But belief in light quanta went against the enormous and continuing success of Maxwell’s classical wave theory of the electromagnetic field. What’s more, taking light quanta seriously inevitably brought the coupled problems of discontinuity and unpredictability into physics. Classical waves always behaved smoothly, gradually, seamlessly. Light quanta, if such things there were, necessarily came and went abruptly, without apparent reason or cause. Here is the root of a problem that was to plague Einstein for the rest of his life. He believed in the reality of light quanta sooner than anyone else, but he rebelled more strenuously than anyone else against the implication that light quanta inevitably bring spontaneity and probability into physics.
Insisting on the reality of light quanta, Einstein traveled for many years a lonely road. Physicists, meanwhile, puzzled over electromagnetic radiation, radioactivity, the structure of atoms, indeed the structure of basic physics generally. Theorists, Planck dolefully reported in 1910, “now work with an audacity unheard of in earlier times; at present no physical law is considered assured beyond doubt, each and every physical truth is open to dispute. It often looks as if the time of chaos again is drawing near in theoretical physics.”
In 1916, in Chicago, Robert A. Millikan carefully measured the photoelectric effect and resoundingly demonstrated that “Einstein’s photoelectric equation…appears in every case to predict exactly the observed results.” Obstinately, though, he concluded that “the semicorpuscular theory by which Einstein arrived at his equation seems at present wholly untenable.” Many other physicists, despite the evidence, agreed with Millikan more than with Einstein.
Adding to the confusion, the Bohr-Sommerfeld atom enjoyed only a few years of untrammeled success. It did enough things sufficiently well that it could not be set aside. But as the 1920s dawned, confidence waned that it could do much beyond the simple case of hydrogen, and that only imperfectly. Perhaps, some physicists began to think, this was just a passing phase. Perhaps the disturbing language of transitions and jumps, of quanta and spontaneity, would soon fade away, allowing physics to deal once again in the familiar certainties of old.
At the end of the war, Arnold Sommerfeld took on a couple of interesting new students. In 1918 Wolfgang Pauli arrived from Vienna. Two years later Werner Heisenberg, a local boy, showed up. Unburdened by the past, these young men would quickly make their presence felt.
Chapter 6
LACK OF KNOWLEDGE IS NO GUARANTEE OF SUCCESS
If Max Planck fervently clung to the culture of science as a way for Germany to rise above the indignity of its downfall, young men like Wolfgang Pauli and Werner Heisenberg found in the pursuit of science a personal escape from the hardships of life in the grim postwar years. Both were children of privilege, sons of university professors. Both enrolled at the University of Munich at a time when that city had survived starvation only to fall into violent anarchy, a cycle of revolution and repression punctuated by assassination. In later memoirs and interviews they do not dwell on these irksome circumstances. For these two young men life meant science, its splendors and frustrations. Science gave them purpose and freedom.
Pauli’s origins were especially conducive to his later career. His father, a professor of medical chemistry in Vienna, was a faculty colleague of Ernst Mach’s and something of a disciple of the old positivist. In 1900 he asked Mach to be godfather to his newly born son. The Paulis were by this time Catholic, having converted from Judaism in hopes of securing themselves against the wave of anti-Semitism sweeping across Viennese society. As many as 10 percent of Austrian Jews converted in this period.
Mach was, the younger Pauli said much later, “a stronger personality than was the Catholic priest. The result seems to be that, in this way, I was baptized as ‘Antimetaphysical’ instead of Roman Catholic.” Mach called himself antimetaphysical because he condemned as metaphysics any suggestion that theory could reveal deep secrets of nature, beyond a mere accounting of experimental facts. Pauli could hardly follow his godfather in embracing anti-atomism, but Mach’s antimetaphysical severity evolved in him into a kind of universal skepticism, a wariness about theorizing that strayed too far from the concrete and the demonstrable. In the early days of quantum theory, this was a debatable virtue. Heisenberg said later that Pauli wanted to hew strictly to the experimental data and maintain mathematical rigor, and in an uncertain and evolving world that was asking too much. Pauli published much less than he might have, Heisenberg said, because so few ideas met his exacting standards. But he was an acute critic and adviser, the “conscience of physics,” as he later became known.
At Gymnasium in Vienna, Pauli’s brilliance in physics and mathematics shone out from the start. Through his father’s influence he obtained advanced tutoring from some of the university physics professors, and by the time he graduated he had already written a cogent paper on the new subject of general relativity. When it came to his continuing education, the University of Vienna did not impress young Pauli. Ludwig Boltzmann had committed suicide in 1906, an outcome of his lifelong mix of depression, hypochondria, and self-described neurasthenia, exacerbated by continuing hostility from Mach and the anti-atomists. The Vienna physics department was but a pale imitation of its former self. Pauli had no sentimental affection for the city. Viennese politics was in chaos, society in tatters. The same was largely true in Munich, but the university there at least possessed a thriving and adventurous department of theoretical physics, led by Sommerfeld. In 1918, with the war not yet truly over, Wolfgang Pauli traveled to Munich and signed on as an undergraduate. Diagnosed with a weak heart, he had avoided military service in the last year of the conflict.
