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.
Let's backtrack quickly to Becquerel and Rutherford. Recall that Becquerel had serendipitously discovered radioactivity in 1896 when he stored some uranium in a drawer where he kept his photographic paper. When the photographic paper came out black, he eventually traced the cause to invisible rays shooting out of the uranium. After the discovery of radioactivity and the elucidation by Rutherford of alpha, beta, and gamma radiation, many physicists the world over concentrated on the beta particles, which were soon identified as electrons.
Where did the electrons come from? Physicists very quickly figured out that the electron was emitted from the nucleus when it underwent a spontaneous change of state. In the 1930s researchers determined that nuclei consist of protons and neutrons, and traced the radioactivity of nuclei to the instability of their constituent protons and neutrons. Obviously, not all nuclei are radioactive. The conservation of energy and the weak force play important roles in whether and how readily a proton or a neutron decays in a nucleus.
In the late 1920s careful before-and-after measurements of radioactive nuclei were made. One measures the mass of the initial nucleus, the mass of the final nucleus, and the energy and mass of the emitted electron (remembering that E = mc2). And here an important discovery was made: it didn't add up. Energy was missing. The input was bigger than the output. Wolfgang Pauli made his (then) daring suggestion that a small neutral object was carrying the energy away.
In 1933 Enrico Fermi put it all together. The electrons were coming from the nucleus, but not directly. What happens is that the neutron in the nucleus decays into a proton, an electron, and the small neutral object that Pauli had invented. Fermi named it the neutrino, meaning "little neutral one." A force is responsible for this reaction in the nucleus, said Fermi, and he called it the weak force. It is enormously feeble compared to the strong nuclear force and electromagnetism. For example, at low energy the weak force is about one thousandth the strength of electromagnetism.
The neutrino, having no charge and almost no mass, could not be directly detected in the 1930s; it can be detected today only with great effort. Though the neutrino's existence was not proven experimentally until the 1950s, most physicists accepted it as a fact because it had to exist to make the bookkeeping come out right. In today's more exotic reactions in accelerators, involving quarks and other weird things, we still assume that any missing energy flies out of the collision in the form of undetectable neutrinos. This artful little dodger seems to leave its invisible signature all over the universe.
But back to the weak force. The decay that Fermi described—neutron gives way to proton, electron, and neutrino (actually, an antineutrino)—occurs routinely with free neutrons. When the neutron is imprisoned in the nucleus, however, it can happen only under special circumstances. Conversely, the proton as a free particle cannot decay (as far as we know). Inside the crowded nucleus, however the bound proton can give rise to a neutron, a positron, and a neutrino. The reason that the free neutron can undergo weak decay is simple energy conservation. The neutron is heavier than the proton, and when a free neutron changes into a proton there is enough additional rest mass energy to make the electron and the antineutrino and send each of them off with a little energy. A free proton has too little mass to do this. However inside the nucleus the presence of all the other guys in effect alters the mass of a bound particle. If the protons and neutrons inside can, by decaying, increase the stability and lower the mass of the nucleus in which they are stuck, they do it. However if the nucleus is already in its lowest mass-energy state, it is stable and nothing happens. It turns out that all the hadrons—the protons, neutrons, and their hundreds of cousins—are induced to decay via the weak force, with the free proton being the only apparent exception.
The theory of the weak force was gradually generalized and, in constant confrontation with new data, evolved to a quantum field theory of the weak force. A new breed of theorists emerging mostly in American universities helped to mold the theory: Feynman, Gell-Mann, Lee, Yang, Schwinger Robert Marshak, and many others. (I keep having this nightmare in which all the theorists I've failed to cite meet in a suburb of Teheran and offer a reward of prompt admission to Theory Heaven for anyone who instantly and totally renormalizes Lederman.)
SLIGHTLY BROKEN SYMMETRY, OR WHY WE ARE ALL HERE
A crucial property of the weak force is parity violation. All the other forces respect this symmetry; that one force can violate it was a shock. Another deep symmetry, one that compares the world to the anti-world, had been demonstrated to fail by the same experiments that showed P (parity) violation. This second symmetry was called C, for charge conjugation. The failure of C symmetry also occurred only with the weak force. Before C violation was demonstrated, it was thought that a world in which all objects are made of antimatter would obey the same laws of physics as the regular old matter world. No, said the data. The weak force doesn't respect that symmetry.
