This is a triumphant chapter, for we come to the end of the road in our search for a basic building block. In the fifties and early sixties, however, we were not feeling so sanguine about finally answering Democritus's riddle. Because of the hundred-hadron headache, the prospect of identifying a few elementary particles seemed pretty dim. Physicists were making much better progress in describing the forces of nature. Four were clearly recognized: gravity, the electromagnetic force, the strong force, and the weak force. Gravity was the domain of astrophysics, for it was too feeble to deal with in accelerator labs. This omission would come to haunt us later. But we were getting the other three forces under control.
The Electric Force
The 1940s had seen the triumph of a quantum theory of the electromagnetic force. The work of Paul Dirac in 1927 successfully blended quantum theory and special relativity in his theory of the electron. However the marriage of quantum theory and electromagnetism, the electromagnetic force, was a stormy one, filled with stubborn problems.
The struggle to unite the two theories was known informally as the War Against Infinities, and by the mid-1940s it involved infinity on one side and, on the other, many of the brightest luminaries in physics: Pauli, Weisskopf, Heisenberg, Hans Bethe, and Dirac, as well as some new rising stars—Richard Feynman at Cornell, Julian Schwinger at Harvard, Freeman Dyson at Princeton, and Sinitiro Tomonaga in Japan. The infinities came from this: simply described, when one calculated the value of certain properties of the electron, the answer according to the new relativistic quantum theories, came out "infinite." Not just big, infinite.
One way to visualize the mathematical quantity called infinity is to think of the total number of integers—and then add one more. There is always one more. Another way, one that was more likely to appear in the calculations of these brilliant but deeply unhappy theorists, is to evaluate a fraction in which the denominator becomes zero. Most pocket calculators will politely inform you—usually with a series of EEEEEEs—that you have done something stupid. Earlier relay-driven mechanical calculators would go into a grinding cacophony that usually terminated in a dense puff of smoke. Theorists saw infinities as a sign that something was deeply wrong with the way the marriage between electromagnetism and quantum theory was being consummated—a metaphor we probably should not pursue, much as we are tempted. In any case, Feynman, Schwinger, and Tomonaga, working separately, achieved victory of a sort in the late 1940s. They finally overcame the inability to calculate the properties of charged particles such as the electron.
A major stimulus to this theoretical breakthrough came from an experiment carried out at Columbia by one of my teachers, Willis Lamb. In the early postwar years, Lamb taught most of the advanced courses and worked on electromagnetic theory. He also designed and carried out, using the wartime radar technology developed at Columbia, a brilliantly precise experiment on the properties of selected energy levels in the hydrogen atom. Lamb's data were to provide a test of some of the most subtle pieces of the newly minted quantum electromagnetic theory, which his experiment served to motivate. I'll skip the details of Lamb's experiment, but I want to emphasize that an experiment was seminal to the exciting creation of a workable theory of the electric force.
What emerged from the theorists was something called "renormalized quantum electrodynamics." Quantum electrodynamics, or QED, enabled theorists to calculate the properties of the electron, or its heavier brother the muon, to ten significant figures beyond the decimal point.
QED was a field theory, and thus it gave us a physical picture of how a force is transmitted between two matter particles, say, two electrons. Newton had problems with the idea of action-at-a-distance, as did Maxwell. What is the mechanism? One of the oh-so-clever ancients, a pal of Democritus's, no doubt, discovered the influence of the moon on the earth's tides and agonized over how that influence could manifest itself through the intervening void. In QED, the field is quantized, that is, broken down into quanta—more particles. These are not matter particles, however. They are particles of the field. They transmit the force by traveling, at the speed of light, between the two interacting matter particles. These are messenger partides, which in QED are called photons. Other forces have their own distinct messengers. Messenger particles are the way we visualize forces.
VIRTUAL PARTICLES
Before we go on, I should explain that there are two manifestations of particles: real and virtual. Real particles can travel from point A to point B. They conserve energy. They make clicks in Geiger counters. Virtual particles do none of these things, as I mentioned in Chapter 6. Messenger particles—force carriers—can be real particles, but more frequently they appear in the theory as virtual particles, so the two terms are often synonymous. It is virtual particles that carry the force message from particle to particle. If there is plenty of energy around, an electron can emit a real photon, which produces a real click in a real Geiger counter. A virtual particle is a logical construct that stems from the permissiveness of quantum physics. According to quantum rules, particles can be created by borrowing the necessary energy. The duration of the loan is governed by Heisenberg's rules, which state that the borrowed energy times the duration of the loan must be greater than Planck's constant divided by twice pi. The equation looks like this: ΔEΔt is greater than h/2π. This means that the larger the amount of energy borrowed, the shorter the time the virtual particle can exist to enjoy it.
