Coming of Age in the Milky Way - Timothy Ferris (2003)

Part III. CREATION

Chapter 16. RUMORS OF PERFECTION

Spirit of BEAUTY, that dost consecrate
   With thine own hues all thou dost shine
                upon
       Of human thought or form, where art
                thou gone?
   Why dost thou pass away, and leave our
                state,
This dim vast vale of tears, vacant and
                desolate?

—Shelley, “Hymn to Intellectual
Beauty”

The Universe is built on a plan the profound symmetry of which is somehow present in the inner structure of our intellect.

—Paul Valéry

           Theoretical physicists, like artists (one is tempted to say, like other artists) are guided in their work by aesthetic as well as rational concerns. “To make any science, something else than pure logic is necessary,” wrote Poincaré, who identified this additional element as intuition, involving “the feeling of mathematical beauty, of the harmony of numbers and forms and of geometric elegance.”1 Heisenberg spoke of “the simplicity and beauty of the mathematical schemes which nature presents us. You must have felt this too,” he told Einstein, “the almost frightening simplicity and wholeness of the relationship which nature suddenly spreads out before us.”2 Paul Dirac, the English theoretical physicist whose relativistic, quantum mechanical description of the electron ranks with the masterpieces of Einstein and Bohr, went so far as to maintain that “it is more important to have beauty in one’s equations than to have them fit experiment.”3*

Aesthetics are notoriously subjective, and the statement that physicists seek beauty in their theories is meaningful only if we can define beauty. Fortunately this can be done, to some extent, for scientific aesthetics are illuminated by the central sun of symmetry.

Symmetry is a venerable and all but bottomless concept, with many implications in both science and art; long after the Chinese-American physicist Chen Ning Yang had won a Nobel Prize for his work in developing a symmetry theory of fields, he was still pointing out that “we do not yet comprehend the full scope of the concept of symmetry” (Yang’s italics).4 In Greek, the word means “the same measure” (sym, meaning “together,” as in symphony, a bringing together of sounds, and metron, for “measurement”); its etymology thus informs us that symmetry involves the repetition of a measurable quantity. But by symmetry the Greeks also meant “due proportion,” suggesting that the repetition involved ought to be harmonious and pleasing; this suggests that a symmetrical relationship is to be judged by a higher aesthetic criterion, an idea to which I will return at the end of this chapter. In twentieth-century science, however, the former aspect of the old definition is emphasized; symmetry is said to exist when a measurable quantity remains invariant (meaning unchanging) under a transformation (meaning an alteration). Because this definition is the most relevant to the subject at hand, I will employ it in discussing all aspects of symmetry, including those that were in general use before there was such a thing as science.

Most of us were first introduced to symmetry through its visual manifestations in geometry and art. When we say, for instance, that a sphere is rotationally symmetrical, we indicate that it possesses a characteristic—in this case, its circular silhouette—that remains invariant throughout the transformation introduced by rotating it. The sphere can be rotated on any axis and to any degree without changing its silhouette, which makes it more symmetrical than, say, a cylinder, which enjoys a similar symmetry only when rotated on its long axis; if rotated on its short axis, the cylinder shrinks to a circle. Translational symmetries, like those found in palm fronds and building facades like that of the Doge’s Palace in Venice, occur when a shape remains invariant when moved (“translated”) a given distance along one axis. (See previous page.)

Symmetries are commonplace in sculpture, beginning with the human nude, which is (approximately) bilaterally symmetrical when viewed from the front or back, and in architecture, as in the cross-shaped floor plans of medieval cathedrals, and they turn up elsewhere in everything from weaving to square dancing. There are many symmetries in music. Bach, in the following passage from the Toccata and Fugue in E Minor, moves little tentlike trios of notes up and down the staff. Except for the occasional difference in a note here and there, the construct is translationally symmetrical: If we were to peel off any one trio and lay it over another, it would fit perfectly:

The first two bars of Claude Debussy’s Deux Arabesques are bilaterally symmetrical both within themselves and relative to each other: The sheet music can be folded vertically at the bar, or midway within each bar, and the notes will still fit atop one another:

Beneath these visible and audible manifestations of symmetry lie deeper mathematical invariances. The spiral patterns found inside the chambered nautilus and on the faces of sunflowers, for instance, are approximated by the Fibonacci series, an arithmetic operation in which each succeeding unit is equal to the total of the preceding two (1, 1, 2, 3, 5, 8 …). The ratio created by dividing any number in such a series by the number that follows it approaches the value 0.618* (see page 306). This, not incidentally, is the formula of the “golden section,” a geometrical proportion that shows up in the Parthenon, the Mona Lisa, and Botticelli’s The Birth of Venus, and is the basis of the octave employed in Western music since the time of Bach. All the fecund diversity of this particular symmetry, expressed in myriad ways from seashells and pine cones to the Well-Tempered Clavier, therefore derives from a single invariance, that of the Fibonacci series. The realization that one abstract symmetry could have such diverse and fruitful manifestations occasioned delight among Renaissance scholars, who cited it as evidence of the efficacy of mathematics and of the subtlety of God’s design. Yet it was only the beginning. Many other abstract symmetries have since been identified in nature—some intact and some “broken,” or flawed—and their effects appear to extend to the very bedrock foundations of matter and energy.