What were the theorists to do? They quickly retreated to a new symmetry: CP symmetry. This says that two physical systems are essentially identical if one is related to the other by simultaneously reflecting all objects in a mirror (P) and also changing all particles to antiparticles (C). CP symmetry, the theorists said, is a much deeper symmetry. Even though nature does not respect C and P separately, simultaneous CP symmetry must endure. It did until 1964 when Val Fitch and James Cronin, two Princeton experimenters studying neutral kaons (a particle my group discovered in Brookhaven experiments in 1956–1958), came upon clear and compelling data that CP symmetry was, in fact, not perfect.
Not perfect? The theorists sulked, but the artist in all of us rejoiced. Artists and architects love to tweak us with canvases or architectural structures that are almost, but not exactly, symmetrical. The asymmetric towers in the otherwise symmetric cathedral at Chartres is a good example. The CP violation effect was small—a few events out of a thousand—but clear, and theorists were back to square one.
I mention CP violation for three reasons. First, it is a good example of what became recognized, in the other forces, as "slightly broken symmetry." If we believe in the intrinsic symmetry of nature, something, some physical agency, must enter to break that symmetry. A closely related agency doesn't actually destroy the symmetry, it just hides it so that nature appears to be asymmetrical. The God Particle is such a disguiser of symmetry. We will return to it in Chapter 8. The second reason for mentioning CP violation is that in the 1990s understanding this concept is one of the most pressing needs for clearing up the problems in our standard model.
The final reason, and the element that brought the Fitch-Cronin experiment to the respectful attention of the Royal Swedish Academy of Science, is that when applied to cosmological models of the evolution of the universe, CP violation explained a puzzle that had plagued astrophysicists for fifty years. Before 1957 a large number of experiments indicated perfect symmetry between matter and antimatter. If matter and antimatter are so symmetric, why is our planet, our solar system, our galaxy, and, evidence indicates, all other galaxies devoid of antimatter? And how could an experiment carried out on Long Island in 1965 explain it all?
Models indicated that as the universe cooled after th
e Big Bang, all the matter and antimatter annihilated, leaving essentially pure radiation, ultimately too cool—too low in energy—to create matter. But matter, that's us! Why are we here? The Fitch-Cronin experiment shows the way out. The symmetry isn't perfect. A slight excess of matter over antimatter (for every 100 million quark-antiquark pairs there is one extra quark) is a result of the slightly broken CP symmetry, and this tiny excess accounts for all the matter in the presently observed universe, including us. Thanks Fitch, thanks Cronin. Splendid fellows.
TRAPPING THE LITTLE NEUTRAL ONE
Much of the detailed information on the weak force was provided by neutrino beams, and herein lies another story. Pauli's 1930 hypothesis—that a small, neutral particle exists that feels only the weak force—was tested in many ways from 1930 to 1960. Precise measurements of an increasingly large number of weakly decaying nuclei and particles tended to confirm the hypothesis that a little neutral thing was escaping from the reaction carrying away energy and momentum. This was a convenient way to understand decay reactions, but could we actually detect neutrinos?
This was no easy task. Neutrinos float through vast thicknesses of matter unscathed because they obey only the weak force, whose short range reduces the probability of a collision enormously. It was estimated that to ensure a collision of a neutrino with matter would require a target of lead one light-year thick! Quite an expensive experiment. However; if we use a very large number of neutrinos, the required thickness to see a collision every once in a while is correspondingly reduced. In the mid-1950s, nuclear reactors were used as intense sources of neutrinos (so much radioactivity!), to which a huge vat of cadmium dichloride (cheaper than a light-year's worth of lead) was exposed. With so many neutrinos (actually, antineutrinos, which is mostly what you get from reactors), it was inevitable that some of them would strike protons, causing inverse beta decay; that is, a positron and a neutron were released. The positron, in its wandering, would eventually find an electron and annihilate into two oppositely moving photons. These fly outward into dry cleaning fluid, which flashes when struck by the photons. The detection of a neutron and a pair of photons represented the first experimental evidence of the neutrino, about thirty-five years after Pauli thought up the critter.
The God Particle: If the Universe Is the Answer, What Is the Question? Page 36