In this view, so-called empty space can be awash with these ghostly objects: virtual photons, virtual electrons and positrons, quarks and antiquarks, even (with oh god how small a probability) virtual golf balls and anti-golf balls. In this swirling, dynamic vacuum, a real particle's properties are modified. Fortunately for sanity and progress, the modifications are very small. Nevertheless, they are measurable, and once this was understood, life became a contest between increasingly precise measurements and ever more patient and determined theoretical calculations. For example, think about a real electron. Around the electron, because of its existence, there is a cloud of transient virtual photons. These notify all and sundry that an electron is present, but they also influence the electron's properties. What's more, a virtual photon can dissolve, very transiently, into an e+ e− pair (a positron and an electron). In a blink of a mosquito's eye, the pair is back together as a photon, but even this evanescent transformation influences the properties of our electron.
In Chapter 5, I wrote the g-value of the electron as calculated theoretically from QED and as measured by inspired experiments. As you may recall, the two figures agreed to eleven places past the decimal. Equally successful was the g-value of the muon. Because the muon is heavier than the electron, it provides an even more incisive test of the concept of messenger particles; the muon's messengers can have higher energy and cause more mischief. The effect is that the field influences the properties of the muon even more strongly. Very abstract stuff, but the agreement between theory and experiment is sensational and indicates the power of the theory.
THE PERSONAL MAGNETISM OF THE MUON
As for the verifying experiment ... On my first sabbatical year (1958–59) I went to CERN in Geneva, using a Ford Fellowship and a Guggenheim Fellowship to supplement my half-salary. CERN was the creation of a twelve-nation European consortium to build and share the expensive facilities required to do high-energy physics. Founded in the late forties, when the rubble of World War II was still warm, this collaboration of former military adversaries became a model for internadonal cooperation in science. There my old sponsor and friend, Gilberto Bernardini, was director of research. My main reason for going was to enjoy Europe, learn to ski, and dabble in this new laboratory nestled on the Swiss-French border just outside of Geneva. Over the next twenty years I spent about four years doing research in this magnificent multilingual facility. Although French, English, Italian, and German were common, the official language of CERN was broken Fortran. Grunts and sign language also worked. I used to contrast CERN and Fermilab as follo
ws: "CERN is a lab of culinary splendor and architectural catastrophe and Fermilab is the other way around." Then I convinced Bob Wilson to hire Gabriel Tortella, the legendary CERN chef and cafeteria manager, as a consultant to Fermilab. CERN and Fermilab are what we like to call cooperative competitors; each loves to hate the other.
At CERN, with Gilberto's help, I organized a "g minus 2" experiment, designed to measure the g-factor of the muon with mind-boggling precision, using some tricks. One trick was made possible by the fact that muons come out of pion decay polarized; that is, the vast majority have spins that point in the same direction relative to their motion. Another clever trick is implied by the tide of the experiment, "Gee minus two" or "Jzay moins deux," as the French call it. The g-value has to do with the strength of the little magnet built into the properties of spinning charged particles like the muon and electron.
Dirac's "crude" theory, remember predicted that the g-value was exactly 2.0. However, as QED evolved, it was found that important but tiny adjustments to Dirac's 2 were required. These small terms appear because the muon or electron "feels" quantum pulsations of the field around it. Recall that a charged particle can emit a messenger photon. This photon, as we saw, can virtually dissolve into a pair of oppositely charged particles—just fleetingly—and then restore itself before anyone can see. The electron, isolated in its void, is perturbed by the virtual photon, influenced by the virtual pair, twisted by die transient magnetic forces. These and other, even more subde, processes in the seething broth of virtual happenings connect the electron, ever so weakly, to all die charged particles that exist The effect is a modification of the electron's properties. In the whimsical linguistics of theoretical physics, the "naked" electron is an imaginary object cut off from the influences of the field, whereas a "dressed" dectron carries die imprint of the universe, but it is all buried in extremely tiny modifications to its bare properties.
In Chapter 5, I described the electron's g-factor. Theorists were even more interested in the muon; because its mass is two hundred times greater, the muon can emit virtual photons, which reach out farther to the more exotic processes. The result of one theorist's labor of many years was the g-factor of the muon:
g = 2(1.001165918)
This result (in 1987) was the culmination of a long sequence of calculations, using the new QED formulations of Feynman and the others. The collection of terms that add up to the sum .001165918 are known as radiative corrections. Once at Columbia we were listening to theorist Abraham Pais lecture on radiative corrections when a janitor entered the hall carrying a wrench. Pais leaned over to ask the man what he wanted. "Bram," someone yelled from the audience, "I think he's here to correct the radiator."
How do we match the theory with experiment? The trick was to find a way to measure the difference of the muon's g-value from 2.0. By finding a way to do this, we are measuring the correction (.001165918) directly rather than as a tiny add-on to a large number. Imagine trying to weigh a penny by first weighing a person carrying a penny and then weighing the person without the penny, then subtracting the second weight from the first. Better to weigh the penny directly. Suppose we trap a muon in an orbit in a magnetic field. The orbiting charge is also a "magnet" with a g-value, which Maxwell's theory says is precisely 2, whereas the spin-related magnet has this minuscule excess above 2. So the muon has two different "magnets": one internal (its spin) and the other external (its orbit). By measuring the spin-magnet while the muon is in its orbital configuration, the 2.0 gets subtracted, allowing us to measure directly the deviation from 2 in the muon, no matter how small.