The Fibonacci series, represented in the abstract (above) is embodied in the architecture of the chambered nautilus (below).

Which brings us back to science. When mathematicians in the early twentieth century began to look more closely at the concept of symmetry, they realized that the laws that science finds in nature are expressions of invariances—and may, therefore, be based on symmetries. This first became evident with regard to the conservation laws: The laws of thermodynamics, for instance, identify a quantity (energy) that remains invariant under a transformation (work). The German mathematician Emmy Noether demonstrated in 1918 that every conservation law implies the existence of a symmetry. The same evidently is true of the other laws as well. As the Hungarian physicist Eugene Wigner put it, “Laws of nature could not exist without principles of invariance,”6 and invariance, keep in mind, is the signature of symmetry.

If natural laws express symmetries, then one ought to be able to search for previously unknown laws by looking for symmetrical relationships (invariances) in nature. Einstein absorbed this lesson in his bones, and employed symmetry as a lamp to guide his way in the creation of new theories. In special relativity (which, we recall, he originally called “invariance theory”), he employed the Lorentz transformations to maintain the invariance of Maxwell’s field equations for observers in motion; in the general theory of relativity he did much the same thing for observers in strong gravitational fields. As his friend Wigner remarked in 1949, speaking at a Princeton celebration in Einstein’s honor, “It is now natural for us to try to derive the laws of nature and to test their validity by means of the laws of invariance, rather than to derive the laws of invariance from what we believe to be the laws of nature.”7

If the symmetry concept was powerful in relativity, it proved to be even more so when applied to the quantum physics of particles and fields. We can appreciate why this would be the case if we consider that subatomic particles of a given variety are indistinguishable from one another. All protons are identical. So are all neutrons and electrons. The same is true of fields; if we have two electromagnetic or gravitational fields with the same quantum numbers, and a trickster switches them while our backs are turned, we can never tell that we have been tricked, for the fields are identical. Inasmuch as identity is a form of invariance, we can, therefore, choose to regard the individual electron or photon as representative of a symmetry group that embraces all its fellow particles of the same species. Moreover, we can look for larger symmetries that might link the various groups involved—revealing, say, a previously undiscerned invariance linking photons and electrons.

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 the 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 later, 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.

“My God! This young boy was claiming that this theory was renormalizable!” Salam recalled, in a 1984 interview with Robert Crease and Charles Mann.

It cut me to the quick! Both of us considered ourselves the experts on renormalizability, wrestling for months with the problem—and here was this slip of a boy who claimed he had renormalized the whole thing! Naturally, I wanted to show he was wrong—which he was. He was completely wrong. As a consequence, I never read anything else by Glashow, which of course turned out to be a mistake.16

Glashow, however, was not easily discouraged, and despite any embarrassment he may have felt at having mistakenly claimed to have solved the renormalization problem, he persisted in searching for links between electromagnetism and the weak force. In this effort he was encouraged by Gell-Mann if by few others. (“What you’re doing is good,” Gell-Mann recalled having told Glashow, over a seafood lunch in Paris, “but people will be very stupid about it.”)17 In 1961, Glashow produced a paper, “Partial-Symmetries of Weak Interactions,”18 that called attention to “remarkable parallels” between electromagnetism and the weak force, depicted them as linked by a broken symmetry, and predicted the existence of the W and Z force-carrying particles—later known as the W+, W, and Z°. These hitherto undetected particles were to play an important role in experimental tests of the unified electroweak theory, but Glashow was unable to predict their masses, which left the experimenters with nothing to go on. Glashow and Gell-Mann then wrote a paper demonstrating that all the symmetries evinced in what are known as noncommutative or Cartan groups correspond to Yang-Mills gauge fields. Their efforts to identify a gauge symmetry group that would embrace both the strong force and Glashow’s protounified electroweak forces, however, came to naught. Glashow, discouraged, set aside his work on electroweak unified theory.

Meanwhile, in 1959, Salam and Ward had, like Glashow, arrived at insights about links between the weak and electromagnetic forces, but had, like Glashow, met with an indifferent response from the scientific community, and likewise grew discouraged. “A broken symmetry breaks your heart,” said Salam.19

The situation then brightened, thanks to new insights into the mechanism of spontaneous symmetry-breaking first presented by Yoichiro Nambu, Jeffrey Goldstone, and others and culminating in work published by Peter Higgs in 1964 and 1966. This research demonstrated that symmetry-breaking events could create new kinds of force-carrying particles, some of them massive. (The particles envisioned by Yang-Mills gauge theory had been massless.) If the particles that carry the weak and electromagnetic forces were related by a broken symmetry, these new tools might make it possible to estimate the masses of the W and Z particles characteristic of the unified, more symmetrical force from which the two forces were thought to have arisen.

