This, much simplified, is the basic concept behind unified field theory, and it is no mere intellectual exercise: Wigner, for one, found that by applying relativistic invariances to quantum mechanics he could organize all known subatomic particles into symmetry groups, classifying them according to their rest mass and their spin. An even more dramatic example of the pathfinding power of symmetry came in 1928, when Dirac derived the relativistic quantum equation of the electron, preserving the symmetries of both special relativity and quantum mechanics, and found that his equation mandated the existence of a positively charged electron. This was the first intimation that there might be such a thing as antimatter, particles with mass and spin identical to those of ordinary matter, but with opposite electrical charge.
Dirac was mathematical to the marrow, an epitome of Karl Friedrich Gauss’s dictum that whenever possible one should count; when out on a stroll with a colleague who remarked that there were fourteen ducks on the lake, Dirac replied, “Fifteen. I saw one going under the water.”8 He was also empirical to a fault; when a newcomer to Cambridge High Table ventured to say, as a conversational icebreaker, “It is very windy, Professor,” Dirac got up, went to the door, opened it, looked out, returned, took his seat, thought for a moment, then replied, “Yes.”9 Yet the concept of antimatter seemed so outlandish that even Dirac initially denied the verdict of his own equations. At first he tried to portray his new particles as but the familiar protons, but this avenue of escape was soon closed off by the German mathematician Herman Weyl (himself the author of a classic treatise on symmetry), who demonstrated that unless Dirac’s theory of the electron was nonsense, there had to be such a thing as antimatter. The question was resolved in symmetry’s favor in 1932, when the antielectrons (called “positrons”) predicted by the Dirac equation were discovered, by Carl Anderson, in a cloud chamber at Caltech. Before the decade was out Dirac and Anderson had won the Nobel Prize.
Just as symmetry can be employed to discern the identity of previously unknown particles, it can guide the search for unknown fields. The foremost application of this realization came with the development of “gauge” field theory, a revolution that has been classed, along with relativity and quantum physics, as the third great theoretical advance in twentieth-century physics.
The first gauge field theory beyond electromagnetism (the term “gauge” has a complex history, and is in any case a misnomer) was invented by Yang and his colleague Robert Mills at Brookhaven National Laboratory in 1954. Yang, a mathematician’s son, grew up in China amid the destitution of the war; he studied statistical and quantum mechanics in K’un-ming, taking notes in unheated lecture halls and subsisting on a bare minimum of food, and once had to dig his schoolbooks out of the ruins of the house his family had been renting when it was demolished by a Japanese bomb. (His family, ensheltered, survived.) While still a student, Yang became fascinated with what is called the gauge invariance of the electromagnetic field—the implicit symmetry from which Einstein had deduced that the velocity of light is the same for all observers.
Yang hoped to identify a similar invariance for the strong nuclear force. A clue that such a thing was possible could be found in the fact that the strong force treats protons and neutrons identically, even though the proton has an electrical charge and the neutron does not—which is to say that the strong force is invariant under transformations of electrical charge. This symmetry, first noted in the 1930s, had been encoded as a quantum number called isospin. It was in this guise that the two particles came to be thought of as but varieties of a single kind of particle, the nucleon, their differences attributable to their differing isospin.
Yang tried for years to generalize gauge invariance by writing a suitably symmetrical equation for the strong force, and each time he failed. Yet the idea would not let him alone. His line of thought, though rather technical, can be depicted in terms of the relationship between a global symmetry, meaning a symmetry that applies everywhere, with a local symmetry, one that applies to a given system at a given place and time. Yang’s question was this: How does the local system “know” about the global symmetry? How, in other words, is a global symmetry communicated to a local system?
