by Thomas Hager
When Pauling came to Munich, Sommerfeld, at fifty-eight years old, was at the height of his power and prestige, director of the Institute of Theoretical Physics in Munich, sage to generations of young students of the atom. But while his work on the Bohr atom and his influential texts on spectroscopy had given him a solid reputation as a quantum thinker, Sommerfeld would never be known as a theorist of the first rank. He was a brilliant mathematician—"If you want to be a physicist, you must do three things," he would say. "First, study mathematics; second, study more mathematics; and third, do the same"— but he used his talents to clean up and clarify the groundbreaking theories of others rather than develop his own novel approaches. This is what he had done with Bohr's atom, picking up another's broad idea and refining it mathematically to make it work better, and he had done the same earlier in his career with everything from the physics of radio waves to a theory of spinning tops. Sommerfeld would never be listed in the histories of quantum physics as more than an important supporting player; he would never win a Nobel Prize. At least one historian would dismiss him as a "mathematical mercenary."
But he was more than that. Like Noyes, he had an uncanny ability to turn raw students into talented scientists. He was an unusually open-minded man who delighted in scouting out new ideas, assessing them with his peers, and quickly presenting the most important of them to his students. He knew everyone in theoretical physics, had collaborated with many of them and corresponded regularly with the rest; the ceaseless flow of information through Munich made it a nerve center for the developing field. He used the letters and prepublication galleys of articles that came in from Einstein, Bohr, Schroedinger, Pauli, and Heisenberg as fodder for his seminars and lectures, letting his students in on new developments well before they appeared in journals.
And Sommerfeld's lectures were legendary. He was not a showman in the classroom, as Pauling would become, but was instead a paragon of organization and clarity. His speaking style was intense enough to hold students' interest, slow enough for them to take careful notes, and reasoned enough to guide them through the major themes of quantum physics without becoming lost in the thickets of paradox that edged the emerging field. At each step he would carefully correlate physical findings with their mathematical interpretations, showing on the blackboard how phenomena in the real world could be explained and illuminated through the use of numbers. During the mid-1920s, Sommerfeld's six-semester lecture cycle on quantum physics was a primer for anyone serious about the field, and Munich was considered one of the three world centers for the study of quantum physics, along with Bohr's institute in Copenhagen and Born's in Goettingen.
As important as his lecture style, however, was Sommerfeld's commitment to working with individual students. Beneath the Prussian facade was a warm, concerned, encouraging teacher, a father figure who invited students to his house for amateur musical recitals (Sommerfeld was a fair pianist), who loved to talk physics at a favorite local cafe, scribbling equations in pencil on the tabletop, and who made time to confer with each student individually, at length, several times each week. During these research discussions he would ask them about their progress, provide direction, and offer encouragement. Sommerfeld was an optimist of a peculiarly German type: He believed in his blood that German science, like German music and philosophy, represented a pinnacle of human achievement and that the rational application of German thinking would eventually solve the mysteries of the atom. It was just a matter of time and approach. He built his students' confidence by focusing their attention on small, solvable problems instead of allowing them to become lost in the complexities of big theories. "When kings go a-building, wagoners have more work," he would say, and he made sure his students were good carpenters before they tried on crowns. If Niels Bohr, increasingly pessimistic about the confusion surrounding his version of the atom in the mid-1920s, was becoming the gloomy philosopher of quantum physics, Sommerfeld was its cheerful engineer.
His program was unparalleled in turning out successful physicists. "What I especially admire about you is that you have, as it were, pounded out of the soil such a large number of young talents," Einstein wrote Sommerfeld in 1922. By one estimate, one-third of all the physicists teaching in Germany in the years before World War II had been through Sommerfeld's institute as either students or assistants. The stars included Laue, Debye, Wolfgang Pauli, Werner Heisenberg, Paul Ewald, Hans Bethe, Paul Epstein, Gregor Wentzel, Walter Heitler, Fritz London, Karl Bechert, and the foreign visitors Edward Condon, Isidor Rabi, Edward Teller, Lawrence Bragg, and Pauling. Many of his students would outdo him in research. All of them would owe him something of their sense of the possible. "I learned mathematics from Born and physics from Bohr," said Heisenberg. "And from Sommerfeld I learned optimism."
