institute of Technology (ETH) from 1928, after serving at the University of Hamburg, Pauli continued his research on wave mechanics. This led in 1933 to another remarkable treatise, published as an encyclopedia article.

## Nuclear Beta Decay and the Neutrino

In December 1930, convinced that a puzzling situation in nuclear beta decay required a "desperate solution," Pauli suggested that a new extremely penetrating neutral particle of very small (perhaps zero) mass accompanied each electron emitted in beta decay. Pauli took this step to account for what appeared to be energy "missing" from the process. Now called the neutrino, Pauli's particle became an ingredient of a new and successful quantum field theory of beta decay worked out by the Italian physicist Enrico Fermi at the end of 1933. (A generalized version of Fermi's theory forms part of the so-called Standard Model of elementary particle interactions developed in the 1970s.)

In 1940 Pauli, fearing a possible German invasion of Switzerland, moved to the Institute for Advanced Study in Princeton, New Jersey, where Einstein was also in residence. He returned in 1945 to the ETH in Zurich, where he remained until his death on December 14, 1958. Pauli had many important accomplishments in physics, and he was also a philosopher. In studying the psychology of creativity, he collaborated with the Swiss psychoanalyst Carl Gustav Jung. Because of the profoundly high standards that he brought to his work, Pauli is sometimes referred to as the "conscience of physics."

*See also:*Neutrino, Discovery of

## Bibliography

Enz, C. P. "W. Pauli's Scientific Work" in *The Physicist's Conception of Nature,* edited by J. Mehra (Reidel, Boston,1973).

Enz, C. P. *No Time to Be Brief: A Scientific Biography of Wolfgang Pauli* (Oxford University Press, New York, 2000).

Fierz, M., and Weisskopf, V.F. *Theoretical Physics in the Twentieth Century* (memorial volume to Pauli)(Interscience, New York, 1960).

Mehra, J., and Rechenberg, H. *The Historical Development of Quantum Mechanics,* Vol. 1, Part 2 (Springer-Verlag, New York, 1982).

Pauli, W. "Remarks on the History of the Exclusion Principle." *Science***103** , 213–215 (1946).

Pauli, W. "Relativitätstheorie" in *Encyclopädie der Mathematis-chen Wissenschaften* 5, Part 2, 539–775 (B.G. Teubner, Leipzig, 1921). English translation: *Theory of Relativity* (Pergamon, New York, 1958).

Pauli, W. *Lectures on Physics,* Vols. 1–6 (MIT Press, Cambridge, MA, 1973).

Pauli, W. "Die allgemeine Prinzipien der Wellenmechanik" in *Handbuch der Physik,* Vol. 24, Part 1, edited by H. Geiger and K. Scheel (Springer-Verlag, Berlin, 1980). English translation: *General Principles of Quantum Mechanics* (Springer-Verlag, New York, 1990).

Peierls, R. E. "Wolfgang Ernst Pauli." *Biographical Memoirs of Fellows of the Royal Society***5** , 175–192 (1959).

Weisskopf, V. F. "Personal Memories of Pauli." *Physics Today***38** , 36–41 (1985).

*Laurie M. Brown*

# Pauli, Wolfgang

# Pauli, Wolfgang

**AMERICAN THEORETICAL PHYSICIST1900–1958**

Wolfgang Ernst Pauli was born in Vienna, Austria, where his father, regarded as one of the founders of colloid chemistry, was employed at the University of Vienna. His godfather was Ernst Mach, a famous physicist, philosopher, and one of the founders of logical positivism; he had a significant influence on Pauli's thinking. In high school Pauli was an outstanding student with a special talent for mathematics and physics. His parents fostered Pauli's appetite for science by hiring a private tutor. The tutor was so successful that within twelve months of beginning his studies at the University of Munich in 1918, Pauli had submitted three original papers on the theory of relativity to a leading physics periodical; all were published before his twentieth birthday.

Pauli received his doctorate in 1921 for theoretical work on the hydrogen molecule ion. He then became an assistant to Max Born at Göttingen. While at Göttingen, Pauli met Niels Bohr, who invited him to work for a year with his group in Copenhagen, Denmark. Once there, Pauli began work on the problem of the anomalous Zeeman effect (how the energy levels of a multielectron atom are split in a magnetic field), work that he continued when in 1923 he moved to a new position at the University of Hamburg. By 1924 he had decided that the current model of atomic structure used by Bohr, which assumed only two numbers and which allowed many electrons to have identical quantum numbers, needed to be modified. He also found that the currently accepted idea that it was the magnetic moment of the core of the atom that was responsible for the splitting of the electron energy levels of the outer electrons, was incorrect. Instead, Pauli proposed a new model that had as its consequence his famous **exclusion principle** .

