Einstein's Genius Club
Page 12
Yet Pauli seems to have been oblivious to the turmoil. At nineteen, he was the resident expert on general relativity. He lectured on it in Sommerfeld's class, wrote his second paper on it in June 1919, and tended to sleep late, enjoying the nightlife and clearly untroubled by missing a few morning lectures. He later recalled the “cheerful mood” of those on their way to and from physics and mathematics conferences. Only rarely did the real world intrude on Sommerfeld's institute, as when extremist students threatened to disrupt a lecture by Einstein, scheduled in late 1921. Einstein wisely decided not to attend.
Pauli had already met Einstein at a 1920 conference in Nauheim. It must have been a heady moment for the young student, at work on the relativity article. The conference was one of several during 1920 at which Einstein was expected to defend general relativity. His name recognition not only among physicists, but among the general populace had increased exponentially when in 1919 Arthur Stanley Eddington was able to measure the bending of light during a solar eclipse, thus confirming Einstein's postulate on gravitational magnetism. Still, with fame came controversy, some of it stirred not by science but by blatant anti-Semitism. The Nauheim conference witnessed a “dramatic… duel between Einstein and Philipp Lenard,” in the words of the mathematician Hermann Weyl. Lenard's anti-Semitism was so virulent that it colored his view of relativity and embittered him against “Jewish physics.” Ironically, it was Einstein, the “Jewish fraud” of relativity, who had been able in 1905 to explain anomalies Lenard observed in his own work on cathode rays.
In Sommerfeld's institute, consisting of not much more than a library, a laboratory, a seminar room, the director's own office, and, of course, a lecture hall, Pauli and his fellow students (Werner Heisenberg among them) learned how to theorize not only on relativity, but on quantum theory as well. It was, of course, the “old” quantum theory first postulated by Bohr in 1913. Bohr's now obsolete atomic model resembled a solar system; its electrons, however, did not follow the rules of classical physics. Sommerfeld was active in the attempt to “manage” Bohr's unwieldy model, suggesting, for instance, elliptical orbits. In the years to follow, Sommerfeld's students, Pauli and Werner Heisenberg among them, rode the wave of quantum theory thoroughly grounded in the rudiments of research. Throughout both of their lives, the very mention of Sommerfeld transformed the usually sardonic Pauli into a deferential and respectful pupil.
In only six semesters, Pauli finished all required coursework. He began his thesis on ionized molecular hydrogen—a little-remembered excursion into quantum theory (Enz remarks that Pauli's ego might have led him to tackle a too-difficult problem). Pauli had distinguished himself sufficiently to be offered an assistantship with Max Born, the physicist whose “probability interpretation” reconciled wave and particle, introduced the notion of probability as a state of knowledge rather than a state of ignorance, and won Born a Nobel Prize in 1954. During the winter of 1921, while completing the thesis, Pauli assisted Born at the University of Göttingen. Until 1933, the university, founded in 1737 by the Hanoverian King George II of England, boasted first-rate mathematics and physics departments: Among other illustrious former faculty was Bernhard Riemann, the nineteenth-century mathematician, whose geometry made Einstein's general relativity theory possible, as we shall see.
Born was fond of Pauli, despite the latter's tendency to sleep late and miss lectures. Much later, Born wrote,
[E]ver since the time he had been my assistant in Göttingen, I had been aware that he was a genius comparable only to Einstein himself. Indeed, from the point of view of pure science he was possibly even greater than Einstein even if as an entirely different type of person he never, in my opinion, attained Einstein's greatness.174
Genius Pauli may have been; still, his somewhat erratic comportment hinted at a psychological imbalance, which surfaced in the early 1930s.
In Göttingen, Pauli and Born collaborated on an important series of calculations that would, in theory, test Niels Bohr's idea of the harmony of atomic motions. The “Göttingen calculations,” based on the celestial mechanics of perturbation (i.e., the effect planets have on each other as opposed to the much greater effect of the sun's gravitation), seemed to contradict Bohr's description of the helium atom. This was one of an increasing number of difficulties facing the Bohr atomic model and his early formulation of quantum theory.