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Optimism was a practical necessity when dealing with the atom. It was becoming increasingly clear that the Bohr-Sommerfeld model, with its orbiting electrons, simply didn't work. The old paradoxes were still unanswered: Why didn't the moving electrons lose energy and fall into the nucleus? Why were some orbits allowed and not others? How did electrons "jump"? And now there were new mysteries. In the early 1920s a French doctoral student, Prince Louis de Broglie, theorized that electrons could behave like waves as well as particles; in other words, that matter, at least at the atomic level, could behave like light. American researchers at the Bell Laboratories proved the point in 1927 when they found that electrons could be diffracted by a crystal, just like light waves or x-rays. In 1923, another American, Arthur Holly Compton, published strong new evidence that light could also behave like a particle. Then the young Dutch researchers Goudsmit and Uhlenbeck offered evidence that electrons had "spin." How could particles also be waves and waves be particles? How could a wave "spin"?
Pauling had heard a great deal about the shortcomings of the Bohr-Sommerfeld atom at Caltech. But until it was all sorted out, he adhered to that model and everything that went with it. Then, in the few months between December 1925, when he still believed that calculations based on the Bohr-Sommerfeld version of quantum theory were "straight-forward and well-grounded," and the summer of 1926, everything changed. Pauling was converted to a new way of thinking about the atom.
It started with his first interview with Sommerfeld. Pauling had taken two years of German at Oregon Agricultural College in addition to what he had learned from his grandparents. Between that and Sommerfeld's minimal English they were able to carry on an adequate conversation. Perhaps, Pauling asked in his beginner’s German, you remember me from your visit to the California Institute of Technology? Unfortunately, the director did not. Sommerfeld asked Pauling to outline his research interests, the things he hoped to accomplish in Munich. Pauling eagerly began talking about a problem he hoped he would be allowed to pursue, following up on work he had done at Caltech on the dielectric constant of hydrogen chloride gas. But, Pauling was surprised to find, Sommerfeld "didn't give my suggestion much heed." The director, like most German scientists, had a somewhat condescending attitude toward American physics in general. ("Don't take all this so seriously," he told one young German physics student who was worrying about going to Berkeley on a fellowship. "Life in America is not so difficult. There any young man can become an assistant professor.") In any case, it was customary in Germany for the professor to assign research projects, not the student. Sommerfeld asked Pauling to give him a few days to think it over and then assigned him a problem Pauling was less interested in, a series of austere calculations related to the spin of the electron.
Pauling pursued the project with the same enthusiasm he brought to the after-school jobs his mother had arranged for him as a teenager: He didn't accomplish much and quit as soon as he could. He was interested in other things. "I was thinking about nearly every theoretical problem that there was," he remembered.
Especially, at that time, a hydrogen chloride problem. Pauling had attempted to come up with a version of quantum theory that accurately predicted t
he effects of an electric field on the motion of polar molecules. His theorizing came close enough to what was found by experiment to convince Pauling that the problem was either with sloppy experimental measurements or his own theoretical tinkering, not with the Bohr-Sommerfeld model of the atom. Just before leaving for Europe he'd thought of adding a magnetic field at right angles to the electric field. If the Bohr-Sommerfeld quantum theory was right, the magnetic field would have a measurable effect on the motion of the molecules—an effect that classical theory said would not be there. This would be important new support for quantum theory. Pauling eventually convinced Sommerfeld to let him work on this problem. "He said that he would present the results next month in Zurich at a congress on magnetism called by Debye," Pauling wrote Noyes on May 22, 1926. "I shall accordingly have to work to have results by then."
Work for a budding theorist like Pauling consisted of hours of sitting at a desk, filling page after page of notebook paper with formulae and drawings, notes and scribbles. "Linus is very busy with his hydrogen chloride problem," Ava Helen wrote on June 2, "and he is at one moment very gleeful and the next very despondent." By June 10, Pauling had verified theoretically that if the Bohr-Sommerfeld model of the atom was correct, the magnetic field should have a large effect. While he waited for news of the confirming experiment from Pasadena, he drafted a paper in German, which Sommerfeld took with him to the Zurich congress on June 21.