Picture a little arrow (the spin axis of the muon) moving in a large circle with the arrow always tangential to the orbit. That's what would happen if g = 2.000 exactly. No matter how many orbits the particle executes, the little spin arrow will always be tangent to the orbit. However if there is ever so small a difference between the true value of g and 2, the arrow will move away from tangency perhaps about a fraction of a degree for each orbit. After say, 250 orbits, the arrow (spin axis) may be pointing toward the center of the orbit, like a radius. Continue the orbital motion, and in 1,000 orbits the arrow will make a full turn (360 degrees) relative to its initial direction as tangent. Thanks to parity violation, we can (triumphantly) detect the direction of the arrow (the muon's spin) by the direction in which the electrons come off when the muon decays. Any angle between the spin axis and a tangent line to the orbit represents a difference between g and 2. A precise measurement of this angle yields a precise measurement of the difference. See? No? Oh well, believe!
The proposed experiment was complicated and ambitious, but in 19–58 it was easy to collect very bright young physicists to help. I returned to the United States in mid-1959 and revisited the experiment in Europe periodically. It went through several phases, each one suggesting the next phase, and didn't really end until 1978, when the final CERN g-value of the muon was published—a triumph of experimental cleverness and determination (sitzfleisch, the Germans call it). The electron's g-value was more precise, but don't forget that electrons are forever and muons stay in the universe for only two millionths of a second. The result?
g = 2(1.001165923 ± .00000008)
The error of eight parts per hundred million clearly covers the theoretical prediction.
All of this is to suggest that QED is a great theory, and it's partly why Feynman, Schwinger, and Tomonaga are considered great physicists. It does have some pockets of mystery, one of which is noteworthy and relevant to our theme. It has to do with these infinities—for example, the electron's mass. Early efforts at quantum field theory calculated a point electron as infinitely heavy. It is as if Santa, manufacturing electrons for the world, must squeeze a certain quantity of negative charge into a very small volume. This takes work! The effort should show up as a huge mass, but the electron, weighing in at 0.511 MeV, or about 10−30 kilograms, is a lightweight, the lowest mass of any particle whose mass is clearly not zero.
Feynman and his colleagues proposed that whenever we see this dreaded infinity appearing, we in effect bypass it by inserting the known mass of the electron. In the real world one could call this fudging. In the world of theory, the word is "‹normalization," a mathematically consistent method for circumventing the embarrassing infinities that a real theory would never have. Don't worry. It worked, and allowed for the super-precise calculations we talked about. Thus, the problem of mass was bypassed—but not solved—and remained behind as a quietly ticking time bomb to be activated by the God Particle.
The Weak Force
One of the mysteries that nagged Rutherford and others was this radioactivity thing. How is it that nuclei and particles decay willy-nilly into other particles? The physicist who first elucidated this question with an explicit theory, in the 1930s, was Enrico Fermi.
There are legions of stories about Fermi's brilliance. At the first nuclear bomb test at Alamogordo, New Mexico, Fermi was lying on the ground about nine miles from the bomb tower. After the bomb went off, he stood up and dropped small pieces of paper on the ground. The pieces fell at his feet in the quiet air; but a few seconds later the shock wave arrived and knocked them a few centimeters away. Fermi calculated the yield of the explosion from the displacement of the paper bits, and his on-the-spot result agreeed closely with the official measurement, which took several days to calculate. (A friend of his, the Italian physicist Emilio Segre, pointed out, however; that Fermi was human. He had trouble figuring out his University of Chicago expense account.)
Like many physicists, Fermi loved making up math games. Alan Wattenberg tells of the time he was eating lunch with a group of physicists when Fermi noticed dirt on the windows and challenged everyone to figure out how thick the dirt could get before it would fall off the window from its own weight. Fermi helped them all get through the exercise, which required starting from fundamental constants of nature, applying the electromagnetic interaction, and proceeding to calculate the dielectric attractions that
keep insulators stuck to each other. At Los Alamos during the Manhattan Project, a physicist ran over a coyote one day in his car. Fermi said it was possible to calculate the total number of coyotes in the desert by keeping track of the vehicle-coyote interactions. These were just like particle collisions, he said. A few rare events yielded clues about the entire population of such particles.
Well, he was very smart, and he has been well recognized. He has more things named after him than anyone I know. Let's see ... there is Fermilab, the Enrico Fermi Institute, fermion particles (all the quarks and leptons), and Fermi statistics (never mind). The fermi is a unit of size equal to 10−13 centimeters. My ultimate fantasy is to leave behind one thing that's named after me. I begged my Columbia colleague T. D. Lee to propose a new particle that, when discovered, would be named the Lee-on. To no avail.
But over and above Fermi's work on the first nuclear reactor beneath the football stadium at the University of Chicago, and his seminal studies of squished coyotes was a contribution more central to the understanding of the universe. Fermi described a new force in nature, the weak force.
The God Particle Page 36