To draw a simile from Yang’s childhood, we could say in economic terms that the poverty imposed upon Yang’s family and their neighbors by the war was a local invariance, embedded in the global invariance of the overall poverty of wartime China. Here the means of communication was the medium of exchange—money, or barter—that propagated the global conditions locally: Yang’s father’s life savings were wiped out by national wartime inflation because they were in a medium (currency in a bank account) that conveyed the general devaluation of the Chinese yuan. What, wondered Yang, might be the means of exchange in physics, the agency that connects local invariances with the wider invariances that form the skeleton of universal natural law?
The answer, Yang ultimately realized, was that the medium that communicates between local and global invariances is nothing other than force itself. This was a wholly new idea. Prior to Yang and Mills, force had been viewed as a given. Yang-Mills gauge theory gave force a raison d’être. It proposed that symmetry is the overweening principle, and that force is but nature’s way of expressing global symmetries in local situations—that force, to speak ideologically, exists in order to maintain the invariances by virtue of which there is such a thing as natural law.
The paper that Yang and Mills originally wrote was limited and flawed and incomplete, and it did not yet fit the experimental results. But in time its problems were cleared up, and its potential beauty and power began to be recognized. Yang-Mills gauge theory offered a new approach to the practice of theoretical physics: What one could now do was to first identify an invariance, the signal of a symmetry; then construct, mathematically, a gauge field capable of maintaining that invariance locally; then derive the characteristics of the particles that would convey such a field; then go and see (or urge the experimenters to go see) whether any such particles actually exist in nature. Viewed from this perspective, Einstein’s photons, the carriers of the electromagnetic force, are gauge particles, messengers of symmetry. So are the gravitons thought to be the carriers of gravitation. But what were the gauge particles of the strong and weak forces?
That question was taken up by one of the first to appreciate the beauty of the Yang-Mills approach, the American physicist Murray Gell-Mann. Some smart scientists (Dirac, Bohr, and the elder Einstein) are modest in demeanor. Others are brash. (Wolfgang Pauli disrupted Yang’s first explication of gauge invariance so persistently that J. Robert Oppenheimer finally had to tell him to shut up and sit down.) Gell-Mann was very smart—he spoke more languages than his friends could keep count of, displayed an expert knowledge of everything from botany to Caucasian carpet-weaving, and was said, with forgivable exaggeration, to rank as a great physicist not because he had any particular aptitude for physics but simply because he deigned to include physics among his many interests—and very brash. From the popular assertion that he was the smartest man in the world Gell-Mann was not predisposed to demur; when he won the Nobel Prize he remarked, echoing Newton’s comment that if he had seen farther than others it was because he stood on the shoulders of giants, that if he, Gell-Mann, could see farther than others it was because he was surrounded by dwarfs. An intellectual wrestler who could stoop to bullying, he corrected strangers on the spellings and pronunciations of their own names, while himself pronouncing foreign terms with such an impeccable accent that he sometimes could not make himself understood.* If such habits tended to build a moat around Gell-Mann, perhaps, like Newton, he needed a moat.
Of Gell-Mann’s scientific acumen and his love for nature there was no doubt, and when he put gauge field theory to work on the strong force the result was a symphony. Combining the Yang-Mills concept with group theory—a group is an ensemble of mathematical entities linked by a symmetry—Gell-Mann found a symmetrical arrangement of hadrons (particles that respond to th
e strong force) that he called “the eightfold way.” (The Israeli physicist Yuval Ne’eman independently reached the same conclusion.) The eightfold way achieved experimental verification when a previously undetected baryon the existence of which it predicted, the omega minus, was subsequently identified in a bubble chamber experiment at Brookhaven.
The symmetry group involved was designated “SU(3)”—“SU” meaning “special unitary” group, one of a set of symmetry groups identified by the French mathematician Elie-Joseph Cartan, and “(3)” meaning that the symmetry operates in three-dimensional internal space.* Investigating SU(3) further, Gell-Mann arrived at the idea that protons and neutrons are each composed of triplets of still smaller particles: Thus did quark theory spring from symmetry’s forehead.