Weinberg in particular was captivated by the concept of spontaneous symmetry breaking. “I fell in love with this idea,” he said in his Nobel Prize address in 1979, “but as often happens with love affairs, at first I was rather confused about its implications.”20 Initially he tried to apply the new symmetry-breaking tools to the strong force. This worked well insofar as global symmetries were concerned—specifically, Weinberg found that he was able to make successful predictions of the scattering of pi mesons—but when he sought to extend the technique to local symmetries, the results were disappointing. “The theory as it was working out was making nonsensical predictions that didn’t look like the strong interactions at all,” Weinberg recalled in a 1985 interview. “I could fiddle with it and make it come out right, but then it looked too ugly to bear.”21 The worst problem was that the particle masses predicted by the breaking of the symmetry group Weinberg was contemplating did not match those of the particles involved in the strong interactions.

But then, in Weinberg’s recollection, “at some point in the fall of 1967, I think while driving to my office at MIT, it occurred to me that I had been applying the right ideas to the wrong problem.”22 The particle descriptions that kept bobbing up out of his equations—one set massive, the other massless—resembled nothing in the strong force, but fit perfectly with the particles that carry the weak and electromagnetic forces. The massless particle was the photon, carrier of electromagnetism; the massive particles were the Ws and Zs. Moreover, Weinberg found, he could calculate the approximate masses of the Ws and Zs. Here, finally, was an electroweak theory that made a verifiable prediction. Salam independently reached a similar conclusion the following year—testimony, Weinberg said, to “the naturalness of the whole theory.”23

With that, the work that would win the 1979 Nobel Prize in physics was complete. Yet little heed was paid to it at first. Weinberg’s paper, the first complete statement of the electroweak theory, was cited not once in the scientific literature for four full years after it appeared. The main reason was that the theory had not yet been shown to be renormalizable. Once that was accomplished—in 1971, when its dolorous infinities were scotched in a heroic effort by the Dutch physicist Gerard’t Hooft—interest in the electroweak theory intensified, and the focus of attention turned to the question of testing the theory through experiment. This called upon those embodiments of big science, the particle accelerators.

Accelerators are to particle physics what telescopes and spectrographs are to astrophysics—both an exploratory tool for finding new things and a supreme court for testing existing theories. Their operating principle is based on Einstein’s E = mc2. One accelerates charged particles to nearly the speed of light by propelling them along an electromagnetic wavefront created by pulsing electromagnets, then smashes them into a target, creating tiny explosions of intense power. New particles condense from the tiny fireball, like raindrops precipitating in a storm cloud, and are recorded by surrounding detectors as they come reeling out. The original detectors were photographic plates; later these were replaced by electronic sensors coupled to computers.

Engaged in the race to test the electroweak theory were researchers at two of the world’s most powerful accelerators—CERN, the European center for nuclear research near Geneva, and Fermilab, named after the physicist Enrico Fermi, on the Illinois plains west of Chicago. Both are proton accelerators.* The protons come from a little bottle of hydrogen gas, small enough for a backpacker to carry, that contains a year’s supply of atoms. Computer-controlled valves release the gas in tiny puffs, each scantier than a baby’s sigh but each containing more protons than there are stars in the Milky Way galaxy. The gas enters the electrically charged cavity of what is called a Cockroft-Walton generator. The field strips the electrons away from the hydrogen atoms and sends the protons speeding down a tunnel and into a pipe the size of a garden hose that describes an enormous circle—three miles in circumference in the case of Fermilab. The protons are accelerated around the ring by pulses sent through surrounding electromagnets, while focusing magnets gather them to a beam thinner than a pencil lead. When they reach a velocity approaching that of light—at which point, thanks to special relativity effects, their mass has increased by some three hundred times—they are diverted from the ring and slammed into a stationary target inside a detector. Their tracks, subjected to yet another magnetic field in the detector, betray their charge and mass and thus their identity.

Though similar in design, the CERN and Fermilab accelerators exemplified rather different styles of doing big science. Fermilab, built under the direction of the American physicist and sculptor Robert Wilson, was conceived and executed as a work of art, an embodiment of the aesthetics of science. A Wilson sculpture, a looming set of steel arches titled “Broken Symmetry,” was erected at the main entrance. The accelerator tunnel, buried underground, was delineated, for purely aesthetic purposes, by an earthwork berm. Within the ring buffalo grazed; swans swam in the waters employed to cool the electromagnets. The administration building, a sweeping, convex tower, was set against the berm like a diamond on an engagement ring; Wilson modeled it on the proportions of Beauvais Cathedral in France. As he recalled his reasons for this decision:

I found a striking similarity between the tight community of cathedral builders and the community of accelerator builders. Both of them were daring innovators, both were fiercely competitive on national lines, but yet both were basically internationalists…. They recognized themselves as technically oriented; one of their slogans was Ars sine scientia nihil est!—art without science is nothing.24

Wilson defended the aesthetics of his creation—which, it should be added, was completed under budget—by drawing further parallels between art and science:

The way that science describes nature is based on aesthetic decisions. Physics is very close to art in the sense that when you examine nature on a small scale, you see a diversity in nature, you see symmetries in nature, you see forms in nature that are just utterly delightful. Eventually, in the way that one looks at sculpture or art, people will also begin to look at those great simple facts.25

CERN, for its part, looked about as aesthetically unified as a Bolshevik boiler factory. Its administration building, slapped together from prefabricated plastic panels and aluminum alloy window frames that bled pepper-gray corrosives in the rain, called to mind less Beauvais Cathedral than the public housing projects of suburban Gorky. Its laboratories were scattered across the landscape, as haphazardly as the debris from a trucking accident, on a plot of land that straddled the French-Swiss border outside Geneva. The prevailing style was late Tower of Babel, with scientists switching from French to German to English in mid-sentence while lunching at the laboratory cafeterias, one of which accepted only French currency and the other only Swiss. Yet for all its air of disorder, CERN worked every bit as well as Fermilab, and by the early 1970s was beginning to surpass it.