The new model had its origins in a new classification of electron levels published in 1924 by Edmond C. Stoner, an English physicist at the University of Leeds who was an expert on the magnetic properties of matter. This classification divides the electrons of an atom into electronic shells using three quantum numbers (n, k1, k2). The first two number are the same as those used by Bohr, and the third one, the inner quantum number k2, was chosen so that twice the sum of the individual k2 numbers became the number of electrons in a subgroup. It was Pauli's genius that allowed him to extend this classification by adding a fourth quantum number (m1), which could have only two values (+1/2 and −1/2). As a result, Pauli was able in 1925 to arrive at the first statement of his exclusion principle, that stated that there cannot be two or more equivalent electrons in an atom for which in strong fields the values of all quantum numbers n, k1, k2, and m1 are the same. Initially, Pauli rejected the notion that the two-valuedness of m1 was due to spin, but after discussing the matter of electron spin with fellow physicists Samuel Goudsmit and George Uhlenbeck, he accepted the idea. The term "exclusion principle" had its origin in Pauli's insistence on each electron having a unique set of quantum numbers. This requirement immediately solved many problems in the interpretation of observed atomic spectra, because it prevented many lines that, according to prior theories, should be seen but never were, to become forbidden.

In 1928 Pauli became professor of **theoretical physics** at the Federal Institute of Technology, Zurich; largely through his efforts it became a leading center for research in theoretical physics. In 1931 he observed that when an electron was emitted from a nucleus, a loss of energy occurred that could not be explained by then-current theories. He proposed that it was due to the existence of another particle which carried no charge and had very low mass. The American physicist Enrico Fermi named this particle the "neutrino"; it was eventually discovered some twenty-five years later.

During World War II Pauli worked at the Institute for Advanced Studies at Princeton in New Jersey; he then returned to Zurich, where he died in 1958.

see also Bohr, Niels; Fermi, Enrico.

*John E. Bloor*

## Bibliography

McMurray, Emily J., ed. (1995). *Notable Twentieth-Century Scientists.* Detroit: Gale Research.

Peierls, Rudolf E. (1959). "Wolfgang Ernst Pauli." In *Biographical Memoirs of Fellows of the Royal Society,* Vol. 5, pp. 175–192. London: Royal Society.

### Internet Resources

"Wolfgang Pauli and Modern Physics." Available from <http://www.ethbib.ethz.ch/exhibit/pauli>.

# Pauli, Wolfgang

# PAULI, WOLFGANG

(*b*. Vienna, Austria, 25 April 1900; *d*. Zurich, Switzerland, 14 December 1958), *physics*. For the original article on Pauli see *DSB*, vol. 10.

Pauli was a leading figure of modern physics from the 1920s through the 1950s. His Nobel Prize, awarded in 1945, recognized the 1924 discovery of the exclusion (or Pauli) principle in atomic physics. Pauli made crucial contributions to quantum mechanics, quantum statistics, and the quantum theory of fields, and he set a broadly recognized standard for critical analyses of those domains. Beginning with the 1921 survey of Albert Einstein’s relativity theory that announced him to the scientific world,

his review articles were widely consulted synthetic accounts. The excellent edition of his correspondence has made it possible to trace his influence in important domains of physics. Since his death, the interest he had in Jungian psychoanalysis has attracted attention as well.

Pauli as scientist and human being is well-described in Markus Fierz’s sympathetic entry in the original *DSB*. Scholars since Fierz have done much work filling out Pauli’s intellectual context. In particular, historical studies of quantum physics have made plain how powerfully Pauli shaped the trajectory from the old (Bohr-Sommerfeld) quantum theory of atomic structure to the new quantum mechanics. John Hendry has examined the exchanges between Pauli and Niels Bohr, and other studies have illuminated Pauli’s influence on Werner Heisenberg from the 1920s onward. Pauli’s work leading to the exclusion principle has been taken up by several historians and followed out to the spin-statistics theorem in Michela Massimi’s philosophical account.

Most attention to Pauli has concentrated on the 1920s, though his role in quantum field theory in the 1930s and beyond was no less significant. His 1932 proposal of the neutrino was one important intervention. Pauli’s greatest contribution to quantum field theory, however, was his systematic and critical exploration of its formalism. Pauli’s extraordinary scientific correspondence, edited by Karl von Meyenn, has many insights, while Charles P. Enz’s scientific biography analyzes Pauli’s publications across his full career. Enz’s biography also provides many personal details. A very valuable set of reflections by colleagues (*Wolfgang Pauli: Das Gewissen der Physik*, 1988) likewise carries the story up to Pauli’s early death.

