The Greatest Story Ever Told—So Far
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Clearly something about the weak interaction is different, but you may wonder if it is worth worrying about. Neutron decay is interesting, but happily the properties of nuclei protect us from it so that stable atoms can exist. Thus it seems to have little impact on everyday lives. Unlike gravity and electromagnetism, we don’t sense it. If the weak interaction were of little other importance, then its anomalous nature could be easily overlooked.
However, the weak interaction, at least as much as gravity and electromagnetism, is directly responsible for our existence. In 1939, Hans Bethe, who would soon help lead the effort to build the atomic bomb, realized that the interactions that broke apart heavy nuclei as the source of the explosive power of the bomb could, under different circumstances, be utilized to build larger nuclei from smaller nuclei. This could release even more energy than was released in the A-bomb.
Up until that time the energy source of the Sun was a mystery. It was well established that the temperature in the solar core could not exceed a few tens of millions of degrees—which may seem extreme, but the energies available to the colliding nuclei at those temperatures had already been achieved in the lab. Moreover, the Sun could not involve simple burning, like a candle.
It had been established as early as the eighteenth century that an object with the mass of the Sun could only burn with its observed brightness for perhaps ten thousand years if it were just something like a burning lump of coal. While that meshed nicely with Bishop Ussher’s estimates for the age of the universe as inferred from the Bible’s tale of creation, geologists and biologists had already established by the mid-nineteenth century that Earth itself was far older. With no apparent new energy source, the longevity and brightness of the Sun was inexplicable.
Enter Hans Bethe. Another of the incredibly talented and prolific theoretical physicists coming out of Germany in the first half of the twentieth century, Bethe was also another doctoral student of Arnold Sommerfeld’s and also went on to win the Nobel Prize. Bethe began his career in chemistry because the introductory physics instruction at his university was poor—a common problem. (I also dropped physics in my first year for the same reason, but happily the physics department at my university let me take a more advanced course the following year.) Bethe switched to physics before moving on to graduate studies and emigrated to the United States to escape the Nazis.
A consummate physicist, Bethe could work through detailed calculations to solve a wide variety of problems on the blackboard, beginning at the upper left of the board and ending at the lower right with almost no erasures. Bethe strongly influenced Richard Feynman, who used to marvel at Bethe’s patient methodological approach to problems. Feynman himself often jumped from the beginning of a problem to the end and worked out the steps in between afterward. Bethe’s solid technical prowess and Feynman’s brilliant insights combined well when they both worked at Los Alamos on the atomic bomb. They would go down the hallway with Feynman loudly countering the patient but persistent Bethe, and their colleagues labeled them “the Battleship and the Torpedo Boat.”
Bethe was legendary when I was a young physicist because even into his nineties he was still writing important physics articles. He was also happy to talk to anyone about physics. When I gave a visiting lecture at Cornell—where Bethe spent most of his professional career—I felt immensely honored when he walked into my office to ask me questions and then listened intently to me, as if I actually had something to offer him.
He was also physically robust. A physicist friend of mine told me of a time he too visited Cornell. One weekend he decided to be ambitious and climb one of the many steep hiking trails near the campus. He was proud of himself for huffing and puffing his way almost to the top until he spied Bethe, then in his late eighties, happily making his way down the trail from the summit.
While I always liked and admired Bethe, in researching material for this book I found two additional happy personal connections that were satisfying enough for me to relate them here. First, I found out that I am in a sense his intellectual grandson, as my undergraduate physics honors thesis adviser, M. K. Sundaresan, was one of his doctoral students. Second, I discovered that Bethe, who had little patience for grand claims made of fundamental results that were carried out without any real motivation or evidence, once wrote a hoax paper while a postdoc poking fun at a paper he deemed ridiculous by the famous physicist Sir Arthur Stanley Eddington. Eddington claimed to “derive” a fundamental constant of electromagnetism using some fundamental principles, but Bethe correctly viewed the claim as nothing other than misguided numerology. Learning this made me feel better about a hoax paper I wrote when I was an assistant professor at Yale, responding to what I thought was an inappropriate paper, published in a distinguished physics journal, that claimed to discover a new force in nature (which indeed later turned out to be false). At the time that Bethe wrote his paper, the physics world took itself a little more seriously, and Bethe and his colleagues were forced to issue an apology. By the time I wrote mine, the only negative reaction I got was from my department chair, who was worried that the Physical Review might actually publish my article.
When he was in his early thirties, Bethe had already established himself as a master physicist with his name attached to a host of results, from the Bethe formula, describing the passage of charged particles through matter, to the Bethe ansatz, a method to obtain exact solutions for certain quantum problems in many-body physics. A series of reviews he cowrote on the state of the nascent field of nuclear physics in 1936 remained authoritative for some time and became known as Bethe’s Bible. (Unlike the conventional Bible, it made testable predictions, and it was eventually replaced as scientific progress was made.)