It was in this fevered context that the two laboratories raced to test the predictions of the electroweak theory. The new force-carrying particles postulated by the electroweak theory, the W+ W-, and Z°, were massive, meaning that it would take a lot of energy to bring them into existence in an accelerator collision. In 1971, no accelerator could yet summon up sufficient energy to create W and Z particles, if they existed. In the meantime, however, the experimentalists could hope to discern the existence of the Z indirectly, by identifying the effects, in accelerator collisions, of “neutral currents.” This consisted of searching through thousands of accelerator events for evidence of the few neutral current interactions in which the Z° would have played a role. Encouraged by Weinberg’s estimation that such events “are just on the edge of observability,” a team working under the experimental physicist Paul Musset at the CERN accelerator began staying up nights, examining thousands of photographs of particle interactions. After a year’s work they were finally rewarded when the myopic Musset, who scrutinized the particle tracks with his nose almost touching the print, discerned a kink in the recorded path of a particle that gave away its identity as a pion rather than a muon, indicating that it had emerged from a neutral current reaction. Salam learned of the result shortly after arriving at Aix-en-Provence, where he was to attend a physics conference. He was lugging his suitcase to a student hostel near the train station when a car stopped next to him. Musset looked out and said, “Are you Salam?” Salam said yes. “Get into the car,” Musset said. “I have news for you. We have found neutral currents.”26

This was welcome news to Salam, Glashow, and Weinberg, but it nevertheless fell short of fully vindicating the electroweak theory, for other theories also predicted the existence of neutral currents. The Weinberg-Salam theory surpassed its predecessors in predicting the mass of the carriers of the electroweak force—about 80 GeV for the Ws and 90 GeV for the Z. (A GeV is one billion electron volts; in this context, it is convenient to express mass in terms of energy.) The Ws and Zs were known collectively as intermediate vector bosons. To produce enough intermediate vector bosons to make their detection likely would require a particle accelerator with a minimum energy of some 500 to 1,000 GeV.

Neither accelerator could reach this level, but both were hurriedly being souped up to approach it, by means of a daring new technique involving the collision of protons, not with a stationary target, but with an oncoming stream of antiprotons. The universe, so far as we can tell, contains only trace amounts of antimatter—this in itself is one of nature’s more intriguing broken symmetries —but antimatter can be created in accelerator collisions, and by the 1970s accelerator engineers were beginning to talk of collecting the antiprotons they created and then colliding them with protons coming the other way. Since matter and antimatter particles annihilate each other when they meet, the result would be to greatly boost the effective power of the accelerator.

Fermilab approached the problem methodically. They would first install new magnets to increase the power of the accelerator to 1,000 GeV (equal to one teraelectron volt, or one TeV), and only thereafter take on the more hazardous business of trying to make and store antimatter. CERN proceeded in a more intrepid fashion, going for a matter-antimatter collider right away. Wilson, with his customary gentility, wished them well: “May they reach meaningful luminosity and may they find the elusive intermediate boson,” he wrote. “We will exult with them if they do.”27 CERN officials, with equal courtliness, described the Fermilab plan as “a project of great vision being attacked with courage and enthusiasm.”28 But behind the pleasantries raged a fierce competition between rival teams of the world’s brightest and most egocentric scientists and engineers.

Of these, few were brighter—and none more egocentric—than Carlo Rubbia, the driving force behind the CERN effort. Born in northern Italy in 1934 of Austrian parents, Rubbia was by nature an internationalist (“I have an accent in every language,” he said) who felt at home cajoling and browbeating the scores of scientists who made up his enormous research teams, among them Italian, French, English, German, and Chinese researchers, a Finn, a Welshman, and a Sicilian. A driven man, Rubbia traveled ceaselessly, flying from CERN to Harvard to Berkeley to Fermilab to Rome so incessantly that friends who monitored his progress calculated that he had a lifetime average velocity of over forty miles per hour. (“Ah,” he said, settling into his seat one morning, “my first flight of the day!”) Massive and energetic and constantly in motion, he resembled nothing so much as a human proton: Like Rutherford, who told his tailor, “Every year I grow in girth, and in mentality,” Rubbia ballooned in size until, by 1984, he was boasting that his form now approached the perfection of a Platonic sphere.

