The Dirac equation described not just the behavior of electrons in a quantum electromagnetic field but also the behavior of all charged fermions, that is, all particles that obey Pauli’s exclusion principle. In it, he predicted the existence of antimatter and he explained why particle “spin,” as proposed by Goudsmit and Uhlenbeck, was not simply a convenient way of interpreting the behavior of electrons but actually required by natural law. It was a breathtaking tour de force and firmly established Dirac as one of history’s greatest physicists. He was a mere twenty-four years old at the time.
Only as theorists explored Dirac’s astonishing theory did they come to understand its limitations. The most important one involved the calculation of the “magnetic moment” of an electron, related to the torque an electron “feels” in a magnetic field. The Dirac equation provides a first approximation of the magnetic moment that is reasonably consistent with experimental data, but the calculation requires an iterative process to get greater accuracy. Unfortunately, the mathematics required involves summing a numerical series that does not converge onto a more exact quantity, but, absurdly, approaches infinity. This problem would not be solved either by Dirac or by Fermi or in fact by anyone at all until after World War II, when three brilliant young theorists—Richard Feynman, Julian Schwinger, and Sin-Itiro Tomonaga—cracked the puzzle independently.
FERMI UNDERSTOOD THE IMPORTANCE OF DIRAC’S WORK, BUT IT took him until the winter of 1928–1929 before he set about studying it seriously. Much of the mathematics Dirac used was of his own invention, and Fermi, according to Segrè, found it “alien.” He began to recast Dirac’s theory in his own terms, terms that were mathematically more familiar to him. The private seminars at Via Panisperna became the stage upon which he worked out, aloud in front of an audience consisting of Rasetti, Amaldi, Majorana, Segrè, and Racah, a version of Dirac’s work that would be easier to digest. One must also assume, though Segrè and Amaldi are silent on this, that he spent his early morning pre-breakfast hours at home working intensively on the problem.
By April 1929, Fermi had a preliminary version of his presentation ready for lectures he had been asked to give in Paris. He continued working on it over the next year, and by the time of the 1930 summer school in Ann Arbor, he had built up the presentation to an extensive series of lectures, which he presented there and which were subsequently published in 1932. Fermi eased into the subject matter by comparing an atom and the electromagnetic field to a pendulum and a vibrating string connected by a thin elastic thread, which represented the coupling of the two. If the pendulum is at rest and the string starts to vibrate only slightly, the elastic thread will perturb the pendulum only slightly. But when the string vibrates in tune with the amplitude of the pendulum, the elastic thread carries that energy to the pendulum and causes the pendulum to swing in time with the vibrating string, creating a resonance between the pendulum and the string. This description of how an atom and an electromagnetic field interact with each other formed the basis of Fermi’s interpretation of Dirac’s quantum electrodynamics.
Some seventy years later, Nobel Prize–winning theorist Frank Wilczek would call this description “a masterpiece, instructive and refreshing to read even today.… Everything is done from scratch, starting with harmonic oscillators.”
Hans Bethe, the young German physicist who spent this period in Rome as a post-doc, recounts the impact the paper had on him:
Many of you, like myself, have learned their first field theory from Fermi’s wonderful article in the Reviews of Modern Physics of 1932. It is an example of simplicity in a difficult field which I think is unsurpassed. It came after a number of quite complicated papers and before another set of quite complicated papers on the subject, and without Fermi’s enlightening simplicity I think many of us would never have been able to follow into the depths of field theory. I think I’m one of them.
Eugene Wigner, another quantum theory pioneer who was destined to work closely with Fermi during the Manhattan Project, corroborated Bethe’s assessment:
He disliked complicated theories and avoided them as much as possible. Although he was one of the founders of quantum electrodynamics, he resisted using this theory as long as possible. His article on the Quantum Theory of Radiation in the Reviews of Modern Physics (1932) is a model of many of his addresses and lectures: nobody not fully familiar with the intricacies of the theory could have written it, nobody could have better avoided those intricacies. However, when he tackled a problem which could not be solved without the explicit use of the much disliked concepts of quantum field theories, he accepted this fact and one of his most brilliant papers [on beta decay] is based on quantized fields.
Fermi himself thoroughly understood the Dirac formulation and yet spent two years recasting it in his own terms. As Wigner suggests, he was fully familiar with the mathematical complexity of Dirac’s approach, yet he felt uncomfortable with it and sought a simpler way of explaining it. The issue was not mathematical complexity per se. Fermi was a fine mathematician, able to hold his own with some of the greatest mathematicians of his day. Rather, like almost all of Fermi’s greatest work, the effort of radical simplification was at least in part pedagogically motivated. He worked it out in front of his colleagues and students, slowly and methodically, making sure that his audience followed at each step of the way. The purpose of this exercise was to make the material accessible to others. It was not simply the physicist’s love of simplicity—if he couldn’t teach it to someone else, he felt he didn’t understand it sufficiently himself. Dirac had no such purpose, writing his papers at his own, highly rarified level. Fermi made Dirac comprehensible to physicists who otherwise might not even have bothered slogging through the eccentric physicist’s complex concepts and exotic techniques.