In 1922, Niels Bohr was invited to lecture at Göttingen University. Bohr was at the pinnacle of his career. He had just founded an institute for theoretical physics in Copenhagen, where he taught. He was six months away from being awarded the Nobel Prize for his atomic model. Everyone who was anyone came to the lectures, dubbed the “Bohr Festspiele.” Among those attending were Werner Heisenberg and, of course, Wolfgang Pauli. Bohr was to become the greatest mentor of young physicists in the century. Pauli was thereafter a disciple, colleague, and friend of the Danish scientist. The young Heisenberg and Paul Dirac were also drawn into Bohr's orbit.
Bohr's lectures were exciting but not particularly accessible (one student described Bohr's style as “neither acoustically nor otherwise completely understandable”175). Still, most of the attendees knew Bohr's theories. The lectures were an occasion to discuss, argue, and augment. Pauli must have been active at the conference, since he wrote Bohr immediately after its close, thanking him for answering “the most diverse questions.”176
Those questions, together with Pauli's reputation, led Bohr to invite the twenty-two-year-old prodigy to his new Copenhagen institute for a year. Pauli quickly accepted. In addition to his own work, Pauli spent the year translating Bohr's papers and lectures (including Bohr's Nobel Prize lecture) into German. During his year in Copenhagen, Pauli gained lifelong friends, colleagues, and collaborators. Above all, he became one-third of the trio who would forge a new, more successful quantum theory. Though Pauli and Heisenberg left Copenhagen—Heisenberg went to Leipzig in 1927, Pauli to Hamburg in 1923 and then to Zurich in 1928—the three men met regularly at conferences and corresponded prolifically.
Through it all, Pauli was a “nuclear” force, as it were—not only an incisive theorist, but a critical sounding board, a mediator, an adviser. As a collaborator, he supported and inspired, argued fearlessly, worried the details, and spared no weak postulate his sarcasm and scorn. Silvan Schweber, reviewing a comprehensive history of quantum theory, remarks on
Pauli's staggering contributions to the technical developments (Pauli exclusion principle, solution of the hydrogen atom in matrix mechanics, spin, paramagnetism, quantum electrodynamics,…) and to the resolution of the philosophical problems engendered by the new mechanics of the micro domain. Pauli was the critic par excellence who was at the center of the vast network of correspondents and became the ultimate arbiter of the Kopenhagener Geist der Quantentheorie. 177
Little wonder, then, that Pauli was chosen to write the two volumes on quantum theory for the Handbuch der Physik. The first volume, published in 1926, summarized old quantum theory—the state of quantum physics from Bohr's 1913 atomic model up to 1925. The second volume, published in 1933, summarized the new quantum mechanics and laying out what became known as the “Copenhagen interpretation.” These volumes are bookends to the heady years during which quantum theory revolutionized physics.
As with all scientific theory, the Copenhagen interpretation was the product of many hands and minds—among them, Erwin Schrödinger, who postulated wave mechanics, Paul Dirac, who devised quantum algebra, and Max Born, who “measured” quantum probability. Still, when the Copenhagen interpretation was explained at the Fifth Solvay Conference of 1927, it was primarily the work of Bohr, the “father” of the new quantum theory, and his two “offspring,” Heisenberg and Pauli. Each played his typecast role—Bohr the quixotic and intuitive muse, Heisenberg, the excitable boy wonder, Pauli the indefatigable critic.
It was Heisenberg who devised the linchpins of modern quantum mechanics: matrix mechanics and the uncertainty principle. We will revisit these notion
s in a subsequent chapter; here, we will simplify dramatically. Matrix mechanics involves measurements of quantum states with a twist: They are not observational measurements. Heisenberg fretted over a simple, undeniable fact: We cannot see into an atom to measure it. If we cannot see the atom, he reasoned, efforts to model it were fruitless (rebuking, as sons do, the father—Bohr was an inveterate visualizer). Instead, Heisenberg set out to quantify the only evidence we can observe: the frequencies and intensities of light spectra. To predict the numerical values of atomic energy, he created a system of equations that, with help from Pauli and Max Born, were extended into a “matrix” language. The pretty atomic model of a nucleus and orbiting electrons had been erased and converted into a numerical table.