Pauli arrived in a country on the point of collapse. In Munich on November 8, the socialist leader Kurt Eisner proclaimed a soviet republic in Bavaria, ousting King Ludwig III. The following day a collection of moderate democrats meeting in Weimar announced the foundation of a new democratic Germany. Two days later came the armistice, when Kaiser Wilhelm in Berlin reluctantly stepped down. No one seemed to be in charge. The right wing wanted to restore the monarchy; the left wing wanted a truly communist Germany. In February 1919 Eisner was assassinated by reactionaries. A second Bavarian people’s republic was declared in April, bringing a brief period of red terror as avenging socialists and communists took care of the old regime. Brief, because the militarists returned to crush the socialists two weeks later and embarked on a still fiercer white terror to eradicate the communist scourge.
Heisenberg, then a schoolboy in the city, remembered that “Munich was in a state of utter confusion. On the streets people were shooting at one another, and no one could tell precisely who the contestants were. Political power fluctuated between persons and institutions few of us could have named.”
August 1919 saw the promulgation of the Weimar Constitution, a compromised attempt at democracy that pleased hardly anyone. Right-leaning moderates, such as Max Planck, hankered after the civic certainties of the old Germany and regarded democracy as a polite word for mob rule. The left, wanting socialism in earnest, condemned democracy as pitifully anemic. In elections the following year, extremists on both sides did well, while the moderate middle, beloved by no one, fared poorly.
But a fragile, tentative sense of calm slowly returned. Weimar Germany was never truly stable, but Germans gradually gained some confidence that their country would not fall apart the next day. In Munich, the budding scientists Pauli and Heisenberg, having done their best not to notice the chaos around them, found by degrees that they could breathe a little easier.
Sommerfeld, invited to contribute an encyclopedia article on relativity, turned the task over to his precocious new student—“a downright amazing specimen”—who had already written on the subject. In this way Wolfgang Pauli, a mere undergraduate, composed what was in essence a short book on relativity, setting out the mathematics and physics with an elegance and lucidity that astonished Einstein himself.
But general relativity, Pauli soon concluded
, was not the subject for him. Though intellectually impressive, it was a finished theory, with no practical consequences. (It would be decades before the language of general relativity became commonplace in astrophysics and cosmology, subjects that didn’t exist in 1920.) At Munich, under Sommerfeld’s guidance, Pauli could hardly fail to take up quantum theory instead, with its array of cryptic results, unsolved problems, and half-baked theories. He tackled the ionized hydrogen molecule—two nuclei sharing a single electron. This ferociously difficult problem seemed worthy of his attention. He constructed elaborate and ingenious models, trying to figure out how an electron would orbit in this double system, then trying to understand how quantum rules would apply to the orbits. But he made little progress.
He was hooked, though. He began to profess a certain disdain for Sommerfeld’s program of sifting through spectroscopic data in order to find patterns that he could interpret as quantum rules. Looking beyond hydrogen and helium to other families of elements in the periodic table, Sommerfeld tried to tease out regularities even in these complex cases. He compiled his findings in a fat monograph, Atomic Structure and Spectral Lines—Sommerfeld’s bible, as it became known—in which he consciously likened his efforts both to Kepler’s search for mathematical and geometrical order in the orbits of the planets and to the old Pythagorean belief in numerical harmonies. “What we are listening to nowadays in the language of spectra,” declared Sommerfeld, giving way to a rare flash of purple prose, “is a genuine atomic music of the spheres, a richly proportioned symphony, an order and harmony emerging out of diversity.”
Sommerfeld understood that the search for numerical regularities was a way of laying the groundwork for a deeper theory, just as Kepler’s laws of planetary motion, derived from close scrutiny of the observed motions of the planets, gained their true meaning only when Newton’s inverse square law of gravity gave theoretical foundation to the workings of the solar system. But to the harshly analytical Pauli, Sommerfeld’s strategy was an odd combination of theoretical conservatism and latter-day mysticism. Better, Pauli thought, to try building rational theories from sound principles—although his attempt to find such a theory for ionized molecular hydrogen hadn’t gotten him very far. The way forward was clear to no one.
Because he developed in Munich a lifelong habit of staying out late at bars and cafés, Pauli generally missed morning lectures. Sommerfeld had firm views about proper conduct and insisted that Pauli get up at a decent hour and work while his brain was fresh. Pauli made an effort to comply, but the habit didn’t take, and he reverted to his preferred hours. A tubby young man, Pauli had a tic of rocking back and forth constantly as he sat in his chair and pondered. Sommerfeld concluded that he could not mold his strange, brilliant student into any semblance of what he regarded as normal behavior, and acceded to his late hours and eccentric ways. Pauli referred to Sommerfeld behind his back as a hussar colonel, but to his face showed a lifelong respect and deference that he accorded no one else, not even Einstein.
Sommerfeld was a Prussian by birth, and he looked the part. Short, stocky, and fit, he dressed smartly and had splendid waxed mustaches and a military bearing. Well into his forties he took part eagerly in practices as a reserve army officer. He was a sportsman and an excellent skier. In his youth he had enthusiastically participated in the drinking and dueling that flourished then among student societies.