Rubbia’s hopes of winning a Nobel Prize rested on a conception concocted by an austere CERN engineer named Simon van der Meer. Van der Meer was convinced that one could make antiprotons (albeit at a rate of only one hundred-billionth of a gram of them per day) and keep them in storage until enough had accumulated to collide them with protons in significant numbers. Storing anti-matter would be a tricky business, akin to the old conundrum of how to bottle a universal solvent: If an antiproton made contact with a particle of ordinary matter, both would instantly annihilate. Van der Meer proposed to handle the problem by constructing an antiproton accumulator, a small ring in which the antiprotons could be kept circling for days, suspended in a vacuum in an electromagnetic field. To keep the antiprotons concentrated in tight, secure bundles, Van der Meer proposed a technique called stochastic cooling—stochastic meaning statistical, and cooling meaning reducing random motions among the particles. As little clumps of antiprotons whirled around the storage ring, sensors would detect the drift of those that strayed, and computers would then send a correcting message across the ring to adjust the magnets on the opposite side to correct for the drift. Since the antiprotons were moving at close to the speed of light, the computation would have to be done very quickly, whereupon the message would be sent speeding across the diameter of the storage ring just in time to configure the magnets before the antiproton bundle arrived via the longer, roundabout route. Once a sufficient supply of antiprotons had been collected and concentrated, they could be released into the main ring, accelerated to terminal velocity, and steered into a headlong collision with bunches of protons coming the other way.*

An accelerator speeds subatomic particles—in this case, protons—around a ring, then diverts them to a target inside a detector.

The building of a proton-antiproton collider fed via stochastic cooling represented one of the most audacious endeavors in an age of high technology. Van der Meer himself considered the idea so radical that he originally did not even try to publish it. Many accelerator experts predicted that stochastic cooling would not work, and that if it did, the matter and antimatter bundles would blow each other up the first time they collided, rather than producing the repeated collisions—some fifty thousand of them per second—that would be required to flush out the intermediate vector bosons. (The accelerator would only just get into the energy range of the intermediate vector bosons, and the physicists had to rely upon quantum probabilities to deliver up a detection event.) There were snickers in the audience when Rubbia first proposed constructing an antimatter collider; when he brought up the idea at Fermilab he was invited to leave; and when he and two colleagues submitted a paper on it, the editors of the Physical Review Letters, a leading journal, refused to publish it. But Rubbia kept pushing, despite the high stakes—one hundred million dollars to build the antimatter accumulator and to modify the accelerator, plus another thirty million dollars to build the detectors—and he made it a habit to project an air of robust assurance, keeping his reservations to himself. “Let’s be serious,” he said later. “If we had spelled out these doubts before the project was launched, nobody would have given us the money for it. … I was scared stiff the beam wouldn’t work.”29

A collider sends particles of matter speeding in one direction and particles of antimatter in the opposite direction, smashing them into one another at detector sites located where the beams intersect.

In the end, CERN took the gamble. For three years, while the antiproton ring was being constructed, Rubbia busied himself building the detector, an instrument with the bulk and weight of a Wall Street bank vault, ten meters long by five meters wide and weighing two thousand tons, buried underground and straddling the accelerator tunnel. He worked himself to new depths of exhaustion and twice was nearly electrocuted, but he seldom faltered and he kept learning as he went along. “Look at this place,” he said with pride, once the giant detector was completed. “I know the function of every switch in here.”30

Tests of the proton-antiproton collider began in 1982, and to nearly everybody’s astonishment, the thing worked. The protons and antiprotons collided as promised, producing tiny, intense bursts of energy, and subatomic particles came reeling out of the explosions, peppering the onionskin layers of the detector. Out of a billion such interactions emerged five that held clear evidence of the existence of the elusive W particle. On January 20, 1983, Rubbia stood in the CERN auditorium, in front of a long blackboard bleached with the technicolor palimpsests of thousands of rubbed-out equations, and told his colleagues that the W particle had been detected and the electroweak theory thus confirmed. Detection of the Z soon followed, and the masses of both bosons matched the predictions of the electroweak unified theory. Weinberg, Glashow, and Salam had been right; we live in a universe of broken symmetries, where at least two of the fundamental forces of nature, electromagnetism and the weak nuclear force, have diverged from a single, more symmetrical parent.

The battle of the big accelerators continued in the years that followed. Enormous boring machines toiled in Rembrandtesque gloom beneath the French countryside, digging a tunnel seventeen miles in circumference for a CERN accelerator that would collide electrons with their antimatter opposite numbers, the positrons. Proton accelerators continued to grow as well. The original CERN proton-antiproton machine had achieved an energy of 640 GeV; in America, Fermilab’s proton-antiproton collider, which went into operation in 198S, soon was climbing toward an energy of over 1 TeV. Two years thereafter, the United States began planning a “superconducting super collider” that would attain energies of 20 TeV, flushing out particles forty times more massive than any previously detectable. With a ring fifty miles or more in circumference, the super collider would be the largest machine ever constructed.

The theorists, meanwhile, kept sifting through the particle zoo in search of further hidden symmetries. A number of grandly titled “grand unified” theories (GUTs for short) were written that purported to identify the electroweak and strong nuclear forces as partners in a single, broken gauge symmetry group. The GUTs made a curious prediction: They implied that the proton, always assumed to be stable, instead decays. Its half-life was estimated at some 1032 years. That’s a long time—a thousand billion times the age of the universe—but the prediction could be tested by keeping watch on 1032 protons, one of which ought then to decay each year on the average. To test the grand unified theories, protons accordingly were gathered together, in the form of thousands of tons of filtered water in a tank in a salt mine near Cleveland and in a lead mine in Kamioka, Japan, a thirty-five-ton block of concrete in an iron mine in Minnesota, sheets of iron in a gold mine in India, and stacks of steel bars adjacent to a highway tunnel under Mont Blanc. (The experiments were conducted deep underground to minimize contamination by cosmic rays.) Light-sensing devices were attached to computers programmed to record the telltale flash of light that would be produced by a spontaneously disintegrating proton.