While Heisenberg was thinking up matrix mechanics, Pauli was in the grip of the “anomalous Zeeman effect.” Named after Pieter Zeeman, a Dutch physicist, the Zeeman effect (as distinguished from its anomalous counterpart) is the splitting of a spectral frequency into three symmetrical lines of very slightly differing energy when placed near a magnetic field. This effect can be explained by classical physics, as it was by Zeeman's teacher, Hendrik Lorentz. Zeeman and Lorentz shared the 1902 Nobel Prize for their work.
The Zeeman effect held true for some atoms—for instance, hydrogen. In other cases, the splitting resulted not in three symmetrical lines, but in four or more lines that formed complicated patterns: thus, anomalous—and bedeviling. Pauli later recalled:
A colleague who met me strolling rather aimlessly in the beautiful streets of Copenhagen said to me in a friendly manner, “You look very unhappy”; whereupon I answered fiercely, “How can one look happy when he is thinking about the anomalous Zeeman effect?”178
Not until the concept of electron spin would the anomalies be fully explained. Pauli groped on for several years, identifying the valence electron as the culprit in an article first proposing a “classically not describable kind of two-valuedness” of the electron.179 But what was this “two-valuedness” of the electron? Pauli resisted suggestions of an electron “spin” (thus his deprecation of young Konig) until finally he was convinced, writing to Bohr that he would “capitulate completely.”180
Bohr's now obsolete 1913 atomic model had, in many ways, done its job: It failed the test of “quantization.” Indeed, its visual imprint, based on the solar system, seemed so misleading as to drive physicists away from any proposal that suggested an image. Pauli, a true believer in the quantum, benefited enormously from the swirl of conversation about electrons. In 1924, he read a paper by an English physicist named Edmund Stoner suggesting a distribution of electrons around the nucleus. Pauli was inspired. He set to work formulating the description of electron states that would eventually win him the Nobel Prize.
Known generally as the “exclusion principle,” it was dubbed “exclusion” because it describes what cannot happen: No two electrons can occupy a single quantum state at the same time. The exclusion principle solved a simple but enormously important question: Why do electrons not fall into the nucleus? The answer is that electrons cannot “fall” into another, less-energized state or “orbital” if it is already occupied. More precisely, no two electrons can have the same quantum states within an atomic structure. These states are expressed as the four quantum numbers: (n) the size or level of the orbit, (l) the orbit's shape, (ml) the orbit's orientation, and (ms) the electron's spin direction. Were electrons not excluded from other states, matter would collapse into itself—as, for instance, in black holes, where the exclusion principle does not hold!
The exclusion principle and electron spin answered a number of questions beyond the anomalous Zeeman effect. Most wonderfully, especially for chemists, the exclusion principle gave the periodic table and its arrangement of elements new meaning. Working empirically, from experimental observations, Dmitry Mendeleyev, the Russian chemist who laid out the table in 1869, had arranged the elements in order of atomic mass. He also grouped them vertically by similar properties. When the exclusion principle clarified the energy value (and position) of the valence shell electron (that is, the outer shell, where bonding takes place), the hidden logic of Mendeleyev's table was revealed. His organization seemed amazingly on target. Those elements with the same valence electrons in a shell are similar—lithium and francium, for instance, each have one valence electron and are both alkali metals, though lithium is light, with an atomic number of 3, whereas francium is quite heavy, with an atomic number of 87.
Pauli's exclusion principle was one of the first in a series of interconnected discoveries that grew out of the “new quantum theory.” From 1924 through 1927, Heisenberg, Bohr, Max Born and his assistant Pascual Jordan, Enrico Fermi, Paul Dirac, Erwin Schrödinger, and Pauli, in collaboration or singly, contributed postulates, equations, and theorems to the Copenhagen interpretation. In his role as supercritic, Pauli was Heisenberg's sounding board. Although Heisenberg is credited with creating matrix mechanics, the first complete description of quantum mechanics, Pauli provided the dialectic from which emerged both matrix mechanics and Heisenberg's uncertainty principle of 1927. Indeed, Heisenberg's great insight—that theories must be based on what can be observed—is very Paulian in temperament. While Heisenberg was pondering the “strangely beautiful interior” of atomic phenomena,181 Pauli obsessed over the anomalous Zeeman effect, determined to explain rather than theorize away experimental observations.