One feature of Pauli’s life that has come to prominence is his interest in dreams, archetypes, and the unconscious. Pauli’s correspondence with Carl Gustav Jung has been published, and their relationship has been analyzed in several books. More broadly, Pauli’s collected philosophical writings (published in English and German) have made this side of his thought accessible. A full synthetic treatment is as of 2007 still outstanding.

## SUPPLEMENTARY BIBLIOGRAPHY

### WORKS BY PAULI

With Carl Gustav Jung. *Naturerklärung und Psyche: Synchronizität als ein Prinzip akausaler Zusammenhänge* Zurich: Rascher, 1952. Published as *The Interpretation of Nature and the Psyche*. New York: Pantheon, 1955.

*Aufsätze und Vorträge über Physik und Erkenntnistheorie*. Braunschweig: Vieweg, 1961.

*Collected Scientific Papers*. Edited by R. Kronig and V. F. Weisskopf. New York: Interscience, 1964.

*Wissenschaftlicher Briefwechsel mit Bohr, Einstein, Heisenberg u.a*. 6 vols. Edited by Karl von Meyenn et al. New York: Springer, 1979–2005.

With Carl Gustav Jung. *Wolfgang Pauli and C. G. Jung: Ein*

*Briefwechsel, 1932–1958*. Edited by C. A. Meier. Berlin: Springer, 1992. Translated by David Roscoe as *Atom and Archetype: The Pauli-Jung Letters, 1932–1958*. Princeton, NJ: Princeton University Press, 2001.

*Writings on Physics and Philosophy*. Edited by Charles P. Enz and Karl von Meyenn, translated by Robert Schlapp. Berlin: Springer, 1994.

### OTHER SOURCES

Atmanspacher, H., H. Primas, and E. Wertenschlag Birkenhäuser, eds. *Der Pauli-Jung-Dialog und seine Bedeutung für die moderne Wissenschaft*. Berlin: Springer, 1995.

Enz, Charles P. *No Time to be Brief: A Scientific Biography of Wolfgang Pauli*. Oxford: Oxford University Press, 2002.

Mostly technical, but much personal information.

———, and Karl von Meyenn, eds. *Wolfgang Pauli: Das Gewissen der Physik*. Braunschweig: Vieweg, 1988.Recollections and original documents.

Hendry, John. *The Creation of Quantum Mechanics and the Bohr-Pauli Dialogue*. Dordrecht: D. Reidel, 1984. Laurikainen, Kalervo V. *The Message of the Atoms: Essays on Wolfgang Pauli and the Unspeakable*. Berlin: Springer, 1997.

Massimi, Michela. *Pauli’s Exclusion Principle: The Origin and*

*Validation of a Scientific Principle*. Cambridge, U.K.: Cambridge University Press, 2005. Includes citations to earlier historical literature.

*Cathryn Carson*

# Wolfgang Ernst Pauli

# Wolfgang Ernst Pauli

The Austrian theoretical physicist Wolfgang Ernst Pauli (1900-1958) was awarded the Nobel Prize in Physics for his discovery of the exclusion principle, known as the Pauli principle.

Wolfgang Pauli the son of Wolfgang Joseph Pauli, a professor in the University of Vienna, was born in that city on April 25, 1900. Brilliant at school, he studied theoretical physics in the University of Munich under Arnold Sommerfeld (1918-1921) and graduated as a Doctor of Philosophy. Sommerfeld asked him to write the article on relativity for the *Encyclopedia of Mathematical Sciences.* The article, over 200 pages long, was published in 1921; it was translated into English and Italian in 1958 and is still definitive.

Pauli was an assistant to Max Born at Göttingen (1921-1922) and to Niels Bohr at Copenhagen (1922-1923). He then spent 5 years as a lecturer in the University of Hamburg, and in 1928 he became professor of physics in the Federal Institute of Technology at Zurich.

In 1921 the generally accepted theory of the atom was that advanced by Bohr in 1913. In the case of the hydrogen atom with its single electron, the state of the atom was defined by a single quantum number representing the energy in the possible circular orbits of the electron. By postulating an additional set of quantum numbers Sommerfeld later extended Bohr's theory to cover the elliptical orbits in complex atoms, and a third set was later postulated to explain the atom in a magnetic field. The Bohr-Sommerfeld theory explained the hydrogen atom satisfactorily; but in the case of complex atoms it did not explain the doublet nature of the series of the alkali spectra, nor did it explain the anomalous Zeeman effect which Pauli had tried to elucidate while he was at Copenhagen.