The Yang-Mills equations indicated that gluons, the gauge particles that convey the strong force and so bind the quarks together inside nucleons, ought to be massless, as are photons and gravitons. Why, then, does the strong force make itself felt only over a short range, when light and gravitation are infinite in range? The answer, according to quantum chromodynamics, the new theory of the strong force, is that the strong force increases in strength when the quarks it imprisons try to move apart, rather than growing weaker as do electromagnetism and gravity. This was the origin of the concept of quark confinement and the gluon lattice that we touched on in the last chapter. Quantum chromodynamics illuminated the workings of the weak force as well: The previously mysterious phenomenon of radioactive beta decay could now be interpreted as the conversion of a “down” quark to an “up” quark, changing the neutron, which is made of two down quarks and one up quark, into a proton, which consists of two up and one down quark.
Symmetry, as we shall see, was to play an undiminished role in the further development of quantum field theory, even pointing the way toward a unified, “supersymmetric” theory that might gather all particles and fields under the umbrella of a single set of equations. “Nature,” as Yang wrote,
seems to take advantage of the simple mathematical representation of the symmetry laws. The intrinsic elegance and beautiful perfection of the mathematical reasoning involved and the complexity and depth of the physical consequences are great sources of encouragement to physicists. One learns to hope that nature possesses an order that one may aspire to comprehend.10
But by no means are all nature’s symmetries manifest. We live in an imperfect world, in which many of the symmetries that show up in the equations are found to be broken. Yang himself, working with Tsung Dao Lee, identified a discrete asymmetry in the weak force called parity violation. In 1956, Yang and Lee predicted, on theoretical grounds, that the spin of particles emerging from beta decay events would show a slight preference for one direction over another—i.e., that the weak force does not function symmetrically with regard to spin. Experiments conducted by Chien-Shiung Wu and others promptly confirmed their prediction, bringing the Nobel Prize the following year to Lee and Yang (though not, for some reason, to Wu) and turning renewed attention to the question of why nature is symmetric in some ways but asymmetric in others.
It was by investigating asymmetries that Steven Weinberg, Sheldon Glashow, and Abdus Salam formulated the unified electroweak theory that revealed a kinship between the weak and electromagnetic forces. Weinberg was intrigued by the fact that nature is replete with broken symmetries—asymmetrical relationships that have arisen from the functioning of symmetrical natural laws. The question, Weinberg observed, was how “symmetrical problems can have asymmetrical solutions.”11 Suppose that you take a handful of sharpened pencils, gather them into a perfectly cylindrical bundle, balance them on their points, and let go. For a moment, the arrangement remains rotationally symmetrical: Looking down from above you can walk around it, and all you will see is a circle made of the pencil erasers. But you’d better look quickly, for the symmetry is unstable: In an instant the pencils will fall, and the result will be an asymmetrical tangle like that encountered at the outset of a game of pickup sticks. In this simile, the jumble of fallen pencils is the universe today, and the original bundle is the symmetric state in which the universe is thought to have begun. The physicist’s task is to identify the deeper symmetry hidden beneath the extant broken symmetry. This, indeed, could be the key to writing unified theories of ample scope. “Nothing in physics,” Weinberg wrote in 1977, “seems so hopeful to me as the idea that it is possible for a theory to have a very high degree of symmetry which is hidden from us in ordinary life.”12
The tangled world lines that led Weinberg, Glashow, and Salam to the triumph of the electroweak unified theory were themselves redolent with the tensions and broken symmetries that animate human affairs. Born in the Bronx in 1933, Weinberg attended the Bronx High School of Science, where his close friend was Shelly Glashow. The two went on together to Cornell, then parted when Weinberg went to Princeton and Glashow to Harvard. Aside from their common fascination with science and science fiction they were a study in oppositions, and the differences in their personalities were only magnified once they entered the adult world of theoretical physics. Weinberg was intensely curious, rigorously studious, and compulsively hardworking. He set himself to learning whole branches of physics, less because he saw in them any immediate application to the questions that most concerned him than because he felt that a physicist ought to know these things: Though primarily a particle physicist rather than a relativist, he once wrote a textbook on relativity, in part, he said, to help bridge the gap between general relativity and the theory of elementary particles. His self-discipline extended beyond physics: When he joined the faculty at the University of Texas and found that the furnished house he had rented in Austin came with a study full of books on the American Civil War, he simply read his way through them, emerging as something of an expert on the Civil War. Though painfully individualistic, he cultivated the art of communication, becoming an eloquent public speaker and the author of a best-selling popular science book, The First Three Minutes.