A few days later, Pauling received a telegram. Sommerfeld was calling Pauling to Switzerland to talk over his ideas.
Ava Helen remembered the late-June train ride through the Alps—the vivid green hills, the fields of red poppies, the peasant women in bright blue kerchiefs—and the excitement her husband felt. He was making an impression on Sommerfeld. His ideas were being taken seriously. When they arrived in Zurich, they were asked to dine with the director and a few others at Debye's house. During the next few days, Pauling talked about his work, listened to presentations, and chatted informally with some of the most renowned physicists of Europe. "He listens so intently and gets as excited as can be," Ava Helen wrote. "I like to watch him."
One thing he was excited about was the chance to compare notes with one of the most talked about young physicists in Europe, Wolfgang Pauli. Pauli, the son of a Viennese chemistry professor, began building a reputation at age seventeen, when he stood up after a talk by Einstein on the theory of relativity and said that he thought there was an error in the great man's conclusions. At eighteen he was writing articles on relativity for encyclopedias, and by 1925, at just twenty-five years of age, he assured his place in the history of physics by publishing his "exclusion principle," a far-reaching idea that added a fourth quantum number for describing the state of electrons to the three already postulated in the Bohr-Sommerfeld model and stated that no two electrons could have exactly the same set of quantum numbers. Goudsmit and Uhlenbeck tied Pauli's fourth quantum number to the much-talked-about new property of electrons they called "spin," which they described as the rotation of the electron on its axis. Spin was two-faced, either parallel to the electron's orbit or opposite it. According to the exclusion principle, then, a pair of electrons could share the same orbit as long as they had opposite spin. The idea of paired electrons immediately struck a chord with chemists, or at least those like Pauling, who were familiar with G. N. Lewis's theory of shared electron-pair chemical bonds.
Pauli was also becoming infamous for what one colleague called his "excessive honesty," a tendency to directly, sometimes brutally, attack any idea he considered sloppy. Even as mild a personality as Paul Ehrenfest was put off by Pauli's cutting criticism, telling him, "I like your papers better than you." Since Pauling's paper pointed out shortcomings in Pauli's own ideas about polar molecules, perhaps he should have expected a cool reception.
Pauling bustled up to Pauli during a break in the presentations and began outlining the results of his weeks of feverish work showing that the Bohr-Sommerfeld version of quantum physics was an improvement over the classical scheme. Pauli listened politely and then offered a two-word response: "Not interesting." Perhaps sensing the deflating effect of his comment, he added, "If you'd have thought of this two years ago, you'd be famous." Two years earlier it was still worthwhile to provide support for the Bohr-Sommerfeld atom. But now, at least to bright young European physicists such as Pauli, that version of quantum physics was already dead. It had been killed during the course of the previous year by a formidable new way of thinking called quantum mechanics.
The New Mechanics
Pauli's friend Werner Heisenberg was the prime assassin. Heisenberg and Pauli were scientific siblings of complementary types, Wolfgang the restrained, analytic older brother (older, in fact, by a year and a half), Werner the impulsive revolutionary firebrand. They had parallel student careers: They both earned their doctorates with Sommerfeld in Munich, where Heisenberg, a year or two behind Pauli: became the older student’s friend;; both went on to Goettingen to work with Max Born; both served as Bohr's assistant in Copenhagen. Born was one of the spiritual godfathers of the new physics; both were influenced by his consummate skepticism and utter belief in numbers. Born passed on to his postdoctoral fellows the idea that they shouldn't feel constrained when describing the atom to use concepts of space and time that worked to describe larger-scale events. He also taught them a mathematician's disdain for the messy, illogical paradoxes of the Bohr-Sommerfeld atom. By 1924, Pauli and Heisenberg were calling attempts to keep the Bohr-Sommerfeld atom patched together the "swindle."