Pauli and Heisenberg both independently wrote papers paralleling Fermi’s simplifying approach. Working in the opposite direction, Jordan and Wigner, among others, added an additional layer of complexity to Dirac’s initial formulation. Dirac’s mathematics explained the creation and annihilation of bosons such as photons in electrodynamic processes, offering a mathematical description of what happens when a photon strikes an electron in the outer shell of an atom (it disappears and the electron “moves” to a higher energy state) and when an electron “moves” to a lower energy state (a photon is created out of “nothing”). Jordan and Wigner, significantly, extended the mathematics describing creation and annihilation of particles from bosons to fermions in what was called a “second quantization.” Their contribution was essential to Fermi’s formulation of the beta decay paper in late 1933. Segrè suggests that the time lag between the Ann Arbor conference in 1930 and the 1933 beta decay paper was due to Fermi’s working through the Jordan second quantization approach so that he felt completely comfortable with it. Once he had thoroughly absorbed the difficult methods pioneered by Jordan and Wigner, however, he determined to use them in ways no one anticipated.
ERNEST RUTHERFORD WAS THE FIRST TO CLASSIFY DIFFERENT TYPES of radioactive emissions by their respective ability to penetrate matter. Emissions that were least able to penetrate he called alpha rays. The most penetrative were called gamma rays. Those with medium penetration ability he called beta rays. Rutherford quickly concluded, through a series of classic experiments, that alpha rays are positively charged, with the charge of two protons and the mass of four protons. Later investigation revealed that the alpha particle consists of two protons and two neutrons, emitted from certain overcrowded nuclei. Similar investigation showed that gamma rays were high-energy photons, of which X-rays were a subset. Beta rays were negatively charged and very light compared with the mass of the alpha particles. They were, in fact, electrons.
For a long time, not much more was known about these forms of radiation, largely because the structure of the atom’s nucleus was a mystery. For a time, physicists thought that electrons and protons existed together in the nucleus of the atom, because beta rays seemed to be coming directly from the nu
cleus of radioactive elements. Many tried to explain the existence of electrons within the nucleus, but those explanations raised more questions than they solved.
A series of very precise experiments in the latter half of the 1920s created a beta ray “crisis,” involving the apparent violation of certain laws of conservation that physicists cherish. One of the central conservation laws concerns the conservation of energy. In any physical process, the energy into the process and the energy out of the process must be equal and accounted for. Beta radiation seemed to violate this law. If energy was conserved, the energy of the emitted beta particles should fall within a very narrow range. Every process of beta ray emission was, theoretically, the same as every other one, yet the beta particles emitted fell along a significantly wider spectrum of energy than predicted. That strongly suggested that energy was not being conserved. Imagine baseball batting practice with a machine set to pitch balls at exactly the same speed and in the same direction every time. Yet, suddenly the balls start coming out randomly at different speeds. One would conclude that there is something wrong with the machine.
Some physicists surrendered to the evidence and pronounced that energy was evidently not conserved in this particular interaction. These included Niels Bohr, who ventured this daring, and to physicists distasteful, conclusion in a paper he presented at a major physics conference held by Corbino and Fermi in Rome in 1931. Rutherford, for one, utterly rejected Bohr’s conclusion, but it was only the imaginative Pauli who made a suggestion that would explain beta radiation without violating the principle of energy conservation.
In typically audacious terms, Pauli suggested that another particle was being emitted at the same time as the electron, virtually undetectable because it is neutral and of very small (or even no) mass. He first outlined his idea in a letter to physicists attending a conference in Tübingen, Germany, in December 1930. He called this imaginary particle a “neutron” and proposed that it was carrying the balance of the energy not observed in beta decay, thus salvaging the conservation of energy. The particle we today call the neutron had not yet been discovered. James Chadwick’s sensational discovery took place some two years later, at which point Fermi and his team proposed the name “neutrino”—little neutral one—for Pauli’s hypothetical particle.
Not many people took Pauli’s idea seriously. For some, the whole issue of energy conservation in beta radiation was something, in the words of one eminent physicist, “better not to think about… at all, like new taxes.” Others sided with Bohr and found the idea of a particle that could not be seen and that could penetrate vast distances unimpeded too outlandish to take seriously. Violation of energy conservation was more likely than the existence of such a neutral particle. Further, no one understood the mechanism by which an electron and a neutrino would be emitted. Did they exist in the nucleus all the time, ready to be emitted at the appropriate stimulation? Or were they somehow created within the nucleus and then promptly ejected?