Still, Pauli had time for Heisenberg. Pauli was “generally my severest critic,” said Heisenberg. Pauli's feelings toward Heisenberg were more complex. “When I think about his ideas,” wrote Pauli in a 1924 letter to Bohr, “then I find them dreadful, and I swear about them internally. For he is very unphilosophical, he does not pay attention to clear elaboration of the fundamental assumptions and their relation with the existing theories. However, when I talk with him he pleases me very much….”182 Most of Pauli's letters to Heisenberg seem to have vanished during wartime, a particularly sad loss given Pauli's careful, expansive epistolary style.183 Heisenberg's contribution to the dialogue consisted of thirty-four letters and more than twenty postcards.
Pauli's “staggering contributions” to quantum mechanics continued apace. Yet another oddity reared its head, and Pauli took up the case of the missing momentum. It was a mystery. Experimental data showed that during radioactive processes, the atomic nucleus emits an electron. This is called “beta decay.” It occurs because a neutron transforms into a proton. The atom consequently emits an electron. The energy and momentum of all the particles were measured, but the before and after did not match. A tiny amount of energy had gone missing with the beta decay and could not be accounted for. Some physicists, Bohr among them, seemed willing to give up the sacred principle of the conservation of energy. Demonstrably, they argued, energy was lost, and conservation of energy, like much of classical physics, simply did not work for individual subatomic processes.
Not so, said Pauli. He sought the advice of Lise Meitner, a leading authority on nuclear physics. Her work helped him refute Bohr's contention that beta decay did not follow the conservation of energy except statistically—an idea that offended Pauli's austere scientific sensibility. After battling through the possibilities, he came up with a solution—what he called a “desperate remedy.” He announced his idea in a letter addressed to the Meeting of the Regional Society in Tübingen: “Dear Radioactive Ladies and Gentlemen,” he began. Pauli's wit was famous. The salutation may not have surprised the conferees, but the remedy must have done so:
[T]here might exist in the nuclei electrically neutral particles, which I shall call neutrons, which have spin 1/2, obey the exclusion principle and moreover differ from light quanta in not traveling with the velocity of light. The mass of the neutrons would have to be of the same order as the electronic mass and in any case not greater than 0.01 proton masses.184
Pauli's terminology was soon amended by Enrico Fermi to “neutrino”—in 1932, Sir James Chadwick discovered what he named the neutron, the ne
utral element equal in mass to the proton. Fermi, unlike the “radioactive” conferees, found the neutrino plausible, since it fit into his theory of weak force and the resulting instability in the atomic nucleus.
Not until 1956, two years before Pauli's death, was the neutrino's existence proven experimentally. It was, said Frederick Reines, its codiscoverer, “the most tiny quality of reality ever imagined by a human being.”185 Today, the neutrino is an invaluable tool in astrophysics. So small in mass and so weak in energy, it passes through the densest material as no other entity can, without collision or effect. Even supernovae, which collapse into unimaginable density, release almost all their energy in the form of neutrinos. Whatever information they carry comes from the very core of the explosion. Pauli celebrated the confirmation of the neutrino with champagne and wrote to Reines and Clyde Cowan in Los Alamos, “Everything comes to him who knows how to wait.”
If Pauli's professional work ever suffered from his personal crises, it rarely if ever showed. But crises there were. In 1927, Pauli's father had an affair. His mother's suicide followed soon after. Pauli was stricken, but his anguish remained hidden. The following year, he settled in Zurich, where, despite his reputation as a poor lecturer (his style resembled “a soliloquy… often scarcely… intelligible” to Markus Fierz, then a student186), ETH hired Pauli at the rank of full professor of theoretical physics. In turn, Pauli hired Ralph Kronig to be his assistant for the summer term. They spent the summer as much at play as at work. They were joined by Paul Scherrer, Pauli's nominal department head. Eating, drinking, and concert-going were the usual fare. A favorite haunt was the Kronenhalle, where the famous and infamous among artists (Thomas Mann, James Joyce, Braque, Picasso, Stravinsky) had imbibed.