It was a hard life, waiting for years on end in lead mines and salt mines. (“That’s what they get for choosing to be experimental physicists,” joked one hard-hearted theorist.) The results, moreover, were null, and as years went by and no proton was observed to decay, it became increasingly evident that the GUT theorists had picked the wrong broken symmetries. Meanwhile, looking for something to do while they waited, the experimentalists put their instruments to work detecting neutrinos, a few of which betrayed their presence by smashing into atoms in the vats of water and stacks of concrete and metal that had been assembled to look for proton decay. This came in handy in 1987, when a supernova blazed forth in the Large Magellanic Cloud and a wave of neutrinos was promptly detected at the Kamioka and Lake Erie proton-decay installations. The observation confirmed a theory (authored in part by Bethe, indefatigable student of stars) that Supernovae generate enormous quantities of neutrinos, and gave birth to the new science of observational neutrino astronomy.

The waning of the grand unified theories went widely unmourned. The GUTs had lacked the sweeping simplicity that unified theories are supposed to be all about; like the standard model they were full of arbitrary parameters, and, of course, they left out gravity. What the theorists really wanted was a “superunified” theory that would identify symmetrical family relationships among all four forces.

Elements of just such a theory began to appear, first in the Soviet Union and then independently in the West, in the 1970s. Collectively called “supersymmetry,” these new theories identified a symmetry linking bosons, the carriers of force, with fermions, the stuff of matter. Gravitation was drawn under the umbrella of the theory in 1976, a development that generated widespread excitement. And yet, by the early 1980s, supersymmetry had begun to stall. In itself it could not generate all the known quarks, leptons, and gauge particles, and it introduced even more unexplained terms than had grand unified theories and the standard model. Something was missing.

That something, a few young theorists proposed, was strings. Traditionally, elementary particles like the electron had been regarded as dimensionless points. In string theory, the particles are instead portrayed as extended objects, longer than they are wide —in short, as strings. They can be mistaken for infinitesimal objects because they are very small—only about one Planck length long, which is just about as small as anything can be. The prospect that particles are strings rather than points made an enormous difference, however, in the way their behavior was interpreted. Strings can vibrate, and the rate at which they vibrate, it turned out, can generate the properties of all known particles—and of an infinite variety of other particles as well. The bewildering diversity of the myriad particles was suddenly, if only potentially, unified, by a stroke as simple as a chord struck on Pythagoras’s lyre: All, said the theory, are but differing harmonies of strings.

String theory proffered potential answers to some of the most troubling questions that had been confronting theorists concerned with unification. Why did prior versions of quantum field theory so often generate infinities that had to be “renormalized” away? Because they regarded the elementary particles as having zero dimension: This meant they could draw infinitesimally close together, in which case the energy level of the force being exchanged between them could rise to infinity. Since strings have length, the problem of infinities did not arise in string theory. Why are gravitons spin two and the other force-carrying particles spin one? Because, said the theory, a string can either be open, meaning it has two ends, or closed, meaning that the ends are joined, forming a loop: Open strings can be spin one, closed strings can be spin two. Why has the Yang-Mills gauge field concept enjoyed such broad applicability in understanding the forces? Because a string when in its lowest energy state—straight and nonrotating—acts like a massless, spin-one particle, and that is the description of the gauge particles that convey the Yang-Mills fields. String theory even opened a door toward understanding the conceptual gulf between relativity and quantum mechanics. Indeed, string theory could not work without including gravity. It was an inherently unifying conception.

Subatomic particles, traditionally envisioned as points, are depicted in string theory as extended objects (top). Particles in motion trace out world lines; strings, world sheets (middle). A “Feynman diagram” of pointlike particle interactions consists of lines; for closed (i.e., looplike) strings, the Feynman diagram is tubular (bottom).

The string concept originally was invoked in the 1960s, by theorists who had in mind larger strings whose harmonies might explain the behavior of the rapidly spinning hadrons. At this task it did not fare well, and most physicists soon dropped the idea. One of the few to appreciate its potential was (once again) the perspicacious Murray Gell-Mann, who encouraged the American physicist John Schwarz that even if string theory appeared sterile at present, “somehow, sometime, somewhere, it would still be useful.”31

A breakthrough came in 1974, when Schwarz and the young French physicist Joel Scherk realized that an unwelcome particle that kept turning up in their string equations—its mass zero, its spin two—might be none other than the graviton, the boson that carries gravitation. Schwarz and Scherk then began thinking of strings as being only 10−35 meter long, the “Planck length” at which gravitation becomes as strong as the other forces and, therefore, presumably begins to function in an obviously quantized manner. Though these ideas initially garnered little enthusiasm in the scientific community, Schwarz stubbornly kept returning to the string concept, working on it in collaboration with Michael Green, who was visiting Caltech from the University of London. The concept was so unfashionable that Schwarz and Green apparently were the only two people in the world conducting research into strings at that time. But their efforts finally began to bear fruit, and in the summer of 1984 they were able to demonstrate that anomalies that had troubled other unified field theories canceled out in string theory. This captured attention, and by 1987 strings were the hottest topic in theoretical particle physics.