Chadwick’s discovery of the neutron in the nucleus of the atom provided a clue. Dirac’s quantum electrodynamics, which described the creation and destruction of photons, provided a second clue. Jordan and Wigner’s “second quantization” provided the third clue. By mid-1933, Fermi—who took Pauli’s proposal quite seriously—used everything he had learned over the previous four years and applied it to the problem of beta radiation. His paper, “A Tentative Theory of Beta Rays,” published in late 1933 and early 1934 in scientific journals in Germany and Italy, set out his ideas on the subject. More than eighty years later, it stands as one of the most important achievements of twentieth-century physics.
What Fermi proposed was the existence of a new quantum interaction—an interaction now known as the “weak” interaction because it takes effect only when particles come into extremely close range of each other. This interaction changes neutrons into protons and protons into neutrons. At the very moment that these changes occur, new particles are created and emitted from the nucleus at high energy. When the neutron is changed into a proton, an electron and an antineutrino are emitted. When a proton is changed into a neutron, a positively charged electron (a positron) and a neutrino are emitted. The sum total of the energy of the emitted particles remains constant, but the apportionment of energy among the particles varies according to quantum laws that are a direct consequence of the quantum field theory. The electron and the neutrino (and their antimatter cousins) do not preexist in the nucleus at all. Rather, they are created at the moment of emission. The theory allows one to calculate the likelihood of a neutrino or an antineutrino interacting with matter. That likelihood is so low that a neutrino can travel through millions of miles of lead without interacting at all.
The story of the development and publication of the paper is intriguing. Fermi had been working on the paper through the latter part of 1933. Beta radiation was a major preoccupation of the Solvay conference of October 1933, which Fermi attended, and he and Pauli discussed Pauli’s neutrino idea at length during the conference. By Christmas of that year, Fermi had progressed sufficiently to feel comfortable presenting the main ideas to his Rome colleagues during a group ski vacation. Segrè reports that soon after this holiday Fermi presented the paper to the British journal Nature, because the group at Via Panisperna had decided, following the rise of Hitler in Germany, to boycott German publications even though they remained the most prestigious in the field. According to Segrè, Nature rejected the paper, a reviewer claiming that it was too “speculative.” In response, Fermi sent the paper to the Italian journal Nuovo Cimento and the German Zeitschrift für Physik, both of which published it. This story is so central to the legend of the paper that Wikipedia reports Nature later publicly regretted having rejected it as one of its most egregious editorial errors.
In fact, no such public statement of regret can be found in any back issues of Nature. It is unfortunately impossible to review Nature’s archives to find the rejection letter written by the reviewer, because all records were destroyed in a move to new offices several decades ago. Some historians question the entire story. They observe that at that time Nature accepted only short notes on these types of subjects and was certainly not a forum for a detailed presentation of new quantum field theories. A more logical British publication would have been the Proceedings of the Royal Society of London, which had published all of Dirac’s seminal papers on QED and would have been a logical place for Fermi to submit the beta decay paper. These historians suggest that he may have wanted his German counterparts, particularly people like Born, Heisenberg, and of course Pauli himself, to read the paper first. A white lie—that he had tried but failed to get it published by Nature—would get him off the hook with his young colleagues who were so opposed to publishing anything in German journals and still achieve his main objective.
Whatever the actual history of the paper, the immediate reaction to it within the physics community was somewhat muted. Pauli and Wigner appreciated the achievement for what it was. Fermi had integrated the entire Dirac quantum field framework into his own thinking and applied it ingeniously to the beta radiation problem. The trouble was that the theory seemed almost impossible to verify experimentally. Neutrinos appeared to be impossible to detect. Fermi himself doubted that they ever would be. Although he could take private satisfaction in having mastered QED and used its mathematics to explain another apparently different phenomenon, only in later decades would the true brilliance of the paper come to be appreciated. It was the first hint of the existence of a new, fourth fundamental force of nature, the weak force, which would ultimately take its place alongside gravity, electromagnetism, and the strong force (the force that holds the nucleus of an atom together). Its exploration has resulted in over a dozen Nobel Prizes and some of physics’ biggest surprises.
In the 1970s, Fermi’s future University of Chicago student, Chen Ning Yang, who would help to uncover one of the most surprising secrets of the weak force, asked Fermi’s colleague and friend Eugene Wigner wha
t physicists would remember as Fermi’s most important contribution to the field. Wigner insisted that the beta radiation paper was Fermi’s most important work. Yang disagreed, noting that it was Jordan and Wigner himself who had invented the second quantization with its creation/annihilation operators for fermions. Wigner’s reply: “Yes, yes. But we never dreamed that it could be used in real physics.” Most people would agree with Wigner’s assessment that the beta decay paper remains one of Fermi’s true landmark discoveries.
IN THE MEANTIME, SOME NEWS FROM PARIS CAME TO FERMI’S attention. The Joliot-Curies announced that they had induced radiation by bombarding nonradioactive elements with alpha particles. The news gave Fermi yet another idea.
CHAPTER NINE
GOLDFISH
WELL BEFORE HE BEGAN THINKING ABOUT BETA RAYS, FERMI knew that the next big thing would be nuclear physics.
The Last Man Who Knew Everything Page 13