In 1924-1925 Pauli published his theoretical solution of the anomalous Zeeman effect. To explain it, others had suggested that the third, or magnetic, quantum number should be regarded as having a half-integer value. But Pauli postulated a fourth quantum number, a fourth degree of freedom. This he regarded as having one of two values only—a property he later defined as "two-valuedness not describable classically." He then defined his "principle," which is now usually stated as follows: no two electrons in the same atom can have all four quantum numbers equal. Recognized from the time of its publication as important, it was not at once called the exclusion, or Pauli, principle. In 1925 G. E. Uhlenbeck and S. A. Goudsmit introduced the hypothesis of electron spin, with possible quantum numbers of either + ½ or -½. About this time the new mechanics, as exemplified by Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave equation, was making headway, but these methods did not easily explain the problem of the hydrogen atom because it involved the inverse-square law in the attractive force. In 1926 Pauli solved this problem brilliantly by identifying his hypothetical fourth degree of freedom with Uhlenbeck and Goudsmit's "spin," and since then this degree has been called the spin quantum.

Between 1928 and 1930 Pauli first attempted—partly in collaboration with Heisenberg—to apply the quantum principle to the interaction of radiation and matter. These three papers constituted the first steps in quantum field theory. In the early 1930s, to explain the phenomenon of beta decay of nuclei, by which an unpredictable amount of energy appeared to be lost, Pauli postulated the existence of a neutral particle of low mass but with spin ½ For this particle Enrico Fermi later coined the name "neutrino."

Pauli was visiting professor at the University of Michigan (1931, 1941) and at the Institute for Advanced Study, Princeton (1935-1936, 1940-1945). He received many honors, including the Nobel Prize for Physics in 1945. In 1953 he was elected a Foreign Member of the Royal Society. He died in Zurich on Dec. 15, 1958.

## Further Reading

There is a biography of Pauli in *Nobel Lectures, Physics, 1942-1962* (1964), which also includes his Nobel Lecture. For his work see N. H. de V. Heathcote, *Nobel Prize Winners, Physics, 1901-1950* (1953); B. Hoffmann, *The Strange Story of the Quantum* (2d ed. 1959); and A. d'Abro, *The Rise of the New Physics,* vol. 2 (1951). □

# Pauli, Wolfgang

# PAULI, WOLFGANG

**PAULI, WOLFGANG** (1900–1958), Swiss physicist and Nobel laureate born in Vienna. His father was a physician born in Prague, who changed the family name from Pascheles to Pauli, and his mother, a writer, was born in Vienna. He was educated at the Doebling Gymnasium and received his doctorate in physics from the Ludwig-Maximilian University of Munich supervised by Arnold Sommerfeld (1921). After working for a year with Max Born at the University of Goettingen and a further year with Niels Bohr in Copenhagen, he was a lecturer in physics at the University of Hamburg (1923–28). In 1928 he was appointed professor of theoretical physics at the Federal Institute of Technology, Zurich (1928–40). In 1940 he held a German passport which classified him as 75% Jewish even though it was not stamped "Jewish." The Nazi threat and his failure to obtain Swiss naturalization at the time led him to move to Princeton University (1940–46). Further difficulties concerning his status at his former university were resolved following his receipt of the Nobel Prize and he returned to Zurich for the rest of his career. He served as head of the mathematics and physics section (1950–52). Pauli was one of the most influential theoretical physicists of the 20^{th} century. He showed a precocious command of mathematics and physics while a schoolboy, and his life-long interest in quantum mechanics began at university. Early on he recognized the importance of particle spin in exploring the structure of the atom. He formulated the exclusion principle which states that no two fermions (defined as the elementary particles other than bosons) can have identical quantum numbers. This principle has profound implications for understanding the composition of the periodic table and cosmological issues. He was awarded the 1945 Nobel Prize in physics for this contribution which he was unable to receive personally because of political difficulties over his travel documents from the U.S. Later he predicted the existence of the neutrino, the elusive particle that accounts for the loss of energy in beta decay. He also elucidated the basis of the Zeeman effect whereby the spectral line is split into two or more components when the light source is placed in a magnetic field. This finding facilitated the adaptation of this observation to nuclear physics and astronomy. His work on spinors and the Pauli master equation also had important applications for studying particle spin. His other honors included foreign membership in the Royal Society of London (1953). Pauli was less successful as a teacher because his analytical, non-didactic style was often difficult to follow, and he could be abrasive in scientific discourse and criticism.

Towards the end of his life Pauli became dissatisfied with science and his thoughts and writing incorporated much of his longstanding discourse with Carl Jung which had started for therapeutic reasons. He expressed no specific monotheistic belief but incorporated Jewish mysticism into his general mystical philosophy.

[Michael Denman (2^{nd} ed.)]

# Pauli, Wolfgang

**Pauli, Wolfgang** (1900–58) US physicist, b. Austria. His work on quantum theory led him to formulate (1925) the exclusion principle, which explains the behaviour of electrons in atoms. Pauli received the 1945 Nobel Prize in physics for the work. In 1931, he had predicted the existence of the neutrino, and lived to see the prediction verified in 1956.

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