Glashow, on the other hand, was naturally gregarious, easygoing to the point of indolence, and a stranger to the rigors of study. If Weinberg excelled at Cornell, missing Phi Beta Kappa only because he failed physical education, Glashow barely scraped by; in accepting the Nobel Prize, he thanked “my high school friends Gary Feinberg and Steven Weinberg for making me learn too much too soon of what I might otherwise have never learned at all.”13 He spoke indistinctly, in fragmentary sentences built on an unimposing vocabulary, and smiled perpetually, as if contemplating a private joke. Physics seemed to come to him as naturally and effortlessly as a dream.
Glashow studied at Harvard under the elegant and venturesome Julian Schwinger, called “the Mozart of physics” both for his brilliance and for the uncaring way he wore it. A child prodigy, Schwinger as an adult remained impatient with the fragmented state of quantum physics, and he implored his students and colleagues never to rest until they had arrived at unified theories capable of describing a far wider scope of phenomena through fewer precepts. Even in the 1950s, when the quantum electrodynamics he had helped to create was the rising sun of quantum field theory, Schwinger was writing that
a full understanding … can exist only when the theory of elementary particles has come to a stage of perfection that is presently unimaginable…. No final solution can be anticipated until physical science has met the heroic challenge to comprehend the structure of the sub-microscopic world.14
Glashow absorbed from Schwinger the conviction that the weak and electromagnetic interactions ought to be explicable by means of a single, unified gauge theory.* “A fully acceptable theory” of the two forces, Glashow wrote in his graduate thesis, echoing Schwinger, “… may only be achieved if they are treated together.”15
His thesis completed, Glashow went to Copenhagen to study with Niels Bohr. There he pieced together a unified Yang-Mills theory of the weak and electromagnetic forces. The glaring problem with this theory, as would be the case for Weinberg and others lat
er, was that its equations produced nonsensical infinities. Glashow tried to solve this problem by “renormalizing” his equations. Renormalization is a mathematical procedure that involves canceling the unwanted infinities by introducing other infinities; it smacks of mathematical trickery, but when adroitly manipulated can produce the desired, finite results. Among other credentials, renormalization had played an essential role in the perfection of quantum electrodynamics—which had made some of the most precise predictions ever confirmed by experiment, and had become a model of what a quantum field theory ought to be.* By late 1958 Glashow was satisfied that he had renormalized his unified theory, and he presented a paper saying so the following spring, in London.
In the audience was the Pakistani physicist Abdus Salam, seven years Glashow’s senior but seemingly older, a dignified, composed man in whom strong intellectual currents flowed beneath an exterior of oceanic calm. Born in 1926, the son of a high school English teacher who had prayed nightly to Allah for a son of intellectual brilliance, Salam at age fourteen scored the highest marks in the history of the Punjab University matriculation examination, a feat that brought cheering throngs out to greet him when he bicycled home to the little town of Jhang in what is now Pakistan. While working for his Ph.D., Salam managed to prove the renormalizability of quantum electrodynamics as applied to mesons, an accomplishment that garnered him a reputation as an expert on renormalization. Since then, he and a colleague, John Ward, had devoted considerable effort to the renormalization of a unified theory of the electromagnetic and weak interactions, without success. So when Glashow claimed that he had solved the problem, he got Salam’s attention.
Coming of Age in the Milky Way Page 32