In 1938, Bethe was induced to attend a conference on “stellar energy generation,” though at that time astrophysics was not his chief interest. By the end of the meeting, he had worked out the nuclear processes by which four individual protons (the nuclei of hydrogen atoms) eventually “fuse”—as a result of Fermi’s weak interaction—to form the nucleus of helium, containing two protons and two neutrons. This fusion releases about a million times more energy per atom than is released when coal burns. This allows the Sun to last a million times longer than previous estimates would have permitted, or about 10 billion years instead of ten thousand years. Bethe later showed that other nuclear reactions help power the Sun, including a set that converts carbon to nitrogen and oxygen—the so-called CNO cycle.
The secret of the Sun—the ultimate birth of light in our solar system—had been unveiled. Bethe won the Nobel Prize in 1967, and almost forty years after that, experiments on neutrinos coming from the Sun confirmed Bethe’s predictions. Neutrinos were the key experimental observable that allowed such confirmation. This is because the whole chain begins with a reaction in which two protons collide, and via the weak interaction one of them converts into a neutron, allowing the two to fuse into the nucleus of heavy hydrogen, called deuterium, and release a neutrino and a positron. The positron later interacts in the Sun, but neutrinos, which interact only via the weak interaction, travel right out of the Sun, to Earth and beyond.
Every second of every day, more than 400,000 billion of these neutrinos are passing through your body. Their interaction strength is so weak that they could traverse on average through ten thousand light-years of solid lead before interacting, so most of them travel right through you, and Earth, without anyone’s noticing. But if not for the weak interaction, they would not be produced, the Sun wouldn’t shine, and none of us would be here to care.
So the weak interaction, although extremely weak, nevertheless is largely responsible for our existence. Which is one of the reasons why, when the Fermi interaction, developed to characterize it, and the neutrinos first predicted by it, turned out to both defy common sense, physicists had to stand up and take notice. And they were driven to change our notions of reality itself.
Part Two
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EXODUS
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nbsp; Chapter 11
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DESPERATE TIMES AND DESPERATE MEASURES
To every thing there is a season, and a time for every purpose.
—ECCLESIASTES 3:1
The rapid succession of events during the 1930s, from the discovery of the neutron to probing the nature of neutron decay, as well as the discovery of the neutrino and the consequent discovery of a new and universal short-range weak force in nature, left physicists more confused than inspired. The brilliant march that had led to the unification of electricity and magnetism, and the unification of quantum mechanics and relativity, had been built on exploring the nature of light. Yet it wasn’t clear how the elegant theoretical edifice of quantum electrodynamics could guide considerations of a new force. The weak interaction is far removed from direct human experience and involves new and exotic elementary particles and nuclear transmutations reminiscent of alchemy but, unlike alchemy, testable and reproducible.
The fundamental confusion lay with the nature of the atomic nucleus itself and the question of what held it together. The discovery of the neutron helped resolve the paradox that had earlier seemed to require electrons to be confined in the nucleus to counter the charge of additional protons necessary to produce correct nuclear masses, but the observation of beta decay—which resulted in electrons emerging from nuclei—didn’t help matters.
The realization that in beta decay neutrons became protons in the nucleus clarified matters, but then another question naturally arose: Could this transformation somehow explain the strong binding that held protons and neutrons together inside nuclei?
In spite of the obvious differences between the weak forces and quantum theory of electromagnetism, QED, the remarkable success of QED in describing the behavior of atoms and the interactions of electrons with light colored physicists’ thinking about the new weak force as well. The mathematical symmetries associated with QED worked beautifully to ensure that otherwise worrisome infinities in the calculations arising from the exchange of virtual particles vanished when making predictions of physical quantities. Would something similar work to understand the force binding protons and neutrons in nuclei?
Specifically, if the electromagnetic force was due to the exchange of particles, then it was reasonable to think that the force that held together the nucleus might also be due to the exchange of particles. Werner Heisenberg proposed this idea in 1932 around the time the neutron was discovered. If neutrons and protons could convert into each other, with the proton absorbing an electron to become a neutron, then maybe the exchange of electrons between them might somehow produce a binding force?
A number of well-known problems marred this picture, however. First was the problem of “spin.” If one assumed, as Heisenberg did, that the neutron was essentially made up of a proton and an electron bound together, and since both were spin ½ particles, then adding them together in the neutron, it couldn’t have spin ½ as well, since ½ + ½ can’t equal ½. Heisenberg argued, in desperation, because those were desperate times when it seemed all the conventional rules were breaking down, that the “electron” that was transferred between neutrons and protons, and which bound them together in the nucleus, was somehow different from a free electron and had no spin at all.
In retrospect, this picture has another problem. Heisenberg was motivated to consider electrons binding together neutrons and protons because he was thinking about hydrogen molecules. In hydrogen, two protons are bound together by sharing electrons that orbit them. The problem with using a similar explanation for nuclear binding is one of scale. How could neutrons and protons exchange electrons and be bound together so tightly that their average distance apart is more than one hundred thousand times smaller than the size of hydrogen molecules?