Writing a unified theory is something of an ad hoc affair, like putting up a tent in a high wind; while one sets the pegs, the tent flaps free. Einstein’s relativity required abandoning classical conceptions of space and time; quantum mechanics required abridging classical causality. The odd thing about string theory was very odd indeed: It required that the universe have at least ten dimensions. As we live in a universe of only four dimensions (three of space plus one of time), the theory postulated that the other dimensions were “compactified,” meaning that they had collapsed into structures so tiny that we do not notice them. Weinberg stumped for this idea, and was kidded about it when Howard Georgi, known for his work in grand unified theory, introduced a 1984 Weinberg lecture at Harvard by writing a limerick on the blackboard that read:

Steve Weinberg, returning from Texas
Brings dimensions galore to perplex us.
But the extra ones all
Are rolled up in a ball
So tiny it never affects us.32

Unification of quantum mechanics and general relativity, long a conundrum, appears to be inherent to string theory. It implies that gravitation, explicated in relativity, is produced by open strings (top), while the other, quantum forces are produced by closed strings (middle). Cutting a closed string produces two open strings (bottom), suggesting a natural affinity between the two classes of force.

Hyperdimensionality had first been introduced into unified theory by Theodor Kaluza in Germany in 1919. Kaluza wrote to Einstein, proposing that Einstein’s dream of finding a unified theory of gravitation and electromagnetism might be realized if he worked his equations in five-dimensional space-time. Einstein at first scoffed at the idea, but later reconsidered and helped Kaluza get his paper published. A few years after that, the Swedish physicist Oskar Klein published a quantum version of Kaluza’s work. The resulting Kaluza-Klein theory seemed interesting, but nobody knew what to do with it until the 1970s, when it turned out to be salutary in working on supersymmetry. Soon Kaluza-Klein was on everyone’s lips (with Gell-Mann, in his role as linguistic sentry, chiding colleagues who failed to pronounce it “Ka-woo-sah-Klein”).

Though both string theory in particular and supersymmetry in general invoked higher dimensions, strings had a way of selecting their requisite dimensionality: String theory, it soon became apparent, would work only in two, ten, or twenty-six dimensions, and invoked only two possible symmetry groups—either SO(32) or E8 × E8. When a theory points a finger that decisively, scientists pay attention, and by the late 1980s scores were at work on strings. A great deal of toil lay ahead, but the prospects were bright. “The coming decades,” wrote Schwarz and his superstring co-workers Green and Edward Witten, “are likely to be an exceptional period of intellectual adventure.”33

Such optimism may, of course, prove to have been misplaced. The history of twentieth-century physics is strewn with the bleached bones of theories that were once thought to approach an ultimate answer. Einstein devoted much of the later half of his career to trying to find a unified field theory of gravitation and electromagnetism, with popular expectations running so high that equations from his work in progress were posted in windows along New York’s Fifth Avenue, where they were scrutinized by curious if uncomprehending multitudes. Yet nothing came of it. (Einstein had ignored the quantum principle.) Wolfgang Pauli collaborated with Werner Heisenberg on a unified theory for a while, then was alarmed to hear Heisenberg claim on a radio broadcast that a unified Pauli-Heisenberg theory was close to completion, with only a few technical details remaining to be worked out. Put out by what he regarded as Heisenberg’s hyperbole, Pauli sent George Gamow and other colleagues a page on which he had drawn a blank box. He captioned the drawing with the words, “This is to show the world that I can paint like Titian. Only technical details are missing.”34

Critics of the superstring concept pointed out that claims for its power were based almost entirely upon its internal beauty. The theory had not yet so much as duplicated the achievements of the standard model, nor had it made a single prediction that could be tested by experiment. Supersymmetry did mandate that the universe ought to contain whole families of new particles, among them “selectrons” (supersymmetric counterparts of the electron) and “photinos” (counterparts of the photon), but it did not postulate the hypothetical particles’ masses. The absence of evidence adduced in preliminary searches for supersymmetric particles, like those conducted at the PEP accelerator at Stanford and at PETRA in Hamburg, therefore proved nothing; one could always imagine that the particles were too massive to be produced in these machines, or indeed in any newer and more powerful machines that might be built. The prospects of conducting experiments to test string theory were even more remote: The putative strings themselves had a theoretical mass of more than 1021 times that accessible to existing accelerators, meaning that their detection, using existing technology, would require building an accelerator larger than the solar system. Supersymmetry and string theory were elegant, but if the theorists working on them had to proceed indefinitely without the benefit of what Weinberg called “that wonderful fertilization that we normally get from experiment,”35 they seemed in danger of drifting away into the ionospheric reaches of pure, abstract thought. If that happened, argued Glashow and his Harvard colleague Paul Ginsparg, their tongues only slightly in cheek, “contemplation of superstrings may evolve into an activity as remote from conventional particle physics as particle physics is from chemistry, to be conducted at schools of divinity by future equivalents of medieval theologians.” They added sardonically that “for the first time since the Dark Ages, we can see how our noble search may end, with faith replacing science once again.”36