Heisenberg would end the swindle. He thought the paradoxes arose from trying to relate the increasingly strange experimental results researchers were finding to what was, after all, a made-up model of orbiting electrons. Heisenberg decided to forget about orbits, to forget about models entirely. He wiped the Bohr-Sommerfeld atom from his mind, and on a clean mental slate began working with purely mathematical formulae based only on data that could be observed. No one could see orbiting electrons, but you could see the light they gave off. Heisenberg concentrated on spectral data. In a few legendary days, while isolated on a rocky North Sea island recuperating from hay fever, using only observable data, Heisenberg created a new mathematical approach to describing quantum physics. Cleaned up and expanded by Born and one of his students, Pascual Jordan, Heisenberg's insights became what is called matrix mechanics. The new system was a distinct improvement over the old quantum physics: It not only explained more spectral data with fewer paradoxes; it also appeared to include within itself the principles of classical physics, Newton's old mechanics, as a limiting case. Heisenberg was twenty-four when he created it.
Unfortunately, matrix mechanics was also a bulky, difficult system to use. As an added problem, it seemed to many observers that Heisenberg had done too good a job of divorcing himself from models of the atom. There was a reaction against matrix mechanics because it was too abstract; it didn't relate to any visualizable thing at all. The mathematics seemed to work, but what sort of atom did the formulae describe? There was a good deal of initial skepticism based on the idea that Heisenberg's brainchild might be mathematical doodling ungrounded in physical reality, a spin of fantasy, or as Einstein succinctly termed matrix mechanics, "magic." It didn't appeal to researchers like Pauling, who worked better if they could "see" their atoms. Born had toured the United States in late 1925 explaining matrix mechanics; Pauling had heard him lecture at Caltech before he left. And Pauling, like many physicists (most chemists didn't understand Heisenberg's brainchild at all), wasn't ready to sign on. "It was just too difficult," he remembered. "I couldn't see any way of using matrix mechanics to attack the problems that I was interested in."
As Pauling was sailing to Europe in March 1926, the physics world was jolted again, this time by the publication of what appeared to be an entirely different approach to quantum physics. The author was unlikely. Erwin Schroedinger was a middle-aged, rather old-fashioned Austrian theoretical physicist who had been watching the heret
ical progress of quantum physics with dismay. At age thirty-nine he was already past the prime age for making revolutionary theories, which generally seemed to be made by youngsters like Heisenberg. He did have his oddities: a passion for philosophy (especially Spinoza, Schopenhauer, and the ideas of the Vedanta), a Viennese sense of superiority to almost all other peoples (especially Americans), and a freethinking approach to sex (especially involving women substantially younger than himself). His colleague (and his wife's lover) Hermann Weyl once linked Schroedinger's great quantum mechanical idea to "a late erotic outburst in his life." But he was by temperament more of a reactionary than a revolutionary, a classical physicist at heart who had an instinctive dislike for the paradoxes of quantum thinking. "You surely must understand," he once told Bohr, "that the whole idea of quantum jumps necessarily leads to nonsense."
Schroedinger wanted to abolish Bohr's ideas and explain the atom in classical terms. He thought he had found a way in de Broglie's idea that electrons could behave like waves instead of orbiting like little planets and making those nonsensical jumps. Schroedinger theorized that the nucleus was surrounded by an electron/wave vibrating at a certain frequency, something like the standing wave of a vibrating drum head. Only certain stable frequencies were possible, those that included an integer number of waves; if not, the waves would interfere with each other. Add energy and you boost the electron/wave to the next whole-number frequency; when it falls back, it emits a wavelength of light. In a rush of extraordinary work, Schroedinger developed a mathematical equation in which, by treating the electron as a wave, he was able to derive Bohr's energy levels for the stable state of the hydrogen electron. It was incredible, but the electron, he thought, must be in fact not a point in space but a sort of standing wave smeared around the nucleus. He could measure the shape and density of the wave and found that according to his calculations the hydrogen electron formed a spherical smear of negative energy around the nucleus. His system, which appeared to give just as complete an accounting of atomic reality as Born and Heisenberg's, became known as wave mechanics.