But Sommerfeld’s conservative appearance was deceptive. His mastery of classical physics did not close his mind to innovation. He seized eagerly on Bohr’s ill-founded but marvelously productive model of the atom and employed his extensive and detailed knowledge to turn the simple Bohr atom into a sophisticated theoretical device.
Nor in his personality was Sommerfeld the Prussian he seemed to be. With his students he was friendly and collegial. As well as his regular classes he conducted every week an intense two-hour session on the latest research topics. “A kind of market place to exchange views about the most modern developments” was Heisenberg’s description of these freewheeling discussions. Sommerfeld’s students thus came to learn and criticize at firsthand the ever-changing quantum theory of the atom. He engaged them as contributors to his constantly revised and updated Atomic Structure and Spectral Lines. Not just Pauli and Heisenberg but a remarkable number of other contributors to the nascent quantum theory emerged from the Munich school of theoretical physics.
Sometime in 1920 Sommerfeld would have introduced into his weekly research seminar his latest innovation, a fourth quantum number. In the Bohr-Sommerfeld atom up to that point, electrons were described by three quantum numbers that had straightforward geometrical meaning in terms of the size, ellipticity, and orientation of their orbits. But now Sommerfeld took a fateful step away from such commonsense imagery.
The fourth quantum number derived from Sommerfeld’s scrutiny of the so-called anomalous Zeeman effect displayed by certain multi-electron atoms. (This is a more complicated version of the original Zeeman effect, the splitting of spectral lines in a magnetic field.) Noticing, as was his habit, certain numerical regularities in the spectroscopic data, Sommerfeld devised a new quantum number that seemed to account for the pattern. But this fourth number had no theoretical foundation; it didn’t come with any obvious interpretation in terms of the geometry or mechanics of electron orbits. Straining for a justification, Sommerfeld argued that in these atoms, a single outlying electron took part in all the relevant transitions, while the nucleus and remaining inner electrons formed a composite, invariable core. The whole thing thus looked like a modified kind of hydrogen, and Sommerfeld suggested that the fourth quantum number involved what he vaguely called a “hidden rotation” of the single outlying electron relative to the core.
To Pauli, this was not theory but fantasy. It was one thing to take standard properties of electron orbits and transform them into quantum numbers. It was quite another to invent a quantum number out of whole cloth and only afterward grace it with some dubious, ad hoc interpretation. Did Sommerfeld’s new invention imply that the quantum atom had properties that couldn’t be understood by reference to old-style mechanics? Or did it just mean that quantum theory was coming off the rails?
It might have been around this time that Pauli suggested caustically to Heisenberg that “it’s much easier to find one’s way if one isn’t too familiar with the magnificent unity of classical physics. You have a decided advantage there,” he told his fellow student with a wicked grin, “but then lack of knowledge is no guarantee of success.”
If Pauli arrived in Munich almost as a mature, fully formed physicist, armed with not only deep knowledge but also pronounced opinions, Heisenberg was by contrast talented but dreamy, with a spotty command of his subject. He had thought at first to take up pure mathematics, but in his teens he discovered a small book written by Einstein as an attempt to explain relativity to nonscientists. “My original wish to study mathematics,” he recalled later, “was imperceptibly diverted toward theoretical physics.”
Werner Heisenberg was born at the end of 1901 in the university town of Würzburg, some 150 miles northwest of Munich, where his father taught classics. August Heisenberg was devoted to Bismarckian Germany, a Protestant nation united in moral conduct and the pursuit of commerce. His family lived with proper decorum. They went to church dutifully and regularly, though August later confessed to his two sons that he had never had any particular religious sensibility. Late in life Werner said, with an elegant ambiguity befitting the inventor of the uncertainty principle, that “if someone were to say that I had not been a Christian, he would be wrong. But if someone were to say that I had been a Christian, he would be saying too much.”
In 1910, August Heisenberg was appointed professor of Byzantine philology at the University of Munich, and the family moved to the Bavarian capital. Professor Heisenberg was a good teacher but a fierce disciplinarian. Trapped within his rigid, formal manner lay a volatile temper that flashed out occasionally, usually within the privacy of his famil
y. He pushed Werner and his older brother, Erwin, to compete with each other, in athletics and scholastics, and Erwin mostly had the edge. Only in mathematics, Werner discovered, could he beat Erwin, and this discovery became the foundation for his life. Werner and Erwin were never close. After studying chemistry, Erwin moved to Berlin and fell in with the cult of anthroposophy. As adults, the brothers had only rare and fleeting contacts.
Finishing Gymnasium just as the war was ending, Werner had to serve in the local militia, a ragtag collection of teenagers charged with keeping order in the strife-torn city. It was like playing cops and robbers, he said later; nothing serious. He remembered times “when our families had long since eaten their last piece of bread,” when he and his older brother and other friends would scurry about the shattered city of Munich foraging for food. During the time of the Bavarian soviet, he had sneaked across the battle lines into territory controlled by forces of the German republic, returning with bread, butter, and bacon. Such memories Heisenberg recounted in a matter-of-fact way, as if these adventures had been the stuff of a perfectly ordinary adolescence.
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