Here is another way of thinking about this problem that will be useful to return to later. Recall that electromagnetism is a long-range force. Two electrons on opposite sides of the galaxy experience a repulsion—albeit extremely small—due to the exchange of virtual photons. The quantum theory of electromagnetism makes this possible. Photons are massless, and virtual photons can travel arbitrarily far, carrying arbitrarily small amounts of energy, before they are absorbed again—without violating the Heisenberg uncertainty principle. If the photons were massive, then this would not be possible.
Now if a force between neutrons and protons in nuclei arose due to the absorption and emission of virtual electrons, say, then the force would be short-range because the electrons are massive. How short-range? Well, it works out to be about one hundred times the size of typical nuclei. So, exchanging electrons doesn’t work to produce nuclear-scale forces. As I say, those were desperate times.
Heisenberg’s desperate idea about a strange spinless version of the electron was not lost on a young Japanese physicist, the shy twenty-eight-year-old Hideki Yukawa. Working in 1935 when Japan was just beginning to emerge from centuries of isolation, and just before its imperial designs ignited the war in the Pacific, Yukawa published the first original work in physics to be published by a physicist educated entirely in Japan. No one took notice of the paper for at least two years, yet fourteen years later he won the Nobel Prize for this work, which had by then become noticed, but for the wrong reasons.
Einstein’s visit to Japan in 1922 had cemented Yukawa’s growing interest in physics. When Yukawa was still in high school and searching for material to help him pass examinations in a second foreign language, he found Max Planck’s Introduction to Theoretical Physics in German. He rejoiced in reading both the German and the physics and was aided by his classmate Sin-Itiro Tomonaga, a talented physicist who was his colleague both in high school and later at Kyoto University. Tomonaga was so talented that he would later share the 1965 Nobel Prize with Richard Feynman and Julian Schwinger for demonstrating the mathematical consistency of quantum electrodynamics.
That Yukawa, who had been a student in Japan at a time when many of his instructors did not yet fully understand the emerging field of quantum mechanics, came upon a possible solution to the nuclear-force problem that had been overlooked by Heisenberg, Pauli, and even Fermi was remarkable. I suspect that part of the problem was a phenomenon that has occurred several times in the twentieth century and perhaps before, and perhaps after. When the paradoxes and complexities associated with some physical process begin to seem overwhelming, it is tempting to assume that some new revolution, similar to relativity or quantum mechanics, will require such a dramatic shift in thinking that it doesn’t make sense to push forward with existing techniques.
Fermi, unlike Heisenberg or Pauli, was not looking for a wholesale revolution. He was willing to propose, as he called it, a “tentative theory” of neutron decay that got rid of electrons in the nucleus by allowing them to be spontaneously created during beta decay. He proposed a model that worked, which he knew was just a model and not a complete theory, but it did allow one to do calculations and make predictions. That was the essence of Fermi’s practical style.
Yukawa had followed these developments, translated Heisenberg’s paper on nuclei along with an introduction, and published it in Japan, so the problems of Heisenberg’s proposal were already clear to him. Then in 1934 Yukawa read Fermi’s theory of neutron decay, which catalyzed a new idea in Yukawa’s mind. Perhaps the nuclear force binding protons and neutrons was due not to the exchange of virtual electrons between them, but to the exchange of both the electron and the neutrino that were created when neutrons changed to protons.
Another problem immediately arose, however. Neutron decay is a result of what would become known as the weak interaction, and the force responsible for it is weak. Plugging in values for the possible force that might result between protons and neutrons by the exchange of an electron-neutrino pair made it clear that this force would be far too weak to bind them.
Yukawa then allowed himself to do what none of the others had done. He questioned why the nuclear force, if it, like QED, results from the exchange of virtual particles, had to be
due to the exchange of one or more of the particles already known or assumed to exist. Remembering how loath physicists such as Dirac and Pauli had been to propose new particles, even when they were correct, you can perhaps appreciate how radical Yukawa’s idea was. As Yukawa later described it:
At this period the atomic nucleus was inconsistency itself, quite inexplicable. And why?—because our concept of elementary particle was too narrow. There was no such word in Japanese and we used the English word—it meant proton and electron. From somewhere had come a divine message forbidding us to think about any other particle. To think outside of these limits (except for the photon) was to be arrogant, not to fear the wrath of the gods. It was because the concept that matter continues forever had been a tradition since the times of Democritus and Epicurus. To think about creation of particles other than photons was suspect, and there was a strong inhibition of such thoughts that was almost unconscious.
One of my good physics friends has said that the only time he was able to do complicated calculations was after the birth of each of his children, when he couldn’t sleep anyway, so he stayed up and worked. Thus in October of 1934, just after the birth of his second child and unable to sleep, Yukawa realized that if the range of the strong nuclear force was to be restricted to the size of a nucleus, then any exchanged particle must be far more massive than the electron. The next morning he estimated the mass to be two hundred times the electron mass. It would have to carry an electric charge if it was to be exchanged between neutrons and protons, and it could have no spin, so as not to change the proton’s or neutron’s spin when it was absorbed or emitted.