Nonetheless, hope continued to run high that there is a fundamentally beautiful, symmetrical principle to nature that has generated the particles and forces, and that it can perhaps be glimpsed by the human mind. “Maybe it isn’t true,” Weinberg allowed. “Maybe nature is fundamentally ugly, chaotic and complicated. But if it’s like that, then I want out.”37

Which brings us back to the other Greek definition of symmetry—“due proportion.” To the Greeks, symmetry consisted, not simply of invariance, but of an aesthetically pleasing kind of invariance. This implies that there is a higher order of perfection, a more perfect world, that we glimpse through the windows proffered by symmetry and by which the elegance of any symmetry theory can be gauged. Supersymmetry portrays this ultimate perfection as a hyperdimensional universe, of which our poor imperfect universe is but a paltry shadow. It implies that physicists—in identifying, say, the weak and electromagnetic forces as having arisen from the breaking of the more symmetrical electroweak force, or in finding concealed symmetries cowering in the cramped nuclear precincts where the strong force does its work—are in effect piecing together the shattered potsherds of that perfect world. Indeed, the theory indicates that there may be countless more such debris, in the form of supersymmetric particles that have as yet remained undetected because they interact only weakly or not at all with the particles we are made of and have come to know.

Where, then, is the hyperdimensional universe of perfect symmetry to be found? Certainly not here and now; the world we live in is fraught with broken symmetries, and knows but four dimensions. The answer comes from cosmology, which tells us that the supersymmetric universe, if it existed, belonged to the past. The implication is that the universe began in a state of symmetrical perfection, from which it evolved into the less symmetrical universe we live in. If so, the search for perfect symmetry amounts to a search for the secret of the origin of the universe, and the attention of its acolytes may with good reason turn, like the faces of flowers at dawn, toward the white light of cosmic genesis.

*Dirac meant, of course, not that one should ignore the empirical results altogether, but that a beautiful theory need not be abandoned just because it fails an initial test. He had in mind Erwin Schrödinger’s reluctance to publish his estimable equations of wave mechanics merely because they conflicted with experimental data. “It is most important to have a beautiful theory,” Dirac told the science writer Horace Freeland Judson. “And if the observations don’t support it, don’t be too distressed, but wait a bit and see if some error in the observations doesn’t show up.”5

*The ratio is approximate because the numbers generated by the Fibonacci series are “irrational”—i.e., the ratio upon which they converge cannot be expressed exactly in terms of a fraction. The Pythagoreans discovered irrational numbers, and are said to have been so unsettled by them that they prescribed the death penalty to any of their sect who revealed their existence to the untutored multitudes. Hippasus was banished for defying the ban. He drowned at sea, a fate that the Pythagoreans ascribed to divine retribution.

*Richard Feynman, Gell-Mann’s chief competitor for the title of World’s Smartest Man but a stranger to pretension, once encountered Gell-Mann in the hall outside their offices at Caltech and asked him where he had been on a recent trip; “Moon-TRW-ALGH!” Gell-Mann responded, in a French accent so thick that he sounded as if he were strangling. Feynman—who, like Gell-Mann, was born in New York City—had no idea what he was talking about. “Don’t you think,” he asked Gell-Mann, when at length he had ascertained that Gell-Mann was saying “Montreal,” “that the purpose of language is communication?”

*Quantum interactions customarily are depicted as taking place not in the conventional space that makes up the theater for macroscopic events, but in an assessment complex space described in part by the quantum wave functions. Quarks, for instance, are for convenience depicted as existing in a three-dimensional “color” space described by quantum chromodynamics—color is a quantum number that plays a role in the strong force analogous to that of the charge in electrodynamics—while electrons normally occupy a one-dimensional space the two directions of which represent positive and negative electrical charge.

*Connections between the weak and electromagnetic interactions had been noted before; Fermi in 1933 formulated the first model of the weak force by analogy with electromagnetism. But a great many such threads weave their way through the history of physics, and this book is not the place to attempt to trace more than a few of them.

*Compare, for instance, the value of g, the gyromagnetic ratio of the electron, as predicted by the theory of quantum electrodynamics and as tested experimentally:

Theory: £ = 1.00115965241

Experiment: £ = 1.00115965238, ± 0.00000000026

*Electrons, since they also carry an electrical charge, can also be employed; the resulting explosions are cleaner and therefore easier to study, but as electrons are less massive than protons they collide less violently, and so electron accelerators yield weaker collisions relative to their energy consumption.

After Ernest Walton, an Irish physicist, and John Cockroft, the English physicist who on one fine day in 1932 could be seen stopping strangers on the streets of Cambridge and exclaiming, “We have split the atom! We have split the atom!”

*Since antiprotons have opposite electrical charge, the same sequence of magnetic pulses that kept protons moving clockwise around the ring would keep the antiprotons moving counterclockwise. A somewhat more exotic way of looking at the situation, proposed by Feynman years earlier, was to say that antimatter particles move in reverse time.